技术领域Technical Field
本发明涉及一种配电网鲁棒状态估计方法。特别是涉及一种考虑多源量测的配电网二阶锥规划鲁棒状态估计方法。The present invention relates to a robust state estimation method for a distribution network, and in particular to a second-order cone programming robust state estimation method for a distribution network considering multi-source measurement.
背景技术Background Art
以光伏、风电为代表的可再生能源的蓬勃快速发展，正推动构建以新能源为主体的新型配电系统。光伏、风电等可再生能源具有清洁、低碳等优势，但存在波动性、间歇性的特点，其出力的快速波动使得网络运行状态的变化更为频繁，更高频率的运行状态监视成为新型配电系统的必要功能。在量测设备端，以同步相量量测(PMU)为代表的新型量测具有时间同步、采样频率快、量测精度高等特点，使得高精度、强鲁棒性的运行状态估计成为可能。在此背景下，配电网运行状态估计如何充分利用包含新型PMU量测及配电网传统的数据采集与监视控制系统(SCADA)量测和高级量测体系(AMI)量测，并辨识其中存在的量测坏数据，对提高状态估计精度和鲁棒性具有重要的意义。The rapid development of renewable energy represented by photovoltaic and wind power is promoting the construction of a new distribution system with new energy as the main body. Renewable energy such as photovoltaic and wind power has the advantages of being clean and low-carbon, but it is characterized by volatility and intermittency. The rapid fluctuation of its output makes the network operation status change more frequently, and higher-frequency operation status monitoring has become a necessary function of the new distribution system. On the measurement equipment side, new measurements represented by synchronized phasor measurement (PMU) have the characteristics of time synchronization, fast sampling frequency, and high measurement accuracy, making high-precision and strong robustness of operation status estimation possible. In this context, how to make full use of the new PMU measurement and the traditional data acquisition and monitoring control system (SCADA) measurement and advanced measurement system (AMI) measurement of the distribution network operation status estimation, and identify the bad measurement data, is of great significance to improving the accuracy and robustness of state estimation.
目前，配电网状态估计的目标函数主要包括加权最小二乘估计方法和加权最小绝对值估计方法，相比于加权最小二乘估计方法，加权最小绝对值估计方法对量测坏数据具有一定的鲁棒性，可在估计过程中辨识量测坏数据，但求解速度相对较慢。当前主流的状态估计求解方法为高斯-牛顿法迭代求解法，但其对估计初始点较为敏感，初始点选取不好时存在一定的收敛性问题。因此，为提升包括鲁棒性在内的状态估计性能指标，需要权衡速度、精度及鲁棒性能指标，有必要选取合适的目标函数并挖掘提出相应的求解方法。At present, the objective functions of distribution network state estimation mainly include weighted least squares estimation method and weighted minimum absolute value estimation method. Compared with weighted least squares estimation method, weighted minimum absolute value estimation method has certain robustness to bad measurement data and can identify bad measurement data during the estimation process, but the solution speed is relatively slow. The current mainstream state estimation solution method is the Gauss-Newton iterative solution method, but it is sensitive to the initial point of estimation and has certain convergence problems when the initial point is not well selected. Therefore, in order to improve the state estimation performance indicators including robustness, it is necessary to balance the speed, accuracy and robustness performance indicators. It is necessary to select a suitable objective function and explore and propose a corresponding solution method.
考虑多源量测数据的鲁棒状态估计方法充分考虑新型配电系统的多源量测数据，以加权最小绝对值作为目标函数、采用二阶锥规划方法实现估计求解，可以处理PMU量测给二阶锥规划求解模型带来的变化，实现多源量测数据的综合利用，凸显鲁棒状态估计在量测坏数据辨识、计算求解速度方面的优势。考虑到PMU量测的采样频率远大于SCADA及AMI量测，在状态估计时刻充分利用估计时刻附近的多时间断面PMU量测数据，可避免由于通信故障、量测采集错误等原因导致的单个量测坏数据问题，进一步提升状态估计的鲁棒性。The robust state estimation method considering multi-source measurement data fully considers the multi-source measurement data of the new distribution system, takes the weighted minimum absolute value as the objective function, and adopts the second-order cone programming method to achieve estimation and solution. It can handle the changes brought by PMU measurement to the second-order cone programming solution model, realize the comprehensive utilization of multi-source measurement data, and highlight the advantages of robust state estimation in measurement bad data identification and calculation and solution speed. Considering that the sampling frequency of PMU measurement is much higher than that of SCADA and AMI measurement, making full use of multi-time section PMU measurement data near the estimation time at the state estimation time can avoid the problem of single measurement bad data caused by communication failure, measurement acquisition errors, etc., and further improve the robustness of state estimation.
发明内容Summary of the invention
本发明所要解决的技术问题是，为克服现有技术的不足，提供一种能够进一步提升坏数据辨识性能的考虑多源量测的配电网二阶锥规划鲁棒状态估计方法。The technical problem to be solved by the present invention is to provide a second-order cone programming robust state estimation method for distribution network considering multi-source measurement, which can further improve the bad data identification performance, in order to overcome the shortcomings of the prior art.
