CN113381402B - Node level dispersion method for obtaining minimum state power flow of alternating current power system - Google Patents

Node level dispersion method for obtaining minimum state power flow of alternating current power system Download PDF

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CN113381402B
CN113381402B CN202110599975.0A CN202110599975A CN113381402B CN 113381402 B CN113381402 B CN 113381402B CN 202110599975 A CN202110599975 A CN 202110599975A CN 113381402 B CN113381402 B CN 113381402B
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彭建春
吴鸣寰
江辉
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    • H—ELECTRICITY
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Abstract

A node level dispersion method for obtaining minimum state power flow of an alternating current power system belongs to the field of power engineering, and comprises the steps of firstly, establishing a linear asymptotic equation of node power balance according to the known structure and parameters of the alternating current power system; establishing a quadratic programming model of the minimum state power flow of the alternating current power system according to the linear asymptotic equation and the node voltage; establishing a Lagrange function according to a quadratic programming model; and establishing a node level dispersion iteration formula according to a Lagrange function, and then obtaining the minimum state power flow of the alternating current power system according to the node level dispersion iteration formula. The method enables the solving result of the minimum state power flow of the alternating current power system to be unique and globally optimal, and avoids the defect that the global optimality of the solution of the state power flow in the traditional method is not guaranteed; meanwhile, the solution of the minimum state power flow of the alternating current power system is node-level dispersion and power private information of passive load is leaked.

Description

Node level dispersion method for obtaining minimum state power flow of alternating current power system
Technical Field
The application relates to the field of power engineering, in particular to a node level dispersion method for obtaining minimum state power flow of an alternating current power system.
Background
The state flow of an ac power system is the basis for determining its control reference. At present, the voltage value of the balance node is obtained by intensively solving a nonlinear node power balance equation set based on the artificially given voltage value of the balance node, although the obtaining is reliable, the artificially given voltage value of the balance node cannot ensure that the whole system operates in a state of minimum deviation voltage rated value, and the defect of low working efficiency of equipment is caused; the method is obtained by intensively constructing and solving an optimization model with a nonlinear node power balance equation system as a constraint, but the constraint nonlinearity causes the defect that the global optimality of a state load flow solution is not guaranteed. Meanwhile, the methods need centralized calculation, so that power private data of source load needs to be collected, and the defect of leakage of private information of the source load is caused.
Disclosure of Invention
The embodiment of the application provides a node-level dispersion method for acquiring the minimum state power flow of an alternating current power system, which can solve the problems of low equipment working efficiency, no guarantee on the global optimality of a solution of the state power flow and leakage of power private information of source load in the traditional method for acquiring the minimum state power flow of the alternating current power system.
A first aspect of an embodiment of the present application provides a node-level decentralized method for acquiring a minimum state power flow of an ac power system, including:
according to the known structure and parameters of the alternating current power system, a linear asymptotic equation of node power balance is established;
establishing a quadratic programming model of the minimum state power flow of the alternating current power system according to the linear asymptotic equation and the node voltage;
establishing a Lagrange function according to the quadratic programming model;
and establishing a node level dispersion iteration formula according to the Lagrangian function, and then obtaining the minimum state power flow of the alternating current power system according to the node level dispersion iteration formula.
A second aspect of embodiments of the present application provides a computer-readable storage medium, which stores a computer program, which when executed by a processor, implements the steps of the above node-level decentralized method for acquiring minimum state power flow of an ac power system.
A third aspect of the embodiments of the present application provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements the steps of the above node-level decentralized method for acquiring minimum state power flow of an ac power system when executing the computer program.
