Digital Differential Relaying Scheme for Teed Circuits Based on Voltage and Current Signal Comparison

Digital differential relaying scheme for teed circuits based on voltage and current signal comparison

R.K. Aggarwal, BEng, PhD, CEng, MlEE Prof. A.T. Johns, DSc, PhD, CEng, FlEE

Indexing terms: Transmission lines

Abstract: The paper describes the basis of an alternative approach to the problem of differential protection of teed feeders that involves deriving signals which are functions of both voltages and currents. It is shown that, unlike conventional current differential protection, this approach obviates the need for bias to compensate for capacitance spill current, thus improving the overall performance of the relay. Methods are outlined for compensating for the variable responses of practical transducers. Other practical considerations include the means developed for signal compression to simplify the digital hardware requirements and reduce the bandwidth requirements for digital communication between the three ends. The protection has been developed using CAD techniques, and the methods proposed are readily implemented using present generation signal processing hardware.

List of symbols

Z,, = modal surge impedances y k = modal propagation constants w = angular frequency CT = current transformer CVT = capacitor voltage transformer f, = sampling frequency x = arbitrary line length

Subscript k = 1 (for earth mode); 2, 3 (for aerial modes)

1 Introduction

Multiterminal lines, i.e. teed feeders, often offer considerable economic advantages and environmental benefits over two-terminal lines for EHV power transmission purposes. From a protection point of view, such feeders have always presented difficult problems [l] which, in many cases, are not readily solved using conventional unit or nonunit techniques. Of the alternatives, differential protection is generally regarded as the method that is best suited to teed feeders.

Paper 7562C (P9, P l l ) , first received 27th November 1989 and in revised form 15th June 1990 Dr. R.K. Aggarwal is with the School of Electrical Engineering, Uni- versity of Bath, Claverton Down, Bath BA2 IHU, United Kingdom Prof. A.T. Johns is with the Power and Energy Systems Research Centre, School of Engineering, The City University, Northampton Square, London ECI OHB, United Kingdom

414

Conventional differential protection of teed feeders generally compares signals that are functions of the currents measured at each end of the circuit. These signals are usually combined into a differential and bias signal, the former comprising the sum of the terminal currents. The standard practice of providing a bias signal is to ensure that security is not compromised under conditions where a significant differential signal is generated under healthy conditions, e.g. due to CT saturation and/or circuit shunt capacitance charging current. There are a variety of methods of combining the currents at the ends of a teed feeder to form a bias signal, but in practice there are a number of teed circuits and associated external system operating conditions [ 1, 21 that nevertheless result in the difference between the differential and bias signals being small. The suitable choice of a current bias signal has, in consequence, been a subject of considerable interest over many years [3,4].

The foregoing considerations account, to a large extent, for ongoing interest in the development of alternative and improved methods of protection for three- terminal systems 14-61. More recently, the authors have proposed a new high speed current differential protection scheme for three-terminal lines [7] which addresses some of the limitations and problems (such as those caused by feed-around paths) of the schemes developed by other researchers [4-61. Although all the forementioned methods offer high speed protection for teed circuits, the choice of a suitable bias in current differential protection schemes remains a problem.

The basis of a new approach to the problem of differential protection of teed feeders was first outlined by the authors in Reference 8. The objective of the present paper, however, is to provide more extensive information on the techniques developed and results gained since the technique was first introduced. The method described here involves deriving differential signals that are functions of both voltages and currents measured at each end. It is shown that this approach obviates the need for relay bias to compensate for any capacitance spill current, improves the sensitivity to high resistance faults and removes uncertainties as to the dependability of protection under contingency operating and/or fault conditions. The scheme is based on master and slave principles using a fibre optic link (FOL) as a means of communication between ends. Recent developments in the field of FOLs [9] provide the ability to transmit the instantaneous values of the currents and voltages measured at each end of the feeder to remote locations. It should be mentioned that the master/slave approach has been adopted mainly for economic reasons and has some disadvantage in that it is dependent on the master end being in service, and it cannot tolerate the failure of any communication link.

IEE PROCEEDINGS, Vol. 137, Pt . C , N o . 6, N O V E M B E R 1990

However, where the economies resulting from the afore- mentioned approach are unimportant, the methods described can be equally applied to those with full independent operation at each line end using a triangulated communications system. The equipment has been designed using CAD methods and is readily implemented using digital signal processing hardware. Practical considerations include the means developed for signal compression to considerably simplify the digital hardware and reduce the bandwidth requirements for signal transmission over the FOL, the latter being achieved by employing a relatively low sampling rate. This approach also makes the relay highly flexible, and it can be adapted to work with alternative communication channels (such as microwave) by minor changes in the interfacing hardware.

