Development and hardware implementation of a compensating algorithm for the secondary current of current transformers

Y.C. Kang S.H.Kang J.K.Park A.T.Johns R. K. Agga rwa I

Indexing terms: Current transformers, Compensators, Saturation

Abstract: The conventional method of dealing with current-transformer (CT) saturation is overdimensioning of the core so that CTs can reproduce up to 20 times the rated current without exceeding 10% ratio correction. However, this not only reduces the sensitivity of relays, as some errors may still be present in the secondary current when a severe fault occurs, but also increases the CT size. An algorithm is described for estimating the secondary current corresponding to the CT ratio under CT saturation using the fluxkurrent (hli) curve, and the results of hardware implementation of the algorithm using a digital signal processor are also presented. The main advantage of the algorithm is that it can improve the sensitivity of relays to low-level internal faults, maximise the stability of relays for external faults, and reduce the required CT-core cross-section significantly.

List of symbols

ip(t) = primary current i,(t) = secondary current ie(t) = exciting current i,(t) = magnetising current ikt) = loss current v,(t) = secondary electromagnetic force h(t) = core flux h(tO) = initial core flux Rp = primary-winding resistance R, = secondary-winding resistance 0 IEE, 1996 IEE Proceedings online no. 19960040 Paper first received 13th April 1995 Y.C. Kang and J.C. Park are with the Department of Electrical Engineer- ing, Seoul National University, Shinlimdong, Kwanak Ku, Seoul, 151- 742, Korea S.H. Kang is with the Department of Electrical Engineering, Myong-Ji University, Namri, Yongin Gun, Kyunggi-do, 449-728, Korea A.T. Johns and R.K. Aggarwal are with the School of Electronic & Elec- trical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, UK

RI = loss resistance Rb = resistance of the load Lp = primary-winding leakage inductance L, = secondary-winding leakage inductance L, = magnetising inductance Lb = inductance of the load T, = ideal transformer Zb = impedance of the load Z, = source impedance n = turns of the secondary winding

1 Introduction

Protective relays demand a reasonably accurate replica of the primary current and voltage, in particular when faults occur on the system. For this reason current transformers (CTs) are employed to provide a reduc- tion of the primary current for the relays. However, most conventional iron-cored CTs are not ideal because of their nonlinear excitation characteristics and their ability to retain large flux levels in their cores, known as remanent flux; they are thus prone to satura- tion. Thus many studies on the analysis of the steady- state and transient behaviour of iron-cored CTs have been reported [14].

If a CT is saturated, the ratio error becomes severe; thus it may cause a variety of protective relays to mal- function. The conventional way to deal with the prob- lem is overdimensioning of the core so that CTs can carry up to 20 times the rated current without exceed- ing 10% ratio correction. It implies that increased core cross-section of CTs is necessary to allow larger flux swings to be accommodated when the expected fault- current levels are increased.

The presence of any remanent flux in the core of the CT reduces the available flux swing in one direction and makes the avoidance of saturation during fault conditions more difficult. Thus the level at which satu- ration occurs must be great enough to allow the flux swings needed when large asymmetric fault currents are flowing. There have been many approaches to reducing the required CT-core cross-section without unduly affecting the CT’s ability to cope with large flux swings. In one approach, for example, gapped-core CTs have been used to reduce remanent flux and per- mit the use of a small core cross-section. However, as

IEE Proc.-Elect,. Power Appl., Vol. 143, No. I , January 1996 41

gapped-core CTs have some disadvantages their use may require application considerations; some of them are enumerated in [5].

To date, there is no proper method available that would cope fully with CT saturation; protective-relay engineers have thus to take account of this drawback when drawing up the specifications for relay perform- ance.

