CN113852104B - Three-phase asymmetric power distribution network power flow calculation method - Google Patents

Three-phase asymmetric power distribution network power flow calculation method Download PDF

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CN113852104B
CN113852104B CN202111104300.0A CN202111104300A CN113852104B CN 113852104 B CN113852104 B CN 113852104B CN 202111104300 A CN202111104300 A CN 202111104300A CN 113852104 B CN113852104 B CN 113852104B
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phase
node
matrix
column
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CN113852104A (en
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孙孔明
李玉敦
梁正堂
李娜
黄强
刘萌
李宽
李聪聪
王永波
张婉婕
李晨昊
史方芳
王宏
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Shandong Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Shandong Electric Power Co Ltd
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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
    • H02J3/26—Arrangements for eliminating or reducing asymmetry in polyphase networks
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/50—Arrangements for eliminating or reducing asymmetry in polyphase networks

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  • Power Engineering (AREA)
  • Supply And Distribution Of Alternating Current (AREA)

Abstract

The utility model provides a three-phase asymmetric power distribution network power flow calculation method, based on forward push back design, simultaneously considers the three-phase parameter imbalance and the three-phase topology imbalance in the calculation process, realizes the accurate calculation of power flow, and can provide accurate basic calculation tools for advanced functions of power distribution system topology reconstruction, power distribution network reactive power optimization and the like requiring power flow calculation.

Description

Three-phase asymmetric power distribution network power flow calculation method
Technical Field
The invention relates to the technical field of power flow calculation of power systems, in particular to a power flow calculation method of a three-phase asymmetric power distribution network.
Background
The method is characterized in that the method comprises the steps of obtaining various parameters such as node voltage, line current, power size, flow direction and the like under the condition of normal operation of a power distribution network, and carrying out a large amount of power flow calculation on the premise of realizing advanced application functions of various power distribution networks, such as power distribution network topology reconstruction optimization, reactive compensation device optimization configuration and the like. The power flow calculation of the power distribution network is carried out by adopting a forward push back substitution method, taking line parameters, load parameters and the like as basic conditions, and carrying out iterative calculation until convergence conditions are met. In order to simplify the calculation steps, it is generally assumed that the power distribution network is a three-phase balance system, only one of three phases is used as a calculation object under the condition that the precision requirement is met, only the iteration sequence of the target phase is needed to be determined, and the association direction of three-phase mutual inductance of each branch is not changed. In fact, the three phases of the power distribution network are usually in an asymmetric state, and particularly when the three phases are operated in open loops at different positions, the forward-backward substitution sequence of the three phases and the direction of mutual inductance are changed.
Disclosure of Invention
In order to overcome the defects of the technology, the invention provides a power flow calculation method for an asymmetric power distribution network, which forms respective iterative calculation sequences of three phases and the association direction between three-phase mutual inductances according to a topological structure.
The technical scheme adopted for overcoming the technical problems is as follows:
a three-phase asymmetric power distribution network power flow calculation method comprises the following steps:
a) Acquiring parameters of a power distribution system and a topology structure of the power distribution system;
b) Forming a branch parameter matrix P according to the acquired power distribution system parameters;
c) Forming a branch-node association matrix of each item;
d) Determining a push-forward substitution sequence of each phase;
e) Forming a branch association direction matrix;
f) And calculating to obtain the power flow parameters of the power distribution network and iteratively calculating until convergence conditions are met.
Further, the obtaining the parameters of the power distribution system in the step a) includes: the self impedance and the trans impedance of each branch and the load value of each load node.
Further, the obtaining the topology structure of the power distribution system in the step a) includes: the system nodes and the branches are numbered according to distribution of the topological structure of the power distribution system, the power supply point is numbered 1, the numbers of other n system nodes are respectively n+1, the numbers of branches close to the power supply point are respectively 1, and the numbers of other m branches are respectively m+1.
