=INTRO_MOD_2-Fundamentals=rev2015-June.pdf

Course Outline
1. Introduction to WECC
2. Fundamentals of Electricity
3. Power System Overview
4. Principles of Generation
5. Substation Overview
6. Transformers
7. Power Transmission
8. System Protection
9. Principles of System Operation

2|Fundamentals of Electricity
• Electric Theory, Quantities and Circuit
Elements
• Alternating Current
• Power in AC Circuits
• Three-Phase Circuits
• Electromechanics
3
W E S T E R N E L E C T R I C I T Y C O O R D I N A T I N G C O U N C I L

Electric Theory, Quantities
and Circuit Elements
• Atoms, Electrons, Charge
• Conductors and Insulators
• Current
• Voltage
• Power
• Magnetism and Electromagnetism
• Circuit Components and Resistance
• Circuit Analysis (Ohm’s and Kirchoff’s Laws)
5

Electric Theory, Quantities and Circuit Elements
Electricity
• Electricity is the set of physical phenomena
associated with the presence and flow of
electric charge. Including:
• Lightning and Static electricity
• Electromagnetic induction
• Current
• Electromagnetic radiation and radio waves

Atoms, Electrons, Charge
7

• Matter - has weight and occupies space.
• Matter is composed of atoms.
• Atoms are composed of:
– Electrons(-) orbiting around a nucleus of
Protons(+) and Neutrons.

Electrons have a negative charge
Protons have a positive charge
Opposite charges attract
Like charges repel

An Electric (force) field surrounds any charged
object – it spreads out - weakens with distance.
– Electric field around various shaped objects

• Charge is measured in Coulombs
• 1 Coulomb =1 amp per second
• The charge of one electron is -1.6 X 10-19
Coulombs.
6,250,000,000,000,000,000 electrons!
1 𝐶𝑜𝑢𝑙𝑜𝑚𝑏 =
1
−1.6 ∗ 10−19
= 6.25 ∗ 1018 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠

• Electrons orbiting the nucleus are organized
into shells
• The number of protons in an atom determine
what the element is
• For instance:
– Hydrogen - 1 proton and 1 electron
– Aluminum - 13 protons and 13 electrons

Electrons (negative charge)
Nucleus consisting of: Protons
(positive charge) Neutrons
(neutral charge)
3 Valence Electrons
Shell 1 (2 electrons)
Aluminum Atom (13 Protons)

1 Valence Electron
Copper Atom – 29 Protons

• Free Electrons - jump easily from one atom to
another
• The number of shells, and electrons in each
shell, determine how tightly they are bound to
the atom
• In a good conductor the valence electrons can
be easily forced to move from one atom to the
next

An external force can cause the free electrons to move from
one atom to the next.
friction (static), thermal (thermocouple), light (photocell),
chemical (battery) or electromagnetic (generator)
Force

Conductors and Insulators
17

When it comes to electricity there are
generally two types of material:
–Conductors
–Insulators

A conductor is a material that has a large
number of free electrons that continually jump
to other atoms.
• Good electrical conductors are copper and
aluminum. Gold, silver, and platinum are also
good conductors, but are very expensive

An insulator is a material that has only a few
free electrons. In insulators, the electrons are
tightly bound by the nucleus.
• Good electrical insulators are rubber,
porcelain, glass, and dry wood

• Insulators prevent current from flowing
• Insulators are used to isolate electrical
components and prevent current flow

Electric Theory, Quantities and Circuit
Elements

Insulator Characteristics
Resistance - The ability of the insulator to resist
current leakage through and over the surface of the
insulator material.
Dielectric Strength - The ability to withstand a
maximum voltage without breakdown damage to
the insulator.

Check Your Knowledge:
Fundamentals of Electricity
1. In general are objects charged, or neutral?
Why is that?
2. Where do you see static electricity?
3. What are good conductors? What are good
insulators?
4. What decides which conductor you should
use?
25

Current
Current
Current (I) is the movement of charge through a
conductor. Electrons carry the charge.
• Unit of measurement: Amperes (A)
• One ampere (amp) of current is one coulomb of
charge passing a point on a conductor in one
second
• This measurement is analogous to “gallons or
liters per second” when measuring the flow of
water

Current
Direct Current (DC) flows in only one direction.
• Many uses including: Batteries, electronic
circuits, LED lights, generator excitation systems
and rotors, DC transmission lines – and much
more

Current
Alternating Current (AC) continuously changes
in magnitude and direction.
• AC is used by most lights, appliances and motors.
It is used in the high voltage transmission system
• AC enables use of transformers to change voltage
from high to low and back

Current
Typical Current Levels:
Cell phone battery charger 5/1000 Amps = 5mA = (5 milli-amps)
Sensation .2 - .5mA
Let-go threshold 5mA
Potentially lethal 50mA
40 watt incandescent light bulb .33 Amps
Toaster 10 Amps
Car Starter Motor 100+ Amps
Transmission line conductor 1000 Amps
Lightning Bolt or Ground Fault 20,000+ Amps

Voltage
Voltage (V) is the force that causes electrons to
move.
• Voltage is also referred to as potential difference
or electromotive force (emf or E)
• Unit of measurement: Volts (V)
• Similar to “pounds per square
inch” when measuring water
pressure.
Alessandro Volta (1745–1827)

Voltage Sources

Voltage
Sample Voltage Levels
AA Battery 1.5v
Car Battery 12v
Household 120v
Distribution Feeder Circuit 12.47kV
High Voltage Line 47kV to 500kV
Lightning 1,000,000+
volts

