Improved multi-objective particle swarm optimization method for solving multi-time and space comprehensive energy system scheduling

Abstract

The application discloses an improved multi-objective particle swarm optimization method for solving multi-time-space comprehensive energy system scheduling, and a flow chart is shown in figure one. It is especially related to the fields of operational research, comprehensive energy system, multi-objective optimization, etc. Its components include two parts of model and solving algorithm, wherein the model is a mathematical model of the comprehensive energy system scheduling for the collaborative scheduling multi-time scale rolling optimization of industrial areas, commercial areas and residential areas, and the objective functions are respectively the lowest cost and the lowest carbon emission; the solving algorithm is an improved multi-objective particle swarm optimization algorithm, compared with the traditional algorithm, the local search mechanism is introduced, the storage system is adjusted, and the adaptive adjustment of the inertia weight is adjusted. The model adds the expander to utilize the excess natural gas pressure energy, and compared with the traditional algorithm, the algorithm is more diverse, faster and higher in quality, and effectively solves the problems of the current comprehensive energy system, such as complex environment, too much uncertainty, single target and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to integrated energy systems; in particular, to a multi-time-space multi-objective integrated energy system optimization scheduling. BACKGROUND

[0002] The current global energy production and consumption revolution is deepening, and the energy system is continuously transforming towards green, low-carbon, clean, efficient, intelligent, and diversified. The global energy system is shifting from absolute dominance of fossil energy to low-carbon multi-energy integration, and the new round of energy revolution is characterized by large-scale low-carbon energy, clean traditional energy, diversified energy supply, efficient end-use energy, and intelligent energy system.

[0003] Integrated energy systems (IES) consist of supply side, demand side, energy conversion and storage, and are currently a hot research topic. However, with increasingly complex loads and environments, the scheduling problem of integrated energy systems is gradually developing towards multi-time-space. However, there are still many problems in realizing the operation and scheduling of multi-time-space integrated energy systems, such as too many uncertain parameters, how to design multi-time-space, considering pollution may conflict with cost optimization, etc.

[0004] The scheduling problem of IES is not limited to single time scale optimization, but needs to consider the coordinated optimization of multiple time scales. This includes 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-demand balance between multiple regions. In addition, uncertain factors such as renewable energy output fluctuation and demand side response uncertainty further increase the difficulty of scheduling.

[0005] To solve the above problems, academia and industry have conducted a lot of research and proposed various models and optimization methods. In terms of model construction, researchers have established mathematical models that can represent the complex characteristics of IES based on graph theory, scenario tree method, EMP framework, etc. At the same time, to solve the problem of multi-time-space integration, researchers have proposed multi-time scale rolling scheduling model, two-stage optimization scheduling strategy, etc. to realize the coordinated optimization of different time scales. In addition, to deal with uncertainty, researchers have also introduced distributed robust optimization, fuzzy mathematics theory, model predictive control, etc. to improve the robustness and flexibility of scheduling.

[0006] In the optimization method, traditional algorithms such as particle swarm optimization and firefly algorithm are widely used in the optimization scheduling of IES. 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, dynamic adaptive firefly algorithm, etc. These algorithms perform well in solving multi-objective optimization problems, and can find the optimal balance point between cost, efficiency, environmental protection and other objectives.

[0007] In order to further improve the low-carbon and economic benefits of IES, researchers have also introduced new technical elements such as hydrogen production and pressure energy utilization. These technologies 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 optimization scheduling of IES, and by adjusting the weight coefficient, the contradiction between operation cost and environmental pollution can be balanced. This strategy makes it possible for IES to optimize scheduling under different demand scenarios.

[0008] In summary, multi-objective multi-time and space adaptive comprehensive energy system optimization scheduling is a hot and difficult topic of current research. With the continuous emergence and application of new technologies and methods, the scheduling problem of IES will be more effectively solved, and greater contribution will be made to the green transformation and sustainable development of energy systems. SUMMARY

[0009] In view of the defects in the prior art, the purpose of the present application is to solve the scheduling problem of multi-time and space comprehensive energy system by multi-objective particle swarm optimization.

