Determination of Capacity for Synchronous Phase Modifier

Determination of Capacity for Synchronous Phase Modifier

We already know that synchronous machine can take lagging or leading current depending upon whether it is under excited or overexcited.

If idle running synchronous machine is used for voltage regulation by connecting it in parallel with the load at receiving end of the line then it may take lagging or leading current. When it is used in this manner, it is referred as phase modifier.

Phase modifiers are not designed for driving any mechanical load and are built for highest possible economic speeds. These are equipped with smaller shafts and bearings and high overall efficiency. Its capacity can be calculated as follows. Consider the following phasor diagram shown in Fig. 2.16.1.

When all the quantities such as A, B, P_R , α, β and V_R are known, V_S can be obtained. The above expression can be used for this purpose.

Sometimes voltages at sending end and receiving end are kept constant and

A, B, P_R, α, β and Q_R (load) are given and it is required to find out capacity of phase modifier. In this case the required quantity is Q_R. This net Q_R can be obtained from above equation. From that capacity of phase modifier can be determined.

Example 2.16.1 A 3 phase line has an impedance per phase of (5 + j 20) Ω/phase. The load at the receiving end is 30 MW at 33 kV, 0.8 p.f. lag. Find the sending end voltage. If a synchronous phase modifier is inserted at the receiving end and the voltage at both the ends are maintained at 33 kV. Find the kVAR rating of the modifier for the above load conditions. Also find the maximum load that can be transmitted.

Solution :

If synchronous phase modifier is used so that V_R = V_S =33 kV.

The equation for VS remains same only we will now find Q_R

This is net VAR requirement which is obtained.

Q_Rnet = -20.29 MVAR

We have the equation,

Q_Rnet + Q_C = Q_L

where Q_C is the VAR supplied by phase modifier

Q_C = Q_L - Q_Rnet = (22.5)-(- 20.29)

Q_C = 42.8 MVAR

This must be rating of phase modifier.

Maximum power transmitted is given by,

Example 2.16.2 A 3 phase overhead line has resistance and the reactance per phase of 5 Ω and 25 Ω respectively. The load at the receiving end is 15 MW, 33 kV, 0.8 p.f. lagging. Determine the capacity of the compensation equivalent needed to deliver this load with a sending end voltage of 33 kV.

Solution :

We have, Q_Rnet + Q_C = Q_L

where Q_C is the VAR supplied by the phase modifier

Q_C = Q_L -Q_Rnet = (11.25)-(-6.1327) = 17.38 MVAR

This is the rating of the phase modifier.

Review Question

1. Explain how capacity of synchronous phase modifier can be determined.