A convex hull economic dispatch domain delineation method for grid-connected section of power distribution network

Abstract

The application discloses a convex hull economic dispatch domain delineation method for grid-connected sections of a power distribution network, relates to the technical field of power distribution network dispatching and energy management, and comprises the following steps: obtaining power distribution network equipment, network parameters and source and load uncertainty data, and constructing a deterministic economic dispatch model; through a dual theory, the deterministic economic dispatch model is converted into a compact mathematical optimization form; based on the deterministic economic dispatch model under the mathematical optimization form, a decision-dependent two-stage robust optimization dispatch model is established, and a convex hull economic dispatch domain of a first-stage conventional generator start-stop scheme and second-stage grid-connected section power representation is determined; a normalization reconstruction technology is adopted to convert the decision-dependent optimization model into a decision-independent optimization model, a standard two-stage robust optimization dispatch model is formed, and the convex hull economic dispatch domain is obtained by solving the robust optimization dispatch model and alternately iteratively solving the standard model by using a column constraint generation algorithm. The method improves dispatching economy on the basis of ensuring system safety.

Description

Technical Field

[0001] This invention relates to the field of distribution network dispatching and energy management technology, and in particular to a method for characterizing the convex hull economic dispatch domain of a distribution network connection section. Background Technology

[0002] To achieve the goal of "carbon neutrality," the penetration rate of renewable energy sources such as wind and solar power in the power system has increased significantly. However, their intermittency and uncertainty pose significant challenges to distribution network dispatch. As a core component for accommodating distributed energy resources, the distribution network's flexibility can support the operation of the upstream main grid. Quantifying this flexibility and balancing dispatch security and economy have become key issues in distribution network energy management.

[0003] Existing research often employs methods such as two-stage robust optimization and adjustable robust optimization to address uncertainties in distribution networks, but these methods have significant shortcomings: First, they focus on system operational safety, and the feasible regions they delineate include a large number of extreme and uneconomical scheduling schemes, making them difficult to apply in practical engineering. Second, traditional optimization models are prone to iterative oscillations and non-convergence problems when dealing with decision-dependent uncertainties, failing to meet the requirements of online scheduling. Third, they do not incorporate scheduling costs into the regional delineation objectives, thus failing to provide the upper-level main grid with a scheduling boundary reference that combines safety and economy.

[0004] With the increasing demand for coordinated dispatching of power transmission and distribution networks, there is an urgent need for an optimization method that can accurately quantify the economic dispatching area of ​​the distribution network connection section and solve stably, in order to solve the problems of conservatism, lack of economy and solution efficiency of existing technologies, as well as the problems of "emphasizing safety while ignoring economy" and "easy oscillation and non-convergence in the current research on the dispatching area of ​​distribution networks. Summary of the Invention

[0005] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and provide a method for characterizing the convex hull economic dispatch domain of the grid-connected section of the distribution network. Through two-stage robust modeling and normalization reconstruction technology, the convex hull economic region of the grid-connected line power is delineated on the basis of ensuring system safety, so as to provide guidance for automatic cruise of the upper-level main grid and economic operation of the distribution network.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method for characterizing the convex hull economic dispatch domain of a distribution network section according to the present invention includes:

[0008] Step 1: Obtain uncertainty data on distribution network equipment, network parameters, and source loads; and construct a deterministic economic dispatch model based on the uncertainty data on distribution network equipment, network parameters, and source loads.

[0009] Step 2: Using duality theory, the deterministic economic scheduling model from Step 1 is transformed into a deterministic economic scheduling model under a contractionary optimization form.

[0010] Step 3: Based on the deterministic economic dispatch model under the optimization form in Step 2, establish a decision-dependent two-stage robust optimization dispatch model. The decision-dependent two-stage robust optimization dispatch model includes the generator start-up and shutdown scheme in the first stage and the convex hull economic dispatch domain representing the grid connection section power in the second stage.

[0011] Step 4: Using normalization reconstruction technology, the decision-dependent two-stage robust optimization scheduling model in Step 3 is transformed into a decision-independent two-stage robust optimization scheduling model.

[0012] Step 5: Solve the decision-independent two-stage robust optimization scheduling model, transforming it into a standard model that includes the main problem and sub-problems. Use the column constraint generation algorithm to solve it iteratively to obtain the convex hull economic scheduling domain.

[0013] As a further optimization scheme for the method of characterizing the convex hull economic dispatch domain of the grid-connected section of the distribution network described in this invention, in step 1, the distribution network equipment and network parameters include the operating cost coefficient, power limit, efficiency parameters, and branch resistance and reactance of generators, energy storage, renewable energy units, and grid-connected lines, as well as the power capacity; the source-load uncertainty data include the predicted nominal values ​​and deviation ranges of photovoltaic output and load power.

