CN102842907B - Three-phase decoupling load flow calculation method of power distribution network based on path matrix - Google Patents

Abstract

The invention discloses a three-phase decoupling load flow calculation method of a power distribution network based on a path matrix. The method comprises the following steps: firstly, adopting a symmetrical component method to perform sequence component decoupling on a three-phase unbalanced power distribution network to obtain zero sequence, a power distribution sequence network with positive sequence and negative sequence, and adopting a loop-analysis method based on the path matrix to perform one-phase-sequence component load flow calculation to obtain load flows of the three-sequence networks; and secondly, transforming sequence network load flows in a phase component mode by an inverse transformation principle of the symmetrical component method to obtain three-phase load flows. By using the method, a three-phase unbalanced power distribution network system is decoupled into zero sequence, positive sequence and negative sequence networks, so that large matrix manipulation in the three-phase load flow calculation is avoided, the calculated amount is decreased, and the calculation efficiency is improved. The method has the advantages of clear calculation process, simple programming and fast calculation speed. Finally, a 6-busbar test example verifies the correctness and good convergence; and the method is good in generality and practical applicability.

Description

Three-phase decoupled power flow calculation method for distribution network based on road matrix

technical field

The invention relates to a three-phase decoupling power flow calculation method of a distribution network based on a road matrix, and belongs to the technical field of power system analysis and calculation.

Background technique

Distribution network power flow calculation has been a hot spot in academic research for many years, and distribution network power flow calculation is the basis of distribution network analysis. Because the characteristics of the distribution network are different from those of the transmission network, it generally has a high R/X ratio, three-phase unbalance, and a tree-like network structure with closed-loop design and open-loop operation, so the traditional power flow algorithm for the transmission network cannot be directly applied to power distribution. net. Scholars at home and abroad have proposed various distribution network power flow algorithms according to the characteristics of the distribution network, such as the forward push-back method, the implicit Zbus Gaussian method, the loop impedance method, the improved Newton method, and the fast decoupling method. Among them, the forward-backward method makes full use of the structural characteristics of the distribution network, and it has clear physical concepts, simple programming, no large matrix calculations, fast calculation speed, and good convergence, which is very suitable for solving radial distribution networks. It is widely used due to its trendy and other advantages. At present, the line parameters in the distribution network are basically spatially symmetrical, and generally there is a three-phase imbalance on the load.

Contents of the invention

Purpose of the invention: Aiming at the problems and deficiencies in the prior art, the present invention provides a three-phase decoupled power flow calculation method for distribution network based on road matrix.

Technical solution: A three-phase decoupled power flow calculation method for distribution network based on road matrix, including the following steps:

(3×1阶)，各节点三相电压相量矩阵为

(3n×1阶)，在配电系统序网络中，可以得出电源节点的三序电压矩阵为

(3×1阶)，各节点三序电压矩阵为(3n×1阶)。其中，令a＝e^j2π/3， $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ n为独立节点的个数，则独立支路条数为b＝n。即针对具有N个节点的三相辐射状(树形)配电网，假设首节点是电源且作为参考节点，则独立节点个数为n＝N-1，独立支路条数b＝n。1) Assuming that the first node is a power supply and serves as a reference node, the three-phase voltage phasor matrix of the power supply node is

(3×1 order), the three-phase voltage phasor matrix of each node is

(3n×1 order), in the distribution system sequence network, the three-sequence voltage matrix of the power supply node can be obtained as

(3×1 order), the three-sequence voltage matrix of each node is (3n×1 order). Among them, let a=e ^j2π/3 , $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ n is the number of independent nodes, then the number of independent branches is b=n. That is, for a three-phase radial (tree-shaped) distribution network with N nodes, assuming that the first node is a power source and serves as a reference node, the number of independent nodes is n=N-1, and the number of independent branches b=n.

