Optimal Distributed Control for Continuum Power Systems

Large electrical power networks viewed as continuum systems have been studied under constant voltage magnitude assumptions. The continuum system phase behavior was proved to follow the dynamics of a second order nonlinear wave equation. The latter represents electromechanical wave propagation in large electric power networks. In this paper, we generalize this work to time and space variant voltage magnitudes which is the case in real world applications. The resulting partial differential equations (PDEs) are also wave equations but include more nonlinearity terms. Optimal control theory is used to derive optimality conditions for two optimal control problems. The first problem is when the mechanical power is the control input where the constraint is a constant voltage PDE, while the second problem is when the variant voltage magnitude is the control input under a generalized variant voltage PDE as the optimization constraint. Numerical results are presented to illustrate the performance of the resulting closed loop control systems for large power networks. Due to page size limits we present the optimal control results for the variant voltage swing PDE in a different paper.