Introduction

All the alternators in a power system operate "in synchronism" in steady state. The load electrical load is representative of electrical torque. At steady state the electrical torque and mechanical torque are equal. Now if the electrical torque i.e. load increases beyond limit, the mismatch between the two may result in some of the alternators going out of step. Frequency all over a synchronous power grid is the same in steady state. Maintaining a near-constant frequency (one may allow frequency to vary over a very narrow band) is considered an important requirement of power system operation.
Frequency in a power system is intimately related to the electrical speed of synchronous generators. The difference between mechanical and electrical torques govern acceleration of a rotor of a generator. Therefore to maintain a constant speed, mechanical input and electrical output power need to be continually matched. Electrical load can vary randomly, but the total load versus time roughly follows a trend. For example, total load in a grid can vary over twenty four hours as shown in the figure on the right.
There is a distinctive peak at about 8 pm. This is the typical variation for a particular season of the year. For other seasons, the load profile is different. Also, power systems are not immune to sudden large load or generation throw-offs due to contingencies.
Frequency variation is dependent on several factors which includes the load characteristics and generator prime mover controls.

Why frequency control?

Frequency needs to be maintained near 50 Hz (nominal frequency) for the following reasons:

• Steam turbine blades are designed to operate in a narrow band of frequencies. Deviation of frequency beyond this band may cause gradual or immediate turbine damage. Consequently, protective and control equipment take corrective action in case of under/over frequency. A 50 Hz steam turbine may not be able to withstand frequency deviation of +2 Hz to -2.5 Hz for more than an hour in its entire life!
• Loads and other electrical equipment are usually designed to operate at a particular frequency. Off-nominal frequency operation causes electrical loads to deviate from the desired output. The output of power plant auxiliaries like pumps or fans may reduce, causing reduction in power plant output.

Modes of frequency deviation

When there are two or more alternators present then we know that the frequency of each alternator voltage is same in steady state. But frequencies may be different in transient. But this is not the only deviation in frequency the frequency of whole system may deviate during a certain transient condition. Thus there are two types of motion to be considered when generator rotors are subject to transients :

1. Relative motion between generators: Rotor speeds may not be equal during transients. Exchange of power between generators during transients causes relative rotor movement ("swings"). Relative motion dies down if the system is angular stable. Relative motion needs to be stable so that eventually all rotors move together at a common speed
2. Motion of the center of inertia or the "common motion": Center of inertia frequency can be considered as a definition of "system frequency" under transient conditions. Interestingly, center of Inertia movement is determined ONLY by the OVERALL load-generation-loss balance. Motion of center of inertia may exist even if there is no relative movement between rotors. Conversely it is possible to have relative motion between generator rotors without center of inertia movement.

The two modes described above can be seen as analogous as a simple spring mass system. Velocity of the whole system is analogous to the system frequency. But this is not the only mode possible as we know. There may be a motion of masses with respect to each other this represents relative motion between the generators. This is depicted in the following diagram.