Differential equation based impedance measurement

Differential equation based impedance measurement for series-compensated lines E. Rosolowski

J. Izykowski

B. Kasztenny

M.M. Saha

Member, IEEE [email protected] Wroclaw University of Technology Wroclaw, Poland

Member, IEEE [email protected] Wroclaw University of Technology Wroclaw, Poland

Senior Member, IEEE [email protected] Wroclaw University of Technology Wroclaw, Poland

Senior Member, IEEE [email protected] ABB Automation Products AB Dept. TTD SE-72159 Västerås, Sweden

Abstract - Differential equation based digital algorithms for measurement of a fault loop impedance are studied in relation to their application for protective relaying of seriescompensated lines. Both, single and parallel arrangements of series-compensated lines are taken into consideration. Adaptation of the impedance measurement algorithms to the specific nature of transients in the relaying signals for the seriescompensated lines is presented. Correct measure of the distance to a fault is provided by incorporating the representation of the series-capacitor equipped with Metal-Oxide Varistor into the fault loop model. The algorithms were investigated for a variety of fault conditions. For this purpose the detailed ATP-EMTP models of the series-compensated lines have been developed and used for generating reliable fault data.

Keywords: transmission line, parallel lines, series compensation, digital relaying, fault loop impedance, differential equation I. INTRODUCTION

Series Capacitors (SCs) are installed on long transmission lines for achieving [1]: x increased transmittable power in considerably cheaper way than constructing a new extra line and what is nowadays of vital importance - without violating the environment,

x x x x

improved power system stability, reduced transmission losses, improved voltage control, power flow control more flexible. When a series compensated line suffers a fault behind its SCs, as seen from the relaying point, a fault loop considered by a distance relay contains, depending on type of fault, one or even two complexes of SCs and their overvoltage protecting arresters (Metal-Oxide Varistors (MOVs)). The presence of MOVs makes a fault loop strongly nonlinear and nature of transients of the signals is entirely different than for traditional lines. Moreover, the fault loop impedance measured in the steady state is not a strict geometrical measure of the distance to a fault. Also subsynchronous oscillations may occur under high resistance faults as well as the voltage and/or current inversion, what causes all traditional protection methods to fail. Enhancement of series-compensated line protection calls for development of the fault loop impedance measurement algorithms suitable for such the specific conditions. Both, the dynamic and the steady state features of the measurement as important for that are deeply investigated in this study. The considerations are limited to the single line and the parallel lines arrangements with the SCs installed in the middle (Fig. 1).

A

MOVs

a

a

a)

B

Air-gaps

CTs&AFs (F1)

CVTs&AFs

SCs

(F2)

RELAY

Air-gaps

AB

BB

MOVs CTs&AFs SCs

b)

Z 0m

a

Z 0m

a

Air-gaps MOVs CTs&AFs (F1)

CVTs&AFs

SCs

(F2)

RELAY

AA

Paper BPT99-316-16 accepted for presentation at the IEEE Power Tech '99 Conference, Budapest, Hungary, Aug 29 Sept 2, 1999

BA Fig. 1. Single line (a) and parallel lines (b) studied series-compensated networks

II. THE ATP-EMTP MODELS OF SERIES-COMPENSATED NETWORKS

Fig. 1 presents the one line schematic diagrams of the studied series compensated networks. A brief description of the key components in these circuits follows. The line: 300km, 400kV, 50Hz, compensated in the middle at the degree of 70% was considered for both the arrangements (Fig. 1a and Fig. 1b ). A cascade of fourports, each representing a 50km long line segment, were applied in modeling. The line impedances for the positive and zero sequence assumed the values: ZL1=0.315:/km, 85o; ZL0=1.0265:/km, 75o. Mutual coupling between the parallel lines (Fig. 1b) for the zero sequence was taken as: Z0 m Z L1 . A variety of conditions with respect to the supplying systems were considered. However, in all the tests presented in this paper, the impedances of the local (A) and remote (B) sources have been taken as identical and equal to: Zs1=Zs2=15:, 85o, Zs0=26.6:, 85o. The voltages at the remote source have been delayed by 10o with respect to the local source. The MOVs were modeled as non-linear resistors approximated by the standard voltage-current characteristic: i