Both voltage and current signals proportional only to the two aerial mode [ l o ] voltages and currents are employed. This approach is adopted because, apart from gaining some economy through processing and transmitting only two signals, it also increases the stability of the protection on a healthy circuit from a fault on an adjacent circuit in double-circuit line applications. The latter is achieved by virtue of the the mutual coupling between the two circuits being predominantly associated with the earth mode (the use of which is avoided in this scheme).

At the end of the paper we present the results of simulation testing of the new relay under practical fault conditions and contingency fault operating conditions that commonly pose difficulties for differential protection. Some typical 400 kV applications are considered for these purposes.

2 Relay operating principles

The basic relay operating principle hinges upon deriving signals proportional to the instantaneous values of the aerial mode (i.e. subscript k = 2 or 3) voltages and currents at the three ends of the circuit.

2.1 Fundamental tee-circuit theory Consider a teed-feeder system as shown in Fig. 1 . Using the theory of natural modes [ l o ] , it is shown in Appen- dix 8.1 that, for a healthy circuit, the modal voltages and currents from the tee point T to each of the three termin- als, P, Q and R (assuming homogeneity) are related in the frequency domain by eqns. 1-3 :

vTk(w) + zOk(m)lPTk(m)

= exp ( - Y k ( w ) L P ) [ VPk(m) - zOk(m)zPk(m)l ( l )

vTk(w) + zOk(w)zQTk(m)

= exp ( -yk(w)LQ)CvQk(m) - zOk(0)zQk(m)l ( 2 )

/ I 1

Fig. 1 Basic teed-feeder model

IEE PROCEEDINGS, Vol. 137, P t . C , N o . 6 , N O V E M B E R 1990

CQI - The matrices [ S I - ' and [QI- ' are the inverse of the voltage and current eigenvector matrices [ l l ] . The operation of the relay involves a comparison of the signals S i k , Sh,, and SAk given in eqn. 5. In theory, their sum should be zero under healthy (or external fault) conditions but significantly finite under internal faults, thereby causing tripping.

2.2 Filter functions Consider the signals in terms of values Vp,, I p s , VQs, I , , , VR,, I R s , say, at the secondary of the voltage and current transducers. If the frequency response of the CVT and CT are H,(w) and Hi(w), respectively, and are the same at the three ends, then the three signals given in eqn. 5 can be written in the alternative form

sbk = VPsk(W) + BP ZOk(o)zP,k(o)Hu(w)/Hi(o) (7)

' Q k = C A Q - B Q l VQsk(m)

+ C A Q + BQIZOk(o)zQsk(o)Hu(o)/Hi(o) (8)

+ C A R + BRIZOk(w)zRsk(W)Hu(W)/Hi(w) (9)

' k k = C A R - B R I VRsk(w)

Eqns. 7-9 show that, to compensate for the frequency responses of the transducers, it becomes necessary to

415

effectively filter the signals I p s k , IQ,, and l R s k by the function

= Z O k ( w ) H u ( o ) / H , ( w )

For the transducers, the CT response is a constant over a wide bandwidth (typically 0.1 Hz-10 kHz) and, although the CVT response varies somewhat between transducers, it is nevertheless reasonably constant around the power angular frequency U,. Thus the use of a bandpass filter with a frequency response HB(w), such that H,(o) .+ 0 for (oo - yc) < w d (0, + w,), where w, defines the filter bandwidth at the - 3 dB point, ensures that the rather unpredictable and variable frequency response of the CVT, for frequencies other than those around a,, has little practical effect. Fig. 2 shows the response of the filter used in the prototype equipment. The actual signals compared are therefore filtered versions of those given in eqns. 7-9, and they are

SPk = &k H B ( w ) S Q k = s h k HB(w) sRk = S k k HB(w)

(10)

It should be noted that the exponential terms, A , , B , , . . . , B R in eqns. 5, 7, 8, 9 are also, in essence, filter functions.

Fig. 2 Bandpassfilter characteristics ~ magnitude

phase _ _ - -

2.3 Digital filter implementation To implement the forementioned filter functions in real time as digital filters, it is necessary to realise the functions. It has been found that finite impulse response (FIR) filters are more suited to the types of application considered here than other types of filters, primarily because of their linear phase response and stability and also because the errors arising from quantisation, round-off and coefficient inaccuracies are usually less critical in the realisation of such filters [12].