Power

Power
Power (P) is the rate at which work is being
performed.
• Unit of Measurement: watts (w)
• Power = Voltage x Current
• This means that the electrical
energy is being converted into
another form of energy
(e.g. heat energy, light energy,
mechanical energy, etc.)
James Watt, 1736 -1819

Power

Power
Sample Power Calculation
A Toaster uses 120-volts and allows 10 amps of
current to flow. How much power does it consume?
Instructions: Using the formula for power and
substituting the known values, we have:
𝑃 = 𝑉𝐼
𝑃 = (_____)(_____)
𝑃 = _____________
38

Power
Sample Power Calculation
A Toaster uses 120-volts and allows 10 amps of
current to flow. How much power does it consume?
Instructions: Using the formula for power and
substituting the known values, we have:
𝑃 = 𝑉𝐼
𝑃 = 120𝑉 10𝐴
𝑃 = 1200 𝑊𝑎𝑡𝑡𝑠
39

Power
• A “watt” is an instantaneous value, it is the
power being used at any given instant of time
• A “watt hour” indicates how much power is
being consumed over an hour
watt x time (in hours) = watt hours = energy

Power
Retail Power consumption is typically measured in
kilowatt hours (KWh)
Kilowatts x time (in hours) = Kilowatt hours
Example:
5,000 watts used for 3 hours
5,000 = 5 kW
5 kW x 3 hours = 15 kWh
Wholesale power consumption is typically
measured in megawatt hours (MWh)
41

Power
Example Power Use:
• Small light bulb 40 watts
• Toaster 1000 watts or 1 kW
• Household 5–10kW
• One horsepower 746 watts (.746 kW)
• Wind turbine 1,000 kW or 1.0 MW
• Power Plant 500 MW

Power
Example Power Use:
Small light bulb 40 watts
Toaster 1000 watts or
1 kilowatt (1kW)
Household 5 – 10kW
One horsepower 746 watts
(.746 kW)
Wind turbine 1,000 kW or
1.0 Megawatts (MW)
Combined Cycle Power Plant 500 MW

1. How many volts does a hair dryer use?
2. How many amps?
3. How many watts?
4. How many watts are consumed in a city at
7:00am where 50,000 people are
simultaneously drying their hair to get ready
for work?
44

Magnetism and Electromagnetism

Wherever an electric current exists, a magnetic
field also exists.
• The magnetic field carries the invisible force of
magnetism
• The magnetic field surrounds the conductor

CURRENT FLOW
Whenever current flows through a
conductor, a magnetic field is created
around the conductor.

What happens when you drop a
magnet in a copper tube?

Right hand rule for Magnetic Field around a conductor.
Assumes Current flows from Positive to Negative

Magnetic Field Lines of Force

Electromagnet
52
Current Flow
Battery
+

Electromagnetic Induction
In order to induce current and voltage you need
3-things:
1. Conductor
2. Magnetic field
3. Relative motion between the conductor
and the magnetic field.

Creation of Voltage

N S
Flux Opposite Directions (cancels)
Flux the Same Direction (adds)
Direction of Deflection
Direction
of Deflection
Magnet
Current Carrying
Conductors

• Electromagnetic Induction creates a voltage
or current in a conductor when a magnetic
field changes
• In a transformer, alternating current in one
winding induces a changing magnetic field in
the transformer core
• The changing magnetic field induces an
alternating voltage and current in the second
winding

Basic Transformer Operation
𝑉𝑃𝑟𝑖𝑚𝑎𝑟𝑦=
𝑊𝑖𝑛𝑑𝑖𝑛𝑔𝑠 𝑃𝑟𝑖𝑚𝑎𝑟𝑦
𝑊𝑖𝑛𝑑𝑖𝑛𝑔𝑠 𝑆𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦
𝑉𝑆𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦

Generator - magnetic field of the rotor Induces a
voltage in the stator windings.
• Rotor may be a permanent magnet
• In a large generator, the rotor is a spinning
electromagnet – created by current from the
exciter
Guide Page #

Whenever a magnetic field is moved past a
conductor a voltage is induced in the conductor
Voltmeter
N
S
Motion
+
Magnetic Lines of
Flux
Electromagnetic Induction

Circuit Components and
Properties

Circuit Components and Properties
Resistance (R) is the property of materials that
opposes or resists current by converting electric
energy to heat.
• Unit of Measurement: ohms (Ω)
• A Resistor provides resistance to
the circuit
Georg Ohm, 1789 -1854

Resistance depends on:
Resistivity
Conducting material has very low resistivity, insulators have
very high resistivity.
Length
Decreasing the material's length decreases the resistance.
Cross-sectional area
Increasing the material's cross-sectional area decreases the
resistance.
Temperature
The hotter the wire, the more resistance it exhibits.

