CN102842908B - Three-phase decoupling power flow calculation method for power distribution network containing multiple transformer branches - Google Patents

Abstract

The invention discloses a three-phase decoupling power flow calculation method for a power distribution network containing multiple transformer branches. According to the characteristics of basically symmetrical three-phase line parameters, unbalanced three-phase load and the tree structure of the power distribution network, the method comprises the following steps: performing sequence component decoupling on the three-phase unbalanced network of the power distribution network by a symmetrical component method; in a power distribution three-sequence network model, transforming the transformer branches into the common branches by a phase transformation technology; and calculating the sequence network power flow of the power distribution system by a path matrix-based loop analysis method and transforming sequence component power flow into phase component power flow by an inverse transformation principle so as to realize three-phase decoupling power flow calculation of the three-phase unbalanced system of the power distribution network containing multiple transformer branches and reduce calculated quantity. The method is clear in calculation process, simple in programming and high in calculation speed. The correctness and high convergence property of the method are verified through 34 bus test calculation examples. The method has high generality and practicability.

Description

Three-phase decoupling load flow calculation method for power distribution network containing multiple transformer branches

Technical Field

The invention relates to a three-phase decoupling load flow calculation method for a power distribution network containing multiple transformer branches, and belongs to the field of analysis and calculation of power systems.

Background

The power distribution network flow calculation is always a hotspot of academic research for many years, and is a basis for power distribution network analysis. Because the characteristics of the power distribution network are different from those of the power transmission network, the power distribution network generally has the characteristics of higher R/X ratio, unbalanced three phases and a tree-shaped network structure with closed-loop design and open-loop operation, the traditional power transmission network power flow algorithm cannot be directly applied to the power distribution network. Scholars at home and abroad propose various power distribution network trend algorithms according to the characteristics of a power distribution network, such as a forward-backward substitution method, an implicit Zbus Gaussian method, a loop impedance method, an improved Newton method, a rapid decoupling method and the like. The forward-backward substitution method fully utilizes the structural characteristics of the power distribution network, and has the advantages of clear physical concept, simple programming, no large matrix calculation, high calculation speed, good convergence, suitability for solving the radial power distribution network load flow and the like, so that the forward-backward substitution method is widely applied. The line parameters in a distribution network are basically spatially symmetrical, which is generally characterized by the presence of a three-phase imbalance on the load.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the problems and the defects in the prior art, the invention provides a three-phase decoupling load flow calculation method for a power distribution network with multiple transformer branches.

The technical scheme is as follows: a three-phase decoupling load flow calculation method for a power distribution network containing multiple transformer branches comprises the following steps:

1) the initial node is a power supply and is used as a reference node, and the three-phase voltage phasor matrix of the power supply node is(3 x 1 order), each node three-phase voltage phasor matrix is(3n x 1 order), in the distribution system sequence network, the three-sequence voltage matrix of the power source node can be obtained as(3 x 1 order) and a three-sequence voltage matrix of each node is(3n × 1 order). Wherein, let a ═ e^j2π/3， $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ And n is the number of the independent nodes, and the number of the independent branches is b ═ n. That is, for a three-phase radial (tree) distribution network having N nodes, assuming that the first node is a power source and serves as a reference node, the number of independent nodes is N-1, and the number of independent branches is N.

2) Correspondingly dividing the power distribution network into K blocks of areas according to the number K of transformers in the power distribution network, and sequentially calculating a phase transformation matrix theta of each block of area according to reference nodes and the wiring mode of each transformer_kAnd calculating a decoupling transformation matrix A of each block area_k＝Θ_kA (3 × 3 steps). Wherein K represents the kth block area in the power distribution network, and K belongs to {1,2, …, K }; theta is a phase transformation matrix which is a 3 x 3 diagonal matrix, andθ₀、θ₁and theta₂Zero sequence, positive sequence and negative sequence phase shift quantities in the three-sequence network system are respectively shown, and subscripts of 0,1 and 2 respectively represent the zero sequence, the positive sequence and the negative sequence in the three-sequence network; can also find <math> <mrow> <msubsup> <mi>A</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>A</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>&Theta;</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>.</mo> </mrow> </math>

3) Calculating the network parameters of each sequenceIs a sequence impedance based on branch iForming a diagonal array (n × n order), wherein the superscript s is 0,1 and 2, and respectively represents a zero sequence, a positive sequence and a negative sequence in the sequence network modelAnd (4) sequencing network model. Three-phase impedance of branch iAssuming it belongs to the kth block region, thenWherein, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],$ $Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right];$ wherein A is_kIs a decoupling transformation matrix of the region where the branch i is located.

