Physical Restrictions: Line Flow Limits in Secondary Frequency Control

Abstract

This chapter shows how to design distributed optimal secondary frequency control considering both generation capacity constraints and tie-line flow limits. It shows that the controllers together with the physical dynamics serve as primal–dual updates with saturation for solving the optimization problem. The chapter formulates the optimal frequency control problem in the network balance case, presents the distributed frequency controller, and proves the optimality, uniqueness, and stability of the closed-loop equilibrium. It addresses the asymptotic stability of the closed-loop system, under an additional assumption. The chapter explains a distributed optimal frequency control in the network balance case, which can autonomously restore the nominal frequencies after unknown load disturbances while minimizing the regulation costs. Simulations on a modified Kundur's power system validate the effectiveness of the controller. This approach is also applicable to other problem involving frequency regulation, e.g. control of standalone microgrids or demand-side management.