Power transmission network expansion planning method and system based on improved large M method

Abstract

The invention discloses a power transmission network expansion planning method and system based on an improved large M method, and the method comprises the steps: constructing a target function of a power transmission network source-network collaborative planning model with the minimum total cost; based on the objective function of the power transmission network source-network collaborative planning model, constructing constraint conditions of the power transmission network source-network collaborative planning model; decomposing the power transmission network source-network collaborative planning model into an investment planning main problem and an operation sub-problem by adopting a Benders decomposition algorithm; in the operation sub-problem, setting a large M value range for each large M constraint through a direct current power flow transfer factor matrix; and solving to obtain a power transmission network expansion planning scheme. According to the method, the large M value range of the constraint condition is set aiming at the problem of difficulty in large M method value taking in the power transmission network extension planning modeling process, the feasible solution space of the power transmission network extension planning problem is effectively reduced, and the accuracy and efficiency of model solution are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of power transmission network, relates to power transmission network planning technology, and specifically relates to a power transmission network expansion planning method and system based on an improved large-M method. Background Art

[0002] At present, with the continuous improvement of the penetration rate of new energy and the increase in load demand, the power randomness and volatility of the power grid are also increasing. The current transmission network faces the problem of insufficient equipment and line capacity, which may lead to limited operation and bring risks and challenges to the economic dispatch and flexible operation of the transmission network. In order to meet these challenges, it is urgent to carry out expansion planning on the existing architecture of the transmission network to improve the economic and reliable operation capacity of the transmission network.

[0003] In the modeling process of transmission network expansion planning in the power system, the constraints often involve nonlinear terms of the product of variables, and the big M method is often used for linearization. For the transmission network line expansion planning model, the prior art linearizes the product of the line investment variable and the flow variable. For the transmission network power supply planning model, the prior art linearizes the three-variable product of the line state 0-1 variable, the line number integer variable, and the voltage phase angle variable. For the transmission network source-grid collaborative planning model, the prior art linearizes the product of the voltage phase angle change variable and the susceptance matrix change variable. In general, the above prior arts all use the big M method to realize the linearization of nonlinear terms, and set the big M value between 10^5 and 10^6, which is a relatively large subjective setting value.

[0004] In summary, the existing technology has the following problems: in the field of transmission network expansion planning technology, the value of M in the traditional large-M method is often set to a maximum value based on subjective experience, which easily leads to an overly large solution space for the optimization problem, thereby reducing the solution efficiency and speed. Summary of the invention

[0005] Purpose of the invention: In order to overcome the deficiencies in the prior art, a method and system for transmission network expansion planning based on an improved large-M method is provided.

[0006] Technical solution: To achieve the above object, the present invention provides a transmission network expansion planning method based on the improved large-M method, comprising the following steps:

[0007] S1: To minimize the total cost, construct the objective function of the transmission network source-grid collaborative planning model;

[0008] S2: Based on the objective function of the transmission network source-grid collaborative planning model, considering the four parts of investment, units, DC power flow, and abandoned renewable energy load shedding, the constraints of the transmission network source-grid collaborative planning model are constructed;

[0009] S3: Using the Benders decomposition algorithm, the transmission network source-grid collaborative planning model is decomposed into the investment planning main problem and the operation sub-problem;

[0010] S4: In the operation sub-problem, the range of large M values ​​is set for each large M constraint through the DC power flow transfer factor matrix;

[0011] S5: Based on the large M value range after constraint adjustment, the transmission network expansion planning scheme is solved.

[0012] Furthermore, the transmission network source-grid collaborative planning model in step S1 aims to meet the economic operation of the system by expanding lines and units. The objective function of the transmission network source-grid collaborative planning model is to minimize the total economic cost, which is the sum of investment cost, operation cost, and penalty cost for abandoning new energy and shedding loads. The specific expression is as follows:

[0013]

[0014]

[0015]

[0016]

[0017] Where: represents the investment cost; , For each unit and transmission lines investment costs; , For each unit ,line Construction status, 1 means construction, 0 means no construction; , They represent the candidate generating units and the candidate transmission line sets respectively; Indicates the operating cost; Indicates time The crew contribute; is the unit cost function. The present invention performs piecewise linearization on the unit quadratic cost function, where a , b , c They are the quadratic cost coefficient, the linear cost coefficient, and the constant cost coefficient respectively; Gather for the moment; For the existing generator set collection; represents the penalty cost; Penalty costs for units that abandon wind and solar power; is the unit load shedding penalty cost; Indicates time The amount of wind and solar power curtailment; Indicates time The load shedding capacity; Assemble for new energy units; For load collection.