§ v · P¨ ¸ © V REF ¹

q

(1)

The parameters of (1) assumed the values of q=23, P=1kA, VREF=150kV. Each MOV is protected from overheating by firing the corresponding air-gap by the thermal (overload) protection. The MOV protection was modeled as an energy-based function using the ATP-EMTP MODELS: the energy absorbed by the MOV is integrated and the MOV becomes shunted once this energy reaches its pre-defined limit [5]. Capacitive Voltage Transformers (CVTs), Current Transformers (CTs) and Analog anti-aliasing Filters (AFs) were modeled as well. The CVTs were represented by their 5th order linear models while the CTs were simulated taking into account their saturation branches. The AFs were represented by the 2nd order approximation with the cut-off frequency set at 1 / 3 of the sampling rate - assumed in this study at 1000 Hz. III. FAULT TRANSIENT Two different fault locations with respect to the SCs&MOVs position that cause considerably different phenomena are depicted in Fig. 1. The fault (F1) is considered as occurring in front of SCs&MOVs, while the fault (F2) as behind them as seen from the substation A. A. Faults in front of SCs&MOVs For faults in front of SCs&MOVs (F1), fault loops do not contain SCs&MOVs. Therefore, analogously to the case of traditional uncompensated lines, the fault loop is of the form of the resistive-inductive circuit (under negletion of line shunt capacitances). SCs&MOVs even placed outside fault loops, influence to some extent the fault loop impedance measurement by means of the remote line end infeed. It is worth to notice that the infeed has to be taken

into account for accurate fault location aimed at pinpointing the fault position for post-fault inspection and repairs of the line. On the other hand, for protection purposes the infeed effect is being usually neglected. This is especially justified for faults with low fault resistances. Generally, the faults in front of SCs&MOVs (F1) can be considered as not differing much from the faults on uncompensated lines. Therefore, fault loop impedance measurement under such the faults (F1) can be performed with the variety of algorithms dedicated for application in protective relaying of uncompensated lines [2]. B. Faults behind SCs&MOVs The substantial difference appears for faults behind SCs&MOVs (F2). In this case the type of a fault, in terms whether it is a phase-to-ground or a phase-to-phase, is important for considering the composition of a fault loop. For the phase-to-ground fault the fault loop contains the faulty segment of the line, one SC together with its MOV and the fault resistance. In the case of phase-to-phase faults, the fault loop impedance is being determined on the base of the fault current and the difference of phase voltages taken from the phases involved in a fault. Therefore, for phase-to-phase faults the fault loop contains two complexes of SCs&MOVs. Moreover, for any type of a fault the contents of a particular fault loop changes with passing of time due to the possibility of shunting the SC&MOV scheme by its air-gap. Involvement of SC&MOV or even two such complexes in the fault loop makes the fault loop a strongly nonlinear circuit. As a consequence of that, the nature of transients in the relaying voltage and current signals is completely different in comparison with the phenomena observed for traditional - uncompensated lines. The d.c. disturbances in the relaying signals do not appear at all. Both, voltages and currents are contaminated by the oscillations resulting from nonlinear operation of the MOVs. However, for low current faults the MOVs can operate almost linearly and the subsynchronous oscillations appearing in the relaying signals considerably disturb the measuring process [4]. Thus, measurement under faults behind SCs&MOVs (F2) requires modifications of the impedance measuring algorithms in both the dynamic and steady state aspects. Such the adaptation was presented in [4] where the linear R-L-C model of a fault loop was applied. However, the algorithm developed in [4] suits only for the completely linear cases with the subsynchronous oscillations in the relaying signals. Such the cases are relevant for the faults occurring close to the line far end through comparatively high fault resistances. For all the faults behind SCs&MOVs with moderate and low fault resistances the nonlinear operation of MOVs is observed and there is a need for taking into account such the behavior. IV. FAULT LOOP MODELS

