Multi-region interconnected power system optimal power flow method considering photovoltaic output uncertainty

Abstract

The invention relates to a multi-region interconnected power system optimal power flow method considering photovoltaic output uncertainty. The method comprises the following steps: S1, introducing photovoltaic output uncertainty; s2, reconstructing and simplifying the operation model considering the photovoltaic output uncertainty; s3, decomposing into sub-problems corresponding to each sub-region; s4, determining a projection space; s5, searching an initial vertex set of each sub-region operation space in the projection space; s6, searching residual vertexes of the sub-region by translating the boundary; s7, reconstructing a multi-region interconnected power system operation space considering the photovoltaic output uncertainty; s8, solving an optimization problem in the reconstructed operation space to obtain an optimal solution; and S9, obtaining a power flow parameter under the optimal solution. According to the method, the mathematical model can be reconstructed and simplified while key information is reserved, the problem that a traditional centralized operation solving method cannot be subjected to large-scale joint optimization is solved, and privacy information is effectively protected.

Description

Technical Field

[0001] The present invention relates to the field of power system optimization operation, and more specifically, to an optimal power flow method for a multi-region interconnected power system taking into account the uncertainty of photovoltaic output. Background Art

[0002] With the development of new power systems, the proportion of photovoltaic installed capacity in the power system has continued to increase. While large-scale photovoltaic grid connection brings huge environmental and economic benefits, the strong volatility and uncertainty of photovoltaics also bring difficulties to the dispatching and operation of the power system.

[0003] Centralized dispatching methods can be used to solve the optimal power flow calculation problem of multi-region interconnected power systems. However, for power systems composed of multiple regions, the above centralized methods require all data of each sub-region, and different sub-regions are usually managed by independent operators, which may lead to privacy issues. Therefore, a distributed dispatching method is needed to solve the optimal power flow of multi-region interconnected power systems. Sub-regions only exchange boundary information and public information, and private information is not disclosed to other operators, which can avoid the above privacy issues.

[0004] However, all distributed scheduling methods involve iteration, which may lead to poor computational performance and non-convergence problems. Therefore, it is very important to propose a non-iterative optimal power flow calculation method with good computational performance. The optimal power flow calculation method based on the projection method can solve the above problems, with the advantages of privacy protection, non-iteration, high accuracy, and can reduce the complexity of the model. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an optimal power flow method for a multi-region interconnected power system taking into account the uncertainty of photovoltaic output, which has the advantages of privacy protection, non-iteration, high accuracy, and can reduce the complexity of the model.

[0006] The technical solution adopted by the present invention to solve the technical problem is: constructing an optimal power flow method for a multi-region interconnected power system considering the uncertainty of photovoltaic output, including the following steps:

[0007] S1. Introducing PV output uncertainty into the multi-region interconnected power system operation model without considering PV output uncertainty;

[0008] S2, reconstruct and simplify the operation model considering the uncertainty of photovoltaic output;

[0009] S3, decomposing the reconstructed and simplified multi-region interconnected power system model considering the uncertainty of photovoltaic output into sub-problems corresponding to each sub-region;

[0010] S4, determining the projection space according to the interconnection relationship of each sub-area and the need for privacy protection;

[0011] S5, searching for an initial vertex set of each sub-region operation space in the projection space;

[0012] S6, searching for the remaining vertices of each sub-region by translating the boundary based on the initial vertex set of each sub-region;

[0013] S7, reconstructing the operation space of the multi-regional interconnected power system considering the uncertainty of photovoltaic output in the projection space using the new constraints formed by the found vertices;

[0014] S8. Solve the optimization problem in the reconstructed operation space and obtain the optimal solution;

[0015] S9. Reconstruct the sub-area problem and obtain the flow parameters under the optimal solution.

[0016] According to the above scheme, in step S1, the mathematical expression of the multi-region interconnected power system operation model without considering the uncertainty of photovoltaic output is as follows:

[0017]

[0018]

[0019] Wherein, formula (1) represents the objective function of the optimal power flow of the multi-regional interconnected power system. The objective function minimizes the operating cost of the multi-regional interconnected power system. The operating cost includes the fuel cost of the coal-fired units. Load Shedding Penalty Function and the light abandonment penalty function represents the load shedding power of load j in area a at time t; η B represents the load shedding cost; represents the amount of abandoned light from photovoltaic v in area a at time t; η V represents the cost of abandoned light;

[0020] Formula (2) represents the fuel cost of the unit, which is a quadratic function, PG a,i,t is the output of unit i in area a at time t; b 0,i , b 1,i and b 2,i is the quadratic function coefficient of the unit operating cost;

[0021] Formula (3) represents the unit output power constraint, and is the minimum and maximum output of unit i in area a;

[0022] Formula (4) represents the transmission line capacity constraint, is the maximum transmission power of transmission line l;

[0023] Formula (5) represents the node power balance constraint, PV a,v,t represents the predicted power generation of photovoltaic v in region a at time t without considering the uncertainty of wind power; PB a,j,t represents the power of load j in area a at time t; PL a,l,t represents the power flow of tie line l in area a at time t;

