一种T形连接电力线路的参数估计方法

摘要

一种T形连接电力线路的参数估计方法，属于电力系统线路参数辨识与估计技术领域。本发明利用计算机和T形连接线路三端的数据采集装置，通过程序，首先输入T形连接线路多个负荷水平下多个时段的SCADA量测数据，然后求解加权最小二乘估计模型得到T形连接线路参数在一个负荷水平下的估计值，即估计值的一个样本，再计算多个估计值样本的均值，利用样本方差系数作为参数估计精度的收敛判据，最后得到T形连接线路参数的估计值。本发明方法能有效估计T形连接线路的参数，并具有方法简单，计算速度快，估计精度高，数值稳定性好，工程实用性强，便于推广应用等特点。本发明可广泛应用于任何安装有数据采集装置的T形连接电力线路的参数估计。

主权项

1.一种T形连接电力线路的参数估计方法，利用计算机和T形连接电力线路三端的数据采集装置，对T形连接电力线路的参数进行估计，其特征在于其具体的方法步骤如下：(1)输入基础数据首先输入待估计T形连接电力线路的基础数据、参数估计计算精度ε及时段数n，要求n≥3；所述的T形连接电力线路的基础数据为：T形连接电力线路单位长度电阻r的上限r_max和下限r_min，单位长度电抗x的上限x_max和下限x_min，单位长度电纳b的上限b_max和下限b_min，T形连接电力线路三条支路长度的上限l_1max、l_2max、l_3max和下限l_1min、l_2min、l_3min，电压幅值的量测值、支路有功功率及无功功率量测的权重系数W_u，W_p和W_q，以及T形连接电力线路三端多个时段的SCADA量测数据，即T形连接电力线路三端节点的电压幅值、三条支路首端的有功功率和无功功率；(2)初始化循环变量第(1)步完成后，初始化循环变量h，令h=1；循环过程中，h代表不同的负荷水平，计算得到T形连接电力线路参数在一个负荷水平下的估计值后，即得到估计值的一个样本后，循环变量h增加1，即令h=h+1，继续计算T形连接电力线路参数在下一个负荷水平下的估计值，如此循环，直至满足参数估计的计算精度要求为止；(3)读入第h个负荷水平下n个时段的SCADA量测数据第(2)步完成后，读入第h个负荷水平下T形连接电力线路三端n个时段的SCADA量测数据，即T形连接电力线路三端节点i、节点j和节点k电压幅值的量测值U_i¹，U_i²，…，U_iⁿ，U_j¹，U_j²，…，U_jⁿ，U_k¹，U_k²，…，U_kⁿ，三条支路首端的有功功率P_io¹，P_io²，…P_ioⁿ，P_jo¹，P_jo²，…，P_joⁿ，P_ko¹，P_ko²，…，P_koⁿ，以及三条支路首端的无功功率Q_io¹，Q_io²，…Q_ioⁿ，Q_jo¹，Q_jo²，…，Q_joⁿ，Q_ko¹，Q_ko²，…，Q_koⁿ；(4)计算T形连接电力线路单位长度参数估计值的第h个样本第(3)步完成后，按下式建立T形连接电力线路参数的加权最小二乘估计模型：$\min J\left(x\right)=W_u\underset{m=1}{\overset{n}{\Sigma }}[{(v_i-U_i^m)}^2+{(v_j-U_j^m)}^2+{(v_k-U_k^m)}^2]$$+W_p\underset{m=1}{\overset{n}{\Sigma }}[{({\hat{P}}_{\mathrm{io}}-P_{\mathrm{io}}^m)}^2+{({\hat{P}}_{\mathrm{jo}}-P_{\mathrm{jo}}^m)}^2+{({\hat{P}}_{\mathrm{ko}}-P_{\mathrm{ko}}^m)}^2]$    (1)$+W_q\underset{m=1}{\overset{n}{\Sigma }}[{({\hat{Q}}_{\mathrm{io}}-Q_{\mathrm{io}}^m)}^2+{({\hat{Q}}_{\mathrm{jo}}-Q_{\mathrm{jo}}^m)}^2+{({\hat{Q}}_{\mathrm{ko}}-Q_{\mathrm{ko}}^m)}^2]$$s.t.\left\{\begin{array}{c}{\hat{P}}_{\mathrm{oi}}+{\hat{P}}_{\mathrm{oj}}+{\hat{P}}_{\mathrm{ok}}=0\\ {\hat{Q}}_{\mathrm{oi}}+{\hat{Q}}_{\mathrm{oj}}+{\hat{Q}}_{\mathrm{ok}}=0\\ r_{\min }<r^{\left(h\right)}<r_{\max }\\ x_{\min }<x^{\left(h\right)}<x_{\max }\\ b_{\min }<b^{\left(h\right)}<b_{\max }\\ l_{1\min }<l_1^{\left(h\right)}<l_{1\max }\\ l_{2\min }<l_2^{\left(h\right)}<l_{2\max }\\ l_{3\min }<l_3^{\left(h\right)}<l_{3\max }\end{array}\right.