A Transmission Network Expansion Planning Method and System Based on Improved Big M Method

Abstract

The present invention discloses a transmission network expansion planning method and system based on an improved big M method, the method comprising: constructing an objective function of a transmission network source-network collaborative planning model with the minimum total cost; constructing constraints of the transmission network source-network collaborative planning model based on the objective function of the transmission network source-network collaborative planning model; using the Benders decomposition algorithm to decompose the transmission network source-network collaborative planning model into an investment planning main problem and an operation sub-problem; in the operation sub-problem, adjusting the big M value range for each big M constraint through a DC power flow transfer factor matrix; and solving to obtain a transmission network expansion planning scheme. Aiming at the problem of the difficulty of taking values ​​of the big M method in the modeling process of transmission network expansion planning, the present invention adjusts the big M value range of the constraint condition, effectively narrows the feasible solution space of the transmission network expansion planning problem, and significantly improves the accuracy and efficiency of model solving.

Description

Technical Field

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

[0002] At present, with the continuous increase in the penetration rate of new energy and the increase in load demand, the power randomness and volatility of the power grid also increase. The current power transmission network faces the problem of insufficient capacity of equipment and lines, which may lead to restricted operation and bring risks and challenges to the economic dispatching and flexible operation of the power transmission network. To address these challenges, it is urgent to carry out expansion planning on the existing architecture of the power transmission network to improve the economic and reliable operation ability of the power transmission network.

[0003] In the process of modeling the power transmission network expansion planning in the power system, the constraint conditions often involve non-linear terms of variable products, and the big M method is often used for linearization. For the power transmission network line expansion planning model, the prior art linearizes the product of the line investment variable and the power flow variable. For the power transmission network power source planning model, the prior art linearizes the product of the line state 0-1 variable, the line number integer variable, and the voltage phase angle variable. For the power transmission network source-network collaborative planning model, the prior art linearizes the product of the voltage phase angle change variable and the susceptance matrix change variable. Generally speaking, the above prior arts all use the big M method to achieve the linearization of non-linear 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 prior art has the following problems: in the field of power transmission network expansion planning technology, the M value in the traditional big M method is often set as a maximum value according to 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] Object of the Invention: In order to overcome the deficiencies in the prior art, the present invention provides a power transmission network expansion planning method and system based on an improved big M method.

[0006] Technical Solution: To achieve the above object, the present invention provides a power transmission network expansion planning method based on an improved big M method, including the following steps:

[0007] S1: Construct the objective function of the power transmission network source-network collaborative planning model with the minimum total cost;

[0008] S2: Based on the objective function of the power transmission network source-network collaborative planning model, considering four parts: investment, unit, DC power flow, and new energy abandonment and load shedding, construct the constraint conditions of the power transmission network source-network collaborative planning model;

[0009] S3: Use the Benders decomposition algorithm to decompose the transmission network source-network collaborative planning model into an investment planning master problem and an operation sub-problem;

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

[0011] S5: Based on the range of the large M value set after constraint tuning, solve to obtain the transmission network expansion planning scheme.

[0012] Furthermore, the transmission network source-network 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-network collaborative planning model is to minimize the total economic cost, which is the sum of the investment cost, operation cost, and penalty cost for abandoning new energy and shedding load. The specific expression is as follows:

[0013]

[0014]

[0015]

[0016]

[0017] In the formula: represents the investment cost; , are the investment costs of unit and transmission line respectively; , are the investment statuses of unit , line respectively, 1 means built, 0 means not built; , represent the candidate unit set and candidate transmission line set respectively; represents the operation cost; represents the time output of unit ; is the unit cost function. In the present invention, the quadratic cost function of the unit is piecewise linearized, where a , b , c are the quadratic term cost coefficient, linear term cost coefficient, and constant term cost coefficient respectively; is the time set; is the existing generator set; represents the penalty cost; is the unit penalty cost for wind and light abandonment; is the unit penalty cost for load shedding; The curtailment of wind and solar power at time ; The load shedding at time ; is the set of new energy units; is the set of loads.

