2006 International Conference on Power System Technology

Measured Impedance by Distance Relay Considering Double n: Model of the Line

Capacitance S. Jamali, Fellow, IEE, and H . Shateri, Member, IEE

Abstract-- This paper investigate the measured impedance by distance relay considering the transmission line capacitance by utilizing a double i~ model for the line. The distance relay ideal tripping characteristic is therefore presented. The measured impedance and the tripping characteristic are compared with those in the case of not considering the line capacitance. In the case of zero fault resistance, the deviation of the measured impedance from its exact value caused by the line capacitance is also investigated.

Index Terms--Distance protection, Fault resistance, Line capacitance, Measured impedance, Transmission line.

T HE measured impedance at the relaying point is the basis of the distance protection operation. There are several

factors affecting the measured impedance at the relaying point. Some of these factors are related to the power system parameters prior to the fault instance, which can be categorized into two groups. First group is the structural conditions, represented by the short circuit levels at the transmission line ends, whereas the second group is the operational condtions, represented by the line load angle and the voltage magnitude ratio at the line ends. In addtion to the power system parameters, the fault resistance could greatly influence the measured impedance, in such a way that for zero fault resistance, the power system parameters do not affect the measured impedance. In other words, power system parameters affect the measured impedance only in the presence of the fault resistance, and as the fault resistance increases, the impact of power system parameters becomes more severe.

An adaptive distance protection is introduced to solve the problems caused by presence of the fault resistance [2]. Since the fault resistance is an unknown parameter,, [2] presented an ideal tripping characteristic for &stance relays, for a definite range of fault resistance, e.g. 0-200 ohms.

References [3]-[5] discuss the adaptive &stance protection from various points of view. For example, [4] presented a fixed quadrilateral characteristic according to the ideal tripping characteristic. Applying the artificial intelligent techniques, [5]

The authors are with the Center of Excellence for Power Systems Automation and Operation, the Department of Electrical Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran, (e-mails: sjamali@iust.ac.ir, and shateri@iust.ac.ir).

tried to identify the boundaries of the ideal tripping characteristic presented in [2].

The effect of line capacitance is neglected in the all works reported in [I]-[5], though some considered the line capacitance in the short circuit impedances at the line ends. Therefore, either the line capacitance is neglected, or the line capacitive current which flows through the distance relay current transformers is neglected. This paper intends to investigate the validity of t h~s assumption by considering the line capacitance in the impedance measurements while changing the power system conditions.

11. MEASURED IMPEDANCE AT RELAYING POINT AND LINE CAPACITANCE CONSIDERATION

In the case of zero fault resistance, the measured impedance by distance relay is the exact impedance of the line section between the fault and the relaying points. According to Fig. 1 this impedance is equal to pZIL, where p is per unit length of the line section between the fault and the relaying points, and ZIL is the line positive sequence impedance in ohms.

L - Fig. 1. Equivalent circuit f i r single phase to earth fault

For a non-zero fault resistance, the measured impedance at the relaying point is not equal to the mentioned magnitude. In this case, the structural and operational conditions of the power system affect the measured impedance. The operational conditions prior to the fault instance can be represented by the load angle of the line, 6, and the ratio of the voltage magnitude at the line ends, h, or in general EB / E A = he"'. The structural conditions are evaluated by the short circuit levels at the line ends, SsA and SsB. With respect to Fig. 1 and Fig. 2, the measured impedance at the relaying point can be expressed by the following equations. More detailed calculations can be found in [2].

1-4244-01 11-9/06/$20.0002006 IEEE.

I I I

Fig. 2. Equivalent circuit of phase A to ground fault

It can be seen that for zero fault resistance, the measured impedance at the relaying point is equal to the impedance of the line section located between the relaying and the fault points. As it can be seen from (l l ) , the power system conditions only affect the measured impedance in the presence of fault resistance.

