Distributed energy system source load coordinated optimization method based on quasi-potential game method

Abstract

The invention discloses a distributed energy system source load coordinated optimization method based on a quasi-potential game method, and the method comprises the steps: constructing a distributed energy system model, inputting system parameters, and predicting renewable energy power generation and initial load demands. In a source side optimization stage, a leader layer potential function of a quasi-potential game is established by taking minimization of source side cost # imgabs0 # as a target, and an initial power generation plan is generated by comprehensively considering economical efficiency and carbon emission constraints; and then, based on a scheduling result, calculating a carbon potential epsilon t of each node and a dynamic carbon emission factor # imgabs1 # of each stage, optimizing a load side response based on an LCDR scheme, constructing a local potential function of a follower layer, reflecting a relationship between a user profit maximization target and carbon emission, and adjusting user behaviors through a distributed decision. And the updated load demand is fed back to the source side, and the source side optimizes the output plan of each unit based on the updated load, so that an iterative process of source side potential function optimization-load side equilibrium response is formed, and an optimal scheduling strategy and scheduling result of the energy supply side are obtained. According to the framework, the global consistency requirement of a traditional potential game is relaxed, independent optimization of source-load two sides under the guidance of respective potential functions is allowed, and a Nash equilibrium state is finally achieved only by ensuring monotonous convergence of total potential energy of a system in an iteration process. According to the method, the convergence advantage of the potential game is reserved, the method is also adapted to the characteristics of a source-load heterogeneous decision subject, efficient consumption of renewable energy and collaborative optimization of carbon emission are realized through bidirectional transmission of the carbon potential signal, and the overall efficiency of the system is remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of distributed energy system source-load optimization, and in particular relates to a distributed energy system source-load coordination optimization method based on a quasi-potential game method. Background Art

[0002] Reducing carbon emissions from the power sector is not only feasible but also essential to combating climate change.

[0003] The deployment of carbon capture and storage (CCS) technology has been recognized as an integral strategy for reducing carbon emissions, and therefore plays a key role in the pursuit of net-zero carbon goals. In the energy sector, CCS technology can be used to transform traditional coal-fired power plants into carbon capture power plants (CCPPs), enabling them to operate flexibly while reducing their own carbon emissions. This enhancement not only significantly increases the utilization of renewable energy systems (RES) but also plays a crucial role in ensuring that the power grid is not forced to consume excess renewable energy output.

[0004] To improve the overall energy efficiency and economic benefits of distributed energy systems (DES), extensive research has been conducted on optimizing the energy side of these systems. Ding et al. discussed a two-stage power dispatch model for hybrid renewable energy systems, examining the impact of ancillary service markets on the distribution of economic benefits, with the goal of improving the sustainability and low-carbon nature of power systems. Zhang et al. developed a carbon recycling system that combines power-to-gas (P2G), carbon capture, and a supercritical CO2 process to improve the energy conversion efficiency of integrated energy systems. Considering uncertainties in global carbon taxes, carbon prices, and load, a two-stage planning model for combined power and natural gas systems demonstrated its effectiveness, robustness, and sensitivity. Other literature has evaluated the effectiveness of combined heat and power plants equipped with various carbon capture technologies. Others have proposed a new concept of a committed carbon emission operating region for integrated energy systems, which can intuitively represent the low-carbon feasible space. Furthermore, a new stochastic optimization scheduling model based on three-dimensional equilibrium has been proposed, providing decision makers with an effective tool for solving multi-objective scheduling problems in DES. These studies have made significant contributions to the low-carbon optimization of DES, but they have all overlooked the impact of load-side responses on the system's low-carbon level.

[0005] Experts emphasized the important role of load-side demand response (DR), particularly in managing energy consumption and enhancing power system resilience. Wu et al. introduced a hierarchical dispatch model for a system of post-combustion carbon capture power plants, designed to provide decarbonization and flexibility across different timeframes. Furthermore, Li et al. demonstrated the efficacy of a comprehensive demand response exchange mechanism that accounts for seasonal variation and uncertainty in emissions reduction and its economic advantages as a novel low-carbon dispatch approach. Chen et al. examined existing carbon trading schemes and proposed a dispatch model that integrates combined heat and power (CHP), CCS, and P2G subsystems, including flexible load participation. This model aims to reduce peak and off-peak load variations, alleviate stress on energy supply equipment, and optimize system operation. Addressing the pervasive uncertainty in the coordinated dispatch of economic and carbon emissions in integrated heat and power systems, Yang et al. designed a multi-objective optimization model that combines CCPPs with multiple energy demand response mechanisms. This approach not only boosts renewable energy output but also significantly reduces CO2 emissions.

[0006] In summary, current research in this field primarily focuses on one-sided modeling and optimization to improve the economic efficiency of DES. However, the inverse relationship between economic dispatch and carbon reduction poses significant challenges to achieving optimal balance between energy and carbon benefits. These studies often fail to fully examine the impact of economic behavior on carbon emissions. This gap is particularly evident in studies specifically addressing source-load coordination, which primarily examine load-side dynamics from an electricity perspective, focusing on price incentives within DR mechanisms, while neglecting carbon emissions. Furthermore, the increasing inclusion of RES and their inherent uncertainties highlight the shortcomings of traditional optimization methods in DES. Wei et al. proposed a coordinated optimization scheduling algorithm to improve the convergence performance of large-scale microgrid P2P trading problems. However, as an improvement on the traditional ADMM, it is often difficult to verify the existence of Nash equilibrium points in its game process. Xu et al. proposed an interactive energy management method for multi-energy microgrids (MEMGs) to simultaneously provide MEMG operators with optimal energy dispatch and pricing strategies. A limitation of this study is that it only considers the Stackelberg game approach with a single leader and a single follower, which has not been effectively applied in actual electricity trading markets. To address these challenges, we introduce a source-load coordination optimization framework for low-carbon economic dispatch that integrates low-carbon demand response (LCDR) and quasi-potential game approaches. Summary of the Invention

[0007] In order to overcome the shortcomings of the existing technology, different from the traditional electricity price driving mechanism, the present invention provides a distributed energy system source-load coordination optimization method based on the quasi-potential game method. The method of the present invention is based on a carbon-centric perspective and establishes a practical LCDR method, combining a hierarchical carbon trading system with a comprehensive carbon quota; the method uses a novel full-node carbon potential calculation to determine the dynamic carbon emission factor (DCEF) of the DES, and by using DCEF as a guiding signal, it aims to guide users towards a low-carbon energy consumption trend, thereby improving the low-carbon economic performance of the load side.

[0008] Within a hierarchical economic optimization framework based on the Stackelberg game, the flexible operation of CCPP on the power supply side and LCDR on the load side is coordinated. The upper layer of the framework operates based on a hierarchical carbon trading model, with the goal of minimizing costs for energy suppliers while optimizing the power generation plans of various generators. The lower layer focuses on maximizing benefits on the load side, adjusting energy consumption plans based on DCEF, and fully leveraging the low-carbon advantages of both parties.

