Power system dispatching prediction method based on automatic verification and electronic equipment

Abstract

The invention relates to a power system scheduling prediction method based on automatic verification and electronic equipment, and the method comprises the following steps: carrying out formalized data cleaning based on a mathematical logic protocol, and ensuring that the association attribute of each record in a data set accords with the specification of a power system; stipulating the property satisfied by the output of the deep neural network model through sequential logic; training a mapping function from the load demand to the generator output power through a deep neural network model, and verifying whether the property of the protocol is met or not through each training iteration; predicting a scheduling scheme in real time by using the trained deep neural network model based on a real-time load demand; the prediction scheduling scheme is automatically verified in real time; if verification succeeds, putting the predicted scheduling scheme into use, and ending; otherwise, executing a feedback learning mechanism, and further training. Compared with the prior art, the method has the advantages of realizing automatic safety verification of the power system scheduling algorithm, improving the reliability and verifiability of the algorithm and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of power system dispatching, and in particular to a power system dispatching prediction method and electronic equipment based on automated verification. Background Art

[0002] With the increasing complexity of power systems and the continuous growth of demand, the safety and reliability of power system dispatching algorithms have become particularly important. Traditional power dispatching algorithms rely on strict operating procedures and manual monitoring, but with the development of smart grids, automated dispatching algorithms have gradually become mainstream. However, automated dispatching algorithms still face challenges in ensuring system stability and safety. Therefore, it is particularly important to use formal methods to perform automated safety verification of power system dispatching algorithms.

[0003] The main goal of the power system dispatch algorithm is to dynamically adjust the power generation plan according to the real-time load data and the operating status of the generator to meet the load demand and optimize the system operating cost. Common dispatch algorithms include economic dispatch (ED), unit commitment (UC) and load forecasting. The economic dispatch algorithm minimizes the total power generation cost by optimizing the output of the generator while meeting the load demand and system operation constraints. Traditional economic dispatch algorithms usually use Lagrangian relaxation or dynamic programming. These methods need to ensure that the algorithm can operate stably under different input conditions and the output results meet expectations. The unit commitment problem determines which generators should be started in a given time period to minimize the operating cost and meet the load demand. The unit commitment problem is usually solved by mixed integer linear programming (MILP), which needs to consider the startup cost, shutdown cost and operation constraints of the generator. Load forecasting uses machine learning algorithms to predict future load demand based on historical load data and external environmental factors. Common methods include time series analysis and deep learning models. The prediction results directly affect the decision-making of the dispatch algorithm, so its accuracy and reliability are crucial.

[0004] Modal logic extends traditional logic by introducing modal operators such as "may" or "must" to deal with the concepts of necessity and possibility. In modal logic, SVO logic (subject-verb-object logic) is a form of sentence structure, arranged in the order of subject (S), verb (V), and object (O). Dafny is a programming language that supports formal specifications and automatic verification, which is very suitable for modeling and verifying the safety of power system dispatch algorithms. The application of SVO logic in modal logic mainly involves the analysis and reasoning of sentence structure, helping to understand and express complex logical relationships and modal properties. Dafny supports the writing of programs with formal specifications and ensures that the programs comply with the specifications through automatic verification tools. Using Dafny to automatically verify the safety of power system dispatch algorithms mainly includes three steps: defining formal specifications, implementing algorithm logic, and automatic verification. Formal specifications include preconditions, postconditions, and invariants to ensure that the algorithm remains correct and stable during execution. Through Dafny's formalized specifications and automatic verification, potential security vulnerabilities can be discovered and fixed in advance, the reliability and security of the power system dispatching algorithm can be improved, and a solid technical guarantee can be provided for the development of smart grids.

[0005] How to achieve prediction and automated safety verification of power system dispatch has become a technical problem that needs to be solved. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a power system scheduling prediction method and electronic equipment based on automated verification.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] According to one aspect of the present invention, a method for predicting power system dispatch based on automated verification is provided, the method comprising the following steps:

[0009] Step S1, performing formal data cleaning based on mathematical logic conventions to ensure that the associated attributes of each record in the data set meet the specifications of the power system;

[0010] Step S2, reducing the properties satisfied by the output of the deep neural network model through sequential logic, wherein the properties satisfied include the security of power system dispatch and power balance;

[0011] Step S3, using the data processed in step S1 to train the mapping function from load demand to generator output power through a deep neural network model, and verifying whether each training iteration satisfies the properties specified in step S2. If not, the data is fed back to the deep neural network model for annotation and retraining until each iteration meets the properties specified in step S2.

[0012] Step S4, based on the real-time load demand, use the trained deep neural network model to predict the scheduling plan in real time;

[0013] Step S5, automatically and in real time verifying the predicted scheduling plan of step S4;

[0014] Step S6, if the verification is successful, the prediction scheduling scheme is put into use and ends; otherwise, the feedback learning mechanism is executed and returns to step S1 for further training.

[0015] Preferably, the associated attributes of each record in the data set conform to the specifications of the power system, specifically: for each load demand record P load , generator output power P gen The data records should meet basic power system constraints, including load balance and generator capacity limitations. Load balance refers to the balance between the total power generation of the generators and the total load of the system; the capacity limitation of the generator means that the output power of each generator must be within its physical capacity, that is, its output power must be between its rated maximum power and rated minimum power.

[0016] Preferably, the safety in step S2 is specifically: the total power generation in the scheduling scheme matches the total load demand, and the load balance constraint is represented by logical symbols:

[0017]

[0018] Where: t represents time, It means that the system's power generation and load demand must be balanced at all times. represents the output power of the ith generator, n is the number of generators in the system, represents the power demand of the jth load;

[0019] The power balance in step S2 is specifically: the output power of the generator cannot exceed the physical limit, and the power balance constraint is represented by logical symbols:

[0020]

[0021] Where: t is the time variable, It means that at any time t the output power of the generator must be within its allowable range. represents the minimum output power limit of the i-th generator, represents the actual output power of the i-th generator, represents the maximum output power limit of the i-th generator, This means that the data record for each generator i in the system must satisfy this constraint.

