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A high speed power system transmission line protection scheme using a 32-bit microprocessor
Electric Power Systems Research, 21 (1991) 195 - 202
195
A High Speed Power System Transmission Line Protection Scheme Using a 32-bit Microprocessor Y. FRANK WANG and A. H. M. S. ULA
Department of Electrical Engineering, University of Wyoming, Laramie, WY 82071 (U.S.A.) (Received February 21, 1991)
ABSTRACT
The availability of cheap and powerful microprocessors in recent years has led to their increasing use in all aspects of power engineering. In future years they are expected to play an even greater role in power system protection schemes because of their ability to: (1) compare on-line data and come to a logical or quick decision; (2) store information from past events and make an expert decision; (3) combine various complicated tasks, etc. Thus, the application of microprocessors in power system protection is much more attractive than in many other fields. As an example, this paper develops a high speed digital protection scheme for a power transmission line. A signal processing technique is used to analyze the power spectrum of the transient fault currents, which makes it possible to develop a desired digital filtering algorithm using computer-aided design (CAD) techniques and minimize the potential for false tripping due to the steady-state system harmonics. This design was implemented on a 32-bit MVME133 monoboard microcomputer to demonstrate the protection of a model power transmission line.
1. INTRODUCTION
A primary objective of all power systems is to maintain a very high level of continuity of service and, when an intolerable condition occurs, to minimize the outage time. The role of protective relays is to minimize the damage by locating and isolating the fault immediately. Over the years, excellent protection schemes based on analog techniques have been developed, which have contributed towards the outstanding reliability of the 0378-7796/91/$3.50
present power system. Developments in computer relaying which use a digital processor to compute and make decisions can be traced back to the 1960s. In 1969, Rockefeller [1] presented one of the pioneer works in which a central minicomputer was designed to undertake all the protective relaying activities at a substation. With the availability of microprocessors, the idea of a central minicomputer is no longer considered useful. Instead, a microcomputer is used for each separate protective relaying activity because it is more reliable and faster t han the central minicomputer. In the late 1970s and early 1980s, some more digital protective relays were developed [2, 3] based on the principle of distance or impedance relaying, in which the fault impedance between the relay station and the fault point is calculated by considering the steady-state values of the fault voltage and current, while neglecting the fault transient content as noise. Other algorithms use some form of Fourier analysis to extract the fundamental frequency information. These algorithms may not be fast enough to be used on ultra high voltage transmission lines where lightning strikes are very common. Some investigators simply assume the current waveforms to be sinusoidal plus either a constant DC term or an exponentially decaying DC term [2]. Others consider the input signals to have specific harmonics in addition to the fundamental frequency component [3]. In reality, the input signals to the relay are a combination of fundamental frequency and random harmonics, especially during the first few cycles after the inception of a fault. More recent work includes direction comparison and c u r r e n t differential protection schemes where special filters are used and implementation on a 16-bit microcomputer is initiated [4-6]. ~? Elsevier Sequoia/Printed in The Netherlands
196
A
In this paper a fault-detection algorithm is developed for implementation on a 32-bit microcomputer which has significantly higher resolution and speed. A fast algorithm can be potentially beneficial in those protection applications where speed is important. In the design presented here the fast Fourier transform (FFT) is used to obtain the power spectrum analysis of the fault current, which makes it possible to design optimum filters to remove the random harmonics from the fault signals.
B
rc I TRANSFORMER
I AM/METER 8 ~ 1508 DATA VISICOREE~
- -
BREAKER 1
4
2. SYSTEM TRANSIENT ANALYSIS
Power system faults may be categorized as one of four types in order of the frequency of occurrence: (1) single line to ground fault, (2) line to line fault, (3) double line to ground fault, and (4) symmetrical three-phase fault. Generally, the amount of damage caused by a system fault depends on the severity of the fault, which is mostly decided by the magnitude of its current and on the total amount of time the fault exists. One of the best approaches to reduce the amount of damage is the reduction of the fault clearing time, which can be achieved in two ways: (1) reduction of relaying time, that is, the time from fault inception to the occurrence of the breaker tripping, and (2) design of faster circuit breakers, which is beyond the scope of this paper.
Fig. 1. Schematic diagram of the synchronous generator laboratory setup.
same type of fault occurring at various parts of the voltage cycle. During the course of this study all of the four types of faults described above were applied and analyzed. For the sake of brevity, however, only the transient results of the two most frequently occurring faults are presented and discussed here. Figures 2 and 3 show the we/l-known current waveforms due to a single line to ground o-
<
2.1. Transient data acquisition The task of recording real transient data from a power system is very difficult, mainly because the exact occurrence of a fault transient is completely unpredictable. Also, the transient measuring instruments must be very accurate for the relays to operate at any high voltage site where electric and magnetic fields are considerable. A laboratory experiment has been adopted here to get the basic transient data. Figure 1 shows the schematic diagram of this setup, where a DC motor drives a 5-kVA AC synchronous generator which sends power to a load. With the various combinations of breakers indicated as numbers 2 - 9 in the Figure, we can simulate the four different types of transmission line faults and record the transient current waveforms. By closing breaker 1 at different times, we are able to model the
d g Fig. 2. Transient current of a single line to ground fault.
Fig. 3. Transient current of a double line to ground fault.
197
fault and a double line to ground fault, respectively, recorded by a rack-mounted direct recording oscillograph. It is clear that: (1) the current waveforms of these faults are distorted, indicating the presence of harmonics, and (2) each waveform is different, which means that the composition of harmonics in each type of fault is different.
2.2. Fast Fourier transform analysis The FFT is a digital computer program used to derive the sine and cosine series by the use of sampled data input. The FFT is really a time series expressed as an amplitude spectrum. The application of either the discrete Fourier transform (DFT) or the FFT represents the most efficient available method for this type of analysis. The Fourier transform is defined as X(je)) =
i
x(t) exp(-je)t) dt
(1)
The DFT is a one-to-one mapping of any finite sequence {x(n)} (n = 0, 1, 2. . . . . N - 1) of N complex samples onto another sequence defined by N
"o.~""2oo:o
' ;oo'.o " ;g'.o " ~oo:o ~ooo'.o ,ioo'.o' i~,oo:o FRE(IUEIICY
i;oo:o
(IIZ}
Fig. 4. Power spectrum of a single line to ground fault.
9
5
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
FREOUENCY (HZ]
Fig. 5. P o w e r s p e c t r u m of a double line to g r o u n d fault.
