A Probabilistic Interval Power Flow Calculation Method for Distribution Network Considering Correlation

Abstract

The present invention provides a distribution network probability interval power flow calculation method considering correlation, which divides the output interval of distributed wind farms into several sub-intervals and assigns corresponding probabilities to the sub-intervals to construct a focal element model of distributed wind farm output; combines affine arithmetic to transform the distribution network probability interval power flow model based on the focal element model into an affine optimization model for solution, and adopts a parallelogram model, a convex polygon model, and an ellipsoid model to describe the correlation of the output of distributed wind farms, and transforms the correlation model into an affine constraint condition through coordinate transformation and embeds it into the affine optimization model for joint solution; finally, the probability boundary of the distribution network probability interval deliquescence is obtained according to the evidence theory synthesis rule. The function of accurately simulating the impact of the access of distributed wind farms on the distribution of uncertain power flow of the distribution network is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of distribution network uncertainty power flow calculation, and in particular relates to a distribution network probability interval power flow calculation method considering correlation. Background Art

[0002] With the optimization and adjustment of traditional energy structure, distributed energy represented by photovoltaic and wind power has been connected to the distribution network on a large scale. The strong volatility and randomness of its output have aggravated the uncertainty of the distribution network. Therefore, using uncertainty power flow algorithm to analyze the impact of distributed energy on the power flow distribution of the distribution network has become the current focus.

[0003] At present, the uncertainty power flow algorithms of distribution networks are mainly divided into three categories: fuzzy power flow (FPF), probabilistic power flow (PPF), and interval power flow (IPF). Among them, fuzzy power flow describes uncertain variables through membership density functions. It is a type of uncertainty power flow algorithm based on fuzzy set theory. Compared with probabilistic power flow, fuzzy power flow does not require a large amount of historical statistical data, but its modeling is more difficult, and the calculation accuracy and efficiency cannot be guaranteed. It is difficult to use in practice. Probabilistic power flow is an uncertainty power flow algorithm based on probability statistics theory. It mainly works on two aspects: adapting to different probability density functions of uncertain variables and correlation modeling. Interval power flow only needs to input the upper and lower boundary information of uncertain variables. Relatively speaking, modeling is simple and the data demand is small. Probabilistic power flow and interval power flow correspond to the two extreme cases of sufficient and insufficient historical statistical information for solving the input uncertain variables. In actual distribution networks, the historical statistical data of uncertain variables are usually between these two extreme cases. At this time, if interval power flow is used, some historical data will be wasted; if probabilistic power flow is used, the results will be inaccurate due to the lack of uncertain information. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a distribution network probability interval power flow calculation method considering correlation, which is used to accurately simulate the impact of distributed wind farm access on the distribution network uncertainty power flow distribution.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a method for calculating the probability interval power flow of a distribution network considering correlation, comprising the following steps:

[0006] S1: Initialization, input the initial data of the distribution network power flow model, and calculate the correlation coefficient between the outputs of distributed wind farms through historical data;

[0007] S2: Establish basic trust distribution for active power and reactive power of distributed wind farms through evidence theory synthesis rules, assuming the number of division focal elements is n; substitute the basic trust distribution into the power flow equation to construct a probability interval power flow model;

[0008] S3: For the input uncertain variables of different nodes, the joint trust distribution is established through the Cartesian product to obtain the focal domain and corresponding trust of the joint identification framework;

[0009] S4: Establish an affine power flow model under the input of the focal element interval in each focal element domain, embed the constraint condition formulas corresponding to various correlation models into the affine power flow model respectively, and solve the interval power flow solution of the input focal element considering the correlation;

[0010] S5: The belief function Bel and the likelihood function Pl are calculated through evidence theory to construct a probability interval to describe the probability boundary of the interval power flow solution.

[0011] According to the above scheme, in step S2, the specific steps of establishing basic trust distribution are:

[0012] A probabilistic interval power flow model of distribution network is constructed on the basis of evidence theory. The fluctuation interval of input variables is divided into multiple sub-intervals and the corresponding probabilities of the sub-intervals are assigned according to historical statistical data to construct a focal element model of input variables. Then, the interval power flow algorithm is used to solve the interval solution under the corresponding probability of uncertain power flow. Finally, the cumulative likelihood probability distribution and cumulative trust probability distribution are constructed through evidence theory to obtain the probability boundary of the uncertain power flow solution.

[0013] Furthermore, in step S2, the specific steps are:

[0014] S21: Establish the focal element model of input variables: Let [x k ,x k+1 ] is the interval of the input uncertain variable x divided into the kth subinterval of B focal elements; m k is the basic trust corresponding to the kth subinterval. When the focal element x contains only one input uncertain variable, the basic trust distribution BPA of the input focal element is obtained as follows:

[0015]

[0016] The above formula indicates that the input uncertain variable is in the focal element interval [x k ,x k+1 ] has a trust value of m k ;

[0017] When the focal element x i When there are n input uncertain variables, there are different combinations of input variables, and the number of focal elements increases in a power function. is the focal domain consisting of n input uncertain variables; N n is the number of focal elements divided; The joint trust of the focal element domain is the product of the trust corresponding to the subintervals in the focal element domain. The joint trust distribution of the input focal element is obtained through the Cartesian product. The focal element domain and the corresponding joint trust under n input uncertain variables are obtained. The joint trust distribution of the input focal element is obtained as follows:

[0018]

[0019] S21: Establish a probability interval power flow model: The distributed wind farm output active power P at the distribution network node i Wi and reactive power Q Wi When constructing the focal domain, the sub-interval division principle is assumed to be the same and the probability corresponding to the sub-interval is the same; the output active power of the distributed wind farm is assumed to be P Wi , construct P Wi The equivalent interval focal element domain is divided according to the equivalent interval to construct the basic trust distribution. Suppose the distributed wind farm output active power P Wi The basic trust distribution divides N Wi focal element, and focal element The interval radius is equal; are the trust levels of each focal element, Then, each focal element is assigned a basic trust degree, and the distributed wind farm output active power P is established. Wi The trust distribution is:

[0020]

[0021] Assume that there are n distributed wind farms in the distribution network. Any focal domain consisting of the active power output of n distributed wind farms is a multidimensional cube; its multidimensional joint trust distribution is shown in the following formula:

[0022]

[0023] Let N be the number of nodes in the distribution network; S P Represents the set of PQ and PV nodes; S PQ Represents the set of PQ nodes; S PV Represents a set of PV nodes; P Li , are the minimum and maximum active power requirements of the load at node i, respectively; Q Li , are the minimum and maximum reactive power requirements of the load at node i respectively; G ij , B ijare the real and imaginary parts of the elements in the i-th row and j-th column of the node admittance matrix respectively; e i 、f i are the real and imaginary parts of the voltage at node i, respectively; V i is the voltage amplitude of node i; then substitute the above formula into the distribution network power flow equation in rectangular coordinates to obtain:

[0024]

[0025] Furthermore, in step S3, the specific steps are:

[0026] set up is the input uncertainty x i The focal element, N i For the input uncertain variable x i The number of focal elements; then the input uncertain variable x i The identification framework is:

[0027]

[0028] Assume A j The focal element of the joint trust distribution of x, m j A j The joint trust degree; N is the number of focal elements, N = N1 × N2 × … × N n ; Then the joint basic trust distribution of the input uncertainty x is obtained through the Cartesian product, and the n-dimensional joint identification framework Ω of x x for:

[0029]

[0030] Furthermore, in step S4, the specific steps are:

[0031] S41: Establish an affine power flow model:

[0032] set up and is the deterministic power flow solution when the injected power is the center value of the interval, that is, the injected active power Reactive power and They are respectively the active power injected into node j and reactive power The corresponding noise element; and They represent the active power injected into node j respectively. For i and f i The sensitivity coefficient of and Respectively represent the reactive power injected into node j For i and f i sensitivity coefficient and It is directly obtained from the inverse matrix of the Jacobian matrix of the deterministic power flow equation; the affine power flow algorithm is used to solve the interval power flow, and the injected active power at node i is Reactive power l is the index of any subinterval combination in the focal domain, then the real part of the voltage at node i, e i and the imaginary part f i The affine form of is:

[0033]

[0034] set up is the square of the voltage amplitude at PV node i; is the square of the voltage amplitude at node i obtained by the deterministic power flow solution when the injected power is the center value of the interval, is the noise element coefficient after affine operation; is the noise element newly generated after affine operation The noise element coefficient, S n is the newly generated noise element The dimension of the node is ; then substitute the above formula into the power flow equation to reconstruct the node injected active power, reactive power and node voltage equations, and the affine expression is obtained as follows:

[0035]

[0036] According to the fluctuation range of node injection power:

[0037]

[0038] Let inf(·) and sup(·) represent the lower and upper bounds of the interval quantity respectively; Substituting the affine expression into the above formula, we get:

[0039]

[0040]

[0041]

[0042]

[0043] make:

[0044]

[0045] Then the affine power flow constraint corresponding to the lth focal element combination is:

[0046]

[0047] S42: Considering interval correlation: The parallelogram model PM, convex polygon model CPM and ellipsoid model EM are used to model the correlation of the input focal element interval to characterize the impact of correlation on the uncertain power flow distribution.

[0048] Furthermore, in step S42, the specific steps of using the parallelogram model PM to perform correlation modeling on the input focal element interval are:

[0049] Assume two input focal element intervals x w ,y w The input focal element intervals are The radius of the interval; x c ,y c The input focal element intervals are The central value of ; when the two input focal element intervals are independent of each other, the area formed is a rectangle; when there is a correlation between the two input focal element intervals, the area formed shrinks, and this envelope area is described by constructing a parallelogram. The constructed parallelogram model is required to include all sampling points; let a and b represent the length of the semi-diagonal and semi-diagonal of the parallelogram respectively, and define the input focal element interval and The correlation coefficient is:

[0050]

[0051] set up represents the input focal element interval; X c =[x c ,y c ] T is the center value of the interval variable; e = [1 1] T ; Then the mathematical model using parallelogram to describe the envelope area is:

[0052] |ρ -1 T -1 R -1 ΔX|≤e,

[0053]

[0054]

[0055]

[0056] ΔX=XX c ;

[0057] Let δ=[δ1,δ2] T(δ i =[-1,1],i=1,2); the input focus variable in the parallelogram model The correlation mathematical model is converted into:

[0058] X=RTρδ+X c ;

[0059] Assume that the distributed wind farm node injects active power P Wj and P Wk The correlation coefficient between jk ; and The correlation coefficient between jk According to the affine power flow constraint condition, the affine power flow constraint condition without considering the correlation is obtained as follows:

[0060]

[0061] The above formula represents the four boundaries of the rectangle;

[0062] When considering the correlation, the parallelogram is transformed into the corresponding constraint conditions; when the rectangle is transformed into the parallelogram, the positions of the two relative points remain unchanged, and the constraint conditions of the correlation under the parallelogram model are obtained by the linear coordinate transformation; let is the slope of the parallelogram side; the interval Using X=RTρδ+X c right Calculate; then construct have to:

[0063]

[0064] The four sides of the parallelogram are transformed into two constraint expressions; the affine power flow constraint considering PM correlation is:

[0065]

[0066] Furthermore, in step S42, the specific steps of using the convex polygon model CPM to perform correlation modeling on the input focal element interval are:

[0067] The edge blank area is cut by linear constraints, and this part of the area is re-enveloped to form a convex polygon to describe the correlation of the input focal element interval;

[0068] make is the scaling factor; the edges of the convex polygon model are transformed by translation transformation; then the affine power flow constraint considering CPM correlation is:

[0069]

[0070] Furthermore, in step S42, the specific steps of using the ellipsoid model EM to perform correlation modeling on the input focal element interval are:

[0071] Assume D x , D y They are The variance of , then:

[0072] D x =(x w ) 2 ,D y =(y w ) 2 ;

[0073] Let θ be the inclination angle of the ellipsoid, then the major and minor semi-axes r1 and r2 of the ellipse are:

[0074]

[0075] ρ xy For the focal interval The correlation coefficient is:

[0076]

[0077] but The covariance of is:

[0078]

[0079] Let C be the covariance matrix, then the mathematical model of the ellipsoid model is:

[0080] G(X)=(XX c ) T C -1 (XX c )≤1;

[0081] Let Ω be the characteristic matrix of the ellipsoid model, Ω = C -1 ; then L0 is obtained by Cholesky decomposition:

[0082]

[0083] When considering EM correlation, the ellipsoid model is decorrelated and transformed to obtain:

[0084]

[0085] The tilted ellipsoid formula is used to perform nonlinear coordinate transformation on the envelope area of ​​the focus element interval to form the nonlinear constraint condition of the ellipsoid surface envelope. Construct lower and upper bounds for nonlinear constraints, pass For the inclined ellipsoid, the interval number is calculated by the construction formula The affine power flow constraint considering EM correlation is:

[0086]

[0087] According to the above scheme, in step S5, the specific steps are:

[0088] Active power P of distributed wind farm Wi , is between and For any value of and the likelihood function The calculation formulas are:

[0089]

[0090]

[0091] A computer storage medium stores a computer program executable by a computer processor, wherein the computer program executes a distribution network probability interval power flow calculation method considering correlation.

[0092] The beneficial effects of the present invention are:

[0093] 1. A distribution network probability interval power flow calculation method considering correlation of the present invention divides the output interval of the distributed wind farm into several sub-intervals and assigns corresponding probabilities to the sub-intervals, thereby constructing a focal element model of the distributed wind farm output; combining affine arithmetic to transform the distribution network probability interval power flow model based on the focal element model into an affine optimization model for solution, and using a parallelogram model, a convex polygon model, and an ellipsoid model to describe the correlation of the distributed wind farm output, and transforming the correlation model into an affine constraint condition through coordinate transformation and embedding it into the affine optimization model for joint solution; finally, according to the evidence theory synthesis rule, the probability boundary of the distribution network probability interval deliquescence is obtained. The function of accurately simulating the impact of the access of distributed wind farms on the distribution of uncertain power flow of the distribution network is realized.

[0094] 2. The present invention adopts a new probabilistic interval power flow (PIPF) to calculate the uncertainty power flow model with the input uncertain variable as the probability interval, which solves the shortcomings of the existing distribution network uncertainty power flow algorithm and obtains the best comprehensive result. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1is a flow chart of an embodiment of the present invention.

[0096] Figure 2 It is a topological diagram of a 33-node distribution network example according to an embodiment of the present invention.

[0097] Figure 3 Schematic diagram of a parallelogram model according to an embodiment of the present invention.

[0098] Figure 4 Schematic diagram of a convex polygon model according to an embodiment of the present invention.

[0099] Figure 5 Schematic diagram of an ellipsoid model according to an embodiment of the present invention.

[0100] Figure 6 It is a cumulative probability distribution diagram of the voltage amplitude of the node 14 of the IEEE-33 system when the correlation is not considered according to an embodiment of the present invention.

[0101] Figure 7 It is a cumulative probability distribution diagram of the voltage amplitude of the node 14 of the IEEE-33 system when the parallelogram model correlation is considered in an embodiment of the present invention.

[0102] Figure 8 It is a cumulative probability distribution diagram of the voltage amplitude of the node 14 of the IEEE-33 system when the correlation of the convex polygon model is considered in an embodiment of the present invention.