[0022] Preferably, step S3 comprises:

[0023] Assume that the historical data set D after processing in step S1 = {(P loed ,P gen )}, where P load is the historical load demand, P gen = {P 1 ,P 2 ,…,P n} is the output power of each generator under the historical dispatch scheme;

[0024] The goal of the deep neural network model is to learn from the load demand P load To the generator output power P gen The mapping function f θ ,Right now:

[0025] P gen =f θ (P load ),

[0026] Where θ is the parameter of the neural network, including weights and biases;

[0027] During the training process, the loss function L θ Used to measure the generator output power predicted by the deep neural network model The actual output power P gen The error between them is:

[0028]

[0029] By minimizing the loss function L θ , we can get the optimal parameter θ * , so that the deep neural network model can accurately predict the given load P load Generator output power P under gen , specifically:

[0030] θ * =argmin θ L(θ),

[0031] Where argmin is the loss function L θ The set of parameters θ to minimize.

[0032] Preferably, the step S4 comprises:

[0033] For a given current load demand The generator power predicted by the deep neural network model output is:

[0034]

[0035] in, is the mapping function from load demand to generator output, For the scheduling plan, Output the predicted nth generator power for the deep neural network model.

[0036] Preferably, the automated real-time verification process of step S5 includes:

[0037] Step S31, using SVO logic to establish a property description of the power system dispatch algorithm;

[0038] Step S32, constructing a formalized model based on the attribute description of step S31;

[0039] Step S33, constructing a core method for verifying the formal model, and scheduling the core method to verify the formal model.

[0040] More preferably, the process of step S31 includes defining basic symbols, assumptions and premises, expected results, and logical reasoning and proof;

[0041] In the basic notation, the subject is the whale optimization algorithm, the verb is optimize, and the object is the power generation plan;

[0042] The assumptions and premises include: the input generator cost coefficient and load demand are valid, the output power range of the generator is between its minimum and maximum output;

[0043] The desired results are: the total power generation cost is minimized, and the total output of all generators meets the load demand;

[0044] The logical reasoning and proof are specifically as follows: through the optimization process of the power system dispatching algorithm, the optimal solution of the whale population meets the expected result.

[0045] Preferably, the feedback learning mechanism includes: Add the training data set D to get the updated data set, i.e. D new =D∪D fail , for the updated dataset D new Retrain and update the parameters θ of the neural network; represents the output power of the ith generator, represents the power demand of the i-th load.

[0046] Preferably, the verification is successful if the automated real-time verification satisfies the following three conditions at the same time:

[0047] 1) Security attributes

[0048] Verify that the generator output power meets its physical limitations, namely:

[0049]

[0050] is the predicted nth generator power, and are the minimum output power and maximum output power of the ith generator, It means that all generators must meet the conditions of physical limitations;

[0051] 2) Verifiability attributes:

[0052] Verify whether the scheduling scheme can be verified by formal verification tools;

[0053] 3) Optimality properties:

[0054] Verify that the forecast dispatch scheme minimizes the total generation cost:

[0055]

[0056] where a i 、b i and c i denote the secondary cost coefficient, primary cost coefficient and fixed cost coefficient of the i-th generator respectively;

[0057] If the verification is successful, the scheduling plan This is the optimal solution.

[0058] According to another aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the method described above is implemented when the processor executes the program.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] 1) The present invention performs formal data cleaning based on mathematical logic specifications to ensure that the associated attributes of each record in the data set meet the specifications of the power system, and is not limited to traditional data cleaning and filtering; the deep neural network model is learned and trained based on the processed data, and the properties satisfied by the output of the deep neural network model are specified by temporal logic, and the model of each iteration is guaranteed to satisfy the properties to predict the scheduling plan, and the formal verification tool is input for automatic verification, and a feedback learning mechanism is introduced to improve the training of the mapping function. The introduction of the interpretable deep neural network effectively reduces the number of iterations of the traditional whale optimization algorithm, shortens the verification time and improves the verification efficiency. At the same time, the system has stronger adaptability when facing dynamic load demands, and can improve the interpretability of the deep neural network model from data input to data output, thereby improving the reliability and robustness of the scheduling algorithm.

[0061] 2) The present invention uses SVO logic to establish the attribute description of the power system dispatching algorithm, performs formal modeling and verification based on Dafny language rules, realizes the automated safety verification of the power system dispatching algorithm, and improves the accuracy, reliability and optimality of the algorithm.

[0062] 3) The formal model of the present invention is based on the economic dispatch algorithm of whale optimization. By optimizing the output of the generator, it ensures the optimal power generation plan and minimizes the total power generation cost while meeting the load demand of the power system. This automated verification method not only improves the accuracy and stability of the dispatch, but also provides a strong guarantee for the safe and efficient operation of the smart grid, and promotes the development of power system dispatching technology towards a more efficient, smarter and safer direction.

[0063] 4) If the iteration of the deep neural network model of the present invention cannot meet the specified properties, feedback is given to the model for annotation and further training; if the result of verifying the formalized model cannot meet the defined properties, the logic of the scheduling algorithm is modified or constraints are added, and the entire automated verification process is repeated until the defined properties are met, which is helpful for optimizing and improving the scheduling algorithm, thereby promoting the development of power system scheduling technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a basic flow chart of the existing economic dispatch algorithm based on the whale algorithm;

[0065] Figure 2 It is a flow chart of the power system dispatch prediction method based on automated verification of the present invention;

[0066] Figure 3 It is a flow chart of the power system dispatch prediction method based on automated verification of the present invention;

[0067] Figure 4 This is a schematic diagram of the process of establishing a formal model using Dafny in the present invention. DETAILED DESCRIPTION

[0068] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0069] Aiming at the safety problem of power dispatching algorithm, the present invention utilizes SVO logic for modeling and Dafny tool for automated safety verification. By introducing the whale optimization algorithm, the output power of the generator is optimized to ensure the economy and efficiency of the power generation plan.

[0070] In addition, the use of deep learning and feedback learning mechanisms to improve methods has made the formal verification process more intelligent and efficient, promoting the further development of power system dispatching technology.