A double .n model is utilized for considering the transmission line capacitance as shown in Fig. 3.

to pYlL/2, while for the far section th~s quantity is (I-p)YlL/2. Combining the two shunt branches at the fault point, the admittance of t h~s branch is YlL/2. With respect to Fig. 3, a new set of equations are applied:

ZlA = PZlL + 221,

2 + PZ1,YlL (12)

221, Z'IB = ( 1 - PPIL + + - p)z

ISB IL (13)

2 1 , = 22'1,

2 + z 'm YlL (14)

220, ZOA = P ~ O L + 2+pz

0 , OL (15)

ZOB = (1 - P)ZOL + 220,

2 + ( 1 - P)ZO,YOL (16)

Z , - 2 Z I A ~ I B + Z O A ~ O B 2 1 , + z l B ZoA + z o B

(17)

cl = z l B

' l A +'IB (18)

2 CIA =

2 + PZ1,YlL (19)

2 X

2 ClB =

2 + ( 1 - P)Z,,Y~L 2 + 2'1, YlL (20)

Fig. 3 . Equivalent circuit for single phase to earth fault considering line capacitance with double K model

The system of Fig. 3 includes three additional shunt branches, compared to Fig. 1. The fault point divides the line into two sections. Each line section is molded by a .n model. In the near section, the admittance of the shunt branches is equal

It can be seen that in (29), unlike (1 l), the fault resistance is not the only factor causing the measured impedance deviation. Here, even for zero fault resistance, the measured impedance might deviate from its actual value, due to the line capacitance. This somehow depends on the power system conditions and the line length.

Knowing the structural and operational conditions, i.e. the short circuit levels, the load angle, and the voltage ratio, the distance relay ideal tripping characteristic can be defined. This characteristic has four boundaries. First boundary is the measured impedance for zero fault resistance; fault location varies from near end up to the far end of the line. In the second boundary, the fault point is at the far end; fault resistance varies between 0 and 200 ohms. Third boundaly is the result of the fault point variation along the line for the fault resistance of 200 ohms. Forth is achieved by variation of the fault resistance between 0 and 200 ohms for the faults on the near end of the line. Setting distance relay operational characteristic to t h~s one, the relay would not mal-operate.

The tripping characteristic of a distance relay is presented for a practical system. A 400 kV transmission line with the length of 300 km has been used in t h~s study. The various impedances of the line are as follow:

RIL = 0.0301 Q/km XIL = 0.3 178 Q/km RoL = 0.2269 Q/km XoL = 0.7057 Q/km YlL=3.5117 pSkm YoL = 2.9745 pSkm Fig. 4 shows the tripping characteristic when the short

circuit levels at Buses A and B are 20 and 10 GVA, the voltage ratio is 0.96, and the load angle is equal to 16'. The obtained characteristic without considering the line capacitance is also plotted in the dotted form for comparison.

110

0 50 100 150 200 250 300 350 Rewtance, R (Ohms)

Fig. 4. Distance relay tripping characteristic

The characteristic impedance of the line is 9.03 + j 95.61. Considering the line capacitance, the measured impedance for the fault at the line far end with zero fault resistance would be equal to 9.94 + j 100.58. It is evident that both the measured resistance and reactance increase. The increase in the measured resistance, the measured reactance, and the magnitude of measured impedance are 10.04%, 5.2%, and 5.24%, respectively.

Fig. 5 shows the measured impedance characteristic with more details. The measured impedance for the fault points on the 0.1 to 0.9 of the line in the steps of 0.1 and resistance fault variation between 0 and 200 ohms are plotted in dotted form.

Rewtance, R (Ohms) Fig. 5. Detailed distance relay tripping characteristic

Fig. 5 indicates that moving from the near end to the far end, the &stance between the dotted lines varies, or in the other word, the increase in the measured impedance is a function of the fault point. For better observation, Fig. 6 shows the amount of increase in the measured impedance for the various fault points, in the case of zero fault resistance.