Application of classical distance relays for protection of a series-compensated line is troublesome. Regardless the dynamic performance features, the new problem, related to the reach of a protective relay under faults behind SCs&MOVs arrives. In this case significant overreaching may take place what forces to set the first zone very short

and degrades the protection quality. This drawback results from the fact that the fault loop model applied for the classical distance relays (resistive-inductive circuit) does not match the case of a fault with SCs&MOVs in the fault loop. As a result of that, the determined apparent impedance of a fault loop is not a strict geometrical measure of the distance to a fault. Therefore, to resolve this problem, this paper proposes to base the distance relaying on the model of the fault loop which is adequate for those troublesome cases. Fig. 2. presents the models of fault loops for different locations and types of faults for the case of parallel lines. Note that the case of parallel lines as being more general is taken for consideration. The models of fault loops are derived under negletion of the line shunt capacitances what is justified for protection purposes. For faults in front of SCs&MOVs (Fig. 2a, b) the fault loop apparent impedance (R, X) is determined on the base of signals composed analogously as for uncompensated lines, namely:

i=ip h+k 0 i0 +k 0m i0 _ p a r a l

i=ip h 1-ip h 2

R

X

a)

b)

v=v p h 1-v p h 2

c)

R comp

ip h

Xcomp

vv

voltage (vph) and the signal (iph+ k0i0+ k0mi0_paral) being the phase current (iph) compensated for the zero sequence component of the faulted line (k0i0) and for the zero sequence component of the parallel healthy line (k0mi0_paral) are used, where:

v=vph

vph_comp k 0 i0 + k 0m i0 _ p a r a l

= / , = /

= P , = / i0 , i0_paral - zero sequence current from the faulted and from the healthy lines, respectively.

X

v=v p h

x for the phase-to-ground fault (Fig. 2a): the faulty phase

N

R

vv1

d)

N P

x Fig. 2d, in turn, presents the fault loop model for phaseto-phase faults occurring behind SCs&MOVs. In this case the resistive-inductive impedance of the fault loop (Rcomp, Xcomp) is determined with the voltage signal (vph1_comp-vph2_comp) being the difference of phase voltages but compensated for the voltage drops across the SC&MOV schemes, and currents from the faulty phases (iph1-iph2).

ip h 2 vv2

X comp

v p h 1 _ c o m p -v p h 2 _ c o m p

vph1

vph1_comp

i p h 1 -ip h 2 R c o m p

vph2_comp

the voltages (vph1-vph2) and in the currents (iph1-iph2), calculated for the phases involved in a fault, are used. For faults behind SCs&MOVs there are two cases, as shown in Fig. 2c and d, namely: x Fig. 2c presents the fault loop model for phase-toground faults occurring behind SCs&MOVs. The resistive-inductive impedance of a fault loop (Rcomp, Xcomp) is determined with use of the voltage signal (vph_comp=vph-vv), being the phase voltage from the faulted phase (vph) but compensated for the voltage drop across the SC&MOV (vv) from this phase and the signal (iph+ k0i0+ k0mi0_paral) being the phase current (iph) compensated for the zero sequence component of the faulted line (k0i0) and for the zero sequence component of the healthy line (k0mi0_paral).

vph2

x for the phase-to-phase fault (Fig. 2b): the differences in

ip h 1

Fig. 2. Models of fault loops for: a) phase-to-ground in front of SCs&MOVs, b) phase-to-phase in front of SCs&MOVs, c) phase-to-ground fault behind SCs&MOVs, d) phase-to-phase fault behind SCs&MOVs.

Thus, application of the models for faults behind SCs&MOVs (Fig. 2c and d) requires compensating the phase voltages (vph) for the voltage drop across SC&MOV (vv). In terms of the instantaneous quantities the compensation is performed as:

Y SK B FRPS

Y SK  YY

(2)

Since the voltage drops across the SCs&MOVs are not measurable at the relaying point, they have to be estimated. The estimation can be performed on the base of the phase currents and the parameters of the approximation for the voltage-current characteristic of the MOVs as in [3].