This paper proposes a technique for compensating the secondary current of CTs using the fluxicurrent (U i) curve which can be incorporated within the digital protective-relaying algorithm. The technique estimates accurately the secondary current corresponding to the CT ratio when the CT is saturated both with and with- out the presence of remanent flux, in particular when a smaller CT than the rated value is used and gets more severely saturated because of its size. The CT model is based on the Electromagnetic Transient Program (EMTP) software and the performance of the algo- rithm is tested under a variety of different system and fault conditions on a typical 345 kV Korean transmis- sion system. The paper concludes by validating the CAD technique in real time; this is achieved by imple- menting the technique into a hardware model based on a TMS320C digital signal processor.

2 Compensating algorithm for secondary current of CTs

Fig. 1 shows the equivalent circuit of a CT referred to the secondary [4]. This circuit can be made to represent any CT operating with any load and primary current under steady-state and transient conditions. The excit- ing current ie(t), which causes errors in CTs, is depend- ent on the exciting impedance, presented by the parallel RI - L, branch, which represents the transformer hys- teresis and varies with the core flux h(t) needed to pro- vide the secondary electromagnetic force.

' R'uLm Fig. 3 Equivalent circuit of CTs referred to the secondary

At any instant, the relationship between the primary current ip(t) and the secondary current iS(Q is

-ap(t) 1 . = q t ) 4 G(t ) n

As i,(t) is the input of relays and measured, if ie(t) can be deduced, then the secondary current corresponding to the CT ratio (lln)i,(t) can be estimated.

2.1 If the load of a CT is a resistive-inductive load of the type Zb = Rb + jcoLb, the relationship between h(t) and is(t) is described by the first-order differential equation

Calculation o f the core flux

This relationship will still be valid at any instant, i.e. even when the CT is saturated. Integrating both sides of eqn. 2 from to to t yields

t

X ( t ) - X ( t 0 ) = (R, + Rb) 2, ( t ) d t + (L, +Lb) { 2, ( t ) - i s ( t o ) }

(3)

t o J' As all the circuit parameters such as R,, Rb, L, and Lb are given and i,(t) is measured, if the initial core flux h(to) is calculated, then h(t) can be evaluated using eqn. 3.

2.2 Calculation of the initial core flux In the steady-state, the core flux is a periodic and zero- mean function, i.e.

N A ( t ) = X ( t + N A T ) C A( t0 + kAT) = O (4)

where N is the number of samples per cycle and AT is sampling interval. Letting

k=l

X(t0 + kAT) = A(t0 + kAT) - A(t0) ( 5 ) yields

(6) X{to + ( I C + 1)AT) - X(t0 + kAT)

= X ( t 0 + ( k + 1)AT) - X ( t 0 + SAT)

Summing k(to + kAT) from k = 1 to N gives: N

X ( t 0 + SAT) k=l

= { X ( t o + AT) - X ( t 0 ) ) + . . . + { X ( t o + N A T ) - X ( t 0 ) )

(7) N

= E X(t, + kAT) - NX(t0) k=l

As the core flux is a zero-mean function (eqn. 4), eqn. 7 becomes

k = l

As h(t,) can be obtained from eqn. 8 using a periodic- ity of the core flux with a cycle window of the second- ary current in the steady-state, after one cycle h(t) can be calculated using eqn. 3 even when the CT is satu- rated.

2.3 Compensating algorithm using flux/ current curve h/ i ) It is well known that there is no direct way of estimat- ing accurately the secondary current corresponding to the CT ratio in real time employing the measured sec- ondary-current values and the CT magnetic-circuit parameters, owing to the complex magnetic process. However, using the hli curve, it can be estimated cor- rectly in real time.

The h/i curve relates the magnetising current to a core flux, which in turn can be transformed from the VlI curve given by the manufacturer. The hysteresis- loop characteristic of the core is shown in Fig. 2. In saturated regions, as the hysteresis characteristic becomes single-valued, the magnetising current is the same as the exciting current. However, in unsaturated regions the exciting current has two different values for every value of the flux. The difference between the magnetising current and the exciting current is equal to

IEE Proc -Electr Power Appl, Vol 143, No I , January I996 42

or less than half the width of the major loop of the hys- teresis. In practice, since the width of the major loop of the hysteresis is so small, the difference between them is even smaller so that the magnetising current can be assumed to be the same as the exciting current.