[0071] The commonly used Dafny syntax rules are shown in the following table.

[0072] Table 1

[0073]

[0074]

[0075] As mentioned above, the basic grammatical rules of Dafny formal specification are simple and clear, easy to define, and have been successfully applied to the security verification of some well-known algorithms.

[0076] In order to further improve the accuracy and robustness of the power dispatching algorithm, and to address the problem of weak interpretability of deep learning models, the present invention further proposes an improved verification scheme combined with interpretable deep learning. Interpretable deep learning can firstly perform logical screening, cleaning and filtering of the training data, and then use the learning training model of the processed data to extract the properties that the trained model needs to ensure and characterize them with temporal logic. The model detection tool is used to ensure that the model of each iteration meets the properties and predict possible scheduling schemes, thereby not only shortening the verification time and improving the verification efficiency, but also improving the interpretability of the deep learning model from the data input to the data output stage.

[0077] By introducing interpretable deep learning, not only can the number of iterations of the traditional whale optimization algorithm be effectively reduced, but the system can also have stronger adaptability when facing dynamic load requirements, while improving the interpretability of the deep learning model.

[0078] Example 1

[0079] This embodiment relates to a power system dispatch prediction method based on automated verification, such as Figure 2 , including the following steps:

[0080] Step S1, data logic legitimacy check: Formal data cleaning is performed based on mathematical logic conventions to ensure that the associated attributes of each record in the data set conform to the specifications of the power system.

[0081] Before training data, we must first ensure the compliance of the data. By using mathematical logic to regulate the power system dispatch data, we check whether the attribute relationship in each data record conforms to the specifications of the conventional power system. This check is no longer limited to traditional data cleaning methods (such as deleting invalid data), but verifies the correlation between data through formal means to ensure the integrity and correctness of the data. For example, for each load demand record P load , generator output power P gen The data records should satisfy basic power system constraints, such as load balancing, generator capacity limitations, etc. Specifically,

[0082] 1) In the power system, load balance refers to the balance between the total power generation of the generator and the total load of the system. A common mathematical logic formula for load balance can be expressed as:

[0083]

[0084] in: represents the output power of the i-th generator, and n is the number of generators in the system. represents the power demand of the jth load, and m is the number of loads in the system. In this formula, the left side is the total output power of all generators, and the right side is the power demand of all loads. The requirement for load balancing is that these two totals are equal to ensure that power generation meets demand.

[0085] 2) The capacity limitation of the generator means that the output power of each generator must be within its physical capacity, that is, its output power cannot exceed its rated maximum power or be lower than its rated minimum power.

[0086]

[0087] in: represents the minimum output power limit of the i-th generator, represents the actual output power of the i-th generator, Represents the maximum output power limit of the i-th generator.

[0088] Step S2: Deep neural network model output property specification

[0089] In the training process of the deep neural network model, temporal logic is used to reduce the properties that the model output needs to satisfy and convert them into mathematical logic formulas. These properties include the safety of power system scheduling, power balance, etc. Specifically,

[0090] 1) Power balance: The output power of the generator cannot exceed the physical limit (such as the maximum and minimum output range of the generator).

[0091] This restriction can be expressed in mathematical logic as follows:

[0092]

[0093] in: represents the minimum output power limit of the i-th generator, represents the actual output power of the i-th generator, represents the maximum output power limit of the i-th generator, This means that the data record for each generator i in the system must satisfy this constraint.

[0094] In addition, if the data record contains time, it is necessary to consider the capacity limitation of the generator at different time points. The time variable t can be added and the formula becomes:

[0095]

[0096] Where t is the time variable, It means that at any time t, the output power of the generator must be within its allowed range. Exceeding these ranges may cause the generator to be overloaded, inefficient, or even damaged. The goal of this mathematical formula is to ensure that the output power of each generator is within a reasonable operating range to maintain the safety and stability of the system.

[0097] 2) Security of power system dispatch: The total power generation in the dispatch plan should match the total load demand.

[0098] To convert it into a mathematical logic formula, the load balancing constraint can be expressed using logical symbols:

[0099]

[0100] Where: t represents time, load balancing can be a time-varying constraint, It means that at all times, the system's power generation and load demand must be balanced. The meaning of this mathematical logic formula is that at every moment of system operation, the total power output of all generators must be equal to the total power demand of all loads to ensure the stability and reliability of the system during operation. Therefore, all data records should satisfy the above mathematical logic formula.

[0101] These specifications will serve as the basis for subsequent verification, and model checking tools will be used during deep neural network model training to ensure that each model iteration conforms to these properties.

[0102] Step S3, data training process: The historical scheduling data is trained through the Deep Neural Networks (DNN) model to learn the nonlinear relationship between generator output and system load.

[0103] The core of using deep neural network models to predict scheduling solutions is to train the neural network model through a large amount of historical scheduling data. Assume that the historical data set D = {(P load ,P gen )}, where: P load is the historical load demand, P gen = {P 1 ,P 2 ,…,P n} is the output power of each generator under the historical dispatch scheme.

[0104] The goal of the deep neural network model is to learn from the load demand P load To the generator output power P gen The mapping function f θ ,Right now:

[0105] P gen =f θ (P load ),

[0106] Where θ is the parameters of the neural network, including weights and biases.

[0107] During the training process, the loss function L θ Used to measure the generator output power predicted by the model The actual output power P gen The error between . Mean Squared Error (MSE) based on the common loss function:

[0108]

[0109] By minimizing the loss function L θ , we can get the optimal parameter θ * , so that the model can accurately predict the given load P load Generator output power P under gen , specifically:

[0110] θ * =argmin θ L(θ),

[0111] Where argmin is the independent variable value of a function to achieve the minimum value, here is the loss function L θ The set of parameters θ to minimize.

[0112] In each training iteration, the model checking tool checks whether the output of the DNN satisfies the logical specifications defined in step S2. If it is found that it does not meet the requirements, the sample is returned and the model is retrained until each iteration meets the specifications.

[0113] Step S4, real-time prediction of scheduling plan: Based on the real-time load demand, the deep neural network model predicts a feasible scheduling plan (generator output power) in real time as the initial input.