[0018] Furthermore, the constraints of the transmission network source-network collaborative planning model in step S2 include:

[0019] Investment constraints:

[0020] For the expanded units and transmission lines, the total investment cost should not exceed the upper limit:

[0021]

[0022]

[0023] Where: , For each unit and transmission lines investment ceiling;

[0024] Unit constraints:

[0025] The unit should meet the upper and lower output constraints:

[0026]

[0027] Where: , For each unit Upper and lower limits of output;

[0028] In addition, the unit should meet the climbing constraints:

[0029]

[0030]

[0031] Where: , For each unit Upward and downward climbing rates;

[0032] DC power flow constraints:

[0033] First, the node power balance constraint should be satisfied:

[0034]

[0035] Where: Indicates in the scene s,time t Lower energy storage j Charging power; Indicates in the scene s ,time t Lower energy storage j The discharge power; Indicates time of new energy output; Indicates time Load; Indicates at time Branch The power flowing through , , and They are the generator set, energy storage, new energy unit and load set located at node n respectively; is the line set; s(l) and r(l) are the sending end and receiving end of branch l respectively;

[0036] Secondly, for existing lines, the power flow constraints should be met:

[0037]

[0038]

[0039] Where: For Line Susceptance; , They are the voltage phase angles at the sending and receiving ends of branch l at time t respectively; For Line The maximum current allowed to pass;

[0040] For the expansion line, the power flow constraints should also be met:

[0041]

[0042]

[0043] Where: is a large number used to linearize nonlinear constraints;

[0044] Finally, the phase angle constraint should be satisfied:

[0045]

[0046]

[0047] Where: is the voltage phase angle of node n at time t; is the reference node voltage phase angle at time t;

[0048] Constraints for abandoning renewable energy and shedding loads:

[0049] The amount of abandoned new energy and load shedding should be within the limit:

[0050]

[0051]

[0052] Furthermore, the transmission network source-grid collaborative planning model constructed above is a mixed integer linear programming problem, which can be decomposed using the Benders decomposition algorithm.

[0053] Benders decomposition algorithm is a decomposition method for solving large-scale optimization problems. It is used to decompose problems with large-scale complex structures into two parts - a main problem and one (or more) sub-problems. Benders decomposition reduces computational complexity by decomposing complex problems into sub-problems that are easier to solve, and is particularly suitable for large-scale optimization problems with complex constraints.

[0054] The objective function of the main investment planning problem in step S3 is:

[0055]

[0056] Where: is the auxiliary variable introduced;

[0057] The constraints include investment constraints and Benders optimal cut constraints returned from running subproblems;

[0058] The investment constraints are:

[0059]

[0060]

[0061] The above investment planning main problem (without the Benders optimal cut constraint) is written in a compact form:

[0062]

[0063] Where: The coefficient matrix of the objective function of the main problem of investment planning; The decision variables for the main investment planning problem, including the line investment variables , Unit investment variables , auxiliary variables ; The coefficient matrix of the constraints for the main investment planning problem; is the constant term of the constraints of the main investment planning problem;

[0064] The Benders optimal cut constraints returned from running the subproblem are:

[0065]

[0066] Where: The decision variables for running the subproblem The value of the dual variable can be obtained by running the subproblem. The meaning of other variables in the Benders optimal cut constraint can be found in equations (22) and (41). It is worth mentioning that the running subproblem always has a solution, so only the Benders optimal cut is returned to the main investment planning problem, and no Benders feasible cut is returned.

[0067] Therefore, the complete investment planning problem can be written in a compact form as:

[0068]

[0069] In summary, the main investment planning problem is a mixed integer linear programming problem.

