Optimal power flow(OPF) is the fundamental mathematical model to optimize power system operations.Based on conic relaxation, Taylor series expansion and McCormick envelope, we propose three convex OPF models to improv...Optimal power flow(OPF) is the fundamental mathematical model to optimize power system operations.Based on conic relaxation, Taylor series expansion and McCormick envelope, we propose three convex OPF models to improve the performance of the second-order cone alternating current OPF(SOC-ACOPF) model. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods.A heuristic algorithm to recover feasible ACOPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The proposed SOC-ACOPF models are examined through IEEE case studies under various load scenarios and power network congestions. The quality of solutions from the proposed SOC-ACOPF models is evaluated using MATPOWER(local optimality) and LINDOGLOBAL(global optimality). We also compare numerically the proposed SOC-ACOPF models with other two convex ACOPF models in the literature.The numerical results show robust performance of the proposed SOCACOPF models and the feasible solution recovery algorithm.展开更多
Combined heat and electricity operation with variable mass flow rates promotes flexibility,economy,and sustainability through synergies between electric power systems(EPSs)and district heating systems(DHSs).Such combi...Combined heat and electricity operation with variable mass flow rates promotes flexibility,economy,and sustainability through synergies between electric power systems(EPSs)and district heating systems(DHSs).Such combined operation presents a highly nonlinear and nonconvex optimization problem,mainly due to the bilinear terms in the heat flow model—that is,the product of the mass flow rate and the nodal temperature.Existing methods,such as nonlinear optimization,generalized Benders decomposition,and convex relaxation,still present challenges in achieving a satisfactory performance in terms of solution quality and computational efficiency.To resolve this problem,we herein first reformulate the district heating network model through an equivalent transformation and variable substitution.The reformulated model has only one set of nonconvex constraints with reduced bilinear terms,and the remaining constraints are linear.Such a reformulation not only ensures optimality,but also accelerates the solving process.To relax the remaining bilinear constraints,we then apply McCormick envelopes and obtain an objective lower bound of the reformulated model.To improve the quality of the McCormick relaxation,we employ a piecewise McCormick technique that partitions the domain of one of the variables of the bilinear terms into several disjoint regions in order to derive strengthened lower and upper bounds of the partitioned variables.We propose a heuristic tightening method to further constrict the strengthened bounds derived from the piecewise McCormick technique and recover a nearby feasible solution.Case studies show that,compared with the interior point method and the method implemented in a global bilinear solver,the proposed tightening McCormick method quickly solves the heat–electricity operation problem with an acceptable feasibility check and optimality.展开更多
电-热综合能源系统(integrated electricity and heat system,IEHS)可以有效促进可再生能源消纳。构建区域供热系统精细化模型与合理的可再生能源不确定性出力模型是调度IEHS的两个难点。该文首先提出计及可变流量调节模式的IEHS条件分...电-热综合能源系统(integrated electricity and heat system,IEHS)可以有效促进可再生能源消纳。构建区域供热系统精细化模型与合理的可再生能源不确定性出力模型是调度IEHS的两个难点。该文首先提出计及可变流量调节模式的IEHS条件分布鲁棒优化调度模型,主要有两点改进:通过构建基于修正模糊集的条件分布鲁棒模型建模可再生能源预测误差与其预测出力信息之间的内在依赖性,提升调度结果安全性与最优性;基于流体能量守恒方程与一阶隐式迎风格式建立可变流量调节模式下的IEHS调度模型,以期充分挖掘区域供热系统的灵活性,促进可再生能源消纳。所构建的IEHS调度模型为含有大量非线性约束的条件分布鲁棒模型,难以直接求解。对此,通过对偶理论与条件风险价值近似方法将条件分布鲁棒模型转化为含非线性约束的确定性模型,并提出自适应McCormick算法用以求解非线性约束。通过不同规模案例仿真表明,所提模型能够降低IEHS的调度成本,所提算法在保证可行性的条件下快速求出问题的近似最优解,最优间隙小于千分之一。展开更多
文摘Optimal power flow(OPF) is the fundamental mathematical model to optimize power system operations.Based on conic relaxation, Taylor series expansion and McCormick envelope, we propose three convex OPF models to improve the performance of the second-order cone alternating current OPF(SOC-ACOPF) model. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods.A heuristic algorithm to recover feasible ACOPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The proposed SOC-ACOPF models are examined through IEEE case studies under various load scenarios and power network congestions. The quality of solutions from the proposed SOC-ACOPF models is evaluated using MATPOWER(local optimality) and LINDOGLOBAL(global optimality). We also compare numerically the proposed SOC-ACOPF models with other two convex ACOPF models in the literature.The numerical results show robust performance of the proposed SOCACOPF models and the feasible solution recovery algorithm.
基金This work was supported by the Science and Technology Program of State Grid Corporation of China(522300190008).
文摘Combined heat and electricity operation with variable mass flow rates promotes flexibility,economy,and sustainability through synergies between electric power systems(EPSs)and district heating systems(DHSs).Such combined operation presents a highly nonlinear and nonconvex optimization problem,mainly due to the bilinear terms in the heat flow model—that is,the product of the mass flow rate and the nodal temperature.Existing methods,such as nonlinear optimization,generalized Benders decomposition,and convex relaxation,still present challenges in achieving a satisfactory performance in terms of solution quality and computational efficiency.To resolve this problem,we herein first reformulate the district heating network model through an equivalent transformation and variable substitution.The reformulated model has only one set of nonconvex constraints with reduced bilinear terms,and the remaining constraints are linear.Such a reformulation not only ensures optimality,but also accelerates the solving process.To relax the remaining bilinear constraints,we then apply McCormick envelopes and obtain an objective lower bound of the reformulated model.To improve the quality of the McCormick relaxation,we employ a piecewise McCormick technique that partitions the domain of one of the variables of the bilinear terms into several disjoint regions in order to derive strengthened lower and upper bounds of the partitioned variables.We propose a heuristic tightening method to further constrict the strengthened bounds derived from the piecewise McCormick technique and recover a nearby feasible solution.Case studies show that,compared with the interior point method and the method implemented in a global bilinear solver,the proposed tightening McCormick method quickly solves the heat–electricity operation problem with an acceptable feasibility check and optimality.
文摘电-热综合能源系统(integrated electricity and heat system,IEHS)可以有效促进可再生能源消纳。构建区域供热系统精细化模型与合理的可再生能源不确定性出力模型是调度IEHS的两个难点。该文首先提出计及可变流量调节模式的IEHS条件分布鲁棒优化调度模型,主要有两点改进:通过构建基于修正模糊集的条件分布鲁棒模型建模可再生能源预测误差与其预测出力信息之间的内在依赖性,提升调度结果安全性与最优性;基于流体能量守恒方程与一阶隐式迎风格式建立可变流量调节模式下的IEHS调度模型,以期充分挖掘区域供热系统的灵活性,促进可再生能源消纳。所构建的IEHS调度模型为含有大量非线性约束的条件分布鲁棒模型,难以直接求解。对此,通过对偶理论与条件风险价值近似方法将条件分布鲁棒模型转化为含非线性约束的确定性模型,并提出自适应McCormick算法用以求解非线性约束。通过不同规模案例仿真表明,所提模型能够降低IEHS的调度成本,所提算法在保证可行性的条件下快速求出问题的近似最优解,最优间隙小于千分之一。
