计及N-1线路故障的连续时间随机安全约束机组组合问题的双层分解算法

Two-layer Decomposition Algorithm for Continuous-time Stochastic Security-constrained Unit Commitment Considering N-1 Line Contingency

伴随着可再生能源装机规模逐步扩大,电力系统的随机性和波动性进一步增强。为了制定更准确的机组启停和发电计划,保证系统运行安全,建立计及N-1线路故障的连续时间随机安全约束机组组合模型。首先采用Bernstein多项式将该无限维的连续时间优化模型转化为有限维的混合整数线性规划(mixed integer linear programming,MILP)模型。由于转化后的模型维度极高,为高效求解该模型,提出逐步对冲-Benders分解(progressive hedging-Bendersdecom-position, PH-BD)双层分解算法:外层采用逐步对冲(progressive hedging,PH)算法对场景打捆后的“场景束”进行分解,实现每个场景束对应问题的并行计算;内层采用Benders分解(Benders decomposition,BD)算法将每个场景束对应问题分解为无线路约束主问题和可并行求解的线路约束子问题。最后在IEEE118节点系统中进行算例验证。结果表明,与离散时间模型相比,连续时间随机安全约束机组组合模型可以更准确地制定机组启停和发电计划以及设置备用容量;与传统PH算法相比,所提出的PH-BD算法显著降低了求解时间。

With the gradual expansion of renewable energy installations,the randomness and volatility of the power systems are further enhanced.In order to make more accurate scheduling decisions and ensure the safety of the system operation,a continuous time stochastic security constraint unit commitment model considering N-1 line contingency is established.Firstly,the Bernstein polynomials are used to transform the infinite dimensional continuous time optimization model into a finite dimensional Mixed Integer Linear programming(MILP)model.Due to the high dimension of the transformed model,a two-layer Progressive Hedging-Benders decomposition algorithm(PH-BD)is proposed to efficiently solve the model:In the outer layer,the Progressive Hedging(PH)algorithm is used to decompose the"scenario bundles"after bundling the scenarios,realizing the parallel calculation of the corresponding problem of each scenario bundle.In the inner layer,the Benders decomposition(BD)algorithm is used to decompose the corresponding problem of each scenario bundle into a main problem without line constraints and the sub-problems with line constraints that can be solved in parallel.Finally,an example is given in the IEEE 118-bus system.The results show that compared with the discrete time model,the continuous time stochastic security constraint unit commitment model makes more accurate scheduling decisions.Compared with the traditional PH algorithm,the proposed PH-BD algorithm significantly reduces the solution time.