An Application of Digital Computers to Breaker-Fail Protection

IFAC Symposium 1977 Melbourne, 21-25 February 1977

An Application of Digital Computers to Breaker-Fail Protection IF MORRISON Associate Professor, Department of Electric Power Engineering, University of New South Wales, Sydney

GA MUSTAPHA Senior Lecturer, Department of Electrical Engineering , University of Lagos and

G.C . DEWSNAP Associate Professor, Department of Electric Power Engineering, University of New South Wales , Sydney Sm-~FY The paper d es cribe s a technique f o r dete ct in g changes in power s yst e m c urrents or voltage s . The techni q ue is based upon the calculation of th e rate of rise of these quantities at their own zero c rossings and is referred to as "current (or voltage) derivative relaying".

The t ec hnique emerged from a study of the possible use of digital computers for back-up protection, wher e it is used to detect the fa il ur e of a circuit breaker to interrupt the flow of fault current. The technique is found to be suitable also for realisation as a r e lative ly simple electroni c circuit. 1

assumes r e liable rel ay op er a tion. In most power s ys tems, back-up protection is a lso applied to r e lay operation; there are var i ous forms of this rel ay b ac k-up protection, both lo ca l and remote. Cir c uit breaker back-up becomes rel e vant on c e a circuit breaker trip signal has been initiated and is intended to ensure that the circuit bre a ker clears the fault, or that further circuit brea ker operations are initiated to clear the faulted zone.

INTRODUCTION

In c reasing attention is being focu s sed o n the possibility of using on-line digital computers in power system protection and other substation c ontrol functions. One main objective of the pres e nt paper is to describe digital relaying techni~ues suitabl e for local circuit breaker back-up protection. Th e re are undoubtedly a large number of ways in which a digital computer could be used to monitor the clearance or non-clearance of a fault by a local circuit breaker. Two of the more obvious approaches encounter serious diffi c ulties: -

2

THEORY

The calculation of the rate of rise of phase currents at their zero crossings involves the location of the zero crossings and c alculation of the amplitud e of the first derivatives at these p o ints.

the use of auxiliary contact currents, the absence or presence of which may indicate whether the breaker has removed the fault or not. The main objections to the use of this techniqu e are first, the possibility of a fault in the contacts themselves, and second, for both relay and breaker back-up protection by digital computer, their monitoring necessitates the provision of additional AID converter channels as well as data storage locations, which limits the size of system that can be protected by a given computer.

For digital computer analysis, two basic methods of locating the zero crossings suggest themselves, either checking when the sign of two successive sampled values changes from positive to negative or using an a nalogue zero c rossing detector circuit and employin g its output to initialise sampling. If, for example the c urrent changes sign between sample values i , i + taken at times t , t + , k k 1 k k l then the rate of change of current at the zero crossing c an be shown to be given by (see Appendix):

- the use of the presence or absence of fault current itself. In this case digital sampling rates will have to be synchronized (a difficult task to achieve) to the system frequency, otherwise, if sampling is random, it is possible to sample at current zero crossings and hence presume erroneously that the fault current has ceased.

i'

o

.,

~k

i

-.

k

-'

~k+l ~k

(.

~k+l

,

-

i ') k

( 1)

where the dashes denote differentiation and the subscripts k, k+l denote sampling instants t , t + • k 1 k

In this paper it is shown that if the rate of change of fault current measured at its zero crossings is used as the criterion of fault current, the above problems are eliminated; this technique is described more fully in the following sections.

Alternatively if the sampling is initiated by'a zero crossing detector, and the derivatives are calculated or measured at times t , t ,then k equation (1) still holds (see Appendi~+lfor derivation).

The development of this digital technique for local circuit breaker back-up protection has also led to its realisation as an electronic analogue device. This, it is thought, may be used in conjunction with modern system back-up protection equipment to obtain improved operating times.