[0014] The objective function of the deterministic economic scheduling model is to minimize the total operating cost, as expressed below:

[0015] (1)

[0016] in, The objective function of the deterministic economic dispatch model for distribution networks is to minimize the total operating cost, where y is the set of decision variables. For generator power, These represent the energy storage charging and discharging power, respectively. These represent the power purchased and sold through the grid connection, respectively; t is the time period number, and i is the node number. This is the generator operating cost coefficient. This is the energy storage degradation cost coefficient. These refer to the grid-connected power purchase price and the power sales price; Let I be the total number of time periods in the scheduling cycle, and let I be the number of nodes in the distribution network. The duration of a single time period;

[0017] The constraints of the deterministic economic scheduling model include:

[0018] 1) Generator constraints:

[0019] (2)

[0020] (3)

[0021] (4)

[0022] Equation (2) represents the active power range of the generator, where Let be the minimum and maximum power coefficients of the generator at node i. Let represent the start / stop status of the generator at node i during time period t. Let be the active power output of the generator at node i during time period t; Equation (3) represents the reactive power output range of the generator, where Let be the maximum and minimum power factors of the generator at the i-th node. Let be the reactive power output of the generator at node i during time period t; Equation (4) represents the active power ramp-up rate range of the generator, where Let be the maximum landslide and ramp rates of the generator at the i-th node; Let be the initial power output of the generator at the i-th node, set to 0. Let be the active power generated by the generator at node i during time period t-1;

[0023] 2) Energy storage constraints:

[0024] (5)

[0025] (6)

[0026] (7)

[0027] (8)

[0028] Equation (5) represents the active power range of the energy storage unit, where Let be the charging active power and discharging active power of the energy storage unit at the i-th node during time period t; Let be the maximum charging active power and the maximum discharging active power of the energy storage unit at the i-th node; Equation (6) represents the reactive power range of the energy storage unit, where Let be the reactive power of the energy storage unit at the i-th node during time period t; Let be the minimum power factor of the energy storage unit at the i-th node; Equation (7) represents the state-of-charge expression of the energy storage unit, where Let represent the state of charge of the energy storage unit at node i during time period t. Let represent the state of charge of the energy storage unit at node i during time period t-1. Let be the charging efficiency of the energy storage unit at the i-th node. Let be the discharge efficiency of the energy storage unit at the i-th node; Equation (8) represents the range of the energy storage state of charge. Let be the minimum and maximum states of charge of the energy storage unit at the i-th node; For the energy storage unit at the i-th node at the end of the cycle The capacity and initial state of charge;

[0029] 3) Renewable energy and load constraints:

[0030] (9)

[0031] (10)

[0032] Equation (9) represents the reactive power range of renewable energy units, where Let be the active power of the renewable energy unit at node i during time period t. Let be the reactive power of the renewable energy unit at node i during time period t; Let be the minimum power factor of the renewable energy unit at the i-th node; Equation (10) is the expression for the reactive power of the load, where Let be the active power of the load at node i during time period t; Let be the reactive power of the load at node i during time period t; Let be the power factor of the load at the i-th node. Let be the power factor of the load at the i-th node;

[0033] 4) Grid connection constraints:

[0034] (11)

[0035] (12)

[0036] Equation (11) represents the active power range of the grid-connected line, where Let be the positive and negative active power of the grid-connected line of the i-th node during time period t; Let be the upper limit of the forward active power and the upper limit of the reverse active power of the grid-connected line at the i-th node; Equation (12) represents the range of the apparent power of the grid-connected line. Let be the reactive power of the grid-connected line of the i-th node. Let be the apparent power limit of the grid-connected line of the i-th node;

[0037] 5) Distribution network line constraints:

[0038] (13)

[0039] (14)

[0040] (15)

[0041] (16)

[0042] (17)

[0043] Equation (13) represents the active power balance constraint of the distribution network lines, where Let be the active power of the renewable energy unit at node i during time period t; Let be the active power of the load at node i during time period t; These are the charging active power and discharging active power of the energy storage unit at the i-th node during time period t, respectively. Let be the active power of the generator at the i-th node during time period t; These are the forward and reverse active power of the grid-connected line of the i-th node during time period t; Let be the active power of the line from node i to node j during time period t; Let be the resistance of the line from node i to node j; Let be the current of the line from node i to node j during time period t; Equation (14) represents the reactive power balance constraint of the network line, where Let be the reactive power of the renewable energy unit at node i during time period t. Let be the reactive power of the load at node i during time period t; Let be the reactive power output of the energy storage unit at the i-th node during time period t. Let be the reactive power output of the generator at node i during time period t. Let be the reactive power of the grid-connected line of the i-th node during time period t. Let be the reactive power of the line from node i to node j during time period t; Equation (15) represents the voltage change at the node, where Let be the reactance of the line from node i to node j. Let be the square of the line voltage from node i to node j. Let be the imaginary part of the admittance of the line from node i to node j. Let be the current in the line from node i to node j during time period t. Let be the square of the minimum voltage and the square of the maximum voltage from node i to node j during time interval t. Let be the maximum current of the line from node i to node j; Equation (16) represents the constraint of the line apparent power; Equation (17) represents the boundary constraints of the line voltage and current. Let be the active power of the line from node s to node i during time period t. Let be the resistance of the line from the s-th node to the i-th node. Let be the current in the line from node s to node i during time period t. Let i be the set of all branches flowing into the i-th node. Let i be the set of all branches flowing out of the i-th node. Let be the reactive power of the line from node s to node i during time period t. Let be the reactance of the line from the s-th node to the i-th node. Let be the square of the voltage amplitude of the j-th node during time period t. Let be the square of the voltage amplitude of the i-th node during time period t. , These are the minimum and maximum values ​​of the square of the voltage amplitude at the i-th node.

[0044] As a further optimization scheme for the method of characterizing the convex hull economic dispatch domain of the distribution network section described in this invention, step 2, through duality theory, transforms the deterministic economic dispatch model of step 1 into a compact optimization form of deterministic economic dispatch model M1.

