CN109659943B - Admittance matrix calculation method for power system load flow calculation - Google Patents
Admittance matrix calculation method for power system load flow calculation Download PDFInfo
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- CN109659943B CN109659943B CN201710942153.1A CN201710942153A CN109659943B CN 109659943 B CN109659943 B CN 109659943B CN 201710942153 A CN201710942153 A CN 201710942153A CN 109659943 B CN109659943 B CN 109659943B
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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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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
Abstract
The invention discloses an admittance matrix calculation method for power flow calculation of a power system, which comprises the following steps: reading a first node number array I, a last node number array J, a resistance array R, a reactance array X, a ground-to-ground sodium array B and a transformer transformation ratio array K of the branch circuit; defining AS and AE AS n multiplied by l sparse matrixes; calculating an admittance array of a branch circuit in series connection with the branch circuit pi-shaped equivalent circuit; calculating a node branch incidence matrix; forming an initial admittance matrix from the series branches; calculating the ground admittance arrays of the first node and the last node of the directional branch; forming an admittance array to ground for each node and modifying the admittance matrix. The method provided by the invention is realized on a Matlab platform, and is convenient for scientific researchers to test and analyze the calculation result by using various tools and functions of the Matlab. The admittance matrix calculation provided by the invention adopts matrix operation and complex operation, so that program codes are reduced, programming is simplified, and the program is clearer; the matrix operation also greatly improves the calculation speed.
Description
Technical Field
The invention relates to an admittance matrix calculation method for power system load flow calculation, in particular to an admittance matrix calculation method based on Matlab load flow calculation, which is suitable for research purposes.
Background
Power system load flow calculation is a basic calculation for studying the steady-state operation of a power system, and determines the operation state of the whole network according to given operation conditions and network structures. The power flow calculation is also the basis of other analyses of the power system, and the power flow calculation is used in safety analysis, transient stability analysis and the like. The power flow calculation is a basic analysis tool for power system analysis, and researchers often perform further research on the basis of the power flow calculation. Practical commercial software is written by adopting a high-level programming language such as C language and the like and adopts a high-level technology such as sparse matrix technology, node optimized numbering and the like. Although the technologies can greatly improve the speed of tidal current calculation and reduce the memory occupation amount, programming is very troublesome, modification and maintenance are difficult, and new functions are not easy to increase, so that the technology is not suitable for being used for research purposes by scientific researchers.
Matlab software takes a matrix as the most basic data unit, can conveniently process various matrix and vector operations, and also can conveniently and naturally process complex types, the instruction expression of the Matlab software is very close to the common form in mathematics, and a large number of common and practical functions bring great convenience to programming. Matlab software is simple and easy to use, codes are short and small, operation is easy, programming and debugging are easy, computing functions are strong, meanwhile, the method has very strong visual graphic processing and interactive functions, an efficient programming tool is provided for scientific research and engineering application, the method becomes a basic tool and a preferred platform in many scientific fields at present, and the method is widely applied to various scientific and engineering computing fields. In order to meet the requirement that more and more scientific researchers need to further research on a Matlab platform based on load flow calculation, a load flow calculation method which is based on Matlab software and easy to program, modify and debug is urgently needed.
The current commonly used load flow calculation methods of the Newton method and the rapid decomposition method are based on a node voltage method, and a node admittance matrix is required to be obtained.
The node admittance matrix is:
in the formula, YikThe method comprises the following steps that (1) a node admittance matrix element is used, when a subscript i is not equal to k, mutual admittance between a node i and a node k is used, and when the subscript i is equal to k, self-admittance of the node i is used; n is the number of nodes.
The admittance matrix elements can be calculated by adopting an additional branch method, namely, all branches are scanned in sequence, and each branch is scanned, and an admittance increment is added on the basis of the original admittance matrix elements. Because the transmission line and the transformer branch belong to branches, the transmission line and the transformer branch are generally used as branch data to be input in a unified manner. For distinction, the node number of the non-standard transformation ratio side of the transformer branch is added with a negative number.
