Concepts of SVC Voltage Control
5.2 VOLTAGE CONTROL
5.2.4 Influence of the SVC on the System Voltage
5.2.4.1 Coupling Transformer Ignored The SVC behaves like a con- trolled susceptance, and its effectiveness in regulating the system voltage is dependent on the relative strength of the connected ac system. The system strength or equivalent system impedance, as seen from the SVC bus, primar- ily determines the magnitude of voltage variation caused by the change in the SVC reactive current. This can be understood [5] from the simplistic represen- tation of the power system and SVC shown in Fig. 5.2(a). In this representation, the effect of the coupling transformer is ignored and the SVC is modeled as a variable susceptance at the high-voltage bus. The SVC is considered absorbing reactive power from the ac system while it operates in the inductive mode.
The SVC bus voltage, VSVC, is given by Eq. (5.7). Linearizing Eq. (5.7)
150 CONCEPTS OF SVC VOLTAGE CONTROL
VSVC
(a) Power System
ISVC
ISVC1
SVC1 SVC2
ISVC 2
(c) SVC1 VSVC
SVC1 + SVC2
System Load Line
ISVC
B A
C e
SVC2
Controls Voltage SVC1
Controls Voltage SVC2
(b) SVC1
VSVC
SVC1 + SVC2
System Load Line
ISVC SVC2
Controls Voltage
B A e C
SVC2
SVC1 Controls Voltage
Figure 5.4 (a) Two parallel-connected SVCs at a system bus; (b) two SVCs in par- allel with differenceεin the reference-voltage setpoints without current droop; and (c) two SVCs in parallel with current droop and with differenceεin the reference-voltage setpoints.
VOLTAGE CONTROL 151 gives the variation in the VSVC as a function of change in the SVC current, ISVC. Thus for the constant-equivalent-source voltageVs,
DVSVCc−XsDISVC (5.8)
The VSVC is also related toISVCthrough the SVC reactance,BSVC, as follows:
ISVCcBSVCVSVC (5.9)
For incremental changes, Eq. (5.9) is linearized to give
DISVCcBSVC0DVSVC+DBSVCVSVC0 (5.10) SubstitutingDISVCfrom Eq. (5.10) in Eq. (5.8),
DVSVC
DBSVC c −VSVC0
ESCR +BSVC0 (5.11)
where the effective short-circuit ratio (ESCR) is defined as
ESCRc 1
(−DVSVC
/
DISVC)c 1
Xs cBs (5.12)
where Bs cthe equivalent system susceptance
5.2.4.2 Coupling Transformer Considered As shown in Fig. 5.5, the representation of the SVC coupling transformer creates a low-voltage bus con- nected to the SVC and the transformer reactanceXT is separated fromXs. The high-voltage side,VH, is then related to low-voltage side, VSVC, as
XS VH
BSVC ISVC
VSVC XT
Figure 5.5 Representation of the power system and the SVC, including the coupling transformer.
152 CONCEPTS OF SVC VOLTAGE CONTROL
VSVC
VH c 1
1+XTBSVC (5.13)
Linearizing Eq. (5.13) gives
DVSVC(1 +XTBSVC0) +VSVC0XTDBSVCcDVH (5.14) Substituting Eq. (5.14) and the expression VSVC0
/
VH0 from Eq. (5.13) in Eq.(5.11) results in DVH
DBSVC c −VH0
(ESCR +BSVC0) 冢11−+XXTTESCRBSVC0 冣 (5.15)
5.2.4.3 The System Gain The effect of the SVC on system voltage can also be evaluated in an alternate [11] (though approximate) manner, as follows in Eq. (5.16). Equations (5.7) and (5.9) can be combined to give
VSVCc Vs(1
/
BSVC)(Xs+ 1
/
BSVC)c Vs
(1 +BSVC
/
ESCR) (5.16)whereXs is the equivalent short-circuit impedance of the system in shunt with the capacitive reactance of SVC.
For ac systems, generally ESCR >> BSVC (or effectively, Xs << 1
/
BSVC).Thus Eq. (5.16) can be expanded as
VSVC⬵VS冢1− ESCRBSVC 冣 (5.17)
The change in SVC bus voltage,DV, is then given by
DVcVS−VSVC (5.18)
or
DVc VSBSVC
ESCR (5.19)
or
DVcKNBSVC (5.20)
where KN is defined as the “system gain” and is expressed as
VOLTAGE CONTROL 153
KN c VS
ESCR c VS
BS (5.21)
The system gain, KN, thus relates the deviation in SVC bus voltage to SVC susceptance. An increase in inductive susceptance,BSVC, causesDVto become more positive, thereby leading to a drop in the SVC bus voltage. In fact, Eq.
(5.20) can be obtained from Eq. (5.11) if it is assumed that
VSVC0⬵VS and ESCR>>BSVC0 (5.22)
and understanding that
DVc−DVSVC (5.23)
The foregoing derived expression for system gain can be used to arrive at a preliminary design of an SVC voltage regulator. However, it may, be noted that the system gain KN depends on the equivalent system voltageVSand equiva- lent impedance XS—both of which are subject to change with the dynamically varying power-system configuration. The gain KN is thus not a constant and, in fact, varies in a certain range. A weak ac system would correspond to a high system gain; a strong ac system would result in a relatively lower system gain.
Equation (5.21) was derived based on the absolute values of the various parameters involved. For control studies, it is desirable to derive a correspond- ing equation based on per-unit values of different variables. Let the base volt- age,Vb, and base susceptance, Bb, be chosen as
VbcVnominal (5.24)
where Vnominal cthe rated bus voltage
BbcBmax−Bmin (5.25)
where Bmax c the maximum susceptance of the SVC (fully capacitive) Bminc the minimum susceptance of the SVC (fully inductive) The per-unit system gain is therefore given from Eq. (5.21) as
KN c VS Vb
Bb
BS (5.26)
Multiplying and dividing Eq. (5.20) by V2b,
154 CONCEPTS OF SVC VOLTAGE CONTROL
KN c VS Vb
Bb BS
V2b V2b c VS
Vb
QSVC BSVSVb
Vb VS
(5.27)
or
KN c VSQSVC VbSc Vb
VS
(5.28)
where Scc the short-circuit power
c the base voltage . the short-circuit current c Vb. (BSVS)
AssumingVS
/
Vb is close to unity, which is usually the case in power systems, the per-unit system gain is expressed asKN c DVSVC
BSVC c QSVC Sc
pu (5.29)
It should be noted that the system gain will change with variations in network configuration, line switchings, and any event that may change the system short- circuit level at the SVC bus.