Optimum compensation to improve line loadability

Electric Power Systems Research, 20 (1990) 73 - 80

73

Optimum Compensation to Improve Line Loadability G. DURGA PRASAD, S. H. JANGAMASHETTI and V. G. RAO Electrical Engineering Department, Indian Institute of Technology, Kharagpur 721 302 (India) C. S. INDULKARand S. C. TRIPATHY Electrical Engineering Department, Indian Institute of Technology, New Delhi 110 016 (India) (Received March 13, 1990)

ABSTRACT This paper presents 'optimum compensation requirement' (OCR) curves to select the optimum series and shunt compensation to be employed for different loading conditions of E H V A C transmission systems. The OCR curves enable improvements to be made to the system loadability from the points of view of compensation effectiveness, total compensation M V A R requirement, line voltage profile and efficiency of power transmission. The results are reported for three compensation schemes selected from the point of view of voltage stability. The OCR curves are also shown for voltages of 760 and 1100kV under different operating conditions.

Keywords: expansion planning, transmission expansion, utility application. INTRODUCTION Augmentation of power transfer capability of EHV AC transmission systems by the use of series and shunt compensation is well known [1- 4]. In transmission systems the role of this equipment is to reduce the series reactance and shunt susceptance of the lines artificially so as to improve the system stability and voltage control, increase the efficiency of power transmission, facilitate line energization and reduce temporary and transient overvoltages. For the planning and operation of long distance transmission systems, it is necessary to determine not only the most appropriate compensation schemes, but also the optimum degree of compensation to be employed for different loading conditions. 0378-7796/90/$3.50

Even though much work has been done in this area [5], information is not available on the optimum selection of series and shunt compensation to be employed for different loading conditions from the operation point of view. Furthermore, the optimum selection has to be in such a way that the total M V A R requirement is lower, the line voltage profile is well within the limits, the power transmission efficiency is high and the system stability is improved. In this paper a simple graphical way of selecting the optimum degree of series and shunt compensation from 'optimum compensation requirement' (OCR) curves is presented. Different compensation schemes of varying lengths, up to 1800 km, built on a modular basis by cascading a variable number of compensated line sections (1- 3) are considered. After examining various compensation schemes [1], three schemes were selected from the point of view of voltage stability. The results are reported for line operation at surge impedance loading and a line angle of 30% chosen from the point of view of stability, for three different transmission voltage levels of 500, 760 and 1100 kV. The O C R curves are also shown for 760 and 1100 k V under different operating conditions.

COMPENSATION SCHEMES AND LINE DATA Compensation schemes Various compensation schemes [1] were considered, but only three schemes were selected from the point of view of voltage stability. The transmission systems t h a t were considered to obtain the OCR curves are shown in Fig. 1; they are built on a modular © ElsevierSequoia/Printedin The

Netherlands

74

voltages are controlled to remain at the rated value; the power that can be transmitted over a given line will then be AVW ' 600

A2"~ 600

A3 • 600

BI~600

82 w~800

B3 • 600

C1~600

C2.600

C3~600

P = 0.5 V2/LXL

Fig. 1. Compensation schemes A, B and C for the transmission lines.

basis for lengths up to 1800 km by cascading the compensated line sections (1-3).

Line data The line data [6, 7] for different EHV transmission voltages, used for obtaining the OCR curves for all the compensation schemes, are given in Table 1.

(2)

From the above equation (2), it follows that when the length of the line increases for any given operating voltage, the power handling capacity of the line will decrease rapidly. In order to improve the line loadability of the surge impedance load (SIL), or an even greater load, the line must be compensated in such a way that the loading on the line is always made equal to the actual load. For a series and shunt compensated transmission line, the degree of series compensation is given by

K.~ = XclXL

(3)

and the degree of shunt compensation is given by

K.h = BriBe IMPROVEMENT OF LINE LOADABILITY

In this section certain fundamentals are reviewed for the sake of completeness and ready reference.

