Power Distribution System Reliability Practical Methods And Applications Ali A Chowdhury

Power Distribution System Reliability Practical
Methods And Applications Ali A Chowdhury
download
https://ebookbell.com/product/power-distribution-system-
reliability-practical-methods-and-applications-ali-a-
chowdhury-4310320
Explore and download more ebooks at ebookbell.com

Here are some recommended products that we believe you will be
interested in. You can click the link to download.
Intelligent Coordinated Control Of Complex Uncertain Systems For Power
Distribution And Network Reliability 1st Edition Meng Xiangping
https://ebookbell.com/product/intelligent-coordinated-control-of-
complex-uncertain-systems-for-power-distribution-and-network-
reliability-1st-edition-meng-xiangping-5433166
Power Distribution System State Estimation Elizete Maria Loureno
https://ebookbell.com/product/power-distribution-system-state-
estimation-elizete-maria-loureno-46714916
Electric Power Distribution System Engineering 2nd Edition Turan Gnen
https://ebookbell.com/product/electric-power-distribution-system-
engineering-2nd-edition-turan-gnen-4728276
Electric Power Distribution System Engineering Second Edition Turan
Gonen
https://ebookbell.com/product/electric-power-distribution-system-
engineering-second-edition-turan-gonen-5445144

Distribution System Modeling And Analysis Electric Power Engineering
Series 1st Edition William H Kersting
https://ebookbell.com/product/distribution-system-modeling-and-
analysis-electric-power-engineering-series-1st-edition-william-h-
kersting-2215184
Terrorism And The Electric Power Delivery System 1st Edition National
Research Council Division On Engineering And Physical Sciences Board
On Energy And Environmental Systems Committee On Enhancing The
Robustness And Resilience Of Future Electrical Transmission And
Distribution In The United States To Terrorist
https://ebookbell.com/product/terrorism-and-the-electric-power-
delivery-system-1st-edition-national-research-council-division-on-
engineering-and-physical-sciences-board-on-energy-and-environmental-
systems-committee-on-enhancing-the-robustness-and-resilience-of-
future-electrical-transmission-and-distribution-in-the-united-states-
to-terrorist-51396980
Electrical Power Distribution Systems 8th Edition V Kamaraju
https://ebookbell.com/product/electrical-power-distribution-
systems-8th-edition-v-kamaraju-10945164
Power Quality In Power Distribution Systems Concepts And Applications
1st Edition Mahesh Kumar Mishra
https://ebookbell.com/product/power-quality-in-power-distribution-
systems-concepts-and-applications-1st-edition-mahesh-kumar-
mishra-52392032
Resiliency Of Power Distribution Systems Anurag K Srivastava
https://ebookbell.com/product/resiliency-of-power-distribution-
systems-anurag-k-srivastava-53545902

POWER DISTRIBUTION
SYSTEM RELIABILITY

BOOKS IN THE IEEE PRESS SERIES ON POWER ENGINEERING
Principles of Electric Machines with Power Electronic Applications, Second Edition
M. E. El-Hawary
Pulse Width Modulation for Power Converters: Principles and Practice
D. Grahame Holmes and Thomas Lipo
Analysis of Electric Machinery and Drive Systems, Second Edition
Paul C. Krause, Oleg Wasynczuk, and Scott D. Sudhoff
Risk Assessment for Power Systems: Models, Methods, and Applications
Wenyuan Li
Optimization Principles: Practical Applications to the Operations of Markets of the Electric
Power Industry
Narayan S. Rau
Electric Economics: Regulation and Deregulation
Geoffrey Rothwell and Tomas Gomez
Electric Power Systems: Analysis and Control
Fabio Saccomanno
Electrical Insulation for Rotating Machines: Design, Evaluation, Aging, Testing,
and Repair
Greg Stone, Edward A. Boulter, Ian Culbert, and Hussein Dhirani
Signal Processing of Power Quality Disturbances
Math H. J. Bollen and Irene Y. H. Gu
Instantaneous Power Theory and Applications to Power Conditioning
Hirofumi Akagi, Edson H. Watanabe and Mauricio Aredes
Maintaining Mission Critical Systems in a 24/7 Environment
Peter M. Curtis
Elements of Tidal-Electric Engineering
Robert H. Clark
Handbook of Large Turbo-Generator Operation and Maintenance, Second Edition
Geoff Klempner and Isidor Kerszenbaum
Introduction to Electrical Power Systems
Mohamed E. El-Hawary
Modeling and Control of Fuel Cells: Distributed Generation Applications
M. Hashem Nehrir and Caisheng Wang
Power Distribution System Reliability: Practical Methods and Applications
Ali A. Chowdhury and Don O. Koval

POWER DISTRIBUTION
SYSTEM RELIABILITY
Practical Methods
and Applications
Ali A. Chowdhury
Don O. Koval
IEEE Press

IEEE Press
445 Hoes Lane
Piscataway, NJ 08854
IEEE Press Editorial Board
Lajos Hanzo, Editor in Chief
R. Abari T. Chen O. Malik
J. Anderson T. G. Croda S. Nahavandi
S. Basu S. Farshchi M. S. Newman
A. Chatterjee B. M. Hammerli W. Reeve
Kenneth Moore, Director of IEEE Book and Information Services (BIS)
Jeanne Audino, Project Editor
Technical Reviewers
Ward Jewell, Wichita State University
Fred Vaneldik, University of Alberta
Copyright Ó 2009 by the Institute of Electrical and Electronics Engineers, Inc.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved.
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any
means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted
under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of
the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web
at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions
Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-
6008, or online at http://www.wiley.com/go/permission.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in
preparing this book, they make no representations or warranties with respect to the accuracy or completeness of
the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a
particular purpose. No warranty may be created or extended by sales representatives or written sales materials.
The advice and strategies contained herein may not be suitable for your situation. You should consult with a
professionalwhere appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other
commercial damages, including but not limited to special, incidental, consequential, or other damages.
Forgeneral information on our other productsand services or for technicalsupport, please contact our Customer
Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax
(317) 572-4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print
may not be available in electronic formats. For more information about Wiley products, visit our web site
at www.wiley.com.
Library of Congress Cataloging-in-Publication Data is available.
ISBN 978-0470-29228-0
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1

To my wife Razia, daughter Fariha, late parents Hesamuddin Ahmed and
Mahfuza Khatun, late elder brother Ali Hyder, and late older sister Chemon
Ara Chowdhury
—Ali A. Chowdhury
To my wife Vivian, my mother Katherine, and late father Peter Koval
—Don. O. Koval

CONTENTS
Preface xix
1 OUTLINE OF THE BOOK 1
1.1 Introduction 1
1.2 Reliability Assessment of Power Systems 2
1.2.1 Generation System Reliability Assessment 2
1.2.2 Transmission System Reliability Assessment 3
1.2.3 Distribution System Reliability Assessment 4
1.3 Organization of the Chapters 5
1.4 Conclusions 10
References 11
2 FUNDAMENTALS OF PROBABILITY AND STATISTICS 13
2.1 Concept of Frequency 13
2.1.1 Introduction 13
2.1.2 Concept of Class 15
2.1.3 Frequency Graphs 15
2.1.4 Cumulative Frequency Distribution Model 15
2.2 Important Parameters of Frequency Distribution 15
2.2.1 Mean 16
2.2.2 Median 16
2.2.3 Mode 16
2.2.4 Standard Deviation 16
2.2.5 Variance 17
2.3 Theory of Probability 17
2.3.1 Concept 17
2.3.2 Probability Laws and Theorems 18
2.4 Probability Distribution Model 19
2.4.1 Random Variable 19
2.4.2 Probability Density Function 20

2.4.3 Parameters of Probability Distributions 21
2.4.4 The Binomial Distribution 22
2.4.5 The Poisson Distribution 25
2.4.6 The Exponential Distribution 26
2.4.7 The Normal Distribution 27
2.5 Sampling Theory 29
2.5.1 Concepts of Population and Sample 29
2.5.2 Random Sampling Model 29
2.5.3 Sampling Distributions 29
2.5.4 Concept of Conﬁdence Limit 32
2.5.5 Estimation of Population Statistic 32
2.5.6 Computation of Sample Size 34
2.6 Statistical Decision Making 36
2.6.1 Procedure of Decision Making 37
2.6.2 Types of Error 37
2.6.3 Control of Errors 42
2.7 Conclusions 42
References 42
3 RELIABILITY PRINCIPLES 45
3.1 Failure Rate Model 45
3.1.1 Concept and Model 45
3.1.2 Concept of Bathtub Curve 46
3.2 Concept of Reliability of Population 47
3.2.1 Theory of First Principles 47
3.2.2 Reliability Model 50
3.2.3 The Poisson Probability Distribution 52
3.2.4 Reliability of Equal Time Steps 53
3.3 Mean Time to Failures 54
3.4 Reliability of Complex Systems 55
3.4.1 Series Systems 55
3.4.2 Parallel Systems 56
3.4.3 Partially Redundant Systems 58
3.4.4 Bayes’ Theorem 60
3.5 Standby System Modeling 62
3.5.1 Background 62
3.5.2 Spares for One Unit 62
3.5.3 Spares for Multiple Interchangeable Units 63
viii CONTENTS

3.6 Concepts of Availability and Dependability 65
3.6.1 Mean Time to Repair 65
3.6.2 Availability Model 66
3.6.3 Markov Model 66
3.6.4 Concept of Dependability 67
3.6.5 Design Considerations 68
3.7 Reliability Measurement 68
3.7.1 Concept 68
3.7.2 Accuracy of Observed Data 69
3.7.3 Conﬁdence Limit of Failure Rate 69
3.7.4 Chi-Square Distribution 70
3.8 Conclusions 77
References 77
4 APPLICATIONS OF SIMPLE RELIABILITY MODELS 79
4.1 Equipment Failure Mechanism 79
4.1.2 Utilization of Forced Outage Statistics 80
4.1.3 Failure Rate Computation 80
4.2 Availability of Equipment 81
4.2.1 Availability Considerations and Requirements 81
4.2.2 Availability Model 82
4.2.3 Long-Run Availability 83
4.3 Oil Circuit Recloser (OCR) Maintenance Issues 85
4.3.2 Study Methods 85
4.4 Distribution Pole Maintenance Practices 86
4.5 Procedures for Ground Testing 87
4.5.1 Concept 87
4.5.2 Statistical Methods For Ground Testing 87
4.6 Insulators Maintenance 87
4.6.1 Background 87
4.6.2 Inspection Program for Insulators 87
4.6.3 Voltage Surges On Lines 88
4.6.4 Critical Flashover 89
4.6.5 Number of Insulators in a String 91
4.7 Customer Service Outages 93
4.7.1 Background 93
CONTENTS ix

4.7.2 Popular Distribution Reliability Indices 93
4.7.3 Reliability Criteria 94
4.7.4 Cost of Interruption Concept 95
4.8 Conclusions 95
References 96
5 ENGINEERING ECONOMICS 97
5.1 Introduction 97
5.2 Concept of Interest and Equivalent 98
5.3 Common Terms 98
5.4 Formulas for Computing Interest 98
5.5 Annual Cost 101
5.5.1 Concept of Annual Cost 101
5.5.2 Alternatives with Different Life Times 102
5.6 Present Value (PV) Concept 103
5.7 Theory of Rate of Return 105
5.8 Cost–Beneﬁt Analysis Approach 106
5.9 Financial Risk Assessment 107
5.9.1 Basic Concept 107
5.9.2 Principles 107
5.9.3 Concept of Risk Aversion 108
5.10 Conclusions 108
References 109
6 RELIABILITY ANALYSIS OF COMPLEX NETWORK
CONFIGURATIONS 111
6.1 Introduction 111
6.2 State Enumeration Methodologies 112
6.2.1 Basic Assumptions: Criteria for System Success—Power is
Delivered to All Loads 112
6.3 Network Reduction Methods 115
6.3.1 Path Enumeration Methods: Minimum Tie Set 116
6.3.2 Path Enumeration Methods: Minimum Cut Set 121
6.4 Bayes’ Theorem in Reliability 129
6.5 Construction of Fault Tree Diagram 139
6.5.1 Basic Rules for Combining the Probability of Independent
Input Failure Events to Evaluate the Probability
of a Single-Output Failure Event 140
x CONTENTS

6.6 The Application of Conditional Probability Theory to System
Operating Conﬁgurations 146
6.7 Conclusions 151
References 151
7 DESIGNING RELIABILITY INTO INDUSTRIAL AND COMMERCIAL
POWER SYSTEMS 153
7.2 Example 1: Simple Radial Distribution System 154
7.2.1 Description of a Simple Radial System 155
7.2.2 Results: Simple Radial System Example 1 155
7.2.3 Conclusions: Simple Radial System Example 1 155
7.3 Example 2: Reliability Analysis of a Primary Selective
System to the 13.8 kV Utility Supply 156
7.3.1 Description: Primary Selective System to the 13.8 kV
Utility Supply 157
7.3.2 Results: A Primary Selective System to the 13.8 kV
Utility Supply 158
7.3.3 Conclusions: Primary Selective System to 13.8 kV
Utility Supply 159
7.4 Example 3: A Primary Selective System to the Load Side of
a 13.8 kV Circuit Breaker 161
7.4.1 Description of a Primary Selective System to the Load
Side of a 13.8 kV Circuit Breaker 161
7.4.2 Results: Primary Selective System to Load Side of 13.8 kV
Circuit Breaker 162
7.4.3 Conclusions: A Primary Selective System to the Load Side
of a 13.8 kV Circuit Breaker 163
7.5 Example 4: Primary Selective System to the Primary
of the Transformer 163
7.5.1 Description of a Primary Selective System to the Primary
7.5.2 Results: A Primary Selective System to the Primary
7.5.3 Conclusions: Primary Selective system to Primary
of Transformer 164
7.6 Example 5: A Secondary Selective System 164
7.6.1 Description of a Secondary Selective System 164
7.6.2 Results: A Secondary Selective System 165
7.6.3 Conclusions: A Secondary Selective System 165
CONTENTS xi

7.7 Example 6: A Simple Radial System with Spares 166
7.7.1 Description of a Simple Radial System with Spares 166
7.7.2 Results: A Simple Radial System with Spares 167
7.7.3 Conclusions: Simple Radial System with Spares 167
7.8 Example 7: A Simple Radial System with Cogeneration 168
7.8.1 Description of a Simple Radial System with Cogeneration 168
7.8.2 Results: Simple Radial System with Cogeneration 168
7.8.3 Conclusions: A Simple Radial System with Cogeneration 169
7.9 Reliability Evaluation of Miscellaneous System Configurations 170
References 188
8 ZONE BRANCH RELIABILITY METHODOLOGY 191
8.2 Zone Branch Concepts 192
8.3 Industrial System Study 196
8.4 Application of Zone Branch Methodology: Case Studies 201
8.4.1 Case 1: Design “A”—Simple Radial Substation Configuration 202
8.4.2 Case 2: Design “B”—Dual Supply Radial—Single Bus 208
8.4.3 Case 3: Design “C”—Dual Supply Radial with Tiebreaker 215
8.4.4 Case 4: Design “D”—Dual Supply Loop with Tiebreaker 219
8.4.5 Case 5: Design “E”—Dual Supply Primary Selective 225
8.4.6 Case 6: Design “F”—Double Bus/Double Breaker Radial 232
8.4.7 Case 7: Design “G”—Double Bus/Double Breaker Loop 235
8.4.8 Case 8: Design “H”—Double Bus/Breaker Primary Selective 242
8.5 Conclusions 251
References 252
9 EQUIPMENT OUTAGE STATISTICS 255
9.2 Interruption Data Collection Scheme 256
9.3 Typical Distribution Equipment Outage Statistics 259
9.4 Conclusions 265
References 265
10 HISTORICAL ASSESSMENT 267
10.2 Automatic Outage Management System 268
10.2.1 Definitions of Terms and Performance Indices 269
xii CONTENTS

10.2.2 Customer-Oriented Indices 269
10.2.3 Classification of Interruption as to Causes 270
10.3 Historical Assessment 271
10.3.1 A Utility Corporate Level Analysis 272
10.3.2 Utility Region-Level Analysis 279
10.4 Crew Center-Level Analysis 282
10.5 Development of a Composite Index for Reliability Performance
Analysis at the Circuit Level 282
References 283
11 DETERMINISTIC CRITERIA 285
11.2 Current Distribution Planning and Design Criteria 286
11.2.1 Outage Data Collection and Reporting 287
11.2.2 Reliability Indices 287
11.2.3 Targets for Customer Service Reliability 288
11.2.4 Examples of Distribution Reliability Standards in a
Deregulated Market 288
11.3 Reliability Cost Versus Reliability Benefit Trade-Offs
in Distribution System Planning 290
11.4 Alternative Feed Requirements for Overhead Distribution Systems 293
11.5 Examples of Deterministic Planning Guidelines for Alternative
Feed Requirements 294
11.5.1 Reliability of Supply to 25 kV Buses 294
11.5.2 Reliability of Supply to Towns/Cities 295
11.5.3 Reliability of Supply to Large Users and Industrial
Customers 295
11.6 Value-Based Alternative Feeder Requirements Planning 295
11.6.1 Customer Interruption Cost Data 297
11.6.2 An Illustrative Example for Justification of an Alternate
Feed to a Major City 298
References 299
12 IMPORTANT FACTORS RELATED TO DISTRIBUTION
STANDARDS 301
12.2 Relevant Issues and Factors in Establishing Distribution
Reliability Standards 304
CONTENTS xiii