The transmission line adopts a pi-shaped equivalent circuit as shown in figure 2, and the admittance of the series branch of the mth branch is set as
ym＝1/zm＝1/(rm+jxm) (2)
In the formula, rm，xm，zmRespectively the resistance, reactance and impedance of the equivalent circuit of the power transmission line.
When the mth transmission line is added, the calculation formula of the admittance matrix element is as follows:
in the formula, subscripts i and j respectively represent the first node number i of the branchmAnd last node number jmNode number with minus sign removed, bmAnd for the ground-to-ground susceptance of the equivalent circuit of the power transmission line, the symbol "←" represents that the right-end calculation result is assigned to the left-end variable.
The transformer branches are represented by equivalent circuits of ideal transformer series-connected equivalent impedance as shown in fig. 3, and are divided into 4 cases according to the positions of the variable ratio and the equivalent impedance, wherein fig. 3(a) and 3(b) show that the equivalent impedance is positioned on the standard variable ratio side (namely side 1), and fig. 3(c) and 3(d) show that the equivalent impedance is positioned on the non-standard variable ratio side (namely side k)mSide). To reduce the complexity of programming, the transformation ratios of FIG. 3(c) and FIG. 3(d) are usually converted to (1/k)m): 1, thereby changing the equivalent circuits shown in fig. 3(c) and 3(d) to those shown in fig. 3(a) and 3 (b). FIGS. 4(a) and 4(b) are pi-shaped equivalent circuits to the circuits shown in FIGS. 3(a) and 3(b), respectively, where y ism＝1/(rm+j xm)。
As shown in fig. 3(a), when the transformation ratio k ismWhen the first node i side is located, a calculation formula for obtaining the admittance matrix element of the mth transformer branch according to the pi-shaped equivalent circuit diagram 4(a) is as follows:
in the formula, kmIs the transformation ratio of the transformer branch.
When the transformation ratio k is as shown in FIG. 3(b)mWhen the voltage is positioned at the j side of the tail node, a calculation formula for obtaining the admittance matrix element of the mth transformer branch according to the pi-shaped equivalent circuit diagram 4(b) is as follows:
as shown in fig. 1 to 5, the conventional power flow calculation method mainly includes the following steps:
A. inputting original data and initializing voltage;
the original data comprises branch data of a line and a transformer, node injection active power and reactive power, node voltage amplitude, node reactive compensation data, convergence precision and maximum iteration times;
the method comprises the following steps that a power transmission line and a transformer branch are used as branch data to be input in a unified mode and used for distinguishing, and a negative sign is added to a node number of a non-standard transformation ratio side of the transformer branch;
according to the characteristics of the nodes of the power system, the nodes of the power system are divided into 3 types by load flow calculation: the node with known active power and reactive power and unknown node voltage amplitude and voltage phase angle is called PQ node; the node with known active power and voltage amplitude and unknown node reactive power and voltage phase angle is called a PV node; the node with known voltage amplitude and voltage phase angle and unknown active power and reactive power is called a balance node.
The voltage initialization adopts flat start, namely the voltage amplitudes of the PV node and the balance node are set values, and the voltage amplitude of the PQ node is 1.0; the phase angle for all voltages takes 0.0. The unit of the phase angle is radian, and the unit of other quantities is a per unit value.
B. Forming a node admittance matrix;
the steps of forming the node admittance matrix are as follows:
b1, setting branch count m to be 1;
b2, taking the first node number i of branch mmLast node number jmAnd let i ═ im|、j＝|jm|；
B3 resistance r of branch mmReactance xmAnd order ym＝1/(rm+j xm)；
B4, judging branch mFirst node number imLast node number jmIf both are greater than 0, if not, go to step B7;
b5, grounding electric quantity B of branch mm；
B6, calculating node admittance matrix elements corresponding to the nodes at the two ends of the power transmission line according to the formula (2) and the formula (3);
b7, judging the first node number i of the branch mmIf not, go to step B10;
b8, taking the transformation ratio k of the transformer branch mm；
B9, calculating node admittance matrix elements corresponding to nodes at two ends of the transformer branch circuit according to the formula (2) and the formula (4);
b10, judging the end node number j of the branch mmIf not, go to step B13;
b11, taking the transformation ratio k of the transformer branch mm；
B12, calculating node admittance matrix elements corresponding to nodes at two ends of the transformer branch circuit according to the formula (2) and the formula (5);
b13, let m be m + 1.