positive-saturation :

. * I

iqat ive saturation

negative- , / 1, saturatio region

& A : nr

:point Fig. 2 Major-hysteresis-loop characteristic a Positive-saturation point b Positive-saturation region c Negative-saturation point d Negative-saturation region

As the core flux is evaluated from eqn. 3, the mag- netising current can thus be obtained from the hli curve. Thus, using eqn. 1, the secondary current corre- sponding to the CT ratio can be estimated by simply adding the magnetising current to the measured sec- ondary current. In the process of calculating the mag- netising current from the W i curve, piecewise linearisation of the latter reduces the load of calcula- tion, facilitating its estimation in real time.

As the proposed algorithm compensates the errors produced by the exciting current in saturated regions, it can estimate the correct secondary current accurately even when a CT is saturated.

As, conventionally, CTs are used up to the knee point of the hli curve, the required core cross-section must be increased in proportion to the expected level of the fault current in order to avoid saturation. This inevitably increases the size of the CT. The magnetising inductance in saturated regions is much smaller than that in unsaturated regions; this means that in satu- rated regions the core flux increases very slightly even though the fault current increases very significantly. Thus, as the algorithm estimates the correct secondary current even though small CTs are used and become saturated faster than bigger ones, if characteristics of cores are known in the region, the proposed algorithm can reduce the required CT-core cross-section signifi- cantly.

10 GVA 7 GVA

I , I 2km / 98 km

Zs I CT

Fig.3 345kV transmission system studied

3 System configuration and CT-model implementation

Fig. 3 shows the 345 kV-transmission-system configu- ration studied. For all the cases, the fault assumed is an

‘A’-phase-to-earth fault at a distance 2 km from the P bus and the system frequency is 60 Hz. The primary and secondary currents of a CT are generated using EMTP and the sampling rate used is 64 samples per cycle.

Kezunovic et al. [6] have introduced several digital models of CTs based on EMTP modelling techniques, and Fig. 4 shows the model used in this paper. Type-96 element accounts not only for the saturation but also for the hysteresis and requires the hysteresis curve. In this paper an EMTP auxiliary subroutine HYSDAT is used to obtain hysteresis characteristics from the known VII curve.

Ls CTS Rp Lp Tr.

CTI

CTO 1 1 ’ I ’

Fig.4 EMTP-based CT model

4

X - 3 (2.6 A, 3.378 Vs) +

magnetising current Fig.5 Ui curve of the CSOO CT

As C800 CTs are employed as the rated accuracy class on the 345 kV Korean transmission system, a C800 (20005, R2 = 0.72Q) CT is used for the case studies presented here, and its Wi curve is shown in Fig. 5. As shown, the saturation point (2.6 A, 3.378Vs) on the curve is determined for use with this CT model. As a load of the C800 CT, a resistive-inductive load of value (4 f j7) i2 is used.

4

As the proposed algorithm can be used in digital pro- tective-relaying algorithms, an antialiasing lowpass fil- ter which is between the CT and analogue-digital converter in digital relays was designed with a cutoff frequency of 360Hz corresponding to the sixth har- monic, to perform the case studies presented here. This design was chosen because the distorted secondary cur- rents, when analysed, showed that the magnitudes of harmonics higher than the sixth are less than 5% of the fundamental frequency. All the measured secondary currents are filtered by the designed second-order But- terworth filter.

During the first cycle, the initial core flux is evalu- ated with the secondary current in the steady state using eqn. 8. Thereafter, at every sampling interval, the core flux is calculated using eqn. 3 from the simulated secondary current, and then the magnetising current is obtained from the hli curve in Fig. 5. Finally, the sec-

Case studies and error analysis

IEE Proc-Electr. Power Appl.. Vol. 143, No. I , January 1996 43

ondary current corresponding to the CT ratio is esti- mated using eqn. 1. To assess the accuracy of the estimated secondary current, the ratio error given by eqn. 9 is calculated at every sampling interval:

The algorithm was tested for a variety of cases such as fault-inception angle, primary time constant, sampling frequency, remanent flux and a smaller-size CT.