Further, in step b), column 1 of the branch parameter matrix P is the branch number, columns 2 to 4 are A, B, C-phase loads of the branch end nodes, columns 5 to 7 are A, B, C-phase self-impedances, and columns 8 to 10 are mutual impedances of the AB, BC and CA phases, respectively.
Further, three phases in step c) form a branch-node correlation matrix M respectively bna 、M bnb 、M bnc Branch-node association matrix M bna 、M bnb 、M bnc All branches of the behavior in (a) are arranged in ascending order according to branch numbers, and a branch-node association matrix M bna 、M bnb 、M bnc All the nodes are arranged in ascending order of node numbers, elements in the matrix are 0, 1, -1,0 represents that the nodes are irrelevant to the branch, 1 represents that the nodes are power supply nodes of the branch, and-1 represents that the nodes are load nodes of the branch.
Further, the method for determining the forward-push substitution sequence of each phase in the step d) is as follows:
d-1) establishing a null vector S eq The vector dimension is equal to the branch number;
d-2) in the branchNode association matrix M bna 、M bnb 、M bnc Starting from the first column, judging whether the sum of the columns is-1, if so, searching the row where the element-1 in the column is located, setting all non-zero elements in the row to zero, and filling the branch number corresponding to the row into the vector S eq If not, continuing to carry out next column judgment until all columns are completed;
d-3) judging the branch-node association matrix M bna 、M bnb 、M bnc If the matrix is 0, repeating the step d-2) if the matrix is not 0, and ending the operation if the matrix is 0.
Further, the method for forming the branch association direction matrix in the step e) includes:
e-1) R is abc Representing an association direction matrix among three-phase lines, wherein the number of lines of the matrix is equal to the number of branches, and the number of columns is 3;
e-2) starting from the first branch, through the A-phase branch-node correlation matrix M bna And B-phase branch-node association matrix M bnb Judging whether the first node and the last node of the A phase and the B phase of the branch are the same, if so, the branch is in R abc The first column of the corresponding row is set to 1, if the first node and the last node of the A phase and the B phase of the branch are opposite, the branch is arranged at R abc The first column of the corresponding row in the branch is set to be-1, if the first node and the last node of the A phase and the B phase of the branch are neither identical nor opposite, the branch is arranged at R abc The first column of the corresponding row is set to 0;
e-3) starting from the first branch, through the B-phase branch-node correlation matrix M bnb And C-phase branch-node association matrix M bnc Judging whether the first node and the last node of the B phase and the C phase of the branch are the same, if so, the branch is in R abc The second column of the corresponding row is set to 1, if the head node and the tail node of the B phase and the C phase of the branch are opposite, the branch is arranged at R abc The second column of the corresponding row is set to-1, if the first node and the last node of the B phase and the C phase of the branch are neither identical nor opposite, the branch is at R abc The second column of the corresponding row is set to 0;
e-4) starting from the first branch, through the C-phase branch-sectionPoint association matrix M bnc And A-phase branch-node association matrix M bna Judging whether the first node and the last node of the C phase and the A phase of the branch are the same, if so, the branch is in R abc The third column of the corresponding row is set to 1, if the first node and the last node of the C phase and the A phase of the branch are opposite, the branch is arranged at R abc The third column of the corresponding row is set to-1, if the first node and the last node of the B phase and the C phase of the branch are neither identical nor opposite, the branch is at R abc The third column of the corresponding row is set to 0;
e-5) repeating steps e-2) to e-4) for each branch until all branches are processed.