B14, judging whether m is larger than the branch number l, if m is not larger than l, returning to the step B2; otherwise, ending.
C. Carrying out load flow calculation and iteration main program;
according to different methods for load flow calculation, a polar coordinate Newton method, a rectangular coordinate Newton method and a rapid decomposition method can be adopted for load flow calculation.
D. Calculating the active power and the reactive power of the balance node and the reactive power of the PV node;
the active power and reactive power of the balance nodes and the reactive power of the PV nodes are unknown and need to be calculated.
E. Calculating active power and reactive power of each branch;
F. and outputting the calculation result, and ending.
The load flow calculation software directly realized by adopting the principle has low calculation speed, and the commercially used load flow calculation software adopts a sparse matrix technology and a node optimized numbering technology, is complex and is not suitable for scientific research by scientific researchers on the basis of the sparse matrix technology and the node optimized numbering technology. Therefore, chinese patents ZL201710557623.2, ZL201710557642.5, and ZL201710557622.8 respectively propose a polar newton method load flow calculation method, a rectangular newton method load flow calculation method, and a fast decomposition method load flow calculation method based on Matlab, which can make full use of the features of Matlab's unique excellence matrix operation and complex operation, and adopt Matlab's sparse matrix technology and equation solving algorithm to design a compact load flow calculation method with faster calculation speed, so as to provide a load flow calculation method easy to modify and maintain for researchers who further study on the basis of load flow calculation, and the features are as follows:
1. the method is realized on a Matlab platform, so that scientific research personnel can conveniently test and analyze the calculation result by using various tools and functions provided by the Matlab;
2. most functions adopt matrix operation and complex operation, so that program codes are reduced, programming is simplified, programs are clearer, and scientific research personnel can modify the programs, debug and improve the programs and add new functions conveniently;
3. matrix operation and Matlab sparse matrix technology are adopted, and an equation solving algorithm of Matlab is directly called, so that the calculation speed is greatly improved.
The flow calculation methods based on Matlab provided by the above patents provide three types of flow calculation methods based on Matlab platform, which are easy to modify and maintain and have faster calculation speed, for scientific researchers engaged in electric power system research. The methods are realized by adopting Matlab, the characteristics of Matlab excellence in matrix operation and complex operation are fully utilized, and a sparse matrix technology and an equation solving algorithm provided by Matlab are used, so that the programming is greatly simplified, and the calculation speed is improved. However, when the admittance matrix is calculated by the load flow calculation methods, matrix operation is not realized, the admittance matrix calculation speed is relatively slow, and the calculation speed is still to be further improved.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an admittance matrix calculation method based on Matlab matrix operation, which fully utilizes the characteristic of Matlab that is specially good at matrix operation and achieves the purpose of improving the calculation speed of load flow calculation.
In order to achieve the purpose, the technical scheme of the invention is as follows: an admittance matrix calculation method for power flow calculation of an electric power system adopts matrix operation. The following derives the formula for calculating the admittance matrix using matrix operations.
An admittance matrix of an electric power network can be obtained by a node branch incidence matrix and a branch admittance, in order to obtain the node branch incidence matrix, the direction of a branch in the electric power network is firstly specified, the direction of a transmission line is that a first node points to a last node, the direction of a transformer branch is that a node on a non-standard transformation ratio k side of a transformer points to a node on a standard transformation ratio 1 side, the direction of the transformer branch shown in fig. 3(a) is that the first node points to the last node, and the direction of the transformer branch shown in fig. 3(b) is that the last node points to the first node.
