Mani V. Venkatasubramanian Washington State University Pullman WA

Transcription

1 Mani V. Venkatasubramanian Washington State University Pullman WA 1

2 Motivation Real-time detection and analysis of events and oscillations Fully utilize all available PMU measurements Simultaneous multi-dimensional processing needed for root cause analysis Complex interactions of large-scale power systems Fast multi-dimensional algorithms needed 2

3 Oscillation Monitoring System PMU PMU PMU PMU PMU OMS OpenPDC Historian SQL Database Published PMU OMS as action adapters built into OpenPDC v.2 3

4 Entergy 5 Hz mode Mode frequency changes during some days

5 5.45 Hz mode shape

6 5 Hz mode shape different mode

7 June IPC Results

8 June WECC Comtrade data

9 June 13th PSD Singular Values from WECC data

10 June 13th 0.37 Hz oscillations at Generator

11 Mode Shapes on June 13, Hz at Near Zero Damping Ratio (7.30 am to 8.00 am) 0.4 Hz at Near 8% Damping Ratio (10 am to 11 am)

12 Generator MW Oscillations Operated in rough zone when wind power output high. Vortex effect in Francis turbine when water flow level is low Air compressor to keep oscillations low to nil 5 to 25 MW oscillations observed at 0.37 Hz Tricky for ambient mode monitoring engines Mode shape analysis critical Multi-dimensional analysis crucial

13 Mode Energy Trending for Ringdown Analysis (METRA) Zaid Tashman and Mani Venkatasubramanian Washington State University Pullman WA 13

14 PMU Based Modal Analysis Ambient Data Ringdown data Nonlinearity Ringdown Data Time (sec) Ambient Data 14

15 Complementary Engines Event Analysis Engine (EAE) Prony, Matrix Pencil, HTLS, ERA, Multi-dimensional Fourier Ringdown Algorithm (MFRA), and Modal Energy Trending for Ringdown Analysis (METRA). Aimed at events resulting in sudden changes in damping Damping Monitor Engine (DME) Ambient noise based. Continuous. Provides early warning on poorly damped modes. Frequency Domain Decomposition (FDD), Distributed Frequency Domain Optimization (DFDO), and Recursive Adaptive Stochastic Subspace Identification (RASSI) 15

16 Voltage (kv) Ringdown Analysis Linear Response Time (sec) Mode Hz + Mode Hz + Mode Hz n y t = A j e σ jt cos (ω j t + φ j ) j=1 n y t = R j e λ jt j=1 n y k = R j z j k j=1 z j = e λ jδt, λ j = σ j + jω j 16

17 Prony Algorithm First applied to power systems by John Hauer Commonly used method in many domains Fits a linear combination of damped sinusoids Sensitive to noise in measurements Fits exponential sinusoids to additive noise by over-fitting 17

18 Event Analysis Engine at WSU Consistent Oscillation detected at 352s with 1.18 Hz and 0.09 % Damping ratio 18

19 Existing Ringdown Algorithms Prony, Matrix Pencil, ERA, and HTLS High levels of noise maybe an issue CPU intensive and not scalable Can handle only a limited number of PMUs Selection of model order can be an issue How to analyze ringdown responses from hundreds of PMUs simultaneously? New algorithms developed (MFRA and METRA) 19

20 Multidimensional Fourier Ringdown Analysis (MFRA) Designed for automatic real-time analysis of hundreds of PMU signals simultaneously. Frequency Domain vs Time Domain. Tracks energy trends of each dominant mode during events over time in frequency domain analysis. Not CPU intensive. Fast Processing Time. Recent paper in IEEE Trans. Power Systems Extension from a single signal method by Peter O`Shea 20

21 Magnitude 50 Algorithm Steps 1 0 y n = A j e σ jn/fs cos 2πf j n/fs + φ j G 50 T 50 FFT F k = y(n) Freq (Hz) Freq (Hz) 1 Estimate: - Amplitude Aj - Frequency fj N 1 n= e j2πkn N Estimate: - Phase фj Phase (rad) T = 2/fj, G = 1/fj Least Square Fit 3.5 σ

22 Multidimensional Example Three synthetic signals with one common 1 Hz mode at 2% damping ratio N seconds = ig, i=1,2,3,... T seconds 1.0 Hz 2.0 % 0.5 Hz 5.0 % 0.25 Hz 3.0 % 0.35 Hz 4.0 % G = 1/f = 1/1 = 1 second 22

23 Mode Decay Rate The Logarithmic Fourier Magnitude of the 1 Hz mode decays as window slides through the data t = 0 sec t = 5 sec Signal 1 Signal 2 Signal 3 23

24 Least Square Fit The Damping Ratio (ζ) can be calculated by finding the energy decay slope using a least square fit 24

25 Modal Energy Trending for Ringdown Analysis (METRA) METRA proposed in this paper Track trend of oscillation mode energy measure seen in power spectrum density SVD of PSD matrix as in Frequency Domain Decomposition (FDD) algorithm to get overall energy measures for each dominant mode from multiple PMU signals Robust under noisy conditions 25

26 Example Three synthetic signals with one common 0.5 Hz mode at 2% damping ratio N seconds = ig, i=1,2,3,... T seconds 0.5 Hz 2.0 % 0.75 Hz 4.0 % 1.00 Hz 3.0 % 1.25 Hz 2.0 % G = 1/2f = 1/1 = 1 second 26

27 Least Square Fit The Damping Ratio (ζ) can be calculated by finding the slope of the power spectrum decay using a least square fit 27

28 Case Study I METRA Rest 28

29 Case Study I 29

30 Case Study II METRA Rest 30

31 Case Study II 31

32 Conclusion We thank Entergy and Idaho Power Company for sharing their system results with community Emphasis: Fully utilize all available PMU measurements Simultaneous multi-dimensional processing needed for root cause analysis Complex interactions of large-scale power systems challenging Fast multi-dimensional oscillation monitoring algorithms needed 32