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

[0019] Investment constraint conditions:

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

[0021]

[0022]

[0023] Where: , are the investment upper limits of unit and transmission line respectively;

[0024] Unit constraint conditions:

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

[0026]

[0027] Where: , are the upper and lower limits of the output of unit respectively;

[0028] In addition, the unit should meet the ramping constraint:

[0029]

[0030]

[0031] Where: , are the upward and downward ramping rates of unit respectively;

[0032] DC power flow constraint conditions:

[0033] First of all, the node power balance constraint should be met:

[0034]

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

[0036] Secondly, for existing lines, the power flow constraint should be satisfied:

[0037]

[0038]

[0039] In the formula: is the susceptance of the line ; , are respectively the phase angles of the sending end and receiving end node voltages of branch l at time t; is the maximum power flow allowed through the line ;

[0040] For the extended line, the power flow constraint should also be satisfied:

[0041]

[0042]

[0043] In the formula: is a very large number used to linearize the non - linear constraint;

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

[0045]

[0046]

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

[0048] Constraint condition for abandoning new energy and shedding load:

[0049] For the amount of abandoned new energy and the amount of load shedding, they should be within the restricted range:

[0050]

[0051]

[0052] Furthermore, the constructed transmission network source-network collaborative planning model above is a mixed-integer linear programming problem, and the Benders decomposition algorithm can be used to decompose it.

[0053] The Benders decomposition algorithm is a decomposition method for solving large-scale optimization problems. It decomposes a problem with a large-scale complex structure into two parts - a master problem and one (or more) subproblems. Benders decomposition reduces the computational complexity by decomposing a complex problem into more easily solvable subproblems, and is particularly suitable for large-scale optimization problems with complex constraints.

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

[0055]

[0056] In the formula: is the introduced auxiliary variable;

[0057] The constraint conditions include investment constraint conditions and the Benders optimal cut constraint returned from the operation subproblem;

[0058] The investment constraint conditions are:

[0059]

[0060]

[0061] Write the above investment planning master problem (excluding the Benders optimal cut constraint) in a compact form:

[0062]

[0063] In the formula: is the coefficient matrix of the objective function of the investment planning master problem; is the decision variable of the investment planning master problem, including the line investment variable and the unit investment variable and the auxiliary variable ; is the coefficient matrix of the constraint conditions of the investment planning master problem; The constant term of the constraint condition of the investment planning main problem;

[0064] The Benders optimal cut constraint returned from the operation sub-problem is:

[0065]

[0066] Where: is the decision variable of the operation sub-problem The value of the dual variable of can be obtained by solving the operation sub-problem. The meanings of other variables in the Benders optimal cut constraint can be seen in Equations (22) and (41). It is worth mentioning that the operation sub-problem always has a solution, so it will only return the Benders optimal cut to the investment planning main problem, rather than the Benders feasible cut.

[0067] Therefore, writing the complete investment planning main problem in a compact form is:

[0068]

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

[0070] The objective function of the operation sub-problem is:

[0071]

[0072]

[0073]

[0074]

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

[0076] The constraint conditions include unit, DC power flow, and new energy abandonment and load shedding constraint conditions:

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Write the above operation sub - problem in a compact form:

[0090]

[0091] Where: is the coefficient matrix of the objective function of the operation sub - problem; is the decision variable of the operation sub - problem, including , , , , , , ; is the coefficient matrix of the constraint conditions of the operation sub - problem; is the constant term of the constraint conditions of the operation sub - problem; is the investment planning solution obtained from the main problem of the investment plan, including the line investment planning solution , the unit investment planning solution .

[0092] For the equality constraints in the operation sub - problem, they can be equivalently split into two inequality constraints, thus reduced to the form of . Exemplarily, for , it can be equivalently split into and these two inequality constraints.