[0103] Fig. 9 It is a cumulative probability distribution diagram of the voltage amplitude of the node 14 of the IEEE-33 system when the correlation of the ellipsoid model is considered in an embodiment of the present invention. DETAILED DESCRIPTION

[0104] In order to more clearly illustrate the technical solution and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and a 33-node system as an example. The specific examples described here are only used to explain the present invention and are not used to limit the present invention.

[0105] See also Figure 1 According to an embodiment of the present invention, a probability interval power flow calculation method for a distribution network considering correlation is provided. First, a focal element model of the distributed wind farm output is constructed by dividing the output interval of the distributed wind farm into a plurality of sub-intervals and assigning corresponding probabilities to the sub-intervals. The probability interval power flow model of the distribution network based on the focal element model is converted into an affine optimization model for solution by combining affine arithmetic, and a parallelogram model, a convex polygon model, and an ellipsoid model are used to describe the correlation of the output of the distributed wind farm. The correlation model is converted into an affine constraint condition through coordinate transformation and embedded into the affine optimization model for joint solution. Finally, the probability boundary of the probability interval deliquescence of the distribution network is obtained according to the synthesis rule of evidence theory.

[0106] The calculation process is as follows Figure 1 As shown, taking a 33-node system as an example, Figure 2 The specific steps are as follows:

[0107] Step 1: Initialization: input the initial data of the distribution network power flow model and calculate the correlation coefficient between the outputs of distributed wind farms through historical data;

[0108] Considering the uncertainty of the injected power of the distributed wind farm and the load demand power, it is assumed that the fluctuation range of the load demand power is ±10% of its expected value. Distributed wind farm 1 and distributed wind farm 2 are connected to nodes 14 and 32 of the IEEE-33 node distribution network, and the output active power of the distributed wind farms is in the range of [0,1000]kW and [0,800]kW. Considering the correlation between the injected active power of the two distributed wind farms, the correlation coefficient of PM is -0.2, and the upper and lower scaling coefficient of CPM is 1.1; in order to verify the superiority of EM in describing the correlation of input variables, the correlation coefficient of EM can be obtained as -0.75 while ensuring that the envelope area is close to that of CPM and can include all sampling points.

[0109] Step 2: Establish basic trust allocation for active power and reactive power of distributed wind farms through evidence theory synthesis rules, assuming that the number of focal units is n. Substitute the basic trust allocation into the power flow equation to construct a probability interval power flow model; Tables 1 to 4 give the basic trust allocation of 2, 4, 8, and 16 focal units of the output active power of distributed wind farms in the IEEE-33 node distribution network;

[0110] Table 1 Basic trust distribution table of the output active power of distributed wind farm with two focal units

[0111]

[0112]

[0113] Table 2 Basic trust distribution table of the output active power of distributed wind farms with 4 focal units

[0114]

[0115] Table 3 Basic trust distribution table of the output active power of distributed wind farm with 8 focal units

[0116]

[0117] Table 4 Basic trust distribution table of the output active power of the distributed wind farm with 16 focal units

[0118]

[0119]

[0120] Table 5 Probability intervals of PIPF variable values ​​for different correlation models

[0121]

[0122] (1) Establishing basic trust distribution: The present invention constructs a distribution network probability interval power flow model based on evidence theory. The fluctuation interval of the input variable is divided into multiple sub-intervals, and the corresponding probabilities of the sub-intervals are assigned according to historical statistical data. In this way, a focal element model of the input variable is constructed. Then, the interval power flow algorithm is used to solve the interval solution under the corresponding probability of the uncertain power flow. Finally, the cumulative likelihood probability distribution and the cumulative trust probability distribution are constructed through evidence theory to obtain the probability boundary of the uncertain power flow solution.

[0123] ① Establish a focal element model of input variables:

[0124] When the focal element x contains only one input uncertain variable, the basic probability assignment (BPA) of the input focal element is obtained as:

[0125]

[0126] In the formula, [x k ,x k+1 ] is the interval of the input uncertain variable x divided into the kth subinterval of B focal elements; m k is the basic trust corresponding to the kth subinterval. The above formula indicates that the input uncertain variable is in the focal element interval [x k ,x k+1 ] has a trust value of m k .

[0127] When the focal element x i When there are n input uncertain variables, there are different combinations between the input variables, and the number of focal elements increases in a power function. The joint trust distribution of the input focal elements is obtained through the Cartesian product, and the focal element domain and the corresponding joint trust under n input uncertain variables are obtained. At this time, the joint trust distribution of the input focal elements is obtained as follows:

[0128]

[0129] In the formula, is the focal region composed of n input uncertain variables; N n is the number of focal elements divided; is the joint trust of the focal domain, that is, the product of the trust corresponding to the subintervals in the focal domain.