[0114] After training, the deep neural network model can be used to predict the dispatch plan of the power system in real time. The deep neural network model outputs the predicted generator power where f θ is the mapping function from load demand to generator output.

[0115] The scheduling scheme It will be used as input to enter the Dafny formal verification process, where Output the predicted nth generator power for the deep neural network model.

[0116] Step S5: Automatically verify the predicted scheduling plan

[0117] During the automated verification phase, Dafny will use the SVO logic to predict the scheduling plan predicted by the neural network. The key to verification is to ensure that the scheduling solution meets the following three main properties:

[0118] 1) Safety attributes:

[0119] Verify that the generator output power meets its physical limitations, namely:

[0120]

[0121] in, and are the minimum output power and maximum output power of the ith generator, This means that all generators must meet physical constraints.

[0122] 2) Verifiability:

[0123] Verify whether the scheduling scheme can be verified by formal verification tools. For example, verify the power balance constraint:

[0124] 3) Optimality:

[0125] Verify that the forecast dispatch scheme minimizes the total generation cost:

[0126]

[0127] Among them, a i It represents the quadratic cost coefficient of the i-th generator, which is related to the quadratic term of the generator's output power and is used to describe the nonlinear cost of the generator. Usually, the power generation cost is the part that is proportional to the square of the power, because the energy consumption of the generator increases with the increase of the output power;

[0128] b i It represents the primary cost coefficient of the i-th generator, which is proportional to the output power of the generator and describes the linear cost, that is, the cost of generating electricity at a fixed power level;

[0129] c i It represents the fixed cost of the ith generator, or the constant cost. It represents the fixed cost of the generator regardless of its output power, including maintenance and startup costs, etc. This cost is fixed even if the power generation is zero.

[0130] If the verification is successful, the scheduling plan This is the optimal solution.

[0131] Step S6, feedback learning mechanism: if the verification fails, feedback the error samples for further training to improve the prediction accuracy; if the verification succeeds, the process ends.

[0132] If the scheduling solution predicted by the deep neural network model is found during the formal verification process If certain constraints are not met, the failed samples will be fed back to the deep neural network model for further training. This feedback mechanism can gradually improve the prediction ability of the deep learning model, especially in the face of complex load change scenarios, improving scheduling accuracy and verification efficiency.

[0133] The process of reusing and relearning failed samples can be expressed as:

[0134] (i) Failure sample set

[0135] (ii) Add the failed samples back into the training dataset D new =D∪D fail ,

[0136] (iii) For the updated dataset D new Retrain and update the network parameters θ to improve the generalization ability of the model.

[0137] In step S5, Dafny is selected as a verification tool to verify the predicted scheduling plan in real time, including:

[0138] First, a formal model is established to describe the components of the power system, such as generators, power lines, and load demand, and the logic of the dispatch algorithm is defined to explain how to adjust the generator output and power line load distribution according to real-time conditions. On this basis, Dafny is selected as a verification tool to verify the model using its formal specification and automatic verification functions.

[0139] Next, the model is converted into a form recognizable by Dafny, for example, by using Dafny's program structure and logic specifications to represent the model.

[0140] Then, select the verification attributes, such as "Can the system maintain stable operation under given load demand?" and "Can the system adjust the power line load distribution in time when the generator output changes?" When running the Dafny tool for verification, the tool will automatically detect whether the selected verification attributes are met and give the verification results.

[0141] In step S5, Dafny is used to analyze and verify the security of the power system dispatching algorithm, including the following steps:

[0142] 1. Establish a formal model: Establish a formal model to describe the components of the power system, such as generators, power lines, and load demand, and define the logic of the scheduling algorithm to explain how to adjust the generator output and power line load distribution according to real-time conditions.

[0143] 2. Select a verification tool: Select Dafny as the verification tool and use its formal specification and automatic verification functions to verify the model.

[0144] 3. Model conversion: Convert the model into a form recognizable by Dafny, and use Dafny's program structure and logical specifications to represent the model.

[0145] 4. Select verification attributes: Select verification attributes, such as "Can the system maintain stable operation under given load demand?" and "Can the system adjust the power line load distribution in time when the generator output changes?"

[0146] 5. Run the verification tool: Run the Dafny tool for verification. The tool will automatically detect whether the selected verification attributes are met and give the verification results.

[0147] Through Dafny's formal specification, the security and design correctness of the power dispatching algorithm can be automatically verified to ensure the stability and security of the algorithm.

[0148] In step S6, based on the verification results, we analyze and make necessary corrections. If it is found that the system cannot meet the verification properties in some cases, the logic of the scheduling algorithm is modified or constraints are added as needed. Finally, the verification results of the tool are explained.

[0149] Example 2

[0150] This embodiment relates to a power system dispatch prediction method based on automated verification. The power system dispatch algorithm adopts an economic dispatch algorithm based on the whale algorithm. The basic idea is as follows: The whale optimization algorithm (WOA) simulates the hunting behavior of humpback whales, including encirclement, spiral bubble net and random search mechanism. The economic dispatch algorithm based on the whale algorithm ensures that the load demand is met and the total power generation cost is minimized by optimizing the generator output.

[0151] As attached Figure 1 , the economic dispatch algorithm includes the following steps:

[0152] Step S101, initialization: initializing the whale population position and fitness value.

[0153] Step S102, calculating fitness: calculating the fitness value of each whale according to the total power generation cost.

[0154] Step S103, updating the location, including

[0155] Encirclement mechanism: simulates the behavior of whales encircling their prey after discovering it, and adjusts the position through the formula:

[0156]

[0157] in, is the current optimal position, A and C are coefficient vectors, and Represent the current position and the updated position at the next moment respectively.

[0158] Spiral Bubble Net Attack Mechanism: Simulates the behavior of a whale spiraling around its prey, adjusting its position through the formula:

[0159]

[0160] Where b and l are the helical constants.

[0161] Random search mechanism: simulates the random search behavior of whales when no prey is found, and adjusts the position through the formula:

[0162]

[0163] Among them, the lower_bound function returns the first position in the container that is greater than or equal to the target value, and the upper_bound function returns the first position in the container that is greater than the target value.

