Global Optimality of Inverter Dynamic Voltage Support

TL;DR

This paper formulates the inverter dynamic voltage support problem as a nonconvex optimization, analytically explores its global optimum, and proposes a real-time control solution validated through simulations.

Contribution

It provides a novel analytical framework for global optimality in inverter DVS control, including closed-form solutions and conditions for different scenarios.

Findings

The global optimum has three distinct scenarios based on system parameters.

Closed-form solutions are derived for two scenarios, enabling real-time implementation.

Simulations demonstrate the effectiveness and robustness of the proposed optimal control.

Abstract

This paper investigates the dynamic voltage support (DVS) control of inverter-based resources (IBRs) under voltage sags to enhance the low-voltage ride-through performance. We first revisit the prevalent droop control from an optimization perspective to elaborate on why it usually suffers from suboptimality. Then, we formulate the DVS problem as an optimization program that maximizes the positive-sequence voltage magnitude at the point of common coupling (PCC) subject to the current, active power, and stability constraints. The program is inherently nonconvex due to the active power limits, of which the global optimality is not guaranteed by off-the-shelf solvers. In this context, we perform the optimality analysis to explore the global optimum analytically. It is found that the unique global optimum has three scenarios/stages (S1--S3), which depends on the specific relationship among grid voltage, grid strength, as well as physical limits of IBRs. The closed-form solutions in S1 and S3 are derived and the optimality conditions for S2 are provided, which guarantees the optimality and compatibility with the fast real-time control. We implement the optimum with a grid-connected photovoltaic (PV) power plant by integrating a DVS controller. Dynamic simulations are carried out under different scenarios to test our proposal and compare it with other existing methods. Additionally, the robustness of optimality against model errors is discussed and numerically demonstrated.