CN114566968A - Polar coordinate Newton method load flow calculation method suitable for research purpose - Google Patents

Polar coordinate Newton method load flow calculation method suitable for research purpose Download PDF

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CN114566968A
CN114566968A CN202210109051.2A CN202210109051A CN114566968A CN 114566968 A CN114566968 A CN 114566968A CN 202210109051 A CN202210109051 A CN 202210109051A CN 114566968 A CN114566968 A CN 114566968A
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unbalance
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姚玉斌
任田峰
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Dalian Maritime University
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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
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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
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
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Abstract

The invention discloses a polar coordinate Newton method load flow calculation method suitable for research purposes, and provides a Newton method load flow calculation method which is easy to modify and maintain for scientific researchers who carry out further research on the basis of polar coordinate Newton method load flow calculation. For an electric power system with n nodes, the node number is independent of the node type, a Jacobian matrix of load flow calculation is stored according to (2n) x (2n), the row element corresponding to the delta Q and the column element corresponding to the delta U of the PV node are both 0, the row element and the column element related to the balance node are both 0, but the diagonal element is not clear, and the original calculation value is reserved. Therefore, the linear equation with excellent performance provided by the programming language can be used for solving the correction equation of the load flow calculation, the programming difficulty is reduced, the calculation speed is increased, and the reliability of the algorithm is ensured. The embodiment shows that the linear equation provided by the programming language can be used for solving the function solution correction equation, so that the load flow calculation speed is increased, and the programming difficulty is reduced.

Description

Polar coordinate Newton method load flow calculation method suitable for research purpose
Technical Field
The invention relates to a Newton method load flow calculation method for a power system, in particular to a polar coordinate Newton method load flow calculation method suitable for research purposes.
Background
The 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 power system according to the given operation condition and network structure of the power system. The power flow calculation is also the basis of other analyses of the power system, such as safety analysis, transient stability analysis and the like. The Newton method becomes the mainstream method of the current load flow calculation due to the advantages of reliable convergence, high calculation speed and moderate memory requirement. The Newton method is divided into two forms of polar coordinates and rectangular coordinates, and the Newton method load flow calculation of the two forms is widely applied to a power system.
In polar coordinate newton method load flow calculation, the voltage of the node i is expressed by adopting a polar coordinate as follows:
Figure BDA0003494688300000011
as shown in fig. 1, a conventional polar newton method load flow calculation method mainly includes the following steps:
A. raw data and initialization voltage are input.
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 injected into the node and is called as a PQ node; the node with known node injection active power and voltage amplitude and unknown node injection reactive power and voltage phase angle is called PV node; the node with known node voltage amplitude and voltage phase angle and unknown node injection 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 given values, and the voltage amplitude of the PQ node is 1.0; the voltage phase angle of all nodes takes 0.0. The voltage phase angle is here in units of radians, other quantities being per unit.
B. A node admittance matrix is formed.
C. The iteration count t is set to 0.
D. Calculating the node power and the node power unbalance amount to obtain the maximum unbalance amount delta Wmax。
The node power calculation formula is as follows:
Figure BDA0003494688300000021
in the formula, Pi、QiRespectively the active power and the reactive power of the node i; u shapei、UkThe voltage amplitudes of the node i and the node k are respectively; thetaik＝θi-θk，θiAnd thetakVoltage phase angles of the node i and the node k respectively; gik、BikAre respectively node admittance matrix elements YikThe real and imaginary parts of (c); n is the number of nodes.
Setting No. 1-m nodes as PQ nodes, No. m + 1-n-1 nodes as PV nodes, No. n nodes as balance nodes, and the calculation formula of the node power unbalance amount is as follows:
Figure BDA0003494688300000022
in the formula,. DELTA.Pi、ΔQiRespectively the active power unbalance amount and the reactive power unbalance amount of the node i; pis、QisThe node i is given injected active power and injected reactive power, respectively.
The balance nodes do not participate in iterative computation, and the power unbalance of the nodes does not need to be computed.
And calculating the maximum value of the absolute value in the power unbalance of each node, which is called as the maximum unbalance.
