一种使用局部降阶的微电网不确定性下最优控制的高效方法

摘要

针对微电网在不确定性条件下的最优容量配置与功率调度问题，控制领域已有广泛研究。通常，该最优控制问题被建模为混合整数规划，以描述储能系统中出现的逻辑约束，并采用场景法等数值方法进行近似求解。本文针对包含逻辑约束且存在用户用电需求、光伏发电出力、电网电价及电池效率不确定性的鲁棒微电网容量与功率调度最优控制问题，提出并比较了两种建模方案。第一种方案采用二进制变量与大M约束，构建混合整数线性规划模型；第二种方案通过引入附加建模变量与非凸约束，对逻辑约束进行精确光滑重构，将问题转化为连续非线性规划。在此基础上，我们提出一种改进的局部约简算法，用于求解上述两类问题。通过基于10万样本蒙特卡洛模拟的求解结果对比评估，两种方案均取得了理想效果，平均可行性验证率均超过90%。

English

The problem of optimal sizing and power scheduling in microgrids subject to uncertainties is well known to the control community. Commonly, the optimal control problem is cast as a mixed-integer program to model the logical constraints arising in energy storage systems, and is then solved approximately using numerical methods such as the scenario approach. In this paper, we propose and compare two formulations of a robust microgrid sizing and power scheduling optimal control problem with logical constraints and uncertainties in the user's power demand, solar power generation, grid electricity prices and battery efficiencies. The first formulation uses binary variables and big-M constraints, leading to a mixed-integer linear program. The second formulation casts the problem as a continuous nonlinear program through an exact smooth reformulation of the logical constraints, consisting of additional modelling variables and non-convex constraints. We then propose a novel local reduction algorithm, extending an existing method, to solve both problems. The two formulations are compared by evaluating the solutions returned by local reduction using 100,000-sample Monte Carlo simulations and achieve promising results, with both averaging feasibility rates above 90%.