Probability optimal power flow calculation method and system based on semi-definite programming-point estimation method

Abstract

The invention relates to the technical field of power system optimization, in particular to a probabilistic optimal power flow calculation method and system based on a semi-definite programming-point estimation method. The method comprises the following steps: establishing an uncertainty model of a random signal load, and counting a dimension n of an input random variable load; calculating the high-order moment of the random variable load according to the uncertainty model of the random signal load; for each random variable load, generating three estimation points and corresponding weights of each random variable load based on the calculated high-order moment; the optimal power flow is calculated once for the estimation point of each random variable load, a result is stored, the number of sample points is 2n + 1, a power flow equation is converted into an SDP convex relaxation model, an objective function is established to minimize power generation cost or network loss, and the optimal power flow is obtained through solving. According to the method, the high-order moment information of the random variable is efficiently sampled by using the three-point estimation method, so that the calculation efficiency of the probabilistic optimal power flow of the large-scale power system is remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system optimization, in particular to a probability optimal power flow calculation method and system based on semi-definite programming-point estimation method. BACKGROUND

[0002] Traditional optimal power flow (OPF) model is based on deterministic assumption, which is difficult to deal with uncertain factors such as new energy output and load fluctuation. The probability optimal power flow can reflect the system operation risk more comprehensively by quantifying the statistical characteristics of random variables, but its calculation complexity is high. The existing technology has the following problems: the semi-definite programming (SDP) method can guarantee the global optimality of the solution, but the calculation scale is large, and the solving time increases exponentially with the system scale; Monte Carlo simulation needs a large number of samples, and the calculation efficiency is low; the point estimation method (such as two-point estimation) ignores the high-order moment information, and the precision is limited; the application of parallel computing technology in probability optimal power flow has not been fully tapped, especially how to allocate the calculation task under the SDP framework to speed up the solution still lacks effective solutions. SUMMARY

[0003] In view of the problems in the prior art, the present application provides a probability optimal power flow calculation method and system based on semi-definite programming-point estimation method. The specific technical scheme is as follows: A probability optimal power flow calculation method based on semi-definite programming-point estimation method, comprising the following steps: Step S1, establishing an uncertainty model of random signal load, and counting the dimension of input random variable load ; Step S2, calculating the high-order moment of the random variable load according to the uncertainty model of the random signal load; Step S3, for each random variable load, generating three estimation points and corresponding weights of each random variable load based on the calculated high-order moment; Step S4, calculating the optimal power flow for each estimation point of the random variable load and saving the results, the number of sample points is 2n+1, converting the power flow equation into an SDP convex relaxation model, establishing the objective function as minimizing the generation cost or network loss, and solving to obtain the optimal power flow.

[0004] Preferably, the uncertainty model of the random signal load in step S1 is as follows: The uncertainty model of the load adopts normal distribution, and the cumulative distribution function is as follows: ; Wherein, P(x≤x0) represents the probability that the load is less than or equal to a certain value , and and are the mean and standard deviation of the load respectively.

[0005] Preferably, the higher-order moments of the random variable loading in step S2 include the mean, standard deviation, skewness, and kurtosis of the random variable loading; let... Loading of random variables of Moment of order, when hour, These are the mean, standard deviation, skewness, and kurtosis of the loading of the random variable, respectively.

[0006] Preferably, the skewness of the random variable loading is calculated as follows: ; in, Load of the k-th random variable skewness, Load of the k-th random variable The mean, Load of the k-th random variable Standard deviation; This represents the expected value.

[0007] Preferably, the kurtosis of the random variable loading is calculated as follows: ; in, Load of the k-th random variable peak, Load of the k-th random variable The mean, Load of the k-th random variable Standard deviation; This represents the expected value.

[0008] Preferably, in step S3, the generation of three estimation points and corresponding weights for each random variable loading based on the calculated higher-order moments is as follows: ; ; in, Load of the k-th random variable of Weighting coefficients of the step moment, Load of the k-th random variable The i-th estimated point, For random variable loading hit point The probability of.

