CN114421483A - Analytic probabilistic power flow calculation method, device and storage medium - Google Patents

Analytic probabilistic power flow calculation method, device and storage medium Download PDF

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CN114421483A
CN114421483A CN202210126978.7A CN202210126978A CN114421483A CN 114421483 A CN114421483 A CN 114421483A CN 202210126978 A CN202210126978 A CN 202210126978A CN 114421483 A CN114421483 A CN 114421483A
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杨银国
陆秋瑜
伍双喜
朱誉
林英明
于珍
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Guangdong Power Grid Co Ltd
Electric Power Dispatch Control Center of Guangdong Power Grid Co Ltd
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Abstract

The invention discloses an analytic probability load flow calculation method, an analytic probability load flow calculation device and a storage medium. According to the method, after the mapping relation between the injection power of the node and the operation state of the power system is determined through the linear power flow model, the operation state of the power system is corrected by adopting a first-order polynomial fitting correction method, so that the corrected operation state of the power system is closer to the real operation state, the linear power flow model is updated according to the mapping relation between the injection power of the node and the corrected operation state of the power system, and the analytic probability power flow calculation is carried out by utilizing the updated linear power flow model, so that the probability power flow calculation precision is effectively improved.

Description

Analytic probabilistic power flow calculation method, device and storage medium
Technical Field
The invention relates to the technical field of power system operation analysis, in particular to an analytic probability load flow calculation method, an analytic probability load flow calculation device and a storage medium.
Background
The large-scale wind power integration can bring non-negligible randomness to a power system. One of the effects of this randomness of injected power during power system operation is that it causes line transmission power fluctuations and even line overload. In order to quantitatively evaluate the line power Flow out-of-limit risk caused by the wind power randomness, a probability power Flow (PLF) calculation method is adopted to analyze the operation condition of the power system after the wind power integration. A commonly used probabilistic power flow calculation Method is Monte Carlo Simulation (MCSM). The biggest disadvantage of the Monte Carlo simulation method is that large-scale sampling data is needed, and the time is long. In order to quickly and accurately perform probability load flow calculation, particularly to calculate the joint probability distribution of power of a plurality of lines, the development of an analytic probability load flow calculation method is urgently required. However, the existing analytic probabilistic power flow calculation method usually only uses a linear power flow model to realize the mapping of the node injection power to the operation state of the power system, is deficient in calculation accuracy, and how to effectively improve the probabilistic power flow calculation accuracy becomes a current research hotspot.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an analytic probability load flow calculation method, an analytic probability load flow calculation device and a storage medium, which can effectively improve the probability load flow calculation precision.
In order to solve the above technical problem, in a first aspect, an embodiment of the present invention provides an analytic probability power flow calculation method, including:
according to the injection power of a node accessed to a power system, constructing a Gaussian mixture model, obtaining a parameter set of the Gaussian mixture model according to historical data of the injection power of the node by adopting an EM (effective electromagnetic range) algorithm, and updating the Gaussian mixture model based on the parameter set;
constructing a linear power flow model according to the conductance and susceptance information of the power system and the injection power of the node, and determining a mapping relation between the injection power of the node and the running state of the power system through the linear power flow model;
correcting the running state of the power system by adopting a first-order polynomial fitting correction method, and updating the linear power flow model according to the mapping relation between the injection power of the node and the corrected running state of the power system;
and mapping the probability distribution of the injection power of the node to the probability distribution of the operation state of the corrected power system through the Gaussian mixture model and the linear power flow model to obtain the probability power flow of the operation state of the power system.
Further, the gaussian mixture model is:
Figure BDA0003500462650000021
wherein, ω isjIs the weight coefficient of the jth Gaussian component, ωj>0，
Figure BDA0003500462650000022
J is the total number of Gaussian components;
Figure BDA0003500462650000023
Nj(. h) is the jth Gaussian component, X is the injection power of the node, μj、σjRespectively, a mean vector and a covariance matrix of the jth gaussian component, W is the dimension of the injection power of the node, det (.) is a matrix determinant, and T represents a transpose of the matrix.
