Two Machine Power System (With Diagram) | Electrical Engineering

A system having two machines can be replaced by an equivalent system having one machine connected to an infinite bus such that the swing equation and swing curves of angular displacement between the two machines are the same for both systems.

This is shown below:

A simple two-machine system connected through a transmission line having reactance X_T is shown in Fig. 7.25. Each machine is represented by its transient reactance and voltage behind transient reactance. The mechanical power input to the generator is P_s and its electrical power output is P_E.

Since both electrical and mechanical losses are generator neglected, the electrical power input to the motor is equal to the electrical output of generator, i.e., P_E and its mechanical power output equals the power input to the generating machine, i.e., P_s. Torque angles are measured positively in the direction of rotation.

Let δ₁, M₁, P_A1 be the quantities referred to generator and δ₂, M₂ and P_A2 for the motor.

The swing equation for the two machines can be written as –  

The relative torque angle between the two rotor axes,

δ = δ₁ – δ₂                                                                                             ….(7.47)

Expressing the acceleration of generator relative to the motor as the algebraic difference of their accelerations which must be equal to the acceleration of the equivalent single generator relative to the infinite bus, the following equation can be obtained –  

Equation (7.49) is the same as the swing equation for a single machine connected to an infinite bus with equivalent inertia constant.

Further, the electrical power transfer is given as –  

Thus, the two machine system shown in Fig. 7.23 is equivalent to a single generator of angular momentum M and voltage (behind transient reactance) E₁ connected to an infinite bus of voltage E₂ and the transfer reactance between the generator and infinite bus, i.e., X = X’_1d + X_T + X’_2x