In recent European and American countries, research on FACTS (Flexible AC Transmission System) apparatus using power electronics techniques is becoming active. One of the objectives is to increase transmitted power through power system using control equipment such as TCSC (Thyristor Controlled Series Capacitor and UPFC (Unified Power Flow Controller). This attempt may be available in power systems which are tightly connected through many loops.
This paper deals with the optimality of load flow control of power system with many loops . In this paper, three kinds of linear or nonlinear programming problems are formulated. The first one is the maximum flow problem under the condition that growth rate of each generation and load node is given. The second one aims at minimizing the var-loss of the whole power system using FACTS apparatus under the condition that the power system transmits the maximum power obtained in the first problem. The third problem is to minimize the capacity of installed FACTS apparatus under the condition that var-loss of power system is kept equal to the minimum value obtained in the second problem. In this problem, installation points and capacities of FACTS apparatus are assumed as the only controllable parameters.
At first, the effects of FACTS apparatus from the viewpoints of the first and second problems axe discussed and some important results are obtained. Secondly, using these obtained results, three problems shown above are formulated into linear or nonlinear programming problems in three steps using DC flow calculation method. Each problem is solved sequentially using the results obtained in each previous step. Thirdly an example of calculation is shown using model power system. The solutions obtained above are compared with those, obtained by using the conventional AC flow calculation to study the calculation accuracy of the proposed method. Finally, the first and the third problems are formulated into two steps linear or nonlinear problems. It is demonstrated that the solution is not always equal to the solution of the problems in three steps discussed before.
The proposed formulations can be used not only for the determination of optimal installation points and optimal installed capacities of FACTS apparatus but also for the evaluation of FACTS apparatus from the points of load flow control in large scale power systems because the proposed techniques are simple and all of the constraints are linear and sparse.