CN109980650B - Load flow calculation method of radiation type power distribution system - Google Patents
Load flow calculation method of radiation type power distribution system Download PDFInfo
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- CN109980650B CN109980650B CN201910424449.3A CN201910424449A CN109980650B CN 109980650 B CN109980650 B CN 109980650B CN 201910424449 A CN201910424449 A CN 201910424449A CN 109980650 B CN109980650 B CN 109980650B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
Abstract
The invention discloses a power flow calculation method of a radiation type power distribution system, which carries out power flow calculation aiming at a power distribution system in one direction of a power distribution network area, firstly, according to the characteristics of the radiation type power distribution system, a circuit model of the radiation type power distribution system is established, the topological structure of the radiation type power distribution system is reasonably numbered, the initial data of a circuit is represented by using a matrix form, particularly the data description of the topological relation of the circuit, the logical relation of graphic connection in the circuit model is clear and definite, the introduction of an incidence matrix realizes the programming design of a path searching process, and the initial data matrix is used as the only data input, so that the whole program design is direct and simple; in the calculation process, the algebraic operation of matrix elements is utilized to solve the voltages of all load nodes and the power flows of all branches of the power distribution network, so that the program calculation time is less, and the convergence speed is higher.
Description
Technical Field
The invention relates to the technical field of low-voltage power distribution, in particular to a method for calculating a power flow of a radiation type power distribution system.
Background
At present, the calculation of the tidal current of the power distribution network is an important basis for analysis and economic operation of the power distribution network system. Network reconstruction, fault processing, reactive power optimization, state estimation, line loss analysis and the like of the power distribution network all need to use the result of power distribution network load flow calculation. A power flow calculation method with excellent performance is the key of power distribution system management. With the increasing importance of the power distribution network management by the power department, the research of load flow calculation specially aiming at the power distribution network is widely developed. Because the power distribution network is an intermediate link of a power transmission network and an electric energy user, the voltage grade is lower than that of the power transmission network, a network structure is in a tree-shaped and multi-branch unidirectional radial structure in steady-state operation, the R/X value of a line is higher, and most of the R/X values are larger than 1; the low-voltage distribution transformer is mostly positioned in a load center, power is supplied from the low-voltage side of the distribution transformer to multiple directions, an outlet bus of a superior transformer substation of a distribution system can be regarded as an infinite power supply, the power supply in the multiple directions can be separately calculated, the tide of the low-voltage distribution network flows to the load from the low-voltage side of the distribution transformer, and the tide flow on a line has unidirectionality.
Students at home and abroad propose various power distribution network trend algorithms such as a Newton method, an improved PQ decoupling method, a loop impedance method, a forward-backward substitution method and the like according to the characteristics of a power distribution network. But the Newton method needs to form an admittance matrix, and the diagonal advantage of the Jacobian matrix does not exist, so that convergence is difficult; the improved PQ decoupling method introduces a compensation technology to a circuit with a large R/X value, the algorithm is complex, and the advantages of small calculation amount and reliable convergence of the original quick decoupling method are lost; the loop impedance method requires complex node and branch numbering and is time consuming. In comparison, the forward-backward substitution power flow algorithm fully utilizes the radial structural characteristics of the network, the physical concept of the method is clear, but the power distribution system has huge structure and more branches, the search of system structural data in the calculation process influences the calculation speed of the power flow, the power loss of the branch is calculated when the data are pushed forward each time, the calculation of a data matrix is directly related, and the occupied space is large and time is long.
Disclosure of Invention
The invention aims to provide a method for calculating the power flow of a radiation type power distribution system, which can be used for quickly and efficiently calculating the power flow of a power distribution network, and has the advantages of high convergence speed and less time consumption.
The technical scheme adopted by the invention is as follows:
a radiation type power distribution system power flow calculation method specifically comprises the following steps:
establishing a circuit model of a power distribution system according to the characteristics of a radiation type power distribution system, taking the low-voltage side of a distribution transformer as a potential node and a balance node in load flow calculation, wherein equivalence is that the voltage amplitude and the phase angle are constant known quantities and the three-phase voltage is assumed to be symmetrical; all loads on the feeder line are equivalent to concentrated loads of branch end nodes, and are constant power, namely PQ loads, which are simply referred to as node loads; the feeder line branch adopts a centralized parameter model, and according to the characteristics of a radiation type power distribution system, only one potential node in the power distribution system is a balance node, the other nodes are load nodes, and the power flow in the power distribution system flows from the potential node to the load nodes. Each branch in the power distribution system is connected with two nodes in the system, a power flow outflow node is called a branch initial end node, a power flow inflow node is called a branch tail end node, and each node is connected with at most two branches.