Basically, FIR filters involve determining the time- domain impulse responses of the various filter functions (from a knowledge of their frequency responses) to determine the appropriate weighting coefficients which are then combined digitally with the digitised input voltage and current signals, using direct convolution, thus determining the outputs of the appropriate filters. To avoid unnecessary long group delays, care needs to be taken to determine the lowest possible order filters (i.e. minimum number of coefficients) that would approximate the functions. Appendix 8.2 gives the process of convolution in some detail.

2.4 Phase -modal transformation For phase to modal transformation, the [SI- ' and [ Q ] matrices shown in eqn. 2 are complex functions of frequency and therefore, in theory, should also be realised as filter functions. However, studies have shown that the matrix terms are near real quantities with little variation in magnitude above power frequency. Thus, from a practical point of view, it is sufficient to precompute the matrix terms from a knowledge of the series impedance and shunt admittance matrices [ Z ] and [ Y ] at power frequency, for a particular line configuration, and simply multiply the phase values of voltage and current samples by the appropriate real parts of the terms to obtain the modal quantities.

2.5 Decision logic As mentioned in Section 2.1, the signals from the three ends, should theoretically sum to zero under all healthy conditions (including external faults), i.e. S p k + S Q k

+ SRk = 0. However, owing to quantisation, transducer and filtering errors etc., it is necessary to apply a small threshold T,, to the sum of the signals. Thus, in its sim- plest form, the relay would give a trip output if

I S P k + S Q k + S R k I = D k > T h (1 1)

One of the advantages of using composite signals based on both voltages and currents is that, unlike more conventional differential protection schemes, there is no longer any need to implement elaborate and complex decision logic into the relay. In this scheme, an extensive series of studies have shown that a simple logic check in which, if the criterion of eqn. 11 is satisfied for two con- secutive samples, a trip decision can be safely initiated. This simple logic is sufficient also to ensure relay stability for all practically encountered external faults, including a degree of tolerance to CT saturation at an end.

3 Relay description

The complete protection scheme is as shown in Fig. 3. The equipment at the slave ends transmit voltage and current data and receive any direct intertripping signal generated at the master end where the tripping decision is made. Although in the scheme described here, the end R is proposed as the master end, the choice is not critical and in practice any one of the three ends can be chosen without affecting the relay performance. A sampling frequency f, of 500Hz provides a satisfactory response, without imposing undue demands on both hadware and signal transmission requirements. An analogue prefilter with a second-order lowpass Butterworth characteristic and a 250 Hz cutoff frequency has been used to ensure that signal aliasing effects have no detrimental effects on performance.

The transmission of the two aerial mode signals, from each slave end ( S Q z , SQ, from end Q and S , , , S p , from end P ) to the master end, at the 500 Hz sampling rate with a 14 bit A/D conversion (13 bits + sign bit), requires a data transmission rate of at least 14 kbit/s. In practice, this would be achieved over two channels of a standard modem, each with a capability of transmitting 64 kbit/s. The use of the latter would also allow sufficient spare capacity for performing error detection, byte synchro- nisation etc. The direct intertripping signal from the master to slave ends is of necessity a very high security signal which, owing to the very large bandwidth and virtual noise immunity of the FOL, can be transmitted with minimal delay over two separate channels devoted

IEE PROCEEDINGS, Vol. 137, Pt. C, No . 6, NOVEMBER 11990 416

to this function. By this means, a secure intertrip signal can be asserted at any slave end after modem delay (typically 1-2 ms) plus an FOL signal delay correspond- ing to data transmission at approximately the speed of light.

(slave)

current I voltage interface

S lHand MUX

I multiplexer

(L

U C

0

Lo 0

.-

-_- _-__-__ A / D - _ _ _ _ _ _ _ _ _ - I 1 rl ~digito;vertor analogue to

phaselrnodal transformation

signal mix signal r n i x

t

decision logic

I-

O@ signal rn ix

to 'cB

1 to CB

Block schematic diagram of complete protection scheme Fig. 3 CB = circuit breaker

3.1 Digital processing The digital part comprises FIR filters and a decision process. The modal mixing software is arranged to combine the phase variations of currents and voltages to effect the phase-modal transformations according to eqn. 6. The implementation of the FIR filters has already been described in Section 2.3. The decision logic at the master end compares the magnitude of the sum of the three signals for each mode separately, against a threshold as in eqn. 1 1 . To compensate for the channel/modem delays and any sampled data mismatch, it is necessary to incur- porate the compensating delays Tp, TQ, TR at the master end. The final trip decision T, is asserted and transmitted when one or other of the modal measurands indicates the presence of an internal fault.

