Voltage Stabilization in Microgrids via Quadratic Droop Control

TL;DR

This paper introduces a quadratic droop control method for microgrid voltage stabilization, providing explicit solutions, stability analysis, and demonstrating optimality and power sharing properties across various network configurations.

Contribution

It proposes a novel quadratic droop controller for microgrids, linking equilibrium points to optimization solutions and analyzing stability and power sharing in arbitrary topologies.

Findings

Exact correspondence between equilibrium points and reduced power flow solutions

Controller achieves proportional load sharing in low-gain limit

Robustness confirmed through numerical simulations

Abstract

We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a one-to-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.