论文标题
混合整数线性编程的多参数分析：传输计划和拥塞控制的应用
Multi-parametric Analysis for Mixed Integer Linear Programming: An Application to Transmission Planning and Congestion Control
论文作者
论文摘要
增强现有传输线是对抗传输充血并保证传输安全性随需求增加并提高可再生能源的有用工具。这项研究涉及选择其容量应扩大的线路的选择，以及从独立系统操作员（ISO）的角度来看，考虑到传输线约束，发电和需求平衡条件，并将坡道和启动坡道汇率，关闭坡道速率，坡道降低速度限制和最低降低和最低限度的时间，以最小化系统成本。为此，我们开发了ISO单元承诺和经济调度模型，并将其作为混合整数线性编程（MILP）问题的右侧不确定性多个参数分析。我们首先放松二进制变量以连续变量，并采用拉格朗日方法和Karush-Kuhn-tucker条件，以获得最佳的解决方案（最佳决策变量和目标函数）以及与主动和无效约束相关的关键区域。此外，我们通过确定每个节点处的问题上限，然后比较上限和下限之间的差异，并在决策者的耐受误差范围内达到近似最佳解决方案，从而扩展传统分支和界限方法。另外，目标函数在每行参数上的第一个衍生物用于告知各行的选择，以减轻拥塞和最大化社会福利。最后，通过平衡目标函数的成本率与参数的成本率和划分升级成本来选择容量升级量。我们的发现得到了数值模拟的支持，并为传输线计划提供了决策指导。
Enhancing existing transmission lines is a useful tool to combat transmission congestion and guarantee transmission security with increasing demand and boosting the renewable energy source. This study concerns the selection of lines whose capacity should be expanded and by how much from the perspective of independent system operator (ISO) to minimize the system cost with the consideration of transmission line constraints and electricity generation and demand balance conditions, and incorporating ramp-up and startup ramp rates, shutdown ramp rates, ramp-down rate limits and minimum up and minimum down times. For that purpose, we develop the ISO unit commitment and economic dispatch model and show it as a right-hand side uncertainty multiple parametric analysis for the mixed integer linear programming (MILP) problem. We first relax the binary variable to continuous variables and employ the Lagrange method and Karush-Kuhn-Tucker conditions to obtain optimal solutions (optimal decision variables and objective function) and critical regions associated with active and inactive constraints. Further, we extend the traditional branch and bound method for the large-scale MILP problem by determining the upper bound of the problem at each node, then comparing the difference between the upper and lower bounds and reaching the approximate optimal solution within the decision makers' tolerated error range. In additional, the objective function's first derivative on the parameters of each line is used to inform the selection of lines to ease congestion and maximize social welfare. Finally, the amount of capacity upgrade will be chosen by balancing the cost-reduction rate of the objective function on parameters and the cost of the line upgrade. Our findings are supported by numerical simulation and provide transmission line planners with decision-making guidance.