12.2.1 Data Pool 305
12.2.2 Definitions of Terms 307
12.2.3 System Characteristics 308
12.2.4 Outage Data Collection Systems 308
12.3 Performance Indices at Different System Levels of a Utility 309
12.4 Performance Indices for Different Utility Types 314
References 315
13 STANDARDS FOR REREGULATED DISTRIBUTION UTILITY 317
13.2 Cost of Service Regulation versus Performance-Based
Regulation 318
13.3 A Reward/Penalty Structure in the Performance-Based Rates 319
13.4 Historical SAIFI and SAIDI Data and their Distributions 322
13.5 Computation of System Risks Based on Historical
Reliability Indices 323
13.6 Cause Contributions to SAIFI and SAIDI Indices 329
References 335
14 CUSTOMER INTERRUPTION COST MODELS FOR LOAD POINT
RELIABILITY ASSESSMENT 337
14.2 Customer Interruption Cost 338
14.3 Series and Parallel System Model Equations 339
14.4 Dedicated Distribution Radial Feeder Configuration 340
14.5 Distribution Radial Feeder Configuration Serving
Multiple Customers 341
14.6 Distribution Radial Feeder Configuration Serving Multiple
Customers with Manual Sectionalizing 342
14.7 Distribution Radial Feeder Configuration Serving Multiple
Customers with Automatic Sectionalizing 345
14.8 Distribution System Looped Radial Feeders 347
14.8.1 Operating Procedures 347
14.8.2 Feeder Characteristics: Looped Radial Feeders—Manual
Sectionalizing 347
References 355
xiv CONTENTS

15 VALUE-BASED PREDICTIVE RELIABILITY ASSESSMENT 357
15.2 Value-Based Reliability Planning 358
15.3 Distribution System Conﬁguration Characteristics 360
15.4 Case Studies 362
15.5 Illustrative Example System Problem and Its Reliability
Calculations 368
15.5.1 Operating Procedures 369
References 374
16 ISOLATION AND RESTORATION PROCEDURES 375
16.2 Distribution System Characteristics 378
16.2.1 Distribution Load Transfer Characteristics 379
16.2.2 Operating Procedures: Line Section Outages 380
16.2.3 Feeder Circuit Reliability Data 380
16.2.4 Cost of Load Point Interruptions 381
16.3 Case Studies 381
16.3.1 Case Study 1 381
16.3.2 Case Study 2 384
16.3.3 Case Study 3 388
16.4 Major Substation Outages 389
16.5 Summary of Load Point Interruption Costs 391
References 393
17 MESHED DISTRIBUTION SYSTEM RELIABILITY 395
17.2 Value-Based Reliability Assessment in a Deregulated Environment 396
17.3 The Characteristics of the Illustrative Urban Distribution System 397
17.4 Discussion of Results 400
17.5 Feeder and Transformer Loading Levels 401
17.6 Bus and Feeder Tie Analysis 402
17.6.1 Tie Costs and Descriptions 402
17.7 Maintenance 403
17.7.1 Single Transformer 403
17.7.2 Conductor Sizing 403
CONTENTS xv

17.8 Feeders with Nonfused (Lateral) Three-Phase Branches 404
17.9 Feeder Tie Placement 404
17.10 Finding Optimum Section Length 406
17.10.1 Definition of Terms 407
17.11 Feeder and Transformer Loading 408
17.12 Feeder Tie Cost Calculation 409
17.13 Effects of Tie Maintenance 410
17.14 Additional Ties for Feeders with Three-Phase Branches 411
17.14.1 Definition of Terms 412
References 413
18 RADIAL FEEDER RECONFIGURATION ANALYSIS 415
18.2 Predictive Feeder Reliability Analysis 416
18.3 Reliability Data and Assumptions 418
18.4 Reliability Assessment for an Illustrative Distribution Feeder 419
18.4.1 Base Case Circuit Description 419
18.4.2 Circuit Tie 47-2 419
18.4.3 Circuit Tie 46-1 420
18.4.4 Circuit Tie 43-2 421
18.4.5 Circuit Tie 102-3 421
18.4.6 Base Case Reliability 421
18.5 Alternative Improvement Options Analysis 422
18.5.1 Incremental Improvement Alternative 1: Add Distribution
Automation Switch 422
18.5.2 Incremental Improvement Alternative 2: Add
Sectionalizing Switch 423
18.5.3 Incremental Alternative 3: Relocate Recloser 255 424
18.5.4 Incremental Improvement Alternative 4:
Place 2 New Switches 425
18.6 Summary of the Illustrative Feeder Reliability Performance
Improvement Alternatives 425
References 426
19 DISTRIBUTED GENERATION 427
19.2 Problem Definition 428
xvi CONTENTS

19.3 Illustrative Distribution System Conﬁguration Characteristics 430
19.4 Reliability Assessment Model 432
19.4.1 Reliability Indices 433
19.4.2 Reliability Data 433
19.5 Discussion of Results 433
19.5.1 Equivalent Distributed Generation Reinforcement
Alternative 434
References 438
20 MODELS FOR SPARE EQUIPMENT 441
20.2 Development of Probabilistic Models for Determining
Optimal Number of Transformer Spares 442
20.2.1 Reliability Criterion Model for Determining the Optimal
Number of Transformer Spares 442
20.2.2 Mean Time Between Failures (MTBFu) Criterion Model
for Determining the Optimal Number of Transformer Spares 443
20.2.3 Determination of Optimal Transformer Spares Based
on the Model of Statistical Economics 444
20.3 Optimal Transformer Spares for Illustrative 72 kV Distribution
Transformer Systems 445
on the Minimum Reliability Criterion 446
on the Minimum MTBFu Criterion 447
on the Criterion of Statistical Economics 448
References 451
21 VOLTAGE SAGS AND SURGES AT INDUSTRIAL
AND COMMERCIAL SITES 453
21.2 ANSI/IEEE Standard 446—IEEE Orange Book 454
21.2.1 Typical Range for Input Power Quality and Load
Parameters of Major Computer Manufacturers 454
21.2.2 Typical Design Goals of Power Conscious Computer
Manufacturers (Often Called the CBEMA Curve) 454
21.3 IEEE Standard 493-2007—IEEE Gold Book 455
21.3.1 Background 455
CONTENTS xvii

21.3.2 Case Study: Radial Distribution System 459
21.4 Frequency of Voltage Sags 461
21.4.1 Industrial Customer Group 462
21.4.2 Commercial Customer Group 463
21.5 Example Voltage Sag Problem: Voltage Sag Analysis
of Utility and Industrial Distribution Systems 464
21.5.1 Utility Distribution Systems 464
21.5.2 Industrial Distribution System 470
21.6 Frequency and Duration of Voltage Sags and Surges at
Industrial Sites: Canadian National Power Quality Survey 472
21.6.1 Background 472
21.6.2 Voltage Sags and Surges (Time of Day) 473
21.6.3 Voltage Sags and Surges (Day of Week) 475
21.6.4 Frequency of Disturbances Monitored on Primary
and Secondary Sides of Industrial Sites 478
21.7 Scatter Plots of Voltage Sag Levels as a Function of Duration 479
21.8 Scatter Plots of Voltage Surge Levels as a Function of Duration 479
21.9 Primary and Secondary Voltage Sages Statistical Characteristics 480
21.10 Primary and Secondary Voltage Surges Statistical Characteristics 481
References 486
SELECTED PROBLEMS AND ANSWERS 489
Problem Set for Chapters 2 and 3 489
Answers to Problem Set for Chapters 2 and 3 493
Problem Set for Chapter 4 494
Answers to Problem Set for Chapter 4 496
Index 519
xviii CONTENTS

PREFACE
Historically, the attention to distribution reliability planning was proportional to the
operating voltage of utilities and the primary focus was on generation and transmission
reliability studies. It has, however, been reported in the technical literature that
approximately 80% of the customer interruptions occur due to the problems in the
distribution system. Under the new era of deregulation of power utilities, the focus has
shifted to distribution systems to economically provide a reliable service. There are not
many textbooks in theworld dealing with topics in power distribution reliability planning
and operation. We found that many of the theoretical examples presented in the literature
were not representativeofactual distributionsystems. These anomalies raise the question
of their credibility in modeling these systems. There are reliability programs for
calculating customer reliability indices. The details and the assumptions, however,
made in some of these computer programs are not revealed. We found in many cases the
results of these programs were incorrect. The basic intention of this book is to provide the
theory and detailed longhand calculations and their assumptions with many examples
that are required in planning and operating distribution system reliably (i.e., reliability
cost versus reliability worth) and to validate the results generated by commercial
computer programs.
This book evolved from many practical reliability problems and reports written
by us while working for various utilities (e.g., Alberta Power Ltd, BC Hydro, SaskPower,
and MidAmerican Energy Company) in North America over the past 40 years.
Some of the book materials evolved from the content of the reliability courses taught
by Dr. Don Koval at the University of Alberta. The book has been written for senior-level
undergraduate and graduate-level power engineering students, as well as practicing
engineers in the electric power utility industry. It can serve as a complete textbook for
either a one-semester or two-semester course.
It is impossible to cover all aspects of distribution system reliability in a single book.
The book attempts to include the most important topics of fundamentals of probability
and statistics, reliability principles, applications of simple reliability models, engineer-
ing economics, reliability analysis of complex network configurations, designing
reliability into industrial and commercial power systems, application of zone
branch reliability methodology, equipment outage statistics, historical assessment,
deterministic planning criteria, important factors related to distribution standards,
standards for re-regulated distribution utility, customer interruption cost models for
load point reliability assessment, value-based predictive reliability assessment,
isolation and restoration procedures, meshed distribution system layout, radial feeder

reconfiguration analysis, distributed generation, models for spare equipment, and
voltage sags and surges at industrial and commercial sites that are routinely dealt by
distribution engineers in planning, operating and designing distribution systems. The
special feature of this book is that many of the numerical examples are based on actual
utility data and are presented throughout all chapters in an easy-to-understand manner.
Selected problem sets with answers are provided at the end of the book to enable the
reader to Review and self-test the material in many of the chapters of the book. The
problems range from straightforward applications, similar to the examples in the text, to
quite challenging problems requiring insight and refined problem-solving skills. We
strongly believe that the book will prove very useful to power distribution engineers in
their daily engineering functions of planning, operating, designing, and maintaining
distribution systems.
ACKNOWLEDGMENTS
We are grateful to Dr. Fred VanEldik, professor emeritus, University of Alberta for his
editing skills and valuable suggestions in the writing of this book. We are most grateful to
numerous colleagues and friends: Yakout Mansour, president and CEO of California
Independent System Operator; John Propst, Brent Hughes, and Peter Hill of BC Hydro;
Charles Heising, an independent consultant; Doug Hollands of SaskPower; Dr. Roy
Billinton of the University of Saskatchewan; Dr. James McCalley of the Iowa State
University; Dr. Ward Jewell of the Wichita State University; Dr. S.S. Venkata of the
University of Washington; Dr. Anil Pahwa of the Kansas State University; Dr. Chanan
Singh of the Texas A&M University; Dr. Armando M. Leite Da Silva of Universidade
Federal de Itajubá; Dr. Gomaa Hamoud of Hydro One; Dr. Damir Novosel, Dr. Richard
Brown, James Burke, and H. Lee Willis of Quanta Technology; James Averweg, Richard
Polesky, Tom Mielnik, Brian Shell, Dan Custer, James Hettrick, and James Mack of
MidAmerican Energy; R.M. Godfrey of SNC LAVALIN; Cheryl Warren of National
Grid; C.V. Chung of Seattle City Light; John Vitagliano of Canadian Electricity
Association; Pat O'Donnell, independent consultant; J.P. Ratusz, Andy Swenky, Angie
Kirkwood, and Lance Barker of EPCOR; Tony Palladino and Murray Golden of Atco
Electric; Ibrahim Ali Khan of IK Power Systems Solutions; Roger Bergeron of IREQ; Dr.
Turan Gonen of Sacramento State; Bill Braun of Owens Corning; Robert Arno of EYP
Mission Critical Facilities, Inc.; Ariel Malanot of ABB, Switzerland; David Mildenberger
of AltaLink, Laverne Stetson of University of Nebraska, Lincoln, Glenn Staines of
Stantec; Lou Heimer and Michele Ransum of Public Works and Government Services
Canada; Darcy Braun of ETAP; Dr. Costas Vournas of the National Technical University,
Athens; Professor George E. Lasker, president of IIAS; Dr. Mohamed Hamza, president
of IASTED; and the members of the Gold Book Working Group (IEEE Standard
493-2007) for their keen interest and invaluable suggestions over the many years. We
express our kindest appreciations and gratitude to Dr. Mohammed E. El-Hawary, series
editor; Jeanne Audino, project editor; and Steve Welch, acquisitions editor of IEEE Press
for their constant encouragement and deep interest in our manuscript.
xx PREFACE

We are particularly grateful to all the undergraduate and graduate students in the
Department of Electrical and Computer Engineering at the University of Alberta for their
valuable suggestions, research works, and validation of many of the reliability concepts
over the years. Particular thanks go to Cameron Chung, Cindy Zhang, Joseph Dong,
Tahir Siddique, Imran Khan, Catalin Statineanu, Jack Zheng, Jianguo Qiu, Mihaela
Ciulei, Haizhen Wang, Kai Yao, Bin Shen, Meina Xiao, Xiaodong Liu, Ming Wu, Vikas
Gautam, Zhengzhao Lu, Shrinivasa Binnamangale, Aman Gill, Sukhjeet Toor, Fatima
Ghousia, Delia Cinca, Faraz Akhtar, Tushar Chaitanya, and many other undergraduate
and graduate students. Our sincere thanks go to Pamela McCready of California
Independent System Operator for meticulously proofreading the entire manuscript.
Finally, our deepest appreciations go to our wives and family for their limitless
patience and understanding while we were working on this book.
ALI A. CHOWDHURY
DON O. KOVAL
Folsom, California
Edmonton, Alberta, Canada,
March 2009
PREFACE xxi

1
OUTLINE OF THE BOOK
1.1 INTRODUCTION
Reliability is an abstract term meaning endurance, dependability, and good performance.
For engineering systems, however, it is more than an abstract term; it is something that
can be computed, measured, evaluated, planned, and designed into a piece of equipment
or a system. Reliability means the ability of a system to perform the function it is
designed for under the operating conditions encountered during its projected lifetime.
Historically, a power system has been divided into three almost independent areas of
operation as follows:
1. Generation System: facilities for the generation of electricity from economical
energy sources.
2. Transmission System: transportation system to move large energy blocks from
generation facilities to specific geographical areas.
3. Distribution System: within a specific geographical area distribute the energy to
individual consumers (e.g., residential, commercial, industrial, etc.).
Power Distribution System Reliability. By Ali A. Chowdhury and Don O. Koval
Copyright Ó 2009 the Institute of Electrical and Electronics Engineers, Inc.

Ideally, a power system’s reliability from the viewpoint of consumers means
uninterrupted supply of power from thegeneration, transmission, or distribution systems.
In reality, the key indicators of a power system’s reliability for consumers are the
frequency and duration of interruptions at their point of utilization (i.e., their load point).
From an engineering viewpoint, the question is how do you determine mathematically
the frequency and duration of load point interruptions? The ‘‘how to‚ assessment for
distribution systems with practical examples is the subject of this book.
1.2 RELIABILITY ASSESSMENT OF POWER SYSTEMS
The basic function of a power system is to supply its customers with electrical energy as
economically and as reliably as possible. There were some simple applications of
probability methods to calculations of generation reserve capacity since 1940s; however,
the real interest in power system reliability evaluation started to take off only after 1965,
most notably influenced by the New York City blackout that year. Reliability mathe-
matics is constantly evolving to accommodate technical changes in operations and
configurations of power systems. At present, renewable energy sources such as wind and
photovoltaic systems have a significant impact on the operation of generation, trans-
mission, and distribution systems.
At present, deregulation is forcing electric utilities into uncharted waters. For the
first time, the customer is looking for value-added services from their utilities or they will
start shopping around. Failure to recognize customer needs has caused a great number of
business failures in numerous industries. The electric industries’ movement toward a
competitive market forces all related businesses to assess their focus, strengths, weak-
nesses, and strategies. One of the major challenges to electric utilities is to increase the
market value of the services they providewith the right amount of reliability and to lower
their costs of operation, maintenance, and construction to provide customers electricity
at lower rates. For any power system supplying a specific mix of customers, there is an
optimum value of reliability that would result in lowest combined costs. Quantitative
value-based reliability planning concepts presented in this book are an attempt to achieve
this optimum reliability in power systems.
1.2.1 Generation System Reliability Assessment
In evaluating generation capacity adequacy, the commonly accepted definition of failure
is ‘‘loss of load,‚which is an outage due to capacity inadequacy. The reliability is defined
in terms of the loss of load probability in a giventime interval, usually a year, or the loss of
load expectation (LOLE) in days per year. For a loss of load to occur, the system capacity
has to fall to a level due to scheduled maintenance and/or forced outages of other
generating units by a margin exceeding the spinning reserve to meet the system peak
load. Even then, there may not be an outage because the system load is not always at its
peak. To calculate the amount of time when the capacity cannot meet the actual load of
the time, the load duration curve has to be brought into the picture. The most commonly
used generation reliability index of LOLE can be calculated if all parameters, namely,
2 OUTLINE OF THE BOOK

