Power System Protection Part-III Numerical Relaying and Digital Protection of Power Systems: Theory and Applications

Dr. K.S.Swarup Department of Electrical Engineering Indian Institute of Technology Madras Chennai 600036 Email: swarup@ee.iitm.ac.in http://www.ee.iitm.ac.in/people/faculty/shantiswarup.html
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Contents
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Introduction to Power System Protection Numerical Relaying Principles Digital Protection Algorithms Numerical Relaying vs Digital Protection Suitability Applications Methodology Design Development Implementation Case Studies
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Need for Power System Protection

Electrical power system consists of generators, transformers, transmission and distribution lines, etc. Short circuits and other abnormal conditions often occur on a power system. The heavy currents associated with short circuits are likely to damage the equipment. Hence it is necessary to provide suitable protective relays and circuit breakers for the protection of each section of power system. If a fault occurs in an element of a power system, an automatic protective device is needed to isolate the faulty element as quickly as possible to keep the healthy section of the system in normal operation.

What is a Protection System ?

A protective system includes circuit breakers and relays to isolate the faulty section of the system from the healthy sections. A circuit breaker can disconnect the faulty element for the system as designated by the relay. The function of a protective relay is to detect and locate a fault and issue a command to the circuit breaker to disconnect the faulty element. A relay constantly monitors the electrical quantities and senses the abnormal conditions on a power system.

Power System Relaying

Digital/Computer Relaying History
Contemplated in late 1960s Introductory papers by Rockefeller Digital Distance Protection relay by Mann and Morrison in 1971 Digital Relays by Westinghouse and Pacific Gas & Electric Company in 1972 Kalman Filter based approaches by Girgis and Brown in 1982 Latest being Traveling wave based and Wavelet based techniques
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NUMERICAL RELAYING

Block Diagram of a Numerical Relay

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Development Cycle of a new Numerical Relay

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I. Numerical Relaying Algorithms

Over-Current Protection Distance Protection Differential Protection

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Numerical Over-current Protection

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i. Over-Current Protection
Procedure: 1) Step down the current or the voltage

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signal. Low-pass analogue filtering. Analog to digital conversion. Find FFT. Select the sampling rate (N) and current pick up value(Ipu). Find weights of fundamental sine and cosine waves. W1sine (1) to W1sine (N); W1cos (1) to W1cos(N). A0 = 0, A1 = 0 = B1. Read nth sample value. A0 = A0 + W1 (n), A1 = A1 + W1sine (n)*Sample(n), B1 = B1 + W1cos(n)*Sample(n). n = n + 1. If (n > N) go to (d) else a0 = A0/N, a1 = 2*A1/N, b1 = 2*B1/N. F1 = a1^2 + b1^2, Q = arc tan (b1/a1). If (F1 > Ipu) trip signal else go to (c). If above condition is true then start the relay.
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ii. Distance Protection

Procedure: Read current and voltage at three different instants. Calculate impedance Zi. Determine the sampling period ( T sampling ), frequency of the signal ( W ). Follow the above given procedure to determine the corresponding magnitudes. These be In-1, In, In+1,Vn-1,Vn, Vn+1. Now Vm = sqrt [ Vn^2 + (( Vn-1 + Vn+1 )/(2*T sampling*W))^2]. Now Im = sqrt [ In^2 + (( In-1 + In+1 )/(2*Tsampling*W))^2]. Calculate effective impedance ( Z). If ( Z > Zi) issue trip else go to (1).

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Numerical Transformer Differential Protection

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iii. Differential Protection

Procedure: Read percentage bias (B). Read pickup value of current ( Ipu ). Read I primary. Step down the current signal. Low-pass analogue filtering. Analog to digital conversion. Store the samples in buffer. Find FFT. Select the sampling rate (N). Define the pickup value ( Ipu ). Find weights of fundamental sine and cosine waves. W1sine (1) to W1sine (N); W1cos (1) to W1cos (N). A0 = 0, A1 = 0 = B1. Read nth sample value. A0 = A0 + W1(n), A1 = A1 + W1sine(n)*Sample(n), B1 = B1 + W1cos(n)*Sample(n). n = n + 1. If(n > N) go to (d) else a0 = A0/N, a1 = 2*A1/N, b1 = 2*B1/N. F1 = a1^2 + b1^2, Q1= arc tan (b1/a1). Read I secondary. Find its magnitude is F2 and phase is Q2 as for the case of I primary. I spill = F1 ~ F2. I circulating = (F1 + F2)/2. If ( I spill > ( B * I circulation + Ipu ) then trip signal is issued else go to (3). So the relay is started accordingly.
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Protective Relay Example

IMPLEMENTATION OF PROTECTION MODULE IN MATLAB

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NOISY SIGNAL AND DENOISED SIGNAL.