Compared with the prior art, the embodiment of the application has the beneficial effects that: the minimum state tide of the alternating current power system is obtained, so that the working efficiency of the equipment is improved; because a quadratic programming model of the minimum state power flow of the alternating current power system is established by adopting a linear asymptotic equation, the solving result of the minimum state power flow of the alternating current power system is unique and globally optimal, and the defect that the global optimality of the solution of the state power flow is not guaranteed is avoided; meanwhile, because a node level dispersion iterative formula is established, the solving of the minimum state load flow of the alternating current power system is node level dispersion and power private information leakage of passive load.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a flowchart of an implementation of a node-level decentralized method for acquiring a minimum state power flow of an ac power system according to an embodiment of the present application;
FIG. 2 is a schematic structural diagram of a common model of an AC power system according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a terminal device according to an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Referring to fig. 1, fig. 1 is a flowchart of an implementation of a node-level decentralized method for obtaining a minimum state power flow of an ac power system according to an embodiment of the present invention. The node-level decentralized method for obtaining the minimum state power flow of the alternating current power system as shown in the figure can comprise the following steps:
in step 101, a linear asymptotic equation for the node power balance is established based on known configurations and parameters of the ac power system.
In a specific implementation, step 101 may include step a1 and step B1.
In step a1, according to the branch admittance parameter of the ac power system, the voltage amplitude at the two ends of the branch, and the voltage phase angle at the two ends of the branch, a linear asymptotic expression of the branch transmission power is established by applying the electric power definitional formula and removing the coupling term therein:
Pij＝αijVi+βijVj+γijθi+δijθj
Figure BDA0003092387520000031
wherein, PijActive power transmitted for branch ij; qijThe reactive power transmitted for branch ij; i and j are serial numbers of nodes in the alternating current power system, and belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of nodes in the alternating current power system; gijIs the conductance parameter of branch ij; bijIs the susceptance parameter of branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of node i; vjIs the voltage magnitude variable of node j; thetajIs the voltage phase angle variable of node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha (alpha) ("alpha")ijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of the branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 nd modified admittance of determined branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd corrected admittance of the branch ij; deltaijIs according to deltaij＝bijViVj[ 3 ] determinationThe 4 th modified admittance of branch ij;
Figure BDA0003092387520000041
is according to
Figure BDA0003092387520000042
Figure BDA0003092387520000043
A 5 th modified admittance of the determined leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of leg ij determined; chi shapeijIs according to chiij＝-gijViVj3 determining the 7 th corrected admittance of the branch ij; psiijIs according to psiij＝gijViVj(ii)/3 an 8 th modified admittance of branch ij; viAnd VjAre voltage per unit. gijAnd bijAre known power system parameters.
By transforming the non-linear electric power definitional expression into a linear asymptotic expression, the problem that an optimization planning model using a non-linear equation as a constraint is difficult to solve is avoided.
In step B1, according to the linear asymptotic expression and the branch connection structure of the ac power system, a linear asymptotic equation of the power balance of the node i is established as follows according to Kirchhoff's current law:
Figure BDA0003092387520000044
Figure BDA0003092387520000045
wherein, PGiIs the active power parameter of the power supply connected to node i; qGiReactive power of power supply connected to node iA parameter; pDiAn active power parameter for a load connected to node i; qDiIs the reactive power parameter of the load connected to node i. QGi、QDi、PGiAnd PDiAre known power system parameters.
The linear asymptotic equation for the node power balance is a linear equation with respect to the node voltage amplitude and the phase angle, and approaches the true value as the node voltage amplitude and the phase angle approach, approaching the exact node power balance equation obtained according to the electric power definition and Kirchhoff's law of current. This is because the above-described linear asymptotic equation is referred to as a linear asymptotic equation for node power balance.
In step 102, a quadratic programming model of the minimum state power flow of the alternating current power system is established according to the linear asymptotic equation and the node voltage.
