Transcript
WPRC 2007
Power System Frequency Measurement for Frequency Relaying
Spark Xue, Bogdan Kasztenny, Ilia Voloh and Dapo Oyenuga
GE Multilin
Organization of the presentation
Frequency definition and signal models
Requirement on frequency measurement
Review of frequency measurement methods
Simulation tests on four typical algorithms
Frequency relay design and test
The general definition of frequency
General definition: The number of cycles or alterations per unit time of a wave or oscillation.
Frequency for arbitrary signal including aperiodic signal
Instantaneous Frequency
Fourier Transform Rotating phasor
Power system frequency
Generator frequencyA
VA
A
B
B C
C
VBVC
The frequency of ith node in the system
Use rotating phasor for ith node voltage
The frequency is:
Power system frequency
System frequency:
Node frequency:
Apparent frequency: what a relay ‘sees’
Signal models - 1
Signal with harmonics/noise and dc components
Basic signal model
or
Signal models - 2
Three-phase model based on Clarke transform
Three-phase model based on positive seq. component
The frequency relaying
Under/over frequency relays (generator protection,
load shedding scheme, etc.)
Over-excitation protection
Synchrocheck relays
Phasor measurement units
Phasor-based numerical relays
Requirements for frequency measurement
The measured frequency or frequency rate-of-change should be the true reflections of the power system state
The accuracy should be good enough under system steady state and dynamic conditions
The frequency estimation should be fast enough to follow the actual frequency change to satisfy the need of the intended application
The frequency tracking for generator protection should have wide range to handle generator starting-up and shutting-down
The frequency measurement should be stable and robust when the signal is distorted
Frequency measurement algorithms
Zero-crossing
Digital Fourier transform (DFT) with compensation
Signal decomposition
Signal demodulation
Phase locked loop
Nonlinear iterative methods (LES, LMS, Newton, Kalman filter, etc.)
Artificial intelligence (NN, Fuzzy, GA)
Wavelet transform
And more …
Review 1: Zero-crossing methods
Simple, not affected by signal amplitude variation, relatively less susceptible to harmonics and noise
Highly susceptible to dc component and phase abnormity
Accurate localization zero-crossings is critical
Polynomial interpolating / linear interpolating
Has delay for frequency estimation
Review 2 - 1: DFT with compensation
Frequency is derived as phasor rotating speed
Review 2 - 2: DFT with compensation
Leakage error occurs if the sampling frequency is not an integer multiple the signal frequency
Frequency domain for a 60Hz signal (fs = 3840Hz)
Frequency domain for a 59Hz signal (fs = 3840Hz)
Magnitudes of the phasors for 60Hz / 59Hz signals (fs = 3840Hz)
Angles of the phasors for 60Hz / 59Hz signals (fs = 3840Hz)
Review 2 - 3: DFT with compensation
To compensate leakage error, there are four main approaches:
The DFT method is susceptible to harmonics and noise
The window length is fixed, the sampling frequency is updatedThe sampling frequency is fixed, the window length is updatedBoth the sampling frequency and the window length are fixed,
the data are re-sampled Both the sampling frequency and the window length are fixed,
the leakage error is compensated analytically
Review 3: Signal decomposition
Original signal Orthogonal signals Frequency
The different filter gains at off-nominal frequencies would bring error
Good results can be achieved after error compensation
Sine Filter
Cosine Filter
Input signal v(t) f
v
v
1
2
E.g.
Review 4: Signal demodulation and PLL
It can achieve high accuracy, insusceptible to harmonics / noise
The low-pass filter design is critical
Signal demodulation
The Phase locked loop (PLL)
Highly accurate and insusceptible to harmonics and noise
The dynamic response may be slow
Review 5-1: Non-linear iterative methods
Non-linear iterative methods:
Least error squares (LES) methods
Least mean squares (LMS) methods
Newton type methods
Kalman filters
And more …
A common feature: iteratively minimize the error between model estimations and the observations (sample values).
They could be highly accurate and relatively robust, but the convergence could be slow and computational cost could be high
Review 5-2: A example - Newton method
Signal model:
The parameters to be estimated:
Objective function:
Parameters updating:
Updating step:
Performance evaluation
Three aspects: the accuracy, the estimation latency and the robustness
The accuracy
1mHz resolution 1mHz accuracy
The maximum error and the average error
Use benchmark signals to check the accuracy, the latency and the robustness, e.g.,
The signal frequency is modulated by a 1.0Hz swing
The signal amplitude is modulated by a 1.5Hz swing
The signal is contaminated by 3rd, 5th, 7th harmonics and noise
The signal contains dc component
The signal contains 25Hz low frequency component
Simulation tests
Four typical algorithms are selected
Zero-crossing with linear interpolation (ZC)
DFT with compensation (SDFT, proposed by Yang & Liu)
Signal decomposing (SDC, proposed by Szafran)
Signal demodulation (SDM, using a 6-order IIR filter with more
than 100dB stop-band attenuation)
Platform: MATLAB
Sampling Frequency: 3840Hz
Additional filters are NOT used
Test 1: Stationary signal with off-nominal frequencies
Use basic signal model
f = 61.5Hz, 59.3Hz, 58.1Hz, 45.2Hz, 20.3Hz
Test 2: Track the frequency change
Test 3: Both frequency and amplitude are time-varying
Test 4: The frequency step change test
Frequency change from 60Hz to 59.5Hz within one sampling interval
Test 5: Signal containing harmonics
Test 6: Signal containing low-frequency components
Test 7: Signal containing dc component
Test 8: Signal containing impulsive noise
Test 9: Power system simulation test – the model
G
Hydraulic Turbine
Excitation System
Meter
Voltage Source 1500MVA, 230kV
Transformer210MVA
13.8kV/230kV
Synchronuous Machine
200MVA/13.8kV
Test 9: Power system simulation test
ZC
SDFT
SDC
SDM
Rotor speed
Digital frequency relay / element design
Pre-filtering: to clean up and to fix distortions
Band-pass filter (e.g. 20-65Hz passband)
The stop band attenuation should be reasonably high (e.g. 20-40dB)
Additional impulsive noise detector
Post filtering: low-pass filter or moving average filter to improve accuracy
Security conditions: to remove abnormal frequency
The rate-of-change (df/dt) needs additional filtering and security check
Test an actual relay : case 1
The analytical test signal
Contains dc component, harmonics, white noise, impulsive noise,
Both frequency and amplitude are oscillating
Produced by MATLAB, saved in comtrade file, played back by RTDS
The tracking frequency
Test an actual relay : case 2
The voltage signal from model simulation
The tracking frequency
Tests recommendations
The steady-state signal test with off-nominal frequencies
Check the basic accuracy, verify the resolution, the measurement range
The frequency ramping-down test
Ramping step up to 0.1Hz and ramping rate up to 5Hz/s
Check the dynamic accuracy
Check the operating time
The robustness test
Add 3rd, 5th, 7th harmonics (5% each) and noise (SNR=40-60dB)
The playback test
Summary
Power system frequency is not an instantaneous value, even though the concept of instantaneous frequency could be utilized for frequency estimation.
For various numerical algorithms based on signal periodicity orinstantaneous frequency, the common goal is to pursue high accuracy and fast estimation, under the condition of robustness.
In fact, it is necessary to use a few cycles of data to derive the frequency, in order to obtain stable measurement under various signal conditions.
For frequency relay design, the balance between the accuracy and the group delay need to be achieved, filters and security check conditions are needed.
The frequency relay needs to be tested under adverse signal conditions.
……
Thank you, questions?