Inductance (L) is the property of an electrical
circuit that opposes change in current. The unit
of inductance is the Henry (H).
• Any component that we use for its inductive
property is called an inductor
• In the Power system, an inductor is sometimes
also called a reactor

• An Inductor (L) is a coil of wire that creates a
magnetic field when current is applied
• The changing magnetic field of an Inductor opposes
the voltage that is trying to force current in the wire
• An inductor opposes a change in current
𝑉 = 𝐿
𝑑𝐼
𝑑𝑡
(Voltage equals Inductor size times rate-of-change of
Current)

Capacitance (C) is the property of an electrical circuit that
opposes change in voltage.
• Unit of Measurement: Farads(F)
A Capacitor stores electrical charge.
• A Capacitor consists of two metal plates separated by
an insulating layer.
𝑉 = 1/(2𝜋𝑓𝐶) 𝐼𝑑𝑡
(Voltage builds up as current flows into the Capacitor)

• The value of capacitance in a circuit is measured in
capacitive units called farads.
• The farad is named after Michael Faraday, a 19th
century British physicist, who is credited with
developing the method of measuring capacitance.
• Farad determined that a capacitor has a
value of one farad of capacitance if
one volt of potential difference
applied across its plates moved one
coulomb of electrons from one plate to
the other.
Michael Faraday

• A Capacitor consists of two conducting metal
plates with an insulating sheet of material in
between.
• When current is applied across the terminals,
charge flows from one side to the other.
• Over time as charge builds on the capacitor,
voltage increases.

Circuit Components and Properties: Capacitor Construction
Conducting Plates(electrodes)
Insulating Dielectric

Capacitors come in all sizes and shapes…

=INTRO_MOD_2-Fundamentals=rev2015-June.pdf

Chemical Battery Operation
In the battery, two different
metals, called ELECTRODES are
placed in a chemical solution
called the ELECTROLYTE.
• The metals react differently.
• One loses electrons and
develops a positive charge,
the other attracts electrons
and develops a negative
charge.

This results in a DIFFERENCE
IN POTENTIAL (Voltage)
between the two
electrodes.
When a conductor is
attached to the electrodes
of the battery, electrons
flow from the negative
electrode to the positive
electrode.
V

Circuit Analysis - Series and Parallel Circuits

Circuit Analysis: Series and Parallel Circuits

A series circuit is a circuit that has only one path for
current to flow.
Current Flow
160V
+
Circuit Analysis: Series Circuit

Total resistance of the circuit (RT)?
RT =
R1 R2
R3
R4
R5
160V
+
5  + 10  + 40  + 20  + 5 
R1 + R2 + R3 + R4 + R5
RT =
RT = 80 
5 10
40
20
5
Circuit Analysis: Series Circuit

A parallel circuit is a circuit that has more than
one path for current to flow.
120V 50 100 300
CURRENT FLOW
2.4A
1.2A
0.4A
4.0A 1.6A 0.4A
Circuit Analysis: Parallel Circuit

R1 R2 R3
120V 50 100 300
1
RT
= +
1
R3
+
1
R2
1
R1
1
RT
= +
1
300
+
1
100
1
50
1
RT
= 0.02 0.0033
0.01
+ +
1
0.0333
=
RT
0.0333
1
RT
=
=
RT 30
Circuit Analysis: Parallel Circuit

Ohm’s Law and
Kirchoff’s Law
83

Ohm’s Law
Ohm's Law:
– Voltage Drop = Current * Resistance
Kirchhoff's Laws:
– Sum of current entering a junction equals the sum
of current leaving the junction.
– Sum of voltage drops equals the applied voltage.
84

Ohm’s Law
Ohm’s law, named after Mr.
Georg Ohm, a German
mathematician and physicist.
1789 -1854.
He defined the basic
relationship between power,
voltage, current and
resistance.
The principles apply to AC, DC
or RF (radio frequency).

Ohm’s Law
V = IR
I = V/R
R = V/I
Where:
V = Voltage in Volts
I = Current in Amps
R = Resistance in Ohms
86

E
I R
Ohm’s Law: Pie or Triangle

Quick question
How much current is flowing in the toaster
circuit?
I = __ amps

Quick question
How much current is flowing in the toaster
circuit?
I = 10 amps

Kirchhoff's Current Law: the sum of the currents
entering a junction equals the sum of the
currents leaving a junction.
• For series circuits - the current is the same at
all points
• For parallel circuits - the total current in a
parallel circuit is equal to the sum of the
currents in each branch
Kirchoff’s Law

Gustav Kirchoff was a German
Physicist 1824 – 1887.
He developed laws for circuit
analysis as well as other laws for
“black body” radiation and
thermochemistry.
Kirchoff’s Law

Kirchhoff’s Voltage Law states:
• The voltage difference across a resistor is
called a voltage drop
• In series circuits, the sum of the voltage drops
around the circuit is equal to the applied
voltage
• In parallel circuits, the voltage drops across all
the branches are the same
Kirchoff’s Law

1. A blow drier uses 120 Volts and draws 10 amps. What is its
resistance?
2. How much power does it use?
3. How much would it cost to run the blow drier for one hour?
4. If you had two similar blow dryers plugged in to the wall –
would they be in series or parallel?
5. How many amps total would they use?
6. If you re-wired the blow dryers to put one in series with the
other, what would be the total resistance?
7. How much current would flow through the circuit?
8. What would the voltage across each dryer be?
9. What would be the total power used?
93

Alternating Current
• Generating AC Current
• Sine Waves
• RMS Values
• Phase Relationship
• Right Triangle Relationships
• Impedance–Resistance, Inductance,
Capacitance

Alternating Current (AC)
Alternating Current (AC) periodically changes
direction of flow and magnitude.
• AC voltage produces an alternating current
• AC power is produced by alternating current
and alternating voltage

Generating AC Current
96

N
S
0° 90° 180° 270° 360°
Time
Rotation
0°
90°
270°
+
_
180°
Amplitude
of Voltage
or Current
0V
Generator

