Design of the SVC Voltage Regulator

Concepts of SVC Voltage Control

5.2 VOLTAGE CONTROL

5.2.5 Design of the SVC Voltage Regulator

154 CONCEPTS OF SVC VOLTAGE CONTROL

KN c V_S Vb

B_b BS

V²_b V²_b c V_S

Vb

Q_SVC BSVSVb

V_b V_S

(5.27)

or

KN c V_SQ_SVC V_bS_c Vb

V_S

(5.28)

where S_cc 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 as

KN c DV_SVC

BSVC c Q_SVC 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.

VOLTAGE CONTROL 155

dc-Side Filters

Voltage- Magnitude Transducer

ac-Side Filters V_ac

SVC HV Bus

X_T

V_meas (pu)

per-unit TCR Conduction

B_TCR X_TCR B_CTSC

X_TSC B_TSC1

B_TSC2 B_TSC3 B_min

B_max V_ref (pu)

TCR−TSC Logic K_R B_TOT

1+sT_R

where

B_min= B_SVC at the TCR only B_max= B_SVC at all TSCs only B_TOT= B_max − B_min

− +

B_{SVC 0} V_e

B_CTSC

X_TSC B_CTSC

X_TSC Σ

+ Other Control Inputs

K_R= the static gain (full range for the voltage change of 1/K_R)

T_R= the regulator time constant

B_{SVC 0}= the net susceptance at the SVC HV bus B_TSC−^TOT

I_SVC

Figure 5.6 Basic elements of SVC voltage-regulation control with TSC.

KSLc the current droop (pu)

TRc the regulator time constant (s) An additional term-transient gain,K_T, is defined as

KT c K_R

T_R (5.31)

In the integrator–current-droop model, the voltage regulator is described as an integratorG′R(s), with the following explicit current-feedback loop:

G′R(s)c 1 sRR

(5.32) where R_R cthe response rate (ms

/

^pu)

The regulator time constant,TR, and the response rate,RR, are related as T_Rc R_R

KSL

(5.33) 5.2.5.1 Simplistic Design Based On System Gain This design method- ology, proposed in ref. [11], considers a proportional–integral (PI) controller with an explicit current feedback similar to that described in the previous sec- tion. This method is calledsimplisticbecause it models the power system by a

156 CONCEPTS OF SVC VOLTAGE CONTROL

(c) 1 sR_R V_SL

B_ref

K_SL V_meas V_ref ⁻

Σ

B_min B_max V_e

+

I_SVC

(b) 1

sR_R B_ref

V_SL

K_SL V_meas

V_ref ⁻

−

B_min B_max V_e

+ Σ

(a) V_meas

V_ref

B_ref K_R

1 + sT_R

− Σ

B_min B_max V_e

+

Figure 5.7 Alternate voltage-regulator forms: (a) a gain–time constant; (b) an integra- tor with susceptance-droop feedback; and (c) an integrator with current-droop feedback.

pure reactance or equivalent gain and does not account for the effect of genera- tor dynamics on controller performance. This method is, however, highly impor- tant, as it explains very clearly the influence of system strength and current- droop on the speed of controller response.

The block diagram of an SVC-compensated power system is shown in Fig.

5.8(a). It is assumed that

1. the change in system voltageDV caused by the SVC is small;

2. the SVC bus voltage is very close to the nominal-rated voltage, that is, VSVC⬵1pu; and

3. the variations in the SVC reference voltage are also quite small.

VOLTAGE CONTROL 157

V_ref Σ Measurement

H_I

Measurement H_V

Regulator

G_R G_Y

Y_C Y_L

I V Power System Disturbances Slope

K_SL

Vadd Variable Admittance

Y_Lmin < Y_L < Y_Lmax

Σ Σ

+ + − +

+ +

+

(a)

Variable Admittance Y_Lmin < Y_L < Y_Lmax

Σ

Measurement H_M

Regulator

G_R G_Y

Y_L= I_L

Power System G_N

Disturbances

+ Σ−

+ + V₀

V_Z Σ

+ −

V_ref

∆V

V_add

−

∆V

+

Slope K_SL

(b)

Figure 5.8 (a) A block diagram of the system voltage controller incorporating an SVC and (b) a simplified block diagram of the system voltage controller forV−∼Vrated.

Then, the currents I_L, in the TCR, and I_C, in the TSC, are given by IL cYLVSVC≈YL in pu (5.34) I_C cY_CV_SVC≈Y_C in pu (5.35) An equivalent circuit of the SVC-compensated system is depicted in Fig.