[0045] (18)

[0046] (19)

[0047] (20)

[0048] In this context, the superscript T represents the transpose, and the objective function and constraints in M1 are expressed in matrix form. Equation (18) is the compressed matrix representation of Equation (1), where y is the set of decision variables and A is the coefficient vector. Equations (19)-(20) integrate formulas (2)-(17). In Equation (19), G, H, and J are coefficient matrices, where... , To represent the set of uncertain parameters, , This is the set of start-stop state parameters for the generator. Let f represent the start-up command, stop-up command, and start / stop status of the generator at node i during time period t, respectively, and f be a constraint constant vector. The dual vectors are: Equation (20) corresponds to the second-order cone constraints (12) and (16), where L, m, and n are coefficient matrices. As dual variables;

[0049] The derivation of the dual problem of M1 is as follows:

[0050] (twenty one)

[0051] In equation (21), Let be the dimension of equation (21). , , It is a coefficient matrix;

[0052] M1 is a second-order cone programming problem, a convex optimization problem that satisfies strong duality. The primal-dual optimality condition of M1 is expressed as:

[0053] (twenty two)

[0054] The optimality condition transforms the solution of the convex second-order cone programming M1 into the solution of equation (22). For a given u and x, the optimal solution of M1 can be obtained by using equation (22).

[0055] As a further optimization of the convex hull economic dispatch domain characterization method for a distribution network connection section described in this invention, step 3 includes:

[0056] The decision-dependent two-stage robust optimization scheduling model is as follows:

[0057] (twenty three)

[0058] Limited to:

[0059] (twenty four)

[0060] (25)

[0061] (26)

[0062] (27)

[0063] (28)

[0064] (29)

[0065] In equation (23), P represents a decision-dependent two-stage robust optimization scheduling model. , This is the set of generator start-stop constraints for the first stage, where Let represent the start-up command, stop-up command, and start / stop status of the generator at node i during time period t, respectively; Equation (24) represents the minimum start-up time constraint, where Let be the minimum start-up time of the generator at the i-th node; Equation (25) represents the minimum downtime constraint, where Let be the minimum downtime of the generator at the i-th node; Equation (26) represents the maximum uptime constraint, where Let be the maximum start-up time of the generator at the i-th node; Equation (27) represents The logical relationship between them, among which Let be the start-stop state of the generator at node i during time period t-1; Equation (28) represents the definition of the set of uncertainty parameters u, where This is a set of source-load uncertainties, including photovoltaic output limitations and load power limitations. Let be the active power of the renewable energy unit at node i during time period t. Let be the upper and lower limits of the active power of the renewable energy unit at the i-th node during time period t; Let be the active power demand of the i-th node during time period t. Let be the upper and lower limits of the active power demand of the i-th node during time period t; Equation (29) describes the column vector using half-space representation, where Let be the column vector of the optimal active power and reactive power of the grid-connected section during time period t. For non-slack variables, when Grid connection line It falls within the convex hull region. The reactive power of the grid-connected line; the convex hull economic operating domain constraint is... ,in The coefficient matrix, For coefficient vectors; It is the transpose of a vector consisting entirely of 1s. The index is the number of iterations. This represents the start / stop status of the generator at the i-th node during the initial period.

[0066] As a further optimization scheme for the convex hull economic dispatch domain characterization method of the distribution network connection section described in this invention, step 4 includes: further simplifying the decision-dependent two-stage robust optimization dispatch model developed in step 3 to P1:

[0067] (30)

[0068] (31)

[0069] (32)

[0070] (33)

[0071] (34)

[0072] In equation (30), P1 is a robust model with decision dependencies, x is the set of generator start-stop state parameters, w is the set of uncertainty-related variables, and y is the set of decision variables. As dual variables, This represents the dual variable corresponding to the second-order cone constraint; , Let B be the set of nonnegative slack variables, and let B be the coefficient matrix of the slack variables. is a constant matrix vector; C, b, E, d, g, h are coefficient matrices, and Ξ, Ξ' are uncertain sets;

[0073] Constraints (31)-(34) are matrix expressions of equations (24)-(29); the set of uncertain variables w related to problem P1 is affected by x in equation (33), and the two-stage robust optimization model involves decision-dependent uncertainty; P1 is transformed into a two-stage robust optimization model using the standardization reconstruction technique; P1 is equivalently transformed into a two-stage robust optimization model P2 in the following form:

[0074] (35)

[0075] In equation (35), w is the set of variables related to uncertainty. Let be a constant matrix vector, Θ' be the set of uncertainties, Θ' is no longer affected by x, and w' represent decision-independent uncertainty variables.

[0076] As a further optimization of the convex hull economic dispatch domain characterization method for a distribution network connection section described in this invention, step 5 includes:

[0077] Step 501): Based on the column constraint generation algorithm, ... The problem is decomposed into a main problem (MP) and subproblems (SP) and solved iteratively. Subproblems (SP) are solved using the output of the main problem. Given quantities To find the optimal solution for MP, we solve for the optimal uncertainty scenario and slack variables, as shown in the following expression:

[0078] (36)

[0079] Step 502): The main problem MP is output as subproblems. To add a new vertex, update the convex hull region and optimize x. The optimal uncertainty of SP is given by the following expression:

[0080] (37)

[0081] in, For the number of iterations, For the objective function variable, The constraint matrix vector of the main problem; Let be the dual variable of the worst-case uncertainty scenario obtained from solving the subproblem in the l-th iteration. The worst-case uncertainty variable value obtained by solving the subproblem in the l-th iteration. These are the values ​​of the uncertain variables after normalization.

[0082] Step 503): Using Matlab, call the YALMIP toolbox and CPLEX solver to iteratively solve MP and SP until convergence. Output the convex hull economic scheduling domain of the grid-connected line interface.