The other possibility of taking into account the presence of SCs&MOVs in the fault loops under the faults behind them relies in application of the fundamental frequency equivalenting of SCs&MOVs [5] - Fig. 3. The parallel connection of a fixed series capacitor and its nonlinear protecting resistor MOV (Fig. 3a) was represented for the steady state by the fundamental frequency equivalent (Fig. 3b). The equivalent is of the form of a series branch with the resistance RV and the reactance XV, both dependent on the amplitude of a fault current. Fundamental frequency currents and voltage drops denoted in the original scheme (Fig. 3a) and in the equivalent (Fig. 3b) match. V. DIFFERENTIAL EQUATION BASED IMPEDANCE ALGORITHMS

5

A. R-L model of the fault loop for faults in front of SCs&MOVs It was checked that fault loop impedance measurement under faults in front of SCs&MOVs can be performed with the variety algorithms dedicated for uncompensated lines. The differential equation based algorithms were taken into consideration in this study as they can provide fast settling time of the measurement and thus to fulfill the requirements imposed by the contemporary high speed digital relays. For the linear R-L model of the fault loop as in Fig. 2a and b the following differential equation stands: di( t ) Ri( t )  L v( t ) (3) dt where: R, L - fault loop resistance and inductance to be estimated, i(t), v(t) - fault loop current and voltage signals composed according to the fault type (Fig. 2a, b). C

a)

b)

Iv

Iv

MOV

Xv

Rv

Vv

Vv 40

Resistance, Reactance (:)

c)

Variety of digital implementations of (3) can be used, namely by applying: 1. Least Error Squares (LES) approach [4], 2. digitalization of (3) for the two consecutive sampling instants [2], 3. digitalization of (3) for the single sampling instant but in combination with decoupling the relaying signals into the orthogonal components [2]. Variety of digital representations of (3) can be originated since different digital differentiation rules as well filtration and pre-filtration techniques can be used. On the base of the extensive study [2] and its verification for the parallel line case, the third version from the above listed possibilities has been selected for usage:

G E  G  E D  G   D G 

Rv

(4)

1 1 a2 > is ( k )  i s ( k  1 )@ >ic ( k )  ic ( k  1 )@ 2 2 1 1 b1 b2 > v s ( k )  v s ( k  1 )@ > v c ( k )  v c ( k  1 )@ 2 2 1 1 d1 d2 >i s ( k )  is ( k  1 )@ > ic ( k )  ic ( k  1 )@ T T k - marker of the time instant, Z1 - radian fundamental frequency. The subscripts s, c in (4) denote quadratic (sine) and direct (cosine) orthogonal components. The half-cycle sine/cosine filters have been used to extract the orthogonal components of both current and voltage signals. B. Nonlinear R-L-C model of the fault loop for faults behind SCs&MOVs For the faults occurring behind SCs&MOVs (Fig. 2c and d) the following differential equation stands: di( t ) Rcomp i( t )  Lcomp v comp ( t ) (5) dt where: vcomp(t) - the classic relay input voltage but compensated for the voltage drop(s) across the circuit(s) of SC&MOV (Fig. 2c and d). Digital algorithm for the fault loop model (5) is analogous as for the R-L model (3). The only difference is that the coefficients involving the voltage signal from (4) are now:

E

0

D  E  D E Z D  G   D G  

a1

E

20

;

   

>

YFRPS B V  N  YFRPS B V  N   @ (6)

> YFRPS B F  N  YFRPS B F  N   @

-20

C. Linear R-L model with compensation for the nonlinearity of SC&MOV designed for faults behind SCs&MOVs

-40

Xv -60

-80 0

2000

4000

6000

8000

10000

Amplitude of Current Entering SC&MOV (A)

Fig. 3. Equivalenting of SC&MOV: a) the original scheme, b) the fundamental frequency equivalent circuit, c) the equivalent characteristic.

