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930 Samuel N. Ndubisi and Marcel .U. Agu ⎡ 1 ⎢ − ⎡V� ⎤ G t ⎡X� ⎤ τ 1 ⎢ ⎢ ⎥ ⎢ ⎥ ⎢ F = ⎢V� F ⎥ = ⎢X� 2⎥ = ⎢ 0 ⎢ b� () t ⎥ ⎢ X� ⎥ ⎢ ⎣ ⎦ ⎣ 3 ⎦ ⎢ −1 ⎢ ⎣ KG τ G 1 K E − + u τ E τ E 0 ⎤ 0 ⎥ ⎥ ⎡0⎤ ⎥ 0 + ⎢ ⎥ ⎥ ⎢ 0 ⎥ Vd ⎥ ⎢⎣ 1⎥ ⎥ ⎦ 0 ⎥ ⎦ ⎡ 1 F = ⎢− ⎣ τ G y = CX K G × X 1 + × X 2 ; τ G 1 K ⎤ E − × X 2 + × u( index); Vd ( index) − X ( 1) ⎥ τ E τ E ⎦ () ( ) ( ) ; 4. Simulation Results The performance of the FAVR controller is examined through simulation using MATLAB software package developed based on the exciter and generator models of fig.5. It is worth noting that the FAVR here considers only the deviations of the terminal voltage for its set point and the liveliness of the control signal. However, during major disturbances the rotor angle of the generator with respect to the infinite busbar of the power system is disturbed significantly and can take sometime to settle down following the event. It is known that conventional AVR (CAVR) controller can reduce the damping torque of the generator if it uses only the terminal voltage as its feedback signal resulting to reduction of damping of rotor oscillations. This has to be examined sufficiently in a later work. Two set of tests are carried out A. Voltage v Sudden terminal ariation With this sudden terminal voltage change, four tests were carried out 1. With CAVR, the amplifier transfer function is given by K A (22) 1+ τ AS and K A = 10 , τ A = 0. 1, K E = 1, τ E = 0. 4 , KG = 1 , τG = 0. 1, K R = 1, τ R = 0. 05 has the response shown below. Figure 6: Terminal voltage step response for CAVR. 2. A stabilizer is connected between the exciter output and the input summer with a step input signal. The stabilizer transfer function is 2S (23) 0. 04S + 1 (20) (21)
A Rule-Based Fuzzy Automatic Voltage Regulator for Power System Stability 931 The response is shown below with its time domain specifications Figure 7: Terminal Voltage step response of CAVR with stabilizer 3. A PID is connected in series with the amplifier. The PID parameters are K P = 10 , K I = 0. 25 and K D = 0. 28 . Figure 8: Terminal voltage step response with PID controller. 4. With the FAVR of fig 4, the response to a step input is shown below with the time specifications. Figure 9: (a) Terminal and desired voltage step response with FAVR (b) Fuzzy input voltage to the generator
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