$    (2)式中：x=[v_i,v_j,v_k,v_o,θ_i,θ_j,θ_k,r^(h),x^(h),b^(h),l₁^(h),l₂^(h),l₃^(h)]为估计模型的变量，其中，v_i,v_j,v_k分别为T形连接电力线路三个端节点的电压幅值，v_o为T形连接点的电压幅值，θ_i,θ_j,θ_k分别为三个端节点相对于T节点的电压相角；r^(h),x^(h),b^(h)为T形连接电力线路单位长度电阻、电抗及电纳估计值的第h个样本；l₁^(h),l₂^(h),l₃^(h)为T形连接电力线路三条支路长度估计值的第h个样本；W_u，W_p和W_q分别为电压幅值的量测值、支路有功功率及无功功率量测的权重系数，r_max和r_min为单位长度电阻的上限和下限；x_max和x_min为单位长度电抗的上限和下限；l_1max，l_2max和l_3max分别为三条支路长度的上限；l_1min，l_2min和l_3min分别为三条支路长度的下限；U_i^m,U_j^m和U_k^m分别为第m个时段T形连接电力线路三端节点i，节点j和节点k的电压幅值的量测值，P_i^m,P_j^m和P_k^m分别为第m个时段T形连接电力线路三条支路首端有功功率的量测值，Q_i^m,Q_j^m和Q_k^m分别为第m个时段T形连接电力线路三条支路首端无功功率的量测值；和分别为T形连接电力线路三条支路首端有功功率的估计值，和分别为T形连接电力线路三条支路首端无功功率的估计值，和分别为T形连接电力线路三条支路末端有功功率的估计值，和分别为T形连接电力线路三条支路末端无功功率的估计值，这些功率估计值的表达式如下：$\left\{\begin{array}{c}{\hat{P}}_{\mathrm{io}}=v_i^2{g}_1^{\left(h\right)}-v_i{v}_o{g}_1^{\left(h\right)}\cos {\theta }_i-v_i{v}_o{b}_1^{\left(h\right)}\sin {\theta }_i\\ {\hat{P}}_{\mathrm{jo}}=v_j^2{g}_2^{\left(h\right)}-v_j{v}_o{g}_2^{\left(h\right)}\cos {\theta }_j-v_j{v}_o{b}_2^{\left(h\right)}{\sin \theta }_j\\ {\hat{P}}_{\mathrm{ko}}=v_k^2{g}_3^{\left(h\right)}-v_k{v}_o{g}_3^{\left(h\right)}\cos {\theta }_k-v_k{v}_o{b}_3^{\left(h\right)}{\sin \theta }_k\\ {\hat{Q}}_{\mathrm{io}}=-v_i^2(b_1^{\left(h\right)}+y_1^{\left(h\right)})-v_i{v}_o{g}_1^{\left(h\right)}\sin {\theta }_i+v_i{v}_o{b}_1^{\left(h\right)}\cos {\theta }_i\\ {\hat{Q}}_{\mathrm{jo}}={-v}_j^2(b_2^{\left(h\right)}+y_2^{\left(h\right)})-v_j{v}_o{g}_2^{\left(h\right)}{\sin \theta }_j+v_j{v}_o{b}_2^{\left(h\right)}{\cos \theta }_j\\ {\hat{Q}}_{\mathrm{ko}}={-v}_k^2(b_3^{\left(h\right)}+y_3^{\left(h\right)})-v_k{v}_o{g}_3^{\left(h\right)}{\sin \theta }_k+v_k{v}_o{b}_3^{\left(h\right)}{\cos \theta }_k\end{array}\right.$    (3)$\left\{\begin{array}{c}{\hat{P}}_{\mathrm{oi}}=v_o^2{g}_1^{\left(h\right)}-v_o{v}_i{g}_1^{\left(h\right)}{\cos \theta }_i+v_o{v}_i{b}_1^{\left(h\right)}{\sin \theta }_i\\ {\hat{P}}_{\mathrm{oj}}=v_o^2{g}_2^{\left(h\right)}-v_o{v}_j{g}_2^{\left(h\right)}{\cos \theta }_j+v_o{v}_j{b}_2^{\left(h\right)}{\sin \theta }_j\\ {\hat{P}}_{\mathrm{ok}}=v_o^2{g}_3^{\left(h\right)}-v_o{v}_k{g}_3^{\left(h\right)}{\cos \theta }_k+v_o{v}_k{b}_3^{\left(h\right)}{\sin \theta }_k\\ {\hat{Q}}_{\mathrm{oi}}={-v}_o^2(b_1^{\left(h\right)}+y_1^{\left(h\right)})+v_o{v}_i{g}_1^{\left(h\right)}{\sin \theta }_i+v_o{v}_j{b}_1^{\left(h\right)}{\cos \theta }_i\\ {\hat{Q}}_{\mathrm{oj}}={-v}_o^2(b_2^{\left(h\right)}+y_2^{\left(h\right)})+v_o{v}_j{g}_2^{\left(h\right)}{\sin \theta }_j+v_o{v}_j{b}_2^{\left(h\right)}{\cos \theta }_j\\ {\hat{Q}}_{\mathrm{ok}}={-v}_o^2(b_3^{\left(h\right)}+y_3^{\left(h\right)})+v_o{v}_k{g}_3^{\left(h\right)}{\sin \theta }_k+v_o{v}_k{b}_3^{\left(h\right)}{\cos \theta }_k\end{array}\right.