4. I Error analysis for various fault-inception angles The DC component has far more influence on severe CT saturation than AC fault current and depends on the fault-inception angle. Figs. 6-1 1 show the results of two different fault-inception angles at 0 and 45"; the primary time constants in both the cases are 20ms.

"V

60 2 40 2- 20 $ 0 2 -20

-40

19.01 52.34 85.68 119.01 152.34 time,ms

Error analysis for a 0" fault and primary time constant of 20ms: Fig.6 primary current

4 ul =-- - ? i 2 .+- 0

-2 I I 19.01 52.34 85.68 119.01 152.34

time,ms Fig.7 core flux

Error analysis for a 0" fault and primary time constant of 20ms:

200

2- 100

5 0 c U

-1 00

19.01 52.34 85.68 119.01 152.34 time,ms

Fig.$ compensated and measured secondary currents a Compensated secondary current b Measured secondary current

Error analysis for a 0" fault and primary time constant of20ms:

19.01 52.34 85.68 119.01 152.34 time,ms

Fig.9 ratio error

Error analysis for a OOfauLt and primary time constant of20ms:

4

C -- 100

$ 0 U

-100 f I

19.01 52.34 85.68 119.01 152.34 time,ms

Fig.10 2Oms: compensated and measured secondary currents a Compensated secondary current b Measured secondary current

Error analysis for a 45" fault and primary time constant of

19.01 52.34 85.68 119.01 152.34 t ime, ms

Fig.11 20ms: ratio error

Error analysis for a 45" fault and primary time constant of

As the DC component for a 0" fault is larger than that for a 45" fault, the degree of CT saturation for the former case is more severe than for the latter. As shown in Fig. 7 (for a 0" fault), the core flux exceeds the saturation value (3.378Vs), causing CT saturation. However, the algorithm estimates with high accuracy the secondary current corresponding to the CT ratio from the distorted secondary current. The ratio errors in the two cases are small (4 1.5%) as shown by Figs. 9 and 11; the results clearly indicate that the algorithm performs very satisfactorily for different levels of satu- ration arising as a result of differing fault-inception angles.

4.2 Error analysis for different primary time constants (X/R ratios) In EHV systems, the primary time constant can be large and increases as the transmission voltages increase. The time constant ranges from several tens of milliseconds up to maximum of about 200ms. Severe CT saturation will ensue if the time constant is long and the DC component is high. Figs. 12-17 show the results of two different primary time constants of lOOms and 200ms, respectively. As expected, the sec- ondary current for the 200ms time constant is more severely saturated than that for the lO0ms time con- stant. However, the proposed algorithm is very effec- tive in estimating accurately the correct secondary current from the distorted secondary current even when the time constant is very large and the DC component is so high. The ratio errors in these two cases are less than 1.5%, as shown by Figs. 15 and 17.

n 1

6 6o y. 40 = 20 E 5 0

..2

* -20 -40

1901 52 34 8568 11901 152 34 t i m e , m s

Fig. 12 l0Oms primary current

Error analysis for a fault at 0" and primary time constant of

44 1EE Proc-Electr. Power Appl, Vol. 143, No. 1, January 1996

U - I 19.01 52.34 85.68 119.01 152.34

time, ms Fig.13 100ms: core flux

Error analysis for a fault at 0" and primary time constant of

2 - : - b o n i

200 Q 2 100 E 2 0

-1 00

.- 3 - 2 1

-4.