forced outage rates of different generating units, the load forecast, the load duration
curve, the spinning reserve, and the other refinements deemed necessary (e.g., reliability
of the transmission system), are known. Significant research has gone into developing
reliability assessment tools and models applied to generating capacity adequacy over the
past four decades. Electric utilities are routinely performing probabilistic assessments of
generation reserve margin requirements using the sophisticated tools based on Monte
Carlo simulation and contingency enumeration approaches. Recent developments in
generating capacity adequacy assessment include, but are not confined to, novel models
for energy limited units such as wind, solar, geothermal, and other exotic energy
technologies and merchant plant modeling as well as capacity market design models
for deregulated markets. The system planning engineer can then decide if the level of
reliability is adequate and also determine the effect of alternative actions such as
increasing the spinning reserve, adding a generating unit, and changing the maintenance
schedules and interconnections with other areas.
1.2.2 Transmission System Reliability Assessment
In earlier reliability works on generation capacity adequacy assessments, only the energy
production systems were considered. The transmission and distribution systems were
ignored. In a mathematical sense, the transmission and distribution systems were
implicitly assumed to be perfectly reliable, which in reality was not true. Determining
the probability of system capacity outage levels based on the forced outage rates of the
generators alone will lead to overly optimistic results.
The transmission system consists of high-voltage transmission lines and terminal
stations including different equipment and control. The average forced failure rate and
outage duration of each component such as line sections, transformers, and circuit
breakers of the transmission system can be computed and the reliability of a load point
can be calculated using an appropriate reliability model.
The load point reliability depends on the reliability of the individual component;
however, it also depends on other factors. The two most important factors are system
configuration and environment. The transmission system is a network of lines and
equipment. Failure of one component does not necessarily render the system failure.
There is a lot of inherent redundancy in other parts of the transmission system. Another
factor in transmission system reliability is the weather and environment under which it is
subjected to operate. The failures of many outdoor components are caused by lightning,
snow, high winds, and so on. In addition, failures are not always independent as generally
assumed instatisticalcalculations.Thefailureofonecomponentmayincreasethechance
offailureofanother.Onetypeofsuchdependentfailuresisthecommon-modefailure,that
is, failure of more than one component due to the same cause, which generally happens
moreoftenininclementweatherthaninfairweather.Intheanalysisoftransmissionsystem
reliability, therefore, different failure rates are assigned to different weather conditions,
and the dependency of failures, at least in adverseweather, has to be taken into account. It
canbeseenthatadetailedanalysiscanbeverycomplexanditgetsmorecomplexwhenthe
composite generation and transmission system is taken together. The use of powerful
computersisalmostmandatoryforanysystemreliabilityanalysis.Significantworkshave
RELIABILITY ASSESSMENT OF POWER SYSTEMS 3

been done in probabilistic assessments of transmission systems to augment the current
deterministic criteria in planning and designing of transmission systems.
1.2.3 Distribution System Reliability Assessment
The application of reliability concepts to distribution systems differsfrom generation and
transmission applications in that it is more customer load point oriented instead of being
system oriented, and the local distribution system is considered rather than the whole
integrated system involving the generation and transmission facilities. Generation and
transmission reliability also emphasizes capacity and loss of load probability, with some
attention paid to components, whereas distribution reliability looks at all facets of
engineering: design, planning, and operations. Because the distribution system is less
complex than the integrated generation and transmission system, the probability
mathematics involved is much simpler than that required forgeneration and transmission
reliability assessments.
It is important to note that the distribution system is a vital link between the bulk
power system and its customers. In many cases, these links are radial in nature that makes
them vulnerable to customer interruptions due to a single outage event. A radial
distribution circuit generally uses main feeders and lateral distributors to supply
customer energy requirements. In the past, the distribution segment of a power system
received considerably less attention in terms of reliability planning compared to
generation and transmission segments. The basic reason behind this is the fact that
generation and transmission segments are very capital intensive, and outages in these
segments can cause widespread catastrophic economic consequences for society.
It has been reported in the literature that more than 80% of all customer interruptions
occur due to failures in the distribution system. The distribution segment has been the
weakest link between the source of supply and the customer load points. Though a single
distribution system reinforcement scheme is relatively inexpensive compared to a
generation or a transmission improvement scheme, an electric utility normally spends
a large sum of capital and maintenance budget collectively on a huge number of
distribution improvement projects.
At present, in many electric utilities, acceptable levels of service continuity are
determined by comparing the actual interruption frequency and duration indices with
arbitrary targets. For example, monthly reports on service continuity statistics produced
by many utilities contain the arbitrary targets of system reliability indices for perfor-
mance comparison purposes. It has long been recognized especially in the deregulated
market environment that rules of thumb and implicit criteria cannot be applied in a
consistent manner to the very large number of capital and maintenance investment and
operating decisions that are routinely made. Though some reliability programs with
limited capabilities are available, virtually no utilities perform distribution system
expansion studies using probabilistic models. Unlike bulk transmission system that is
subject to North American Electric Reliability Council’s deterministic criteria in
planning and designing the transmission systems, the distribution system is not subject
to any established planning standards. Distribution utilities are required only to furnish
historical distribution system performance indices to regulatory agencies.

There are ample opportunities for distribution utilities to judiciously invest in
distribution system expansion activities to meet the future load growth by using the
probabilistic reliability methods that would eliminate the risk of over/underinvestment in
the system while providing the optimum service reliability at the right cost. The
reluctance of electric utilities to use the reliability methods in planning and designing
distribution systems is due to the prevailing perception that it requires sophisticated
probabilistic computer tools and trained engineers in power system reliability engineer-
ing. This book intends to eliminate this misperception and presents practical probabilis-
tic reliability models for planning and designing distribution systems.
The applications of the developed reliability models presented in this book are
illustrated using hand calculations that require no sophisticated computer tools and
virtually little or no knowledge of probability mathematics. Problem sets and answers are
provided at the end of the book to test the reader’s ability to solve reliability problems in
distribution systems.
1.3 ORGANIZATION OF THE CHAPTERS
Two approaches to reliability evaluation of distribution systems are normally used,
namely, historical assessment and predictive assessment. Historical assessment involves
the collection and analysis of distribution system outage and customer interruption data.
It is essential for electric utilities to measure actual distribution system reliability
performance levels and define performance indicators to assess the basic function of
providing cost-effective and reliable power supply to all customer types. Historical
assessment generally is described as measuring the past performance of a system by
consistently logging the frequency, duration, and causes of system component failures
and customer interruptions. Predictive reliability assessment, however, combines his-
torical component outage data and mathematical models to estimate the performance of
designated configurations. Predictivetechniques therefore rely on twobasic types of data
to compute service reliability: component reliability parameters and network physical
configurations.
This book deals with both historical and predictive distribution system reliability
assessments. Simple and easy-to-use practical reliability models have been developed
and their applications illustrated using practical distribution system networks. Virtually
all reliability calculations have been performed by hand and no sophisticated computer
programs are necessary. A simple but realistic live distribution system has been
frequently used to illustrate the application of different reliability models developed
and presented in this book. For the convenience of the readers, the mathematical
reliability models and formulas relevant to particular applications have been repeated
in chapters where necessary to maintain the flow of understanding the models and
concepts. Each chapter is independent of other chapters, and cross-referencing different
chapters is not required to understand the new concepts presented in a particular chapter.
The applications of the novel concept of reliability cost–reliability worth or commonly
known as the value-based reliability model are extensively discussed and illustrated with
many numerical examples in this book.
ORGANIZATION OF THE CHAPTERS 5

The book is organized as follows:
Chapter 1 presents the basic definition of the term ‘‘reliability‚and its application to
power systems. The current state of the reliability methodology applications in
generation, transmission, and distribution segments of the power system is briefly
described.
Chapters 2 and 3 very briefly describe fundamentals of probability theories and
reliability principles. Although the basic probability and reliability models presented
with numerical examples in Chapters 2 and 3 are available in many textbooks, these
models are repeated in these chapters to help the readers understand the models that will
be used extensively in the later chapters of this book. The majority of systems in the real
world do not have a simple structure or are operated by complex operational logic. For
solving complexnetworks or systems, additional modeling and evaluation techniques are
required to evaluate the reliability of such networks or systems. Chapters 2 and 3 also
include models to assess the reliability complex network configurations. The basic
models for complex network solutions have been illustrated using numerical examples.
Chapter 4 illustrates the applications of the probability and statistical models
presented in Chapters 2 and 3 using simple numerical examples in distribution system
planning and designing. Distribution system planners will be able to utilize the
probability and statistical models by using hand calculations in real-life situations.
Chapter 5 presents the basic engineering economics models. The economics
concepts and models related to distribution system planning and design are illustrated
with numerous simple examples. The novel value-based reliability model presented in
later chapters is based on economic theories discussed in Chapter 5.
In Chapter 6, the basic models for complex network solutions are illustrated
using numerous numerical examples. Chapter 6 introduces models to assess the
reliability complex network configurations. Some of the common methodologies in
practice are (1) state enumeration methods (event-space methods), (2) network reduction
methods, and (3) path enumeration methods.
In Chapter 7, a description is given of how to make quantitative reliability and
availability predictions for proposed new configurations of industrial and commercial
power distribution systems. Several examples are worked out, including a simple radial
system, a primary selective system, and a secondary selective system. The simple
radial system that was analyzed had an average number of forced hours of downtime per
year that was 19 times larger than a secondary selective system; the failure rate was
6 times larger. The importance of two separate power supply sources from the electric
utility provider has been identified and analyzed. This approach could be used to assist in
cost–reliability trade-off decisions in the design of power distribution systems.
Chapter 8 presents a zone branch methodology that overcomes many of these
limitations and applies the methodology to a large industrial plant power system
configuration. There are many methods available for evaluating the frequency and
duration of load point interruptions within a given industrial power system configuration.
However, as systems become larger and more interconnected, these existing methods can
become computationally bound and limited in their ability to assess the impact of
unreliable protective equipment and unreliable protection coordination schemes on
individual load point reliability indices within a given plant configuration. These

methods also may not often account for complex isolation and restoration procedures
within an industrial plant configuration that are included in the zone branch reliability
methodology.
Chapter 9 deals with the types of data needed for distribution system’s predictive
reliability assessments and presents typical distribution component outage statistics in
urban and rural environments for use in predictive reliability analysis. This database is
the result of comprehensive synthesis of a large number of industry data available in
different technical publications. The distribution system is an important part of the total
electric supply system as it provides the final link between a utility’s bulk transmission
system and its ultimate customers. All quantitative reliability assessments require
numerical data. Historical assessment generally analyzes discrete interruption events
occurring at specific locations over specific time periods. Predictive assessment deter-
mines the long-term behavior of systems by combining component failure rates and the
duration of repair, restoration, switching, and isolation activities for the electric utility’s
distribution system for given system configurations to calculate average reliability
performance. Accurate component outage data are therefore the key to distribution
system predictive performance analysis. In addition to the physical configuration of the
distribution network, the reliability characteristics of system components, the operation
of protection equipment, and the availability of alternative supplies with adequate
capacity also have a significant impact on service reliability.
In Chapter 10, the methodology used to assess the historical reliability performance
ofa practical utility’s electric distribution system is outlined. Included in the discussion is
an overview of the process used to collect and organize the required interruption data as
well as a description of the performance indices calculated for use in the causal
assessment. Various components of reliability performance assessment are described,
including reliability indices, comparison between years of operation, comparisons of the
averages at different levels of the system, and outage cause and component failures.
The application of the calculated performance statistics in planning, operating, and
maintaining distribution systems is also described.
Chapter 11 provides a brief overview of current deterministic planning practices in
utility distribution system planning and design. The chapter also introduces a probabi-
listic customer value-based approach to alternative feed requirements planning for
overhead distribution networks to illustrate the advantages of probabilistic planning.
Chapter 12 identifies a number of pertinent factors and issues taken into account in
establishing distribution reliability standards and illustrates the issues and factors
considered in using historical reliability performance data. Actual utility data are used
in the illustrations. The development of standard distribution reliability metric values, for
example, System Average Interruption Frequency Index (SAIFI), System Average
Interruption Duration Index (SAIDI), and Customer Average Interruption Duration
Index (CAIDI), against which all utilities can compare performance, can be problematic
without strict adherence to a national or international standard (e.g., IEEE Standard
1366). This issue has been discussed in Chapter 11. At present, there are many
differences between data collection processes and characteristics of utility systems
to make comparisons against such standard metric values impossible for many
utilities. Rather, the development of uniform standard metric values, which utilities

compare to their own historical reliability performance indices, is more practical. If
cross-comparisons between utilities are desirable, a number of issues and factors
associated with individual utilities must be taken into consideration when establishing
distribution reliability standards.
Chapter 13 identifies a number of factors and issues that should be considered in
generating a PBR (performance-based rate making) plan for a distribution utility. A brief
analysis of cause contributions to reliability indices is also performed and presented in
this chapter. The historic reliability-based PBR framework developed in this chapter will
find practical applications in the emerging deregulated electricity market. In an attempt
to reregulate the distribution segment of an electric power system, public utility
commissions (PUCs) in a number of states in the United States are increasingly adopting
a reward/penalty framework to guarantee acceptable electric supply reliability. This
reward/penalty framework is commonly known as PBR. A PBR framework is introduced
to provide distribution utilities with incentives for economic efficiency gains in the
competitive generation and transmission markets. A distribution utility’s historical
reliability performance records could be used to create practical PBR mechanisms.
The chapter presents actual reliability performance history from two different utilities to
develop PBR frameworks for use in a reregulated environment. An analysis of financial
risk related to historic reliability data is presented by including reliability index
probability distributions in a PBR plan.
Chapter 14 presents the basic concepts and applications for computing load point
customer reliability indices and interruption costs. Case studies showing the applications
of load point reliability index calculations including customer interruption costs in
distribution system planning are described in detail. The practical distribution system
used in this chapter to illustrate the computation of the load point customer interruptions
costs has been extensively applied in Chapters 15, 16 and 19 for demonstrating
value-based predictive system planning methods, probabilistic distribution network
isolation, and restoration procedures and for determining distributed generation (DG)
equivalence to replace a distribution feeder requirement.
Chapter 15 presents a series of case studies of an actual industrial load area supplied
by two feeder circuits originating from two alternate substations. A basic conclusion of
this chapter is that expansion plans of an industrial distribution system can be optimized
in terms of reliability by using an economic criterion in which the sum of both the
industrial facility interruptions and the utility system costs is minimized. Society is
becoming increasingly dependent on a cost-effective reliable electric power supply.
Unreliable electric power supplies can be extremely costly to electric utilities and their
customers. Predictive reliability assessment combines historical outage data and
mathematical models to estimate the performance of specific network and system
configurations. Chapter 15 has expanded the customer interruption cost methodology
presented in Chapter 14 and applied to a practical distribution in illustrating the
value-based assessment of proposed modifications to an existing industrial distribution
system configuration to minimize the costs of interruptions to both the utility and the
utility’s industrial customers.
Chapter 16 presents a new restoration methodology for distribution system
configurations that maximizes the amount of load that can be restored after a grid

blackout, substation outage, and distribution feeder line section outages and evaluates the
cost of load point interruptions considering feeder islanding and substation capacity
constraints. Several case studies with restoration tables have been presented and
discussed to clearly reveal the impact of distribution system capacity constraints on
load point reliability indices and the cost of load point interruptions. A recent report on
the U.S.–Canada blackout on August 14, 2003 revealed that the duration of restoring the
Eastern Interconnect to a normal operating configuration was lengthy and complicated.
One of the difficulties in modeling a power system is to represent the significant changes
in loading patterns that present themselves during the restoration process after a major
outage. The capacity of the equipment may be adequate during normal operating
conditions; however, it may be severely compromised during restoration procedures,
particularly the restoration of thousands of distribution system feeder circuits.
Chapter 17 presents a customer cost–benefit probabilistic approach to designing
meshed urban distribution systems. The customer value-based reliability methodology is
illustrated using a practical urban distribution system of a Canadian utility. Achieving
high distribution reliability levels and concurrently minimizing capital costs can be
viewed as a problem of optimization. Using mathematical models and simulations, a
comparison of design concepts can be performed to compute the optimal feeder section
length, feeder loading level, and distribution substation transformer loading level. The
number of feeder ties and feeder tie placement in a meshed network are also optimized
through the models. The overall outcome of this analysis is that capital costs can then be
directed toward system improvements that will be most cost-effective in improving
distribution system reliability.
Chapter 18 discusses a reliability methodology to improve the radial distribution
feeder reliability performance normally prevailing in a rural environment using a simple
illustrative feeder configuration. As indicated earlier, historical distribution feeder
reliability assessment generally summarizes discrete interruption events occurring at
specific locations over specific time periods, whereas predictive assessment estimates
the long-term behavior of systems by combining component failure rates and repair
(restoration) times that describe the central tendency of an entire distribution of possible
values with feeder configurations. The outage time due to component failures can
substantially be reduced by protection and sectionalizing schemes. The time required to
isolate a faulted component by isolation and switching action is known as switching or
restoration time. The provision of alternative supply in radial networks normally
enhances the load point reliability. Fuses usually protect the lateral distributors
connected to the customers.
Chapter 19 delves into a reliability model for determining the DG equivalence to a
distribution facility for use in distribution system planning studies in the new competitive
environment. The primary objective of any electric utility company in the new competi-
tive environment is to increase the market value of the services by providing the right
amount of reliability and, at the same time, lower its costs of operation, maintenance, and
construction of new facilities to provide customers its services at lower rates. The electric
utility company will strive to achieve this objective by many means, one of which is to
defer the capital distribution facility requirements in favor of a DG solution by an
independent power producer (IPP) to meet the growing customer load demand. In this

case,the distribution capital investment deferral creditreceivedby the IPP will depend on
the incremental system reliability improvement rendered by the DG solution. In other
words, the size, location, and reliability of the DG will be based on the comparable
incremental reliability provided by the distribution solution under considerations.
Chapter 20 discusses probabilistic models developed based on Poisson probability
distribution for determining the optimal number of transformer spares for distribution
transformer systems. To maintain adequate service reliability, a distribution utility needs
to maintain a certain number of distribution equipment in its inventory as spare
equipment. The outage of a transformer is a random event, and the probability
mathematics can best describe this type of failure process. The developed models have
been described by using illustrative 72 kV distribution transformer systems. Industry
average catastrophic transformer failure rate and a 1-year transformer repair or procure-
ment time have been used in examples considered in the chapter. Among the models
developed for determining the optimum number of transformer spares, the statistical
economics model provides the best result as it attempts to minimize the total system cost
including the cost of spares carried in the system.
Chapter 21 deals with service quality issues in terms of voltage sags and surges.
A voltage sag may be caused by a switching operation involving heavy currents or by
the operation of protective devices (including autoreclosers) resulting from faults. These
events may emanate from the consumer’s systems or from the public supply network.
Voltage sags and short supply interruptions may disturb the equipment connected to the
supply network and cause a consumer interruption. The conclusions of this chapter are
that some of the inconveniences created by power quality problems are made worse by
the fact that restarting an industrial process may take from a few minutes to a few hours.
This chapter attempts to answer many questions asked by a utility’s industrial customers.
The answers presented in Chapter 21 are based on the statistical characteristics of
the Canadian National Power Quality Survey.
1.4 CONCLUSIONS
This chapter has introduced the basic definition of the term ‘‘reliability‚in a more generic
form. The application of reliability techniques to power systems performance assessment
was discussed briefly. Power generation system reliability evaluation by using the
reliability techniques using the 1 day in 10 years loss of load expectation criterion is
an accepted practice in the electric power industry. Reliability assessments in transmis-
sion systems have made great strides in recent years, and sophisticated computer models
are available for large-scale transmission system assessments. With the recent movement
toward competition in the electric energy market, increasing attention is being paid to the
utilization of probabilistic reliability techniques in distribution system assessments and
performance-based rate makings. This book is an attempt to achieve the objective of
providing distribution planning engineers simple and easy-to-use reliability models that
can be applied in routine distribution system cost–benefit enhancement planning without
resorting to sophisticated computer tools. The reliability concepts and models developed
and illustrated with practical system examples do not require knowledge of probability

mathematics, and virtually all reliability assessment tasks can be performed by hand
calculations. It is important to note that the book does not purport to cover every known
and available method in distribution system reliability planning, as it would require a text
of infinite length.
REFERENCES
1. R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems, 2nd edition, Plenum
Press, New York, 1996.
2. J. Endrenyi, Reliability in Electric Power Systems, John Wiley & Sons, Ltd., Chichester, 1978.
3. T. G€
onen, Electric Power Distribution System Engineering, McGraw Hill, New York, 1986.
4. J. J. Burke, Power Distribution Engineering: Fundamentals and Applications, Marcel Dekker,
Inc., New York, 1994.
5. R. E. Brown, Electric Power Distribution Reliability, Marcel Dekker, Inc., New York, 2002.
6. G. J. Anders, Probability Concepts in Electric Power Systems, John Wiley & Sons, Inc.,
New York, 1990.
REFERENCES 11