[0024] Formula (6) represents the climbing constraint, RD a,i represents the downward ramp rate of coal-fired unit i in area a; RU a,i represents the upward ramp rate of coal-fired unit i in region a; Δt represents the scheduling interval;

[0025] Formula (7) represents the interconnection constraint between sub-regions, Φ(s l ) represents the sub-area number where the starting node sl of the tie line l is located; Φ(e l ) represents the sub-area number where the terminal node el of the tie line l is located;

[0026] The operation model with the introduction of PV output uncertainty is as follows:

[0027]

[0028] Wherein, formula (8) represents the objective function considering the uncertainty of photovoltaic output, the goal is to minimize the operating cost in the worst case of the uncertainty set, ΔPG a,i,t It represents the output deviation of unit i in region a at time t due to the deviation of photovoltaic output from the predicted value; It represents the load shedding deviation caused by the PV output deviation from the predicted value at time t in region i. ΔPV represents the amount of abandoned photovoltaic power generated by the photovoltaic output deviation from the predicted value in region i at time t; a,v,t It represents the amount by which the photovoltaic v in region a deviates from the predicted value at time t;

[0029] Formula (9) represents the amount by which the unit output deviates from the deterministic model, KG a,i represents the balance factor of unit i in region a, which is a constant related to the unit capacity;

[0030] Constrain the PV in (2)-(7) a,v,t and PG a,i,t Replace with (PV a,v,t +ΔPV a,v,t ) and (PG a,i,t +ΔPG a,i,t ), other variables are also replaced with values ​​that deviate from the predicted values, such as PLa,l,t Replace with (PL a,l,t +ΔPL a,l,t ), etc. The multi-regional interconnected power system constraints considering the uncertainty of photovoltaic output are composed of constraint (9) and the replaced constraints (2)-(7), and the model objective function is (8).

[0031] According to the above scheme, in step S2, the process of reconstructing and simplifying the operation model considering the uncertainty of photovoltaic output includes the following steps:

[0032] S201. Write the centralized operation model of the multi-regional interconnected power system without considering the uncertainty of photovoltaic output into the following form:

[0033]

[0034] Where n represents the number of regions in the multi-regional interconnected power system; α a A represents the vector composed of variables in sub-region a, where the elements are private variables of each sub-region; χ represents the vector composed of interconnected variables between sub-regions, where the elements are public variables; a is the coefficient parameter vector corresponding to each variable in each sub-region in the objective function; B 1 ,B 2 ,B 3 ,…,B 2n is the coefficient matrix corresponding to each variable in the constraint; C 1 ,C 2 ,…,C 2n is a vector consisting of constants in each constraint;

[0035] S202. Considering the uncertainty of photovoltaic output, the centralized operation model of the multi-regional interconnected power system will be rewritten as formula (11):

[0036]

[0037] Where ΔPV a is the deviation of photovoltaic output from the predicted value caused by the uncertainty of photovoltaic output in region a; is the minimum deviation of the photovoltaic output in area a from the predicted value; is the maximum deviation of the photovoltaic output in region a from the predicted value, where B 2n+1 ΔPV 1 ,B 2n+2 ΔPV 2 ,…,B 3n ΔPV n The term indicates that the photovoltaic output fluctuates by ΔPV a The amount of fluctuation in other variables caused by

[0038] S203, only consider ΔPVa The two worst cases are and like and When the constraints can be satisfied, then All constraints can be satisfied, and the uncertainty model (11) is simplified to the deterministic model (12):

[0039]

[0040] in:

[0041]

[0042] According to the above solution, in step S3, the sub-regions correspond to the sub-problems as follows:

[0043]

[0044] To hide the private variable information in the objective function, a new public variable y is defined 1 , rewrite the region 1 subproblem as follows:

[0045]

[0046] in, This is a customized value based on actual conditions. This setting is to avoid unbounded running space after rewriting.

[0047] According to the above scheme, in step S4, the projection space is determined by the interconnection relationship between each sub-area and the need for privacy protection: to protect the privacy of each subsystem, hide their respective private variables, select public variables x and y 1 As variables that make up the projection space, private variables can be hidden.

[0048] According to the above scheme, in step S5, the process of searching for the initial vertex set of each sub-region operation space in the projection space includes the following steps:

[0049] S501, set initial vertex set is an empty set;

[0050] S502, select one of the public variables y a ;

[0051] S503, assign a suitable initial value x to other public variables x except those in step S502 init , this initial value must be within the feasible domain of the variable χ;

[0052] S504. Combined with the conditions of step S503, solve the maximum and minimum values ​​of the variables selected in step S502, that is, solve the following problem:

[0053]

[0054] What you get and Together with the initial values ​​of other public variables, two initial vertices are formed. and Add these two initial vertices to the initial vertex set

[0055] S505. Repeat steps S502-S504, and perform the same operation on other public variables to obtain a complete initial vertex set of region a. The number of vertices in the initial vertex set is denoted by N 0 ;

[0056] S506. In order to facilitate the subsequent calculation of the normal vector outside the boundary, the coordinate origin is translated to the inside of the convex hull formed by the initial vertex set:

[0057]

[0058] in, is the initial vertex set of region a The i-th vertex in .