[0070] The objective function of running the subproblem is:

[0071]

[0072]

[0073]

[0074]

[0075] Where: The source-grid investment cost determined for the main investment planning problem; The line investment planning scheme determined by the main investment planning problem; The unit investment planning scheme is determined by the main investment planning problem.

[0076] Constraints include unit, DC power flow, and new energy load shedding constraints:

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] The above operation subproblem can be written in a compact form:

[0090]

[0091] Where: is the coefficient matrix of the objective function for running the subproblem; The decision variables for running subproblems include , , , , , , ; is the coefficient matrix of the constraints for the running subproblem; is the constant term for the constraints of the running subproblem; The investment planning scheme obtained for the main investment planning problem, including the line investment planning scheme , Unit Investment Planning Scheme .

[0092] For the equality constraint in the running subproblem, it can be equivalently split into two inequality constraints, which can be classified as For example, for , which can be equivalently decomposed into and These two inequality constraints.

[0093] In summary, the operation subproblem is a linear programming problem.

[0094] Furthermore, the step S4 specifically includes:

[0095] For formula (35), it is necessary to select a suitable large M value. A large M value that is too large will make the constraints too loose, resulting in an overly large search space for the optimization problem, which will slow down the model convergence; a large M value that is too small may make the problem unsolvable or unable to find the global optimal solution, affecting the accuracy of the results. Therefore, in order to ensure the accuracy and solution efficiency of the model, it is necessary to select a reasonable large M value for the constraint. The details are as follows:

[0096] Rewrite formula (35) as:

[0097]

[0098] Where: , They are The maximum and minimum values ​​of

[0099] According to the DC power flow transfer factor matrix (SF matrix), we get:

[0100]

[0101] Where: is the element in the nth row and lth column of the SF matrix, which means: in DC power flow analysis, the sensitivity of the power change of branch l in the system to the power change of node n; is the net injected power of node n at time t;

[0102] For the upper and lower limits of the line power flow, we get:

[0103] )

[0104]

[0105] Where: , are the maximum and minimum values ​​of the net injected power at node n, respectively; , The setting method is as follows:

[0106] for , set all candidate units to be connected to the grid, the unit connected to node n is taken as the maximum power, the output of the new energy unit is taken as the maximum value of the historical data, and the load is taken as the minimum value of the historical data;

[0107]

[0108] for , set the unit connected to node n to take the minimum power, the output of the new energy unit to take the minimum value of historical data, and the load to take the maximum value of historical data:

[0109]

[0110] According to the phase angle constraint of formula (37), we have:

[0111]

[0112] In summary, the range of large M values ​​in formula (35) is obtained:

[0113]

[0114]

[0115] Furthermore, the step S5 specifically includes:

[0116] A1: Let auxiliary variable , , upper bound , the lower bound , and set the algorithm convergence threshold ;

[0117] A2: Solve the main investment planning problem and obtain the objective function The value of, and the value of the investment planning decision variable , ,renew ;

[0118] A3: , (That is, ) into the running subproblem, solve the running subproblem, and get the objective function The value of , and the value of the decision variable of the running sub-problem (that is, The values ​​of the dual variables of the decision variables of the running subproblem ,renew ;

[0119] A4: Bring in the main investment planning problem and update the Benders optimal cut constraints of the main investment planning problem;

[0120] A5: Check convergence; if converged, , the algorithm ends and outputs the transmission network expansion planning scheme; otherwise, return to step S2 until the algorithm converges to a solution that meets the accuracy requirements.

[0121] It should be noted that the main investment planning problem is a mixed integer linear programming problem, and the running subproblem is a linear programming problem, both of which can be solved by calling commercial solvers, such as Gurobi, Cplex, etc. In the running subproblem, the value of the decision variable of the running subproblem (that is, the value obtained by x in equation (41)) can be called by the commercial solver to directly obtain the value of the dual variable of the decision variable of the running subproblem .

[0122] In addition, the transmission network expansion planning scheme includes the expansion results of lines and units, as well as the total construction cost.

[0123] The present invention also provides a transmission network expansion planning system based on the improved large-M method, comprising:

[0124] An objective function building module is used to build the objective function of the transmission network source-grid collaborative planning model;

[0125] The constraint condition construction module is used to construct the constraint conditions of the transmission network source-grid collaborative planning model;

[0126] Benders decomposition module, used to decompose the transmission network source-grid collaborative planning model into the main investment planning problem and the operation sub-problem;

[0127] A value range determination module, used for adjusting the large M value range for each large M constraint;

[0128] The planning solution module is used to solve the transmission network expansion planning solution.

