Improved multi-target particle swarm solution multi-spatio-temporal integrated energy system scheduling method

Abstract

The invention discloses an improved multi-target particle swarm solving multi-spatio-temporal integrated energy system scheduling method. A flow chart is as shown in Figure 1. The method particularly relates to the fields of operational research, comprehensive energy systems, multi-objective optimization and the like. The method comprises a model part and a solving algorithm part, the model is a comprehensive energy system scheduling mathematical model of industrial district, commercial district and residential district collaborative scheduling multi-time scale rolling optimization, and objective functions are the lowest cost and the lowest carbon emission respectively; a solution algorithm is an improved multi-target particle swarm optimization algorithm, and compared with a traditional algorithm, a local search mechanism is introduced, a storage system is adjusted, and self-adaptive adjustment of inertia weight is achieved. According to the model, the expansion machine is added, redundant natural gas pressure energy is utilized, meanwhile, compared with a traditional algorithm, the algorithm is higher in diversity, higher in speed and higher in quality, and the problems that an existing comprehensive energy system is complex in environment, excessive in uncertainty, single in target and the like are effectively solved.

Description

Technical Field

[0001] The present invention relates to an integrated energy system, and in particular to an optimized scheduling of a multi-temporal and multi-objective integrated energy system. Background Art

[0002] At present, the global energy production and consumption revolution is deepening, and the energy system continues to transform towards green, low-carbon, clean, efficient, smart and diversified directions. The global energy system is changing from the absolute dominance of fossil energy to the integration of low-carbon and multi-energy. The new round of energy revolution presents the characteristics of low-carbon energy scale, traditional energy cleanliness, energy supply diversification, terminal energy efficiency and energy system intelligence.

[0003] The integrated energy system consists of three parts: supply side, demand side, and energy conversion and storage. It is a hot research issue today. However, with the increasingly complex load and environment, the scheduling problem of the integrated energy system is gradually developing in the direction of multi-time and space. However, in realizing the operation and scheduling of the multi-time and space integrated energy system, there are still many problems, such as too many uncertain parameters, how to design multi-time and space, and the conflict between pollution and cost optimization.

[0004] The scheduling problem of IES is no longer limited to the optimization of a single time scale, but requires the coordinated optimization of multiple time scales. This includes multiple levels such as long-term planning, medium-term scheduling and short-term real-time adjustment. At the same time, the spatial distribution also increases the complexity of scheduling, such as energy flow and supply and demand balance between multiple regions. In addition, uncertain factors such as the output fluctuation of renewable energy and the uncertainty of demand-side response further increase the difficulty of scheduling.

[0005] To solve the above problems, academia and industry have conducted a lot of research and proposed a variety of models and optimization methods. In terms of model construction, researchers have established a mathematical model that can characterize the complex characteristics of IES based on graph theory, scenario tree method, EMP framework and other theories. At the same time, in response to the problem of multi-time and space fusion, a multi-time scale rolling scheduling model and a two-stage optimization scheduling strategy were proposed to achieve collaborative optimization on different time scales. In addition, in order to deal with uncertainty problems, researchers have also introduced methods such as distributed robust optimization, fuzzy mathematics theory, and model predictive control to improve the robustness and flexibility of scheduling.

[0006] In terms of optimization methods, traditional algorithms such as particle swarm optimization and firefly algorithm are widely used in IES optimization scheduling. In order to further improve the performance and adaptability of the algorithm, researchers have also proposed a variety of improved algorithms and hybrid algorithms, such as binary particle swarm optimization and dynamic adaptive firefly algorithm. These algorithms perform well in solving multi-objective optimization problems and can find the optimal balance between multiple objectives such as cost, efficiency, and environmental protection.

[0007] In order to further improve the low-carbon nature and economic benefits of IES, researchers have also introduced new technical elements such as hydrogen production and pressure energy utilization. These technologies can not only reduce carbon emissions, but also improve the overall energy efficiency of the system. At the same time, multi-objective optimization strategies are widely used in the optimal scheduling of IES, balancing the contradiction between operating costs and environmental pollution by adjusting weight coefficients. This strategy makes it possible to optimize the scheduling of IES in different demand scenarios.

[0008] In summary, the optimization and dispatch of multi-objective, multi-temporal and multi-spatial adaptive integrated energy systems is a hot topic and a difficult point in current research. With the continuous emergence and application of new technologies and methods, the dispatching problem of IES will be solved more effectively, making greater contributions to the green transformation and sustainable development of energy systems. Summary of the invention

[0009] In view of the defects existing in the prior art, the purpose of the present invention is to solve the scheduling problem of multi-temporal and spatial integrated energy systems through a multi-objective particle swarm algorithm.

[0010] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0011] An improved multi-objective particle swarm solution for multi-temporal and multi-spatial integrated energy system scheduling method includes the following steps: firstly, a mathematical programming model of a multi-objective multi-temporal and multi-spatial integrated energy system is established, and the basic components are photovoltaic power generation, wind power generation, gas turbines, electrolyzers, expanders, electric refrigerators, absorption refrigerators, batteries, heat storage tanks, cold storage tanks, and gas storage tanks; the supply side is the power grid, gas grid, and heat grid. The load side is the electric load, heat load, gas load, and cold load; the decision variables are the real-time power of each component, the storage state of the storage system, and the energy flow between each area; the constraints are the design principles of each component itself and the energy balance between output and use under the condition of meeting the load side demand; the objective function is the lowest scheduling cost and the lowest carbon emission under the condition of meeting the load side.

[0012] In particular, a natural gas pressure energy power generation system was added during the construction of the mathematical model, which converted the previously unused natural gas pressure energy into electrical energy to participate in the overall energy supply and demand balance of the integrated energy system.

[0013] The photovoltaic power generation model is:

[0014]

[0015] Where G(t) is the light intensity; T cell is the photovoltaic panel temperature; T amb (t) is the ambient temperature; NOCT is the set temperature; E PV (t) is the photovoltaic power generation power; PMP REF is the rated power; γ PV is the temperature coefficient; μ DA For conversion efficiency.

[0016] The wind power generation model is:

[0017]

[0018] In the formula, is the fan output power, v ci 、v co , v, are cut-in wind speed, cut-out wind speed and rated wind speed respectively; P r is the rated output power; a and b are wind speed correlation coefficients.