N
S
0° 90° 180° 270° 360°
Time
+
_
Current Flow
_
+
Amplitude
of Voltage
or Current
90°
270°
0°
180°
Generator

N S
0° 90° 180° 270° 360°
Amplitude
of Voltage
or Current
Time
+
_
0V
90°
270°
0°
180°
Generator

N
S
0° 90° 180° 270° 360°
Time
+
_
Current Flow
+
_
Amplitude
of Voltage
or Current
90°
270°
0°
180°
Generator

0° 90° 180° 270° 360°
Time
+
_
Current Flow
+
_
N
S
Amplitude
of Voltage
or Current
90°
270°
0°
180°
Generator

0° 90° 180° 270° 360°
Time
0° (360°)
+
_
N
S
Amplitude
of Voltage
or Current
0V
90°
270°
180°
Generator

Sine Waves
106

A Sine Wave is a curve that describes a smooth
repetitive oscillation.
Sine Waves

A Sine Wave shows the height of the circle at a
given angle.
𝐴1 0º
90º
180º
270º
0º
90º
180º
270º
𝐴2
𝐴3
𝐴1 𝐴2 𝐴3
Sine Waves

𝐴1
0º
90º
180º
270º
0º
90º
180º
270º
𝐴1
Spinning Generator Rotor Sine Wave Voltage
Rotor
Rotor Angle = Phase Angle
Spinning Generator Rotor creates a Sine Wave Voltage
Sine Waves

A Cycle is the part of a waveform that does not
repeat or duplicate itself. In the time it takes to
complete one cycle, the current:
builds from zero to the maximum amplitude in
one direction
decays back to zero
builds to the maximum amplitude in the opposite
direction
decays back to zero again
Sine Waves

• The Period (T) is the time required to
complete one cycle
• Frequency (f) is the rate at which the cycles
are produced
• Frequency is measured in Hertz (Hz). One
hertz equals one cycle per second
Sine Waves

Frequency (f) and period (T) are related by the
following equations:
f = 1/T
T = 1/f
Sine Waves

Amplitude
– peak
– peak-to-peak
– RMS (Effective Value)
Sine Waves

Maximum
Negative Value
Peak-to-Peak
Maximum
Positive Value
Peak
AC Power Sine Wave

RMS Values
115

RMS (Effective) Value
• The effective or root mean square (RMS) is the
amount of AC current or voltage that has the
same effect as a given amount of DC current or
voltage in producing heat in a resistive circuit
• Effective value (RMS) is the most common way of
specifying the amount of AC
• One amp of effective AC and one amp of DC
produce the same power when flowing through
equal resistors

• The Root Mean Square (RMS) Value is the
Effective value
• To calculate the RMS value of a waveform,
Square the instantaneous values over one
period, average them to provide the Mean, and
take the square Root of the mean
• RMS value is 70.7% of Peak value
𝐼𝑟𝑚𝑠 =
2
2
𝐼𝑝 = .707 𝐼𝑝
RMS Values

RMS Value
70.7% of
Peak Voltage
Zero
Alternating Current
RMS (Effective) Value

VP-P = 340 V
Vpeak = 170 V
Vpeak = 170 V
VRMS = .707 x 170 V = 120.2 V
Vrms = 120 V
Alternating Current
Household Voltage

60
50
40
30
20
10
0
-10
-20
Average Power 25 Watts
10 Volts, 7.07V rms
5 Amps, 3.53A rms
RMS Voltage * RMS Current = Average Power
0 30 60 90 120 150 180 210 240 270 300 330 360
50 Watts Peak Power

Phase Relationship
121

Phase Relations
Phase Angle is the angle difference between
two sine waves with the same frequency
• Phase Angle is sometimes called phase
relation
• Phase angle is the portion of a cycle that has
elapsed since another wave passed through a
given value

Phase Angle Between Two Generators
𝐴1 0º
90º
180º
270º
𝐴1
Two Generators - Out of Phase Sine Wave Voltages
Gen 1
Relative Rotor Angle = Phase Angle
Gen 2
Gen 1
Gen 2

𝐴1
0º
90º
180º
270º
𝐴1
Two Generators – Out of Phase Sine Wave Voltages
Gen 1
Relative Rotor Angle = Phase Angle
Gen 2
Gen 1
Gen 2
Angle between Generators stays the same while they both rotate

Figure 2.8: Phase Angle
V1 = Generator #1
V2 = Generator #2
Phase Relations

In-Phase - the phase angle between two
generators is zero degrees
• The generated voltages cross zero at the same
time

Out-of-Phase means that the phase angle
between two generators is not zero degrees.
• The generated voltages cross zero at different
times
• Only applies if the two waveforms have the
same frequency

A phasor is a line representing a rotating
quantity (voltage or current) for which:
Length represents magnitude
Direction represents the phase angle (in electrical
degrees)
Zero electrical degrees are on the right side of the
horizontal axis
Rotation is counterclockwise
Phase Relations

A phasor is similar to an arrow drawn on the
end of a spinning shaft
• A strobe light flashes once each time the shaft
does a full revolution
Phase Relations

𝐴1
0º
90º
180º
270º
0º
90º
180º
270º
𝐴1
Spinning Generator Rotor Sine Wave Voltage
Phasor
Phase Relations

Since phasors rotate in a counterclockwise direction,
the phasor diagram above shows the current leading
the voltage by 30º.
30°
90º
180º
270º
Phasors – Voltage and Current
Voltage Phasor
Current Phasor
Phase Relations

