Fast solution method for unit commitment based on lagrangian relaxation and neural network

Abstract

The present application relates to the technical field of power system optimization scheduling, in particular to a unit commitment fast solution method based on Lagrange relaxation and neural network, comprising: establishing a security constrained unit commitment model, Lagrange relaxation of system level constraints, and decomposition into single unit sub-problems; according to the multipliers, constructing aggregated marginal cost, and establishing its mapping with start-up and shutdown sequence; based on minimum switch-on time, constructing state transition diagram, enumerating feasible paths and numbering; offline training of neural network; in online solution, calculating aggregated marginal cost to input network to obtain path number and map into start-up and shutdown sequence, solving out power and updating multipliers to convergence, and finally adjusting to obtain feasible solution; the present application significantly reduces online solution calculation time of security constrained unit commitment problem while maintaining solution quality.

Description

Technical Field

[0001] This invention relates to the field of power system optimization scheduling technology, and in particular to a method for fast solution of unit combination based on Lagrange relaxation and neural networks. Background Technology

[0002] Security-Constrained Unit Commitment (SCUC) is a fundamental problem in power system optimization scheduling. Its objective is to determine the start-up and shutdown status and output level of each unit across multiple time periods, minimizing system operating costs, while satisfying constraints such as load balance, transmission security, unit output limits, ramping constraints, and minimum start-up / shutdown times. This problem typically manifests as a large-scale mixed-integer optimization problem, and its difficulty increases significantly with larger system scales, more scheduling periods, or a greater number of network security constraints. Current engineering practices primarily rely on commercial solvers based on mixed-integer linear programming (such as Gurobi), which rely on enumeration search mechanisms like branch and bound. In the worst case, the computational complexity increases exponentially with the size of the integer variables, making it difficult to obtain a stable and satisfactory solution within a finite time. While Lagrange relaxation methods can reduce problem coupling through decomposition, traditional methods still require repeatedly solving numerous single-unit subproblems with integer variables in each iteration, resulting in a high online computational burden when the number of units is large and the scheduling periods are long. While machine learning-assisted methods introduced in recent years have shown some effectiveness, they typically rely on a large number of historical running cases for training, and the training results are strongly correlated with system topology, load level, network parameters, etc. When the system structure or scenario changes, retraining or correction is required, which limits their universality and transferability. Summary of the Invention

[0003] This invention provides a fast solution method for unit combination based on Lagrange relaxation and neural networks, which is used to solve the problems of high computational complexity, heavy iterative burden of traditional Lagrange relaxation, and poor transferability of machine learning methods that rely on historical data in existing safety constraint unit combination solution methods.

[0004] The objective of this invention can be achieved through the following technical solutions:

[0005] The first aspect of this invention is to provide a fast solution method for unit combination based on Lagrange relaxation and neural networks, comprising: The system acquires physical parameters, network topology, load forecast data, and operational economic indicators of the power system; it then constructs a safety-constrained unit combination model using the physical parameters, network topology, load forecast data, and operational economic indicators; the safety-constrained unit combination model includes: an objective function for the unit combination problem, system-level constraints, and individual unit constraints. Lagrange multipliers are introduced into the system-level constraints in the safety-constrained unit combination model to perform Lagrange relaxation, decomposing the original problem into multiple single-unit relaxation subproblems, and obtaining a single-unit relaxation subproblem model; The aggregate marginal cost is obtained based on the Lagrange multipliers and the network transmission correlation coefficients in the network topology. Based on the minimum start-up and shutdown time constraints of a single unit in the physical parameters, a state transition diagram is constructed, all feasible start-up and shutdown paths that satisfy the minimum start-up and shutdown time constraints are enumerated and numbered, and a one-to-one correspondence between path numbers and start-up and shutdown sequences is established. By solving the single-unit slack subproblem model, the optimal start-up and shutdown sequence and its corresponding path number under different combinations of aggregate marginal cost and initial state of the unit are obtained, forming a training sample set. A neural network model is trained for each unit to fit the mapping relationship from aggregate marginal cost and initial state to path number. During the online solution process, the start-stop sequence is predicted by the trained neural network model based on the current Lagrange multipliers, and then the output force variables are solved and the system-level constraint violation is calculated. The violation is used to determine whether convergence has occurred. If convergence has not occurred, the multipliers are updated and the iteration is repeated until the convergence condition is met, at which point the iteration stops and an approximate solution at convergence is determined. If the approximate solution still violates system-level constraints after the iteration stops, the start-stop sequence obtained by the iteration is adjusted based on the state transition diagram to construct a feasible solution of the unit combination model that satisfies the original safety constraints.

[0006] Furthermore, the specific process of determining the approximate solution at convergence includes: Step 1: During the online solution process, calculate the aggregate marginal cost corresponding to each unit based on the current Lagrange multipliers, input the corresponding neural network model to obtain the path number, and then use the path number to look up the state transition diagram to determine the start-up and shutdown sequence of a single unit. Step 2: Substitute the start-stop sequence determined in Step 1 into the single-unit slack subproblem model. At this point, the model degenerates into a linear programming problem, and the continuous output variables are obtained by solving it. Step 3: Substitute the output variables obtained in Step 2 back into the original equations or inequalities of the load balance constraints and transmission safety constraints in the safety constraint unit combination model, and calculate the violation of each constraint. Step 4: Determine whether the sum of the absolute values ​​of all violations is less than the preset convergence tolerance. If so, stop the iteration and output the current start / stop sequence and output sequence as an approximate solution. Otherwise, update the Lagrange multipliers using the subgradient method based on the violation quantities, and return the updated Lagrange multipliers to Step 1 for the next round of iteration.

[0007] Furthermore, training a neural network model for each unit separately includes: The aggregated marginal cost, initial start-up time, and initial power generation in the input neural network model are processed to obtain the processed aggregated marginal cost, initial start-up time, and initial power generation. Training samples are generated using the processed aggregated marginal cost, initial start-up time, initial power generation, and the corresponding optimal start-up / shutdown sequence and its corresponding path number. Neural network models are trained for each unit to obtain the trained neural network model for each unit. The optimal start-up and shutdown sequence is determined using a single-unit slack subproblem model.

[0008] Furthermore, the process for handling the aggregation marginal cost includes: The effective range of values ​​for aggregate marginal cost is determined, and aggregate marginal costs exceeding the effective range are truncated before normalization is performed; this is to avoid interference from extreme values ​​on neural network predictions. The effective range of values ​​for the aggregation marginal cost is as follows:

[0009] In the formula, This represents the aggregate marginal cost of unit i in time period t. This represents the coefficient of the first-order term in the fuel cost function of unit i. This represents the effective range expansion factor, which is a preset value. The normalization process is specifically expressed by the following formula:

[0010] In the formula, This represents the aggregated marginal cost of unit i after processing in time period t, which is the value input to the neural network.

[0011] Furthermore, the process for processing the initial power-on / off time includes: The effective range of initial power-on / off time is determined, and the initial power-on / off time exceeding the effective range is truncated. Then, it is converted into neural network input through mapping rules to avoid interference from extreme values ​​in the prediction. The valid range of initial power-on / off time values ​​is as follows:

[0012] In the formula, This indicates the initial start-up and shutdown time of unit i. Indicates the minimum shutdown time. Indicates the minimum boot time; The specific formula for the neural network input mapping rule based on the initial power-on / off time is as follows:

[0013] In the formula, This represents the initial on / off time of unit i after processing, i.e., the value input to the neural network.

[0014] Furthermore, the initial power generation process includes: The effective range of initial power generation is determined, and initial power generation exceeding the effective range is truncated before normalization is performed; this is to avoid interference from extreme values ​​on neural network prediction. The effective range of initial power generation is as follows:

[0015] In the formula, This represents the initial generating power of unit i. This represents the minimum output of unit i. This indicates the maximum output of unit i; The normalization process is specifically expressed by the following formula:

[0016] In the formula, This represents the initial power generation of unit i after processing, i.e., the value input to the neural network.

[0017] Furthermore, the feasibility adjustment of the iteratively obtained start-up and shutdown sequence based on the state transition diagram includes: locating the time period when system-level constraints are violated, selecting the units that need to be adjusted according to the level of fuel costs, adjusting the nodes along the decision path in the state transition diagram, while ensuring that the minimum start-up and shutdown time constraints are not violated.

[0018] Furthermore, the path numbers are enumerated using a depth-first search order, so that the start and stop sequences corresponding to two paths with adjacent numbers are most physically similar.

[0019] A second aspect of the present invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method for rapid solution of unit combination based on Lagrange relaxation and neural networks.

[0020] A third aspect of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for rapid solution of unit combination based on Lagrange relaxation and neural networks.