Further, the step f) includes the steps of:
f-1) is represented by the formulaCalculating to obtain the i-th branch end apparent power S i S in the formula i,load Load power for the i-th branch end node, S t Apparent power for the ith branch downstream, the tth adjacent branch, n b The number of adjacent branches downstream of the ith branch;
f-2) passing through the formulaCalculating the current of the ith branch>In->Is the i-th branch end node voltage;
f-3) passing through the formula
Iteratively calculating the i-th branch end node voltage, whereFor the voltage of the initial end node of the ith branch, P (i, 5) is the data of the ith row and the 5 th column in the branch parameter matrix P, P (i, 8) is the data of the ith row and the 8 th column in the branch parameter matrix P, R abc (i, 1) is an associated direction matrix R abc Data of the ith row and the 1 st column in the branch parameter matrix P, P (i, 9) is data of the ith row and the 9 th column in the branch parameter matrix P, R abc (i, 2) is an associated direction matrix R abc Data of the ith row and the 2 nd column in the branch parameter matrix P, P (i, 10) is data of the ith row and the 10 th column in the branch parameter matrix P, R abc (i, 3) is an associated direction matrix R abc Data of the ith row and the 3 rd column;
f-4) passing through the formulaIteratively calculating the i-th branch end apparent power, < +.>Is->Conjugation of (2);
f-5) passing through the formulaCalculating the difference between the node voltage and the last voltage after iteration, wherein delta is the real part of the voltage, delta is the imaginary part of the voltage, and V i t Is->T-th iteration of V i t-1 Is->T-1 th iteration of (2);
f-6) determining whether or not it satisfiesIf not, repeating step f-1), if yes, ending the calculation, V set Is a convergence standard value。
The beneficial effects of the invention are as follows: based on the forward-push back design, the conditions of three-phase parameter imbalance and three-phase topology imbalance are simultaneously considered in the calculation process, so that the accurate calculation of the power flow is realized, and an accurate basic calculation tool can be provided for advanced functions of power flow calculation such as power distribution system topology reconstruction and power distribution network reactive power optimization.
Detailed Description
The present invention will be further described below.
A three-phase asymmetric power distribution network power flow calculation method comprises the following steps:
a) Acquiring parameters of a power distribution system and a topology structure of the power distribution system;
b) Forming a branch parameter matrix P according to the acquired power distribution system parameters;
c) Forming a branch-node association matrix of each item;
d) Determining a push-forward substitution sequence of each phase;
e) Forming a branch association direction matrix;
f) And calculating to obtain the power flow parameters of the power distribution network and iteratively calculating until convergence conditions are met.
The method is suitable for load flow calculation of the three-phase asymmetric distribution network. The power distribution network is different from a high-voltage power transmission network, three phases of the power distribution network have unbalance phenomenon, the three phases are generally simplified into a symmetrical system when the power flow of the power distribution network is calculated at present, and a forward-push back substitution method is adopted to calculate only one phase, so that the calculated amount is reduced, but the accuracy of a calculation result is not high. Based on forward-push back design, the method simultaneously considers the conditions of three-phase parameter imbalance and three-phase topology imbalance in the calculation process, realizes accurate calculation of power flow, and can provide an accurate basic calculation tool for advanced functions of power flow calculation such as power distribution system topology reconstruction, power distribution network reactive power optimization and the like.
Example 1:
the obtaining of the power distribution system parameters in the step a) comprises the following steps: the self impedance and the trans impedance of each branch and the load value of each load node.
Example 2:
the obtaining of the topology of the power distribution system in step a) comprises: the system nodes and the branches are numbered according to distribution of the topological structure of the power distribution system, the power supply point is numbered 1, the numbers of other n system nodes are respectively n+1, the numbers of branches close to the power supply point are respectively 1, and the numbers of other m branches are respectively m+1. The nodes refer to power points and branch point-and-click load points in the system, and the branches are lines among the nodes.
Example 3:
in the step b), the 1 st column of the branch parameter matrix P is the branch number, the 2 nd to 4 th columns are A, B, C phase loads of the branch end nodes respectively, the 5 th to 7 th columns are A, B, C phase self-impedances respectively, and the 8 th to 10 th columns are mutual impedances of AB, BC and CA phases respectively.