[0019] The electrolyzer model is:

[0020]

[0021] In the formula, is the hydrogen production power of the electrolyzer; η ED is the hydrogen flow rate per unit time in the electrolyzer; J ED is the current density of the electrolytic cell; V m is the gas molar volume; c1, c2, k1, k2 are coefficients related to Faraday efficiency, c1 = 50, c2 = 1, k1 = 2.5, k2 = 6.25 × 10-6; c is the conversion constant, c = 0.08988 kg / m2; z is the number of electrons transferred in the reaction; F is the Faraday constant, F = 96485 Cmol; V ED is the working voltage of the electrolytic cell; A is the diaphragm area of ​​the electrolytic cell.

[0022] The absorption chiller model is:

[0023] P AR (t) = P WHB,c (t)η AR (5)

[0024] Where P AR represents the cooling power of the absorption refrigeration unit at time t; P WHB,c represents the output power of the waste heat boiler for refrigeration at time t; η AR Represents the refrigeration efficiency of the absorption chiller.

[0025] The electric refrigerator model is:

[0026] C EC (t) = P EC (t)COP ec (6)

[0027] In the formula, C EC represents the cooling power of the electric refrigerator at time t; P EC Represents the electrical power consumed by the refrigerator at time t; COP ec Refrigeration coefficient of electric refrigerator.

[0028] The expander model is:

[0029]

[0030] Where, Q is the natural gas flow rate; C p is the specific heat capacity of gas; P in With P out are the inlet and outlet pressures respectively; T in is the inlet temperature; k is the natural gas index; there is energy loss in the process of converting pressure energy into electrical energy, which is reflected in the expander efficiency μ tur and generator efficiency μ g superior.

[0031]

[0032] Formula 8 represents the cost of the expander under different operating conditions, which is mainly determined by factors such as the inlet and outlet pressures of natural gas and the flow rate of natural gas.

[0033] The gas turbine model is:

[0034]

[0035] In the formula, Power generation capacity of gas turbine, L gas is the lower calorific value of natural gas, η MT is the power generation efficiency of the gas turbine, is the volume of natural gas consumed by the gas turbine.

[0036] The energy storage model is:

[0037]

[0038] In the above formula, is the energy storage type, including electric energy storage ESS, thermal energy storage TES, cold energy storage CSS, and gas energy storage GSS; γ0 is the ratio of initial energy storage to energy storage capacity; For Node The installed capacity of energy storage of type; is the energy storage at time t; Indicates the charging and discharging power of energy storage equipment; They are the charging efficiency and discharging efficiency of energy storage respectively; is the self-loss factor of energy storage; are the ratio of minimum energy storage / maximum energy storage and energy storage capacity respectively.

[0039] The carbon emission model is:

[0040] Traditional carbon emission calculation methods mainly take into account the two major carbon sources of external grid electricity and external grid gas, while new energy power generation and energy storage devices are usually ignored because they produce almost no carbon emissions during operation. However, the above devices will generate carbon emissions during product production, transportation, installation, and dismantling and recycling. From the perspective of full life cycle carbon emissions, it is necessary to convert them into account to further restrict system carbon emissions.

[0041]

[0042] Where: and are the carbon emissions at time t under scenario s and the total amount of natural gas consumed by each device; a1, a2, a3 and a4 are the carbon emission factors of external grid electricity purchase, external grid gas purchase, photovoltaic power generation and energy storage operation.

[0043] The cost model is:

[0044] F cell =∑ m C buy +C om +C loss (17)

[0045] C om =∑ m P m ×δ m (18)

[0046] C om =∑ m P m ×θ m (19)

[0047] In the formula, C buy is the purchase cost; C om is the maintenance cost; C loss is the loss cost; m is the maintenance factor; θ m is the loss factor; m is each component. The cost is a periodic cost, and the full life cycle cost needs to be calculated.

[0048] The present invention uniquely realizes the coordinated coordination of energy flow in multiple regions under multiple time scales and combines the two advantages of the lowest dispatching cost and the lowest pollution. Multi-objective refers to the two objectives of dispatching cost and environmental pollution, multi-region refers to the coordinated dispatching of energy flow between three regions, and multi-time scale refers to the cyclic dispatching method of three levels of time.

[0049] The mathematical models of the three areas are composed separately, which together constitute the mathematical planning model of the multi-objective and multi-temporal and multi-space integrated energy system.

[0050] Preferably, the multi-objective particle swarm algorithm is improved.

[0051] The multi-objective particle swarm optimization algorithm (MOPSO) is a meta-heuristic algorithm for solving multi-objective optimization problems. It is an extension of the standard particle swarm optimization algorithm (PSO). PSO is an optimization algorithm based on swarm intelligence, which simulates the behavior of bird flocks or fish schools and searches for the optimal solution in the solution space through cooperation and information sharing.

[0052] v i =v i +c1×rand()×(pbest i -x i )+c2×rand()×(gbest i -x i ) (20)

[0053] x i =x i +v i (twenty one)

[0054] Where i = 1, 2, ..., N, N is the total number of particles in the group; v i is the speed of the particle; rand() is a random number between (0, 1); x i is the current position of the particle; c1 and c2 are learning factors, usually c1=C2=2; v i The maximum value of v max (greater than 0), if v i Greater than v max , then Formula 20 and Formula 21 are the standard forms of PSO.

[0055] MOPSO introduces the concept of multi-objective optimization problems, which enables the algorithm to solve complex optimization problems with multiple conflicting objectives. The core idea of ​​MOPSO is to simulate the movement of particles in the solution space and maintain a Pareto optimal solution set, that is, a set of solutions that cannot be improved. The characteristic of this set is that it is the optimal solution when no other solution can be better than it in all objectives. To achieve this, MOPSO introduces a fitness function to evaluate the quality of the solution and measures the pros and cons of the solutions through the Pareto dominance relationship. This relationship means that one solution is better than another solution in one objective, but worse than it in another objective.

[0056] When it comes to multi-objective optimization, the design of the fitness function is critical. The fitness function needs to take into account not only the optimization of a single objective, but also the balance between multiple objectives. Generally, the fitness function should be able to evaluate the performance of the solution on multiple objectives and give a comprehensive fitness value based on the specific needs of the problem. The following is an example of a multi-objective fitness function, assuming that we have two objectives to optimize: minimizing the function f1(x) and maximizing the function f2(x):

[0057] Fitness = w2×f1(x)+w2×(1-f2(x)) (22)

[0058] In order to maintain the diversity of the solution set, MOPSO can also adopt some techniques, such as diversity maintenance mechanism and solution aggregation technology. These techniques help to ensure that as many high-quality solutions as possible are found on the entire Pareto frontier, rather than just the local optimal solution.

