Sensitivity to Power-System Parameters

Concepts of SVC Voltage Control

5.3 EFFECT OF NETWORK RESONANCES ON THE CONTROLLER RESPONSE

5.3.2 Sensitivity to Power-System Parameters

The influence of power-system parameters on the transient response of the SVC voltage regulator, with varying regulator gains K_T [4], [5], is depicted in Fig.

5.15. The SVC bus-voltage transducer output and the voltage-regulator output, B_ref, responses are presented for three kinds of power-systems: a very weak system (ESCR₀ c0.7 pu,F_r0 c80Hz); a moderately weak system (ESCR₀ c 1.6 pu,F_r0c110Hz); and a strong system (ESCR₀ c2.5 pu,F_r0 c180Hz). For each system configuration, the responses are presented for four widely different

EFFECT OF NETWORK RESONANCES ON THE CONTROLLER RESPONSE 167

Z_s

Z_T

5 7

TCR Filters

200 Mile 200 Mile

(a)

(b) 0.01

10 60 100 1000

0.1 1 10

F_{r 0}

Z (pu on TCR) Z_T

Z_S 1 ESCR₀

Frequeny (Hz)

Figure 5.13 (a) A single-line diagram of an SVC-compensated system and (b) impedance-versus-frequency characteristics for an SVC-compensated system.

values of the SVC controller transient gain K_T{c1

/

^{(KSL .TR})}, that is, K_T c 30, 100, 300, and 1000 pu

/

^s

/

pu. For each combination of system strength and controller-transient gain, the SVC voltage response is obtained for a 3-phase fault applied at 50 ms and cleared at 100 ms. All the foregoing SVC responses are determined for a TCR-average conduction (operating susceptance) B_T0 of 0.3 pu.

168 CONCEPTS OF SVC VOLTAGE CONTROL

0.1 0.1

1 10 100

1 10

Frequency, pu F_r

Z (pu on SIL)

1 ESCR

With B_C B_C

X_S = 0.2 pu Z

Without B_C Length

(b) 0

0 1 2 3 4 5

1 2 3 4 5

ESCR, pu (SIL)

Resonant Frequency, pu (60 Hz)

500 400

300 200

150

50 miles 0

miles

0.4 B_C= 0.2

B_C= B_C= 0

0.6 0.8 1.0 1.2 Length = 100 miles

(a)

Figure 5.14 Plots illustrating the relationships of (a) ESCR and (b)Fr0to parameters of a system with long lines.

EFFECT OF NETWORK RESONANCES ON THE CONTROLLER RESPONSE 169

0 0.5 1

0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 0

0.5 1

0 0.5 1 0

1 2

0 1 2

0 1 2

0

0 0.25 0 0.25 0 0.25

0.5 1

0 0.5 1

0 0.5 1 0

1 2

0 1 2

0 1 2

0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 0

0.5 1

0.0 0.5 1

0 0.5 1 0

1 2

0 1 2

0 1 2

0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 0

0.5 1

0.0 0.5 1

0.0 0.5 1 0

1 2

0 1 2

0 1 2 Power System Parameters

Time (s) Voltage Transducer

Regulator Output Regulator Output Regulator Output

Regulator Output Regulator Output Regulator Output

Regulator Output Regulator Output Regulator Output

Regulator Output Regulator Output Regulator Output

Voltage Transducer Voltage Transducer

Voltage Transducer Voltage Transducer Voltage Transducer

Voltage Transducer Voltage Transducer Voltage Transducer

Voltage Transducer Voltage Transducer Voltage Transducer ESCR₀= 2.5 pu

F_{r 0}= 180 Hz

ESCR₀= 1.6 pu F_{r 0}= 110 Hz

ESCR₀= 0.7 pu F_{r 0}= 80 Hz

KT = 1000 pu/s TR = 0.02 s

KT = 300 pu/s TR = 0.067 s

KT = 100 pu/s TR = 0.2 s

KT = 30 pu/s TR = 0.67 s

Voltage-Regulator Transient Gain

Figure 5.15 Effect of power-system characteristics on SVC transient response with B_T0c0.3 pu.