The node branch incidence matrix of the power network is
In the formula, the row number corresponds to the node number, the column number corresponds to the branch number, aikRepresenting the association of nodes and branches, aik1 denotes that branch k is connected from node i, aikWith-1 meaning that branch k is connected to node i, aikWhere 0 indicates that the branch k is not directly connected to the node i, n is the node number, and l is the branch number.
When no branch to ground is included in the power network, the admittance matrix is
Y1＝AYBDAT (7)
In the formula, YBDAdmittance arrays Y for series branchesBThe diagonal matrix is formed and the superscript T represents the transpose of the matrix.
Admittance of series branch of the equivalent circuit of the mth transmission line is
ym＝1/zm＝1/(rm+jxm) (8)
In the formula, rm，xm，zmRespectively the resistance, reactance and impedance of the equivalent circuit of the power transmission line.
As can be seen from the pi-shaped equivalent circuits of the transformers shown in FIGS. 4(a) and 4(b), the serial branch admittance of the pi-shaped equivalent circuit of the mth transformer branch is
y′m＝1/zm/km＝1/(rm+jxm)/km (9)
In the formula, rm，xm，zm，kmRespectively the resistance, reactance, impedance and transformation ratio of the equivalent circuit of the transformer branch.
The transmission line can be regarded as a transformation ratio kmThe series branch admittance of the pi-shaped equivalent circuits of the transmission line and the transformer branch can be uniformly written in the form of the formula (9) for the 1 transformer branch.
The matrix represents the serial branch admittance array of the branch pi-shaped equivalent circuit as
YB＝1·/(R+jX)·/K (10)
In the formula, R is a branch resistance array, X is a branch reactance array, K is a branch transformation ratio array, the transformation ratio of the power transmission line is 1, and-/' represents the division of corresponding elements of the two arrays;
since the pi-shaped equivalent circuits of the transmission line and the transformer both comprise the ground branch, the admittance of the ground branch should be added to the self-admittance elements of the admittance matrix.
To calculate the node-to-ground branch admittance, the following matrices (11) and (12) are formed.
In the formula, AS represents the incidence matrix of the first node and the branch of the directional branch, the row number corresponds to the node number, the column number corresponds to the branch number, aikRepresenting the incidence relation of the node and the branch, if the branch k is connected from the node i, aik1, otherwise, aik＝0。
In the formula, AE represents the incidence matrix of the tail node and the branch of the directional branch, the row number corresponds to the node number, the column number corresponds to the branch number, aikRepresenting the incidence relation of the node and the branch, if the branch k is connected to the node i, aik1, otherwise, aik＝0。
According to the definitions of the formula (6), the formula (11) and the formula (12), the node branch incidence matrix is
A＝AS-AE (13)
As can be seen from FIG. 2, the admittance to ground is the same on both sides of the equivalent circuit of the transmission line, namely
ys＝ye＝jbm/2 (14)
In the formula, ys is the first node of the directional branch to ground susceptance, and ye is the last node of the directional branch to ground susceptance.
As can be seen from FIGS. 4(a) and 4(b), the ground admittance of the k-side node of the nonstandard transformation ratio of the pi-shaped equivalent circuit of the transformer branch is
The ground admittance of a node at the standard transformation ratio 1 side of the pi-shaped equivalent circuit of the transformer branch is
The formula (14) -formula (16) are integrated, and the ground admittance array of the first node and the last node of the directional branch obtained by writing the matrix form is
YS＝YB·*(1-K)·/K+jB/2 (17)
YE＝YB·*(K-1)+jB/2 (18)
In the formula, B is a ground-ground electric array, the value of the transformer branch B is 0, and "·" represents the multiplication of the corresponding elements of the two arrays.