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

[0011] An improved multi-objective particle swarm optimization method for solving multi-time and space comprehensive energy system scheduling, comprising the following steps: first, a mathematical programming model of multi-objective multi-time and space comprehensive energy system is established, the basic components are photovoltaic power generation, wind power generation, gas turbine, electrolytic cell, expander, electric refrigerator, absorption refrigerator, battery, hot storage tank, cold storage tank, gas storage tank; the supply side is power grid, gas network, heat network. The load side is electric load, heat load, gas load, cold load; the decision variable is the real-time power of each component, the storage state of the storage system and the energy flow between each region, the constraint is the design principle of each component itself and the energy balance of output and effort under the condition of meeting the demand of the load side; the objective function is to minimize the scheduling cost and minimize the carbon emission under the condition of meeting the load side.

[0012] In particular, a natural gas pressure energy power generation system is added in the process of constructing the mathematical model, which converts the previously unused natural gas pressure energy into electric energy to participate in the overall energy supply and demand balance of the comprehensive energy system.

[0013] The photovoltaic power generation model is:

[0014]

[0015] In the formula, 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 is the conversion efficiency.

[0016] The wind power generation model is:

[0017]

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

[0019] The electrolytic cell model is:

[0020]

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

[0022] The absorption refrigeration machine model is:

[0023] P AR (t) = P WHB,c (t) η AR (5)

[0024] In the formula, P AR represents the refrigeration 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 refrigeration machine.

[0025] The model of the electric refrigerator is:

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

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

[0028] The model of the expander is:

[0029]

[0030] In the formula, Q is the flow rate of natural gas; C p is the specific heat capacity of the gas; P in and 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 electric energy, which is reflected in the expander efficiency μ tur and the generator efficiency μ g .

[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 model of the gas turbine is:

[0034]

[0035] In the formula, is the power generation of the gas turbine, L gas is the low heat 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 model of energy storage is:

[0037]

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

[0039] The carbon emission model is as follows:

[0040] Traditional carbon emission calculation methods primarily consider the two major carbon sources: electricity and gas purchased from the external grid. New energy power generation and energy storage devices are typically ignored because they generate almost no carbon emissions during operation. However, these devices generate carbon emissions during product manufacturing, transportation, installation, and dismantling and recycling. From a life-cycle carbon emission perspective, it is necessary to include these emissions to further control system carbon emissions.

[0041]

[0042] In the formula: and A1 represents the carbon emissions at time t under scenario s, and B2 represents the total amount of natural gas consumed by each device. A3 and B4 represent the carbon emission factors for electricity purchased from the external grid, gas purchased from the external grid, photovoltaic power generation, and energy storage operation, respectively.

[0043] The cost model is as follows:

[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 For purchase cost; C om To maintain costs; C loss For loss cost; δ m For maintenance factors; θ m is the loss factor; m represents each component. The cost is a periodic cost, and the total life-cycle cost needs to be calculated.

[0048] This invention uniquely achieves coordinated energy flow across multiple regions at multiple time scales, combining the advantages of lowest scheduling cost and minimal pollution. "Multi-objective" refers to the dual objectives of scheduling cost and environmental pollution; "multi-regional" refers to the coordinated scheduling of energy flow among three regions; and "multi-time scale" refers to a cyclical scheduling method across three time levels.

[0049] The three regions are used to form mathematical models, which together constitute a mathematical planning model for a multi-objective, multi-temporal integrated energy system.

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

[0051] Multi-objective Particle Swarm Optimization (MOPSO) is a metaheuristic algorithm for solving multi-objective optimization problems. It is an extension of the standard Particle Swarm Optimization (PSO) algorithm. PSO is an optimization algorithm based on swarm intelligence, simulating the behavior of flocks of birds or schools of fish, searching 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] In the formula, i = 1, 2, ..., N, where N is the total number of particles in the group; v i It represents the particle's velocity; rand() is a random number between (0, 1); x i c1 is the particle's current position; c1 and c2 are learning factors, usually c1 = c2 = 2; v i The maximum value is v max (greater than 0), if v i Greater than v max Then, Formulas 20 and 21 are the standard forms of PSO.

[0055] MOPSO introduces the concept of multi-objective optimization problems, enabling 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 set of Pareto-optimal solutions, which are the set of solutions that cannot be improved. This set is characterized by being the best solution in the absence of other solutions that are better in all objectives. To achieve this, MOPSO introduces a fitness function to evaluate the quality of solutions and a Pareto dominance relation to measure the superiority of solutions over each other. This relation refers to a solution being better in one objective and worse in another objective than another solution.