[0129] Beneficial effects: Compared with the prior art, the present invention aims to solve the problem of difficulty in selecting the value of the big M method in the modeling process of transmission network expansion planning, adjusts the big M value range of the constraint conditions, effectively narrows the feasible solution space of the transmission network expansion planning problem, and significantly improves the accuracy and efficiency of the model solution. On the basis of ensuring the accuracy of the solution of the expansion planning scheme, the solution efficiency of the expansion planning scheme is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] Figure 1 It is a schematic diagram of the process of the present invention;

[0131] Figure 2 This is the modified Garver 6-node system network topology diagram;

[0132] Figure 3 The expansion planning result diagram for the modified Garver 6-node system;

[0133] Figure 4 Frequency distribution diagram of values ​​taken to improve the Big M method. DETAILED DESCRIPTION

[0134] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0135] Embodiment 1:

[0136] like Figure 1 As shown, this embodiment provides a transmission network expansion planning method based on the improved large-M method, comprising the following steps:

[0137] S1: To minimize the total cost, construct the objective function of the transmission network source-grid collaborative planning model;

[0138] The transmission network source-grid collaborative planning model aims to meet the economic operation of the system by expanding lines and units. The objective function of the transmission network source-grid collaborative planning model is to minimize the total economic cost, which is the sum of investment cost, operation cost, and penalty cost of abandoning new energy and shedding load. The specific expression is as follows:

[0139]

[0140]

[0141]

[0142]

[0143] Where: represents the investment cost; , For each unit and transmission lines investment costs; , For each unit ,line Construction status, 1 means construction, 0 means no construction; , They represent the candidate generating units and the candidate transmission line sets respectively; Indicates the operating cost; Indicates time The crew contribute; is the unit cost function. The present invention performs piecewise linearization on the unit quadratic cost function, where a , b , c They are the quadratic cost coefficient, the linear cost coefficient, and the constant cost coefficient respectively; Gather for the moment; For the existing generator set collection; represents the penalty cost; Penalty costs for units that abandon wind and solar power; is the unit load shedding penalty cost; Indicates time The amount of wind and solar power curtailment; Indicates time The load shedding capacity; Assemble for new energy units; For load collection.

[0144] S2: Based on the objective function of the transmission network source-grid collaborative planning model, considering the four parts of investment, units, DC power flow, and abandoned renewable energy load shedding, the constraints of the transmission network source-grid collaborative planning model are constructed;

[0145] The constraints for the build include:

[0146] 1. Investment constraints:

[0147] For the expanded units and transmission lines, the total investment cost should not exceed the upper limit:

[0148]

[0149]

[0150] Where: , For each unit and transmission lines investment ceiling;

[0151] 2. Unit constraints:

[0152] The unit should meet the upper and lower output constraints:

[0153]

[0154] Where: , For each unit Upper and lower limits of output;

[0155] In addition, the unit should meet the climbing constraints:

[0156]

[0157]

[0158] Where: , For each unit Upward and downward climbing rates;

[0159] 3. DC power flow constraints:

[0160] First, the node power balance constraint should be satisfied:

[0161]

[0162] Where: Indicates in the scene s ,time t Lower energy storage j Charging power; Indicates in the scene s ,time t Lower energy storage j The discharge power; Indicates time of new energy output; Indicates time Load; Indicates at time Branch The power flowing through , , and They are the generator set, energy storage, new energy unit and load set located at node n respectively; is the line set; s(l) and r(l) are the sending end and receiving end of branch l respectively;

[0163] Secondly, for existing lines, the power flow constraints should be met:

[0164]

[0165]

[0166] Where: For Line Susceptance; , They are the voltage phase angles at the sending and receiving ends of branch l at time t respectively; For Line The maximum current allowed to pass;

[0167] For the expansion line, the power flow constraints should also be met:

[0168]

[0169]

[0170] Where: is a large number used to linearize nonlinear constraints;