Example 4:
in step c), three phases form branch-node associated matrix M respectively bna 、M bnb 、M bnc Branch-node association matrix M bna 、M bnb 、M bnc All branches of the behavior in (a) are arranged in ascending order according to branch numbers, and a branch-node association matrix M bna 、M bnb 、M bnc All nodes are arranged in ascending order of node numbers, elements in the matrix are 0, 1, -1,0 indicates that the nodes are irrelevant to the branch, 1 indicates that the nodes are power supply (upstream) nodes of the branch, and-1 indicates that the nodes are load (downstream) nodes of the branch.
Example 5:
the method for determining the forward-push substitution sequence of each phase in the step d) is as follows:
d-1) establishing a null vector S eq The vector dimension is equal to the branch number;
d-2) correlation matrix M between branches and nodes bna 、M bnb 、M bnc Starting from the first column, judging whether the sum of the columns is-1, if so, searching the row where the element-1 in the column is located, setting all non-zero elements in the row to zero, and filling the branch number corresponding to the row into the vector S eq If not, continuing to carry out next column judgment until all columns are completed;
d-3) judging the branch-node association matrix M bna 、M bnb 、M bnc Whether or not it is 0 matrixAnd (3) repeating the step d-2) if the matrix is not 0, and ending the operation if the matrix is 0. S is S eq The sequence of the middle branch number is the sequence of the forward pushing process, and the reverse substitution sequence is opposite.
Example 6:
the method for forming the branch association direction matrix in the step e) comprises the following steps:
e-1) R is abc Representing an association direction matrix among three-phase lines, wherein the number of lines of the matrix is equal to the number of branches, and the number of columns is 3;
e-2) starting from the first branch, through the A-phase branch-node correlation matrix M bna And B-phase branch-node association matrix M bnb Judging whether the first node and the last node of the A phase and the B phase of the branch are the same, if so, the branch is in R abc The first column of the corresponding row is set to 1, if the first node and the last node of the A phase and the B phase of the branch are opposite, the branch is arranged at R abc The first column of the corresponding row in the branch is set to be-1, if the first node and the last node of the A phase and the B phase of the branch are neither identical nor opposite, the branch is arranged at R abc The first column of the corresponding row is set to 0;
e-3) starting from the first branch, through the B-phase branch-node correlation matrix M bnb And C-phase branch-node association matrix M bnc Judging whether the first node and the last node of the B phase and the C phase of the branch are the same, if so, the branch is in R abc The second column of the corresponding row is set to 1, if the head node and the tail node of the B phase and the C phase of the branch are opposite, the branch is arranged at R abc The second column of the corresponding row is set to-1, if the first node and the last node of the B phase and the C phase of the branch are neither identical nor opposite, the branch is at R abc The second column of the corresponding row is set to 0;
e-4) starting from the first branch, through the C-phase branch-node correlation matrix M bnc And A-phase branch-node association matrix M bna Judging whether the first node and the last node of the C phase and the A phase of the branch are the same, if so, the branch is in R abc The third column of the corresponding row is set to 1, if the first node and the last node of the C phase and the A phase of the branch are opposite, the branch is arranged at R abc The third column of the corresponding row is set to-1 if the branch B-phase and C-phaseThe first node and the last node are neither identical nor opposite, then the branch is at R abc The third column of the corresponding row is set to 0;
e-5) repeating steps e-2) to e-4) for each branch until all branches are processed.