1
X(k) = ~ x(n)W,~ k" n
?o
(2)
0
where
W,= exp(-j2~/n) = cos(2~/n) - j sin(2~/n) The FFT is a computationally efficient DFT and, for large values of N, is always preferred. In general, reasonably small time steps yield results with less than 1% error with the FFT, which is accurate enough for this study. Figures 4 and 5 show the power spectrum graphs obtained by applying the FFT on the fault currents of Figs. 2 and 3. The power spectrum graphs show the presence of the DC component, the second, third, and fourth harmonics, and other sub- and superharmonics, along with the fundamental frequency [7].
2.3. Static system harmonics and traveling wave effects Static system harmonics are the harmonics present in the power system at normal steadystate operation. The existence of harmonics in
static systems has, in general, been ignored by most relay designers, but this was only acceptable in the past when almost all the system parameters were linear. Today's power system harmonics problem is being caused increasingly by the vast increase in nonlinear loads, which include silicon-controlled rectifiers (SCRs), power transistors, arc furnaces, solar photovoltaic and wind power producers. The saturation effects in converters, transformers and shunt reactors can also produce harmonics, the range of which is very broad. Owing to the substantial increase in these nonlinear loads, it is becoming clear t h a t the system harmonics are becoming a very serious problem, representing potentially damaging effects to the power network and its individual components. The traveling waves in a transmission line also affect the voltage and current waveshape during a fault, appearing as a noise or harmonic whose frequency is mainly determined by the source impedance and the transmission line length. But the harmonic caused by the traveling waves has less affect on the current waveshape, the usual relay
198
signal, than on the voltage waveshape, and the harmonic frequencies usually fall between 100 and 1000 Hz [8].
3. DIGITAL S I G N A L P R O C E S S I N G
In an actual system, the relay input signals are seriously distorted right after fault inception and can be viewed as a combination of the fundamental frequency and a wide-ranging frequency spectrum [2, 7, 8]. Several techniques are available for filtering noisy signals, such as least square errors, Fourier methods, the Motrison method, cascaded filter method, Kalman filter, etc. [2- 3, 9- 11]. For this study a simple bandpass digital filter is used so that the order and complexity of the filter can be adjusted to match the characteristics of the real system by reprogramming the algorithm in the microcomputer. Although filters can be analog or digital as well as hybrid, this flexibility of a digital filter allows us to adopt discrete digital processing techniques which permit the realization of a filtering function with fast transient characteristics and limited impulse response times and also satisfy the requirements for high sensitivity and reliability. 3.1. Sampling theorem The selection of a sampling rate is dependent on the highest frequency content of the signal to be sampled. This is guided by the well-known Nyquist sampling theorem which states that if the sampling of the analog input is at a speed slower than twice the highest frequency component, a phenomenon known as aliasing occurs. Fortunately, in a power system, the current or voltage transformers usually have a limited frequency response so that the noise content above, say, 1 kHz, may not appear at the relay terminals. Solid-state relays are most sensitive to noise, since there are no longer mechanical and magnetic time constants to slow down the fast transients. Considering the popularity of these relays, it is safer to avoid the possible aliasing errors by using a lowpass analog filter such as a simple low cost RC filter prior to sampling. The cutoff frequency, which equals one-half of the sampling frequency, f~, is given by fc = 1/2~RC
(3)
The values of R and C can be decided if the sampling frequency, fs, is known. The optimum sampling frequency in the power system fault signal is not obvious, and is related to the power spectrum content of the signal. Higher rates are preferred, but are hampered by the limitations of the hardware, especially when three currents and three voltages need to be sampled at the same time. By analyzing the power spectrum of the fault transient data, it can be seen that most of the signal's energy is contained in the lower part of the spectrum (below I kHz). In order to keep the system designed here more general, the sampling rate is selected as 3200Hz [4, 10, 12]. According to a rule of thumb, f~ is chosen as 1/4-1/10 of the sampling rate and, using this value, the parameters of the R C lowpass filter can be determined. 3.2. Digital filtering The speed and accuracy of a filter are always in conflict. Increased accuracy and a steeper slope can be attained by increasing the order of the filter at the expense of a longer filter algorithm execution time, which slows the overall relaying speed. For an acceptable accuracy, the lowest order should be chosen to maximize the speed. The order of the filter is, therefore, subject to change, based on the characteristics of the system where it is to be used. As the system characteristics change with future additions to the transmission and distribution networks, the digital bandpass filter can be easily adapted to match the new network conditions. An infinite-impulse response (IIR) elliptic filter is chosen here for the main reason that it is fast, while it is stable and has a linear phase r e l a t i o n s h i p - - a n important factor in producing a satisfactory waveshape for the decisionmaking process. A digital filter design program is developed, based on the above method, which gives the order of the filter and the coefficients of the transfer function and plots the frequency response for optimization given the specifications. There are other general-purpose digital filter design programs and software packages readily available, but the program developed here provides the most desirable coefficients,, which is critical if the digital filter is to work properly and avoid truncation and round-off error problems in the integer arithmetic operation.
199
To m e e t a g i v e n s p e c i f i c a t i o n of low a n d h i g h c u t o f f f r e q u e n c i e s of 50 a n d 80 Hz, respectively, the digital b a n d p a s s elliptic filter t r a n s f e r f u n c t i o n is g i v e n by H(z) -
y(z) 0
X(z) r.j
A4Z4 + A3Z3 + A2Z2 + A1Z + Ao
= B4 Z4 -t- B 3 Z 3 + B 2 Z 2 + B 1 Z + ~
~/
~
Time, ms
Ho
(4) w h e r e the coefficients are:
Fig. 6. Filtered t r a n s i e n t c u r r e n t of a double line to g r o u n d fault.
H 0 = 0.10022 A 0 = 0.169, A3 = - 0 . 6 7 1 , B 0 = 0.165, B 3 = -0.679,
A1 = - 0 . 6 7 1 ,
%"
A2 = 0.100
A4 = 0.169 B 1 -~
-0.663,
%
B2 = 0.100
B4 = 0.173
T h e d i s c r e t e - t i m e o u t p u t , y(n), is r e a l i z e d by t a k i n g the i n v e r s e Z t r a n s f o r m f r o m the transfer f u n c t i o n of the digital filter:
%
~-% %
y ( n ) = { [ A 4 x ( n ) + A 3 x ( n - 1) + A 2 x ( n - 2)
"olo ~ 2oo'.0 " :,oo'.o
;,~;o'.o " 8oo:o ,~(;o'.o ~o'.o FREQUENCY
,~,oo'.o ,6oo'.o
(TIZ]
+ n 1x ( n - 3) + A o x ( n - 4)]H 0 - B 3 y ( n - 1) - B 2 y ( n - 2) - B l y ( n
- 3)
Fig. 7. P o w e r s p e c t r u m of a filtered double line to g r o u n d fault.
