CN114511418A - Method for calculating short-circuit current of power distribution network containing inverter type distributed power supply - Google Patents

Method for calculating short-circuit current of power distribution network containing inverter type distributed power supply Download PDF

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CN114511418A
CN114511418A CN202210143031.7A CN202210143031A CN114511418A CN 114511418 A CN114511418 A CN 114511418A CN 202210143031 A CN202210143031 A CN 202210143031A CN 114511418 A CN114511418 A CN 114511418A
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node
voltage
positive sequence
sequence
positive
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朱健
刘江东
吴成国
肖仕武
孔伯骏
朱金鑫
王升波
丰颖
薛钟兵
李培培
刘恒门
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Yangzhou Power Supply Branch Of State Grid Jiangsu Electric Power Co ltd
State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
North China Electric Power University
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Yangzhou Power Supply Branch Of State Grid Jiangsu Electric Power Co ltd
State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
North China Electric Power University
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06QINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06Electricity, gas or water supply
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/16Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02HEMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
    • H02H1/00Details of emergency protective circuit arrangements
    • H02H1/0007Details of emergency protective circuit arrangements concerning the detecting means
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02HEMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
    • H02H1/00Details of emergency protective circuit arrangements
    • H02H1/0092Details of emergency protective circuit arrangements concerning the data processing means, e.g. expert systems, neural networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02HEMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
    • H02H7/00Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions
    • H02H7/26Sectionalised protection of cable or line systems, e.g. for disconnecting a section on which a short-circuit, earth fault, or arc discharge has occured
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management

Abstract

The method for calculating the short-circuit current of the distribution network containing the inverter type distributed power supply comprises the following steps: step 1: establishing an output characteristic equation of the distributed power supply, a node admittance matrix of the network and a fault point boundary condition; step 2: on the basis of the step 1, circularly calculating by using a linear iteration method; and step 3: on the basis of the steps 1 and 2, performing second-order convergence iterative calculation based on a Newton-Raphson principle and a positive sequence amplification network node voltage equation, and calculating to obtain each node voltage and branch current of a positive sequence network; and 4, step 4: and (3) calculating the node voltage and the branch current of the negative sequence zero sequence network based on the calculation result of the step (3) and by combining the fault point boundary condition of the step (1), synthesizing the fault node phase voltage and the branch fault current of the power distribution network by using a symmetric component method, and outputting a result. The method provides reference basis for power distribution network fault location, fault diagnosis and the like through accurate short circuit calculation results.

Description

Method for calculating short-circuit current of power distribution network containing inverter type distributed power supply
Technical Field
The invention relates to the field of grid-connected short circuit calculation of an inverter type distributed power supply, in particular to a second-order convergence iteration method for short circuit calculation of a power distribution network containing the inverter type distributed power supply.
Background
With the proposal of national double-carbon targets, the permeability of Distributed power supplies is higher and higher, more and more Inverter-type Distributed power supplies (IIDG) are connected to an active power distribution network, and the fault current of the IIDG is more and more important in the calculation of the short-circuit current of the power distribution network. In the calculation of the short-circuit current of the power grid, the short-circuit current cannot be simply ignored or the output current of the short-circuit current cannot be replaced by 1.2 times of rated current.
In a power grid, an inverter type distributed power supply is merged into the power grid by means of power electronic devices, the amplitude of output current of the inverter type distributed power supply is controlled, the phase of the output current is controlled, so that the fault current characteristic of the inverter type distributed power supply is greatly different from that of a traditional alternating current synchronous generator, and a complex nonlinear relation exists between the output current of the inverter type distributed power supply and the voltage of a grid-connected point.
Meanwhile, with the development of a novel double-high power system, the traditional power distribution network gradually develops into an active power distribution network with an active control function, the original single-power-supply less annular network is used as a distribution network, the original single-power-supply less annular network is changed into a multi-power-supply multi-loop network, and the size and the direction of short-circuit current can also be changed. The change of the short-circuit current can affect the relay protection of the power distribution network, possibly causes the false operation of the relay protection, and the relay protection fixed value needs to be reset according to the calculation result of the short-circuit current of the power distribution network containing the distributed power supply.
For the above problems, some current methods use a linear iteration method based on a node impedance matrix to calculate the short-circuit current, and as the scale of the power grid is enlarged and the permeability of the distributed power supply is increased, the method comprises the following steps: (1) the iterative convergence is reduced, and the convergence speed is too low; (2) the nodal impedance matrix is difficult to form and as a full matrix, the demand on system computational memory increases. Therefore, under the background of increasing the permeability of new energy in the future, the existing linear iteration method based on the node impedance matrix is not suitable for short-circuit current calculation of a large-scale power grid in the future.
Disclosure of Invention
Aiming at the problems, the invention provides a method for calculating the short-circuit current of a power distribution network containing an inverter type distributed power supply.
The technical scheme of the invention is as follows: the method comprises the following steps:
step 1: establishing an output characteristic equation of the distributed power supply, a node admittance matrix of the network and a fault point boundary condition;
step 2: on the basis of the step 1, calculating by using a linear iteration method to obtain positive sequence voltages of all nodes and phase angles of the positive sequence voltages of all nodes;
and step 3: on the basis of the steps 1 and 2, performing second-order convergence iterative calculation based on a Newton-Raphson principle and a positive sequence amplification network node voltage equation, and calculating to obtain each node voltage and branch current of a positive sequence network;
and 4, step 4: and (3) calculating the node voltage and the branch current of the negative sequence zero sequence network based on the calculation result of the step (3) and by combining the fault point boundary condition of the step (1), synthesizing the fault node phase voltage and the branch fault current of the power distribution network by using a symmetric component method, and outputting a result.