Example 7:
the step f) comprises the following steps:
f-1) is represented by the formulaCalculating to obtain the i-th branch end apparent power S i S in the formula i,load Load power for the i-th branch end node, S t Apparent power for the ith branch downstream, the tth adjacent branch, n b The number of adjacent branches downstream of the ith branch;
f-2) passing through the formulaCalculating the current of the ith branch>In->Is the i-th branch end node voltage;
f-3) passing through the formula
Iteratively calculating the i-th branch end node voltage, whereFor the voltage of the initial end node of the ith branch, P (i, 5) is the data of the ith row and the 5 th column in the branch parameter matrix P, P (i, 8) is the data of the ith row and the 8 th column in the branch parameter matrix P, R abc (i, 1) is an associated direction matrix R abc The data of the ith row and the 1 st column in the matrix P is that P (i, 9) is the ith row and the 1 st column in the branch parameter matrix PData of 9 columns, R abc (i, 2) is an associated direction matrix R abc Data of the ith row and the 2 nd column in the branch parameter matrix P, P (i, 10) is data of the ith row and the 10 th column in the branch parameter matrix P, R abc (i, 3) is an associated direction matrix R abc Data of the ith row and the 3 rd column;
f-4) passing through the formulaIteratively calculating the i-th branch end apparent power, < +.>Is->Conjugation of (2);
f-5) passing through the formulaCalculating the difference between the node voltage and the last voltage after iteration, wherein delta is the real part of the voltage, delta is the imaginary part of the voltage, and V i t Is->T-th iteration of V i t-1 Is->T-1 th iteration of (2);
f-6) determining whether or not it satisfiesIf not, repeating step f-1), if yes, ending the calculation, V set Is a convergence standard value.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. The power flow calculation method of the three-phase asymmetric power distribution network is characterized by comprising the following steps of:
a) Acquiring parameters of a power distribution system and a topology structure of the power distribution system;
b) Forming a branch parameter matrix P according to the acquired power distribution system parameters;
c) Forming a branch-node association matrix of each item;
d) Determining a push-forward substitution sequence of each phase;
e) Forming a branch association direction matrix;
f) Calculating to obtain power flow parameters of the power distribution network and iteratively calculating until convergence conditions are met;
the method for forming the branch association direction matrix in the step e) comprises the following steps:
e-1) R is abc Representing an association direction matrix among three-phase lines, wherein the number of lines of the matrix is equal to the number of branches, and the number of columns is 3;
e-2) starting from the first branch, through the A-phase branch-node correlation matrix M bna And B-phase branch-node association matrix M bnb Judging whether the first node and the last node of the A phase and the B phase of the branch are the same, if so, the branch is in R abc The first column of the corresponding row is set to 1, if the first node and the last node of the A phase and the B phase of the branch are opposite, the branch is arranged at R abc The first column of the corresponding row in the branch is set to be-1, if the first node and the last node of the A phase and the B phase of the branch are neither identical nor opposite, the branch is arranged at R abc The first column of the corresponding row is set to 0;
e-3) starting from the first branch, through the B-phase branch-node correlation matrix M bnb And C-phase branch-node association matrix M bnc Judging whether the first node and the last node of the B phase and the C phase of the branch are the same, if so, the branch is in R abc The second column of the corresponding row is set to 1, if the first node and the last node of the B phase and the C phase of the branch areConversely, then the branch is at R abc The second column of the corresponding row is set to-1, if the first node and the last node of the B phase and the C phase of the branch are neither identical nor opposite, the branch is at R abc The second column of the corresponding row is set to 0;
e-4) starting from the first branch, through the C-phase branch-node correlation matrix M bnc And A-phase branch-node association matrix M bna Judging whether the first node and the last node of the C phase and the A phase of the branch are the same, if so, the branch is in R abc The third column of the corresponding row is set to 1, if the first node and the last node of the C phase and the A phase of the branch are opposite, the branch is arranged at R abc The third column of the corresponding row is set to-1, if the first node and the last node of the B phase and the C phase of the branch are neither identical nor opposite, the branch is at R abc The third column of the corresponding row is set to 0;