Mathematical approach The power that can be transmitted on an uncompensated line decreases with increasing distance [8]. The power handling capacity of a long EHV AC transmission line is given by P = V. Vr sin O/LXL

(1)

Normally, considering the transient stability, the line angle 0 is limited to about 30° and TABLE 1 Line data System voltage (kV)

f(Hz) r (~/km) l (mH/km) c (pF/km) g ~ D - 1 k m - 1)

X/R Z (D) SIL (MW)

500

760

1100

50.00000 0.02383 1.14524 0.01569 0.00105 15.09000 270.12000 925.49000

50.00000 0.01220 0.89763 0.01285 0.01910 23.11000 264.20000 2186.21000

50.00000 0.00299 0.72893 0.00108 0.00146 76.58000 258.80000 4675.42600

(4)

The effective impedance Z and admittance Y of a compensated line section are, respectively, Z = r + jwl(1 - K..)

(5)

Y = g + jwc(1 - K.h)

(6)

Accordingly, the compensated line characteristic impedance Zc and its corresponding surge impedance load Pc are

Zc = [~ + j-Jc°l(1~-~c( l ~-~,h) K~) j

(7)

and

(8)

Pc=

It can be seen from eqn. (8) t h a t the surge impedance load is a function of the degree of series and shunt compensation. Therefore, loading on the line can be improved by controlling the characteristic impedance of the line equal to t h a t of the load, and the corresponding power delivered in terms of the overall generalized constants [8] is given by

p, = Iv.I IVrl cost8 -IBI

_

V~2

IAII "1 costs -IBI

The line phase angle 0 can be obtained by equating the real part of Pc from eqn. (8) to the receiving-end power in eqn. (9), and is

75 given by

O -- fl - c°s- l[Pc ~ lAl 'Vl2 c°s(fl - °~) ll~--~121( Read line c~to and ~.ronsm;ssion System nf~rmatian

By taking the receiving-end voltage as the reference and the sending-end voltage as 170, the sending-end current I, and the receivingend current Ir can easily be derived as

Ir=(V~-AVR)/~//3B

(11)

1_8= (DV.

(12)

-

VR)/~/~ B

and the total MVAR requirement of the transmission system is given by

Qc, = 3.0Ic,2Xc,/2.0

(13)

and

s~ualrculate characteristic impedance Zc and ge irnpe.4qnce loading Pc eqn.(7) & (8)

L

Colculoie the overall ABCD c,onstants and the hne ong e B, eqn (10

~

the inlermediote voffages and currents I rn ABCD constan[s to ob~.oin Qcond QL! Create on output file : Ksh,Kse ' I~,p¢ ,Qc ,QL Nm~n ,Vma x,'l~ tr

QL = 3.0IL 2 X 2.0/Br

(14)

where Ic, is the total capacitor current and IL is the total inductor current. The efficiency of power transmission, which is the ratio of power received at the receiving end to the power injected at the sending end, is given by ~tr "~-(Pr/Ps)

L..__~Vory the degree of Series and shunt\'-> • compensation from 0 ~ to 100 ~ /

x

100

(15)

Implementation aspects Assuming the voltage magnitudes to be the same at both ends, the sending-end voltage angle can readily be obtained from eqn. (10). By using the generalized line constants the intermediate voltages and currents can be used to obtain the ratings of the total compensated series and shunt reactive power requirements. By varying the series and shunt compensation from 0 to 100% the values of line angle, power delivered, total MVAR requirement, voltage minimum and maximum and the efficiency of power transmission may be calculated for the improved line loadability condition: the compensated line characteristic impedance is made equal to that of the load. This will maintain flat voltage profiles and prevent undervoltages and normal frequency overvoltages. The sequence of computations for computer implementation to improve the line loadability is shown in the form of a simplified flowchart in Fig. 2.