[0059] Preferably, in the improved MOPSO algorithm, a local search mechanism is introduced to enhance the combination of the global search capability and the local search capability of the algorithm.

[0060] The improved method of the present invention is adaptive mutation rate regulation of sinusoidal periodic convergence factor; first, the mutation rate pmu is calculated according to the current number of iterations and the total number of iterations, and an initial mutation rate pmuinit and a final mutation rate pmufinal are defined, and then the initial mutation rate is gradually reduced to the final mutation rate in a sinusoidal distribution during the iteration process, as shown in the formula. The mutation rate decreases with the increase of the number of iterations, so that a wider search is performed in the early stage of the iteration, and a more local search is performed in the later stage of the iteration. Then, for each particle, it is determined whether to perform a mutation operation according to the mutation rate; if the random number is greater than the mutation rate, a mutation is performed. For the particle selected for mutation, a dimension is randomly selected, and the value of the dimension is adjusted according to the mutation rate. The adjusted value is randomly generated within the upper and lower bounds of the dimension. Finally, "damping" is performed by gradually reducing the mutation rate to control the amplitude of the mutation operation.

[0061]

[0062] Where τ is the parameter factor, cycle is the total number of iterations, and i is the i-th iteration in progress.

[0063] Preferably, in order to increase the diversity of solutions, the improved multi-objective particle swarm algorithm optimizes the archive, calculates the crowdedness of the solution, and optimizes and replaces the solutions in the grid with higher crowdedness. Thus, a relatively dispersed set of solutions is retained to improve the search ability of particles, which helps to optimize the quality and diversity of solutions.

[0064] Preferably, the inertia weight is adaptively changed.

[0065] Inertia Weight is a parameter in the particle swarm optimization (PSO) algorithm, usually represented by ω. It controls the proportion of the current velocity of the particle to be retained during the update, thereby affecting the behavior of the particle in the search space. Traditional methods generally fix it, while the present invention adopts a unique nonlinear adaptive periodic strategy to increase or decrease the inertia weight according to the actual situation of the particle swarm.

[0066]

[0067] where ω new and ω old are the new and old inertia weights, respectively, and ΔG is the rate of change of the number of current non-disposable solutions. When it is less than T, there is no significant change, and when it is greater than T, there is a significant change. Through the degree of change in the number of particle swarm optimal solutions, the size of the inertia weight is adaptively controlled to achieve the effect of merging global search and local search.

[0068] On the basis of the above technical solution, compared with the prior art, the advantages of the present invention are:

[0069] A multi-objective, multi-region, and multi-time-scale coordinated optimization scheduling method is proposed. The present invention uniquely realizes the coordinated cooperation of energy flows in multiple regions under multiple time scales and combines the two advantages of lowest scheduling cost and lowest pollution. The natural gas pressure energy is uniquely converted into electrical energy, increasing the proportion of clean energy. This method effectively responds to the uncertainty of supply-side demand response through sophisticated energy flow management and time-tiered optimization strategies, while also solving the inherent volatility and intermittent challenges of renewable distributed energy systems. This innovative scheduling strategy not only improves the overall operating efficiency of the energy system, but also enhances its flexibility and reliability, providing strong support for achieving energy transformation and sustainable development goals.

[0070] The present invention successfully introduced an optimized multi-objective particle swarm algorithm, which has achieved significant improvements in both computing speed and solution quality. Specifically, compared with traditional methods, the algorithm's computing speed has increased by 37.63%, which provides significant advantages in complex application scenarios that require fast solutions. At the same time, the algorithm also performs well in the diversity and quality of solutions, can generate a more diverse solution set, and find candidate solutions that are closer to the true optimal solution, thereby enhancing the globality of the search and the convergence of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 The design process of the present invention;

[0072] Figure 2 This is a simplified topological diagram of a multi-temporal and spatial integrated energy system (taking an industrial zone as an example);

[0073] Figure 3 It is a multi-time scale scheduling flow chart;

[0074] Figure 4 To compare the improved particle swarm algorithm with the traditional particle swarm algorithm;

[0075] Figure 5 To improve the particle swarm algorithm and compare it with the genetic algorithm;

[0076] Figure 6 is the Pareto solution diagram;

[0077] Figure 7 Flowchart for finding the optimal compromise solution;

[0078] Figure 8 It is the balance diagram of electricity supply and demand in industrial area;

[0079] Fig. 9 It is the heat supply and demand balance diagram for industrial areas;

[0080] Fig.10 It is the gas supply and demand balance diagram for industrial areas;

[0081] Fig.11 It is the balance diagram of cold energy supply and demand in industrial area;

[0082] Fig.12 Changes in carbon emissions for industrial, residential, and commercial areas;

[0083] Fig.13 This is the carbon emission distribution map of different components in the industrial area;

[0084] Fig.14 Surface graph of 24-hour cost and carbon emissions. DETAILED DESCRIPTION

[0085] The present invention combines the technical fields of integrated energy system, operations research, multi-objective optimization, deep learning, etc., specifically the following points:

[0086] 1. Energy system optimization and scheduling

[0087] Integrated energy system: This algorithm is aimed at integrated energy systems, which usually contain multiple energy forms (such as electricity, heat, cold, gas, etc.) and multiple energy conversion equipment (such as generators, boilers, refrigerators, etc.). The optimal scheduling of integrated energy systems aims to achieve efficient use of energy and stable operation of the system.

[0088] Multi-temporal and spatial characteristics: Consider multi-temporal and spatial factors, that is, the energy demand and supply at different times and in different spaces (such as different regions and different users), and optimize the scheduling of the system.

[0089] 2. Multi-objective optimization

[0090] Multi-objective optimization theory: This algorithm aims to solve multi-objective optimization problems, that is, to optimize multiple conflicting or mutually constrained objectives at the same time. In the optimization and scheduling of multi-temporal and multi-objective integrated energy systems, these objectives may include economy, environmental protection, reliability, etc.

