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Basim T. Kadhem | 33

inferred that the 14th order reduced order model is a wise shown in Figs. 10(a,b), without and with a full order LQG
decision that doesn't introduce a lot of mistake. The error controller for the 29th, respectively, and the electromechanical
bound at the 14th reduced order is equal. torque (?Te) is shown in Figs. 11 (a, b)

?@(M() - @.(M()? = 0.026964 Figs. 12a and 12b depict the torque between the
The "ideal" eigenvalues for the closed-loop system based low-pressure turbine and the generator (?Tig) when the order of
on the reduced-order system with LQR state feedback are the LQG controller is reduced to third and fourteenth,
presented in Table I. The eigenvalue for the open loop system respectively, and the electromechanical torque (?Te) is shown
demonstrates that all modes are only marginally stable because in Figs. 13 (a, b)
the system is open loop without any additional signal to the
excitation system, TCSC and SVC. The controller ends up having the same order as the
open-loop system because it is based on full state feedback
(during the design phase, not the implementation phase). The
LQG belongs to order 29. A controller decrease is feasible in
many situations. To achieve a balanced state-space realization,
the controller state-space model can be normalized via a
similarity transformation [13–15].

In order to lower the model's order, states that can be
eliminated are indicated by the balanced realization. The
complete order controller in this system is of 29th order. As a
result, the controller's order can be lowered from 29 to just 14
with negligible performance loss. Fig.14 display the
performance of the reduced-order robust controller.

Fig.9. Controller reduction error bound.

TABLE I
EIGENVALUE OF OPEN LOOP AND CLOSED LOOP FOR REDUCED

ORDER REGULATOR

Mode 1 Mode 2 Mode 3

@125 rad/sec @174 rad/sec @191 rad/sec

Open loop -0.06733 -0.02514 -0.020288

Closed loop with -7.2484 -0.6856 -1.4146
Full order 29 th
Closed loop with -6.9585 -0.66597 -1.3661 (a) Without controller.

Order 14 th -5.3898 -0.5286 -1.1234 (b) With full order controller.
Closed loop with Fig.10: Torque between the low-pressure turbine and the
-4.2458 -0.40775 -0.81285
Order 12 th generator (?Tlg) at 3-phase short circuit.
Closed loop with -1.3449 -0.12783 -0.33268

Order 9 th -1. 2074 -0.058126 -0.073612

Closed loop with
Order 6 th

Closed loop with
Order 3 rd

VI. STUDY RESULTS

Full-order robust control and reduced order robust control
are the two control strategies that have been studied. Here is
the simulated scenario. Up to the time t = 1 second, the system
is in a steady state. At time t = 1 seconds, a three phase short
circuit is injected at the generator terminal for 0.1 seconds, and
the controller is not in operation. The controller is activated
when t = 3 seconds.

The system response for a three-phase short circuit
occurring at time = 1 second is shown in Fig. 10. The torque
between the low-pressure turbine and the generator (?Tig) is