本发明所采用的技术方案是：一种考虑多源量测的配电网二阶锥规划鲁棒状态估计方法，包括如下步骤：The technical solution adopted by the present invention is: a second-order cone programming robust state estimation method for distribution network considering multi-source measurement, comprising the following steps:
1)对于给定的包含多源量测数据的有源配电网，输入配电网的拓扑连接关系，线路阻抗参数，负荷、分布式电源的接入位置信息及多源量测数据的配置信息；1) For a given active distribution network containing multi-source measurement data, input the topological connection relationship of the distribution network, line impedance parameters, access location information of loads and distributed generation, and configuration information of the multi-source measurement data;
2)依据步骤1)提供的配电网的拓扑连接关系和多源量测数据的配置信息，确定二阶锥规划鲁棒状态估计状态变量x；2) determining a second-order cone programming robust state estimation state variable x according to the topological connection relationship of the distribution network and the configuration information of the multi-source measurement data provided in step 1);
3)获取估计时刻t多源量测数据的计算量测值z[t]、计算权重w[t]，构建多源量测数据与二阶锥规划鲁棒状态估计状态变量x之间的量测约束；构建零注入节点与二阶锥规划鲁棒状态估计状态变量x之间的零注入约束；3) Obtain the calculated measurement value z[t] and the calculated weight w[t] of the multi-source measurement data at the estimation time t, construct the measurement constraint between the multi-source measurement data and the second-order cone programming robust state estimation state variable x; construct the zero injection constraint between the zero injection node and the second-order cone programming robust state estimation state variable x;
4)以多源量测数据的计算量测值与估计值之间的残差加权最小绝对值为目标函数，采用二阶锥规划算法求解估计时刻t的鲁棒状态估计问题；4) Taking the weighted minimum absolute value of the residual between the calculated measurement value and the estimated value of the multi-source measurement data as the objective function, the second-order cone programming algorithm is used to solve the robust state estimation problem at the estimation time t;
5)将估计时刻t的二阶锥规划鲁棒状态估计状态变量x的估计结果转换为节点电压幅值和相角估计结果。5) The estimation result of the second-order cone programming robust state estimation state variable x at the estimation time t is converted into the node voltage amplitude and phase angle estimation results.
本发明的考虑多源量测的配电网二阶锥规划鲁棒状态估计方法，构建了加权最小绝对值目标函数下二阶锥规划方法求解的鲁棒状态估计方法，综合考虑配电网中的PMU量测数据、SCADA量测数据和AMI量测数据，引入节点电压状态变量、线路状态变量及节点注入电流幅值状态变量，采用二阶旋转锥规划方法求解，加快了状态估计的求解速度，实现了估计过程中的量测坏数据辨识；在求解过程中引入多时间断面PMU量测数据，在传统加权最小绝对值目标函数状态估计的基础上进一步提升了坏数据辨识性能。The second-order cone programming robust state estimation method for distribution network considering multi-source measurement of the present invention constructs a robust state estimation method for solving the second-order cone programming method under the weighted minimum absolute value objective function, comprehensively considers PMU measurement data, SCADA measurement data and AMI measurement data in the distribution network, introduces node voltage state variables, line state variables and node injection current amplitude state variables, and adopts the second-order rotating cone programming method for solution, which speeds up the solution speed of state estimation and realizes the identification of bad measurement data in the estimation process; multi-time section PMU measurement data are introduced in the solution process, and the bad data identification performance is further improved on the basis of traditional weighted minimum absolute value objective function state estimation.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1是本发明考虑多源量测的配电网二阶锥规划鲁棒状态估计方法的流程图；1 is a flow chart of a robust state estimation method for distribution network second-order cone programming considering multi-source measurement according to the present invention;
图2是IEEE33节点算例的网络拓扑连接和量测配置情况图。Figure 2 is a diagram of the network topology connection and measurement configuration of the IEEE33 node example.
具体实施方式DETAILED DESCRIPTION
下面结合实施例和附图对本发明的考虑多源量测的配电网二阶锥规划鲁棒状态估计方法做出详细说明。The robust state estimation method of distribution network second-order cone programming considering multi-source measurement of the present invention is described in detail below in conjunction with the embodiments and drawings.
如图1所示，本发明的考虑多源量测的配电网二阶锥规划鲁棒状态估计方法，包括如下步骤：As shown in FIG1 , the second-order cone programming robust state estimation method for distribution network considering multi-source measurement of the present invention comprises the following steps:
1)对于给定的包含多源量测数据的有源配电网，输入配电网的拓扑连接关系，线路阻抗参数，负荷、分布式电源的接入位置信息及多源量测数据的配置信息；所述的多源量测包括传统量测和同步相量测量装置(PMU)量测，传统量测包括数据采集与监视控制系统(SCADA)量测和高级量测体系(AMI)量测。1) For a given active distribution network containing multi-source measurement data, the topological connection relationship of the input distribution network, line impedance parameters, access location information of loads and distributed generation, and configuration information of the multi-source measurement data; the multi-source measurement includes traditional measurement and synchronized phasor measurement unit (PMU) measurement, and the traditional measurement includes data acquisition and supervision control system (SCADA) measurement and advanced measurement architecture (AMI) measurement.