The step 1 comprises the following steps:
1.1, establishing an equation of the port output characteristic of the IIDG in the low voltage ride through period
Figure BDA0003507246660000021
1.2, establishing node branch incidence matrix A of each sequence networki(i ═ 1,2,0) and original branch admittance matrix
Figure BDA0003507246660000022
(i-1, 2,0), according to
Figure BDA0003507246660000023
Establishing node admittance matrix Y of each sequence network1 i(i=1,2,0);
1.3 establishing fault point boundary conditions according to fault types
Figure BDA0003507246660000024
The step 2 comprises the following steps:
2.1 setting initial positive sequence output current value of IIDG
Figure BDA0003507246660000025
Set to 0;
2.2, substituting the positive sequence output current value of the IIDG into the positive sequence network node voltage equation Y1U+=I+To obtain the normal component of positive sequence voltage of each node
Figure BDA0003507246660000026
2.3 substituting into the positive sequence current solving formula to obtain the positive sequence current of the short circuit point
Figure BDA0003507246660000027
Simultaneous fault point boundary condition f and node voltage equation Y of each sequence network1 iUi=Ii(i is 1,2,0) solving the positive and negative zero sequence voltage fault components of each node after the iteration
Figure BDA0003507246660000028
(i=1,2,0);
2.4 according to
Figure BDA0003507246660000029
Calculating the voltage of each sequence considering the IIDG short-circuit current
Figure BDA00035072466600000210
(i=1,2,0);
2.5 according to the new node positive sequence voltage formula
Figure BDA00035072466600000211
Updating the positive sequence current value of the IIDG output
Figure BDA00035072466600000212
Returning to the step 2.2 for recalculation, and circulating for 2 times in total;
2.6 outputting the positive sequence voltage U of each node(1)And phase angle theta of positive sequence voltage of each node(1)
The step 3 comprises the following steps:
3.1, connecting the negative sequence zero sequence network as a whole to the positive as equivalent impedanceIn the sequence network, a positive sequence network node voltage equation at the moment is established
Figure BDA00035072466600000213
And simplifying the positive sequence network node voltage equation into
Figure BDA00035072466600000214
And the real part and the imaginary part of each equation are listed;
3.2, carrying out derivation on the nonlinear equation set F to obtain a Jacobi matrix J;
3.3, will be the positive sequence voltage
Figure BDA0003507246660000031
And phase angle
Figure BDA0003507246660000032
Substituting into the nonlinear equation set F and the Jacobi matrix J to obtain the unbalance amount Delta F of the equation set at the moment(k)And each element value in the Jacobi matrix J;
3.4 according to
Figure BDA0003507246660000033
Solving for new positive sequence voltage
Figure BDA0003507246660000034
And phase angle
Figure BDA0003507246660000035
3.5, judging whether the iteration error is established or not, and if so, outputting a new positive sequence voltage at the moment
Figure BDA0003507246660000036
And phase angle
Figure BDA0003507246660000037
Otherwise, return to step 3.3.
The step 4 comprises the following steps:
4.1 solving the positive sequence current of the fault point
Figure BDA0003507246660000038
And according to the boundary condition f of the fault point and the node voltage equation Y of the negative sequence zero sequence network1 iUi=Ii(i is 2,0) solving the negative sequence zero sequence voltage of each node;
4.2, synthesizing three-phase voltage of each node according to a symmetrical component method;
and 4.3, finishing the calculation.
In step 1.1, an equation of port output characteristics of the IIDG during low voltage ride through is established
Figure BDA0003507246660000039
Figure BDA00035072466600000310
Wherein, INA rated current value of the inverter; theta is a positive sequence voltage phase angle of a grid-connected point; u shape(1)Is the per unit value of the positive sequence voltage of the grid-connected point;
Figure BDA00035072466600000311
step 1.3, establishing fault point boundary conditions according to fault types
Figure BDA00035072466600000312
When the single-phase grounding short circuit occurs, the positive and negative zero sequence voltage currents of the fault point satisfy the following relation:
Figure BDA00035072466600000313
in the formula (I), the compound is shown in the specification,
Figure BDA00035072466600000314
positive and negative zero sequence voltages of a fault point are respectively;
Figure BDA00035072466600000315
positive and negative zero sequence currents of fault points are respectively.
In step 2.2, substituting the positive sequence output current value of the IIDG into the positive sequence network node voltage equation Y1 1U+=I+To obtain the normal component of positive sequence voltage of each node
Figure BDA0003507246660000041
Figure BDA0003507246660000042
Wherein, Y1 1A node admittance matrix for the positive sequence network; zSIs the system impedance;
Figure BDA0003507246660000043
is the positive sequence current output by the distributed power supply.