Step 102 comprises: and establishing a quadratic programming model of the minimum state power flow of the alternating current power system by taking a linear asymptotic equation as a constraint and taking the minimum sum of the squares of the offset of the node voltage amplitude relative to 1 and the square sum of the phase angle of the node voltage as an objective function:
Figure BDA0003092387520000051
Figure BDA0003092387520000052
Figure BDA0003092387520000053
and the node numbered n is an alternating current power system power balance node. i and j are serial numbers of nodes in the alternating current power system, and belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of nodes in the alternating current power system; gijIs the conductance parameter of branch ij; bijIs the susceptance parameter of branch ij; viIs the voltage amplitude variable of node i; theta.theta.iIs the voltage phase angle variable of node i; vjIs the voltage magnitude variable of node j; thetajIs the voltage phase angle variable of node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 the 1 st modified admittance of the determined branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 nd modified admittance of determined branch ij; gamma rayijIs according to gammaij＝-bijViVj3 the 3 rd modified admittance of the determined branch ij; deltaijIs according to deltaij＝bijViVj3 determining the 4 th corrected admittance of the branch ij;
Figure BDA0003092387520000054
is according to
Figure BDA0003092387520000055
Figure BDA0003092387520000056
A 5 th modified admittance of the determined branch ij; phi is aijIs in accordance with phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi3 the 6 th modified admittance of the determined branch ij; chi shapeijIs according to chiij＝-gijViVj3 determining the 7 th corrected admittance of the branch ij; psiijIs according to psiij＝gijViVj(ii)/3 an 8 th modified admittance of branch ij; viAnd VjAre voltage per unit. PGiIs the active power parameter of the power supply connected to node i; qGiA reactive power parameter for a power supply connected to node i; pDiAn active power parameter for a load connected to node i; qDiIs the reactive power parameter of the load connected to node i. g is a radical of formulaij、bij、QGi、QDi、PGiAnd PDiAre known power system parameters.
By the quadratic programming model, under the constraint of a linear asymptotic equation which meets the node power balance, the node voltage amplitude value is stably changed, and the node voltage phase angle is minimum.
The quadratic term coefficients of the objective function in the quadratic programming model are all larger than zero, so the quadratic term coefficients are convex functions, and the constraint condition is a linear equation, so the quadratic programming model is convex quadratic programming. According to the optimization theory, the local optimal solution is only and is the global optimal solution. Therefore, the stagnation point of the lagrangian function of the quadratic programming model is the only globally optimal solution.
In step 103, a lagrangian function is established according to a quadratic programming model.
Step 103 comprises: according to a quadratic programming model, the following Lagrangian function is established according to the definition of the Lagrangian function.
Figure BDA0003092387520000061
Wherein the content of the first and second substances,
Figure BDA0003092387520000062
is the lagrange function; lambda [ alpha ]iA Lagrange multiplier of an active power balance equation corresponding to the node i; xiiLagrange multipliers for the reactive power balance equations of the corresponding node i; the node numbered n is an ac power system power balance node. i and j are serial numbers of nodes in the alternating current power system, and belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of nodes in the alternating current power system; gijIs the conductance parameter of branch ij; bijAs a branch ij of a susceptanceCounting; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of node i; vjIs the voltage magnitude variable of node j; thetajIs the voltage phase angle variable of node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of the branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 nd modified admittance of determined branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd corrected admittance of the branch ij; deltaijIs according to deltaij＝bijViVj3 determining the 4 th corrected admittance of the branch ij;
Figure BDA0003092387520000063
is according to
Figure BDA0003092387520000064
Figure BDA0003092387520000065
A 5 th modified admittance of the determined leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of leg ij determined; chi shapeijIs according to chiij＝-gijViVj3 determining the 7 th corrected admittance of the branch ij; psiijIs according to psiij＝gijViVj[ 3 ] determined branchThe 8 th modified admittance of way ij; viAnd VjAre voltage per unit. PtiIs the active power parameter of the power supply connected to node i; qGiA reactive power parameter for a power supply connected to node i; pDiAn active power parameter for a load connected to node i; qDiIs the reactive power parameter of the load connected to node i. gij、bij、QGi、QDi、PGiAnd PDiAre known power system parameters.