2
FUNDAMENTALS OF
PROBABILITY AND STATISTICS
2.1 CONCEPT OF FREQUENCY
2.1.1 Introduction
In recent years, there has been a significant increase in public awareness on the subject
of probability and statistics. At present, nearly all high school mathematics courses
introduce some elementary level of probability and statistics topics to many students,
while at the university level, many liberal arts disciplines such as geography and
sociology require some knowledge of probability and statistical mathematics from
college-bound students. Moreover, probability and statistical mathematics are being
increasingly used by almost all academic disciplines. There are relatively few science
or social science disciplines that do not require knowledge of probability and statistics.
This chapter will introduce some basic theories associated with probability and
statistics.
It is a well-known fact that things in nature exhibit variations. People have different
heights, earn different incomes, and machines turn out parts that are not perfectly
identical—the list can go on infinitely. To analyze the data, we divide them into groups
and count the number of occurrences in each group. Consider two examples. In a bag of
Power Distribution System Reliability. By Ali A. Chowdhury and Don O. Koval
Copyright 2009 the Institute of Electrical and Electronics Engineers, Inc.

marbles, there are five blue ones, seven red ones, and three white ones; second, the
duration of distribution feeder outages for a particular substation lasted 8 times
between 0 and 1 h, 15 times between 1 and 2 h, 5 times between 2 and 3 h, and 3
times between 3 and 4 h, as illustrated in Fig. 2.1. In the first example, the groups
are classified by a qualitative characteristic, the color of the marble. We have the
information on how many marbles of each color there are, but that is the end. There is no
relationship between the groups. The second example is different. The groups are
classified by a quantitative characteristic, the duration of the outages, and there is a
quantitative relationship between the groups. It is this kind of classification that lends
itself to analysis. The groups are called classes and the number in each group is called
the frequency. This frequency can also be converted to relative frequency in percentage
of the total population. The classification of a group of items by some quantitative
characteristic is called a frequency distribution.
Duration of feeder outages in hours
Frequency
of
the
duration
of
feeder
outages
5
0
10
15
0 1 2 3 4
Figure 2.1. Frequency histogram of duration of feeder outages.
0
Relative
frequency
of
occurrences
0.3226
0.1613
0.4839
Relative
frequency
of
the
duration
of
feeder
outages
4
3
2
1
0
Figure 2.2. Relative frequency histogram of duration of feeder outages.
14 FUNDAMENTALS OF PROBABILITY AND STATISTICS

2.1.2 Concept of Class
The classes in the duration of feeder outages example have a class width of 1 h. The width
can be made narrower to havea more detailed description of the duration offeeder outages
resulting in more classes. In general, the classes have equal widths and are consecutive.
There are also classes that are discrete numbers instead ofintervals, for example, age
of students (age rounded off to integers). As long as the discrete numbers are arranged
in some consecutive order, they form a frequency distribution that can be analyzed
systematically.
2.1.3 Frequency Graphs
The relationship between frequency or relative frequency and class can be shown
graphically as illustrated in Fig. 2.2. If shown as a bargraph, it is a histogram. Histograms
can also be used for qualitatively defined classes. If the midpoints of consecutive classes
are joined together with a line, it becomes a line graph. Sometimes the line graph is
smoothened, and an approximate, continuous frequency distribution is obtained. Line
graphs have no meaning if the classes are not quantitatively related.
2.1.4 Cumulative Frequency Distribution Model
Instead of the frequency of a class, the sum of frequencies of all proceedings or
subsequent classes can be shown as illustrated in Fig. 2.3. Cumulative frequency
distributions have a lot of applications, one of which is the load duration curve used
in generation capacity adequacy studies.
2.2 IMPORTANT PARAMETERS OF FREQUENCY DISTRIBUTION
The basic objective of constructing a frequency distribution is to analyze the pattern
of variation of a phenomenon. This pattern can be defined by several parameters.
0
Cumulative
frequency
of
occurrences
0.7419
0.2581
0.9032
1.0000
Cumulative
frequency
of
the
duration
of
feeder
outages
4
3
2
1
0
Figure 2.3. Cumulative frequency histogram of duration of feeder outages.
IMPORTANT PARAMETERS OF FREQUENCY DISTRIBUTION 15

2.2.1 Mean
Mean refers to the arithmetic mean or expected value. It is computed by summing the
values of all observations or items and by dividing the sum by the total number of
observations or items. In most frequency distributions, the values fall into different class
intervals, and the summation is done by calculating the product of the value of a class
and its frequency and summing over all classes. This sum will then be divided by the
total frequency. Mathematically, if Xi is the value of the ith class and fi is the frequency
of the ith class, then
Mean ¼
X
fixi
X
fi
ð2:1Þ
The mean represents the average value of each item in that frequency distribution,
such as the average height of a group of students in a class, the average income of
employees in a company, and so on.
2.2.2 Median
Median is thevalue of the middle item when all the items are arranged in either ascending
or descending order. It is the 50% point of the spectrum; so there are an equal number of
items on both sides of the median.
2.2.3 Mode
Mode is the value in a frequency distribution that occurs most often, that is, the value of
the class with the highest frequency. When represented in a graph form, it is the class
value corresponding to the highest point of the curve.
2.2.4 Standard Deviation
Standard deviation is a measure of the extent of variation in a frequency distribution.
It is defined as the square root of the average of squared deviations of the frequency
distribution. A deviation is the difference between the value of an item and the meanvalue,
and it could be negative. The squared deviation is the square of that and is always positive.
The average of squared deviations is obtained by summing all the squared deviations
in the frequency distribution and dividing by the number of items. Mathematically,
Standard deviation ¼ s ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
X
fiðxi ~
xÞ2
X
fi
v
u
u
t ; where ~
x is the mean ð2:2Þ
The standard deviation is therefore a measure of the spread of the items about the
mean. For example, the three numbers 20, 25, and 30 have a mean of 25. The mean gives
a fairly good approximation of the three individual numbers. The numbers 5, 10, and 60
also have a mean of 25, but the mean does not come close to giving an indication of what

the individual numbers are. The standard deviation tells the story; in the former case, it is
4.08, in the latter case, it is 24.83.
Problem 2.1
The following chart shows the seniority of 40 workers at a plant:
Seniority 1 2 3 4 5 6 8 9 11 15 18 20
Number 2 2 4 6 6 10 3 2 1 2 1 1
What is the average seniority?
What is the standard deviation?
Solution:
Average seniority ¼
x ¼
P
fixi
P
fi
¼
ð2 1Þ þ ð2 2Þ þ ð4 3Þ þ ð6 4Þ þ þ ð1 20Þ
2 þ 2 þ 6 þ 6 þ þ 1
¼ 6:33
Standard deviation ¼ s ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
fiðxi
xÞ2
P
fi
v
u
u
t
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ð1 6:33Þ2
þ 2ð2 6:33Þ2
þ 4ð3 6:33Þ2
þ þ 1ð18 6:33Þ2
þ 1ð20 6:33Þ2
2 þ 2 þ 4 þ þ 1 þ 1
v
u
u
t
¼ 4:19
2.2.5 Variance
Variance is the square of the standard deviation and has more direct applications in some
statistical analyses than the standard deviation.
2.3 THEORY OF PROBABILITY
2.3.1 Concept
Probability in simple terms is a measure of how likely it is for an event to happen or take
place. The approach used is normally a relative frequency approach, that is, the number
THEORY OF PROBABILITY 17

of outcomes in which the event of interest will take place expressed as a percentage
(or decimal) of the total number of possible outcomes assuming implicitly that all
outcomes are equally likely.
There are two kinds of situations usually encountered in this method. The first
one is when the number of outcomes is finite, and the probability is known exactly, for
example, the probability of rolling a “six” in a backgammon game in which two dice
are used is 5/36. The second situation is when the number of outcomes is infinite,
such as the probability of having a sunny day on Chinese New Year’s Day. The total
number of outcomes is all the Chinese New Year’s Day from the beginning of the
world to eternity, which is infinite and impossible to count, so the probability can only
be estimated from a limited account of past data. If in the past 10 years, 8 years have a
sunny Chinese New Year’s Day, the probability of having a sunny day on the next
Chinese New Year’s Day will be estimated to be 0.8. If, however, records of the past
25 years were used, it might be found that 22 years had sunny Chinese New Year’s
Day, giving a probability of 0.88. In this example, there is no exact probability as
there was for the rolling dice.
2.3.2 Probability Laws and Theorems
There are many laws and theorems pertaining to probability. The examples listed
below are some of the most fundamental and most frequently used. No rigorous
mathematical derivations are given.
1. The probability of an event occurring and probability of that event not occurring
always add up to 1.
PðAÞ þ Pð
AÞ ¼ 1:0 ð2:3Þ
2. The probability of event A or event B or both occurring is equal to the probability
of event A occurring plus the probability of event B occurring minus the
probability of both events occurring simultaneously.
PðA [ BÞ ¼ PðAÞ þ PðBÞ PðA; BÞ ð2:4Þ
3. The probability of two independent events both occurring is equal to the product
of the individual probabilities.
PðA BÞ ¼ PðAÞPðBÞ ð2:5Þ
4. The probability of event A given that event B has occurred is equal to the
probability of A and B both occurring divided by the probability of event B
occurring.
PðAjBÞ ¼
PðA BÞ
PðBÞ
ð2:6Þ

This is known as the conditional probability. No independence between A and B is
assumed. In fact, rearranging the terms gives the probability of both events A and
B occurring when A and B are not independent.
Someexampleswillclarifythelasttwotheorems.Supposethereare400boysand400
girls in a school and suppose one-quarter of the students wear glasses. The probability that
a studentpickedatrandomwillbea girlwearingglassesis1/2 1/4 ¼ 1/8accordingtothe
third theorem. The theorem applies because the two attributes are independent.
Now suppose 300 of the boys and 100 of the girls are interested in computer games.
The school has 400 students out of 800 who like computergames. However, if a student is
picked at random, the probability of finding a boy who is interested in computer games
is not 400/800 400/800 ¼ 0.25. It should be 300/800 ¼ 0.375 from first principles.
The Product Rule does not apply here because the two events, being a boy and being
interested in computer games, are not independent—boys seem to be more interested in
computer games than girls. Instead, the conditional probability of the fourth theorem
should be used.
Pðboy likes computer gamesÞ ¼ Pðboyjcomputer gamesÞ
Pðlikes computer gamesÞ
¼ 300=400 400=800
¼ 0:375
It does not matter which event is the dependent one and which event is the
independent one. The results will be identical:
Pðlikes computer games boyÞ ¼ Pðlikes computer gamesjboyÞ PðboyÞ
¼ 300=400 400=800
¼ 0:375
2.4 PROBABILITY DISTRIBUTION MODEL
2.4.1 Random Variable
Most probability and statistical problems involve a number that canvary between a range
of values. This number is the value of the item under consideration and is determined by
a random process and hence it is called a random variable. The random variable can take
on any value within the range, but the probability that it will assume a certainvalue varies
depending on what value it assumes. Using the backgammon example again, the possible
rolls of the two dice are from “two” to “twelve” but probability of each roll is not the
same as illustrated in Fig. 2.4. If the probability is plotted against the roll, the graph
given in Fig. 2.5 will be obtained.
The graph is called a probability distribution. This probability distribution is a
discrete one because the values of the rolls can only be integers. If the random variable is
continuous and can take on any value within the range, then it will be a continuous
probability distribution.
PROBABILITY DISTRIBUTION MODEL 19

2.4.2 Probability Density Function
In a discrete probability distribution, the ordinate of the random variable represents the
probability that the random variable will take on that particular value, for example, the
bar height of the roll “seven” in Fig. 2.5 is 0.1667 (one-sixth), which is the probability of
rolling a “seven.” The sum of the heights of all the bars is 1. This representation runs into
difficulty with continuous probability distributions. Since the random variable can
assume an infinite number of possible values, the sum of all these probabilities will
12
11
10
9
8
7
6
5
4
3
2
Sum of faces of two dice tossed
Probability
of
occurrence
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Figure 2.5. Probability distribution of the sum of faces of two dice tossed.
Face value of die #1
6
5
4
3
2
1
1 2 6
5
4
3 7
2 6
5
4
3 7 8
3 6
5
4 7 9
8
4 6
5 7 10
9
8
5 6 7 11
10
9
8
Face
value
of
die
#2
6 7 11
10
9
8 12
Sum of two die faces for a
single roll
Figure 2.4. Sum of two die faces for a single roll as a function of the face value of the die #2.

add up to infinity. The way to overcome this problem is by introducing the probability
density function.
In a probability density function, the ordinate of the random variable x represents the
probability density and not the probability itself. The probability is represented by the
area under the curve, so the probability of x falling between A and B is the area under
the curve between x ¼ A and x ¼ B, and the probability of the random variable being
equal to a certain value exactly is zero because the area of a line is zero. The area under
the entire curve is, of course, equal to 1. The probability density function can usually be
represented by a mathematical expression, for example,
fðxÞ ¼
1
a
e x=a
ð2:7Þ
The area under the curve from point A to point B can be found by integration.
Probability ðA x BÞ ¼
Z B
A
fðxÞ dx ð2:8Þ
For application purposes, there are tables for the calculation of area under the curve as
long as the end limits are known.
For discrete probability distributions, there are no continuous curves, just bars at
the discrete values that the random variable may take on. The heights of the bars are
the respective probabilities and no integration is necessary. For ascertaining cumulative
probabilities, however, it is required to calculate the heights of the bars separately and
sum them up whereas with a continuous probability density function, all that has to be
done is integration between the proper limits. For common discrete probability dis-
tributions, there are standard tables for cumulative probabilities.
2.4.3 Parameters of Probability Distributions
The mean of a probability distribution is the average value of the random variable. It is
analogous to the mean of a frequency distribution. For a discrete distribution, the mean
value of the random variable is given by

x ¼
X
PðxiÞxi ð2:9Þ
For a continuous probability distribution,

x ¼
Z
xfðxÞ dx ð2:10Þ
The mean is not necessarily in the middle of the range of possible x’s. However,
there is an equal chance for the random variable x to fall on the lower side of x as on the
higher side. In a continuous probability distribution, this means the area under the curve
is divided into two equal halves at x ¼
x.