Lme Length, P @u) Fig. 6. Increase in measured resistance, reactance, and impedance magnitude

Here, the increase in the measured resistance, reactance, and impedance magnitude are shown by dotted, dashed, and full curves, respectively. It can be seen that the impedance deviation is a function of fault location. Because of different deviation of the measured resistance and reactance, the angle of the measured impedance varies as well as its magnitude.

IV. MEASURED IMPEDANCE VARIATIONS

Once the operational conditions of a power system has changed, for instance, due to load level changes, the load angle and the voltage ratio would vary. Otherwise, when a switching takes place in the network that changes the topology i f network; short circuit levels at the line ends would also vary. As operational or structural conditions of the network vary, the measured impedance would change. Therefore, the tripping characteristic of the line also would vary.

Fig. 7 shows the tripping characteristic for three &fferent power system operational conditions, with the same structural conditions as Fig. 4. In Fig. 7 , curve (1) is the tripping characteristic of Fig. 4. When the load angle increases from

16" to 22" and the voltage ratio decreases from 0.96 to 0.94, curve (2) would be resulted. On the other hand, when load decreases, curve (3) is resulted for 6 = 10" and h = 0.98.

:::I , , , , , , , \I -30

-40 0 50 100 150 200 250 300 350 400 450

Rewtqce,,R (Ohms Fig. 7. Tripping characteristic variation wtk changes in power system

It can be seen that as the power system conditions change, the tripping characteristic also varies. The amount of increases in the measured resistance, reactance, and impedance magnitude for above three conditions are presented in Fig. 8.

, , ,

0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 h e P (PU)

Fig. 8. Variation in amount of increase in measured resistance, reactance, and impedance magnitude, with changes in power system

It can be seen that as the power system loading varies, the amount of increases does not change considerably. Three curves are so close that it is hard to observe any discrimination.

Usually load angle and voltage ratio have a close relation with each other, since the former determines active load and the latter shows reactive power flow of a transmission line, knowing power factor is usually constant. Here, the effect of these factors on the boundaly fault resistance curve is discussed separately. In addition to the operational and the structural conditions are also considered.

A. LoadAngle

Once the load level of a transmission line increases, the load angle also increases, and vice versa. If power flow direction in a transmission line reversed, the sign of load angle is inversed. Fig. 9 shows the effect of the load angle variation on the tripping characteristic. Here, load angle takes the values 25", 15", 5", -5", -15" and -25".

-3000 1 -2000 -1000 0 1000 2000 3000 4000 5000

Res~stmdnce, R (Ohms)

Fig. 9. Tripping characteristic variation, load angle changes

It can be seen that as the load angles varies, the tripping characteristic changes considerably. In the case of negative load angles, the tripping characteristic is in crescent shape.

Fig. 10 shows the amount of increase in the measured resistance, reactance, and impedance magnitude. The load angles are the same as Fig. 9.

Lme Lepgth, P @u) Fig. 10. Increase in measured resistance, reactance, and impedance

magnitude, load angle changes

It can be seen that as the load angle decreases, changing from positive to negative value, the increase in the measured resistance increases. The amounts of increases in the measured resistance are 9.97%, 10.05%, 10.14%, 10.26%, 10.39%, and 10.53%. On the other hand, the increase in the measured reactance, decrease as the load angle decrease. The increases in the measured reactance are 5.21%, 5.19%, 5.18%, 5.17%, 5.17%, and 5.16%. The increase in the measured impedance magnitude varies similar to the measured reactance and is equal to 5.25%, 5.24%, 5.23%, 5.22%, 5.21%, and 5.21%.

B. Voltage Ratio

Variation of the voltage ratio of transmission line affects the reactive power flow through the line. The amount of reactive power flowing through the line increases as this factor decreases (for ratios lower than 1). If t h~s ratio is higher than 1, it means that the reactive power flow direction is inversed. In order to show the impact of voltage ratio, the magnitudes of 0.95, 1.00 and 11.05 are considered for this factor, while the other parameters are the same as Fig. 4.