19.01 52.34 85.68 119.01 152.34 time, ms

Fig.14 lO0ms: compensated and measured secondary currents a Compensated secondary current b Measured secondary current

Error analysis for a fault at 0" and primary time constant of

- 4 t I 19.01 52.34 85.68 119.01 152.34

time,ms Fig.15 100ms: ratio error

Error analysis for a fault at 0" and primary time constant of

I 1 200

5 = 100 E! u o

-1 00

c

3

19.01 52.34 85.68 119.01 152.34 time,ms

Fig.16 200ms: compensated and measured secondary currents a Compensated secondary current b Measured secondary current

Error analysis for a fault at 0" and primary time constant of

;-" 4 t

-4 7 19.01 52.34 85.68 119.01 152.34

time, ms Fig. 17 200ms: ratio error

Error analysis for a fault at 0" and primary time constant of

4.3 Error analysis for differing sampling frequencies The technique presented herein is based on the trape- zoidal rule for calculating the integration of eqn. 3 , essentially to reduce the load of calculation. As the slope of the magnetisation curve in the saturated region is very small, small errors of flux calculation cause large errors when the magnetising current is obtained

IEE Proc.-Electr. Power Appl., Vol. 143, No. I , January 1996

from the magnetisation curve. Thus the performance of the algorithm is dependent on the accuracy of the flux calculation. As the error is increased in proportion to the time step according to the trapezoidal rule, error analysis was performed for several sampling frequen- cies in the case of a 0" fault with the primary time con- stant of 20ms, and the results are shown in Figs. 18 and 19. It is apparent from the results that the accu- racy of the secondary current is nearly identical for sampling based on either 64 or 128 samples per cycle. However, the error is doubled to nearly 3% when 32 samples per cycle are employed; this would be expected because of the large numerical errors introduced in the use of the trapezoidal rule for a low sampling fre- quency.

1

3 4 t

I -41 1 I

18.23 51.56 84.90 118.23 151.56 time,ms

Fig. 19 128 sample/s

Ratio errors for a 0" fault with primary time constant of 20ms at

4.4 Error analysis with remanent flux As mentioned in Section 1 the presence of remanent flux makes the avoidance of CT saturation more diffi- cult, and there are several conditions that may leave behind remanent flux in CT cores. For example, fault clearance may leave behind a large remanence in the core; on autoreclosure thereafter, the CT could present a distorted secondary current. Thus, to ascertain the performance of the proposed algorithm, two examples of reclose operation (assuming a permanent fault) were chosen to perform error analysis with remanent flux (primary time constants in both the cases being 200ms), and their results are presented in Figs. 20-26.

For a 90" fault, there is no DC component and the CT is not saturated before the clearance of the fault, as shown in Fig. 22. After clearance, there exists a rema- nence in the core and its value is 1.9Vs (57% rema- nence) at the instant of reclosure (Fig. 21), which causes the CT to saturate after reclosure. However, the algorithm successfully compensates the distorted sec- ondary current and the errors are small, as shown by Fig. 23 (4 1.5%).

For a 0" fault, the core flux is so large that the CT is saturated before fault clearance. After clearance, the core flux decays to 3.17Vs at the instant of reclosure, which contributes a very significant remanence (94Y0). The CT is saturated after reclosure as well as before clearance of the fault. Moreover, in this case, when the fault is cleared and the primary current becomes zero, a unidirectional transient current (depending on the core

45

flux at the instant of fault clearance) flows in the sec- ondary (Fig. 26); this may delay the reset of very sensi- tive high-speed overcurrent relays utilised in breaker- failure protective schemes. However, the proposed algorithm is effective in compensating the very highly distorted secondary current arising as a result of severe CT saturation, again as shown by Fig. 26.

I 1

19.01 52.34 85.68 119.01 152.34 time, ms

Fig.20 Error analysis with remanentjlux for fault at 904 primary time constant of Zooms, fault clearance at 62ms and reclosure at I37ms: pri- mary current

4 m :- 2 3 - .,..

