xue_ppt

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?