[0091] Pareto frontier solution set: Through algorithmic solving, a set of Pareto frontier solution sets can be obtained. These solutions achieve the optimal balance between multiple objectives and provide decision makers with a variety of feasible options.

[0092] 3. Particle Swarm Optimization Algorithm

[0093] Particle Swarm Optimization (PSO): Particle Swarm Optimization is an optimization algorithm based on swarm intelligence. It simulates the foraging behavior of bird flocks to find the optimal solution to the problem. The algorithm has the advantages of fewer parameter settings, fast search speed, and easy engineering implementation.

[0094] Improved Multi-Objective Particle Swarm Optimization (MOPSO): Improvements have been made to address the problems of the traditional PSO algorithm in dealing with multi-objective optimization problems (such as slow convergence, local optimal solution problems, etc.). These improvements may include the introduction of random black hole strategies, dynamic updating of inertia weights and learning factors, NSGA-II non-dominated sorting, crowding distance sorting, selection of leader particles, and small probability random mutations.

[0095] 4. Mathematical modeling and simulation

[0096] Mathematical modeling: In order to optimize the system scheduling, it is first necessary to establish a mathematical model of the comprehensive energy system, including energy flow model, equipment model and system constraint model.

[0097] Simulation technology: Through simulation technology, the operating status and scheduling process of the system can be simulated to verify the effectiveness and feasibility of the algorithm.

[0098] 5. Artificial Intelligence and Machine Learning

[0099] Intelligent optimization algorithm: The multi-objective particle swarm algorithm itself is an intelligent optimization algorithm that solves complex problems by simulating group behavior in nature.

[0100] Machine learning technology: In the process of algorithm improvement, machine learning technology may be introduced to enhance the algorithm's search ability and adaptability, such as dynamically adjusting algorithm parameters through an adaptive parameter adjustment mechanism.

[0101] In summary, "An improved multi-objective particle swarm algorithm for solving the problem of optimizing and dispatching multi-temporal and multi-objective integrated energy systems" involves multiple technical fields such as energy system optimization and dispatching, multi-objective optimization, particle swarm optimization algorithm, mathematical modeling and simulation, and artificial intelligence and machine learning. The cross-integration of these technical fields provides strong support for the optimal dispatching of integrated energy systems.

[0102] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0103] The embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0104] [Example 1]

[0105] An improved multi-objective particle swarm solution method for multi-temporal and multi-spatial integrated energy system scheduling is proposed, and its implementation steps are as follows.

[0106] Step 1: Establish a mathematical programming model for a multi-objective, multi-temporal and multi-spatial integrated energy system.

[0107] like Figure 2As shown, this figure is a simplified diagram of the energy flow topology of the industrial zone. From the figure, we can see the components of the model mentioned in this invention, among which the supply side is composed of the power grid, gas network, and heat network; the load side is composed of electric load, heat load, gas load, and cold load; the middle components are photovoltaic power generation, wind power generation, gas turbine, expander, electrolyzer, absorption refrigerator, electric refrigerator, and energy storage equipment for electricity, heat, gas, and cold. Compared with residential areas, commercial areas do not have a large supply of natural gas, so there is no pressure energy, and the rest is the same as the industrial area. At the same time, energy can flow between the three areas, thus forming a complete model of a multi-regional integrated energy system.

[0108] In particular, a natural gas pressure energy power generation system was added during the construction of the mathematical model, which converted the previously unused natural gas pressure energy into electrical energy to participate in the overall energy supply and demand balance of the integrated energy system.

[0109] The photovoltaic power generation model is:

[0110]

[0111] Where G(t) is the light intensity; T ceu is the photovoltaic panel temperature; T amb (t) is the ambient temperature; NOCT is the set temperature; E PV (t) is the photovoltaic power generation power; PMP REF is the rated power; YPV is the temperature coefficient; μDA is the conversion efficiency.

[0112] The wind power generation model is:

[0113]

[0114] In the formula, is the fan output power, v ci 、v co , v, are cut-in wind speed, cut-out wind speed and rated wind speed respectively; P r is the rated output power; a and b are wind speed correlation coefficients.

[0115] The electrolyzer model is:

[0116]

[0117] In the formula, is the hydrogen production power of the electrolyzer; η ED is the hydrogen flow rate per unit time in the electrolyzer; J ED is the current density of the electrolytic cell; V mis the gas molar volume; c1, c2, k1, k2 are coefficients related to Faraday efficiency, c1 = 50, c2 = 1, k1 = 2.5, k2 = 6.25 × 10-6; c is the conversion constant, c = 0.08988 kg / m2; z is the number of electrons transferred in the reaction; F is the Faraday constant, F = 96485 Cmol; V ED is the working voltage of the electrolytic cell; A is the diaphragm area of ​​the electrolytic cell.

[0118] The absorption chiller model is:

[0119] P AR (t) = P WHB，c (t)η AR (5)

[0120] Where P AR represents the cooling power of the absorption refrigeration unit at time t; P WHB,c represents the output power of the waste heat boiler for refrigeration at time t; η AR Represents the refrigeration efficiency of the absorption chiller.

[0121] The electric refrigerator model is:

[0122] C Ec (t) = P EC (t)COP ec (6)

[0123] In the formula, C EC represents the cooling power of the electric refrigerator at time t; P EC Represents the electrical power consumed by the refrigerator at time t; COP ec Refrigeration coefficient of electric refrigerator.

[0124] The expander model is:

[0125]

[0126] Where, Q is the natural gas flow rate; C p is the specific heat capacity of gas; P in With P out The inlet and outlet pressures are: T in is the inlet temperature; k is the natural gas index; there is energy loss in the process of converting pressure energy into electrical energy, which is reflected in the expander efficiency μ tur and generator efficiency μ g superior.

[0127]

[0128] Formula 8 represents the cost of the expander under different operating conditions, which is mainly determined by factors such as the inlet and outlet pressures of natural gas and the flow rate of natural gas.

[0129] The gas turbine model is:

[0130]

[0131] In the formula, Power generation capacity of gas turbine, L gas is the lower calorific value of natural gas, η MT is the power generation efficiency of the gas turbine, is the volume of natural gas consumed by the gas turbine.