[0009] The original optimization problem of the hierarchical multi-leader and multi-follower Stackelberg game framework is transformed into a quasi-potential game model. The existence of the Nash equilibrium of this game model is proved, and the consistency of the Nash equilibrium solution with the optimal solution of the model is demonstrated. In addition, through benchmark analysis of typical cases, it is found that the solution time of the algorithm in DES of different scales increases linearly, and the time complexity of the algorithm is close to O(n).

[0010] In order to achieve the above object, the technical solution of the present invention is:

[0011] A distributed energy system source-load coordination optimization method based on a quasi-potential game method comprises the following steps:

[0012] S1: Build a distributed energy system model, input system parameters, and predict renewable energy generation and initial load demand. Based on the initial data k=1, Optimize the source side and schedule it. In the source side optimization phase, the source side cost Minimize the leader layer potential function of the quasi-potential game, comprehensively consider economic and carbon emission constraints, and generate the initial power generation plan;

[0013] S2: Establish a quasi-potential game model;

[0014] S3: Load side optimization, calculate the carbon potential ε of each node based on the scheduling results t and the dynamic carbon emission factors at each stage Based on the LCDR scheme, the load-side response is optimized, a local potential function of the follower layer is constructed to reflect the relationship between the user's profit maximization goal and carbon emissions, and user behavior is adjusted through distributed decision-making;

[0015] S4: Update the load demand and transfer it to the source side;

[0016] S5: Source-side optimization: The source optimizes the output plan of each unit based on the updated load to minimize the source-side cost, thus forming an iterative process of "source-side potential function optimization-load-side balanced response" to obtain the optimal scheduling strategy and scheduling results on the energy supply side;

[0017] S6: The system determines whether Nash equilibrium is reached. If so, the system outputs the final optimization result; if not, the system returns to step S2 and re-optimizes based on the updated state information.

[0018] In the present invention, within the distributed energy system, its power supply side is composed of distributed power sources such as wind energy, solar energy, and energy storage. High-carbon emission power plants are transformed into carbon capture power plants. Carbon capture power plants capture the CO2 generated during the power generation process, thereby improving power generation efficiency and reducing the carbon emissions of DES. On the demand side, a low-carbon demand response (LCDR) method is introduced to replace the traditional price-driven demand response.

[0019] The beneficial effects of the present invention are:

[0020] 1. Low-carbon demand response can flexibly adjust load demand in different time periods, and can indirectly guide the formulation of unit output plans that are conducive to reducing carbon emissions and improving the renewable energy absorption rate.

[0021] 2. Using carbon capture equipment to capture carbon dioxide from direct exhaust gases from thermal power units significantly reduces the carbon emissions of the power system and the reduction rate of wind turbines and photovoltaic power generation, but it also increases the total fossil fuel consumption in the system.

[0022] 3. Under the carbon trading environment, carbon capture power plants are considered to be coordinated with low-carbon demand response to low-carbon dispatch, and the output of low-carbon units during off-peak hours is replaced by the output of high-carbon units during peak hours. Compared with the traditional power system, the comprehensive operating costs and total carbon emissions are reduced by 7.2% and 87.7% respectively, with significant emission reduction effects and ensuring the economic efficiency of system operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is an improved IEEE-39 node system.

[0024] Figure 2 is the predicted power for a typical day.

[0025] Figure 3 Comparison of PDR in scene 2 and LCDR in scene 3.

[0026] Figure 4 is the total power output for different scenarios.

[0027] Figure 5 is the renewable energy utilization rate in different scenarios.

[0028] Figure 6 It is a comparison of the carbon emission results after optimization.

[0029] Figure 7 is the carbon emissions under different carbon prices.

[0030] Figure 8 is the total cost under different carbon prices.

[0031] Figure 9 is the carbon capture efficiency of the IEEE-118 node system.

[0032] Figure 10 The present invention is a flow chart of a distributed energy system source-load coordination optimization method based on quasi-potential game method. DETAILED DESCRIPTION

[0033] The present invention will be further described below with reference to the accompanying drawings.

[0034] Reference Figures 1 to 10 A distributed energy system source-load coordination optimization method based on a quasi-potential game method comprises the following steps:

[0035] S1: Construct a distributed energy system model, input system parameters, predict renewable energy generation and initial load demand, based on initial data k = 1, Optimize the scheduling of the source side. In the source side optimization stage, the source side cost Minimize the leader layer potential function of the quasi-potential game, comprehensively consider economic and carbon emission constraints, and generate the initial power generation plan;

[0036] In step S1, the system includes the following components:

[0037] S1-1. Mathematical Model of a Flexible Operation Carbon Capture Power Plant: This approach allows the MEA solution to absorb CO2 during peak load periods and subsequently store it in a dedicated solution reservoir. During off-peak periods, the accumulated CO2 is transferred to a regeneration tower for extraction and capture. This operating strategy significantly improves CO2 capture efficiency, expands the net output range of CCPPs, and increases the utilization of RES. Taking into account the actual power consumption requirements of DES, the energy consumption of CCPPs in flexible operation mode is defined as follows:

[0038]

[0039] 0≤δ i≤1 (5)

[0040] In formula (1) represents the total output power of coal-fired power plant i in period t. When unit i is converted into CCPP, Divided into three categories: Net output Carbon capture energy consumption and fixed energy consumption When unit i represents a conventional coal-fired power plant, and will be 0;

[0041] In equation (2), The total mass of CO2 captured during period t Directly related, ω i represents the coefficient of carbon capture energy consumption, equation (3) explains Including CO2 generated by power generation, Also includes CO2 generated by the solution storage tank, In this case, β i represents the CO2 capture coefficient, δ i represents the split ratio of flue gas, equation (4) expresses and Proportional, e i represents carbon emission intensity, (5) specifies the δ of CCPPs i Should remain in the range of 0 to 1;

[0042] In order to achieve flexible operation modes of CCPPs, a solution storage is introduced in this work, where CO2 is dissolved in the MEA and becomes a liquid compound. The mass of CO2 extracted from the solution storage is calculated based on the volume of the solution. The modeling of this basic component is shown below:

[0043]

[0044] Equation (6) expresses the relationship between CO2 mass and MEA solution volume, represents the MEA solution required by carbon capture power plant i to absorb carbon dioxide during period t, the molar mass of MEA and CO2 ((M mea ) and (M CO2 )) is the key to understanding their interaction. The CO2 absorption efficiency of the absorption tower is expressed as η i In addition, the concentration of MEA solution is expressed as N mea Its density is expressed as D mea Indicates that, the corresponding constraints are as follows:

[0045]

[0046] Equation (7) describes the dynamic volumes of rich and lean solutions in the solution reservoir at any given time t, and represent the volume of rich solution and lean solution of carbon capture power plant i in time period t; (8) establish operating volume limits for rich solution and lean solution, and the capacity of solution storage in each carbon capture power plant is expressed as V i ,Finally, equation (9) stipulates that the volume of the solution should remain unchanged after 24 hours;

[0047] S1-2. Low-Carbon Demand Response Mathematical Model: The LCDR method utilizes DCEF to modify electricity consumption behavior. By guiding users to adjust their electricity usage, LCDR directly impacts the carbon emissions of the DES. While carbon emissions primarily come from sources, loads, especially end users, generate significant amounts of CO2 emissions through their consumption patterns. Users utilize DCEF to understand the indirect carbon emissions associated with their electricity consumption. This not only allows end users to better understand their carbon footprint but also enables comprehensive tracking of emissions within the DES. This insight is crucial for optimizing future energy consumption and can be a valuable tool for reducing the environmental impact of electricity consumption.