2)依据步骤1)提供的配电网的拓扑连接关系和多源量测数据的配置信息，确定二阶锥规划鲁棒状态估计状态变量x；2) determining a second-order cone programming robust state estimation state variable x according to the topological connection relationship of the distribution network and the configuration information of the multi-source measurement data provided in step 1);
所述的确定二阶锥规划鲁棒状态估计状态变量x为：The second-order cone programming robust state estimation state variable x is determined as:
x＝[V，Kl，Ll，Km，Lm]T (1)x=[V, Kl , Ll , Km , Lm ]T (1)
式中，V为节点电压状态变量，为节点i的p相电压状态变量，i为节点编号，为配电网节点集合，p为相序编号，为相序集合，为节点i的p相电压幅值；Kl、Ll分别为线路状态变量，分别为线路ij的p相状态变量，i、j分别为线路ij的首端节点和末端节点，为配电网线路集合，为节点j的p相电压幅值，分别为节点i、j的p相电压相角；Km、Lm分别为节点注入电流幅值量测状态变量，分别为节点注入电流幅值量测关联的连接节点s和c的p相状态变量，分别为节点s、c的p相电压幅值，分别为节点s、c的p相电压相角，s∈lr，c∈lr，c＞s，s和c均为节点r的连接节点，r为节点注入电流幅值量测关联的节点，为节点注入电流幅值量测关联的节点集合，为节点r的连接节点集合；[·]T为元素“·”的转置。Where V is the node voltage state variable, is the p-phase voltage state variable of node i, i is the node number, is the set of distribution network nodes, p is the phase sequence number, is a phase sequence set, is the p-phase voltage amplitude of node i; Kl and Ll are line state variables, are the p-phase state variables of line ij, i and j are the head node and the terminal node of line ij respectively, is the distribution network line collection, is the p-phase voltage amplitude at node j, are the p-phase voltage phase angles of nodes i and j respectively; Km and Lm are the state variables for measuring the amplitude of the node injected current respectively, The p-phase state variables of the connected nodes s and c are measured for the node injection current amplitude, respectively. are the p-phase voltage amplitudes at nodes s and c, respectively. are the p-phase voltage phase angles of nodes s and c, s∈lr , c∈lr , c＞s, s and c are both connected nodes of node r, r is the node associated with the node injection current amplitude measurement, The node set associated with the node injection current amplitude measurement, is the set of connected nodes of node r; [·]T is the transpose of element “·”.
3)获取估计时刻t多源量测数据的计算量测值z[t]、计算权重w[t]，构建多源量测数据与二阶锥规划鲁棒状态估计状态变量x之间的量测约束；构建零注入节点与二阶锥规划鲁棒状态估计状态变量x之间的零注入约束；其中，3) Obtain the calculated measurement value z[t] and the calculated weight w[t] of the multi-source measurement data at the estimation time t, construct the measurement constraint between the multi-source measurement data and the second-order cone programming robust state estimation state variable x; construct the zero injection constraint between the zero injection node and the second-order cone programming robust state estimation state variable x; wherein,
所述的获取估计时刻t多源量测数据的计算量测值z[t]、计算权重w[t]，构建多源量测数据与二阶锥规划鲁棒状态估计状态变量x之间的量测约束，具体表示为：The calculation of the measurement value z[t] and the weight w[t] of the multi-source measurement data at the estimated time t, and the construction of the measurement constraint between the multi-source measurement data and the second-order cone programming robust state estimation state variable x, are specifically expressed as:
3.1)估计时刻t多源量测数据的计算量测值z[t]、计算权重w[t]表示为：3.1) The calculated measurement value z[t] and the calculated weight w[t] of the multi-source measurement data at the estimated time t are expressed as:
式中，分别为估计时刻t第a个传统量测的计算量测值、计算权重，a＝1，2，...，M，M为传统量测的数目，分别为估计时刻t第y个同步相量测量装置量测的计算量测值、计算权重，Y为同步相量测量装置量测的数目；In the formula, are the calculated measurement value and the calculated weight of the ath traditional measurement at the estimation time t, respectively, a=1, 2, ..., M, M is the number of traditional measurements, are the calculated measurement value and the calculated weight of the yth synchronized phasor measurement device measurement at the estimation time t, respectively, and Y is the number of synchronized phasor measurement device measurements;
3.2)对于任意的第a个传统量测，根据量测类型分别设置估计时刻t的计算量测值、计算权重及量测约束：3.2) For any a-th traditional measurement, set the calculated measurement value, calculation weight and measurement constraint at the estimated time t according to the measurement type:
3.2.1)若a为关联节点i的p相电压幅值量测，则令为估计时刻t节点i的p相电压幅值量测的量测值，为节点i的p相电压幅值量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.1) If a is the measured voltage amplitude of phase p associated with node i, then let is the measured value of the p-phase voltage amplitude at node i at the estimated time t, is the error standard deviation of the p-phase voltage amplitude measurement at node i; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
式中，为节点i的p相电压状态变量，为估计时刻t第a个传统量测的残差；In the formula, is the p-phase voltage state variable of node i, is the residual of the ath traditional measurement at time t;
3.2.2)若a为关联节点i的p相注入有功功率量测，则令为估计时刻t节点i的p相注入有功功率量测的量测值，为节点i的p相注入有功功率量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.2) If a is the p-phase injected active power measurement associated with node i, then let is the measured value of the p-phase injected active power measurement at node i at the estimated time t, is the error standard deviation of the p-phase injected active power measurement of node i; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