E. Judging the absolute value of the maximum unbalance | Delta WmaxWhether | is less than the convergence precision ε; if the precision is less than the convergence precision epsilon, executing a step I; otherwise, step F is performed.
F. Forming a jacobian matrix J.
The basic equation of the load flow calculation is a nonlinear equation, and a successive linearization method is generally adopted for iterative solution.
And (3) obtaining a correction equation (3) through linearization, and solving the correction quantity of the voltage amplitude and the phase angle.
Figure BDA0003494688300000031
Wherein J is a Jacobian matrix of (n + m-1) × (n + m-1) order, and H, N, M, L are four partitioned submatrices of the Jacobian matrix respectively, and the dimensions are (n-1) × (n-1) order, (n-1) × m order, mx (n-1) order, and mx order, respectively; Δ θ ═ Δ θ1,…,Δθn-1]TThe upper mark T represents transposition for the column vector of the phase angle correction quantity of the node voltage; delta U/U ═ delta U1/U1,…,ΔUm/Um]TDividing the node voltage amplitude correction quantity by the column vector of the node voltage amplitude; Δ P ═ Δ P1,…,ΔPn-1]TThe active power unbalance column vector of the node is obtained; Δ Q ═ Δ Q1,…,ΔQm]TIs a column vector of node reactive power unbalance.
The formula for calculating the elements of the jacobian matrix J (i ≠ J) is as follows:
Figure BDA0003494688300000032
Figure BDA0003494688300000033
Figure BDA0003494688300000034
Figure BDA0003494688300000035
in the formula (I), the compound is shown in the specification,
Figure BDA0003494688300000036
is active of node iThe partial derivative of the amount of power imbalance to the voltage phase angle of node j;
Figure BDA0003494688300000037
is the partial derivative of the active power unbalance of the node i to the voltage amplitude of the node j;
Figure BDA0003494688300000038
Is the partial derivative of the reactive power unbalance of the node i to the voltage phase angle of the node j;
Figure BDA0003494688300000039
is the partial derivative of the amount of reactive power imbalance at node i to the voltage magnitude at node j.
The formula for calculating the elements of the jacobian matrix J (when i equals J) is as follows:
Figure BDA0003494688300000041
Figure BDA0003494688300000042
Figure BDA0003494688300000043
Figure BDA0003494688300000044
in the formula (I), the compound is shown in the specification,
Figure BDA0003494688300000045
the partial derivative of the active power unbalance amount of the node i to the voltage phase angle of the node i is obtained;
Figure BDA0003494688300000046
is the partial derivative of the active power unbalance amount of the node i to the voltage amplitude of the node i;
Figure BDA0003494688300000047
is the partial derivative of the reactive power unbalance of the node i to the voltage phase angle of the node i;
Figure BDA0003494688300000048
is the partial derivative of the amount of reactive power imbalance at node i to the voltage magnitude at node i.
Or by the following formula:
Figure BDA0003494688300000049
Figure BDA00034946883000000410
Figure BDA00034946883000000411
Figure BDA00034946883000000412
in the formula, Pi、QiAnd respectively calculating the active power and the reactive power of the node i according to the formula (1).
G. And solving a correction equation and correcting the node voltage amplitude U and the phase angle theta.
And (4) solving a correction equation (3) to obtain the node voltage amplitude and the voltage phase angle correction quantity.
The node voltage amplitude and voltage phase angle correction formula is as follows:
Figure BDA0003494688300000051
in the formula, superscript (t) represents the t iteration; delta UiAnd Δ θiThe voltage amplitude correction and the voltage phase angle correction of the node i are respectively.
H. And D, making t equal to t +1, and returning to the step D for the next iteration.
I. Output node and branch data.
In the linear equation shown in equation (3), the PQ node has related Δ P and Δ Q equations, the PV node has only Δ P equation, and neither Δ P nor Δ Q equation related to the balanced node exists. Therefore, not every node has Δ P and Δ Q equations, nor does it need to solve for Δ θ and Δ U. Therefore, the corresponding relation between the node and the equation needs to be determined according to the type of the node, the type is changed, the corresponding relation is also changed, and great troubles are brought to programming and debugging. Although the first m nodes can be defined as PQ nodes, nodes m +1 to n-1 are PV nodes, and node n is a balance node. However, this provides that when data is input, it may be necessary to renumber the nodes according to this specification; in addition, when the node type changes, the corresponding relationship between the node and the equation needs to be readjusted.