[0021] Compared with existing technologies, the beneficial effects of this invention are: acquiring the physical parameters, network topology, load forecasting data, and operational economic indicators of the power system; constructing a safety-constrained unit combination model using the physical parameters, network topology, load forecasting data, and operational economic indicators; the safety-constrained unit combination model includes: the objective function of the unit combination problem, system-level constraints, and single-unit constraints; clarifying the input parameters and mathematical form of the problem, providing a standardized basis for subsequent optimization; introducing Lagrange multipliers to perform Lagrange relaxation on the system-level constraints in the safety-constrained unit combination model, decomposing the original problem into multiple single-unit relaxation subproblems, obtaining a single-unit relaxation subproblem model; and reducing the complexity of the problem. System-level coupling decomposes complex problems into independently solvable sub-problems for individual units, reducing the difficulty of solving them. Aggregate marginal costs are obtained based on Lagrange multipliers and network transmission correlation coefficients in the network topology. The fusion of Lagrange multipliers and network parameters establishes an economic signal connecting system-level information and individual unit decisions. A state transition diagram is constructed based on the minimum start-up / shutdown time constraints for individual units in the physical parameters. All feasible start-up / shutdown paths satisfying the minimum start-up / shutdown time constraints are enumerated and numbered, establishing a one-to-one correspondence between path numbers and start-up / shutdown sequences. This ensures that all enumerated paths strictly satisfy the minimum start-up / shutdown time constraints, providing a discrete, feasible, and physically ordered output encoding space for the neural network. By solving the individual unit... A unit slack subproblem model is used to obtain the optimal start-stop sequence and its corresponding path number under different combinations of aggregate marginal cost and initial state of the unit, forming a training sample set. A neural network model is trained for each unit to fit the mapping relationship from aggregate marginal cost and initial state to path number. The subproblem solution is transformed into fast forward propagation, avoiding repeated solutions to mixed integer programming in online iteration. Furthermore, the training does not rely on historical system data, and the model can be reused across systems. During the online solution process, the start-stop sequence is predicted based on the current Lagrange multiplier using the trained neural network model, thereby solving for the output variable and calculating the system-level constraint violation. The violation amount is used to determine whether convergence has occurred; if convergence has not occurred, the multiplier is updated. The iteration is repeated until the convergence condition is met, at which point the iteration stops and an approximate solution at convergence is determined. This significantly reduces online computation time, achieves rapid convergence, and ensures solution quality through violation feedback. After iteration stops, if the approximate solution still violates system-level constraints, the start-stop sequence obtained from the iteration is adjusted based on the state transition diagram to construct a feasible solution for the unit combination model that satisfies the original safety constraints. While maintaining the constraints of individual units, system-level violations are corrected, and a globally feasible solution that satisfies all original constraints is finally obtained. This solves the problems of high computational complexity, heavy burden of traditional Lagrange relaxation iteration, and poor transferability of machine learning methods that rely on historical data in existing safety constraint unit combination solution methods. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart illustrating the steps of the method for rapid solution of unit combination based on Lagrange relaxation and neural network provided for this invention; Figure 2 A schematic diagram illustrating the mapping relationship between aggregated marginal cost and the start-up and shutdown solution of a single unit; Figure 3 This is a schematic diagram illustrating the iterative solution process for the slack subproblem of a single unit. Figure 4 A schematic diagram of a multilayer perceptron structure used to learn the mapping relationship between aggregated marginal cost and single unit start-stop operation; Figure 5 A state transition diagram for single-unit start-up and shutdown decisions constructed based on minimum start-up and shutdown time constraints; Figure 6 Schematic diagram of the process for determining the load balancing marginal units; Figure 7 This is a schematic diagram of single-unit start-up and shutdown path adjustment based on the state transition diagram; Figure 8 This is a flowchart illustrating the online solution process. Detailed Implementation

[0024] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0025] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0026] To address the problems existing in the background technology, a fast solution method for unit combination based on Lagrange relaxation and neural networks was designed, which has important practical significance.

[0027] like Figure 1 As shown, the first aspect of the present invention is to provide a fast solution method for unit combination based on Lagrange relaxation and neural networks, comprising the following steps: Step S1: Obtain the physical parameters, network topology, load forecast data, and operating economic indicators of the power system; construct a safety-constrained unit combination model using the physical parameters, network topology, load forecast data, and operating economic indicators; the safety-constrained unit combination model includes: the objective function of the unit combination problem, system-level constraints, and single-unit constraints.

[0028] It should be noted that because the safety-constrained unit combination problem includes unit start-up and shutdown states (0-1 integer variables) and power generation (continuous variables), and is subject to the coupled influence of multiple constraints such as load balance, transmission security, upper and lower limits of output, ramping, and minimum start-up and shutdown time, it is difficult to solve directly. Therefore, in order to transform the problem into a standardized mathematical form that can be used for subsequent Lagrange relaxation and neural network modeling, it is first necessary to establish a safety-constrained unit combination model that includes all decision variables, objective functions, and constraints.

[0029] Specifically, the model is constructed as follows: 1. Define the scheduling period: Determine the number T of discrete scheduling periods included in the scheduling period, and the system load demand for each period; 2. Define decision variables: Unit start-up / shutdown status variable, taking values ​​of 0 or 1, representing the start-up or shutdown status of unit i during time period t. Unit output variable. , is a continuous variable, representing the active power output of unit i in time period t; 3. Establish the objective function: Set the minimum total operating cost of all units within the scheduling cycle, including start-up and shutdown costs and fuel costs; 4. Add system-level constraints: System-level constraints include load balancing constraints and transmission security constraints; Load balancing constraint: The total power generation of the system in each time period is equal to the total load demand; Transmission security constraint: The power flow of each line or section does not exceed its thermal stability limit, calculated by the power transmission distribution factor. 5. Add single-unit operation constraints: Single-unit operation constraints include power generation capacity constraints, ramp-up constraints, and minimum start-up time constraints; Power generation capacity constraints: Output must be between the unit's minimum and maximum output; Ramp-up constraints: Output variation between adjacent time periods must not exceed the unit's ramp-up capacity; Minimum start-up time constraints: After the unit is started, it must remain in the started state for at least a certain number of time periods, and after it is shut down, it must remain in the shut-down state for at least a certain number of time periods. 6. Integration Model: Integrate the above objective function and all constraints into a complete mathematical model to provide standardized input for subsequent Lagrange relaxation.

[0030] Among them, a safety-constrained unit combination model is constructed based on the physical parameters of the power system (unit ramp rate, upper and lower limits of output, minimum start-up and shutdown time, etc.), network topology (transmission line parameters, power transmission distribution factor), load forecast data (system load demand in each time period), and operating economic indicators (unit start-up and shutdown costs, fuel cost function).

[0031] The objective function in the safety-constrained unit combination model is specifically expressed by the following formula:

[0032] In the formula, This represents the start-up and shutdown cost of generator set i during the scheduling period t. This represents the fuel cost of generator set i during the scheduling period t. This is a variable representing the start-up or shutdown status of generator unit i during the scheduling period t (1 for start-up, 0 for shutdown). is a continuous variable, representing the active power output of generator unit i during the scheduling period t; The total number of all generator sets. This represents the total number of time periods within the scheduling cycle. This represents a minimum-value function, which determines the optimal parameters when the value within the square brackets is minimized. and .

[0033] The constraints in the safety-constrained unit combination model include system-level constraints and individual unit operation constraints. System-level constraints include load balancing constraints and transmission security constraints, while individual unit operation constraints include unit power generation capacity constraints, unit ramp-up constraints, and minimum start-up and shutdown time constraints.

[0034] The load balancing constraint is specifically expressed by the following formula:

[0035] In the formula, This represents the active power load demand of load node m during scheduling period t. The total number of all load nodes; Here, T is the index of the scheduling period, and T is the total number of periods within the scheduling period. This represents the set of all scheduled time periods. Wherein, This indicates that the constraint condition holds true for every scheduling period t. Wherein, It is a universal quantifier, meaning "for each" or "any one"; It belongs to the symbol, indicating "is an element in...".

[0036] The transmission security constraints are specifically expressed by the following formula:

[0037]

[0038] In the formula, Indicates generator set i is paired with transmission line The positive power transmission distribution factor; This indicates that load node m is connected to the transmission line. The power distribution factor; Indicates power transmission line Thermal limit; This represents the total number of all transmission lines. This represents the set of all power transmission lines.