为基于支路i的序阻抗

形成的对角阵(n×n阶)，其中，上标s＝0,1,2，分别表示序网络模型中的零序、正序和负序网络模型。支路i的三相阻抗为则有

其中， $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],$ $Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right].$ 2) Calculate the network parameters of each sequence

is the sequence impedance based on branch i

The formed diagonal matrix (n×n order), where the superscript s=0, 1, 2, respectively represent the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model. The three-phase impedance of branch i is then there is

in, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& {\mathrm{<figure-callout\; id="2"\; label="Z\; bi"\; filenames="HDA00002125894800021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{\mathrm{bi}}^{}\end{array}\right],$ $Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right].$

3) In the decoupled sequence network model circuit, calculate the road matrix T _s of each sequence network; in addition, for the node whose injected sequence current is zero, delete the row corresponding to the node in the road matrix T _s of each sequence network After going, a new matrix is formed as T _sg . Among them, the subscript s=0, 1, 2 respectively represent the zero-sequence, positive-sequence and negative-sequence networks in the sequence network model.

4) Calculate the impedance sensitivity matrix in each sequence network

5) Assign an initial value to the three-phase voltage of each node of the distribution network Where E _n =[E,E,...,E] ^T , there are n E in total, and E is a 3×3 unit matrix.

其中

是节点i各相注入功率，

是节点i各相并联导纳之和，p＝a,b,c，i＝1,2,…,m。m为节点注入序电流不为零的节点个数，d为迭代次数变量。6) Calculate the current of each phase injected by node i during d iterations

in

is the injected power of each phase of node i,

It is the sum of the parallel admittance of each phase of node i, p=a,b,c, i=1,2,...,m. m is the number of nodes whose injected sequence current is not zero, and d is the iteration number variable.

i＝1,2,…,m。7) Calculate the sequence currents injected by node i during d iterations

i=1,2,...,m.

其中，

为d次迭代时去除注入序电流为零的节点后形成的新注入序电流矩阵(m×1阶)，m为节点注入序电流不为零的节点个数，上标s＝0,1,2，分别表示序网络模型中的零序、正序和负序网络模型。8) Calculate d iterations

in,

is the new injected sequence current matrix (m×1 order) formed after removing the nodes whose injected sequence current is zero during d iterations, m is the number of nodes whose injected sequence current is not zero, superscript s=0,1, 2, respectively represent the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model.

9) Calculate d iterations Among them, 1 _n =[1,1,…,1] ^T , a total of n 1s; s=0,1,2, respectively representing the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model.

i＝1,2,…,n。10) Calculate the three-phase voltage phasor of node i at d iterations based on the inverse transformation

i=1,2,...,n.

幅值之差是否满足收敛精度要求，满足结束迭代；不满足转步骤6)。11) judgment and

Whether the amplitude difference meets the convergence accuracy requirement, and the iteration ends; if not, go to step 6).

Beneficial effects: Compared with the prior art, the present invention proposes a three-phase decoupling power flow calculation method based on the road matrix, which combines the loop analysis method based on the road matrix and the sequence component decoupling analysis method, through Decoupling the three-phase unbalanced distribution network system into zero-sequence, positive-sequence and negative-sequence networks avoids large matrix operations in the calculation process, and considers the three-phase unbalance of the distribution network to reduce the amount of calculation. Improved computational efficiency. The calculation process of the whole invention is clear, the programming is simple, and the calculation speed is fast. Using the symmetrical component method to calculate the three-phase decoupled power flow will have a good calculation advantage. It can decompose a group of asymmetric "a", "b", and "c" three-phase components into three groups of three-phase symmetrical sequence components , then the calculation of three-phase power flow becomes the calculation of one phase in three sets of three-phase symmetrical sequence components. Therefore, the calculation amount of the three-phase unbalanced power flow calculation of the distribution network will be reduced by 2/3, and it can bring faster calculation speed to the three-phase power flow calculation of the distribution network while maintaining good convergence. Finally, the correctness and good convergence of the present invention are verified through the 6-bus test example, and at the same time, it has good versatility and practicability.

Description of drawings

Fig. 1 is method flowchart of the present invention;

Figure 2 shows the 6-bus three-phase unbalanced distribution network system.

Detailed ways

Below in conjunction with specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalent forms of the present invention All modifications fall within the scope defined by the appended claims of the present application.