[0132] The energy storage model is:

[0133]

[0134] In the above formula, is the energy storage type, including electric energy storage ESS, thermal energy storage TES, cold energy storage CSS, and gas energy storage GSS; γ0 is the ratio of initial energy storage to energy storage capacity; For Node The installed capacity of energy storage of type; is the energy storage at time t; Indicates the charging and discharging power of energy storage equipment; They are the charging efficiency and discharging efficiency of energy storage respectively; is the self-loss factor of energy storage; are the ratio of minimum energy storage / maximum energy storage and energy storage capacity respectively.

[0135] The carbon emission model is:

[0136] Traditional carbon emission calculation methods mainly take into account the two major carbon sources of external grid electricity and external grid gas, while new energy power generation and energy storage devices are usually ignored because they produce almost no carbon emissions during operation. However, the above devices will generate carbon emissions during product production, transportation, installation, and dismantling and recycling. From the perspective of full life cycle carbon emissions, it is necessary to convert them into account to further restrict system carbon emissions.

[0137]

[0138] Where: and are the carbon emissions at time t under scenario s and the total amount of natural gas consumed by each device; a1, a2, a3 and a4 are the carbon emission factors of external grid electricity purchase, external grid gas purchase, photovoltaic power generation and energy storage operation.

[0139] The cost model is:

[0140] F cell =∑ m C buy +C om +Closs (17)

[0141] C om =∑ m P m ×δ m (18)

[0142] C om =∑ m P m ×θ m (19)

[0143] In the formula, C buy is the purchase cost; m is the maintenance cost; C loss is the loss cost; m is the maintenance factor; θ m is the loss factor; m is each component. The cost is a periodic cost, and the full life cycle cost needs to be calculated.

[0144] The present invention uniquely realizes the coordinated coordination of energy flow in multiple regions under multiple time scales and combines the two advantages of the lowest dispatching cost and the lowest pollution. Multi-objective refers to the two objectives of dispatching cost and environmental pollution, multi-region refers to the coordinated dispatching of energy flow between three regions, and multi-time scale refers to the cyclic dispatching method of three levels of time.

[0145] The mathematical models of the three areas are composed separately, which together constitute the mathematical planning model of the multi-objective and multi-temporal and multi-space integrated energy system.

[0146] Step 2: Establish a multi-time scale scheduling plan.

[0147] like Figure 3 As shown in the figure, this is a multi-time scale scheduling scheme for a multi-regional integrated energy system, thereby realizing a multi-time and space integrated energy system. The cyclic scheduling scheme is divided into three parts: day-ahead, mid-day, and real-time, with time scales of 1 hour, 15 minutes, and 5 minutes respectively. Day-ahead scheduling mainly predicts the fluctuation of energy prices through changes in load, and at the same time, with a cycle of 24 hours and a time scale of 1 hour, determines the scheduling strategy for the integrated energy system based on the predicted price fluctuations. Based on the day-ahead scheduling, mid-day scheduling schedules the energy flow between the three zones based on the uncertainty of non-renewable energy, and performs cyclic scheduling with a cycle of 1 hour and a time scale of 15 minutes.

[0148] Step three, improve the existing multi-objective particle swarm optimization method.

[0149] The multi-objective particle swarm optimization algorithm (MOPSO) is a meta-heuristic algorithm for solving multi-objective optimization problems. It is an extension of the standard particle swarm optimization algorithm (PSO). PSO is an optimization algorithm based on swarm intelligence, which simulates the behavior of bird flocks or fish schools and searches for the optimal solution in the solution space through cooperation and information sharing.

[0150] v i =v i +c1×rand()×(pbest i -x i )+c2×rand()×(gbest i -x i ) (20)

[0151] x i =x i +v i (twenty one)

[0152] Where i = 1, 2, ..., N, N is the total number of particles in the group; v i is the speed of the particle; rand() is a random number between (0, 1); x i is the current position of the particle; c1 and c2 are learning factors, usually c1=c2=2; v i The maximum value of v max (greater than 0), if v i Greater than v max , then Formula 20 and Formula 21 are the standard forms of PSO.

[0153] MOPSO introduces the concept of multi-objective optimization problems, which enables the algorithm to solve complex optimization problems with multiple conflicting objectives. The core idea of ​​MOPSO is to simulate the movement of particles in the solution space and maintain a Pareto optimal solution set, that is, a set of solutions that cannot be improved. The characteristic of this set is that it is the optimal solution when no other solution can be better than it in all objectives. To achieve this, MOPSO introduces a fitness function to evaluate the quality of the solution and measures the pros and cons of the solutions through the Pareto dominance relationship. This relationship means that one solution is better than another solution in one objective, but worse than it in another objective.

[0154] When it comes to multi-objective optimization, the design of the fitness function is critical. The fitness function needs to take into account not only the optimization of a single objective, but also the balance between multiple objectives. Generally, the fitness function should be able to evaluate the performance of the solution on multiple objectives and give a comprehensive fitness value based on the specific needs of the problem. The following is an example of a multi-objective fitness function, assuming that we have two objectives to optimize: minimizing the function f1(x) and maximizing the function f2(x):

[0155] Fitness = w2×f1(x)+w2×(1-f2(x)) (22)

[0156] In order to maintain the diversity of the solution set, MOPSO can also adopt some techniques, such as diversity maintenance mechanism and solution aggregation technology. These techniques help to ensure that as many high-quality solutions as possible are found on the entire Pareto frontier, rather than just the local optimal solution.

[0157] In the improved MOPSO algorithm, a local search mechanism is introduced to enhance the combination of the global search capability and the local search capability of the algorithm. Specifically, by dynamically adjusting the mutation rate, the global search is gradually converted to the local search during the iteration process. The improved method of the present invention is the adaptive mutation rate adjustment of the sinusoidal periodic convergence factor; first, according to the current number of iterations and the total number of iterations, the mutation rate pmu is calculated, and an initial mutation rate pmuinit and a final mutation rate pmufinal are defined, and then the initial mutation rate is gradually reduced to the final mutation rate in a sinusoidal distribution during the iteration process, as shown in the formula. The mutation rate decreases with the increase of the number of iterations, so that a wider search can be performed in the early stage of the iteration, and a more local search can be performed in the later stage of the iteration. Then, for each particle, it is determined whether to perform the mutation operation according to the mutation rate; if the random number is greater than the mutation rate, the mutation is performed. For the particle selected for mutation, a dimension is randomly selected, and the value of the dimension is adjusted according to the mutation rate. The adjusted value is randomly generated within the upper and lower bounds of the dimension. Finally, "damping" is performed by gradually reducing the mutation rate to control the amplitude of the mutation operation.