[0039] The power transmission distribution factor (PTDF) is calculated using the network topology parameters and line impedance parameters of the power system (these parameters are derived from official data provided by the power grid planning or operation departments). Both are typically calculated in advance using a DC power flow model based on the node admittance matrix and line reactance parameters, and are used as constant parameters in the optimization model. The thermal limit of the transmission line is derived from the line design parameters provided by the power grid planning or dispatching departments, representing the maximum allowable thermally stable transmission power of the line; it is also used as a constant in the optimization model.

[0040] The unit's power generation capacity constraint is specifically expressed by the following formula:

[0041] In the formula, This represents the minimum output of generator set i. This represents the maximum output of generator set i; This represents the set of all generator sets.

[0042] The unit's climb constraint is specifically expressed by the following formula:

[0043] In the formula, This represents the active power output of generator unit i during the dispatch period t-1; This indicates the start-up or shutdown status of generator set i during the scheduling period t-1; This represents the upper limit of the upward ramp rate of generator set i (the maximum output that can be increased per unit time period). This represents the upper limit of the downward ramp rate of generator set i (the maximum output that can be reduced per unit time period).

[0044] The minimum power-on / off time constraint is specifically expressed by the following formula:

[0045] In the formula, This indicates the unit's start-up or shutdown status during the corresponding scheduling period. This represents the set of the unit's on / off status across all scheduling periods. Indicates the sequence of start / stop states of the unit. Must belong to a set This refers to all feasible start-up and shutdown sequences that satisfy the conditions of minimum power-on time and minimum power-off time. (Set) The construction is based on the minimum start / stop time constraint of each unit, and is obtained by enumerating all feasible paths through the state transition diagram.

[0046] Step S2: Introduce Lagrange multipliers to perform Lagrange relaxation on the system-level constraints in the safety constraint unit combination model, decompose the original problem into multiple single-unit relaxation sub-problems, and obtain the single-unit relaxation sub-problem model.

[0047] It should be noted that because the system-level constraints (load balancing constraints and transmission security constraints) in the original safety-constrained unit combination model couple the decision variables of each unit together, making it difficult to solve the problem independently for each unit, in order to weaken or eliminate the coupling relationship between units, the original problem is decomposed into multiple independent solvable single-unit subproblems. Therefore, Lagrange multipliers are introduced into the system-level constraints and incorporated as penalty terms into the objective function, and Lagrange relaxation and problem decomposition operations are performed.

[0048] Specifically, the decomposition process is as follows: 1. Identify system-level constraints (also known as system-level coupling constraints): From the SCUC model established in the above steps, filter out the constraints that couple the units together, namely load balancing constraints and transmission security constraints; 2. Introduce Lagrange multipliers: Introduce Lagrange multipliers for the load balancing constraints of each scheduling period t. (Unrestricted real numbers); for each transmission line The transmission security constraints for each scheduling period t introduce non-negative Lagrange multipliers. and (These correspond to the upper and lower limits of the power flow constraints for the line, respectively). 3. Construct the Lagrange function: Multiply the system-level constraints by the corresponding Lagrange multipliers, remove them from the constraints, and add them to the objective function to form the Lagrange function; 4. Merging and rearranging multiplier terms: Merging the terms in the Lagrange function that are related to the decision variables; 5. Decomposition by unit: Since the single-unit operation constraints (generating capacity, ramp-up, minimum start-up time) only involve the single unit itself, and the Lagrange function can be decomposed into the sum of independent terms of each unit except for the constant term, the Lagrange function minimization problem is decomposed into multiple independent single-unit slack subproblems by unit. 6. Output the relaxation subproblem for a single unit: For each unit i, its subproblem takes the form: Objective function: Start-up and shutdown costs of the unit + fuel costs + multiplier-related terms; Constraints: upper and lower limits of the unit's output, ramp-up constraint, and minimum start-up / start-up time constraint; Decision variable: The start-up and shutdown status of the unit and contribution .

[0049] Lagrange relaxation is performed on the system-level constraints in the safety-constrained unit combination model to decompose the original problem (referring to the complete safety-constrained unit combination (SCUC) model established in step S1, i.e., the original optimization problem that includes all unit start-up and shutdown variables, output variables, objective functions, and all constraints (system-level constraints + single unit constraints)) into multiple single unit relaxation sub-problems.

[0050] Specifically, the system-level constraints in the safety-constrained unit combination model are subjected to Lagrange relaxation to obtain the relaxed Lagrange function; then the relaxed Lagrange function is decomposed by unit (that is, the original problem is decomposed into multiple single-unit relaxation sub-problems) to obtain multiple independent single-unit relaxation sub-problem models (each sub-problem contains only the decision variables and constraints of a single unit).

[0051] The specific process of performing Lagrange relaxation is as follows: Introducing Lagrange multipliers for the load balancing constraints of each scheduling period t (Unrestricted real numbers).

[0052] For each transmission line The transmission security constraints for each scheduling period t introduce non-negative Lagrange multipliers. and (These correspond to the upper and lower limits of the power flow constraints for the line, respectively); where, , and These multipliers originate from the principle of Lagrange relaxation—by adding system-level constraints as penalty terms to the objective function, the originally coupled constraints are relaxed, decomposing into individual machine subproblems. The load balancing constraint is an equality constraint. The is a real number; the power flow constraint is an inequality constraint. ≥0, ≥0. The multipliers are updated during the iteration process based on the constraint violation, in order to guide the optimization to converge to a feasible solution.

[0053] Constructing the Lagrange function: Multiply the system-level constraints by their corresponding Lagrange multipliers, remove them from the constraints, and add them to the objective function to form the Lagrange function; the Lagrange function is specifically expressed by the formula:

[0054]

[0055]

[0056]

[0057]

[0058] In the formula, This represents the Lagrange multiplier corresponding to the load balance constraint during time period t; Indicates the line The Lagrange multiplier (non-negative) corresponding to the upper limit constraint of the positive direction power flow in time period t; Indicates the line The Lagrange multiplier (non-negative) corresponding to the upper limit constraint of the reverse power flow in time period t; It is a Lagrange function.

[0059] in, The original objective function; This is a penalty term for load balancing constraints, which is incurred when the total power generation is not in balance with the load demand. This is a penalty for exceeding the limit in the positive direction of the line's power flow; a penalty is incurred when the power flow in the line exceeds the upper limit. This is a penalty for the reverse flow of power exceeding the limit. The penalty is incurred when the power flow of the line is below the lower limit (i.e., the reverse flow exceeds the limit).

[0060] By combining and rearranging the multipliers in the Lagrange function, we obtain an equivalent form of the Lagrange function; the specific formula for the equivalent form of the Lagrange function is as follows:

[0061] In the formula, This represents a constant term that is independent of the decision variable.

[0062] The constant term, which is independent of the decision variables, is specifically expressed by the following formula:

[0063] The relaxed Lagrange function is decomposed by unit, resulting in multiple independent unit-level relaxation subproblems. Since the unit-level operating constraints (generating capacity, ramp-up, minimum start-up time) only involve the unit itself, and the Lagrange function, except for the constant term, can be broken down into the sum of independent terms for each unit, the Lagrange function minimization problem is decomposed into multiple independent unit-level relaxation subproblems.

[0064] The mathematical expression for the Lagrange function minimization problem (a mathematical expression in the form of the summation of multiple independent single-unit slack subproblems) is as follows:

[0065] In the formula, Indicates taking The minimum corresponding and .

[0066] It should be noted that, through the Lagrange relaxation process described above, the system-level constraints in the original safety-constrained unit combination model are transformed into penalty terms in the objective function. This weakens the coupling relationships between units in the original problem, providing a foundation for subsequent decomposition by individual units. In the Lagrange relaxation, since the system-level constraints have been relaxed into the objective function, the remaining constraints that have not been relaxed are mainly related to the physical operating characteristics of individual units, including unit power generation capacity constraints, unit ramp-up constraints, and minimum start-up / shutdown time constraints. These constraints are only related to the start-up / shutdown state and power generation of the corresponding individual unit.

[0067] Therefore, given the Lagrange multipliers, the Lagrange function can be decomposed according to the unit, resulting in independent single-unit slack problems for each unit. The mathematical expression for the single-unit slack problem of any given unit is as follows:

[0068] It should be noted that the decision variables of the single-unit slack subproblem include the start-up and shutdown state variables and the power generation variables of the unit during the scheduling cycle; its objective function includes the start-up and shutdown cost of the unit itself, the fuel cost, and the multiplier terms introduced by the Lagrange multipliers; its constraints include the power generation capacity constraint, the ramp-up constraint, and the minimum start-up and shutdown time constraint of the unit.

[0069] Through the above decomposition, the original safety-constrained unit combination problem is transformed into multiple smaller-scale single-unit slack problems. Compared to the original problem, the number of constraints and decision variables in the single-unit slack problems is significantly reduced, which helps to reduce computational complexity.

