Mani V. Venkatasubramanian

Washington State University

Pullman WA

1

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

Oscillation Monitoring System

OMS

OpenPDC

PMU

PMU

PMU

PMU

PMU

PMU OMS as action adapters built into OpenPDC v.2

Historian

SQL Database

Published

3

Entergy 5 Hz mode

Mode frequency changes during some days

5.45 Hz mode shape

5 Hz mode shape – different mode

June 13 2013 IPC Results

June 13 2013 WECC Comtrade data

June 13th PSD Singular Values from WECC data

June 13th 0.37 Hz oscillations at Generator

Mode Shapes on June 13, 2013

0.37 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)

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

Mode Energy Trending for Ringdown

Analysis (METRA)

Zaid Tashman and Mani Venkatasubramanian

Washington State University

Pullman WA

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•Ambient Data

•Ringdown data

PMU Based Modal Analysis

10 20 30 40 50 60 70 8021.9

22

22.1

Time (sec)

Ambient Data

Ringdown Data Nonlinearity

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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)

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𝑦 𝑡 = 𝐴𝑗𝑒−𝜎𝑗𝑡cos (𝜔𝑗𝑡 + 𝜙𝑗)

𝑛

𝑗=1

Ringdown Analysis

𝑦 𝑡 = 𝑅𝑗𝑒λ𝑗𝑡

𝑛

𝑗=1

𝑦 𝑘 = 𝑅𝑗𝑧𝑗𝑘

𝑛

𝑗=1

𝑧𝑗 = 𝑒𝜆𝑗Δ𝑡, 𝜆𝑗 = 𝜎𝑗 + 𝑗𝜔𝑗

0 10 20 30 40 50 60490

500

510

520

530

Time (sec)

Voltage (

kV

)

0 5 10 15 20-0.4

-0.2

0

0.2

0.4

0 5 10 15 20-0.5

0

0.5

1

Mode 1

1.6 Hz

+

Mode 2

0.7 Hz

+

Mode 3

0.4 Hz

0 5 10 15 20-1

-0.5

0

0.5

1

Linear Response

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•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

Prony Algorithm

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Event Analysis Engine at WSU Consistent Oscillation detected at

352s with 1.18 Hz and 0.09 % Damping ratio

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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)

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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

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0 2 4 6 8 10-1

0

1

0 0.5 10

50

100

0 0.5 1-2

0

2

4

0 0.5 10

10

20

30

40

50

0 0.5 10

10

20

30

40

50

0 0.5 10

10

20

30

40

50

0 0.5 10

10

20

30

40

50

2 4 6 8 10 123

3.5

4

Algorithm Steps 𝑦 𝑛 = 𝑨𝒋𝑒

−𝝈𝒋𝑛/𝐹𝑠 cos 2𝜋𝒇𝑗𝑛/𝐹𝑠 + 𝝓𝒋

T G

𝐹 𝑘 = 𝑦(𝑛)

𝑁−1

𝑛=0

𝑒−𝑗2𝜋kn𝑁

FFT

Estimate:

- Amplitude Aj

- Frequency fj

Estimate:

- Phase фj

T = 2/fj, G = 1/fj

Freq (Hz) Freq (Hz)

Phase

(rad)

Magnitude

Least Square Fit

σ

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Multidimensional Example

• Three synthetic signals with one common 1 Hz

mode at 2% damping ratio

0.5 Hz

5.0 %

0.25 Hz 3.0 %

0.35 Hz 4.0 %

G = 1/f = 1/1 = 1 second

1.0 Hz

2.0 %

T seconds N seconds = iG, i=1,2,3,...

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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

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Least Square Fit

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

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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

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Example • Three synthetic signals with one common 0.5

Hz mode at 2% damping ratio

0.75 Hz

4.0 %

1.00 Hz 3.0 %

1.25 Hz 2.0 %

G = 1/2f = 1/1 = 1 second

0.5 Hz

2.0 %

T seconds N seconds = iG, i=1,2,3,...

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Least Square Fit

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

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Case Study I

METRA Rest 28

Case Study I

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Case Study II

METRA Rest 30

Case Study II

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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

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