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

[0094] Furthermore, step S4 specifically includes:

[0095] For Equation (35), it is necessary to select an appropriate large M value. An overly large large M value will make the constraint conditions too loose, resulting in an overly large search space for the optimization problem, and thus the model will have a slow convergence speed; an overly small large M value may make the problem have no solution or fail to find the global optimal solution, affecting the accuracy of the results. Therefore, to ensure the accuracy of the model and the solution efficiency, it is aimed to select a reasonable large M value for the constraint. Specifically as follows:

[0096] Rewrite Equation (35) as:

[0097]

[0098] In the formula: 、 are respectively the maximum and minimum values;

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

[0100]

[0101] In the formula: is the element in the nth row and lth column of the SF matrix, and its meaning is: in the 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 injection power of node n at time t;

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

[0103] )

[0104]

[0105] In the formula: 、 are respectively the maximum and minimum values of the net injection power of node n; 、 The setting method is as follows:

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

[0107]

[0108] For , set the units connected to node n to be the minimum power, the output of new energy units is taken as the minimum value of historical data, and the load is taken as the maximum value of historical data:

[0109]

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

[0111]

[0112] In summary, the value range of the big M in Equation (35) is obtained:

[0113]

[0114]

[0115] Furthermore, the specific steps of step S5 include:

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

[0117] A2: Solve the main problem of the investment plan to obtain the value of the objective function , and the values of the investment plan decision variables , , and update ;

[0118] A3: Substitute , (which is in Equation (41)) into the operation sub-problem, solve the operation sub-problem to obtain the value of the objective function , and the values of the operation sub-problem decision variables (which is the value obtained for in Equation (41)), and the values of the dual variables of the operation sub-problem decision variables , and update ;

[0119] A4: Substitute into the main problem of the investment plan, and update the Benders optimal cut constraint of the main problem of the investment plan;

[0120] A5: Check the convergence situation; if it converges, that is, , then 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 operation sub-problem is a linear programming problem. Both can be solved by calling commercial solvers, such as Gurobi, Cplex, etc. In the operation sub-problem, by using the value of the decision variable of the operation sub-problem (i.e., the value obtained for x in Equation (41)), a commercial solver can be called to directly obtain the value of the dual variable of the decision variable of the operation sub-problem. 。

[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 an improved big M method, including:

[0124] An objective function construction module for constructing the objective function of the transmission network source-network collaborative planning model;

[0125] A constraint condition construction module for constructing the constraint conditions of the transmission network source-network collaborative planning model;

[0126] A Benders decomposition module for decomposing the transmission network source-network collaborative planning model into a main investment planning problem and an operation sub-problem;

[0127] A value range determination module for setting the value range of big M for each big M constraint;

[0128] A planning scheme solving module for solving the transmission network expansion planning scheme.

[0129] Beneficial effects: Compared with the prior art, the present invention addresses the problem of difficult big M method value selection in the transmission network expansion planning modeling process, tunes the value range of big M for the constraint conditions therein, effectively reduces the feasible solution space of the transmission network expansion planning problem, significantly improves the accuracy and efficiency of model solving, and greatly improves the solving efficiency of the expansion planning scheme on the basis of ensuring the accuracy of the expansion planning scheme solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] Figure 1 is a schematic flow chart of the method of the present invention;

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

[0132] Figure 3 is a modified expansion planning result diagram of the Garver 6-node system;

[0133] Figure 4 is a frequency distribution diagram of the improved big M method value; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0134] The present invention will be further illustrated 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 not to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification made by those skilled in the art fall within the scope defined by the appended claims of this application.