[0070] However, the single-unit slack problem still contains integer variables representing start-up and shutdown states, especially the minimum start-up time constraint, which introduces integer logic coupling across time periods. Therefore, the single-unit slack problem is essentially still a mixed-integer linear programming problem. When there are many generator units, long scheduling periods, or a large number of Lagrange relaxation iterations, traditional Lagrange relaxation methods still need to repeatedly solve a large number of single-unit slack problems containing integer variables, resulting in a still high online computational burden.

[0071] Based on this problem, this invention further utilizes the characteristic that the constraint structure of the single-unit relaxation subproblem remains unchanged in different iterations and only the multipliers in the objective function change, to construct a mapping relationship from aggregated marginal cost to single-unit solution, and uses a neural network to learn this mapping relationship offline, so as to reduce the repeated calls to the mixed integer linear programming subproblem in the online solution stage.

[0072] Step S3: Obtain the aggregate marginal cost based on the Lagrange multipliers and the network transmission correlation coefficients in the network topology.

[0073] It should be noted that, given the Lagrange multipliers, the optimal start-stop sequence of the single-unit slack problem is determined solely by the aggregated marginal cost, and this mapping is system-independent (does not depend on historical data). Therefore, to avoid repeatedly solving the mixed-integer programming subproblem in each iteration, we construct a mapping relationship from the aggregated marginal cost to the single-unit start-stop sequence, laying the foundation for subsequent offline learning of this mapping using neural networks.

[0074] Specifically, the process of determining the mapping relationship is as follows.

[0075] 1. Define the expression for aggregated marginal cost: Construct the aggregated marginal cost based on the Lagrange multipliers and network transmission correlation coefficients; the aggregated marginal cost is specifically expressed as:

[0076] In the formula, This represents the aggregate marginal cost of generator set i during scheduling period t.

[0077] Given the unit's physical parameters, scheduling cycle, initial start-up and shutdown states, and initial output, the constraints of the single-unit slack subproblem remain unchanged, and its start-up and shutdown sequence is mainly determined by the aggregated marginal cost. This provides a theoretical basis for subsequent neural network learning of the single-unit start-up and shutdown sequence.

[0078] Based on the defined aggregate marginal cost, the solution process of the single-unit slack problem can be further expressed as an input-output mapping relationship (the mapping relationship between the input of the single-unit slack problem and the start-up and shutdown sequence of the single unit); this mapping relationship can be expressed by the following formula:

[0079]

[0080] In the formula, This indicates the initial start-up and shutdown time of generator set i. This represents the initial generating power of generator set i. This represents the objective function value of the subproblem. The sign function represents the value of the independent variable that minimizes the objective function; This represents the aggregate marginal cost of generator set i. Indicates the start / stop sequence. Represents the output sequence.

[0081] Among them, the start-stop sequence is a one-dimensional sequence consisting of the start-stop status (0 or 1) of the units in each scheduling period, with a length of T equal to the total number of scheduling periods, for example [1,1,0,0,1]; the output sequence is a one-dimensional sequence consisting of the active power output (continuous value) of the units in each scheduling period, with a length of T, for example [100,95.5,0,0,80.3] (unit: MW).

[0082] This mapping relationship has the following characteristics: 1) Uniqueness: Given the physical parameters, initial state and scheduling cycle of a single unit, each aggregated marginal cost corresponds to a unique feasible single unit solution; 2) System independence: This mapping only depends on the parameters of the individual unit and the aggregated marginal cost, and does not depend on the historical operating data of the system; 3) Online computability: By training a neural network, this mapping relationship can quickly predict the start-up and shutdown sequence of a single unit in the online stage, avoiding the need to repeatedly solve mixed integer linear programming subproblems with integer variables.

[0083] like Figure 2As shown in the diagram, the mapping relationship between aggregate marginal cost and single-unit solution is illustrated. The horizontal axis represents aggregate marginal cost, and the vertical axis represents the start-up and shutdown sequence of a single unit. Each curve corresponds to a single-unit subproblem under different initial states.

[0084] Define aggregate marginal cost (a linear combination of Lagrange multipliers and network transmission correlation coefficients), and prove that under the premise of fixed unit parameters, initial state, and scheduling cycle, the optimal start-up and shutdown sequence of a single unit subproblem is determined solely by aggregate marginal cost, thus establishing an "input → output" mapping relationship.

[0085] Step S4: Construct a state transition diagram based on the minimum start-up and shutdown time constraints of a single unit in the physical parameters, enumerate all feasible start-up and shutdown paths that satisfy the minimum start-up and shutdown time constraints and number them, and establish a one-to-one correspondence between path numbers and start-up and shutdown sequences; by solving the single unit slack subproblem model, obtain the optimal start-up and shutdown sequences and their corresponding path numbers under different combinations of aggregate marginal costs and initial state of the unit, form a training sample set, and train a neural network model for each unit to fit the mapping relationship from aggregate marginal costs and initial state to path numbers.

[0086] It should be noted that, because there is a complex and unexpressed nonlinear mapping relationship between the optimal start-stop sequence and the aggregate marginal cost in the single-unit slack subproblem, and this mapping relationship is system-independent and learnable, in order to avoid repeatedly solving the mixed integer programming subproblem and achieve fast prediction in the online solution stage, the neural network model is trained offline, allowing the network to learn the mapping from the aggregate marginal cost and the initial state to the optimal start-stop path number.

[0087] Specifically, the process of determining the dataset and training the model is as follows.

[0088] 1. Construct a neural network model; build a separate Multilayer Perceptron (MLP) for each unit; each MLP contains an input layer, at least one hidden layer, and an output layer; the input layer receives the aggregated marginal cost sequence and the unit's initial state encoding, the hidden layer extracts higher-order features through a non-linear activation function, and the output layer uses softmax normalization to output the probability distribution of each start-stop path number; the structure of the MLP is as follows. Figure 4 As shown. The training objective is to minimize the cross-entropy loss between the predicted path number and the actual path number obtained from the MLP solution; all unit models share the network structure but have independent parameters, ensuring a balance between generalization ability and unit specificity.

[0089] The input layer consists of T+2 neurons, each corresponding to a marginal cost of aggregation over T time periods. (t=1,2,...,T), initial power-on / off time Initial power generation A hidden layer contains R neurons; the output layer contains one neuron whose value f determines which group of solutions the classification result falls into for that input. .

[0090] 2. Establish start / stop decoding methods; It should be noted that, due to the constraint of minimum start-up and shutdown time, among all possible binary combinations of generator unit start-up / shutdown states in all time periods within the dispatch cycle, only a few unit combinations satisfy the minimum start-up and shutdown time constraint. It is feasible. And all feasible solutions are based on the mapping relationship. Since the input data is entirely contained within the feasible solution set that satisfies the minimum power-on / off time constraint, we consider having a neural network MLP build the input data. A feasible solution that satisfies the minimum power-on / off time constraint. The correspondence between them.

[0091] Specifically, a state transition diagram is constructed based on the minimum start-up time, minimum shutdown time, and total number of scheduling periods for each unit (one state transition diagram is constructed for each unit). Within the state transition diagram, a depth-first search (DFS) algorithm is used to enumerate all feasible start-up and shutdown paths that satisfy the minimum start-up time constraint. The depth-first search algorithm is a well-known technique and will not be elaborated upon here.

[0092] Number each path (0, 1, 2, ..., N) 1) Establish a one-to-one correspondence between path numbers and start / stop sequences; normalize the path numbers to the [0,1] interval and use them as the output labels of the neural network.

[0093] The implementation process of enumerating start / stop paths and codes is as follows: like Figure 5 As shown in the diagram, this state transition diagram typically contains multiple stages, with circles (black dots) representing different states within each stage. Each stage represents a generator unit performing a start-up / shutdown operation and remaining in the on / off state for a period of time until the next shutdown / start-up operation. Each circle represents the time period during which the start-up / shutdown operation occurred in the current stage. Specifically, for a state transition diagram with a total scheduling period of T, the circle labeled T+1 indicates that the unit will remain in that state until the end of the scheduling cycle after completing the start-up / shutdown operation of the previous stage. For example, Figure 5In the red path, the circle labeled 2 in the second stage indicates that the unit was started up during time period 2; the circle labeled T-1 in the third stage indicates that the unit remained in the started state until time period T-1 and will be shut down in the next time period; the circle labeled T+1 in the fourth stage indicates that the unit will remain in the shut-down state until the end of the scheduling cycle. Therefore, the entire red path represents one unit combination solution. The connections between different stages in this state transition diagram must satisfy the minimum power-on / off time constraint, i.e., for stages with a minimum power-on time... and minimum shutdown time For the generator unit, during the startup phase, the circle labeled 't' can only be connected to the next phase where the circle is labeled with a number greater than or equal to 't'. The circle and the T+1 circle, during the shutdown phase, the circle labeled 't' can only be connected to the circle labeled 't' or 't' in the next phase. The circles and T+1 circles. The state transition diagram established by this method satisfies the condition that any path corresponds to a feasible solution with minimum on / off time. And all solutions that satisfy the minimum power-on / off time constraint Each of these can correspond to a specific path in the diagram. Therefore... Figure 5 This fully represents the minimum power-on / off time based on a total scheduling period of T. and All feasible solutions under the unit Therefore, by searching all paths in the state transition graph, it is easy to find feasible solutions. The enumeration of .

