A robust optimization method for active distribution networks based on generalized linear polyhedron sets

Abstract

The present invention provides a robust optimization method for active distribution networks based on a generalized linear polyhedron set. On the basis of the traditional polyhedron set, the boundary of the polyhedron uncertainty set is reconstructed through the distribution envelope diagram of the correlation of distributed photovoltaic output. Further, in view of the conservative problem of the correlation polyhedron uncertainty set, a generalized linear polyhedron uncertainty set is established to describe the correlation of distributed photovoltaic output. The effectiveness of the generalized linear polyhedron set proposed by the present invention is verified by a calculation example system, and the function of quantifying the influence of the correlation of distributed photovoltaic output on the optimization result in the polyhedron set is realized. The generalized linear polyhedron set of the present invention not only covers the entire range of photovoltaic output fluctuations, but also reduces the blank areas with low probability of distributed photovoltaic output fluctuations. The cost of abandoned light is the lowest, and the network loss cost is lower, and the total system cost is the lowest, that is, the robustness of the optimization result is increased, and the conservatism of the optimization result is reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of distributed power generation grid connection, and in particular relates to a robust optimization method for an active distribution network based on a generalized linear polyhedron set. Background Art

[0002] With the large-scale development and high-proportion access of new energy, the operation of the power grid faces the risk of random disturbances due to its volatility and randomness. On the distribution network side, the traditional distribution network will gradually upgrade to an active distribution network with interactive supply and demand, making the operation mode of the distribution network more diversified. How to effectively overcome the uncertainty of new energy and ensure the safe and economical operation of the distribution network has become a difficult problem that needs to be solved urgently.

[0003] In order to deal with the uncertainty of distributed photovoltaic output, the uncertainty optimization methods of distribution networks are mainly divided into stochastic optimization methods and robust optimization methods. Robust optimization methods usually use polyhedron sets to describe the uncertainty of distributed photovoltaics. Since there is no need to obtain the probability distribution of distributed photovoltaic output and avoid the curse of dimensionality caused by a large number of scenarios, they have attracted more and more attention. The impact of different uncertainty sets on the robust optimization results is very obvious. When the uncertainty set is more refined, the model complexity is higher and the solution is more difficult. When the uncertainty set is wider, the optimal solution is more conservative and less economical. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a robust optimization method for an active distribution network based on a generalized linear polyhedron set, which is used to quantify the influence of the correlation of distributed photovoltaic output on the optimization result in the polyhedron set.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a robust optimization method for active distribution network based on generalized linear polyhedron set, comprising the following steps: S1: initializing the system, inputting active distribution network line parameters, distributed photovoltaic parameters, battery energy storage parameters, group switching capacitor parameters, static VAR compensator parameters, on-load tap-changing transformer parameters and load prediction reference value;

[0006] S2: Establish a distributed photovoltaic output correlation polyhedron model. The specific steps include:

[0007] S21: Establish a distributed photovoltaic output correlation polyhedron set to describe the uncertainty of distributed photovoltaic output;

[0008] S22: Reconstruct the boundary of the polyhedron set in combination with the correlation distribution envelope diagram, establish a generalized linear polyhedron set describing the correlation of distributed photovoltaic output, reduce the proportion of blank areas of the envelope, and increase the proportion of areas around the diagonal of the envelope to solve the problem of excessive conservatism;

[0009] S3: Construct an adjustable robust optimization model for active distribution network, including the comprehensive cost objective function of active distribution network and the operation constraints of active distribution network;

[0010] S4: A linear affine mechanism is used in the active distribution network adjustable robust optimization model to establish the relationship between the adjustable decision variables and the uncertainty variables. According to the linear affine mechanism and the distributed photovoltaic output correlation polyhedron model established in step S2, an active distribution network affine adjustable robust optimization model is constructed.

[0011] S5: Solve the affine adjustable robust optimization model of active distribution network based on generalized linear polyhedron set, analyze the influence of generalized linear polyhedron set on the affine adjustable robust optimization results of active distribution network, and output the optimization results.

[0012] According to the above scheme, in step S21, the specific steps are:

[0013] set up is the active power of the distributed photovoltaic connected to node j at time t; is the expected output value of distributed photovoltaic power; is the maximum value of the distributed photovoltaic output fluctuation; z j,t is the uncertain parameter of distributed output; Γ is the polyhedron set uncertainty; then the distributed photovoltaic output correlation polyhedron set is as follows:

[0014]

[0015] Suppose there are n uncertain parameters about distributed photovoltaic output, ρ jk,t represents the uncertain parameter z about the distributed photovoltaic output j,t and z k,t The correlation between them ranges from [-1,1]; then the distributed photovoltaic output correlation polyhedron set is expressed as:

[0016]

[0017] Furthermore, in step S21, n=2;

[0018] Take two uncertain parameters z1 and z2 about distributed photovoltaic output to determine a polyhedron uncertainty set, ρ is the correlation coefficient between the uncertain parameters z1 and z2 of distributed photovoltaic output; use the historical data of distributed photovoltaic output to obtain the correlation matrix of distributed photovoltaic output, randomly sample z1 and z2 with different ρ, and obtain the correlation distribution envelope diagram of the uncertain output parameters z1 and z2;

[0019] If there is no correlation between distributed photovoltaic outputs, |ρ|=0, |z j,t|≤1, the distribution of the uncertain parameters of distributed photovoltaic output forms a square area with a side length of 1;

[0020] When the correlation increases positively, the uncertain parameters are concentrated around the straight line y = x;

[0021] When the correlation decreases in the negative direction, the uncertain parameters are concentrated around the straight line y = -x;

[0022] If there is correlation between distributed photovoltaic outputs, the distributed photovoltaic output fluctuation sampling points are concentrated around the diagonal of the correlation distribution envelope diagram of the uncertain parameters; by bending the boundary of the polyhedron, the area around the diagonal covers more distributed photovoltaic output fluctuation sampling points than the area far from the diagonal; this reconstructed polyhedron set makes the uncertain parameters of distributed photovoltaic output more concentrated around the diagonal; when the correlation coefficient of distributed photovoltaic output is larger, the boundary of the polyhedron set is more curved, and the shape of the reconstructed polyhedron set depends on the strength of the correlation between distributed photovoltaic outputs, that is, the correlation polyhedron set;

[0023] The uncertainty set is taken in the first quadrant of the rectangular coordinate system to analyze the mathematical expression of the correlation polyhedron set; line segments L1 and L2 represent the boundaries of the correlation polyhedron set respectively; line segment L3 represents the boundary of the polyhedron set with the same uncertainty Γ; line segments L4 and L5 represent the boundaries of the correlation polyhedron set when the correlation coefficient of distributed photovoltaic output is the largest; the coordinates of point P1 are (0, Γ), the coordinates of point P2 are (1, 1), and the coordinates of point P3 are (Γ, 0); then the equations of L3, L4 and L5 are expressed as:

[0024] L3:z2=-z1+Γ,

[0025] L4:z2=(1-Γ)z1+Γ,

[0026]

[0027] make It is the straight line L i If the correlation coefficient satisfies 0≤|ρ|≤1 and the uncertainty Γ∈[0,2], the range of the slopes of L1 and L2 is:

[0028]

[0029]

[0030] From the above formula, we can see that in the range of 0≤|ρ|≤1 and Γ∈[0,2], L1 is between L3 and L4, and L2 is between L3 and L5; is an increasing function of |ρ|, It is a decreasing function of |ρ|. The stronger the correlation between distributed photovoltaic outputs, The bigger, The smaller it is, the closer L1 is to L4 and L2 is to L5, so that the area around the diagonal of the correlation distribution envelope of the uncertain parameters covered by it is larger, and the optimization result is more conservative; therefore, the slopes of L1 and L2 are:

[0031]

[0032] Then the equations for L1 and L2 are expressed as:

[0033] L1:z2=((2-Γ)|ρ|-1)z1+Γ,

[0034]

[0035] In summary, substituting the equations of L1 and L2 into the polyhedron uncertainty set, the expression of the correlation polyhedron set formed by the two uncertain parameters of distributed photovoltaic output is obtained as follows:

[0036]

[0037] Furthermore, in step S22, the specific steps are:

[0038] Suppose there are n uncertain parameters about distributed photovoltaic output, and define parameter β c (β c ∈[0,1]) is used to control the range of the envelope of the generalized linear polyhedron set, and the generalized linear polyhedron set is expressed as:

[0039]

[0040] Furthermore, in step S22, n=2;

[0041] Suppose the point with the smallest horizontal coordinate among the points where the correlation distribution envelope formed by the uncertain parameters z1 and z2 intersects with the straight line y=1 is H1(x H ,1); The point with the smallest ordinate among the points where the correlation distribution envelope intersects the straight line x=1 is H1(1,y H ); Let the point with the largest ordinate among the points where the correlation distribution envelope intersects the y-axis be D1(0,y D ); The point with the largest horizontal coordinate among the points where the correlation distribution envelope intersects the x-axis is D2(x D ,0); when point R1 fluctuates between points D1 and P1, and point R2 fluctuates directly between points D2 and P3, the set composed of points R1, R2, H1 and H2 is a generalized linear polyhedron set;

[0042] The generalized linear polyhedron set envelops all areas of the correlation distribution diagram formed by the uncertain parameters z1 and z2, increasing the robustness of the optimization result. When point R1 is closer to point D1 and point R2 is closer to point D2, the improved correlation polyhedron set envelops fewer blank areas, reducing the conservatism of the optimization result. When the correlation coefficient is determined, the line segment is controlled by adjusting the position of point R1 and point R2. and line segments The envelope range controls the conservatism of the optimization results;

[0043] Define parameter β c (β c ∈[0,1]) calculates the ordinate value of point R1 and the abscissa value of point R2 to control the line segment and line segments The locations are as follows:

[0044] y im =(Γ-y D )β c +y D ,

[0045] x im =(Γ-x D )β c +x D ,

[0046] set up Line and The slope of the line segment and line segments The slope of is given by:

[0047]

[0048]

[0049] and The equation is expressed as:

[0050]

[0051] Boundary and parameter x of a set of generalized linear polyhedra D ,y D 、x H and H The boundary of the correlation polyhedron set is related to the correlation coefficient ρ. In order to control the boundary of the generalized linear polyhedron set through the correlation coefficient ρ, the Monte Carlo method is used to establish the parameter x D ,y D 、x H ,yH The linear regression relationship between ρ and the correlation coefficient is shown in the following formula:

[0052]

[0053] It is expressed as the correlation coefficient ρ and The equation is:

[0054]

[0055] The above expression and Substituting the equation into the polyhedron set, we get the expression of the generalized linear polyhedron set formed by two uncertain parameters:

[0056]

[0057] According to the above scheme, in step S3, the specific steps are:

[0058] S31: Let c loss , and c PV are the network loss cost coefficient, the main network power purchase cost coefficient and the abandoned light penalty cost coefficient respectively; r ij is the resistance of branch (i, j); I ij,t is the current of branch (i, j) at time t; is the active power purchased from the main grid at the gateway at node j at time t; Ω L is the line set; Ω TR is the set of distribution and transformation gateway nodes; T is the number of scheduling operation periods; considering the network loss cost, power purchase cost, abandoned light penalty cost and BESS cycle life daily depreciation cost, the comprehensive cost objective function of the active distribution network is constructed as shown in the following formula:

[0059]

[0060] S32: Active distribution network operation constraints include second-order cone relaxation power flow constraints, node voltage and branch current constraints, distributed photovoltaic operation constraints, BESS operation constraints considering cycle life degradation, group switching capacitor CB operation constraints, SVC operation constraints, distribution network gateway power constraints and OLTC operation constraints; specifically:

[0061] S321: Let set u(j) be the set of head nodes of the branch with j as the terminal node in the distribution network; let set v(j) be the set of terminal nodes of the branch with j as the head node in the distribution network; V i,t =(U i,t ) 2 , U j,t is the voltage amplitude; Pij,t , Q ij,t are the active power and reactive power of branch (i, j) at time t respectively; l ij,t =(I ij,t ) 2 , I ij,t is the current of branch (i, j) at time t; P j,t , Q j,t are the active power and reactive power injected into node j respectively; is the reactive power injected into the main grid by the gateway at node j at time t; are the continuous compensation power of the SVC connected to node j and the discrete compensation power of the group switching capacitor bank CB respectively; ij is the reactance of branch (i, j); then the second-order cone relaxed power flow constraint is:

[0062]

[0063] S322: Set are the upper and lower limits of the voltage amplitude at node j respectively; is the upper limit of the current amplitude of branch (i, j); then the node voltage and branch current constraints are:

[0064]

[0065] S323: Set are the reactive power of distributed photovoltaic connected to node j at time t; is the predicted power value of the distributed photovoltaic connected to node j at time t; is the apparent power of the distributed photovoltaic inverter connected to node j; θ j is the power factor angle of the distributed photovoltaic inverter connected to the j node; Ω PV represents the set of distributed photovoltaic access nodes; then the distributed photovoltaic operation constraints are:

[0066]

[0067] S324: BESS operation constraints considering cycle life degradation, including:

[0068] S3241: The life cycle cost of BESS includes the investment cost of BESS and its auxiliary equipment, which is determined by the rated capacity and rated power of BESS; They represent the rated capacity and rated power of the BESS at node j respectively; Ω ESSis the installation node set of BESS; the BESS life cycle cost is converted to daily according to the total number of days in a year, and the loss cost caused by the charge and discharge process in one day on the cycle life is the BESS cycle life daily loss cost C ESS :

[0069]

[0070] set up They represent the unit capacity investment cost and unit power investment cost of BESS at node j respectively; r is the discount rate; is the cycle life of BESS at node j; then the annualized investment cost per unit capacity of BESS at node j is and annualized investment cost per unit power They are:

[0071]

[0072] set up The equivalent number of cycles of a battery in a day based on different depths of discharge; and is the linear fitting coefficient of each term; for the daily depreciation cost of BESS cycle life C ESS Linearization yields:

[0073]

[0074] S3242: BESS has charging state, discharging state and static state. In static state, it neither charges nor discharges. Introduce 0-1 variable Indicates that the BESS at node j is in the charging state during period t, a 0-1 variable It means that the BESS at node j is in the discharging state in time period t. Since the BESS can only be in one of the three states at the same time, we have:

[0075]

[0076] set up are the upper and lower limits of the charging power of BESS at node j respectively; are the upper and lower limits of BESS discharge power at node j respectively; are the charging and discharging powers of BESS at node j in time period t respectively; BESS is also subject to the constraints of charging and discharging rate, energy balance and charging and discharging process during operation, which are respectively expressed as:

[0077]

[0078] set up is the charge state of the BESS at node j at time t; η ch,j , η dis,j are the charging and discharging efficiencies of BESS at node j, respectively; Δt is the scheduling time interval; They are the upper and lower limits of the state of charge of the BESS at node j:

[0079]

[0080] S325: The group switching capacitor CB is a discrete reactive power compensation mechanical device, and its frequent operation times need to be limited to extend its service life; is the compensation power of the CB connected to node j at time t; is the number of CBs connected to node j in operation at time t; is the compensation power of each group of CBs connected to node j at time t; is the limit of the number of CB operations within T cycles in one day; then the group switching capacitor CB constraint is:

[0081]

[0082]

[0083] S326: Set are the lower and upper limits of the adjustable reactive power of the SVC connected to node j, respectively. Considering the operation constraints of the continuously regulated reactive compensation device SVC, the following table shows the operation constraints of the SVC:

[0084]

[0085] S327: The power constraint of the distribution network gateway is to control the power of the distribution network gateway within a certain range to suppress the impact of power fluctuations of the distribution network on the main network. are the upper and lower limits of the active power at the node j of the distribution network respectively; are the upper and lower limits of the gateway reactive power at the j node of the distribution network, respectively. The power constraint of the distribution network gateway is:

[0086]

[0087] S328: Add an on-load tap-changing transformer between nodes i and j, add an auxiliary node o, and set V o,t is the square of the voltage amplitude of the auxiliary node o at time t; N ij,t is the optimal gear of the transformer of branch (i, j) at time t, which is an integer variable; Δk ij k is the increment of each level of the transformer tap of branch (i, j); ij,tK is the transformation ratio of the transformer of branch (i, j) at time t; ij is the number of gears of the transformer tap of branch (i, j); are the upper and lower limits of the transformer ratio of branch (i, j) respectively; then the OLTC operation constraint is:

[0088] V o,t =V i,t -2(r ij P ij,t +x ij Q ij,t )+[(r ij ) 2 +(x ij ) 2 ]l ij,t ,

[0089]

[0090] 0≤N ij,t ≤K ij ,

[0091]

[0092] Furthermore, in step S4, the specific steps are:

[0093] S41: Set j,t As the affine proportional coefficient, the adjustable decision variables are established in the adjustable robust optimization model of active distribution network. The uncertainty of distributed photovoltaic active output z j,t The linear affine relationship between them, the adjustable decision variables are adjusted within the adjustable range according to the linear affine rule to reduce the blindness of optimization, as shown in the following formula:

[0094]

[0095] For any uncertain quantity in the uncertainty set, the above constraints hold to simplify the model structure;

[0096] S42: Lowercase bold letters represent column vectors, uppercase bold letters represent matrices; let Represents an unadjustable decision variable, which is a decision variable made before the uncertainty variable is obtained; represents the adjustable decision variable, which is the decision variable that changes in real time after the uncertainty variable is obtained; c1 and c2 represent the coefficient matrix corresponding to the objective function; g is the coefficient matrix of the variables under the corresponding constraints; r, h c 、w cis a constant column vector; based on the linear affine mechanism and the distributed photovoltaic output correlation polyhedron model established in step S2, the vector form of the active distribution network affine adjustable robust optimization model is obtained:

[0097]

[0098] represents the constraints only related to x, including BESS operation constraints, branch power balance constraints and voltage drop constraints in the second-order cone power flow model, node voltage and branch current constraints, and OLTC operation constraints;

[0099] Represents the second-order cone relaxation constraint in the second-order cone power flow model;

[0100] It represents the coupling constraint condition between x and y, and the node injection power balance constraint in the second-order cone power flow model;

[0101] represents the constraints only related to y, including SVC operation constraints, gateway power constraints and BESS operation constraints.

[0102] Furthermore, in step S5, the specific steps are:

[0103] set up and is the coefficient matrix The parameters corresponding to the i-th row and j-th column of ; is a constant vector h c The i-th row of ; The constraints in the vector form of the affine adjustable robust optimization model for active distribution networks are Including the uncertainty z, for z∈Z Polyhedral , the inequality constraint is robust if and only if its robust counterpart constraint holds, i.e.

[0104]

[0105] When Z Polyhedral When is a polyhedral uncertain set, the above maximization problem is equivalent to:

[0106]

[0107] make Then the above formula is transformed into:

[0108]

[0109] set up and is the dual variable; the robust equivalent problem of the maximization problem obtained by using the dual theory is:

[0110]

[0111] Through robust equivalence, the max constraints with uncertain variables are converted into corresponding deterministic min constraints, which are then integrated with the min term of the objective function into a unified form. The active distribution network affine adjustable robust optimization model based on polyhedron sets is converted into a deterministic mixed integer second-order cone programming model, which can then be directly solved by calling the commercial solver Gurobi.

[0112] When Z Polyhedral When it is a set of correlation polyhedra and a set of generalized linear polyhedra, the uncertainty constraints are transformed into deterministic constraints through robust equivalence.

[0113] Furthermore, in step S5, the specific steps are:

[0114] When Z Polyhedral When is a set of related polyhedrons, the maximization problem is equivalently written as:

[0115]

[0116] set up and is the dual variable; the robust equivalence problem of the above equation is obtained by using the dual theory:

[0117]

[0118] Through robust equivalence, the max term constraint containing uncertain variables is converted into the deterministic min term constraint shown in the above formula, and integrated with the min term of the objective function into a unified form.

[0119] A computer storage medium stores a computer program executable by a computer processor, wherein the computer program executes a robust optimization method for an active distribution network based on a generalized linear polyhedron set.

[0120] The beneficial effects of the present invention are:

[0121] 1. The present invention discloses a robust optimization method for an active distribution network based on a generalized linear polyhedron set. On the basis of a traditional polyhedron set, the boundary of the polyhedron uncertainty set is reconstructed through the correlation distribution envelope diagram of distributed photovoltaic output. Furthermore, in view of the conservative problem of the correlation polyhedron uncertainty set, a generalized linear polyhedron uncertainty set is established to describe the correlation of distributed photovoltaic output. The effectiveness of the generalized linear polyhedron set proposed by the present invention is verified through a calculation example system, and the function of quantifying the influence of the correlation of distributed photovoltaic output on the optimization result in the polyhedron set is realized.

[0122] 2. Under the same uncertainty, compared with the traditional polyhedron uncertainty set AARO method that does not consider the correlation of distributed photovoltaics, the correlation polyhedron uncertainty set AARO method has the lowest penalty cost for abandoning light, but the highest network loss cost, and the total system cost increases, which increases the conservatism of the optimization result; the generalized linear polyhedron set of the present invention not only covers the entire range of photovoltaic output fluctuations, but also reduces the blank areas where the probability of distributed photovoltaic output fluctuations is low. Therefore, the generalized linear polyhedron set AARO method has the lowest abandonment cost, and the network loss cost is lower than that of the correlation polyhedron uncertainty set AARO method, and the total system cost is the lowest. To a certain extent, it increases the robustness of the optimization result and reduces the conservatism of the optimization result. BRIEF DESCRIPTION OF THE DRAWINGS

[0123] Figure 1 is a flow chart of an embodiment of the present invention.

[0124] Figure 2 It is a topological diagram of a 33-node distribution network example according to an embodiment of the present invention.

[0125] Figure 3 Graph showing the influence of the uncertainty of an embodiment of the present invention on the uncertain set of polyhedra.

[0126] Figure 4 is an envelope diagram of the uncertainty parameter correlation distribution of an embodiment of the present invention.

[0127] Figure 5 Detailed Description of the Invention The present invention relates to a correlation polyhedral uncertainty set and a polyhedral uncertainty set graph.

[0128] Figure 6 It is a boundary setting diagram of the correlation polyhedron uncertainty set according to an embodiment of the present invention.

[0129] Figure 7 It is an envelope range diagram of the correlation polyhedron set according to an embodiment of the present invention.

[0130] Figure 8 It is a boundary setting diagram of a generalized linear polyhedron set according to an embodiment of the present invention.

[0131] Fig. 9 Graphs showing different envelope ranges of a generalized linear polyhedron set according to an embodiment of the present invention.

[0132] Fig.10 It is a diagram of daily depreciation cost of BESS cycle life under different correlations in a 33-node system of an embodiment of the present invention.

[0133] Fig.11 It is a network loss cost diagram under different correlations in a 33-node system of an embodiment of the present invention.

[0134] Fig.12It is a graph of abandoned light costs under different correlations in a 33-node system in an embodiment of the present invention.

[0135] Fig.13 It is a diagram of the total system cost under different correlations in a 33-node system of an embodiment of the present invention. DETAILED DESCRIPTION

[0136] In order to more clearly illustrate the technical solution and advantages of the present invention, the following will be combined with the attached Figure 2 The specific examples described here are only used to explain the present invention, and are not used to limit the present invention.

[0137] See also Figure 1 , a robust optimization method for an active distribution network based on a generalized linear polyhedron set according to an embodiment of the present invention comprises the following steps:

[0138] Step 1: Initialization, input the line parameters of the 33-node distribution network and the load forecast reference value; assume that the reference voltage is 12.66kV and the reference power is 10MV. Two distributed photovoltaics are connected to nodes 17 and 30, with a capacity of 1500kVA. The on-load tap changer ratio adjustment range is 0.95 to 1.05, and its tap position is divided into 10 gears, with a change value of 0.01 for each gear. A static VAR compensator (SVC) is connected to node 26, and the reactive compensation range of the static VAR compensator is -200 to 300kvar. Two group switching capacitors (CB) are connected to nodes 4 and 21 respectively. The single group compensation power of CB is 50kvar, the maximum number of compensation groups is 4, and the upper limit of the number of CB actions in one day is 5 times. Two battery energy storage systems are connected to nodes 15 and 32, with a charging and discharging power of 0 to 240kW, a rated capacity of 1200kVA, a charging efficiency of 90%, and a discharging efficiency of 100%.