RESULTS AND DISCUSSION The digital computer results are obtained by using the procedure described above,

O6toi, O.C.R. curves by plotting the contours of C'onstont power" and Line ang •

Fig. 2. Simplified flowchart for the OCR curves. shown in Fig. 2, for three different compensation schemes A, B and C of line lengths variable between 600 and 1800 km by cascading compensated line sections of 600 km each (as shown in Fig. 1). The results of the performance of the different compensation schemes in terms of series and shunt compensation, the MVAR requirement, the maximum voltage rise and the efficiency of power transmission are tabulated in Table 2 for an operating point of 100% surge impedance loading and line angle equal to 30 ° (chosen from the point of view of stability). From Table 2 it can be observed that the minimum and maximum voltages over the entire length of the transmission line are within the operating limits. Furthermore, when the length of the transmission line increases for the same power transmitted, the degree of series and shunt compensation to be provided increases, for the same transmission voltage level. Also, it can be observed that the degree of series and shunt compensation decreases with increase in the transmission voltage levels for the same length of line. When planning a long distance EHV AC power transmission line for a particular purpose, the results in Table 2 may be used to choose the best compensation scheme.

2

0.40 0.35 0.34

0.75 0.65 0.71

0.90 0.75 0.65

A 2 x 600 B 2 x 600 C 2 x600

A 3 x 600 B 3 x 600 C 3 x600

0.87 0.75 0.83

0.75 0.65 0.70

0.40 0.35 0.34

925 925 925

925 925 925

925 925 925

3454 2039 1540

1431 1080 1053

319 274 241

Qc

1863 1833 1218

1090 1028 1034

298 264 251

QL

604 579 625

535 546 585

504 511 535

Vmax

375 474 497

500 490 499

488 498 500

Vmin

77.4 64.5 82.6

87.7 89.8 89.4

94.5 94.8 94.9

~tr

0.78 0.70 0.75

0.64 0.58 0.60

0.20 0.20 0.18

Kse

0.78 0.70 0.75

0.64 0.58 0.60

0.20 0.20 0.18

2164 2184 2184

2164 2164 2184

2184 2184 2164

Pc

3855 3244 2531

1994 1732 1632

290 289 250

Qc

Ksh

Pc

Kse

K~

Voltage = 760 kV

Voltage = 500 kV

A 1 x 600 B 1 x 600 C 1 x600

Scheme (Fig. 1)

O p t i m u m compensation values for 100% surge impedance load and line angle 0 = 30 °

TABLE

3221 3101 2098

1778 1682 1681

290 281 252

QL

789 790 642

770 764 822

762 764 776

Vmax

691 751 759

721 758 759

756 759 759

90.1 91.1 91.8

93.7 94.0 94.6

96.9 96.9 98.8

Vmin ~tr

0.70 0.65 0.68

0.52 0.56 0.50

0.02 0.02 0.02

Kse

0.70 0.65 0.68

0.52 0.50 0.50

0.02 0.02 0.02

Ksh

4075 4675 4675

4685 4675 4675

4675 4675 4675

Pc

5582 4961 3253

2681 2526 2382

56 56" 49

Qc

Voltage = 1105 kV

5177 4995 3384

2574 2527 2467

49 49 49

QL

1100 1129 1162

1100 1115 1144

1100 1100 1101

Vmax

1065 1100 1100

1082 1099 1100

1099 1099 1105

Vmin

97.2 97.3 98.0

98.1 98.2 98.6

99.1 99.1 99.3

?~tr

77 1.0

1.0

P6p

..~

0.8

0.8 = ' ~

'° I

P,

u~

== t3.

0.6

0.6

0.4

0.4

0.2

0.2

y.,

E 0 u

un

Y

0

0 0.2

0 °/o

0.4

shunt

(a)

0.6

0.8

compensation

Scheme-

%

-'~4

O.

0 . 8 1.0 0.4 0.6 compensation

shunt

Scheme- C

Scheme- B

A

1.0 0.8

/k 0.2

0

0.8 12 0.2 0.4 0.6 % shunt compensation

0

1.0

o: 0+

L

r

0.6

E o

0,6

O.L

0,2

O.

