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 decoupling load flow calculation method for power distribution network based on road matrix

Technical Field

The invention relates to a three-phase decoupling load flow calculation method for a power distribution network based on a road matrix, and belongs to the technical 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 the current distribution network are basically spatially symmetrical, and generally three-phase imbalance exists 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 based on a road matrix.

The technical scheme is as follows: a three-phase decoupling load flow calculation method for a power distribution network based on a road matrix 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) Calculating the network parameters of each sequence

Is a sequence impedance based on branch i

And 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 iThen there is

Wherein, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],$ $Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right].$

3) 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.

4) Calculating an impedance sensitivity matrix in each sequence net

5) 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.

6) Calculating each phase current injected by the node i in d iterations

Wherein

Is the injected power of each phase at node i,

is 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.

7) Calculating each sequence current injected by the node i in d iterations

i＝1,2,…,m。

8) Calculating d iterations

Wherein,

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.

9) 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.

10) Calculating node i three-phase voltage phasor in d iterations based on inverse transformation

i＝1,2,…,n。

11) Judgment ofAnd

whether 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 6).

Has the advantages that: compared with the prior art, the method for calculating the three-phase decoupling load flow of the power distribution network based on the road matrix combines a loop analysis method and a sequence component decoupling analysis method based on the road matrix, and decouples a three-phase unbalanced power distribution network system into a zero sequence network, a positive sequence network and a negative sequence network, so that large matrix operation in the calculation process is avoided, the three-phase unbalance of the power distribution network is considered, the calculated amount is reduced, and the calculation efficiency is improved. The whole calculation process is clear, programming is simple, and calculation speed is high. The three-phase decoupling load flow calculation by using the symmetrical component method has good calculation advantages, and a group of asymmetrical three-phase components of 'a', 'b' and 'c' can be decomposed into three groups of three-phase symmetrical sequence components, so that the three-phase load flow calculation becomes calculation of one phase of the three groups of three-phase symmetrical sequence components. Therefore, the calculation amount of the three-phase unbalanced power flow calculation of the power distribution network is reduced 2/3, and under the condition that good convergence is kept, the calculation speed can be increased for the three-phase power flow calculation of the power distribution network. Finally, the correctness and the good convergence of the invention are verified through a 6-bus test example, and meanwhile, the invention has good universality and practicability.

Drawings

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

fig. 2 is the three-phase unbalanced distribution network system of the 6 buses.

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， $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ 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) Calculating the network parameters of each sequence

Is 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 iThen there is

Wherein, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],$ $Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right].$

3) 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.

4) Calculating an impedance sensitivity matrix in each sequence net

5) 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.

6) Calculating each phase current injected by the node i in d iterations

Wherein

Is the injected power of each phase at node i,is 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.

7) Calculating each sequence current injected by the node i in d iterations

i＝1,2,…,m。

8) Calculating d iterations

Wherein,

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 for step 8) 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), let

Is 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 current

The 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) gives

However, 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 i

The 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> <msubsup> <mi>&Delta;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> <msubsup> <mi>&Delta;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>

9) calculating d iterations

Wherein 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.

10) Calculating node i three-phase voltage phasor in d iterations based on inverse transformation

i＝1,2,…,n。

11) Judgment of

And

whether the difference in amplitude meets the convergence accuracy requirement. The end of iteration is satisfied; not satisfying go to step 6).

Example analysis

FIG. 2 shows a 6-bus three-phase unbalanced distribution network system, a transformer Y_n-y_nAnd (4) wiring mode, and resetting line parameters, so that the line space is symmetrical, namely mutual inductance between phases is completely symmetrical, and three-phase load is unbalanced.

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

Table 1 load flow calculation results of the algorithm

Claims (1)

1. A power distribution network three-phase decoupling load flow calculation method based on a road matrix 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 is

Each node has a three-phase voltage phasor matrix of

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

Each node has a three-sequence voltage matrix of

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, 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) calculating the network parameters of each sequence

Is a sequence impedance based on branch i

Forming 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 i

Then there is $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}={\mathrm{AZ}}_{\mathrm{bi}}^{a,b,c}{A}^{-1},$ Wherein, $Z_{\mathrm{bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{bi}}^0& 0& 0\\ 0& Z_{\mathrm{bi}}^1& 0\\ 0& 0& Z_{\mathrm{bi}}^2\end{array}\right],$

$Z_{\mathrm{bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{iaa}}& Z_{\mathrm{iab}}& Z_{\mathrm{iac}}\\ Z_{\mathrm{iba}}& Z_{\mathrm{ibb}}& Z_{\mathrm{ibc}}\\ Z_{\mathrm{ica}}& Z_{\mathrm{icb}}& Z_{\mathrm{icc}}\end{array}\right];$

3) 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;

4) calculating an impedance sensitivity matrix in each sequence net

5) Giving initial value to three-phase voltage of each node of power distribution network

Wherein E_n＝[E,E,…,E]^TN E, E being a 3 × 3 identity matrix;

6) calculating each phase current injected by the node i in d iterationsWherein

Is the injected power of each phase at node i,

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

is 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;

7) calculating each sequence current injected by the node i in d iterations

i＝1,2,…,m；

8) Calculating d iterations

Wherein,

the new injection sequence current matrix is formed after removing the node with the injection sequence current being zero in d iterations,

the sequence voltage difference matrix is generated from a power supply node to each independent node during d iterations, 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;

9) calculating d iterations

Wherein,for each node sequence voltage matrix found during d iterations, 1_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;

10) calculating node i three-phase voltage phasor in d iterations based on inverse transformation

i＝1,2,…,n；

11) Judgment ofAnd

whether the difference of the amplitude values meets the requirement of convergence precision or not meets the requirement of ending iteration; not satisfying step 6); wherein,and

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

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