[0009] Preferably, the step S4 is calculated once for each random variable load estimation point optimal power flow and save the results, the number of sample points is 2n+1, the power flow equation is converted into SDP convex relaxation model, the objective function is established to minimize the generation cost or network loss, and the optimal power flow is solved, specifically including the following steps: Inequality constraints are established, specifically as follows: ; Wherein: is the system node set, is the system generator node set, is the reactive power supply node set; , is the active power and reactive power of node ; , is the real part and imaginary part of the voltage of node ; is the voltage of node ; Relaxation variables , , , , , are introduced, and the inequality constraints are converted into equality constraints; constant variables , are introduced, and the linear terms are expressed as quadratic terms; The converted SDP convex relaxation model is as follows: ; Wherein, the objective function is network loss, , , is the fuel cost coefficient of generator unit , is the system node set, is the system generator node set, , is the active power and reactive power of node ; , is the active and reactive load of node ; , is the conductance and susceptance of branch composed of node ; , is the real part and imaginary part of the voltage of node ; , , Balance the real and imaginary parts of the node voltage; represents the maximum value of the variable, represents the minimum value of the variable; , is a constant variable; is the voltage of the node .

[0010] Group the relevant variables and auxiliary variables, respectively , , , : ; Let , the variable matrix of the SDP is ; the SDP model can be obtained: ; Wherein is the objective function matrix; is the equality constraint matrix; call the SDP software package SDPARA to calculate the optimal solution of power flow .

[0011] A probability optimal power flow calculation system based on semi-definite programming-point estimation method, applying the method, comprising: An uncertainty modeling module for establishing an uncertainty model of random signal load, and counting the dimension of input random variable load ; A high-order moment calculation module for calculating the high-order moment of the random variable load according to the uncertainty model of the random signal load; A three-point estimation module for generating three estimation points and corresponding weights of each random variable load based on the calculated high-order moment for each random variable load; A power flow calculation module for calculating an optimal power flow for each estimation point of the random variable load and saving the result, the number of sample points being 2n+1, converting the power flow equation into an SDP convex relaxation model, establishing an objective function for minimizing the generation cost or network loss, and solving to obtain the optimal power flow.

[0012] A computer readable storage medium, the computer readable storage medium comprising a stored program, wherein the computer readable storage medium controls the device where the computer readable storage medium is located to execute the probability optimal power flow calculation method based on semi-definite programming-point estimation method when the program is running.

[0013] A processor for running a program, wherein the program executes the probability optimal power flow calculation method based on semi-definite programming-point estimation method when the program is running.

[0014] Compared with the prior art, the present application has the following advantages: The method of the present application significantly improves the calculation efficiency of the probabilistic optimal power flow of a large-scale power system by efficiently sampling the high-order moment information of a random variable using a three-point estimation method, and is suitable for operation risk assessment and optimal scheduling of a power system containing a high proportion of new energy.

[0015] The present application has the advantages of efficient parallel architecture: by double parallelism of task level (estimation point) and data level (Schur equation), the multi-core / distributed computing resources are fully utilized to solve the SDP calculation bottleneck; high-precision probability modeling: the three-point estimation method uses fourth-order moment information, which reduces the error by more than 50% compared with the traditional two-point estimation method; strong compatibility: the existing SDP solver (such as SDPARA) and parallel computing library can be directly called without reconstructing the optimization algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the description of the embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn according to the actual proportions.

[0017] Figure 1 The present application is a method flowchart.

[0018] Figure 2 The present application is a method and SDP-MCS comparison result graph.

[0019] Figure 3 The present application is a system schematic diagram. DETAILED DESCRIPTION

[0020] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0021] It should be understood that when used in the present specification and the appended claims, the terms "comprise" and "include" indicate the presence of the described features, integers, steps, operations, elements, and / or components, but do not exclude one or more other features, integers, steps, operations, elements, components, and / or sets thereof.

[0022] It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used in this specification and the appended claims, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

[0023] It is further to be understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items, and that the term "at least one of' denotes one, or a plurality of, or any combination of the elements it introduces.

[0024] A probabilistic optimal power flow calculation method based on semi-definite programming-point estimation method, comprising the following steps: Step S1, establishing an uncertainty model of random signal load, and counting the dimension of input random variable load The uncertainty model of random signal load is specifically as follows: The uncertainty model of load adopts normal distribution, and the cumulative distribution function is specifically as follows: ; Wherein, represents the probability that the load is less than or equal to a certain value , and are the mean and standard deviation of the load respectively.

