Integrated energy system multi-objective scheduling method and device guided by rule language

Abstract

This invention provides a method and apparatus for multi-objective scheduling of integrated energy systems guided by rule-based language. The method includes: establishing a mathematical model for multi-objective scheduling of an integrated energy system (IES); transforming the mathematical model of IES multi-objective scheduling optimization into a Markov Decision Process (MDP) process using a Large Language Model (LLM), and constructing an LLM agent for multi-objective guided interaction; solving the MDP process of IES multi-objective scheduling optimization using the LLM agent and the Multi-Objective Deep Deterministic Policy Gradient Algorithm (DDPG), to obtain the decision scheme for IES multi-objective scheduling. This invention, by combining LLM and deep reinforcement learning models, can effectively guide human multi-objective preferences during IES scheduling optimization, providing theoretical and technical support for scheduling departments and personnel to arrange actual power grid generation plans.

Description

Technical Field

[0001] This invention relates to the field of energy system scheduling technology, and in particular to a method and apparatus for multi-objective scheduling of integrated energy systems guided by rule-based language. Background Technology

[0002] Integrated Energy System (IES) scheduling is typically defined as a complex Multi-Objective (MO) optimization problem. The objectives are tightly coupled through decision variables, and optimizing one objective often requires compromise on others. Furthermore, the unit differences between objectives make it difficult to objectively compare the merits of solutions to multi-objective problems. Existing research on IES scheduling usually simplifies multiple objectives, such as minimizing cost and environmental impact, into a single objective for optimization, or employs heuristic algorithms to solve for the Pareto front.

[0003] Energy Emission Management Systems (IES) need to coordinate the coupled operation of different energy forms, possess the ability to manage uncertainties on both the source and load sides, and balance the flexibility, efficiency, and economy of system operation. Therefore, IES energy dispatch management has become a key technology for achieving carbon emission reduction targets. To balance the contradiction between carbon emission reduction and economic operation, multi-objective optimization has become a key element in formulating IES dispatch schemes.

[0004] The integrated energy system scheduling optimization problem is a multi-objective and multi-constraint optimization problem, mathematically described as follows:

[0005]

[0006] In the formula, f n Let (X) represent the nth objective. Q(X) are the inequality constraints that need to be satisfied, and P(X) are the equality constraints that need to be satisfied.

[0007] Generally, the objective function of the comprehensive energy optimization problem can be summarized into three types of objective functions, namely:

[0008] i) Economic objectives. Economic objectives are generally system operating costs. Operating costs encompass the total lifecycle costs of equipment operation and external energy purchases.

[0009] ii) Reliability Objectives. For IES (Environmental Engineering Systems) that include renewable energy equipment, the ideal operating state is one where the system is self-sufficient and there is no curtailment of wind or solar power. However, due to uncertainties in the system, actual operating conditions often deviate from the scheduling plan. Therefore, the degree of load imbalance within the system is used to reflect the degree of deviation between the scheduling results and the ideal operating state; the lower the degree of load imbalance within the system, the better the performance of the scheduling scheme.

[0010] iii) Environmental objectives. Environmental objectives are relatively easy to calculate and can be reflected in the objective functions of many similar models. For IES optimal scheduling, system carbon emissions are generally considered.

[0011] Common multi-objective optimization methods include linear weighted methods, Pareto front methods, and hierarchical processing methods. Currently, one existing technology for solving the aforementioned IES scheduling optimization problem includes a power dispatch intelligent response method and system based on a large language model. The method involves: constructing a power dispatch large language model; selecting the ChatGLM-6B language model; constructing a power dispatch knowledge graph; power dispatch personnel inputting voice or text-based questions; the power dispatch large language model calling the power dispatch knowledge graph to generate specific commands or answers; and providing feedback to relevant personnel via a display screen and / or audio. By using ChatGLM-6B as the large language model and incorporating a power dispatch knowledge graph into it, intelligent question-and-answer and timely response in the power dispatch field can be achieved, improving the work efficiency of power dispatch personnel and filling knowledge gaps.

[0012] Another existing solution to the aforementioned IES scheduling optimization problem includes a multi-objective scheduling optimization method for hybrid energy systems based on deep reinforcement learning. The method comprises the following steps: Step 1: Establishing a model of an integrated electric-thermal energy system; Step 2: Establishing a model of an integrated electrical energy system; Step 3: Establishing an optimization model for the integrated electric-thermal-gas energy system, with a reasonable structure that uses the heating network and gas supply network as energy storage for the power grid, thereby ensuring smooth grid connection for large-scale wind power, improving the system's capacity to absorb renewable energy, and guaranteeing the stability and economy of grid operation.

[0013] The shortcomings of the existing solutions to the aforementioned IES scheduling optimization problem include: The method of transforming multiple objectives into a single objective typically requires determining parameters such as weights and coefficients to integrate the multiple objectives. However, the determination of these parameters is often subjective and uncertain, making it difficult to find an objective and accurate method. This may lead to the final single-objective result failing to accurately reflect the essential characteristics of the multiple objectives. Furthermore, complex relationships and interactions may exist between the objectives in a multi-objective problem, and simply transforming it into a single objective will result in the loss of much important information. For example, some objectives may be overemphasized or ignored during the transformation process, causing the obtained single-objective solution to perform poorly on other unconsidered objectives. In practical problems, the importance and priority of multiple objectives may change over time or with environmental variations. However, traditional multi-objective to single-objective methods are usually based on fixed parameters and weights, making it difficult to flexibly adapt to such dynamic changes, resulting in poor adaptability and robustness of the solution.

[0014] The Pareto method states that all solutions on the Pareto front are non-inferior, meaning no single solution is superior to another across all objectives. However, this also presents a problem: it's impossible to directly evaluate the superiority or inferiority of solutions on the Pareto front, making it difficult to determine which solution is best suited for the specific problem. In practice, decision-makers often need to select a specific solution on the Pareto front, but lack clear standards and methods for this selection. The methods mentioned above rely heavily on fixed-weight control, and in particular, they cannot provide direct adjustments based on human language rules and preferences. Summary of the Invention

[0015] Embodiments of the present invention provide a method and apparatus for multi-objective scheduling of integrated energy systems guided by rule language, so as to effectively guide IES scheduling by utilizing human multi-objective preferences.

