Optimal Multisine Probing Signal Design for Power System Electromechanical Mode Estimation
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The document discusses optimal multisine probing signal design for estimating electromechanical modes in power systems to improve stability and avoid blackouts. It emphasizes real-time monitoring using phasor measurement units (PMUs) and presents conclusions on the benefits of probing signals for enhanced accuracy in mode estimation. Additionally, it highlights the relationship between probing signal characteristics and the accuracy of estimating critical damping ratios in power systems.
![49.85
49.9
49.95
50
50.05
50.1
50.15
08:00:00 08:05:00 08:10:00 08:15:00
f[Hz]
20110219_0755-0825
Freq. Mettlen Freq. Brindisi Freq. Kassoe
Why do we care ?
PMU Data
Oscillations if lightly damped can lead to a system black-out
Occupy transmission capacities, increase losses, wear and tear
February 19th 2011 – North-South Inter-Area Oscillation
Continuous monitoring of frequency and damping = indicators!](https://image.slidesharecdn.com/2017hicsspresentationv1-170821140004/85/Optimal-Multisine-Probing-Signal-Design-for-Power-System-Electromechanical-Mode-Estimation-4-320.jpg)
![Chief Joseph Dynamic Breaker – “The Toaster”
PDCI Modulation (HVDC) Probing Test @ WECC
Ref. BPA, WECC, John Pierre (UW), PNNL
WOW!
I want one
of those!
[BPA] “It can consume 1,440 MW - more than the
output of Bonneville Dam. It's only capable of staying on
for 3 seconds - beyond that, it would destroy itself.”](https://image.slidesharecdn.com/2017hicsspresentationv1-170821140004/85/Optimal-Multisine-Probing-Signal-Design-for-Power-System-Electromechanical-Mode-Estimation-13-320.jpg)
Optimal Multisine Probing Signal Design for Power System Electromechanical Mode Estimation
- 1. KTH ROYAL INSTITUTE OF TECHNOLOGY Vedran S. Peric, Xavier Bombois, and Luigi Vanfretti https://www.kth.se/profile/luigiv/ Associate Professor & Docent Department of Electric Power & Energy Systems (EPE) KTH Royal Institute of Technology Stockholm, Sweden Optimal Multisine Probing Signal Design for Power System Electromechanical Mode Estimation Electrical Energy Systems Track - Monitoring Control and Protection Minitrack Large Scale Dynamics and Control Session
- 2. Outline 1 • Low frequency electromechanical oscillations 2 • Electromechanical mode estimation 3 • Optimal probing design 6 • Conclusions
- 3. Oscillations • General phenomenon • Excitation types • Omnipresent random excitation (ambient) • Intrinsic property of the system (modes) Frequency Damping
- 4. 49.85 49.9 49.95 50 50.05 50.1 50.15 08:00:00 08:05:00 08:10:00 08:15:00 f[Hz] 20110219_0755-0825 Freq. Mettlen Freq. Brindisi Freq. Kassoe Why do we care ? PMU Data Oscillations if lightly damped can lead to a system black-out Occupy transmission capacities, increase losses, wear and tear February 19th 2011 – North-South Inter-Area Oscillation Continuous monitoring of frequency and damping = indicators!
- 5. How to continuously monitor? Estimate modes (freq. and damping) 350 400 450 500 550 600 650 700 750 800 1100 1200 1300 1400 Time (sec.) Power Transfer (MW) Alarm System Unstable 0.27 Hz 7% Damping (Ambient) 0.264 Hz 3.46% Damping (Transient) 0.252 Hz 1.2% Damping (Ambient) 15:42:03 – K-A Line Trip 15:47:36 – R-L Line Trip McNary Generation Trip 15:48:51 Out-of-step Separation
- 6. Outline 1 • Low frequency electromechanical oscillations 2 • Electromechanical mode estimation 3 • Optimal probing design 6 • Conclusions
- 7. Application Objectives Avoid black-outs Real-time monitoring Decision support tools Control actions
- 9. M. S. Almas, M. Baudette, L. Vanfretti, S. L⊘vlund and J. O. Gjerde, "Synchrophasor network, laboratory and software applications developed in the STRONg2rid project," 2014 IEEE PES General Meeting | Conference & Exposition, National Harbor, MD, 2014, pp. 1-5. doi: 10.1109/PESGM.2014.6938835 Ø Power system or real-time simulator Ø Phasor measurement units (PMUs). Ø Phasor data concentrator (PDC) S3DK PMU 1 PMU 2 PMU n PDC Comm. Network IEEE C37.118 Protocol KTH SmarTS Lab Test-Bed and Application Prototyping Real system Real time simulator User application Source Measurements Comm. Infrastructure Decoder Ø Communication Network Ø Software Development Kit (SDK) Ø User applications
- 10. Sample Mode Estimator Prototype GUI Communication Configuration L. Vanfretti, V. H. Aarstrand, M. S. Almas, V. S. Perić and J. O. Gjerde, "A software development toolkit for real-time synchrophasor applications," PowerTech (POWERTECH), 2013 IEEE Grenoble, Grenoble, 2013, pp. 1-6. doi: 10.1109/PTC.2013.6652191 V. S. Perić, M. Baudette, L. Vanfretti, J. O. Gjerde and S. Løvlund, "Implementation and testing of a real-time mode estimation algorithm using ambient PMU data,"Power Systems Conference (PSC), 2014 Clemson University, Clemson, SC, 2014, pp. 1-5. doi: 10.1109/PSC.2014.6808116 Mode Estimator https://github.com/SmarTS- Lab-Parapluie/S3DK/releases S3DK: Real-time mediator + LabView Library Available as Open Source Software:
- 11. Ambient data-based mode estimation • Assumptions: – The system operates in quasi steady state period – Behavior of the system is modeled by a linear model – System is excited only by small load changes modeled as white noise Power System H(jω) Load Changes Measurements • The model of measured stochastic signal is determined by a model set and set of parameters. • Most common model set is: 𝑯 𝒛 = 𝑩 𝒛 𝑨 𝒛 = ∑ 𝒃 𝒌 𝒛)𝒌𝒒 𝒌+𝟎 𝟏 + ∑ 𝒂 𝒌 𝒛)𝒌𝒑 𝒌+𝟎
- 12. Probing-based mode estimation Power system dx/dt=Ax+Bu y=Cx+Du Inputs (load noise) Outputs (PMUs) Deterministic signal Exactly known excitation brings new information that can be used for improved mode identification Probing signals FACTS devices AVR Turbine governors H(θ,z) G(θ,z) e(t) y(t) u(t) - designed input signal Aggregated load noise Single output model
- 13. Chief Joseph Dynamic Breaker – “The Toaster” PDCI Modulation (HVDC) Probing Test @ WECC Ref. BPA, WECC, John Pierre (UW), PNNL WOW! I want one of those! [BPA] “It can consume 1,440 MW - more than the output of Bonneville Dam. It's only capable of staying on for 3 seconds - beyond that, it would destroy itself.”