The standard deviation is defined in the sameway as that for frequency distributions.
s ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
ðxi
xÞ2
PðxiÞ
q
ð2:11Þ
For a continuous distribution, this becomes
s ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Z
ðx
x2ÞfðxÞ dx
s
ð2:12Þ
2.4.4 The Binomial Distribution
An example will illustrate this probability distribution very clearly. Consider the
probability of rolling a fair die and getting a “six” two times out of three tosses. Work
from first principle:
Probability of rolling a “six” ¼ 1/6
Probability of not rolling a “six,” that is, X ¼ 5/6
To get two “sixes” out of three tosses, there are three ways:
6 6 X, Probability ¼ 1/6 1/6 5/6 ¼ 5/216
6 X 6, Probability ¼ 1/6 5/6 1/6 ¼ 5/216
X 6 6, Probability ¼ 5/6 1/6 1/6 ¼ 5/216
The probabilities of the three sequences are the same. Each consists of the
probability of rolling a “six” raised to the power 2 (the number of “sixes” required)
times the probability of not rolling a “six” raised to the power of 1 (the number of
“non-sixes” required). The number of sequences is the number of possible combinations
of two objects out of three. Multiply the three terms together and we get the required
probability. Total probability ¼ 3 (1/6)2
(5/6) ¼ 5/72.
The process can be generalized by the binomial theorem as follows:
PðxÞ ¼ nCxpx
ð1 pÞn x
ð2:13Þ
where n is the number of trials, x is the number of successful trials required, nCx ¼
n!/(n x)!x!) is the number of combinations of x objects out of n, and p is the
probability of success.
This term is readily recognized as the px
term in the expansion of the binomial term
[p þ (1 p)]n
. For the above example,
ð1=6 þ 5=6Þ3
¼ ð1=6Þ3
þ 3ð1=6Þ2
ð5=6Þ þ 3ð1=6Þð5=6Þ2
þ ð5=6Þ3
This is no coincidence. In fact, the first term represents the probability of rolling
three “sixes,” the second term two “sixes” and one “non-six,” the third term one “six”

and two “non-sixes,” and the fourth term three “non-sixes.” Since that covers all
possibilities, the sum of all these probabilities must be 1. That is automatically true
because [p þ (1 p)]n
is always equal to 1 regardless of what p and n are. The plot of
P(x) versus x for all the n terms is a binomial probability distribution and is shown in
Fig. 2.6.
Here, n and p are the parameters of the distribution that determine the shape of the
binomial distribution. The mean of the distribution is
P
PðxiÞxi ¼ p and the standard
deviation s ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pð1 pÞ
p
. Calculation of individual terms of the binomial distribution is
not too difficult with a calculator. Calculations of the cumulative probability can be
tedious, but there are tables available. Also for large n, the binomial distributions can be
approximated by other distributions.
Problem 2.2
It is known that 5% of the insulators are defective. What is the probability of finding three or
more defective insulators in a string of five?
Solution:
Defective rate p ¼ 0.2.
Probability of finding three or more defectives in five is given by
PðxÞ ¼ nCxpx
ð1 pÞn x
ðSection 2:4:4Þ
0
1
2
3
Number of “sixs” in three tosses of a die, x
Probability
of
occurrence
p(x)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
Figure 2.6. Binomial probability distribution n ¼ 3, p ¼ 1/6.

Pð3Þ ¼ 5C3ð0:2Þ3
ð0:8Þ5 3
¼
5 4 3 2 1
ð3 2 1Þ ð2 1Þ
ð0:2Þ3
ð0:8Þ2
¼ 0:0011
Pð4Þ ¼ 5C4ð0:2Þ4
ð0:9Þ5 4
¼ 5ð0:2Þ4 ð0:8Þ
¼ 0:0064
Pð5Þ ¼ 5C5ð0:2Þ5
ð0:8Þ0
¼ 0:00032
Probability of three or more defectives
¼ Pð3Þ þ Pð4Þ þ Pð5Þ
¼ 0:00782
¼ 0:782%
Problem 2.3
If there are three good insulators in a string of four, for 72 kV line, the probability of flashover is
quite small (0.02%). On a 72 kV line, salvaged insulators with 10% defectives are used. What is the
probability that a string will have fewer than three good insulators? The engineering manager
decides to add one unit to each string. How does that help?
Solution:
If percentage of defectives is 10, probabilities of getting zero, one, or two good insulators in a string
of five are
Pð0Þ ¼ 4 C0ð0:8Þ0
ð0:2Þ4
¼ð0:2Þ4
¼0:0016
Pð1Þ ¼ 4 C1ð0:8Þ1
ð0:2Þ3
¼4 0:8 0:008¼0:0256
Pð2Þ ¼ 4 C2ð0:8Þ2
ð0:2Þ2
¼0:1536
Pð0Þ þ Pð1Þ þ Pð2Þ ¼ 0:0016 þ 0:0256 þ 0:1536 ¼ 0:1808 ¼ 18:08%
If length of string is increased to 5,
P(0) ¼ 5C0(0.8)0
(0.2)5
¼ 0.00032
P(1) ¼ 5C1(0.8)1
(0.2)4
¼ 0.0064
P(2) ¼ 5C2(0.8)2
(0.2)3
¼ 0.0512

The probability of having less than three good insulators is
Pð0Þ þ Pð1Þ þ Pð2Þ ¼ 0:0579 ¼ 5:79%
The probability of inadequate insulation drops from over 18.08% to 5.79%.
2.4.5 The Poisson Distribution
Poisson distribution is a discrete probability distribution with an infinite number of
possible points for the random variable. The probability that the random variable will
take on a value x is given by
PðxÞ ¼
mx
e m
x!
ð2:14Þ
where m is a parameter of the distribution. Indeed, it is the mean and the standard
deviation that are
ffiffiffiffi
m
p
. The Poisson distribution describes the probability of occurrence
of a random eventfor a specified number of times within a given interval of time or scope.
Although the average number of occurrences is m in the long run, there is always a chance
that for a particular interval, the number of occurrences is something other than m.
For example, during a lightning storm, there are, say, two strokes per minute on an
average, that is, m ¼ 2; but for any given minute, there is always a chance that there are
0, 1, 2, 3, . . . strokes. In fact,
P(0) ¼ 13.5335%
P(1) ¼ 27.0671%
P(2) ¼ 27.0671%
P(3) ¼ 18.0447%
P(4) ¼ 9.0224%
P(5) ¼ 3.6089%
Like the binomial distribution, the Poisson distribution can be approximated by
continuous probability distributions. It is used as an approximation for the binomial
distribution in many cases. There are tables giving the cumulative probabilities.
Problem 2.4
The failure of power transformers is assumed to follow a Poisson probability distribution. Suppose
on average, a transformer fails once every 5 years. What is the probability that it will not fail in the
next 12 months? That it will fail once in the next 24 months?
Solution:
Failure rate ¼ once in 5 years
¼ 0:2=year
Number of expected failures in 12 months ¼ 0.2.

Probability of having zero failures is given by
Pð0Þ ¼
ð0:2Þ0
e 0:2
0!
¼ 0:8187
Number of expected failures in 24 months ¼ 0.2 2 ¼ 0.4.
Probability of having exactly one failure in that period is
Pð1Þ ¼
ð0:4Þ1
e 0:4
1!
¼ 0:2681
2.4.6 The Exponential Distribution
The exponential distribution is a continuous probability density function (i.e., the area
indicates the probability) given by the formula
fðxÞ ¼ l e lx
ð2:15Þ
where l is a parameter of this probability function. It extends from 0 to ? and is
illustrated in Fig. 2.7.
The exponential distribution describes a probability that decreases exponentially
with increasing x. That probability is indicated by the area under the curve to the right
of x, which extends to ? as illustrated in Fig. 2.8.
RðxÞ ¼
Z?
x
l e lx
dx ¼ e lx
ð2:16Þ
f(x)
0
λ
λ
e
– x
Exponential
density
function
x
Figure 2.7. Exponential distribution.

where R(x) is the probability that the random variable is greater than x and Q(x) is the
probability that the random variable is less than or equal to x.
The mean of the exponential distribution can be found from the formula
m ¼
Z?
0
xl e lx
dx ¼
1
l
ð2:17Þ
The standard deviation is given by
s ¼
Z?
0
x
1
l
2
l e lx
dx ¼
1
l
ð2:18Þ
The parameter l and the mean 1/l all have significant physical meanings when the
exponential distribution is applied to reliability assessments.
2.4.7 The Normal Distribution
Normal distribution is the most widely used probability distribution due to the fact that
most things that are phenomena in nature tend to follow this distribution. It is a good
approximation for many other distributions such as the binomial when the population is
large. It is a continuous distribution; hence, the curve is the probability density function
that takes on a symmetrical bell shape as illustrated in Fig. 2.9. The mathematical
formula for the probability density function is
fðxÞ ¼
1
ffiffiffiffiffiffiffiffiffi
2ps
p e ðx mÞ2
=2s2
ð2:19Þ
x
R(x)
f(x)
0 x
λe–λx
Exponential
density
function
Q(x)
Figure 2.8. Areas under the exponential density function. Note: Q(x) ¼ 1 R(x) because the
total area under the density function equals 1.

There are two parameters with this distribution, m and s. It can be proved that the
mean is m and the standard deviation is s. Being symmetrical, the mean m naturally
coincides with the midpoint of the bell-shaped curve. The area under the curve represents
probability. The curve extends from ? to ?; however, the areas at the tail ends are
negligible. Over 99% of the area falls within 3s, that is, three standard deviations from
the mean. Very often, instead of using the actual value of x, measurement is done in terms
of standard deviations from the mean and is called z. The mean becomes zero on this
normalized scale as shown in Fig. 2.10. If the mean value of the normal curve is set at
zero and all deviations are measured from the mean in terms of standard deviations,
the equation for the normal curve in standard form for Y becomes
Y ¼
1
ffiffiffiffiffiffi
2p
p

e z2
=2
; where z ¼ ðx mÞ=s ð2:20Þ
For example, suppose m ¼ 520 and s ¼ 11. A value of x ¼ 492.5 is 2.5 standard
deviations below the mean. On the normalized scale, x ¼ 492.5 simply becomes
z ¼ 2.5. There are tables for computing the area under a normal distribution curve,
and these tables are all based on the normalized scale.
x
µ
f(x)
−∞
∞ ∞
Figure 2.9. Normal probability density function.
Figure 2.10. Normalized normal probability density function. The area from z ¼ 1 to z ¼ 1 is
68.28%; from z ¼ 2 to z ¼ 2 is 95.48%; and from z ¼ 3 to z ¼ 3 is 99.76%.

Problem 2.5
In a normal distribution, what percentage is within 1.6 standard deviations from the mean?
Solution:
Refer to the normal distribution shown in Table 2.1.
z ¼ 1:6 corresponds to 0:4452
This is the shaded area.
The question says “within 1.6 standard deviations from the mean,” which includes the other
side of the mean (i.e., area corresponding to z ¼ 1.6).
So the area within 1:6 standard deviation from the mean
¼ 0:4452 2
¼ 0:8904
¼ 89:04%
2.5 SAMPLING THEORY
2.5.1 Concepts of Population and Sample
In statistics, the totality of things, persons, events, or other items under study is called the
population. There is certain information about the population that needs to be ascer-
tained. This information can be collected from the entire population; however, this is
often impractical and sometimes impossible, so sampling is used. A sample is a part of
the population selected so that inferences can be made from it about the entire population.
2.5.2 Random Sampling Model
In order for the information provided by the sample to be an accurate representation
of the population, there are two fundamental requirements, namely, the sample must be
a part of the population and there must be no bias in selecting the sample, that is, it should
be a random sample.
To achieve the accuracy desired, there are other principles and rules to follow, such
as the sample size to use and the techniques to select the sample. It must be recognized
that there is always the probability of error in sampling because part of the population has
been missed out. The error, however, can be predicted and controlled. If decisions are
made based on sampling information, the probability of error will be known and the risk
can hence be gauged. Sampling methods can be designed to suit the need. On the
contrary, a complete census is not always free of error in practice, and these errors are
hard to predict and control.
2.5.3 Sampling Distributions
When a sample is selected and the characteristics of interest of each unit in the sample
are observed or tested, a set of statistics such as mean, standard deviation, and so on
SAMPLING THEORY 29

T
A
B
L
E
2.1.
Areas
for
Standard
Normal
Probability
Distribution
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.0000
0.0040
0.0080
0.0120
0.0160
0.0199
0.0239
0.0279
0.0319
0.0359
0.1
0.0398
0.0438
0.0478
0.0517
0.0557
0.0596
0.0636
0.0675
0.0714
0.0753
0.2
0.0793
0.0832
0.0871
0.0910
0.0948
0.0987
0.1026
0.1064
0.1103
0.1141
0.3
0.1179
0.1217
0.1255
0.1293
0.1331
0.1368
0.1406
0.1443
0.1480
0.1517
0.4
0.1554
0.1591
0.1628
0.1664
0.1700
0.1736
0.1772
0.1808
0.1844
0.1879
0.5
0.1915
0.1950
0.1985
0.2019
0.2054
0.2088
0.2123
0.2157
0.2190
0.2224
0.6
0.2257
0.2291
0.2324
0.2357
0.2389
0.2422
0.2454
0.2486
0.2518
0.2549
0.7
0.2580
0.2612
0.2642
0.2673
0.2704
0.2734
0.2764
0.2794
0.2823
0.2852
0.8
0.2881
0.2910
0.2939
0.2967
0.2995
0.3023
0.3051
0.3078
0.3106
0.3133
0.9
0.3159
0.3186
0.3212
0.3238
0.3264
0.3289
0.3315
0.3340
0.3365
0.3389
1.0
0.3413
0.3438
0.3461
0.3485
0.3508
0.3531
0.3554
0.3577
0.3599
0.3621
1.1
0.3643
0.3665
0.3686
0.3708
0.3729
0.3749
0.3770
0.3790
0.3810
0.3830
1.2
0.3849
0.3869
0.3888
0.907
0.3925
0.3944
0.3962
0.3980
0.3997
0.4015
1.3
0.4032
0.4049
0.4066
0.4082
0.4099
0.4115
0.4131
0.4147
0.4162
0.4177
1.4
0.4192
0.4207
0.4222
0.4236
0.4251
0.4265
0.4279
0.4292
0.4306
0.4319
1.5
0.4332
0.4345
0.4357
0.4370
0.4382
0.4394
0.4406
0.4418
0.4429
0.4441
1.6
0.4452
0.4463
0.4474
0.4484
0.4495
0.4505
0.4515
0.4525
0.4535
0.4545
(Continued
)

T
A
B
L
E
2.1.
(Continued)
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1.7
0.4554
0.4564
0.4573
0.4582
0.4591
0.4599
0.4608
0.4616
0.4625
0.4633
1.8
0.4641
0.4649
0.4656
0.4664
0.4671
0.4678
0.4686
0.4693
0.4699
0.4706
1.9
0.4713
0.4719
0.4726
0.4732
0.4738
0.4744
0.4750
0.4756
0.4761
0.4767
2.0
0.4772
0.4778
0.4783
0.4788
0.4793
0.4798
0.4803
0.4808
0.4812
0.4817
2.1
0.4821
0.4826
0.4830
0.4834
0.4838
0.4842
0.4846
0.4850
0.4854
0.4857
2.2
0.4861
0.4864
0.4868
0.4871
0.4875
0.4878
0.4881
0.4884
0.4887
0.4890
2.3
0.4893
0.4896
0.4898
0.4901
0.4904
0.4906
0.4909
0.4911
0.4913
0.4916
2.4
0.4918
0.4920
0.4922
0.4925
0.4927
0.4929
0.4931
0.4932
0.4934
0.4936
2.5
0.4938
0.4940
0.4941
0.4943
0.4945
0.4946
0.4948
0.4949
0.4951
0.4952
2.6
0.4953
0.4955
0.4956
0.4957
0.4959
0.4960
0.4961
0.4962
0.4963
0.4964
2.7
0.4965
0.4966
0.4967
0.4968
0.4969
0.4970
0.4971
0.4972
0.4973
0.4974
2.8
0.4974
0.4975
0.4976
0.4977
0.4977
0.4978
0.4979
0.4979
0.4980
0.4981
2.9
0.4981
0.4982
0.4982
0.4983
0.4984
0.4984
0.4985
0.4985
0.4986
0.4986
3.0
0.49865
0.4987
0.4987
0.4988
0.4988
0.4989
0.4989
0.4989
0.4990
0.4990
4.0
0.4999683
Illustration:
For
z
¼
1.93,
shaded
area
is
0.4732
out
of
a
total
area
of
1.