IEE PROCEEDINGS, Vo l . 137, P t . C , N o . 6 , N O V E M B E R 1990

3.2 Hardware implementation The relay design has been performed using CAD techniques and recent work on its implementation using a 16 bit TMS320 10 microcomputer system has been initiated. The latter was chosen because the TMS320 10 digital signal processor is specifically designed [13] to carry out the filtering processes of the type used in the relaying scheme described here.

The voltage and current signals produced by a prog- rammable transmission line are passed through analogue voltage and current interfaces. The voltage interface comprises fixed ratio transformers/antialiasing filters, and the current interface module comprises transformer-reactors and compensating networks that are arranged to inte- grate the output of the former. Antialiasing filters are again employed. Each phase voltage and current signal is fed to a sample/hold circuit and analogue multiplexed into a single 14 bit analogue to digital convertor. Beyond this, the microprocessor performs the various digital processes as described in Section 3.1.

4

4.1 Applications considered The results presented in this paper relate to the teed- feeder applications shown in Fig. 4. These circuits com-

System and relay setting parameters

5GVA - lOOkm = 20km- 20GVA

0 1 GVA

( 1 )

5GVA - 100km = - 20 km- 20 GVA

a I E 0 LD

1 1 GVA

( 1 1 1 )

Typical tee configurations studied Fig. 4

417

prise typical 400 kV vertical construction lines of the type commonly used on the UK supergrid system. Details of the line construction are given in reference 11, and the relevant parameters used are

(i) earth resistivity (assumed homogeneous) = 100 Om (ii) system frequency = 50 Hz (iii) source X / R ratio = 30; source sequence imped-

(iv) nominal CVT and CT ratios = 400/0.11 and ance ratio Zs0/Z,, = 0.5

2000/1, respectively.

4.2 Relay parameters The current and voltage gains K , and K , of the interface modules are the only application dependent settings that the scheme possesses.

4.2.1 Current gain, Ki This is set so that there is no case where current clipping occurs at any end for external faults. The latter require- ment is met by first performing a simple steady-state study to determine the maximum possible external fault current. For example, if in the tee configuraton of Fig. 4(i) the short circuit levels quoted are the respective absolute maximum levels, then the maximum possible through- fault current would occur at end R for a solid three-phase fault on the R busbar. This would give a maximum secondary current at end R of approximately 25 A in any one phase, allowing for current doubling under conditions of full exponential transient offset. Thus, to ensure that the signals are kept within the & 10 V range of linearity, K i will be set to a value of

(12) Using the value of K , shown in eqn. 12 guarantees absolute stability for all external faults and the relay retains its sensitivity to low level faults.

4.2.2 Voltage gain K, With a standard 63.5 V RMS secondary VT, the maximum input voltage to the voltage/voltage interface,

K i = 10/25 = 0.4 volts per secondary ampere

100 I 100

0 I O -100 , -100

-300 I -300 I

allowing for an overvoltage factor of 2, is

V,, = [2 x 63.5 x J(2)] = 180V (13) To ensure linearity within the thus set to

10 V, the value of K , is

(14) K , = 10/180 = 0.056 volts per secondary volt

end P b, c

0

-5

-1 0

4.2.3 Threshold level T, This fixed level has been determined largely by means of an extensive CAD exercise to determine the stability of the scheme for extreme out-of-zone faults and also its ability to respond quickly to internal faults. The setting

must be sufficiently high to ensure that any noise in the differential signal D, (eqn. 11) is ignored. The prin- cipal noise sources are analogue circuit noise and harmo- nics generated by the CVT, CT (including a degree of saturation for the CT) and voltage and current interface modules. In the broader sense, residual differential signal components caused by sample data mismatch and quantisation errors are effectively also noise sources that combine to corrupt the basic signals. A consideration of these factors has led to the conclusion that the required value of Th is 1000 quantum levels. The 213 conversion process leads to a quantisation level of approximately 1.2 mV, and the resulting pick-up level of 1.2 V is well above the total noise level expected in the equipment as a whole.

5 Relay response studies

The modelling techniques used for obtaining the instantaneous values of the voltages and currents at each end of the tee circuit are essentially an extension of those used for plain feeder applications as outlined in Reference 11.