Estimating on-line the voltage drop(s) across the circuit(s) of SC&MOV and using (4) in connection with (6) makes that the nonlinear character of the fault loop is taken into account. However, there is a possibility of avoiding the estimation procedure. This can be accomplished by using the algorithm (4) (suitable for faults in front of SCs&MOVs) but with its adequate adaptation to the case of faults behind SCs&MOVs, what can be done with ap-

plying the fundamental frequency equivalent of the SC&MOV circuit. For the phase-to-ground faults the compensation procedure can be derived basing on the fault loop equation which in the phasor notation is of the form:  Rcomp

(7)

V ph  Z v (| I ph | ) I ph

Using the algorithm (4) one obtains the estimated impedance for the considered phase-to-ground faults as: V ph

(8)

I ph  k 0 I 0  k 0 m I 0 _ paral

Such the estimated impedance (R, X) (according to (8)) is not a measure of the distance to fault and thus, the following compensating procedure has to be accomplished:

§

· ¸ I ph  k 0 I 0  k0 m I0 _ paral ¸¹ I ph

Rcomp

R  real ¨¨ Z v (| I ph | )

X comp

§ · I ph ¸ X  imag ¨¨ Z v (| I ph | ) I ph  k0 I0  k 0 m I 0 _ paral ¸¹ ©

©

:



    



Fig. 4 and 5 illustrate the performance of the measurement for the parallel series-compensated lines. The phase-to-ground faults behind SCs&MOVs through fault resistance of 10: at the distance 0.5p.u. - just behind the SCs&MOVs (Fig. 4) and at 0.833p.u. line length (Fig. 5) are considered. Measurement of the two conditional impedances (without and with the compensation) together with the estimated equivalent (Rv, Xv) is shown.



;FRPS 5 ; 5FRPS



VI. EXAMPLES OF FAULT LOOP IMPEDANCE ESTIMATION

5HVLVWDQFH 5HDFWDQFH 







(10)

As a result of the compensation (9) or (10) the calculated impedance (Rcomp, Xcomp) provides adequate measure of the distance to fault and can be used for protection.

:



5HVLVWDQFH 5HDFWDQFH 

(9)

; 5 ;FRPS 5FRPS



§ Z v1 (| I ph1| ) I ph1  Z v 2 (| I ph 2 | ) I ph 2 · ¸¸ X  imag ¨¨ I ph1  I ph 2 © ¹

X comp

 jX comp  I ph  k0 I0  k0 m I 0 _ paral

R  jX

For phase-to-phase faults the compensation is: § Z v1 (| I ph1| ) I ph1  Z v 2 (| I ph 2 | ) I ph 2 · ¸¸ Rcomp R  real ¨¨ I ph1  I ph 2 © ¹

5Y 











;Y







3RVWIDXOW 7LPH PV







3RVWIDXOW 7LPH PV

Fig. 4. Fault loop impedance measurement under fault behind SCs&MOVs at the location: 0.5p.u.

; 5 ;FRPS 5FRPS



;FRPS





:



5HVLVWDQFH 5HDFWDQFH 

:

5HVLVWDQFH 5HDFWDQFH 



5



5FRPS



;

   





3RVWIDXOW 7LPH PV





5Y







;Y











  3RVWIDXOW 7LPH PV

Fig. 5. Fault loop impedance measurement under fault behind SCs&MOVs at the location: 0.833p.u.



Z Zcomp

%$ d=1

Reactance ( : )



d = ( 1 / 2 )-

d=5/6



d=4/6 d=2/6

d = ( 1 / 2 )+



d=1/6 



$$ 





Resistance ( : )



Fig. 6. Locations of the conditional impedances.