Further, the linear power flow model is:
Figure BDA0003500462650000024
wherein θ and V are the voltage phase angle and the voltage amplitude of the node, P, Q is the active power and the reactive power of the injected power of the node, the subscript R represents the set of nodes V θ, K represents the set of nodes PV and V θ, S represents the set of nodes PV and PQ,
Figure BDA0003500462650000025
representing a set formed by PQ nodes, wherein a V theta node represents a given voltage amplitude and a given voltage phase, active power and reactive power are nodes of a quantity to be solved, a PV node represents a given active power and voltage amplitude, a given reactive power and voltage phase are nodes of the quantity to be solved, a PQ node represents a given active power and reactive power, and a given voltage amplitude and voltage phase are nodes of the quantity to be solved; the lambda and the C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure BDA0003500462650000031
G. b is a conductance matrix and a susceptance matrix respectively, the superscript' represents the susceptance matrix neglecting all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.
Further, the mapping relationship between the injected power of the node and the operation state of the power system is as follows:
Figure BDA0003500462650000032
wherein Y is the operating state of the power system, X is the injected power of the node,
Figure BDA0003500462650000033
beta and gamma are preset parameters, and T represents the transposition of the matrix.
Further, the correcting the operating state of the power system by using a first-order polynomial fitting correction method specifically includes:
randomly generating a plurality of groups of power data as the injection power of a plurality of groups of nodes, obtaining the actual operation state of a plurality of groups of power systems by adopting an alternating current power flow calculation method, and obtaining the theoretical operation state of the plurality of groups of power systems through the linear power flow model;
substituting the actual operating states of the multiple groups of power systems and the theoretical operating states of the multiple groups of power systems into a predefined first-order polynomial equation to obtain coefficients of the first-order polynomial equation, and updating the first-order polynomial equation based on the coefficients;
and after the running state of the power system is obtained through the linear power flow model, substituting the running state of the power system into the first-order polynomial equation to obtain the corrected running state of the power system.
Further, the first order polynomial equation is:
Y(AC)＝ρY+ζ；
wherein, Y(AC)Is the actual operating state of the power system, Y is the theoretical operating state of the power system, ρ and
Figure BDA0003500462650000041
are all the coefficients.
Further, the corrected operation state of the power system is as follows:
Figure BDA0003500462650000042
wherein X is the injection power of the node, and Λ and C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure BDA0003500462650000043
beta and gamma are preset parameters, T represents the transpose of a matrix, N is the sum of the number of PV nodes and PQ nodes, M is the number of PQ nodes, PV nodes represent nodes with given active power and voltage amplitude, the given reactive power and voltage phase are the quantity to be solved, PQ nodes represent nodes with given active power and reactive power, and the given voltage amplitude and voltage phase are the quantity to be solved.
Further, the parameter set includes weight coefficients, mean vectors, and covariance matrices of respective gaussian components.
In a second aspect, an embodiment of the present invention provides an analytic probability power flow calculation apparatus, including:
the Gaussian mixture model building module is used for building a Gaussian mixture model according to the injection power of a node accessed to the power system, obtaining a parameter set of the Gaussian mixture model according to the historical data of the injection power of the node by adopting an EM (effective electromagnetic field) algorithm, and updating the Gaussian mixture model based on the parameter set;
the linear power flow model building module is used for building a linear power flow model according to the conductance and susceptance information of the power system and the injection power of the node so as to determine the mapping relation between the injection power of the node and the running state of the power system through the linear power flow model;
the operation state correction module is used for correcting the operation state of the power system by adopting a first-order polynomial fitting correction method and updating the linear power flow model according to the mapping relation between the injection power of the node and the corrected operation state of the power system;
and the probability power flow calculation module is used for mapping the probability distribution of the injection power of the node to the probability distribution of the corrected operation state of the power system through the Gaussian mixture model and the linear power flow model so as to obtain the probability power flow of the operation state of the power system.
In a third aspect, an embodiment of the present invention provides a computer-readable storage medium including a stored computer program; wherein, when the computer program runs, the device where the computer readable storage medium is located is controlled to execute the analytic probability power flow calculation method.