[0135] Embodiment 1:

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

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

[0138] The transmission network source-network 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-network collaborative planning model is to minimize the total economic cost, which is the sum of the investment cost, operation cost, and penalty cost for cutting off new energy load. The specific expression is as follows:

[0139]

[0140]

[0141]

[0142]

[0143] In the formula: represents the investment cost; , are respectively the investment costs of unit and transmission line ; , are respectively the construction states of unit , line , 1 means constructed, 0 means not constructed; , respectively represent the sets of candidate units and candidate transmission lines; represents the operation cost; represents the output of unit at time ; is the unit cost function. In the present invention, the quadratic cost function of the unit is piecewise linearized, where a , b , c are respectively the quadratic term cost coefficient, the linear term cost coefficient, and the constant term cost coefficient; is the set of times; is the set of existing generator sets; represents the penalty cost; is the penalty cost per unit of wind and light curtailment; is the penalty cost per unit of load shedding; represents the time of wind and light curtailment; represents the time of load shedding; is the set of new energy generator sets; is the set of loads.

[0144] S2: Based on the objective function of the source-network collaborative planning model of the transmission network, considering four parts: investment, generator sets, DC power flow, and new energy curtailment and load shedding, construct the constraint conditions of the source-network collaborative planning model of the transmission network;

[0145] The constructed constraint conditions include:

[0146] 1. Investment constraint conditions:

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

[0148]

[0149]

[0150] In the formula: , are respectively the upper limits of investment for the generator set and the transmission line ;

[0151] 2. Generator set constraint conditions:

[0152] The generator set should satisfy the upper and lower limits of output constraints:

[0153]

[0154] In the formula: , are respectively the upper and lower limits of the output of the generator set ;

[0155] In addition, the generator set should satisfy the ramping constraint:

[0156]

[0157]

[0158] In the formula: , are respectively the upward and downward ramping rates of the generator set ;

[0159] 3. DC power flow constraint conditions:

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

[0161]

[0162] In the formula: represents the charging power of the energy storage s at time t in scenario j ; represents the discharging power of the energy storage s at time t in scenario j ; represents the new energy output at time ; represents the load at time ; represents the power flowing through branch at time ; , , and are the sets of generator sets, energy storage, new energy units, and loads located at node n, respectively; is the set of lines; s(l) and r(l) are the sending end and receiving end of branch l, respectively;

[0163] Secondly, for existing lines, the power flow constraint should be satisfied:

[0164]

[0165]

[0166] In the formula: is the susceptance of line ; , are the phase angles of the node voltages at the sending end and receiving end of branch l at time t, respectively; is the maximum power flow allowed through line ;

[0167] For the extended lines, the power flow constraint should also be satisfied:

[0168]

[0169]

[0170] In the formula: is a very large number used to linearize the non - linear constraint;

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

[0172]

[0173]

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

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

[0176] For the amount of abandoned new energy and the amount of load shedding, they should be within the restricted range:

[0177]

[0178]

[0179] S3: Adopt the Benders decomposition algorithm to decompose the source-network collaborative planning model of the power transmission network into the main investment planning problem and the operation sub-problem;

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

[0181]

[0182] In the formula: is the introduced auxiliary variable;

[0183] The constraint conditions include investment constraint conditions and the Benders optimal cut constraint returned from the operation sub-problem;

[0184] The investment constraint conditions are:

[0185]

[0186]

[0187] Write the above main investment planning problem (excluding the Benders optimal cut constraint) in a compact form:

[0188]

[0189] In the formula: is the coefficient matrix of the objective function of the main investment planning problem; is the decision variable of the main investment planning problem, including the line investment variable and the unit investment variable and the auxiliary variable ; is the coefficient matrix of the constraint conditions of the main investment planning problem; The constant term of the constraint condition of the investment planning master problem.

[0190] The Benders optimal cut constraint returned from the operating subproblem is:

[0191]

[0192] In the formula: is the decision variable of the operating subproblem The value of the dual variable can be obtained by solving the operating subproblem. The meanings of other variables in the Benders optimal cut constraint can be seen in Eqs. (22) and (41). It is worth mentioning that the operating subproblem always has a solution, so it will only return the Benders optimal cut to the investment planning master problem, rather than the Benders feasible cut.