[0016] To achieve the above objectives, the present invention adopts the following technical solution.

[0017] According to one aspect of the present invention, a multi-objective scheduling method for an integrated energy system guided by a rule-based language is provided, characterized in that it includes:

[0018] Establish a mathematical model for multi-objective scheduling of the integrated energy system (IES);

[0019] By combining the large language model LLM, the mathematical model of IES multi-objective scheduling optimization is transformed into a Markov decision process (MDP) to construct an LLM agent for multi-objective guided interaction.

[0020] The LLM agent uses the Multi-Objective Deep Deterministic Policy Gradient Algorithm (DDPG) to solve the MDP process of IES multi-objective scheduling optimization, thereby obtaining the decision scheme for IES multi-objective scheduling.

[0021] Preferably, the mathematical model for establishing IES multi-objective scheduling includes:

[0022] Considering the objectives of economy, reliability, and environmental protection, a mathematical model for IES multi-objective scheduling is constructed, and the objective function of the mathematical model is set as shown in equation (1):

[0023]

[0024] In the formula, p HB ,p EB ,p BES For CHP, HB, EB, and BES power; η BES Q BES For BES efficiency and capacity; C buy C NG The unit cost of purchasing electricity / natural gas; p buy,t M NG,t For the quantity of electricity / natural gas purchased; C CHP C HB C EB For the operation and maintenance costs of CHP, HB, and EB. Emission grid Emission NG Carbon emissions per unit of electricity / natural gas. load,e,t p load,h,t For electricity / heat load demand;

[0025] Considering the IES system balance constraints and the operational constraints of various types of generating units and lines, the constraints for IES multi-objective scheduling are determined, including:

[0026] IES system equilibrium constraints:

[0027]

[0028] Line constraints:

[0029] |P grid,t |≤P grid,max M NG,t ≤M NG max (3)

[0030] Operating constraints for various types of generating units:

[0031]

[0032] In the formula, p CHP ,pHB ,p EB ,p BES Power ratings for CHP, HB, EB, and BES;

[0033]

[0034] In the formula, η BES Q BES For BES efficiency and capacity.

[0035] Preferably, the process of transforming the mathematical model of IES multi-objective scheduling optimization into MDP by combining LLM includes:

[0036] The mathematical model of IES multi-objective scheduling optimization is transformed into an MDP process, defining the state space, action space, and reward function of the MDP process, including:

[0037] Define the state space:

[0038]

[0039] Define the action space:

[0040]

[0041] The reward function is defined as consisting of an objective function and constraints / penalties. The objective function is constructed by calculating economic costs, the degree of load imbalance within the system, and carbon emissions. The constraints / penalties are the penalties imposed on the agent for violating constraints.

[0042] R(n)=R t (n)+R P (n) (9)

[0043] In the formula: R(n) is the reward function obtained from the nth power generation plan, R t (n) represents the objective function reward obtained from the nth power generation plan, Rn P (n) represents the constraint penalty obtained from the nth power generation plan;

[0044] The objective function part of the MDP process is obtained as follows:

[0045] R t (n)=―λ var ·σ 2 (n)―λ t ·T(n)―λ m ·M(n) (10)

[0046] In the formula: λ var λ is the scaling factor for the economic cost function. t λ is the scaling factor for the function of load imbalance within the system. mThis is the scaling factor for the carbon emissions function;

[0047] The constraint penalties for the MDP process are:

[0048] R P =―F B (P max +P soc +P load (11)

[0049] In the formula: F B To constrain the scaling factor of the penalty function, P max P is a penalty for various generating units and lines exceeding operating constraints. mis As a penalty for violating the charging and discharging constraints of the energy storage system, P con This becomes a penalty for violating the balance constraint.

[0050] Preferably, the construction of the LLM agent for multi-objective guided interaction includes:

[0051] The training of the DRL agent is guided by dialogue with the LLM agent. The background c and the question q are preset according to the content of the dialogue with the LLM agent. The background c includes the rules and regulations for IES multi-objective scheduling, and the question q includes the IES multi-objective scheduling results and the weighting coefficient of the reward function.

[0052] The LLM agent uses the concept of Token x to model text. The LLM agent's answer comes from the distribution of a generative model:

[0053]

[0054] Where x1, x2, ..., x n It is a series of tokens obtained from the vocabulary by applying probabilistic chain rules;

[0055] Tokens are obtained through iterative sampling x i+1 and iteratively change x i+1 Input model with sample x i+2 To generate:

[0056]

[0057] Sample sequence x i+1 ,...,x i+n The generated text is the output of the LLM agent. The output of the LLM agent is parsed into numerical scores of the weights of multiple objective functions, i.e.:

[0058] w i (c,q i ) = parse W {xi+1 ,…,x i+n |a,s,c,q i} (14)

[0059] a is the action space (Formula 8); s is the state space (Formula 7); c is the preset background; q is the question; i is the dialogue turn; parse W The function represents the answer generated by the LLM agent within the given action space, state space, context, and problem.

[0060] Quantifying the rewards and penalties for DRL agents:

[0061] R target =―∑ i w i (a,s,z,q j )·Q i (s,a) (15)

[0062] Among them, R target Represents a target output with weighted multiple rewards, and a quantitative DRL agent reward.

[0063] Preferably, the step of solving the MDP process of IES multi-objective scheduling optimization using the LLM agent with the Multi-Objective Deep Deterministic Policy Gradient Algorithm (DDPG) to obtain the decision scheme for IES multi-objective scheduling includes:

[0064] The multi-objective DDPG algorithm is used to solve the MDP process of IES multi-objective scheduling optimization. The DDPG algorithm is defined by one Actor network, multiple Critic networks, target network, loss function and empirical replay part.