[0094] After enumerating and numbering all paths in the state transition graph, feasible solutions can be identified. This is represented by a one-dimensional variable, corresponding to the output layer variable f of the MLP. During enumeration, this invention employs a depth-first search traversal order: first, it traverses the path at the bottom containing the state with the smallest label, records this path as 0, then backtracks to the previously reached state node, and then traverses the next branch, numbering them sequentially. If the unit contains N feasible solutions... Then we can get the number as The decision path. At the same time, this path numbering method can largely guarantee that two adjacent paths correspond to the two most similar sets of solutions. For example in Figure 5 In the case where the fourth stage is the final power-on operation, what are the solutions for the two paths numbered 0 and 1? The only difference is the time period during which the second power-on operation occurs. and time period The paths differ by only one time period, while all other power-on and power-off operations occur within the same time period. This property makes the order of path numbers, to some extent, consistent with actual physical properties, which helps reduce the learning curve for different feasible solutions by the neural network. The difficulty of classifying different input values ​​using this as a classification criterion. Furthermore, the path number is normalized to obtain a value range of... encoding This corresponds to the range of the activation function in the MLP. Therefore, what the neural network essentially needs to learn is the mapping relationship between aggregated marginal cost and initial state to path number, i.e., from the current single-unit subproblem... Corresponding to the optimal single-unit solution This further corresponds to the solution's number in the state transition diagram. Finally, it corresponds to the normalized code of the number. As the output of the neural network.

[0095] The normalization process for path numbers is specifically expressed by the following formula:

[0096] Specifically, the mapping relationship between aggregated marginal cost and initial state to path number is a normalized encoding of the aggregated marginal cost, initial start-up and shutdown time and initial power generation under the current single unit subproblem, which is mapped to the path number of the state transition diagram corresponding to the optimal single unit start-up and shutdown sequence. The mapping relationship between the aggregated marginal cost and the initial state to the path number is specifically expressed by the following formula:

[0097] 3. Generate training dataset offline; It should be noted that, for a known generator set, determining the solution to its individual unit subproblems requires... Three variables. Among them, the initial start-up and shutdown time of the unit. and the initial generating power of the unit These are all related only to the characteristics of the generating unit itself and are not affected by system-level variables such as load demand and power transmission distribution; while Although the above expression includes power transfer distribution This is a system-level variable, but after calculating the Lagrange multipliers... and A linear combination of After obtaining the actual value, the process of determining the single-unit solution based on the input-output mapping relationship is essentially based only on the single-unit sub-problem and is independent of the system. Therefore, the method of learning the mapping relationship between aggregated marginal cost and initial state to path number through neural network has the following characteristics: 1) It requires training a neural network separately for each generator set in the system, and the neural networks of different sets are independent of each other; 2) The single-unit solution provided by the neural network during training and use is not affected by system-level variables, such as changes in load demand, the introduction of new nodes in the power grid, transmission line breaks or short circuits caused by unexpected factors; 3) After the generator set trained with the neural network is migrated to other systems, the neural network can still be used. If a generator set is added or replaced in the system, it is only necessary to train the neural network separately for the new generator set. This achieves the system independence of the fast algorithm of this invention.

[0098] Specifically, the aggregated marginal cost in the input neural network model (t=1,2,...,T), initial power-on / off time Initial power generation The data is processed separately to obtain the aggregated marginal cost, initial start-up and shutdown time, and initial power generation. Training samples are generated using these data, along with the corresponding optimal start-up and shutdown sequences for each unit. A neural network model is then trained for each unit to obtain the trained neural network model for each unit.

[0099] The process of handling the initial power-on / off time includes: Consider a system with a known minimum power-on / off time. and The unit's initial start-up and shutdown time The following conditions must be met (i.e., the valid range of initial power-on / off time is):

[0100] In the formula, This indicates the initial start-up and shutdown time of unit i. Indicates the minimum shutdown time. This indicates the minimum boot time.

[0101] For initial power-on time greater than or equal to and the initial shutdown time is greater than or equal to In both scenarios, the power-on / off decision for time period 1 will not violate the minimum power-on / off time constraint under any circumstances; therefore, they are uniformly stipulated separately. and In order to be based on Construct the corresponding neural network input information, and define the neural network input mapping rules based on the initial power-on / off time for different... Determine the corresponding neural network input values A more specific and intuitive correspondence is shown in Table 1. Therefore, its value range is... .

[0102] The specific formula for the neural network input mapping rule based on the initial power-on / off time is as follows:

[0103] In the formula, This represents the initial power-on / off time after processing, i.e., the value input to the neural network.

[0104] Table 1. Relationship between initial power-on / off time and corresponding neural network input values

[0105] for Larger cases: When When the timing is positive, the unit has been initially powered on for a relatively long time, and only needs to remain powered on for a shorter period within the current scheduling cycle to meet the minimum start-up and shutdown time constraints. During time period 1, the unit can be started and stopped. Conversely, when... When the value is negative, the unit has been initially shut down for a longer period, and only needs to remain shut down for a shorter time within the current scheduling cycle. At that time, the unit can be started and stopped during time period 1. Therefore, for near or In both cases, the operating characteristics of the unit are very similar, and their corresponding It is designed to be the closest among the rules mentioned above.

[0106] for Smaller cases: When When the timing is positive, the initial start-up time of the unit is relatively short. The unit must maintain a longer start-up state before its first shutdown within the current scheduling cycle, thus leading to... It is fixed at 1 in the first few periods. Conversely, when When the value is negative, the initial shutdown time of the unit is short, and the unit must remain in a longer shutdown state before its first startup in the current scheduling cycle, thus leading to... The value is fixed at 0 for the first few periods. The difference in the unit's operating characteristics is greatest under these two conditions, therefore its corresponding... The neural network input mapping rules with initial power-on and power-off times are closest to 1 and 0 respectively to highlight this significant difference. Based on this, the neural network input mapping rules with initial power-on and power-off times make... To a certain extent with The monotonic variation is beneficial for neural networks to learn the initial on / off time characteristics of the unit.

[0107] The process of processing the initial power generation includes: Consider a generator with a known maximum power output. and minimum power generation The generating unit's power output in its start-up state meets the generating capacity constraint. Therefore, when the unit's initial state is start-up, its initial generating power output is... The following conditions must be met (i.e., the effective range of initial power generation):

[0108] In the formula, This represents the initial generating power of unit i. This represents the minimum output of unit i. This indicates the maximum output of unit i; The initial power generation was normalized using the maximum and minimum value normalization method. Processing is performed to determine the different initial power-on conditions. Corresponding neural network input values The maximum and minimum value normalization method is specifically expressed by the following formula:

[0109] In the formula, This represents the initial power generation of unit i after processing, i.e., the value input to the neural network.

[0110] If the unit's initial state is shutdown, then The rules of the maximum-minimum normalization method do not apply. And at this point, since there must be... Therefore, the information that the unit's initial state is shutdown is obtained only through input values. This allows for complete expression, enabling the training and use of the neural network. Therefore, when When, input value It does not take effect, and is fixed. .