-60 \ I -101 I

0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 400 Res?s@dpce, R ( O b s ) Rewtance, R (Ohms)

Fig. 11. Tripping characteristic variation, voltage ratio changes Fig. 13. Tripping characteristic variation, short circuit ratio changes

It can be seen that as the voltage ratio varies, the tripping It can be seen that as the short circuit level at the far end of characteristic changes, but it does not change as the case of the line varies, the tripping characteristic changes considerably load angle variation. and it approaches to a quadrilateral for low ratios.

Fig. 12 shows the amount of increase in the measured Fig. 14 shows the amount of increase in the measured resistance, reactance, and impedance magnitude for voltage resistance, reactance, and impedance magnitude for the above ratios of 0.95, 1.00, and 1.05. far end short circuit levels.

, , , , , , , ,

, , , , , , , , , ,

0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1

h e Lepgth, P (PU) Fig. 12. Increase in measured resistance, reactance, and impedance

magnitude, voltage ratio changes

It can be seen that as the voltage ratio increases, from 0.95 to 1.05, the measured resistance is less increased. The amounts of increases in the measured resistance are equal to 10.05%, 10.0 1%, and 9.97%. The increase in the measured reactance is also less, as the voltage ratio decrease. The increases in the measured reactance are 5.20%, 5.19%, and 5.19%. The increase in the measured impedance magnitude varies similar to the measured resistance and reactance. The measured impedance magnitude is equal to 5.24%, 5.24%, and 5.23%.

C. Structural Conditions

As mentioned, structural condtions are governed by short circuit levels at the line ends. There are two aspects about the short circuit levels at the line ends; their ratio and their magnitude. In order to study the effect of short circuit levels ratio at the line ends, the short circuit level of the far end is changed as other parameters are the same as Fig. 4. Fig. 13 shows the variation of the tripping characteristic for the far end short circuit levels of 50, 20, 10, 5, 1, 0.1, and 0.001 GVA.

0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1

h e P (PU)

Fig. 14. Increase in measured resistance, reactance, and impedance magnitude, short circuit ratio changes

It can be seen that as the short circuit level at the far end decreases, there is also less increase in the measured resistance also. The amounts of increases in the measured resistance are 10.04%, 10.04%, 10.04%, 10.04%, 10.02%, 10.00% and 9.97%. The increase in the measured reactance is reduced as the short circuit level decreases. The increases in the measured reactance are 5.20%, 5.20%, 5.20%, 5.19%, 5.18%, 5.17%, and 5.17%. The increase in the measured impedance magnitude varies similar to two previous cases and is equal to 5.24%, 5.24%, 5.24%, 5.24%, 5.22%, 5.21%, and 5.21%.

The other aspect of the short circuit levels is their magnitudes. In order to study th~s aspect, short circuit levels are assumed to be (200, loo), (20,lO) and (2,l) GVA, with the same operational conditions as before.

It can be seen that as the short circuit magnitudes vary, the tripping characteristic changes considerably approaching to a quadrilateral for low magnitudes, similar to the previous case.

Fig. 16 shows the amount of increase in the measured resistance, reactance, and impedance magnitude for the

mentioned short circuit magnitudes.

-101 I 0 50 100 150 200 250 300 350 400

Res~stmdnce, R (Ohms)

Fig. 15. Tripping characteristic variation, short circuit magnitude changes

-40 I 0 50 100 150 200 250 300 350 400 450

Rewtance, R (Ohms)

Fig. 17. Tripping characteristic variation, line length changes

, , , , , , ,

, , , ,,

0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1

Lme Length, P @u) Fig. 16. Increase in measured resistance, reactance, and impedance

magnitude, short circuit magnitude changes

It can be seen that as the short circuit magnitudes decrease, the increase in the measured resistance also reduces and for low magnitudes the measured resistance decreases, instead of increasing. The amounts of increases in the measured resistance are 10.80%, 10.04%, and 1.64%. The increase in the measured reactance, also decrease as the short circuit level decrease. The increases in the measured reactance are 5.30%, 5.20%, and 4.55%. The increase in the measured impedance magnitude varies similar to measured reactance and is equal to 5.30%, 5.24%, and 4.52%.