- B o Y ( n - 4)] } / B 4
F i g u r e 6 s h o w s the filtered t r a n s i e n t curr e n t of the d o u b l e line to g r o u n d f a u l t by i m p l e m e n t i n g the a b o v e e q u a t i o n in the M V M E 1 3 3 system. A l t h o u g h the filter allows the signals t h r o u g h w i t h o u t a n y significant delay, it a l t e r s t h e m a g n i t u d e s of the f a u l t c u r r e n t s o m e w h a t . E v e n so, the first filtered p e a k o c c u r r i n g a b o u t 5 ms a f t e r f a u l t incept i o n h a s a m a g n i t u d e of - 4 0 A , m o r e t h a n t h r e e times the r a t e d c u r r e n t of 13.2 A, w h i c h is e n o u g h to m a k e a q u i c k trip decision. In addition, it is c l e a r f r o m the p o w e r s p e c t r u m s h o w n in Fig. 7 t h a t all the h a r m o n i c s h a v e b e e n filtered o u t s a t i s f a c t o r i l y . Therefore, the decision to trip is b a s e d solely on fundamental frequency information, thereby a v o i d i n g a n y possible false t r i p due to s t a t i c s y s t e m h a r m o n i c s , t r a n s i e n t spikes or traveling w a v e effects.
4. RELAY O P E R A T I N G S E T T I N G S
T h e f u n d a m e n t a l o b j e c t i v e of s y s t e m prot e c t i o n is to i s o l a t e a f a u l t e d a r e a in the
s y s t e m quickly so t h a t the r e s t of the s y s t e m c a n be left i n t a c t to c o n t i n u e service. To choose the r e l a y ' s o p e r a t i n g s e t t i n g s is a c o m p l e x task: the o b j e c t i v e is to o p e r a t e as fast as possible to p r o t e c t the p r i m a r y zone, while h a v i n g a r e a s o n a b l e delay for f a u l t s in the b a c k u p area. T h e s e t t i n g s are n o t o n l y r e q u i r e d to be below the v a l u e of the f a u l t c u r r e n t for w h i c h t h e y s h o u l d o p e r a t e , b u t also s h o u l d n o t o p e r a t e for a n y n o r m a l or t o l e r a b l e conditions. In some e x t r e m e cases, t h e s e r e q u i r e m e n t s p r o v i d e v e r y n a r r o w margins, w h i c h is e s p e c i a l l y t r u e w h e n t h e r e is a l a r g e v a r i a t i o n b e t w e e n the c u r r e n t s at maxim u m a n d m i n i m u m far-end faults. T h e maxim u m v a l u e s of the f a u l t c u r r e n t o p e r a t i n g c o n d i t i o n o c c u r at the p e a k l o a d periods w h e n all the g e n e r a t o r s a n d lines are in service, while t h e m i n i m u m f a u l t c u r r e n t s o c c u r w h e n some of the g e n e r a t o r s a n d lines are o u t of service due to light l o a d c o n d i t i o n s [13]. The overcurrent protection relay designed h e r e c a n p r o t e c t n o t o n l y the p r i m a r y zone, b u t also t h e b a c k u p zone, as s h o w n in Fig. 8. C u r v e 1 d e n o t e s t h e f a u l t c u r r e n t at the
200 Locat ioi~ i
F
Location 2
A
v
L sE-"~0,:l,:2,:~ Dd
I
i
I.A Curve
1 /
Curve
2/
I fBmax I3
I fCmin 0
Fig. 8. Digital overcurrent protection characteristics. m a x i m u m o p e r a t i n g c o n d i t i o n w h e n the worst fault occurs, while c u r v e 2 indicates the fault c u r r e n t at the m i n i m u m o p e r a t i n g c o n d i t i o n w h e n a least severe fault occurs. We define !fBma x a s the m a x i m u m far-end fault c u r r e n t at bus B and / f B m i n a s the m i n i m u m far-end fault c u r r e n t at bus B, while Ifcm~x and I~cmin are similar q u a n t i t i e s defined at bus C. The t h r e s h o l d coefficients for r e l a y 1 are selected a r b i t r a r i l y as listed below for use in this study, but they can be c h a n g e d easily by o t h e r users based on t h e i r field e x p e r i e n c e and specific power system analysis characteristics; for example, in ref. 14 and its discussions, t h r e s h o l d coefficients of 1.2- 1.7 are used [14]: I0 = 1.2IfB. . . .
I1 = 1.1Ifcma x
I2 =
I3 = 1.1Ifcmi n
1,2Immin,
F i g u r e 9 explains this o p e r a t i n g principle, where time delay 1 is the delay for faults o c c u r r i n g in the b a c k u p area, for example, n e a r bus B on the BC line. Time delay 2, on the o t h e r hand, is set so t h a t r e l a y 1 can act as the b a c k u p for r e l a y 2, t h e r e b y satisfying b o t h selectivity and reliability.