[0083] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0084] (1) Distributed energy access enables the distribution network to have scheduling flexibility, and its coordinated operation with the main grid depends on the quantification of the scheduling capability of the grid-connected line interface. Existing research on distribution network scheduling areas mostly focuses on operational safety, and the constructed feasible domains contain a large number of extreme uneconomical schemes. They have problems such as strong conservatism, poor economic efficiency and weak engineering practicality. Moreover, when dealing with decision-making that depends on uncertainty, the algorithm is prone to non-convergence, making it difficult to meet the main grid's precise requirements for the economic scheduling boundary of the distribution network.

[0085] (2) This method proposes a two-stage robust optimization model to delineate the convex hull economic dispatch region of the grid-connected line interface. On the one hand, under the premise of satisfying safety constraints, it eliminates uneconomical dispatch schemes, avoids excessive conservatism in the feasible region, and clarifies the economic dispatch range of the distribution network to the main grid. On the other hand, it transforms decision-dependent uncertainty into decision-independent uncertainty through normalization reconstruction technology, solves the oscillation and non-convergence problems of traditional column constraint generation algorithms, and ensures solution efficiency. At the same time, this region can provide a clear basis for the automatic cruise dispatch of the main grid and the economic evaluation of distribution network operation, ensuring the economic operation of the power grid under strong uncertainty and improving the engineering practicality and economy of distribution network dispatch. Attached Figure Description

[0086] Figure 1 This is a flowchart of an embodiment of the present invention. Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0088] As shown in Figure 1, an embodiment of the method of the present invention includes the following steps:

[0089] A method for characterizing the convex hull economic dispatch domain of a distribution network section, characterized by comprising:

[0090] Step 1: Obtain uncertainty data on distribution network equipment, network parameters, and source loads; and construct a deterministic economic dispatch model based on the uncertainty data on distribution network equipment, network parameters, and source loads.

[0091] In step 1, the distribution network equipment and network parameters include the operating cost coefficient, power limit, efficiency parameters, and branch resistance, reactance, and power capacity of generators, energy storage, renewable energy units, and grid connection lines; the source-load uncertainty data includes the predicted nominal values ​​and deviation ranges of photovoltaic output and load power.

[0092] The objective function of the deterministic economic scheduling model is to minimize the total operating cost, as expressed below:

[0093] (1)

[0094] in, The objective function of the deterministic economic dispatch model for distribution networks is to minimize the total operating cost, where y is the set of decision variables. For generator power, These represent the energy storage charging and discharging power, respectively. These represent the power purchased and sold through the grid connection, respectively; t is the time period number, and i is the node number. This is the generator operating cost coefficient. This is the energy storage degradation cost coefficient. These refer to the grid-connected electricity purchase price and the electricity sales price; Let I be the total number of time periods in the scheduling cycle, and let I be the number of nodes in the distribution network. The duration of a single time period;

[0095] The constraints of the deterministic economic scheduling model include:

[0096] 1) Generator constraints:

[0097] (2)

[0098] (3)

[0099] (4)

[0100] Equation (2) represents the active power range of the generator, where Let be the minimum and maximum power coefficients of the generator at node i. Let represent the start / stop status of the generator at node i during time period t. Let be the active power output of the generator at node i during time period t; Equation (3) represents the reactive power output range of the generator, where Let be the maximum and minimum power factors of the generator at the i-th node. Let be the reactive power output of the generator at node i during time period t; Equation (4) represents the active power ramp-up rate range of the generator, where Let be the maximum landslide and ramp rates of the generator at the i-th node; Let be the initial power output of the generator at the i-th node, set to 0. Let be the active power generated by the generator at node i during time period t-1;

[0101] 2) Energy storage constraints:

[0102] (5)

[0103] (6)

[0104] (7)

[0105] (8)

[0106] Equation (5) represents the active power range of the energy storage unit, where Let be the charging active power and discharging active power of the energy storage unit at the i-th node during time period t; Let be the maximum charging active power and the maximum discharging active power of the energy storage unit at the i-th node; Equation (6) represents the reactive power range of the energy storage unit, where Let be the reactive power of the energy storage unit at the i-th node during time period t; Let be the minimum power factor of the energy storage unit at the i-th node; Equation (7) represents the state-of-charge expression of the energy storage unit, where Let represent the state of charge of the energy storage unit at node i during time period t. Let represent the state of charge of the energy storage unit at node i during time period t-1. Let be the charging efficiency of the energy storage unit at the i-th node. Let be the discharge efficiency of the energy storage unit at the i-th node; Equation (8) represents the range of the energy storage state of charge. Let be the minimum and maximum states of charge of the energy storage unit at the i-th node; For the energy storage unit at the i-th node at the end of the cycle The capacity and initial state of charge;

[0107] 3) Renewable energy and load constraints:

[0108] (9)

[0109] (10)

[0110] Equation (9) represents the reactive power range of renewable energy units, where Let be the active power of the renewable energy unit at node i during time period t. Let be the reactive power of the renewable energy unit at node i during time period t; Let be the minimum power factor of the renewable energy unit at the i-th node; Equation (10) is the expression for the reactive power of the load, where Let be the active power of the load at node i during time period t; Let be the reactive power of the load at node i during time period t; Let be the power factor of the load at the i-th node. Let be the power factor of the load at the i-th node;

[0111] 4) Grid connection constraints:

[0112] (11)

[0113] (12)

[0114] Equation (11) represents the active power range of the grid-connected line, where Let be the forward and reverse active power of the grid-connected line of the i-th node during time period t; Let be the upper limit of the forward active power and the upper limit of the reverse active power of the grid-connected line at the i-th node; Equation (12) represents the range of the apparent power of the grid-connected line. Let be the reactive power of the grid-connected line of the i-th node. Let be the apparent power limit of the grid-connected line of the i-th node;