0

-2 19.01 52.34 85.68 119.01 152.34

time,ms Fig.21 Error analysis with remanentjlux for fault at 904 primary time constant of 200ms, fault clearance at 62ms and reclosure at 137ms: core flux

100 2 50 F O 2 -50

-100 -1501 I

time,ms 19.01 52.34 85.68 119.01 152.3L

Fig.22 Error analysis with remanent flux for fault at 90: primary time constant of 200ms, fault clearance at 62ms and reclosure at 137ms: com- pensated and measured secondary currents a Compensated secondary current b Measured secondary current

4 s $ 2 $ 0 0 LI -2 F

-4 19.01 52.34 85.68 119.01 152.34

t ime,ms Fig. 23 Error analysis with remanent flux for fault at 904 primary time constant of 200ms, fault clearance at 62 ms and reclosure at 137ms: ratio error

time,ms Fig.24 Error analysis with remanent flux for fault at 09 primary time constant of 200ms, fault clearance at 48 ms and reclosure at 137ms: pri- mary curi'ent

46

19.01 52.34 85.68 119.01 152.34 time,ms

Fig.25 Error analysis with remanent flux for fault at OD, primary time constant of 200ms, fault clearance ai 48 ms and reclosure at 137ms: cole frux

i 1 19.01 52.34 85.68 119.01 152.34

time, ms Fig.26 Error analysis with remanent flux for fault at 04 primary time constant of 200ms, fault clearance at 48 ms and reclosure at I37ms: com- pensated and measured secondary currents a Compensated secondary current b Measured secondary current

The results of the above two studies clearly show that the proposed algorithm correctly estimates the correct secondary current even though there exists high rema- nent flux in the core.

4.5 Error analysis with small CTs As the algorithm compensates the distorted secondary current even in the saturated region, it can estimate the secondary current corresponding to the CT ratio even when a small CT is used resulting in more severe satu- ration. To prove this, a C200 (2000:5, R, = 0.56452) CT whose core cross-section is one-quarter of that of a C800 CT, is used in the same model system. A resistive inductive of value (1 + j1.7) f2 is used as a load of the C200 CT and the hli curve of the C200 is shown in Fig. 27. In this case the point of value (2.0 A, 0.713Vs) on the curve is selected as the saturation point of the C200 CT to generate the hysteresis characteristic using HYS- DAT.

t

X - 3 saturation point (2.0 A , 0.7 13 Vs) *

magnetising current Fig.27 V i curve of C200 CT

In exactly the same manner as in the previous cases, at every sampling interval, the proposed algorithm esti- mates the secondary current corresponding to the CT ratio using the hli curve in Fig. 27 and the ratio error of eqn. 9 is evaluated.

IEE €'roc.-Electr. Power AppL, Vol. 143, No. I , January 1996

To compare the results for the C800 and C200 CTs, the following three case studies were performed for the same conditions as in the previous studies except for the CT size. Figs. 28-35 show the results.

801 1

6 6o

$ 0

=. 40 = 20 E!

-20 -4 0

U

-601 I 19.01 52.34 85.68 119.01 152.34

time,ms Fig.28 time constant of 20ms: primary current

Error analysis with the C200 CT for fault at 0" and primary

1.61 1

2 0.8

- 0

X 3 -

-0.81 I 19.01 52.34 85.68 119.01 152.34

time,ms Fig.29 time constant of 20ms: coreflux

Error analysis with the C200 CT for fault at 0" and prinzary

200

- 100 6 L C E 5 0

-100 I 1

19.01 52.34 85.68 119.01 152.34 t i m e , m s

Fig.30 time constant of 20ms: compensated and measured secondary currents a Compensated secondary current b Measured secondary current

Error analysis with the C200 CT for fault at 0" and primary

z 4t

I I 19.01 52.34 85.68 119.01 152.34

time,ms Fig.31 time constunt of 20nzs: ratio erroi

Error analysis with the C200 CT for ,fault at 0" and primary

200

; 100

5 0

-1 00 I I

19.01 52.34 85.68 119.01 152.34 time, ms

Fig.32 time constant of 200ms: compensated and measured secondary currents a Compensated secondary current b Measured secondary current