The embodiment of the invention has the following beneficial effects:
the method comprises the steps of constructing a Gaussian mixture model according to injection power of a node accessed into the power system, adopting an EM (effective magnetic field) algorithm, obtaining a parameter set of the Gaussian mixture model according to historical data of the injection power of the node, updating the Gaussian mixture model based on the parameter set, constructing a linear power flow model according to conductance, susceptance information and the injection power of the node of the power system, determining a mapping relation between the injection power of the node and an operation state of the power system through the linear power flow model, correcting the operation state of the power system by adopting a first-order polynomial fitting correction method, updating the linear power flow model according to the mapping relation between the injection power of the node and the corrected operation state of the power system, mapping probability distribution of the injection power of the node to the corrected probability distribution of the operation state of the power system through the Gaussian mixture model and the linear power flow model, and obtaining the probability load flow of the operation state of the power system, and finishing the calculation of the probability load flow. Compared with the prior art, the embodiment of the invention adopts the first-order polynomial fitting correction method to correct the operation state of the power system after the mapping relation between the injection power of the node and the operation state of the power system is determined through the linear power flow model, so that the corrected operation state of the power system is closer to the real operation state, the linear power flow model is updated according to the mapping relation between the injection power of the node and the corrected operation state of the power system, and the analytic probability power flow calculation is carried out by using the updated linear power flow model, thereby effectively improving the probability power flow calculation precision.
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Fig. 1 is a schematic flow chart of an analytic probabilistic power flow calculation method according to a first embodiment of the present invention;
fig. 2 is a schematic structural diagram of an analytic probability power flow calculation apparatus according to a second embodiment of the present invention.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that, the step numbers in the text are only for convenience of explanation of the specific embodiments, and do not serve to limit the execution sequence of the steps. The method provided by the embodiment can be executed by the relevant terminal device, and the following description takes a processor as an execution subject as an example.
As shown in fig. 1, the first embodiment provides an analytic probabilistic power flow calculation method, including steps S1 to S4:
s1, constructing a Gaussian mixture model according to the injection power of the node accessed to the power system, obtaining a parameter set of the Gaussian mixture model according to the historical data of the injection power of the node by adopting an EM (effective electromagnetic range) algorithm, and updating the Gaussian mixture model based on the parameter set;
s2, constructing a linear power flow model according to the conductance and susceptance information of the power system and the injection power of the nodes, and determining the mapping relation between the injection power of the nodes and the running state of the power system through the linear power flow model;
s3, correcting the running state of the power system by adopting a first-order polynomial fitting correction method, and updating a linear power flow model according to the mapping relation between the injection power of the node and the corrected running state of the power system;
and S4, mapping the probability distribution of the injection power of the nodes to the probability distribution of the operation state of the corrected power system through a Gaussian mixture model and a linear power flow model to obtain the probability power flow of the operation state of the power system.
According to the method, after the mapping relation between the injection power of the node and the operation state of the power system is determined through the linear power flow model, the operation state of the power system is corrected by adopting a first-order polynomial fitting correction method, so that the corrected operation state of the power system is closer to the real operation state, the linear power flow model is updated according to the mapping relation between the injection power of the node and the corrected operation state of the power system, and the analytic probability power flow calculation is carried out by utilizing the updated linear power flow model, so that the probability power flow calculation precision is effectively improved.
In a preferred embodiment, the gaussian mixture model is:
Figure BDA0003500462650000061
wherein, ω isjIs the weight coefficient of the jth Gaussian component, ωj>0，
Figure BDA0003500462650000062
J is the total number of Gaussian components;
Figure BDA0003500462650000071
Nj(. h) is the j-th Gaussian component, X is the injection power of the node, μj、σjMean vector and covariance matrix of the jth gaussian component, W is dimension of injection power of the node, det (.) is matrix determinant, and T represents transpose of the matrix.
In a preferred embodiment of this embodiment, the parameter set includes a weight coefficient, a mean vector, and a covariance matrix of each gaussian component.
Illustratively, a Gaussian Mixture Model (GMM) is used to describe the joint probability distribution of a random vector X, which is defined as a convex combination of multiple Gaussian distribution functions, denoted by Ω ═ ω { (ω) } byj,μj,σj(ii) a J ═ 1,2, … J } is the tunable parameter set for GMM.