Therefore, Chinese patent CN201010509556.5 proposes a Newton method load flow calculation method suitable for research purposes, and provides a Newton method load flow calculation algorithm which is easy to modify and maintain for scientific researchers who further research on the basis of polar coordinate Newton method load flow calculation. The Jacobian matrix of load flow calculation of the patent is stored according to (2n) x (2n), elements of a row corresponding to a PV node delta Q and a column corresponding to a delta U are both 0, and elements of the row and the column related to a balance node are also both 0, so that although the memory demand is increased, the corresponding relation between the nodes and the rows and columns of an equation coefficient matrix can be simplified, the programming difficulty is greatly reduced, and the calculation amount is not increased. When the correction equation of the load flow calculation is solved, the row with the main diagonal element of 0 in the Jacobian matrix is skipped through judgment (the main diagonal element of 0 indicates that the row elements are all 0 and no corresponding equation exists), and no processing is performed.
Although the method of the chinese patent CN201010509556.5 simplifies the corresponding relationship between the nodes and the rows and columns of the equation coefficient matrix, and greatly reduces the programming difficulty, when solving the load flow calculation correction equation, special processing is required, and the linear equation with excellent performance provided by the programming language cannot be used to solve the function.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a polar coordinate Newton method load flow calculation method suitable for research purposes, and provides a polar coordinate Newton method load flow calculation algorithm which is easy to modify and maintain for scientific researchers who further research on the basis of polar coordinate Newton method load flow calculation.
In order to achieve the above object, the present invention improves the jacobian matrix as follows: the Jacobian matrix is stored according to (2n) x (2n), elements of a row corresponding to the PV node delta Q and a column corresponding to the delta U are all 0, elements of the row and the column related to the balance node are all 0, but the diagonal elements are not cleared, and the original calculated value is reserved. Therefore, the linear equation solving function with excellent performance provided by the programming language can be used for solving the correction equation of the power flow calculation.
The technical scheme of the invention is as follows: a polar coordinate Newton method load flow calculation method suitable for research purposes comprises the following steps:
A. Raw data and an initialization voltage are input.
B. A node admittance matrix is formed.
C. The iteration count t is set to 0.
D. Calculating the node power and the node power unbalance amount to obtain the maximum unbalance amount delta Wmax。
The node power is calculated according to the formula (1), and the node power unbalance is calculated according to the formula (17).
Figure BDA0003494688300000061
In the formula,. DELTA.Pi、ΔQiRespectively the active power unbalance amount and the reactive power unbalance amount of the node i; pis、QisThe node i is given injected active power and injected reactive power, respectively.
The balance nodes do not participate in iterative computation, and the power unbalance of the nodes does not need to be computed.
Delta P and delta Q are both n-dimensional vectors, and the active power unbalance amount delta P corresponding to the balance node iiSetting 0; balance nodei or the reactive power unbalance amount delta Q corresponding to the PV node iiAnd setting 0.
Calculating the maximum value of the absolute value of the active power unbalance and the reactive power unbalance of each node as the maximum unbalance delta Wmax。
E. Judging the absolute value | Delta W of the maximum unbalance amountmaxWhether | is less than convergence precision ε; if the convergence precision is smaller than the convergence precision epsilon, executing a step I; otherwise, executing step F.
F. Forming a jacobian matrix J.
The procedure for forming the jacobian matrix J is as follows:
f1, calculating Jacobian matrix elements according to the formula (18) to the formula (25) without considering the node type to form a Jacobian matrix J of (2n) x (2 n);
Figure BDA0003494688300000071
Figure BDA0003494688300000072
Figure BDA0003494688300000073
Figure BDA0003494688300000074
In the formula, Ji,jThe element is the ith row and the jth column of the Jacobian matrix;
Figure BDA0003494688300000075
is the partial derivative of the active power unbalance of the node i to the voltage phase angle of the node j;
Figure BDA0003494688300000076
is the partial derivative of the active power unbalance of the node i to the voltage amplitude of the node j;
Figure BDA0003494688300000077
is the partial derivative of the reactive power unbalance of the node i to the voltage phase angle of the node j;
Figure BDA0003494688300000078
is the partial derivative of the amount of reactive power imbalance at node i to the voltage magnitude at node j.