Right Triangle Relationships
132

Right Triangles
A Right Triangle has one corner with a 90º
Angle.
q
adjacent
opposite
Symbol for a
right angle (900)

Right Triangles
The right triangle can be used to represent:
– Resistance vs Reactance
– Real versus Reactive portion of Current and
Voltage
– Real and Reactive Power

The right triangle can be used to represent the
resistive, reactive, and Resulting total.
Right Triangles
Real
Reactive

Right Triangles
Angles total 180º
450
450
900
1800
600
300
900
1800

Right Triangles
q
adjacent
opposite
theta (q)

Right Triangles
The Pythagorean Theorem states that the square of the
hypotenuse of a right triangle is equal to the sum of the
squares of the remaining two sides.
q
adjacent
opposite
Pythagorean Theorem

Right Triangles
The Pythagorean
Theorem states that
the square of the
hypotenuse of a right
triangle is equal to the
sum of the squares of
the remaining two
sides.
q
adjacent
opposite
9
16
25
hypotenuse2
= + opposite2
adjacent2

Right Triangles
140
Pythagorean Theorem

Right Triangles
Using our formula, we could find the value of any side if
we know the value of the other two sides.
q
A
B
Pythagorean Theorem
C2 = A2 + B2
C2 = A2 + B2
or
A2 = C2 - B2
or
B2
= C2 - A2

Right Triangles
Generators produce Mega-Watts and Mega-Vars.
Use the right triangle to find the values.
q
MW
MVAR
Pythagorean Theorem
MVA2 = MW2 + MVAR2
MVA2 = MW2 + MVAR2
MVA2
= - MVAR2
MVA2
= MW2
-
MW2
MVAR2

Right Triangles
If a generator was producing 100 MW and 50 MVAR we
could calculate the MVA using our formula.
q
100 MW
50
MVAR
MVA2 = 1002
+ 502
MVA2 = 10,000 + 2,500
MVA2 = 12,500
MVA = 111.8
Pythagorean Theorem

q
adjacent
opposite
Sine and Cosine
Sine q =
opposite
hypotenuse
Cosine q =
adjacent
hypotenuse
Right Triangles

This ratio of Adjacent side to Hypotenuse establishes the slope of the angle
q
4
Sine and Cosine
5
4
cosine q =
Right Triangles

Determine the angle theta using the inverse of the cosine of theta the arccosine.
q
4
Sine and Cosine
cosine q =
5
4
cosine q = 0.8
arccosine 0.8 = 36.860
36.90
q = 36.90
Right Triangles

q
4
Sine and Cosine
36.90
900
1800
900
36.90
53.10
-
Right Triangles

We can solve for all angles and sides given only one side
and one angle
q
36.90
Right Triangles

Right Triangles
q
36.90
arccosine q = 36.90
cosine q (36.9) = 0.8
a = 0.8 X 5
a = 4
a
o

Right Triangles
q
36.90
a = 4
o2 = h2 - a2
o2 = 25 - 16
o2 = 9
o = 3
o
O = 5 sin(36.9) = 3
OR

Right Triangles
Summary
• A right triangle has one right angle (90º)
• The sum of the angles of any triangle equals 1800
• The sides of a right triangle are named the hypotenuse,
adjacent and opposite side.
• The hypotenuse of any right triangle will always be the longest
side.
• The square of the hypotenuse is equal to the sum of the
squares of the remaining two sides
• The sine equals the ratio of the opposite side to the hypotenuse
• The cosine equals the ratio of the adjacent side to the
hypotenuse

Right Triangles
Practice Question
q
41.40
Solve the unknown sides and angles of this right
triangle using the methods we have learned in this
module on right triangles.

Resistive, Reactive, and Total Impedance
Right Triangles
Resistance R
Reactance X
Application to Electricity

Total Voltage drop equals the voltage drop across resistor
squared plus voltage drop across reactor squared.
Right Triangles
I*R = VR
I*X = VX

Apparent Power = Real Power + Reactive Power (Vars)
Right Triangles
I*VR=Real Power =MWatts
I*VX=Reactive
Power = MVars

1. In a right triangle with the adjacent side equal to 5 and
the opposite side equal to 12, what is the length of the
hypotenuse?
2. Can you prove graphically that the Pythagorean
Theorem is true?
3. What is the sine of 45 degrees?
4. With a hypotenuse of one and an adjacent side of .5,
what is the angle? The opposite side?
156

Impedance
Resistance, Inductance, Capacitance
157

Impedance
Impedance (Z) is the total opposition to current.
• Impedance is the vector sum of the resistance
and reactance
• Impedance is represented by a Z and measured in
ohms (Ω)
Real R
Reactive X

Impedance
• Impedance of resistors is independent of
whether the current is AC or DC
• Impedance of inductors and capacitors
depends on the rate-of-change or frequency
of the voltage

Impedance
• Impedance of capacitors and inductors is also
called reactance
• Reactance depends on frequency
𝑋𝐶 =
1
2𝜋𝑓𝐶
- Current Leads the Voltage
𝑋𝐿 = 2𝜋𝑓𝐿 - Voltage Leads the Current

Impedance
Inductive Reactance(XL) opposes change in current. It
is measured in ohms(Ω).
• Reactance does not convert the electrical energy into
heat energy
• The reactor temporarily stores the energy in the
expanding magnetic field, then gives it back when
the field collapses

Impedance
Applied
EMF
Counter EMF
I
XL
Inductors are devices that oppose changes in
current flow using a magnetic field.