[0059] According to the above scheme, in step S6, the steps of searching for the remaining vertices of each sub-region by translating the boundary based on the initial vertex set of each sub-region are as follows:

[0060] S601, set the number of cycles r a = 0, and the vertex set Initialize to

[0061] S602, r a =r a +1;

[0062] S603, solve the vertex set The convex hull of

[0063] S604, respectively solve the external normal vector corresponding to each boundary surface of the convex hull in step S603:

[0064]

[0065] in, For the rth a The vertex matrix that forms the convex hull boundary surface s in the second cycle, For the rth aThe external normal vector of the convex hull boundary surface s in the second cycle, when the coordinate origin is located inside the convex hull, the normal vector obtained by formula (18) is the external normal vector. This condition has been guaranteed by formula (17);

[0066] S605, respectively along the outer normal vector of each boundary surface s of the convex hull Directionally search outward for the convex hull vertex farthest from the boundary surface s, that is, solve the objective function (19) under the constraints of model (15);

[0067]

[0068] In addition, Corresponding The value is recorded as

[0069] S606, because the vertex obtained in step S605 It must be on or outside the boundary surface of the convex hull obtained in step S603, so Established; when On the boundary surface Not a new vertex; when Outside the boundary surface is the new vertex found, that is, when When formula (20) is satisfied, it means that a new vertex is searched;

[0070]

[0071] Among them, ε 1 is a small positive number that satisfies equation (20) The corresponding vertex Add to Vertex Set

[0072]

[0073] S607, repeat steps S602-S606. When formula (21) is satisfied, it means that there are no new vertices outside the precision requirement range, and the loop is terminated:

[0074]

[0075] Among them, ε 2 is the residual error of vertex search, ε 2 The larger the value, the shorter the calculation time, but the lower the solution accuracy, and vice versa. 2 = 0, the vertex set in the projected space obtained It is completely precise and can fully and accurately describe the operating space of the original optimization problem after projection.

[0076] According to the above scheme, in step S7, the steps of reconstructing the operation space of the multi-region interconnected power system considering the uncertainty of photovoltaic output in the projection space using the new constraints formed by the found vertices are as follows:

[0077] S701, build vertex set The convex hull of denoted by ;

[0078] S702, solving the normal vector outside the boundary of the convex hull:

[0079]

[0080] in, is the vertex matrix that constitutes the convex hull boundary surface s, is the external normal vector of the convex hull boundary surface s;

[0081] S703, the constraints after running space projection of sub-regional problem of multi-region interconnected power system are as follows:

[0082]

[0083] It can be seen that private variables have been hidden, and the constraints after running space projection only contain public variables;

[0084] S704. Each sub-region provides the information obtained in step S703 to the central operator.

[0085] According to the above scheme, in step S8, the steps of solving the optimization problem in the reconstructed operation space are as follows:

[0086] The central operator combines the spatial constraint information of each sub-problem into the reconstructed convex hull (25) after projection, and further obtains the reconstructed optimization problem (24)-(25);

[0087]

[0088] The reconstruction optimization problem (24)-(25) obtained by the central operator contains only public variables, and the privacy of each subsystem is effectively protected. The reconstruction optimization problem (24)-(25) is completely equivalent to model (12) and contains the optimality information of the original model. The central operator can obtain the public variable y under the optimal cost by solving the reconstruction optimization problem (24)-(25). a and the value of χ, denoted as and χ * .

[0089] According to the above solution, in step S9, the steps of reconstructing the sub-region problem are as follows:

[0090] The central operator will find χ *Return to each sub-region operator, each sub-region operator will * Substitute the values ​​of into each sub-region problem (14) to obtain the reconstructed sub-problem, and substitute into the public variable χ * After the value of is determined, each sub-problem can be solved independently of other sub-systems. By solving the reconstruction sub-problem, operators in each sub-region can obtain the optimal power flow in their respective regions.

[0091] The implementation of the optimal power flow method for a multi-region interconnected power system considering the uncertainty of photovoltaic output of the present invention has the following beneficial effects:

[0092] 1. The present invention proposes an optimal power flow method for a multi-region interconnected power system considering the uncertainty of photovoltaic output. This method obtains an equivalent optimization problem containing only public variables through projection transformation, hides the private variables of each sub-region, and effectively protects the privacy of each sub-region;

[0093] 2. The present invention proposes an optimal power flow method for a multi-region interconnected power system considering the uncertainty of photovoltaic output. The operating space after projection using this method is an equivalent operating space containing the optimality information of the original optimization problem, thus achieving a higher accuracy and ensuring the accuracy of the dimensionality reduction projection method;