[0164] Step S104, iteration: repeat the fitness calculation and position update steps until the termination condition is met.

[0165] Step S105, output the optimal solution: after the iteration is completed, the optimal generator output solution is output.

[0166] The present invention proposes an automated security verification method for the security of the above economic dispatch algorithm, such as Figure 3 , including the following steps:

[0167] Step S31, by analyzing the power system dispatch algorithm (economic dispatch algorithm based on the whale algorithm), the properties of the power system dispatch algorithm are described using SVO logic, including defining basic symbols, assumptions and premises, expected results, logical reasoning and proof.

[0168] (a) Definition of symbols

[0169] S: Subject - Whale Optimization Algorithm (WOA)

[0170] V: Verb - Optimization

[0171] O: Object - Generation Schedule

[0172] G:Whale Population

[0173] F: Fitness Function

[0174] P i : Output power of the ith generator

[0175] C i :The cost coefficient of the i-th generator (a i ,b i )

[0176] D: Load Demand.

[0177] (b) Define assumptions and premises

[0178] H 1 : The input generator cost factor and load demand are valid:

[0179]

[0180] H 2 : The output power range of a generator is between its minimum and maximum output:

[0181]

[0182] (c) Define the expected results

[0183] R 1 :Total power generation cost is minimized:

[0184] R 2 :All generator outputs meet load requirements:

[0185] (d) Logical reasoning and proof

[0186] Specifically, the SVO logical symbolic representation includes:

[0187] Step S31-1, define subject, verb and object:

[0188] S: Whale Optimization Algorithm (WOA)

[0189] V: Optimization

[0190] O: Generate schedule (Generation Schedule).

[0191] Step S31-2, verifying that the total power generation cost is minimized:

[0192] Premise 1 ):

[0193] Action (V): Optimize P with WOA i , so that minimize;

[0194] Expected result (R 1 ): reach a minimum;

[0195] Proof: Through the iterative process of WOA, the whale population continuously updates its position and gradually approaches the optimal solution for the total power generation cost.

[0196] Step S31-3, verify that the load requirement is met:

[0197] Premise 2 ): D is a known condition and is fixed;

[0198] Action (V): Use WOA to adjust Pi , so that

[0199] Expected result (R 2 ):

[0200] Proof: Through the optimization process of WOA, the optimal solution of the whale population will satisfy the total output equal to the load demand D.

[0201] Through SVO logic, the verification process of the economic dispatch algorithm based on the whale algorithm can be structured and clearly expressed. The separation of subject, verb, and object makes the logical reasoning clearer and easier to understand, thus ensuring that the algorithm can meet the expected results in all cases.

[0202] Step S32, based on the attribute description of the power system dispatching algorithm, a formal model is constructed using Dafny language rules.

[0203] In order to formally verify the economic scheduling algorithm based on the whale algorithm, Dafny is used to model, define properties, and verify the correctness of the algorithm.

[0204] The following are the basic steps to establish a formal model. Figure 4 shown.

[0205] Step S32-1, initializing variables and parameters, including:

[0206] Define the number of generators, the output power range of the generators, and the cost coefficient of the generators;

[0207] Initialize the positions and fitness values ​​of the whale population.

[0208] Step S32-2, define a fitness function and calculate a fitness value according to the total power generation cost.

[0209] Step S32-3, define the position update rules, including: encirclement mechanism, spiral bubble net attack mechanism and random search mechanism.

[0210] Step S32-4, define the iterative process:

[0211] The fitness calculation and position update steps are repeated until the termination condition is met.

[0212] Step S33, Dafny language rules, ten core methods (Methods) of constructing a formal model.

[0213] The core methods for constructing formal models based on the Dafny language are shown in Table 2.

[0214] Table 2

[0215]

[0216]

[0217] The basic constants are defined as follows:

[0218] const numGenerators:int:=3; / / define the number of generators

[0219] const maxIterations:int:=100; / / define the maximum number of iterations

[0220] const loadDemand:int:=500; / / define load demand

[0221] The basic initial conditions for the generator output power range and cost factor are as follows:

[0222] var P_min:array <int>:=[100,150,200]; / / Minimum output power of generator

[0223] var P_max:array <int>:=[400,350,500]; / / Maximum output power of the generator

[0224] var a:array <int>:=[10,20,30]; / / cost coefficient a

[0225] var b:array <int>:=[5,10,15]; / / cost coefficient b

[0226] The whale population and fitness are defined as follows:

[0227] var population:array <array <int>>; / / Define whale population

[0228] var fitness:array <int>; / / Define fitness.

[0229] The specific implementation of each method is introduced below.

[0230] The first core method: define a method called InitializePopulation

[0231] This method is used to initialize a population. The population is a two-dimensional integer array population, with a dimension of numGenerators×numGenerators, which is used to represent the status of multiple generators. Another one-dimensional integer array fitness, with a size of numGenerators, is used to represent the fitness value of each generator.

[0232] In this method, we first create the population array and the fitness array. Then, we use two nested for loops to initialize the values ​​in the population array. For each generator i and each generator j, we set the value of population[i][j] to the middle value between P_min[j] and P_max[j], that is, P_min[j] +

[0233] (P_max[j] - P_min[j]) / 2. Thus, the initial position of each generator is in the middle of its range.

[0234]

[0235]

[0236] The second core method: define a method called CalculateFitness

[0237] This method is used to calculate the fitness value (total cost) of each generator in the population. This method iterates over each generator in the population array, calculates its fitness value and stores it in the fitness array. Specifically, this method first uses a for loop to iterate over all generators i, ranging from 0 to numGenerators-1. At the beginning of each iteration, a local variable totalCost is declared and initialized to 0 to store the total cost of the current generator. Then, another nested for loop is used to iterate over all possible states j of the current generator i, also ranging from 0 to numGenerators-1. In the inner loop, the cost of the current state j is calculated according to the formula a[j]+b[j]*population[i][j] and added to totalCost, where a[j] and b[j] are coefficients related to the generator state, and population[i][j] is the value of generator i in state j. After the inner loop ends, the accumulated total cost totalCost is assigned to fitness[i], which represents the fitness value of generator i.