4) Calculating road matrix T of each sequence network in each decoupled sequence network model circuit_s(ii) a And for nodes with zero injection sequence current, the road matrix T of each sequence network_sDeleting the row corresponding to the node to form a new matrix T_sg. Where, subscript s is 0,1,2, which respectively represents the zero sequence, positive sequence and negative sequence networks in the sequence network model.

5) Calculating an impedance sensitivity matrix in each sequence net

6) Giving initial value to three-phase voltage of each node of power distribution networkWherein E_n＝[E，E，…,E]^TN total E, E being a 3X 3 identity matrix。

7) Calculating each phase current injected by the node i in d iterationsWhereinIs the injected power of each phase of node i, Y_i ^pIs the sum of the parallel admittances of the node i, p is a, b, c, i is 1,2, …, m. m is the number of nodes with the node injection sequence current not being zero, and d is an iteration number variable.

8) Calculating each sequence current injected by the node i in d iterationsi is 1,2, …, m. Wherein A is_kIs a decoupling transformation matrix of the area where the node i is located.

9) Calculating d iterationsWherein,and a new injection sequence current matrix (m × 1 order) formed by removing nodes with zero injection sequence current in d iterations, wherein m is the number of nodes with non-zero node injection sequence current, and the superscript s is 0,1 and 2, and respectively represents a zero sequence network model, a positive sequence network model and a negative sequence network model in the sequence network model.

10) Calculating d iterationsWherein 1 is_n＝[1,1,…,1]^TN is 1; and s is 0,1 and 2, and respectively represents a zero sequence network model, a positive sequence network model and a negative sequence network model in the sequence network model.

11) Calculating node i three-phase voltage phasor in d iterations based on inverse transformationi is 1,2, …, n. Wherein A is_kIs a decoupling transformation matrix of the area where the node i is located.

12) Judgment ofAndwhether the difference of the amplitude values meets the requirement of convergence precision or not meets the requirement of ending iteration; not satisfying go to step 7).

Has the advantages that: compared with the prior art, the three-phase decoupling load flow calculation method for the power distribution network containing the multi-transformer branch circuits, which is provided by the invention, combines a loop analysis method and a sequence component decoupling analysis method based on a road matrix, and simplifies the transformer removal by utilizing a phase transformation technology in a decoupling sequence network, thereby realizing the treatment of taking the transformer branch circuits as common branch circuits and realizing the three-phase load flow calculation of the power distribution network containing the multi-transformer branch circuits. On one hand, the three-phase decoupling load flow calculation by using the symmetric component method has good calculation advantages, and a group of asymmetric three-phase components of 'a', 'b' and 'c' can be decomposed into three groups of three-phase symmetric sequence components, so that the three-phase load flow calculation becomes calculation of one phase of the three groups of three-phase symmetric sequence components. Therefore, the calculation amount of the three-phase unbalanced power flow calculation of the power distribution network can be reduced 2/3, and under the condition that better convergence is kept, the calculation speed can be increased for the three-phase power flow calculation of the power distribution network. On the other hand, in the distribution sequence network, the conversion of the transformer branch into the common branch is easier, and no matter what wiring mode the transformer is in, the transformer branch can be converted into the common branch for calculation after being processed by the phase conversion technology. Therefore, the method has the advantages of less calculation amount, high calculation efficiency, and good universality and practicability. The whole calculation process is clear, programming is simple, and calculation speed is high. Finally, the correctness and good convergence of the invention are verified by 34 bus test examples.

