The problem associated with economic dispatch of battery energy storage systems (BESSs) in alternating current (AC) distribution networks is addressed in this paper through convex optimization. The exact nonlinear programming model that represents the economic dispatch problem is transformed into a second-order cone programming (SOCP) model, thereby guaranteeing the global optimal solution-finding due to the conic (i.e., convex) structure of the solution space. The proposed economic dispatch model of the BESS considers the possibility of injecting/absorbing active and reactive power, in turn, enabling the dynamical apparent power compensation in the distribution network. A basic control design based on passivity-based control theory is introduced in order to show the possibility of independently controlling both powers (i.e., active and reactive). The computational validation of the proposed SOCP model in a medium-voltage test feeder composed of 33 nodes demonstrates the efficiency of convex optimization for solving nonlinear programming models via conic approximations. All numerical validations have been carried out in the general algebraic modeling system.

中文翻译：

---

用于交流配电网中视在功率补偿的BESS经济调度问题的二阶锥规划重构

本文通过凸优化解决了与交流配电网中电池储能系统（BESS）的经济调度有关的问题。代表经济调度问题的精确非线性规划模型被转换为二阶锥规划（SOCP）模型，从而由于解空间的圆锥（即凸）结构而保证了全局最优解查找。提出的BESS经济调度模型考虑了注入/吸收有功和无功功率的可能性，进而实现了配电网的动态视在功率补偿。为了说明独立控制两种功率（即有功和无功）的可能性，引入了基于无源控制理论的基本控制设计。在一个由33个节点组成的中压测试馈线中，所提出的SOCP模型的计算验证证明了凸优化通过圆锥近似求解非线性规划模型的效率。所有数值验证均已在通用代数建模系统中进行。