D. Line Length

The effects of the operational and structural condtions have been studied in the previous sub-sections. The line length cannot be considered as a variable parameter of lines, but to study the effective parameters, the line length is also considered.

Fig. 17 shows the tripping characteristic for the line lengths of 100,200,300, and 400 km.

It can be that as the line length increases, the covered region by tripping characteristic also increases in both resistance and reactance axis.

Fig. 18 shows the amount of increase in the measured resistance, reactance, and impedance magnitude for the mentioned line lengths.

0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1

Lme Length P @u) Fig. 18. Increase in measured resistance, reactance, and impedance

magnitude, line length changes

It can be seen that as the line length increases, the increase in the measured resistance, reactance, and the magnitude of impedance also increases. The amounts of increases in the measured resistance are 0.87%, 4.10%, 10.04%, and 19.39%. The increases in the measured reactance are 0.54%, 2.23%, 5.20%, and 9.65%. The increase in the measured impedance magnitude is equal to 0.54%, 2.25%, 5.24%, and 9.74%.

In this paper the measured impedance at the relaying point has been presented, considering the line capacitance in the form of double .n model. This impedance depends on the power system operational and structural conditions. The operational and structural conditions influence the tripping characteristic considerably, but they are not so effective on the measured impedance for faults at the far end of the line with zero fault resistance, only the magnitudes of the short circuit levels affect this value. On the other hand, line length is a critical parameter in the case of far end measured impedance deviation. The results have shown that the deviation of the characteristic impedance is considerable, in the range of 10% for a 400 km line, and it should be considered in the design of distance protection.

VI. REFERENCES

[l] Zhang Zhizhe, C. Deshu, "An adaptive approach in digital distance protection", IEEE Trans. Power Dehvery, vol. 6, no. 1, pp. 135-142, Jan. 1991.

[2] Y. Q. Xia, K. K. Li, A. K. David, "Adaptive relay setting for stand-alone digital distance protection", IEEE Trans. Power Dehvery, vol. 9, no. 1, pp. 480-491, Jan. 1994.

[3] S. Jamali, "A fast adaptive digital distance protection", in Proc. 2001 IEE 7th Internatlonal Conference on Developments In Power System Protection, pp. 149-152.

[4] Chang-Ho Jung, Dong-Joon Shin, Jin-0 Kim, "Adaptive setting of digital relay for transmission line protection", in Proc. 2000 IEEE Internatlonal Conference on Power System Technology, PowerCon2000, vol. 3, pp. 1465-1468.

[5] K. K. Li, L. L. Lai, A. K. David, "Stand alone intelligent digital distance relay", IEEE Trans. Power Systems, vol. 15, no. 1, pp. 137-142, Feb. 2000.

VII. BIOGRAPHIES

Sadegh Jamali, was born in 1956 in Tehran, Iran. He received his BSc from Sharif university of Technology in Tehran in 1979, MSc from UMIST, Manchester, UK in 1986 and PhD from City University, London, UK in 1990, all in Electrical Engineering. Dr. Jamali is currently an Associate Professor in the Department of Electrical Engineering at Iran University of Science and Technology in Tehran. Dr. Jamali is a Fellow of the

Institution of Electrical Engineers (IEE) and the IEE Council Representative in Iran. His field of interest includes Power System Protection and Distribution Systems.

Hossein Shateri, was born in 1979 in Karaj, Iran. He received his BSc and MSc from Iran

, University of Science and Technology in Tehran in r I 2001 and 2003, respectively a l l in Electrical

Engineering. He is currently worlung towards a Phd degree in the Department of Electrical Engineering at Iran University of Science and Technology (IUST) in Tehran, Iran since Sep. 2004 and the research assistant of Digital Power Svstem

Protection Lab. H. Shateri is a Member of the Gstitution of ~ l e k i c a l Engineers (IEE). His field of interest includes Power System Protection, and Distribution Systems Protection and Automation.