The mathematical expression of GMM is shown in formula (1):
Figure BDA0003500462650000072
in the formula (1), ω isjIs the weight coefficient of the jth Gaussian component, ωj>0，
Figure BDA0003500462650000073
J is the total number of Gaussian components;
Figure BDA0003500462650000074
Nj(. h) is the j-th Gaussian component, X is the injection power of the node, μj、σjMean vector and covariance matrix of the jth gaussian component, W is dimension of injection power of the node, det (.) is matrix determinant, and T represents transpose of the matrix.
In a preferred embodiment of this embodiment, the parameter set includes a weight coefficient, a mean vector, and a covariance matrix of each gaussian component.
It will be appreciated that determining the parameter set Ω of the GMM is a typical parameter estimation problem. If the random variable X is characterized by a GMM as shown in equation (1) and the random variable Y is a linear transformation of X satisfying Y ═ AX + C, then the distribution of Y is also a GMM whose components are each the mean a μj+ C, covariance matrix of A ∑jATWith a weight coefficient of ωj。
Based on the historical data of X, a parameter set for the GMM may be obtained using a maximum likelihood estimation technique. Typical algorithms include Expectation Maximization (EM) algorithms. And the EM algorithm finally realizes the estimation of the GMM parameters through iterative calculation of the E step and the M step.
Illustratively, the k-th iterative computation process for the j-th gaussian component in the GMM is as follows:
Figure BDA0003500462650000081
Figure BDA0003500462650000082
Figure BDA0003500462650000083
Figure BDA0003500462650000084
wherein the content of the first and second substances,
Figure BDA0003500462650000085
is the nth history data.
In a preferred embodiment, the linear power flow model is:
Figure BDA0003500462650000086
wherein, theta and V are respectively the voltage phase angle and the voltage amplitude of the node, P, Q is respectively the active power and the reactive power in the injected power of the node, the subscript R represents the set formed by the nodes of V theta, K represents the set formed by the nodes of PV and V theta, S represents the set formed by the nodes of PV and PQ,
Figure BDA0003500462650000087
representing a set formed by PQ nodes, wherein a V theta node represents a given voltage amplitude and a given voltage phase, active power and reactive power are nodes of a quantity to be solved, a PV node represents a given active power and voltage amplitude, a given reactive power and voltage phase are nodes of the quantity to be solved, a PQ node represents a given active power and reactive power, and a given voltage amplitude and voltage phase are nodes of the quantity to be solved; the lambda and the C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure BDA0003500462650000088
G. b is a conductance matrix and a susceptance matrix respectively, the superscript' represents the susceptance matrix neglecting all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.
Illustratively, the linear Power Flow model is a linear Power Flow (DLPF) model independent of voltage phase angle decoupling of an operating point, and a mathematical expression of the linear Power Flow model is as shown in formula (6):
Figure BDA0003500462650000089
in the formula (6), θ and V are the voltage phase angle and the voltage amplitude of the node, P, Q is the active power and the reactive power of the injected power of the node, the subscript R represents the set of the nodes V θ, K represents the set of the nodes PV and V θ, S represents the set of the nodes PV and PQ,
Figure BDA0003500462650000091
representing a set formed by PQ nodes, wherein a V theta node represents a given voltage amplitude and a given voltage phase, active power and reactive power are nodes of a quantity to be solved, a PV node represents a given active power and voltage amplitude, a given reactive power and voltage phase are nodes of the quantity to be solved, a PQ node represents a given active power and reactive power, and a given voltage amplitude and voltage phase are nodes of the quantity to be solved; the lambda and the C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure BDA0003500462650000092
G. b is a conductance matrix and a susceptance matrix respectively, the superscript' represents the susceptance matrix neglecting all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.
In a preferred embodiment, the mapping relationship between the injected power of the node and the operation state of the power system is as follows:
Figure BDA0003500462650000093
wherein Y is the operation state of the power system, X is the injection power of the node,
Figure BDA0003500462650000094
beta and gamma are preset parameters, and T represents the transposition of the matrix.
