COORDINATION OF CONTROLS FOR THE OPTIMUM STABILIZATION OF POWER SYSTEMS

Abstract

Since the beginning of this decade quite a good number of research papers have been published for the development of optimal contro llers for the synchronous machine- system. Side by side work has also boon carried out to assess qualitatively as vrell as quantatively the stabilizing signal for the synchronous machine system based on other methods of control theory. Whatever may be the mode of tackling the problem, the goal remains same. It is required to extend the dynamic stability limit and to improve system transient performance under large disturbance. Though the use of optimal con trol theory is more systematic in nature (in comparison to other methods) so far as the physical realization of the optimal contro ller is concerned it often poses problem. Normally the controller requires realization of all the states and the associated gains aro also very high. So by using appropriate limiters if this problem is taken care of, the resultant control may load to some suboptimal result. BUt still with a systematic design desired objective may be fulfilled to a larger.ejetcnt. If the existing control systems (like basic excitation control system and speed-governing system for input power control) fitted with synchronous machine are re tained as far as possible, the necessary optimal or suboptimal con trollers may be formulated to ensure proper and effective coordina tion with these controls. Based on these ideas following works have been carried out. In the first stage of development of optimal controllers for the synchronous machine system, proportional-integral-derivative type has been realized based on the linear system model. This controller merits over the earlier reported p-i-d controllers, because of no constraint on the selection of number of outputs of the system. It has been observed that for a particular relation of outputs and states, of course, the proposed p-i-d realization is unique. Other wise, in general, it yiolds a suboptimal control. As the system model fecnsidered is linear, possibility of increasing (small per turbation) dynamic stability has been stressed by designing the controller corresponding to a point in the vicinity of the limit

line. Analysis of the system with p-i-d controllers in terms of synchronizing and damping components of restraining (electrical) torque also justifies for the improvement of dynamic stability of the system. It has been observed that the controller actuated by speed deviation signal and based on the principle of proportional -integral-derivative realization helps the system in restoring back to steady stable condition after large transient fl*ot«rfe«M by way or continuous control of the interceptor""valve of'aturbogenerator sot. Further work with linear model, utilizing a state-dependent state weighting matrix, has helped in the construction of state as well as disturbance adaptive controllers for single-machine as well as multi-machine system. Disturbance adaptation over and above state adaptation, by way of realization of the disturbance to the syutem indirectly, has resulted in the improvement of dynamic performance of the system to alarge extent. For the multi-machine system, tak ing atwo-machine system as an example, possibility of decentralized suboptimal adaptive control has been explored in order to sake the overall control system much more reliable. Application of the theo ries of minimum error excitation and minimum norm successively to the states and disturbances of the multi-machine system has made it possible to design suboptimal controllers for individual machinos. For small disturbances, the result obtained with this type of com plete localized control is quite optinistif (i.e., quite close to that obtained with exact state as well as disturbance adaptive opti mal control). Subsequently ageneral controller capable of meeting the challenge of input as well as output disturbance in an optimal way has boon designed for the synchronous machine system in order that stability of the system is improved under small load / input mechanical pother variation as well as under large output variation such as transient fault condition. This gain adjusting general adaptive controller clearly shows the superiority of it over the ordinary proportional controller with fixed gain. In the second stage of work, keeping the nonlinear performance cq.ua( v) tions intact, anonlinear proportional-integral controller for the machine has been developed. This has been achieved on the basis of nonlinear optimal control techniques alongwith the classical con cept of integral feedback over raid above usual proportional feed back system. Following a standard synthesis procedure the constant coefficients of this P-i controller have been evaluated. Performance of a synchronous machine delivering power to an infinite bus .and equipped with speed-governor and fast-acting exciter to accept the additional coordinated control signals shows effectiveness of the designed controller under small as well as large disturbance. And as the original nonlinear performance equations have been used, the designed controller is expected to be equally effective over awide range of operating conditions. It may be observed that the above mentioned controller has got twice the number of states variables to be dealt with (because of the additional integral states). Thus the question of overall relia bility of the designed control system needs proper attention. This problem becomes much more acute when the possibility of development of this type of controller for the multi-machino system is to be explored. So while dealing with the nonlinear multi-machino system in general, talcing the advantage of fast-acting exciters having com paratively smaller time constants and larger gains, basic nonlinear differential equations have been formulated in terms of certain small parameter. This small parameter has been neglected subsequently to give rise to reduced order system in the process of separation of slow and fast dynamics in the problem. Later on by way of partial linearization a timo-dependent suboptimal controller has boon design ed taking the example of atwo-machine system subjected to alargo trojasient disturbance. From the above mentioned study it may be concluded that with the help of p-l-d regulator (energized from the output) it is possible to raise the dynamic stability limit of the synchronous machine system. Again with the assessment of disturbance indirectly, appli cation of stat3 as well as disturbance adaptive controller results in improvement in both df&ariic performance as well as transient per( vi) formance under large disturbance. However for successful operation over a wide range, nonlinear proprtional-integral controller may be used for smaller system while for multi-machine system by separa ting slow and fast dynamics of the system time-dependent controller, may be developed for use to meet the challenge of large disturbance*