[0025] Step S2, calculating the high-order moments of random variable load according to the uncertainty model of random signal load. The high-order moments of random variable load include the mean of random variable load, the standard deviation of random variable load, the skewness of random variable load, and the kurtosis of random variable load; let be the moment of random variable load , when , are the mean, standard deviation, skewness and kurtosis of random variable load respectively.

[0026] The calculation method of the skewness of random variable load is as follows: ; Wherein, is the skewness of the kth random variable load , is the mean of the kth random variable load , is the standard deviation of the kth random variable load ; denotes the expected value.

[0027] The calculation method of the kurtosis of random variable load is as follows: ; wherein, is the kth random variable load kurtosis.

[0028] Step S3, for each random variable load, generating 3 estimation points and corresponding weights of each random variable load based on the calculated higher moments. Generating 3 estimation points and corresponding weights of each random variable load based on the calculated higher moments is specifically as follows: ; ; wherein, is the weight coefficient of the kth random variable load kurtosis, is the i th estimation point of the kth random variable load is the probability of taking point in the random variable load . Step S4, calculating the power flow for each estimation point of the random variable load and saving the results, the number of sample points is 2n+1, converting the power flow equation into an SDP convex relaxation model, establishing the objective function as minimizing the generation cost or network loss, and solving to obtain the optimal power flow. Specifically, it includes the following steps: Establishing inequality constraints, specifically as follows:

[0029] ; wherein: is the system node set, is the system generator node set, is the reactive power source node set; , is the active power and reactive power of node ; , is the real part and imaginary part of the voltage of node ; is the voltage of node ; introducing relaxation variables , , , , , , , , converting the inequality constraints into equality constraints; introducing constant variables , , expressing the linear term as a quadratic term; The converted SDP convex relaxation model is as follows: ; wherein the objective function is the network loss, 、 、 is the fuel cost coefficient of the generator group , is the set of system nodes, is the set of system generator nodes, 、 is the active power and the reactive power of the node ; 、 is the active and reactive load of the node ; 、 is the conductance and the susceptance of the branch composed of the node and the node ; 、 is the real part and the imaginary part of the voltage of the node ; 、 is the real part and the imaginary part of the voltage of the balanced node; represents the maximum value of a variable, represents the minimum value of a variable; 、 is a constant variable; is the voltage of the node . Group the relevant variables and auxiliary variables, respectively as

[0030] 、 、 、 : ; Let , the variable matrix of the SDP is ; the SDP model can be obtained as follows: ; wherein is the objective function matrix; is the equality constraint matrix; call the SDP software package SDPARA to calculate, and the optimal solution of the power flow is obtained .

[0031] The embodiment sums up the objective function values of each estimation point The electricity purchase cost is weighted to calculate the mean value and the standard deviation, and the specific process is as follows: In the formula: represents the load sample​ the mean of the mean of the standard deviation of represents that only one random variable is changed each time, and the rest of the random variables take the mean value, and the value of the objective function (the cost of purchasing electricity) obtained.

[0032] In order to highlight the performance of the algorithm of the present application, the semi-definite programming-Monte Carlo simulation (SDP-MCS) method is selected as a comparative algorithm. The IEEE 30 and IEEE 118 node systems are taken as research objects, which have 27 and 115 load nodes respectively. The load nodes are subject to normal distribution, and the mean value is the predicted value, and the standard deviation is 5% of the mean value.

[0033] The results are shown in Figure 2 In the IEEE 30 node system, the semi-definite programming-point estimation method (SDP-PEM) proposed in the present application can complete the probabilistic optimal power flow calculation in only 0.6 seconds, while the traditional semi-definite programming-Monte Carlo simulation (SDP-MCS) method takes about 40 seconds. The core of the efficiency improvement is that the three-point estimation method only needs 55 samples (2x27+1), which is reduced by 94.5% compared with the 1000 times sampling of the Monte Carlo simulation, and the calculation load is reduced from the root. In the IEEE 118 node system, the calculation time (313.2 seconds) of SDP-PEM is 15.4 times shorter than that (4827.5 seconds) of SDP-MCS, which verifies the scaling advantage of the technical scheme. In terms of accuracy, SDP-PEM achieves a relative error of 0.5% and 0.8% in IEEE 30 and 118 systems respectively, which is slightly higher than that of SDP-MCS (0.1% / 0.15%), but fully meets the engineering requirements: with a precision loss of 0.7%, the efficiency is improved by 15.4-66.7 times, solving the long-standing contradiction between high precision requirement and exponential calculation complexity in the field of probabilistic optimal power flow. Especially in the power system containing wind, light and storage, when the dimension of random variable increases sharply, this balancing strategy has significant engineering value.