[0158]

[0159] Where τ is the parameter factor, cycle is the total number of iterations, and i is the i-th iteration in progress.

[0160] In order to increase the diversity of solutions, the improved multi-objective particle swarm algorithm optimizes the archive, calculates the crowdedness of the solution, and optimizes and replaces the solutions in the grid with higher crowdedness. In this way, a relatively dispersed set of solutions is retained to improve the search ability of particles, which helps to optimize the quality and diversity of solutions.

[0161] Inertia Weight is a parameter in the particle swarm optimization (PSO) algorithm, usually represented by ω. It controls the proportion of the current velocity of the particle to be retained during the update, thereby affecting the behavior of the particle in the search space. Traditional methods generally fix it, while the present invention adopts a unique nonlinear adaptive periodic strategy to increase or decrease the inertia weight according to the actual situation of the particle swarm.

[0162]

[0163] where ω new and ω old are the new and old inertia weights, respectively, and ΔG is the rate of change of the number of current non-disposable solutions. When it is less than T, there is no significant change, and when it is greater than T, there is a significant change. Through the degree of change in the number of particle swarm optimal solutions, the size of the inertia weight is adaptively controlled to achieve the effect of merging global search and local search.

[0164] like Figure 4 , Figure 5 As shown in the figure, this paper uses the standard test function Sphere to compare the basic PSO algorithm and the improved PSO algorithm to verify the convergence and stability of the algorithm proposed in this section.

[0165] The expression of the standard test function Sphere is as follows:

[0166]

[0167] As can be seen from the figure, the basic SMPSO algorithm and the improved MOPSO algorithm in the Sphere function have two curves. The latter converges faster and has a more uniform convergence effect. The basic MOPSO algorithm in the Rastrigrin function cannot converge to 0, while the improved MOPSO algorithm can converge to 0 quickly. When MOPSO is compared with the genetic algorithm NSGA2, it has stronger dispersion. In summary, the improvement of this algorithm has a better effect on convergence and global adaptability.

[0168] Step 4: Determine the optimal compromise solution among the Pareto solutions.

[0169] like Figure 6 As shown in the figure, it is the Pareto frontier of the multi-temporal and multi-objective integrated energy system. Figure (1) is the process solution, in which the red dot is the current optimal solution, and the blue dot is the dominant solution, that is, the solution set that has been optimized. Figure (2) is the Pareto solution set formed after one hundred iterations, and the Pareto frontier composed of non-dominated solutions.

[0170] In order to better analyze the operating rules of the system, the present invention solves the optimal compromise solution of the system and performs sensitivity analysis on it. The concept of the optimal compromise solution is Pareto optimality, and the formula for obtaining it is as follows.

[0171]

[0172] Among them, w1 and w2 are the weights of the two objectives respectively. This time, the entropy weight method is used to determine the weight parameters. As an objective weighting method, the entropy weight method mainly determines the weights of each indicator in the multi-indicator evaluation system based on the principle of information entropy. Figure 7 As shown in FIG. 1 , the process of determining weights using the entropy weight method is shown in FIG. 1 .

[0173] Step 5: Conduct sensitivity analysis on the results.

[0174] like Figure 8 , Fig. 9 , Fig.10 , Fig.11 As shown in the figure, they are the energy supply and demand balance diagrams taking the industrial zone as an example in the day-ahead dispatch.

[0175] by Figure 8 For example, the power supply and demand diagram shows that photovoltaic power output is concentrated between 6 am and 6 pm, when solar energy can be converted into electricity. Since it is an industrial area, natural gas will have pressure energy generated after expansion and converted into electricity for use. Since natural gas is a stable supply, the pressure energy generated by natural gas is also a stable supply and demand. In addition to the necessary electrical load, the electricity demand also includes electrolytic hydrogen and electric refrigerators, and gas turbines can provide part of the electricity for the supply side. Due to the stable power supply of pressure energy, part of the pressure on the power grid is shared, and the pressure between other areas can be reduced.

[0176] by Fig. 9 For example, the industrial area has no demand for heat load, and the main heat supply is absorption chillers. The absorption chillers require more heat energy from 6:00 to 22:00, which is related to the increase in temperature at noon and the heavy workload of the factory during the day. Since the gas turbine has a lower operating power at night and the price of the heating network is lower at night, the gas turbine output is lower.

[0177] by Fig.10 For example, the demand for natural gas is mainly composed of gas load and gas turbines. Since natural gas is basically purchased from the gas grid, it is a considerable cost. According to the daytime production requirements, the gas load required from 6:00 to 21:00 is higher, and the gas load is lower at night.

[0178] by Fig.11 For example, according to production requirements, the cooling load covers the whole day, but due to the high ambient temperature during the day, the cooling load during the day also increases, reaching its peak at 13:00. The supply side mainly consists of two methods: electric refrigeration and absorption refrigeration. Due to the high carbon emissions generated by electric refrigeration, absorption chillers account for a larger proportion of refrigeration.

[0179] Fig.12 The carbon emission trends of the three districts within 24 hours. In the 24-hour monitoring, the carbon emission data of industrial areas, commercial areas and residential areas showed different characteristics and trends. The carbon emission in the industrial area is the highest and fluctuates greatly. The emission peak coincides with the peak period of industrial production activities. Although it decreases at night, it still maintains a high emission level. The carbon emission in the commercial area is relatively stable. The emission is higher during daytime working hours and evening business activities, and significantly lower at night. The carbon emission in the residential area changes with the changes in residents' activities. The emission is lowest from night to early morning, and reaches a peak from dusk to night due to the increase in residents' daily activities. Overall, the peak carbon emission in the industrial area is significantly higher than that in the commercial area and residential area, while the difference between the commercial area and the residential area is relatively small. In order to reduce carbon emissions, each region should take measures such as optimizing production processes, rationally planning commercial activities, and encouraging energy-saving and low-carbon lifestyles. At the same time, the government should also strengthen supervision and management to promote the development of a low-carbon economy. The implementation of these measures will help reduce carbon emissions, protect the environment and achieve sustainable development.

