Numerical Prof. Kothari

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11/27/2009

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NUMERICAL RELAYS

(Microprocessor based technologyapplied to relaying)

Prof. M.L.Kothari

Deptt of Electrical Engineering

Indian Institute of TechnologyDelhi

New Delhi INDIA

Visiting Professor, HelsinkiUniversity of Technology

OUTLINE OF THE LESSON

• Brief History of Microprocessor based

Relays.

• Benefits of Microprocessor basedRelays.

• Shortcomings of Microprocessor based

Relays.



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OUTLINE OF LESSON

• Introduction to Relaying Algorithms

• Phasor Estimation Techniques (Algorithmsfor Protective relaying)

• Peak Measurement Scheme

• Asynchronous –sample Algorithms

• Peak and Phase Computing with Data

Samples.• Linear Estimation

• Wave form Model

OUTLINE OF LESSON

• Relaying as parameter estimation

• Fourier algorithms

• Differential equation algorithm



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• Major Functional Blocks of a typical

Microprocessor based Relay

• Phasor Estimation Techniques

• Time Domain Algorithms or Modelling

Algorithms

REFERENCES

• IEEE WG116 Report –

Understanding microprocessor –

based technology applied to

relaying, February 2004.

• A.G.Phadke and J.S. Thorp,

“Computer Relaying for Power

systems,Taunton,UK:Research

studies Press and NewYork: John

Wiley and Sons,1988.



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• M.S.Suchdeva (coordinator)IEEETutorial Courses Text,

• Computer Relaying,New Jersey: IEEEPublication No. 79EH0148-7-PWR,1979

• Microprocessor Relays and Protection

Systems, New Jersey,IEEEPublication No. 88EH0269-1-PWR,1988

• Advancements in Microprocessor

Based Protection and Communication,

New Jersey,IEEE Publication No.

97TP120-0,1997



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BRIEF HISTORY OF MICROPROCESSOR

BASED RELAYS

• In late 1960’s researchers ventured into

the use of computers for power system

protection.

• The advances in VLSI technology and

software techniques in 1970’s led to the

development of microprocessor based

relays that were first offered as

commercial devices in 1979.



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• Multifunction relays were introduced in the

late 1980s. These devices reduced the

product and installation costs drastically

• This trend continued until now and has

converted microprocessor relays as

powerful tools in modern substations.

• At this time, several trends are emerging.

These include

• Common hardware platforms

• Configuring the software to perform

different functions.

• Integrating protection with substation

control.

• Application of Fiber optic cables.



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NUMERICAL RELAYS

• Microprocessor based relays are called

Numerical relays specifically if the

calculate algorithm numerically.

BENEFITS OF MICROPROCESSORBASED RELAYS

• Multiple functions.

• Cost

• Custom logic scheme

• Panel space



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• Burden on instrument transformers

• Sequence of events and oscillography

• Self monitoring and self –testing.

MULTIPLE FUNCTIONS

• Multiple setting groups

• Programmable logic

• Adaptive logic

• Self monitoring



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• Self – testing

• Sequence of events recording and

Oscillography

• Ability to communicate with other

relays and control computers

COST

• The cost per function of microprocessor

based relays is lower compared to the

cost of electromechanical and solid state

counterparts.

• The reduction in cost is due to the lower

cost of components,and production

techniques



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CUSTOM LOGIC SCHEMES

• A major feature of microprocessor –

based-relays that was not available in

previous technologies is the ability to

develop their own logic schemes,including

dynamic changes in that logic

PANEL SPACE

• Significantly less panel space.

• The reduction in size is a result of the high

level of integration in hardware and theability of using one physical device for

performing multiple protection functions.



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BURDEN ON INSTRUMENTTRANSFORMERS

• Microprocessor –based relays place

significantly less burden on instrument

transformers than the burden placed by

relays of the previous technologies

• They also require fewer CTs and PTs

because some operating quantities, such

as zero sequence currents and voltages

are derived by numerical techniques.