[0094] 3. The present invention proposes an optimal power flow method for a multi-region interconnected power system considering the uncertainty of photovoltaic output. The method avoids iteration and solves the problem of excessive iterations and possible non-convergence in traditional distributed optimization methods using iterations. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0096] Figure 1 is a flow chart of an optimal power flow method for a multi-region interconnected power system considering the uncertainty of photovoltaic output according to the present invention;

[0097] Figure 2 It is a topological diagram of a 6-6 node two-region interconnected power system of the present invention according to the optimal power flow method of a multi-region interconnected power system taking into account the uncertainty of photovoltaic output. DETAILED DESCRIPTION

[0098] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0099] like Figure 1 As shown, the optimal power flow method of the multi-region interconnected power system considering the uncertainty of photovoltaic output of the present invention was tested in a 6-6 node two-region interconnected power system and a 118-145 node two-region interconnected power system. The topology diagram of the 6-6 node two-region interconnected power system is shown in Figure 2As shown, region 1 has four conventional units, seven transmission lines and one photovoltaic unit, region 2 has three conventional units, eleven transmission lines and one photovoltaic unit, and the two regions are interconnected by one transmission line. 118-145 Region 1 of the two-region interconnected power system has fifty-four conventional units, one hundred and eighty-six transmission lines and eighteen photovoltaic units, region 2 has fifty conventional units, four hundred and fifty-three transmission lines and fourteen photovoltaic units, and the two regions are interconnected by one transmission line. Two situations are set to illustrate the effectiveness of the present invention:

[0100] The first case: using the centralized operation model to directly solve;

[0101] The second case: using the dimension reduction projection method to solve;

[0102] In the 6-6 node two-region interconnected power system and the 118-145 node two-region interconnected power system, the optimal power flow method of the multi-region interconnected power system considering the uncertainty of photovoltaic output is proposed in the second case. Figure 1 As shown, the specific steps include:

[0103] S1. The uncertainty of photovoltaic output is introduced into the operation model of multi-regional interconnected power system without considering the uncertainty of photovoltaic output.

[0104] The mathematical expression of the multi-regional interconnected power system operation model without considering the uncertainty of photovoltaic output is as follows:

[0105]

[0106]

[0107] Wherein, formula (1) represents the objective function of the optimal power flow of the multi-regional interconnected power system. The objective function minimizes the operating cost of the multi-regional interconnected power system. The operating cost includes the fuel cost of the coal-fired units. Load Shedding Penalty Function and the light abandonment penalty function represents the load shedding power of load j in area a at time t; η B represents the load shedding cost; represents the amount of abandoned light from photovoltaic v in area a at time t; η V Indicates the cost of abandoned light.

[0108] Formula (2) represents the fuel cost of the unit, which is a quadratic function. a,i,t is the output of unit i in area a at time t; b 0,i , b 1,i and b 2,i is the quadratic function coefficient of the unit operating cost.

[0109] Formula (3) represents the unit output power constraint. and are the minimum and maximum output values ​​of unit i in region a.

[0110] Equation (4) represents the transmission line capacity constraint. is the maximum transmission power of transmission line l.

[0111] Formula (5) represents the node power balance constraint. a,v,t represents the predicted power generation of photovoltaic v in region a at time t without considering the uncertainty of wind power; PB a,j,t represents the power of load j in area a at time t; PL a,l,t Represents the power flow of tie line l in area a at time t.

[0112] Formula (6) represents the climbing constraint. a,i represents the downward ramp rate of coal-fired unit i in area a; RU a,i represents the upward climbing rate of coal-fired unit i in area a; Δt represents the scheduling interval.

[0113] Formula (7) represents the interconnection constraints between sub-regions. l ) represents the sub-area number where the starting node sl of the tie line l is located; Φ(e l ) represents the sub-area number where the terminal node el of the tie line l is located.

[0114] The operation model with the introduction of PV output uncertainty is as follows:

[0115]

[0116] Among them, formula (8) represents the objective function considering the uncertainty of photovoltaic output, and the goal is to minimize the operating cost in the worst case of the uncertainty set. a,i,t It represents the output deviation of unit i in region a at time t due to the deviation of photovoltaic output from the predicted value; It represents the load shedding deviation caused by the PV output deviation from the predicted value at time t in region i. ΔPV represents the amount of abandoned photovoltaic power generated by the photovoltaic output deviation from the predicted value in region i at time t; a,v,t It represents the amount by which the photovoltaic power v in region a deviates from the predicted value at time t.

[0117] Equation (9) represents the amount by which the unit output deviates from the deterministic model. a,i It represents the balance factor of unit i in area a, which is a constant related to the unit capacity.

[0118] Constrain the PV in (2)-(7) a,v,t and PGa,i,t Replace with (PV a,v,t +ΔPV a,v,t ) and (PG a,i,t +ΔPG a,i,t ). In addition, other variables are also replaced with values ​​that deviate from the predicted values, such as PL a,l,t Replace with (PL a,l,t +ΔPL a,l,t ) etc. The multi-regional interconnected power system constraints considering the uncertainty of photovoltaic output are composed of constraint (9) and replaced constraints (2)-(7), and the model objective function is (8).