Step 2.3, substituting the positive sequence current solving formula to obtain the positive sequence current of the short circuit point
Figure BDA0003507246660000044
Simultaneous fault point boundary condition f and node voltage equation Y of each sequence network1 iUi=Ii(i is 1,2,0) solving the positive and negative zero sequence voltage fault components of each node after the iteration
Figure BDA0003507246660000045
(i ═ 1,2,0), the positive sequence current solving formulas under the single-phase short circuit, the two-phase interphase short circuit and the two-phase grounding short circuit are respectively as follows:
Figure BDA0003507246660000046
Figure BDA0003507246660000047
Figure BDA0003507246660000048
Figure BDA0003507246660000049
wherein the content of the first and second substances,
Figure BDA00035072466600000410
the normal component value of the positive sequence voltage of the fault point is obtained; z∑1、Z∑2、Z∑0Positive and negative zero sequence equivalent impedances respectively; y is1 i(i is 1,2,0) is a positive and negative zero sequence network node admittance matrix respectively;
Figure BDA00035072466600000411
(i is 1,2,0) is a positive and negative zero sequence voltage fault component of the node;
Figure BDA00035072466600000412
and (i is 1,2 and 0) is the positive and negative zero sequence current of the fault point.
In step 2.6, positive sequence voltage U of each node is output(1)And phase angle theta of positive sequence voltage of each node(1)
Figure BDA0003507246660000051
Wherein, U(1)For positive sequence voltage of each node, theta(1)Is the phase angle of the positive sequence voltage of each node.
Step 3.1, connecting the negative sequence zero sequence network as a whole in a positive sequence network as equivalent impedance, and establishing a node voltage equation of the positive sequence network at the moment
Figure BDA0003507246660000052
Simplifying the positive sequence network node voltage equation into
Figure BDA0003507246660000053
And the real part and the imaginary part of each equation are listed as follows:
Figure BDA0003507246660000054
Figure BDA0003507246660000055
wherein f is a fault point; zsIs the system impedance;
Figure BDA0003507246660000061
injecting a positive sequence current of the positive sequence network into the IIDG;
in this case, F is a positive sequence voltage containing each node
Figure BDA0003507246660000062
And phase angle
Figure BDA0003507246660000063
A 2 n-dimensional nonlinear system of equations.
In step 3.2, the nonlinear equation set F is derived to obtain a Jacobi matrix J, and the Jacobi matrix J is set
Figure BDA0003507246660000064
Yij=Gij+jBij
For non-IIDG access nodes:
Figure BDA0003507246660000065
for an IIDG access node:
Figure BDA0003507246660000066
then:
Figure BDA0003507246660000067
in step 3.3, the positive sequence voltage is applied
Figure BDA0003507246660000068
And phase angle
Figure BDA0003507246660000069
Substituting the obtained data into a nonlinear equation set F and a Jacobi matrix J to obtain the unbalance amount delta F of the equation set at the moment(k)And the values of the elements in the Jacobi matrix J:
Figure BDA00035072466600000610
wherein the content of the first and second substances,
Figure BDA00035072466600000611
the positive sequence voltage and phase angle for the kth iteration of each node.
In step 3.4, according to
Figure BDA00035072466600000612
Solving for a new positive sequence node voltage
Figure BDA00035072466600000613
And positive sequence voltage phase angle
Figure BDA00035072466600000614
Figure BDA00035072466600000615
In step 3.5, judging whether the iteration error meets the precision requirement, and if so, outputting the new positive sequence node voltage at the moment
Figure BDA0003507246660000071
And positive sequence voltage phase angle
Figure BDA0003507246660000072
Otherwise, returning to the step 3.3;
wherein the iteration error is
Figure BDA0003507246660000073
In step 4.1, the positive sequence current of the fault point is solved
Figure BDA0003507246660000074
And according to the boundary condition f of the fault point and the node voltage equation Y of the negative sequence zero sequence network1 iUi=Ii(i is 2,0) solving the negative sequence zero sequence voltage of each node;
Figure BDA0003507246660000075
Figure BDA0003507246660000076
wherein the content of the first and second substances,
Figure BDA0003507246660000077
positive sequence voltage and phase angle for fault adjacent node;
Figure BDA0003507246660000078
positive sequence voltage and phase angle for fault point; y is(f-1)fAdmittance of the line between the two; y is1 i(i is 2,0) is a negative sequence zero sequence network node admittance matrix respectively;
Figure BDA0003507246660000079
(i is 2,0) is a positive and negative zero sequence voltage fault component of the node;
Figure BDA00035072466600000710
and (i is 2,0) is the fault point negative sequence zero sequence current.
Step 4.2, synthesizing three-phase voltage of each node according to a symmetrical component method;
Figure BDA00035072466600000711
wherein,
Figure BDA00035072466600000712
Three phase voltages of each node; a ═ ej120°
Compared with the current linear iteration short circuit calculation method, the method has the following advantages: (1) the advantage of sparsity of the node admittance matrix is fully utilized, the requirement of calculation on a memory is reduced, and the calculation speed is improved; (2) the method is based on the Newton-Raphson principle, so that the method has the characteristic of second-order convergence, and the convergence speed is greatly improved.
According to the invention, reference basis is provided for power distribution network fault positioning, fault diagnosis, selection of distribution network equipment, distribution network relay protection, reclosing, short circuit level control and the like through an accurate short circuit calculation result.
Drawings
FIG. 1 is a logic diagram of a second-order convergence iteration method including short-circuit calculation of an inverter type distributed power distribution network in the method of the invention;
FIG. 2 is a diagram of a grid architecture used in the method of the present invention;
fig. 3 is a comparative analysis diagram of the second-order convergence iteration and linear iteration convergence speed of the inverter-type distributed power distribution network short-circuit calculation included in the method.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples.