[0111] The process of handling the marginal cost of aggregation includes: Since the feasible solutions to the single-machine subproblem can only be decision paths in the state transition diagram, there are only a finite number of such paths. Therefore, when other parameters in the subproblem are already determined, Decoding a single unit The impact will only occur within a certain range. Therefore There exists a finite effective range, namely Whether too large or too small, any value it takes will correspond to a certain extreme single-machine group solution. Essentially, This represents the aggregate marginal cost of the generator unit, which is related to the generator unit's fuel cost function. coefficient of the first term Closely related. This invention uses To define The effective range is as follows (i.e., the effective range of values ​​for the aggregate marginal cost):

[0112] In the formula, This represents the aggregate marginal cost of unit i in time period t. This represents the coefficient of the first-order term in the fuel cost function of unit i. This represents the effective range expansion factor, which is a preset value. In the formula, the parameter Decision made The size of the effective range of input data for a neural network should preferably be selected as a larger value to ensure... The entire effective range is covered. It should be noted that as long as... The effective range is fully covered, and no matter how large the range is, it will not affect the solution given by the neural network to the sub-problem of the single unit after the final training. The result will not affect the training speed of the neural network. This is because if If the value is too large, the training dataset will not cover the area covered by the dataset. The scope will also expand accordingly, requiring more training data and longer training time to ensure the neural network can learn fully. and the optimal solution The mapping relationship between them. This invention aims to... To improve training efficiency, a more compact value range was adopted, and preliminary experiments were conducted using numerical simulation methods. Specifically, the simulated cases were solved using the original Lagrange relaxation method, and all errors encountered during the solution process were recorded. Value. Based on simulation experiments, it is recommended to... Set to 20%. Because... The analysis of the values ​​is based on the coefficients. This is a characteristic of a single unit, not a characteristic of the entire system, therefore The determination of the effective range remains unaffected by system-level constraints, satisfying system independence.

[0113] Finally, the linear normalization method of aggregated marginal cost is used to... Normalization is performed to determine the corresponding neural network input values. The linear normalization method for aggregate marginal cost is specifically expressed by the following formula:

[0114] In the formula, The expansion coefficient represents the effective range; where, This represents the aggregated marginal cost of unit i after processing in time period t, which is the value input to the neural network.

[0115] Training samples are generated by processing the aggregated marginal cost, initial start-up and shutdown time, initial power generation, and corresponding optimal single-unit start-up and shutdown sequence. Neural network models are then trained for each unit to obtain the trained neural network model for each unit.

[0116] When creating a training dataset for a single unit, firstly, a set of values ​​is randomly generated within the above-mentioned valid range. Then, based on the above processing methods, the corresponding neural network input values ​​are determined. Since the optimal solution to the above single-machine subproblem is only determined by... It is determined that each set is generated. Each of these is equivalent to generating a subproblem. The corresponding solution is obtained by solving the subproblem using mixed-integer linear programming. Furthermore, the corresponding neural network output value f is obtained based on the aggregation marginal cost and the mapping relationship between the initial state and the path number.

[0117] For scheduling periods containing The unit combination problem for each time period, the input layer of MLP includes The hidden layer contains one variable, while the output layer contains one variable. Therefore, the hidden layer in the MLP used in this invention contains... The number of neurons in the hidden layer is approximately equal to the average number of neurons in the input and output layers, adhering to the empirical formula of the trade-off rule for single-hidden-layer MLPs. This structure ensures that the MLP has the ability to learn the mapping relationship between aggregated marginal costs and initial states to path numbers, while maintaining moderate complexity, ensuring a certain level of training efficiency while avoiding underfitting and overfitting. The Sigmoid function is used as the activation function for the MLP.

[0118] The Xavier initialization method was used for initializing the weight and bias matrices to ensure compatibility with the Sigmoid activation function. During training, for each training round, a set of input values ​​was first... The MLP is input and propagated forward to obtain the predicted values ​​of the output layer. The loss value is calculated using the mean squared error loss function.

[0119] It can be observed that the entire dataset generation process only utilizes parameters relevant to a single unit, without relying on any historical case data, and neural network training can be performed once a complete dataset is available. Therefore, the entire process of dataset creation and neural network training can be carried out completely offline.

[0120] A state transition graph is constructed based on the minimum start-up and shutdown time constraint, and all feasible start-up and shutdown paths are enumerated and numbered. Input variables such as aggregated marginal cost are randomly generated, and the optimal path number is obtained as a label by solving subproblems using mixed-integer programming. A multilayer perceptron (MLP) is trained separately for each unit to fit a nonlinear mapping of "aggregated marginal cost + initial state → path number". The training data depends only on the parameters of a single unit and does not require historical system operation data.

[0121] Step S5: During the online solution process, the start-stop sequence is predicted by the trained neural network model based on the current Lagrange multipliers, and then the output force variables are solved and the system-level constraint violation is calculated; the violation is used to determine whether convergence has occurred; if convergence has not occurred, the multipliers are updated and the iteration is repeated until the convergence condition is met, at which point the iteration stops and an approximate solution at convergence is determined.

[0122] It should be noted that since the neural network model has been built through offline training, and this model can quickly output the optimal start-stop sequence for a single unit based on the current Lagrange multipliers, in order to avoid repeatedly calling the mixed integer programming solver and significantly reducing the computation time during the online solution process, the trained neural network is directly used to predict the start-stop sequence in each iteration, then the continuous output variables are solved and the system-level constraint violation is calculated, and then the Lagrange multipliers are updated based on the violation until the convergence criteria are met.

[0123] Specifically, firstly, redundant transmission security constraints are eliminated to obtain a reduced constraint set. Then, based on the marginal unit fuel cost and KKT conditions, the Lagrange multipliers are initialized through marginal unit determination and zeroing operations. Next, based on the initialized Lagrange multipliers and the initial state of a single unit, the start-stop sequence and output sequence of each unit are obtained by calculating the aggregated marginal cost, inputting it into the neural network for forward propagation, back-mapping the path number, looking up the state transition diagram to obtain the start-stop sequence, and solving the linear programming problem to obtain the output. Then, based on the unit output results, the deviation is calculated by substituting it into the constraint formula to obtain the system-level constraint violation amount. Based on the comparison between the violation amount and the convergence tolerance, the result of convergence is obtained by judging whether the convergence is successful through a threshold. If convergence is not achieved, the step size is calculated and the Lagrange multipliers are updated using the subgradient method based on the violation amount and the iteration round, and the updated multipliers are obtained and the solution is returned to be solved again. If convergence is achieved, the current start-stop sequence and output sequence are output as an approximate solution.

[0124] The specific process of determining the approximate solution at convergence includes: Step 1: During the online solution process, calculate the aggregate marginal cost corresponding to each unit based on the current Lagrange multipliers, input the corresponding neural network model to obtain the path number, and then use the path number to look up the state transition diagram to determine the start-up and shutdown sequence of a single unit. Step 2: Substitute the start-stop sequence determined in Step 1 into the single-unit slack subproblem model. At this point, the model degenerates into a linear programming problem, and the continuous output variables are obtained by solving it. Step 3: Substitute the output variables obtained in Step 2 back into the original equations or inequalities of the load balance constraints and transmission safety constraints in the safety constraint unit combination model, and calculate the violation of each constraint. Step 4: Determine whether the sum of the absolute values ​​of all violations is less than the preset convergence tolerance. If so, stop the iteration and output the current start / stop sequence and output sequence as an approximate solution. Otherwise, update the Lagrange multipliers using the subgradient method based on the violation quantities, and return the updated Lagrange multipliers to Step 1 for the next round of iteration.

[0125] The specific operation process of step S5 is as follows: S501, remove redundant transmission security constraints; First, redundant constraint identification methods are used to eliminate ineffective transmission security constraints, resulting in a reduced set of constraints (reducing the problem size).

[0126] S502, initialize the Lagrange multipliers; Based on the marginal unit fuel cost and the Karush-Kuhn-Tucker conditions, the Lagrange multipliers are initialized through marginal unit determination and zeroing operations; the process of initializing the Lagrange multipliers is as follows: Record the iteration rounds Before the first iteration, the Lagrange multipliers are... Initialize to the marginal unit cost. Specifically, to minimize fuel costs in the objective function, the system will prioritize selecting the coefficients of the linear term in the fuel cost function. Smaller units will provide the power. Therefore, all units will be arranged in order. The marginal units are sorted from smallest to largest, and the selection of marginal units is determined by the constraints imposed on them. Specifically, the constraints for selecting marginal units are as follows:

[0127] In the formula, This represents the j-th unit in this sequence, i.e. Let j be the smallest generating unit. For time period t, if the load balance constraint can be satisfied, then the total load must not exceed the sum of the maximum generating power of all generating units; therefore, there must exist an integer... The constraints for selecting marginal units are satisfied. Then the units... This refers to marginal units, and the process for determining their status can be carried out by... Figure 6 Intuitive display, The initial value is set to the coefficient of the first term of its fuel cost function. .

[0128] Furthermore, according to the KKT conditions (Karush-Kuhn-Tucker conditions), the multipliers corresponding to the transport security constraints... It is non-negative, and its value of 0 indicates that the constraint has no effect. This invention sets... and The initial value of is 0, so that the transmission security constraint does not produce a penalty term in the initial state. The relaxation subproblem is closest to the original problem structure, which is beneficial to the simplicity of solution and the stability of iteration.

[0129] S503, Solve the single-unit slack subproblem; In the original Lagrange relaxation method, the single-unit relaxation subproblem needs to be solved using a mixed-integer linear programming method. However, the method of this invention directly provides integer solutions to the subproblem using a neural network. This transforms the subproblem into a pure linear programming problem that only requires solving p, significantly reducing computational complexity.