[0056] The design of the fitness function is crucial when dealing with multi-objective optimization. The fitness function needs to consider not only the optimization of individual objectives but also the balance between multiple objectives. Typically, the fitness function should be able to evaluate the performance of solutions on multiple objectives and give a comprehensive fitness value according to the specific needs of the problem. Here is an example of a multi-objective fitness function, assuming we have two objectives to optimize: minimizing function f1(x) and maximizing function f2(x):

[0057] Fitness = w1 x f1(x) + w2 x (1 - f2(x)) (22)

[0058] To maintain the diversity of the solution set, MOPSO can also employ techniques such as diversity preservation mechanisms and solution aggregation techniques. These techniques help ensure that as many high-quality solutions as possible are found across the entire Pareto front, not just local optimal solutions.

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

[0060] The improved method of the present application is a sine periodic convergence factor adaptive mutation rate adjustment. First, according to the current iteration number and the total iteration number, the mutation rate pmu is calculated, and by defining an initial mutation rate pmuinit and a final mutation rate pmufinal, 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 iteration number, so as to carry out a more extensive search in the early iteration and a more local search in the later iteration. Next, 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, the mutation is performed. For the selected particle to be mutated, 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, the mutation operation is controlled by gradually reducing the mutation rate in the form of "damping".

[0061]

[0062] where τ is a parameter factor, cycle is the total number of iterations, and i is the i th iteration being performed.

[0063] Preferably, in order to increase the diversity of solutions, the improved multi-objective particle swarm algorithm optimizes the archive, and by calculating the crowding degree of the solution, the solution in the grid with high crowding degree is replaced, so that a relatively dispersed solution set is retained, thereby improving the search ability of the particles and helping to improve the quality and diversity of the optimized solution.

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

[0065] The inertia weight (Inertia Weight) is a parameter in the particle swarm optimization (PSO) algorithm, usually represented by ω. It controls the proportion of the current speed of the particle that is retained in the update, thereby affecting the behavior of the particle in the search space. The traditional method generally fixes it, and the present application uses a unique nonlinear adaptive periodic strategy to make the inertia weight increase or decrease with 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 change rate of the current non-dominated solution quantity, which is not significantly changed when it is less than T, and is significantly changed when it is greater than T. By the degree of change of the population number of the best solution of the particle swarm, the size of the inertia weight is adaptively controlled, achieving the effect of combining global search and local search.

[0068] Based on the above technical solutions, compared with the prior art, the present application has the following advantages:

[0069] A multi-objective multi-region multi-time scale coordinated optimization scheduling method is proposed, which uniquely realizes the energy flow circulation coordination of multi-regions in the case of multi-time scale and combines the advantages of the lowest scheduling cost and the smallest pollution. The unique conversion of natural gas pressure energy into electric energy increases the proportion of clean energy. This method effectively deals with the uncertainty of supply-side demand response through fine energy flow management and time gradient optimization strategy, and also solves the inherent volatility and intermittency challenges of renewable distributed energy systems. This innovative scheduling strategy not only improves the overall operation efficiency of the energy system, but also enhances its flexibility and reliability, providing strong support for energy transformation and sustainable development goals.

[0070] The application successfully puts forward an optimized multi-objective particle swarm algorithm, which realizes significant improvement in operation speed and solution quality. Specifically, compared with the traditional method, the operation speed of the algorithm is improved by 37.63%, which provides a significant advantage in complex application scenarios that require fast solution. At the same time, the algorithm also performs well in the diversity and quality of the solution, can generate a more diverse solution set, and find a candidate solution closer to the real optimal solution, thereby enhancing the global search and convergence of the algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0071] Figure 1 The design process of the application;

[0072] Figure 2 The multi-time and space comprehensive energy system topology diagram (industrial area as an example);

[0073] Figure 3 The multi-time scale scheduling flowchart;

[0074] Figure 4 Comparison of improved particle swarm and traditional particle swarm algorithm;

[0075] Figure 5 Comparison of improved particle swarm algorithm and genetic algorithm;

[0076] Figure 6 Pareto solution set diagram;

[0077] Figure 7 Flowchart for solving optimal compromise solution;

