一種在不確定性下使用局部縮減法進行微電網最佳控制的高效方法

摘要

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在控制领域广为人知。通常，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，并通过数值方法（例如场景法）近似求解。本文针对具有逻辑约束以及用户用电需求、太阳能发电量、电网电价及电池效率不确定性的鲁棒微电网容量配置与功率调度最优控制问题，提出并比较了两种建模形式。第一种形式采用二进制变量与大M约束，构成混合整数线性规划。第二种形式通过一种精确光滑的逻辑约束重构方法，将问题转化为连续非线性规划，其中包含额外的建模变量和非凸约束。随后，我们提出一种新颖的局部约简算法，对既有方法进行了扩展，以求解上述两种问题。通过基于10万样本蒙特卡洛仿真的解评估对两种形式进行了比较，二者均取得了令人满意的结果，平均可行率均超过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%.