[0048] The definition of the LCDR method is detailed below, focusing on its application in DES. At its core, the source side of DES delivers electricity to meet the needs of end users. At the same time, it transfers the responsibility for carbon emissions to users through carbon flows to promote the transfer of responsibility for carbon emissions generated by energy production. This method is based on the theory of carbon emission flow analysis, which cleverly links carbon emissions on the source side with electricity consumption on the load side. The basic concept of this method is to track the carbon footprint of power flows, so that users can recognize the indirect carbon emissions related to their electricity consumption behavior;

[0049] The dynamic carbon emission factor plays an important role in the low-carbon demand response strategy. The dynamic carbon emission factor is calculated by averaging the spatial load based on the carbon potential of each node, expressed as:

[0050]

[0051] represents the carbon emission factor of the power system in period t, Z is the set of all nodes in the power system, is the power load consumption of node j in period t, ε j,t represents the carbon potential of node j in the power system during period t;

[0052] To elaborate on ε j,tThe carbon potential of a power plant is calculated by multiplying the power generation of the power plant by its respective carbon emission intensity. However, this method is improved by adding CCPPs that capture CO2. When CO2 is captured by CCPPs during period t, the carbon potential associated with the nodes connected to these power plants will decrease. Assuming that coal-fired power plant i and renewable energy i are interconnected with node j, the improved carbon potential of this node during period t is expressed in equation (11):

[0053]

[0054] J + represents all nodes connected to node j in the power system, represents the forward power flow from node s to node j during period t, is the power input to node j by coal-fired unit i during period t, is the power input from renewable energy generator i to node j during period t;

[0055] S1-3. Source-side optimization scheduling model:

[0056] S1-3-1. Source-side objective function: The source side includes the output of traditional coal-fired power plants, CCPPs, and RES to meet the total load demand. An optimal scheduling model is established, whose main goal is to minimize the total operating cost of the source side in DES, denoted as

[0057]

[0058] C1 represents the coal consumption cost of coal-fired power plants, C2 represents the total cost of coal-fired unit startup and shutdown, C3 represents the penalty cost for renewable energy reduction, C4 represents the solvent loss cost of carbon capture power plants, and C5 represents the depreciation cost of carbon capture power plants. The detailed formula for each cost component is as follows:

[0059]

[0060] In equation (13), N g The variable X represents the number of coal-fired units. i,t Indicates the on / off status of the i-th coal-fired unit in period t, which can be 0 or 1; a i 、b i and c i is the coal consumption characteristic parameter of coal-fired unit i. In equation (14), τ represents the unit start-up and shutdown cost coefficient, N res represents the number of renewable energy units (i.e. wind turbines (WTs) and photovoltaic (PVs)), and the penalty cost per unit of renewable energy reduction is τ re Given, and represent the predicted and actual power output of the RES unit, respectively. In equation (16), the coefficients Corresponding to the unit solvent loss cost in the CCS process, represents the amount of solvent consumed per ton of CO2 captured, as shown in equation (17), the depreciation rate of CCPP equipment is represented by r, and the cost coefficients of CCS equipment (without solution storage) and with solution storage are represented by τ ccs and τ so Indicates that, finally, Y1 and Y2 refer to the depreciation years of CCS equipment (without solution storage) and with solution storage, respectively;

[0061] The integration of market mechanisms into power system reform is aimed at balancing the system's low-carbon goals and economic development. A stepped carbon trading mechanism has been introduced, with a tiered carbon pricing model and a carbon trading quota system. See Equations (18) and (19) for details. The common goal of these models is to improve the energy efficiency of power generation units and reduce emissions, thereby promoting a broader global trend:

[0062]

[0063] λ represents the carbon trading base price, q represents the carbon emissions exceeding the system quota, l represents the length of the carbon emission interval, α represents the increase in the step-by-step carbon trading price, and E total represents the total carbon emissions of the system, ξ represents the carbon quota coefficient, and C7 in equation (20) describes the carbon emission reduction incentive cost after the source side provides the LCDR method;

[0064] On the source side, based on the carbon reduction incentive price λ and the reduced carbon emissions achieved through the LCDR method Pay carbon reduction incentives to end users on the load side;

[0065] S1-3-2. Source side constraints:

[0066] After the low-carbon demand response, the output of each generator set on the source side is adjusted to meet the real-time demand on the load side. The corresponding power balance constraints are as follows:

[0067]

[0068] Among them, N b Indicates the number of battery energy storage (BES) units, and Respectively represent the charging and discharging power of the i-th BES unit at time t. represents the total load at time t after LCDR;

[0069] The power generation constraints related to the coal-fired units are as follows: constraints (22)-(24) specify the output and operating cycle of the coal-fired units, constraints (25)-(26) define the output power limit of the RES power generation, and finally, constraints (27)-(30) determine the power flow parameters of the DES;

[0070]

[0071]

[0072] θ ref =0 (30)

[0073] and are the minimum and maximum output power of coal-fired unit i, is the maximum ramp rate of coal-fired unit i, and is the minimum startup and shutdown time of coal-fired unit i, is the maximum ramp rate of renewable energy unit i, θ s,t and θ j,t is the voltage phase angle between nodes s and j at time t, z sj is the impedance of the line connecting node s and node j, is the maximum transmission power from node s to node j, Represents the voltage phase angle limit value of node s. θ ref is the equilibrium node voltage phase angle;

[0074] CCPPs are essentially improvements on traditional coal-fired power plants. Therefore, in addition to meeting the constraints previously specified for coal-fired units, it is also crucial to consider the unique energy consumption model and the constraints associated with the CCPPs solution storage. The specific model that controls the flexible operation of CCPPs is detailed in equations (1)-(9). The operating constraints of the BES are detailed in equations (31)-(36). (31) defines the calculation of the BES state of charge (SOC). Equations (32)-(33) set the charging and discharging power limits. Equation (34) indicates that the BES is prohibited from charging and discharging simultaneously. The SOC limit is specified by equation (35). Finally, equation (36) ensures that the SOC capacity remains unchanged after the end of the dispatch period.

[0075]

[0076]

[0077] S i,0 =S i,24 ,i∈N b (36)

[0078] Among them, S i,t is the state of charge of the i-th energy storage battery at time t, and is the charging and discharging efficiency of the i-th energy storage battery, and represents the charging and discharging power of the i-th energy storage battery at time t, and is the charge and discharge state of the i-th energy storage battery at time t, and its value is a 0 / 1 variable; and is the maximum charge and discharge power allowed for the i-th energy storage battery, and Represents the minimum and maximum state of charge of the i-th energy storage battery;

[0079] S1-4. Load-side Low-Carbon Demand Response Model: After adjusting the generation plan for each period on the source side, the load side implements a low-carbon demand response strategy and adjusts its electricity consumption behavior to maximize the benefits of end users. This improvement utilizes a dynamic carbon emission factor derived from the carbon emission flow to guide the power system to implement low-carbon scheduling and facilitate carbon footprint tracking.