式中，f为节点i的前序连接节点，j为节点i的后序连接节点，和分别为节点i的前序连接节点集合和后序连接节点集合，分别为线路fi的p相电导、电纳，分别为线路ij的p相电导、电纳，分别为线路fi的p相状态变量，分别为线路ij的p相状态变量；In the formula, f is the previous connection node of node i, j is the subsequent connection node of node i, and are the pre-order connection node set and post-order connection node set of node i respectively, are the p-phase conductance and susceptance of line fi respectively, are the p-phase conductance and susceptance of line ij, are the p-phase state variables of line fi, are the p-phase state variables of line ij respectively;
3.2.3)若a为关联节点i的p相注入无功功率量测，则令为估计时刻t节点i的p相注入无功功率量测的量测值，为节点i的p相注入无功功率量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.3) If a is the p-phase injected reactive power measurement associated with node i, then let is the measured value of the reactive power injected into the p-phase of the node i at the estimated time t, is the error standard deviation of the reactive power measurement of phase p injected at node i; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
式中，为线路fi的p相并联电纳，为线路ij的p相并联电纳；In the formula, is the p-phase shunt susceptance of line fi, is the p-phase shunt susceptance of line ij;
3.2.4)若a为关联线路ij的p相首端有功功率量测，则令为估计时刻t线路ij的p相首端有功功率量测的量测值，为线路ij的p相首端有功功率量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.4) If a is the active power measurement at the first end of phase p of the associated line ij, then let is the measured value of the active power measurement at the first end of the p-phase line ij at time t, is the error standard deviation of the active power measurement at the first end of phase p of line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.2.5)若a为关联线路ij的p相末端有功功率量测，则令为估计时刻t线路ij的p相末端有功功率量测的量测值，为线路ij的p相末端有功功率量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.5) If a is the active power measurement at the end of phase p of the associated line ij, then let is the measured value of the active power measurement at the end of phase p of line ij at time t, is the error standard deviation of the active power measurement at the end of phase p of line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
式中，为节点j的p相电压状态变量；In the formula, is the p-phase voltage state variable of node j;
3.2.6)若a为关联线路ij的p相首端无功功率量测，则令为估计时刻t线路ij的p相首端无功功率量测的量测值，为线路ij的p相首端无功功率量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.6) If a is the reactive power measurement at the first end of phase p of the associated line ij, then let is the measured value of reactive power measurement at the first end of phase p of line ij at time t, is the error standard deviation of the reactive power measurement at the first end of phase p of line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.2.7)若a为关联线路ij的p相末端无功功率量测，则令为估计时刻t线路ij的p相末端无功功率量测的量测值，为线路ij的p相末端无功功率量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.7) If a is the reactive power measurement at the end of phase p of the associated line ij, then let is the measured value of reactive power measurement at the end of phase p of line ij at time t, is the error standard deviation of the reactive power measurement at the end of phase p of line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.2.8)若a为关联线路ij的p相首端电流幅值量测，则令为估计时刻t线路ij的p相首端电流幅值量测的量测值，为线路ij的p相首端电流幅值量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.8) If a is the measured current amplitude of the first end of the p-phase of the associated line ij, then let is the measured value of the current amplitude of the first end of the p-phase line ij at the estimated time t, is the standard deviation of the error of the current amplitude measurement at the first end of the p-phase of line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.2.9)若a为关联线路ij的p相末端电流幅值量测，则令为估计时刻t线路ij的p相末端电流幅值量测的量测值，为线路ij的p相末端电流幅值量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.2.9) If a is the measured current amplitude at the end of phase p of the associated line ij, then let is the measured value of the current amplitude at the end of the p-phase line ij at the estimated time t, is the standard deviation of the error of the current amplitude measurement at the end of phase p of line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.3)对于任意的第y个同步相量测量装置量测，y＝1，2，...，Y，估计时刻t的计算量测值计算权重进一步表达为：3.3) For any y-th synchrophasor measurement, y=1, 2, ..., Y, estimate the calculated measurement value at time t Calculating weights Further expressed as:
式中，分别为时刻t-DT第y个同步相量测量装置量测的计算量测值、计算权重，分别为时刻t-(D-1)T第y个同步相量测量装置量测的计算量测值、计算权重，分别为时刻t+dT第y个同步相量测量装置量测的计算量测值、计算权重，分别为时刻t+DT第y个同步相量测量装置量测的计算量测值、计算权重，d为多时间断面同步相量测量装置量测系数变量，d＝-D，...，-1，0，1，...，D，D为多时间断面同步相量测量装置量测系数，T为同步相量测量装置量测采样时间间隔；对于任意的第y个同步相量测量装置量测，根据量测类型分别设置时刻t+dT的计算量测值、计算权重及量测约束，d＝-D，...，-1，0，1，...，D：In the formula, are the calculated measurement value and the calculated weight measured by the yth synchronized phasor measurement device at time t-DT, respectively. are respectively the calculated measurement value and the calculated weight measured by the yth synchronized phasor measurement device at time t-(D-1)T, are the calculated measurement value and the calculated weight measured by the yth synchronized phasor measurement device at time t+dT, respectively. are respectively the calculated measurement value and the calculated weight of the y-th synchronized phasor measurement device at time t+DT, d is the measurement coefficient variable of the multi-time section synchronized phasor measurement device, d=-D, ..., -1, 0, 1, ..., D, D is the measurement coefficient of the multi-time section synchronized phasor measurement device, and T is the measurement sampling time interval of the synchronized phasor measurement device; for any y-th synchronized phasor measurement device measurement, the calculated measurement value, the calculated weight and the measurement constraint at time t+dT are set according to the measurement type, d=-D, ..., -1, 0, 1, ..., D:
3.3.1)若y为关联节点i的p相同步相量测量装置电压幅值量测，则令为时刻t+dT节点i的p相同步相量测量装置电压幅值量测的量测值，为节点i的p相同步相量测量装置电压幅值量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.3.1) If y is the voltage amplitude measurement of the p-phase synchronous phasor measurement device associated with node i, then let is the measured value of the voltage amplitude measured by the p-phase synchronous phasor measurement device at node i at time t+dT, is the error standard deviation of the voltage amplitude measurement of the p-phase synchronous phasor measurement device at node i; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
式中，为时刻t+dT第y个同步相量测量装置量测的残差；In the formula, is the residual measured by the yth synchronized phasor measurement device at time t+dT;
3.3.2)若y为关联线路ij的p相首端同步相量测量装置电流幅值量测，则令为时刻t+dT线路ij的p相首端同步相量测量装置电流幅值量测的量测值，为线路ij的p相首端同步相量测量装置电流幅值量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.3.2) If y is the current amplitude measured by the synchronous phasor measurement device at the first end of the p-phase of the associated line ij, then let is the measured value of the current amplitude measured by the synchronous phasor measuring device at the first end of the p-phase line ij at time t+dT, is the error standard deviation of the current amplitude measurement of the synchronous phasor measurement device at the first end of the p-phase line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.3.3)若y为关联线路ij的p相末端同步相量测量装置电流幅值量测，则令为时刻t+dT线路ij的p相末端同步相量测量装置电流幅值量测的量测值，为线路ij的p相末端同步相量测量装置电流幅值量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.3.3) If y is the current amplitude measured by the synchronous phasor measuring device at the end of phase p of the associated line ij, then let is the measured value of the current amplitude measured by the synchronous phasor measuring device at the end of the p-phase line ij at time t+dT, is the error standard deviation of the current amplitude measurement of the synchronous phasor measurement device at the end of the p-phase of the line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.3.4)若y为关联节点i的p相同步相量测量装置注入电流幅值量测，则令为时刻t+dT节点i的p相同步相量测量装置注入电流幅值量测的量测值，为节点i的p相同步相量测量装置注入电流幅值量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：3.3.4) If y is the current amplitude measurement injected by the p-phase synchronous phasor measurement device associated with node i, then let is the measured value of the current amplitude measurement injected by the p-phase synchronous phasor measurement device at the node i at the time t+dT, The error standard deviation of the current amplitude measurement injected by the p-phase synchronous phasor measurement device of node i; calculate the measurement value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
式中，为节点i的连接线路集合的电导之和，为节点i的连接线路集合的电纳与并联电纳之和，为节点i的连接节点集合；s和c均为节点i的连接节点，分别为节点注入电流幅值量测关联的连接节点s和c的p相状态变量；分别为线路is的p相电导、电纳，分别为线路ic的p相电导、电纳；In the formula, is the sum of the conductances of the set of connecting lines of node i, is the sum of the susceptance and shunt susceptance of the set of connected lines at node i, is the set of connected nodes of node i; s and c are both connected nodes of node i, The p-phase state variables of the connected nodes s and c associated with the node injection current amplitude measurement are respectively; are the p-phase conductance and susceptance of line is respectively, are the p-phase conductance and susceptance of line ic respectively;
3.3.5)若y为关联线路ij的p相首端等值同步相量测量装置有功功率量测，则令：3.3.5) If y is the active power measurement of the equivalent synchronous phasor measurement device at the first end of the p-phase of the associated line ij, then let:
式中，为时刻t+dT节点i的p相同步相量测量装置电压相角量测的量测值，为时刻t+dT线路ij的p相首端同步相量测量装置电流相角量测的量测值；令：In the formula, is the measured value of the voltage phase angle measured by the p-phase synchronous phasor measurement device at node i at time t+dT, is the measured value of the current phase angle measured by the synchronous phasor measurement device at the first end of the p-phase line ij at time t+dT; let:
式中，为节点i的p相同步相量测量装置电压相角量测的误差标准差，为线路ij的p相首端同步相量测量装置电流相角量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：In the formula, is the error standard deviation of the voltage phase angle measurement of the p-phase synchronous phasor measurement device at node i, is the error standard deviation of the current phase angle measurement of the synchronous phasor measurement device at the first end of the p-phase line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.3.6)若y为关联线路ij的p相末端等值同步相量测量装置有功功率量测，则令：3.3.6) If y is the active power measurement of the equivalent synchronous phasor measurement device at the end of the p-phase of the associated line ij, then let:
式中，为时刻t+dT节点j的p相同步相量测量装置电压幅值量测的量测值，为时刻t+dT节点j的p相同步相量测量装置电压相角量测的量测值，为时刻t+dT线路ij的p相末端同步相量测量装置电流相角量测的量测值；令：In the formula, is the measured value of the voltage amplitude measured by the p-phase synchronous phasor measurement device at node j at time t+dT, is the measured value of the voltage phase angle of the p-phase synchronous phasor measurement device at node j at time t+dT, is the measured value of the current phase angle measured by the synchronous phasor measurement device at the end of the p-phase line ij at time t+dT; let:
式中，为节点j的p相同步相量测量装置电压幅值量测的误差标准差，为节点j的p相同步相量测量装置电压相角量测的误差标准差，为线路ij的p相末端同步相量测量装置电流相角量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：In the formula, is the error standard deviation of the voltage amplitude measurement of the p-phase synchronous phasor measurement device at node j, is the error standard deviation of the voltage phase angle measurement of the p-phase synchronous phasor measurement device at node j, is the error standard deviation of the current phase angle measurement of the synchronous phasor measurement device at the p-phase end of line ij; calculate the measured value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.3.7)若y为关联线路ij的p相首端等值同步相量测量装置无功功率量测，则令：3.3.7) If y is the reactive power measurement of the equivalent synchronous phasor measurement device at the first end of phase p of the associated line ij, then let:
计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：Calculate measurement value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.3.8)若y为关联线路ij的p相末端等值同步相量测量装置无功功率量测，则令：3.3.8) If y is the reactive power measurement of the equivalent synchronous phasor measurement device at the end of phase p of the associated line ij, then let:
计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：Calculate measurement value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.3.9)若y为关联节点i的p相等值同步相量测量装置注入有功功率量测，则令：3.3.9) If y is the active power measurement injected by the p-phase synchronous phasor measurement device associated with node i, then let:
式中，为时刻t+dT节点i的p相同步相量测量装置注入电流相角量测的量测值；In the formula, The measured value of the current phase angle measurement injected by the p-phase synchronous phasor measurement device at the node i at the time t+dT;
式中，为节点i的p相同步相量测量装置注入电流相角量测的误差标准差；计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：In the formula, The error standard deviation of the current phase angle measurement injected into the p-phase synchronous phasor measurement device of node i; calculate the measurement value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
3.3.10)若y为关联节点i的p相等值同步相量测量装置注入无功功率量测，则令：3.3.10) If y is the reactive power measurement injected by the p-phase synchronous phasor measurement device associated with node i, then let:
计算量测值与二阶锥规划鲁棒状态估计状态变量x之间的量测约束满足：Calculate measurement value The measurement constraints between the state variables x and the second-order cone programming robust state estimation are satisfied:
所述的构建零注入节点与二阶锥规划鲁棒状态估计状态变量x之间的零注入约束表示为：The zero injection constraint between the constructed zero injection node and the second-order cone programming robust state estimation state variable x is expressed as:
3.4)针对网络中任意的节点判断节点i是否存在负荷和分布式电源，若节点i不存在负荷和分布式电源，则节点i为零注入节点，形成零注入节点i与二阶锥规划鲁棒状态估计状态变量x之间的零注入约束：3.4) For any node in the network Determine whether there is load and distributed power at node i. If there is no load and distributed power at node i, node i is a zero injection node, forming a zero injection constraint between the zero injection node i and the second-order cone programming robust state estimation state variable x:
式中，f为节点i的前序连接节点，j为节点i的后序连接节点，和分别为节点i的前序连接节点集合和后序连接节点集合；分别为线路fi的p相电导、电纳、并联电纳，分别为线路ij的p相电导、电纳、并联电纳；为节点i的p相电压状态变量，分别为线路fi的p相状态变量，分别为线路ij的p相状态变量。In the formula, f is the previous connection node of node i, j is the subsequent connection node of node i, and They are respectively the pre-order connected node set and the post-order connected node set of node i; are the p-phase conductance, susceptance and shunt susceptance of line fi respectively, are the p-phase conductance, susceptance and shunt susceptance of line ij respectively; is the p-phase voltage state variable of node i, are the p-phase state variables of line fi, are the p-phase state variables of line ij respectively.