The formula for calculating the elements (i ═ J) of the jacobian matrix J is as follows:
Figure BDA0003494688300000079
Figure BDA0003494688300000081
Figure BDA0003494688300000082
Figure BDA0003494688300000083
in the formula (I), the compound is shown in the specification,
Figure BDA0003494688300000084
the partial derivative of the active power unbalance of the node i to the voltage phase angle of the node i is obtained;
Figure BDA0003494688300000085
the partial derivative of the active power unbalance of the node i to the voltage amplitude of the node i is obtained;
Figure BDA0003494688300000086
is the partial derivative of the reactive power unbalance of the node i to the voltage phase angle of the node i;
Figure BDA0003494688300000087
is the partial derivative of the amount of reactive power imbalance at node i to the voltage magnitude at node i.
F2, setting the node count i to 1;
f3, judging whether the node i is a balanced node, if not, turning to the step F10;
f4, setting count k to 1;
f5, determining whether k is true, and if so, going to step F8;
f6, let Jacobian matrix i the row the k the column element Ji,k＝0；
F7, order Jk,i＝0；
F8, let k be k + 1;
F9, judging whether k is larger than 2n, if k is larger than 2n, turning to step F10; otherwise, return to step F5;
f10, judging whether the node i is a PQ node, if so, turning to the step F17;
f11, setting count k to 1;
f12, determining whether k is n + i, if so, going to step F15;
f13, order Jn+i,k＝0；
F14, order Jk,n+i＝0；
F15, let k be k + 1;
f16, judging whether k is larger than 2n, if k is larger than 2n, turning to step F17; otherwise, return to step F12;
f17, let i ═ i + 1;
f18, judging whether i is larger than n, if i is larger than n, turning to the step G; otherwise, return to step F3.
G. And solving a correction equation (26) and correcting the node voltage amplitude U and the phase angle theta according to an equation (27).
Figure BDA0003494688300000091
Wherein J is a Jacobian matrix of order (2n) × (2 n); Δ θ ═ Δ θ1,…,Δθn]TFor the column vector of the phase angle correction of the node voltage, the superscript T representsTransposition is carried out; delta U/U ═ delta U1/U1,…,ΔUn/Un]TDividing the node voltage amplitude correction quantity by the column vector of the node voltage amplitude; Δ P ═ Δ P1,…,ΔPn]TThe active power unbalance column vector of the node is obtained; Δ Q ═ Δ Q1,…,ΔQn]TIs a column vector of node reactive power unbalance. The node voltage amplitude and voltage phase angle correction formula is as follows:
Figure BDA0003494688300000092
in the formula, superscript (t) represents the t iteration; delta UiAnd Δ θiThe voltage amplitude correction and the voltage phase angle correction of the node i are respectively.
H. And D, making t equal to t +1, and returning to the step D for the next iteration.
I. Output node and branch data.
Compared with the prior art, the invention has the following beneficial effects:
1. the Jacobian matrix of load flow calculation is stored according to (2n) x (2n), so that the corresponding relation between the nodes and the rows and columns of the equation coefficient matrix can be simplified, the programming difficulty is greatly reduced, and the calculation amount is not increased.
2. For the equation without PV nodes or balance nodes, the other elements except the diagonal elements in the corresponding row of the Jacobian matrix are all 0, which is used to indicate that no corresponding equation exists. Because the diagonal element is not 0, the linear equation solving function provided by the programming language can be used for solving the correction equation of the load flow calculation, and the programming difficulty can be greatly reduced. The linear equation solving function provided by the programming language is optimized, the calculation speed is high, the stability is high, and the calculation speed and the program stability of the load flow calculation can be greatly improved.