[0180] Fig.13 This is the distribution map of carbon emissions of different components in industrial areas. The sources of carbon emissions in industrial areas are diverse, among which the purchase of electricity, gas and heat dominate, accounting for 28.13%, 30.14% and 24.15% respectively. Gas turbines, as important equipment for industrial production, also account for 14.80% of carbon emissions. In contrast, the carbon emissions of clean energy such as electric refrigerators, photovoltaics and wind power account for very low proportions, at 2.67%, 0.06% and 0.06% respectively. This shows that in carbon emissions in industrial areas, traditional energy consumption is still the main source, while the use of clean energy still needs to be strengthened. In order to reduce carbon emissions, the energy structure should be further optimized and the proportion of clean energy should be increased.

[0181] Fig.14 The figure is a 24-hour cost and carbon emission surface diagram. In the 24-hour time period, the carbon emissions and cost data of this study showed significant volatility. Carbon emissions experienced multiple ups and downs in a day, with peaks occurring at the 8th and 19th hours. These two periods are likely to coincide with the peak periods of production activity intensity and energy consumption patterns, such as concentrated periods of industrial production or busy periods of commercial activities. The valley values ​​of carbon emissions occurred at the 23rd and 2nd hours, reflecting a reduction in production activities or a low period of energy use, such as factory shutdowns at night and reduced electricity consumption by residents.

[0182] Cost data also fluctuates significantly, but its peak hours are mainly concentrated in the noon, evening and night, which is related to the peak of energy consumption, electricity price fluctuations (such as peak-valley electricity price differences) or specific changes in production efficiency during this period. Due to the increase in electricity consumption in residential areas in the evening, the cost is higher, but there is still a gap compared to the midday when production tasks are heavy. It is worth noting that although there is a certain positive correlation between carbon emissions and costs, the fluctuations of the two are not completely synchronized. This difference may be due to the combined influence of multiple factors, including energy types (such as the mixed use of natural gas and renewable energy), fluctuations in production efficiency, and electricity price policies.

[0183] The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims. Anything not described in the present invention is applicable to the prior art.

Claims

1. An improved multi-objective particle swarm solution method for multi-temporal and multi-spatial integrated energy system scheduling, comprising the following steps: A multi-objective, multi-temporal and multi-space integrated energy system scheduling optimization mathematical model is established. In particular, an expander structure is proposed for the unused natural gas pressure energy, which converts the pressure energy into electrical energy to participate in the energy supply and demand balance. After the model is established, the improved multi-objective particle swarm algorithm of the present invention is used to solve its optimal scheduling scheme and conduct a sensitivity analysis. The basic components of the mathematical programming model include photovoltaic power generation, wind power generation, gas turbines, electrolyzers, expanders, electric refrigerators, absorption refrigerators, batteries, heat storage tanks, cold storage tanks, and gas storage tanks; the supply side is the power grid, gas grid, and heat grid; the load side is the electric load, heat load, gas load, and cold load; the decision variables are the real-time power of each component, the storage state of the storage system, and the energy flow between the areas; the constraints are the design principles of each component itself and the energy balance between output and use under the condition of meeting the load side requirements; The objective function is to minimize the dispatch cost and the carbon emission when the load is met; In particular, a natural gas pressure energy power generation system was added during the construction of the mathematical model, which converts the previously unused natural gas pressure energy into electrical energy to participate in the overall energy supply and demand balance of the integrated energy system; The photovoltaic power generation model is: Where G(t) is the light intensity; T cell (t) is the temperature of the photovoltaic panel; T amb (t) is the ambient temperature; NOCT is the set temperature; E PV (t) is the photovoltaic power generation power; PMP REF is the rated power; γ PV is the temperature coefficient; μ DA is the conversion efficiency; The wind power generation model is: In the formula, is the fan output power, v ci 、v co , v, are cut-in wind speed, cut-out wind speed and rated wind speed respectively; P r is the rated output power; a and b are wind speed correlation coefficients. The electrolyzer model is: In the formula, is the hydrogen production power of the electrolyzer; η ED is the hydrogen flow rate per unit time in the electrolyzer; J ED is the current density of the electrolytic cell; V m is the gas molar volume; c1, c2, k1, k2 are coefficients related to Faraday efficiency, c1 = 50, c2 = 1, k1 = 2.5, k2 = 6.25 × 10-6; c is the conversion constant, c = 0.08988 kg / m2; z is the number of electrons transferred in the reaction; F is the Faraday constant, F = 96485 Cmol; V ED is the working voltage of the electrolytic cell; A is the diaphragm area of ​​the electrolytic cell; The absorption chiller model is: P AR (t)=P WHB,c (t)η AR (5) Where P AR represents the cooling power of the absorption refrigeration unit at time t; P WHB，c represents the output power of the waste heat boiler for refrigeration at time t; η AR Represents the refrigeration efficiency of the absorption chiller; The electric refrigerator model is: C EC (t)=P EC (t)COP ec (6) In the formula, C EC represents the cooling power of the electric refrigerator at time t; P EC Represents the electrical power consumed by the refrigerator at time t; COP ec Refrigeration coefficient of electric refrigerator; The expander model is: Where, Q is the natural gas flow rate; C p is the specific heat capacity of gas; P in With P out are the inlet and outlet pressures respectively; T in is the inlet temperature; k is the natural gas index; there is energy loss in the process of converting pressure energy into electrical energy, which is reflected in the expander efficiency μ tur and generator efficiency μ g superior; Formula 6 represents the cost of the expander under different operating conditions, which is mainly determined by factors such as the inlet and outlet pressures of natural gas and the flow rate of natural gas; The gas turbine model is: In the formula, Power generation capacity of gas turbine, L gas is the lower calorific value of natural gas, η MT is the power generation efficiency of the gas turbine, is the volume of natural gas consumed by the gas turbine; The energy storage model is: In the above formula, is the energy storage type, including electric energy storage ESS, thermal energy storage TES, cold energy storage CSS, and gas energy storage GSS; γ0 is the ratio of initial energy storage to energy storage capacity; is the installed capacity of energy storage of type at node φ; is the energy storage at time t; Indicates the charging and discharging power of energy storage equipment; They are the charging efficiency and discharging efficiency of energy storage respectively; is the self-loss factor of energy storage; They are the ratio of minimum energy storage / maximum energy storage and energy storage capacity: The carbon emission model is: Traditional carbon emission calculation methods mainly take into account the two major carbon sources of electricity and gas purchased from the external network, while new energy power generation and energy storage devices are usually ignored because they produce almost no carbon emissions during operation; however, the above devices will generate carbon emissions during the product production, transportation, installation, and dismantling and recycling processes. From the perspective of carbon emissions throughout the life cycle, it is necessary to convert them into account to further restrict system carbon emissions; Where: and are the carbon emissions at time t under scenario s and the total amount of natural gas consumed by each device; a1, a2, a3 and a4 are the carbon emission factors of external grid electricity purchase, external grid gas purchase, photovoltaic power generation and energy storage operation respectively; The cost model is: F cell =∑ m C buy +C om +C loss (17) C om =∑ m P m ×δ m (18) C om =∑ m P m ×θ m (19) In the formula, C buy is the purchase cost; Com is the maintenance cost; C loss is the loss cost; m is the maintenance factor; θ m is the loss factor; m is each component. The cost is the periodic cost, and the full life cycle cost needs to be calculated; The present invention uniquely realizes the coordinated coordination of energy flow in multiple regions under multiple time scales and combines the two advantages of the lowest dispatching cost and the lowest pollution; the multi-objective refers to the two objectives of dispatching cost and environmental pollution, the multi-region refers to the coordinated dispatching of energy flow between three regions, and the multi-time scale refers to the cyclic dispatching method of three levels of time; The mathematical models of the three areas are composed separately, which together constitute the mathematical planning model of the multi-objective and multi-temporal and multi-space integrated energy system.