Fig. 1 is the general flowchart of the present invention, specifically comprises the following steps:

(3×1阶)，各节点三相电压相量矩阵为

(3n×1阶)，在配电系统序网络中，可以得出电源节点的三序电压矩阵为

(3×1阶)，各节点三序电压矩阵为

(3n×1阶)。其中，令a＝e^j2π/3， $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ n为独立节点的个数，则独立支路条数为b＝n。即针对具有N个节点的三相辐射状(树形)配电网，假设首节点是电源且作为参考节点，则独立节点个数为n＝N-1，独立支路条数b＝n。1) Assuming that the first node is a power supply and serves as a reference node, the three-phase voltage phasor matrix of the power supply node is

(3×1 order), the three-phase voltage phasor matrix of each node is

(3n×1 order), in the distribution system sequence network, the three-sequence voltage matrix of the power supply node can be obtained as

(3×1 order), the three-sequence voltage matrix of each node is

(3n×1 order). Among them, let a=e ^j2π/3 , $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ n is the number of independent nodes, then the number of independent branches is b=n. That is, for a three-phase radial (tree-shaped) distribution network with N nodes, assuming that the first node is a power source and serves as a reference node, the number of independent nodes is n=N-1, and the number of independent branches b=n.

为基于支路i的序阻抗形成的对角阵(n×n阶)，其中，上标s＝0,1,2，分别表示序网络模型中的零序、正序和负序网络模型。支路i的三相阻抗为则有

其中， $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],$ $Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right].$ 2) Calculate the network parameters of each sequence

is the sequence impedance based on branch i The formed diagonal matrix (n×n order), where the superscript s=0, 1, 2, respectively represent the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model. The three-phase impedance of branch i is then there is

in, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& {\mathrm{<figure-callout\; id="2"\; label="Z\; bi"\; filenames="HDA00002125894800021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{\mathrm{bi}}^{}\end{array}\right],$ $Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right].$

3) In the decoupled sequence network model circuit, calculate the road matrix T _s of each sequence network; in addition, for the node whose injected sequence current is zero, delete the row corresponding to the node in the road matrix T _s of each sequence network After going, a new matrix is formed as T _sg . Among them, the subscript s=0, 1, 2 respectively represent the zero-sequence, positive-sequence and negative-sequence networks in the sequence network model.

4) Calculate the impedance sensitivity matrix in each sequence network

5) Assign an initial value to the three-phase voltage of each node of the distribution network Where E _n =[E,E,...,E] ^T , there are n E in total, and E is a 3×3 unit matrix.

其中

是节点i各相注入功率，是节点i各相并联导纳之和，p＝a,b,c，i＝1,2,…,m。m为节点注入序电流不为零的节点个数，d为迭代次数变量。6) Calculate the current of each phase injected by node i during d iterations

in

is the injected power of each phase of node i, It is the sum of the parallel admittance of each phase of node i, p=a,b,c, i=1,2,...,m. m is the number of nodes whose injected sequence current is not zero, and d is the iteration number variable.

i＝1,2,…,m。7) Calculate the sequence currents injected by node i during d iterations

i=1,2,...,m.

其中，

为d次迭代时去除注入序电流为零的节点后形成的新注入序电流矩阵(m×1阶)，m为节点注入序电流不为零的节点个数，上标s＝0,1,2，分别表示序网络模型中的零序、正序和负序网络模型。8) Calculate d iterations

in,

is the new injected sequence current matrix (m×1 order) formed after removing the nodes whose injected sequence current is zero during d iterations, m is the number of nodes whose injected sequence current is not zero, superscript s=0,1, 2, respectively represent the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model.

The formula derivation of step 8) is as follows:

For a three-phase radial (tree-shaped) distribution network with N nodes, assuming that the first node is a power source and serves as a reference node, the number of independent nodes is n=N-1, and the number of independent branches b=n. The road of a node refers to the set of branches on the path that the node passes along the tree to the root. The road of the node emphasizes the branches on the path. For a given tree, the road of the node is unique, and the road of the node It is only composed of tree branches, and the road is described by the road matrix T. The road matrix T is an n×n order square matrix. It is assumed that the positive direction of the road is from the power point to each node, and the positive direction of each branch is the same as the positive direction of the road. If the branch j is on the road i, then T( i,j)=1, otherwise T(i,j)=0. The road matrix T is a sparse lower triangular matrix, and the memory requirement can be reduced by using sparse technology.

