馈线区段故障的快速准确辨识对于提升配电网可靠性与自愈性有重要作用。针对基于逻辑关系的间接故障定位方法在数值稳定性和决策效率上的不足,该文基于代数关系描述和互补约束理论构建了配电网故障区段定位的互补约束新模型,其优势在于...馈线区段故障的快速准确辨识对于提升配电网可靠性与自愈性有重要作用。针对基于逻辑关系的间接故障定位方法在数值稳定性和决策效率上的不足,该文基于代数关系描述和互补约束理论构建了配电网故障区段定位的互补约束新模型,其优势在于:1)避免了对群体智能算法的过分依赖,可采用数值稳定性好的梯度算法优化求解;2)利用互补约束条件将离散变量松弛为连续变量,降低了故障定位问题决策时的复杂性。在此基础上,提出基于扰动因子的故障定位模型光滑化求解算法。仿真表明,新模型和决策算法不仅能够实现馈线故障区段的准确高容错性辨识,且进行优化决策时具有数值稳定性好、优化效率高的优点,在大规模配电网故障定位中有良好的应用前景。Fast and exact feeder fault location method plays an important role in enhancing reliability and self-healing of distribution network.Logic relationship based conventional indirect fault location model and method has the drawbacks of excessive reliance on swarm intelligence algorithm in optimization computation,numerical optimization instability and low decision-making efficiency.In order to overcome the above shortcomings,on basis of algebra relationship description and complementary theory,a novel complementarity constraints fault location model is proposed as follows:1min()()1,0[(1),(2),,()],[(1),(2),,()],0,,i N S i N N f KB x x x NκκκN=?=???+=⊥=?==?≥∈∈?X∑X X X X X XκκκκRκR(1)Because the feasible points of the above complementarity constraints model can not satisfy the nonlinear programming constraint specification,the optimal solution can not be obtained by using the nonlinear programming to satisfy the Karush-Kuhn-Tucker(KKT)condition.In order to solve the novel fault location model effectively used by nonlinear programming directly,the Fischer-Burmeister auxiliary function with the perturbation factor is used to transform the complementarity constraints fault location model into a continuous smoothing model,which can satisfy the B-stability point.The smoothing model for fault location with complementarity constraints can be expressed as:212 2 2min(,,)()()()()11 2 0()()0[(1),(2),,()][(1),(2),,()][(1),(2),,()],0,N i N N F f i f x x x N N Nφφεφκκκεεε=?=+??=??+=??-++=??=?=?=??=?≥??∈∈?∑X X X XεX XκεX XκεεεκκεκRεR(2)In this model,the feasible point satisfies the nonlinear constraint specification,which can be solved by nonlinear programming directly.When the value of the perturbation factor tends to zero and the KKT extremum condition is established,the optimal decision vector of the fault location model can be obtained,so that the feeder fault section can be found.The correctness and effectiveness of the fault location model with complementarity constraints are verified by(sequence quadratic program)SQP in Matlab2010 a simulation platform.The simulation study shows that:1)The novel model of distribution network fault location based on the theory of complementarity constraints can effectively reflect the correlation characteristics between the causal devices,which can accurately locate the fault section of the feeder fault,and has high fault tolerance.2)The model is proposed based on relational algebra description modeling,so in optimization decision process can avoid the fault identification model excessive reliance on swarm intelligence algorithm in optimization computation,in which the gradient algorithm with good numerical stability can be used,which has the advantage in numerical stability.3)By through the feeder fault status information complementarity constraints conditions,the fault identification model can be transformed from discrete optimization space to continuous optimization space,which can effectively reduce the complexity of fault location model in optimization decision.4)The smoothing method based on the perturbation factor auxiliary penalty function can improve the non-smoothing characteristics of the complementarity constraints model,which can lead the optimal value to converge to the stable point,so as to accurately locate the feeder fault section.5)The novel fault location model and decision method proposed in this paper can be applied to the feeder fault location problem in large scale distribution network.展开更多
文摘馈线区段故障的快速准确辨识对于提升配电网可靠性与自愈性有重要作用。针对基于逻辑关系的间接故障定位方法在数值稳定性和决策效率上的不足,该文基于代数关系描述和互补约束理论构建了配电网故障区段定位的互补约束新模型,其优势在于:1)避免了对群体智能算法的过分依赖,可采用数值稳定性好的梯度算法优化求解;2)利用互补约束条件将离散变量松弛为连续变量,降低了故障定位问题决策时的复杂性。在此基础上,提出基于扰动因子的故障定位模型光滑化求解算法。仿真表明,新模型和决策算法不仅能够实现馈线故障区段的准确高容错性辨识,且进行优化决策时具有数值稳定性好、优化效率高的优点,在大规模配电网故障定位中有良好的应用前景。Fast and exact feeder fault location method plays an important role in enhancing reliability and self-healing of distribution network.Logic relationship based conventional indirect fault location model and method has the drawbacks of excessive reliance on swarm intelligence algorithm in optimization computation,numerical optimization instability and low decision-making efficiency.In order to overcome the above shortcomings,on basis of algebra relationship description and complementary theory,a novel complementarity constraints fault location model is proposed as follows:1min()()1,0[(1),(2),,()],[(1),(2),,()],0,,i N S i N N f KB x x x NκκκN=?=???+=⊥=?==?≥∈∈?X∑X X X X X XκκκκRκR(1)Because the feasible points of the above complementarity constraints model can not satisfy the nonlinear programming constraint specification,the optimal solution can not be obtained by using the nonlinear programming to satisfy the Karush-Kuhn-Tucker(KKT)condition.In order to solve the novel fault location model effectively used by nonlinear programming directly,the Fischer-Burmeister auxiliary function with the perturbation factor is used to transform the complementarity constraints fault location model into a continuous smoothing model,which can satisfy the B-stability point.The smoothing model for fault location with complementarity constraints can be expressed as:212 2 2min(,,)()()()()11 2 0()()0[(1),(2),,()][(1),(2),,()][(1),(2),,()],0,N i N N F f i f x x x N N Nφφεφκκκεεε=?=+??=??+=??-++=??=?=?=??=?≥??∈∈?∑X X X XεX XκεX XκεεεκκεκRεR(2)In this model,the feasible point satisfies the nonlinear constraint specification,which can be solved by nonlinear programming directly.When the value of the perturbation factor tends to zero and the KKT extremum condition is established,the optimal decision vector of the fault location model can be obtained,so that the feeder fault section can be found.The correctness and effectiveness of the fault location model with complementarity constraints are verified by(sequence quadratic program)SQP in Matlab2010 a simulation platform.The simulation study shows that:1)The novel model of distribution network fault location based on the theory of complementarity constraints can effectively reflect the correlation characteristics between the causal devices,which can accurately locate the fault section of the feeder fault,and has high fault tolerance.2)The model is proposed based on relational algebra description modeling,so in optimization decision process can avoid the fault identification model excessive reliance on swarm intelligence algorithm in optimization computation,in which the gradient algorithm with good numerical stability can be used,which has the advantage in numerical stability.3)By through the feeder fault status information complementarity constraints conditions,the fault identification model can be transformed from discrete optimization space to continuous optimization space,which can effectively reduce the complexity of fault location model in optimization decision.4)The smoothing method based on the perturbation factor auxiliary penalty function can improve the non-smoothing characteristics of the complementarity constraints model,which can lead the optimal value to converge to the stable point,so as to accurately locate the feeder fault section.5)The novel fault location model and decision method proposed in this paper can be applied to the feeder fault location problem in large scale distribution network.