[0080] S1-4-1. Load-side objective function: When implementing low-carbon demand response, the load party aims to maximize the load-side benefits, as shown in formula (37).

[0081]

[0082] Equation (38) shows how the carbon emissions of the system are reduced, where represents the load reduction and increase at time t after the low-carbon demand response, which emphasizes the key role of power load demand management in reducing carbon emissions;

[0083] S1-4-2. Load-side constraints: The load change constraints after implementing the low-carbon demand response method are as follows:

[0084]

[0085]

[0086] Wherein, equation (39) specifies that the load change should be kept within the upper limit of the load change, which is expressed as According to equation (40), at time t, the load increase should not exceed the maximum allowable load The load reduction shall not exceed That is, the initial load before LCDR. Equation (41) indicates that the total load change in a single day should be kept within the limit of ζ. Finally, equation (42) describes that load increase and decrease cannot occur at the same time;

[0087] S2: Establishing a quasi-potential game model. The establishment of the quasi-potential game model includes the following processes:

[0088] S2-1. In this study, the model is formulated as a mixed-integer nonlinear programming problem. To address this complexity, a multi-leader and multi-follower hierarchical Stackelberg game model framework is employed, which accounts for the complex interactions between the source and load terminals. Furthermore, it is demonstrated that the proposed hierarchical Stackelberg game model can be solved using an efficient quasi-potential game method.

[0089] Initially, the source side formulates an output plan for each generator unit. The load side then adjusts the load based on a dynamic carbon emission factor based on a low-carbon demand response model. These changes in energy demand prompt a reassessment of each unit's generation plan. The Stackelberg game, a component of non-cooperative game theory, is a mathematical framework for analyzing these interactive decision-making processes. The multi-agent entities operating power plants play the role of leaders, while active end users play the role of followers in the established hierarchical multi-leader, multi-follower Stackelberg game model G, as follows:

[0090]

[0091] Participants: The game consists of i participants, where i is an element in the set U = (X∪Y), where X represents the set of source participants and Y corresponds to the set of load participants.

[0092] Strategy set: For the source side that plays the role of leader, the strategy includes the unit output formulated in 24 hours, which is mathematically expressed as The individual strategy of leader i is given by x i Indicates that, except for participant i, all other participants’ combined strategies are included in x -i In, x -i ={x i′ |i′∈U,i′≠i}=(x1,...,x i-1 ,x i+1 ,...,x N ), accordingly, the strategies of the load-side followers are characterized by their load responses, expressed as

[0093] Benefit: For the objective function, the benefit structure of the source This is described in detail in Equation (12). Similarly, the benefit on the load side is As stated in equation (37), adopting strategy x i When , the payoff of participant i is The payoffs of all participants are represented by given;

[0094] In general, Stackelberg games exhibit an inherent power asymmetry, where the leader exerts influence but does not fully control the followers; each follower independently solves an optimization problem that considers both the leader's strategy and the strategies of the other followers; thus, for any given strategy set x = (x1, ..., x N ), the equilibrium set of followers is S(x i ,x -i )=S(x) means, y i is the expected strategy profile of all followers from the perspective of leader i;

[0095] In this Stackelberg game, it is assumed that an ideal leader minimizes Maximize at the same time Therefore, the original goal for leader i in (12) is reformulated as

[0096]

[0097] Participants independently decide on strategies that are in their own interests, with the goal of maximizing their respective benefits. This process continues until they reach the Nash equilibrium, which is defined as follows:

[0098] Definition (Nash Equilibrium): A strategy set A Nash equilibrium is formed, where no participant can benefit from unilaterally changing their strategy. Formally speaking, this is when the conditions of each participant i are in the strategy set S i For all x i 、y i All are established, indicating that there is no motivation to deviate;

[0099]

[0100] S2-2. Quasi-Position Game:

[0101] Before determining the Nash equilibrium in the proposed multi-leader multi-follower Stackelberg hierarchical game, it is necessary to verify that the game indeed supports the existence of at least one Nash equilibrium;

[0102] Finding a Nash equilibrium is challenging. In the field of non-cooperative games, quasi-potential games are noteworthy because they guarantee the existence of at least one pure strategy Nash equilibrium, characterized by the existence of a global situation function that coordinates the payoffs of all players. If a quasi-potential function is successfully established, it will make the hierarchical Stackelberg game model a quasi-potential game.

[0103] The quasi-potential game is defined as: Consider a multi-leader multi-follower game G, where the players’ goals are expressed as If G is a quasi-potential game, then:

[0104] (i) There exists a function Φ(·) such that for all i = 1, ..., N, all x∈X and x i ∈X i , equation remain unchanged;

[0105] (ii) For i=1,...,N, there exists a function And the function z(x,y i ), so that the goal of each player i Given as

[0106] The function Φ is used as a potential function, and the combination Φ+z is called a quasi-potential function;

[0107] Corollary: The hierarchical Stackelberg game G is a quasi-potential game, and the quasi-potential function benefit is Φ(i)+z;

[0108] Proof: Consider and

[0109]

[0110] Similarly, the difference in potential functions is expressed as:

[0111]

[0112] Expanding it, we get:

[0113]

[0114] because Condition (i) is satisfied, and the proof of condition (ii) follows a similar rationale, thus proving that the hierarchical Stackelberg game G is a quasi-potential game, and Φ(i)+z acts as a quasi-potential function;

[0115] The existence theorem of the global equilibrium of G is: consider G as a quasi-potential game with multiple leaders and multiple followers, define U as the set of fixed points (x, y) in the strategy space, assume that U is a non-empty set, and for each i∈N, is a continuous function, if There exists a minimum (for example, if Φ is a compact function on U or U is compact), then G has at least one equilibrium point;

[0116] Under certain conditions, the existence of a global equilibrium of the Stackelberg game can be proved. These conditions include the continuity and convexity of the objective function and the non-emptiness of the strategy set. These conditions have been rigorously proved in several references and further establish the existence and consistency of global equilibria and global minima. In summary, the hierarchical Stackelberg game G we proposed guarantees a unique global equilibrium solution and optimal result.

[0117] S3: Load side optimization. Calculate the carbon potential ε of each node based on the scheduling results. t and the dynamic carbon emission factors at each stage Based on the LCDR scheme, the load-side response is optimized, a local potential function of the follower layer is constructed to reflect the relationship between the user's profit maximization goal and carbon emissions, and user behavior is adjusted through distributed decision-making;

[0118] S4: Update the load demand and transfer it to the source side;

[0119] S5: Source-side optimization. The source optimizes the output plan of each unit based on the updated load to minimize the source-side cost, thus forming an iterative process of "source-side potential function optimization-load-side balanced response" to obtain the optimal scheduling strategy and scheduling results on the energy supply side;

[0120] S6: The system determines whether Nash equilibrium is reached. If so, the system outputs the final optimization result; if not, the system returns to step S2 and re-optimizes based on the updated state information.