¢#

0

0.4

0.2

0

0.6

0.8

1.0

0

Scheme - A 1.0

0.4

=/o s h u n t

o/= shunt compensation

(b)

0.2

O.g 1.0

0.6

0

compensation

Scheme- B

e]

E

0.6

0.6

0.6

I=l

0.4

0.41

0.4

0.2

0.2

0.2

~

0 0.2

0

%

= 0.4

0.8

0 0.2

0

1.0

%

shunt c o m p e n s a t i o n

(c)

e6

0 0.6

Scheme- A The f o l l o w i n g legend is f o l l o w e d

for

0.4

0.S

0,8

1.0

0

shunt compensation Scheme- B

compensated

power

0.2 %

0.4

0.6

0.8

1.0

shunt compensation Scheme- C

Pc and Line a n g l e 8

P1 = 250/0 of SIL

P4 = 100°1o of

SIL

e 1 = 10 °

e4

P2 = 5 0 %

of SIL

PS = 125=/°

of

SIL

02

= 20 °

0 5 = 50 °

P3 : 7 5 %

of SIL

P6

of

SIL

e 3 = 30 °

e G = 60 °

=150e/o

1.0

0. 8

9.8

0 ~t

13.8

6Z e=

0.8

P4

0.6

compensation

1.0 ele6

0

0.4

Scheme- C

1.0

•

8 ul

0.2

o/0 s h u n t

= 40 °

Fig. 3. O p t i m u m compensation requirement curves for 760 kV: (a) 1 × 600 kin; (b) 2 x 600 kin; (c) 3 x 600 kin.

The optimum compensation curves are shown for EHV transmission voltages of 760 and 1100 kV in Figs. 3 and 4, respectively, for all the systems considered. These OCR curves

are obtained stant power 100%, 125% loading and

by plotting the contours of condelivered for 25%, 50%, 75%, and 150% of surge impedance constant line angles of 10°, 20°,

78 0

1,0

"~ 0 s

8

O.B

o~0.6

6

0.6

u

0.4 2 o~

0.2

0-2 0

0

0

(a)

0

0

0.2 0./0.6 0.8 1.0 % shunt compensation

0.2

%

0.4

shunt

0,fi

0.8

1.0

0

compensation

0.2

0.4

=/o shunt

Scheme- B

Scheme- A

0.6

0.8

1.0

compensation

Scheme - C

1.0

1.0

0.8

0.8

E 0.6 O V

0,6

0.6

0.4

0.4

0,2

0.2

1,0

= o

0.2

p6. X

0.8

//~/n

o

0 0

0.2 0. 0.6 0.8 % shunt compensation

0

0,2

0

1.0

%

0,8

1.0

0.2

shunt compensation

Scheme- A

(b)

O.G

O.

0.8

0 8

0.6

0 6

0.6

,~ 0 . 4

0

0./~

0.2

0

0.t

0.0

0

0.2

% (c)

0.4

0.6

0.6

0

1.0

shunt compensation

81 ¸

012

II

0.4

=/o shunt

O.G

i

!

1.0

0.8

compensation.

0

0.4

0.2 %

Scheme- B

Scheme- A The f o l l o w i n g legend

.0

0.8

(

I/

G

0.8

1.0

I

0I

0.

Scheme- C

Scheme- B

1,0 -

i

0.4

% s h u n t compensation

0.6

0.8

1.0

shunt compensation Scheme - C

is f o l l o w e d for compensated powerPcand t h e a n g l e O

P1 : 25 °/o of

SIL

P/,

: 100 °/o of SIL

01 = 10 °

0/.

= 40 °

P2 : 5 0 %

of

SIL

P5

= 125%

of SIL

02 = 20 °

0 5 = 50 °

P3 : 7 5 %

of

SIL

P6 = 150%

of S I L

0 3 = 30 °

06

= 60 °

Fig. 4. Optimum compensation curves for 1100 kV: (a) 1 x 600 km; (b) 2 x 600 kin; (c) 3 x 600 km.

30 ° , 40 ° , 50 ° and 60 ° by v a r y i n g the degree of series and shunt compensation from 0 to

100%.