IEE Proc.-Electr. Power Appl., Vol. 143, No. 1, January 1996

Error analysis with the C200 CT for fault at 0" and primary

s 4t

19.01 52.34 85.68 119.01 152.34 time, ms

Fig.33 time constant of 200ms: ratio error

Error analysis with the C200 CT for fault at 0" and primary

150

100 50

g o -50

-1 00

19.01 52.34 85.68 119.01 152.34

Fig.34 Error anulysis with the C200 CT for fault at 90" and primary time constant of 200 ms with fault clearance at 62ms and reclosure at 137ms: compensated and measured secondary currents a Compensated secondary current b Measured secondary current

time,ms

1

19.01 52.34 85.68 119.01 152.34 time, m s

Fig.35 Error analysis with the C200 CT .for fault at 90" and primary time constant of 200ms with fault clearance at 62ms and reclosure at 137ms: ratio error

The first case is a 0" fault with the primary time con- stant of 20ms; these are the same conditions as those used for evaluating the results shown in Figs. 6-9. As expected, since the load of value (1 + j1.7) C2 is used, the core flux is also nearly one-quarter of that shown in Fig. 7. Since a smaller CT is used, the CT core reaches saturation faster and the degree of saturation is more severe than was the case for the corresponding much larger C800 CT, as shown by Fig. 30. However, the proposed algorithm accurately estimates the secondary current and the errors for the estimated secondary cur- rent are again small and comparable with those for the C800 CT, as shown by Fig. 31 (2 1.5%).

The second case is a 0" fault with the primary time constant of 200ms; these conditions correspond to the results shown in Figs. 16 and 17. As a smaller CT is used, the time constant is very large and the DC com- ponent is so high that the degree of saturation is much more severe than in the previous case. The algorithm, however, successfully compensates the distorted sec- ondary currents even for such an extreme case and the errors are again small (2 2.5%).

The third case is a 90" fault with the primary time constant of 200ms, which correspond to the conditions used for the results shown in Figs. 20-23. Here, in marked contrast to the situation with the C800 CT, for which there was no saturation, the CT is saturated before clearance as a direct consequence of a smaller CT being employed in this case (Fig. 34). After clear-

41

ance of the fault, there exists a remanence in the core and its value is 0.568Vs (80% remanence) at the instant of reclosure, which is again larger than in the previous example with the C800 CT, again causing CT satura- tion. The algorithm successfully compensates the sec- ondary current (Fig. 34) and the errors offered are small and identical to those in the previous case of (2800, as shown by Fig. 35 (I 1.5).

The results of the foregoing three cases indicate that the proposed algorithm successfully estimates the sec- ondary current corresponding to the CT ratio even though a smaller CT is used, resulting in a higher severity of CT saturation than in the previous cases; it is thus apparent that the proposed algorithm can be employed very effectively in applications in which, owing to economic and/or physical constraints, smaller size CTs have to be used.

a~dware implementation

As mentioned in Section 2.3, the algorithm can be implemented in real time. To prove this, prototype hardware has been implemented and tested by using a TMS320C digital signal processor. Fig. 36 shows the block diagram of the hardware implementation using the TMS320C. The three-phase analogue currents con- verted from the EMTP output data using the program- mable transmission line (PTL) are injected into the TMS320C.

display

U Fig. 36 ital signal processor BIO: branch inpuffoutput EOC: end of conversion EVM: evaluation module INT: interrupt

Block diagram of hardware implementation using TMS32OC dig-

LPF: lowpass filter MUX: multiplexer PC: program counter SIH: sample and hold

To compare the results of the hardware implementa- tion and simulation, two cases were chosen, and their results are shown in Figs. 3740; these cases are for a 0" fault with the primary time constants of 50ms and 200ms, respectively. The complete compensating algo- rithm for three-phase secondary currents is executed in real time on the digital processor in approximately 6 3 p ; this corresponds to 24% of the duty cycle of the processor based on the sample period of 2 6 0 ~ ~ i.e. 3.8kHz (this is the sampling frequency used here). This effectively means that, in practice, the time required to implement the main relaying functions within the hard- ware, in conjunction with this technique, would be more than adequate.