Secondly, numbering branches and nodes in the topological structure of the circuit model according to the circuit model of the power distribution system, wherein the branches are numbered from the branch connected with the potential node in sequence as 1,2,3,4 \8230 \ 8230, b and b are the number of the branches of the power distribution system; the potential node is numbered 0, and the load nodes corresponding to the tail ends of the branches are sequentially numbered 1,2,3,4 \8230, 8230, n-1, n are the number of the nodes of the power distribution system; according to the characteristics of a radiation type power distribution system, b = n-1 is provided, and for the sake of simplicity and convenience of subsequent procedures, the branch numbers are the same as the numbers of the connected end nodes during numbering;
and expressing the topological structure and specific parameters of the circuit model by an initial data matrix DS, wherein the initial data matrix DS is a matrix with b rows and 5 columns, and the ith row is as follows: DS (i) = [ x, NS (x), NR (x), Z (x), S (NR (x)) ]; i =1,2,..., b; x is the number of the ith branch, NS (x) is the number of the starting node of the ith branch, and NR (x) is the number of the tail end node of the ith branch, then NR (x) = i; z (x) is the impedance of the ith branch, and S (NR (x)) is the complex power loaded by a node with a tail end node of the branch being NR (x);
step three, constructing a node branch incidence matrix NB of the power distribution system through the initial data matrix DS, wherein the node branch incidence matrix NB is a matrix with n rows and b columns, and the ith row and ith column of elements NB (j, i) of the jth row are as follows:
wherein j =1,2,.. Wherein, n, i =1,2,.. Wherein, b;
step four, constructing a path matrix P through which the power flow from the potential node to the load node flows according to the node branch incidence matrix NB, wherein the path matrix P is a matrix of (n-1) rows and b columns, and the element P (j, i) of the jth row and the ith column is as follows:
wherein j =1,2, ·., n-1, i =1,2,... ·., b;
the decision that the power flow from potential node 0 to load node j flows through the branch comprises the following steps:
1) Traversing the (j + 1) th row element NB (j,: in the NB matrix, if NB (j, y) =1, the y end node of the branch can be determined to be j;
2) Traversing the y-th column element NB (: y) in the NB matrix, and if NB (z, y) = -1, determining that the y starting end node of the branch is (z-1);
3) Traversing the z-th row element NB (z,: in the NB matrix), if NB (z, t) =1, the end node of the branch t can be determined to be (z-1);
4) Repeating the steps 2 and 3 until the node at the starting end of the branch circuit is a potential node 0;
the current path from potential node 0 to load node j is potential node 0 \ 8230 \8230 \ 8230, branch t, node (z-1), branch y, load node j;
constructing a branch impedance matrix ZP through which the power flow from the potential node to the load node flows and a complex power matrix SB of the node load according to the path matrix P and the initial data matrix DS; the branch impedance matrix ZP is a matrix of (n-1) rows and b columns, and the element ZP (j, i) in the ith row and ith column is:
ZP (j, i) = P (j, i) × Z (i); the complex power matrix SB of the node load is a matrix with b rows and (n-1) columns, the element SB (i, j) of the ith row and the jth column is as follows:
SB(i,j)＝P(i,j)*S(j)；
wherein Z (i) = DS (i, 4) is the impedance of the ith branch; s (j) = DS (i, 5) is the node load complex power of a j node, wherein the end node of a branch i is j; j =1,2, ·., n-1, i =1,2, ·. · b;
step six, calculating the voltage of each load node and the power flow of each branch of the radiation type power distribution system, and specifically comprising the following steps:
1) Setting the initial voltage value of each load node as V 1 ，V 2 ，…V j ，…V n-1 Wherein V is j Representing the initial voltage value of a load node j, constructing a node voltage matrix V, wherein the node voltage matrix V is a matrix with 1 row and (n-1) column, and the j-th column comprises the following elements:
V(1,j)＝V j
wherein j =1, 2.... N-1;
2) Further, a node voltage conjugate matrix VC can be obtained, wherein the node voltage conjugate matrix is a matrix with 1 row, n-1 columns and j-th column elements:
VC(1,j)＝V * (1,j)