[0171] Finally, the phase angle constraint should be satisfied:

[0172]

[0173]

[0174] Where: is the voltage phase angle of node n at time t; is the reference node voltage phase angle at time t;

[0175] 4. Constraints for abandoning new energy and shedding loads:

[0176] The amount of abandoned new energy and load shedding should be within the limit:

[0177]

[0178]

[0179] S3: Using the Benders decomposition algorithm, the transmission network source-grid collaborative planning model is decomposed into the investment planning main problem and the operation sub-problem;

[0180] The objective function of the main investment planning problem is:

[0181]

[0182] Where: is the auxiliary variable introduced;

[0183] The constraints include investment constraints and Benders optimal cut constraints returned from running subproblems;

[0184] The investment constraints are:

[0185]

[0186]

[0187] The above investment planning main problem (without the Benders optimal cut constraint) is written in a compact form:

[0188]

[0189] Where: The coefficient matrix of the objective function of the main problem of investment planning; The decision variables for the main investment planning problem, including the line investment variables , Unit investment variables , auxiliary variables ; The coefficient matrix of the constraints for the main investment planning problem; is the constant term for the constraints of the main investment planning problem.

[0190] The Benders optimal cut constraints returned from running the subproblem are:

[0191]

[0192] Where: The decision variables for running the subproblem The value of the dual variable can be obtained by running the subproblem. The meaning of other variables in the Benders optimal cut constraint can be found in equations (22) and (41). It is worth mentioning that the running subproblem always has a solution, so only the Benders optimal cut is returned to the main investment planning problem, and no Benders feasible cut is returned.

[0193] Therefore, the complete investment planning main problem can be written in a compact form as:

[0194]

[0195] In summary, the main investment planning problem is a mixed integer linear programming problem.

[0196] The objective function of running the subproblem is:

[0197]

[0198]

[0199]

[0200]

[0201] Where: The source-grid investment cost determined for the main investment planning problem; The line investment planning scheme determined by the main investment planning problem; The unit investment planning scheme is determined by the main investment planning problem.

[0202] Constraints include unit, DC power flow, and load shedding constraints of abandoned renewable energy sources:

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215] The above operation subproblem can be written in a compact form:

[0216]

[0217] Where: is the coefficient matrix of the objective function for running the subproblem; The decision variables for running subproblems include , , , , , , ; is the coefficient matrix of the constraints for the running subproblem; is the constant term for the constraints of the running subproblem; The investment planning scheme obtained for the main investment planning problem, including the line investment planning scheme , Unit Investment Planning Scheme .

[0218] For the equality constraint in the running subproblem, it can be equivalently split into two inequality constraints, which can be classified as For example, for , which can be equivalently decomposed into and These two inequality constraints.

[0219] In summary, the operation subproblem is a linear programming problem.

[0220] S4: In the operation sub-problem, the range of large M values ​​is set for each large M constraint through the DC power flow transfer factor matrix;

[0221] Rewrite formula (35) as:

[0222]

[0223] Where: , They are The maximum and minimum values ​​of

[0224] According to the DC power flow transfer factor matrix (SF matrix), we get:

[0225]

[0226] Where: is the element in the nth row and lth column of the SF matrix, which means: in DC power flow analysis, the sensitivity of the power change of branch l in the system to the power change of node n; is the net injected power of node n at time t;

[0227] For the upper and lower limits of the line power flow, we get:

[0228]

[0229]

[0230] Where: , are the maximum and minimum values ​​of the net injected power at node n, respectively; , The setting method is as follows:

[0231] for , set all candidate units to be connected to the grid, the unit connected to node n is taken as the maximum power, the output of the new energy unit is taken as the maximum value of the historical data, and the load is taken as the minimum value of the historical data;

[0232]

[0233] for , set the unit connected to node n to take the minimum power, the output of the new energy unit to take the minimum value of historical data, and the load to take the maximum value of historical data:

[0234]

[0235] According to the phase angle constraint of formula (37), we have:

[0236]

[0237] In summary, the range of large M values ​​in formula (35) is obtained:

[0238]

[0239]

[0240] S5: Solve and obtain the transmission network expansion planning scheme, which specifically includes:

[0241] A1: Let auxiliary variable , , upper bound , the lower bound , and set the algorithm convergence threshold ;

[0242] A2: Solve the main investment planning problem and obtain the objective function The value of, and the value of the investment planning decision variable , ,renew ;

[0243] A3: , (That is, ) into the running subproblem, solve the running subproblem, and get the objective function The value of the decision variable of the subproblem (i.e., the value obtained by x in equation (41)), and the value of the dual variable of the decision variable of the subproblem ,renew ;

[0244] A4: Bring in the main investment planning problem and update the Benders optimal cut constraints of the main investment planning problem;

[0245] A5: Check convergence; if converged, , the algorithm ends and outputs the transmission network expansion planning scheme; otherwise, return to step S2 until the algorithm converges to a solution that meets the accuracy requirements.

[0246] It should be noted that the main investment planning problem is a mixed integer linear programming problem, and the running subproblem is a linear programming problem, both of which can be solved by calling commercial solvers, such as Gurobi, Cplex, etc. In the running subproblem, the value of the decision variable of the running subproblem (that is, the value obtained by x in equation (41)) can be called by the commercial solver to directly obtain the value of the dual variable of the decision variable of the running subproblem .

[0247] In addition, the transmission network expansion planning scheme includes the expansion results of lines and units, as well as the total construction cost.

[0248] Embodiment 2:

[0249] Based on the transmission network expansion planning method of embodiment 1, this embodiment provides a transmission network expansion planning system based on the improved big-M method, including:

[0250] An objective function building module is used to build the objective function of the transmission network source-grid collaborative planning model;

[0251] The constraint condition construction module is used to construct the constraint conditions of the transmission network source-grid collaborative planning model;

[0252] Benders decomposition module, used to decompose the transmission network source-grid collaborative planning model into investment planning main problem and operation sub-problems;

[0253] A value range determination module, used for adjusting the large M value range for each large M constraint;

[0254] The planning solution module is used to solve the transmission network expansion planning solution.

[0255] Embodiment 3:

[0256] This embodiment uses the power transmission network expansion planning method of embodiment 1 and the power transmission network expansion planning system of embodiment 2 as examples, as follows:

[0257] This example adopts a modified Garver 6-node system. The modified Garver 6-node system includes 6 nodes and 6 built lines, of which node 6 is an isolated node. This example is based on this system, taking node 1 as a balancing node, and adding new energy units to nodes 2 and 4. The network topology is as follows: Figure 2 shown.

[0258] The specific parameters of this embodiment are set as follows:

[0259] Set time interval The parameters of the built lines, built units, candidate lines, and candidate units are shown in Tables 1 to 4 respectively:

[0260] Table 1 Parameters of the built lines

[0261]

[0262] Table 2 Parameters of the built units

[0263]

[0264] Table 3 Parameters of the lines to be built

[0265]

[0266] Table 4 Parameters of units to be built

[0267]

[0268] first, Figure 3 Table 5 shows the expansion planning result of this embodiment:

[0269] Table 5 Modified Garver 6-node network planning results

[0270]

[0271] from Figure 3 It can be seen from Table 5 that a new unit CG2 is added at node 5 of the modified Garver6 node system as an additional resource supply; in addition, a line is expanded between nodes 1 and 3, nodes 2 and 5, nodes 2 and 6, nodes 4 and 6, and nodes 5 and 6 respectively to change the distribution of power flow in the power grid and improve the economic and reliable operation capability of the transmission network.

[0272] In order to verify the effect of the solution of the present invention, this embodiment compares the performance difference between the improved large M method proposed by the present invention and the existing large M method. In the existing large M method, this embodiment sets M = 10^5.

[0273] Figure 4 The frequency distribution of large M values ​​calculated using the improved large M method is shown.

[0274] from Figure 4 It can be seen that in the modified Garver 6-node system, more than 90% of the M values ​​are less than 100. Compared with the existing large-M method, the improved large-M method can adaptively adjust the appropriate M value for each constraint, thereby avoiding excessive M values. Therefore, the improved method can significantly alleviate the problem of over-relaxation of constraints caused by the existing large-M method when modeling extended planning problems.

