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<p>The substantial and uneven integration of single-phase photovoltaic inverters (S-PVIs) into distribution systems (DS) has significantly increased voltage unbalance (VU) and voltage magnitude variations. This study proposes a coordinated control framework for managing complex unbalanced DS by integrating single-phase and three-phase PV inverters (S/T-PVIs), on-load tap changers (OLTC), and step voltage regulators (SVRs) through a model predictive control (MPC) strategy. The control problem is formulated as a Mixed-Integer Nonlinear Programming (MINLP) model, enabling precise coordination of OLTC and SVRs tap positions along with the active and reactive power outputs of each S/T-PVI phase. To efficiently solve the MINLP, a Modified Mixed-Variable Particle Swarm Optimization (MMVPSO) algorithm is developed, featuring distinct update strategies for discrete and continuous variables. The relationship between the voltage unbalance factor (VUF) and power injections is established through a VUF sensitivity matrix, while the influence of tap changes on the VUF is quantified via an analytical sensitivity model. The proposed framework is validated through time-series simulations on a modified IEEE 123-bus distribution system, augmented with additional S/T-PVIs and subjected to dynamic solar irradiance profiles. The results demonstrate that the control strategy reduces the cumulative daily VUF by up to 35.88% on sunny days and 29.07% on cloudy days, while maintaining voltage magnitudes within the standard range of 0.95–1.05&#xa0;p.u. Furthermore, the number of daily tap changing operations is limited to 67 on sunny days and 70 on cloudy days, thereby preserving device integrity and ensuring that control actions remain feasible within the 15-min operational interval required for real-time implementation.</p>

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A model predictive control approach solved via modified mixed-variable PSO for voltage unbalance mitigation in an unbalanced distribution system with high photovoltaic penetration

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Yassir Maataoui,
  • Sara Dankir,
  • Hamid Chekenbah,
  • Vicenç Puig,
  • Rafik Lasri

摘要

The substantial and uneven integration of single-phase photovoltaic inverters (S-PVIs) into distribution systems (DS) has significantly increased voltage unbalance (VU) and voltage magnitude variations. This study proposes a coordinated control framework for managing complex unbalanced DS by integrating single-phase and three-phase PV inverters (S/T-PVIs), on-load tap changers (OLTC), and step voltage regulators (SVRs) through a model predictive control (MPC) strategy. The control problem is formulated as a Mixed-Integer Nonlinear Programming (MINLP) model, enabling precise coordination of OLTC and SVRs tap positions along with the active and reactive power outputs of each S/T-PVI phase. To efficiently solve the MINLP, a Modified Mixed-Variable Particle Swarm Optimization (MMVPSO) algorithm is developed, featuring distinct update strategies for discrete and continuous variables. The relationship between the voltage unbalance factor (VUF) and power injections is established through a VUF sensitivity matrix, while the influence of tap changes on the VUF is quantified via an analytical sensitivity model. The proposed framework is validated through time-series simulations on a modified IEEE 123-bus distribution system, augmented with additional S/T-PVIs and subjected to dynamic solar irradiance profiles. The results demonstrate that the control strategy reduces the cumulative daily VUF by up to 35.88% on sunny days and 29.07% on cloudy days, while maintaining voltage magnitudes within the standard range of 0.95–1.05 p.u. Furthermore, the number of daily tap changing operations is limited to 67 on sunny days and 70 on cloudy days, thereby preserving device integrity and ensuring that control actions remain feasible within the 15-min operational interval required for real-time implementation.