基于半正定规划的交直流主动配电网三相有功无功联合优化

Three-Phase Active-Reactive Power Optimization of AC-DC Active Distribution Network Based on Semi-Definite Programming

交直流主动配电网作为未来配电网的主要发展形态,实现其有功无功资源的协同优化控制具有重要的研究意义。然而配电网负荷单相接入和分布式发电三相功率不一致,将导致配电网三相不平衡现象越发严重。为了应对交直流主动配电网的三相不平衡问题,提出考虑相间耦合与三相不平衡度限制的三相有功无功联合优化方法。首先,建立考虑相间耦合的原始三相潮流模型并对其进行升维映射;其次,采用半正定松弛方法,推导了交直流主动配电网各子系统的完整三相潮流模型以及序分量形式下的三相电压不平衡度约束;再次,提出以总运行成本最小化为目标函数的交直流主动配电网三相有功无功联合优化模型;最后,采用改进IEEE 33节点、69节点、141节点和1056节点交直流配电网算例分析,验证了该文所提方法的有效性。

As the main outlook of the future distribution network,it is of great research value to jointly allocate active-reactive power resources of AC-DC active distribution network.However,the access of single-phase load and the three-phase power inconsistency of distributed generation will lead to more severe three-phase unbalance situation in the distribution network.To deal with the three-phase unbalance problem in AC-DC active distribution network,a joint three-phase active and reactive power optimization method is proposed,which takes the phase-to-phase coupling relationship and the three-phase unbalance factor limitation into account.Firstly,the original three-phase power flow model considering the phase-to-phase coupling relationship is established and the model is mapped to a high-dimensional space then.Secondly,the complete symmetrical three-phase power flow model of each subsystem of AC-DC active distribution network and the symmetrical three-phase voltage unbalance factor constraints are derived using the semidefinite programming.Then,a joint three-phase active-reactive power optimization model of AC-DC active distribution network with the objective of minimizing the total network operation cost is proposed.To verify the accuracy and effectiveness of the proposed method,the maximum relaxation deviation and maximum logarithmic relaxation mismatch results are firstly demonstrated via case studies on the modified IEEE 33-bus AC-DC distribution system.Under different unbalanced circumstances,the maximum relaxation deviations of the proposed method are always lower than 10-7 with the corresponding relaxation mismatch under 10-5.Besides,the results of voltage deviation percentage of the proposed method are lower than the results of the standard three-phase SDP method.Moreover,in contrast to the traditional three-phase decoupled model,the proposed method is able to obtain a smaller operation cost results,e.g.,4.489%and 13.188%reduction on operation cost and transmission loss cost under 20%-line impedance unbalance circumstance,and more real voltage results.And it can effectively limit the three-phase unbalance of the system voltage with the voltage unbalance factor model always under the pre-set 2%threshold at the same time.To further verify the calculation performances on large scale systems,case studies are carried out on the modified IEEE 69-,141-and 1056-bus AC-DC distribution systems.Compared with the standard three-phase SDP method,the proposed method can provide more accurate optimization results while the computing time do not increase too much.Meanwhile,compared with the linearized model,the average mismatches are always smaller,which indicates the infeasibility of the linearized model.The following conclusions can be drawn from the simulation analysis:(1)Under different three-phase unbalance circumstances,the proposed method can guarantee the relaxation accuracy of the algorithm and gain better performances on accuracies compared with the standard three-phase SDP method.(2)The proposed method can obtain a smaller operation cost and more real bus voltages compared with the traditional three-phase decoupled model,which indicates its’applicability in the actual operation states of the AC-DC distribution network.(3)The effectiveness of the three-phase voltage unbalance limitation constraint is verified which consequently proves that the proposed model satisfies the actual operation requirements of the AC-DC distribution network.(4)In large-scale AC-DC distribution test systems,the proposed method is superior on calculation accuracy,but has no evident disadvantages on calculation speed performance.