A number of fault conditions were simulated using ATP-EMTP and location of both the conditional impedances was studied. Fig. 6 shows as an example the locations of the impedances under phase (a) to ground faults applied at different locations on the line (d - distance in p.u.). The obtained picture of the locations is a solid base for development of the logic unit of the protective relay designed for series-compensated lines. VII. CONCLUSIONS

x

ATP-EMTP models of the single and the mutually coupled parallel series-compensated lines have been developed to generate reliable fault data for versatile testing of the impedance measuring algorithms. x Impedance measurement algorithms based on the differential equation technique suitable for seriescompensated lines were developed and investigated. The algorithms utilize two different fault loop models for the fault occurring in front of SCs&MOVs or behind them, respectively. For faults behind SCs&MOVs the compensation for the presence of SCs&MOVs in the fault loops is introduced. Fundamental frequency equivalenting is applied for that. x Locations of the estimated conditional fault loop impedances were studied for variety of fault conditions. VIII. REFERENCES [1] CIGRE SC-34 WG-04, „Application guide on protection of complex transmission network configurations”, CIGRE materials, August 1990 [2] E. Rosolowski, B. Kasztenny, J. Izykowski and M.M.Saha, "Comparative analysis of impedance algorithms for series compensated lines", Proceedings of the Power System Protection Conference, pp.21-26, 1996, Bled, Slovenia [3] F. Ghassemi, J. Goodarzi and A.T. Johns, "Method for eliminating the effect of MOV operation on digital distance relays when used in series compensated lines", Proceedings of the Universities Power Engineering Conference, pp.113116, September 10-12 , 1997, Manchester, UK [4] J. Izykowski, E. Rosolowski, M.M. Saha, L. Eriksson, "Study of transient simulation of series compensated network for investigation of digital protective relays", Proceedings of the Power Tech Conference, pp. 479-484, June 18-22, 1995, Stockholm [5] M.M. Saha, J. Izykowski, E. Rosolowski, B. Kasztenny, "A new accurate fault locating algorithm for series compensated lines", IEEE Trans. Power Delivery, vol.14, no. 3, July 1999, pp. 789-797

IX. BIOGRAPHIES Eugeniusz Rosolowski (M’97) was born in 1947 in Poland. He received his M.Sc. degree in Electrical Engineering from the Wroclaw University of Technology (WUT) in 1972 where he is presently an Associate Professor. From 1974 to 1977, he studied in Kiev Politechnical Institute from which he received his Ph.D. in 1978. In 1993 he received D.Sc. from the Wroclaw University of Technology. His research interests are in power system analysis and microprocessor application in power systems. Currently he is a Director of the Institute of Electric Power Engineering of WUT. Jan Izykowski (M’97) was born in Poland in 1949. He received his M.Sc. and Ph.D. degrees from the Wroclaw University of Technology in 1973 and in 1976 respectively. In 1973 he joined Institute of Electrical Engineering of the Wroclaw University of Technology where he is presently an Assistant Professor. His research interest are in power system protection, fault locators and transient phenomena of instrument transformers.

Bogdan Kasztenny (M'95, SM’98) received his M.Sc. (89) and Ph.D. (92) degrees (both with honors) from the Wroclaw University of Technology, Poland, where he is a faculty member of the Department of Electrical Engineering since 1989. In 1994 he was with Southern Illinois University in Carbondale as a Visiting Assistant Professor. During the academic year 1997/98 Dr.Kasztenny was with Texas A&M University as a Senior Fulbright Fellow, and then, till 1999 - as a Visiting Assistant Professor. Murari Mohan Saha was born in 1947 in Bangladesh. He received B.Sc.E.E. from Bangladesh University of Technology (BUET), Dhaka in 1968 and completed M.Sc.E.E. in 1970. In 1972 he completed M.S.E.E and in 1975 he was awarded with Ph.D. from The Technical University of Warsaw, Poland. He joined ASEA, Sweden in 1975 as a Development Engineer and currently is a Senior Research and Development Engineer at ABB Automation Products AB, Substation Division, Vasteras, Sweden. He is a Senior Member of IEEE, a Member of IEE and an individual member of CIGRE from Sweden. He is a registered European Engineer (EURING) and a Chartered Engineer (CEng). His areas of interest are measuring transformers, power system analysis and simulation, and digital protective relays.