170 CONCEPTS OF SVC VOLTAGE CONTROL

5.3.2.1 Response Variation With Regulator Transient Gain, K_T For the strong system (ESCR0 c2.5 pu), the SVC response is very sluggish forKT

c30pu

/

^s

/

pu, but quite fast forKT c1000pu

/

^s

/

pu. For the moderately weak system (ESCR0 c 1.6 pu), the response for KT c30pu

/

^s

/

pu is less sluggish;

however, as the gain is increased, the response becomes faster but also becomes oscillatory forKT c300pu

/

^s

/

pu and unstable forKT c1000 pu

/

^s

/

pu. At this high value of K_T, the voltage-regulator susceptance output increases substan- tially and starts hitting the susceptance limits. For the very weak system (ESCR₀ c0.7 pu), the SVC response is reasonably fast for the lowest selected gain, that is,K_T c30pu

/

^s

/

pu; it becomes oscillatory at a slightly increased value of gain K_Tc100pu

/

^s

/

pu, unstable if the gain is increased further toK_T c300pu

/

^s

/

^pu

and 1000 pu

/

^s

/

pu. The stability limit ofK_T is much lower with weak systems than it is with strong systems.

5.3.2.2 Response Variation With System Strength, ESCR₀ For the reg- ulator gainKT c30pu

/

^s

/

pu, as the system strength ESCR0 decreases from 2.5 pu to 0.7 pu, the SVC response tends to become faster. ForKT c100pu

/

^s

/

^pu,

however, the sluggish response for the strong system (ESCR0c2.5 pu) becomes quicker for the system with medium strength (ESCR0 c1.6 pu) and oscillatory for the weak system (ESCR0c0.7 pu). With a high gainKTc1000pu

/

^s

/

^{pu, the}

SVC response is very fast, with acceptable overshoot for the strong system, but it becomes oscillatory and eventually unstable as the system strength declines.

From the foregoing studies, the following are illustrated

1. The SVC response, in general, becomes faster with the increase in trans- ient gain of the voltage regulator.

2. If the gain is made very large, the SVC response may become oscillatory or even unstable.

3. A sluggish SVC response for a strong system becomes faster as the sys- tem strength deteriorates. If the regulator gain is optimized for a high system strength, the SVC response may become unstable for a weak sys- tem, implying that the SVC regulator gain should always be optimized for the weakest system state to ensure the stable response for any variation in system strength. The only repercussion of this strategy is that the SVC response will become slower as the system strength increases. However, this problem can be resolved through a variable gain strategy.

5.3.2.3 Voltage-Sensitivity Transfer Function The effect of the network resonance can be understood in terms of the voltage-sensitivity transfer func- tion, which relates the SVC voltage-regulator output, DB_CV, to the output of the voltage-magnitude transducer, DV_meas. This transfer function essentially includes the characteristics of the network. The Bode plots for this transfer func- tion corresponding to two power-system configurations having different reso- nant frequencies—80 Hz and 110 Hz—are illustrated in Fig. 5.16.

EFFECT OF NETWORK RESONANCES ON THE CONTROLLER RESPONSE 171

−40^° at 20 Hz

−100^° at 20 Hz 10

0

−10

−20

100 0

−100

−200

−300

−400

10

Modulation Frequency (Hz) 100

−6.2 dB

F_{r 0}= 110 Hz, ESCR₀= 1.6 pu

Phase (deg.) F_{r 0}= 80 Hz, ESCR₀= 1 pu

∆V_meas/∆B_CV Transfer Function

−2.5 dB

+2 dB peak Magnitude (dB)

Figure 5.16 Effect of power-system response characteristics on voltage-sensitivity transfer function.

The two systems exhibit different steady-state gains for low-modulating fre- quencies. In case of the weak-system configuration (ESCR0c1.0 pu), the effect of first-resonant frequency,Fr0 c80Hz, is manifested as a peak in the gain at 20 Hz, which is the lower sideband (80 − 60 Hz) of the network resonance.

At this modulating frequency, there occurs not only a large gain amplification of 45 dB over the steady-state gain, but also a significantly large phase lag of 100⁸, leading to a small stability margin. In comparison, the phase lag of the strong system at 20 Hz is just 40⁸. Thus for the weak system, if the phase lag associated with the voltage regulator and the various firing delays at 20 Hz is shown to be 80⁸(resulting in an overall phase lag of 180⁸in the voltage-control loop), an instability will occur.

Within the voltage-control loop, the frequency characteristics of the power system resemble that of a second-order control filter having a break frequency at the lower sideband of the network-resonant frequency. Since the phase lag

172 CONCEPTS OF SVC VOLTAGE CONTROL

of the network block at the break frequency (20 Hz) is fairly large, the stability margin of the voltage-controller loop deteriorates substantially.