In step 104, a node-level decentralized iterative formula is established according to the lagrangian function, and then the minimum state power flow of the alternating current power system is obtained according to the node-level decentralized iterative formula.
In particular implementations, step 104 may include step A2 and step B2.
In step a2, according to the lagrange function, the following set of stagnation point equations is established according to the definition of the stagnation point:
Figure BDA0003092387520000071
wherein the content of the first and second substances,
Figure BDA0003092387520000072
is the lagrange function; lambda [ alpha ]iA Lagrange multiplier of an active power balance equation corresponding to the node i; xiiLagrange multipliers for the reactive power balance equations of the corresponding node i; the node numbered n is an ac power system power balance node. i and j are serial numbers of nodes in the alternating current power system, and belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of nodes in the alternating current power system; gijIs the conductance parameter of branch ij; bijIs the susceptance parameter of branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of node i; vjIs the voltage magnitude variable of node j; thetajIs the voltage phase angle variable of node j; xiijIs according to xiij＝sinθij-θi+θjAdmittance of determined branch ijA correction factor; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of the branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 nd modified admittance of determined branch ij; gamma rayijIs according to gammaij＝-bijViVf3 determining the 3 rd corrected admittance of the branch ij; delta. for the preparation of a coatingijIs according to deltaij＝bijViVj3 determining the 4 th corrected admittance of the branch ij;
Figure BDA0003092387520000073
is according to
Figure BDA0003092387520000074
Figure BDA0003092387520000081
A 5 th modified admittance of the determined leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of leg ij determined; chi shapeijIs according to chiij＝-gijViVj3 determining the 7 th corrected admittance of the branch ij; psiijIs according to psiij＝gijViVj3 the 8 th modified admittance of the determined branch ij; viAnd VjAre voltage per unit. PGiIs the active power parameter of the power supply connected to node i; qGiA reactive power parameter for a power supply connected to node i; pDiAn active power parameter for a load connected to node i; qDiFor loads connected to node iA reactive power parameter; gij、bij、QGi、QDi、PGiAnd PDiAre known power system parameters.
And solving the stationary point equation set to obtain the value of each variable when the target function takes the minimum value.
In step B2, based on the stagnation equation set, the following node-level decentralized iterative formula is established, and then the minimum state power flow of the ac power system is obtained according to the node-level decentralized iterative formula:
Figure BDA0003092387520000082
wherein, (t +1) represents the iteration result of the t +1 step; (t) representing the iteration result of the t step; sigma is an inertia parameter which is more than 0 and less than 1; omegaiIs the number set of all the neighbor nodes of the node with the number i; omeganIs the number set of all neighbor nodes of the node numbered n.
And (4) carrying out iterative calculation according to the node level dispersion iterative formula until convergence, wherein the vector formed by the final solution of the voltages of all nodes of the obtained alternating current power system is the vector representing the minimum state power flow of the alternating current power system. Therefore, the node level dispersion acquisition of the minimum state power flow of the alternating current power system is realized.
Step B2 converts the continuous equation set (stagnation equation set) into a discrete iterative expression (node-level discrete iterative formula) according to the control theory. Calculating theta of the node with the number i according to the node level dispersion iterative formulai、Vi、λiAnd xiiThen, only the number is required to belong to the set ΩiThe voltage amplitude and the phase angle of the node (namely, only the neighbor node is needed) and the Lagrange multiplier, and source load power private data of the neighbor node are not needed. Calculating thetanAnd VnThe same applies to the case. Therefore, the node level dispersion iterative formula is node level dispersion, and source load power private information of the neighbor nodes is not leaked. The method is just called as the section for acquiring the minimum state power flow of the alternating current power systemThe reason of the point level dispersion method.