[0193] Therefore, the complete investment planning master problem is written in a compact form as:

[0194]

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

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

[0197]

[0198]

[0199]

[0200]

[0201] In the formula: is the source-network investment cost determined by the investment planning master problem; is the line investment planning scheme determined by the investment planning master problem; is the unit investment planning scheme determined by the investment planning master problem.

[0202] The constraint conditions include unit, DC power flow, and new energy abandonment and load shedding constraint conditions:

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215] Write the above operation sub - problem in a compact form:

[0216]

[0217] Where: is the coefficient matrix of the objective function of the operation sub - problem; is the decision variable of the operation sub - problem, including , , , , , , ; is the coefficient matrix of the constraint conditions of the operation sub - problem; is the constant term of the constraint conditions of the operation sub - problem; is the investment planning solution obtained from the main problem of investment planning, including the line investment planning solution , the unit investment planning solution .

[0218] For the equality constraints in the operation sub - problem, they can be equivalently split into two inequality constraints, thus reduced to the form of . Exemplarily, for , it can be equivalently split into and these two inequality constraints.

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

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

[0221] Rewrite Equation (35) as:

[0222]

[0223] In the formula: and are respectively the maximum and minimum values;

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

[0225]

[0226] In the formula: is the element in the nth row and lth column of the SF matrix, and its meaning is: in the 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 injection power of node n at time t;

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

[0228]

[0229]

[0230] In the formula: and are respectively the maximum and minimum values of the net injection power of node n; and are set as follows:

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

[0232]

[0233] For set the units connected to node n to be taken as the minimum power, the output of new energy units is taken as the minimum value of historical data, and the load is taken as the maximum value of historical data:

[0234]

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

[0236]

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

[0238]

[0239]

[0240] S5: Obtain the transmission network expansion planning scheme, specifically including:

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

[0242] A2: Solve the main investment planning problem to obtain the value of the objective function , and the values of the investment planning decision variables , , update ;

[0243] A3: Substitute , (i.e., in Equation (41)) into the operation sub-problem, solve the operation sub-problem to obtain the value of the objective function , and the values of the operation sub-problem decision variables (i.e., the value of x obtained in Equation (41)), and the values of the dual variables of the operation sub-problem decision variables , update ;

[0244] A4: Substitute into the main investment planning problem to update the Benders optimal cut constraint of the main investment planning problem;

[0245] A5: Check the convergence situation; if it converges, i.e., , then the algorithm ends and outputs the transmission network expansion planning scheme; otherwise, go back 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 operation sub-problem is a linear programming problem. Both can be solved by calling commercial solvers, such as Gurobi, Cplex, etc. In the operation sub-problem, through the values of the operation sub-problem decision variables (i.e., the value of x obtained in Equation (41)), the commercial solver can be called to directly obtain the values of the dual variables of the operation sub-problem decision variables .

[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] Example 2:

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

[0250] An objective function construction module, configured to construct an objective function of a source-network collaborative planning model for a transmission network;

[0251] A constraint condition construction module, configured to construct constraint conditions of a source-network collaborative planning model for a transmission network;

[0252] A Benders decomposition module, configured to decompose a source-network collaborative planning model for a transmission network into an investment planning master problem and an operation sub-problem;

[0253] A value range determination module, configured to set a value range for each large M constraint;

[0254] A planning scheme solving module, configured to solve and obtain a transmission network expansion planning scheme.

[0255] Example 3:

[0256] This example applies the transmission network expansion planning method of Example 1 and the transmission network expansion planning system of Example 2, specifically as follows:

[0257] This example uses a modified Garver 6-node system. The modified Garver 6-node system includes 6 nodes and 6 existing lines, where node 6 is an isolated node. Based on this system, node 1 is taken as the balancing node, and new energy units are added to nodes 2 and 4. Its network topology is as Figure 2 shown.