[0078] Figure 8 Industrial area electric energy supply and demand balance diagram;

[0079] Figure 9 Industrial area heat energy supply and demand balance diagram;

[0080] Figure 10 Industrial area gas energy supply and demand balance diagram;

[0081] Figure 11 Industrial area cold energy supply and demand balance diagram;

[0082] Figure 12 Carbon emission changes in industrial area, residential area and commercial area;

[0083] Figure 13 Industrial area different component carbon emission distribution diagram;

[0084] Figure 14 24-hour cost and carbon emission surface diagram. DETAILED DESCRIPTION

[0085] The invention combines the fields of integrated energy systems, operations research, multi-objective optimization, and deep learning. Specifically, it involves the following points:

[0086] 1. Energy system optimization and scheduling

[0087] Integrated energy system: The algorithm targets integrated energy systems, which typically include multiple energy forms (such as electricity, heat, cold, gas, etc.) and multiple energy conversion devices (such as generators, boilers, refrigerators, etc.). The optimization and scheduling of integrated energy systems aim to achieve efficient energy utilization and stable system operation.

[0088] Multi-time and space characteristics: The algorithm considers multiple time and space factors, i.e., energy demand and supply under different times and different spaces (such as different regions, different users), to optimize and schedule the system.

[0089] 2. Multi-objective optimization

[0090] Multi-objective optimization theory: The algorithm aims to solve multi-objective optimization problems, i.e., optimizing multiple conflicting or interdependent objectives simultaneously. In the multi-time and space multi-objective integrated energy system optimization and scheduling, these objectives may include economic efficiency, environmental protection, and reliability.

[0091] Pareto frontier solution set: Through the algorithm, a set of Pareto frontier solutions can be obtained, which achieve an optimal balance between multiple objectives and provide decision-makers with multiple feasible options.

[0092] 3. Particle swarm optimization algorithm

[0093] Particle swarm optimization algorithm (PSO): Particle swarm optimization is a swarm intelligence-based optimization algorithm that simulates the foraging behavior of bird flocks to find the optimal solution to a problem. This algorithm has the advantages of few parameters, fast search speed, and easy engineering implementation.

[0094] Improved multi-objective particle swarm optimization algorithm (MOPSO): To address the problems of traditional PSO algorithms in handling multi-objective optimization problems (such as slow convergence speed and local optimal solution), improvements have been made. These improvements may include the introduction of random black hole strategy, dynamic updating of inertia weight and learning factor, NSGA-II non-dominated sorting, crowded distance sorting, leader particle selection, and small probability random mutation methods.

[0095] 4. Mathematical modeling and simulation

[0096] Mathematical modeling: To optimize and schedule the system, a mathematical model of the integrated energy system needs to be established, including energy flow models, device models, and system constraint models.

[0097] Simulation technology: Through simulation technology, the running state 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: Multi-objective particle swarm optimization algorithm itself is an intelligent optimization algorithm, which solves complex problems by simulating group behavior in nature.

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

[0101] In summary, "an improved multi-objective particle swarm optimization algorithm for solving multi-time and space multi-objective comprehensive energy system optimization scheduling problem" involves multiple technical fields such as energy system optimization and scheduling, multi-objective optimization, particle swarm optimization algorithm, mathematical modeling and simulation, and artificial intelligence and machine learning. The cross-fusion of these technical fields provides strong support for the optimization and scheduling of comprehensive energy systems.

[0102] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below in combination 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 the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0103] The embodiments of the present application will be further described in detail below in combination with the drawings.

[0104]

Embodiment 1

[0105] An improved multi-objective particle swarm optimization method for solving multi-time and space comprehensive energy system scheduling, the implementation steps are as follows.

[0106] Step one establishes the mathematical programming model of multi-objective multi-time and space comprehensive energy system.

[0107] For example Figure 2As shown, the figure is a simple diagram of energy flow topology of industrial area, from which the components of the model mentioned in the present application can be seen, wherein the supply side is composed of power grid, gas grid and heat grid; the load side is composed of electric load, heat load, gas load and cold load; the components in the middle are respectively photovoltaic power generation, wind power generation, gas turbine, expander, electrolyzer, absorption refrigerator, electric refrigerator and energy storage devices of electricity, heat, gas and cold. Compared with residential area, commercial area has no large supply of natural gas, so there is no pressure energy, and the rest is the same as industrial area. At the same time, energy can flow among the three areas, thus forming a complete model of multi-area integrated energy system.

