Coupling Load-Following Control with OPF

TL;DR

This paper introduces LQR-OPF, a novel optimization framework that integrates load-following control costs into the power flow problem, resulting in more cost-effective and stable power system operation.

Contribution

The paper develops a linearized, semidefinite programming approach that jointly optimizes steady-state setpoints and feedback control laws considering load-following costs.

Findings

LQR-OPF reduces overall control costs.

It improves frequency stability.

It outperforms separate OPF and control schemes.

Abstract

In this paper, the optimal power flow (OPF) problem is augmented to account for the costs associated with the load-following control of a power network. Load-following control costs are expressed through the linear quadratic regulator (LQR). The power network is described by a set of nonlinear differential algebraic equations (DAEs). By linearizing the DAEs around a known equilibrium, a linearized OPF that accounts for steady-state operational constraints is formulated first. This linearized OPF is then augmented by a set of linear matrix inequalities that are algebraically equivalent to the implementation of an LQR controller. The resulting formulation, termed LQR-OPF, is a semidefinite program which furnishes optimal steady-state setpoints and an optimal feedback law to steer the system to the new steady state with minimum load-following control costs. Numerical tests demonstrate that the setpoints computed by LQR-OPF result in lower overall costs and frequency deviations compared to the setpoints of a scheme where OPF and load-following control are considered separately.