WHAT? WHY? HOW??What are “Low Frequency Modes”?Why we need to identify them?How can we identify these modes?
DEFINITION Variationin load causes the fluctuation in electromechanical dynamics of the system. Operation modes under these low level fluctuations called “Low frequency Modes”.
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).
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 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.
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).
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.
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.