Each node in the power network has an admittance array Y0 of branch path
Y0＝AS·YS+AE·YE (19)
Adding the diagonal elements of the node admittance matrix of the pi-shaped equivalent circuit series branch of the power network branch to the admittance of each node to the ground branch to obtain a complete node admittance matrix, wherein the calculation formula is as follows:
Y1ii＝Y1ii+Y0i i＝1,…,n (20)
the invention adopts matrix operation to form an admittance matrix, which comprises the following steps:
b1, reading branch first node number array I, tail node number array J, resistance array R, reactance array X, ground-to-ground capacitor array B and transformer transformation ratio array K;
the first node number array I, the last node number array J, the resistance array R, the reactance array X, the earth-ground sodium array B and the transformer transformation ratio array K are used for storing the first node numbers I of all the branches in sequence respectivelymLast node number jmResistance rmReactance xmGround-to-ground susceptance bmTransformer transformation ratio kmTransformer branch to ground susceptance bmIs 0, the nonstandard transformation ratio k of the transformermNode number of side plus negative number, transformation ratio k of power transmission linemSetting the subscript m as the serial number of the branch circuit to be 1;
b2, defining AS and AE AS n x l order sparse matrixes;
b3, setting branch count m to be 1;
b4, judging the first node number I of the branch mmIf not, go to step B6;
b5, let I ═ Im|、j＝|JmGo to step B7;
b6, let i ═ Jm|、j＝|Im|；
B7, let ASim＝1、AEjm＝1；
B8, let m be m + 1;
b9, judging whether m is larger than the branch number l, if m is not larger than l, returning to the step B4;
b10, calculating a branch pi-shaped equivalent circuit series branch admittance array;
series branch admittance array Y for calculating branch pi-shaped equivalent circuit by formula (10)B；
B11, calculating a node branch incidence matrix;
calculating a node branch incidence matrix A by using the formula (13);
b12, forming an initial admittance matrix by the serial branches;
calculating an initial admittance matrix Y1 formed by the serial branches of the branch pi-shaped equivalent circuit by using the formula (7);
b13, calculating the ground admittance arrays of the first node and the last node of the directional branch;
calculating the ground admittance arrays YS and YE of the first node and the last node of the directional branch by using an equation (17) and an equation (18) respectively;
b14, forming an array of node pair ground admittance;
calculating the node pair ground admittance array Y0 using equation (19);
b15, setting the node count m to 1;
b16, let Y1mm＝Y1mm+Y0m；
B17, let m be m + 1;
b18, judging whether m is larger than the number n of nodes, if m is not larger than n, returning to the step B16; otherwise, ending.
Compared with the prior art, the invention has the following beneficial effects:
1. the method provided by the invention is realized on a Matlab platform, and is convenient for scientific researchers to test and analyze the calculation result by using various tools and functions provided by Matlab.
2. The admittance matrix calculation provided by the invention adopts matrix operation and complex operation, reduces program codes, simplifies programming and makes the program clearer; the use of matrix operations also greatly increases the computational speed.
Drawings
The invention is shown in figure 6. Wherein:
fig. 1 is a flowchart of a conventional power flow calculation.
Fig. 2 is an equivalent circuit diagram of a transmission line.
Fig. 3 is an equivalent circuit diagram of a transformer branch.
Fig. 4 is a pi-shaped equivalent circuit diagram of a transformer branch.
Fig. 5 is a flow chart of forming an admittance matrix from a current power flow calculation.
Fig. 6 is a flow chart of the present invention for forming an admittance matrix.
Detailed Description
The invention is further described with reference to the drawings, and a 10428 node actual system example is calculated according to the flow shown in fig. 1 and fig. 6, and the example has 10428 nodes and 10436 branches.
The method and the prior patent method are adopted to calculate the 10428 node actual system calculation example, the load flow calculation adopts a polar coordinate Newton method, the unit of the time phase angle is calculated to be radian, other quantities adopt per unit value, and the convergence precision is 0.00001. The two load flow calculation methods respectively comprise:
the method comprises the following steps: in the method of the Chinese patent ZL201710557623.2, the admittance matrix calculation adopts a circular structure and complex operation;
the method 2 comprises the following steps: in the method, complex operation and matrix operation are adopted for admittance matrix calculation.