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SEQUENCE OF EVENTS ANDOSCILLOGRAPHY

• Reporting features ,including sequence

of events recording and oscillography

are natural byproduct of microprocessor

based protection systems

SELF- MONITORING AND SELF-TESTING

• Microprocessor–based-relays have the

ability to perform self-monitoring and self-

testing functions.



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• These features reduce the need for

routine maintenance because the relays

automatically take themselves out of

service and alert the operators of the

problem when they detect functionalabnormalities (Fail in safe mode).

SHORTCOMINGS OF MICROPROCESSORBASED RELAYS

• Short life cycle.

• Susceptibility to transients

• Settings and Testing Complexity



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SHORT LIFE CYCLE.

• Microprocessor- based devices ,including

protection systems have short life cycle.

While each generation of microprocessor-

based systems increase the functionality

compared with previous generation,the

pace of change makes the equipmentobsolete in shorter times.

SETTINGS AND TESTING COMPLEXITY

• The multifunction microprocessor –based

relays have a significant number of

settings.The increased number of settingsmay pose problems in managing the

settings and in conducting functional tests.



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• Setting management software is

generally available to create, transfer,and

track the relay settings.

MAJOR FUNCTIONAL BLOCKS OF A

TYPICAL MICROPROCESSOR RELAY



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BLOCK DIAGRAM OF A TYPICAL

MICROPROCESSOR -RELAY



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ANALOG INPUT SUBSYSTEM

• Electrically isolates the relay from the power

system.

• Reduces the level of the input voltages

• Converts currents to equivalent voltages

• Removes high frequency components

from the signal using analog filters.

• Anti-aliasing filters (low pass filters) are

used.



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ANALOG INTERFACE

• The outputs of the analog input

subsystems are applied to the analog

interface,which includes:

• Amplifiers

• Multiplexers

• Analog to digital (A/D) converters

DIGITAL INPUT SUBSYSTEM

• The status of the isolators and circuit

breakers in the power system is provided

to the relay via the digital input subsystem

and are read into the microcomputer

memory.



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MICROPROCESSOR

• The relaying algorithm,which is a part of

the software ,process the acquired

information.

• The relaying algorithm uses signal

processing techniques to estimate the

magnitudes and angles of voltage and

current phasors and impedances.

• The computed quantities are compared

with pre-specified settings to decide

whether the power system is experiencing

a fault or not.If it is ,the relay sends a

command to open one or more circuit

breakers for isolating the faulted zone of

the power system.



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DIGITAL OUTPUT SUBSYSTEM

• The trip output is transmitted to the power

system through digital output subsystem.

ROM and RAM

• The settings and other vital information

are stored in in the non-volatile memory

of the relay (ROM)

• Random –access memory (RAM) is used

for storing data temporarily.



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POWER SUPPLY

• The power supply to a relaying

microcomputer must be available even

when the system supply is interrupted.

• Uninterrupted power supply is made

available to the relay.

INTRODUCTION TO RELAYINGALGORITHMS

• Assume for the moment that one wishes

to perform simple over current protection

using a computer.

• That is, if the current magnitude

exceeds some user –selected

threshold,a trip output is to be initiated.



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PEAK MEASUREMENT SCHEME

DEFICIENCIES OF PEAKMEASUREMENT SCHEME

• In order to find out the peak,the relaying

processor required special interfacing hard

ware-zero crossing detector’s and timingor differentiating devices in addition to

normal hardware.



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• Any transient distortion present during the

sampling would disrupt the measurement.

ASYNCHRONOUS –SAMPLEALGORITHMS

• Asynchronous signal processingalgorithm need not be synchronized tothe periodic waveform being measured.