2. The improved multi-objective particle swarm solution method for multi-temporal and multi-spatial integrated energy system scheduling as claimed in claim 1, characterized in that: The improved multi-objective particle swarm algorithm is: By improving the adaptive mutation rate adjustment and the adaptive inertia weight adjustment, the traditional algorithm can expand the local search mechanism, speed up the search and improve the population quality. The multi-objective particle swarm optimization algorithm (MOPSO) is a meta-heuristic algorithm for solving multi-objective optimization problems. It is an extension of the standard particle swarm optimization algorithm (PSO). PSO is an optimization algorithm based on swarm intelligence, which simulates the behavior of bird flocks or fish schools and searches for the optimal solution in the solution space through cooperation and information sharing. v i =v i +c1×rand()×(pbest i -x i )+c2×rand()×(gbest i -x i ) (20) x i =x i +v i (21) Where i = 1, 2, ..., N, N is the total number of particles in the group; v i is the speed of the particle, rand() is a random number between (0, 1); i is the current position of the particle; c1 and c2 are learning factors, usually c1=c2=2; v i The maximum value of v max (greater than 0), if v i Greater than v max , then Formula 20 and Formula 21 are the standard forms of PSO; MOPSO introduces the concept of multi-objective optimization problems, which enables the algorithm to solve complex optimization problems with multiple conflicting objectives. The core idea of ​​MOPSO is to simulate the movement of particles in the solution space and maintain a Pareto optimal solution set, that is, a set of solutions that cannot be improved. The characteristic of this set is that it is the optimal solution when no other solution can be better than it in all objectives. To achieve this, MOPSO introduces a fitness function to evaluate the quality of the solution and measures the pros and cons of the solutions through the Pareto dominance relationship. This relationship means that one solution is better than another solution in one objective, but worse than it in another objective. When it comes to multi-objective optimization, the design of the fitness function is critical. The fitness function needs to take into account not only the optimization of a single objective, but also the balance between multiple objectives. Generally, the fitness function should be able to evaluate the performance of the solution on multiple objectives and give a comprehensive fitness value based on the specific needs of the problem. The following is an example of a multi-objective fitness function, assuming that we have two objectives to optimize: minimizing the function f1(x) and maximizing the function f2(x): Fitness = w2×f1(x)+w2×(1-f2(x)) (22) In order to maintain the diversity of the solution set, MOPSO can also adopt some techniques, such as diversity preservation mechanism and solution aggregation technology; these techniques help to ensure that as many high-quality solutions as possible are found on the entire Pareto frontier, rather than just the local optimal solution.

3. The improved multi-objective particle swarm algorithm according to claim 2, characterized in that: In the improved MOPSO algorithm, a local search mechanism is introduced to enhance the combination of the global search capability and the local search capability of the algorithm; the improved method of the present invention is the adaptive mutation rate adjustment of the sinusoidal periodic convergence factor; first, according to the current number of iterations and the total number of iterations, the mutation rate pmu is calculated, by defining an initial mutation rate pmuinit and a final mutation rate pmufinal, and then the initial mutation rate is gradually reduced linearly to the final mutation rate during the iteration process, as shown in the formula; the mutation rate decreases with the increase of the number of iterations, so as to perform a wider search in the early iteration and a more local search in the later iteration; then, for each particle, decide whether to perform the mutation operation according to the mutation rate; if the random number is greater than the mutation rate, perform mutation; for the particle selected for mutation, randomly select a dimension and adjust the value of the dimension according to the mutation rate. The adjusted value is randomly generated within the upper and lower bounds of the dimension: finally, "damping" is performed by gradually reducing the mutation rate to control the amplitude of the mutation operation. Where τ is the parameter factor, cycle is the total number of iterations, and i is the i-th iteration in progress.

4. The improved multi-objective particle swarm algorithm according to claim 2, characterized in that: In order to increase the diversity of solutions, the improved multi-objective particle swarm algorithm optimizes the archive, and by calculating the crowdedness of the solution, optimizes and replaces the solution in the grid with higher crowdedness; thereby retaining a relatively scattered set of solutions to improve the search ability of particles, which helps to optimize the quality and diversity of solutions; Inertia Weight is a parameter in the particle swarm optimization (PSO) algorithm, usually represented by ω. It controls the proportion of the current velocity of the particle to be retained during the update, thereby affecting the behavior of the particle in the search space. Traditional methods generally fix it, but the present invention adopts a unique nonlinear adaptive periodic strategy to increase or decrease the inertia weight according to the actual situation of the particle swarm; where ω new and ω old are the new and old inertia weights, respectively, and ΔG is the rate of change of the number of current non-disposable solutions. When it is less than T, there is no significant change, and when it is greater than T, there is a significant change. Through the degree of change in the number of particle swarm optimal solutions, the size of the inertia weight is adaptively controlled to achieve the effect of merging global search and local search.

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