The calculation time of the load flow calculation and the admittance matrix calculation of the two methods is shown in table 1, and the calculation time of the load flow calculation does not comprise the time for reading and outputting data.
TABLE 1 comparison of load flow calculation time by two polar coordinate Newton method
As can be seen from table 1, the method disclosed in chinese patent ZL201710557623.2 takes a long time to calculate the admittance matrix, accounting for 79.1% of the calculation time of the power flow, and accounting for most of the calculation time of the power flow; the method adopts the matrix operation technology to calculate the admittance matrix, so that the calculation speed of the admittance matrix is obviously improved, and the calculation time of the admittance matrix accounts for 42.4 percent of the calculation time of the load flow. The admittance matrix calculation time of the invention is 1/5 of the method of patent 201710557623.2.
The present invention can be implemented in any version of the MATLAB programming language, but it is suggested to use a newer version of the MATLAB language.
The present invention is not limited to the embodiment, and any equivalent idea or change within the technical scope of the present invention is to be regarded as the protection scope of the present invention.
Claims (1)
1. An admittance matrix calculation method for power flow calculation of an electric power system is characterized in that: the method comprises the following steps:
b1, reading branch first node number array I, tail node number array J, resistance array R, reactance array X, ground-to-ground capacitor array B and transformer transformation ratio array K;
the first node number array I, the last node number array J, the resistance array R, the reactance array X, the earth-ground sodium array B and the transformer transformation ratio array K are used for storing the first node numbers I of all the branches in sequence respectivelymLast node number jmResistance rmReactance xmGround-to-ground susceptance bmTransformer transformation ratio kmWherein the transformer branch is grounded bmIs 0, the nonstandard transformation ratio k of the transformermNode number of side plus negative number, transformation ratio k of power transmission linemSetting the subscript m as the serial number of the branch circuit to be 1;
b2, defining AS and AE AS n x l order sparse matrixes, wherein the matrix AS is an incidence matrix of a first node and a branch of the directional branch, the matrix AE is an incidence matrix of a last node and the branch of the directional branch, n is the number of nodes, and l is the number of branches; (ii) a
B3, setting branch count m to be 1;
b4, judging the first node number I of the branch mmIf not, go to step B6;
b5, let I ═ Im|、j＝|JmGo to step B7;
b6, let i ═ Jm|、j＝|Im|；
B7, let ASim＝1、AEjm＝1；
B8, let m be m + 1;
b9, judging whether m is larger than the branch number l, if m is not larger than l, returning to the step B4;
b10, calculating a branch pi-shaped equivalent circuit series branch admittance array;
series branch admittance array Y of branch pi-shaped equivalent circuitBComprises the following steps:
YB＝1·/(R+jX)·/K (1)
in the formula, "·/" represents the division of the corresponding elements of the two arrays;
b11, calculating a node branch incidence matrix;
the node branch incidence matrix A is as follows:
A＝AS-AE (2)
b12, forming an initial admittance matrix by the serial branches;
the initial admittance matrix Y1 formed by the branch pi-shaped equivalent circuit series branches is:
Y1＝AYBDAT (3)
in the formula, YBDAdmittance arrays Y for series branchesBForming a diagonal matrix, and using superscript T to represent transposition of the matrix;
b13, calculating the ground admittance arrays of the first node and the last node of the directional branch;
the ground admittance arrays YS and YE of the first node and the last node of the directional branch are respectively as follows:
YS＝YB·*(1-K)·/K+jB/2 (4)
YE＝YB·*(K-1)+jB/2 (5)
in the formula, "· represents multiplication of corresponding elements of the two arrays;
b14, forming an array of node pair ground admittance;
node-to-ground admittance array Y0 is:
Y0＝AS·YS+AE·YE (6)
b15, setting the node count m to 1;
b16, let Y1mm＝Y1mm+Y0m；
B17, let m be m + 1;
b18, judging whether m is larger than the number n of nodes, if m is not larger than n, returning to the step B16; otherwise, ending.
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