The load-frequency control is a matter of interest in power system operation as it addresses the problem of controlling the system in response to the disturbances. A well-known solution to this problem is feedback stabilization through Linear Quadratic Regulator. The observability condition has to be satisfied for the implementation of LQR, but for certain cases of multi-source power systems this criteria fails. Also, to obtain the desired response, proper selection of the weighting matrices Q and R for LQR controller is inevitable. On a trial and error based choice of these matrices, the classical optimal controller may fail to achieve an optimum set point tracking, due to the absence of an integral control action. In this paper, a balanced reduction technique is proposed to obtain a minimal realization of the unobservable system, which makes the optimal control design possible for the control of change in frequency. Thus the paper also applies PID output feedback controller designed through LQR. The impact of reduction for minimal realization and the LQR based PID controller in the frequency stabilization of the considered systems are highlighted in this paper through pertinent cases.

负载频率控制是电力系统运行中的一个重要问题，因为它解决了控制系统以响应干扰的问题。这个问题的一个众所周知的解决方案是通过线性二次稳压器实现反馈稳定。LQR 的实施必须满足可观察性条件，但对于多源电力系统的某些情况，此标准不成立。此外，要获得所需的响应，请正确选择权重矩阵Q和R对于 LQR 控制器是不可避免的。在这些矩阵的基于试错的选择中，由于缺少积分控制动作，经典最优控制器可能无法实现最优设定点跟踪。本文提出了一种平衡缩减技术来获得不可观测系统的最小实现，从而使控制频率变化的最优控制设计成为可能。因此本文也应用了通过LQR设计的PID输出反馈控制器。本文通过相关案例强调了最小实现减少和基于 LQR 的 PID 控制器对所考虑系统的频率稳定的影响。