Impedance
This form of Ohm's Law applies to inductive
reactance:
𝑉 = 𝐼𝑋𝐿
Where:
• V and I = Voltage and current, respectively
• 𝑋𝐿 = 2𝜋𝑓𝐿= Inductive Reactance
• 𝜋 = Constant (approximately 3.14)
• f = Frequency
• L = Inductance
The Current lags the voltage by 90º
V
I XL

Inductance
The current lags the voltage by 90º in this example.

Applied Voltage
Current Lags Voltage by a Maximum 90°
Circuit Current
The maximum amount that the inductance can cause
the current to lag behind the voltage is 90°
Inductance

E L I
E = Voltage L = Inductance I = Current
Voltage leads the current in an inductive circuit.
ELI the ICE man
(A catchy memorable phrase)
(The hard part is remembering why I=Current and E=Voltage)
Impedance

Impedance
Capacitive Reactance (Xc) opposes change in
voltage. It is measured in ohms(Ω).
• Reactance does not convert the electrical
energy into heat energy
• The capacitor temporarily stores the energy
in the electric field between its plates, then
gives it back when the field collapses

Impedance
Capacitors are devices that store electrical charge.
They oppose a change of voltage.
+
+
Voltage

The following form of Ohm's Law applies to capacitive
reactance:
𝑉 = 𝐼𝑋𝐶
Where:
• V and I = Voltage and current, respectively.
• 𝑋𝐶 = 1/(2𝜋𝑓𝐶)= Capacitive Reactance
• 𝜋 = Constant (approximately 3.14)
• f = Frequency
• C = Capacitance
Current can lead the voltage by up to 90º.
V
I XC
Impedance

Similar to inductive reactance, capacitive reactance
depends on frequency.
– Increasing the frequency decreases the capacitive
reactance.
Definition: Susceptance
• There are times when using the reciprocal of XC
makes calculations easier
• The reciprocal of XC is BC and is called susceptance
So now: I = VBC
Impedance

E L I
I = Current C = Capacitance E = Voltage
Current leads the voltage in a capacitive circuit.
ELI the ICE man
(A catchy memorable phrase)
(The hard part is remembering why I=Current and E=Voltage)
Impedance

1. With a Voltage of 120 volts, Resistance of
10Ω and Inductive Reactance of 5Ω. What is
the current?
2. Does the current lead or lag the voltage?
3. What is the angle between the current and
the voltage legs of the triangle?
178

Power in AC Circuits
• Resistive Circuits - Watts
• Reactive Circuits – VARS
• Complex Power
• Power Triangle
• Power Factor
• VARs – Effect on Voltage
• Voltage Collapse

Resistive Circuits - Watts
184

Power is the rate at which work is performed it
is measured in watts.
• In a resistive circuit, the current and voltage
are in phase.
• Real Power is the power consumed by the
resistance in a circuit.
Resistive Circuits

60
50
40
30
20
10
0
-10
-20
Average Power 25 Watts
10 Volts, 7.07V rms
5 Amps, 3.53A rms
REAL POWER IN A RESISTIVE CIRCUIT
0 30 60 90 120 150 180 210 240 270 300 330 360
50 Watts

Resistive Circuits
Real power is calculated using the following
equations:
𝑃 = 𝐼𝑉 = 𝐼 𝐼𝑅 = 𝐼2
R
𝑃 =
𝑉𝑉
𝑅
=
𝑉2
𝑅
187

• Losses are dissipated as heat in transmission
lines and transformers
• I2R = Heating Losses
• Most circuits are not entirely resistive – they
contain reactance
Resistive Circuits

Reactive Circuits - VARs
189

Reactance causes a phase shift between voltage
and the current.
Reactive Circuits

Reactive Circuits
𝑉 = 𝐼𝑅 + 𝐼𝑋 < 90°
IR
IX
V
90° Note: Reactive
Impedance of a
Transmission line is
much larger then the
resistance.

Reactive Circuits
Reactive Power is the power used to support
the magnetic and electric fields found in
inductive and capacitive loads throughout a
power system.
• Reactive power is measured in
volt-amps-reactive (Vars)

Complex Power
193

Complex Power
Complex Power = Real Power + Reactive Power.
• Unlike resistors; inductors and capacitors do
not consume power, they store and release
energy
• In a resistive circuit, the current and voltage
are in phase. But that is not the case in a
reactive circuit

Complex Power
• Reactive Power supports the magnetic
and electric fields found in inductive and
capacitive loads
• Reactive power is measured in volt-
amperes reactive (Vars)
195

Complex Power
We use phasors and right triangle relationships to
break the current and voltage into resistive and
reactive parts.
𝐴1
0º
90º
180º
270º
0º
90º
180º
270º
𝐴1
Rotor

Current leads Voltage by 30º
30°
90º
180º
270º
Current Leads the Voltage
Voltage Phasor
Current Phasor
Complex Power
Capacitive Circuit

30°
Voltage Phasor
Total Current Phasor
Complex Power
Part of the Current is in-phase with the voltage. Part of the
Current is out-of-phase with the voltage.
IX=Out of Phase Current
IR=In Phase Current

30°
Complex Power
Part of the Current is in-phase with the voltage. Part of the
Current is out-of-phase with the voltage.
VIX=Reactive Power = VARS
VIR= Real Power = Watts
Leading!

