Power System Stability

Power System Stability

AU : April-2000, Dec.-13

The term stability with respect to the transmission line refers to the stable operation of the power system with sending end and receiving end terminals in synchronism with each other. When this synchronism is lost it is said to be the unstable operation. The stability limit corresponds to maximum power flow possible without losing the stability.

Consider the generator supplying power to the load through the transmission line as shown in Fig. 2.19.1.

The load may consist of either impedance, Load induction motor or synchronous motor. With the load of the type static impedance, there is limit for generator to supply power to the load but the system can never lose synchronism or become unstable. Similarly for the induction motor there is limit and it can become unstable only when motor stalls but it can never lose the synchronism. But for synchronous motor type of load, it can cause unstability and loss of synchronism.

Thus it is required that under steady state and under dynamic conditions, the synchronism must be maintained.

The steady state stability limit refers to maximum power transfer that is possible with small changes in power flow or gradual disturbance, without losing stability. The transient stability refers to the maximum power transfer that is possible for given amount of sudden or large changes in power disturbance without loss of stability. The voltage stability corresponds to limit on maximum power transfer through the transmission line beyond which the voltage collapses and stability is lost.

1. Power Angle Diagram

We have already seen that after neglecting resistance and shunt admittance of the line the power at the receiving end is given by,

P_R = | V_S | |V_R | / X_L sin δ

The angle δ is called phase angle or the torque angle or load angle between sending and receiving end voltages.

With increase in load, angle & also increases. But it has limit beyond which power flow is not increased. This upper limit is called stability limit. The variation of power flow with angle & is shown in Fig. 2.19.2.

From the above equation it can be clearly seen that when δ = 0, P_R is also zero while when δ = 90° then P_R is maximum when 8 goes beyond 90°, PR goes on reducing and at δ =180°, it reduces to zero.

When there is sudden change in transmission system, change in load, tripping of generator or load, sudden switching load, any fault etc. brings about oscillations in angle 8. If load angle 8 goes beyond 90°, the synchronism is lost and the transmission system fails to transfer the power. P_m is called steady state stability limit and is given by,

P_m = | V_S | |V_R | / X_L

Transient state stability is one half of steady state stability,

If the mechanical power input to the alternator and the load on the system is unchanged for arbitrary disturbances, the system returns to the stable working point. With large disturbance the operating point is shifted and the system becomes unstable.

Example 2.19.1 A 3 phase overhead line has a reactance of 13 Ω per phase. If the voltage at the two ends are maintained at 33 kV, calculate the maximum steady state power that can be transmitted over the line.

 AU: April-2000

Solution: The given values are

Review Questions

1. Write a short note on power angle curve.

2. Write a note on stability of a power system.

AU: Dec.-13, Marks 6