[0258] The specific parameter settings of this example are as follows:

[0259] Let the time interval be . The parameters of the existing lines, existing units, candidate lines, and candidate units are shown in Tables 1 to 4 respectively:

[0260] Table 1 Parameters of Existing Lines

[0261]

[0262] Table 2 Parameters of Existing Units

[0263]

[0264] Table 3 Parameters of Lines to be Built

[0265]

[0266] Table 4 Parameters of Units to be Built

[0267]

[0268] First, Figure 3 and Table 5 show the expansion planning results of this example:

[0269] Table 5 Revised Garver 6-Node Network Planning Results

[0270]

[0271] From Figure 3 As can be seen from and Table 5, a new unit CG2 is added at Node 5 of the revised Garver 6-node system as a new resource supply. In addition, a new line is built between Node 1 and 3, Node 2 and 5, Node 2 and 6, Node 4 and 6, and Node 5 and 6 respectively, changing the power flow distribution in the power grid and improving the economic and reliable operation ability of the transmission grid.

[0272] To verify the effectiveness of the proposed solution of the present invention, this embodiment compares the performance differences between the improved big-M method proposed by the present invention and the existing big-M method. In the existing big-M method, M = 10^5 is set in this embodiment.

[0273] Figure 4 Shows the frequency distribution of the big-M values calculated using the improved big-M method.

[0274] From Figure 4 As can be seen, in the revised Garver 6-node system, more than 90% of the M values are less than 100. Compared with the existing big-M method, the improved big-M method can adaptively set appropriate M values for each constraint, thus avoiding excessive M values. Therefore, this improved method can significantly alleviate the problem of over-relaxation of constraints caused by the existing big-M method in the modeling of expansion 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] Based on the results in Table 6, the following conclusions can be drawn:

[0279] In terms of calculation speed, the calculation time of the existing big-M method is 445 seconds, while the calculation time of the improved big-M method is 82 seconds. The improved big-M method significantly shortens the solution time, improves the solution efficiency of the expansion planning scheme, and the improvement amplitude is more than 5 times.