[0130] For each unit, the current multiplier and Calculated and will The input values ​​of the neural network are obtained by normalizing the values ​​using the method described in S2. The neural network will output its corresponding value f. Then, according to the inverse mapping formula from the neural network output value to the path number, the corresponding single-unit solution number n is obtained. The decision path corresponding to number n in the state transition diagram is the solved single-unit solution. (Based on the initial Lagrange multipliers and the initial state of a single unit after initialization, the start-up and shutdown sequences and output sequences of each unit are obtained by calculating the aggregated marginal cost, inputting the neural network forward propagation, back mapping the path number, looking up the state transition diagram to obtain the start-up and shutdown sequence, and solving the linear programming problem to obtain the power output.)

[0131] The inverse mapping formula from the neural network output value to the path number is specifically expressed as follows:

[0132] In the formula, It is the result of reverse derivation of the path number. This represents the rounding symbol. Since the decision path number n is a discrete quantity, its corresponding normalized mapping f is also a discrete quantity. Therefore, the method of this invention selects the single-unit solution that best matches the neural network output value f. As a result of the sub-problem decision.

[0133] S504, calculate the violation amount; Then, based on the unit output results, the deviation is calculated by substituting into the constraint formula (load balance constraint and transmission safety constraint) to obtain the system-level constraint violation amount; based on the comparison between the violation amount and the convergence tolerance, the result of convergence is obtained by judging the threshold.

[0134] The specific formula for system-level constraint violation is as follows:

[0135]

[0136]

[0137] In the formula, This represents the load balance violation during time period t, indicating the deviation between the system's total power generation and total load demand. This represents the amount of positive power flow violation on line l during time period t, indicating the degree to which the positive power flow on the line exceeds its upper limit. It represents the amount of reverse power flow violation of line l during time period t, and indicates the degree to which the reverse power flow (i.e., the absolute value of the negative direction power flow) exceeds its upper limit.

[0138] The convergence is determined by comparing the violation amount with the convergence tolerance and using a threshold to determine whether convergence has occurred. The convergence formula is specifically expressed as follows:

[0139] In the formula, This indicates the convergence tolerance (empirical preset value). It is the absolute value symbol.

[0140] S505, update the multipliers; Determined based on the amount of violation of system-level constraints This serves as the subgradient direction for multiplier updates. For each update step, the sum of the objective functions of the subproblems under the current multiplier is calculated; specifically, the sum of the objective functions is expressed by the formula:

[0141] The process of determining the subgradient and step size can be expressed by the following formula:

[0142]

[0143]

[0144] In the formula, This refers to the current iteration round; This represents the theoretically optimal objective function value for the subproblem. Step size; This is the step size decay coefficient, ensuring that the iteration step size gradually decreases with each round; For the current iteration The constraint violation amount (subgradient); The Euclidean norm is used to constrain the violation quantity and normalize the step size, making the step size reasonable and unaffected by the magnitude of the absolute value of the violation quantity. This is an empirical coefficient used to control the step size decay rate. Its value is determined based on algorithm experience and is generally set through simulation or prior testing. The decay exponent controls the rate at which the step size decays; It is the decay exponent, used to control the step size decay with each iteration. The specific values ​​of the curve are determined through simulation experience. The initial step size, The initial marginal cost of aggregation, The initial aggregation marginal cost corresponds to the theoretically optimal objective function value of the subproblem.

[0145] Multiplier update is performed by determining the subgradient and step size, where the update process is specifically expressed by the following formula:

[0146]

[0147]

[0148] In the formula: and They must be non-negative values ​​because they correspond to inequality constraints. If or If a negative value appears after the update, it needs to be corrected to 0. Update the multiplier and record the iteration rounds. Proceed to step S503.

[0149] In the online solution process, the aggregated marginal cost of each unit is calculated based on the current Lagrange multipliers, input into the corresponding neural network model, and the path number is directly output and mapped to a start-stop sequence that satisfies the constraints. Subsequently, the continuous output variables (pure linear programming) are solved, and the system-level constraint violations are calculated. If the violation exceeds the tolerance, the Lagrange multipliers are updated using the subgradient method, and this step is repeated until convergence.

[0150] Step S6: After the iteration stops, if the approximate solution still violates the system-level constraints, the start-stop sequence obtained by the iteration is adjusted based on the state transition diagram to construct a feasible solution of the unit combination model that satisfies the original safety constraints.

[0151] It should be noted that, although the approximate solution obtained by neural network prediction and Lagrange iteration in step S5 satisfies the constraints of the single unit itself, it may not satisfy the system-level constraints (such as load balancing or transmission security). Therefore, in order to ensure that the final solution can satisfy all the constraints in the original security constraint unit combination model, it is necessary to make feasibility adjustments to the start-up and shutdown sequence obtained by the iteration based on the state transition diagram in order to construct a globally feasible solution that satisfies all the original constraints.

[0152] The feasibility adjustment of the iteratively obtained start-up and shutdown sequence based on the state transition diagram includes: locating the time period when system-level constraints are violated, selecting the units that need to be adjusted according to the level of fuel costs, adjusting the nodes along the decision path in the state transition diagram, while ensuring that the minimum start-up and shutdown time constraints are not violated.

[0153] Due to approximate solution The solution is obtained by solving individual subproblems of each unit. Therefore, this solution may not be feasible for the entire system, so it needs to be adjusted to obtain a globally feasible solution. Since each path in the state transition diagram corresponds to a feasible unit solution that satisfies the minimum on / off time constraint, this invention proposes a heuristic strategy based on the state transition diagram to ensure that unit constraints are not violated when constructing a globally feasible solution.

[0154] 1) Identify the individual units requiring adjustment: First, locate the time period in which the system-level constraints are violated, and then observe the on / off status of each individual unit during that period. For the second equation in the formula for the system-level constraint violation, if there is a positive violation, it indicates that the unit's power generation is too high. In this case, several units that are currently running should be shut down. Since the objective function requires the power generation cost to be minimized, the units with the highest fuel costs during that period should be shut down first, until the violation amount drops to 0. Similarly, for the third equation in the formula for the system-level constraint violation, if there is a positive violation, it indicates that the unit's power generation is too low. The coefficient of the first-order term of the fuel cost function should be activated first. The smallest unit. Furthermore, since a good approximate solution has already been obtained... Furthermore, load balancing constraints are easier to satisfy than transmission security constraints, so there is usually no need to adjust for load balancing violations in time period t.

[0155] 2) Determine the single-unit decision paths requiring adjustment based on the state transition diagram: The state transition diagram describes all decision paths that satisfy the minimum start-up / start-up time constraint. Therefore, in this adjustment strategy, the object being adjusted is not the start-up / start-up state within a certain time period, but rather the nodes traversed by the decision path. The adjustment strategy is as follows: Figure 3-7 As shown: the red dashed line represents the approximate solution for a certain unit. The corresponding decision path indicates that the unit is initially shut down, turns on during time period 2, and shuts down at the end of time period T. If, according to 1), the decision is made to shut down the unit during time period 2 while keeping its state unchanged during other time periods, then the connection point of the decision path in the second stage will be adjusted to node 3, and other stages only need to ensure that the minimum start-up / shutdown time constraint is satisfied. At this point, a new decision path is obtained, as follows: Figure 7 The red solid line indicates this. The overall flowchart of this solution is shown below. Figure 8 As shown.

[0156] An embodiment of the present invention is provided below. The present invention was tested on an IEEE 24-node system, an IEEE 118-node system, and a Polish 2383-node system. Basic information about these case systems is shown in Table 2, with the number of scheduling periods being [missing information]. .