The invention provides a second-order convergence iteration method for short circuit calculation of a distribution network containing an inverter type distributed power supply, which is carried out by an iteration method based on a Newton-Raphson principle. The present invention will be described in detail with reference to the accompanying drawings.
The invention comprises the following steps:
step 1: establishing an output characteristic equation of the distributed power supply, a node admittance matrix of the network and boundary conditions of fault points, and providing preconditions of short circuit calculation for the steps 2 and 3;
step 2: on the basis of the step 1, circularly calculating for 2-3 times by using a linear iteration method, calculating to obtain positive sequence voltages of all nodes and phase angles of the positive sequence voltages of all nodes, and providing an initial value condition for the step 3;
and step 3: on the basis of the steps 1 and 2, performing second-order convergence iterative calculation based on a Newton-Raphson principle and a positive sequence amplification network node voltage equation, and calculating to obtain each node voltage and branch current of a positive sequence network;
and 4, step 4: and (3) calculating the node voltage and the branch current of the negative sequence zero sequence network based on the calculation result of the step (3) and by combining the fault point boundary condition of the step (1), synthesizing the fault node phase voltage and the branch fault current of the power distribution network by using a symmetric component method, and outputting a result.
The distributed power supply is equivalent to a controlled current source, the positive sequence output current of the controlled current source and the positive sequence voltage of the terminal of the controlled current source are in a nonlinear relation, a positive sequence augmentation network node voltage equation reflecting the fault type is established, a second-order convergence fast iterative algorithm adapting to the nonlinear relation of the distributed power supply is provided based on the Newton-Raphson principle, and accurate node voltages and branch currents are obtained through calculation. The method is based on the Newton-Raphson principle and the symmetric component method, the defect that the traditional IIDG power grid short circuit calculation convergence is slow is overcome, the accuracy of the calculation result is improved, and the working reliability of the power distribution network is improved.
As shown in fig. 1, the method specifically comprises the following steps:
the step 1 comprises the following steps: 1.1, establishing an equation of the port output characteristic of the IIDG in the low voltage ride through period
Figure BDA0003507246660000081
Namely, the functional relation between the positive sequence current output by the distributed power supply during the short-circuit fault of the power distribution network and the positive sequence voltage of the grid-connected point of the distributed power supply;
1.2, establishing node branch incidence matrix A of each sequence networki(i ═ 1,2,0) and original branch admittance matrix
Figure BDA0003507246660000082
(i ═ 1,2,0) according to
Figure BDA0003507246660000083
Establishing node admittance matrix Y of each sequence network1 i(i=1,2,0);
1.3 establishing fault point boundary conditions according to fault types
Figure BDA0003507246660000084
The step 2 comprises the following steps: 2.1 setting initial positive sequence output current value of IIDG
Figure BDA0003507246660000085
Generally given as 0; because the initial voltage value is not sensitive to the initial positive output value of the IIDG in the process of selecting the initial voltage value for the subsequent second-order iteration, the initial voltage value can be generally 0;
2.2, substituting the positive sequence output current value of the IIDG into the positive sequence network node voltage equation Y1U+=I+To obtain the normal component of positive sequence voltage of each node
Figure BDA0003507246660000091
2.3 substituting into the positive sequence current solving formula to obtain the positive sequence current of the short circuit point
Figure BDA0003507246660000092
Simultaneous fault point boundary condition f and node voltage equation Y of each sequence network1 iUi=Ii(i is 1,2,0) solving the positive and negative zero sequence voltage fault components of each node after the iteration
Figure BDA0003507246660000093
(i=1,2,0);
2.4 according to
Figure BDA0003507246660000094
Calculating the voltage of each sequence considering the IIDG short-circuit current
Figure BDA0003507246660000095
(i=1,2,0);
2.5 according to the new node positive sequence voltage formula
Figure BDA0003507246660000096
Updating the positive sequence current value of the IIDG output
Figure BDA0003507246660000097
Returning to the step 2.2 for recalculation, and circulating for 2-3 times in total;
2.6 outputting the positive sequence voltage U of each node(1)And phase angle theta of positive sequence voltage of each node(1)
Step 2 adopts a conventional iterative method taking the distributed power into account, which is generally called linear iteration because it has the characteristic of first-order convergence. The second-order convergence iterative method provided by the invention is sensitive to the initial value, so that the method is used for calculating 2-3 times to select a proper initial value, namely the amplitude and the phase angle of the positive sequence voltage of each node.
And (3) equating the distributed power supply in a normal network by using the superposition theorem in the step 2.
The step 3 comprises the following steps: 3.1, connecting the negative sequence zero sequence network as a whole in a positive sequence network as equivalent impedance, and establishing a node voltage equation of the positive sequence network at the moment
Figure BDA0003507246660000098
And simplifying the positive sequence network node voltage equation into
Figure BDA0003507246660000099
And the real part and the imaginary part of each equation are listed;
3.2, carrying out derivation on the nonlinear equation set F to obtain a Jacobi matrix J;
3.3, will be the positive sequence voltage
Figure BDA00035072466600000910
And phase angle
Figure BDA00035072466600000911
Substituting into the nonlinear equation set F and the Jacobi matrix J to obtain the unbalance amount Delta F of the equation set at the moment(k)And each element value in the Jacobi matrix J;
3.4 according to
Figure BDA00035072466600000912
Solving for new positive sequence voltage
Figure BDA00035072466600000913
And phase angle
Figure BDA00035072466600000914
3.5, judging iteration errors
Figure BDA00035072466600000915
If yes, outputting the new positive sequence voltage
Figure BDA00035072466600000916
And phase angle
Figure BDA00035072466600000917
Otherwise, return to step 3.3.