$    (4)式中：g₁^(h),g₂^(h)和g₃^(h)分别为T形连接电力线路三条支路的串联电导，b₁^(h),b₂^(h)和b₃^(h)分别为T形连接电力线路三条支路的串联电纳，y₁^(h),y₂^(h)和y₃^(h)分别为T形连接电力线路三条支路的对地电纳，其表达式为：$\left\{\begin{array}{c}{g}_1^{\left(h\right)}=\frac{r^{\left(h\right)}{l}_1^{\left(h\right)}}{{\left(r^{\left(h\right)}{l}_1^{\left(h\right)}\right)}^2+{\left(x^{\left(h\right)}{l}_1^{\left(h\right)}\right)}^2},b_1^{\left(h\right)}=\frac{{-x}^{\left(h\right)}{l}_1^{\left(h\right)}}{{\left(r^{\left(h\right)}{l}_1^{\left(h\right)}\right)}^2+{\left(x^{\left(h\right)}{l}_1^{\left(h\right)}\right)}^2},y_1^{\left(h\right)}=\frac{b^{\left(h\right)}{l}_1^{\left(h\right)}}{2}\\ g_2^{\left(h\right)}=\frac{r^{\left(h\right)}{l}_2^{\left(h\right)}}{{\left(r^{\left(h\right)}{l}_2^{\left(h\right)}\right)}^2+{\left(x^{\left(h\right)}{l}_2^{\left(h\right)}\right)}^2},b_2^{\left(h\right)}=\frac{-x^{\left(h\right)}{l}_2^{\left(h\right)}}{{\left(r^{\left(h\right)}{l}_2^{\left(h\right)}\right)}^2+{\left(x^{\left(h\right)}{l}_2^{\left(h\right)}\right)}^2},y_2^{\left(h\right)}=\frac{b^{\left(h\right)}{l}_2^{\left(h\right)}}{2}\\ g_3^{\left(h\right)}=\frac{r^{\left(h\right)}{l}_3^{\left(h\right)}}{{\left(r^{\left(h\right)}{l}_3^{\left(h\right)}\right)}^2+{\left(x^{\left(h\right)}{l}_3^{\left(h\right)}\right)}^2},b_3^{\left(h\right)}=\frac{-x^{\left(h\right)}{l}_3^{\left(h\right)}}{{\left(r^{\left(h\right)}{l}_3^{\left(h\right)}\right)}^2+{\left(x^{\left(h\right)}{l}_3^{\left(h\right)}\right)}^2},y_3^{\left(h\right)}=\frac{b^{\left(h\right)}{l}_3^{\left(h\right)}}{2}\end{array}\right.$    (5)求解式(1)-(5)所示的T形连接电力线路参数的加权最小二乘估计模型，得到T形连接电力线路单位长度参数估计值的第h个样本，即单位长度电阻、电抗和电纳估计值的第h个样本r^(h),x^(h)和b^(h)，以及三条支路长度估计值的第h个样本l₁^(h),l₂^(h)和l₃^(h)；(5)计算T形连接电力线路全长参数估计值的第h个样本第(4)步完成后，按下式计算T形连接电力线路三条支路全长参数估计值的第h个样本：$\left\{\begin{array}{c}{R}_1^{\left(h\right)}=r^{\left(h\right)}{l}_1^{\left(h\right)},X_1^{\left(h\right)}=x^{\left(h\right)}{l}_1^{\left(h\right)},B_1^{\left(h\right)}=b^{\left(h\right)}{l}_1^{\left(h\right)}\\ R_2^{\left(h\right)}=r^{\left(h\right)}{l}_2^{\left(h\right)},X_2^{\left(h\right)}=x^{\left(h\right)}{l}_2^{\left(h\right)},B_2^{\left(h\right)}=b^{\left(h\right)}{l}_2^{\left(h\right)}\\ R_3^{\left(h\right)}=r^{\left(h\right)}{l}_3^{\left(h\right)},X_3^{\left(h\right)}=x^{\left(h\right)}{l}_3^{\left(h\right)},B_3^{\left(h\right)}=b^{\left(h\right)}{l}_3^{\left(h\right)}\end{array}\right.