[0034] Embodiment 2: As shown in Figure 3 based on the same inventive concept as embodiment 1, the present embodiment provides a probabilistic optimal power flow calculation system based on semi-definite programming-point estimation method, which applies the method, comprising: an uncertainty modeling module for establishing an uncertainty model of the random signal load, and counting the dimension of the input random variable load ; a high-order moment calculation module for calculating the high-order moment of the random variable load according to the uncertainty model of the random signal load; ​​a three-point estimation module configured to generate three estimation points and corresponding weights for each random variable load based on the calculated higher order moments; a power flow calculation module configured to calculate a power flow for each estimation point of each random variable load and save the results, the number of sample points being 2n+1, convert the power flow equation into an SDP convex relaxation model, and establish an objective function for minimizing generation cost or network loss to obtain an optimal power flow.

[0035] Embodiment 3 Based on the same inventive concept as Embodiment 1, this embodiment provides a computer readable storage medium comprising a stored program, wherein the program, when executed, controls a device in which the computer readable storage medium is located to perform the probabilistic optimal power flow calculation method based on the semi-definite programming-point estimation method.

[0036] Embodiment 4 Based on the same inventive concept as Embodiment 1, this embodiment provides a processor configured to execute a program, wherein the program, when executed, performs the probabilistic optimal power flow calculation method based on the semi-definite programming-point estimation method.

[0037] Those skilled in the art can appreciate that the units of the examples described in conjunction with the embodiments disclosed herein can be realized in electronic hardware, computer software or a combination of both. In order to clearly illustrate the interchangeability of hardware and software, the components of the examples have been described in general terms in the above description. Whether the functions are realized in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0038] In the embodiments provided in the present application, it should be understood that the division of units is only a logical functional division, and actual implementation can have another division manner, for example, multiple units can be combined into one unit, one unit can be split into multiple units, or some features can be ignored, etc.

[0039] In addition, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or software functional unit.

[0040] The integrated unit, if implemented in the form of a software function unit and sold or used as an independent product, can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or say the part that contributes to the prior art or the whole or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a mobile hard disk, a magnetic disk or an optical disk, and various media that can store program codes.

[0041] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope of the claims and the specification of the present application.

Claims

1. A probabilistic optimal power flow calculation method based on semi-definite programming-point estimation method, characterized in that, The method comprises the following steps: Step S1, establishing an uncertainty model of random signal load, counting the dimension n of input random variable load; Step S2, calculating high-order moments of the random variable load according to the uncertainty model of the random signal load; Step S3, for each random variable load, generating three estimation points and corresponding weights of each random variable load based on the calculated high-order moments; Step S4, calculating the optimal power flow for each estimation point of the random variable load and saving the results, the number of sample points is 2n+1, converting the power flow equation into an SDP convex relaxation model, establishing the objective function as minimizing the power generation cost or network loss, and solving to obtain the optimal power flow.

2. The probabilistic optimal power flow calculation method based on semi-definite programming-point estimation method according to claim 1, characterized in that, The uncertainty model of the random signal load in the step S1 is specifically as follows: The uncertainty model of the load adopts a normal distribution, and the cumulative distribution function is specifically as follows: Wherein, G(x) represents the probability of the load being less than or equal to a specific value x, μ and σ are the mean and standard deviation of the load respectively.

3. The probabilistic optimal power flow calculation method based on semi-definite programming-point estimation method according to claim 1, wherein, The high-order moment of the random variable load in the step S2 includes the mean of the random variable load, the standard deviation of the random variable load, the skewness of the random variable load, and the kurtosis of the random variable load; let λ k,i be the i-th moment of the random variable load X k , when i = 1, 2, 3, 4, λ k,i is the mean, the standard deviation, the skewness, and the kurtosis of the random variable load, respectively.

