# A Sensitivity Matrix Approach Using Two-Stage Optimization for Voltage Regulation of LV Networks with High PV Penetration

ENERGIES（2021）

Abstract

The occurrence of voltage violations is a major deterrent for absorbing more rooftop solar power into smart Low-Voltage Distribution Grids (LVDGs). Recent studies have focused on decentralized control methods to solve this problem due to the high computational time in performing load flows in centralized control techniques. To address this issue, a novel sensitivity matrix was developed to estimate the voltages of the network by replacing load flow simulations. In this paper, a Centralized Active, Reactive Power Management System (CARPMS) is proposed to optimally utilize the reactive power capability of smart Photovoltaic (PV) inverters with minimal active power curtailment to mitigate the voltage violation problem. The developed sensitivity matrix is able to reduce the time consumed by 55.1% compared to load flow simulations, enabling near-real-time control optimization. Given the large solution space of power systems, a novel two-stage optimization is proposed, where the solution space is narrowed down by a Feasible Region Search (FRS) step, followed by Particle Swarm Optimization (PSO). The failure of standalone PSO to converge to a feasible solution for 34% of the scenarios evaluated further validates the necessity of the two-stage optimization using FRS. The performance of the proposed methodology was analysed in comparison to the load flow method to demonstrate the accuracy and the capability of the optimization algorithm to mitigate voltage violations in near-real time. The deviations of the mean voltages of the proposed methodology from the load flow method were: 6.5x10-3 p.u for reactive power control using Q-injection, 1.02x10-2 p.u for reactive power control using Q-absorption, and 0 p.u for active power curtailment case.

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Key words

smart grid, renewable energy integration, rooftop solar PV, PV inverter control, voltage violation

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