[0065] Multiple reward functions are introduced into the DDPG algorithm, namely:

[0066] Q(s,a)=[Q1(s,a),Q2(s,a),...,Q m (s,a)] (16)

[0067] The Q-value function of reinforcement learning is represented as Q(s,a), with m objective functions and m Q-values;

[0068] The Actor network learns the optimal policy π(a|s), while the Critic network evaluates the quality of this policy using the Q-function Q(s,a). Its update rule follows the Bellman equation, and the target network has parameters θ. target The update method will gradually converge towards the online network parameter θ.

[0069] Define experience replay, construct a replay storage area, and store the state, action, reward and next state sampled from the environment each time in the replay buffer. The state space is the set of all possible states that the agent can be in, the action space is the set of all actions that the agent can take in each state, the state transition probability describes the probability that the agent will transition to the next state after taking a certain action in a certain state, and the reward function defines the immediate reward that the agent will receive after taking a certain action in a certain state.

[0070] The reinforcement learning reward R is learned through Equations 16 and 15. The agent is guided by language and rules to learn the optimal policy, which is the optimal sequence of actions a to be taken from each state. t :

[0071]

[0072] According to another aspect of the present invention, a multi-objective scheduling device for an integrated energy system guided by a rule-based language is provided, comprising:

[0073] The mathematical model building module is used to establish a mathematical model for the multi-objective scheduling of the Integrated Energy System (IES).

[0074] The LLM agent building module is used to combine the large language model LLM to transform the mathematical model of IES multi-objective scheduling optimization into an MDP process, and build an LLM agent for multi-objective guided interaction.

[0075] The decision scheme acquisition module is used to solve the MDP process of IES multi-objective scheduling optimization by the LLM agent using the multi-objective deep deterministic policy gradient algorithm (DDPG) to obtain the decision scheme of IES multi-objective scheduling.

[0076] Preferably, the mathematical model construction module is specifically used to construct a mathematical model for IES multi-objective scheduling, taking into account economic, reliability, and environmental protection objectives, and setting the objective function of the mathematical model as shown in equation (1):

[0077]

[0078] In the formula, p HB ,p EB ,p BES For CHP, HB, EB, and BES power; η BES Q BES For BES efficiency and capacity; C buy C NG The unit cost of purchasing electricity / natural gas; p buy,t M NG,t For the quantity of electricity / natural gas purchased; C CHP CHB C EB For the operation and maintenance costs of CHP, HB, and EB. Emission grid Emission NG Carbon emissions per unit of electricity / natural gas. load,e,t p load,h,t For electricity / heat load demand;

[0079] Considering the IES system balance constraints and the operational constraints of various types of generating units and lines, the constraints for IES multi-objective scheduling are determined, including:

[0080] IES system equilibrium constraints:

[0081]

[0082] Line constraints:

[0083] |P grid,t |≤P grid,max M NG,t ≤M NG max (3)

[0084] Operating constraints for various types of generating units:

[0085]

[0086] In the formula, p CHP ,p HB ,p EB ,p BES Power ratings for CHP, HB, EB, and BES;

[0087]

[0088] In the formula, η BES Q BES For BES efficiency and capacity.

[0089] Preferably, the LLM agent construction module is specifically used to transform the mathematical model of IES multi-objective scheduling optimization into an MDP process, defining the state space, action space, and reward function of the MDP process, including:

[0090] Define the state space:

[0091]

[0092] Define the action space:

[0093]

[0094] The reward function is defined as consisting of an objective function and constraints / penalties. The objective function is constructed by calculating economic costs, the degree of load imbalance within the system, and carbon emissions. The constraints / penalties are the penalties imposed on the agent for violating constraints.

[0095] R(n)=R t (n)+R P (n) (9)

[0096] In the formula: R(n) is the reward function obtained from the nth power generation plan, R t (n) represents the objective function reward obtained from the nth power generation plan, Rn P (n) represents the constraint penalty obtained from the nth power generation plan;

[0097] The objective function part of the MDP process is obtained as follows:

[0098] R t (n)=―λ var ·σ 2 (n)―λ t ·T(n)―λ m ·M(n) (10)

[0099] In the formula: λ var λ is the scaling factor for the economic cost function. t λ is the scaling factor for the function of load imbalance within the system. m This is the scaling factor for the carbon emissions function;

[0100] The constraint penalties for the MDP process are:

[0101] R P =―F B (P max +P soc +P load (11)

[0102] In the formula: F B To constrain the scaling factor of the penalty function, P max P is a penalty for various generating units and lines exceeding operating constraints. mis As a penalty for violating the charging and discharging constraints of the energy storage system, P con This becomes a penalty for violating balance constraints;

[0103] The training of the DRL agent is guided by dialogue with the LLM agent. The background c and the question q are preset according to the content of the dialogue with the LLM agent. The background c includes the rules and regulations for IES multi-objective scheduling, and the question q includes the IES multi-objective scheduling results and the weighting coefficient of the reward function.

[0104] The LLM agent uses the concept of Token x to model text. The LLM agent's answer comes from the distribution of a generative model:

[0105]

[0106] Where x1, x2, ..., x n It is a series of tokens obtained from the vocabulary by applying probabilistic chain rules;

[0107] Tokens are obtained through iterative sampling x i+1 and iteratively change x i+1 Input model with sample x i+2 To generate:

[0108]

[0109] Sample sequence x i+1 ,...,x i+n The generated text is the output of the LLM agent. The output of the LLM agent is parsed into numerical scores of the weights of multiple objective functions, i.e.:

[0110] w i (c,q i ) = parse W {x i+1 ,…,x i+n |a,s,c,q i} (14)

[0111] a is the action space (Formula 8); s is the state space (Formula 7); c is the preset background; q is the question; i is the dialogue turn; parse W The function represents the answer generated by the LLM agent within the given action space, state space, context, and problem.