the complex power conjugate matrix of the node load is SC, the complex power conjugate matrix SC of the node load is a matrix of b rows and (n-1) columns, the ith row and the jth column have the following elements:
SC(i,j)＝SB * (i,j)
wherein i =1,2,..., b; j =1, say, n-1;
3) Calculating to obtain a current matrix LC, wherein the current matrix LC is a matrix of b rows and (n-1) columns, and the element of the ith row and the jth column is as follows:
LC(i,j)＝SC(i,j)/VC(1,j)
the branch current matrix FC is a matrix with b rows and 1 column, and the ith row element is:
wherein i =1, 2.... B; j =1,.. N-1;
4) Calculating to obtain a voltage drop matrix D, a total voltage drop matrix M and a voltage matrix T; a voltage drop matrix D, a total voltage drop matrix M and a voltage matrix T are matrixes of n-1 rows and b columns;
D(j,i)＝ZP(j,i)*FC(i,1)
T(j,i)＝V 0 -M(j,i)
calculating to obtain a new node voltage matrix Vnew, wherein the new node voltage matrix Vnew is a matrix of 1 row (n-1) column, and the j-th column element: vnew (1, j) = min (T (j, 1), T (j, 2),.. T (j, (n-1)))
Wherein, V 0 I =1,2, a. j =1, say, n-1; l =1, 2.... I;
5) Determining a convergence condition, selecting the error precision of the system to be delta, judging whether the absolute value of Vnew (1, j) -V (1, j) | ≦ delta is true, if not, then V (1, j) = Vnew (1, j) and returning to the step 2);
otherwise, the voltage of each load node and the power flow of each branch of the radiation type power distribution system can be obtained:
the voltage at node j is U j ＝V(1,j)
The ith branch current is Il i ＝FC(i,1)
The ith branch has a power flow of
Wherein i =1, 2.... B; j =1,.. N-1.
The method establishes a circuit model of the power distribution system according to the characteristics of the power distribution system, numbers nodes and branches in the circuit model of the power distribution system, and expresses initial data of a circuit by using a matrix form, particularly the datamation description of a circuit topological structure, so that the logical relation of graph connection in the circuit model is clear and definite, the introduction of an incidence matrix realizes the programmed design of a path searching process, and the initial data matrix is used as the unique data input, so that the whole program design is direct and simple; in the calculation process, the algebraic operation of the matrix elements is utilized to solve the load flow of each branch and the voltage of each load node of the power distribution network, so that the program calculation time is less, and the convergence speed is higher.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention;
fig. 2 is a schematic circuit model diagram of a radiation-type power distribution system according to an embodiment of the present invention;
fig. 3 is a schematic diagram illustrating a circuit model branch node numbering of a radiation-type power distribution system according to an embodiment of the present invention;
fig. 4 is a schematic diagram illustrating a determination of a branch path for a power flow from a potential node to a load node 9 in a power distribution system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
As shown in fig. 1,2 and 3, the present invention comprises the following steps:
establishing a circuit model of a power distribution system according to the characteristics of a radiation type power distribution system, taking the low-voltage side of a distribution transformer as a potential node and a balance node in load flow calculation, wherein equivalence is that the voltage amplitude and the phase angle are constant known quantities and the three-phase voltage is assumed to be symmetrical; all loads on the feeder line are equivalent to concentrated loads of branch end nodes, and are constant power, namely PQ loads, which are simply referred to as node loads; the feeder line branch adopts a centralized parameter model, and according to the characteristics of a radiation type power distribution system, only one potential node in the power distribution system is a balance node, the other nodes are load nodes, and the power flow in the power distribution system flows from the potential node to the load nodes. Each branch in the power distribution system is connected with two nodes in the system, a power flow outflow node is called a branch initial end node, a power flow inflow node is called a branch tail end node, and each node is connected with at most two branches.