5. DIGITAL PROTECTION IMPLEMENTATION T h e choice of h a r d w a r e to be used in the system has to meet some specifications, such as speed, a c c u r a c y , and ease of use. The evolution of m i c r o p r o c e s s o r a r c h i t e c t u r e has progressed at an incredible pace in r e c e n t years. Eight-bit m i c r o p r o c e s s o r s h a v e been used v e r y widely in i n d u s t r i a l applications, but t h e i r principal s h o r t c o m i n g is the r e l a t i v e l y slow flow calculations, especially in m u l t i p l i c a t i o n and division calculations, t h e r e b y m a k i n g
[, Y
L GIVE TRIP SIGNAL I
Fig. 9. Flowchart of the overcurrent protection scheme. t h e m u n s u i t a b l e for use in high speed r e l a y p r o t e c t i o n applications. A fully f u n c t i o n a l MVME133 32-bit single-board m i c r o c o m p u t e r , with MC68020 and MC68881 built in so as to h a v e floating-point a r i t h m e t i c ability, is used here to simulate and d e m o n s t r a t e the protection software package. The MVME133 is a selfstanding m i c r o c o m p u t e r with o n b o a r d RAM and ROM which are accessed t h r o u g h the local VMEbus. This is also a s t a n d a r d V M E b u s card and d a t a can be t r a n s f e r r e d t h r o u g h the V M E b u s i n t e r f a c e to communicate with e x t e r n a l devices. The t h r e e prog r a m m a b l e 8-bit timers inside the MVME133 can be used individually or cascaded to provide variable system time i n t e r v a l s and real-time s i m u l a t i o n and d e m o n s t r a t i o n , and are used to m e a s u r e the d e c i s i o n m a k i n g time in this project. The a l g o r i t h m of the digital bandpass filter for i m p l e m e n t a t i o n in the m i c r o c o m p u t e r is derived from eqn. (5), which can be f u r t h e r simplified as y(n)
= fox(n)
+ fl x ( n
-
1) +
f2x(n
+ f~x(n
-
3) +
f4x(n
+ gly(n
-
1) +
g2y(n
-
2)
+ g~y(n
-
3) +
g4y(n
-
4)
-
2)
4)
-
(6)
201 SET DIGITAL FILTER COEFFICIENTS] SET THRESHOLDS (]0,Ii,12,131
I
SA}~LEDATA
]
EXECUTE FILTER
1
FIND A~SDLUTE MAXIMUM VALUE 1
Fig. 10. Flowchart of the digital protection software.
The decision process algorithm is based on Fig. 9, but a routine which finds the maximum absolute value is needed here to get the peak value. Then, logic decisions are performed according to the threshold coefficients (I0-I3). For the example used here, time delay 1 is set for 2 ms and time delay 2 for 3 ms. The software for the digital section is written in assembly language to be executed on the MVME133. The flowchart for this software is shown in Fig. 10, where the digital filter coefficients and the thresholds are to be set by the user. In the demonstration of the analog implementation of the protection scheme, a simulated power system is set up, consisting of an
i ~
.-
DIGITAL PART
LINE
D/A I''" CONVERTER
DIGITAL BANDFASS FILTER
RELAY TRIP SIGNAL
Fig. 11. A digital relay protection block diagram.
A/D converter, a D/A converter, a current transducer, a relay which is normally closed, and a simulated power transmission line. The schematic diagram of this power system protection scheme is shown in Fig. 11. The A/D and D/A converters are built on the MPV901 standard VMEbus card. They are 12-bits long in digital form and need to be extended to 32-bits. Both of the analog signal ranges are set as + 10 V and - 1 0 V. The conversion time of the A/D converter is about 25 ps and the D/A converter takes about 3 ps to complete the conversion. The principle of the simulated protection scheme presented here is easily extendible to more complicated power systems, where the transmission line fault can be one of the four discussed in the earlier sections, as the thresholds of the digital protective relays can be reset and the software algorithms can be reprogrammed very easily by the operators. This versatility and adaptability are the main advantages t hat digital relay protection has over analog relay protection.
6. CONCLUSIONS Over the years, excellent protection schemes based on analog techniques have been developed, which contributed towards the outstanding reliability of present power systems. The availability of cheap and powerful microprocessors in recent years has led to their increasing use in all aspects of power engineering. They are expected to play an even greater role in power system protection schemes because of the need for logical and quick decisions. As an example, this paper has presented a complete procedure for designing a fast digital o v e r c u r r e n t protection scheme for a power transmission line. A signal processing technique is used to analyze the power spectrum of the transient fault currents. This allows a desired digital filter to be developed using computer-aided design techniques and minimizes the potential for false tripping due to the steady-state system harmonics. The fast, simple, and low cost o v e r c u r r e n t protection device presented in the paper was implemented on a 32-bit monoboard MVME133 microcomputer, which is a standard VMEbus card using a 68020 microprocessor.
202
The flexibility, versatility and adpatability of a digital protection scheme allows easy resetting of any existing digital relay thresholds to accommodate future changes in the system configuration due to any additions and/or changes in operating conditions. Although the example used in the paper to demonstrate the digital protection scheme was that of instantaneous overcurrent (IOC) settings, other protection schemes such as ground overcurrent, differential, distance, directional, backup, etc. can also be readily implemented, singly or in combination, by simply reprogramming the software.
5
6
7
8 9
10 REFERENCES 1 G. D. Rockefeller, Fault protection with a digital computer, I E E E Trans., P A S - 8 8 (1969) 438- 461. 2 M. Mir and P. J. McCleer, Simulation methods for optimum performance estimation of analog and compurer impedance relays, I E E E Trans., PAS-103 (1984) 1147 - 1154. 3 M. S. Sachdev and M. A. Baribeau, A new algorithm for digital impedance relays, I E E E Trans., PAS-98 (1979) 2232- 2240. 4 A. T. Johns and M. A. Martin, A new approach to E.H.V. direction comparison protection using digital
11
12
13 14
signal processing techniques, I E E E Trans., P W R D - t (1986) 24 - 34. R. K. Aggarwal and A. T. Johns, The development and application of directional protection for series compensated transmission systems, I E E E Trans., P W R D - 2 (1987) 1037 - 1045. J. S. Thorp and A. G. Phadke, A microprocessor based three-phase transformer differential relay, I E E E Trans., PAS-101 (1982) 426-432. A. Kumar, Time delay compensation for high speed digital protection, IEEE Trans., P W R D - I (1986) 68 - 73. G. W. Swife, The spectra of fault-induced transients, I E E E Trans., P A S - 9 8 (1979) 940- 947. M. S. Sachdev, Kalman filtering applied to power system measurements for relaying, I E E E Trans., P A S 104 (1985) 3565 - 3573. B. J. Cory and A. M. Ranjbar, Filters for digital protection of long transmission lines, I E E E P E S Summer Meeting, Vancouver, Canada, 1979, Paper No. A 79 416-9. R. K. Aggarwal and A. T. Johns, The development of a new high speed 3-terminal line protection scheme, I E E E Trans., PWRD-1 (1986) 125- 134. J. Carr and R. V. Jackson, Frequency domain analysis applied to digital transmission line protection, I E E E Trans., PAS-94 (1975) 1157- 1166. J. L. Blackburn, Protection Relaying, Principles and Applications, Marcel Dekker, New York, 1987. C. H. Griffin, Principles of ground relaying for high voltage and extra high voltage transmission lines, I E E E Trans., PAS-102 (1983) 420- 432.