[0115] 5) Distribution network line constraints:

[0116] (13)

[0117] (14)

[0118] (15)

[0119] (16)

[0120] (17)

[0121] Equation (13) represents the active power balance constraint of the distribution network lines, where Let be the active power of the renewable energy unit at node i during time period t; Let be the active power of the load at node i during time period t; These are the charging active power and discharging active power of the energy storage unit at the i-th node during time period t, respectively. Let be the active power of the generator at the i-th node during time period t; These are the forward and reverse active power of the grid-connected line of the i-th node during time period t; Let be the active power of the line from node i to node j during time period t; Let be the resistance of the line from node i to node j; Let be the current of the line from node i to node j during time period t; Equation (14) represents the reactive power balance constraint of the network line, where Let be the reactive power of the renewable energy unit at node i during time period t. Let be the reactive power of the load at node i during time period t; Let be the reactive power output of the energy storage unit at the i-th node during time period t. Let be the reactive power output of the generator at node i during time period t. Let be the reactive power of the grid-connected line of the i-th node during time period t. Let be the reactive power of the line from node i to node j during time period t; Equation (15) represents the voltage change at the node, where Let be the reactance of the line from node i to node j. Let be the square of the line voltage from node i to node j. Let be the imaginary part of the admittance of the line from node i to node j. Let be the current in the line from node i to node j during time period t. Let be the square of the minimum voltage and the square of the maximum voltage from node i to node j during time interval t. Let be the maximum current of the line from node i to node j; Equation (16) represents the constraint of the line apparent power; Equation (17) represents the boundary constraints of the line voltage and current. Let be the active power of the line from node s to node i during time period t. Let be the resistance of the line from the s-th node to the i-th node. Let be the current in the line from node s to node i during time period t. Let i be the set of all branches flowing into the i-th node. Let i be the set of all branches flowing out of the i-th node. Let be the reactive power of the line from node s to node i during time period t. Let be the reactance of the line from the s-th node to the i-th node. Let be the square of the voltage amplitude of the j-th node during time period t. Let be the square of the voltage amplitude of the i-th node during time period t. , These are the minimum and maximum values ​​of the square of the voltage amplitude at the i-th node.

[0122] Step 2: Using duality theory, the deterministic economic scheduling model from Step 1 is transformed into a deterministic economic scheduling model under a contractionary optimization form.

[0123] In step 2, the deterministic economic scheduling model from step 1 is transformed into a deterministic economic scheduling model M1 under a contractionary optimization form using duality theory.

[0124] (18)

[0125] (19)

[0126] (20)

[0127] In this context, the superscript T represents the transpose, and the objective function and constraints in M1 are expressed in matrix form. Equation (18) is the compressed matrix representation of Equation (1), where y is the set of decision variables and A is the coefficient vector. Equations (19)-(20) integrate formulas (2)-(17). In Equation (19), G, H, and J are coefficient matrices, where... , To represent the set of uncertain parameters, , This is the set of start-stop state parameters for the generator. Let f represent the start-up command, stop-up command, and start / stop status of the generator at node i during time period t, respectively, and f be a constraint constant vector. The dual vectors are: Equation (20) corresponds to the second-order cone constraints (12) and (16), where L, m, and n are coefficient matrices. As dual variables;

[0128] The derivation of the dual problem of M1 is as follows:

[0129] (twenty one)

[0130] In equation (21), Let be the dimension of equation (21). , , It is a coefficient matrix;

[0131] M1 is a second-order cone programming problem, a convex optimization problem that satisfies strong duality. The primal-dual optimality condition of M1 is expressed as:

[0132] (twenty two)

[0133] The optimality condition transforms the solution of the convex second-order cone programming M1 into the solution of equation (22). For a given u and x, the optimal solution of M1 can be obtained by using equation (22).

[0134] Step 3: Based on the deterministic economic dispatch model under the optimization form in Step 2, establish a decision-dependent two-stage robust optimization dispatch model. The decision-dependent two-stage robust optimization dispatch model includes the generator start-up and shutdown scheme in the first stage and the convex hull economic dispatch domain representing the grid-connected section power in the second stage; as detailed below:

[0135] The decision-dependent two-stage robust optimization scheduling model is as follows:

[0136] (twenty three)

[0137] Limited to:

[0138] (twenty four)

[0139] (25)

[0140] (26)

[0141] (27)

[0142] (28)

[0143] (29)

[0144] In equation (23), P represents a decision-dependent two-stage robust optimization scheduling model. , This is the set of generator start-stop constraints for the first stage, where Let represent the start-up command, stop-up command, and start / stop status of the generator at node i during time period t, respectively; Equation (24) represents the minimum start-up time constraint, where Let be the minimum start-up time of the generator at the i-th node; Equation (25) represents the minimum downtime constraint, where Let be the minimum downtime of the generator at the i-th node; Equation (26) represents the maximum uptime constraint, where Let be the maximum start-up time of the generator at the i-th node; Equation (27) represents The logical relationship between them, among which Let be the start-stop state of the generator at node i during time period t-1; Equation (28) represents the definition of the set of uncertainty parameters u, where This is a set of source-load uncertainties, including photovoltaic output limitations and load power limitations. Let be the active power of the renewable energy unit at node i during time period t. Let be the upper and lower limits of the active power of the renewable energy unit at the i-th node during time period t; Let be the active power demand of the i-th node during time period t. Let be the upper and lower limits of the active power demand of the i-th node during time period t; Equation (29) describes the column vector using half-space representation, where Let be the column vector of the optimal active power and reactive power of the grid-connected section during time period t. For non-slack variables, when Grid connection line It falls within the convex hull region. The reactive power of the grid-connected line; the convex hull economic operating domain constraint is... ,in The coefficient matrix, For coefficient vectors; It is the transpose of a vector consisting entirely of 1s. The index is the number of iterations. This represents the start / stop status of the generator at the i-th node during the initial period.