[0139] Step 2: Establish a distributed photovoltaic output correlation polyhedron model: mainly includes establishing a distributed photovoltaic output correlation polyhedron set and a generalized linear polyhedron set of photovoltaic output correlation.

[0140] (1) Establishing a polyhedron set of distributed photovoltaic output correlation: A polyhedron set is used to describe the uncertainty of distributed photovoltaic output, as shown in the following formula.

[0141]

[0142] In the formula, is the active power of the distributed photovoltaic connected to node j at time t; is the expected output value of distributed photovoltaic power; is the maximum value of the distributed photovoltaic output fluctuation; z j,tis the uncertain parameter of distributed output; Γ is the polyhedron set uncertainty.

[0143] For the convenience of analysis, let ρ be the correlation coefficient between distributed photovoltaic outputs, and take two uncertain parameters z1 and z2 to determine a polyhedron uncertainty set, such as Figure 3 The present invention assumes that the correlation matrix of distributed photovoltaic output can be obtained using the historical data of distributed photovoltaic output, and z1 and z2 are randomly sampled with different ρ to obtain the correlation distribution envelope diagram of z1 and z2, as shown in Figure 4 shown.

[0144] Depend on Figure 4 It can be seen that when there is no correlation between the distributed photovoltaic outputs, due to |z j,t |≤1, the distribution of the uncertain parameters of distributed photovoltaic output forms a square area with a side length of 1. When the correlation increases positively or decreases negatively, the uncertain parameters are concentrated around the straight line y=x or the straight line y=-x, respectively.

[0145] Due to the correlation between distributed photovoltaic outputs, the sampling points of distributed photovoltaic output fluctuations are concentrated around the diagonal of the correlation distribution envelope of the uncertain parameters. Therefore, by bending the boundary of the polyhedron, the area around the diagonal covers more distributed photovoltaic output fluctuation sampling points than the area far from the diagonal. This reconstructed polyhedron uncertainty set can make the uncertain parameters of distributed photovoltaic output more concentrated around the diagonal, without increasing the uncertainty Γ to cover the blank areas with low probability of distributed photovoltaic output fluctuations. Figure 5 As shown in Figure 2, when the correlation coefficient of distributed photovoltaic output is larger, the boundary of the polyhedron uncertainty set should be more curved. Therefore, the shape of the reconstructed polyhedron uncertainty set depends on the strength of the correlation between the distributed photovoltaic outputs, that is, the correlation polyhedron uncertainty set.

[0146] In order to derive the mathematical expression of the photovoltaic output correlation polyhedron set, the uncertainty set is taken in the first quadrant of the rectangular coordinate system to analyze the mathematical expression of the correlation polyhedron uncertainty set (the same applies to other quadrants), as follows: Figure 6 As shown in the figure, line segments L1 and L2 represent the boundaries of the correlation polyhedron uncertainty set; line segment L3 represents the boundary of the polyhedron uncertainty set with the same uncertainty Γ; line segments L4 and L5 respectively represent the boundaries of the correlation polyhedron set when the correlation coefficient of distributed photovoltaic output is the largest; the coordinates of point P1 are (0, Γ), the coordinates of point P2 are (1, 1), and the coordinates of point P3 are (Γ, 0). Then the equations of L3, L4 and L5 can be expressed as:

[0147] L3:z2=-z1+Γ

[0148] L4:z2=(1-Γ)z1+Γ

[0149]

[0150] exist Figure 6 In, order It is the straight line L i Since the correlation coefficient satisfies 0≤|ρ|≤1 and the uncertainty Γ∈[0,2], the range of the slopes of L1 and L2 is:

[0151]

[0152] From the above formula, we can get that in the range of 0≤|ρ|≤1 and Γ∈[0,2], L1 is between L3 and L4, and L2 is between L3 and L5. In addition, is an increasing function of |ρ|, It is a decreasing function of |ρ|. The stronger the correlation between distributed photovoltaic outputs, The bigger, The smaller it is, the closer L1 is to L4 and L2 is to L5, so that the area around the diagonal of the correlation distribution envelope of the uncertain parameters covered by it is larger, and the optimization result will be more conservative. Therefore, the slopes of L1 and L2 are:

[0153]

[0154] Then the equations for L1 and L2 can be expressed as:

[0155] L1:z2=((2-Γ)|ρ|-1)z1+Γ

[0156]

[0157] In summary, by substituting the equations of L1 and L2 into the polyhedron uncertainty set, we can obtain the expression of the correlation polyhedron uncertainty set formed by the two uncertain parameters of distributed photovoltaic output:

[0158]

[0159] Note that in the above formula, if there is no correlation between the distributed photovoltaic outputs, that is, |ρ| = 0, the uncertainty set expressed by this formula is the same as the polyhedron uncertainty set.

[0160] Furthermore, if the two uncertain parameters are extended to n uncertain parameters, the proposed correlation polyhedron uncertainty set can be expressed as:

[0161]

[0162] In the formula, ρ jk,tRepresents the uncertain parameter z j,t and z k,t The correlation between them is in the range of [-1,1].

[0163] (2) Establishing a generalized linear polyhedron set of photovoltaic output correlation: Although the polyhedron uncertainty set of distributed photovoltaic output correlation proposed in (1) takes into account the correlation between distributed photovoltaic outputs, its envelope has certain defects. Taking the first quadrant of the rectangular coordinate system as an example, Figure 7 As shown in . On the one hand, the correlation polyhedron uncertainty set only envelops a part of the area around the diagonal of the correlation distribution envelope diagram of the uncertain parameters, and does not envelop the part with a high probability of distributed photovoltaic output fluctuation, such as Figure 7 The dark area in the figure will reduce the robustness of the optimization result. On the other hand, the proportion of the part with low probability of distributed photovoltaic output fluctuation is still high, such as Figure 7 The empty area within the boundary of the correlation polyhedron in , which will increase the conservatism of the optimization results.

[0164] In order to further solve the problem of poor robustness and high conservatism of the above correlation polyhedron uncertainty set, the present invention will improve the above correlation polyhedron uncertainty set so that the proportion of the blank area of ​​its envelope is reduced and the proportion of the area around the envelope diagonal is increased. The specific method is as follows Figure 8 As shown. Let the point with the smallest horizontal coordinate among the points where the correlation distribution envelope formed by the uncertain parameters z1 and z2 intersects with the straight line y=1 be H1(x H ,1); Similarly, the point with the smallest ordinate among the points where the correlation distribution envelope intersects the straight line x=1 is H1(1,y H ). Let the point with the largest ordinate among the points where the correlation distribution envelope intersects the y-axis be D1(0,y D ); Similarly, the point with the largest horizontal coordinate among the points where the correlation distribution envelope intersects the x-axis is D2(x D ,0). When point R1 fluctuates between points D1 and P1, and point R2 fluctuates directly between points D2 and P3, the set composed of points R1, R2, H1 and H2 is a generalized linear polyhedron set.

[0165] from Figure 8 It can be seen that the generalized linear polyhedron set envelops all areas of the correlation distribution diagram formed by the uncertain parameters z1 and z2, increasing the robustness of the optimization results. And when point R1 is closer to point D1 and point R2 is closer to point D2, the blank area enveloping the improved correlation polyhedron uncertainty set is smaller, reducing the conservatism of the optimization results.

[0166] When the correlation coefficient is determined, the line segment can be controlled by adjusting the positions of points R1 and R2. and line segments The envelope range of , thereby controlling the conservatism of the optimization results, such as Fig. 9 shown.

[0167] Therefore, define the parameter β c (β c ∈[0,1]) calculates the ordinate value of point R1 and the abscissa value of point R2 to control the line segment and line segments The locations are as follows:

[0168] y im =(Γ-y D )β c +y D

[0169] x im =(Γ-x D )β c +x D

[0170] Then the line segment and line segments The slope of can be obtained by using the following formula:

[0171]

[0172] In the formula, Line and The slope of .