5.1 Typical fault study Fig. 5 typifies the signal waveforms when an internal a-earth fault (at voltage maximum point-on-wave) occurs

1 pr imary currents I

pr imary voltages ' I p r imary voltages I pr imary currents teeconf Fig &(I) I tee conf Fig 4 (11) I tee conf Fig4 ( I ) I tee conf Fig 4 (11)

> Y

M 300 m 2 100 $ 0 5 -100 0

c -300 L -

> Y v; 300

c 100

aJ B : o 5 -100 5 4 -300

300 300

100 100 0 0

I -100 I ! -300

-100

-300

0 40 80 120 . I

0 40 80 120 (Ill) (VI) tl

z 6

g o ,c

- 4 2 2

" -2 .E -4

-6

3

-

3 2 1 0 C

-1 -2 -3

0 40 80 120 ~ , m s (Id

a a =. b.c 2 . 4 ? o end Q

a -4

-8

U

.- -

3 2 1 0

-1 -2 -3

end R

418 IEE PROCEEDINGS, Vol. 137, Pt. C, N o . 6, N O V E M B E R 1990

close to end P on the two alternative circuits shown in Figs. 4(i) and 4(ii). The primary system voltages for the two configurations are nearly identical. However, com- paring the primary system currents for the two configurations, it will be seen from Figs. S(vii)-(xii) that for a fault on the circuit with a feed-around path, i.e. for circuit in Fig. 4(ii), there is effectively a current outfeed at end R. Such conditions, of course, commonly pose problems for nonunit protection. Furthermore, for some alternative fault conditions on the tee circuit of Fig. qii) (for which the current at end R undergoes a transition from one direction of current flow to another), the current at end R is small and the distribution of currents then becomes similar to a plain two-ended circuit. In such cases the differential and bias quantities in a conventional current differential scheme are nearly identical, which in turn often causes difficulties in maintaining dependability and security. It is later shown that, for the scheme described herein, the relay performance is unaffected when one end of the tee is out of service.

A comparison of Figs. S(xiii)-(xv) with Figs. S(xviit (xix) clearly shows that the relay measurements at the three ends are little different for faults on the two alternative circuits. However, for both the circuits the sum of the measurands at the master end lie well above the pick-up level, with the assertion of a trip decision in approximately 16 ms after a fault in both cases (see Figs. (xvi) and (xx)). This operating time also includes a channel/ modem delay of approximately 3 ms.

Although, in reality, the primary system waveforms (voltages in particular as shown in Figs. S(i)-(vi)) contain significant high frequency components for the fault condition considered here, very little of these appear in the relay signals S. This is because there is extensive filtering

signals for tee conf FigL(1)

signals for tee conf Fig & ( i t )

x103

signals Sp

0 LO 80 120 0 40 80 120 tirne,rns

Fig. 5 a-earth fault near maximum of a-phase voltage and close to end P; T, = fault inception time; Th = threshold

IEE PROCEEDINGS, Vol. 137, Pt . C , No. 6, NOVEMBER I990

Relay waveforms for typical internal fault

employed at both the analogue and digital stages, and the sampling rates are relatively low.

5.2 Relay stability and operating times An extensive series of studies using the circuits shown in Figs. 4(i) and (ii) have shown that the relay is stable for all through-faults. Fig. 6 shows the variations of the relay measurands S ( t ) (at the three ends) and the differential signal D(t) at the master end when an external a-phase- earth fault has occurred close to end P. The signals are nearly identical for both configurations and the differential signals are well below the threshold for both modes, thus restaining relay operation.

signals for tee conf Fig4 (I) conf Fig L ( 1 1 )

signals for tee

15 10 5 0

-5 -1 0

signals Sp

signals So

5 signals D

0 0

I

0 LO 80 120 0 LO 80 120 tirne,rns

Fig. 6 a-earth fault near minimum of a-phase voltage and close to end P; T, = fault inception time; Th = threshold

Typical external fault relay signals

Investigations into the effect of sampled data mismatch have indicated that the relay is completely stable under external faults for compensation delay drifts in Tp, TQ and TR of up to 2 ms, which is the maximum drift likely to be encountered in practice.

Fig. 7a shows how the relay responds to internal faults (faults on circuit 4(ii)) that occur at the maximum and minimum of the prefault system voltages. The relay operating times are almost identical for both phase-earth and pure phase faults (the former being slightly higher than the latter) and are more or less independent of the fault position for both types of fault.

Fig. 7b shows the variation of the relay operating time with point-on-wave of fault, for faults near the T-point. In common with the previous study, the results clearly show that the operating times are again almost independent of the fault inception angle. These features are particularly important in many practical applications such as high-speed autoreclosure schemes, the successful application of which can often depend on fast, near simulta-

419

neous tripping of the circuit breakers at all ends for all types of fault conditions.