• Sample and derivative calculations• Sinusoidal curve- fitting

• Fourier Algorithms

• Differential –Equation Algorithm

• Least Squares Fitting Algorithms



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ASYNCHRONOUS –SAMPLEALGORITHM

m oi=I sin t

'

o m o

dii = I cos t

dt=

2'

2 2

m

o

iI i +

=

-1 o

i '

i =tan

i

PEAK AND PHASE COMPUTING WITHDATA SAMPLES.



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' k+1 k-1

k

i -ii =

2 t∆

DATA WINDOW



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TWO KEY QUESTIONS?

• What Algorithm results are produced

during the transition interval when some of

the samples are taken after fault inceptionand some remain from before

inception.(i.e.when the data window

includes the fault inception time) ?



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• How well will the algorithm work when

noise and transients are present ?

LINEAR ESTIMATION

b=Ax+e

•A and b are known, e=error

•X is to be determined

•Sum of the squared errors



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( ) ( )TT

e e= b-Ax b-Ax

( )( )T T Tb -x A b-AX=

T T T T T T=x A Ax-x A b-b Ax+b b

( )^ -1

T Tx = A A A b

( )-1

T TA A A is PSEUDO inverse of A

The ‘x’ that minimizes can beobtained by taking partial derivativesof with respect to componentsof ‘x’ and equating to zero.

Te e

Te e

The result is



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WAVE FORM MODEL

Suppose y(t) is assumed to be of the form

c sWhere Y and Y are real numbers

Further, assume that samples are taken at

-t , 0 , andt

( ) c 0 s 0y t =Y cos t+Y sin t

( )

( )( )

-1

0

1

y =y -t

y =y 0y =y t

The samples are related toc sY and Y

through



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-1

c

0

s

1

y cos -sinY

y = 1 0Y

cos siny

0where, = t

Least square solution is

^1 0 -1

c 2

y cos+y +y cosY =

1+2cos

^1 -1

s

y -yY =

2sin



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( )

( )

θ

θ

θ θ

sin2

cos21

sincos

11

^

2

11

^

−+

−+

−=

+

++=

k k k

s

k k k k

c

y yY

y y yY

• The above approach uses three terms asa means of filtering out higher frequencyharmonics or random perturbations intheprocessed signal.

• The algorithm described has a datawindow of three samples.

• As a new sample becomes available ,theoldest of the original sample set isdiscarded and the new sample is added tothe set.



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• Note that each window contains exactlythree samples of data.

• The compued values using the data set(i.e. data window containing both prefaultpost-fault data ) have no meaning.

• Using the windowing process,thecomputer must complete the evaluation in

time ∆t ,which sets a specification forcomputer speed that limits the complexityof the computation.

RELAYING AS PARAMETER ESTIMATION

( ) ( )

( )

N

n n

n=1

N

k n n

n=1

y t = Y s t + (t)

or y = Y s k t + (t)

∈

∈



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1 0

2 0

3 0

4 0

R- t

LN

s (t)=cos

ts (t)=sin t

s (t)=cos2 t

s (t)=sin2 t

s (t)=e

Other harmonics

The exponentialoffset

The problem then is to estimate the

coefficient from the

measurements.

nY



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1 1 2 N

N2 1 2

k 1 2 N

1 1

2 2

N k

y s (t) s (t) s (t)s (2t)y s (2t) s (2t)

y s (k t) s (k t) s (Kt)

Y

Y

Y

= ×

∈

∈ +

∈

[y]=[s][Y]+[ ]∈

[ ]( ) [ ]-1

T T[ Y]= s [s] s [y]

∧

The matrix can be computed

off-line and stored

[ ]( ) [ ]-1

T Ts [s] s



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FOURIER ALGORITHM

• If only the fundamental and harmonics are

included in the signal set [sn(t)] and even

number of samples spanning a full period is

used, then

( ) ( ) ( )K

T

i jijk=1

s s = s k t s k t

K= ; i=j

2

= 0 ; i j≠

K=number of samples spanning over a

full period



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FOURIER FULL CYCLE ALGORITHM

( )

( )