Drawings

FIG. 1 is a flow chart of a method of the present invention;

FIG. 2 is a three-phase unbalanced distribution system with 34 bus lines including multiple transformer branches;

FIG. 3 is a three-phase voltage distribution diagram of each node after power flow convergence under the Case1 condition;

fig. 4 is a three-phase voltage distribution diagram of each node after power flow convergence under the Case5 condition.

Detailed Description

The present invention is further illustrated by the following examples, which are intended to be purely exemplary and are not intended to limit the scope of the invention, as various equivalent modifications of the invention will occur to those skilled in the art upon reading the present disclosure and fall within the scope of the appended claims.

Fig. 1 is a general flow chart of the present invention, which specifically includes the following steps:

1) the initial node is a power supply and is used as a reference node, and the three-phase voltage phasor matrix of the power supply node is(3 x 1 order), each node three-phase voltage phasor matrix is(3n x 1 order), in the distribution system sequence network, the three-sequence voltage matrix of the power source node can be obtained as(3 x 1 order) and a three-sequence voltage matrix of each node is(3n × 1 order). Wherein, 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 the independent nodes,the number of the independent branches is b ═ n. That is, for a three-phase radial (tree) distribution network having N nodes, assuming that the first node is a power source and serves as a reference node, the number of independent nodes is N-1, and the number of independent branches is N.

2) Correspondingly dividing the power distribution network into K blocks of areas according to the number K of transformers in the power distribution network, and sequentially calculating a phase transformation matrix theta of each block of area according to reference nodes and the wiring mode of each transformer_kAnd calculating a decoupling transformation matrix A of each block area_k＝Θ_kA (3 × 3 steps). Wherein K represents the kth block area in the power distribution network, and K belongs to {1,2, …, K }; theta is a phase transformation matrix which is a 3 x 3 diagonal matrix, andθ₀、θ₁and theta₂Zero sequence, positive sequence and negative sequence phase shift quantities in the three-sequence network system are respectively shown, and subscripts of 0,1 and 2 respectively represent the zero sequence, the positive sequence and the negative sequence in the three-sequence network; can also find <math> <mrow> <msubsup> <mi>A</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>A</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>&Theta;</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>.</mo> </mrow> </math>

3) Calculating the network parameters of each sequenceIs a sequence impedance based on branch iAnd forming a diagonal array (n × n order), wherein the superscript s is 0,1 and 2, and respectively represents a zero sequence network model, a positive sequence network model and a negative sequence network model in the sequence network model. Three-phase impedance of branch iAssuming it belongs to the kth block region, thenWherein, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],$ $Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right];$ wherein A is_kIs a decoupling transformation matrix of the region where the branch i is located.

4) Calculating road matrix T of each sequence network in each decoupled sequence network model circuit_s(ii) a And for nodes with zero injection sequence current, the road matrix T of each sequence network_sDeleting the row corresponding to the node to form a new matrix T_sg. Where, subscript s is 0,1,2, which respectively represents the zero sequence, positive sequence and negative sequence networks in the sequence network model.

5) Calculating an impedance sensitivity matrix in each sequence net

6) Giving initial value to three-phase voltage of each node of power distribution networkWherein E_n＝[E,E,…,E]^TN total E, E being a 3 × 3 identity matrix.

7) Calculating d iteration time sectionsPhase current injected at point iWhereinIs the injected power of each phase of node i, Y_i ^pIs the sum of the parallel admittances of the node i, p is a, b, c, i is 1,2, …, m. m is the number of nodes with the node injection sequence current not being zero, and d is an iteration number variable.

8) Calculating each sequence current injected by the node i in d iterationsi is 1,2, …, m. Wherein A is_kIs a decoupling transformation matrix of the area where the node i is located.

9) Calculating d iterationsWherein,and a new injection sequence current matrix (m × 1 order) formed by removing nodes with zero injection sequence current in d iterations, wherein m is the number of nodes with non-zero node injection sequence current, and the superscript s is 0,1 and 2, and respectively represents a zero sequence network model, a positive sequence network model and a negative sequence network model in the sequence network model.