[0130] ② Establish a probability interval power flow model:

[0131] The output active power P of the distributed wind farm at the distribution network node i Wi and reactive power Q Wi When constructing the focal domain, it is assumed that the sub-interval division principle is the same and the probability corresponding to the sub-interval is the same. Wi For example, construct P Wi The equivalent interval focal element domain is constructed according to the equivalent interval division, that is, the interval radius of each focal element is equal. The basic trust degree allocation is assigned to each focal element to establish the distributed wind farm output active power P Wi The trust distribution is:

[0132]

[0133] In the formula, the distributed wind farm output active power P Wi The basic trust distribution divides N Wi focal element, and focal element The interval radius is equal; are the trust levels of the corresponding focal elements,

[0134] Assuming that there are n distributed wind farms in the distribution network, the multi-dimensional joint trust distribution is as follows:

[0135]

[0136] In the formula, Represents any focal element domain composed of the active power output of n distributed wind farms, which is a multidimensional cube. Substituting the above formula into the distribution network power flow equation in rectangular coordinates, we can get:

[0137]

[0138] Where: N is the number of distribution network nodes; S P Represents the set of PQ and PV nodes; S PQ Represents the set of PQ nodes; S PV Represents a set of PV nodes; P Li , are the minimum and maximum active power demands of the load at node i, respectively; Q Li , are the minimum and maximum reactive power requirements of the load at node i; G ij , B ij are the real and imaginary parts of the elements in the i-th row and j-th column of the node admittance matrix respectively; e i 、f i are the real and imaginary parts of the voltage at node i, respectively; V i is the voltage amplitude at node i.

[0139] Step 3: For the input uncertain variables of different nodes, the joint trust distribution is established through the Cartesian product to obtain the focal domain and corresponding trust of the joint identification framework;

[0140] Enter the uncertain variable x i The identification framework can be set as:

[0141]

[0142] Where: is the input uncertainty x i The focal element; N i For the input uncertain variable x i The number of focal elements.

[0143] The joint basic trust distribution of the input uncertainty x is obtained through the Cartesian product, and the n-dimensional joint identification framework Ω of x x for:

[0144]

[0145] Where: A j The focal element of the joint trust distribution of x, m j A j The joint trust degree; N is the number of focal elements, N = N1 × N2 × … × N n .

[0146] Step 4: Establish an affine power flow model under the input of the focal element interval of each focal element domain, further embed the constraint condition formulas corresponding to the three correlation models into the affine power flow model respectively, and solve the interval power flow solution of the input focal element considering the correlation;

[0147] ① Establish an affine power flow model:

[0148] Depend on Any input of a focus unit group in the focal unit domain corresponds to an interval power flow model. Therefore, by inputting the focus unit model, the probability interval power flow model of the distribution network can be converted into several interval power flow models for solution. In order to avoid the interval expansion problem of the traditional interval power flow algorithm, the present invention adopts the affine power flow algorithm to solve the interval power flow, and the injected active power at the node i is Reactive power l is the index of any subinterval combination in the focal domain, then the real part of the voltage at node i, e i and the imaginary part f i The affine form of is:

[0149]

[0150] Where: and is the deterministic power flow solution when the injected power is the center value of the interval, that is, the injected active power Reactive power and They are respectively the active power injected into node j and reactive power The corresponding noise element; and They represent the active power injected into node j respectively. For i and f i The sensitivity coefficient of and Respectively represent the reactive power injected into node j For i and f i These four sensitivity coefficients can be directly obtained from the inverse matrix of the Jacobian matrix of the deterministic power flow equation.

[0151] Further substituting it into the power flow equation to reconstruct the node injected active power, reactive power and node voltage equation, the affine expression is obtained as follows:

[0152]

[0153] Where: is the square of the voltage amplitude at PV node i; is the square of the voltage amplitude at node i obtained by the deterministic power flow solution when the injected power is the center value of the interval, is the noise element coefficient after affine operation; is the noise element newly generated after affine operation The noise element coefficient, S n is the newly generated noise element The dimension of .

[0154] According to the fluctuation range of the node injection power, we can get:

[0155]

[0156] Substituting the affine expression into the above formula, we can get:

[0157]

[0158]

[0159]

[0160]

[0161] In the formula, inf(·) and sup(·) represent the lower and upper bounds of the interval quantity, respectively.

[0162]

[0163] Therefore, the affine power flow constraint corresponding to the lth focal element combination is:

[0164]

[0165] ② Consider interval correlation:

[0166] The present invention adopts Parallelogram Model (PM), Convex Polygon Model (CPM) and Ellipsoidal Model (EM) to respectively model the correlation of input focal element intervals, so as to characterize the influence of correlation on the distribution of uncertain power flow.

[0167] Assume two input focal element intervals x w ,y w The input focal element intervals are The radius of the interval; x c ,y c The input focal element intervals are When the two input focal element intervals are independent of each other, the area they form is Figure 3 When there is a correlation between the two input focal element intervals, the area formed will shrink, and a parallelogram can be constructed to describe this envelope area. The constructed parallelogram model is required to include all sampling points. Input focal element interval and The correlation coefficient can be defined as:

[0168]

[0169] Where a and b represent the length of the half diagonal and half diagonal of the parallelogram, respectively.

[0170] The mathematical model using a parallelogram to describe the envelope area is:

[0171] |ρ -1 T -1 R -1 ΔX|≤e

[0172]

[0173]

[0174]

[0175] ΔX=XX c

[0176] Where: represents the input focal element interval; X c =[x c ,y c ] T is the center value of the interval variable; e = [1 1] T .

[0177] The input focus variable in the parallelogram model The correlation mathematical model is converted into:

[0178] X=RTρδ+X c

[0179] Where δ=[δ1,δ2] T (δ i =[-1,1],i=1,2).

