The document discusses low frequency modes in power systems, which refer to oscillations between 0.1-2 Hz caused by fluctuations in load. It is important to identify these modes to increase transmission capacity and ensure stability. Identification can be done offline using ambient data or online using phasor measurement data. Common online methods include FFT, Kalman filtering, and Prony analysis, but they have limitations. Noise space decomposition and modified Prony analysis are proposed for more accurate identification using phasor data from PMUs.

1. WHAT? WHY? HOW??
What are “Low Frequency Modes”?
Why we need to identify them?
How can we identify these modes?

2. DEFINITION
 Variationin load causes the fluctuation
in electromechanical dynamics of the
system.
 Operation modes under these low
level fluctuations called “Low
frequency Modes”.

3. CLASSIFICATION
Low Frequency modes
Inner Area mode Local plant
 Inner Area mode: Oscillation frequency (0.1 to 0.7 Hz).
 Local Plant: Oscillation frequency (0.8 to 2 Hz).

4. 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.

5. METHODS OF IDENTIFICATION
Approaches
Off-line approach On-line approach
 Off-line approach:
1. Utilize ambient data.
2. Require time window of 10-20 min.
3. Not much accurate at estimation of modes.

6. 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.).

7. METHODS
 On-line methods which utilize the real time data
obtain from the Phasor Data Concentrator (PDC).
1. FFT (Fast Fourier Transform)
2. Kalman Filter
3. Hilbert Method
4. Prony Methods
 All these methods have some limitation in
estimation of low frequency modes.

8. 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.

9. 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).

10. BLOCK DIAGRAM

11. 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.

12. CONTINUE…


13. NOISE SPACE DECOMPOSITION METHOD


14. SIMULATION RESULTS
Samples vs. Damping Samples vs. Frequency

15. 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.

16. BLOCK DIAGRAM

17. CONTINUE…
Samples vs. Damping Samples vs. Frequency

18. RESULT COMPARISON
Samples vs. Damping Samples vs. Frequency

19. THANK YOU