3. The nodes of the load flow calculation are flexibly numbered, the numbering is irrelevant to the node type, the balancing node is the last node without requiring the PQ node to be numbered in the front, and the original numbering of the system nodes is not required to be changed according to the program design requirement.
Drawings
The invention is shown in figure 2. Wherein:
fig. 1 is a flow chart of a conventional polar newton method load flow calculation.
Fig. 2 is a block flow diagram of the jacobian matrix formation of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. According to the flow chart of polar coordinate Newton method load flow calculation shown in figure 1 and the flow chart of Jacobian matrix formation of the invention shown in figure 2, load flow calculation is carried out on an actual large-scale power grid. The actual large-scale power grid is provided with 445 nodes which contain a large number of small impedance branches, and in order to enable the conventional load flow calculation method to calculate, the small impedance branches are changed into normal branches. The convergence accuracy of the power flow calculation is 0.00001.
For comparison, the following 3 methods are adopted to perform load flow calculation on the actual large-scale power grid:
the conventional method comprises the following steps: a conventional polar coordinate Newton method load flow calculation method;
the patented method comprises the following steps: the method of patent CN 201010509556.5;
the comparison method comprises the following steps: the method of patent CN201010509556.5 is adopted, but the correction equation solution of the power flow calculation adopts Matlab linear equation solution function.
All the load flow calculation methods are programmed by adopting M files of Matlab, and the calculation time of different load flow calculation methods is shown in a table 1.
TABLE 1 calculation time(s) for different load flow calculation methods
Method Conventional methodMethod of making Patented method Comparison method The invention
Calculating time 13.237416 13.143264 The coefficient matrix is singular and cannot be solved 0.339362
As can be seen from Table 1, for the modified 445-node actual power system calculation example, the calculation time of the conventional polar coordinate Newton method load flow calculation method is close to that of the patented method. Some diagonal elements in the Jacobian matrix of the comparison method are 0, so that the coefficient matrix of the correction equation is singular, and the linear equation provided by a programming language can not be used for solving the function.
The present invention can be implemented using any programming language and programming environment, such as the M-file programming languages of C, C + +, FORTRAN, Delphi, MATLAB, and the like. The development environment may employ Visual C + +, Borland C + + Builder, Visual FORTRAN, MATLAB, and the like.
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. A polar coordinate Newton method load flow calculation method suitable for research purposes is characterized in that: the method comprises the following steps:
A. Inputting original data and an initialization voltage;
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 injected into the node and is called as a PQ node; the node with known node injection active power and voltage amplitude and unknown node injection reactive power and voltage phase angle is called PV node; the node with known node voltage amplitude and voltage phase angle and unknown node injection 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 voltage phase angles of all the nodes are 0.0; the unit of the voltage phase angle is radian, and other quantities adopt per unit values;
B. forming a node admittance matrix;
C. setting an iteration count t to be 0;
D. calculating the node power and the node power unbalance amount to obtain the maximum unbalance amount delta Wmax；
The node power calculation formula is as follows:
Figure FDA0003494688290000011
in the formula, Pi、QiRespectively the active power and the reactive power of the node i; u shapei、UkThe voltage amplitudes of the node i and the node k are respectively; thetaik＝θi-θk，θiAnd thetakVoltage phase angles of the node i and the node k respectively; g ik、BikRespectively, node admittance matrix elements YikThe real and imaginary parts of (c); n is the number of nodes;
the calculation formula of the node power unbalance is as follows:
Figure FDA0003494688290000021
in the formula,. DELTA.Pi、ΔQiRespectively the active power unbalance amount and the reactive power unbalance amount of the node i; pis、QisInjecting active power and injection respectively given for node iInputting reactive power;
the balance nodes do not participate in iterative computation, and the power unbalance of the nodes does not need to be computed;