195
A High Speed Power System Transmission Line Protection Scheme Using a 32-bit Microprocessor Y. FRANK WANG and A. H. M. S. ULA
Department of Electrical Engineering, University of Wyoming, Laramie, WY 82071 (U.S.A.) (Received February 21, 1991)
ABSTRACT
The availability of cheap and powerful microprocessors in recent years has led to their increasing use in all aspects of power engineering. In future years they are expected to play an even greater role in power system protection schemes because of their ability to: (1) compare on-line data and come to a logical or quick decision; (2) store information from past events and make an expert decision; (3) combine various complicated tasks, etc. Thus, the application of microprocessors in power system protection is much more attractive than in many other fields. As an example, this paper develops a high speed digital protection scheme for a power transmission line. A signal processing technique is used to analyze the power spectrum of the transient fault currents, which makes it possible to develop a desired digital filtering algorithm using computer-aided design (CAD) techniques and minimize the potential for false tripping due to the steady-state system harmonics. This design was implemented on a 32-bit MVME133 monoboard microcomputer to demonstrate the protection of a model power transmission line.
1. INTRODUCTION
A primary objective of all power systems is to maintain a very high level of continuity of service and, when an intolerable condition occurs, to minimize the outage time. The role of protective relays is to minimize the damage by locating and isolating the fault immediately. Over the years, excellent protection schemes based on analog techniques have been developed, which have contributed towards the outstanding reliability of the 0378-7796/91/$3.50
present power system. Developments in computer relaying which use a digital processor to compute and make decisions can be traced back to the 1960s. In 1969, Rockefeller [1] presented one of the pioneer works in which a central minicomputer was designed to undertake all the protective relaying activities at a substation. With the availability of microprocessors, the idea of a central minicomputer is no longer considered useful. Instead, a microcomputer is used for each separate protective relaying activity because it is more reliable and faster t han the central minicomputer. In the late 1970s and early 1980s, some more digital protective relays were developed [2, 3] based on the principle of distance or impedance relaying, in which the fault impedance between the relay station and the fault point is calculated by considering the steady-state values of the fault voltage and current, while neglecting the fault transient content as noise. Other algorithms use some form of Fourier analysis to extract the fundamental frequency information. These algorithms may not be fast enough to be used on ultra high voltage transmission lines where lightning strikes are very common. Some investigators simply assume the current waveforms to be sinusoidal plus either a constant DC term or an exponentially decaying DC term [2]. Others consider the input signals to have specific harmonics in addition to the fundamental frequency component [3]. In reality, the input signals to the relay are a combination of fundamental frequency and random harmonics, especially during the first few cycles after the inception of a fault. More recent work includes direction comparison and c u r r e n t differential protection schemes where special filters are used and implementation on a 16-bit microcomputer is initiated [4-6]. ~? Elsevier Sequoia/Printed in The Netherlands
196
A
In this paper a fault-detection algorithm is developed for implementation on a 32-bit microcomputer which has significantly higher resolution and speed. A fast algorithm can be potentially beneficial in those protection applications where speed is important. In the design presented here the fast Fourier transform (FFT) is used to obtain the power spectrum analysis of the fault current, which makes it possible to design optimum filters to remove the random harmonics from the fault signals.
B
rc I TRANSFORMER
I AM/METER 8 ~ 1508 DATA VISICOREE~
- -
BREAKER 1
4
2. SYSTEM TRANSIENT ANALYSIS
Power system faults may be categorized as one of four types in order of the frequency of occurrence: (1) single line to ground fault, (2) line to line fault, (3) double line to ground fault, and (4) symmetrical three-phase fault. Generally, the amount of damage caused by a system fault depends on the severity of the fault, which is mostly decided by the magnitude of its current and on the total amount of time the fault exists. One of the best approaches to reduce the amount of damage is the reduction of the fault clearing time, which can be achieved in two ways: (1) reduction of relaying time, that is, the time from fault inception to the occurrence of the breaker tripping, and (2) design of faster circuit breakers, which is beyond the scope of this paper.
Fig. 1. Schematic diagram of the synchronous generator laboratory setup.
same type of fault occurring at various parts of the voltage cycle. During the course of this study all of the four types of faults described above were applied and analyzed. For the sake of brevity, however, only the transient results of the two most frequently occurring faults are presented and discussed here. Figures 2 and 3 show the we/l-known current waveforms due to a single line to ground o-
<
2.1. Transient data acquisition The task of recording real transient data from a power system is very difficult, mainly because the exact occurrence of a fault transient is completely unpredictable. Also, the transient measuring instruments must be very accurate for the relays to operate at any high voltage site where electric and magnetic fields are considerable. A laboratory experiment has been adopted here to get the basic transient data. Figure 1 shows the schematic diagram of this setup, where a DC motor drives a 5-kVA AC synchronous generator which sends power to a load. With the various combinations of breakers indicated as numbers 2 - 9 in the Figure, we can simulate the four different types of transmission line faults and record the transient current waveforms. By closing breaker 1 at different times, we are able to model the
d g Fig. 2. Transient current of a single line to ground fault.
Fig. 3. Transient current of a double line to ground fault.
197
fault and a double line to ground fault, respectively, recorded by a rack-mounted direct recording oscillograph. It is clear that: (1) the current waveforms of these faults are distorted, indicating the presence of harmonics, and (2) each waveform is different, which means that the composition of harmonics in each type of fault is different.
2.2. Fast Fourier transform analysis The FFT is a digital computer program used to derive the sine and cosine series by the use of sampled data input. The FFT is really a time series expressed as an amplitude spectrum. The application of either the discrete Fourier transform (DFT) or the FFT represents the most efficient available method for this type of analysis. The Fourier transform is defined as X(je)) =
i
x(t) exp(-je)t) dt
(1)
The DFT is a one-to-one mapping of any finite sequence {x(n)} (n = 0, 1, 2. . . . . N - 1) of N complex samples onto another sequence defined by N
"o.~""2oo:o
' ;oo'.o " ;g'.o " ~oo:o ~ooo'.o ,ioo'.o' i~,oo:o FRE(IUEIICY
i;oo:o
(IIZ}
Fig. 4. Power spectrum of a single line to ground fault.
9
5
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
FREOUENCY (HZ]
Fig. 5. P o w e r s p e c t r u m of a double line to g r o u n d fault.