5.8(b). The following simplifications are made:

1. The voltage- and current-measurement systems are considered identical.

2. The TSC switchings are ignored, and the droop effect of the capacitive current is merged withVref.

158 CONCEPTS OF SVC VOLTAGE CONTROL

3. The only variable considered is the inductive currentIL, which reduces the system bus voltage by DV as given by Eqs. (5.18)–(5.20). The effect of constant-capacitive SVC current on the SVC bus voltage is incorporated in V0. The influence of any power-system disturbance,Vz, is neglected.

The thyristor phase control is denoted byGY, as already explained in Chapter 4, and is given by

GY(s)c e^{−s Td}

1+s T_Y (5.36)

where Tdc the thyristor dead time (cone-twelfth cycle time) TY c the thyristor firing-delay time caused by the sequential

switching of thyristors (⬵one-quarter cycle time)

A PI controller that gives the fastest stable response for the weakest system configuration having gainKNmax is determined [11] as

GR(s)cKp

{

^{1+ s T1Y}

}

^{c− 2(KSL+1KNmax)}

{

^{1+ s T1Y}

}

^(5.37)

The overall closed-loop transfer function, GW(s), of the control system for incremental variations is given by

G_W(s)c DV(s) DV_ref(s)

c K_NG_RG_Y 1+ (KSL+KN)GRGYHM

(5.38) where H_Mc the transfer function of the measurement system

To obtain the response time of the control system only, the largest time con- stants are considered. Thus

G_W(s)_⬵ KN

(K_SL+K_N) s TW

1+s T_W (5.39)

where

T_W c2冢^{KSLKSL++KNKNmax}冣 ^{TY (5.40)}

Hence for a change in the reference voltageDV_ref, the SVC bus voltage varies as

VOLTAGE CONTROL 159

DVc KN

K_SL+K_N DV_ref(1−e^−t/^TW) (5.41) The following conclusions are drawn from the foregoing analysis:

1. A change in the DV_ref causes the SVC bus voltage to vary by k . V_ref because of the current droop, wherekcK_N

/

^(KSL+KN).

2. The fastest response is obtained whenKN cKNmax (i.e., for the weakest system state). In this case, the response time constant,TWopt, is obtained from Eq. (5.40) asT_Woptc2T_yc8.33 ms for a 60-Hz system frequency.

The settling time (to 95% of the step change)_⬵3T_Wopt c 25 ms c 1.5 cycle time.

The voltage controller is expected to maintain stability under all reasonably realizable network configurations and to ensure a rapid response under those conditions. Hence the voltage controller is optimized for the lowest system short-circuit level.

Equation (5.36) can be rewritten as T_W

2TY c T_W

TWopt c K_SL+K_Nmax KSL+KN

(5.42) Dividing the numerator and denominator on the right-hand side byK_Nmax, we get

TW

T_Wopt c

K_SL KNmax

+ 1 K_SL

K_Nmax + K_N K_Nmax

(5.43)

From Eq. (5.29), it follows that

KNmaxc Q_SVC

S_cmin (5.44)

Substituting Eqs. (5.29) and (5.44) in Eq. (5.43) gives

TW

TWopt c

K_SL K_Nmax + 1 K_SL

K_Nmax +S_cmin S_c

(5.45)

A plot of the normalized-response time constant,T_W

/

^TWopt, as a function of the normalized-system short-circuit level,Sc

/

^Scmin, is shown in Fig. 5.9. This

160 CONCEPTS OF SVC VOLTAGE CONTROL

1 2 3 4 5

Short - Circuit Level : S_C S_{C min} Danger

of Instability 1

2 3 4 5 6

ResponsetR tRopt

Optimal Regulator Setting for S_{C min}: t_{R opt}, Approximately 1.5 Cycles; No Overshoot

K_SL= 0 K_{N max}: All Values

K_SL= 4% K_{N max} = 0.2

K_SL= 10% K_{N max} = 0.2 K_SL= 10% K_{N max} = 0.1

6

Figure 5.9 Effect of the system short-circuit level on the SVC response time.

plot shows the influence of the network short-circuit level and current droop on the SVC response time.

For a given short-circuit level, the control response time increases (becomes slow) with decreasing values of the current slope. The response time is also enhanced as the system strength increases relative to the weakest network state.

If a larger current slope is chosen (of course, at the expense of voltage regula- tion), the increase in response time with system strength is comparatively lower.