[0238]

[0239] The third core method: define a method called FindBestWhale

[0240] This method is used to find the generator with the smallest fitness value in the population, that is, the optimal whale, and return its index. The specific process is as follows: First, the return value bestIndex is defined to store the index of the optimal whale and initialize it to 0. Next, the local variable minFitness is defined to store the currently found minimum fitness value and initialize it to fitness[0]. Then, a for loop is used to traverse from 1 to numGenerators-1, that is, to traverse all generators except the first generator. In the loop, determine whether the fitness value fitness[i] of the current generator is less than minFitness. If so, update minFitness to the fitness value of the current generator, and update bestIndex to the index i of the current generator. After the loop ends, return bestIndex, which is the index of the generator with the smallest fitness value.

[0241]

[0242] The fourth core method: define a method called UpdatePositionEncircling

[0243] This method is used to update the position of the generator according to the strategy around the prey. This method receives a parameter bestIndex, which represents the index of the generator with the smallest fitness value (that is, the optimal whale). The specific process is as follows: First, use a for loop to traverse all generators i, ranging from 0 to numGenerators-1. In the loop, first check whether the current generator i is not the optimal whale (that is, i!=bestIndex). If so, enter the inner loop. The inner loop traverses all possible states j of the current generator i, also ranging from 0 to numGenerators-1. In the inner loop, two variables A and C are calculated. The value of A is 2*(bestIndex+1)-(i+1), which represents the offset based on the position of the optimal whale. The value of C is 2*(j+1), which represents a constant factor. Then, the formula is used to update the value of the current generator i in state j: population[i][j]:=population[bestIndex][j]-A*|C*population[bestIndex][j]-population[i][j]|. This formula is based on the position of the best whale, population[bestIndex][j], and combines the calculation results of A and C to adjust the position of the current generator through absolute value calculation.

[0244]

[0245] Fifth core method: define a method called UpdatePositionBubbleNet

[0246] This method is used to update the position of the generator according to the bubble net attack strategy. It receives a parameter bestIndex, which represents the index of the generator with the smallest fitness value (i.e., the optimal whale). The specific process is as follows: First, use a for loop to traverse all generators i, ranging from 0 to numGenerators-1. In the loop, first check whether the current generator i is not the optimal whale (i.e., i!=bestIndex). If so, enter the inner loop. The inner loop traverses all possible states j of the current generator i, also ranging from 0 to numGenerators-1. In the inner loop, two variables are defined: b is set to a constant 1, and the value of l is (bestIndex+1)-(i+1), which represents the position difference between generator i and the optimal whale. Then, use the formula to update the value of the current generator i in state j:

[0247] population[i][j]:=|population[bestIndex][j]-population[i][j]|*e ( b*l ) *cos(2*pi*l)+population[bestIndex][j]; / / Update the position of generator i in state j

[0248] Among them, |population[bestIndex][j]-population[i][j]| is used to calculate the absolute value of the position difference between the current generator i and the best whale in state j; e(b*l) is used to calculate the natural exponential function, where the exponent is b*l; cos(2*pi*l) is used to calculate the cosine function, where the parameter is 2*pi*l. The result of the multiplication of the above three plus population[bestIndex][j] is used to get the updated position of generator i in state j.

[0249]

[0250] The sixth core method: define a method called UpdatePositionBubbleNet

[0251] This method is used to randomly update the position of each generator in the population. The method traverses all generators and all their states through two nested for loops, and randomly updates the position of each state. Specifically, the position update is achieved by generating a random number within the minimum and maximum range of the generator, with the formula P_min[j]+(P_max[j]-P_min[j])*rand(). In this way, the position of each generator will be randomized within its allowed range, simulating the random movement behavior of whales when searching for prey.

[0252]

[0253] The seventh core method: define a method called HasConverged

[0254] This method is used to determine whether the population has converged and returns a Boolean value converged. Specifically, this method iterates through the fitness values ​​of all generators and checks whether there is a generator whose fitness value is less than a predefined threshold (for example, 0.001). If such a generator is found, converged is set to true and the loop is exited; otherwise, converged remains false. The purpose of this method is to determine whether the optimization process has reached the expected convergence conditions.

[0255]

[0256] The eighth core method: define a method called EconomicDispatchAlgorithm

[0257] This method is used to solve the economic dispatch problem and return the best solution bestSolution. The method first initializes the population, then updates the population state in multiple iterations, and terminates the iteration when the convergence condition is met. The specific process is as follows: First, call the InitializePopulation method to initialize the population. Then enter a loop, iterating from 0 to maxIterations-1. In each iteration, first call the CalculateFitness method to calculate the fitness value of each generator in the current population. Then call the FindBestWhale method to find the index bestIndex of the generator with the smallest fitness value in the current population (that is, the best whale). Then call the UpdatePositionEncircling, UpdatePositionBubbleNet, and UpdatePositionRandom methods in sequence to adjust the position of the generator in the population according to the surrounding prey, bubble net attack, and random update strategies, respectively. At the end of each iteration, call the HasConverged method to check whether the population has converged. If the convergence condition is met (that is, the fitness value of at least one generator is less than the predefined threshold), then jump out of the loop. After the iteration is completed, the FindBestWhale method is called to find the index of the best whale again and return its position as the best solution bestSolution.

[0258]

[0259]

[0260] Ninth core method: Define a method called VerifySolution

[0261] This method is used to verify whether the optimal solution bestSolution meets the given load demand loadDemand and returns a Boolean value valid, indicating the validity of the solution. The specific process is as follows:

[0262] First, initialize the return value valid to true, indicating that the hypothetical solution is valid. Next, define a local variable totalOutput, initialized to 0, to accumulate the total output of the generator. Then, use a for loop to iterate over all generators, from 0 to numGenerators-1, and accumulate the output value of each generator in the bestSolution array in the loop and add it to totalOutput. After the loop ends, check whether totalOutput is equal to loadDemand. If the total output is not equal to the load demand, set valid to false, indicating that the solution is invalid.

