# Stability of an Electric Power System

## Stability of an Electric Power System

the ability of an electric power system to reestablish the initial state (or one practically identical) after any disturbance manifested as a deviation from the initial parameter values for the system’s operation.

The electric power sources in a power system are usually synchronous generators, which are coupled together by a common electric network in such a way that the rotors of all generators are in synchronized rotation. This mode, called the normal, or steady-state, mode, should be stable; that is, the power system must return to the initial state (or one practically identical) every time after a deviation from the steady-state mode. The deviations may be associated with a variation in load, short circuits, disconnections of power transmission lines, and similar causes. The system’s stability is usually diminished by an increase in the load (the power delivered by the generators) and a decrease in the voltage (an increase in the power consumed or a decrease in the excitation of the generators); specific limit, or critical, values can be determined for each power system for these quantities or for associated quantities that characterize the stability limit. A power system can operate reliably if a specific stability margin is provided for it, that is, if the parameters of the operating mode and the system itself differ sufficiently from the critical values. Various measures are taken to ensure the stability of an electric power system, such as designing the system with an adequate stability margin, regulating the excitation of the generators automatically, and using automated counteremergency equipment.

In the analysis of the stability of an electric power system, a distinction is made between static, dynamic, and overall system stability. Static stability covers the case of small disturbances, that is, those for which the system under consideration may be regarded as linear. It is analyzed with the general methods developed by A. M. Liapunov to solve stability problems. In engineering practice the stability of an electric power system is sometimes analyzed by a simple determination of the presence or absence of stability; the approach is oriented toward practical stability criteria, with certain assumptions based on experience, for example, the impossibility of self-oscillation in the system and the frequency invariance of the system’s electric current. Static stability is studied with the aid of digital and analogue computers.

Dynamic stability evaluates the behavior of an electric power system after the occurrence of strong disturbances that arise as a result of short circuits, disconnections of power transmission lines, and the like. In the analysis of dynamic stability (the system is generally considered to be nonlinear), it is necessary to integrate high-order nonlinear transcendental functions; analogue computers and AC evaluation models are used for this purpose. In the majority of cases special algorithms and programs are developed that permit the calculations to be performed on digital computers. The programs are validated by comparing calculated results with experimental results on a real system or on a physical model of the system.

Overall system stability evaluates the stability of an electric power system when the synchronism of some of the working generators has been lost. The normal operating mode in this case is subsequently reestablished without disconnecting major system elements. Calculations of the overall system stability are quite approximate because of their complexity; they are designed to reveal unacceptable effects on equipment and to find a set of measures that will eliminate the asynchronous operating mode.

The static stability of an electric power system can be improved primarily by the use of power regulation; dynamic stability can be improved by forcing the excitation of the generators, by quickly disconnecting faulty sections, by using special braking devices on the generators, and by disconnecting some of the generators and part of the load. An improvement in the overall system stability, which is usually regarded as an improvement in the ruggedness of an electric power system, is achieved primarily by controlling the power produced by the generators that have lost synchronism and by automatically disconnecting some power consumers.

Stability problems occur in the design of all types of electric power systems, including high-voltage ground systems, shipboard systems, and aircraft systems.

### REFERENCES

Markovich, I. M. Rezhimy energeticheskikh sistem, 4th ed. Moscow, 1969.
Venikov, V. A. Perekhodnye elektromekhanicheskieprotsessy v elektricheskikh sistemakh, 2nd ed. Moscow, 1970.

V. A. VENIKOV

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