[0121] In step S6, the Nash equilibrium solution process is: when the system meets the Nash equilibrium condition, that is, When the change in source-side revenue before and after the iteration is less than the set threshold ζ, the iteration is considered to have converged and the system has reached the optimal state. If not, jump to step S2 and optimize again;

[0122] The proposed source-load coordination scheduling framework is evaluated through case simulations on modified IEEE-39 and IEEE-118 node systems, which aims to optimize energy distribution and reliability in response to dynamic demand and the integration of renewable energy; the traditional coal-fired power plants G1 and G2 are converted into carbon capture power plants, such as Figure 1 As shown in Figure 2; In addition, renewable energy sources are integrated by introducing six wind farms and three photovoltaic power generation installations with capacities of 200 MW and 150 MW respectively. This integration marks the adaptability of our framework to different energy sources and enhances sustainability. The power forecasts of the power load, WT and PV in a typical day in the distributed energy system are shown in Figure 2. Figure 2 As shown;

[0123] MATLAB (version 2023b) combined with the YALMIP toolbox and the GUROBI solver (version 10.0.0) was used. For comparative analysis, six representative cases were selected, as shown in Table 1 , where “√” indicates that a specific subsystem is included, while “×” indicates that it is not.

[0124] Table 1 shows the simulation cases.

[0125]

[0126]

[0127] 1) Scenario 1: No carbon capture power plant and no low-carbon demand response considerations;

[0128] 2) Scenario 2: Adding a price demand response method to Scenario 1 to shift load from peak to valley;

[0129] Scenario 3: Introducing LCDR on the load side to guide users to change load status using DCEF as a signal;

[0130] 4) Scenario 4: There is no solution storage, and CCPPs are incorporated into the source side in flue gas bypass mode;

[0131] 5) Scenario 5: Using CCPPs in flexible operation mode;

[0132] 6) Scenario 6: Our proposed framework, where CCPPs operate in a comprehensive flexible mode on the source side and LCDR is introduced on the load side;

[0133] Specifically, the parameters discussed in this example are detailed in Table 2. The relevant data for each coal-fired power plant (including CCPPs) are shown in Table 3.

[0134] Table 2 shows the experimental parameter settings.

[0135]

[0136] Table 3 is the parameters of each coal-fired unit

[0137]

[0138]

[0139] A. Scheduling Result Analysis

[0140] Analysis of Scenario 1 shows that without carbon capture capacity, the DES reaches peak carbon emissions and renewable energy curtailment rates. This inability to capture CO2 from power plants prevents the system from generating revenue by selling additional carbon emission allowances, resulting in the highest carbon emission costs.

[0141] The introduction of PDR in Scenario 2 significantly increases the system's renewable energy output, thereby reducing carbon emissions. Although this approach compensates for the load with additional renewable energy during peak hours, the carbon reduction effect is limited and renewable energy is still restricted. This suggests that the low-carbon potential of the system in this case needs further exploration;

[0142] In the third case (Scenario 3), LCDR is introduced on the load side, which uses DCEF as a signal to help users improve their energy consumption behavior. First, the effect of LCDR is similar to that of PDR in Scenario 2. However, the advantage of LCDR is that it allows users to directly understand the carbon emissions related to their electricity consumption, including carbon emissions from the supply side, which makes it possible to fully track carbon footprints. The guiding signals of electricity price-based demand response and low-carbon demand response and their corresponding load transfer effects are shown in Figure 2. Figure 3 As shown in Figure 2, although the introduction of LCDR can shift some of the load, it still faces a situation of high carbon emissions. Therefore, it is necessary to consider combining LCDR with the deployment of CCPPs at the source end.

[0143] In the fourth case (Scenario 4), CCPPs are incorporated at the source, e.g. Figure 4 As shown in Scenario 4, the output of CCPPs significantly exceeds that of power plants with higher carbon emissions, which results in most of the CO2 emissions within the system being captured and collected by CCS equipment, thereby promoting low-carbon operation of the system. Although CCPPs can effectively capture the CO2 produced during the power generation process in this case, their carbon capture flexibility is limited. They cannot maximize the absorption of renewable energy during off-peak periods, which shows that there is still room for optimization in DES.

[0144] In the fifth case (Scenario 5), CCPPs equipped with liquid storage tanks can facilitate the flexible shifting of carbon capture energy consumption by storing CO2 produced during peak periods and capturing it during off-peak periods. This approach provides two main advantages: first, it can increase the net output of CCPPs during peak periods to meet load demand; second, it allows the minimum net output of CCPPs to be reduced during off-peak periods to absorb more renewable energy. The dispatch results show that this strategy significantly enhances the low-carbon operation of the system. However, some high-carbon power plants still need to operate during peak periods, and the system continues to experience renewable energy curtailment.

[0145] The framework proposed in Scenario 6 provides further improvements to the shortcomings found in the previous scenarios. By shifting load from peak hours to off-peak hours and replacing the output of high-carbon units during peak hours with the output of low-carbon units during off-peak hours, a greater reduction in carbon emissions is achieved. Compared with Scenario 1, Scenario 3, and Scenario 5, carbon emissions in Scenario 6 are reduced by 87.6%, 87.2%, and 16%, respectively. Simulation results show that load demand is mainly met by the output of low-carbon units (i.e., CCPPs and RES units);

[0146] The optimized dispatch results for various scenarios, including the RES curtailment rate θ, are shown in Table 4. Compared to Scenario 1, the renewable energy curtailment rates in Scenarios 2 and 3 (using PDR and LCDR, respectively) are reduced by 2.32% and 2.15%, respectively, indicating similar impacts on renewable energy consumption. Notably, Scenario 4, which employs a CCPP splitting mode, shows a 2.95% reduction in renewable energy curtailment, 1.19% lower than Scenario 1. This reduction is attributed to the operation of low-carbon power plants CCPP1 and CCPP2, which consume electricity to capture CO2 during low-demand periods, thereby reducing the plant's minimum net output and enhancing renewable energy absorption. Furthermore, Scenario 5 includes a solution storage tank to enhance carbon capture flexibility, capturing CO2 during peak periods for use during low-demand periods. This strategy effectively reduces the plant's net output constraints and improves renewable energy generation efficiency. Compared to Scenario 1, the renewable energy curtailment rate is reduced by 4.13%. Finally, Scenario 6 demonstrates full utilization of renewable energy in every period, highlighting the effectiveness of the proposed source-load coordinated low-carbon dispatch approach in optimizing renewable energy consumption.

[0147] Table 4 Optimization scheduling results under different conditions

[0148]

[0149] In order to accurately quantify the renewable energy output under different circumstances, we introduce the renewable energy curtailment rate θ. The mathematical formula of this rate is as follows:

[0150]

[0151] Figure 5The impact of different scenarios on RES utilization efficiency is illustrated, showing the different levels of RES curtailment observed from scenarios 1 to 6. Notably, scenario 6 achieves 100% RES utilization through the coordinated use of CCPPs and LCDRs. LCDRs enhance off-peak load absorption from renewable energy, while the flexible operation of CCPPs maximizes CO2 capture during periods of low demand. This coordinated framework effectively reduces the net output constraints of power plants and ensures full renewable energy integration by eliminating waste, representing a significant step towards optimizing renewable energy management.