Another Random Document on
Scribd Without Any Related Topics

In the Congressional Library, Washington,
D. C
The Smithsonian Institution was formally created by Act of Congress,
August 10, 1846, the corporation being composed of the President,
Vice-President, members of the Cabinet and Chief Justice, who are
constituted the establishment, made responsible for the duty of
the increase and diffusion of knowledge among men. The
Institution is administered by a Board of Regents, including in
addition three Senators, three members of the House, and six
citizens appointed by Congress; the presiding officer, called the

Chancellor, being usually the Chief Justice, and the secretary of the
board is the Executive Officer. The late eminent Professor Joseph
Henry was elected secretary in 1846, and he designed the plan and
scope of the Institution, continuing as its executive head until his
death in 1878. His statue stands in the grounds near the entrance.
Two other secretaries followed him, Spencer F. Baird (who was
twenty-seven years assistant secretary), and upon his death Samuel
P. Langley, in 1888. The ornate building of red Seneca brownstone, a
fine castellated structure in the Renaissance style, was designed in
1847 and finished in 1855. Its grand front stretches about four
hundred and fifty feet, and its nine towers and turrets, rising from
seventy-five to one hundred and fifty feet, stand up prettily behind
the groves of trees. This original building contains a museum of
natural history and anthropology. In connection with it there is
another elaborate structure over three hundred feet square—the
National Museum—containing numerous courts, surrounding a
central rotunda, beneath which a fountain plashes. This is under the
same management, and directly supported by the Government, the
design being to perfect a collection much like the British Museum,
but paying more attention to American antiquities and products. This
adjunct museum began with the gifts by foreign Governments to the
Philadelphia Centennial Exposition in 1876, most of them being still
preserved there. The Smithsonian Trust Fund now approximates
$1,000,000, and there are various other gifts and bequests held in
the Treasury for various scientific purposes similarly administered.
Briefly stated, the plan of Professor Henry was to increase
knowledge by original investigations and study, either in science or
literature, and to diffuse knowledge not only through the United
States, but everywhere, and especially by promoting an interchange
of thought among the learned in all nations, with no restriction in
favor of any one branch of knowledge. A leading feature of his plan
was to assist men of science in making original researches, to
publish them in a series of volumes, and to give a copy of them to
every first-class library on the face of the earth. There is said to be
probably not a scientific observer of any standing in the United

States to whom the Institution has not at some time extended a
helping hand, and this aid also goes liberally across the Atlantic. As
income grew, the scope has been enlarged. In the various museums
there is a particularly good collection of American ethnology, and a
most elaborate display of American fossils, minerals, animals, birds
and antiquities. There are also shown by the Fish Commission
specimens of the fishing implements and fishery methods of all
nations, an exhibition which is unexcelled in these special
departments. Many specifically interesting things are in the National
Museum. The personal effects of Washington, Jackson and General
Grant are there. Benjamin Franklin's old printing-press is preserved
in a somewhat dilapidated condition, and there is also the first
railway engine sent from England to the United States, the original
John Bull, built by Stephenson Son at Newcastle-on-Tyne in
June, 1831, and sent out as Engine No. 1 for the Camden and
Amboy Railroad crossing New Jersey, now a part of the Pennsylvania
Railroad. It weighs ten tons, and has four driving-wheels of fifty-four
inches diameter. This relic, after being used on the railroad for forty
years, until improved machinery superseded it, has been given the
Government as a national heirloom. Among the anthropological
collections is a chronologically arranged series illustrating American
history from the period of the discovery to the present day. This
includes George Catlin's famous collection of six hundred paintings,
illustrating the manners and customs of the North American Indians.
One of the most important features of the work of this most
interesting establishment is its active participation in all the great
International Expositions by the loan to them of valuable exhibits
under Government direction and control.
THE SOLDIERS' HOME AND WASHINGTON MONUMENT.
The city of Washington, with progressing years, is becoming more
and more the popular residential city of the country. It is one of the
most beautiful and attractive, the admirable plan, with the wide
asphalted streets, lined with trees, opening up vista views of grand

public buildings, statues, monuments or leafy parks, making it
specially popular. The northern and northwestern sections, on the
higher grounds, have consequently spread far beyond the Executive
Mansion, being filled with rows of elaborate and costly residences,
the homes of leading public men. The streets are kept scrupulously
clean, while at the intersections are circles, triangles and little
squares, which are availed of for pretty parks, and usually contain
statues of distinguished Americans. Among the noted residence
streets are Vermont, Massachusetts and Connecticut Avenues and K
Street and Sixteenth Street, all in the northwestern district. Among
the many statues adorning the small parks and circles are those of
Washington, Farragut, Scott, Thomas, McPherson, Dupont, Logan,
Franklin, Hancock, Grant, Rawlins and Martin Luther, the latter a
replica of the figure in the Reformation Monument at Worms.
To the northward the suburbs rise to Columbia Heights, with an
elevated plateau beyond, where there is a Government park
covering nearly a square mile of rolling surface, and surrounding one
of the noted rural retreats on the borders of the Capital, the
Soldiers' Home. This is an asylum and hospital for disabled and
superannuated soldiers of the American regular army, containing
usually about six hundred of them, and founded by General Winfield
Scott, whose statue adorns the grounds. Its cottages have been
favorite retiring-places of the Presidents in the warm weather. Amid
lovely surroundings the veterans are comfortably housed, and in the
adjacent cemetery thousands of them have been buried. Scott's
statue stands upon the southern brow of the plateau, where a ridge
is thrust out in a commanding situation; and from here the old
commander of the army forty and fifty years ago gazes intently over
the lower ground to the city three miles away, with the lofty Capitol
dome and Washington Monument rising to his level, while beyond
them the broad and placid Potomac winds between its wooded
shores. This is the most elevated spot near Washington, overlooking
a wide landscape. In the cemetery at the Soldiers' Home sleeps
General Logan, among the thousands of other veterans. To the
westward the beautiful gorge of Rock Creek is cut down, and beyond

is Georgetown, with its noted University, founded by the Jesuits in
1789, and having about seven hundred students. In the Oak Hill
Cemetery, at Georgetown, is the grave of John Howard Payne, the
author of Home, Sweet Home, who died in 1852. Far away over
the Potomac, in the Arlington National Cemetery, are the graves of
Generals Sherman and Sheridan.
Down near the Potomac, on the Mall, to the westward of the
Smithsonian turrets, is the extensive brick and brownstone building
representing the dominant industry of the United States, which gives
the politicians so much anxiety in catering for votes—the Agricultural
Department. Here are spacious gardens and greenhouses, an
arboretum and herbarium, the adjacent buildings also containing an
agricultural museum. As over three-fifths of the men in the United
States are farmers and farm-workers, and many others are in the
adjunct industries, it has become a popular saying in Washington
that if you wish to scare Congress you need only shake a cow's tail
at it. This department has grown into an enormous distributing office
for seeds and cuttings, crop reports and farming information. Among
its curiosities is the Sequoia Tree Tower, formed of a section of a
Sequoia or Big Tree of California, which was three hundred feet high
and twenty-six feet in diameter at the base.
Behind the Agricultural Department, and rising almost at the river
bank, and in front of the Executive Mansion, is the noted
Washington Monument, its pointed apex elevated five hundred and
fifty-five feet. This is a square and gradually tapering shaft,
constructed of white Maryland marble, the walls fifteen feet thick at
the base and eighteen inches at the top, the pyramidal apex being
fifty-five feet high and capped with a piece of aluminum. Its
construction was begun in 1848, abandoned in 1855, resumed in
1877 and finished in 1884, at a total cost of $1,300,000. The lower
walls contain stones contributed by public corporations and
organizations, many being sent by States and foreign nations, and
bearing suitable inscriptions in memory of Washington. A fatiguing
stairway of nine hundred steps leads to the top, and there is also a

slow-moving elevator. From the little square windows, just below the
apex, there is a grand view over the surrounding country. Afar off to
the northwest is seen the long hazy wall of the Blue Ridge or
Kittatinny Mountain range, its prominent peak, the Sugar Loaf, being
fifty miles distant. To the eastward is the Capitol and its surmounting
dome, over a mile away, while the city spreads all around the view
below, like a toy town, its streets crossing as on a chess-board, and
cut into gores and triangles by the broad, diagonal avenues lined
with trees, the houses being interspersed with many foliage-covered
spaces. Coming from the northwest the Potomac passes nearly at
the foot of the monument, with Arlington Heights over on the distant
Virginia shore, and the broad river channel flowing away to the
southwest until lost among the winding forest-clad shores below
Alexandria. From this elevated perch can be got an excellent idea of
the peculiarities of the town, its vast plan and long intervals of
space, so that there is quite plainly shown why the practical Yankee
race calls it the City of Magnificent Distances. Possibly one of the
best descriptions of Washington and its characteristics is that of the
poet in the Washington Post:

A city well named of magnificent distances;
Of boulevards, palaces, fountains and trees;
Of sunshine and moonlight whose subtle insistence is—
Bask in our radiance! Be lulled by our breeze!
A city like Athens set down in Arcadia;
White temples and porticoes gleaming 'mid groves;
Where nymphs glide and smile as though quite unafraid o' you,
The home of the Muses, the Graces, the Loves;
The centre of Politics, Letters and Sciences;
Elysium of Arts, yet the Lobbyist's Dream;
Where gather the clans whose only reliance is
Gold and the dross that sweeps down with its stream;
An isle of the lotus, where every-day business
Sails on its course all unvexed by simoons;
No bustle or roar, no mad-whirling dizziness
O'er velvety streets like Venetian lagoons;
A town where from nothing whatever they bar women,
From riding a bicycle—tending a bar;
Ex-cooks queen society—ladies are charwomen—
For such the plain facts as too often they are.
A city where applicants, moody, disconsolate,
Swoop eager for office and senseless to shame;
The heeler quite certain of getting his consulate,
Although, to be sure, he can't sign his name;
A town where all types of humanity congregate;
The millionaire lolling on cushions of ease;
The tramp loping by at a wolfish and hungry gait;
And mankind in general a' go as you please.
A city in short of most strange inconsistencies;
Condensing the history of man since the fall;
A city, however, whose piece de resistance is
This—'tis the best and the fairest of all.

THE POTOMAC AND THE ALLEGHENIES.
The Potomac is one of the chief among the many rivers draining the
Allegheny Mountains. It originates in two branches, rising in West
Virginia and uniting northwest of Cumberland; is nearly four hundred
miles long; has remarkably picturesque scenery in the magnificent
gorges and reaches of its upper waters; breaks through range after
range of the Alleghenies, and after reaching the lowlands becomes a
tidal estuary for a hundred miles of its final course, broadening to six
and eight and ultimately sixteen miles wide at its mouth in the
Chesapeake. Washington is near the head of tidewater, one hundred
and twenty-five miles from the bay; and for almost its entire course
the Potomac is an interstate boundary, between Maryland and West
Virginia and Virginia. Its name is Indian, referring to its use in their
primitive navigation, the original word Petomok meaning they are
coming by water—they draw near in canoes. The Alleghenies,
where this noted river originates, are a remarkable geological
formation. The Atlantic Coast of the United States has a general
trend from the northeast to the southwest, with bordering sand
beaches, and back of them a broad band of pines. Then, towards
the northwest, the land gradually rises, being formed in successive
ridges, with intervening valleys, until it reaches the Alleghenies. The
great ranges of this mountain chain, which is geologically known as
the Appalachian System, run almost parallel to the coast for over a
thousand miles, from the White Mountains of New Hampshire down
to Alabama. They are noted mountains, not very high, but of
remarkable construction, and are said to be much older in geological
formation than the Alps or the Andes. They are composed of series
of parallel ridges, one beyond the other, and all following the same
general course, like the successive waves of the ocean. For long
distances these ridges run in perfectly straight lines, and then, as
one may curve around into a new direction, all the others curve with
it. The intervening valleys are as remarkable in their parallelism as
the ridges enclosing them. From the seaboard to the mountains the
ranges of hills are of the same general character, but with less

elevation, gentler slopes, and in most cases narrower and much
more fertile valleys.
The South Mountain, an irregular and in some parts broken-down
ridge, is the outpost of the Alleghenies, while the great Blue Ridge is
their eastern buttress. The latter is about twenty miles northwest of
the South Mountain, and is the famous Kittatinny range, named by
the Indians, and in their figurative language meaning the endless
chain of hills. It stretches from the Catskills in New York southwest
to Alabama, a distance of eight hundred miles, a veritable backbone
for the Atlantic seaboard, its rounded ridgy peaks rising sometimes
twenty-five hundred feet north of the Carolinas, and much higher in
those States. It stands up like a great blue wall against the
northwestern horizon, deeply notched where the rivers flow out, and
is the eastern border for the mountain chain of numerous parallel
ridges of varying heights and characteristics that stretch in rows
behind it, covering a width of a hundred miles or more. Within this
chain is the vast store of minerals that has done so much to create
American wealth—the coal and iron, the ores and metals, that are in
exhaustless supply, and upon the surface grew the forests of timber
that were used in building the seaboard cities, but are now nearly all
cut off. The great Atlantic Coast rivers rise among these mountain
ridges, break through the Kittatinny and flow down to the ocean,
while the streams on their western slopes drain into the Mississippi
Valley. The Hudson breaks through the Kittatinny outcrop at the
West Point Highlands, the Delaware forces a passage at the Water
Gap, the Lehigh at the Lehigh Gap, below Mauch Chunk; the
Schuylkill at Port Clinton, the Susquehanna at Dauphin, above
Harrisburg, and the Potomac at Harper's Ferry. All these rivers either
rise among or force their winding passages through the various
ranges behind the great Blue Ridge, and also through the South
Mountain and the successive parallel ranges of lower hills that are
met on their way to the coast, so that all in their courses display
most picturesque valleys.

HARPER'S FERRY AND JOHN BROWN.
The Potomac, having flowed more than two hundred miles through
beautiful gorges and the finest scenery of these mountains, finally
breaks out at Harper's Ferry, receiving here its chief tributary, the
Shenandoah, coming up from Virginia, the Potomac River passage of
the Blue Ridge being described by Thomas Jefferson as one of the
most stupendous scenes in nature. The Shenandoah—its name
meaning the stream passing among the spruce-pines—flows
through the fertile and famous Valley of Virginia, noted for its
many battles and active movements of troops during the Civil War,
when the rival forces, as fortunes changed, chased each other up
and down the Valley; and Harper's Ferry, at the confluence of the
rivers, and the towering Maryland Heights on the northern side and
the Loudon Heights on the Virginia side, the great buttresses of the
river passage, being generally held as a northern border fortress.
These huge mountain walls rise fifteen hundred feet above the town,
which has a population of about two thousand.
Harper's Ferry was also the scene of John Brown's raid, which was
practically the opening act of the Civil War, although actual hostilities
did not begin until more than a year afterwards. Old John Brown of
Osawatomie was a tanner, an unsettled and adventurous spirit and
foe of slavery, born in Connecticut in 1800, but who, at the same
time, was one of the most upright and zealous men that ever lived.
In his wanderings he migrated to Kansas in 1855, where he lived at
Osawatomie, and fought against the pro-slavery party. His house
was burnt and his son killed in the Kansas border wars, and he made
bloody reprisals. Smarting under his wrongs, he became the master-
spirit of a convention which met at Chatham, Canada, in May, 1859,
and organized an invasion of Virginia to liberate the slaves. Having
formed his plans, he rented a farmhouse in July about six miles from
Harper's Ferry, and gathered his forces together. On the night of
October 16th, with twenty-two associates, six being negroes, he
crossed the bridge into Harper's Ferry, and captured the arsenal and
armory of the Virginia militia, intending to liberate the slaves and

occupy the heights of the Blue Ridge as a base of operations against
their owners. A detachment of United States marines were next day
sent to the aid of the militia, and, after two days' desultory
hostilities, some of his party were killed, and Brown and the
survivors were captured and given up to the Virginia authorities for
trial. His final stand was made in a small engine-house, known as
John Brown's Fort, which was exhibited at the Chicago Exposition
in 1893. Brown and six of his associates were hanged at the county-
seat, Charlestown, seven miles southwest of Harper's Ferry, on
December 2d, Brown facing death with the greatest serenity. His raid
failed, but it was potential in disclosing the bitter feeling between
the North and the South, and it furnished the theme for the most
popular and inspiring song of the Civil War:
John Brown's body lies mouldering in the grave,
But his soul goes marching on.
THE GREAT FALLS AND ALEXANDRIA.
The Potomac continues its picturesque course below Harper's Ferry,
and passes the Point of Rocks, a promontory of the Catoctin
Mountain, a prolongation of the Blue Ridge. There were battles
fought all about, the most noted being at South Mountain and
Antietam, to the northward, in September, 1862; while it was at
Frederick, fifteen miles away, during this campaign, that Barbara
Frietchie was said to have waved the flag as Stonewall Jackson
marched through the town, immortalized in Whittier's poem. Here is
buried Francis Scott Key, author of the Star-Spangled Banner, who
died in 1843, and a handsome monument was erected to his
memory in 1898. The Potomac reaches its Great Falls about fifteen
miles above Washington, where it descends eighty feet in about two
miles, including a fine cataract thirty-five feet high. Below this is the
Cabin John Bridge, with one of the largest stone arches in the

world, of two hundred and twenty feet span, built for the
Washington Aqueduct, carrying the city water supply from the Great
Falls. On Wesley Heights, to the northward, the new American
University of the Methodist Church is being constructed.
Below Washington, the river passes the ancient city of Alexandria, a
quaint old Virginian town, which was formerly of considerable
commercial importance, but is now quiet and restful, and cherishing
chiefly the memory of George Washington, who lived at Mount
Vernon, a few miles below, and was its almost daily visitor to
transact his business and go to church and entertainments. The
tradition is that Madison, who was chairman of the Committee of
Congress, selected Alexandria for the Federal City, intending to
erect the Capitol on Shooters' Hill, a mile out of town, as grand an
elevation as the hill in Washington; but he was overruled by the
President because the latter hesitated to thus favor his native State.
Had Madison had his way, the town probably would not now be so
sleepy. The modest little steeple of Christ Church, where Washington
was a vestryman, rises back of the town, and his pew, No. 5, is still
shown, for which, when the church was built and consecrated in
1773, the records show that he paid thirty-six pounds, ten shillings.
To construct this church and another at the Falls, the vestry of
Fairfax parish, in 1766, levied an assessment of 31,185 pounds of
tobacco, and the rector's salary was also paid in tobacco. After the
Revolution, to help support the church, Washington and seven
others signed an agreement in the vestry-book to each pay five
pounds annual rental for the pews they owned. Robert E. Lee was
baptized and confirmed and attended Sunday-school in this old
church, and tablets in memory of Washington and Lee were inserted
in the church wall in 1870. At the Carey House, near the river,
Washington, in 1755, received from General Braddock, who had
come up there from Hampton Roads, his first commission as an aide
to that commander, with the rank of Major, just before starting on
the ill-starred expedition into Western Pennsylvania. Alexandria has
probably fifteen thousand people, and on the outskirts is another
mournful relic of the Civil War, a Soldiers' Cemetery, with four

thousand graves. Below Alexandria, the Hunting Creek flows into the
Potomac, this stream having given Washington's home its original
name of the Hunting Creek Estate.
WASHINGTON'S HOME AND TOMB.
Mount Vernon, the home and burial-place of George Washington, is
seventeen miles below the city of Washington, the mansion-house,
being in full view, standing among the trees on the top of a bluff,
rising about two hundred feet above the river. As the steamboat
approaches, its bell is tolled, this being the universal custom on
nearing or passing Washington's tomb. It originated in the reverence
of a British officer, Commodore Gordon, who, during the invasion of
the Capital in August, 1814, sailed past Mount Vernon, and as a
mark of respect for the dead had the bell of his ship, the Sea
Horse, tolled. The Hunting Creek Estate was originally a domain
of about eight thousand acres; and Augustine Washington, dying in
1743, bequeathed it to Lawrence Washington, who, having served in
the Spanish wars under Admiral Vernon, named it Mount Vernon in
his honor. George Washington was born in 1732, in Westmoreland
County, farther down the Potomac, and when a boy lived near
Fredericksburg, on the Rappahannock River. In 1752 he inherited
Mount Vernon from Lawrence, and after his death the estate passed
to his nephew, Bushrod Washington, subsequently descending to
other members of the family. Congress repeatedly endeavored to
have Washington's remains removed to the crypt under the rotunda
of the Capitol originally constructed for their reception, but the
family always refused, knowing it was his desire to rest at Mount
Vernon. The grounds and buildings being in danger of falling into
dilapidation, and the estate passing under control of strangers, a
patriotic movement began throughout the country for the purchase
of the portion containing the tomb and mansion. The Virginia
Legislature, in 1856, passed an act authorizing the sale, and under
the auspices of a number of energetic ladies who formed the Mount
Vernon Association, assisted by the oratory of Edward Everett, who