1
X(k) = ~ x(n)W,~ k" n
?o
(2)
0
where
W,= exp(-j2~/n) = cos(2~/n) - j sin(2~/n) The FFT is a computationally efficient DFT and, for large values of N, is always preferred. In general, reasonably small time steps yield results with less than 1% error with the FFT, which is accurate enough for this study. Figures 4 and 5 show the power spectrum graphs obtained by applying the FFT on the fault currents of Figs. 2 and 3. The power spectrum graphs show the presence of the DC component, the second, third, and fourth harmonics, and other sub- and superharmonics, along with the fundamental frequency [7].
2.3. Static system harmonics and traveling wave effects Static system harmonics are the harmonics present in the power system at normal steadystate operation. The existence of harmonics in
static systems has, in general, been ignored by most relay designers, but this was only acceptable in the past when almost all the system parameters were linear. Today's power system harmonics problem is being caused increasingly by the vast increase in nonlinear loads, which include silicon-controlled rectifiers (SCRs), power transistors, arc furnaces, solar photovoltaic and wind power producers. The saturation effects in converters, transformers and shunt reactors can also produce harmonics, the range of which is very broad. Owing to the substantial increase in these nonlinear loads, it is becoming clear t h a t the system harmonics are becoming a very serious problem, representing potentially damaging effects to the power network and its individual components. The traveling waves in a transmission line also affect the voltage and current waveshape during a fault, appearing as a noise or harmonic whose frequency is mainly determined by the source impedance and the transmission line length. But the harmonic caused by the traveling waves has less affect on the current waveshape, the usual relay
198
signal, than on the voltage waveshape, and the harmonic frequencies usually fall between 100 and 1000 Hz [8].
3. DIGITAL S I G N A L P R O C E S S I N G
In an actual system, the relay input signals are seriously distorted right after fault inception and can be viewed as a combination of the fundamental frequency and a wide-ranging frequency spectrum [2, 7, 8]. Several techniques are available for filtering noisy signals, such as least square errors, Fourier methods, the Motrison method, cascaded filter method, Kalman filter, etc. [2- 3, 9- 11]. For this study a simple bandpass digital filter is used so that the order and complexity of the filter can be adjusted to match the characteristics of the real system by reprogramming the algorithm in the microcomputer. Although filters can be analog or digital as well as hybrid, this flexibility of a digital filter allows us to adopt discrete digital processing techniques which permit the realization of a filtering function with fast transient characteristics and limited impulse response times and also satisfy the requirements for high sensitivity and reliability. 3.1. Sampling theorem The selection of a sampling rate is dependent on the highest frequency content of the signal to be sampled. This is guided by the well-known Nyquist sampling theorem which states that if the sampling of the analog input is at a speed slower than twice the highest frequency component, a phenomenon known as aliasing occurs. Fortunately, in a power system, the current or voltage transformers usually have a limited frequency response so that the noise content above, say, 1 kHz, may not appear at the relay terminals. Solid-state relays are most sensitive to noise, since there are no longer mechanical and magnetic time constants to slow down the fast transients. Considering the popularity of these relays, it is safer to avoid the possible aliasing errors by using a lowpass analog filter such as a simple low cost RC filter prior to sampling. The cutoff frequency, which equals one-half of the sampling frequency, f~, is given by fc = 1/2~RC
(3)
The values of R and C can be decided if the sampling frequency, fs, is known. The optimum sampling frequency in the power system fault signal is not obvious, and is related to the power spectrum content of the signal. Higher rates are preferred, but are hampered by the limitations of the hardware, especially when three currents and three voltages need to be sampled at the same time. By analyzing the power spectrum of the fault transient data, it can be seen that most of the signal's energy is contained in the lower part of the spectrum (below I kHz). In order to keep the system designed here more general, the sampling rate is selected as 3200Hz [4, 10, 12]. According to a rule of thumb, f~ is chosen as 1/4-1/10 of the sampling rate and, using this value, the parameters of the R C lowpass filter can be determined. 3.2. Digital filtering The speed and accuracy of a filter are always in conflict. Increased accuracy and a steeper slope can be attained by increasing the order of the filter at the expense of a longer filter algorithm execution time, which slows the overall relaying speed. For an acceptable accuracy, the lowest order should be chosen to maximize the speed. The order of the filter is, therefore, subject to change, based on the characteristics of the system where it is to be used. As the system characteristics change with future additions to the transmission and distribution networks, the digital bandpass filter can be easily adapted to match the new network conditions. An infinite-impulse response (IIR) elliptic filter is chosen here for the main reason that it is fast, while it is stable and has a linear phase r e l a t i o n s h i p - - a n important factor in producing a satisfactory waveshape for the decisionmaking process. A digital filter design program is developed, based on the above method, which gives the order of the filter and the coefficients of the transfer function and plots the frequency response for optimization given the specifications. There are other general-purpose digital filter design programs and software packages readily available, but the program developed here provides the most desirable coefficients,, which is critical if the digital filter is to work properly and avoid truncation and round-off error problems in the integer arithmetic operation.
199
To m e e t a g i v e n s p e c i f i c a t i o n of low a n d h i g h c u t o f f f r e q u e n c i e s of 50 a n d 80 Hz, respectively, the digital b a n d p a s s elliptic filter t r a n s f e r f u n c t i o n is g i v e n by H(z) -
y(z) 0
X(z) r.j
A4Z4 + A3Z3 + A2Z2 + A1Z + Ao
= B4 Z4 -t- B 3 Z 3 + B 2 Z 2 + B 1 Z + ~
~/
~
Time, ms
Ho
(4) w h e r e the coefficients are:
Fig. 6. Filtered t r a n s i e n t c u r r e n t of a double line to g r o u n d fault.
H 0 = 0.10022 A 0 = 0.169, A3 = - 0 . 6 7 1 , B 0 = 0.165, B 3 = -0.679,
A1 = - 0 . 6 7 1 ,
%"
A2 = 0.100
A4 = 0.169 B 1 -~
-0.663,
%
B2 = 0.100
B4 = 0.173
T h e d i s c r e t e - t i m e o u t p u t , y(n), is r e a l i z e d by t a k i n g the i n v e r s e Z t r a n s f o r m f r o m the transfer f u n c t i o n of the digital filter:
%
~-% %
y ( n ) = { [ A 4 x ( n ) + A 3 x ( n - 1) + A 2 x ( n - 2)
"olo ~ 2oo'.0 " :,oo'.o
;,~;o'.o " 8oo:o ,~(;o'.o ~o'.o FREQUENCY
,~,oo'.o ,6oo'.o
(TIZ]
+ n 1x ( n - 3) + A o x ( n - 4)]H 0 - B 3 y ( n - 1) - B 2 y ( n - 2) - B l y ( n
- 3)
Fig. 7. P o w e r s p e c t r u m of a filtered double line to g r o u n d fault.