[0173] therefore, and The equation can be expressed as:

[0174]

[0175] From the above formula, we can see that the boundary of the generalized linear polyhedron set is related to the parameter x D ,y D 、x H and H The boundary of the uncertainty set of the correlation polyhedron is related to the correlation coefficient ρ. In order to make the boundary of the generalized linear polyhedron set also controllable by the correlation coefficient ρ, the Monte Carlo method can be used to establish the parameter x D ,y D 、x H ,y H The linear regression relationship between ρ and the correlation coefficient is shown in the following formula:

[0176]

[0177] It is expressed as the correlation coefficient ρ and The equation is:

[0178]

[0179] In summary, the above formula and Substituting the equation into the polyhedron uncertainty set, we can get the expression of the generalized linear polyhedron set formed by two uncertain parameters:

[0180]

[0181] Furthermore, if the two uncertain parameters are extended to n uncertain parameters, the set of generalized linear polyhedra can be expressed as:

[0182]

[0183] Step 3: Construct an economic dispatch model for active distribution networks.

[0184] (1) Active distribution network comprehensive cost objective function

[0185] The present invention considers network loss cost, power purchase cost, abandoned light penalty cost and BESS cycle life daily depreciation cost to construct the optimization objective function of the active distribution network, as shown in the following formula.

[0186]

[0187] Where: c loss , and c PV are the network loss cost coefficient, the main network power purchase cost coefficient and the abandoned light penalty cost coefficient respectively; r ij is the resistance of branch (i, j); I ij,t is the current of branch (i, j) at time t; is the active power purchased from the main grid at the gateway at node j at time t; Ω L is the line set; Ω TR is the set of distribution and transformation gateway nodes; T is the number of scheduling operation time periods.

[0188] (2) Active distribution network operation constraints

[0189] ① Second-order cone relaxation power flow constraint

[0190]

[0191] Where: set u(j) is the set of head nodes of the branch with j as the terminal node in the distribution network; set v(j) is the set of terminal nodes of the branch with j as the head node in the distribution network; V i,t =(U i,t ) 2 , U j,t is the voltage amplitude; P ij,t , Q ij,t are the active power and reactive power of branch (i, j) at time t respectively; l ij,t =(I ij,t ) 2 , I ij,t is the current of branch (i, j) at time t; P j,t , Q j,t are the active power and reactive power injected into node j respectively; is the reactive power injected into the main grid by the gateway at node j at time t; are the continuous compensation power of the SVC connected to node j and the discrete compensation power of the group switching capacitor bank CB respectively; ij is the reactance of branch (i, j).

[0192] ②Node voltage and branch current constraints

[0193]

[0194] Where: are the upper and lower limits of the voltage amplitude at node j respectively; is the upper limit of the current amplitude of branch (i, j).

[0195] ③Distributed photovoltaic operation constraints

[0196]

[0197] Where: are the reactive power of distributed photovoltaic connected to node j at time t; is the predicted power value of the distributed photovoltaic connected to node j at time t; is the apparent power of the distributed photovoltaic inverter connected to node j; θ j is the power factor angle of the distributed photovoltaic inverter connected to the j node; Ω PV Represents a collection of distributed photovoltaic access nodes.

[0198] ④ BESS operation constraints considering cycle life degradation

[0199] 1) Daily depreciation cost of BESS cycle life

[0200] BESS cycle life daily depreciation cost C ESSThe main cost is the loss caused by the charge and discharge process within one day. Here, the BESS life cycle cost is converted to daily based on 365 days. The BESS life cycle cost is mainly composed of the investment cost of BESS and its auxiliary equipment, which is determined by the rated capacity and rated power of BESS, that is,

[0201]

[0202] Where: They represent the rated capacity and rated power of the BESS at node j respectively; Ω ESS It is the installation node set of BESS; They represent the annualized investment cost per unit capacity and per unit power of the BESS at node j, and the calculation formulas are

[0203]

[0204] Where: They represent the unit capacity investment cost and unit power investment cost of BESS at node j respectively; r is the discount rate; is the cycle life of the BESS at node j.

[0205] Further analysis of the daily depreciation cost C of the BESS cycle life ESS Linearize to get

[0206]

[0207] In the formula, The equivalent number of cycles of a battery in a day based on different depths of discharge; and are the linear fitting coefficients of each order.

[0208] 2) BESS operation constraints

[0209] BESS has three states: charging, discharging and static (neither charging nor discharging). 0-1 variables are introduced Indicates that the BESS at node j is in the charging state during period t, a 0-1 variable It means that the BESS at node j is in the discharge state in time period t. Since the BESS can only be in one of the three states at the same time, there is

[0210]

[0211] During operation, BESS is also subject to the constraints of charge and discharge rate, energy balance and charge and discharge process, which can be expressed as

[0212]

[0213] Where: are the upper and lower limits of the charging power of BESS at node j respectively; are the upper and lower limits of BESS discharge power at node j respectively; are the charging and discharging powers of the BESS at node j in time period t, respectively.

[0214]

[0215] Where: is the charge state of the BESS at node j at time t; η ch,j , η dis,j are the charging and discharging efficiencies of BESS at node j, respectively; Δt is the scheduling time interval; are the upper and lower limits of the state of charge of the BESS at node j respectively.

[0216] ⑤ Group switching capacitor (CB) operation constraints

[0217] The group switching capacitor is a discrete reactive power compensation mechanical device. Its frequent operation times need to be limited to extend its service life. The specific constraints are:

[0218]

[0219] Where: is the compensation power of the CB connected to node j at time t; is the number of CBs connected to node j in operation at time t; is the compensation power of each group of CBs connected to node j at time t; The limit on the number of CB actions within T cycles in one day.

[0220] ⑥SVC operation constraints

[0221] Further consider the continuously regulated reactive power compensation device SVC, whose operating constraints are

[0222]

[0223] In the formula, are the lower limit and upper limit of the adjustable reactive power of the SVC connected to node j respectively.

[0224] ⑦Power constraints of power distribution gateway ports

[0225] In order to suppress the impact of power fluctuations in the distribution network on the main grid, it is necessary to control the power of the distribution network gateway within a certain range, that is,

[0226]

[0227] Where: are the upper and lower limits of the active power at the node j of the distribution network respectively; are the upper and lower limits of the reactive power at the node j in the distribution network.

[0228] ⑧OLTC operation constraints

[0229] An on-load tap-changing transformer is added between nodes i and j, and an auxiliary node o is added. The OLTC operation has the following constraints.

[0230] V o,t =V i,t -2(r ij P ij,t +x ij Q ij,t )+[(r ij ) 2 +(x ij ) 2 ]l ij,t

[0231]

[0232] 0≤N ij,t ≤K ij

[0233]

[0234] Where V o,t is the square of the voltage amplitude of the auxiliary node o at time t; N ij,t is the optimal gear of the transformer of branch (i, j) at time t, which is an integer variable; Δk ij k is the increment of each level of the transformer tap of branch (i, j); ij,t K is the transformation ratio of the transformer of branch (i, j) at time t; ij is the number of gears of the transformer tap of branch (i, j); They are the upper and lower limits of the transformer ratio of branch (i, j) respectively.

[0235] Step 4: Based on the distribution network optimization model and linear affine strategy established in the first two steps, the decision variables are divided into adjustable decision variables and non-adjustable decision variables to construct an affine adjustable robust scheduling model for the active distribution network.

[0236] The traditional active distribution network adjustable robust optimization model is divided into adjustable decision variables and non-adjustable decision variables according to the decision variables. The non-adjustable decision variables cannot change regardless of how the uncertainty variables change. Therefore, the non-adjustable decision variables are determined before the uncertainty variables are realized; while the adjustable decision variables are based on the set of uncertainty variables and are adjusted along with the uncertainty variables. Therefore, in essence, the traditional active distribution network adjustable robust optimization model is a two-stage optimization model that requires iterative solution.

[0237] To this end, the present invention proposes an active distribution network affine adjustable robust optimization model AARO, which uses a linear affine mechanism to establish the relationship between adjustable decision variables and uncertainty variables, so that the adjustable decision variables are adjusted within the adjustable range according to the linear affine rule, instead of making irregular decisions within the entire adjustable range. Therefore, the AARO operation model of the present invention establishes the adjustable decision variables in the distribution network The uncertainty of distributed photovoltaic active output z j,t The linear affine relationship between them can reduce the blindness of optimization, as shown in the following formula.

[0238]

[0239] Where: j,t is the affine scale coefficient.