E"- 1 5 - a,

E

; 10 : t Q

0 20 40 60 80 100 120

fault distance from end P , km

a

180"

I 270"

b

Fig. 7 a Effect of fault position __ b-c phase fault at ubcpo. and U&,,

a-earth fault at uao.

Relay performance for internal faults b Effect of point-on-wave fault -b-c phase fault

a-earth fault Faults near the T-point

_ _ _ _ a-earth fault at uag,,~ ~ _ ~ _

5.3 Effect of source capacity Fig. 8 shows the relay performance when the source capacity at end P is varied for faults on circuit 4(ii). It is evident that the source capacity has virtually no effect on

Open

10 t 3

0 10 20 30 40 50 source capacity at end P, GVA faultat 25kmfrom end R

Fig. 8 a-earth fault at uno^

nflm a-earth fault at unv with both ends P and R open ~ b-c phase fault, b-c earth fault at ubrW 000 b-c phase fault, b-c earth fault at uko. with both ends P and R open

Effect of source capacity ~~~~

relay performance. This is also true irrespective of the type of fault.

As mentioned previously, in Teed-feeder protection, it is important that the relay performance be satisfactory in the likely event of a fault occurring on a circuit when one leg of the tee is out of service or when a line is energised from one end only onto a permanent fault. The results shown in Fig. 8 clearly indicate that the relay gives satisfactory performance when one end is open and also when a fault occurs with two ends open. The same is true for external faults. This very important feature can be wholly attributed to the presence of very significant voltage components at the three ends, irrespective of the breaker status.

5.4 Effect of fault arc resistance As evident from Fig. 9, the relay responds to high levels of fault arc resistance, typically up to 200 R and 600 Q for single-phase-earth and double-phase-earth faults, respectively. This is attained because, unlike conventional current differential protection with a bias, the signals comprise both voltage and current components. As would be expected, a much better coverage is attained for the double-phase-eart h faults than the single-phase-eart h faults as the levels of fault currents for the former are generally higher. The 'stepped' response, particularly for the latter types of fault, is due to a reduction in the magnitude of the relay measurands at higher fault resistances.

200 400 600 fault arc resistance.0 fault near T point

Fig. 9 Fault arc resistance coverage a-earth fault at uago. b-c earth fault at ukv

~ -~~

Faults near the T-point

5.5 Effect of CT saturation Conventional differential protection can maloperate if current distortion at an end occurs as a result of CT saturation. Fig. 1qi) shows the CT core flux when a purely resistive burden of 30 VA is assumed in the CT model at end Q. The CT model is arranged so that the incremental core flux (d$c/di,) tends to zero when the magnetising current (i,) establishes a core flux density of 1 TS. This represents a more severe condition than is often encountered in practice because it results in a total collapse of the output current during the time when the core is satu- rated (as seen from Fig. lqii)). Figs. lO(iiiHv), however, clearly show that this has little effect on relay stability for the external fault considered. This is particularly evident from Fig. lqvi) which shows that the differential signals are small, i.e. below the pickup threshold.

When considering the effect on internal faults, although CT saturation very severely distorts the current waveforms, as shown by Figs. ll(iHii), the differential signals are nevertheless well above pickup level and as a

420 IEE PROCEEDINGS, Vol. 137, Pt. C , No. 6, NOVEMBER 1990

consequence, the relay operating times are largely unaffected (Figs. 1 l(iiiHvi)).

C T transient xlo-~ core f lux CT output current

Tc L e n d Q TS U

a. 1 ::c I .. ..c _ .

10 10 Lo Lo - - P 5 E 5

$ 0 s o - -

'0 -5 6 -5

?lo = -10

x102 XlO* Th Lo 10

l5 1 signalss 5 IsignalsD 4

2 0

5 5 C

t!me,ms

. . ( V I ) -15 ! time,ms

(V)

Fig. 10 Effect of CT saturationfor external fault b-c phase fault at vbc0.; external fault close to end Q T, = fault inception time; T. = CT saturation period; collapse; Th = threshold

= CT secondary currents

The immunity of the relay to CT saturation can again be largely attributed to the presence of the very significant voltage components in the relay measurands, that render any adverse effects caused by current distortion relatively insignificant.

In very exceptional cases, where there is a likelihood that the degree of saturation may exceed that normally encountered, it is possible to further enhance relay stability for external faults by employing modified decision logic processing techniques similar to those developed in connection with the current differential three-ended circuit protection described in Reference 7. The latter approach would of course add to the complexity of the relay.