3

DIGITAL TECHNIQUE

The main objective here is to use equation (1) to indicate the removal or non-removal of fault current by the associated circuit breaker. Equation (1) is seen to involve derivatives at the two sampled points k and (k + 1). Numerical analysts give several ways of calculating derivatives (e.g. References (1) and (2). In general, these methods

The technique described in this paper is intended to monitor the operation of the circuit br e aker, and

322

ar e series expressions of forward, backward or

coils simulate source and line impedances respectively. A resistive load of 100~ per phase is available at the end of the line and with the help of the point on wave control circuit, faults of any type can be applied to the system. The load was chosen to give a ratio of fault to pre-fault current of about 20:1. The current and voltage signals from a sequencp of faults of different phase of incidence, were recorded on a high performance magnetic taperecorder. The data was then played back into an analogue to digital (A/D) converter which sampled the current wave at 0.5ms intervals for 2 cycles before and 5 cycles after each fault and output this data onto paper tape. The tape has then processed off-line on a large batch processing computer.

c en tral differences, the actual formulas for nu merical differentiation being obtained by d if ferentiating the appropriate interpolation f o rmula. Isaacson and Keller (Ref. (2) show that in t erpolation errors are least near the centre of t h~ interval of interrolation and that an analogous r ~s ult is true for numeric~l differentiation, thus i n theory it seems advisable to use formulas of the c <,!1 tral difference type. However, for real-time cc~ puter implementation it may be advantageous to use backward differences since existing samples can bt· used for immedi a te derivative calculation . T~e

zero crossings of the current wav~ form are to located in this case using the first method d ~sc ribed in Section 2. This is achieved by mul tiplying two successiv e sampled values and c omparing the product with zero. If the product is l ~s s or equal to zero, then the wave form is pre sumed to have crossed the zero a xis. If, o n the o th er hand, the product is positive, the routine is c~n tinued until the logical c ondition for zero c r o ssing is fulfilled. Once a zero crossing is d ~ tected, the rate of rise of current at the two s ucc essive sampled values are computed and the rate of rise at the zero c rossing is calculated. The r ilt io K of this value to that obtained at the Frevious zero crossing is compared with a pres e t The possible presence of a fault in the val ue. p ro tected system is indicated \vhen the comparison y ie lds a ratio greater than or equal to the preset va lue. A time delay Y, corresponding to the circuit br e aker clearance time in cycles, is allowed for by c o unting the number of zero c rossings K, until 2Kl e quals Y. On the final zero crossing, Ehe ratio K f o r this zero crossing is computed and again compared with the preset value. If this comparison s hows a final value of K 3till greater than the pr e set one, then it may be inferred that the circuit breaker has not cleared the fault and a signal to trip is issued to all the circuit breakers connected t o the bus-bar to which ~he faulted breaker is co nnected. If, on the other hand, the comparison s hows a value of K less than the preset one, the c i rcuit-breaker associated with the faulted section i s assumed to have opened or be in the process of d o ing so and a signal to reset the detection routine i s issued instead. b~

In addition to the faults on the model transmission line, several recordings were taken on single-phaseto-ground faults on Electricity Commission of New South Wales grid. The faults were at l32KV at the end of a 23 mile transmission line that was on open circuit prior to the inceptio~ of the fault. These recordings were processed in a manner similar to that described above.

fp= sample point of fault.

Figure 1

..., 600.

:00

10:

3 phase fault-model line

.,,,'

,;

Q)

"" --er ;:J

..... 400

0 Q)

.... Ul

300

The parameter K referred to in the above is the r a tio of the rate of rise of the expected minimum f a ult current at its zero crossings to the rate of r i se of maximum load current at its zero crossings. Th is ratio is also proportional to that of expected mi nimum fault current and the maximum load current ( e .g. for local test systems K la y in the range 1.8-2.25) .

100

0

...,Cl

fp= s.lmpLe pOint of f.!Ult.

ro

0:;

o

The time delay Y sets the margin of time allowed for t h e circuit breaker to operate, thus the point at ,,'h ich th::- final comparison is made can be selected as required, by altering the value of Y in the pr ogramme, depending on the type and make of the c ircuit breaker. 3.1

"

.....

200

Figure 2

2 phase to ground fault-model line

Rate of rise of fault current at the zero crossing for typical faults on a 3 phase system. Figure 1 to 4 show the characteristic response of the technique when applied to typical faults on a 3- phase system. The response characteristic for each of these faults indicates first, that a transition occurs in the magnitude of the rate of rise of current at the zero crossing following the inception of a fault and secondly, that the magnitude remains constant for each of the 3-phases before and after the fault inception (but possibly at different values). The fore-going therefore indicate that the magnitude of the rate of rise of currents at their zero crossings is independent of the type and phase of incidence of the fault and only depends on the amplitude of the pre-fault

Off-Line Test Results

I n order to test the techniques described above, a lumped - element model transmission line was used to ac quire data simulating a faulted line, the model be ing representative of EHV lines of less than 150 miles with X/R = 10. The system is provided with a po int-on-wave fault incidence control circuit, e nabling faults of different DC off-set to be ap plied to the system. Each phase of the line cn nsists of a high X/R ratio coil (14mH, 0.25Q in se ries with a smaller coil (4.3mH, 0.5n). These

323

600

.jJ

~

soof t.do ':)


300 - ~ )..j

....