- B o Y ( n - 4)] } / B 4
F i g u r e 6 s h o w s the filtered t r a n s i e n t curr e n t of the d o u b l e line to g r o u n d f a u l t by i m p l e m e n t i n g the a b o v e e q u a t i o n in the M V M E 1 3 3 system. A l t h o u g h the filter allows the signals t h r o u g h w i t h o u t a n y significant delay, it a l t e r s t h e m a g n i t u d e s of the f a u l t c u r r e n t s o m e w h a t . E v e n so, the first filtered p e a k o c c u r r i n g a b o u t 5 ms a f t e r f a u l t incept i o n h a s a m a g n i t u d e of - 4 0 A , m o r e t h a n t h r e e times the r a t e d c u r r e n t of 13.2 A, w h i c h is e n o u g h to m a k e a q u i c k trip decision. In addition, it is c l e a r f r o m the p o w e r s p e c t r u m s h o w n in Fig. 7 t h a t all the h a r m o n i c s h a v e b e e n filtered o u t s a t i s f a c t o r i l y . Therefore, the decision to trip is b a s e d solely on fundamental frequency information, thereby a v o i d i n g a n y possible false t r i p due to s t a t i c s y s t e m h a r m o n i c s , t r a n s i e n t spikes or traveling w a v e effects.
4. RELAY O P E R A T I N G S E T T I N G S
T h e f u n d a m e n t a l o b j e c t i v e of s y s t e m prot e c t i o n is to i s o l a t e a f a u l t e d a r e a in the
s y s t e m quickly so t h a t the r e s t of the s y s t e m c a n be left i n t a c t to c o n t i n u e service. To choose the r e l a y ' s o p e r a t i n g s e t t i n g s is a c o m p l e x task: the o b j e c t i v e is to o p e r a t e as fast as possible to p r o t e c t the p r i m a r y zone, while h a v i n g a r e a s o n a b l e delay for f a u l t s in the b a c k u p area. T h e s e t t i n g s are n o t o n l y r e q u i r e d to be below the v a l u e of the f a u l t c u r r e n t for w h i c h t h e y s h o u l d o p e r a t e , b u t also s h o u l d n o t o p e r a t e for a n y n o r m a l or t o l e r a b l e conditions. In some e x t r e m e cases, t h e s e r e q u i r e m e n t s p r o v i d e v e r y n a r r o w margins, w h i c h is e s p e c i a l l y t r u e w h e n t h e r e is a l a r g e v a r i a t i o n b e t w e e n the c u r r e n t s at maxim u m a n d m i n i m u m far-end faults. T h e maxim u m v a l u e s of the f a u l t c u r r e n t o p e r a t i n g c o n d i t i o n o c c u r at the p e a k l o a d periods w h e n all the g e n e r a t o r s a n d lines are in service, while t h e m i n i m u m f a u l t c u r r e n t s o c c u r w h e n some of the g e n e r a t o r s a n d lines are o u t of service due to light l o a d c o n d i t i o n s [13]. The overcurrent protection relay designed h e r e c a n p r o t e c t n o t o n l y the p r i m a r y zone, b u t also t h e b a c k u p zone, as s h o w n in Fig. 8. C u r v e 1 d e n o t e s t h e f a u l t c u r r e n t at the
200 Locat ioi~ i
F
Location 2
A
v
L sE-"~0,:l,:2,:~ Dd
I
i
I.A Curve
1 /
Curve
2/
I fBmax I3
I fCmin 0
Fig. 8. Digital overcurrent protection characteristics. m a x i m u m o p e r a t i n g c o n d i t i o n w h e n the worst fault occurs, while c u r v e 2 indicates the fault c u r r e n t at the m i n i m u m o p e r a t i n g c o n d i t i o n w h e n a least severe fault occurs. We define !fBma x a s the m a x i m u m far-end fault c u r r e n t at bus B and / f B m i n a s the m i n i m u m far-end fault c u r r e n t at bus B, while Ifcm~x and I~cmin are similar q u a n t i t i e s defined at bus C. The t h r e s h o l d coefficients for r e l a y 1 are selected a r b i t r a r i l y as listed below for use in this study, but they can be c h a n g e d easily by o t h e r users based on t h e i r field e x p e r i e n c e and specific power system analysis characteristics; for example, in ref. 14 and its discussions, t h r e s h o l d coefficients of 1.2- 1.7 are used [14]: I0 = 1.2IfB. . . .
I1 = 1.1Ifcma x
I2 =
I3 = 1.1Ifcmi n
1,2Immin,
F i g u r e 9 explains this o p e r a t i n g principle, where time delay 1 is the delay for faults o c c u r r i n g in the b a c k u p area, for example, n e a r bus B on the BC line. Time delay 2, on the o t h e r hand, is set so t h a t r e l a y 1 can act as the b a c k u p for r e l a y 2, t h e r e b y satisfying b o t h selectivity and reliability.