Numbering branches and nodes in a circuit model topological structure according to a circuit model of the power distribution system, wherein the branches are numbered from branches connected with potential nodes in sequence as 1,2,3,4 \8230 \ 8230b, b and b are the number of the branches of the power distribution system; the potential node is numbered as 0, and the load nodes corresponding to the tail ends of the branches are numbered as 1,2,3,4 \8230, 8230, n-1 and n are the number of the nodes of the power distribution system in sequence; in the figures, the distinction between parentheses is made for distinguishing between the two, but the two are the same corresponding reference numerals in actual use. B = n-1 is provided according to the characteristics of the radiation type power distribution system, and for the sake of simplicity and convenience of subsequent procedures, the branch numbers are the same as the numbers of the connected end nodes; in the figures, the distinction between parentheses is made for distinguishing between the two, but the two are the same corresponding reference numerals in actual use.
And expressing the topological structure and specific parameters of the circuit model through an initial data matrix DS, wherein the initial data matrix DS is a matrix with b rows and 5 columns, and the ith row is as follows: DS (i) = [ x, NS (x), NR (x), Z (x), S (NR (x)) ]; i =1, 2.... B; x is the serial number of the ith branch, NS (x) is the serial number of the starting node of the ith branch, and NR (x) is the serial number of the tail end node of the ith branch, then NR (x) = i; z (x) is the ith branch impedance, and S (NR (x)) is the complex power loaded by a node with a branch tail end node of NR (x);
step three, constructing a node branch incidence matrix NB of the power distribution system through the initial data matrix DS, wherein the node branch incidence matrix NB is a matrix with n rows and b columns, and the ith row and ith column of elements NB (j, i) of the jth row are as follows:
wherein j =1,2, ·., n, i =1,2,. ·., b;
step four, constructing a path matrix P through which the power flow from the potential node to the load node flows according to the node branch incidence matrix NB, wherein the path matrix P is a matrix of (n-1) rows and b columns, and the element P (j, i) of the jth row and the ith column is as follows:
wherein j =1,2, ·., n-1, i =1,2, ·.. ·, b;
the decision that the power flow from potential node 0 to load node j flows through the branch comprises the following steps:
5) Traversing the (j + 1) th row element NB (j) in the NB matrix, and if NB (j, y) =1, determining that the y end node of the branch is j;
6) Traversing the y-th column element NB (: y) in the NB matrix, and if NB (z, y) = -1, determining that the y starting end node of the branch is (z-1);
7) Traversing the z-th row element NB (z,: in the NB matrix, if NB (z, t) =1, the end node of the branch t can be determined to be (z-1);
8) Repeating the steps 2 and 3 until the node at the starting end of the branch circuit is a potential node 0;
the current path from potential node 0 to load node j is potential node 0 \ 8230 \8230 \ 8230, branch t, node (z-1), branch y, load node j;
constructing a branch impedance matrix ZP through which the power flow from the potential node to the load node flows and a complex power matrix SB of the node load according to the path matrix P and the initial data matrix DS; the branch impedance matrix ZP is a matrix of (n-1) rows and b columns, and the element ZP (j, i) in the jth row and ith column is:
ZP (j, i) = P (j, i) × Z (i); the complex power matrix SB of the node load is a matrix of b rows and (n-1) columns, the element SB (i, j) of the ith row and the jth column is:
SB(i,j)＝P(i,j)*S(j)；
wherein Z (i) = DS (i, 4) is the impedance of the ith branch; s (j) = DS (i, 5) is the node load complex power of a j node, wherein the end node of a branch i is j; j =1,2,. ·, n-1, i =1,2, ·. ·, b;
step six, calculating the voltage of each load node and the power flow of each branch of the radiation type power distribution system, and specifically comprising the following steps:
1) Setting the initial voltage value of each load node as V 1 ，V 2 ，…V j ，…V n-1 Wherein V is j Representing the initial voltage value of a load node j, constructing a node voltage matrix V, wherein the node voltage matrix V is a matrix with 1 row and (n-1) column, and the j-th column comprises the following elements:
V(1,j)＝V j
wherein j =1, 2.... N-1;
2) Further, a node voltage conjugate matrix VC can be obtained, wherein the node voltage conjugate matrix is a matrix with 1 row, n-1 columns and j-th column elements:
VC(1,j)＝V*(1,j)
the complex power conjugate matrix of the node load is SC, the complex power conjugate matrix SC of the node load is a matrix of b rows and (n-1) columns, the ith row and the jth column have the following elements:
SC(i,j)＝SB*(i,j)
wherein i =1,2,..., b; j =1, say, n-1;
3) Calculating to obtain a current matrix LC, wherein the current matrix LC is a matrix of b rows and (n-1) columns, and the ith row and the jth column have the following elements:
LC(i,j)＝SC(i,j)/VC(1,j)
the branch current matrix FC is a matrix with b rows and 1 column, and the ith row element is:
wherein i =1,2,..., b; j =1, say, n-1;
4) Calculating to obtain a voltage drop matrix D, a total voltage drop matrix M and a voltage matrix T; the voltage drop matrix D, the total voltage drop matrix M and the voltage matrix T are matrixes of n-1 rows and b columns;
D(j,i)＝ZP(j,i)*FC(i,1)
T(j,i)＝V 0 -M(j,i)
calculating to obtain a new node voltage matrix Vnew, wherein the new node voltage matrix Vnew is 1 row, a matrix of (n-1) columns and an element of the jth column: vnew (1, j) = min (T (j, 1), T (j, 2),.. T (j, (n-1)))
Wherein, V 0 I =1,2, a. j =1,.. N-1; l =1,2,...., i;
5) Determining a convergence condition, selecting the error precision of the system to be delta, judging whether the absolute value of Vnew (1, j) -V (1, j) | ≦ delta is true, if not, then V (1, j) = Vnew (1, j) and returning to the step 2);
otherwise, the voltage of each load node and the power flow of each branch of the radiation type power distribution system can be obtained:
the voltage at node j is U j ＝V(1,j)
The ith branch current is Il i ＝FC(i,1)
The ith branch has a power flow of
Wherein i =1, 2.... B; j =1, say, n-1.
To further illustrate the present invention, reference is made to the following examples, which are intended to be illustrative only and are not intended to be limiting.
Referring to fig. 1, a method for calculating a power flow of a radiation-type power distribution system specifically includes the following steps:
step one, a simplified circuit model of a radial power distribution system is presented herein and can be seen in fig. 2.
Taking the low-voltage side of the distribution transformer as a potential node 1, equating to a constant known quantity of voltage amplitude and phase angle, and assuming that three-phase voltage is symmetrical; all loads on the feeder line are equivalent to node loads 2 and are constant power, namely PQ loads, and feeder line branches adopt a centralized parameter model, so that only one potential node 1 exists in the power distribution network, and the rest nodes are load nodes 3; each branch 4 in the power distribution system is connected with two nodes in the system, a power flow outflow node is called a branch initial end node 5, and a power flow inflow node is called a branch tail end node 6;
numbering branches and nodes in a topological structure of the radiation type power distribution system circuit model shown in the figure 2, wherein the branches are numbered 1,2 \8230; 9 from branches connected with potential nodes in sequence, and the number b of the branches of the power distribution system is 9; the potential node is numbered 0, the corresponding branch tail end nodes are numbered 1,3,4 \8230 \ 8230:9 in sequence, the node number n of the power distribution system is 10, and the power distribution system comprises one potential node and 9 load nodes; for the sake of simplicity of subsequent procedures, the numbering here is carried out such that the branch number is the same as the number of the connected end node;
and expressing the topological relation and specific parameters of the circuit model through the initial data matrix DS as follows:
wherein, the initial data matrix DS is a matrix with 9 rows and 5 columns, Z (i) is the i-th branch impedance, S (j) is the complex power of the node load whose end node is j, where i = j if the end node of branch i is j; i =1,2, 9, j =1,2, 9;
step three, a node branch incidence matrix NB of the power distribution system can be constructed through the initial data matrix DS as follows:
step four, constructing a path matrix P through which the power flow from the potential node to the load node flows according to the node branch incidence matrix NB as follows:
referring to fig. 4, taking the determination process of the power flow flowing through the branch from the potential node 0 to the node 9 as an example, the specific determination process includes the following steps:
1) Traversing the 10 th row element NB (10,: NB (10, 9) = 1) in the NB matrix, it may be determined that the end node of branch 9 is 9;
2) Traversing the 9 th column element NB (: 9) in the NB matrix, NB (4, 9) = -1, the node of the starting end of the branch 9 can be determined to be 3;
3) Traversing row 4 element NB (4,: NB (4, 3) =1 in NB matrix, branch 3 end node may be determined to be 3;
4) Traversing the 3 rd column element NB (: 3) in the NB matrix, NB (3, 3) = -1, and the starting node of the branch 3 can be determined to be 2;
5) Traversing the 2 nd row element NB (3,: NB (3, 2) =1 in the NB matrix, it may be determined that the end node of branch 2 is 2;
6) Traversing the 2 nd column element NB (: 2) in the NB matrix, NB (2, 2) = -1, and determining that the starting end node of the branch 2 is 1;
7) Traversing the 2 nd row element NB (2,: NB (2, 1) =1 in the NB matrix, it may be determined that the end node of branch 1 is 1;
8) Traversing the 1 st column element NB (: 1) in the NB matrix, NB (1, 1) = -1, and determining that the starting end node of the branch 1 is 0;
the power flow from potential node 0 to node j is routed through potential node 0, branch 1, node 1, branch 2, node 2, branch 3, node 3, branch 9, node 9.
Step five, constructing a branch impedance matrix ZP through which the tidal current from the potential node to the load node flows and a load complex power matrix SB of the node according to the path matrix P and the initial data matrix DS as follows:
step six, calculating the current of each branch circuit and the voltage of each load node of the power distribution network, specifically comprising
1) The initial value of the voltage of other load nodes is set to be V in sequence 1 ，V 2 …V j …V n-1 Wherein, V j And expressing the j-th node voltage initial value, and constructing a node voltage matrix V.
2) Further, a node voltage conjugate matrix VC can be obtained, where the node voltage conjugate matrix is a matrix of 1 row and 9 columns, where the jth column includes:
VC(1,j)＝V * (1,j)
the node load complex power conjugate matrix is SC, the node load complex power conjugate matrix SC is a 9-row and 9-column matrix, wherein the ith row and the jth column have the following elements:
SC(i,j)＝SB * (i,j)
wherein i =1, 2.... 9; j =1,.. 9;
3) The current matrix LC, the branch current matrix FC,
LC(i,j)＝SC(i,j)/VC(1,j)
wherein i =1,2, ·.,9; j =1,.., 9;
for writing convenience, it is not assumed here that:
4) Calculating to obtain a voltage drop matrix D, a total voltage drop matrix M and a voltage matrix T; a voltage drop matrix D, a total voltage drop matrix M and a voltage matrix T are 9 rows and 9 columns of matrixes;
D(j,i)＝ZP(j,i)*FC(i,1)
T(j,i)＝V 0 -M(j,i)
calculating to obtain a new node voltage matrix Vnew, wherein the new node voltage matrix Vnew is a matrix with 1 row and 9 columns, and the j-th column of elements: vnew (1, j) = min (T (j, 1), T (j, 2),.. T (j, (n-1)))
Wherein the content of the first and second substances,
M(1)＝Z(1)*Il(1)
M(2)＝Z(1)*Il(1)+Z(2)*Il(2)
M(3)＝Z(1)*Il(1)+Z(2)*Il(2)+Z(3)*Il(3)
M(4)＝Z(1)*Il(1)+Z(2)*Il(2)+Z(3)*Il(3)+Z(4)*Il(4)
M(5)＝Z(1)*Il(1)+Z(5)*Il(5)
M(6)＝Z(1)*Il(1)+Z(5)*Il(5)+Z(6)*Il(6)
M(7)＝Z(1)*Il(1)+Z(7)*Il(7)
M(8)＝Z(1)*Il(1)+Z(2)*Il(2)+Z(8)*Il(8)
M(9)＝Z(1)*Il(1)+Z(2)*Il(2)+Z(3)*Il(3)+Z(9)*Il(9)
wherein, V 0 I =1, 2.... 9 for voltage measurements at the outlet of the low-side transformer of the power distribution system; j =1,.. 9;
l＝1,2,......,i；
Vnew(1,j)
＝[V 0 -M(1) V 0 -M(2) V 0 -M(3) V 0 -M(4) V 0 -M(5) V 0 -M(6) V 0 -M(7) V 0 -M(8) V 0 -M(9)]
5) Determining convergence conditions, selecting error precision of a system as delta, judging whether the absolute value Vnew (1, j) -V (1, j) | is less than or equal to delta,
if not, V (1, j) = Vnew (1, j) and return to step 2);
otherwise, the voltages of all load nodes and the power flow of all branches of the radiation type power distribution system can be obtained:
the voltage at node j is U j ＝V(1,j)
The ith branch current is Il i ＝FC(i,1)
The ith branch has a complex power of
Wherein i =1, 2.... B; j =1,.. N-1.
