Calculation of Shunt Reactor Capacity in 400kV Power System Using EMTP

Hung-Sok Park*, Bong-Hee Lee*, Young-Seon Cho*, Sang-Ok Han**

Abstract A temporary over-voltage is an oscillatory phase-to-ground or phase-to-phase over-voltage that is relatively long duration and is undamped or only weakly damped. Temporary over-voltages usually originate from faults, sudden charge of load, ferranti effect, linear resonance, ferroresonance, open conductor, induced resonance from coupled circuits and so forth. The steady voltage at the open end of an uncompensated transmission line is always higher than the voltage at the sending end. This phenomenon is known as the ferranti effect, and it occurs because the capacitive charging current flows through the series inductance of the line. On an open line, over-voltages due to the ferranti effect are sinusoidal in nature. Shunt reactors are generally provided on long EHV transmission lines to limit over-voltages during the line energization, load rejection and under light load conditions. As examined in over-voltages due to Ferranti effect, 430km transmission line in Libya 400kV system needs application of shunt reactors to limit over-voltages during the line energization. The reactors are typically rated to compensate 50 to 90% of the line capacitance. For determining rating of shunt reactor, we have studied the over-voltages at the open end of the planned 430km 400kV transmission line that is compensated by 60 to 80% through two line connected shunt reactors. Keywords: Compensation, EMTP, Ferranti Effect, MCOV, Shunt Reactor, (un)Transpose

1. Introduction There are many factors affecting temporary over-voltages that may be considered in insulation. In this paper, temporary over-voltages by Ferranti effect are analyzed to examine whether compensated reactors are required or not at the 400kV transmission lines in Libya.

The Ferranti effect is a phenomenon where the steady voltage at the open end of an uncompensated transmission line is always higher than the voltage at the sending end. It occurs as a result of the capacitive charging current flowing through the inductance of the line and the resulting over-voltage increases according to the increase in line length.[5][6][8]

To examine the temporary over-voltages due to the Ferranti effect, we assumed the following :

The voltage at sending end : 1.0 ~ 1.025 [p.u.] Transmission line is either transposed or untransposed MCOV(Maximum Continuous Operating Voltage) : 1.1 [p.u.] Line lengths as shown in Table I

Table I The lengths of transmission lines Section Length[km]

Case 1 Hooms - GMMA 430 Case 2 Hooms - Tripoli 119 Case 3 GMMA - Hoon 170 Case 4 Hoon - Gulf 298 Case 5 Misutra - Hooms 99 Case 6 Tripoli - EL Rwais 88.33

2. A Brief Review of Ferranti Effect

A long transmission line draws a substantial quantity of charging current. If such a line is open circuited or very lightly loaded at the receiving end, the voltage at receiving end may become greater than voltage at sending end. This is known as Ferranti Effect and is due to the voltage drop across the line inductance (due to charging current) being in phase with the sending end voltages. Therefore both capacitance and inductance is responsible to produce this phenomenon.[1][7]

The capacitance (and charging current is negligible in short line but significant in medium line and appreciable in long line by equivalent - model.[1]

* Overseas Project Section, Power System Construction Office, KEPCO, Korea.(parkhs@kepco.co.kr)

** Dept. of Electrical Engineering, Chung-Nam Natl University, Korea.(sohan@cnu.ac.kr) It is proportional to the square of lengths of lines, that is,

V kx2, where x is the length of line and k is a constant

for all voltage levels (actually, k 1/2 2LC, where, =2f, and LC is the propagation constant). This approximation is valid for lines less than about 500 miles in length.[2][3]

3. Result of Ferranti Effect Analysis

In this paper, Ferranti Effect analysis was performed by using the data of clause 4. Next four figures show the over-voltages due to Ferranti Effect for Libya 400kV Transmission line. These figures is classified by sending end voltage(1.0 or 1.025 p.u.) and transposed or not. And we could conform which section exceeded MCOV(Maximum Continuous Operating Voltage : 1.1 p.u.) in Table II.[5]

1.0001.0201.0401.0601.0801.1001.1201.1401.160

SEND 10 20 30 40 50 60 70 80 90 100Rate of distance[%]

P.U.

430km119km170km298km99km88.33km

( a) sending end voltage 1.0 p.u

1.0001.0201.0401.0601.0801.1001.1201.1401.160

SEND 10 20 30 40 50 60 70 80 90 100Rate of distance[%]

P.U.

430km119km170km298km99km88.33km

( b) sending end voltage 1.025 p.u

Fig. 1 The over-voltages due to Ferranti Effect of transposed line

1.0001.0251.0501.0751.1001.1251.1501.175

SEND 10 20 30 40 50 60 70 80 90 100Rate of distance[%]

P.U.