[0112] Quantifying the rewards and penalties for DRL agents:

[0113] R target =―∑ i w i (a,s,z,q j )·Q i (s,a) (15)

[0114] Among them, R target Represents a target output with weighted multiple rewards, and a quantitative DRL agent reward.

[0115] Preferably, the decision scheme acquisition module is specifically used to solve the MDP process of IES multi-objective scheduling optimization using the multi-objective DDPG algorithm, and to define one Actor network, multiple Critic networks, target network, loss function and experience replay part to determine the DDPG algorithm;

[0116] Multiple reward functions are introduced into the DDPG algorithm, namely:

[0117] Q(s,a)=[Q1(s,a),Q2(s,a),...,Q m (s,a)] (16)

[0118] The Q-value function of reinforcement learning is represented as Q(s,a), with m objective functions and m Q-values;

[0119] The Actor network learns the optimal policy π(a|s), while the Critic network evaluates the quality of this policy using the Q-function Q(s,a). Its update rule follows the Bellman equation, and the target network has parameters θ. target The update method will gradually converge towards the online network parameter θ.

[0120] Define experience replay, construct a replay storage area, and store the state, action, reward and next state sampled from the environment each time in the replay buffer. The state space is the set of all possible states that the agent can be in, the action space is the set of all actions that the agent can take in each state, the state transition probability describes the probability that the agent will transition to the next state after taking a certain action in a certain state, and the reward function defines the immediate reward that the agent will receive after taking a certain action in a certain state.

[0121] The reinforcement learning reward R is learned through Equations 16 and 15. The agent is guided by language and rules to learn the optimal policy, which is the optimal sequence of actions a to be taken from each state. t :

[0122]

[0123] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the multi-objective scheduling method for an integrated energy system guided by a rule-based language.

[0124] As can be seen from the technical solutions provided by the embodiments of the present invention above, the present invention, by combining LLM and deep reinforcement learning models, can better realize the guidance of human multi-objective preferences in the IES scheduling optimization process, and provide theoretical and technical support for scheduling departments and personnel to arrange actual power grid generation plans.

[0125] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0126] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments 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.

[0127] Figure 1 The flowchart of a multi-objective scheduling method for an integrated energy system guided by rule language, which utilizes GPT (Generative Pre-trained Transformer) and DRL (Deep Reinforcement Learning) in an embodiment of the present invention, is provided.

[0128] Figure 2 This is a schematic diagram of prompt words for the IES multi-target JSON generation problem provided in an embodiment of the present invention;

[0129] Figure 3 This is a schematic diagram of the weighted inference result of an agent provided in an embodiment of the present invention. Detailed Implementation

[0130] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0131] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0132] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0133] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0134] This invention focuses on LLM (Large Language Model) technology, proposes a method to simulate human evaluation of multiple objectives, and combines it with DRL (Deep Reinforcement Learning) to propose a comprehensive energy system multi-objective scheduling method that considers multiple objective factors such as operating costs, carbon emissions, and reliability.

[0135] This invention aims to simulate the human evaluation process of multiple objectives using LLM (Limited Learning Model) to train and balance different objectives in IES (Independent Evaluator) scheduling in real time. By constructing and training a DRL (Digital Relationship Management) agent, it solves multi-objective IES scheduling guided by knowledge rules in real time and provides humans with adjustment strategies that offer interpretable language output for different objectives.

[0136] The flowchart of a multi-objective scheduling method for an integrated energy system guided by rule language, provided by this invention, is shown below. Figure 1 As shown, the processing steps include the following:

[0137] Step S101: Establish a mathematical model for IES multi-objective scheduling.

[0138] Step S102: Combine the mathematical model of IES multi-objective scheduling optimization with LLM to perform MDP (Markov Decision Process) modeling, and transform the mathematical model of IES multi-objective scheduling optimization into an MDP process.

[0139] Step S103: Solve the MDP process of IES multi-objective scheduling optimization using the multi-objective DDPG (Deep Deterministic Policy Gradient) algorithm to obtain the decision scheme for IES multi-objective scheduling.

[0140] Step S104: Verify the effectiveness of the proposed method for multi-objective scheduling decision scheme of IES using a certain electrothermal IES system.

[0141] Specifically, S101 above includes the following sub-steps:

[0142] S1011, considering the objectives of economy, reliability and environmental protection, the objective function of IES multi-objective scheduling is determined as shown in equation (1):

[0143]

[0144] In the formula, p HB ,p EB ,p BES For CHP, HB, EB, and BES power; η BES Q BES For BES efficiency and capacity;

[0145] C buy C NG The unit cost of purchasing electricity / natural gas; p buy,t M NG,t For the quantity of electricity / natural gas purchased; C CHP ,

[0146] C HB C EB For the operation and maintenance costs of CHP, HB, and EB; Emission grid Emission NG Carbon emissions per unit of electricity / natural gas; p load,e,t p load,h,t For electricity / heat load demand;

[0147] S1012, considering the IES system balance constraints and the operational constraints of various types of units and lines, determine the constraints for IES multi-objective scheduling, including:

[0148] IES system equilibrium constraints:

[0149]

[0150] Line constraints:

[0151] |P grid,t |≤P grid,max M NG,t ≤M NG max (3)

[0152] Operating constraints for various types of generating units:

[0153]

[0154] In the formula, p CHP ,p HB ,p EB ,p BES Power for CHP, HB, EB, and BES.

[0155]

[0156] In the formula, η BES Q BES For BES efficiency and capacity.

[0157] Specifically, S102 above includes the following sub-steps:

[0158] S1021 transforms the mathematical model of IES multi-objective scheduling optimization into a Markov decision process, defining the state space, action space, and reward function. This includes:

[0159] Define the state space:

[0160]

[0161] Define the action space:

[0162]

[0163] The reward function for an agent should be divided into two parts: an objective function, which is composed of calculations based on economic costs, the degree of load imbalance within the system, and carbon emissions; and a penalty function, which mainly penalizes the agent for violating constraints. Adding the reward function and the penalty function together yields the following reward function:

[0164] R(n)=R t (n)+RP (n) (9)

[0165] In the formula: R(n) is the reward function obtained from the nth power generation plan, R t (n) represents the objective function reward obtained from the nth power generation plan, Rn P (n) represents the constraint penalty obtained from the nth power generation plan.