200

fp= sample point of fault.

o

B

100

«l

<.

~

. '

_.1£"1'~'.6.=-~.11~~-,__ ~:::-~_-=-. _ . _ . __ .

o - --m=-~-::-:JQL-=Co--s'o 60 fp

7b~ y!Q~t1cyc1eafter

100 -lIt-t:a

f :lult Figure 3

sample pOint

Single phase to ground fault-model line.

800

70J . jJ

s::

600

~ )..j

::>

500- u

....

o

400

Q)

en

fp

·rl

300

= SdmplQ of

)..j

....0

Figure 4

pOint

fault.

Single phase to ground fault-high voltage system.

Rate of rise of fault current at the zero crossing for typical faults on a 3 phase system. current and its frequency. These quantities are in themselves functions of the properties of the line, system conditions, and the type of load. Other results (notshown) from the analysis of the 132kV transmission line faults confirm these deductions. Figure 5 shows the flow chart for the off-line program used to analyse the faults on the model and the 132kV lines. This indicates the concept of detecting a fault in anyone of the 3-phases and counting the number of zero crossings in this phas e until 2KI equals Y. After this, the final comparis0n is made to determine whether the circuit breaker has cleared the fault or not.

4

ANALOGUE TECHNIQUE

During the development of the digital technique described in Section 3, it was decided that an analogue realisation based on a modified form of the digital technique could be constructed using electronic circuit elements. The resulting Current Derivative Relay (CDR) could be used in conjunction with present local back-up protection equipment to provide a faster back-up operating time following circuit breaker failure. Basically, the technique used in the design of the CDR is to employ a zero crossing detector circui t to locate the zero crossings of the input relaying cvrrent wave- form; and a gate and gating circllit to s ample the amplitude of thp current wave -f orm ImS after each of these zero crossings. Since the sampling time is fixed by using fixed value circuit elements, th e amplitucles measured at these points are assumed to be proportional to the rate of rise of current at

Figure 5

Circuit breaker back-up protectionflow diagram.

the zero crossings . The inception of a fault in the protected system is detected when any of these measured amplitudes is greater than a preset value; and the removal of the fault indic a ted when the output from the detector is zero as a result of the rate of rise becoming less than the preset value. Figure 6 shows the block-circuit-diagram of the CDR. A differenti~ting circuit could have been used instead of the gate and gating circuit, but the use of this would have meant that amplitude errors due to th e presence of high frequency noi se components in the cnrrent wave would be amplified

324

by such a circuit, the amplification being proportional to the frequency of the components.

burden so that the CT secondary voltage is sufficiently large t o drive it into saturation

tranS(nJ ssion lines

v

,::l_______~_ltzvel dunng fault.

rm zero cross'lng r - - ~etector

.~

1mSgate

f---

and g2.ting

Itim~?l

timlH

r-' ci~\Jit

I (S~t zt L-To !c eSlred i bus-bdr

I-'--+---~cont ro l I , ci~uit.

iv,!lue) i multi-trip re la y

1 I bus-bar

11 :. -_- -=..J Figure 6 4.1

level after rerrovdl·

'A'

Block diagram of current derivative relay (CDR).

Experimental Test Results of the CDR

for most of the fault duration. Pick-up again occurs at the first zero crossing after the, fault inception and within a time of lms. The CDR is found to perform satisfactorily under this abnormal system condition. The drop-out times of both the CDR and the output relay are again of the order of lOms.

The pick-up and reset times of the CDR were investigated when single phase faults of various angles of incidence (hence various DC offsets) were applied. The tests were carried out under the following conditions:(i)

the model line carried no load current prior to fault inception so that on opening the fault contactor, the fault current reduces to zero. This simulates the practical case in which a fault is successfully cleared by the associated circuit breaker and the fault current reduces to zero in the faulted section. It is found that pick-up occurs at the first zero crossing of the fault current; leading to a time delay of only lms (i.e. sampling time) after fault inception. The pick-up response of the sensitive output relay is also found to correspond to that of the CDR. The drop-out time of both relays is seen to be about lOms ,

(ii)

The magnitude of the fault current is normally measured at the relaying point by monitoring the voltage across at CT burden and the magnetising current of the CT is also derived from the fault current . Under some conditions it is possible that the CT will be forced into saturation. This case is simulated by increasing the CT resistive