Illustratively, the injection power of each node is described by using a linear power flow model shown in formula (6)
Figure BDA0003500462650000095
And the power systemOperating state of the system
Figure BDA0003500462650000096
The mapping relationship between them. The active power P injected by each node is considered in consideration of the randomness of the injected power of the wind driven generatorSAnd reactive power QLSatisfy formulas (8), (9), respectively:
Figure BDA0003500462650000097
Figure BDA0003500462650000098
wherein the content of the first and second substances,
Figure BDA0003500462650000101
Figure BDA0003500462650000102
Figure BDA0003500462650000103
Figure BDA0003500462650000104
both β and γ are known amounts.
And forming an Λ and C matrix according to the conductance and susceptance information of the power system, thereby forming a DLPF model expression shown in a formula (6).
And (3) constructing a linear transformation relation between Y and X as shown in the formula (7) according to the DLPF model expression.
In a preferred embodiment, the correcting the operating state of the power system by using a first-order polynomial fitting correction method specifically includes: randomly generating a plurality of groups of power data as the injection power of a plurality of groups of nodes, obtaining the actual operation state of a plurality of groups of power systems by adopting an alternating current power flow calculation method, and obtaining the theoretical operation state of the plurality of groups of power systems through a linear power flow model; substituting the actual operating states of the multiple groups of power systems and the theoretical operating states of the multiple groups of power systems into a predefined first-order polynomial equation to obtain coefficients of the first-order polynomial equation, and updating the first-order polynomial equation based on the coefficients; and after the running state of the power system is obtained through the linear power flow model, substituting the running state of the power system into a first-order polynomial equation to obtain the corrected running state of the power system.
In a preferred implementation of this embodiment, the first order polynomial equation is:
Y(AC)＝ρY+ζ (10)；
wherein, Y(AC)Is the actual operating state of the power system, Y is the theoretical operating state of the power system, ρ and
Figure BDA0003500462650000105
are all coefficients.
In a preferred embodiment of this embodiment, the corrected operation state of the power system is:
Figure BDA0003500462650000106
wherein X is the injection power of the node, and Λ and C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure BDA0003500462650000107
beta and gamma are preset parameters, T represents the transpose of a matrix, N is the sum of the number of PV nodes and PQ nodes, M is the number of PQ nodes, PV nodes represent nodes with given active power and voltage amplitude, the given reactive power and voltage phase are the quantity to be solved, PQ nodes represent nodes with given active power and reactive power, and the given voltage amplitude and voltage phase are the quantity to be solved.
Illustratively, a first-order polynomial fitting correction method is adopted to correct the operation state of the power system obtained by the DLPF model, specifically as follows:
firstly, the injection power of the H group node is randomly generated
Figure BDA0003500462650000111
Where H may take on a smaller number, such as 12.
Then, according to the injection power of different nodes of the H group, the actual operation state of the H group power system is obtained by using an alternating current load flow calculation method:
Figure BDA0003500462650000112
and obtaining the theoretical running state Y of the H groups of power systems by using a DLPF model:
Figure BDA0003500462650000113
reasonably assume Y(AC)And Y satisfies the affine transformation relation:
Figure BDA0003500462650000114
finally, using H group Y(AC)And Y, rho and rho are obtained by first order polynomial fitting
Figure BDA0003500462650000115
The operation state Y of the power system obtained by the DLPF model is corrected to obtain a calculation result Y of the alternating current power flow(AC)Almost identical operating states Y of an electrical systempI.e. with Y(AC)As the true operating state, the corrected Y is compared with the electric power system operating state Y obtained by the DLPF modelpAnd Y(AC)Almost completely consistent, thereby being beneficial to realizing high-precision linear power flow calculation.
Deducing nodes according to DLPFExpression (7) between injected power X and operating state Y of the power system, in combination with Y(AC)And affine transformation relation (14) satisfied between Y, obtaining an expression of the operation state of the high-precision electric power system as shown in equation (15):
Figure BDA0003500462650000116
in combination with the linear invariance of the GMM, the probability distribution of the injected power X of a node can be analytically mapped to the operating state Y of the power systempProbability distribution of (2). Due to YpAnd Y(AC)Almost completely consistent, thereby realizing high-precision analytic probability load flow calculation.