[0180] Assume that the distributed wind farm node injects active power P Wj and P Wk The correlation coefficient between jk .at this time and The correlation coefficient between them is also ρ jk According to the affine power flow constraint condition, the affine power flow constraint condition without considering the correlation can be obtained as follows:

[0181]

[0182] like Figure 3 As shown, the above formula represents the four boundaries of rectangle ABCD. When considering the correlation, it is necessary to Figure 3 The parallelogram in is transformed into the corresponding constraints. When the rectangle ABCD is transformed into the parallelogram AECD, the positions of the two relative points A and C remain unchanged, and the constraints of correlation under the parallelogram model can be obtained by linear coordinate transformation. We can get:

[0183]

[0184] In the formula, is the slope of the parallelogram side; the interval Using X=RTρδ+X c right Calculated.

[0185] This method can transform the four sides AE, AD, DE, and CD of the parallelogram into two constraint expressions. The affine power flow constraint considering PM correlation is:

[0186]

[0187] When PM is used to describe the correlation of the input focal element interval, there is a blank area on the edge of the parallelogram, which will cause the use of PM to expand the envelope area of ​​the sampling point, making the interval result conservative. Figure 4 As shown, the edge blank area is cut by linear constraints, and this part of the area is re-enveloped to form a convex polygon AGHCIJ to describe the input focal element interval correlation, which is more accurate than the area enveloping PM, and the interval result will be more precise. The essence of CPM is to perform linear cutting on the basis of PM, and its mathematical model is the same as that of PM.

[0188] The edges GH and IJ of the convex polygon model cannot be directly calculated by the above method, but can be transformed by translation transformation. is the scaling factor. Affine power flow constraints considering CPM correlation:

[0189]

[0190] PM and CPM are both linear models. In actual situations, there is a nonlinear relationship in the correlation of the input focal element intervals. There is a certain degree of conservatism in using PM and CPM to describe the correlation of the input focal element intervals. The ellipsoid model can well describe the nonlinear relationship of the input focal element intervals. Therefore, the present invention introduces the ellipsoid model to describe the correlation of the input focal element intervals.

[0191] The mathematical model of the ellipsoid model is:

[0192] G(X)=(XX c ) T C -1 (XX c )≤1

[0193] Where C is the covariance matrix. The covariance of is:

[0194]

[0195] Where D x , D y They are The variance of θ is the inclination angle of the ellipsoid; ρ is the xy For the focal interval The correlation coefficient is calculated as follows:

[0196] D x =(x w ) 2

[0197]

[0198] like Figure 5 As shown, the major and minor semi-axes r1 and r2 of the ellipse are:

[0199]

[0200] When considering EM correlation, the ellipsoid model is decorrelated and transformed to obtain:

[0201]

[0202] In the formula, L0 is obtained by Cholesky decomposition, that is:

[0203]

[0204] Where Ω is the characteristic matrix of the ellipsoid model, Ω = C -1 .

[0205] The tilted ellipsoid formula is used to perform nonlinear coordinate transformation on the envelope area of ​​the focus element interval to form the nonlinear constraint condition of the ellipsoid surface envelope. Construct lower and upper bounds for nonlinear constraints, pass For the inclined ellipsoid, the interval number is calculated by the construction formula The affine power flow constraint considering EM correlation is:

[0206]

[0207] Step 5: Calculate the belief function (Bel) and likelihood function (Pl) through evidence theory to construct a probability interval to describe the probability boundary of the interval power flow solution.

[0208] The active power P of the distributed wind farm Wi For example, is between and For any value of and the likelihood function The calculation formula is:

[0209]

[0210]

[0211] from Figures 6 to 9It can be seen that, whether considering the correlation and or considering the correlation of PM, CPM, and EM, as the number of focal element intervals of the distributed wind farm output power increases, the probability interval of the power flow solution obtained by the distribution network probability interval power flow algorithm gradually becomes smaller, and the cumulative trust function curve and the cumulative likelihood function curve gradually become smoother. According to this trend, it can be judged that when the obtained uncertainty information of the distributed wind farm output power is sufficient, that is, when the number of divided focal elements approaches infinity, the cumulative trust function curve and the cumulative likelihood function curve will overlap into a smooth cumulative probability distribution curve, and evolve into the probability distribution of the probability power flow; when the obtained uncertainty information of the distributed wind farm output power is very little, that is, when the number of divided focal elements is 1, the cumulative likelihood function curve and the cumulative trust function curve evolve into the upper and lower boundary distribution of the interval power flow. Therefore, the proposed probability interval power flow is a new type of uncertainty power flow algorithm between the interval power flow and the probability power flow, which realizes the organic unity of the two.

[0212] Table 1 gives the probability intervals of PIPF power flow solution values ​​under 2, 4, 8, and 16 focal elements when different correlation models are used. When the voltage amplitude of node 14 is less than 0.92pu, the probability interval under 2 focal elements is [0, 0.7574] without considering the correlation, which means that the maximum probability of the voltage amplitude of node 14 being less than 0.92pu is 0.7574, and the minimum probability is 0; but when considering the three types of correlation models, the probability interval under 2 focal elements is [0, 0.5821], which is smaller than the probability interval without considering the correlation. This also confirms the impact of the correlation of the output of distributed wind farms on the probability interval power flow results of the distribution network. Moreover, as the number of focal elements increases, the probability interval of the uncertainty power flow results of the distribution network becomes narrower and narrower, which is consistent with the Figures 6 to 9 Comparing the probability intervals of the distribution network flow results under the three types of correlation models, the probability intervals of the distribution network uncertainty flow results in the ellipsoid model are at least less than or equal to the convex polygon model and the parallelogram model. This shows that the ellipsoid model forms a curve envelope area through nonlinear constraints, which can better describe the correlation of distributed wind farm output than the convex polygon model and parallelogram model formed by linear constraints.