4)以多源量测数据的计算量测值与估计值之间的残差加权最小绝对值为目标函数，采用二阶锥规划算法求解估计时刻t的鲁棒状态估计问题；4) Taking the weighted minimum absolute value of the residual between the calculated measurement value and the estimated value of the multi-source measurement data as the objective function, the second-order cone programming algorithm is used to solve the robust state estimation problem at the estimation time t;
所述的以多源量测数据的计算量测值与估计值之间的残差加权最小绝对值为目标函数，采用二阶锥规划算法求解估计时刻t的鲁棒状态估计问题，表示为：The objective function is the weighted minimum absolute value of the residual between the calculated measurement value and the estimated value of the multi-source measurement data. The second-order cone programming algorithm is used to solve the robust state estimation problem at the estimation time t, which is expressed as:
式中，J(x)为鲁棒状态估计的目标函数，λl为线路状态变量的权重系数，Kl为线路状态变量，λm为节点注入电流幅值量测状态变量的权重系数，Km为节点注入电流幅值量测状态变量，u、v分别为二阶锥规划鲁棒状态估计引入的辅助变量，u+v＝|r[t]|，v-u＝r[t]，r[t]为估计时刻t多源量测数据的残差，为估计时刻t第a个传统量测的残差，M为传统量测的数目，为估计时刻t第y个同步相量测量装置量测的残差，Y为同步相量测量装置量测的数目；z[t]＝Hx+v-u为所述的多源量测数据与二阶锥规划鲁棒状态估计状态变量x之间的量测约束公式(4)～(12)、(15)～(24)的紧凑格式，H为量测约束矩阵；Cx＝0为所述的零注入节点与二阶锥规划鲁棒状态估计状态变量x之间的零注入约束公式(25)～(26)的紧凑格式，C为零注入约束矩阵；为节点i、j的p相电压状态变量，分别为线路ij的p相状态变量，为配电网线路集合，p为相序编号，为相序集合，分别为节点s、c的p相电压状态变量，分别为节点注入电流幅值量测关联的连接节点s和c的p相状态变量，s和c均为节点r的连接节点，r为节点注入电流幅值量测关联的节点，为节点注入电流幅值量测关联的节点集合，为节点r的连接节点集合；[·]T为元素“·”的转置。Where J(x) is the objective function of robust state estimation, λl is the weight coefficient of line state variable, Kl is the line state variable, λm is the weight coefficient of node injection current amplitude measurement state variable, Km is the node injection current amplitude measurement state variable, u and v are auxiliary variables introduced by second-order cone programming robust state estimation, respectively. u+v＝|r[t]|, vu＝r[t], r[t] is the residual of the multi-source measurement data at the estimated time t, is the residual of the ath traditional measurement at time t, M is the number of traditional measurements, is the residual measured by the yth synchronized phasor measurement device at the estimated time t, Y is the number of measurements of the synchronized phasor measurement device; z[t]=Hx+vu is the compact format of the measurement constraint formulas (4) to (12), (15) to (24) between the multi-source measurement data and the second-order cone programming robust state estimation state variable x, H is the measurement constraint matrix; Cx=0 is the compact format of the zero injection constraint formulas (25) to (26) between the zero injection node and the second-order cone programming robust state estimation state variable x, C is the zero injection constraint matrix; is the p-phase voltage state variable of nodes i and j, are the p-phase state variables of line ij, is the distribution network line set, p is the phase sequence number, is a phase sequence set, are the p-phase voltage state variables of nodes s and c respectively, are the p-phase state variables of the connection nodes s and c associated with the node injection current amplitude measurement, s and c are both connection nodes of node r, and r is the node associated with the node injection current amplitude measurement, The node set associated with the node injection current amplitude measurement, is the set of connected nodes of node r; [·]T is the transpose of element “·”.