[0275] Table 6 shows the comparison of the calculation time and solution results using the existing big M method and the improved big M method:

[0276] Table 6 Comparison of calculation time and solution results

[0277]

[0278] According to the results in Table 6, the following conclusions can be drawn:

[0279] In terms of calculation speed, the existing big-M method takes 445 seconds to calculate, while the improved big-M method takes 82 seconds. The improved big-M method significantly shortens the solution time and improves the solution efficiency of the extended planning scheme by more than 5 times.

[0280] Judging from the solution results, the planning schemes and objective function values ​​of the existing and improved big-M methods are the same or very close, indicating that the improved big-M method can fully relax the constraints while ensuring that the selected M value is within a reasonable range, thereby ensuring the accuracy and reliability of the solution.

Claims

1. A transmission network expansion planning method based on the improved big M method, characterized in that: The steps include: S1: To minimize the total cost, construct the objective function of the transmission network source-grid collaborative planning model; S2: Based on the objective function of the transmission network source-grid collaborative planning model, considering the four parts of investment, units, DC power flow, and abandoned renewable energy load shedding, the constraints of the transmission network source-grid collaborative planning model are constructed; S3: Using the Benders decomposition algorithm, the transmission network source-grid collaborative planning model is decomposed into the investment planning main problem and the operation sub-problem; S4: In the operation sub-problem, the range of large M values ​​is set for each large M constraint through the DC power flow transfer factor matrix; S5: Based on the large M value range after constraint adjustment, the transmission network expansion planning scheme is solved.

2. A transmission network expansion planning method based on the improved large-M method according to claim 1, characterized in that: The objective function of the transmission network source-grid collaborative planning model in step S1 is to minimize the total economic cost, which is the sum of investment cost, operation cost, and penalty cost for abandoning new energy and shedding loads. The specific expression is as follows: ； ； ； ； Where: represents the investment cost; , For each unit and transmission lines investment costs; , For each unit ,line Construction status, 1 means construction, 0 means no construction; , They represent the candidate generating units and the candidate transmission line sets respectively; Indicates the operating cost; Indicates time The crew contribute; is the unit cost function, and the quadratic cost function of the unit is piecewise linearized, where a , b , c They are the quadratic cost coefficient, the linear cost coefficient, and the constant cost coefficient respectively; Gather for the moment; For the existing generator set collection; represents the penalty cost; Penalty costs for units that abandon wind and solar power; is the unit load shedding penalty cost; Indicates time The amount of wind and solar power curtailment; Indicates time The load shedding capacity; Assemble for new energy units; For load collection.

3. A transmission network expansion planning method based on the improved large-M method according to claim 2, characterized in that: The constraints of the transmission network source-network collaborative planning model in step S2 include: Investment constraints: For the expanded units and transmission lines, the total investment cost shall not exceed the upper limit: ； ； Where: , For each unit and transmission lines investment ceiling; Unit constraints: The unit meets the upper and lower output constraints: ； Where: , For each unit Upper and lower limits of output; The unit meets the climbing constraints: ； ； Where: , For each unit Upward and downward climbing rates; DC power flow constraints: Satisfy the node power balance constraint: ； Where: Indicates in the scene s ,time t Lower energy storage j Charging power; Indicates in the scene s ,time t Lower energy storage j The discharge power; Indicates time of new energy output; Indicates time Load; Indicates at time Branch The power flowing through , , and They are the generator set, energy storage, new energy unit and load set located at node n respectively; is the line set; s(l) and r(l) are the sending end and receiving end of branch l respectively; For existing lines, satisfy the power flow constraints: ； ； Where: For line Susceptance; , They are the voltage phase angles at the sending and receiving ends of branch l at time t respectively; For line The maximum current allowed to pass; For the expansion line, meet the power flow constraints: ； ； Where: is a number used to linearize nonlinear constraints; Satisfy the phase angle constraint: ； ； Where: is the voltage phase angle of node n at time t; is the reference node voltage phase angle at time t; Constraints for abandoning renewable energy and shedding loads: For abandoned new energy and load shedding, within the limits: ； 。 4. A transmission network expansion planning method based on the improved large-M method according to claim 3, characterized in that: The objective function of the main investment planning problem in step S3 is: ； Where: is the auxiliary variable introduced; The constraints include investment constraints and Benders optimal cut constraints returned from running subproblems; The investment constraints are: ； ； The above investment planning main problem can be written in a compact form: ； Where: The coefficient matrix of the objective function of the main problem of investment planning; The decision variables for the main investment planning problem, including the line investment variables , Unit investment variables , auxiliary variables ; The coefficient matrix of the constraints for the main investment planning problem; is the constant term of the constraints of the main investment planning problem; The Benders optimal cut constraints returned from running the subproblem are: ； Where: The decision variables for running subproblems The value of the dual variable of is obtained by running the subproblem; The complete investment planning problem can be written in compact form as: ； The main investment planning problem is a mixed integer linear programming problem.

