Stability of an Electric Power System

Electric power is generated by synchronous generators, also called alternators. These generators are synchronized with the rest of the system and the voltage, frequency, and the phase sequence of the system as a whole is the same. 

"Stability of an electrical power system is the ability of the system to return back to normal state after being subjected to a disturbance."

Or in other words stability is the tendency of a power system to develop restoring forces equal to or greater than the disturbing forces to maintain the state of equilibrium. If the forces tending to hold these synchronous machines in synchronism with one another are sufficient to overcome the disturbing forces, the system remains stable. 

Thus, we can say that the problem of stability is concerned with the behavior of a synchronous machine after a disturbance.  The disturbance can be a gradual change in power, occurrence of a fault in a line, sudden removal of loads etc.

Types of Stability:

Stability is generally divided into two major classes:

1.      Steady state stability, and

2.      Transient state stability.

Steady state stability refers to the ability of the power system to regain synchronism after a small and slow change in the system operating conditions. This slow disturbance can be a gradual power change. The study of steady state stability is mainly concerned with the determination of the upper limit of the loading on the machine before losing synchronism. 

An extension of steady state stability is dynamic stability which is concerned with small disturbances but lasting for a long time with the inclusion of automatic control devices. Small disturbances such as variation in loads, change in turbine speed etc. are continually occurring in a power system. These disturbances are quite small to knock the system out of synchronism but do excite the system into the state of natural oscillations. If the amplitude of these oscillations is below a certain value they die out quickly and the system is dynamically stable. Dynamic system study has to be carried out for 5 to 10 seconds and sometimes up to 30 seconds. 
  

Transient stability deals with the effect of large, sudden disturbances such as the occurrence of a fault, the sudden removal of a line or loads. Transient studies are needed to ensure that the system can withstand the conditions following a major disturbance. The angle between the rotor axis and the resultant magnetic field axis is known as power angle or torque angle. Under normal conditions, the relative position of these two axes is fixed. During any disturbance, rotor will decelerate or accelerate with respect to the synchronously rotating air gap mmf, and a relative motion begins. If after this oscillatory phase, the rotor locks back into synchronous speed, the generator will maintain its stability. If the disturbance is created by a change in generation, load, or in network conditions, the rotor comes to a new operating power angle relative to the synchronously revolving field. If there is no net change in power, the rotor returns to its original position.   

Often such studies are conducted when a new generating plant or transmission system is planned. These studies are needed to determine the nature of the required relaying system, critical clearing time of circuit breakers, voltage level of systems, and the available transfer capacity between the various power systems.

Basics of Shunt Reactive Compensation

Purpose of providing Reactive Compensation:

The purpose of providing reactive compensation is to change the natural electrical characteristics of a transmission line. Shunt connected capacitors are used to maintain the voltage of the transmission system at desired levels during the loaded condition whereas shunt connected reactors are employed to reduce line overvoltages under light load or no-load conditions.

The voltage sag is largest at the midpoint for an uncompensated transmission line. Thus, the optimum location to place a shunt compensator is at the midpoint. Also, the compensator at the midpoint segments the line into two equal sections for each of which the maximum transmittable power is the same. The midpoint shunt compensation can significantly increase the transmittable power but the reactive power demand on the compensator increases rapidly with the increase in transmitted power.

Multiple shunt compensators can be placed on the transmission line located equidistance from each other. With the increase in number of compensators and hence the segments of the line, the voltage profile of the line approaches a flat profile. Theoretically the power which can be transferred over a transmission line doubles with each doubling of the segment. Such a system however would become too complex and costly.

Machine Angle Oscillation in Under-damped Power System:

In an under-damped power system, a small disturbance may cause the machine angle to oscillate around its steady-state value at the natural frequency of the entire electro-mechanical system. This oscillation of angle results in a corresponding sustained power oscillation. By appropriate variations in the shunt reactive compensation and hence in the voltage of the transmission line, the accelerating and decelerating swings of the disturbed machine or machines can be neutralized. 

When the oscillating generator accelerates and the machine angle increases, the electric power transferred must be increased to compensate for the excess mechanical input power. On the other hand the power transmitted must be reduced to counter the reduced mechanical input when the generator decelerates and the angle decreases. 

Thus, with appropriate and fast controls, shunt reactive compensation is able to change the power flow in a system during and following dynamic disturbances. This increases the transient stability and damps the power oscillations. Hence reactive or VAr compensation is used for voltage regulation at the midpoint or at some intermediate locations in the transmission line and at the end of a radial transmission line to avoid voltage instability, to increase transient stability and to damp power oscillations.

Ref: Hingorani and Gyugyi, “Understanding FACTS”, John Wiley & Sons, UK