According to the embodiment of the application, firstly, a linear asymptotic equation of node power balance is established according to the known structure and parameters of an alternating current power system; establishing a quadratic programming model of the minimum state power flow of the alternating current power system according to the linear asymptotic equation and the node voltage; establishing a Lagrange function according to a quadratic programming model; and establishing a node level dispersion iteration formula according to a Lagrange function, and then obtaining the minimum state power flow of the alternating current power system according to the node level dispersion iteration formula. The minimum state tide of the alternating current power system is obtained, so that the working efficiency of the equipment is improved; because a quadratic programming model of the minimum state power flow of the alternating current power system is established by adopting a linear asymptotic equation, the solving result of the minimum state power flow of the alternating current power system is unique and globally optimal, and the defect that the global optimality of the solution of the state power flow is not guaranteed is avoided; meanwhile, because a node level dispersion iterative formula is established, the solving of the minimum state load flow of the alternating current power system is node level dispersion and power private information leakage of passive load.
A second aspect of the embodiments of the present application provides a computer-readable storage medium, which stores a computer program, and the computer program, when executed by a processor, implements the steps of the above node-level decentralized method for acquiring minimum state power flow of an ac power system.
Fig. 3 is a schematic diagram of a terminal device provided in a third aspect of an embodiment of the present application. The terminal device 3 of this embodiment includes: a processor 30, a memory 31 and a computer program 32 stored in the memory 31 and executable on the processor 30, wherein the processor 30 executes the computer program 32 to implement the steps of the above-mentioned node-level decentralized method embodiment of obtaining a minimum state power flow of an ac power system, such as the steps 101 to 104 shown in fig. 1. It will be understood by those skilled in the art that fig. 3 is merely an example of the terminal device 3 and does not constitute a limitation of the terminal device 3. The terminal device 3 includes, but is not limited to, a processor 30, a memory 31, and a computer program 32 stored in the memory 31 and operable on the processor 30, for example, the terminal device is a server, a computer, a palm computer, and a combination of the input output device and the network access device, which have the computer program 32 stored on its own memory or on an external removable memory.
The above-mentioned embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the exemplary embodiments of the present application and are intended to be included within the scope of the present application.

Claims (3)

1. A node-level dispersion method for obtaining the minimum state power flow of an alternating current power system is characterized by comprising the following steps:
according to the known structure and parameters of the alternating current power system, a linear asymptotic equation of node power balance is established;
establishing a quadratic programming model of the minimum state power flow of the alternating current power system according to the linear asymptotic equation and the node voltage;
establishing a Lagrange function according to the quadratic programming model;
establishing a node level dispersion iteration formula according to the Lagrangian function, and then obtaining the minimum state power flow of the alternating current power system according to the node level dispersion iteration formula;
the linear asymptotic equation for establishing the node power balance according to the known structure and parameters of the alternating current power system comprises:
according to the branch admittance parameters of the alternating current power system, the voltage amplitudes at two ends of the branch and the voltage phase angles at two ends of the branch, an electric power definition formula is applied, and coupling terms in the electric power definition formula are removed, so that the following linear asymptotic expression of the branch transmission power is established:
Pij＝αijVi+βijVj+γijθi+δijθj
Figure FDA0003534875240000011
wherein, PijActive power transmitted for branch ij; qijThe reactive power transmitted for the branch ij; i and j are serial numbers of nodes in the alternating current power system, and both belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of the nodes in the alternating current power system; gijIs the conductance parameter of the branch ij; bijIs the susceptance parameter of said branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of the node i; vjIs the voltage magnitude variable of node j; thetajIs a voltage phase angle variable of the node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of said branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 determining the 2 nd modified admittance of the branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd modified admittance of the branch ij; deltaijIs according to deltaij＝bijViVj3 determining the 4 th modified admittance of said branch ij;