In the step 3, the node positive sequence voltage is in a polar coordinate form, because the positive sequence network node voltage equation is an equation set with the positive sequence voltage amplitude and the phase angle as unknowns, for the positive sequence network, if the positive sequence network node voltage equation contains N nodes, the positive sequence network node voltage equation contains 2N unknowns (N node positive sequence voltage amplitudes and N node positive sequence voltage phase angles) and also has 2N equations (N real parts and N imaginary parts), because the distributed power supply causes network nonlinearity, an iteration method is required to be applied for solving, and the fast convergence of calculation can be realized by using the iteration method with the second-order convergence characteristic.
Step 4 comprises the following steps: 4.1 solving the positive sequence current of the fault point
Figure BDA0003507246660000101
And according to the boundary condition f of the fault point and the node voltage equation Y of the negative sequence zero sequence network1 iUi=Ii(i is 2,0) solving the negative sequence zero sequence voltage of each node;
4.2, synthesizing three-phase voltage of each node according to a symmetrical component method;
and 4.3, finishing the calculation.
In step 1.1, an equation of port output characteristics of the IIDG during low voltage ride through is established
Figure BDA0003507246660000102
Figure BDA0003507246660000103
Wherein, INA rated current value of the inverter; theta is a positive sequence voltage phase angle of a grid-connected point; u shape(1)Is the per unit value of the positive sequence voltage of the grid-connected point;
Figure BDA0003507246660000104
and 4, on the basis of the positive sequence voltage of each node obtained in the step 3, obtaining the positive sequence current of a fault point, obtaining the negative sequence current and the zero sequence current on the basis of the boundary condition of the fault point, for example, under the condition of single-phase grounding, the negative sequence zero sequence current is equal to the positive sequence current, obtaining the voltage of each node in the negative sequence zero sequence network and the branch current at the moment, and finally, uniformly synthesizing the node voltage phase component and the branch current phase component by using a symmetrical component method.
Step 1.3, according to the fault type, establishing fault point boundary condition
Figure BDA0003507246660000105
When the single-phase grounding short circuit occurs, the positive and negative zero sequence voltage currents of the fault point satisfy the following relation:
Figure BDA0003507246660000106
in the formula (I), the compound is shown in the specification,
Figure BDA0003507246660000107
positive and negative zero sequence voltages of a fault point are respectively;
Figure BDA0003507246660000108
positive and negative zero sequence currents of fault points are respectively.
In step 2.2, substituting the positive sequence output current value of the IIDG into the positive sequence network node voltage equation Y1 1U+=I+To obtain the normal component of positive sequence voltage of each node
Figure BDA0003507246660000109
Figure BDA0003507246660000042
Wherein, Y1 1A node admittance matrix for the positive sequence network; zSIs the system impedance;
Figure BDA0003507246660000112
is the positive sequence current output by the distributed power supply.
Step 2.3, substituting the positive sequence current solving formula to obtain the positive sequence current of the short circuit point
Figure BDA0003507246660000113
Simultaneous fault point boundary condition f and node voltage equation Y of each sequence network1 iUi=Ii(i is 1,2,0) solving the positive and negative zero sequence voltage fault components of each node after the iteration
Figure BDA0003507246660000114
(i ═ 1,2,0), the positive sequence current solving formulas under the single-phase short circuit, the two-phase interphase short circuit and the two-phase grounding short circuit are respectively as follows:
Figure BDA0003507246660000115
Figure BDA0003507246660000116
Figure BDA0003507246660000117
Figure BDA0003507246660000118
wherein the content of the first and second substances,
Figure BDA0003507246660000119
the normal component value of the positive sequence voltage of the fault point is obtained; z∑1、Z∑2、Z∑0Positive and negative zero sequence equivalent impedances respectively; y is1 i(i is 1,2,0) is a positive and negative zero sequence network node admittance matrix respectively;
Figure BDA00035072466600001110
(i is 1,2,0) is a positive and negative zero sequence voltage fault component of the node;
Figure BDA00035072466600001111
and (i is 1,2 and 0) is the positive and negative zero-sequence current of the fault point.
In step 2.6, positive sequence voltage U of each node is output(1)And phase angle theta of positive sequence voltage of each node(1)
Figure BDA00035072466600001112
Wherein, U(1)For positive sequence voltage of each node, theta(1)Is the phase angle of the positive sequence voltage of each node.
Step 3.1, connecting the negative sequence zero sequence network as a whole in a positive sequence network as equivalent impedance, and establishing a node voltage equation of the positive sequence network at the moment
Figure BDA0003507246660000121
Simplifying the positive sequence network node voltage equation into
Figure BDA0003507246660000122
And the real part and the imaginary part of each equation are listed as follows:
Figure BDA0003507246660000123
Figure BDA0003507246660000124
wherein f is a fault point; zsIs the system impedance;
Figure BDA0003507246660000125
injecting a positive sequence current of the positive sequence network into the IIDG;
in this case, F is a positive sequence voltage containing each node
Figure BDA0003507246660000126
And phase angle
Figure BDA0003507246660000127
A 2 n-dimensional nonlinear system of equations.