- 14. Outline 1 • Low frequency electromechanical oscillations 2 • Electromechanical mode estimation 3 • Optimal probing design 6 • Conclusions
- 15. Ø Model structure of the power system o ARMAX Mathematical formulation and sketch Ø Optimization problem: Solution: model representing the power system ( , ) ( , ) ( ) ( ) ( ) ( , ) ( , ) B z C z y t u t e t A z D z q q q q = + Contain information about the critical modes/poles Model (parameters) Measurements Minimization Error - Parameter variation Model response Measured response min 5 1 𝑁 8 𝜀 𝑡, 𝜃 = > ?+@ 𝜀(𝑡, 𝜃) = 𝑦(𝑡) − 𝑦 ⌢ (𝑡|𝑡 − 1G X. Bombois, G. Scorletti, M. Gevers, P.M.J. Van den Hof and R. Hildebrand, “Least costly identification experiment for control”, Automatica, vol.42, no.10, pp.1651-1662, Oct. 2006.
- 16. p p q p p w q w q w w q w q w p p w s - - - æ ö æ ö = +ç ÷ ç ÷ç ÷ ç ÷ è ø è F ø ò ò 6 4 4 4 4 4 4 4 7 4 4 4 4 4 4 48 6 4 4 4 4 4 7 4 4 4 4 48 1 * * 0 0 0 02 1 ( , ) ( , ) ( , ) ( , ) 2 ( 2 )u u eu e N N P F F d F F Probing Ambien d t Optimal probing: problem formulation Ø Objective: Identify the critical damping ratio of G(z) H(θ,z) G(θ,z) e(t) y(t) u(t) - input signal load measurement How should the probing signal look like ? Spectrum influences accuracy q -1 P Good estimate q -1 P Bad estimate wF ( )u wF ( )u There is a limit how strong probing can be Stronger probing provides better accuracy Probing Ambient
- 17. y(t) H(z) Poles ζ ARMA Pθ Pζ • Important: • Covariance matrix depends directly on the estimated model Addendum Note: Covariance Matrix Computation V. S. Perić, X. Bombois and L. Vanfretti, "Optimal Signal Selection for Power System Ambient Mode Estimation Using a Prediction Error Criterion," in IEEE Transactions on Power Systems, vol. 31, no. 4, pp. 2621-2633, July 2016.doi: 10.1109/TPWRS.2015.2477490
- 18. Spectrum calculation of the probing signal 1) Control effort 2) System disturbance 3) Accuracy Objective function p p p p w w w w p p- - æ ö æ ö = F + Fç ÷ ç ÷ç ÷ ç ÷ è ø è ø ò ò 2 1 2 (t) min ( ) (s) ( ) 2 2u uu k k J d G d Constraint: var( ) T i i i e P e rq z = < r - tolerance Input power Output power (frequency deviation) Ø Requirements : Optimization problem in a form of LMI The solution is the power spectrum of the probing signal Accuracy constraints Accuracy: damping ration estimation variance!
- 19. Time domain probing signal realization Ø Spectrum calculation (solved) Ø Time domain signal realization LMI Signal realization max var(ζ) Multisine ACF (rd) min(upeak 2 /urms 2 ) FIR filter min(║ r-rd║2 ) white noise - e(t) u(t) u(t) u(t) Probing Φu(ω) calculation
- 20. White noise Minimized function var{u(t)} var{y(t)} var{uy(t)} var{u(t)} 10410 1179.8 101850 1441.6 var{y(t)} 1.6761 2.0915 1.2425 1.5980 var{uy(t)} 6881.1 7981.4 52167 2318.8 Optimal probing signal design results The same accuracy obtained with the 5-7 times weaker excitation The same input power provides 4-5 times better accuracy (0.25*10-5) Damping variance < 10-5 Benefits of the proposed method KTH Nordic 32 Minimized input power Minimized disturbance 2 critical modes 0.5Hz & 0.76Hz Reactive power probing
- 21. Conclusions • A comprehensive way of dealing with mode estimation uncertainty • Estimation variance is the measure of accuracy • Probing signals improve mode estimation accuracy • Multisine probing signal parameterization • The spectrum and not time domain probing signal determines accuracy of the mode estimation procedure • Optimal spectrum determined as a solution of an LMI optimization problem