[0152] In summary, the approach of this embodiment can serve as a strategic integration of innovation on the energy supply side and LCDR on the load side to improve the energy supply efficiency and sustainability of DES. Based on the discussed analysis and scheduling results, it is clear that the proposed source-load coordination optimization framework (Scenario 6) demonstrates a comprehensive approach to minimize carbon emissions while ensuring economic feasibility and maximizing resource utilization.

[0153] B. Analysis of low-carbon optimization results

[0154] The changes of DCEF under different conditions are as follows Figure 6 The figure shows that applying DR strategies on the load side, especially in scenarios 2 and 3, effectively reduces carbon emissions during peak periods. However, these scenarios also show a reliance on high-carbon emission generators, which leads to increased CO2 emissions during low-demand periods when DR strategies are implemented.

[0155] Although the split-flow carbon capture device can significantly reduce system CO2 emissions, its limited capture capacity prevents it from fully meeting the low-carbon requirements of the DES. In contrast, Scenario 5 adds a solution storage tank to Scenario 4, increasing the flexibility of carbon capture. This allows CO2 to be captured at any time, further reducing system carbon emissions.

[0156] Scenario 6 expands Scenario 5 with LCDR, reducing the output of high-carbon power plants by shifting loads during peak hours. During off-peak hours, these high-carbon emissions are replaced by low-carbon emissions from CCPP1 and CCPP2. Therefore, Scenario 6 has the lowest carbon emissions. This analysis verifies the effectiveness of the proposed source-load coordinated low-carbon dispatch framework (Scenario 6) in achieving substantial reductions in system carbon emissions.

[0157] In order to further study the impact of carbon trading prices on emission reduction plans, the changes in total carbon emissions and related costs under different scenarios and different carbon trading price levels are analyzed.

[0158] Figure 7The relationship between carbon emissions and carbon prices under each scenario is described. The data shows that carbon emission trends remain relatively stable in Scenarios 1, 2, and 3. This stability suggests that when carbon trading revenue is lower than capture costs, CCPPs choose to release CO2 into the atmosphere rather than capture it. Specifically, when the carbon price is less than $9, Scenario 6 exhibits higher carbon emissions than Scenario 5. This is because during periods of low load, CCPP1 and CCPP2 always operate at their lower output limits due to low carbon revenue and high startup and shutdown costs. In Scenario 5, CCPP1 and CCPP2 still have the ability to capture carbon dioxide generated by the system after meeting load demand and absorbing renewable energy. However, in Scenario 6, the introduction of low-carbon demand response increases the load during off-peak periods, which means that the output of CCPP1 and CCPP2 can only meet load demand and cannot capture carbon, resulting in relatively high carbon emissions.

[0159] The relationship between the total system cost and the carbon base price is as follows: Figure 8 As shown, it can be seen that the total cost of scenario 6 shows a trend of first increasing and then decreasing with the carbon price. This is because when the carbon price is less than 9$, the carbon emission decrease rate is less than the carbon price increase rate. Therefore, the carbon emission cost of scenario 6 shows an upward trend when the carbon price is less than 9$.

[0160] Furthermore, compared to Scenario 5, Scenario 6 consistently maintains lower total costs across a wide range of carbon prices. This is primarily due to the introduction of low-carbon demand response, which reduces reliance on high-cost, high-carbon-emitting power plants. As shown in Table 4, the operating costs of these high-carbon power plants are much higher than those of CCPPs. Therefore, despite higher carbon emissions compared to Scenario 5, Scenario 6 still achieves lower total costs due to the reduced expenses associated with the output of high-carbon power plants.

[0161] C. Large-scale system scalability verification

[0162] To verify the feasibility of the proposed framework and algorithm in real-world power systems and other complex, large-scale environments, we used an IEEE-118 bus power system as a case study for performance evaluation. For a comprehensive evaluation, we used the IEEE 39 bus model as a benchmark to compare the performance of our framework. We focused on comparing the performance of Scenario 3 and Scenario 6 on IEEE-39 and IEEE-118 bus nodes, as detailed in Table 5.

[0163] Table 5 shows the solution time

[0164]

[0165]

[0166] The data presented in Table 5 show that the solution time of the proposed framework increases linearly with the expansion of the system scale, thus demonstrating the scalability of this method to large-scale power systems; compared with Scenario 3, the framework requires more iterations and longer solution time. This increase can be attributed to the inclusion of carbon capture equipment, which, despite the increased complexity, produces significant improvements in carbon capture efficiency and economic dispatch results.

[0167] Figure 9 The carbon capture efficiency of the IEEE-118 bus system under scenarios 4, 5, and 6 is described. During the daytime peak load period, the DES in scenario 4, without a solution storage tank, can only generate electricity to meet the load demand but cannot capture carbon dioxide. In contrast, scenario 6, which adopts the LCDR method, achieves a higher carbon capture efficiency, 4.6% higher than scenario 5. In summary, the introduced source-load coordinated low-carbon system demonstrates significant carbon capture efficiency in the IEEE-118 bus system. Furthermore, the proposed framework demonstrates sufficient scalability and applicability to large-scale complex systems, highlighting its potential as a powerful solution for enhancing low-carbon initiatives in DES.

[0168] This embodiment presents a method for optimizing source-load coordination in a distributed energy system, aiming to significantly reduce carbon emissions. This is achieved by converting high-carbon-emitting power plants into CCPPs and incorporating practical LCDR technology. The MINLP problem is initially modeled as minimizing total cost while reducing carbon emissions. This problem is then reformulated as a hierarchical multi-leader, multi-follower Stackelberg game and solved using an efficient quasi-potential game algorithm.

[0169] Simulations in an IEEE 39-bus system demonstrate that our approach significantly reduces total system cost and CO2 emissions, highlighting the effectiveness of combining CCPPs with solution storage tanks to enhance carbon management and employing LCDR to optimize RES utilization. Furthermore, the application of our framework in a large-scale IEEE 118-bus system demonstrates its strong scalability and effectiveness in complex energy networks, indicating its potential for widespread adoption in decarbonization efforts.

[0170] Although the embodiments of the present invention have been shown and described above, it can be understood that the contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept, and the scope of protection of the present invention should not be regarded as limited to the specific forms described in the embodiments. The scope of protection of the present invention also includes equivalent technical means that can be thought of by those skilled in the art based on the inventive concept.