$    (6)式中：R₁^(h),R₂^(h)和R₃^(h)分别为T形连接电力线路三条支路电阻估计值的第h个样本，X₁^(h),X₂^(h)和X₃^(h)分别为T形连接电力线路三条支路电抗估计值的第h个样本，B₁^(h),B₂^(h)和B₃^(h)分别为T形连接电力线路三条支路电纳估计值的第h个样本；(6)校验参数估计值的精度第(5)步完成后，校验T形连接电力线路参数估计值的计算精度，具体步骤如下：首先计算前N个估计值样本的均值，计算公式为：$\left\{\begin{array}{c}{\bar{R}}_1=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{R_1}^{\left(h\right)},{\bar{X}}_1=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{X_1}^{\left(h\right)},{\bar{B}}_1=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{B_1}^{\left(h\right)}\\ {\bar{R}}_2=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{R_2}^{\left(h\right)},{\bar{X}}_2=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{X_2}^{\left(h\right)},{\bar{B}}_2=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{B_2}^{\left(h\right)}\\ {\bar{R}}_3=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{R_3}^{\left(h\right)},{\bar{X}}_3=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{X_3}^{\left(h\right)},{\bar{B}}_3=\frac{1}{N}\underset{h=1}{\overset{N}{\Sigma }}{B_3}^{\left(h\right)}\end{array}\right.$    (7)式中：和分别T形连接电力线路三条支路电阻估计值的均值，和分别T形连接电力线路三条支路电抗估计值的均值，和分别T形连接电力线路三条支路电纳估计值的均值；然后计算线路参数估计值均值的方差系数，计算公式如下：$\left\{\begin{array}{c}{\eta }_{R1}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(R_1^{\left(h\right)}-{\bar{R}}_1)}^2}}{{\bar{R}}_1},{\eta }_{R2}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(R_2^{\left(h\right)}-{\bar{R}}_2)}^2}}{{\bar{R}}_2},{\eta }_{R3}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(R_3^{\left(h\right)}-{\bar{R}}_3)}^2}}{{\bar{R}}_3}\\ {\eta }_{X1}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(X_1^{\left(h\right)}-{\bar{X}}_1)}^2}}{{\bar{X}}_1},{\eta }_{X2}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(X_2^{\left(h\right)}-{\bar{X}}_2)}^2}}{{\bar{X}}_2},{\eta }_{X3}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(X_3^{\left(h\right)}-{\bar{X}}_3)}^2}}{{\bar{X}}_3}\\ {\eta }_{B1}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(B_1^{\left(h\right)}-{\bar{B}}_1)}^2}}{{\bar{B}}_1},{\eta }_{B2}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(B_2^{\left(h\right)}-{\bar{B}}_2)}^2}}{{\bar{B}}_2},{\eta }_{B3}=\frac{\sqrt{\frac{1}{N(N-1)}\underset{h=1}{\overset{N}{\Sigma }}{(B_3^{\left(h\right)}-{\bar{B}}_3)}^2}}{{\bar{B}}_3}\end{array}\right.$    (8)η＝max(η_R1,η_R2,η_R3,η_X1,η_X2,η_X3,η_B1,η_B2,η_B3)    (9)式中：η_R1,η_R2和η_R3分别为和的方差系数，η_X1,η_X2和η_X3分别为和的方差系数，η_B1,η_B2和η_B3分别为和的方差系数，η为前述方差系数的最大值，其中，前述方差系数包括：η_R1，η_R2，η_R3，η_X1，η_X2，η_X3，η_B1，η_B2，η_B3；最后校验方差系数的最大值η：当η小于第(1)步输入的参数估计计算精度ε时，则第(6)步由公式(7)计算出的和即为三条支路电阻的估计值，和即为三条支路电抗的估计值，和即为三条支路电纳的估计值；否则，返回第(3)步，继续读入第h+1个负荷水平下n个时段的SCADA数据，计算T形连接电力线路参数估计值的第h+1个样本和方差系数，如此循环，直至η小于计算精度ε为止，第(6)步公式(7)的计算结果即为T形连接电力线路参数的估计值；(7)输出T形连接电力线路的参数估计值第(6)步完成后，输出第(6)步公式(7)的计算结果，即输出T形连接电力线路的参数估计值。