It can be seen from Figs. 3 and 4 that the optimum degree of series and s h u n t compensation to be e m p l o y e d for different power trans-

79 fer capabilities and operating line angles can easily be found for the respective transmission voltages. Also, from these curves, the line loadability can be increased easily, without sacrificing the stability margin, by changing the degree of compensation along the same operating line angle. For example, it can be seen from Fig. 4(b) for 1100 kV, 100% SIL, and a line angle of 30 °, that the optimum degrees of series and shunt compensation to be employed are both 50%. For this case, the line loadability can be increased from 100% SIL to 125% SIL by changing the degrees of series and shunt compensation to 61% and 38%, respectively, for the same stability limit line angle of 30 °. Finally, it can be concluded that the OCR curves can easily be obtained for any transmission voltage level, operation frequency, power delivery, length of line, and any type of compensation scheme. Furthermore, it can be observed from the OCR curves shown in Figs. 3 and 4 that the performance of the compensation scheme B is slightly better than that of the other schemes from the point of view of voltage stability and compensation requirements.

sation for any operating load condition in such a way that the M V A R requirement is a m i n i m u m and the efficiency of transmission is high. Furthermore, the curves can also be used to improve the line loadability without sacrificing the stability margin. These curves can easily be obtained for any type of compensation scheme of varying length, different transmission voltage, frequency and any value of the receiving-end voltage. NOMENCLATURE

A,B,C,D Bc Br C

/ g

Ic IL I.,Ir Kse

K~h CONCLUSIONS

This paper presents 'optimum compensation requirement' (OCR) curves to choose not only the best compensation scheme but also the optimum degree of series and shunt compensation to be employed for different loading conditions. The OCR curves are based on the principle that the compensated line impedance should always be equal to the actual impedance of the load. Thus, the voltage profiles are maintained well within the operating limits and the line loadability is improved. Three compensation schemes of different lengths up to 1800km are considered for transmission voltages of 500, 760 and 1100 kV. The optimum series and shunt compensation requirements are presented for an operating condition of 100% surge impedance loading and a line angle of 30 °. Also, the compensation curves are shown for transmission voltages of 760 and 1100 kV for different operating conditions. It can be concluded that the OCR curves will enable us to choose the optimum compen-

L l P

Pc P~ P~ Qc QL R r V

v~,v~ X

x~ x~ Y Z

z~

generalized circuit constants total line shunt capacitive susceptance, ~ - 1 total line susceptance of all shunt reactors, ~ - 1 line capacitance, #F/km frequency, Hz line conductance, #~1-1 km -1 total capacitor current, A total inductor current, A sending- and receiving-end currents, A degree of series compensation degree of shunt compensation length of line, km line inductance, mH/km uncompensated power delivered, MW surge impedance loading (real part of SIL), MW receiving-end power, MW power injected at sending end, MW total capacitive MVAR requirement total shunt MVAR requirement total line resistance, fl line resistance, ~ / k m line voltage, k V sending- and receiving-end voltages, k V total line series reactance, total line series capacitive reactance, total line series inductive reactance, f/ effective line shunt admittance, f/-1 effective line series impedance, f~ characteristic impedance, f/

80

~tr 09

angles of circuit constants A, B efficiency of transmission line angle, deg angular frequency, rad/s

REFERENCES i F. llliceto and E. Cinieri, Comparative analysis of series and shunt compensation schemes for A.C. transmission system, IEEE Trans., PAS-96 (1977) 1819- 1830. 2 E. W. Kimbark, A new look at shunt compensation, IEEE Trans., PAS-102 (1983) 212- 218.

3 E. C. Star, Discussion of 'A new look at shunt compensation', IEEE Trans., PAS-102 (1983) 218. 4 B. S. Ashok Kumar, K. Parthasarathy, F. S. P r a b h a k a r a and H. P. Khincha, Effectiveness of series capacitors in long distance tranmission lines, IEEE Trans., PAS-89 (1970) 941- 951. 5 IEEE VAR Management Working Group Report, Bibliography on reactive power and voltage control, IEEE Trans., PWRS-2 (1987) 361 - 370. 6 B. M. Weedy, Electric Power Systems, Wiley, Chichester, U.K., 3rd edn., 1987. 7 R. D. Begamudre, Extra High Voltage A.C. Transmis. sion Engineering, Wiley Eastern, New Delhi, 1987. 8 W. D. Stevenson, Elements of Power System Analysis, McGraw-Hill, Tokyo, 4th edn., 1987.