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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