5.6 Relay performance in double -circuit applications In double-circuit line applications, there is a possibility of relay instability on the healthy circuit when a fault occurs on an adjacent circuit. This is particularly so for certain types of earth faults which can produce quite a strong mutual coupling effect between the faulted and healthy circuits, primarily caused by the presence of earth mode components. However, for the scheme described herein, this potential problem is avoided by the use of the two aerial modes only. Fig. 12 clearly shows that, for the type of fault considered, (fault on circuit shown in Fig. qiii)), the differential signals on the healthy circuit lie well

IEE PROCEEDINGS, Vol. 137, Pt. C, No. 6, NOVEMBER 1990

CT transient core CT output current end 0 x10-4 flux end 0

30 :. 20

s. ; 10

2 0 2 0

8

C

X U

e -10 8 $ -20

E 8 -4

-8 -30

x103 15 1 signals sp

x104 8 1 signals so 6

- C O L 10

5 2 s o 5 O 6 -5 5 -2

U & -L

$ 5 -

-6 -1 0

-1 5 -8

x103 x t o L

LO 80

time,ms ( V I )

-3 J time,ms

( V )

Fig. 11 Three-phase-earth fault close to end Q T, = fault inception time; Th = threshold

Effect of CT saturationfor internalfault

x103

a, -

x l O L L

2

0 Th

, 0 40 80 120

tirne,rns

healthy circuit signals

x103

end Q signais

so

a, -

s 6 ' J L

2 0 end R

signais -2 -4 -6

SR

signals 'h

800 0

400 3 2 0

I 1 0 40 80 120

iirne.rns

Fig. 12 b-c earth fault at ukIW ; fault at 40 km from end P T, = fault inception lime; Th = threshold

Relay signals for fault on double circuit line

42 1

below the threshold, thus preventing any maloperation. An extensive series of studies has shown the healthy circuit protection remains stable for all types of practically encountered faults on the adjacent circuit.

6 Conclusions

A new differential teed-feeder protection scheme, which uses both voltage and current signals, has been described. The signals can be derived from limited bandwidth transducers and the means for compensating, in particular for the variable response of CVTs, is given. The signals are compared over a standard FOL, and particular emphasis has been placed on designing the scheme to minimise the number of channels required. The relatively low signal channel bandwidth requirements, however, enable the scheme to be satisfactorily applied with alternative sig- nalling channels, e.g. microwave. The operation of the scheme has been modelled in a computer simulation and work is proceeding on testing under actual operating conditions.

The computer results clearly shows that by basing the differential signals on both voltages and currents, thus obviating the need for bias, the dependency of the protection scheme on both circuit configuration and contingency operating conditions is removed. Other important findings in relation to the relay described are

(i) high levels of fault resistance coverage, particularly when compared to conventional current differential protection with a bias

(ii) performance largely independent of source capacity, fault position and fault inception angle

(iii) immunity to the presence of ‘feed-around’ paths (iv) tolerance to a high level of CT saturation (v) satisfactory performance in double-circuit line

applications.

7

1

2

3

4

5

6

7

8

9

10

11

12

13

422

References

IEEE study committee report on ‘Protection aspects of multiterminal lines’. IEEE report 79, 1979 Westinghouse Electric Corporation, ‘Applied protective relaying’ (Westinghouse Electric Corporation, 1979), chapter 17 GRAY, C.B. : ‘Circulating current pilot-wire differential protection of multi-end circuits’, Proc. IEE, September 1969, 116, (9), pp. 1521- 1526 GELFAND, Y.S., NAUMOV, A.M., and RUBINCHICK, V.A.: ‘Multi-terminal transmission line protective relaying’. CIGRE paper 34-08, September 1982 CORROYER, C., and CHOREL, H.: ‘Protection of multi-terminal EHV links’. CIGRE paper 34-01, September 1982 ESZLARGALYOS, J., and EINARSSON, E.: ‘Ultra high speed protection of three-terminal lines’. ClGRE paper 34-06, September 1982 AGGARWAL, R.K., and JOHNS, A.T.: ‘The development of a new high speed 3-terminal line protection scheme’, IEEE Trans. on Power Delioery, 1986, 1, (l), pp. 125-133 AGGARWAL, R.K., and JOHNS, A.T.: ‘A new approach to teed feeder protection using composite current and voltage signal comparison’. Proc. IEE 4th International Conf. on power system protection, April 1989, Edinburgh, pp. 125-129 BENNDORF, H., DAGEFORDE, M.G., DORING, H., and PFEIFFER, T.: ‘Fibre-optic for transmission of information on high voltage overhead power lines’. CICRE paper 35-09, 1980 WEDEPOHL, L.M.: ‘Application of matrix methods to the solution of travelling wave phenomena in polyphase systems’, Proc. IEE, 1963,110, pp. 22W2212 JOHNS, A.T., and AGGARWAL, R.K.: ‘Digital simulation of faulted EHV transmission lines with particular reference to very high speed protection’, Proc. IEE, April 1976, 123, pp. 353-359 RABINER, L.R.: ‘Techniques for designing finite duration impulse response digital filters’, IEEE Trans. on Communication Technology,