Current Lags Voltage by 30º
30°
90º
180º
270º
Current Lags the Voltage
Voltage Phasor
Current Phasor
Complex Power
Inductive Circuit

30°
Complex Power
Lagging
Inductive Circuit

Complex Power
• When voltage and current are not in phase or in
sync, there are two components:
• Real or active power is measured in Watts
• Reactive (sometimes referred to as imaginary)
power is measured in VARs
• The combination (vector product) is Complex Power
or Apparent Power
• The term “Power” normally refers to active power

Complex Power
Real power does the work; it does the heating,
lighting, and turning of motors, etc.
It is measured in Watts

Complex Power
Reactive power supports magnetic and electric
fields required for AC systems to function.
It is measured in:
Volt-Amperes-Reactive (VARs)

Power Triangle
205

Angle between Apparent Power and Real Power is Ɵ
Ɵ
Power Triangle

Power Factor
207

Power Factor (PF) is the ratio of real power to
apparent power.
Power factor =
𝑊𝑎𝑡𝑡𝑠
𝑉𝐴
Power Factor
Ɵ
VARS
Watts

The Power Factor (cos Ө) = Real/Apparent
Power Factor

To serve Manufacturer A, the utility must
provide the following volt-amperes.
Power Factor

To serve this load, the utility's conductors must
be able to carry the following current:
Power Factor

Manufacturer B uses the same real power (2 MW) as
Manufacturer A and, therefore, pays the same amount to the
utility. However, Manufacturer B requires a different amount of
apparent power.
Power Factor

And, the current drawn by Manufacturer B is:
Power Factor

Manufacturer B draws much less current to obtain
the same real power.
Utilities design their transmission and distribution
systems based on the apparent power and the
current they must deliver.
Since utilities bill their customers for the true power
used, utilities encourage the use of high-power
factor systems.
Power Factor

VARs – Effect on Voltage
215

VAR Effect on Voltage Control
Reactive power supply is the most important
element in controlling voltage.
Why?
If I put a lagging reactive current that is 90º out
of phase through a reactive line impedance that
is 90º out of phase, it results in a 180º voltage
drop.
216

Current In Phase with Voltage
90º
180º
270º
Receiving End Voltage Phasor
Current Phasor
VAR effect on Voltage Control
Resistive Load

Current In Phase with Voltage
90º
180º
270º
Voltage Drop due to Line Resistance
(Parallel to Current)
Sending End Voltage
Current Phasor
Resistive Load
Voltage Drop due to Line Reactance
(90º to Current)
Receiving End Voltage

Load Current Lags Voltage by 30º
30°
90º
180º
270º
Current Lags the Voltage
Receiving End Voltage Phasor
Current Phasor
Inductive Load

30°
90º
180º
270º
Voltage Drop due to Line Resistance
(Parallel to Current)
Receiving End Voltage
Load Current
Inductive Load
Sending End Voltage
Voltage Drop due to Line Reactance
(90º to Current)

30°
90º
180º
270º
Lagging Load Current
Voltage Drop High VARS
Voltage Drop Low VARS

VAR Effect on Voltage Control
Voltage fluctuates due to:
Load
• Consumes VARs
• More load, more VARs used
Lines – inductive impedance
• More load, more VAR losses
• Loss of a transmission line means other lines load
heavier and we experience even more VAR losses

Voltage Collapse
223

Voltage Collapse – when the grid system
experiences an uncontrollable reduction
in voltage due to a deficiency in reactive
power (VARS).
Voltage Collapse
Real Real Real Real
VAR
VAR
VAR No VAR

WHAT are VARs?
System Operator and Engineering Terms
• Volt Amp Reactive
• Reactive Power
• Imaginary Power
• Part of Complex Power
• Part of Apparent Power
225

WHAT are VARs?
VAR analogy --- Building a roof
Flat roof with no vertical load is OK
(Voltage is OK)
Flat roof with vertical load (VARS) Sags
(Voltage Sags)
Slanted roof with VARS added to
compensate for load VARS is ok

WHAT are VARs?
• VARs support the system and pull down or
push up the voltage
• When circuits result in the current leading the
voltage, voltage rises as VARs increase
• When circuits result in the current lagging the
voltage, voltage decreases as VARs are
consumed

Why do WE need Reactive Power
“Reactive power (VARs) is required to maintain
the voltage to deliver active power (watts)
through transmission lines. Motor loads and
other loads require reactive power to convert
the flow of electrons into useful work. When
there is not enough reactive power, the voltage
sags down and it is not possible to push the
power demanded by loads through the lines.”
(“Signatures of the Blackout of 2003”, Roger C. Dugan et. al.)

Importance of Reactive Power
• Refers to the circulating power in the grid that does
no useful work
• Results from energy storage elements in the power
grid (mainly inductors and capacitors)
• It must be controlled to prevent voltage problems.
• Reactive power levels have an effect on voltage
collapse
• The reactive power flow should be minimized to
reduce losses. This ensures that the system operates
efficiently

Reactive Power is a Byproduct of AC systems
• Transformers, transmission lines, and motors require reactive
power.
• Transformers and transmission lines introduce inductance as
well as resistance.
• Both oppose the flow of current
• Must raise the voltage higher to push the power through the
inductance of the lines.
• Unless capacitance is introduced to offset inductance
• The farther the transmission of power, the higher the voltage
needs to be raised.