Claims

1. A distributed energy system source-load coordination optimization method based on quasi-potential game method, characterized by: The method comprises the following steps: S1: Construct a distributed energy system model, input system parameters, predict renewable energy generation and initial load demand, based on initial data k = 1, Optimize the scheduling of the source side; in the source side optimization stage, the source side cost Minimize the leader layer potential function of the quasi-potential game, comprehensively consider economic and carbon emission constraints, and generate the initial power generation plan; S2: Establish a quasi-potential game model; S3: Load side optimization, calculate the carbon potential ε of each node based on the scheduling results t and the dynamic carbon emission factors at each stage Based on the LCDR scheme, the load-side response is optimized, a local potential function of the follower layer is constructed to reflect the relationship between the user's profit maximization goal and carbon emissions, and user behavior is adjusted through distributed decision-making; S4: Update the load demand and transfer it to the source side; S5: Source-side optimization: The source optimizes the output plan of each unit based on the updated load to minimize the source-side cost, thus forming an iterative process of "source-side potential function optimization-load-side balanced response" to obtain the optimal scheduling strategy and scheduling results on the energy supply side; S6: The system determines whether Nash equilibrium is reached. If so, the system outputs the final optimization result; if not, the system returns to step S2 and re-optimizes based on the updated state information.

2. A distributed energy system source-load coordination optimization method based on quasi-potential game method according to claim 1, characterized in that: In step S1, the system includes the following components: S1-1. Mathematical Model of a Flexible Operation Carbon Capture Power Plant: This approach allows the ethanolamine (MEA) solution to absorb CO2 during peak load periods and subsequently store it in a dedicated solution reservoir. During off-peak periods, the accumulated CO2 is transferred to a regeneration tower for extraction and capture. Taking into account the actual power consumption requirements of DES, the energy consumption of CCPPs in flexible operation mode is defined as follows: In formula (1) represents the total output power of coal-fired power plant i in period t. When unit i is converted into CCPP, Divided into three categories: Net output Carbon capture energy consumption and fixed energy consumption When unit i represents a conventional coal-fired power plant, and will be 0; In equation (2), The total mass of CO2 captured during period t Directly related, ω i represents the coefficient of carbon capture energy consumption, equation (3) explains Including CO2 generated by power generation, Also includes CO2 generated by the solution storage tank, β i represents the CO2 capture coefficient, δ i represents the split ratio of flue gas, equation (4) expresses and Proportional, e i represents carbon emission intensity, (5) specifies the δ of CCPPs i Should remain in the range of 0 to 1; In order to achieve flexible operation modes of CCPPs, a solution storage is introduced, where CO2 is dissolved in the MEA and becomes a liquid compound. The mass of CO2 extracted from the solution storage is calculated based on the volume of the solution. The modeling of this basic component is shown below: Equation (6) expresses the relationship between CO2 mass and MEA solution volume, M represents the molar mass of MEA solution and CO2 required by carbon capture power plant i to absorb carbon dioxide during period t. mea and M CO2 The key to understanding their interaction is to use η to express the CO2 absorption efficiency of the absorption tower. i In addition, the concentration of MEA solution is expressed as N mea Its density is expressed as D mea The constraints are as follows: Equation (7) describes the dynamic volumes of rich and lean solutions in the solution reservoir at any given time t, and represent the volumes of rich solution and lean solution of carbon capture power plant i in time period t, (8) establishes the operating volume limits for rich solution and lean solution, and the capacity of the solution storage in each carbon capture power plant is expressed as V i ,Finally, equation (9) stipulates that the volume of the solution should remain unchanged after 24 hours; S1-2. Low-carbon demand response mathematical model: The dynamic carbon emission factor plays an important role in the low-carbon demand response strategy. The dynamic carbon emission factor is calculated by averaging the spatial load based on the carbon potential of each node, expressed as: represents the carbon emission factor of the power system in period t, Z is the set of all nodes in the power system, is the power load consumption of node j in period t, ε j,t represents the carbon potential of node j in the power system during period t; Assuming that coal-fired power plant i and renewable energy i are interconnected with node j, the improved carbon potential of the node in period t is expressed in equation (11), J + represents all nodes connected to node j in the power system, represents the forward power flow from node s to node j during period t, is the power input to node j by coal-fired unit i during period t, is the power input from renewable energy generator i to node j during period t; S1-3. Source-side optimization scheduling model; S1-4. Load-side low-carbon demand response model: After adjusting the power generation plan for each period on the source side, the load side implements a low-carbon demand response strategy and adjusts its electricity consumption behavior to maximize the interests of end users. This improvement utilizes the dynamic carbon emission factor derived from the carbon emission flow to guide the power system to conduct low-carbon scheduling to facilitate carbon footprint tracking.

3. A distributed energy system source-load coordination optimization method based on quasi-potential game method according to claim 2, characterized in that: The process of S1-3 is as follows: S1-3-1. Source-side objective function: The source side includes the output of traditional coal-fired power plants, CCPPs, and RES to meet the total load demand. An optimal scheduling model is established, whose main goal is to minimize the total operating cost of the source side in DES, denoted as C1 represents the coal consumption cost of coal-fired power plants, C2 represents the total cost of coal-fired unit startup and shutdown, C3 represents the penalty cost for renewable energy reduction, C4 represents the solvent loss cost of carbon capture power plants, and C5 represents the depreciation cost of carbon capture power plants. The detailed formula for each cost component is as follows: In equation (13), N g The variable X represents the number of coal-fired units. i,t Indicates the on / off status of the i-th coal-fired unit in period t, which can be 0 or 1. i 、b i and c i is the coal consumption characteristic parameter of coal-fired unit i. In equation (14), τ represents the unit start-up and shutdown cost coefficient, N res Represents the number of renewable energy units WTs and photovoltaic PVs, and the unit new energy reduction penalty cost is τ re Given, and represent the predicted and actual power output of the RES unit, respectively. In equation (16), the coefficients Corresponding to the unit solvent loss cost in the CCS process, represents the amount of solvent consumed per ton of CO2 captured, as shown in equation (17), the depreciation rate of CCPP equipment is represented by r, and the cost coefficients of CCS equipment (without solution storage) and with solution storage are represented by τ ccs and τ so Indicates that, finally, Y1 and Y2 refer to the depreciation years of CCS equipment (without solution storage) and with solution storage, respectively; The integration of market mechanisms into power system reform is aimed at balancing the system's low-carbon goals and economic development. A stepped carbon trading mechanism is introduced, which adopts a tiered carbon pricing model and a carbon trading quota system. See Equations (18) and (19) for details: λ represents the carbon trading base price, q represents the carbon emissions exceeding the system quota, l represents the length of the carbon emission interval, α represents the increase in the step-by-step carbon trading price, and E total represents the total carbon emissions of the system, ξ represents the carbon quota coefficient, and C7 in equation (20) describes the carbon emission reduction incentive cost after the source side provides the LCDR method; On the source side, based on the carbon reduction incentive price λ and the reduced carbon emissions achieved through the LCDR method Pay carbon reduction incentives to end users on the load side; S1-3-2. Source side constraints: After the low-carbon demand response, the output of each generator set on the source side is adjusted to meet the real-time demand on the load side. The corresponding power balance constraints are as follows: Among them, N b Indicates the number of battery energy storage BES units, and Respectively represent the charging and discharging power of the i-th BES unit at time t. represents the total load at time t after LCDR; The power generation constraints related to the coal-fired units are as follows: Constraints (22)-(24) specify the output and operating cycle of the coal-fired units, constraints (25)-(26) define the output power limit of the RES power generation, and finally, constraints (27)-(30) determine the power flow parameters of the DES. i ref =0 (30) and are the minimum and maximum output power of coal-fired unit i, is the maximum ramp rate of coal-fired unit i, T i on and T i off is the minimum startup and shutdown time of coal-fired unit i, is the maximum ramp rate of renewable energy unit i, θ s,t and θ j,t is the voltage phase angle between nodes s and j at time t, z sj is the impedance of the line connecting node s and node j, is the maximum transmission power from node s to node j, Represents the voltage phase angle limit value of node s, θ ref is the equilibrium node voltage phase angle; The operating limits of the BES are given in equations (31)-(36). (31) defines the calculation of the BES state of charge (SOC). Equations (32)-(33) set the charging and discharging power limits. Equation (34) prohibits the BES from charging and discharging simultaneously. The SOC limit is specified by equation (35). Finally, equation (36) ensures that the SOC capacity remains unchanged after the end of the dispatch period. S i,0 =S i,24 ,i∈N b (36) Among them, S i,t is the state of charge of the i-th energy storage battery at time t, and is the charging and discharging efficiency of the i-th energy storage battery, and represents the charging and discharging power of the i-th energy storage battery at time t, and is the charge and discharge state of the i-th energy storage battery at time t, and its value is a 0 / 1 variable. and is the maximum charge and discharge power allowed for the i-th energy storage battery, and Represents the minimum and maximum state of charge of the i-th energy storage battery.