[0166] Based on this, scaling by a certain proportion yields the objective function part as follows:

[0167] R t (n)=―λ var ·σ 2 (n)―λ t ·T(n)―λ m ·M(n) (10)

[0168] In the formula: λ var λ is the scaling factor for the economic cost function. t λ is the scaling factor for the function of load imbalance within the system. m is the scaling factor for the carbon emissions function.

[0169] The constraints and penalties are as follows:

[0170] R P =―F B (P max +P soc +P load (11)

[0171] In the formula: F B To constrain the scaling factor of the penalty function, P max P is a penalty for various generating units and lines exceeding operating constraints. mis As a penalty for violating the charging and discharging constraints of the energy storage system, P con This becomes a penalty for violating the balance constraint.

[0172] S1022, Construct an LLM agent for multi-objective guided interaction.

[0173] After transforming the mathematical model of IES multi-objective scheduling optimization into an MDP process, an LLM agent can be used to derive the MDP process. The DRL agent can be trained by engaging in dialogue between humans and the LLM agent, leveraging human multi-objective preferences and rule-based language guidance.

[0174] The LLM agent uses the concept of Token x to model text, i.e., a pre-set background c and a question q. The LLM agent's answer comes from a distribution derived from a generative model:

[0175]

[0176] Where x1,x2,...,x n It is a series of tokens obtained from the vocabulary by applying probabilistic chain rules.

[0177] Tokens are obtained through iterative sampling x i+1 and iteratively set x i+1 Input model with sample x i+2 To generate:

[0178]

[0179] Sample sequence x i+1 ,...,x i+n The generated text is the output of the LLM agent and can be formatted as JavaScript Object Notation (i.e., JSON).

[0180] Given a preset background c and a question q, an input token is defined. Both background c and question q represent the content of a dialogue between a human and an LLM agent. Background c mainly refers to the rules and regulations used in IES multi-objective scheduling. Question q mainly represents the current IES multi-objective scheduling results and the weighting coefficients of the reward function.

[0181] The output JSON can be parsed into numerical scores of the weights of multiple objective functions, i.e.:

[0182] w i (c,q i ) = parse W {x i+1 ,…,x i+n |a,s,c,q i} (14)

[0183] a is the action space (Formula 8); s is the state space (Formula 7); c is the preset background; q is the question; i is the dialogue turn; parse W A function represents the answer generated by an LLM agent within the given action space, state space, context, and problem.

[0184] The parsing function converts the LLM answer into numerical values ​​with string explanations. By integrating the parsed explanations into the rewards and constraints, the LLM answer output has two parts: one is the weights of each objective in the multi-objective optimization problem. The weights, presented as text by the LLM, are converted into numerical values ​​for each objective weight using JSON. These objective weights are used to calculate the rewards and penalties in the DRL agent (i.e., Equation 15). The other part is the LLM's explanation of the multi-objective problem and the weights—that is, why the LLM agent gives these weights.

[0185] The rewards and penalties for violating constraints for the DRL agent are quantified as follows:

[0186] R target =―∑ i w i (a,s,z,q j )·Q i (s,a) (15)

[0187] Among them, R target Represents a target output with weighted multiple rewards, and a quantitative DRL agent reward.

[0188] Specifically, step S103 above includes the following sub-steps:

[0189] The multi-objective scheduling optimization (MDP) process of IES is solved using the multi-objective DDPG algorithm, and the solution yields the action space at that moment.

[0190]

[0191] include:

[0192] The DDPG algorithm is determined by defining one Actor network, multiple Critic networks, a target network, a loss function, and an empirical replay component.

[0193] Multiple reward functions are introduced into the DDPG algorithm, namely:

[0194] Q(s,a)=[Q1(s,a),Q2(s,a),...,Q m (s,a)] (16)

[0195] The Q-value function in reinforcement learning is represented as Q(s,a). Since it is a multi-objective problem, there are m objective functions, and therefore m Q-values.

[0196] The Actor network learns the optimal policy π(a|s), while the Critic network evaluates the quality of the policy based on the Q function Q(s,a), and its update rule follows the Bellman equation.

[0197] target network parameters θ target By gradually aligning with the online network parameter θ using a soft update approach, DDPG's ability to find near-optimal strategies in complex IES scheduling environments is improved.

[0198] Define experience replay and construct a replay storage area to store the quadruple data (state, action, reward, next state) obtained from each sampling of the environment into the replay buffer.

[0199] MDP is a mathematical framework for describing sequential decision problems. It consists of four main elements: state space (S), action space (A), state transition probabilities (P), and reward function (R). The state space is the set of all possible states that an agent can be in; the action space is the set of all actions that the agent can take in each state; the state transition probabilities describe the probability that the agent will transition to the next state after taking an action in a given state; and the reward function defines the immediate reward that the agent receives after taking an action in a given state.

[0200] Formulas 16 and 15 implement the reinforcement learning reward R. The reward function is a key factor guiding the agent's behavior. It provides the agent with a goal-oriented signal, telling it which behaviors are "good" and which are "bad." In MDP, the agent's goal is to maximize long-term cumulative reward. Through the reinforcement learning reward R learned using Formulas 16 and 15, this invention can guide the agent to learn the optimal policy through language and rules, i.e., the optimal sequence of actions to take starting from each state.

[0201] Specifically, S104 above includes the following steps.

[0202] The LLM agent, based on ChatGLM-4-9B and programmed in Python, was tested on a computer using an NVIDIA RTX A5000 graphics card and an Intel(R)Xeon(R)W-2295CPU@3.00GHz processor.

