Fig. 1. Power system model.

A power system model under consideration in this paper is shown in Fig. 1. This is the system considered in [1, 2] except for a capacitor in parallel with the load. An infinite bus is a source of invariable frequency and voltage magnitude. A major bus of a power system of very large capacity compared with the rating of the machine under consideration is approximately an infinite bus. In the figure, , which is chosen as reference, is the magnitude and angle of voltage of the infinite bus, and is the magnitude and angle of terminal voltage of the load. The transmission lines connected to the generator and infinite bus terminals have resistances and reactances.

*2.1. Generator model* (digest)

Fig. 2. 2-pole model of a generator; definition of coordinates and windings.

A two-pole model of a generator is shown in Fig. 2. The symbol *a*-*a*', *b*-*b*' and *c*-*c*', represent armature windings, *f*-*f*' represents the filed winding, and *kd*-*kd*' and *kq*-*kq*' represent damper windings. The reference position of the *d* axis of the rotor is the direction of the negative flux linkage relative to the assumed positive direction of the armature current of phase *a*. All variables and constants for the armature, each of which has three components corresponding to three phases, are projected along the *d* and *q* axes of the rotor by Park's transformation [4-7]. All variables and constants for the rotor are equivalently converted into the quantities for the stator, and are normalized by the bases for the stator [7].

The data of the generator we use here are found in Unit no. F18 of Table D.3 of [6]. The type of the generator is a fossil steam unit with a General Electric SCR excitation system. The size of the generator given in [2] is 500MW, and that of our generator is 560MW.

*2.2. AVR model* (digest)

Fig. 3. Block diagram of AVR control device.

Equations for the generator and AVR

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