Based on the same inventive concept as the first embodiment, the second embodiment provides an analytic probabilistic power flow calculation device as shown in fig. 2, including: the gaussian mixture model establishing module 21 is configured to establish a gaussian mixture model according to injection power of a node accessed to the power system, obtain a parameter set of the gaussian mixture model according to historical data of the injection power of the node by using an EM algorithm, and update the gaussian mixture model based on the parameter set; a linear power flow model building module 22, configured to build a linear power flow model according to the conductance and susceptance information of the power system and the injection power of the node, so as to determine a mapping relationship between the injection power of the node and the operating state of the power system through the linear power flow model; the operating state correcting module 23 is configured to correct the operating state of the power system by using a first-order polynomial fitting correction method, and update the linear power flow model according to a mapping relationship between the injection power of the node and the corrected operating state of the power system; and a probability power flow calculation module 24, configured to map, through the gaussian mixture model and the linear power flow model, the probability distribution of the injected power of the node to the probability distribution of the corrected operation state of the power system, so as to obtain the probability power flow of the operation state of the power system.
In a preferred embodiment, the gaussian mixture model is:
Figure BDA0003500462650000121
wherein, ω isjIs the weight coefficient of the jth Gaussian component, ωj>0，
Figure BDA0003500462650000122
J is the total number of Gaussian components;
Figure BDA0003500462650000123
Nj(. h) is the j-th Gaussian component, X is the injection power of the node, μj、σjMean vector and covariance matrix of the jth gaussian component, W is dimension of injection power of the node, det (.) is matrix determinant, and T represents transpose of the matrix.
In a preferred embodiment of this embodiment, the parameter set includes a weight coefficient, a mean vector, and a covariance matrix of each gaussian component.
In a preferred embodiment, the linear power flow model is:
Figure BDA0003500462650000124
wherein, theta and V are respectively the voltage phase angle and the voltage amplitude of the node, P, Q is respectively the active power and the reactive power in the injected power of the node, the subscript R represents the set formed by the nodes of V theta, K represents the set formed by the nodes of PV and V theta, S represents the set formed by the nodes of PV and PQ,
Figure BDA0003500462650000131
representing a set of PQ nodes, the Vtheta node representing a voltage magnitude and voltage phase setting, active and reactive power being the nodes of the quantity to be demanded, the PV node representing an active and voltage magnitude setting, reactive and voltage phase being the nodes of the quantity to be demanded, the PQ node representing an active and reactive power setting, a voltage magnitude and voltage phase settingIs a node to be metered; the lambda and the C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure BDA0003500462650000132
G. b is a conductance matrix and a susceptance matrix respectively, the superscript' represents the susceptance matrix neglecting all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.
In a preferred embodiment, the mapping relationship between the injected power of the node and the operation state of the power system is as follows:
Figure BDA0003500462650000133
wherein Y is the operation state of the power system, X is the injection power of the node,
Figure BDA0003500462650000134
beta and gamma are preset parameters, and T represents the transposition of the matrix.
In a preferred embodiment, the correcting the operating state of the power system by using a first-order polynomial fitting correction method specifically includes: randomly generating a plurality of groups of power data as the injection power of a plurality of groups of nodes, obtaining the actual operation state of a plurality of groups of power systems by adopting an alternating current power flow calculation method, and obtaining the theoretical operation state of the plurality of groups of power systems through a linear power flow model; substituting the actual operating states of the multiple groups of power systems and the theoretical operating states of the multiple groups of power systems into a predefined first-order polynomial equation to obtain coefficients of the first-order polynomial equation, and updating the first-order polynomial equation based on the coefficients; and after the running state of the power system is obtained through the linear power flow model, substituting the running state of the power system into a first-order polynomial equation to obtain the corrected running state of the power system.
In a preferred implementation of this embodiment, the first order polynomial equation is:
Y(AC)＝ρY+ζ (19)；
in a preferred embodiment of this embodiment, the corrected operation state of the power system is:
Figure BDA0003500462650000141
wherein X is the injection power of the node, and Λ and C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure BDA0003500462650000142
beta and gamma are preset parameters, T represents the transpose of a matrix, N is the sum of the number of PV nodes and PQ nodes, M is the number of PQ nodes, PV nodes represent nodes with given active power and voltage amplitude, the given reactive power and voltage phase are the quantity to be solved, PQ nodes represent nodes with given active power and reactive power, and the given voltage amplitude and voltage phase are the quantity to be solved.