4. The distributed energy system source-load coordination optimization method based on quasi-potential game method according to claim 2, characterized in that: The process of S1-4 is as follows: S1-4-1. Load-side objective function: When implementing low-carbon demand response, the load party aims to maximize the load-side benefits, as shown in formula (37). Equation (38) shows how the carbon emissions of the system are reduced, where represents the load reduction and increase at time t after the low-carbon demand response, which emphasizes the key role of power load demand management in reducing carbon emissions; S1-4-2. Load-side constraints: The load change constraints after implementing the low-carbon demand response method are as follows: Wherein, equation (39) specifies that the load change should be kept within the upper limit of the load change, which is expressed as According to equation (40), at time t, the load increase should not exceed the maximum allowable load The load reduction shall not exceed P t load , which is the initial load before LCDR, equation (41) indicates that the total load change in a single day should be kept within the limit of ζ, and finally, equation (42) describes that load increase and decrease cannot occur at the same time.

5. A distributed energy system source-load coordination optimization method based on quasi-potential game method according to any one of claims 1 to 4, characterized in that: In step S2, establishing the quasi-potential game model includes the following process: S2-1. The model is established as a mixed-integer nonlinear programming problem. To address this complexity, a hierarchical Stackelberg game model framework with multiple leaders and multiple followers is adopted. This framework considers the complex interactions between the source and load ends, and proves that the described hierarchical Stackelberg game model can be solved using an effective quasi-potential game method; The source side formulates an output plan for each generator unit, and the load side adjusts the load according to the dynamic carbon emission factor based on the low-carbon demand response model. These changes in energy demand prompt a reassessment of the power generation plan of each unit. The Stackelberg game is an integral part of non-cooperative game theory and a mathematical framework for analyzing these interactive decision-making processes. The multi-agent entities operating the power plant play the role of leader, while the active end users play the role of follower in the established hierarchical multi-leader multi-follower Stackelberg game model G, as follows: Participants: The game consists of i participants, where i is an element in the set U = (X∪Y), where X represents the set of source participants and Y corresponds to the set of load participants. Strategy set: For the source side that plays the role of leader, the strategy includes the unit output formulated in 24 hours, which is mathematically expressed as The individual strategy of leader i is given by x i Indicates that, except for participant i, all other participants’ combined strategies are included in x -i In, x -i ={x i′ |i′∈U,i′≠i}=(x1,...,x i-1 ,x i+1 ,...,x N ), accordingly, the strategies of the load-side followers are characterized by their load responses, expressed as y i ={P t lcdr }; Benefit: For the objective function, the benefit structure of the source Detailed in equation (12), similarly, the benefit on the load side is As stated in equation (37), adopting strategy x i When , the payoff of participant i is given by The payoffs of all participants are represented by given; The Stackelberg game exhibits an inherent power asymmetry, where the leader exerts influence but does not fully control the followers. Each follower independently solves an optimization problem that considers both the leader's strategy and the strategies of the other followers. Thus, for any given strategy set x = (x1, ..., x N ), the equilibrium set of followers is S(x i ,x -i )=S(x) means, y i is the expected strategy profile of all followers from the perspective of leader i; In this Stackelberg game, it is assumed that an ideal leader minimizes Maximize at the same time Therefore, the original goal for leader i in (12) is reformulated as Participants independently decide on strategies that are in their own interests, with the goal of maximizing their respective benefits. This process continues until they reach the Nash equilibrium, which is defined as follows: Nash equilibrium is defined as: a strategy set (x * ,y * )={x * ,y * |i∈U} constitutes a Nash equilibrium, at which point no participant can benefit from unilaterally changing their strategy. Formally speaking, this is when the conditions of each participant i are in the strategy set S i For all x i 、y i All are established, indicating that there is no motivation to deviate, S2-2. Quasi-Position Game: Before determining a Nash equilibrium in a multi-leader multi-follower Stackelberg hierarchical game, verify that the game indeed supports the existence of at least one Nash equilibrium; The quasi-potential game is defined as: Consider a multi-leader multi-follower game G, where the players’ goals are expressed as It means that if G is a quasi-potential game, then: (i) There exists a function Φ(·) such that for all i = 1, ..., N, all x∈X and x i ∈X i , equation remain unchanged; (ii) For i=1,...,N, there exists a function And the function z(x,y i ), so that the goal of each player i Given as The function Φ is used as the potential function, and the combination Φ+z is called the quasi-potential function; Corollary: The hierarchical Stackelberg game G is a quasi-potential game, and the quasi-potential function benefit is Φ(i)+z; Proof: Consider and Similarly, the difference in potential functions is expressed as: ΔΦ=Φ(x i ′,x -i )-Φ(x i ,x -i ) (47) Expanding it, we get: because Condition (i) is satisfied, and the proof of condition (ii) follows a similar rationale, thus proving that the hierarchical Stackelberg game G is a quasi-potential game, and Φ(i)+z acts as a quasi-potential function; The existence theorem of the global equilibrium of G is: consider G as a quasi-potential game with multiple leaders and multiple followers, define U as the set of fixed points (x, y) in the strategy space, assume that U is a non-empty set, and for each i∈N, is a continuous function, if If there is a minimum (for example, if Φ is a compact function on U or U is compact), then G has at least one equilibrium point.

6. A distributed energy system source-load coordination optimization method based on quasi-potential game method according to claim 1 or 2, characterized in that: In step S6, the Nash equilibrium solution process is: when the system meets the Nash equilibrium condition, that is, When the change in source-side revenue before and after the iteration is less than the set threshold ζ, it is considered that the iteration has converged and the system has reached the optimal state. If it is not satisfied, jump to step S2 and optimize again.

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