Modal optimization of AVR for synchronous generator using the finite gradient

Traditional power systems consist of few centralized power plants, passive grid and uncontrollable passive loads. It is expected that deep penetration of modern trends like distributed generation, SmartGrids and microgrids will lead to a plenty highly automated power units. Each of them should be equipped with effective controllers. Like many years before PID controllers remain relevant and popular despite many others technologies, because they are based on well proven, reliable and clear practice. But PID controllers should be well tuned in order to keep stability of the unit and the entire grid. Existing methods usually assume that the control parameters are chosen at first, then the controlled unit is tested on applicability and stability. Classical methods (D-decomposition et al.) are quite effective for only one or two tunable parameters. The method proposed in this paper is based on the optimization concept of modal design. We consider Hurwitz function (control system relative stability), which is determined by the rightmost pole location and depends on the parameters of the controller. Its minimization using finite gradient method represents a complicated optimization problem. Number of the rightmost poles defines dimension of the manifold. When several poles is almost on the same vertical, we are approaching the zerodimensional manifold: points of global or local extrema. The described method is suitable to various problems of parametric optimization. The authors previously tested it in the control of various plants such as multilink mathematical and inverted pendulums. In the article it is used to optimize PDD2 controller for the linear model of a synchronous generator; similarly it can be used for optimization of PID controllers and other structure ones.