[0240] The AARO operation model of the distribution network is equivalent to adding an affine linear decision-making mechanism to the traditional adjustable robust optimization model of the distribution network, that is, the above constraints are valid for any uncertain quantity in the uncertainty set, which simplifies the model structure.

[0241] Lowercase bold letters represent column vectors, and uppercase bold letters represent matrices. Define x as an unadjustable decision variable and y as an adjustable decision variable. Based on the distribution network optimization model and linear affine strategy established in step 2, the vector form of the distribution network AARO operation model is obtained.

[0242]

[0243] Where: Represents an unadjustable decision variable, which is a decision variable made before the uncertainty variable is obtained; represents the adjustable decision variable, which is the decision variable that changes in real time after the uncertainty variable is obtained; c1 and c2 represent the coefficient matrix corresponding to the objective function; g is the coefficient matrix of the variables under the corresponding constraints; r, h c 、w cis a constant column vector. The constraints in the first row of constraints represent constraints related only to x, including BESS operation constraints, branch power balance constraints and voltage drop constraints in the second-order cone power flow model, node voltage and branch current constraints, and OLTC operation constraints; the constraints in the second row of constraints represent second-order cone relaxation constraints in the second-order cone power flow model; the constraints in the third row of constraints represent coupling constraints related to x and y, and node injection power balance constraints in the second-order cone power flow model; the constraints in the fourth row of constraints represent constraints related only to y, including SVC operation constraints, gateway power constraints, and BESS operation constraints.

[0244] Step 5: Solve the constructed affine adjustable robust optimization model of active distribution network based on generalized linear polyhedron set and output the optimization results.

[0245] The third constraint in the vector form of the AARO operation model contains the uncertainty z. For z∈Z Polyhedral , the inequality constraint is robust if and only if its robust counterpart constraint holds, i.e.

[0246]

[0247] In the formula, and is the coefficient matrix The parameters corresponding to the i-th row and j-th column of ; is a constant vector h c The i-th row of .

[0248] When Z Polyhedral When is a polyhedral uncertain set, the above maximization problem can be equivalently written as:

[0249]

[0250] make Then the above formula is transformed into:

[0251]

[0252] Using duality theory, we can get the robust counterpart of the maximization problem as follows:

[0253]

[0254] In the formula, and is the dual variable.

[0255] It can be seen from the above formula that the max term constraints containing uncertain variables are converted into corresponding deterministic min term constraints through robust equivalence, which can be integrated with the min term of the objective function into a unified form. Therefore, the AARO model of the active distribution network based on the polyhedral uncertainty set is converted into a deterministic mixed integer second-order cone programming model, which can be directly solved by calling the commercial solver Gurobi.

[0256] When Z Polyhedral When it is a correlation polyhedron uncertain set and a generalized linear polyhedron set, the uncertainty constraints can also be transformed into deterministic constraints through robust equivalence. Here, the correlation polyhedron uncertain set is used as an example to illustrate, and the maximization problem can be equivalently written as:

[0257]

[0258] Using duality theory, we can get the robust equivalence problem of the above equation as follows:

[0259]

[0260] In the formula, and is the dual variable.

[0261] Similarly, the max term constraint containing uncertain variables can be converted into the deterministic min term constraint shown in the above formula through robust equivalence, which can be integrated with the min term of the objective function into a unified form.

[0262] Table 1 The influence of uncertainty Γ on various costs

[0263]

[0264] Uncertainty is used to limit the size of the disturbance range of the polyhedron uncertain centralized distributed photovoltaic output. From Table 1, it can be seen that with the increase of the polyhedron uncertainty Γ, the daily depreciation cost of the BESS cycle life remains unchanged; the network loss cost gradually increases; the power purchase cost increases slightly; and the penalty cost of abandoned light gradually decreases. This is because the increase of the polyhedron uncertainty Γ will lead to an increase in the fluctuation range of photovoltaic output, and the excessive photovoltaic output will cause the distribution network to be unable to absorb it locally. At this time, the excess photovoltaic power needs to be transmitted to the load node far away from the photovoltaic power station for absorption, resulting in an increase in branch current. At this time, in order to achieve power balance, the gateway power needs to be slightly increased, so the network loss cost increases and the power purchase cost increases slightly. As the distributed photovoltaic output increases, the amount of abandoned photovoltaic power will decrease, which reduces the penalty cost of abandoned light. However, due to the constraints of its capacity, charge and discharge rate, etc., BESS is difficult to respond to the large-scale fluctuations of distributed photovoltaics, and the daily depreciation cost of BESS cycle life is not affected.

[0265] The size of the correlation coefficient will affect the curvature of the boundary of the correlation polyhedron uncertainty set of distributed photovoltaic output, thereby affecting the envelope range of the correlation polyhedron uncertainty set, resulting in corresponding changes in the optimization results. Figures 10 to 13 As shown in the figure, when the correlation coefficient between distributed photovoltaic outputs is ρ = 0.1 and ρ = 0.4, due to the weak correlation between distributed photovoltaic outputs, the curvature of the boundary of the correlation polyhedron uncertainty set is small, and the fluctuation range of distributed photovoltaic output has almost no change under the polyhedron uncertainty set and the correlation polyhedron uncertainty set, resulting in almost the same costs. When the correlation coefficient between distributed photovoltaic outputs gradually increases, the curvature of the boundary of the correlation polyhedron uncertainty set gradually increases, and the correlation polyhedron uncertainty set envelopes more parts of distributed photovoltaic outputs with correlation. Therefore, as the distributed photovoltaic output increases, the amount of abandoned photovoltaic power will decrease, and the branch current will increase, which will reduce the penalty cost of abandoned photovoltaic power and increase the network loss cost. On the other hand, due to the increase in the correlation of distributed photovoltaic output, the blank area with a small probability of distributed photovoltaic output fluctuation in the correlation polyhedron uncertainty set envelope also increases, resulting in an increase in the total cost of the system and an increase in the conservatism of the optimization results.

[0266] Table 2 Comparison of the impact of polyhedron set, correlation polyhedron set and generalized linear polyhedron set of the present invention on various costs

[0267]

[0268] Table 2 shows the various costs under the three polyhedral uncertainty sets. It can be seen that among the three polyhedral uncertainty sets, the abandoned light cost and the total system cost are the smallest when the generalized linear polyhedron set is used, and the daily depreciation cost of the BESS cycle life and the electricity purchase cost remain unchanged. Because the generalized linear polyhedron set contains the entire range of the distributed photovoltaic output correlation distribution map, it takes into account the situation where the distributed photovoltaic output fluctuation is the largest, and at the same time reduces the blank area where the probability of distributed photovoltaic output fluctuation is small. Although the distributed photovoltaic output increases, most of the photovoltaic output is consumed locally, and only a small part of the photovoltaic output is transmitted to other load nodes. At this time, the distributed photovoltaic output can meet the power balance of the distribution network. Therefore, the abandoned light cost becomes smaller, the daily depreciation cost of the BESS cycle life and the electricity purchase cost remain unchanged, and the total system cost also decreases accordingly. When β c When increases, the blank area with low probability of distributed photovoltaic output fluctuation increases, and the envelope range of the generalized linear polyhedron set also increases, resulting in a further increase in distributed photovoltaic output. However, at this time, most of the photovoltaic output cannot be consumed locally and needs to be transmitted to other load nodes, resulting in a decrease in the cost of abandoned light while increasing the network loss cost, and the total system cost remains basically unchanged. It can be concluded that the generalized linear polyhedron set enhances the robustness of the optimization result while reducing its conservatism.