[0203] The Chain of Thought Prompt and Few-shot Prompt methods are used to ask the LLM agent questions q. That is, the LLM model is provided with a small set of examples and asked to reason step by step to improve its performance on weight generation problems.

[0204] To verify the effectiveness of the proposed method, a case study was conducted on the IES multi-target JSON generation problem, with specific hints as follows: Figure 2As shown. It is known that the weights of each objective in the previous round were 1 / 3. After LLM analysis of the objective weights, the current round state, and the preset multi-objective requirement background c, the agent obtains the following... Figure 3 The weighted inference results are shown, along with a human-understandable explanation.

[0205] This invention also provides a multi-objective scheduling device for an integrated energy system guided by rule-based language, comprising:

[0206] The mathematical model building module is used to establish a mathematical model for the multi-objective scheduling of the Integrated Energy System (IES).

[0207] The LLM agent building module is used to combine the large language model LLM to transform the mathematical model of IES multi-objective scheduling optimization into an MDP process, and build an LLM agent for multi-objective guided interaction.

[0208] The decision scheme acquisition module is used to solve the MDP process of IES multi-objective scheduling optimization by the LLM agent using the multi-objective deep deterministic policy gradient algorithm (DDPG) to obtain the decision scheme of IES multi-objective scheduling.

[0209] The mathematical model construction module is specifically used to construct a mathematical model for IES multi-objective scheduling, taking into account economic, reliability, and environmental objectives. The objective function of the mathematical model is set as shown in equation (1):

[0210]

[0211] In the formula, p HB ,p EB ,p BES For CHP, HB, EB, and BES power; η BES Q BES For BES efficiency and capacity; C buy C NG The unit cost of purchasing electricity / natural gas; p buy,t M NG,t For the quantity of electricity / natural gas purchased; C CHP C HB C EB For the operation and maintenance costs of CHP, HB, and EB. Emission grid Emission NG Carbon emissions per unit of electricity / natural gas. load,e,t p load,h,t For electricity / heat load demand;

[0212] Considering the IES system balance constraints and the operational constraints of various types of generating units and lines, the constraints for IES multi-objective scheduling are determined, including:

[0213] IES system equilibrium constraints:

[0214]

[0215] Line constraints:

[0216] |P grid,t |≤P grid,max M NG,t ≤M NG,max (3)

[0217] Operating constraints for various types of generating units:

[0218]

[0219] In the formula, p CHP ,p HB ,p EB ,p BES Power ratings for CHP, HB, EB, and BES;

[0220]

[0221] In the formula, η BES Q BES For BES efficiency and capacity.

[0222] The LLM agent construction module is specifically used to transform the mathematical model of IES multi-objective scheduling optimization into an MDP process, defining the state space, action space, and reward function of the MDP process, including:

[0223] Define the state space:

[0224]

[0225] Define the action space:

[0226]

[0227] The reward function is defined as consisting of an objective function and constraints / penalties. The objective function is constructed by calculating economic costs, the degree of load imbalance within the system, and carbon emissions. The constraints / penalties are the penalties imposed on the agent for violating constraints.

[0228] R(n)=R t (n)+R P (n) (9)

[0229] In the formula: R(n) is the reward function obtained from the nth power generation plan, R t (n) represents the objective function reward obtained from the nth power generation plan, Rn P (n) represents the constraint penalty obtained from the nth power generation plan;

[0230] The objective function part of the MDP process is obtained as follows:

[0231] R t (n)=―λ var ·σ 2 (n)―λ t ·T(n)―λ m ·M(n) (10)

[0232] In the formula: λ var λ is the scaling factor for the economic cost function. t λ is the scaling factor for the function of load imbalance within the system. m This is the scaling factor for the carbon emissions function;

[0233] The constraint penalties for the MDP process are:

[0234] R P =―F B (P max +P soc +P load (11)

[0235] In the formula: F B To constrain the scaling factor of the penalty function, P max P is a penalty for various generating units and lines exceeding operating constraints. mis As a penalty for violating the charging and discharging constraints of the energy storage system, P con This becomes a penalty for violating balance constraints;

[0236] The training of the DRL agent is guided by dialogue with the LLM agent. The background c and the question q are preset according to the content of the dialogue with the LLM agent. The background c includes the rules and regulations for IES multi-objective scheduling, and the question q includes the IES multi-objective scheduling results and the weighting coefficient of the reward function.

[0237] The LLM agent uses the concept of Token x to model text. The LLM agent's answer comes from the distribution of a generative model:

[0238]

[0239] Where x1, x2, ..., x n It is a series of tokens obtained from the vocabulary by applying probabilistic chain rules;

[0240] Tokens are obtained through iterative sampling x i+1 and iteratively change x i+1 Input model with sample x i+2 To generate:

[0241]

[0242] Sample sequence x i+1 ,…,x i+n The generated text is the output of the LLM agent. The output of the LLM agent is parsed into numerical scores of the weights of multiple objective functions, i.e.:

[0243] w i (c,q i ) = parse W {x i+1 ,…,x i+n |a,s,c,q i} (14)

[0244] a is the action space (Formula 8); s is the state space (Formula 7); c is the preset background; q is the question; i is the dialogue turn; parse W The function represents the answer generated by the LLM agent within the given action space, state space, context, and problem.

[0245] Quantifying the rewards and penalties for DRL agents:

[0246] R target =―∑ i w i (a,s,z,q j )·Q i (s,a) (15)

[0247] Among them, R target Represents a target output with weighted multiple rewards, and a quantitative DRL agent reward.

[0248] The decision scheme acquisition module is specifically used to solve the MDP process of IES multi-objective scheduling optimization using the multi-objective DDPG algorithm, and defines one Actor network, multiple Critic networks, target network, loss function and experience replay part to determine the DDPG algorithm;

[0249] Multiple reward functions are introduced into the DDPG algorithm, namely:

[0250] Q(s,a)=[Q1(s,a),Q2(s,a),...,Q m (s,a)] (16)

[0251] The Q-value function of reinforcement learning is represented as Q(s,a), with m objective functions and m Q-values;

[0252] The Actor network learns the optimal policy π(a|s), while the Critic network evaluates the quality of this policy using the Q-function Q(s,a). Its update rule follows the Bellman equation, and the target network has parameters θ. target The update method will gradually converge towards the online network parameter θ.