为支路序电流向量矩阵(n×1阶)，在解耦的各序网模型电路中，可以获得各序网络的道路矩阵分别为T₀、T₁和T₂，并依据KCL电流定律，支路序电流与节点注入序电流

满足如下等式：In the power distribution network, set Inject the sequence current vector matrix (n×1 order) into the node, set

is the branch sequence current vector matrix (n×1 order), in the decoupled sequence network model circuit, the road matrix of each sequence network can be obtained as T ₀ , T ₁ and T ₂ respectively, and according to the KCL current law, branch sequence current Inject sequence currents with nodes

Satisfy the following equation:

${\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, s=0, 1, 2, respectively represent the zero-sequence, positive-sequence and negative-sequence networks in the sequence network model.

之间的关联，但是，在实际系统中不是每个节点都有注入序电流，对于注入序电流为零的节点，在各序网的道路矩阵T_s中把该节点所对应行删去后形成新矩阵为T_sg，此时式(1)变为Equation (1) gives

However, in the actual system, not every node has injected sequence current. For a node whose injected sequence current is zero, delete the row corresponding to the node in the road matrix T _s of each sequence network to form The new matrix is T _sg , and formula (1) becomes

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sg</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; g</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

为去除注入序电流为零的节点后形成的新注入序电流矩阵(m×1阶)，m为节点注入序电流不为零的节点个数。In formula (2)

It is a new injected sequence current matrix (m×1 order) formed after removing the nodes whose injected sequence current is zero, m is the number of nodes whose injected sequence current is not zero.

For any radial power distribution system sequence component circuit model, based on Ohm's law,

${\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

为配电网支路序电压矩阵(n×1阶)；为基于支路i的序阻抗

形成的对角阵(n×n阶)，s＝0,1,2，分别表示序网络模型中的零序、正序和负序网络模型。in,

is the distribution network branch sequence voltage matrix (n×1 order); is the sequence impedance based on branch i

The formed diagonal matrix (n×n order), s=0, 1, 2, respectively represents the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model.

(3×1阶)，各节点三相电压相量矩阵为

(3n×1阶)，在配电序网络中，可以得出电源节点的三序电压矩阵为

(3×1阶)，各节点三序电压矩阵为

(3n×1阶)，那么，在各序网络模型中，可知任一节点与电源节点的序电压差等于从此节点开始沿着该节点的道路到达电源节点所经支路的支路序电压之和，即(设1_n＝[1,1,…,1]^T，共n个1；s＝0,1,2，分别表示序网络模型中的零序、正序和负序网络模型)：Let the three-phase voltage phasor matrix of the power supply node be

(3×1 order), the three-phase voltage phasor matrix of each node is

(3n×1 order), in the power distribution sequence network, the three-sequence voltage matrix of the power supply node can be obtained as

(3×1 order), the three-sequence voltage matrix of each node is

(3n×1 order), then, in each sequence network model, it can be known that the sequence voltage difference between any node and the power node is equal to the difference between the sequence voltages of the branches along the path from this node to the power node. and, that is (set 1 _n =[1,1,…,1] ^T , a total of n 1s; s=0,1,2, respectively representing the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model) :

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 1</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sg</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; g</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Delta;Z</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}}_{\mathrm{<span\; class="notranslate">\; g</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

定义为各序网中阻抗灵敏性矩阵：in,

Defined as the impedance sensitivity matrix in each sequence network:

${\mathrm{<span\; class="notranslate">\; \&Delta;Z</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; sg</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 1</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

其中，1_n＝[1,1,…,1]^T，共n个1；s＝0,1,2，分别表示序网络模型中的零序、正序和负序网络模型。9) Calculate d iterations

Among them, 1 _n =[1,1,…,1] ^T , a total of n 1s; s=0,1,2, respectively representing the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model.

i＝1,2,…,n。10) Calculate the three-phase voltage phasor of node i at d iterations based on the inverse transformation

i=1,2,...,n.

