The Research Of Optimal PMU Placement

With the development of smart grid,the requirement for power reliability is more and more higher.State estimation provides a guarantee for the security of power systems.However,in state estimation,measurement data gathered from substations must make the system fully observable.Traditional energy management system can provide necessary measurement data for state estimation,but can not monitor the dynamic behavior of the system in real time.The application of phasor measurement unit(PMU)has created favorable conditions for safe operation of the power system.PMU can measure the voltage vector of installed bus and the current vector of branches connecting to this bus and has higher measuring frequency and accuracy.However,it is neither economical nor necessary to install PMU at each bus in the system.And there exists communication burden.So it is very important to study the optimal PMU placement.For optimal PMU placement,the definition and judgment method of observability is first given in this paper.And the effect of zero injection on the observability of the system and PMU placement is analyzed in detail,which helps to use zero injection buses to reduce the number of PMU.Then,the mathematical model with and without considering zero injection is given and by modifying the mathematical model,mathematical model considering measurements losses and limitation of PMU measurement channel are obtained.Finally,all conditions are simulated and results are analyzed in detail.In order to enhance the flexibility of system configuration and obtain several phasor measurement units(PMU)configuration schemes both considering the number of PMU and redundancy value,which are suitable for different situations,a novel PMU configuration method based on the system topology model and matrix elements operation is proposed.The proposed method can be divided into three stages to make the system completely observable.In each stage,the connection information between buses and buses with different degrees such as leaf nodes and isolated bus,where degrees indicate the number of branches connected to this bus,are applied to obtain different PMU placements.Especially,the extent of links between buses is proposed in stage II,which helps to obtain optimal PMU placement.And each stage all considers the effect of zero injection buses.In order to further reduce thenumber of PMU,a novel redundancy check method is put forward for this program.In the configuration process,an operational configuration way based on the binary matrix established by network connectivity matrix,PMU configuration vector,observability bus vector and zero injection bus vector is applied to avoid the effect of model change on the algorithm and enhance the flexibility of this algorithm.And a variety of configuration schemes are also obtained.The application of matrix elements operation such as “and” or“sum” accelerates the speed of operation.In order to guarantee the observability of the system when zero injection is lost or topology model changes,a novel additional PMU configuration method combining the system topology model and mathematical model is proposed.The proposed method first analyzes the effect of the losses of zero injection and change of topology model on system observability.And the zero injection buses with and without applications are proposed by the numerical analysis.To obtain unobservable buses,the way based on the mathematical model is put forward and based on the unobservable buses,additional PMU placements with the minimum number of PMU and maximum redundancy are given by topology model.The zero injection buses without applications are applied to reduce the number of additional PMU.Finally,by simulation of standard system,the additional PMU placements are obtained.