Figure shows the final result of the simulation. It shows the noisy signal in the upper half and the de-noised signal in the lower half. The lower half signals magnitude is calculated and a relay is started accordingly.
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DIGITAL PROTECTION

Digital Algorithms
Sinusoidal Wave Based Algorithms Differential and Distance Protection 1. Sample and First Derivative Method 2. First and Second Derivative Method 3. Two Sample Technique 4. Three Sample Technique

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Digital Algorithms
Fourier Analysis Based Algorithms - Fundamental component extraction 1. Full Cycle Window

2. Half Cycle Window 3. Sub-Cycle Window

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Digital Algorithms
Least Square based methods - Fundamental component extraction Differential equation based methods Mostly used for Transmission Line Protection Traveling wave based methods - Mostly used for Transmission Line Protection

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Digital Algorithms
Transmission Line Protection Using Traveling Waves

Internal Fault

External Fault

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Benefits of Digital Relaying

Reliability Flexibility Self checking and Diagnosis Improved performance Cost/benefit considerations

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Computer Relaying Architecture

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Substation Computer Hierarchy

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Digital Protection :Basic Elements

Basic components of Digital Relay : 1. Signal Processing Subsystem

Signal Processing Subsystem

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Conversion Subsystem

Conversion Subsystem

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Digital Processing Relay Subsystem

Digital Processing Relay Subsystem

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BASIC COMPONENTS OF A DIGITAL RELAY

TRANSDICER

I. SIGNAL CONDITIONING SUBSYSTEM

SURGE PROTECTIVE CIRCUIT

LP FILTER

ANALOGUE MULTIPLEXER

SAMPLE & HOLD CIRCUIT

II. CONVERTION SUBSYSTEM

A/D CONVERTER

DIGITAL MULTIPLEXER

III. DIGITAL PROCESSING RELAY SUBSYSTEM

D/O

D/I

MEMORY

CPU

D/A

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Signal Conditioning
Transducers CT, PT Surge Protection Units capacitors, isolation transformers, zener diodes Typical Arrangement

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Signal Conversion
Sampling Sampling Theory Sample and Hold Principle
Control Pulses Signal to be Sampled

Sampling Circuit
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Signal Output
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Mathematical Background
Finite Differences
Let value of a function y=f(x) at x=k be fk, then

Forward Difference
First Order nth Order

f k = f k +1 f k

Backward Difference
First Order nth Order

n f k = n 1 f k +1 n 1 f k
f k = f k f k 1

Central Difference
First Order nth Order

n f k = n 1 f k n 1 f k 1
f k = f k +1/ 2 f k 1/ 2
n f k = n 1 f k +1/ 2 n 1 f k 1/ 2
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Mathematical Background
Interpolation
Forward Interpolation Backward Interpolation
f k +1 = f ( xk + h) f k 1 = f ( xk h)
f k = 1 1 1 ( 2 + 3 ...) f k h 2 3

Numerical Differentiation Curve Fitting and Smoothing

Least Square Method for Representing Data

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Mathematical Background
Fourier Analysis

Periodic Waveform

Fourier Coefficients for /T = 1/2

Fourier Coefficients for /T = 1/4

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Mathematical Background
Concept of Moving Data Window 3 sample data window W1 Pre Fault W2, W3 Pre and Post Fault W4 Post Fault

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Sampling Theorem
sampling,min2signal (pure signals) sampling,min2signal,max (distorted signals)

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DSP Based Digital Relay

CASE STUDY 1 COMPUTER RELAYING FOR POWER SYSTEM PROTECTION USING DIGITAL SIGNAL PROCESSING TECHNIQUES
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Case Study 1: COMPUTER RELAYING FOR POWER SYSTEM PROTECTION USING DIGITAL SIGNAL PROCESSING TECHNIQUES
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Digital Protection :Basic Elements

Basic components of Digital Relay : 1. Signal Processing Subsystem

Signal Processing Subsystem

2.

Conversion Subsystem

Conversion Subsystem

3.

Digital Processing Relay Subsystem

Digital Processing Relay Subsystem

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Working of DSP Based Protection

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DIGITAL RELAY UNIT

VA VB VC VO IA IB IC IO
Auxiliary Transformer Unit
filter S/H

CPU
MEMORY

filter

S/H

filter

S/H

A/D
M U X

filter

S/H

I D B

D/I

filter

S/H

CLK
filter S/H

D/O

Ry

filter

S/H

TAP

filter

S/H

Auxiliary Relay Unit Digital Relay Unit

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HARDWARE MODEL FOR DSP BASED MULTIFUNCTION RELAYING

PC BUS ANALOG INPUT SUB SYSTEM (DIGITAL SIMULATOR) TMS 320C50 DIGITAL SIGNAL PROCESSOR CONTROLLER
C programs

MAT LAB Programs

DIGITAL I\P ANALOG I\P V&I DIGITAL O\P RELAYS AND CIRCUIT BREAKERS

HARD WARE INPUT SUB SYSTEM (SCALED DOWN SUBSTATION MODEL)

HUMAN INTERFACE

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SETUP FOR COMPUTER RELAYING USING DSP TECHNIQUES

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Development of Relay test programs using the DSP TMS320C50 kit

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Block Diagram for Over current Relay

Input signal Input current signal Comparator Reference signal Delay Trip signal RMS

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MAT LAB SIMULATION BLOCK DIAGRAM FOR OVER CURRENT RELAY

1-Phase Clock InputSignal From File |u| Abs >= 255 Compare To Constant Multiphase Clock S/H Sample and Hold

Clk Up Cnt Rst Counter type converter double Combinatorial Logic >= 50 Compare To Constant1 Scope

The Time Delay need not be fixed. It can be variable, depedning on the kind of overcurrent relay.

Product

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Procured DSP TMS320C50 Kit from Vi Micro Systems

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