A third embodiment provides a computer-readable storage medium comprising a stored computer program; when the computer program runs, the device where the computer readable storage medium is located is controlled to execute the analytic probability power flow calculation method according to the first embodiment, and the same beneficial effects as those of the analytic probability power flow calculation method can be achieved.
In summary, the embodiment of the present invention has the following advantages:
the method comprises the steps of constructing a Gaussian mixture model according to injection power of a node accessed into the power system, adopting an EM (effective magnetic field) algorithm, obtaining a parameter set of the Gaussian mixture model according to historical data of the injection power of the node, updating the Gaussian mixture model based on the parameter set, constructing a linear power flow model according to conductance, susceptance information and the injection power of the node of the power system, determining a mapping relation between the injection power of the node and an operation state of the power system through the linear power flow model, correcting the operation state of the power system by adopting a first-order polynomial fitting correction method, updating the linear power flow model according to the mapping relation between the injection power of the node and the corrected operation state of the power system, mapping probability distribution of the injection power of the node to the corrected probability distribution of the operation state of the power system through the Gaussian mixture model and the linear power flow model, and obtaining the probability load flow of the operation state of the power system, and finishing the calculation of the probability load flow. According to the embodiment of the invention, after the mapping relation between the injection power of the node and the operation state of the power system is determined through the linear power flow model, the operation state of the power system is corrected by adopting a first-order polynomial fitting correction method, so that the corrected operation state of the power system is closer to the real operation state, the linear power flow model is updated according to the mapping relation between the injection power of the node and the corrected operation state of the power system, and the analytic formula probability power flow calculation is carried out by utilizing the updated linear power flow model, so that the probability power flow calculation precision is effectively improved.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
It will be understood by those skilled in the art that all or part of the processes of the above embodiments may be implemented by hardware related to instructions of a computer program, and the computer program may be stored in a computer readable storage medium, and when executed, may include the processes of the above embodiments. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.

Claims (10)

1. An analytic probability power flow calculation method is characterized by comprising the following steps:
according to the injection power of a node accessed to a power system, constructing a Gaussian mixture model, obtaining a parameter set of the Gaussian mixture model according to historical data of the injection power of the node by adopting an EM (effective electromagnetic range) algorithm, and updating the Gaussian mixture model based on the parameter set;
constructing a linear power flow model according to the conductance and susceptance information of the power system and the injection power of the node, and determining a mapping relation between the injection power of the node and the running state of the power system through the linear power flow model;
correcting the running state of the power system by adopting a first-order polynomial fitting correction method, and updating the linear power flow model according to the mapping relation between the injection power of the node and the corrected running state of the power system;
and mapping the probability distribution of the injection power of the node to the probability distribution of the operation state of the corrected power system through the Gaussian mixture model and the linear power flow model to obtain the probability power flow of the operation state of the power system.
2. The analytical probabilistic power flow calculation method of claim 1, wherein the gaussian mixture model is:
Figure FDA0003500462640000011
wherein, ω isjIs the weight coefficient of the jth Gaussian component, ωj＞0，
Figure FDA0003500462640000012
J is the total number of Gaussian components;
Figure FDA0003500462640000013
Nj(. h) is the jth Gaussian component, X is the injection power of the node, μj、σjRespectively, a mean vector and a covariance matrix of the jth gaussian component, W is the dimension of the injection power of the node, det (.) is a matrix determinant, and T represents a transpose of the matrix.
3. The analytical probabilistic power flow calculation method of claim 1, wherein the linear power flow model is:
Figure FDA0003500462640000021
wherein θ and V are the voltage phase angle and the voltage amplitude of the node, P, Q is the active power and the reactive power of the injected power of the node, the subscript R represents the set of nodes V θ, K represents the set of nodes PV and V θ, S represents the set of nodes PV and PQ,
Figure FDA0003500462640000022
representing a set formed by PQ nodes, wherein a V theta node represents a given voltage amplitude and a given voltage phase, active power and reactive power are nodes of a quantity to be solved, a PV node represents a given active power and voltage amplitude, a given reactive power and voltage phase are nodes of the quantity to be solved, a PQ node represents a given active power and reactive power, and a given voltage amplitude and voltage phase are nodes of the quantity to be solved; the lambda and the C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure FDA0003500462640000023
G. b is a conductance matrix and a susceptance matrix respectively, the superscript' represents the susceptance matrix neglecting all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.
