Definition of Frequency

Definition of Frequency
What determines grid frequency?s

While it has been stressed that frequency is the same in steady state throughout a synchronous grid, two very interesting questions need to be answered:

→ What is the precise value of frequency to which a system will settle?
→ How does the "system frequency" vary during transients? How does one obtain a useful definition of frequency when individual generators speeds can be different during transients?

To understand this we need to look at the basic governing equations of synchronous machines in a system.

We know that for the ith generator,



Note : P_mi and P_ei denote the per unit mechanical and electrical powers respectively



It was seen that steady state frequency is determined by the load-generation-loss balance equation. For analysis under transient conditions, consider the analytical development and illustrative analogy given below.

There are two types of motion to be considered when generator rotors are subject to transients :

a) Relative motion between generators: Rotor speeds may not be equal during transients. Exchange of power between generators during transients causes relative rotor movement ("swings"). This phenomenon was considered in the previous module. 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.

b) Motion of the center of inertia or the "common motion": If we sum up the swing equations of individual generators, we obtain:


Interestingly, center of Inertia movement is determined ONLY by the 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.

Center of inertia frequency can be considered as a definition of "system frequency" under transient conditions. You can verify that under equilibrium conditions, i.e., when all machines settle to a common speed we, center of inertia frequency also equals we.

In this module, we will concentrate on center of inertia movement and not on relative motion between rotors. We shall assume that relative motion is stable ( machines stay in synchronism). 
We illustrate the concept of "system frequency" as a quantity affected by the aggregate of forces acting on the system by the familiar mass - spring analogy.