[0145] Step 4: Using normalization reconstruction technology, the decision-dependent two-stage robust optimization scheduling model in Step 3 is transformed into a decision-independent two-stage robust optimization scheduling model; specifically as follows:

[0146] The decision-dependent two-stage robust optimization scheduling model developed in step 3 is further simplified to P1:

[0147] (30)

[0148] (31)

[0149] (32)

[0150] (33)

[0151] (34)

[0152] In equation (30), P1 is a robust model with decision dependencies, x is the set of generator start-stop state parameters, w is the set of uncertainty-related variables, and y is the set of decision variables. As dual variables, This represents the dual variable corresponding to the second-order cone constraint; , Let B be the set of nonnegative slack variables, and let B be the coefficient matrix of the slack variables. is a constant matrix vector; C, b, E, d, g, h are coefficient matrices, and Ξ, Ξ' are uncertain sets;

[0153] Constraints (31)-(34) are matrix expressions of equations (24)-(29); the set of uncertain variables w related to problem P1 is affected by x in equation (33), and the two-stage robust optimization model involves decision-dependent uncertainty; P1 is transformed into a two-stage robust optimization model using the standardization reconstruction technique; P1 is equivalently transformed into a two-stage robust optimization model P2 in the following form:

[0154] (35)

[0155] In equation (35), w is the set of variables related to uncertainty. Let be a constant matrix vector, Θ' be the set of uncertainties, Θ' is no longer affected by x, and w' represent decision-independent uncertainty variables.

[0156] Step 5: Solve the decision-independent two-stage robust optimization scheduling model, transforming it into a standard model including the main problem and subproblems. Use a column constraint generation algorithm to iteratively solve the model to obtain the convex hull economic scheduling domain; details are as follows:

[0157] Step 501): Based on the column constraint generation algorithm, ... The problem is decomposed into a main problem (MP) and a subproblem (SP) that is solved iteratively. The subproblem (SP) is solved using the output of the main problem. Given quantities To find the optimal solution for MP, we solve for the optimal uncertainty scenario and slack variables, as shown in the following expression:

[0158] (36)

[0159] Step 502): The main problem MP is output as subproblems. To add a new vertex, update the convex hull region and optimize x. The optimal uncertainty of SP is given by the following expression:

[0160] (37)

[0161] In the formula, For the number of iterations, For the objective function variable, The constraint matrix vector of the main problem; Let be the dual variable of the worst-case uncertainty scenario obtained from solving the subproblem in the l-th iteration. The worst-case uncertainty variable value obtained by solving the subproblem in the l-th iteration. These are the values ​​of the uncertain variables after normalization.

[0162] Step 503): Using Matlab, call the YALMIP toolbox and CPLEX solver to iteratively solve MP and SP until convergence. Output the convex hull economic scheduling domain of the grid-connected line interface.

[0163] This invention proposes a two-stage robust optimization scheduling model for distribution networks, taking into account the uncertainties of distributed energy sources and loads. The model constructs an uncertainty set based on the prediction deviation intervals of distributed energy output and load. The first stage determines the start-up and shutdown schemes of conventional generators, and the second stage optimizes the operating power of each equipment unit and defines the optimal power convex hull of the grid connection. By utilizing normalized reconstruction technology to improve the column constraint generation algorithm for efficient solution, it is possible to obtain the economical scheduling area of ​​the distribution network convex hull and the available scheduling boundaries and ranges of the main grid under uncertain scenarios.

[0164] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the specific embodiments described above. The specific embodiments and descriptions in the specification are merely for further illustrating the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the claims and their equivalents.

[0165] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for characterizing the convex hull economic dispatch domain of a distribution network section, characterized in that, include: Step 1: Obtain uncertainty data on distribution network equipment, network parameters, and source loads; and construct a deterministic economic dispatch model based on the uncertainty data on distribution network equipment, network parameters, and source loads. Step 2: Using duality theory, the deterministic economic scheduling model from Step 1 is transformed into a deterministic economic scheduling model under a contractionary optimization form. Step 3: Based on the deterministic economic dispatch model under the optimization form in Step 2, establish a decision-dependent two-stage robust optimization dispatch model. The decision-dependent two-stage robust optimization dispatch model includes the generator start-up and shutdown scheme in the first stage and the convex hull economic dispatch domain representing the grid connection section power in the second stage. Step 4: Using normalization reconstruction technology, the decision-dependent two-stage robust optimization scheduling model in Step 3 is transformed into a decision-independent two-stage robust optimization scheduling model. Step 5: Solve the decision-independent two-stage robust optimization scheduling model, transforming it into a standard model that includes the main problem and sub-problems. Use the column constraint generation algorithm to solve it iteratively to obtain the convex hull economic scheduling domain.