If the weakest network states are chosen to be those with very low short-circuit levels, then the response time exhibits a much sharper increase with increasing system strength.

On the basis of the preceding observations, it is concluded that a large value of slope should be chosen, preferably in the 3–5% range. Furthermore, the weakest network should also be identified judiciously. If an unduly weak sys- tem, especially that encountered while rebuilding a network after a major sys- tem collapse, is chosen as the weakest network state, the response time will be unusually longer when realistic system states are existent.

Example 5.1 An SVC connected to a 735-kV system has a reactive-power

VOLTAGE CONTROL 161 range of 350 MVAR production to 100 MVA absorption. The droop is set to 4%. The system short-circuit level is specified as follows:

• The maximum short-circuit current: 50 kA.

• The minimum short-circuit current under normal operating conditions: 5 kA.

• The minimum short-circuit current during system restoration after loss of a transmission line: 500 A.

From these specifications,

1. Determine the per-unit regulator gain that ensures stable operation from 5kA to 50 kA system short-circuit current.

2. Show the change of voltage-control response for the system variation and regulator setting in item 1 of this sublist.

3. Determine the per-unit regulator gain for stable operation in the system short-circuit-level range 500 A to 50 kA.

4. Show the change of the voltage-control response for item 1.

Solution 5.1

Item 1 The system gain is given from Eq. (5.29) as K_N c QSVC

S_c pu (5.46)

where Sc c^f3VbIc

Scminc^f3 . 735 . 10³ . 5 . 10³ c6365MVA (5.47) Scmaxc^f3 . 735 . 10³ . 50 . 10³ c63653MVA (5.48) KNmaxc Q_SVC

Scmin c 350−(−100)

6365 c0.0707pu (5.49)

KNminc Q_SVC

Scmax c 350−(−100)

63653 c0.00707pu (5.50) The regulator is optimized forK_Nmax. Thus the proportional gain of the voltage regulator, as given from Eq. (5.37), is

K_pc− 1

2(K_SL+K_Nmax) c− 1

2(0.04+ 0.0707) c−4.52 (5.51)

162 CONCEPTS OF SVC VOLTAGE CONTROL

Item 2 The variation in response speed is calculated as follows from Eq.

(5.42):

T_W

2TY c K_SL+K_Nmax

KSL+KN c 0.04+ 0.0707

0.04+KN c 0.111 0.04+KN

(5.52) For

K_N cK_Nmaxc0.0707, TW

2T_Y c1 (5.53)

For

KN cKNmin c0.00707, T_W

2T_Y c2.36 (5.54) This demonstrates that the SVC response can slow down by a factor of 2.36 if the system short-circuit current changes from 5 kA to 50 kA.

Item 3 If the weakest network state is chosen to correspond to a short-circuit current of 500 A,

KNmaxc Q_SVC

S_cmin c 350−(−100)

f

3 . 735 . 0.5 c0.070pu (5.55) The proportional gain of the voltage regulator is

K_pc− 1

2(KSL+KNmax) c− 1

2(0.04+ 0.707) c−0.669 (5.56) Item 4 The change of response speed is

TW

2T_Y c KSL+KNmax

K_SL+K_N c 0.04+ 0.707

0.04+K_N c 0.747

0.04+K_N (5.57) For

KN cKNmaxc0.0707, T_W

2T_Y c 0.747

0.04+ 0.707 c1 (5.58) For

KN cKNminc0.00707, T_W

2TY c 0.747

0.04+ 0.00707 c15.86 (5.59) The system configuration with the 500-A short-circuit level is definitely

EFFECT OF NETWORK RESONANCES ON THE CONTROLLER RESPONSE 163 abnormal and should not be chosen as the weakest network state for optimizing the regulator parameters. Otherwise, a very slow response (approximately 16 times the optimum) would result during the strong system condition.

5.2.5.2 Design That Considers Generator Dynamics A technique often resorted to for designing the voltage regulator of the SVC, by including the impact of generator dynamics, consists of the following steps:

1. Deriving a system model linearized around an operating point.

2. Obtaining the stability range of parameters of the preselected voltage- regulator structure from eigenvalue analysis.

3. Determining the best regulator parameters within the stability range that result in a fast response with acceptable overshoot.

4. Validating of the voltage-regulator performance through a detailed non- linear simulation of the system.

A case study of voltage-regulator design for an SVC located at the mid- line in a single-machine infinite-bus (SMIB) system [12], [13] is presented in Appendix A of this book.

5.3 EFFECT OF NETWORK RESONANCES ON THE CONTROLLER