In distribution systems with high penetrations of solar energy, co-optimizing the operation of voltage regulators (VRs) with off-unity power factor inverters of photovoltaics (PVs) becomes imperative for confining nodal voltages within ANSI limits and ensuring an adequate number of tap actions. The framework proposed in this article minimizes the energy import from the substation (or maximizes the solar utility), the line losses, and the diurnal VR actions (VRAs) to reduce their maintenance costs and optimally coordinate with PV Var compensation. This is subject to the physical and security constraints of unbalanced distribution systems for which we build upon the rank-relaxed semidefinite programming branch flow model (SDP BFM). Departing from approximate VR models, we formulate an accurate model with nonuniformly-operated discrete tap positions. We overcome the computational complexity of solving the multi-time MISDP problem and the trilinearity emanating from VR incorporation by the application of Generalized Benders Decomposition (GBD). Also, to efficiently accommodate a large instance of binary variables, we accelerate the GBD's convergence with additional constraints on tap positions to reduce the search region. The merits of the proposed algorithm are demonstrated on the modified IEEE 37-bus and 123-bus test feeders for an hourly day-ahead optimization.

中文翻译：

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不平衡配电系统中稳压器与光伏的多次协同优化


在太阳能高渗透率的配电系统中，为了将节点电压限制在 ANSI 限制范围内并确保足够数量的分接动作，必须共同优化电压调节器 (VR) 与光伏 (PV) 功率因数非单位逆变器的运行。本文提出的框架最大限度地减少了变电站的能源输入（或最大限度地提高了太阳能效用）、线路损耗和日间 VR 动作 (VRA)，以降低其维护成本并与光伏无功补偿实现最佳协调。这受到不平衡分配系统的物理和安全约束，为此我们构建了秩松弛半定规划分支流模型（SDP BFM）。与近似 VR 模型不同，我们制定了具有非均匀操作的离散抽头位置的精确模型。我们通过应用广义 Benders 分解 (GBD) 克服了求解多次 MISDP 问题的计算复杂性以及 VR 合并带来的三线性性。此外，为了有效地容纳二进制变量的大型实例，我们通过对抽头位置的附加约束来加速 GBD 的收敛，以减少搜索区域。所提出算法的优点在改进的 IEEE 37 总线和 123 总线测试馈线上进行了验证，用于每小时的提前优化。