# Distributed Optimal Load Frequency Control Considering Nonsmooth Cost Functions

## TL;DR

This paper develops a distributed control method for power system frequency regulation that effectively handles nonsmooth cost functions using the Clark generalized gradient, ensuring optimality and stability.

## Contribution

It introduces a novel distributed control approach for nonsmooth cost functions in power systems, with proven optimality and stability.

## Key findings

- Effective frequency regulation in IEEE 68-bus system
- Handles nonsmooth cost functions with generalized gradient
- Ensures asymptotic stability of the control system

## 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 regard, 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 using the Clark generalized gradient. We also prove the optimality of the equilibrium of the closed-loop system as well as its asymptotic stability. Simulations carried out on the IEEE 68-bus system verifies the effectiveness of the proposed method.