430km119km170km298km99km88.33km

( a) sending end voltage 1.0 p.u

1.0001.0251.0501.0751.1001.1251.1501.175

SEND 10 20 30 40 50 60 70 80 90 100Rate of distance[%]

P.U.

430km119km170km298km99km88.33km

( b) sending end voltage 1.025 p.u

Fig. 2 The over-voltages due to Ferranti Effect of untransposed line

Table II Results of Ferranti Effect Analysis

Section Length[km] Line

Condition

SendingEnd

Voltage[P.U.]

Open End

Voltage[P.U.]

1.025 1.137Untransposed 1.051 1.165

1.0 1.115Hooms GMMA

430 Transposed

1.025 1.1431.005 1.013

Untransposed 1.030 1.038

1.0 1.025Hooms Tripoli

119 Transposed

1.025 1.0331.041 1.058

Untransposed 1.067 1.0841.000 1.017

GMMA Hoon

170 Transposed

1.025 1.0421.015 1.066

Untransposed 1.040 1.093

1.0 1.053Hoon

Gulf 298

Transposed 1.025 1.0791.004 1.010

Untransposed 1.029 1.0351.000 1.006

Misutra Hooms

99 Transposed

1.025 1.0311.012 1.017

Untransposed 1.038 1.0421.000 1.004

Tripoli EL Rwais

88.33Transposed

1.025 1.030 As examined in over-voltages due to the Ferranti effect,

the 430km transmission line in the Libya 400kV system requires the application of shunt reactors to limit over-voltages during the line energization.[5]

4. Modeling of 400kV power system

The reactors are typically rated to compensate 50 to 90%

of the line capacitance. For determining the rating of the shunt reactor, we studied the over-voltages at the receiving end of the planned 430km Hooms-GMMA 400kV transmission line that is compensated by 60 to 80% through two line connected shunt reactors as shown in Fig. 3.

Fig. 3 Transmission line compensated by shunt reactors 4.1 Equivalent source

In the 400kV power system, to input line voltage 400kV

we calculated 400kV RMS peak voltage. 1.0 p.u. set 400kV RMS peak voltage (326.599kV) at sending end. By setting a 30 phase difference in sending and receiving an equivalent source, the 400kV system was able to pass the current.[4][5]

4.2 Equivalent impedance

Equivalent impedance used in this paper is provided by

PSS/E data for Libyan 400kV power system. Table II Equivalent Impedance(430km, 298km)

Equivalent Z [ohm] Transmission Line Length

[km] Sending end Receiving end

Z+ = 139.65

Z0 = 111.72

Z+ = 1478

Z0 = 1183 Z+ = 69.8

Z0 = 55.85

Z+ = 739

Z0 = 591.5430

Z+ = 34.9

Z0 = 27.925

Z+ = 369.5

Z0 = 295.75 Z+ = 519

Z0 = 415

Z+ = 519

Z0 = 415

Z+ = 259.5

Z0 = 207.5

Z+ = 259.5

Z0 = 207.5 298

Z+ = 129.75

Z0 = 103.75

Z+ = 129.75

Z0 = 103.75

4.3 Transmission line data a) Conductor and wire reference

Table III. Conductor and Wire

Conductor & Wire R in[] Rout []

Resis [ohm/km DC]

ACSR 410 Coot 0.18923 1.3208 0.1986 Overhead grounding wire 0.48 0.87 0.3

b) Tower reference

51.27m

41.27m

1.00m

6.28m

11.38m

Fig. 4 Tower model design in 400kV transmission line

4.4 Selection of Shunt Reactor Capacity a) Calculation 1

In 430km transmission line, line charge capacity QC = 279.6[Mvar], shunt reactor capacitor for compensating 100% (charge

capacity) is

QL = QC 1.0(100%) = 279.6[Mvar] If we install Shunt Reactor by two unit, capacity for one

unit QL' is

QL' = 279.6/2 unit = 139.8[Mvar] Shunt reactor for one unit become about 140 [Mvar]. Shunt Reactance is

Q = VI , V = XL I( I = V / XL)

according to above two formula

XL = V2 / QL' = (400kV)2 / 140 = 1142.86[].

b) Calculation 2

Shunt reactor capacity for compensating 80% (charge capacity) is

QL = QC 0.8 = 223.68[Mvar] QL' = 223.68/2 unit = 111.84[Mvar]

Shunt Reactor capacity for one unit becomes about

112[Mvar].