[0119] S2. Reconstruct and simplify the operation model considering the uncertainty of photovoltaic output. It includes the following steps:

[0120] S201. Write the centralized operation model of the multi-regional interconnected power system without considering the uncertainty of photovoltaic output into the following form:

[0121]

[0122] Where n represents the number of regions in the multi-regional interconnected power system; α a A represents the vector composed of variables in sub-region a, where the elements are private variables of each sub-region; χ represents the vector composed of interconnected variables between sub-regions, where the elements are public variables; a is the coefficient parameter vector corresponding to each variable in each sub-region in the objective function; B 1 ,B 2 ,B 3 ,…,B 2n is the coefficient matrix corresponding to each variable in the constraint; C 1 ,C 2 ,…,C 2n is a vector consisting of the constants in each constraint.

[0123] S202. Considering the uncertainty of photovoltaic output, the centralized operation model of the multi-regional interconnected power system will be rewritten as formula (11):

[0124]

[0125] Where ΔPV a is the deviation of photovoltaic output from the predicted value caused by the uncertainty of photovoltaic output in region a; is the minimum deviation of the photovoltaic output in area a from the predicted value; is the maximum deviation of the photovoltaic output in region a from the predicted value. 2n+1 ΔPV 1 ,B 2n+2 ΔPV 2 ,…,B 3nΔPV n The term indicates that the photovoltaic output fluctuates by ΔPV a The amount of fluctuation in other variables caused by.

[0126] S203, only consider ΔPV a The two worst cases are and like and When the constraints can be satisfied, then All constraints can be satisfied. Therefore, the uncertainty model (11) can be simplified to the deterministic model (12):

[0127]

[0128] in:

[0129]

[0130] S3. Decompose the reconstructed and simplified multi-region interconnected power system model considering the uncertainty of photovoltaic output into sub-problems corresponding to each sub-region.

[0131] Taking sub-area 1 as an example, the corresponding sub-problem is:

[0132]

[0133] In order to hide the private variable information in the objective function, a new public variable y is defined 1 , rewrite the region 1 subproblem as follows:

[0134]

[0135] in, This is a customized value based on actual conditions. This setting is to avoid the situation where the running space is unbounded after rewriting.

[0136] S4. Determine the projection space based on the interconnection relationship between each sub-area and the need for privacy protection.

[0137] In the context of the problem discussed in this invention, in order to protect the privacy of each subsystem, it is necessary to hide the private variables of each subsystem. Therefore, the public variables x and y are selected. 1 As variables that constitute the projection space, private variables can be hidden. The same applies to other sub-areas.

[0138] S5. Find the initial vertex set of each sub-region operation space in the projection space:

[0139] S501, set initial vertex set Is an empty set.

[0140] S502, select one of the public variables (with y a for example).

[0141] S503, assign a suitable initial value x to other public variables x except those in step S502 init , this initial value must be within the feasible region of the variable χ.

[0142] S504. Combined with the conditions of step S503, the maximum and minimum values ​​of the variables selected in step S502 are solved, that is, the following problem is solved (taking sub-area 1 as an example):

[0143]

[0144] What you get and Together with the initial values ​​of other public variables, two initial vertices are formed. and Add these two initial vertices to the initial vertex set

[0145] S505, repeat steps S502-S504, and perform the same operation on other public variables (such as variables in vector x) to obtain a complete initial vertex set of region a. The number of vertices in the initial vertex set is denoted by N 0 .

[0146] S506. In order to facilitate the subsequent calculation of the normal vector outside the boundary, the coordinate origin is translated to the inside of the convex hull formed by the initial vertex set:

[0147]

[0148] in, is the initial vertex set of region a The i-th vertex in .

[0149] S6. Based on the initial vertex set of each sub-region, find the remaining vertices of the sub-region by translating the boundary. The steps are as follows:

[0150] S601, set the number of cycles r a = 0, and the vertex set Initialize to

[0151] S602, r a =r a +1

[0152] S603, solve the vertex set Constructed convex hull.

[0153] S604, respectively solve the external normal vector corresponding to each boundary surface of the convex hull in S603:

[0154]

[0155] in, For the rth a The vertex matrix that forms the convex hull boundary surface s in the second cycle, For the rth a The external normal vector of the convex hull boundary surface s in the second cycle. When the coordinate origin is inside the convex hull, the normal vector obtained by equation (18) is the external normal vector. This condition is guaranteed by equation (17).

[0156] S605, respectively along the outer normal vector of each boundary surface s of the convex hull The convex hull vertex farthest from the boundary surface s is searched outward, that is, the objective function (19) is solved under the constraints of the model (15).

[0157]

[0158] In addition, Corresponding The value is recorded as

[0159] S606, because the vertex obtained in step S605 It must be on or outside the boundary surface of the convex hull obtained in step S603, so Established. On the boundary surface Not a new vertex; when Outside the boundary surface is the new vertex found. When formula (20) is satisfied, it means that a new vertex is searched.