4. The probabilistic optimal power flow calculation method based on semi-definite programming-point estimation method according to claim 3, characterized in that, The skewness of the random variable load is calculated in the following manner: where λ k,3 is the skewness of the kth random variable load X k , μ k is the mean of the kth random variable load X k , σ k is the standard deviation of the kth random variable load X k ; and E[·] denotes the expected value.

5. The probabilistic optimal power flow calculation method based on semi-definite programming-point estimation method according to claim 1, wherein, The kurtosis of the random variable load is calculated in the following manner: where λ k,4 is the kurtosis of the kth random variable load X k , μ k is the mean of the kth random variable load X k , σ k is the standard deviation of the kth random variable load X k ; and E[·] denotes the expected value.

6. The probabilistic optimal power flow calculation method based on semi-definite programming-point estimation method according to claim 3, wherein, The three estimation points and corresponding weights of each random variable load generated based on the calculated high-order moments in the step S3 are specifically as follows: x k,i = μ k + ξ k,i σ k , i = 1, 2, 3; where ξ k,i is the weight coefficient of the i-th moment of the k-th random variable load X k , x k,i is the i-th estimation point of the k-th random variable load X k , p k,i is the probability of taking the point x k in the random variable load X k,i .

7. The probabilistic optimal power flow calculation method based on semi-definite programming-point estimation method according to claim 1, wherein, The step S4 of calculating the optimal power flow for each estimation point of the random variable load and saving the results, the number of sample points is 2n+1, converting the power flow equation into an SDP convex relaxation model, establishing the objective function as minimizing the power generation cost or network loss, and solving to obtain the optimal power flow specifically comprises the following steps: Inequality constraints are established, which are specifically as follows: where: S B is the set of system nodes, S G is the set of system generator nodes, S R is the set of reactive power source nodes; P Gi , Q Ri are the active and reactive power at node i; e i , f i are the real and imaginary parts of the voltage at node i; V i is the voltage at node i; introduce slack variables u Gi , l Gi , u Ri , l Ri , u Bi , l Bi convert inequality constraints to equality constraints; introduce constant variables V Gi = 1, V Ri = 1, express linear terms as quadratic terms; The converted SDP convex relaxation model is as follows: wherein the objective function is network loss, a 2i , a 1i , a 0i is the fuel cost coefficient of generator unit i, S B is the system node set, S G is the system generator node set, P Gi , Q Ri is the active power and reactive power of node i; P Di , Q Di is the active and reactive load of node i; G ij , B ij is the conductance and susceptance of the ij branch composed of node i and node j; e i , f i is the real part and imaginary part of the voltage of node i; e s , f s is the real part and imaginary part of the voltage of the balanced node; represents the maximum value of a variable, (·) represents the minimum value of a variable; V Gi , V Ri is a constant variable; V i is the voltage of node i. Grouping the related variables and auxiliary variables, respectively let x1, x2, x3, x4: Let x = [x1, x2, x3, x4] T , the variable matrix of SDP is X = xx T ; the SDP model is obtained: Where A0is the objective function matrix; A i is the equality constraint matrix; the SDP software package SDPARA is called to calculate the optimal solution X * of power flow.

8. A probabilistic optimal power flow calculation system based on semi-definite programming-point estimation method, characterized in that, The method of any one of claims 1 to 7 comprises: An uncertainty modeling module is configured to establish an uncertainty model of random signal load, count the dimension n of input random variable load; a high-order moment calculation module is configured to calculate high-order moments of the random variable load according to the uncertainty model of the random signal load; A three-point estimation module is configured to generate three estimation points and corresponding weights of each random variable load based on the calculated high-order moments for each random variable load; A power flow calculation module is configured to calculate the optimal power flow for each estimation point of the random variable load and save the results, the number of sample points is 2n+1, convert the power flow equation into an SDP convex relaxation model, establish the objective function as minimizing the power generation cost or network loss, and solve to obtain the optimal power flow.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium comprises a stored program, wherein when the program runs, the computer readable storage medium controls the device where the computer readable storage medium is located to execute the probabilistic optimal power flow calculation method based on the semi-definite programming-point estimation method of any one of claims 1 to 7.

10. A processor, comprising: The processor is configured to run a program, wherein when the program runs, the processor executes the probabilistic optimal power flow calculation method based on the semi-definite programming-point estimation method of any one of claims 1 to 7.

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