The formula in step 9) is derived as follows:

for a three-phase radial (tree) power distribution network with N nodes, assuming that a first node is a power supply and serves as a reference node, the number of independent nodes is N-1, and the number of independent branches is b-N. The road of a node is a branch set on a path which the node passes along the tree to the root, the road of the node emphasizes the branch on the path, the road of the node is unique for a given tree, the road of the node only consists of branch branches of the tree, and the road matrix T is used for describing the road. The road matrix T is an n × n-order matrix, assuming that the positive directions of the roads all point to nodes from power supply points, the positive directions of the branches are the same as the positive direction of the road, if the branch j is on the road i, T (i, j) is 1, otherwise T (i, j) is 0. The road matrix T is a sparse lower triangular matrix, and the memory requirement can be reduced by using a sparse technology.

In the distribution sequence network, it is providedThe node is injected with a sequence current vector matrix (n x 1 order), letIs a branch sequence current vector matrix (n multiplied by 1 order), and can obtain the road matrix of each sequence network as T in each decoupled sequence network model circuit₀、T₁And T₂And branch sequence current according to KCL current lawAnd node injection sequence currentThe following equation is satisfied:

<math> <mrow> <msubsup> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>b</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msubsup> <mi>T</mi> <mi>s</mi> <mi>T</mi> </msubsup> <msubsup> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>n</mi> <mi>s</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

where, s is 0,1,2, which respectively represent the zero sequence, positive sequence and negative sequence networks in the sequence network model.

Formula (1) givesHowever, in the actual system, the injection sequence current does not exist in each node, and for the nodes with zero injection sequence current, the road matrix T in each sequence net_sDeleting the row corresponding to the node to form a new matrix T_sgWhen this time, the formula (1) becomes

<math> <mrow> <msubsup> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>b</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msubsup> <mi>T</mi> <mi>sg</mi> <mi>T</mi> </msubsup> <msubsup> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>g</mi> <mi>s</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

In the formula (2)In order to remove a new injection sequence current matrix (m multiplied by 1 order) formed after the nodes with injection sequence current of zero are removed, m is the number of the nodes with the injection sequence current of non-zero nodes.

For any radial distribution system sequence component circuit model, there are

<math> <mrow> <msubsup> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>b</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msubsup> <mi>Z</mi> <mi>b</mi> <mi>s</mi> </msubsup> <msubsup> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>b</mi> <mi>s</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein,a distribution network branch sequence voltage matrix (n multiplied by 1 order);is a sequence impedance based on branch iThe diagonal matrix (n × n order), s is 0,1,2, and represents the zero sequence, positive sequence, and negative sequence network models in the sequence network model, respectively.

Setting a three-phase voltage phasor matrix of a power supply node as(3 x 1 order), each node three-phase voltage phasor matrix is(3n x 1 order), in the distribution sequence network, a three-sequence voltage matrix of power source nodes can be obtained as(3 x 1 order) and a three-sequence voltage matrix of each node is(order 3n × 1), then, in each sequence network model, it can be known that the sequence voltage difference between any node and the power supply node is equal to the sum of branch sequence voltages of branches from the node to the power supply node along the road of the node, i.e. (set to 1)_n＝[1,1,…,1]^TN is 1; s is 0,1,2, representing the zero, positive and negative sequence network models in the sequence network model, respectively):

<math> <mrow> <mi>&Delta;</mi> <msubsup> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>n</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msub> <mn>1</mn> <mi>n</mi> </msub> <msubsup> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mn>0</mn> <mi>s</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>n</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msub> <mi>T</mi> <mi>s</mi> </msub> <msubsup> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>b</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msub> <mi>T</mi> <mi>s</mi> </msub> <msubsup> <mi>Z</mi> <mi>b</mi> <mi>s</mi> </msubsup> <msubsup> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>b</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msub> <mi>T</mi> <mi>s</mi> </msub> <msubsup> <mi>Z</mi> <mi>b</mi> <mi>s</mi> </msubsup> <msubsup> <mi>T</mi> <mi>sg</mi> <mi>T</mi> </msubsup> <msubsup> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>g</mi> <mi>s</mi> </msubsup> <mo>=</mo> <mi>&Delta;</mi> <msubsup> <mi>Z</mi> <mi>t</mi> <mi>s</mi> </msubsup> <msubsup> <mover> <mi>I</mi> <mo>&CenterDot;</mo> </mover> <mi>g</mi> <mi>s</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,defined as the impedance sensitivity matrix in each ordered net:

<math> <mrow> <mi>&Delta;</mi> <msubsup> <mi>Z</mi> <mi>t</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msub> <mi>T</mi> <mi>s</mi> </msub> <msubsup> <mi>Z</mi> <mi>b</mi> <mi>s</mi> </msubsup> <msubsup> <mi>T</mi> <mi>sg</mi> <mi>T</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>n</mi> <mi>s</mi> </msubsup> <mo>=</mo> <msub> <mn>1</mn> <mi>n</mi> </msub> <msubsup> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mn>0</mn> <mi>s</mi> </msubsup> <mo>-</mo> <mi>&Delta;</mi> <msubsup> <mover> <mi>U</mi> <mo>&CenterDot;</mo> </mover> <mi>n</mi> <mi>s</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>

10) calculating d iterationsWherein 1 is_n＝[1,1,…,1]^TN is 1; and s is 0,1 and 2, and respectively represents a zero sequence network model, a positive sequence network model and a negative sequence network model in the sequence network model.

11) Calculating a node i three-phase voltage phase at d iterations based on inverse transformationMeasurement ofi is 1,2, …, n. Wherein A is_kIs a decoupling transformation matrix of the area where the node i is located.

12) Judgment ofAndwhether the difference in amplitude meets the convergence accuracy requirement. The end of iteration is satisfied; not satisfying go to step 7).

Example analysis

For example, as shown in fig. 2, a 34-bus three-phase unbalanced distribution network including multiple transformer branches is obtained, some adjustments are made to the system, a three-phase voltage regulator is removed, and a loop condition is not considered at all, assuming that the system is operated in an open loop mode, line parameters are symmetric, that is, impedance matrices of phase components of the lines are completely symmetric, and three-phase loads are unbalanced, so that the system is relatively close to a domestic distribution network system.

In the figure 2, T1 is positioned in a step-down transformer substation, and in order to reflect and be suitable for the characteristics of a domestic three-phase unbalanced distribution network, T1 adopts delta-Y common in domestic current main step-down transformer substations_gThe voltage of 69kV is reduced to 24.9kV, and the capacity is 2500 kVA. The rated transformation ratios of the three transformers T2-T4 are the same, and 24.9kV is reduced to 4.16 kV. The total load of the system is 1379kW and 878kvar, and the distribution is unbalanced. For simulation comparative analysis, transformer T1 was fixed at delta-Y_gArranged such that transformers T2-T4 are at Y_g-Y_g、△-Y_gAnd Y-delta, wherein 27 groups of combination forms are selected from the three configurations, as shown in Table 1, and the partial combination forms are shown in Table 1, and the convergence situation of the power flow calculation based on the algorithm of the invention is shown in Table 2.

TABLE 1 arrangement of transformers T1-T4

Iteration times after power flow convergence of bus system of table 234

It can be seen from table 2 that the convergence is not very different under different configurations, and the algorithm herein has better convergence performance.

Fig. 3 and 4 are distribution diagrams of voltages of phases a, B and C at nodes after convergence of power flow calculation under the conditions of Case1 and Case5, respectively, and it can be seen from comparison between fig. 3 and 4 that the voltage distribution of the phases a, B and C at the nodes is relatively balanced in Case5, while the voltage difference of the phases C at the Case1 is relatively large, wherein the voltage of the phase C at a part of the nodes is obviously excessively low (less than 0.9), so that the problem that the voltage of the single phase at the nodes of a three-phase unbalanced distribution system is excessively low can be solved by carrying out different combination configurations on transformers.