2. The method for characterizing the convex hull economic dispatch domain of a distribution network section according to claim 1, characterized in that, In step 1, the distribution network equipment and network parameters include the operating cost coefficient, power limit, efficiency parameters, and branch resistance, reactance, and power capacity of generators, energy storage, renewable energy units, and grid-connected lines; the source-load uncertainty data includes the predicted nominal values ​​and deviation ranges of photovoltaic output and load power. The objective function of the deterministic economic scheduling model is to minimize the total operating cost, as expressed below: （1）； in, The objective function of the deterministic economic dispatch model for distribution networks is to minimize the total operating cost, where y is the set of decision variables. For generator power, These represent the energy storage charging and discharging power, respectively. These represent the power purchased and sold through the grid connection, respectively; t is the time period number, and i is the node number. This is the generator operating cost coefficient. This is the energy storage degradation cost coefficient. These refer to the grid-connected power purchase price and the power sales price; Let I be the total number of time periods in the scheduling cycle, and let I be the number of nodes in the distribution network. The duration of a single time period; The constraints of the deterministic economic scheduling model include: 1) Generator constraints: （2）； （3）； （4）； Equation (2) represents the active power range of the generator, where Let be the minimum and maximum power coefficients of the generator at node i. Let represent the start / stop status of the generator at node i during time period t. Let be the active power output of the generator at node i during time period t; Equation (3) represents the reactive power output range of the generator, where Let be the maximum and minimum power factors of the generator at the i-th node. Let be the reactive power output of the generator at node i during time period t; Equation (4) represents the active power ramp-up rate range of the generator, where Let be the maximum landslide and ramp rates of the generator at the i-th node; Let be the initial power output of the generator at the i-th node, set to 0. Let be the active power generated by the generator at node i during time period t-1; 2) Energy storage constraints: （5）； （6）； （7）； （8）； Equation (5) represents the active power range of the energy storage unit, where Let be the charging active power and discharging active power of the energy storage unit at the i-th node during time period t; Let be the maximum charging active power and the maximum discharging active power of the energy storage unit at the i-th node; Equation (6) represents the reactive power range of the energy storage unit, where Let be the reactive power of the energy storage unit at the i-th node during time period t; Let be the minimum power factor of the energy storage unit at the i-th node; Equation (7) represents the state-of-charge expression of the energy storage unit, where Let represent the state of charge of the energy storage unit at node i during time period t. Let represent the state of charge of the energy storage unit at node i during time period t-1. Let be the charging efficiency of the energy storage unit at the i-th node. Let be the discharge efficiency of the energy storage unit at the i-th node; Equation (8) represents the range of the energy storage state of charge. Let be the minimum and maximum states of charge of the energy storage unit at the i-th node; For the energy storage unit at the i-th node at the end of the cycle The capacity and initial state of charge; 3) Renewable energy and load constraints: （9）； （10）； Equation (9) represents the reactive power range of renewable energy units, where Let be the active power of the renewable energy unit at node i during time period t. Let be the reactive power of the renewable energy unit at node i during time period t; Let be the minimum power factor of the renewable energy unit at the i-th node; Equation (10) is the expression for the reactive power of the load, where Let be the active power of the load at node i during time period t; Let be the reactive power of the load at node i during time period t; Let be the power factor of the load at the i-th node. Let be the power factor of the load at the i-th node; 4) Grid connection constraints: （11）； （12）； Equation (11) represents the active power range of the grid-connected line, where Let be the positive and negative active power of the grid-connected line of the i-th node during time period t; Let be the upper limit of the forward active power and the upper limit of the reverse active power of the grid-connected line at the i-th node; Equation (12) represents the range of the apparent power of the grid-connected line. Let be the reactive power of the grid-connected line of the i-th node. Let be the apparent power limit of the grid-connected line of the i-th node; 5) Distribution network line constraints: （13）； （14）； （15）； （16）； （17）； Equation (13) represents the active power balance constraint of the distribution network lines, where Let be the active power of the renewable energy unit at node i during time period t; Let be the active power of the load at node i during time period t; These are the charging active power and discharging active power of the energy storage unit at the i-th node during time period t, respectively. Let be the active power of the generator at the i-th node during time period t; These are the forward and reverse active power of the grid-connected line of the i-th node during time period t; Let be the active power of the line from node i to node j during time period t; Let be the resistance of the line from node i to node j; Let be the current of the line from node i to node j during time period t; Equation (14) represents the reactive power balance constraint of the network line, where Let be the reactive power of the renewable energy unit at node i during time period t. Let be the reactive power of the load at node i during time period t; Let be the reactive power output of the energy storage unit at the i-th node during time period t. Let be the reactive power output of the generator at node i during time period t. Let be the reactive power of the grid-connected line of the i-th node during time period t. Let be the reactive power of the line from node i to node j during time period t; Equation (15) represents the voltage change at the node, where Let be the reactance of the line from node i to node j. Let be the square of the line voltage from node i to node j. Let be the imaginary part of the admittance of the line from node i to node j. Let be the current in the line from node i to node j during time period t. Let be the square of the minimum voltage and the square of the maximum voltage from node i to node j during time interval t. Let be the maximum current of the line from node i to node j; Equation (16) represents the constraint of the line apparent power; Equation (17) represents the boundary constraints of the line voltage and current. Let be the active power of the line from node s to node i during time period t. Let be the resistance of the line from the s-th node to the i-th node. Let be the current in the line from node s to node i during time period t. Let i be the set of all branches flowing into the i-th node. Let i be the set of all branches flowing out of the i-th node. Let be the reactive power of the line from node s to node i during time period t. Let be the reactance of the line from the s-th node to the i-th node. Let be the square of the voltage amplitude of the j-th node during time period t. Let be the square of the voltage amplitude of the i-th node during time period t. , These are the minimum and maximum values ​​of the square of the voltage amplitude at the i-th node.