[0213] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0214] The above embodiments are only used to illustrate the design ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. A method for calculating the probability interval power flow of a distribution network considering correlation, characterized in that: The following steps are involved: S1: Initialization, input the initial data of the distribution network power flow model, and calculate the correlation coefficient between the outputs of distributed wind farms through historical data; S2: Establish basic trust distribution for active power and reactive power of distributed wind farms through evidence theory synthesis rules, assuming the number of division focal elements is n; substitute the basic trust distribution into the power flow equation to construct a probability interval power flow model; The specific steps to establish a basic trust distribution are: Based on the theory of evidence, a probability interval power flow model of the distribution network is constructed. The fluctuation interval of the input variable is divided into multiple sub-intervals, and the corresponding probabilities of the sub-intervals are assigned according to historical statistical data. In this way, the focal element model of the input variable is constructed. Then, the interval power flow algorithm is used to solve the interval solution under the corresponding probability of the uncertain power flow. Finally, the cumulative likelihood probability distribution and cumulative trust probability distribution are constructed through the theory of evidence to obtain the probability boundary of the uncertain power flow solution. The specific steps are: S21: Establish the focal element model of input variables: Let [x k ,x k+1 ] is the interval of the input uncertain variable x divided into the kth subinterval of B focal elements; m k is the basic trust corresponding to the kth subinterval. When the focal element x contains only one input uncertain variable, the basic trust distribution BPA of the input focal element is obtained as follows: The above formula indicates that the input uncertain variable is in the focal element interval [x k ,x k+1 ] has a trust value of m k ; When the focal element x i When there are n input uncertain variables, there are different combinations of input variables, and the number of focal elements increases in a power function. is the focal domain consisting of n input uncertain variables; N n is the number of focal elements divided; The joint trust of the focal element domain is the product of the trust corresponding to the subintervals in the focal element domain. The joint trust distribution of the input focal element is obtained through the Cartesian product. The focal element domain and the corresponding joint trust under n input uncertain variables are obtained. The joint trust distribution of the input focal element is obtained as follows: S22: Establish a probability interval power flow model: The distributed wind farm output active power P at the distribution network node i Wi and reactive power Q Wi When constructing the focal domain, the sub-interval division principle is assumed to be the same and the probability corresponding to the sub-interval is the same; the output active power of the distributed wind farm is assumed to be P Wi , construct P Wi The equivalent interval focal element domain is divided according to the equivalent interval to construct the basic trust distribution. Suppose the distributed wind farm output active power P Wi The basic trust distribution divides N Wi focal element, and focal element The interval radius is equal; are the trust levels of each focal element, Then, each focal element is assigned a basic trust degree, and the distributed wind farm output active power P is established. Wi The trust distribution is: Assume that there are n distributed wind farms in the distribution network. ……、 Any focal element domain consisting of the active power output of n distributed wind farms is a multidimensional cube; Its multi-dimensional joint trust distribution is shown as follows: Let N be the number of nodes in the distribution network; S P Represents the set of PQ and PV nodes; S PQ Represents the set of PQ nodes; S PV Represents a set of PV nodes; P Li , are the minimum and maximum active power requirements of the load at node i, respectively; Q Li , are the minimum and maximum reactive power requirements of the load at node i respectively; G ij , B ij are the real and imaginary parts of the elements in the i-th row and j-th column of the node admittance matrix respectively; e i 、f i are the real and imaginary parts of the voltage at node i, respectively; V i is the voltage amplitude of node i; then substitute the above formula into the distribution network power flow equation in rectangular coordinates to obtain: S3: For the input uncertain variables of different nodes, a joint trust degree distribution is established through Cartesian product to obtain the focal domain and corresponding trust degree of the joint identification framework; the specific steps are: set up is the input uncertainty x i The focal element, N i For the input uncertain variable x i The number of focal elements; then the input uncertain variable x i The identification framework is: Assume A j The focal element of the joint trust distribution of x, m j A j The joint trust degree; N is the number of focal elements, N = N1 × N2 × … × N n ; Then the joint basic trust distribution of the input uncertainty x is obtained through the Cartesian product, and the n-dimensional joint identification framework Ω of x x for: S4: Establish an affine power flow model under the input of the focal element interval in each focal element domain, embed the constraint condition formulas corresponding to various correlation models into the affine power flow model respectively, and solve the interval power flow solution of the input focal element considering the correlation; the specific steps are: S41: Establish an affine power flow model: set up and is the deterministic power flow solution when the injected power is the center value of the interval, that is, the injected active power Reactive power and They are respectively the active power injected into node j and reactive power The corresponding noise element; and They represent the active power injected into node j respectively. For i and f i The sensitivity coefficient of and Respectively represent the reactive power injected into node j For i and f i sensitivity coefficient and It is directly obtained from the inverse matrix of the Jacobian matrix of the deterministic power flow equation; the affine power flow algorithm is used to solve the interval power flow, and the injected active power at node i is Reactive power l is the index of any subinterval combination in the focal domain, then the real part of the voltage at node i, e i and the imaginary part f i The affine form of is: set up is the square of the voltage amplitude at PV node i; is the square of the voltage amplitude at node i obtained by the deterministic power flow solution when the injected power is the center value of the interval, is the noise element coefficient after affine operation; is the noise element newly generated after affine operation The noise element coefficient, S n is the newly generated noise element The dimension of the node is ; then substitute the above formula into the power flow equation to reconstruct the node injected active power, reactive power and node voltage equations, and the affine expression is obtained as follows: According to the fluctuation range of node injection power: Let inf(·) and sup(·) represent the lower and upper bounds of the interval quantity respectively; Substituting the affine expression into the above formula, we get: make: Then the affine power flow constraint corresponding to the lth focal element combination is: S42: Considering interval correlation: The parallelogram model PM, convex polygon model CPM and ellipsoid model EM are used to model the correlation of the input focal element interval to characterize the impact of correlation on the distribution of uncertain power flow; S5: Calculate the belief function Bel and the likelihood function Pl through evidence theory to construct a probability interval to describe the probability boundary of the interval power flow solution; the specific steps are: Active power P of distributed wind farm Wi , is between and For any value of and the likelihood function The calculation formulas are:

2. A method for calculating the probability interval power flow of a distribution network considering correlation according to claim 1, characterized in that: In step S42, the specific steps of using the parallelogram model PM to perform correlation modeling on the input focal element interval are: Assume two input focal element intervals x w ,y w The input focal element intervals are The radius of the interval; x c ,y c The input focal element intervals are The central value of ; when the two input focal element intervals are independent of each other, the area formed is a rectangle; when there is a correlation between the two input focal element intervals, the area formed shrinks, and this envelope area is described by constructing a parallelogram. The constructed parallelogram model is required to include all sampling points; let a and b represent the length of the semi-diagonal and semi-diagonal of the parallelogram respectively, and define the input focal element interval and The correlation coefficient is: set up represents the input focal element interval; X c =[x c ,y c ] T is the center value of the interval variable; e = [1 1] T ; Then the mathematical model using parallelogram to describe the envelope area is: |ρ -1 T -1 R -1 ΔX|≤e, ΔX=X-X c ; Let d = [d1,d2] T (d i (=[-1,1],i=1,2); The input focus variable in the parallelogram model The correlation mathematical model is converted into: X=RTρδ+X c ; Assume that the distributed wind farm node injects active power P Wj and P Wk The correlation coefficient between jk ; and The correlation coefficient between jk According to the affine power flow constraint condition, the affine power flow constraint condition without considering the correlation is obtained as follows: The above formula represents the four boundaries of the rectangle; When considering the correlation, the parallelogram is transformed into the corresponding constraint conditions; when the rectangle is transformed into the parallelogram, the positions of the two relative points remain unchanged, and the constraint conditions of the correlation under the parallelogram model are obtained by the linear coordinate transformation; let is the slope of the parallelogram side; the interval Using X=RTρδ+X c right Calculate; then construct have to: The four sides of the parallelogram are transformed into two constraint expressions; the affine power flow constraint considering PM correlation is:

3. The method for calculating the probability interval power flow of a distribution network considering correlation according to claim 1 is characterized in that: In step S42, the specific steps of using the convex polygon model CPM to perform correlation modeling on the input focal element interval are: The edge blank area is cut by linear constraints, and this part of the area is re-enveloped to form a convex polygon to describe the correlation of the input focal element interval; make is the scaling factor; the edges of the convex polygon model are transformed by translation transformation; then the affine power flow constraint considering CPM correlation is:

4. The method for calculating the probability interval power flow of a distribution network considering correlation according to claim 1 is characterized in that: In step S42, the specific steps of using the ellipsoid model EM to perform correlation modeling on the input focal element interval are: Assume D x , D y They are The variance of , then: D x =(x w ) 2 ,D y =(y w ) 2 ; Let θ be the inclination angle of the ellipsoid, then the major and minor semi-axes r1 and r2 of the ellipse are: ρ xy For the focal interval The correlation coefficient is: but The covariance of is: Let C be the covariance matrix, then the mathematical model of the ellipsoid model is: G(X)=(X-X c ) T C -1 (X-X c )≤1; Let Ω be the characteristic matrix of the ellipsoid model, Ω = C -1 ; then L0 is obtained by Cholesky decomposition: When considering EM correlation, the ellipsoid model is decorrelated and transformed to obtain: The tilted ellipsoid formula is used to perform nonlinear coordinate transformation on the envelope area of ​​the focus element interval to form the nonlinear constraint condition of the ellipsoid surface envelope. Construct lower and upper bounds for nonlinear constraints, pass For the inclined ellipsoid, the interval number is calculated by the construction formula The affine power flow constraint considering EM correlation is:

5. A computer storage medium, characterized in that: A computer program executable by a computer processor is stored therein, and the computer program executes a distribution network probability interval power flow calculation method considering correlation as described in any one of claims 1 to 4.

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