e-5) repeating steps e-2) to e-4) for each branch until all branches are processed;
the step f) comprises the following steps:
f-1) is represented by the formulaCalculating to obtain the i-th branch end apparent power S i S in the formula i,load Load power for the i-th branch end node, S t Apparent power for the ith branch downstream, the tth adjacent branch, n b The number of adjacent branches downstream of the ith branch;
f-2) passing through the formulaCalculating the current of the ith branch>In->Is the i-th branch end node voltage;
f-3) passing through the formula
Iteratively calculating the i-th branch end node voltage, whereFor the voltage of the initial end node of the ith branch, P (i, 5) is the data of the ith row and the 5 th column in the branch parameter matrix P, P (i, 8) is the data of the ith row and the 8 th column in the branch parameter matrix P, R abc (i, 1) is an associated direction matrix R abc Data of the ith row and the 1 st column in the branch parameter matrix P, P (i, 9) is data of the ith row and the 9 th column in the branch parameter matrix P, R abc (i, 2) is an associated direction matrix R abc Data of the ith row and the 2 nd column in the branch parameter matrix P, P (i, 10) is data of the ith row and the 10 th column in the branch parameter matrix P, R abc (i, 3) is an associated direction matrix R abc Data of the ith row and the 3 rd column;
f-4) passing through the formulaIteratively calculating the i-th branch end apparent power, < +.>Is->Conjugation of (2); f-5) by the formula->Calculating the difference between the node voltage and the last voltage after iteration, wherein delta is the real part of the voltage, delta is the imaginary part of the voltage, and V i t Is->Is t-th iteration of->Is->T-1 th iteration of (2);
f-6) determining whether or not it satisfiesIf not, repeating step f-1), if yes, ending the calculation, V set Is a convergence standard value.
2. The method for calculating power flow of a three-phase asymmetric power distribution network according to claim 1, wherein the obtaining of the power distribution system parameters in step a) includes: the self impedance and the trans impedance of each branch and the load value of each load node.
3. The method for calculating the power flow of a three-phase asymmetric power distribution network according to claim 2, wherein the obtaining of the topology of the power distribution system in step a) includes: the system nodes and the branches are numbered according to distribution of the topological structure of the power distribution system, the power supply point is numbered 1, the numbers of other n system nodes are respectively n+1, the numbers of branches close to the power supply point are respectively 1, and the numbers of other m branches are respectively m+1.
4. A three-phase asymmetric power distribution network power flow calculation method according to claim 3, characterized in that: in the step b), the 1 st column of the branch parameter matrix P is the branch number, the 2 nd to 4 th columns are A, B, C phase loads of the branch end nodes respectively, the 5 th to 7 th columns are A, B, C phase self-impedances respectively, and the 8 th to 10 th columns are mutual impedances of AB, BC and CA phases respectively.
5. The method for power flow calculation of a three-phase asymmetric power distribution network according to claim 1, wherein in step c), three phases form a branch-node correlation matrix M, respectively bna 、M bnb 、M bnc Branch-node association matrix M bna 、M bnb 、M bnc All branches of the behavior in (a) are arranged in ascending order according to branch numbers, and a branch-node association matrix M bna 、M bnb 、M bnc All the nodes are arranged in ascending order of node numbers, elements in the matrix are 0, 1, -1,0 represents that the nodes are irrelevant to the branch, 1 represents that the nodes are power supply nodes of the branch, and-1 represents that the nodes are load nodes of the branch.
6. The three-phase asymmetric power distribution network power flow calculation method according to claim 5, wherein the steps of
d) The method for determining the forward push substitution sequence of each phase is as follows:
d-1) establishing a null vector S eq The vector dimension is equal to the branch number;
d-2) correlation matrix M between branches and nodes bna 、M bnb 、M bnc Starting from the first column, judging whether the sum of the columns is-1, if so, searching the row where the element-1 in the column is located, setting all non-zero elements in the row to zero, and filling the branch number corresponding to the row into the vector S eq If not, continuing to carry out next column judgment until all columns are completed;
d-3) judging the branch-node association matrix M bna 、M bnb 、M bnc If the matrix is 0, repeating the step d-2) if the matrix is not 0, and ending the operation if the matrix is 0.
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