[0253] Define experience replay, construct a replay storage area, and store the state, action, reward and next state sampled from the environment each time in the replay buffer. The state space is the set of all possible states that the agent can be in, the action space is the set of all actions that the agent can take in each state, the state transition probability describes the probability that the agent will transition to the next state after taking a certain action in a certain state, and the reward function defines the immediate reward that the agent will receive after taking a certain action in a certain state.

[0254] The reinforcement learning reward R is learned through Equations 16 and 15. The agent is guided by language and rules to learn the optimal policy, which is the optimal sequence of actions a to be taken from each state. t :

[0255]

[0256] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the multi-objective scheduling method for an integrated energy system guided by a rule-based language as described above.

[0257] In summary, this invention provides a multi-objective scheduling method for integrated energy systems guided by rule-based language using GPT and DRL, effectively solving the problem that quantitative modeling research on multi-objective scheduling struggles to effectively simulate the comprehensive thinking process of humans in a loop regarding multiple objectives. The model and method proposed in this invention can better realize the guidance of human multi-objective preferences, providing theoretical and technical support for scheduling departments and personnel to arrange actual power grid generation plans.

[0258] This method can quickly adjust the weights and priorities of multiple objectives based on real-time data and feedback. In practical applications, when the environment or conditions of the problem change, this method can promptly detect and adjust the optimization strategy of multiple objectives accordingly to adapt to the new situation. This dynamic adaptability can improve the effectiveness and practicality of multi-objective optimization.

[0259] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0260] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0261] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0262] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-objective scheduling method for an integrated energy system guided by rule-based language, characterized in that, include: Establish a mathematical model for multi-objective scheduling of the integrated energy system (IES); By combining the large language model LLM, the mathematical model of IES multi-objective scheduling optimization is transformed into a Markov decision process (MDP) to construct an LLM agent for multi-objective guided interaction. The LLM agent uses the Multi-Objective Deep Deterministic Policy Gradient Algorithm (DDPG) to solve the MDP process of IES multi-objective scheduling optimization, thereby obtaining the decision scheme for IES multi-objective scheduling. The process of transforming the mathematical model of IES multi-objective scheduling optimization into an MDP process by combining LLM includes: The mathematical model of IES multi-objective scheduling optimization is transformed into an MDP process, defining the state space, action space, and reward function of the MDP process, including: Define the state space: （7） Define the action space: （8） The reward function is defined as consisting of an objective function and constraints / penalties. The objective function is constructed by calculating economic costs, the degree of load imbalance within the system, and carbon emissions. The constraints / penalties are the penalties imposed on the agent for violating constraints. （9） In the formula: For the first n The reward function obtained from the power generation plan, For the first n The objective function reward obtained from the power generation plan, For the first n Constraints and penalties imposed on the power generation plan; The objective function part of the MDP process is obtained as follows: （10） In the formula: is the scaling factor for the economic cost function. This is the scaling factor for the function of the degree of load imbalance within the system. The scaling factor for the carbon emissions function; The constraint penalties for the MDP process are: （11） In the formula: To constrain the scaling factor of the penalty function, Penalties for various generating units and lines exceeding operational constraints. Penalties for violating the charging and discharging constraints of energy storage systems, This becomes a penalty for violating balance constraints; The construction of the LLM agent for multi-objective guided interaction includes: The training of the DRL agent is guided by dialogue with the LLM agent. The background c and the question q are preset according to the content of the dialogue with the LLM agent. The background c includes the rules and regulations for IES multi-objective scheduling, and the question q includes the IES multi-objective scheduling results and the weighting coefficient of the reward function. LLM agents utilize tokens x Using the concept of text modeling, the LLM agent's answers come from a distribution of a generative model: （12） wherein, is a series of tokens Token obtained from the vocabulary by applying the probability chain rule; Tokens are generated by iterating sampling and iteratively inputting the model to sample from: （13） Sampling sequence The generated text is the output of the LLM agent, and the output of the LLM agent is parsed into numerical scores for a plurality of objective function weights, i.e.: （14） It is the action space, Equation 8; It is the state space, Equation 7; It is a preset background; It's asking a question; It refers to the number of dialogue rounds; The function represents the answer generated by the LLM agent within the given action space, state space, context, and problem. Quantifying the rewards and penalties for DRL agents: （15） wherein, representing a target output containing a weighted plurality of rewards, quantitative DRL agent rewards; The process of solving the MDP process of IES multi-objective scheduling optimization using the LLM agent and the Multi-Objective Deep Deterministic Policy Gradient Algorithm (DDPG) to obtain the decision scheme for IES multi-objective scheduling includes: The multi-objective DDPG algorithm is used to solve the MDP process of IES multi-objective scheduling optimization. The DDPG algorithm is defined by one Actor network, multiple Critic networks, target network, loss function and empirical replay part. Multiple reward functions are introduced into the DDPG algorithm, namely: （16） The Q-value function of reinforcement learning is represented as There are m objective functions, and there are m Q-values; Actor Network Learning Optimal Strategy The Critic network, on the other hand, is based on the Q function. To evaluate the effectiveness of this strategy, its update rule follows the Bellman equation, and the target network parameters... Gradually update online network parameters using a soft update method. Approach; Define experience replay, construct a replay storage area, and store the state, action, reward and next state sampled from the environment each time in the replay buffer. The state space is the set of all possible states that the agent can be in, the action space is the set of all actions that the agent can take in each state, the state transition probability describes the probability that the agent will transition to the next state after taking a certain action in a certain state, and the reward function defines the immediate reward that the agent will receive after taking a certain action in a certain state. The reinforcement learning reward R is learned through Equations 16 and 15. The agent is guided by language and rules to learn the optimal policy, which is the optimal sequence of actions to take starting from each state. : （8）。 2. The method of claim 1, wherein, The mathematical model for establishing IES multi-objective scheduling includes: Considering the objectives of economy, reliability, and environmental protection, a mathematical model for IES multi-objective scheduling is constructed, and the objective function of the mathematical model is set as shown in equation (1): （1） In the formula, , , Power ratings for CHP, HB, EB, and BES; , For BES efficiency and capacity; , The unit cost of purchasing electricity / natural gas; , For the quantity of electricity / natural gas purchased; , , For the operation and maintenance costs of CHP, HB, and EB, , Carbon emissions per unit of electricity / natural gas , For electricity / heat load demand; Considering the IES system balance constraints and the operational constraints of various types of generating units and lines, the constraints for IES multi-objective scheduling are determined, including: IES system equilibrium constraints: （2） Line constraints: （3） Operating constraints for various types of generating units: （4） In the formula, , , , Power ratings for CHP, HB, EB, and BES; （5） （6） In the formula, , BES efficiency and capacity.

