Design Procedure

SUPPLEMENTARY DAMPING CONTROLLER FOR AN SSSC-COMPENSATED TRANSMISSION LINE

7.3 Supplementary Damping Controller

7.3.2 Design Procedure

Having established the resonant characteristics of the SSSC-compensated benchmark system without any supplementary damping controls in section 7.2, it was concluded that the torsional mode that is most significantly affected by torsional interaction with the SSSC, at all values of Xq*, is Mode 4, although the severity of instability in this mode increases at higher compensation levels. A study was then conducted to determine if sufficient damping could be added to the Mode 4 oscillations via supplementary damping control using the SSSC. This section now focuses on the design of such a damping controller for the specific value of SSSC compensating capacitive reactance ofX_q*

=

0.3707 pu, which corresponds to the worst-case instability in Mode 4 in the analyses of the previous section.

In order to implement the SSSC supplementary damping control based on the approach described above, three basic design steps, using the full PSCADIEMTDC system simulation model, were employed:

1. First, a small-amplitude sinusoidal test modulation signal at the torsional frequency of interest (in this case, the Mode 4 frequency of 32.285 Hz) was injected at the input LiXqto the SSSC as shown in Fig. 7.5. The phase lag between this LiXq signal and the resulting oscillations LJT_ein generator electrical torque were then measured. During this part of the test the inertia constant of the generator in the IEEE First Benchmark Model was temporarily set to a very large value in order to prevent the steady-state oscillations in the electrical torque from influencing the speed and rotor angle of the generator - this artificial decoupling technique is the same as that often used when measuring the phase response of a generator for power system stabilizer design purposes.

2. After the open-loop phase lag between the controller input LiXq and electrical torqueLJTe had thus been measured at the frequency of interest, a suitable compensator was then designed to provide phase lead to counteract this phase lag (in other words, the values of time constants TJ

to T₄ in the supplementary damping controller of Fig. 7.4 were so designed). The details of the lead compensator design method are described in Appendix H.

3. Finally, the closed-loop supplementary damping control scheme shown in Fig. 7.4 was then implemented using this lead compensator design on the IEEE First Benchmark Model for the design value of SSSC compensation of X_q* = 0.3707, and its performance evaluated for a range of values of damping controller gain KSSR •

-

I

3·LEVEL 24-PULSE INVERTER SSSC

INTERNAL CONTROLS

1---·

1 sssc

! !

_I

+

I i

_I

_ _ _ _...I

I 1

~o

I i i

!1 ⁺

x'i

} - X...;l.q~L q I

I

I ! I

I

~I

^I

1 I

L - l

[-+-1

I

^L

x, =

^X.O+

"x,

^J

I

f=

32.285 Hz

Fig.7.5: The first step of theSSSCsupplementary damping controller design where a small-amplitude sinusoidal test modulation signal is injected into the input ofLiXq-

7.3.3 Performance Of SSR Damping Control

With the SSSe supplementary damping controller having been designed to damp out Mode 4 oscillations, this section now compares the SSR characteristics of the SSSe, with and without supplementary damping controls, and for different gains of this damping controller.

Fig. 7.6 shows theSSRcharacteristics of the First Benchmark Model when the SSseis providing a set-point value of compensation XqO

=

0.3707pu, but compares the situation when there are no supplementary controls (K_SSR

=

0) to that when the supplementary controls are activated with a gain K_SSR

=

0.1. As has already been seen in Fig. 7.3, theSSSecompensated system is unstable with no supplementary controls. However, Fig. 7.6 now shows that with the damping controls added, the Mode 4 torsional oscillations in the mechanical shaft and electrical torque are clearly more positively damped. Furthermore, the oscillations in the generator speed deviation, LPA-LPB and GEN-EXe torques, shown in Fig. 7.6(b) (e) and (f) respectively, now clearly contain predominately the Mode 1 frequency of 15.71 Hz with significantly less influence from the Mode 4 frequency. Fig. 7.6(a) also illustrates how this has been achieved: the commanded value ofX_q' at the input to theSSSCis modulated in sympathy with the oscillations in the

(a) Commanded Reactance: Xc·

(c) Dead Angle:y (b) Speed Deviation: t:,ro

(d) Machine Electrical Torque Negative: Te

- Without Damping Control

I

- With Damping Control 0.4

~ ^0.3 Q) ^0.2

Q. 0.1 0 10

-

c::: ⁵ :::::>

...

0

Ql

Q. -5

-10 100 enQl Ql

...

50

Cl) Ql

0 0

2

~c::: 1

:::>

...

Ql 0 Q.

-1

(e) Machine Shaft LPA to LPB Torque

-

^c::: 5

:::>

...

Of---....J

Ql Q.

-5

(1) Machine Shaft GEN to EXC Torque

0.2

:g

^0.1

:::::>

...

Ol---J\j

~ ^-0.1 -0.2

o ^{0.2 0.4 0.6 0.8 1 1.2}

Time (s)

1.4 1.6 1.8 2

Fig. 7.6: Performance of the SSSC compensated IEEE Benchmark Model transmission system with no damping control and with damping control and KSSR

=

^{0.1,. XqO}

=

^{0.3707 pu.}

0.4

§

^0.3

Qi ^0.2 c.. ^0.1

0 10

:l: 5

:::>c:: ₀

....Q)

c.. -5 -10 100

lJ) Q) Q).... ₅₀

Cl) Q)

0 0

(a) Commanded Reactance: Xc·

A ,A.A • .It.. I t . A . ,It

- Without Damping Control

I

With Damping Control

(b) Speed Deviation: t"ro

(c) Dead Angle: y

. _.

(d) Machine Electrical Torque: Te

....

Q) 0

c..

-1

3.---,----,---.---,----,----,---r---,---,---,

:l: 2

:::>c:: 1F ' - - -...

(e) Machine Shaft LPA to LPB Torque

5

:l:c::

:::>.... O f - - - - '

c..Q)

-5

(1)Machine Shaft GEN to EXC Torque

-

c:: 0.20.1

::>.... 0 i - - - ' V

cf

^-0.1

-0.2

o ^{0.2 0.4 0.6} 0.8 1 1.2

Time (s)

1.4 1.6 1,8 2

Fig. 7.7:Peiformance of the SSSC compensated IEEE Benchmark Model transmission system with no damping control and with damping control and K_SSR

=

0.15; X_qo

=

0.3707 pu.

generator's speed deviation; the resulting modulation in the inverter's dead angleyis also shown in Fig. 7.6 (c).

Although there is a clear stabilizing influence from the damping controller evident in Fig. 7.6, the torsional oscillations still persist for several seconds after the disturbance even with the damping controller activated. Fig. 7.7 therefore considers whether further improvement in the damping of the torsional oscillations can be obtained by increasing the supplementary controller's gainK_{SSR '}

Fig. 7.7 now shows the SSR characteristics for XqO = 0.3707pu but compares the fixed SSSe compensation (KSSR = 0) to modulated compensation with KSSR = 0.15. The results show that there is in fact further reduction in the amplitude of the Mode 1 (15 Hz) shaft torsional oscillations at the increased value of gain (c.f. Fig. 7.6); however, this comes at the expense of larger excursions in the compensating reactance and generator electrical torque during, and after the application of the fault in the transmission line. Also, there appears to be a less-damped higher frequency mode present in the speed deviation signal in Fig. 7.7 that is not as evident in Fig. 7.6.

Thus, while in principle it is possible to add significant damping to the torsional oscillations using the SSSC's supplementary controller, careful consideration would be required to apply appropriate limits to the magnitude ofLlX_qcommanded at the output of such controls.