delta P and delta Q are both n-dimensional vectors, and the active power unbalance amount delta P corresponding to the balance node iiSetting 0; balance node i or reactive power unbalance amount delta Q corresponding to PV node iiSetting 0; solving the maximum value of the absolute value in the active power unbalance and the reactive power unbalance of each node, which is called as the maximum unbalance;
E. judging the absolute value | Delta W of the maximum unbalance amountmaxWhether | is less than convergence precision ε; if the convergence precision is smaller than the convergence precision epsilon, executing a step I; otherwise, executing step F;
F. forming a Jacobian matrix J;
f1, calculating Jacobian matrix elements according to the formulas (3) to (10) without considering the node types to form a Jacobian matrix J of (2n) x (2 n);
when i ≠ j, the Jacobian matrix element calculation formula is as follows:
Figure FDA0003494688290000022
Figure FDA0003494688290000023
Figure FDA0003494688290000024
Figure FDA0003494688290000025
in the formula, Ji,jThe element is the ith row and the jth column of the Jacobian matrix;
Figure FDA0003494688290000026
active power for node i The partial derivative of the amount of unbalance to the voltage phase angle of the node j;
Figure FDA0003494688290000031
is the partial derivative of the active power unbalance of the node i to the voltage amplitude of the node j;
Figure FDA0003494688290000032
is the partial derivative of the reactive power unbalance of the node i to the voltage phase angle of the node j;
Figure FDA0003494688290000033
is the partial derivative of the reactive power unbalance of the node i to the voltage amplitude of the node j;
when i is J, the formula for calculating the elements of the jacobian matrix J is as follows:
Figure FDA0003494688290000034
Figure FDA0003494688290000035
Figure FDA0003494688290000036
Figure FDA0003494688290000037
in the formula (I), the compound is shown in the specification,
Figure FDA0003494688290000038
the partial derivative of the active power unbalance amount of the node i to the voltage phase angle of the node i is obtained;
Figure FDA0003494688290000039
the partial derivative of the active power unbalance of the node i to the voltage amplitude of the node i is obtained;
Figure FDA00034946882900000310
is the partial derivative of the reactive power unbalance of the node i to the voltage phase angle of the node i;
Figure FDA00034946882900000311
is the partial derivative of the reactive power unbalance of the node i to the voltage amplitude of the node i;
f2, setting the node count i to 1;
f3, judging whether the node i is a balanced node, if not, turning to the step F10;
f4, setting count k to 1;
f5, determining whether k is true, and if so, going to step F8;
f6, let Jacobian matrix i the row the k the column element Ji,k＝0；
F7, order Jk,i＝0；
F8, let k be k + 1;
f9, judging whether k is larger than 2n, if k is larger than 2n, turning to step F10; otherwise, return to step F5;
F10, judging whether the node i is a PQ node, if so, turning to the step F17;
f11, setting count k equal to 1;
f12, determining whether k is n + i, if so, going to step F15;
f13, order Jn+i,k＝0；
F14, order Jk,n+i＝0；
F15, let k be k + 1;
f16, judging whether k is larger than 2n, if k is larger than 2n, turning to step F17; otherwise, return to step F12;
f17, let i ═ i + 1;
f18, judging whether i is larger than n, if i is larger than n, turning to the step G; otherwise, return to step F3;
G. solving a correction equation and correcting the node voltage amplitude U and the phase angle theta;
the correction equation is:
Figure FDA0003494688290000041
wherein J is a Jacobian matrix of order (2n) × (2 n); Δ θ ═ Δ θ1,…,Δθn]TThe upper mark T represents transposition for the column vector of the phase angle correction quantity of the node voltage; delta U/U ═ delta U1/U1,…,ΔUn/Un]TDividing the node voltage amplitude correction quantity by the column vector of the node voltage amplitude; Δ P ═ Δ P1,…,ΔPn]TThe active power unbalance column vector of the node is obtained; Δ Q ═ Δ Q1,…,ΔQn]TThe node reactive power unbalance column vector is obtained;
the node voltage amplitude and voltage phase angle correction formula is as follows:
Figure FDA0003494688290000042
Figure FDA0003494688290000051
in the formula, superscript (t) represents the t iteration; delta UiAnd Δ θiRespectively is the voltage amplitude correction and the voltage phase angle correction of the node i;
H. d, enabling t to be t +1, and returning to the step D for next iteration;
I. Output node and branch data.
CN202210109051.2A 2022-01-29 2022-01-29 Polar coordinate Newton method load flow calculation method suitable for research purpose Pending CN114566968A (en)

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