5. DIGITAL PROTECTION IMPLEMENTATION T h e choice of h a r d w a r e to be used in the system has to meet some specifications, such as speed, a c c u r a c y , and ease of use. The evolution of m i c r o p r o c e s s o r a r c h i t e c t u r e has progressed at an incredible pace in r e c e n t years. Eight-bit m i c r o p r o c e s s o r s h a v e been used v e r y widely in i n d u s t r i a l applications, but t h e i r principal s h o r t c o m i n g is the r e l a t i v e l y slow flow calculations, especially in m u l t i p l i c a t i o n and division calculations, t h e r e b y m a k i n g
[, Y
L GIVE TRIP SIGNAL I
Fig. 9. Flowchart of the overcurrent protection scheme. t h e m u n s u i t a b l e for use in high speed r e l a y p r o t e c t i o n applications. A fully f u n c t i o n a l MVME133 32-bit single-board m i c r o c o m p u t e r , with MC68020 and MC68881 built in so as to h a v e floating-point a r i t h m e t i c ability, is used here to simulate and d e m o n s t r a t e the protection software package. The MVME133 is a selfstanding m i c r o c o m p u t e r with o n b o a r d RAM and ROM which are accessed t h r o u g h the local VMEbus. This is also a s t a n d a r d V M E b u s card and d a t a can be t r a n s f e r r e d t h r o u g h the V M E b u s i n t e r f a c e to communicate with e x t e r n a l devices. The t h r e e prog r a m m a b l e 8-bit timers inside the MVME133 can be used individually or cascaded to provide variable system time i n t e r v a l s and real-time s i m u l a t i o n and d e m o n s t r a t i o n , and are used to m e a s u r e the d e c i s i o n m a k i n g time in this project. The a l g o r i t h m of the digital bandpass filter for i m p l e m e n t a t i o n in the m i c r o c o m p u t e r is derived from eqn. (5), which can be f u r t h e r simplified as y(n)
= fox(n)
+ fl x ( n
-
1) +
f2x(n
+ f~x(n
-
3) +
f4x(n
+ gly(n
-
1) +
g2y(n
-
2)
+ g~y(n
-
3) +
g4y(n
-
4)
-
2)
4)
-
(6)
201 SET DIGITAL FILTER COEFFICIENTS] SET THRESHOLDS (]0,Ii,12,131
I
SA}~LEDATA
]
EXECUTE FILTER
1
FIND A~SDLUTE MAXIMUM VALUE 1
Fig. 10. Flowchart of the digital protection software.
The decision process algorithm is based on Fig. 9, but a routine which finds the maximum absolute value is needed here to get the peak value. Then, logic decisions are performed according to the threshold coefficients (I0-I3). For the example used here, time delay 1 is set for 2 ms and time delay 2 for 3 ms. The software for the digital section is written in assembly language to be executed on the MVME133. The flowchart for this software is shown in Fig. 10, where the digital filter coefficients and the thresholds are to be set by the user. In the demonstration of the analog implementation of the protection scheme, a simulated power system is set up, consisting of an
i ~
.-
DIGITAL PART
LINE
D/A I''" CONVERTER
DIGITAL BANDFASS FILTER
RELAY TRIP SIGNAL
Fig. 11. A digital relay protection block diagram.
A/D converter, a D/A converter, a current transducer, a relay which is normally closed, and a simulated power transmission line. The schematic diagram of this power system protection scheme is shown in Fig. 11. The A/D and D/A converters are built on the MPV901 standard VMEbus card. They are 12-bits long in digital form and need to be extended to 32-bits. Both of the analog signal ranges are set as + 10 V and - 1 0 V. The conversion time of the A/D converter is about 25 ps and the D/A converter takes about 3 ps to complete the conversion. The principle of the simulated protection scheme presented here is easily extendible to more complicated power systems, where the transmission line fault can be one of the four discussed in the earlier sections, as the thresholds of the digital protective relays can be reset and the software algorithms can be reprogrammed very easily by the operators. This versatility and adaptability are the main advantages t hat digital relay protection has over analog relay protection.
6. CONCLUSIONS Over the years, excellent protection schemes based on analog techniques have been developed, which contributed towards the outstanding reliability of present power systems. The availability of cheap and powerful microprocessors in recent years has led to their increasing use in all aspects of power engineering. They are expected to play an even greater role in power system protection schemes because of the need for logical and quick decisions. As an example, this paper has presented a complete procedure for designing a fast digital o v e r c u r r e n t protection scheme for a power transmission line. A signal processing technique is used to analyze the power spectrum of the transient fault currents. This allows a desired digital filter to be developed using computer-aided design techniques and minimizes the potential for false tripping due to the steady-state system harmonics. The fast, simple, and low cost o v e r c u r r e n t protection device presented in the paper was implemented on a 32-bit monoboard MVME133 microcomputer, which is a standard VMEbus card using a 68020 microprocessor.
202
The flexibility, versatility and adpatability of a digital protection scheme allows easy resetting of any existing digital relay thresholds to accommodate future changes in the system configuration due to any additions and/or changes in operating conditions. Although the example used in the paper to demonstrate the digital protection scheme was that of instantaneous overcurrent (IOC) settings, other protection schemes such as ground overcurrent, differential, distance, directional, backup, etc. can also be readily implemented, singly or in combination, by simply reprogramming the software.
5
6
7
8 9
10 REFERENCES 1 G. D. Rockefeller, Fault protection with a digital computer, I E E E Trans., P A S - 8 8 (1969) 438- 461. 2 M. Mir and P. J. McCleer, Simulation methods for optimum performance estimation of analog and compurer impedance relays, I E E E Trans., PAS-103 (1984) 1147 - 1154. 3 M. S. Sachdev and M. A. Baribeau, A new algorithm for digital impedance relays, I E E E Trans., PAS-98 (1979) 2232- 2240. 4 A. T. Johns and M. A. Martin, A new approach to E.H.V. direction comparison protection using digital
11
12
13 14
signal processing techniques, I E E E Trans., P W R D - t (1986) 24 - 34. R. K. Aggarwal and A. T. Johns, The development and application of directional protection for series compensated transmission systems, I E E E Trans., P W R D - 2 (1987) 1037 - 1045. J. S. Thorp and A. G. Phadke, A microprocessor based three-phase transformer differential relay, I E E E Trans., PAS-101 (1982) 426-432. A. Kumar, Time delay compensation for high speed digital protection, IEEE Trans., P W R D - I (1986) 68 - 73. G. W. Swife, The spectra of fault-induced transients, I E E E Trans., P A S - 9 8 (1979) 940- 947. M. S. Sachdev, Kalman filtering applied to power system measurements for relaying, I E E E Trans., P A S 104 (1985) 3565 - 3573. B. J. Cory and A. M. Ranjbar, Filters for digital protection of long transmission lines, I E E E P E S Summer Meeting, Vancouver, Canada, 1979, Paper No. A 79 416-9. R. K. Aggarwal and A. T. Johns, The development of a new high speed 3-terminal line protection scheme, I E E E Trans., PWRD-1 (1986) 125- 134. J. Carr and R. V. Jackson, Frequency domain analysis applied to digital transmission line protection, I E E E Trans., PAS-94 (1975) 1157- 1166. J. L. Blackburn, Protection Relaying, Principles and Applications, Marcel Dekker, New York, 1987. C. H. Griffin, Principles of ground relaying for high voltage and extra high voltage transmission lines, I E E E Trans., PAS-102 (1983) 420- 432.