Figur e 7

(iii) In transmission systems, successive reclosure onto an uncleared fault can set up core flux in the CT which may advance the onset of CT saturation. This condition is simulated on the model system by winding 20 turns of wire round the core of the CT and passing a suitable DC current through them. Figure 7 shows an example of the performance of the CDR and the sensitive output relay under this condition. The residual ampere turns in this case was 200 and was sufficient to bring the CT to the knee of its saturation curve . On applying a maximum DC offset fault, the CT was driven into saturation. It can be seen that under this adverse system condition, the CDR and the output relay still pick-up at the first zero crossing after the inception of the fault with the usual Ims time delay. The reset times of both relays are again seen to be constant at I 10ms.

CDR operation-CT with residual flux IS = CT secondary current, OP

l

= CDR

operation

325

OP

2

= Output

relay.

5

CONCLUSIONS

and at time ~+l

The basic theory of Section 2 and the experimental test results of Sections 3.1, 4.1 indicate that the current (or voltage) derivative relaying technique performs satisfactorily the task of detecting changes in power system current or voltage (with adjustable sensitivity). The performance of the analogue version of the device has been verified under a number of particularly stringent conditions.

w Ipk cos [(wt

k

- 11) + w6t]

(A3)

where 6t is th~ tiree interval between samples. From these two equations it can be shown that, under the assumption that w6t is small;

It is intended to apply the technique to the specific task of circuit breaker back-up protection using a digital computer, with the current and voltage derivative relay either as a programmed function in a computer or as a hard-wired preprocessor.

At zero

The electronic circuit version has a short reset time and offers the possibility of reduced overall operating times if used in conjunction with present analogue schemes for back-up protection. The digital version is ideal for microprocessor appli cation.

where at is the interval between the time tk and the zero crossing.

cross~ng

i~

WI

pk

cos [(wt

- 11) + wot]

k

(M)

, et(i' _ i') i k + 6t k+l k

i

0 = I

o

sin[(wt

pk i

hence Apart from the use of the COR as a component in the chain of local back-up equipment, there are a number of other possible power-system applications of the COR in either its digital or analogue forms, e.g. as a current check or over current relay, or as an under-voltage detector.

at

k

(ik+l i

i'

0

i

k-

(i

-11) + wet]

and since

i~

6t

k

k

k+l

-

-

then

ik)/i~

i ) (i~+l k

-

i~)

(AS)

which is the desired result. 6

REFERENCES

Iron-cored current transformers transmit the DC offset in the primary fault current, and this component often takes many cycles to decay on presenl systems with high X/R ratios. The voltage can also have an offset component, but this is usually smaller than that on the current wave form. The relevant expression for the current, for example, is well known (see references (3) and (4) and is here repeated for convenience:

1. RALSTON, P. (1965) A first course in Numerical Analysis, New York, McGraw-Hill. 2. ISAACSON. E, and KELLER, H.B. (1966) Analysis of Numerical Methods, New York, Wiley. 3. MATHEWS, P. and NELLIST, B.O. (1963) Transients in distance protection. Proc. Inst. Elec. Eng. (London), Vol.llO, pp.407-41B. 4. MATHEWS, P. (1955) Protective Current Transformers and Circuits. London, Chapman & Hall, p.6B7.

At zero crossings

o

N2/N1Ilpk(Sin(wto+u-1Il)-e

-wt /Q 0 s!n(U-1I l

»

(1\6)

7

ACKNOWLEDGEMENT and

The authors wish to acknowledge the financial support of the Electrical Research Board, and indispensable collaboration of colleagues in the State Electricity Commission of Victoria and the Electricity Commission of N.S.W.

B

WN Sin (wt +U-(jll) 2 0 - - 11 k (cos (wt +U-O )+ Q ) l Nl P 0 1 putting (A6) in (A7) therefore:

APPENDIX

I lpk

Pi 1+ -

pk

sin(wt -

11)

(Al)

k=

w I

pk

cos (wt

k

-

11)

(AB)

Equation (AB) is observed to be similar to equation (A4) since t = (t + wot) and hence near the zero o

Then the rate of change of current at time ~ is i

Cos (wt 0 +a-
Q2

Consider a sinusoidal phase current i = I

(A7)

k

crossing, all the accompanying analysis holds; and the rate of rise of current at the zero crossings can be obtained using equation (AS) .

(A2)

326