Reactive Power & Power Factor
• Reactive power is present when the voltage and
current are not in phase
• One waveform leads the other
• Phase angle not equal to Zero Degrees
• Power factor less than unity
• Measured in volt-ampere reactive (VAR)
• Produced when the current waveform leads
voltage waveform (Leading power factor)
• Vice versa, consumed when the current
waveform lags voltage (lagging power factor)

AC Voltage & Current Phase Shift due to Inductance
Current Lags Voltage
Per
Unit
0.00 0.20 0.40 0.60 0.80 1.00
Time
1.00
0.80
0.60
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
V=IR+IXL
Voltage
Current
Power
Φ
V
I

Power
Triangle
True Power = Watts
Reactive
Power =
VARS
θ Phase Angle
Volt-Amperes = (VA) = Apparent Power
Watts = (W) = True Power
Vars = (VARS) = Volt-Amperes Reactive
Power Factor = (PF) = Watts/(Volt Amperes)
Phase Angle = Ɵ = COS-1 (PF) = Angular displacement
between voltage & current

Power Triangle
234

Reactive Power Limitations
• Reactive power does not travel very far
• Usually necessary to produce it close to the location
where it is needed
• A supplier/source close to the location of the need is
in a much better position to provide reactive power
– versus one that is located far from the location of the need
• Reactive power supplies are closely tied to the ability
to deliver real or active power

1. In a Resistive Load the current A) Leads, B) Lags,
C) is in phase with the voltage. T/F?
2. A load consists of a 4 ohms resistor in parallel
with a 3 ohm reactor with a voltage of 10 volts.
a. What is the total Impedance?
b. Current?
c. Real Power?
d. Reactive Power?
e. Power Factor?
236

Three-Phase Circuits
• Definition and Advantages
• Three Phase Connections

WYE vs. Delta

Definition and Advantages
• Almost all electricity is generated and
distributed as three-phase rather than single-
phase
• Cost of three-phase is less than single-phase
• Uses fewer conductors
• Reduces Losses

Phase Neutral
3 – Single Phase Lines
=
1 – 3 Phase Line
Phase
Phase
Phase
Phase Phase
Neutral Neutral
Six Conductors Three Conductors
Neutral Current – returns on
other two phases

Phase A
Phase A= - (Phase B +Phase C)
Neutral Current – returns on
other two phases

• More constant load on the generator shaft.
• Single-phase load on the generator shaft goes
from zero to maximum power and back to zero
with each cycle.
• With three-phase current, at least two of the
phases provide current (and therefore, power) at
any instant.
• Load on a three-phase generator never reduces
to zero. This uniform load allows smoother
operation of the generator…

A Phase C Phase
B Phase

In a three-phase circuit:
• An AC voltage generator produces three evenly
spaced sinusoidal voltages, identical except for a
phase angle difference of 120º
• Three conductors transmit the electric energy.
The conductors are called phases and are
commonly labeled A Phase, B Phase, and C Phase
• Each phase conductor carries its own phase
current

0o
120o
240o
360o
A Phase C Phase
B Phase
Three-Phase Power

A
B
C
A B C
+
Generating 3-Phase Power Waves

1/60th sec.
+
-
vs. Single Phase Power

Three-Phase Power

Interconnected 3-Phase Power
In an AC interconnection, all connected utilities see the
same electrical frequency and all generators operate in
synchronism with each other.

• Definition: Phase-to-Phase and Line Voltages
• The voltages between the outputs of the
generator are called the line voltages
(sometimes called phase-to-phase voltages).
• The line voltages are equal to the phase
voltages.
• When a Delta-connected generator is loaded,
current flows in the loads, lines, and phase
windings.

The line currents are not equal to the phase
currents, because each line carries current from
two phases. The currents from any two phases
are 120° out of phase.
Iline = √3 Iphase
Iline = 1.732 Iphase
(√3 is approximately 1.732)
Three Phase Connections

“Delta” Connection
“A” Phase “B” Phase
“C” Phase

“WYE” Connection

100 Amps
Phase Current = Line Current

13,200 Volts
Line Voltage = Phase Voltage x √3 = PV x 1.732
1.732 Vphase= VLine-Line

Electromechanics
• Definition
• Generators
• Motors
• Synchronous Condenser

Electromechanics
Definition
Electromechanical Energy Conversion is used by
generators and motors.
• This process transforms mechanical energy
into electrical energy and vice versa

Electromechanics
Generators
A simple Generator

Electromechanics
Motors
A simple Motor

Electromechanics
Generators and Motors
A generator converts mechanical energy into
electrical energy.
– A voltage is induced in stator conductors as the
magnetic flux from the rotor moves past them
A motor converts electrical energy into rotary
motion.
– Current-carrying conductors in the rotor
experience a force at right angles to the magnetic
field of the motor

Electromechanics
Synchronous Condenser
A synchronous condenser is a large synchronous
motor.
• A synchronous condenser is used to generate
or absorb VARs
• Operators can control whether it produces or
consumes VARs

1. A conductor is a material that has only a few free valance
electrons that continually jump to other atoms. T/F?
2. What are two materials that are good electrical conductors?
3. An insulator is a material that has a large number of free
valance electrons that continually jump to other atoms. T/F?
4. What are two materials that are good electrical insulators.
5. Whenever current flows in a conductor, what invisible force
surrounds the conductor?
6. In an inductive circuit, does the current lead or lag the
voltage?
7. What is impedance?
276

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