The invention provides a power flow calculation method of a radiation type power distribution system, which is used for carrying out power flow calculation on a power distribution system in one direction of a power distribution network region, firstly, according to the characteristics of the radiation type power distribution system, a circuit model of the radiation type power distribution system is established, the topological structure of the radiation type power distribution system is reasonably numbered, the original data of the power distribution system, including the topological structure relation and the power grid parameters, is stored in a matrix form, and is used as the only data input, a node branch incidence matrix of the power distribution system and a path matrix through which power flow from a potential node to a load node flows are established, and a branch impedance matrix and a complex power matrix of a node load are further constructed; and finally, solving the voltage of each load node and the complex power of each branch of the power distribution system by directly utilizing the algebraic operation of the matrix elements.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (6)
1. A radiation type power distribution system load flow calculation method is characterized in that: the method specifically comprises the following steps:
step one, establishing a circuit model of the radiation type power distribution system according to the characteristics of the radiation type power distribution system: taking the low-voltage side of the distribution transformer as a potential node and a balance node in load flow calculation, wherein the equivalence is that the voltage amplitude and the phase angle are constant known quantities and the three-phase voltage is assumed to be symmetrical; all loads on the feeder line are equivalent to concentrated loads of end nodes of the feeder line, the concentrated loads are referred to as node loads for short, and the feeder line branch adopts a concentrated parameter model; only one potential node is arranged in the radiation type power distribution system, the other nodes are load nodes, and the power flow in the power distribution system flows from the potential node to the load nodes; each branch in the power distribution system is connected with two nodes in the system, a power flow outflow node is called a branch initial end node, a power flow inflow node is called a branch tail end node, and each node is connected with at most two branches;
secondly, numbering branches and nodes of a topological structure in the circuit model according to the circuit model of the radiation type power distribution system, wherein the number of the branches is 1,2,3, 8230starting from the branch connected with the potential node; the potential node is numbered 0, the corresponding branch tail end nodes are numbered 1,2,3,4 \8230insequence, 8230, n-1, n are the node number of the power distribution system; b = n-1 according to the characteristics of the radiation type power distribution system, and the serial number of the branch is the same as that of the tail end node connected with the branch during numbering; expressing the topological structure and specific parameters of the circuit model through an initial data matrix DS;
constructing a node branch incidence matrix NB of the radiation type power distribution system according to the initial data matrix DS;
step four, constructing a path matrix P representing the flowing of the power flow from the potential node to the load node according to the node branch incidence matrix NB;
constructing a branch impedance matrix ZP through which the power flow from the potential node to the load node flows and a complex power matrix SB of the node load according to the path matrix P and the initial data matrix DS;
and step six, calculating the voltage of each load node and the load flow of each branch in the radiation type power distribution system.
2. The method of claim 1, wherein the step of calculating the power flow of the radial power distribution system comprises: in the second step, the initial data matrix DS is a matrix with b rows and 5 columns, where the ith row: DS (i) = [ x, NS (x), NR (x), Z (x), S (NR (x)) ]; i =1, 2.... B; x is the number of the ith branch, NS (x) is the number of the starting node of the ith branch, and NR (x) is the number of the end node of the ith branch, so NR (x) = i, Z (x) is the impedance of the ith branch, and S (NR (x)) is the node load complex power of which the end node is NR (x).