DETTMER, R.: ‘Digital signal processors’, Electron. & Pwr., Feb- ruary 1986, pp. 124-128

1971,19, (2), pp. 188-195

8 Appendix

8.1 Modal circuit theory

8. I . 1 Modal decomposition : A distributed parameter three-phase transmission line can be described in the frequency domain by the following differential equations :

dV(o)/dx = Z ~ ( O ) dl(cu)/dx = Y V(O) (1 5)

The series and shunt parameter matrices Z, Y are evaluated to take account of the presence of any overhead earthwires, and also to include the effect of the frequency variation of both resistive and inductive line earth parameters.

The theory of natural modes [lo] enables eqn. 15 to be effectively decoupled by means of modal transformation matrices S and Q. Thus the phase voltages and currents V(w), I(w) are transformed as

v(0) = sh(W) l(0) = Qlk(O) (16)

(A detailed form of eqn. 16 is as shown in eqn. 6). Com- bining eqns. 15 and 16 gives

dI/ , (w)/dx = s-’ZQZk(w) = ZOk(~)Ik(w) d21/k(w)/dx2 = S - ’ Z Y S ~ / ~ ( O ) = ~~(o)I/,(o)

(17)

(18)

The appropriate modal surge impedances required are readily determined from the matrix product [ZOk] = C y k ] - ‘[Q]-’[Z][S] in which cyk] comprises the square root of the eigenvalues of the matrix product [ Z ] [ Y ] (see Reference 11). It should be noted that both [ZOk] and Cyk] are diagonal matrices.

Eqns. 17 and 18 show that wave propagation in a three-phase line can thus be considered as three independent components, each possessing its own modal propagation constant yk(w) and associated modal surge impedance Zok(w). The voltage differential eqn. 18 has a solution of the form

h(O) = exp[prk(w)xl + x 2 yk(W)xl (19)

Similarly, a solution to the current differential equation is of the form

I d o ) = { X l expl - ydW)x1 - X 2 exp[yk(w)xl)/ZOk(o)

(20)

In eqns. 19 and 20, X , and X , are arbitrary constants.

8.1.2 Fundamental relationships: The arbitrary constants shown in eqns. 19 and 20 can be evaluated from a knowledge of the boundary conditions for a particular transmission system. The system shown in Fig. 1 has the following boundary conditions :

(i) x = 0 at end P, x = L, at point T, for line section PT

(ii) x = 0 at end Q, x = L, at point T, for line section

(iii) x = 0 at end R, x = L, at point T, for line section RT.

Consider line section PT. substitution of the boundary conditions shown in (i) into eqns. 19 and 20 gives

QT

vPk(w) = + X Z ) ‘ P k ( w ) ( x l - x2)/zOk(W) (21)

v’k(o) = {Xl[exp (-7k LP)l + XZ[exp (”?kLP)l)/ZOk(m)

(22) IEE PROCEEDINGS, Vol. 137, P t . C , No. 6, NOVEMBER 1990

step1 Substitution of X , and X , from eqn. 21 into eqn. 22 then finally yields IN(5) IN(4) IN(3) IN(2) IN(1)

W Fig. 13 Digital implementation of FIRfi l ter

Eqns. 23-25, which correspond to eqns. 1-3, are the basic equations that are used to define the operation of the scheme examined in this paper.

8.2 FIR filter implementation A FIR filter performs a simple convolution which is defined as

n - 1

OUT(n) = C(m)IN(n - m) m = O

for n = 0, 1, 2, . .., (2n - 2) (26)

where OUT(n) is the output, IN(n) is the input and C(m) is a set of coefficients attained by filter realisation. The software implementation of the filter is quite simple. The input points and their respective coefficients are multi- plied together and the results are summed, as shown in Fig. 13. The output points are then shifted with respect to the coefficients. One new datum point is entered into the string and the oldest datum point is lost. The multiplication-summation is then repeated to generate the next output point.

IEE PROCEEDINGS, Vol. 137, P t . C , N o . 6 , N O V E M B E R 1990 423

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