Claims (1)

1. A three-phase decoupling load flow calculation method for a power distribution network containing multiple transformer branches is characterized by comprising the following steps:

1) the initial node is a power supply and is used as a reference node, and the three-phase voltage phasor matrix of the power supply node isEach node has a three-phase voltage phasor matrix ofIn the distribution system sequence network, the three-sequence voltage matrix of the power source node is obtained asEach node has a three-sequence voltage matrix ofWherein, 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 the independent nodes, and the number of the independent branches is b ═ n; for a three-phase radial power distribution network with N nodes, assuming that a first node is a power supply and serves as a reference node, the number of independent nodes is N-1, and the number of independent branches is b-N;

2) correspondingly dividing the power distribution network into K blocks of areas according to the number K of transformers in the power distribution network, and sequentially calculating a phase transformation matrix theta of each block of area according to reference nodes and the wiring mode of each transformer_kAnd calculating a decoupling transformation matrix A of each block area_k＝Θ_kA; wherein K represents the kth block area in the power distribution network, and K belongs to {1,2, …, K }; theta is a phase transformation matrix which is a 3 x 3 diagonal matrix, andθ₀、θ₁and theta₂Zero sequence, positive sequence and negative sequence phase shift quantities in the three-sequence network system are respectively shown, and subscripts of 0,1 and 2 respectively represent the zero sequence, the positive sequence and the negative sequence in the three-sequence network; at the same time find <math> <mrow> <msubsup> <mi>A</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>A</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>&Theta;</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>;</mo> </mrow> </math>

3) Calculating the network parameters of each sequence Is a sequence impedance based on branch iForming a diagonal matrix, wherein the superscript s is 0,1 and 2, and respectively represents a zero sequence network model, a positive sequence network model and a negative sequence network model in the sequence network model; three-phase impedance of branch iAssuming it belongs to the kth block region, thenWherein, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right];$ wherein A is_kA decoupling transformation matrix of the area where the branch i is located;

4) calculating road matrix T of each sequence network in each decoupled sequence network model circuit_s(ii) a And for nodes with zero injection sequence current, the road matrix T of each sequence network_sDeleting the row corresponding to the node to form a new matrix T_sg(ii) a The subscript s is 0,1 and 2, and respectively represents a zero sequence, a positive sequence and a negative sequence in the sequence network model;

5) calculating an impedance sensitivity matrix in each sequence net

6) Giving initial value to three-phase voltage of each node of power distribution networkWherein E_n＝[E,E,…,E]^TN E, E being a 3 × 3 identity matrix;

7) calculating each phase current injected by the node i in d iterationsWhereinIs the injected power of each phase at node i,is the phasor, Y, of each phase voltage at node i, which is found at the d-1 th iteration_i ^pIs the sum of the parallel admittances of the node i, p is a, b, c, i is 1,2, …, m; m is the number of nodes with the node injection sequence current not being zero, and d is an iteration number variable;

8) calculating each sequence current injected by the node i in d iterationsi is 1,2, …, m; wherein A is_kA decoupling transformation matrix of the area where the node i is located;

9) calculating d iterationsWherein,a new injection sequence current matrix is formed after nodes with injection sequence currents being zero are removed in d iterations, m is the number of nodes with node injection sequence currents being not zero, and the superscript s is 0,1 and 2, and the zero sequence network model, the positive sequence network model and the negative sequence network model in the sequence network model are respectively represented;

10) calculating d iterationsWherein 1 is_n＝[1,1,…,1]^TN is 1; s is 0,1 and 2, which respectively represent a zero sequence network model, a positive sequence network model and a negative sequence network model in the sequence network model;

11) calculating node i three-phase voltage phasor in d iterations based on inverse transformation1,2, …, n; wherein A is_kIs a decoupled transformation matrix for the region in which node i is located,a node i three-sequence voltage phasor matrix in the d iteration;

12) judgment ofAndwhether the difference between the amplitudes meets the convergence accuracy requirement; the end of iteration is satisfied; not satisfying go to step 7).