traversed the country making a special plea for help, a tract of two
hundred acres was bought for $200,000, being enlarged by
subsequent gifts to two hundred and thirty-five acres. These ladies
and their successors have since taken charge, restoring and
beautifying the estate, which is faithfully preserved as a patriotic
heritage and place of pilgrimage for visitors from all parts of the
world.
The steamboat lands at Washington's wharf at the foot of the bluff,
where he formerly loaded his barges with flour ground at his own
mill, shipping most of it from Alexandria to the West Indies. The
road from the wharf leads up a ravine cut diagonally in the face of
the bluff, directly to Washington's tomb, and alongside the ravine are
several weeping willows that were brought from Napoleon's grave at
St. Helena. Washington's will directed that his tomb shall be built of
brick, and it is a plain square brick structure, with a wide arched
gateway in front and double iron gates. Above is the inscription on a
marble slab, Within this enclosure rests the remains of General
George Washington. The vault is about twelve feet square, the
interior being plainly seen through the gates. It has upon the floor
two large stone coffins, that on the right hand containing
Washington, and that on the left his widow Martha, who survived
him over a year. In a closed vault at the rear are the remains of
numerous relatives, and in front of the tomb monuments are erected
to several of them. No monument marks the hero, but carved upon
the coffin is the American coat-of-arms, with the single word
Washington.
The road, farther ascending the bluff, passes the original tomb, with
the old tombstone antedating Washington and bearing the words
Washington Family. This was the tomb, then containing the
remains, which Lafayette visited in 1824, escorted by a military
guard from Alexandria to Mount Vernon, paying homage to the dead
amid salvos of cannon reverberating across the broad Potomac. It is
a round-topped and slightly elevated oven-shaped vault. The road at
the top of the bluff reaches the mansion, standing in a commanding

position, with a fine view over the river to the Maryland shore. It is a
long wooden house, with an ample porch facing the river. It is built
with simplicity, two stories high, and contains eighteen rooms, there
being a small surmounting cupola for a lookout. The central portion
is the original house built by Lawrence Washington, who called it his
villa, and afterwards George Washington extended it by a large
square wing at each end, and when these were added he gave it the
more dignified title of the Mansion. The house is ninety-six feet
long and thirty feet wide, the porch, extending along the whole
front, fifteen feet wide, its top being even with the roof, thus
covering the windows of both stories. Eight large square wooden
columns support the roof of the porch. Behind the house, on either
side, curved colonnades lead to the kitchens, with other outbuildings
beyond. There are various farm buildings, and a brick barn and
stable, the bricks of which it is built having been brought out from
England about the time Washington was born, being readily carried
in those days as ballast in the vessels coming out for Virginia
tobacco. The front of the mansion faces east, and it has within a
central hall with apartments on either hand. At the back, beyond the
outbuildings and the barn, stretches the carriage road, which in
Washington's time was the main entrance, off to the porter's lodge,
on the high road, at the boundary of the present estate, about
three-quarters of a mile away. Everything is quiet, and in the
thorough repose befitting such a great man's tomb; and this is the
modest mansion on the banks of the Potomac that was the home of
one of the noblest Americans.
THE WASHINGTON RELICS.
As may be supposed, this interesting building is filled with relics. The
most valuable of all of them hangs on the wall of the central hall, in
a small glass case shaped like a lantern—the Key of the Bastille—
which was sent to Washington, as a gift from Lafayette, shortly after
the destruction of the noted prison in 1789. This is the key of the
main entrance, the Porte St. Antoine, an old iron key with a large

handle of peculiar form. This gift was always highly prized at Mount
Vernon, and in sending it Lafayette wrote: It is a tribute which I
owe as a son to my adopted father; as an aide-de-camp to my
general; as a missionary of liberty to its patriarch. The key was
confided to Thomas Paine for transmission, and he sent it together
with a model and drawing of the Bastille. In sending it to
Washington Paine said: That the principles of America opened the
Bastille is not to be doubted, and therefore the key comes to the
right place. The model, which was cut from the granite stones of
the demolished prison, and the drawing, giving a plan of the interior
and its approaches, are also carefully preserved in the house.
The Washington relics are profuse—portraits, busts, old furniture,
swords, pistols and other weapons, camp equipage, uniforms,
clothing, books, autographs and musical instruments, including the
old harpsichord which President Washington bought for two hundred
pounds in London, as a bridal present for his wife's daughter,
Eleanor Parke Custis, whom he adopted. There is also an old
armchair which the Pilgrims brought over in the Mayflower in
1620. Each apartment in the house is named for a State, and cared
for by one of the Lady-Regents of the Association. In the banquet-
hall, which is one of the wings Washington added, is an elaborately-
carved Carrara marble mantel, which was sent him at the time of
building by an English admirer, Samuel Vaughan. It was shipped
from Italy, and the tale is told that on the voyage it fell into the
hands of pirates, who, hearing it was to go to the great American
Washington, sent it along without ransom and uninjured. Rembrandt
Peale's equestrian portrait of Washington with his generals covers
almost the entire end of this hall. Here also is hung the original
proof-sheet of Washington's Farewell Address. Up stairs is the room
where Washington died; the bed on which he expired and every
article of furniture are preserved, including his secretary and writing-
case, toilet-boxes and dressing-stand. Just above this chamber,
under the peaked roof, is the room in which Mrs. Washington died.
Not wishing to occupy the lower room, after his death, she selected
this one, because its dormer window gave a view of his tomb. The

ladies who have taken charge of the place deserve great credit for
their complete restoration; they hold the annual meeting of the
Association in the mansion every May.
As the visitor walks through the old house and about the grounds,
solemn and impressive thoughts arise that are appropriate to this
great American shrine. From the little wooden cupola there is seen
the same view over the broad Potomac upon which Washington so
often gazed. The noble river, two miles wide, seems almost to
surround the estate with its majestic curve, flowing between the
densely-wooded shores. Above Mount Vernon is a projecting bluff,
which Fort Washington surmounts on the opposite shore—a stone
work which he planned—hardly seeming four miles off, it is so
closely visible across the water. In front are the Maryland hills, and
the river then flows to the southward, its broad and winding reaches
being seen afar off, as the southern shores slope upward into the
forest-covered hills of the sacred soil of the proud State of Virginia.
And then the constantly broadening estuary of the grand Potomac
stretches for more than a hundred miles, far beyond the distant
horizon, until it becomes a wide inland sea and unites its waters at
Point Lookout with those of Chesapeake Bay.
MARY, THE MOTHER OF WASHINGTON.
To the southward of the Potomac a short distance, and flowing
almost parallel, is another noted river of Virginia, the Rappahannock,
rising in the foothills of the Blue Ridge, and broadening into a wide
estuary in its lower course. Its chief tributary is the stream which the
colonists named after the good Queen Anne, the Rapid Ann, since
condensed into the Rapidan. The Indians recognized the tidal
estuary of the Rappahannock, for the name means the current has
returned and flowed again, referring to the tidal ebb and flow. Upon
this stream, southward from Washington, is the quaint old city of
Fredericksburg, which has about five thousand inhabitants, and five
times as many graves in the great National Cemetery on Marye's
Heights and in the Confederate Cemetery, mournful relics of the

sanguinary battles fought there in 1862-63. The town dates from
1727, when it was founded at the head of tidewater on the
Rappahannock, where a considerable fall furnishes good water-
power, about one hundred and ten miles from the Chesapeake. But
its chief early memory is of Mary Ball, the mother of Washington,
here having been his boyhood home. A monument has been erected
to her, which it took the country more than a century to complete.
She was born in 1706 on the lower Rappahannock, at Epping Forest,
and Sparks and Irving speak of her as the belle of the Northern
Neck and the rose of Epping Forest. In early life she visited
England, and the story is told that one day while at her brother's
house in Berkshire a gentleman's coach was overturned nearby and
its occupant seriously injured. He was brought into the house and
carefully nursed by Mary Ball until he fully recovered. This gentleman
was Colonel Augustine Washington, of Virginia, a widower with three
sons, and it is recorded in the family Bible that Augustine
Washington and Mary Ball were married the 6th of March, 1730-31.
He brought her to his home in Westmoreland County, where George
was born the next year. His house there was accidentally burnt and
they removed to Fredericksburg, where Augustine died in 1740; but
she lived to a ripe old age, dying there in 1789. When her death was
announced a national movement began to erect a monument, but it
was permitted to lapse until the Washington Centenary in 1832,
when it was revived, and in May, 1833, President Jackson laid the
corner-stone with impressive ceremonies in the presence of a large
assemblage of distinguished people. The monument was started and
partially completed, only again to lapse into desuetude. In 1890 the
project was revived, funds were collected by an association of ladies,
and in May, 1894, a handsome white marble obelisk, fifty feet high,
was created and dedicated. It bears the simple inscription, Mary,
the Mother of Washington.
WILLIAMSBURG AND YORKTOWN.

Again we cross over southward from the Rappahannock to another
broad tidal estuary, an arm of Chesapeake Bay, the York River. This
is formed by two comparatively small rivers, the Mattapony and the
Pamunkey, the latter being the Indian name of York River. It is quite
evident that the Indians who originally frequented and named these
streams did not have as comfortable lives in that region as they
could have wished, for the Mattapony means no bread at all to be
had, and the Pamunkey means where we were all sweating. To
the southward of York River, and between it and James River, is the
famous Peninsula, the locality of the first settlements in Virginia,
the theatre of the closing scene of the War of the Revolution, and
the route taken by General McClellan in his Peninsular campaign of
1862 against Richmond. Williamsburg, which stands on an elevated
plateau about midway of the Peninsula, three or four miles from
each river, was the ancient capital of Virginia, and it has as relics the
old church and magazine of the seventeenth century, and the
venerable College of William and Mary, chartered in 1693, though its
present buildings are mainly modern. This city was named for King
William III., and was fixed as the capital in 1699, the government
removing from Jamestown the next year. In 1780 the capital was
again removed to Richmond. This old city, which was besieged and
captured by McClellan in his march up the Peninsula in May, 1862,
now has about eighteen hundred inhabitants.
Down on the bank of York River, not far from Chesapeake Bay, with
a few remains of the British entrenchments still visible, is Yorktown,
the scene of Cornwallis's surrender, the last conflict of the American
Revolution. Sir Henry Clinton, the British commander-in-chief in
1781, ordered Lord Cornwallis to occupy a strong defensible position
in Virginia, and he established himself at Yorktown on August 1st,
with his army of eight thousand men, supported by several warships
in York River, and strongly fortified not only Yorktown, but also
Gloucester Point, across the river. In September the American and
French forces effected a junction at Williamsburg, marching to the
investment of Yorktown on the 28th. Washington commanded the
besieging forces, numbering about sixteen thousand men, of whom

seven thousand were Frenchmen. Upon their approach the British
abandoned the outworks, and the investment of the town was
completed on the 30th. The first parallel of the siege was established
October 9th, and heavy batteries opened with great effect,
dismounting numerous British guns, and destroying on the night of
the 10th a frigate and three large transports. The second parallel
was opened on the 11th, and on the 14th, by a brilliant movement,
two British redoubts were captured. The French fleet, under Count
De Grasse, in Chesapeake Bay, prevented escape by sea, and
Cornwallis's position became very critical. On the 16th he made a
sortie, which failed, and on the 17th he proposed capitulation. The
terms being arranged, he surrendered October 19th, this deciding
the struggle for American independence. When the British troops
marched out of the place, and passed between the French and
American armies, it is recorded that their bands dolefully played
The World Turned Upside Down. Considering the momentous
results following the capitulation, this may be regarded as prophetic.
Yorktown was again besieged in 1862 by McClellan, and after several
weeks was taken in May, the army then starting on its march up the
Peninsula.

The Natural Bridge, Virginia
THE NATURAL BRIDGE.
The chief river of Virginia is the James, a noble stream, rising in the
Alleghenies and flowing for four hundred and fifty miles from the
western border of the Old Dominion until it falls into Chesapeake Bay
at Hampton Roads. Its sources are in a region noted for mineral
springs, and the union of Jackson and Cowpasture Rivers makes the
James, which flows to the base of the Blue Ridge, and there receives
a smaller tributary, not inappropriately named the Calfpasture River.
The James breaks through the Blue Ridge by a magnificent gorge at

Balcony Falls. Seven miles away, spanning the little stream known as
Cedar Brook, is the famous Natural Bridge, the wonderful arch of
blue limestone two hundred and fifteen feet high, ninety feet wide,
and having a span of a hundred feet thrown across the chasm,
which has given to the county the name of Rockbridge. Overlooking
the river and the bridge and all the country roundabout are the two
noble Peaks of Otter, rising about four thousand feet, the highest
mountains in that part of the Alleghenies. This wonderful bridge is
situated at the extremity of a deep chasm, through which the brook
flows, across the top of which extends the rocky stratum in the form
of a graceful arch. It looks as if the limestone rock had originally
covered the entire stream bed, which then flowed through a
subterranean tunnel, the rest of the limestone roof having fallen in
and been gradually washed away. The bridge is finely situated in a
grand amphitheatre surrounded by mountains. The crown of the
arch is forty feet thick, the rocky walls are perpendicular, and over
the top passes a public road, which, being on the same level as the
immediately adjacent country, one may cross it in a coach without
noticing the bridged chasm beneath. Various large forest trees grow
beneath and under the arch, but are not tall enough to reach it. On
the rocky abutments of the bridge are carved the names of many
persons who had climbed as high as they dared on the steep face of
the precipice. Highest of all, for about seventy years, was the name
of Washington, who, in his youth, ascended about twenty-five feet to
a point never before reached; but this feat was surpassed in 1818 by
James Piper, a college student, who actually climbed from the foot to
the top of the rock. In 1774 Thomas Jefferson obtained a grant of
land from George III. which included the Natural Bridge, and he was
long the owner, building the first house there, a log cabin with two
rooms, one being for the reception of strangers. Jefferson called the
bridge a famous place that will draw the attention of the world;
Chief Justice Marshall described it as God's greatest miracle in
stone; and Henry Clay said it was The bridge not made with
hands, that spans a river, carries a highway, and makes two
mountains one.

THE JAMES RIVER AND POWHATAN.
Following down James River, constantly receiving accessions from
mountain streams, we soon come to Lynchburg, most picturesquely
built on the sloping foothills of the Blue Ridge, and having fine
water-power for its factories, a centre of the great tobacco industry
of Virginia, supporting a population of about twenty thousand
people. Lynchburg was a chief source of supply for Lee's army in
Eastern Virginia until, in February, 1865, Sheridan, by a bold raid,
destroyed the canal and railroads giving it communication; and, after
evacuating Richmond, Lee was endeavoring to reach Lynchburg
when he surrendered at Appomattox, about twenty miles to the
eastward, on April 9, 1865, thus ending the Civil War. The little
village of Appomattox Court House is known in the neighborhood as
Clover Hill. When Lee surrendered, casualties, captures and
desertions had left him barely twenty-seven thousand men, with
only ten thousand muskets, thirty cannon and three hundred and
fifty wagons.
The James River, east of the Blue Ridge, drains a grand agricultural
district, and its coffee-colored waters tell of the rich red soils through
which it comes in the tobacco plantations all the way past Lynchburg
to Richmond. In its earlier history this noted river was called the
Powhatan, and it bears that name on the older maps. Powhatan, the
original word, meant, in the Indian dialect, the falls of the stream
or the falling waters, thus named from the falls and rapids at
Richmond, where the James, in the distance of nine miles, has a
descent of one hundred and sixteen feet, furnishing the magnificent
water-power which is the source of much of the wealth of Virginia's
present capital. The old Indian sachem whose fame is so intertwined
with that of Virginia took his name of Powhatan from the river. His
original name was Wahunsonacock when the colonists first found
him, and he then lived on York River; but it is related that he grew in
power, raised himself to the command of no less than thirty tribes,
and ruled all the country from southward of the James to the
eastward of the Potomac as far as Chesapeake Bay. When he

became great, for he was unquestionably the greatest Virginian of
the seventeenth century, he changed his name and removed to the
James River, just below the edge of Richmond, where, near the river
bank, is now pointed out his home, still called Powhatan. It was here
that the Princess Pocahontas is said to have interfered to save the
life of Captain John Smith. Here still stands a precious relic in the
shape of an old chimney, believed to have been originally built for
the Indian king's cabin by his colonist friends. It is of solid masonry,
and is said to have outlasted several successive cabins which had
been built up against it in Southern style. A number of cedars
growing alongside, tradition describes as shadowing the very stone
on which Smith's head was laid. It may not be generally known that
early in the history of the colony Powhatan was crowned as a king,
there having been brought out from England, for the special
purpose, a crown and a scarlet cloke and apparrell. The writer
recording the ceremony says quaintly: Foule trouble there was to
make him kneele to receive his crowne. At last, by leaning hard on
his shoulders, he a little stooped, and three having the crowne in
their hands, put it on his head. To congratulate their kindnesse, he
gave his old shoes and his mantell to Captaine Newport, telling him
take them as presents to King James in return for his gifts.
THE INDIAN PRINCESS POCAHONTAS.
The James River carries a heavy commerce below Richmond, and
the channel depths of the wayward and very crooked stream are
maintained by an elaborate system of jetties, constructed by the
Government. Both shores show the earthworks that are relics of the
war, and Drewry's Bluff, with Fort Darling, the citadel of the
Confederate defence of the river, is projected across the stream.
Below is Dutch Gap, where the winding river, flowing in a level plain,
makes a double reverse curve, going around a considerable surface
without making much actual progress. Here is the Dutch Gap Canal,
which General Butler cut through the narrowest part of the long
neck of land, thus avoiding Confederate batteries and saving a