K

c k

k=1

K

s k

k=1

2V v cos k

K

2V v sin k

K

∧

∧

=

=

c 0 s 0

c 0 s 0

v(t)=V cos t+Vsin t+Harmonics

i(t)=I cos t+I sin t+Harmonics

0where = t∆

T=sampling period

2 2

c s

2 2

c s

1 1s s

c c

V V|Z|=

I I

V Itan tan

V I

φ

∧ ∧

∧ ∧

∧ ∧

− −

∧ ∧

+

+

= −



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FOURIER ALGORITHMS WITH

SHORTER WINDOWS

• Considering only fundamental frequency

components included in the signal set

^

^

Yc

Ys

( )

( )

K K2

k=1 k=1

K K2

k=1 k=1

k cos(k )sin(k )

cos(k )sin(k ) k

cos

sin

=

-1

*

K

k k=1

K

k k=1

cos(k )

sin(k )

y

y



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With

2=

K

They correspond to full-cycle Fourier algorithm

HALF-CYCLE FOURIER

ALGORITHM

Even number of samples per half cycle

^ K

k k=1

^ K

k k=1

2= cos(k )

c K

2= sin(k )

s K

Y y

Y y



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RECURSIVE FORMS

( ) ( )L

-j k+K-L L

k k=L-K+1

= yeY

Rotate by (K-L)

(L) L~-jk

k k=L-K+1

(L-1) L-1~-jk

k k=L-K

Y =

Y =

y e

y e



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(L) (L-1)~ ~ jK -jL

L L-KY = Y +[y -y ]e e

For full cycle window K=2

(L) (L-1)

~ ~ -jLL L-KY =Y +[y -y ]e

(new) (old)~ ~

cc new old

(new) (old)~ ~

cs new old

Y =Y +[y -y ]cos(L)

Y =Y +[y -y ]sin(L)



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For half cycle window

(new) (old)~ ~

cc new old

(new) (old)~ ~

ss new old

Y =Y +[y +y ]cos(L)

Y =Y +[y +y ]sin(L)

DIFFERENTIAL- EQUATIONALGORITHMS

The differential equation algorithms are

based on a model of the system rather than

on a model of signal.

If we take the single phase model of faulted

line, we can write the differential equation

relating the voltage and current seen by the

relay as



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( ) ( )( )di t

v t =Ri t +L .....................(1)

dt

Since both v(t) and i(t) are measured, it

seems possible that we can estimate

the parameter R and L and hence the

distance to the fault.By integrating equation (1) for two

consecutive intervals:



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( )1 1

0 0

t t

t t 1 0v(t)dt=R i t dt+L[i(t )-i(t )].......(2)

( )2 2

1 1

t t

t t 2 1v(t)dt=R i t dt+L[i(t )-i(t )].......(3)

•If the samples are equally spaced at an

interval t and the trapezoidal rule is used for

integration, viz.

1

0

t

t 1 0 1 0

t tv(t)dt= [v(t )+v(t )]= [v +v ].....(4)

2 2

∆



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Equations (2) and (3) can be written for

samples at k, k+1, k+2 as

( ) ( )

( ) ( )

( )

( )

k+1 k k+1 k k+1 k

k+2 k+1 k+2 k+1 k+2 k+1

t ti +i i -i v +v

R2 2

t L t

i +i i -i v +v2 2

∆ ∆

= ∆ ∆

The three samples of voltage and

current are sufficient to compute

estimate of R and L as

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )k+1 k k+2 k+1 k+2 k+1 k+1 k

k+1 k k+2 k+1 k+2 k+1 k+1 k

v +v i -i - v +v i -i

R=i +i i -i - i +i i -i

( )( ) ( )( )

( )( ) ( )( )k+1 k k+2 k+1 k+2 k+1 k+1 k

k+1 k k+2 k+1 k+2 k+1 k+1 k

i +i v +v - i +i v +vtL=

2 i +i i -i - i +i i -i

Numerical Prof. Kothari

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