[0263]

[0264]

[0265] The tenth core method: define a method called Main

[0266] This method is used to run the entire economic dispatch algorithm and verify the validity of the optimal solution. The specific process is as follows: First, call the EconomicDispatchAlgorithm method to return the optimal solution bestSolution. Then, use the assert statement to call the VerifySolution method to verify the validity of the optimal solution. The VerifySolution method will check whether bestSolution meets the load demand loadDemand. If the verification passes, the assert statement will not throw an error; otherwise, the assert statement will cause an assertion failure error.

[0267]

[0268] Step S34, extracting and verifying the properties of the formalized model of the economic dispatch algorithm based on the whale algorithm based on Dafny, including:

[0269] Step S34-1, defining attributes, including:

[0270] Property 1: Minimize the total power generation cost, similar to H 1 ;

[0271] Property 2: All generator outputs meet the load requirements, similar to the expected result R 2 .

[0272] Step S34-2, verification method, includes:

[0273] 1) Verify that the total power generation cost is minimized: Use the fitness function to calculate the total power generation cost, compare the fitness values ​​of all whale positions, and select the smallest fitness value as the optimal solution.

[0274] 2) Verify that the load requirements are met: Calculate the total output power of the optimal solution and confirm that the total output power is equal to the load requirements.

[0275] Through the above Dafny code and verification process, we can formally characterize and verify the economic dispatch algorithm based on the whale algorithm. Using Dafny's proof function, we can ensure that the algorithm satisfies the defined properties in all cases.

[0276] In step S6, according to the verification result of step S5, the power system dispatching algorithm is analyzed and corrected. If the attributes defined in step S5 cannot be met in some cases, it is necessary to modify the logic of the dispatching algorithm or add constraints, and repeat steps S1 to S6 until the verification attributes are met directly; conclusion analysis is performed based on the unambiguous combing of SVO logic and Dafny formal modeling analysis and verification.

[0277] Constraints include: input constraints, which are mainly used to check the validity of input and determine whether the algorithm has a robust processing mechanism for malicious or erroneous input, such as preventing buffer overflow caused by excessive input and rejecting input in illegal formats; boundary conditions, which are used to judge extreme input behavior.

[0278] Constrain the time and space complexity of the algorithm to minimize the possibility of denial of service attacks DoS, memory leaks, and stack overflows, thereby improving the robustness of the algorithm.

[0279] Based on the verification results, the conclusions of the analysis include:

[0280] Conclusion 1: The Whale Optimization Algorithm (WOA) can effectively optimize the power dispatching algorithm to minimize the total power generation cost.

[0281] In the model implemented in Dafny using the Whale Optimization Algorithm (WOA), the power generation plan is gradually optimized by iteratively calculating and updating the positions of the whale population. In each iteration, the fitness function calculates the total power generation cost, and the algorithm selects the whale position with the smallest fitness value as the current optimal solution. After multiple iterations, a global optimal or near-optimal power generation plan is finally obtained, minimizing the total power generation cost. This unambiguously verifies from a mathematical point of view that WOA can effectively find a power generation plan that minimizes the total power generation cost.

[0282] Conclusion 2: During the optimization process, WOA ensures that all generator outputs meet the given load requirements.

[0283] In Dafny, we define and verify whether the total output power of the optimal solution meets the given load demand. By adding the output power of each generator in the optimal solution, we confirm that the total output power is equal to the load demand. This verification process ensures that the algorithm can meet the actual load demand of the power system while optimizing the total generation cost.

[0284] These conclusions show that WOA is an effective and reliable power dispatch algorithm that can optimize power generation plans, reduce power generation costs, and ensure that the load requirements of the power system are met in practical applications. The reliability and verifiability of the algorithm are further enhanced by combining SVO logic and Dafny for formal modeling and verification.

[0285] In summary, by using the whale optimization algorithm (WOA) combined with SVO logic and Dafny for formal modeling and verification, we proposed a power system dispatch prediction method based on automated verification. This method significantly improves the reliability and verifiability of the electronic system dispatch algorithm, ensures the optimization of the power generation plan and the reduction of costs, and meets the load requirements of the power system. This automated verification method not only improves the accuracy and stability of the dispatch, but also provides a strong guarantee for the safe and efficient operation of the smart grid, and promotes the development of power system dispatch technology towards a more efficient, smarter and safer direction.

[0286] The formal verification process combined with deep learning can be summarized into the following steps:

[0287] Data logic check: Ensure the legitimacy of data, not just limited to traditional data cleaning and filtering

[0288] Initial training: The neural network is trained using historical data sets to learn the relationship between generator output and load demand.

[0289] Real-time prediction: Based on the current load demand, neural networks are used to predict the output power of the generator.

[0290] Formal verification: Use Dafny to verify the prediction results to ensure that the scheduling scheme meets the safety, verifiability and optimality properties of the SVO logic. If the verification fails, the error samples are fed back for further training to improve the prediction accuracy.

[0291] Through the above process, the automatic verification and optimization of the dispatching algorithm can be effectively realized, further improving the accuracy, robustness and intelligence of the power system dispatching. At the same time, the above-mentioned interpretable deep learning can improve the interpretability and robustness of the overall model.

[0292] Example 3

[0293] The electronic device of the present invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in a read-only memory (ROM) or loaded from a storage unit into a random access memory (RAM). In the RAM, various programs and data required for device operation can also be stored. The CPU, ROM and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0294] Multiple components in the device are connected to the I / O interface, including: input units, such as keyboards, mice, etc.; output units, such as various types of displays, speakers, etc.; storage units, such as disks, optical disks, etc.; and communication units, such as network cards, modems, wireless communication transceivers, etc. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunication networks.

[0295] The processing unit performs the various methods and processes described above, such as methods S1 to S6. For example, in some embodiments, methods S1 to S6 may be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed on the device via a ROM and / or a communication unit. When the computer program is loaded into the RAM and executed by the CPU, one or more steps of methods S1 to S6 described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute methods S1 to S6 in any other appropriate manner (e.g., by means of firmware).