Figure FDA0003534875240000021
is according to
Figure FDA0003534875240000022
Determining a 5 th modified admittance of said leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of said branch ij determined; chi shapeijIs according to chiij＝-gijViVj(ii)/3 determining a 7 th modified admittance of said branch ij; psiijIs in accordance with psiij＝gijViVj(iv) the 8 th modified admittance of said branch ij determined; the V isiAnd said VjAre voltage per unit value;
according to the linear asymptotic expression and a branch connection structure of the alternating current power system, establishing a linear asymptotic equation of the power balance of the node i according to a Kirchhoff current law as follows:
Figure FDA0003534875240000023
Figure FDA0003534875240000024
wherein, PGiIs an active power parameter of a power supply connected to the node i; qGiA reactive power parameter for a power source connected to the node i; pDiAn active power parameter for a load connected to the node i; qDiA reactive power parameter for a load connected to the node i;
the establishing of the quadratic programming model of the minimum state power flow of the alternating current power system according to the linear asymptotic equation and the node voltage comprises the following steps:
establishing a quadratic programming model of the minimum state power flow of the alternating current power system by taking the linear asymptotic equation as a constraint and taking the minimum sum of squares of the offset of the node voltage amplitude relative to 1 and the square sum of the phase angle of the node voltage as an objective function, wherein the quadratic programming model comprises the following components:
Figure FDA0003534875240000025
Figure FDA0003534875240000026
Figure FDA0003534875240000027
the node numbered n is a power balance node of the alternating current power system; i and j are numbers of nodes in the alternating current power system, and belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of the nodes in the alternating current power system; gijIs the conductance parameter of the branch ij; bijIs the susceptance parameter of said branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of the node i; vjIs the voltage magnitude variable of node j; thetajIs a voltage phase angle variable of the node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha (alpha) ("alpha")ijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of said branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 determining the 2 nd modified admittance of the branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd modified admittance of the branch ij; deltaijIs according to deltaij＝bijViVj(ii)/3 determining a 4 th modified admittance of said branch ij;
Figure FDA0003534875240000031
is according to
Figure FDA0003534875240000032
Determining a 5 th modified admittance of said leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi3 the 6 th modified admittance of said branch ij; chi shapeijIs according to chiij＝-gijViVj(ii)/3 determining a 7 th modified admittance of said branch ij; psiijIs according to psiij＝gijViVj(iii) an 8 th modified admittance of said branch ij determined; the V isiAnd said VjAre voltage per unit value; pGiIs an active power parameter of a power supply connected to the node i; qGiA reactive power parameter for a power source connected to the node i; pDiAn active power parameter for a load connected to the node i; qDiA reactive power parameter for a load connected to the node i;
the establishing of the Lagrangian function according to the quadratic programming model comprises the following steps:
according to the quadratic programming model, establishing a Lagrangian function according to the definition of the Lagrangian function;
Figure FDA0003534875240000033
wherein the content of the first and second substances,
Figure FDA0003534875240000034
is a pullA Grenarian function; lambda [ alpha ]iA Lagrange multiplier of an active power balance equation corresponding to the node i; xiiA lagrange multiplier of a reactive power balance equation corresponding to the node i; the node with the number n is an alternating current power system power balance node; i and j are serial numbers of nodes in the alternating current power system, and both belong to a set of continuous natural numbers {1,2, …, n }; n is the total number of the nodes in the alternating current power system; gijIs the conductance parameter of the branch ij; bijIs the susceptance parameter of said branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of the node i; vjIs the voltage magnitude variable of node j; thetajIs a voltage phase angle variable of the node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of said branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 determining the 2 nd modified admittance of the branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd modified admittance of the branch ij; deltaijIs according to deltaij＝bijViVj(ii)/3 determining a 4 th modified admittance of said branch ij;