[0157] Table 2 Basic Information of the Case System

[0158] This method was used to solve various test systems, and comparisons were made with the traditional Lagrange relaxation method (LR), the improved method based on neural network assistance (SLR+ML), and the commercial solver (Gurobi). In the tests, the Lagrange relaxation framework used by the LR method, SLR+ML method, and the fast algorithm of this invention was completely consistent, and all performed the same preprocessing to remove redundant transmission security constraints before solving. The only difference between the methods lies in the steps for solving the single-machine subproblem: the LR method uses the Gurobi solver, the SLR+ML method uses a deep neural network (DNN), and the fast algorithm of this invention uses an MLP. The identical solution framework ensures that the performance difference between the different methods depends entirely on the solution strategy of the subproblem, rather than the difference in the Lagrange relaxation method. The solution time for each case is shown in Table 3, and the number of iterations is shown in Table 4. Table 3 Solution time for each case using different methods

[0159] Table 4. Number of iterations for each case using different methods

[0160] As can be seen from Tables 3 and 4: 1) The number of iterations in this invention is almost the same as the original LR method. However, the solution time of the fast algorithm in the IEEE 24-node, IEEE 118-node, and Polish 2383-node systems is reduced by 43.7%, 35.6%, and 20.8% respectively compared to LR. Since the solution process of the combined solutions in all single-unit subproblems is directly completed by the neural network in each iteration, the original mixed-integer linear programming problem is transformed into a pure linear programming problem, thus the fast algorithm significantly reduces the solution time. At the same time, in the three cases, the solution time performance of the fast algorithm is similar to that of SLR+ML, showing a good acceleration effect. 2) Compared with Gurobi, the fast algorithm only performs better in solution time in large-scale problems with 2383 nodes. Since there are relatively few single-unit subproblems for small systems and they are easier to solve in the iteration process, a large proportion of the time in the fast algorithm is used to construct feasible solutions to the original problem, and the effect of iteration acceleration is not obvious. However, due to the small system scale, the solution time of the fast algorithm is still acceptable.

[0161] The target costs obtained by different methods for each case are shown in Table 5.

[0162] Table 5. Target cost of different methods for each case

[0163] Table 5 shows that: 1) Compared with Gurobi, the relative difference in target cost obtained by the present invention in the three case systems is within the range of 0.3%-1.0%. This indicates that the fast algorithm can provide high-quality solutions for large-scale unit combinatorial problems. 2) Compared with the LR method, the relative differences in target cost between the fast algorithm and Gurobi in the IEEE 24-node, IEEE 118-node, and Polish 2383-node systems are 0.07% higher, 0.19% lower, and 0.19% higher, respectively. Compared with SLR+ML, the relative differences are 0.09% higher, 0.06% lower, and 0.35% higher, respectively. The fast algorithm can improve computational efficiency while ensuring solution quality, with accuracy loss remaining within a very small range.

[0164] A second aspect of the present invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a method for rapid solution of unit combination based on Lagrange relaxation and neural networks.

[0165] A third aspect of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements a method for rapidly solving unit combination based on Lagrange relaxation and neural networks.

[0166] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.

[0167] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0168] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0169] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0170] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention.

Claims

1. A fast solution method for unit combination based on Lagrange relaxation and neural networks, characterized in that, include: The system acquires physical parameters, network topology, load forecast data, and operational economic indicators of the power system. The operational economic indicators consist of a function of unit start-up and shutdown costs and fuel costs. Using the physical parameters, network topology, load forecast data, and operational economic indicators, a safety-constrained unit combination model is constructed. The safety-constrained unit combination model includes: an objective function for the unit combination problem, system-level constraints, and individual unit constraints. Lagrange multipliers are introduced into the system-level constraints in the safety-constrained unit combination model to perform Lagrange relaxation, decomposing the original problem into multiple single-unit relaxation subproblems, and obtaining a single-unit relaxation subproblem model; The aggregated marginal cost is obtained based on the Lagrange multipliers and the network transmission correlation coefficients in the network topology; the network transmission correlation coefficients are power transmission distribution factors, which are calculated using the network topology parameters and line impedance parameters of the power system. Based on the minimum start-up and shutdown time constraints of a single unit in the physical parameters, a state transition diagram is constructed, all feasible start-up and shutdown paths that satisfy the minimum start-up and shutdown time constraints are enumerated and numbered, and a one-to-one correspondence between path numbers and start-up and shutdown sequences is established. By solving the single-unit slack subproblem model, the optimal start-up and shutdown sequences and their corresponding path numbers under different combinations of aggregate marginal costs and initial unit states are obtained, forming a training sample set. A neural network model is then trained for each unit to fit the mapping relationship from aggregate marginal costs and initial states to path numbers. The training of the neural network model for each unit includes: The aggregated marginal cost, initial start-up time, and initial power generation in the input neural network model are processed to obtain the processed aggregated marginal cost, initial start-up time, and initial power generation. Training samples are generated using the processed aggregated marginal cost, initial start-up time, initial power generation, and the corresponding optimal start-up / shutdown sequence and its corresponding path number. Neural network models are trained for each unit to obtain the trained neural network model for each unit. The optimal start-up and shutdown sequence is determined using a single-unit slack subproblem model. The process of handling the aggregation marginal cost includes: The effective range of values ​​for aggregate marginal cost is determined, and aggregate marginal costs exceeding the effective range are truncated before normalization is performed; this is to avoid interference from extreme values ​​on neural network predictions. The effective range of values ​​for the aggregation marginal cost is as follows: In the formula, This represents the aggregate marginal cost of unit i in time period t. This represents the coefficient of the first-order term in the fuel cost function of unit i. This represents the effective range expansion factor, which is a preset value. The normalization process is specifically expressed by the following formula: In the formula, This represents the aggregated marginal cost of unit i after processing in time period t, i.e., the value input to the neural network; During the online solution process, the start-stop sequence is predicted by the trained neural network model based on the current Lagrange multipliers, and then the output force variables are solved and the system-level constraint violation is calculated. The violation is used to determine whether convergence has occurred. If convergence has not occurred, the multipliers are updated and the iteration is repeated until the convergence condition is met, at which point the iteration stops and an approximate solution at convergence is determined. If the approximate solution still violates system-level constraints after the iteration stops, the start-stop sequence obtained by the iteration is adjusted based on the state transition diagram to construct a feasible solution of the unit combination model that satisfies the original safety constraints.

2. The method for rapid solution of unit combination based on Lagrange relaxation and neural network according to claim 1, characterized in that, The specific process for determining the approximate solution at convergence includes: Step 1: During the online solution process, calculate the aggregate marginal cost corresponding to each unit based on the current Lagrange multipliers, input the corresponding neural network model to obtain the path number, and then use the path number to look up the state transition diagram to determine the start-up and shutdown sequence of a single unit. Step 2: Substitute the start-stop sequence determined in Step 1 into the single-unit slack subproblem model. At this point, the model degenerates into a linear programming problem, and the continuous output variables are obtained by solving it. Step 3: Substitute the output variables obtained in Step 2 back into the original equations or inequalities of the load balance constraints and transmission safety constraints in the safety constraint unit combination model, and calculate the violation of each constraint. Step 4: Determine whether the sum of the absolute values ​​of all violations is less than the preset convergence tolerance. If so, stop the iteration and output the current start / stop sequence and output sequence as an approximate solution. Otherwise, update the Lagrange multipliers using the subgradient method based on the violation quantities, and return the updated Lagrange multipliers to Step 1 for the next round of iteration.

3. The method for rapid solution of unit combination based on Lagrange relaxation and neural network according to claim 1, characterized in that, The initial power-on / off time processing procedure includes: The effective range of initial power-on / off time is determined, and the initial power-on / off time exceeding the effective range is truncated. Then, it is converted into neural network input through mapping rules to avoid interference from extreme values ​​in the prediction. The valid range of initial power-on / off time values ​​is as follows: In the formula, This indicates the initial start-up and shutdown time of unit i. Indicates the minimum shutdown time. Indicates the minimum boot time; The specific formula for the neural network input mapping rule based on the initial power-on / off time is as follows: In the formula, This represents the initial on / off time of unit i after processing, i.e., the value input to the neural network.

4. The method for rapid solution of unit combination based on Lagrange relaxation and neural network according to claim 1, characterized in that, The initial power generation process includes: The effective range of initial power generation is determined, and initial power generation exceeding the effective range is truncated before normalization is performed; this is to avoid interference from extreme values ​​on neural network prediction. The effective range of initial power generation is as follows: In the formula, This represents the initial generating power of unit i. This represents the minimum output of unit i. This indicates the maximum output of unit i; The normalization process is specifically expressed by the following formula: In the formula, This represents the initial power generation of unit i after processing, i.e., the value input to the neural network.

5. The method for rapid solution of unit combination based on Lagrange relaxation and neural network according to claim 1, characterized in that, The feasibility adjustment of the iteratively obtained start-up and shutdown sequence based on the state transition diagram includes: locating the time period when system-level constraints are violated, selecting the units that need to be adjusted according to the level of fuel costs, adjusting the nodes along the decision path in the state transition diagram, while ensuring that the minimum start-up and shutdown time constraints are not violated.

6. The method for rapid solution of unit combination based on Lagrange relaxation and neural network according to claim 1, characterized in that, The path numbers are enumerated using a depth-first search order, so that two paths with adjacent numbers correspond to the two most similar solutions.

7. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the fast solution method for unit combination based on Lagrange relaxation and neural networks as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the fast solution method for unit combination based on Lagrange relaxation and neural networks as described in any one of claims 1-6.

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