Q = VI , V = XLI ( I = V / XL) XL = V2 / QL' = (400kV)2 / 112 = 1428.571[].

c) Calculation 3

In 298km transmission line, line charge capacity QC = 186.4[Mvar], shunt reactor capacity for compensating 100% (charge

capacity) is

QL = QC 1.0(100%) = 186.4[Mvar] If we install Shunt Reactor with two unit, capacity for

one unit QL' is

QL' = 186.4/2 unit = 93.2[Mvar] Shunt Reactor capacity for one unit becomes about

93.2[Mvar]. Shunt Reactance is

Q = VI , V = XLI ( I = V / XL)

according to above two formula

XL = V2 / QL' = (400kV)2 / 93.2 = 1716.74[].

Like above calculations, if ratio of line charge capacity

compensation was 80%, 70%, 60%, shunt reactor capacity according to ratio of compensation would appear as in Table IV.

Table IV Shunt reactor capacity(430km, 298km)

100% 80% 70% 60%Shunt reactor compensate. line length[km] [Mvar]

430 140 112 98 84

298 93 75 65 56

5. Result of Analysis Fig.5 and Fig. 6 show the shunt reactor compensation of

over-voltages due to Ferranti Effect in transposed and untransposed Libyan 400kV transmission lines as

compensating 80% charge capacity, and show the Ferranti Effect with 1.0 p.u. and 1.025 p.u. at the sending end.

11.021.041.061.081.1

1.121.141.161.18

SEND 10 20 30 40 50 60 70 80 90 100Rate of distance[%]

P.U.

no compensation 80% 70% 60% Fig. 1 Compensated voltages at the open end of

untransposed line

11.021.041.061.081.1

1.121.141.161.18

SEND 10 20 30 40 50 60 70 80 90 100Rate of distance[%]

P.U.

no compensation 80% 70% 60% Fig. 2 Compensated voltages at the open end of

transposed line

Table V. Results for compensation when using shunt

reactors

T/L line Condition

Rating of compensation

Voltage at the

Sending End

Voltage at the

Open End1.025 1.137

No 1.051 1.165 1.020 1.061

60 1.046 1.088 1.020 1.050

70 1.045 1.076 1.019 1.038

Untransposed

80 1.044 1.064 1.000 1.115

No 1.025 1.143 1.000 1.039

60 1.025 1.065 1.000 1.027

70 1.025 1.053 1.000 1.016

Transposed

80 1.025 1.041

6. Conclusion

In this paper, we could confirm the over-voltage due to Ferranti Effect along the transmission line length. According to the reference[2][3], the length causing the over-voltage exceeding MCOV is refered about 500 mile(about 800km), but as a result of this paper the over-voltages exceeding MCOV could be caused in over 300km Libyan 400kV transmission line.

Generally in order to compensate the over-voltages due to Ferranti Effect, the shunt reactors are typically rated to compensate 50 to 90% of the line capacitance, but in this paper transmission line is compensated by 60 to 80% through two line connected shunt reactors.

References

Books: [1] A. Greenwood, "Electrical Transients in Power

Systems, 2nd ed., Rensselaer Polytechnic Institute , Electric Power Engineering Department, New York: John Wiley & Sons, INC, 1991, pp. 444.

[2] M. M. Adibi, A Web-Based Power System Restoration Tutorial, LESSON II, REV 1d ,Energizing High and Extra High Voltage Lines, Maryland, USA

[3] M. M. Adibi, A Web-Based Power System Restoration Tutorial, LESSON III, REV 2A ,Reactive Power Consideration, Maryland, USA

[4] Hermann W. Dommel, EMTP THEORY BOOK,Second Edition, April. 1996

Technical Reports:

[5] E. B. Shim and Y. W. Kang, "Insulation Coordination Case Study for General Electric Company of Libya, Interim Report, KEPRI., Dae-Jeon, Tech. Rep. Jan. 2005.

Papers from Conference Proceedings (Published):

[6] M. Swidan, M. Awad, H. Said, F. Rizk, Temporary Over-voltage Measurements in the 500/400kV Interconnection System, Proceedings of Cigre 1990 session, Paris, France, paper 33-103, 1990.

[7] E. Andersen, S. Bemeryp. S. Lindahl, Synchronous Energization of Shunt Reactors and Shunt Capacitors, CIGRE paper 13-12, 1988.

[8] C. P. Cunyi YU, The Effect of A Shunt Reactor on The Switching Over-voltages of 500 kV Transmission Lines: Case of EGAT 500 kV BSP-CBG-SNO-CHW Transmission Lines, 12CEPS1, PATTAYA, THAILAND, November 1998.