4. The analytical probabilistic power flow calculation method of claim 3 wherein the mapping between the injected power of the node and the operating state of the power system is:
Figure FDA0003500462640000024
wherein Y is the operating state of the power system, X is the injected power of the node,
Figure FDA0003500462640000025
beta and gamma are preset parameters, and T represents the transposition of the matrix.
5. The analytical probabilistic power flow calculation method according to claim 1, wherein the correcting the operation state of the power system by using a first-order polynomial fitting correction method includes:
randomly generating a plurality of groups of power data as the injection power of a plurality of groups of nodes, obtaining the actual operation state of a plurality of groups of power systems by adopting an alternating current power flow calculation method, and obtaining the theoretical operation state of the plurality of groups of power systems through the linear power flow model;
substituting the actual operating states of the multiple groups of power systems and the theoretical operating states of the multiple groups of power systems into a predefined first-order polynomial equation to obtain coefficients of the first-order polynomial equation, and updating the first-order polynomial equation based on the coefficients;
and after the running state of the power system is obtained through the linear power flow model, substituting the running state of the power system into the first-order polynomial equation to obtain the corrected running state of the power system.
6. The analytical probabilistic power flow calculation method of claim 5, wherein the first order polynomial equation is:
Y(AC)＝ρY+ζ；
wherein, Y(AC)Is the actual operating state of the power system, Y is the theoretical operating state of the power system, ρ and
Figure FDA0003500462640000031
are all the coefficients.
7. The analytical probabilistic power flow calculation method according to claim 6, wherein the modified operating state of the power system is:
Figure FDA0003500462640000032
wherein X is the injection power of the node, and Λ and C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure FDA0003500462640000033
beta and gamma are preset parameters, T represents the transpose of a matrix, N is the sum of the number of PV nodes and PQ nodes, M is the number of PQ nodes, PV nodes represent nodes with given active power and voltage amplitude, the given reactive power and voltage phase are the quantity to be solved, PQ nodes represent nodes with given active power and reactive power, and the given voltage amplitude and voltage phase are the quantity to be solved.
8. The analytical probabilistic power flow calculation method of claim 2, wherein the set of parameters includes a weight coefficient, a mean vector and a covariance matrix for each gaussian component.
9. An analytic probability power flow calculation device, comprising:
the Gaussian mixture model building module is used for building a Gaussian mixture model according to the injection power of a node accessed to the power system, obtaining a parameter set of the Gaussian mixture model according to the historical data of the injection power of the node by adopting an EM (effective electromagnetic field) algorithm, and updating the Gaussian mixture model based on the parameter set;
the linear power flow model building module is used for building a linear power flow model according to the conductance and susceptance information of the power system and the injection power of the node so as to determine the mapping relation between the injection power of the node and the running state of the power system through the linear power flow model;
the operation state correction module is used for correcting the operation state of the power system by adopting a first-order polynomial fitting correction method and updating the linear power flow model according to the mapping relation between the injection power of the node and the corrected operation state of the power system;
and the probability power flow calculation module is used for mapping the probability distribution of the injection power of the node to the probability distribution of the corrected operation state of the power system through the Gaussian mixture model and the linear power flow model so as to obtain the probability power flow of the operation state of the power system.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium comprises a stored computer program; wherein, when the computer program runs, the computer readable storage medium is controlled to execute the analytic probability power flow calculation method according to any one of claims 1 to 8.
CN202210126978.7A 2022-02-10 2022-02-10 Analytic probabilistic power flow calculation method, device and storage medium Pending CN114421483A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117313304A (en) * 2023-05-16 2023-12-29 上海交通大学 Gaussian mixture model method for analyzing overall sensitivity of power flow of power distribution network

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117313304A (en) * 2023-05-16 2023-12-29 上海交通大学 Gaussian mixture model method for analyzing overall sensitivity of power flow of power distribution network
CN117313304B (en) * 2023-05-16 2024-03-08 上海交通大学 Gaussian mixture model method for analyzing overall sensitivity of power flow of power distribution network

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