In step 3.2, the nonlinear equation set F is derived to obtain a Jacobi matrix J, and the Jacobi matrix J is set
Figure BDA0003507246660000128
Yij=Gij+jBij
For non-IIDG access nodes:
Figure BDA0003507246660000131
for an IIDG access node:
Figure BDA0003507246660000132
then:
Figure BDA0003507246660000133
in step 3.3, the positive sequence voltage is applied
Figure BDA0003507246660000134
And phase angle
Figure BDA0003507246660000135
Substituting into the nonlinear equation set F and the Jacobi matrix J to obtain the unbalance amount Delta F of the equation set at the moment(k)And the values of the elements in the Jacobi matrix J:
Figure BDA0003507246660000136
wherein the content of the first and second substances,
Figure BDA0003507246660000137
the positive sequence voltage and phase angle for the kth iteration of each node.
In step 3.4, according to
Figure BDA0003507246660000138
Solving for a new positive sequence node voltage
Figure BDA0003507246660000139
And positive sequence voltage phase angle
Figure BDA00035072466600001310
Figure BDA00035072466600001311
In step 3.5, judging whether the iteration error meets the precision requirement, and if so, outputting the new positive sequence node electricity at the momentPress and press
Figure BDA00035072466600001312
And positive sequence voltage phase angle
Figure BDA00035072466600001313
Otherwise, returning to the step 3.3;
wherein the iteration error is
Figure BDA00035072466600001314
In the formula, epsilon is the precision requirement of iterative computation and can be set by people.
In step 4.1, the positive sequence current of the fault point is solved
Figure BDA0003507246660000141
And according to the boundary condition f of the fault point and the node voltage equation Y of the negative sequence zero sequence network1 iUi=Ii(i is 2,0) solving the negative sequence zero sequence voltage of each node;
Figure BDA0003507246660000142
Figure BDA0003507246660000143
wherein the content of the first and second substances,
Figure BDA0003507246660000144
positive sequence voltage and phase angle for fault adjacent node;
Figure BDA0003507246660000145
positive sequence voltage and phase angle for fault point; y is(f-1)fAdmittance of the line between the two; y is1 i(i is 2,0) is a negative sequence zero sequence network node admittance matrix respectively;
Figure BDA0003507246660000146
(i is 2,0) is a positive and negative zero sequence voltage fault component of the node;
Figure BDA0003507246660000147
and (i is 2,0) is the fault point negative sequence zero sequence current.
Step 4.2, synthesizing three-phase voltages of each node according to a symmetrical component method;
Figure BDA0003507246660000148
wherein,
Figure BDA0003507246660000149
Three phase voltages of each node; a ═ ej120°
The structure of the power grid is shown in fig. 2, and the power grid comprises 32 branches and 33 nodes, wherein a red node is a distributed power supply access node, the power supply voltage is 12.66kV, and the system impedance is Zs=2+j2(Ω)
The convergence rates of the second-order convergence iteration method containing the inverter type distributed power distribution network short circuit calculation and the existing linear iteration method are shown in the attached figure 3.
The process of the present invention is illustrated below by means of specific examples. The structural parameters of the power grid are shown in table 1.
TABLE 1 Power grid architecture parameters
Figure BDA00035072466600001410
Figure BDA0003507246660000151
The network comprises 32 branches and 33 nodes, and the reactance and resistance of each branch are shown in the table. The power supply voltage is 12.66kV, and the system impedance is Z s2+ j2 (omega), a short-circuit point is set as node No. 25, and the iteration precision requirement is that epsilon is 1e-9Mesh, netThe net voltage reference is 12.66kV, and the power reference is 10 MVA.
Distributed power supplies are arranged at nodes 19, 20, 21, 22, 26, 27, 28, 29, 30 and 31, the rated capacity of each distributed power supply is 0.2MVA, the second-order convergence iteration provided by the invention can meet the convergence precision requirement only by 5 times, while the existing linear iteration method can meet the convergence precision requirement only by 14 times, and the convergence speed is compared with that shown in figure 3.
The invention provides an iteration method based on a Newton-Raphson principle (namely a Newton-Raphson iteration method), and fully utilizes the advantage of sparsity of a node admittance matrix, and the convergence speed and the calculation speed of the iteration method are far superior to those of the existing linear iteration short circuit calculation methods. Therefore, reference basis is provided for power distribution network fault positioning, fault diagnosis, selection of distribution network equipment, distribution network relay protection, reclosing, short circuit level control and the like through accurate short circuit calculation results. Therefore, the research on the calculation of the short-circuit current of the power distribution network with the distributed power supply has important practical significance.

Claims (17)

1. The method for calculating the short-circuit current of the distribution network containing the inverter type distributed power supply comprises the following steps:
step 1: establishing an output characteristic equation of the distributed power supply, a node admittance matrix of the network and a fault point boundary condition;
step 2: on the basis of the step 1, calculating by using a linear iteration method to obtain positive sequence voltages of all nodes and phase angles of the positive sequence voltages of all nodes;
and step 3: on the basis of the steps 1 and 2, performing second-order convergence iterative calculation based on a Newton-Raphson principle and a positive sequence amplification network node voltage equation, and calculating to obtain each node voltage and branch current of a positive sequence network;
and 4, step 4: and (3) calculating the node voltage and the branch current of the negative sequence zero sequence network based on the calculation result of the step (3) and by combining the fault point boundary condition of the step (1), synthesizing the fault node phase voltage and the branch fault current of the power distribution network by using a symmetric component method, and outputting a result.
2. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 1, wherein the method comprises the following steps: the step 1 comprises the following steps:
1.1, establishing an equation of the port output characteristic of the IIDG in the low voltage ride through period
Figure FDA0003507246650000011
1.2, establishing node branch incidence matrix A of each sequence networki(i ═ 1,2,0) and original branch admittance matrix
Figure FDA0003507246650000012
Figure FDA0003507246650000013
According to
Figure FDA0003507246650000014
Establishing node admittance matrix of each sequence network
Figure FDA0003507246650000015
1.3 establishing fault point boundary conditions according to fault types
Figure FDA0003507246650000016
3. The method for calculating the short-circuit current of the distribution network with the inverter type distributed power supply as claimed in claim 1, wherein the method comprises the following steps: the step 2 comprises the following steps:
2.1 setting initial positive sequence output current value of IIDG
Figure FDA0003507246650000017
Set to 0;
2.2, substituting the positive sequence output current value of the IIDG into the positive sequence network node voltage equation Y1 U+=I+To obtain the normal component of positive sequence voltage of each node
Figure FDA0003507246650000018
2.3 substituting into the positive sequence current solving formula to obtain the positive sequence current of the short circuit point
Figure FDA0003507246650000019
Simultaneous fault point boundary condition f and node voltage equation Y of each sequence network1 iUi=Ii(i is 1,2,0) solving the positive and negative zero sequence voltage fault components of each node after the iteration
Figure FDA00035072466500000110
Figure FDA00035072466500000111
2.4 according to
Figure FDA00035072466500000112
Calculating the voltage of each sequence considering the IIDG short-circuit current
Figure FDA00035072466500000113
2.5 according to the new node positive sequence voltage formula
Figure FDA0003507246650000021
Updating the positive sequence current value of the IIDG output
Figure FDA0003507246650000022
Returning to the step 2.2 for recalculation, and circulating for 2 times in total;
2.6 outputting the positive sequence voltage U of each node(1)And phase angle theta of positive sequence voltage of each node(1)
4. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 1, wherein the method comprises the following steps: the step 3 comprises the following steps:
3.1, connecting the negative sequence zero sequence network as a whole in a positive sequence network as equivalent impedance, and establishing a node voltage equation of the positive sequence network at the moment
Figure FDA0003507246650000023
And simplifying the positive sequence network node voltage equation into
Figure FDA0003507246650000024
And the real part and the imaginary part of each equation are listed;
3.2, carrying out derivation on the nonlinear equation set F to obtain a Jacobi matrix J;
3.3, will be the positive sequence voltage
Figure FDA0003507246650000025
And phase angle
Figure FDA0003507246650000026
Substituting into the nonlinear equation set F and the Jacobi matrix J to obtain the unbalance amount Delta F of the equation set at the moment(k)And each element value in the Jacobi matrix J;
3.4 according to
Figure FDA0003507246650000027
Solving for new positive sequence voltage
Figure FDA0003507246650000028
And phase angle
Figure FDA0003507246650000029
3.5, judging whether the iteration error is established or not, and if so, outputting a new positive sequence voltage at the moment
Figure FDA00035072466500000210
And phase angle
Figure FDA00035072466500000211
Otherwise, the reverse is carried outAnd returning to the step 3.3.
5. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 1, wherein the method comprises the following steps: the step 4 comprises the following steps:
4.1 solving the positive sequence current of the fault point
Figure FDA00035072466500000212
And according to the boundary condition f of the fault point and the node voltage equation Y of the negative sequence zero sequence network1 iUi=Ii(i is 2,0) solving the negative sequence zero sequence voltage of each node;
4.2, synthesizing three-phase voltage of each node according to a symmetrical component method;
and 4.3, finishing the calculation.
6. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 2, wherein the method comprises the following steps: in step 1.1, an equation of port output characteristics of the IIDG during low voltage ride through is established
Figure FDA00035072466500000213
Figure FDA00035072466500000214
Wherein, INA rated current value of the inverter; theta is a positive sequence voltage phase angle of a grid-connected point; u shape(1)Is the per unit value of the positive sequence voltage of the grid-connected point;
Figure FDA0003507246650000031
7. the method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 2, wherein the method comprises the following steps: step 1.3, establishing fault point boundary conditions according to fault types
Figure FDA0003507246650000032
When the single-phase grounding short circuit occurs, the positive and negative zero sequence voltage currents of the fault point satisfy the following relation:
Figure FDA0003507246650000033
in the formula (I), the compound is shown in the specification,
Figure FDA0003507246650000034
positive and negative zero sequence voltages of a fault point are respectively;
Figure FDA0003507246650000035
positive and negative zero sequence currents of fault points are respectively.
8. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 3, wherein the method comprises the following steps: in step 2.2, substituting the positive sequence output current value of the IIDG into the positive sequence network node voltage equation Y1 1U+=I+To obtain the normal component of positive sequence voltage of each node
Figure FDA0003507246650000036
Figure FDA0003507246650000037
Wherein, Y1 1A node admittance matrix for the positive sequence network; zSIs the system impedance;
Figure FDA0003507246650000038
is the positive sequence current output by the distributed power supply.
