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2.1 Single-line Diagram of the Power System

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Figure 1: Single-line diagram of the power system under study

The main elements of this grid are:

• An infinite bus (or busbar)

• A 60 Hz synchronous generator

• A transformer

• Three lines,and

2.2 Power System Parameters

All impedances are in per unit (pu) using a common base of 100 MVA.

The infinite busbar receives active power of 1.0 pu with a lagging power factor of 0.95.

Circuit parameters are shown in Table 1. The per-unit bases of the system are = 100 MVA et = 13800 V.

2.3 Preliminary Calculations

The equation that describes the dynamics of the electromechanical system, in pu, is given as:

It is a differential, non-linear equation because of which is a non-linear function of δ and. The equation includes the possibility of modeling the generator damping. The damping is proportional to the speed of the machine in relation to synchronous speed and constant D. It is assumed that the machine’s mechanical power and internal voltage remain constant during transients.

Before proceeding to real-time simulations, it is useful to perform preliminary calculations on transient stability by determining the following values:

1. The current, in pu, at the infinite bus (bus 2) in steady state.

2. The amplitude and angle of the voltage at generator terminals in steady state.

3. The amplitude and angle of the internal voltage of the generator in steady state.

4. The amplitude and angle of voltage at all buses in steady state.

5. Active and reactive power at buses 2 and 4 in steady state.

6. Mechanical power supplied to the generator turbine atand at (fault occurs at t = 0).

7. The expression of active power flow (sending from generator to the infinite bus) as a function of the generator internal angle.

8. The expression of active power flow (sending from generator to the infinite bus) as a function of the generator internal angle during a fault. Calculate the two cases below:

9. Apply the Equal Area criterion to determine the transient stability for the following two cases (the fault is clearing after six cycles)