[0280] In terms of 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 ensure that the selected M value is within a reasonable range while fully relaxing the constraints, guaranteeing 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; 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 of abandoning new energy and shedding load. The specific expression is as follows: minC inv +C ope +C penal (1) Where: C inv Indicates investment cost; IC g 、IC l are the investment costs of unit g and transmission line l respectively; x g 、x l are the construction status of unit g and line l respectively; Ω g+ ,Ω l+ Respectively represent the candidate units and candidate transmission line sets; C ope represents the operating cost; P g,t represents the unit g output at time t; is the unit cost function, and the quadratic cost function of the unit is piecewise linearized, where a, b, and c are the quadratic cost coefficient, the linear cost coefficient, and the constant cost coefficient, respectively; T is the time set; Ω g C is a collection of existing generator sets; penal represents the penalty cost; c r is the penalty cost for unit wind and solar power abandonment; c d is the unit load shedding penalty cost; Indicates the amount of wind and solar power curtailment at time t; Indicates the load shedding amount at time t; Ω renew For the new energy unit collection; Ω d is the load collection; The constraints of the transmission network source-grid 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: IC gmax 、IC lmax are the investment caps for unit g and transmission line l, respectively; Unit constraints: The unit meets the upper and lower output constraints: P gmin ≤P g,t ≤P gmax (7) Where: P gmax , P gmin They are the upper and lower limits of the unit's g output respectively; The unit meets the climbing constraints: P g,t -P g,t-1 ≤UR g (8) P g,t -P g,t-1 ≥DR g (9) In the formula: UR g ,DR g are the upward and downward climbing rates of unit g respectively; DC power flow constraints: Satisfy the node power balance constraint: Where: represents the charging power of energy storage j in scenario s and time t; represents the square electric power of energy storage j in scenario s and time t; P renew,t represents the new energy output at time t; P d,t represents the load at time t; p t,l represents the power flowing through branch l at time t; and are the generator set, energy storage, new energy unit and load set located at node n respectively; Ω l 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: p s,t,l =B l (i s(t,l) -θ r(t,l) ) (11) -f l,max ≤p t,l ≤f l,max (12) Where: B l is the line susceptance; θ s(t,l) ,θ r(t,l) They are the voltage phase angles at the sending and receiving ends of branch l at time t respectively; f l,max is the maximum flow allowed to pass through line l; For the expansion line, meet the power flow constraints: -(1-x l )M≤p t,l -B l (i s(t,l) -θ r(t,l) )≤(1-x l )M (13) -f l,max x l ≤p t,l ≤f l,max x l (14) Where: M is a number used to linearize nonlinear constraints; Satisfy the phase angle constraint: -π≤θ n,t ≤π (15) i ref,t =0 (16) Where: θ n,t is the voltage phase angle of node n at time t; θ ref,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: The objective function of the main investment planning problem in step S3 is: In the formula: q is the introduced auxiliary variable; 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: c1 is the objective function coefficient matrix of the main investment planning problem; y is the decision variable of the main investment planning problem, including the line investment variable x l , unit investment variable x g , auxiliary variable q; A1 is the coefficient matrix of the constraint conditions of the main problem of investment planning; b1 is the constant term of the constraint conditions of the main problem of investment planning; The Benders optimal cut constraints returned from running the subproblem are: (b2-A1y) T α≤q (23) where: α is the value of the dual variable of the decision variable x of the running subproblem, 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; The objective function of running the subproblem 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: P gmin ≤P g,t ≤P gmax (29) P g,t -P g,t-1 ≤UR g (30) P g,t =P g,t-1 ≥DR g (31) p s,t,l =B l (i s(t,l) -θ r(t,l) (33) -f l,max ≤p t,l ≤f l,max (34) -π≤θ n,t ≤π (37) i ref,t =0 (38) The above operation subproblem can be written in a compact form: Where: c2 is the coefficient matrix of the objective function of the running sub-problem; x is the decision variable of the running sub-problem, including P g,t , p t,l ,θ n,t ; A2 is the coefficient matrix of the constraints of the running sub-problem; b2 is the constant term of the constraints of the running sub-problem; 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; The operation subproblem is a linear programming problem; Step S4 specifically includes: Rewrite formula (35) as: Where: They are p t,l -B l (θ s(t,l) -θ r(t,l) )'s maximum and minimum values; According to the DC power flow transfer factor matrix, we get: Where: SF n,l is the element in the nth row and lth column of the SF matrix, which means: in the DC power flow analysis, the sensitivity of the power change of branch l in the system to the power change of node n; P n,t 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: -2πB l ≤B l (i s(t,l) -θ r(t,l) )≤2πB l (46) The range of large M values ​​in formula (35) is obtained as follows: In equation (44) and equation (45) of step S4, The setting method is as follows: for All candidate units are set 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:

2. A transmission network expansion planning method based on the improved large-M method according to claim 1, characterized in that: The step S5 specifically includes: A1: Set auxiliary variable q = 0, α = 0, upper bound UB = +∞, lower bound LB = -∞, and set the algorithm convergence threshold ε; A2: Solve the main investment planning problem and obtain the objective function f upper The value of, and the value of the investment planning decision variable Update LB = f upper ; A3: Substitute the running subproblem into the problem, solve the running subproblem, and obtain the objective function f lower The value of the decision variable of the running subproblem, and the value of the dual variable of the running subproblem decision variable α, update UB = f lower ; A4: Bring α into the main investment planning problem and update the Benders optimal cut constraint of the main investment planning problem; A5: Check convergence; if converged, that is, UB-LB<ε, 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.

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