[0269] 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 robust optimization method for active distribution network based on generalized linear polyhedron set, characterized by: The following steps are involved: S1: Initialize the system, input active distribution network line parameters, distributed photovoltaic parameters, battery energy storage parameters, group switching capacitor parameters, static VAR compensator parameters, on-load tap-changing transformer parameters and load forecast reference values; S2: Establish a distributed photovoltaic output correlation polyhedron model. The specific steps include: S21: Establish a distributed photovoltaic output correlation polyhedron set to describe the uncertainty of distributed photovoltaic output; the specific steps are: set up is the active power of the distributed photovoltaic connected to node j at time t; is the expected output value of distributed photovoltaic power; is the maximum value of the distributed photovoltaic output fluctuation; z j,t is the uncertain parameter of distributed output; Γ is the polyhedron set uncertainty; then the distributed photovoltaic output correlation polyhedron set is as follows: Suppose there are n uncertain parameters about distributed photovoltaic output, ρ jk,t represents the uncertain parameter z about the distributed photovoltaic output j,t and z k,t The correlation between them ranges from [-1,1]; then the distributed photovoltaic output correlation polyhedron set is expressed as: S22: Reconstruct the boundary of the polyhedron set in combination with the correlation distribution envelope diagram, establish a generalized linear polyhedron set describing the correlation of distributed photovoltaic output, reduce the proportion of blank areas of the envelope, and increase the proportion of areas around the diagonal of the envelope to solve the problem of excessive conservatism; the specific steps are: Suppose there are n uncertain parameters about distributed photovoltaic output, and define parameter β c (β c ∈[0,1]) is used to control the range of the envelope of the generalized linear polyhedron set, and the generalized linear polyhedron set is expressed as: S3: Construct an adjustable robust optimization model for active distribution network, including the comprehensive cost objective function of active distribution network and the operation constraints of active distribution network; S4: A linear affine mechanism is used in the active distribution network adjustable robust optimization model to establish the relationship between the adjustable decision variables and the uncertainty variables. According to the linear affine mechanism and the distributed photovoltaic output correlation polyhedron model established in step S2, an active distribution network affine adjustable robust optimization model is constructed. The specific steps are: S41: Set j,t As the affine proportional coefficient, the adjustable decision variables are established in the adjustable robust optimization model of active distribution network. The uncertainty of distributed photovoltaic active output z j,t The linear affine relationship between them, the adjustable decision variables are adjusted within the adjustable range according to the linear affine rule to reduce the blindness of optimization, as shown in the following formula: For any uncertain quantity in the uncertainty set, the above constraints hold to simplify the model structure; S42: Lowercase bold letters represent column vectors, uppercase bold letters represent matrices; let Represents an unadjustable decision variable, which is a decision variable made before the uncertainty variable is obtained; represents the adjustable decision variable, which is the decision variable that changes in real time after the uncertainty variable is obtained; c1 and c2 represent the coefficient matrix corresponding to the objective function; R, A c , B c , D c , G, C c , g is the coefficient matrix of the variables under the corresponding constraints; r、h c 、w c is a constant column vector; based on the linear affine mechanism and the distributed photovoltaic output correlation polyhedron model established in step S2, the vector form of the active distribution network affine adjustable robust optimization model is obtained: stRx≤r represents the constraints only related to x, including BESS operation constraints, branch power balance constraints and voltage drop constraints in the second-order cone power flow model, node voltage and branch current constraints, and OLTC operation constraints; ||Gx||2≤g T x represents the second-order cone relaxation constraint in the second-order cone power flow model; A c x+B c y c +(D c y c ) T z≤h c Represents the coupling constraint condition related to x and y, and the node Gx injection 2≤g power x balance constraint in the second-order cone power flow model; C c y c ≤w c represents the constraints only related to y, including SVC operation constraints, gateway power constraints and BESS operation constraints; S5: Solve the affine adjustable robust optimization model of active distribution network based on generalized linear polyhedron set, analyze the influence of generalized linear polyhedron set on the affine adjustable robust optimization results of active distribution network, and output the optimization results.

2. The method for robust optimization of active distribution network based on generalized linear polyhedron set according to claim 1, characterized in that: In the step S21, n=2; Take two uncertain parameters z1 and z2 about distributed photovoltaic output to determine a polyhedron uncertainty set, ρ is the correlation coefficient between the uncertain parameters z1 and z2 of distributed photovoltaic output; use the historical data of distributed photovoltaic output to obtain the correlation matrix of distributed photovoltaic output, randomly sample z1 and z2 with different ρ, and obtain the correlation distribution envelope diagram of the uncertain output parameters z1 and z2; If there is no correlation between distributed photovoltaic outputs, |ρ|=0, |z j,t |≤1, the distribution of the uncertain parameters of distributed photovoltaic output forms a square area with a side length of 1; When the correlation increases positively, the uncertain parameters are concentrated around the straight line y = x; When the correlation decreases in the negative direction, the uncertain parameters are concentrated around the straight line y = -x; If there is correlation between distributed photovoltaic outputs, the distributed photovoltaic output fluctuation sampling points are concentrated around the diagonal of the correlation distribution envelope diagram of the uncertain parameters; by bending the boundary of the polyhedron, the area around the diagonal covers more distributed photovoltaic output fluctuation sampling points than the area far from the diagonal; this reconstructed polyhedron set makes the uncertain parameters of distributed photovoltaic output more concentrated around the diagonal; when the correlation coefficient of distributed photovoltaic output is larger, the boundary of the polyhedron set is more curved, and the shape of the reconstructed polyhedron set depends on the strength of the correlation between distributed photovoltaic outputs, that is, the correlation polyhedron set; The uncertainty set is taken in the first quadrant of the rectangular coordinate system to analyze the mathematical expression of the correlation polyhedron set; line segments L1 and L2 represent the boundaries of the correlation polyhedron set respectively; line segment L3 represents the boundary of the polyhedron set with the same uncertainty Γ; line segments L4 and L5 represent the boundaries of the correlation polyhedron set when the correlation coefficient of distributed photovoltaic output is the largest; the coordinates of point P1 are (0, Γ), the coordinates of point P2 are (1, 1), and the coordinates of point P3 are (Γ, 0); then the equations of L3, L4 and L5 are expressed as: L3:z2=-z1+Γ, L4:z2=(1-Γ)z1+Γ, make It is the straight line L i If the correlation coefficient satisfies 0≤|ρ|≤1 and the uncertainty Γ∈[0,2], the range of the slopes of L1 and L2 is: From the above formula, we can see that in the range of 0≤|ρ|≤1 and Γ∈[0,2], L1 is between L3 and L4, and L2 is between L3 and L5; is an increasing function of |ρ|, It is a decreasing function of |ρ|. The stronger the correlation between distributed photovoltaic outputs, The bigger, The smaller it is, the closer L1 is to L4 and L2 is to L5, so that the area around the diagonal of the correlation distribution envelope of the uncertain parameters covered by it is larger, and the optimization result is more conservative; therefore, the slopes of L1 and L2 are: Then the equations for L1 and L2 are expressed as: L1:z2=((2-Γ)|ρ|-1)z1+Γ, In summary, substituting the equations of L1 and L2 into the polyhedron uncertainty set, the expression of the correlation polyhedron set formed by the two uncertain parameters of distributed photovoltaic output is obtained as follows:

3. The method for robust optimization of active distribution network based on generalized linear polyhedron set according to claim 1, characterized in that: In the step S22, let n=2; Suppose the point with the smallest horizontal coordinate among the points where the correlation distribution envelope formed by the uncertain parameters z1 and z2 intersects with the straight line y=1 is H1(x H ,1); The point with the smallest ordinate among the points where the correlation distribution envelope intersects the straight line x=1 is H1(1,y H ); Let the point with the largest ordinate among the points where the correlation distribution envelope intersects the y-axis be D1(0,y D ); The point with the largest horizontal coordinate among the points where the correlation distribution envelope intersects the x-axis is D2(x D ,0); when point R1 fluctuates between points D1 and P1, and point R2 fluctuates directly between points D2 and P3, the set composed of points R1, R2, H1 and H2 is a generalized linear polyhedron set; The generalized linear polyhedron set envelops all areas of the correlation distribution diagram formed by the uncertain parameters z1 and z2, increasing the robustness of the optimization result. When point R1 is closer to point D1 and point R2 is closer to point D2, the improved correlation polyhedron set envelops fewer blank areas, reducing the conservatism of the optimization result. When the correlation coefficient is determined, the line segment is controlled by adjusting the position of point R1 and point R2. and line segments The envelope range controls the conservatism of the optimization results; Define parameter β c (β c ∈[0,1]) calculates the ordinate value of point R1 and the abscissa value of point R2 to control the line segment and line segments The locations are as follows: and im =(Γ-y D )β c +y D , x im =(Γ-x D )b c +x D , set up Line and The slope of the line segment and line segments The slope of is given by: and The equation is expressed as: Boundary and parameter x of a set of generalized linear polyhedra D ,y D 、x H and H The boundary of the correlation polyhedron set is related to the correlation coefficient ρ. In order to control the boundary of the generalized linear polyhedron set through the correlation coefficient ρ, the Monte Carlo method is used to establish the parameter x D ,y D 、x H ,y H The linear regression relationship between ρ and the correlation coefficient is shown in the following formula: It is expressed as the correlation coefficient ρ and The equation is: The above expression and Substituting the equation into the polyhedron set, we get the expression of the generalized linear polyhedron set formed by two uncertain parameters:

4. The method for robust optimization of active distribution network based on generalized linear polyhedron set according to claim 1, characterized in that: In the step S3, the specific steps are: S31: Let c loss , and c PV They are the network loss cost coefficient, the main network power purchase cost coefficient and the abandoned light penalty cost coefficient; r ij is the resistance of branch (i, j); I ij,t is the current of branch (i, j) at time t; is the active power purchased from the main grid at the gateway at node j at time t; Ω L is the line set; Ω TR is the set of distribution and transformation gateway nodes; T is the number of scheduling operation periods; considering the network loss cost, power purchase cost, abandoned light penalty cost and BESS cycle life daily depreciation cost, the comprehensive cost objective function of the active distribution network is constructed as shown in the following formula: S32: Active distribution network operation constraints include second-order cone relaxation power flow constraints, node voltage and branch current constraints, distributed photovoltaic operation constraints, BESS operation constraints considering cycle life degradation, group switching capacitor CB operation constraints, SVC operation constraints, distribution network gateway power constraints and OLTC operation constraints; specifically: S321: Let set u(j) be the set of head nodes of the branch with j as the terminal node in the distribution network; let set v(j) be the set of terminal nodes of the branch with j as the head node in the distribution network; V i,t =(U i,t ) 2 , U j,t is the voltage amplitude; P ij,t , Q ij,t are the active power and reactive power of branch (i, j) at time t respectively; l ij,t =(I ij,t ) 2 , I ij,t is the current of branch (i, j) at time t; P j,t , Q j,t are the active power and reactive power injected into node j respectively; is the reactive power injected into the main grid by the gateway at node j at time t; are the continuous compensation power of the SVC connected to node j and the discrete compensation power of the group switching capacitor bank CB respectively; ij is the reactance of branch (i, j); then the second-order cone relaxed power flow constraint is: S322: Set are the upper and lower limits of the voltage amplitude at node j respectively; is the upper limit of the current amplitude of branch (i, j); then the node voltage and branch current constraints are: S323: Set are the reactive power of distributed photovoltaic connected to node j at time t; is the predicted power value of the distributed photovoltaic connected to node j at time t; is the apparent power of the distributed photovoltaic inverter connected to node j; θ j is the power factor angle of the distributed photovoltaic inverter connected to the j node; Ω PV represents the set of distributed photovoltaic access nodes; then the distributed photovoltaic operation constraints are: S324: BESS operation constraints considering cycle life degradation, including: S3241: The life cycle cost of BESS includes the investment cost of BESS and its auxiliary equipment, which is determined by the rated capacity and rated power of BESS; They represent the rated capacity and rated power of the BESS at node j respectively; Ω ESS is the installation node set of BESS; the BESS life cycle cost is converted to daily according to the total number of days in a year, and the loss cost caused by the charge and discharge process in one day on the cycle life is the BESS cycle life daily loss cost C ESS : set up They represent the unit capacity investment cost and unit power investment cost of BESS at node j respectively; r is the discount rate; is the cycle life of BESS at node j; then the annualized investment cost per unit capacity of BESS at node j is and annualized investment cost per unit power They are: set up The equivalent number of cycles of a battery in a day based on different depths of discharge; and is the linear fitting coefficient of each term; for the daily depreciation cost of BESS cycle life C ESS Linearization yields: S3242: BESS has charging state, discharging state and static state. In static state, it neither charges nor discharges. Introduce 0-1 variable Indicates that the BESS at node j is in the charging state during period t, a 0-1 variable It means that the BESS at node j is in the discharging state in time period t. Since the BESS can only be in one of the three states at the same time, we have: set up are the upper and lower limits of the charging power of BESS at node j respectively; are the upper and lower limits of BESS discharge power at node j respectively; are the charging and discharging powers of BESS at node j in time period t respectively; BESS is also subject to the constraints of charging and discharging rate, energy balance and charging and discharging process during operation, which are respectively expressed as: set up is the charge state of the BESS at node j at time t; η ch,j , η dis,j are the charging and discharging efficiencies of BESS at node j, respectively; Δt is the scheduling time interval; They are the upper and lower limits of the state of charge of the BESS at node j: S325: The group switching capacitor CB is a discrete reactive power compensation mechanical device, and its frequent operation times need to be limited to extend its service life; is the compensation power of the CB connected to node j at time t; is the number of CBs connected to node j in operation at time t; is the compensation power of each group of CBs connected to node j at time t; is the limit of the number of CB operations within T cycles in one day; then the group switching capacitor CB constraint is: S326: Set are the lower and upper limits of the adjustable reactive power of the SVC connected to node j, respectively. Considering the operation constraints of the continuously regulated reactive compensation device SVC, the following table shows the operation constraints of the SVC: S327: The power constraint of the distribution network gateway is to control the power of the distribution network gateway within a certain range to suppress the impact of power fluctuations of the distribution network on the main network. are the upper and lower limits of the active power at the node j of the distribution network respectively; are the upper and lower limits of the gateway reactive power at the j node of the distribution network, respectively. The power constraint of the distribution network gateway is: S328: Add an on-load tap-changing transformer between nodes i and j, add an auxiliary node o, and set V o,t is the square of the voltage amplitude of the auxiliary node o at time t; N ij,t is the optimal gear of the transformer of branch (i, j) at time t, which is an integer variable; Δk ij k is the increment of each level of the transformer tap of branch (i, j); ij,t K is the transformation ratio of the transformer of branch (i, j) at time t; ij is the number of gears of the transformer tap of branch (i, j); are the upper and lower limits of the transformer ratio of branch (i, j) respectively; then the OLTC operation constraint is: V o,t =V i,t -2(r ij P ij,t +x ij Q ij,t )+[(r ij ) 2 +(x ij ) 2 ]l ij,t , 0≤N ij,t ≤K ij , 5. The method for robust optimization of active distribution network based on generalized linear polyhedron set according to claim 1, characterized in that: In the step S5, the specific steps are: set up and T is the coefficient matrix A c , B c , D c The parameters corresponding to the i-th row and j-th column of ; is a constant vector h c The i-th row of ; the vector form of the affine adjustable robust optimization model for active distribution network constraint A c x+B c y c +(D c y c ) T z≤h c Including the uncertainty z, for z∈Z Polyhedral , the inequality constraint is robust if and only if its robust counterpart constraint holds, i.e. When Z Polyhedral When is a polyhedral uncertain set, the above maximization problem is equivalent to: make Then the above formula is transformed into: set up and is the dual variable; the robust equivalent problem of the maximization problem obtained by using the dual theory is: Through robust equivalence, the max constraints with uncertain variables are converted into corresponding deterministic min constraints, which are then integrated with the min term of the objective function into a unified form. The active distribution network affine adjustable robust optimization model based on polyhedron sets is converted into a deterministic mixed integer second-order cone programming model, which can then be directly solved by calling the commercial solver Gurobi. When Z Polyhedral When it is a set of correlation polyhedra and a set of generalized linear polyhedra, the uncertainty constraints are transformed into deterministic constraints through robust equivalence.

6. The method for robust optimization of active distribution network based on generalized linear polyhedron set according to claim 5, characterized in that: In the step S5, the specific steps are: When Z Polyhedral When is a set of related polyhedrons, the maximization problem is equivalently written as: set up and is the dual variable; the robust equivalence problem of the above equation is obtained by using the dual theory: Through robust equivalence, the max term constraint containing uncertain variables is converted into the deterministic min term constraint shown in the above formula, and integrated with the min term of the objective function into a unified form.

7. A computer storage medium, characterized in that: A computer program executable by a computer processor is stored therein, and the computer program executes a robust optimization method for an active distribution network based on a generalized linear polyhedron set as claimed in any one of claims 1 to 6.

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