[0296] The functions described above herein may be performed at least in part by one or more hardware logic components. For example, without limitation, exemplary types of hardware logic components that may be used include: field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), complex programmable logic devices (CPLDs), and the like.

[0297] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code can be executed entirely on the machine, partially on the machine, partially on the machine as a stand-alone software package and partially on a remote machine, or entirely on a remote machine or server.

[0298] In the context of the present invention, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0299] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or substitutions within the technical scope disclosed by the present invention, and these modifications or substitutions should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.< / int> < / int> < / int> < / int> < / int> < / int>

Claims

1. A power system dispatch prediction method based on automated verification, characterized in that: The method comprises the following steps: Step S1, performing formal data cleaning based on mathematical logic conventions to ensure that the associated attributes of each record in the data set meet the specifications of the power system; Step S2, reducing the properties satisfied by the output of the deep neural network model through sequential logic, wherein the properties satisfied include the security of power system dispatch and power balance; Step S3, using the data processed in step S1 to train the mapping function from load demand to generator output power through a deep neural network model, and verifying whether each training iteration satisfies the properties specified in step S2. If not, the data is fed back to the deep neural network model for annotation and retraining until each iteration meets the properties specified in step S2. Step S4, based on the real-time load demand, use the trained deep neural network model to predict the scheduling plan in real time; Step S5, automatically and in real time verifying the predicted scheduling plan of step S4; Step S6, if the verification is successful, the prediction scheduling scheme is put into use and ends; otherwise, the feedback learning mechanism is executed and returns to step S1 for further training.

2. The method for predicting power system dispatch based on automated verification according to claim 1, characterized in that: The associated attributes of each record in the data set conform to the specifications of the power system: for each load demand record P load , generator output power P gen The data records should meet basic power system constraints, including load balance and generator capacity limitations. Load balance refers to the balance between the total power generation of the generators and the total load of the system; the capacity limitation of the generator means that the output power of each generator must be within its physical capacity, that is, its output power must be between its rated maximum power and rated minimum power.

3. The method for predicting power system dispatch based on automated verification according to claim 1, characterized in that: The safety in step S2 is specifically that the total power generation in the scheduling scheme matches the total load demand, and the load balance constraint is represented by logical symbols: Where: t represents time, It means that the system's power generation and load demand must be balanced at all times. represents the output power of the ith generator, n is the number of generators in the system, represents the power demand of the jth load; The power balance in step S2 is specifically: the output power of the generator cannot exceed the physical limit, and the power balance constraint is represented by logical symbols: Where: t is the time variable, It means that at any time t the output power of the generator must be within its allowable range. represents the minimum output power limit of the i-th generator, represents the actual output power of the i-th generator, represents the maximum output power limit of the i-th generator, This means that the data record for each generator i in the system must satisfy this constraint.

4. The method for predicting power system dispatch based on automated verification according to claim 1, characterized in that: The step S3 comprises: Assume that the historical data set D after processing in step S1 = {(P load ,P gen )}, where P load is the historical load demand, P gen = {P1,P2,…,P n } is the output power of each generator under the historical dispatch scheme; The goal of the deep neural network model is to learn from the load demand P load To the generator output power P gen The mapping function f θ ,Right now: P gen =f θ (P load ), Where θ is the parameter of the neural network, including weights and biases; During the training process, the loss function L θ Used to measure the generator output power predicted by the deep neural network model The actual output power P gen The error between them is: By minimizing the loss function L θ , we can get the optimal parameter θ * , so that the deep neural network model can accurately predict the given load P load Generator output power P under gen , specifically: i * =argmin θ L(θ), Where argmin is the loss function L θ The set of parameters θ to minimize.

5. The method for predicting power system dispatch based on automated verification according to claim 1, characterized in that: The step S4 comprises: For a given current load demand The generator power predicted by the deep neural network model output is: in, is the mapping function from load demand to generator output, For the scheduling plan, Output the predicted nth generator power for the deep neural network model.

6. The method for predicting power system dispatch based on automated verification according to claim 1, characterized in that: The automated real-time verification process of step S5 includes: Step S31, using SVO logic to establish a property description of the power system dispatch algorithm; Step S32, constructing a formalized model based on the attribute description of step S31; Step S33, constructing a core method for verifying the formal model, and scheduling the core method to verify the formal model.

7. The method for predicting power system dispatch based on automated verification according to claim 6, characterized in that: The process of step S31 includes defining basic symbols, assumptions and premises, expected results, and logical reasoning and proof; In the basic notation, the subject is the whale optimization algorithm, the verb is optimize, and the object is the power generation plan; The assumptions and premises include: the input generator cost coefficient and load demand are valid, the output power range of the generator is between its minimum and maximum output; The desired results are: the total power generation cost is minimized, and the total output of all generators meets the load demand; The logical reasoning and proof are specifically as follows: through the optimization process of the power system dispatching algorithm, the optimal solution of the whale population meets the expected result.

8. The method for predicting power system dispatch based on automated verification according to claim 1, characterized in that: The feedback learning mechanism includes: Add the training data set D to get the updated data set, i.e. D new =D∪D fail , for the updated dataset D new Retrain and update the parameters θ of the neural network; represents the output power of the ith generator, represents the power demand of the i-th load.

9. The method for predicting power system dispatch based on automated verification according to claim 1, characterized in that: If the automated real-time verification meets the following three conditions at the same time, the verification is considered successful: 1) Security attributes Verify that the generator output power meets its physical limitations, namely: is the predicted nth generator power, and are the minimum output power and maximum output power of the ith generator, It means that all generators must meet the conditions of physical limitations; 2) Verifiability attributes: Verify whether the scheduling scheme can be verified by formal verification tools; 3) Optimality properties: Verify that the forecast dispatch scheme minimizes the total generation cost: where a i 、b i and c i denote the secondary cost coefficient, primary cost coefficient and fixed cost coefficient of the i-th generator respectively; If the verification is successful, the scheduling plan This is the optimal solution.

10. An electronic device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the program, the method according to any one of claims 1 to 9 is implemented.

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