Figure FDA0003534875240000041
is according to
Figure FDA0003534875240000042
Figure FDA0003534875240000043
Determining a 5 th modified admittance of said leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of said branch ij determined; chi shapeijIs according to xij＝-gijViVj3 determining the 7 th modified admittance of said branch ij; psiijIs according to psiij＝gijViVj(iii) an 8 th modified admittance of said branch ij determined; the V isiAnd said VjAre voltage per unit value; pGiIs an active power parameter of a power supply connected to the node i; qGiA reactive power parameter for a power source connected to the node i; pDiAn active power parameter for a load connected to the node i; qDiA reactive power parameter for a load connected to the node i;
the establishing a node-level decentralized iterative formula according to the Lagrangian function, and then obtaining the minimum state power flow of the alternating current power system according to the node-level decentralized iterative formula comprises the following steps:
according to the Lagrange function, establishing the following stagnation point equation set according to the definition of stagnation points:
Figure FDA0003534875240000051
wherein the content of the first and second substances,
Figure FDA0003534875240000052
is the lagrange function; lambda [ alpha ]iA Lagrange multiplier of an active power balance equation corresponding to the node i; xiiA lagrange multiplier of a reactive power balance equation corresponding to the node i; the node with the number n is an alternating current power system power balance node; i and j are serial numbers of nodes in the alternating current power system and belong to continuous natural numbersSet of {1,2, …, n }; n is the total number of the nodes in the alternating current power system; gijIs the conductance parameter of the branch ij; b is a mixture ofijIs the susceptance parameter of said branch ij; viIs the voltage amplitude variable of node i; thetaiIs the voltage phase angle variable of the node i; vjIs the voltage magnitude variable of node j; thetajIs a voltage phase angle variable of the node j; xiijIs according to xiij＝sinθij-θi+θjDetermining admittance correction coefficients of the branch ij; alpha is alphaijIs according to alphaij＝gijVi-gijcosθijVj/2-bijVjθi/3+bijVjθj/3-bijVjξij2 determining the 1 st modified admittance of said branch ij; beta is aijIs according to betaij＝-bijViθi/3-Vigijcosθij/2-bijViθj/3+bijViξij2 determining the 2 nd modified admittance of the branch ij; gamma rayijIs according to gammaij＝-bijViVj3 determining the 3 rd modified admittance of the branch ij; deltaijIs according to deltaij＝bijViVj3 determining the 4 th modified admittance of said branch ij;
Figure FDA0003534875240000053
is according to
Figure FDA0003534875240000054
Figure FDA0003534875240000055
Determining a 5 th modified admittance of said leg ij; phi is aijIs according to phiij＝bijcosθijVi/2-gijViθi/3+gijViθj/3-ξijgijVi(vi) a 6 th modified admittance of said branch ij determined; chi shapeijIs according to chiij＝-gijViVj(ii)/3 determining a 7 th modified admittance of said branch ij; psiijIs according to psiij＝gijViVj(iii) an 8 th modified admittance of said branch ij determined; the V isiAnd said VjAre voltage per unit value; pGiIs an active power parameter of a power supply connected to the node i; qGiA reactive power parameter for a power source connected to the node i; pDiAn active power parameter for a load connected to the node i; qDiA reactive power parameter for a load connected to the node i;
based on the stagnation point equation set, the following node level dispersion iterative formula is established, and then the minimum state power flow of the alternating current power system is obtained according to the node level dispersion iterative formula:
Figure FDA0003534875240000061
wherein, (t +1) represents the iteration result of the t +1 step; (t) representing the iteration result of the t step; sigma is an inertia parameter which is more than 0 and less than 1; omegaiIs the number set of all the neighbor nodes of the node with the number i; omeganIs the number set of all neighbor nodes of the node numbered n.
2. A computer-readable storage medium, storing a computer program, which, when being executed by a processor, carries out the steps of the node-level decentralized method of obtaining a minimum state power flow of an ac power system according to claim 1.
3. A terminal device comprising a memory, a processor and a computer program stored in said memory and executable on said processor, characterized in that said processor when executing said computer program implements the steps of the node-level decentralized method of obtaining a minimum state power flow of an ac power system according to claim 1.
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