3. A rule language guided integrated energy system multi-objective scheduling apparatus, characterized in that, include: The mathematical model building module is used to establish a mathematical model for the multi-objective scheduling of the Integrated Energy System (IES). The LLM agent building module is used to combine the large language model LLM to transform the mathematical model of IES multi-objective scheduling optimization into an MDP process, and build an LLM agent for multi-objective guided interaction. The decision scheme acquisition module is used to solve the MDP process of IES multi-objective scheduling optimization by the LLM agent using the multi-objective deep deterministic policy gradient algorithm (DDPG) to obtain the decision scheme of IES multi-objective scheduling. The LLM agent construction module is specifically used to transform the mathematical model of IES multi-objective scheduling optimization into an MDP process, defining the state space, action space, and reward function of the MDP process, including: Define the state space: （7） Define the action space: （8） The reward function is defined as consisting of an objective function and constraints / penalties. The objective function is constructed by calculating economic costs, the degree of load imbalance within the system, and carbon emissions. The constraints / penalties are the penalties imposed on the agent for violating constraints. （9） In the formula: For the first n The reward function obtained from the power generation plan, For the first n The objective function reward obtained from the power generation plan, For the first n Constraints and penalties imposed on the power generation plan; The objective function part of the MDP process is obtained as follows: （10） In the formula: is the scaling factor for the economic cost function. This is the scaling factor for the function of the degree of load imbalance within the system. The scaling factor for the carbon emissions function; The constraint penalties for the MDP process are: （11） In the formula: To constrain the scaling factor of the penalty function, Penalties for various generating units and lines exceeding operational constraints. Penalties for violating the charging and discharging constraints of energy storage systems, This becomes a penalty for violating balance constraints; The training of the DRL agent is guided by dialogue with the LLM agent. The background c and the question q are preset according to the content of the dialogue with the LLM agent. The background c includes the rules and regulations for IES multi-objective scheduling, and the question q includes the IES multi-objective scheduling results and the weighting coefficient of the reward function. LLM agents model text using the concept of Tokens x The answer from an LLM agent comes from a distribution of a generative model: （12） in, It is a series of tokens obtained from the vocabulary by applying probabilistic chain rules; Tokens are generated by iterating sampling and iteratively inputting the model to sample from （13） Sampling sequence The generated text is the output of the LLM agent, and the output of the LLM agent is parsed into numerical scores for a plurality of objective function weights, i.e.: （14） It is the action space, Equation 8; It is the state space, Equation 7; It is a preset background; It's asking a question; It refers to the number of dialogue rounds; The function represents the answer generated by the LLM agent within the given action space, state space, context, and problem. Quantifying the rewards and penalties for DRL agents: （15） in, Represents a target output with weighted multiple rewards, and a quantitative DRL agent reward; The decision scheme acquisition module is specifically used to solve the MDP process of IES multi-objective scheduling optimization using the multi-objective DDPG algorithm, and defines one Actor network, multiple Critic networks, target network, loss function and experience replay part to determine the DDPG algorithm; Multiple reward functions are introduced into the DDPG algorithm, namely: （16） The Q-value function of reinforcement learning is expressed as: There are m objective functions and m Q values; Actor Network Learning Optimal Strategy The Critic network, on the other hand, is based on the Q function. To evaluate the effectiveness of this strategy, its update rule follows the Bellman equation, and the target network parameters... Gradually update online network parameters using a soft update method. Approach; Define experience replay, construct a replay storage area, and store the state, action, reward and next state sampled from the environment each time in the replay buffer. The state space is the set of all possible states that the agent can be in, the action space is the set of all actions that the agent can take in each state, the state transition probability describes the probability that the agent will transition to the next state after taking a certain action in a certain state, and the reward function defines the immediate reward that the agent will receive after taking a certain action in a certain state. The reinforcement learning reward R is learned through Equations 16 and 15. The agent is guided by language and rules to learn the optimal policy, which is the optimal sequence of actions to take starting from each state. : （8）。 4. The apparatus according to claim 3, characterized in that, The mathematical model construction module is specifically used to construct a mathematical model for IES multi-objective scheduling, taking into account economic, reliability, and environmental objectives. The objective function of the mathematical model is set as shown in equation (1): （1） In the formula, , , Power ratings for CHP, HB, EB, and BES; , For BES efficiency and capacity; , The unit cost of purchasing electricity / natural gas; , For the quantity of electricity / natural gas purchased; , , For the operation and maintenance costs of CHP, HB, and EB, , Carbon emissions per unit of electricity / natural gas , For electricity / heat load demand; Considering the IES system balance constraints and the operational constraints of various types of generating units and lines, the constraints for IES multi-objective scheduling are determined, including: IES system equilibrium constraints: （2） Line constraints: （3） Operating constraints for various types of generating units: （4） In the formula, , , , Power ratings for CHP, HB, EB, and BES; （5） （6） In the formula, , BES efficiency and capacity.

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