3. The method of claim 1, wherein the method further comprises: in the third step, the node branch correlation matrix NB is a matrix with n rows and b columns, and the ith row and ith column of elements NB (j, i) in the jth row are:
4. The method of claim 1, wherein the step of calculating the power flow of the radial power distribution system comprises: the path matrix P in the fourth step is a matrix with (n-1) rows and b columns, and the element P (j, i) in the ith row and the ith column of the jth row is as follows:
traversing the (j + 1) th row element NB (j) in the NB matrix, if NB (j, y) =1, determining that the y end node of the branch is j;
traversing the y-th column element NB (: y) in the NB matrix, and if NB (z, y) = -1, determining that the y starting end node of the branch is (z-1);
traversing the z-th row element NB (z,: in the NB matrix, if NB (z, t) =1, the end node of the branch t can be determined to be (z-1);
and repeating the steps until the starting end node of the branch circuit is determined to be the potential node 0.
5. The method of claim 1, wherein the method further comprises: in the fifth step, the branch impedance matrix ZP is a matrix of (n-1) rows and b columns, and the element ZP (j, i) in the jth row and ith column is:
ZP (j, i) = P (j, i) × Z (i); the complex power matrix SB of the node load is a matrix with b rows and (n-1) columns, the element SB (i, j) = P (i, j) × S (j) in the ith row and the jth column; wherein Z (i) = DS (i, 4) is the impedance of the ith branch; s (j) = DS (i, 5) is the node load complex power of the j node, and the tail end node of the branch i is j; j =1,2, ·., n-1, i =1,2, ·. · b.
6. The method of claim 5, wherein the step of calculating the power flow of the radial power distribution system comprises: the sixth step specifically comprises the following steps: the method specifically comprises the following steps:
6-1, setting the initial voltage value of each load node as V 1 ，V 2 ，…V j ，…V n-1 Wherein V is j Representing the initial voltage value of a load node j, constructing a node voltage matrix V, wherein the node voltage matrix V is a matrix with 1 row and (n-1) column, and the j-th column comprises the following elements:
V(1,j)＝V j
wherein j =1, 2.... N-1;
6-2, a node voltage conjugate matrix VC can be further obtained, wherein the node voltage conjugate matrix is a matrix with 1 row and n-1 columns, and the j th column comprises the following elements:
VC(1,j)＝V * (1,j)
the complex power conjugate matrix of the node load is SC, the complex power conjugate matrix SC of the node load is a matrix of b rows and (n-1) columns, wherein the ith row and the jth column have the following elements:
SC(i,j)＝SB * (i,j)
wherein i =1, 2.... B; j =1,.. N-1;
6-3, calculating to obtain a load current matrix LC, a branch current matrix FC, wherein the load current matrix LC is a matrix with b rows and (n-1) columns, and the ith row and the jth column have the following elements:
LC(i,j)＝SC(i,j)/VC(1,j)
the branch current matrix FC is a matrix of b rows and 1 column, where the ith row element is:
wherein i =1,2,..., b; j =1, say, n-1;
6-4, calculating to obtain a voltage drop matrix D, a total voltage drop matrix M and a voltage matrix T; a voltage drop matrix D, a total voltage drop matrix M and a voltage matrix T are matrixes of n-1 rows and b columns;
D(j,i)＝ZP(j,i)*FC(i,1)
T(j,i)＝V 0 -M(j,i)
calculating to obtain a new node voltage matrix Vnew, wherein the new node voltage matrix Vnew is 1 row, a matrix of (n-1) columns and an element of the jth column: vnew (1, j) = min (T (j, 1), T (j, 2),.. T (j, (n-1)))
Wherein, V 0 I =1,2,. For a voltage measurement at a low side transformer outlet of a radial power distribution system; j =1, say, n-1; l =1, 2.... I;
6-5, determining a convergence condition, selecting the error precision of the system to be delta, judging whether the absolute value of Vnew (1, j) -V (1, j) | ≦ delta is true, if not, then V (1, j) = Vnew (1, j) and returning to the step 6-2);
otherwise, the voltage of each node and the power flow of each branch of the radiation type power distribution system can be obtained:
the voltage at node j is U j ＝V(1,j)
The ith branch current is Il i ＝FC(i,1)
The ith branch has a power flow of
Wherein Z (i) = DS (i, 4) is the impedance of the ith branch; i =1,2,..., b; j =1, say, n-1.
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