3. The method for characterizing the convex hull economic dispatch domain of a distribution network section according to claim 1, characterized in that, Step 2: Using duality theory, the deterministic economic scheduling model from Step 1 is transformed into a deterministic economic scheduling model M1 under a contractionary optimization form. （18）； （19）； （20）； In this context, the superscript T represents the transpose, and the objective function and constraints in M1 are expressed in matrix form. Equation (18) is the compressed matrix representation of Equation (1), where y is the set of decision variables and A is the coefficient vector. Equations (19)-(20) integrate formulas (2)-(17). In Equation (19), G, H, and J are coefficient matrices, where... , To represent the set of uncertain parameters, , This is the set of start-stop state parameters for the generator. Let f represent the start-up command, stop-up command, and start / stop status of the generator at node i during time period t, respectively, and f be a constraint constant vector. The dual vectors are: Equation (20) corresponds to the second-order cone constraints (12) and (16), where L, m, and n are coefficient matrices. As dual variables; The derivation of the dual problem of M1 is as follows: （21）； In equation (21), Let be the dimension of equation (21). , , It is a coefficient matrix; M1 is a second-order cone programming problem, a convex optimization problem that satisfies strong duality. The primal-dual optimality condition of M1 is expressed as: （22）； The optimality condition transforms the solution of the convex second-order cone programming M1 into the solution of equation (22). For a given u and x, the optimal solution of M1 can be obtained by using equation (22).

4. The method for characterizing the convex hull economic dispatch domain of a distribution network section according to claim 1, characterized in that, Step 3 includes: The decision-dependent two-stage robust optimization scheduling model is as follows: （23）； Limited to: （24）； （25）； （26）； （27）； （28）； （29）； In equation (23), P represents a decision-dependent two-stage robust optimization scheduling model. , This is the set of generator start-stop constraints for the first stage, where Let represent the start-up command, stop-up command, and start / stop status of the generator at node i during time period t, respectively; Equation (24) represents the minimum start-up time constraint, where Let be the minimum start-up time of the generator at the i-th node; Equation (25) represents the minimum downtime constraint, where Let be the minimum downtime of the generator at the i-th node; Equation (26) represents the maximum uptime constraint, where Let be the maximum start-up time of the generator at the i-th node; Equation (27) represents The logical relationship between them, among which Let be the start-stop state of the generator at node i during time period t-1; Equation (28) represents the definition of the set of uncertainty parameters u, where This is a set of source-load uncertainties, including photovoltaic output limitations and load power limitations. Let be the active power of the renewable energy unit at node i during time period t. Let be the upper and lower limits of the active power of the renewable energy unit at the i-th node during time period t; Let be the active power demand of the i-th node during time period t. Let be the upper and lower limits of the active power demand of the i-th node during time period t; Equation (29) describes the column vector using half-space representation, where Let be the column vector of the optimal active power and reactive power of the grid-connected section during time period t. For non-slack variables, when Grid connection line It falls within the convex hull region. The reactive power of the grid-connected line; the convex hull economic operating domain constraint is... ,in The coefficient matrix, For coefficient vectors; It is the transpose of a vector consisting entirely of 1s. The index is the number of iterations. This represents the start / stop status of the generator at the i-th node during the initial period.

5. The method for characterizing the convex hull economic dispatch domain of a distribution network section according to claim 1, characterized in that, Step 4 includes: further simplifying the decision-dependent two-stage robust optimization scheduling model developed in Step 3 to P1: （30）； （31）； （32）； （33）； （34）； In equation (30), P1 is a robust model with decision dependencies, x is the set of generator start-stop state parameters, w is the set of uncertainty-related variables, and y is the set of decision variables. As dual variables, This represents the dual variable corresponding to the second-order cone constraint; , Let B be the set of nonnegative slack variables, and let B be the coefficient matrix of the slack variables. is a constant matrix vector; C, b, E, d, g, h are coefficient matrices, and Ξ, Ξ' are uncertain sets; Constraints (31)-(34) are matrix expressions of equations (24)-(29); the set of uncertain variables w related to problem P1 is affected by x in equation (33), and the two-stage robust optimization model involves decision-dependent uncertainty; P1 is transformed into a two-stage robust optimization model using the standardization reconstruction technique; P1 is equivalently transformed into a two-stage robust optimization model P2 in the following form: （35）； In equation (35), w is the set of variables related to uncertainty. Let be a constant matrix vector, Θ' be the set of uncertainties, Θ' is no longer affected by x, and w' represent decision-independent uncertainty variables.

6. The method for characterizing the convex hull economic dispatch domain of a distribution network section according to claim 1, characterized in that, Step 5 includes: Step 501): Based on the column constraint generation algorithm, ... The problem is decomposed into a main problem (MP) and subproblems (SP) and solved iteratively. Subproblems (SP) are solved using the output of the main problem. Given quantities To find the optimal solution for MP, we solve for the optimal uncertainty scenario and slack variables, as shown in the following expression: （36）； Step 502): The main problem MP is output as subproblems. To add a new vertex, update the convex hull region and optimize x. The optimal uncertainty of SP is given by the following expression: (37)； In the formula, For the number of iterations, For the objective function variable, The constraint matrix vector of the main problem; Let be the dual variable of the worst-case uncertainty scenario obtained from solving the subproblem in the l-th iteration. The worst-case uncertainty variable value obtained by solving the subproblem in the l-th iteration. These are the values ​​of the uncertain variables after normalization. Step 503): Using Matlab, call the YALMIP toolbox and CPLEX solver to iteratively solve MP and SP until convergence. Output the convex hull economic scheduling domain of the grid-connected line interface.

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