detour of five and a half miles; it is now used for navigation. Just
below is the large plantation of Varina, where the Indian Princess
Pocahontas lived after her marriage with the Englishman, John Rolfe.
Its fine brick colonial mansion was the headquarters for the
exchange of prisoners during the Civil War.
The brief career of Pocahontas is the great romance of the first
settlement of Virginia. She was the daughter and favorite child of
Powhatan, her name being taken from a running brook, and
meaning the bright streamlet between the hills. When the Indians
captured Captain John Smith she was about twelve years of age. He
made friends of the Indian children, and whittled playthings for
them, so that Pocahontas became greatly interested in him, and the
tale of her saving his life is so closely interwoven with the early
history of the colony that those who declare it apocryphal have not
yet been able to obliterate it from our school-books. Smith being
afterwards liberated, Pocahontas always had a longing for him, was
the medium of getting the colonists food, warned them of plots, and
took an interest in them even after Smith returned to England. The
tale was then told her that Smith was dead. In 1614 Pocahontas,
about nineteen years old, was kidnapped and taken to Jamestown,
in order to carry out a plan of the Governor by which Powhatan, to
save his daughter, would make friendship with the colony, and it
resulted as intended. Pocahontas remained several weeks in the
colony, made the acquaintance of the younger people, and fell in
love with Master John Rolfe. Pocahontas returned to her father, who
consented to the marriage; she was baptized at Jamestown as Lady
Rebecca, and her uncle and two brothers afterwards attended the
wedding, the uncle giving the Indian bride away in the little church
at Jamestown, April 5, 1614. A peace of several years' duration was
the consequence of this union. Two years afterwards Pocahontas
and her husband proceeded to England, where she was an object of
the greatest interest to all classes of people, and was presented at
Court, the Queen warmly receiving her. Captain Smith visited her in
London, and after saluting him she turned away her face and hid it
in her hands, thus continuing for over two hours. This was due to

her surprise at seeing Smith, for there is no doubt her husband was
a party to the deception, he probably thinking she would never
marry him while Smith was living. The winter climate of England was
too severe for her, and when about embarking to return to Virginia
she suddenly died at Gravesend, in March, 1617, aged about twenty-
two. She left one son, Thomas Rolfe, who was educated in London,
and in after life went to Virginia, where he became a man of note
and influence. From him are descended the famous children of
Pocahontas—the First Families of Virginia—the Randolph, Bolling,
Fleming and other families.
SHIRLEY, BERKELEY AND WESTOVER.
The winding James flows by Deep Bottom and Turkey Bend, and one
elongated neck of land after another, passing the noted battlefield of
Malvern Hill, which ended General McClellan's disastrous Seven
Days of battles and retreat from the Chickahominy swamps in 1862.
The great ridge of Malvern Hill stretches away from the river towards
the northwest, and in that final battle which checked the
Confederate pursuit it was a vast amphitheatre terraced with tier
upon tier of artillery, the gunboats in the river joining in the Union
defense. Below, on the other shore, are the spacious lowlands of
Bermuda Hundred, where, in General Grant's significant phrase,
General Butler was bottled up. Here, on the eastern bank, is the
plantation of Shirley, one of the famous Virginian settlements, still
held by the descendants of its colonial owners—the Carters. The
wide and attractive old brick colonial house, with its hipped and
pointed roof, stands behind a fringe of trees along the shore, with
numerous outbuildings constructed around a quadrangle behind. It
is built of bricks brought out from England, is two stories high, with
a capacious front porch, and around the roof are rows of dormer
windows, above which the roof runs from all sides up into a point
between the tall and ample chimneys. The southern view from
Shirley is across the James to the mouth of Appomattox River and
City Point.

The Appomattox originates in the Blue Ridge near Lynchburg, and
flows one hundred and twenty miles eastward to the James, of
which it is the chief tributary. It passes Petersburg twelve miles
southwest of its point of union with the James, this union being at a
high bluff thrust out between the rivers, with abrupt slopes and a
plateau on the top, which is well shaded. Here is the house—the
home of Dr. Epps—used by General Grant as his headquarters during
the operations from the south side of the James against Petersburg
and Lee's army in 1864-65. Grant occupied two little log cabins on
top of the bluff, just east of the house; one his dwelling and the
other his office. One is still there in dilapidation, and the other is
preserved as a relic in Fairmount Park, Philadelphia. A short distance
away is the little town of City Point, with its ruined wharves, where
an enormous business was then done in landing army supplies. To
the eastward the James flows, a steadily broadening stream, past
the sloping shores on the northern bank, where, at Harrison's
Landing, McClellan rested his troops after the Seven Days, having
retreated there from the battle at Malvern Hill. His camps occupied
the plantations of Berkeley and Westover, the former having been
the birthplace of General William Henry Harrison, who was President
of the United States for a few weeks in 1841, the first President who
died in office. The Berkeley House is a spacious and comfortable
mansion, but it lost its grand shade-trees during the war. A short
distance farther down is the quaint old Queen Anne mansion of red
brick, with one wing only, the other having been burnt during the
war; with pointed roof and tall chimneys, standing at the top of a
beautifully sloping bank—Westover House, the most famous of the
old mansions on the James. It was the home of the Byrds—
grandfather, father and son—noted in Virginian colonial history,
whose arms are emblazoned on the iron gates, and who sleep in the
little graveyard alongside. The most renowned of these was the
second, the Honourable William Byrd of Westover, Esquire, who
was the founder of both Richmond and Petersburg.
William Byrd was a man of imposing personal appearance and the
highest character, and his full-length portrait in flowing periwig and

lace ruffles, after Van Dyck, is preserved at Lower Brandon, farther
down the river. He inherited a large landed estate—over fifty
thousand acres—and ample fortune, and was educated in England,
where he was called to the bar at the Middle Temple, and made a
Fellow of the Royal Society. The inscription on his Westover tomb
tells that he was a friend of the learned Earl of Orrery. He held high
offices in Virginia, and possessed the largest private library then in
America. In connection with one Peter Jones, in 1733, he laid out
both Richmond and Petersburg on lands he owned, at the head of
navigation respectively on the James and the Appomattox. He left
profuse journals, published since as the Westover Manuscripts, and
they announce that Petersburg was gratefully named in honor of his
companion-founder, Peter Jones, and that Richmond's name came
from Byrd's vivid recollection of the outlook from Richmond Hill over
the Thames in England, which he found strikingly reproduced in the
soft hills and far-stretching meadows adjoining the rapids of the
James, with the curving sweep of the river as it flowed away from
view behind the glimmering woods. He died in 1744. Westover
House was McClellan's headquarters in 1862. The estates have gone
from Byrd's descendants, but the house has been completely
restored, and is one of the loveliest spots on the James. Major
Augustus Drewry, its recent owner, died in July, 1899, at an
advanced age. Coggins Point projects opposite Westover, and noted
plantations and mansions line the river banks, bearing, with the
counties, well-known English names. Here is the ruined stone Fort
Powhatan, a relic of the War of 1812, with the Unionist earthworks
of 1864-65 on the bluff above it. Then we get among the lowland
swamps, where the cypress trees elevate their conical knees and
roots above the water. The James has become a wide estuary, and
the broad Chickahominy flows in between low shores, draining the
swamps east of Richmond and the James. This was the lick at
which turkeys were plenty, the Indians thus recognizing in the
name of the river the favorite resort of the wild turkey.
THE COLONY OF JAMESTOWN.

We have now come to the region of earliest English settlement in
America, where Newport and Smith, in 1607, planted their colony of
Jamestown upon a low yellow bluff on the northern river bank. It is
thirty-two miles from the mouth of the James River, and the bluff, by
the action of the water, has been made an island. The location was
probably selected because this furnished protection from attacks.
The later encroachments of the river have swept away part of the
site of the early settlement, and a portion of the old church tower
and some tombstones are now the only relics of the ancient town.
The ruins of the tower can be seen on top of the bluff, almost
overgrown with moss and vines. Behind is the wall of the graveyard
where the first settlers were buried. A couple of little cabins are the
only present signs of settlement, the mansion of the Jamestown
plantation being some distance down the river.
When the English colony first came to Jamestown in 1607, they were
hunting for gold and for the northwest passage to the East Indies.
In fact, most of the American colonizing began with these objects.
They had an idea in Europe that America was profuse in gold and
gems. In 1605 a play of Eastward, Ho was performed in London, in
which one of the characters said: I tell thee golde is more plentifull
in Virginia than copper is with us, and for as much redde copper as I
can bring, I will have thrice the weight in golde. All their pannes and
pottes are pure gould, and all the chaines with which they chaine up
their streetes are massie gould; all the prisoners they take are
fettered in golde; and for rubies and diamonds they goe forth in
holidays and gather them by the seashore to hang on their children's
coates and sticke in their children's caps as commonally as our
children wear saffron, gilt brooches, and groates with hoales in
them. The whole party, on landing at Jamestown, started to hunt
for gold. Smith wrote that among the English colonists there was no
talk, no hope, no work, but dig gold, wash gold, refine gold, loade
gold. They found some shining pyrites that deceived them, and
therefore the first ship returning to England carried away a cargo of
shining dirt, found entirely worthless on arrival. The second ship,
after a long debate, they more wisely sent back with a cargo of

cedar. They hunted for the northwest passage, first going up the
James to the falls at the site of Richmond, but returning
disappointed. It was this same hunt for a route to the Pacific which
afterwards took Smith up the Chickahominy, where he got among
the swamps and was captured by the Indians.
The Jamestown colonists met with great discouragements. Most of
them were unfitted for pioneers, and the neighboring swamps gave
them malaria in the hot summer, so that nearly half perished. Smith,
by his courage and enterprise, however, kept the colony alive and
took charge, being their leader until captured by the Indians, and
also afterwards, until his return to England. Among the first
constructions at Jamestown were a storehouse and a church. These,
however, were soon burnt, and a second church and storehouse
were erected in September, 1608. This church was like a barn in
appearance, the base being supported by crotched stakes, and the
walls and roof were made of rafts, sedge and earth, which soon
decayed. When Smith left Jamestown for England in 1609 the place
contained about sixty houses, and was surrounded by a stockade.
Smith early saw the necessity of raising food, and determined to
begin the growing of maize, or Indian corn. Consequently, early in
1608 he prevailed upon two Indians he had captured to teach the
method of planting the corn. Under their direction a tract of about
forty acres was planted in squares, with intervals of four feet
between the holes which received the Indian corn for seed. This
crop grew and was partly harvested, a good deal of it, however,
being eaten green. Thus the Indian invented the method of corn-
planting universally observed in the United States, and this crop of
forty acres of 1608 was the first crop of the great American cereal
grown by white men. Wheat brought out from England was first
planted at Jamestown in 1618 on a field of about thirty acres, this
being the first wheat crop grown in the United States.
Captain John Smith, before he left Jamestown, estimated that there
were about fifty-five hundred Indians within a radius of sixty miles
around the colony, and in his works he enumerates the various

tribes. Describing their mode of life, he wrote that they grew fat or
lean according to the season. When food was abundant, he said,
they stuffed themselves night and day; and, unless unforeseen
emergencies compelled them to arouse, they dropped asleep as
soon as their stomachs were filled. So ravenous were their appetites
that a colonist employing an Indian was compelled to allow him a
quantity of food double that given an English laborer. In a period of
want or hardship, when no food was to be had, the warrior simply
drew his belt more tightly about his waist to try and appease the
pangs of hunger. The Indians, when the colonists arrived, were
found to divide the year into five seasons, according to its varying
character. These were, first, Cattapeuk, the season of blossoms;
second, Cohattayough, the season when the sun rode highest in the
heavens; third, Nepenough, the season when the ears of maize were
large enough to be roasted; fourth, Taquetock, the season of the
falling leaves, when the maize was gathered; and fifth, Cohonk, the
season when long lines of wild geese appeared, flying from the
north, uttering the cry suggesting the name, thus heralding the
winter.
The colony was very unfortunate, and in 1617 was reduced to only
five or six buildings. The church had then decayed and fallen to the
ground, and a third church, fifty by twenty feet, was afterwards
built. Additional settlers were sent out from England in the next two
years, and the Virginians were granted a government of their own,
the new Governor, Sir George Yeardley, arriving in the spring of
1619. The Company in London also sent them a communication
that those cruell laws, by which the ancient planters had soe long
been governed, were now abrogated in favor of those free laws
which his majesties subjects lived under in Englande. It continued
by stating That the planters might have a hande in the governing of
themselves yt was granted that a generall assemblie should be held
yearly once, whereat to be present the governor and counsell with
two burgesses from each plantation, freely to be elected by the
inhabitants thereof, this assemblie to have power to make and
ordaine whatsoever laws and orders should by them be thought

good and profitable for their subsistence. The Governor
consequently summoned the first House of Burgesses in Virginia,
which met at Jamestown, July 30, 1619, the first legislative body in
America. Twenty-two members took their seats in the new church at
Jamestown. They are described as wearing bright-colored silk and
velvet coats, with starched ruffs, and as having kept their hats on as
in the English House of Commons. The Governor sat in the choir,
and with him were several leading men who had been appointed by
the Company on the Governor's Council. They passed various laws,
chiefly about tobacco and taxes, and sent them to England, where
the Company confirmed them, and afterwards, in 1621, granted the
Great Charter, which was the first Constitution of Virginia.
The colonists got into trouble with the Indians in 1622, and having
killed an Indian who murdered a white man, Jamestown was
attacked and the inhabitants massacred, three hundred and forty-
five being killed. Governor Butler, who visited the place not long
after the massacre, wrote that the houses were the worst in the
world, and that the most wretched cottages in England were equal,
if not superior, in appearance and comfort to the finest dwellings in
the colony. The first houses were mostly of bark, imitating those of
the Indian; and, there being neither sawmills to prepare planks nor
nails to fasten them, the later constructions were usually of logs
plastered with mud, with thatched roofs. The more pretentious of
these were built double—two pens and a passage, as they have
been described. As late as 1675 Jamestown had only a few families,
with not more than seventy-five population. Labor was always in
demand there, and at first the laborers were brought out from
England. There was no money, and having early learnt to raise
tobacco from the Indians, this became the chief crop, and, being
sure of sale in England, became the standard of value. Tobacco was
the great export, twenty thousand pounds being exported in 1619,
forty thousand in 1620 and sixty thousand in 1622. Everything was
valued in tobacco, and this continued the practical currency for the
first century. They imported a lot of copper, however, with which to
make small coins for circulation. As the tobacco fluctuated in price in

England, it made a very unstable standard of value. Gradually,
afterwards, large amounts of gold and silver coin came into Virginia
in payment for produce, thus supplanting the tobacco as a standard.
THE VIRGINIAN PLANTERS.
Land was cheap in Virginia in the early days. In 1662 the King of
Mattapony sold his village and five thousand acres to the colonists
for fifty match-coats. During the seventeenth century the value of
land reckoned in tobacco, as sold in England, averaged for cleared
ground about four shillings per acre, the shilling then having a
purchasing power equal to a dollar now. It was at this time that
most of the great Virginian estates along James River were formed,
the colonists securing in some cases large grants. Thus, John Carter
of Lancaster took up 18,570 acres, John Page 5000 acres, Richard
Lee 12,000 acres, William Byrd 15,000 acres, afterwards largely
increased; Robert Beverley 37,000 acres and William Fitzhugh over
50,000 acres. These were the founders of some of the most famous
Virginian families. The demand for labor naturally brought Virginia
within the market of the slave trader, but very few negroes were
there in the earlier period. The first negroes who arrived in Virginia
were disembarked at Jamestown from a Dutch privateer in 1619—
twenty Africans. In 1622 there were twenty-two there, two more
having landed; but it is noted that no negro was killed in the
Jamestown massacre. In 1649 there were only three hundred
negroes in Virginia, and in 1671 there were about two thousand. In
the latter part of the seventeenth century the arrivals of negro slaves
became more frequent—labor being in demand. The records show
that the planters had great difficulty in supplying them with names,
everything being ransacked for the purpose—mythology, history and
geography—and hence the peculiar names they have conferred in
some cases on their descendants. In 1640 a robust African man
when sold commanded 2700 pounds of tobacco, and a female 2500
pounds, averaging, at the then price of tobacco, about seventeen
pounds sterling for the men. Prices afterwards advanced to forty

Welcome to our website – the perfect destination for book lovers and
knowledge seekers. We believe that every book holds a new world,
offering opportunities for learning, discovery, and personal growth.
That’s why we are dedicated to bringing you a diverse collection of
books, ranging from classic literature and specialized publications to
self-development guides and children's books.
More than just a book-buying platform, we strive to be a bridge
connecting you with timeless cultural and intellectual values. With an
elegant, user-friendly interface and a smart search system, you can
quickly find the books that best suit your interests. Additionally,
our special promotions and home delivery services help you save time
and fully enjoy the joy of reading.
Join us on a journey of knowledge exploration, passion nurturing, and
personal growth every day!
ebookbell.com

Power Distribution System Reliability Practical Methods And Applications Ali A Chowdhury

More Related Content

Similar to Power Distribution System Reliability Practical Methods And Applications Ali A Chowdhury (20)

Recently uploaded (20)

Power Distribution System Reliability Practical Methods And Applications Ali A Chowdhury