Figs. 37-40 shows the results of comparison of the simulation and hardware implementation. It is clearly evident from Figs. 38 and 40 that the outputs of the DSP are in close correspondence to those obtained from the CAD studies of Figs. 37 and 39. The small differences in the former case can be attributed to the hardware errors such as those due to quantisation etc. However, the limited number of real-time tests show

48

that the technique developed herein can be incorpo- rated into hardware as part of a digital protection relay.

LVV

Q 4 100 E 2 0

-1 00

19.01 52.34 85.68 119.01 152.34 time,ms

Fig. 37 Compensated and measured secondary currents of simulation and hardware implementation using TMS32010 digital signal processor for 0" fault with primary time constant of 20ms: simulation a Compensated secondary current b Measured secondary current

2 100 E 2 0

-1 00

1 65 129 193 257 321 sample point

Fig. 38 Compensated and measured secondary currents of simulation and hardware implementation using TMS32010 digital signal processor fo r 0" fault with primary time constant of 20ms: hardware implementation a Compensated secondary current b Measured secondary current

t I 200

? 1 5 100 L

7 O O

-1 00 1 19 01 52 34 85 68 11901 15234

t ime ,ms Fig. 39 Compensated and measured secondary currents of simulation and hardware implementation using TMS32010 digital signal processor fo r 0 a fault with primary time constant of 200ms: simulation a Compensated secondary current b Measured secondary current

2ooc n a I Q c = 100 I 0 0

-1 00

2

1 65 129 193 257 321 sampLe point

Fig. 40 Compensated and measured secondary currents of simulation and hardware implementation using TMS32010 digital signal processor for 0" fault with primary time constant of 200112s: hardware implementation a Compensated secondary current b Measured secondary current

6 Conclusions

This paper proposes a novel compensating algorithm for accurate measurement of the CT secondary current; it uses the hii curve of the CT and accurately estimates the secondary current corresponding to the CT ratio, in particular when the CT is saturated. In addition, it can successfully compensate the secondary current even when a smaller CT than the rated size is used, resulting

IEE Proc -Electr Power Appl , Vol 143, No I , January 1996

in secondary currents being more severely distorted. 7 References The results presented clearly demonstrate the ability of

the secondary current even when there is severe CT sat- the technique developed to provide good accuracy in 1 E.E., W E ” Z E.C.3 and ALLEN, D.W.: ‘Methods

for estimating transient performance of practical current trans- former for relaying’, IEEE Trans., 1975, PAS-94, (l), pp. 116- . -

uration, such as under large offset primary currents 122 2 IEEE Power System Relaying Committee: ‘Transient response of

current transformers’, ZEEE Trans., 1977, PAS-96, (6), pp. 1809- 1814

3 POWELL, L.J.: ‘Current transformer burden and saturation’, IEEE Trans., 1979, IA-15, (3), pp. 294-302

4 WRIGHT, A., and CHRISTOPOULOS, C.: ‘Electrical power system protection’ (Chapman & Hall, 1993)

5 IEEE Power System Relaying Committee: ‘Gapped core tran- former characteristics and performance’, IEEE Trans., 1990,

C.W., and PHILLIPS, F.: ‘Experimental evaluation of EMTP- based current transformer models for motective relay transient

and in the presence of remanent flux. Moreover, it is shown that it can be implemented into a digital-signal- processor hardware (such as T M S ~ ~ O C processor) as part of the main protective-relaying algorithm.

As the proposed algorithm estimates the correct sec- ondary current even when a CT is saturated, it can

faults, maximise the stability of relays for external 6 KEZUNOV*C, M.$ KoJoVIC, L.* ABUR, A.$ faults, and make it possible to use a CT with a reduced

improve the sensitivity of relays to low-level internal PWRD-5, (4), pp. 1732-1740

cross-sectional area. study’, IEEE Trans., 1994, PWRD-9, (15, pp. 405-413.

IEE Proc.-Electr. Power Appl.. Vol. 143, No. 1. January 1996 49