一种利用局部优化方法在不确定性条件下对微电网进行最优控制的高效方法
An Efficient Method for the Optimal Control of Microgrids Under Uncertainties using Local Reduction
摘要
在存在不确定性的微电网中，最优规模确定与电力调度问题早已为控制领域所熟知。通常，这一最优控制问题被转化为混合整数规划问题，以模拟能源存储系统中出现的各种约束条件，然后通过数值方法如情景分析法进行近似求解。本文提出了两种具有逻辑约束及用户电力需求、太阳能发电量、电网电价和电池效率等不确定性的微电网规模确定与电力调度最优控制问题的表述方式，并对它们进行了比较。第一种表述方式使用二进制变量和Big-M约束，从而形成混合整数线性规划问题；第二种表述方式则通过精确平滑重构逻辑约束，引入额外的建模变量和非凸约束，将其转化为连续非线性规划问题。我们还提出了一种新的局部简化算法，该算法扩展了现有方法，可用于解决这两种问题。通过使用100,000个样本蒙特卡洛模拟来评估局部简化算法得到的解决方案，发现两种方法的效果都相当好，其平均可行性率均超过90%。
English Abstract
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%.