5)将估计时刻t的二阶锥规划鲁棒状态估计状态变量x的估计结果转换为节点电压幅值和相角估计结果；包括：5) Convert the estimation result of the state variable x of the second-order cone programming robust state estimation at the estimation time t into the node voltage amplitude and phase angle estimation result; including:
5.1)节点电压幅值估计结果：5.1) Node voltage amplitude estimation results:
对于任意的节点节点i的p相电压幅值估计结果为节点i的p相电压状态变量；For any node Estimation result of p-phase voltage amplitude at node i is the p-phase voltage state variable of node i;
5.2)节点电压相角估计结果：5.2) Node voltage phase angle estimation results:
设置源节点的p相电压相角估计结果从配电网源节点开始按照广度优先遍历分别计算各节点的电压相角估计结果；对于任意的线路为配电网线路集合，线路两端节点之间的电压相角估计结果满足：Set the p-phase voltage phase angle estimation result of the source node Starting from the source node of the distribution network, the voltage phase angle estimation results of each node are calculated according to the breadth-first traversal; for any line is a set of distribution network lines, and the voltage phase angle estimation result between the nodes at both ends of the line satisfies:
式中，为线路末端节点j的p相电压相角估计结果，为线路首端节点i的p相电压相角估计结果，分别为线路ij的p相状态变量。In the formula, is the estimated result of the phase angle of the p-phase voltage at the line end node j, is the estimated result of the phase angle of the p-phase voltage at the line head end node i, are the p-phase state variables of line ij respectively.
下面给出具体实例：Here are some specific examples:
采用改进的IEEE 33节点算例对本发明的考虑多源量测的配电网二阶锥规划鲁棒状态估计方法进行验证，配电网拓扑结构和多源量测数据的总体分布情况如图2所示：节点2、3、6为零注入节点；多源量测数据的量测值为潮流计算的基础上叠加满足正态分布的量测误差生成而得，其中，PMU幅值量测的误差标准差为0.1％，PMU相角量测的误差标准差为0.01度，SCADA量测的误差标准差为1％，AMI量测的误差标准差为5％。The improved IEEE 33-node example is used to verify the robust state estimation method of the distribution network second-order cone programming considering multi-source measurement of the present invention. The distribution network topology and the overall distribution of multi-source measurement data are shown in Figure 2: nodes 2, 3, and 6 are zero injection nodes; the measurement values of the multi-source measurement data are generated by superimposing the measurement errors that satisfy the normal distribution on the basis of the power flow calculation, among which the standard deviation of the error of the PMU amplitude measurement is 0.1%, the standard deviation of the error of the PMU phase angle measurement is 0.01 degree, the standard deviation of the error of the SCADA measurement is 1%, and the standard deviation of the error of the AMI measurement is 5%.
为验证本发明的考虑多源量测的配电网二阶锥规划鲁棒状态估计方的鲁棒性能，设置如下的量测坏数据场景：In order to verify the robust performance of the robust state estimation method of the distribution network second-order cone programming considering multi-source measurement of the present invention, the following measurement bad data scenario is set:
场景1：在上述量测误差的基础上，单次状态估计设置单个量测坏数据，进行250次状态估计计算，统计鲁棒状态估计的性能指标。Scenario 1: Based on the above measurement error, a single bad measurement data is set for single state estimation, 250 state estimation calculations are performed, and the performance indicators of robust state estimation are statistically analyzed.
表1单次状态估计设置单个量测坏数据时的鲁棒状态估计性能指标结果Table 1 Results of robust state estimation performance indicators when single state estimation is set with single bad measurement data
表1中，D为多时间断面PMU量测系数。由场景1的分析结果可以看出，相比于其他状态估计方法，本发明的考虑多源量测的配电网二阶锥规划鲁棒状态估计方利用多时间断面PMU量测数据，可有效辨识网络中的单个量测坏数据，并以更短的计算时间获得更高的估计精度。In Table 1, D is the multi-time section PMU measurement coefficient. It can be seen from the analysis results of scenario 1 that, compared with other state estimation methods, the second-order cone programming robust state estimation method for distribution network considering multi-source measurement of the present invention utilizes multi-time section PMU measurement data, can effectively identify single measurement bad data in the network, and obtain higher estimation accuracy with shorter calculation time.
场景2：在上述量测误差的基础上，单次状态估计设置多个相关的量测坏数据，观察鲁棒状态估计算法对量测坏数据的辨识情况。Scenario 2: Based on the above measurement errors, a single state estimation is performed with multiple related bad measurement data to observe how the robust state estimation algorithm identifies the bad measurement data.
表2单次状态估计设置多个相关的量测坏数据时的坏数据辨识结果Table 2 Bad data identification results when multiple related bad measurement data are set for single state estimation
通过上述分析结果可得，本发明的考虑多源量测的配电网二阶锥规划鲁棒状态估计方，通过利用多时间断面PMU量测数据和二阶锥规划方法求解，实现了不同量测坏数据场景下的坏数据辨识，提高了状态估计的精度和对量测坏数据的鲁棒性能。From the above analysis results, it can be obtained that the second-order cone programming robust state estimation method for distribution network considering multi-source measurement of the present invention realizes bad data identification in different measurement bad data scenarios by utilizing multi-time section PMU measurement data and second-order cone programming method for solution, thereby improving the accuracy of state estimation and the robust performance against measurement bad data.
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