Operating Characteristic

Reactive-Power Compensators

3.6 THE FIXED-CAPACITOR–THYRISTOR-CONTROLLED REACTOR (FC–TCR)

3.6.2 Operating Characteristic

3.6.2.1 Without the Step-Down Transformer The operating V-I charac- teristic of an FC–TCR compensator is illustrated in Fig. 3.21. The fixed capac- itor extends the operating-control range of the SVC to the leading side as com-

THE FIXED-CAPACITOR–THYRISTOR-CONTROLLED REACTOR (FC–TCR) 65

TCR HV SVC Bus

Coupling

Transformer MV SVC Bus

Fixed Capacitors High-Pass Filter

Figure 3.20 An FC–TCR SVC.

pared to that shown in Fig. 3.17. The SVC current,I_SVC, can be expressed as a function of system voltage,V, and compensator susceptance,B_SVC, as follows:

I_SVCcVjB_SVC (3.25)

where

B_SVCcB_C+B_TCR and B_C cqC (3.26) Figures 3.21(b) and (c) show the operating characteristic and the susceptance of this type of compensator, respectively, and both also show that var production as well as var absorption is possible. By dimensioning the ratings of the TCR and the capacitor, respectively, the production and absorption ranges can be selected according to the system requirements.

3.6.2.2 With the Step-Down Transformer An FC–TCR SVC is usually connected to the high-voltage power system by means of a step-down coupling transformer, as shown in Fig. 3.22.

The Compensator Susceptance The compensator susceptance, BSVC, is given by

B_SVCc Bj(BC+BTCR)

B_j+B_C+B_TCR c 1 1+B_C+B_TCR

B_j

(B_C+B_TCR) (3.27)

where B_j is the susceptance of the transformer andB_TCR is variable from 0 to BL, according to the firing angles from 180⁸to 90⁸.

66 PRINCIPLES OF CONVENTIONAL REACTIVE-POWER COMPENSATORS

B_C

B_L I_SVC

(a)

Absorption Limit B_SVC = B_C+ B_L a = 90° Production Limit

B_SVC= B_C a = 180^°

V

Overload Range V_ref

Control Range Capacitive Inductive

(b)

a = 180^° B_SVC

(c) B_C

B_C+ B_L

B_TCR B_L

I_SVC V

a = 180° a= 90°

a = 90^°

Figure 3.21 The operating characteristics of an FC–TCR without a coupling trans- former.

From Eq. (3.27), the susceptance limits can be calculated. Susceptance at the production (capacitive) limit, that is, with B_TCR c 0at ac 180⁸, is expressed as

BSVC max c B_jBC

B_j+B_C (3.28)

Susceptance at the absorption (inductive) limit, that is, withBTCRcBL at ac 90⁸, is given by

B_{SVC min}c B_j(B_C+B_L) B_j+BC+BL

(3.29) It must be noted that B_L is a negative quantity. An analysis of Eq. (3.27) shows that the total susceptance B_SVC of the static var compensator does not change linearly withB_TCR. However, if (B_C

/

^{Bj)<<1and (BL}

/

^{Bj)<<1, which}

is usually the case, the nonlinearity is relatively small. This assumption implies that the reactance of the coupling transformer is greatly smaller than the reac-

THE FIXED-CAPACITOR–THYRISTOR-CONTROLLED REACTOR (FC–TCR) 67

Absorption Limit a = 90

°

Production Limit a = 180

°

I_SVC (pu) V (pu)

V_syst V₂

0.95 1.17

1.0 B_j

Capacitive Inductive (b)

B_SVC= B_jB_C B_j+ B_C

B_SVC= Bj(B_C + B_L) Bj + B_C + B_L B_C

B_L

(a) V₂

V_syst

a = 180^° a = 90^°

Figure 3.22 An FC–TCR with a step-down transformer and itsV-Icharacteristics.

tance of either the fixed capacitor or TCR. Equation (3.27) can then be approx- imated by a linear relation, as follows:

B_SVCc冢^{1− BBCj} 冣 ^BC+冢^{1− 2BCB+jBL} 冣 ^{BTCR (3.30)}

The susceptance limits based on the linearized equation (3.30) are

BSVC max c冢^{1− BBCj}冣 ^BC

B_{SVC min} c冢^{1− BCB+jBL} 冣 ^{(BC+BL) (3.31)}

The Transformer-Secondary Voltage The voltage at the secondary of the transformer is

V₂ cI_SVC 1

j(BC+BTCR) (3.32)

The I_SVCcan be expressed as a function of the system voltage V and the total compensator susceptance B_SVC using Eqs. (3.25) and (3.27), as follows. (Note that the secondary voltage is in phase with the system voltage.)

V2 cV B_j

B_j+B_C+B_TCR (3.33)

68 PRINCIPLES OF CONVENTIONAL REACTIVE-POWER COMPENSATORS

At the operating limits of the compensator, the following secondary voltages are found:

V2capcV B_j

Bj+BC −∼V冢^{1− BBCj} 冣 ^(3.34)

V2indcV B_j

B_j+B_C+B_L −∼V冢^{1− BCB+jBL}冣 ^(3.35)

A Practical Example Figure 3.22 gives typical data for an FC–TCR SVC scheme. The characteristic data at the boundaries of the operating range can be calculated from the previously deduced formulas. Note that for the calculation, a per-unit system is used with the following base quantities:

V_basecV_nom (the nominal system voltage)

QbasecQSVC cap (the reactive power at full production at Vnom)

The SVC current and the transformer-secondary voltage are calculated with the assumption that the system voltage is 1 pu.

Production Limit Absorption Limit B_SVCc1pu B_SVCc−0.3pu

ISVCc−1pu ISVCc0.3pu V2 c1.167pu V2 c0.95pu

Figure 3.22 shows the operating characteristic of the SVC with the data of the preceding table. The transformer-leakage reactance is in the range of 15%, and the production side of the compensator is about three times the rating of the absorption side, which can be considered typical. The figure also depicts the transformer-secondary voltage as a function of the total SVC current. It is interesting to note that the voltage has a negative slope if the SVC steady-state characteristic is considered flat. Figure 3.23 illustrates the susceptance charac- teristic. Both the exact characteristic from Eq. (3.27) and the linearized charac- teristic from Eq. (3.30) are displayed. The errors from linearization are clearly visible.

Losses A drawback of the FC–TCR SVC is the circulation of large currents in the FC–TCR loop needed for cancellation of capacitive vars. This results in high steady-state losses, even when the SVC is not exchanging any reactive power with the power system, as shown in Fig. 3.24. Typical losses in an FC–TCR scheme vary from 0.5% to 0.7% of the MVA rating. However, these losses can be min-

THE FIXED-CAPACITOR–THYRISTOR-CONTROLLED REACTOR (FC–TCR) 69

−1.2 −1 −0.8 −0.6 −0.4 −0.2 0

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

a = 90^°

a = 180^°

Exact Equation Linearized Equation

B_TCR (pu)

BSVC (pu)

Figure 3.23 Susceptance characteristics of an FC–TCR SVC with a step-down trans- former.

imized by switching the fixed capacitors through mechanical breakers, ensur- ing that the capacitors are inserted in the compensator circuit only when leading vars are needed. Thus a smaller-size–interpolating TCR can be used, and conse- quently, the steady-state operating losses can be reduced. Those FC–TCRs having a 300-MVA inductive rating have been already installed in the field.

Losses in

Capacitor and Filter

Power Losses

TCR Losses

Step-Down Transformer Losses SVC Reactive Power 1%

Figure 3.24 Losses in an FC–TCR. (Courtesy:The CIGRE.)

70 PRINCIPLES OF CONVENTIONAL REACTIVE-POWER COMPENSATORS

3.7 THE MECHANICALLY SWITCHED CAPACITOR–THYRISTOR-