Power System, Stability of a

the ability of a power system to reestablish the initial state (or one practically identical) after any disturbance or interruption manifested as a deviation from the initial parameter values for the system’s operation. A distinction is made between static and dynamic stability, that is, between the ability to reestablish the initial state after small and strong disturbances, respectively. Stability is a necessary condition for the reliable operation of a power system.

In a steady-state mode the power coming into the system from outside is expended by the load W_l and offsets power losses ΔW. The occurrence of any disturbance in the system produces a deviation in the mode parameters (P). For a disturbance that causes a change in only one parameter (provided only that parameter is important and the change is small), the deviation of the parameters can be treated within linear segments of the power system’s response. If the power being expended W_I + ΔW = ɸ(P) after the mode is disturbed is greater than the maximum power ΔW_g = f(P) that the outside supply can replace, then it is necessary to restore the system to its former mode or one nearly the same. Such a system is said to be stable. The condition for maintaining stability, that is, the stability criterion K, is defined by the inequality ΔW/ΔP > ΔW_g/ΔP, or d(W_g – W)/dP < 0, where W_g – W is called the excess power.

In consideration of a given system, the excess power must be determined on the basis of all pertinent factors; therefore the stability criterion can only be used for specific systems in special cases with some simplifying assumptions. Moreover, the criterion K only determines the existence or absence of stability; it does not provide a direct characterization of the processes occurring in the power system. As a result, special methods and procedures are used to evaluate the stability of power systems. (See alsoSTABILITY OF AN ELECTRIC POWER SYSTEM.)