9. Short-circuit power supply containing inverter type distributed power supply distribution network according to claim 3A flow calculation method, characterized by: step 2.3, substituting the positive sequence current solving formula to obtain the positive sequence current of the short circuit point
Figure FDA0003507246650000039
Simultaneous fault point boundary condition f and node voltage equation Y of each sequence network1 iUi=Ii(i is 1,2,0) solving the positive and negative zero sequence voltage fault components of each node after the iteration
Figure FDA00035072466500000310
The positive sequence current solving formulas under the conditions of single-phase short circuit, two-phase interphase short circuit and two-phase grounding short circuit are respectively as follows:
Figure FDA00035072466500000311
Figure FDA00035072466500000312
Figure FDA00035072466500000313
Figure FDA0003507246650000041
wherein the content of the first and second substances,
Figure FDA0003507246650000042
the normal component value of the positive sequence voltage of the fault point is obtained; z∑1、Z∑2、Z∑0Positive and negative zero sequence equivalent impedances respectively; y is1 i(i is 1,2,0) is a positive and negative zero sequence network node admittance matrix respectively;
Figure FDA0003507246650000043
the fault components of positive and negative zero sequence voltages of the nodes are obtained;
Figure FDA0003507246650000044
positive and negative zero sequence currents of fault points.
10. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 3, wherein the method comprises the following steps: in step 2.6, positive sequence voltage U of each node is output(1)And phase angle theta of positive sequence voltage of each node(1)
Figure FDA0003507246650000045
Wherein, U(1)For positive sequence voltage of each node, theta(1)Is the phase angle of the positive sequence voltage of each node.
11. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 4, wherein the method comprises the following steps: step 3.1, connecting the negative sequence zero sequence network as a whole in a positive sequence network as equivalent impedance, and establishing a node voltage equation of the positive sequence network at the moment
Figure FDA0003507246650000046
Simplifying the positive sequence network node voltage equation into
Figure FDA0003507246650000047
And the real part and the imaginary part of each equation are listed as follows:
Figure FDA0003507246650000048
Figure FDA0003507246650000051
wherein f isA fault point; zsIs the system impedance;
Figure FDA0003507246650000052
injecting a positive sequence current of the positive sequence network into the IIDG;
in this case, F is the positive sequence voltage U containing each nodei (1)And phase angle thetai (1)A 2 n-dimensional nonlinear system of equations.
12. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 4, wherein the method comprises the following steps: in step 3.2, the nonlinear equation set F is derived to obtain a Jacobi matrix J, and the Jacobi matrix J is set
Figure FDA0003507246650000053
Yij=Gij+jBij
For non-IIDG access nodes:
Figure FDA0003507246650000054
for an IIDG access node:
Figure FDA0003507246650000055
then:
Figure FDA0003507246650000061
13. the method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 4, wherein the method comprises the following steps: in step 3.3, the positive sequence voltage is applied
Figure FDA0003507246650000062
And phase angle
Figure FDA0003507246650000063
Substituting into the nonlinear equation set F and the Jacobi matrix J to obtain the unbalance amount Delta F of the equation set at the moment(k)And the values of the elements in the Jacobi matrix J:
Figure FDA0003507246650000064
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003507246650000065
the positive sequence voltage and phase angle for the kth iteration of each node.
14. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 4, wherein the method comprises the following steps: in step 3.4, according to
Figure FDA0003507246650000066
Solving for a new positive sequence node voltage
Figure FDA0003507246650000067
And positive sequence voltage phase angle
Figure FDA0003507246650000068
Figure FDA0003507246650000069
15. The method for calculating the short-circuit current of the distribution network with the inverter type distributed power supply as claimed in claim 4, wherein the method comprises the following steps: in step 3.5, judging whether the iteration error meets the precision requirement, and if so, outputting the new positive sequence node voltage at the moment
Figure FDA00035072466500000610
And positive sequence voltage phase angle
Figure FDA00035072466500000611
Otherwise, returning to the step 3.3;
wherein the iteration error is
Figure FDA00035072466500000612
16. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 5, wherein the method comprises the following steps: in step 4.1, the positive sequence current of the fault point is solved
Figure FDA00035072466500000613
And according to the boundary condition f of the fault point and the node voltage equation Y of the negative sequence zero sequence network1 iUi=Ii(i is 2,0) solving the negative sequence zero sequence voltage of each node;
Figure FDA00035072466500000614
Figure FDA0003507246650000071
wherein the content of the first and second substances,
Figure FDA0003507246650000072
positive sequence voltage and phase angle for fault adjacent node;
Figure FDA0003507246650000073
positive sequence voltage and phase angle for fault point; y is(f-1)fAdmittance of the line between the two; y is1 i(i is 2,0) is a negative sequence zero sequence network node admittance matrix respectively;
Figure FDA0003507246650000074
the fault components of positive and negative zero sequence voltages of the nodes are obtained;
Figure FDA0003507246650000075
is the negative sequence zero sequence current of the fault point.
17. The method for calculating the short-circuit current of the distribution network with the inverter-type distributed power supply according to claim 5, wherein the method comprises the following steps: step 4.2, synthesizing three-phase voltages of each node according to a symmetrical component method;
Figure FDA0003507246650000076
wherein,
Figure FDA0003507246650000077
Three phase voltages of each node; a ═ ej120°
CN202210143031.7A 2022-02-16 2022-02-16 Method for calculating short-circuit current of power distribution network containing inverter type distributed power supply Pending CN114511418A (en)

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Publication number Priority date Publication date Assignee Title
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CN116522043B (en) * 2023-06-27 2023-10-03 中国电力科学研究院有限公司 Short circuit current calculation method and device

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