和

幅值之差是否满足收敛精度要求。满足结束迭代；不满足转步骤6)。11) judgment

and

Whether the amplitude difference meets the convergence accuracy requirement. If it is satisfied, end the iteration; if it is not satisfied, go to step 6).

Case Analysis

Figure 2 shows the 6-bus three-phase unbalanced distribution network system, the transformer Y _n -y _n connection mode, and reset the line parameters to make the line space symmetrical, that is, the mutual inductance between the phases is completely symmetrical, and the three-phase load is unbalanced .

The calculation results based on this algorithm are shown in Table 1. The program converges after 6 iterations, and the convergence accuracy is 10 ^-6 .

Table 1. Power flow calculation results of this algorithm

Claims (1)

1. A three-phase decoupling power flow calculation method for distribution network based on road matrix, is characterized in that, comprises the following steps: 1) Assuming that the first node is a power supply and serves as a reference node, the three-phase voltage phasor matrix of the power supply node is

The three-phase voltage phasor matrix of each node is

In the distribution system sequence network, the three-sequence voltage matrix of the power supply node is obtained as

The three-sequence voltage matrix of each node is

Among them, let a=e ^j2π/3 , $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ n is the number of independent nodes, then the number of independent branches is b=n; that is, for a three-phase radial distribution network with N nodes, assuming that the first node is a power supply and serves as a reference node, the number of independent nodes is n=N-1, the number of independent branches b=n; 2) Calculate the network parameters of each sequence

is the sequence impedance based on branch i

The formed diagonal matrix, where the superscript s=0,1,2 respectively represent the zero-sequence, positive-sequence and negative-sequence network models in the sequence network model; the three-phase impedance of branch i is

then there is $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}={\mathrm{AZ}}_{\mathrm{bi}}^{a,b,c}{A}^{-1},$ in, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],$ ${\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; bi</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; iaa</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; iab</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; iac</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; iba</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; ibb</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; ibc</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; ica</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; icb</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; icc</span>}}\end{array}\right]<span\; class="notranslate">\; ;</span>$ 3) In the decoupled sequence network model circuit, calculate the road matrix T _s of each sequence network; in addition, for the node whose injected sequence current is zero, delete the row corresponding to the node in the road matrix T _s of each sequence network After removal, a new matrix is formed as T _sg ; among them, the subscripts s=0, 1, 2 represent the zero-sequence, positive-sequence and negative-sequence networks in the sequence network model respectively; 4) Calculate the impedance sensitivity matrix in each sequence network

5) Assign an initial value to the three-phase voltage of each node of the distribution network

Where E _n =[E,E,…,E] ^T , there are n E in total, and E is a 3×3 unit matrix; 6) Calculate the current of each phase injected by node i during d iterations in

is the injected power of each phase of node i,

is the voltage phasor of each phase of node i calculated in the d-1th iteration,

is the sum of the parallel admittances of each phase of node i, p=a,b,c, i=1,2,...,m; m is the number of nodes whose injected sequence current is not zero, and d is the iteration number variable; 7) Calculate the sequence currents injected by node i during d iterations

i=1,2,...,m; 8) Calculate the d iteration

in,

is the new injected sequence current matrix formed after removing the nodes whose injected sequence current is zero in d iterations,

is the sequence voltage difference matrix generated from the power supply node to each independent node during d iterations, m is the number of nodes whose sequence current is not zero injected into the node, and the superscript s=0,1,2, respectively denote the sequence network model The zero-sequence, positive-sequence and negative-sequence network models of ; 9) Calculate the d iteration

in, is the sequence voltage matrix of each node obtained during d iterations, 1 _n =[1,1,…,1] ^T , a total of n 1s; s=0,1,2, respectively representing the zero sequence in the sequence network model , positive sequence and negative sequence network models; 10) Calculate the three-phase voltage phasor of node i at d iterations based on the inverse transformation

i=1,2,...,n; 11) Judgment and

Whether the amplitude difference meets the convergence accuracy requirements, and the iteration ends; if not, go to step 6); among them, and

are the three-phase voltage phasor matrices of each node obtained in the d-th iteration and the d-1-th iteration, respectively.

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