5. A transmission network expansion planning method based on the improved large-M method according to claim 4, characterized in that: The objective function of the sub-problem in step S3 is: ； ； ； ； Where: The source-grid investment cost determined for the main investment planning problem; The line investment planning scheme determined by the main investment planning problem; The unit investment planning scheme determined by the main investment planning problem; Constraints include unit, DC power flow, and new energy load shedding constraints: ； ； ； ； ； ； ； ； ； ； ； ； The above operation subproblem can be written in a compact form: ； Where: is the coefficient matrix of the objective function for running the subproblem; The decision variables for running subproblems include , , , , , , ; is the coefficient matrix of the constraints for the running subproblem; is the constant term for the constraints of the running subproblem; The investment planning scheme obtained for the main investment planning problem, including the line investment planning scheme , Unit Investment Planning Scheme ; For the equality constraints in the running subproblem, they are equivalently split into two inequality constraints, which can be classified as form; Run the subproblem as a linear programming problem.

6. A transmission network expansion planning method based on the improved large-M method according to claim 5, characterized in that: The step S4 specifically includes: Rewrite formula (35) as: ； Where: , They are The maximum and minimum values ​​of According to the DC power flow transfer factor matrix, we get: ； Where: is the element in the nth row and lth column of the SF matrix, which means: in DC power flow analysis, the sensitivity of the power change of branch l in the system to the power change of node n; is the net injected power of node n at time t; For the upper and lower limits of the line power flow, we get: ； ； Where: , are the maximum and minimum values ​​of the net injected power at node n, respectively; According to the phase angle constraint of formula (37), we have: ； The range of large M values ​​in formula (35) is obtained as follows: ； 。 7. A transmission network expansion planning method based on the improved large-M method according to claim 6, characterized in that: In equation (44) and equation (45) of step S4, , The setting method is as follows: for , set all candidate units to be connected to the grid, the unit connected to node n is taken as the maximum power, the output of the new energy unit is taken as the maximum value of the historical data, and the load is taken as the minimum value of the historical data; ； for , set the unit connected to node n to take the minimum power, the output of the new energy unit to take the minimum value of historical data, and the load to take the maximum value of historical data: 。 8. A transmission network expansion planning method based on the improved large-M method according to claim 6, characterized in that: The step S5 specifically includes: A1: Let auxiliary variable , , upper bound , the lower bound , and set the algorithm convergence threshold ; A2: Solve the main investment planning problem and obtain the objective function and the values ​​of the investment planning decision variables , ,renew ; A3: , Substitute the running subproblem into the problem, solve the running subproblem, and get the objective function The value of , and the value of the decision variable of the subproblem, and the value of the dual variable of the decision variable of the subproblem ,renew ; A4: Bring in the main investment planning problem and update the Benders optimal cut constraints of the main investment planning problem; A5: Check convergence; if converged, , the algorithm ends and outputs the transmission network expansion planning scheme; otherwise, return to step S2 until the algorithm converges to a solution that meets the accuracy requirements.

9. A transmission network expansion planning system based on the improved Big M method, characterized in that: include: An objective function building module is used to build the objective function of the transmission network source-grid collaborative planning model; The constraint condition construction module is used to construct the constraint conditions of the transmission network source-grid collaborative planning model; Benders decomposition module, used to decompose the transmission network source-grid collaborative planning model into the main investment planning problem and the operation sub-problem; A value range determination module, used for adjusting the large M value range for each large M constraint; The planning solution module is used to solve the transmission network expansion planning solution.

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