WHAT? WHY? HOW??

What are “Low Frequency

Modes”?

Why we need to identify them?

How can we identify these

modes?

DEFINITION

Variation in load causes the fluctuation in electromechanical dynamics of the system.

Operation modes under these low level fluctuations called “Low frequency Modes”.

CLASSIFICATION

Inner Area mode: Oscillation frequency (0.1 to 0.7 Hz).

Local Plant: Oscillation frequency (0.8 to 2 Hz).

Low Frequency modes

Local plantInner Area mode

WHY IDENTIFICATION IS REQUIRED?

Increase transmission capacity: Poorly damped low frequency oscillations reduces the transmission capacity.

Resolve security and stability concerns.

It helps in preventive controls: for proper monitoring and designing of the preventive controllers.

METHODS OF IDENTIFICATION

Off-line approach:

1. Utilize ambient data.

2. Require time window of 10-20 min.

3. Not much accurate at estimation of modes.

Approaches

On-line approachOff-line approach

CONTINUE…

On-line approach:

1. Based on the linearized model of the non-

linear power system.

2. More accurate in estimation of the modes.

3. Require small time window (10-20 sec.).

METHODS

On-line methods which utilize the real time data obtain from the Phasor Data Concentrator (PDC).

1. FFT (Fast Fourier Transform)2. Kalman Filter3. Hilbert Method4. Prony Methods

All these methods have some limitation in estimation of low frequency modes.

LIMITATIONS

FFT has resolution problem for the data with the small samples and does not directly provide the damping information of the mode.

Hilbert methods is obtain using FFT of the signal therefore it has the same resolution limitations.

Very slow response time.

PROPOSED METHODS

Noise Space Decomposition (NSD) Modified Prony Method

But before using them we require Signal in the form of data matrix.

There is also need to know the exact order of the Model.

To do so we use singular value decomposition (SVD).

BLOCK DIAGRAM

PROCEDURE PMUs provide phasor measurements to PDC

through communication channel. Take a block of N most recent samples of the

active power obtained from the PDC. where N is approximately taken to be the ratio

of the phasor data rate of the PMU and the lowest limit of the frequency of the estimator.

Then perform “Down Sampling” to reduce the filter order.

Generates the auto correlation matrix R out of these samples.

CONTINUE…

Now apply SVD on the auto correlation matrix R to know the order of the model.

As result we get singular values

This method estimates the order of the model of the signal by separating the signal subspace from noise subspace based on the magnitude of the singular values.

NOISE SPACE DECOMPOSITION METHOD

Where, where k = 1,…, M and are amplitudes. n = 1….N. and are the attenuation factor and frequency, respectively.

Main idea is to obtain a basis of the noise subspace by using the conditions for a noiseless system.

Which is further used to decompose the singular values in signal space and hence reduces the noise.

SIMULATION RESULTS

Samples vs. Damping Samples vs. Frequency

MODIFIED PRONY METHOD

The basic concept in this method is to express the elements of state space as a function of linear and non-linear parameters.

These parameters are estimated by minimizing the error norm square.

Since both these parameters are independent of each other (as stated in prony method), we fix one variable and use Linear Regression techniques to obtain our solution.

BLOCK DIAGRAM

CONTINUE…

Samples vs. Damping Samples vs. Frequency

RESULT COMPARISON

Samples vs. Damping Samples vs. Frequency

THANK YOU