[0160]

[0161] Among them, ε 1 is a small positive number. The corresponding vertex Add to Vertex Set

[0163] S607, repeat steps S602-S606. When formula (21) is satisfied, it means that there are no new vertices outside the precision requirement range, and the loop is terminated.

[0164]

[0165] Among them, ε 2is the residual of the vertex search. 2 The larger the value, the shorter the calculation time, but the lower the solution accuracy, and vice versa. 2 = 0, the vertex set in the projected space obtained It is completely precise and can fully and accurately describe the operating space of the original optimization problem after projection.

[0166] S7. Use the new constraints formed by the found vertices to reconstruct the operation space of the multi-regional interconnected power system considering the uncertainty of photovoltaic output in the projection space. The steps are as follows:

[0167] S701, build vertex set Represents the convex hull of .

[0168] S702, solving the normal vector outside the boundary of the convex hull:

[0169]

[0170] in, is the vertex matrix that constitutes the convex hull boundary surface s, is the external normal vector of the convex hull boundary surface s.

[0171] S703, the constraints after running space projection of sub-regional problem of multi-region interconnected power system are as follows:

[0172]

[0173] It can be seen that private variables have been hidden, and the constraints after running space projection only contain public variables.

[0174] S704. Each sub-region provides the information obtained in step S703 to the central operator.

[0175] S8. Solve the optimization problem in the reconstructed operation space and obtain the optimal solution. The steps are as follows:

[0176] The central operator projects the spatial constraint information of each subproblem into a reconstructed convex hull (25), and further obtains the reconstructed optimization problems (24)-(25).

[0177]

[0178] The reconstruction optimization problem (24)-(25) obtained by the central operator contains only public variables. Therefore, the privacy of each subsystem is effectively protected. In addition, the reconstruction optimization problem (24)-(25) is completely equivalent to model (12) and contains the optimality information of the original model. By solving the reconstruction optimization problem (24)-(25), the central operator can obtain the public variable y under the optimal cost a and the value of χ, denoted as and χ * .

[0179] S9, reconstruct the sub-region problem and obtain the power flow parameters under the optimal solution. The steps are as follows:

[0180] The central operator will find χ * Return to each sub-region operator. Each sub-region operator will * Substitute the values ​​of into each sub-region problem (14) to obtain the reconstructed sub-problem. Substitute the public variable χ * After the value of is determined, each sub-problem can be solved independently of other sub-systems. By solving the reconstruction sub-problem, operators in each sub-region can obtain the optimal power flow in their respective regions.

[0181] According to the calculation, as shown in Table 1-3, the calculation results of the first case and the second case in the 6-6 node two-region interconnected power system are consistent, which verifies the effectiveness of the present invention. According to the above analysis, it can be seen that the present invention can avoid iteration and protect privacy while ensuring accuracy.

[0182] Table 1 Operating costs ($) of the 6-6 node two-region interconnected power system obtained under different solution methods

[0183]

[0184] Table 2 Output of some conventional units (MW) obtained under different solution methods for the 6-6 node two-region interconnected power system

[0185]

[0186] Table 3. The power of the interconnected power line obtained by different solution methods for the 6-6 node two-region interconnected power system (MW)

[0187]

[0188] As shown in Table 4, the number of variables, number of constraints, calculation time and total cost under predicted output in the first and second cases of the 118-145 node two-region interconnected power system are compared. Among them, the calculation time is the solver calculation time. It can be seen that the number of variables in the second case using the dimensionality reduction projection method is greatly reduced, which greatly simplifies the complexity of the optimization problem. In addition, the privacy of each subsystem is also fully protected. The number of constraints in the second case solved by the dimensionality reduction projection method is much larger than that of Example A, which also makes the transformed running space more compact. Therefore, the calculation time of the second case is shorter than that of the first case, which improves the calculation efficiency. In the 118-145 node two-region interconnected power system, the total cost under predicted output calculated in the two cases is basically the same, and the accuracy of the dimensionality reduction projection method can be guaranteed. In addition, iteration is avoided throughout the calculation process, which solves the problem of excessive iterations and possible non-convergence of traditional distributed optimization methods using iterations. In summary, the optimal power flow method of multi-region interconnected power system considering photovoltaic output uncertainty of the present invention has the advantages of privacy protection, high accuracy and non-iteration.

[0189] Table 4

[0190] The number of variables, number of constraints, calculation time and total cost of the interconnected power system between two regions with 118-145 nodes under different solution methods

[0191]

[0192] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. An optimal power flow method for a multi-region interconnected power system considering the uncertainty of photovoltaic output, characterized in that: The following steps are involved: S1. Introducing PV output uncertainty into the multi-region interconnected power system operation model without considering PV output uncertainty; S2, reconstruct and simplify the operation model considering the uncertainty of photovoltaic output; S3, decomposing the reconstructed and simplified multi-region interconnected power system model considering the uncertainty of photovoltaic output into sub-problems corresponding to each sub-region; S4, determining the projection space according to the interconnection relationship of each sub-area and the need for privacy protection; S5, searching for an initial vertex set of each sub-region operation space in the projection space; S6, searching for the remaining vertices of each sub-region by translating the boundary based on the initial vertex set of each sub-region; S7, reconstructing the operation space of the multi-regional interconnected power system considering the uncertainty of photovoltaic output in the projection space using the new constraints formed by the found vertices; S8. Solve the optimization problem in the reconstructed operation space and obtain the optimal solution; S9. Reconstruct the sub-area problem and obtain the flow parameters under the optimal solution.

2. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1 is characterized in that: In step S1, the mathematical expression of the multi-region interconnected power system operation model without considering the uncertainty of photovoltaic output is as follows: Wherein, formula (1) represents the objective function of the optimal power flow of the multi-regional interconnected power system. The objective function minimizes the operating cost of the multi-regional interconnected power system. The operating cost includes the fuel cost of the coal-fired units. Load Shedding Penalty Function and the light abandonment penalty function represents the load shedding power of load j in area a at time t; η B represents the load shedding cost; represents the amount of abandoned light from photovoltaic v in area a at time t; η V represents the cost of abandoned light; Formula (2) represents the fuel cost of the unit, which is a quadratic function, PG a,i,t is the output of unit i in area a at time t; b 0,i , b 1,i and b 2,i is the quadratic function coefficient of the unit operating cost; Formula (3) represents the unit output power constraint, and is the minimum and maximum output of unit i in area a; Formula (4) represents the transmission line capacity constraint, is the maximum transmission power of transmission line l; Formula (5) represents the node power balance constraint, PV a,v,t represents the predicted power generation of photovoltaic v in region a at time t without considering the uncertainty of wind power; PB a,j,t represents the power of load j in area a at time t; PL a,l,t represents the power flow of tie line l in area a at time t; Formula (6) represents the climbing constraint, RD a,i represents the downward ramp rate of coal-fired unit i in area a; RU a,i represents the upward ramp rate of coal-fired unit i in region a; Δt represents the scheduling interval; Formula (7) represents the interconnection constraint between sub-regions, Φ(s l ) represents the sub-area number where the starting node sl of the tie line l is located; Φ(e l ) represents the sub-area number where the terminal node el of the tie line l is located; The operation model with the introduction of PV output uncertainty is as follows: Wherein, formula (8) represents the objective function considering the uncertainty of photovoltaic output, the goal is to minimize the operating cost in the worst case of the uncertainty set, ΔPG a,i,t It represents the output deviation of unit i in region a at time t due to the deviation of photovoltaic output from the predicted value; It represents the load shedding deviation caused by the PV output deviation from the predicted value at time t in region i. ΔPV represents the amount of abandoned photovoltaic power generated by the photovoltaic output deviation from the predicted value in region i at time t; a,v,t It represents the amount by which the photovoltaic v in region a deviates from the predicted value at time t; Formula (9) represents the amount by which the unit output deviates from the deterministic model, KG a,i represents the balance factor of unit i in region a, which is a constant related to the unit capacity; Constrain the PV in (2)-(7) a,v,t and PG a,i,t Replace with (PV a,v,t +ΔPV a,v,t ) and (PG a,i,t +ΔPG a,i,t ), the multi-regional interconnected power system constraints considering the uncertainty of photovoltaic output are composed of constraint (9) and the replaced constraints (2)-(7), and the model objective function is (8).

3. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1 is characterized in that: In step S2, the process of reconstructing and simplifying the operation model considering the uncertainty of photovoltaic output includes the following steps: S201. Write the centralized operation model of the multi-regional interconnected power system without considering the uncertainty of photovoltaic output as described in claim 2 into the following form: Where n represents the number of regions in the multi-regional interconnected power system; α a A represents the vector composed of variables in sub-region a, where the elements are private variables of each sub-region; χ represents the vector composed of interconnected variables between sub-regions, where the elements are public variables; a is the coefficient parameter vector corresponding to each variable in each sub-region of the objective function; B1, B2, B3, …, B 2n is the coefficient matrix corresponding to each variable in the constraint; C1, C2, …, C 2n is a vector consisting of constants in each constraint; S202. Considering the uncertainty of photovoltaic output, the centralized operation model of the multi-regional interconnected power system will be rewritten as formula (11): Where ΔPV a is the deviation of the photovoltaic output from the predicted value caused by the uncertainty of photovoltaic output in area a; is the minimum deviation of the photovoltaic output in area a from the predicted value; is the maximum deviation of the photovoltaic output in region a from the predicted value, where B 2n+1 ΔPV1,B 2n+2 ΔPV2,…,B 3n ΔPV n The term indicates that the photovoltaic output fluctuates by ΔPV a The amount of fluctuation in other variables caused by S203, only consider ΔPV a The two worst cases are like and When the constraints can be satisfied, then All constraints can be satisfied, and the uncertainty model (11) is simplified to the deterministic model (12): in:

4. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1 is characterized in that: In step S3, the sub-regions correspond to the sub-problems: In order to hide the private variable information in the objective function, a new public variable y1 is defined and the region 1 subproblem is rewritten as follows: in, This is a customized value based on actual conditions. This setting is to avoid unbounded running space after rewriting.

5. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1 is characterized in that: In step S4, the projection space is determined according to the interconnection relationship between the sub-areas and the need for privacy protection: to protect the privacy of each subsystem, the private variables of each subsystem are hidden, and the public variables x and y1 are selected as the variables constituting the projection space, and the private variables can be hidden.

6. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1 is characterized in that: In step S5, the process of searching for the initial vertex set of each sub-region operation space in the projection space includes the following steps: S501, set initial vertex set is an empty set; S502, select one of the public variables y a ; S503, assign a suitable initial value x to other public variables x except those in step S502 init , this initial value must be within the feasible domain of the variable χ; S504. Combined with the conditions of step S503, solve the maximum and minimum values ​​of the variables selected in step S502, that is, solve the following problem: What you get and Together with the initial values ​​of other public variables, two initial vertices are formed. and Add these two initial vertices to the initial vertex set S505. Repeat steps S502-S504 and perform the same operation on other public variables to obtain a complete initial vertex set of region a. The number of vertices in the initial vertex set is recorded as N0; S506. In order to facilitate the subsequent calculation of the normal vector outside the boundary, the coordinate origin is translated to the inside of the convex hull formed by the initial vertex set: in, is the initial vertex set of region a The i-th vertex in .

7. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1 is characterized in that: In step S6, the steps of searching for the remaining vertices of each sub-region by translating the boundary based on the initial vertex set of each sub-region are as follows: S601, set the number of cycles r a = 0, and the vertex set Initialize to S602、r a ＝r a +1； S603, solve the vertex set The convex hull of S604, respectively solve the external normal vector corresponding to each boundary surface of the convex hull in step S603: in, For the rth a The vertex matrix that forms the convex hull boundary surface s in the second cycle, For the rth a The external normal vector of the convex hull boundary surface s in the second cycle, when the coordinate origin is located inside the convex hull, the normal vector obtained by formula (18) is the external normal vector. This condition has been guaranteed by formula (17); S605, respectively along the outer normal vector of each boundary surface s of the convex hull Directionally search outward for the convex hull vertex farthest from the boundary surface s, that is, solve the objective function (19) under the constraints of model (15); In addition, Corresponding The value is recorded as S606, because the vertex obtained in step S605 It must be on or outside the boundary surface of the convex hull obtained in step S603, so Established; when On the boundary surface Not a new vertex; when Outside the boundary surface is the new vertex found, that is, when When formula (20) is satisfied, it means that a new vertex is searched; Among them, ε1 is a very small positive number, which will satisfy the formula (20) The corresponding vertex Add to Vertex Set S607, repeat steps S602-S606. When formula (21) is satisfied, it means that there are no new vertices outside the precision requirement range, and the loop is terminated: Among them, ε2 is the residual error of vertex search. The larger ε2 is, the shorter the calculation time is, but the lower the solution accuracy is, and vice versa. If ε2 = 0, the vertex set in the projection space is obtained. It is completely precise and can fully and accurately describe the operating space of the original optimization problem after projection.

8. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1 is characterized in that: In step S7, the steps of reconstructing the operation space of the multi-region interconnected power system considering the uncertainty of photovoltaic output in the projection space using the new constraints formed by the found vertices are as follows: S701, build vertex set The convex hull of denoted by ; S702, solving the normal vector outside the boundary of the convex hull: in, is the vertex matrix that constitutes the convex hull boundary surface s, is the external normal vector of the convex hull boundary surface s; S703, the constraints after running space projection of sub-regional problem of multi-region interconnected power system are as follows: It can be seen that private variables have been hidden, and the constraints after running space projection only contain public variables; S704. Each sub-region provides the information obtained in step S703 to the central operator.

9. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1, characterized in that: In step S8, the steps of solving the optimization problem in the reconstructed operation space are as follows: The central operator combines the spatial constraint information of each sub-problem into the reconstructed convex hull (25) after projection, and further obtains the reconstructed optimization problem (24)-(25); The reconstruction optimization problem (24)-(25) obtained by the central operator contains only public variables, and the privacy of each subsystem is effectively protected. The reconstruction optimization problem (24)-(25) is completely equivalent to model (12) and contains the optimality information of the original model. The central operator can obtain the public variable y under the optimal cost by solving the reconstruction optimization problem (24)-(25). a and the value of χ, denoted as and χ * .

10. The optimal power flow method for a multi-region interconnected power system considering photovoltaic output uncertainty according to claim 1, characterized in that: In step S9, the steps of reconstructing the sub-region problem are as follows: The central operator will find χ * Return to each sub-region operator, each sub-region operator will * Substitute the values ​​of into each sub-region problem (14) to obtain the reconstructed sub-problem, and substitute into the public variable χ * After the value of is determined, each sub-problem can be solved independently of other sub-systems. By solving the reconstruction sub-problem, operators in each sub-region can obtain the optimal power flow in their respective regions.

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