Abstract
This work addresses the distributed frequency control problem in power systems considering controllable load with a nonsmooth cost. The nonsmoothness exists widely in power systems, such as tiered price, greatly challenging the design of distributed optimal controllers. In this paper, we first formulate an optimization problem that minimizes the nonsmooth regulation cost, where both capacity limits of controllable load and tie-line flow are considered. Then, a distributed controller is derived based on the primal–dual gradient method, where the Clark generalized gradient is utilized to address the nonsmoothness. We also prove the optimality of the equilibrium of the closed-loop system as well as its stability. Simulations carried out on the IEEE 68-bus system verifies the effectiveness of the proposed method.
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