[0108] In particular, a natural gas pressure energy power generation system is added in the process of constructing the mathematical model, which converts the previously unused natural gas pressure energy into electric 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] In the formula, G(t) is the light intensity; T ceu is the temperature of photovoltaic panel; T amb (t) is the ambient temperature; NOCT is the set temperature; E PV (t) is the photovoltaic power; PMP REF is the rated power; YPV is the temperature coefficient; and μDA is the conversion efficiency.

[0112] The wind power generation model is:

[0113]

[0114] In the formula, is the output power of the fan, v ci , v co , v are respectively the cut-in wind speed, the cut-out wind speed and the rated wind speed; P r is the rated output power; and a, b are wind speed related 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 of the electrolyzer per unit time; J ED is the current density of the electrolyzer; and V mV is the working voltage of the electrolytic cell; A is the membrane area of the electrolytic cell. ED V is the working voltage of the electrolytic cell; A is the membrane area of the electrolytic cell.

[0118] The model of the absorption refrigeration machine is:

[0119] P AR (t) = P WHB，c (t)η AR (5)

[0120] P AR represents the refrigeration power of the absorption refrigeration machine 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 refrigeration machine.

[0121] The model of the electric refrigeration machine is:

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

[0123] P EC represents the refrigeration power of the electric refrigeration machine at time t; P EC represents the electric power consumed by the electric refrigeration machine at time t; COP ec is the refrigeration coefficient of the electric refrigeration machine.

[0124] The model of the expander is:

[0125]

[0126] Q is the flow rate of natural gas; C p is the specific heat capacity of the gas; P in and 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 electric energy, which is reflected in the expander efficiency μ tur and the generator efficiency μ g .

[0127]

[0128] Equation 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, the flow rate of natural gas, etc.

[0129] The gas turbine model is:

[0130]

[0131] In the formula, The power generation of the gas turbine, L gas The low heat value of natural gas, η MT The power generation efficiency of the gas turbine, The volume of natural gas consumed by the gas turbine.

[0132] The energy storage model is:

[0133]

[0134] In the above formula, 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 the initial energy storage to the energy storage capacity; The node The installation capacity of the energy storage of type at node ; The energy storage at time t; Indicates the charging and discharging power of the energy storage device; The charging efficiency and discharging efficiency of the energy storage, respectively; The self-loss factor of the energy storage; The ratio of the minimum energy storage / maximum energy storage to the energy storage capacity, respectively.

[0135] The carbon emission model is:

[0136] The traditional carbon emission calculation method mainly considers two carbon sources, i.e., external grid electricity purchase and external grid gas purchase. However, new energy power generation and energy storage devices are usually ignored because they almost do not produce carbon emissions during operation. However, the above devices will produce carbon emissions during product production, transportation, installation, and removal and recycling. From the perspective of whole life cycle carbon emissions, it is necessary to take them into account to further restrict system carbon emissions.

[0137]

[0138] In the formula: And The carbon emission at time t under scenario s and the total amount of natural gas consumed by each device, respectively; 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.

[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 For purchase cost; Co m To maintain costs; C loss For loss cost; δ m For maintenance factors; θ m is the loss factor; m represents each component. The cost is a periodic cost, and the total life-cycle cost needs to be calculated.

[0144] This invention uniquely achieves coordinated energy flow across multiple regions at multiple time scales, combining the advantages of lowest scheduling cost and minimal pollution. "Multi-objective" refers to the dual objectives of scheduling cost and environmental pollution; "multi-regional" refers to the coordinated scheduling of energy flow among three regions; and "multi-time scale" refers to a cyclical scheduling method across three time levels.

[0145] The three regions are used to form mathematical models, which together constitute a mathematical planning model for a multi-objective, multi-temporal integrated energy system.

[0146] Step two: Establish a multi-timescale scheduling scheme.

[0147] like Figure 3 As shown in the figure, this is a multi-timescale scheduling scheme for a multi-regional integrated energy system, thereby realizing a multi-temporal and spatial integrated energy system. This cyclical scheduling scheme is divided into three parts: day-ahead, mid-day, and real-time, with timescales of 1 hour, 15 minutes, and 5 minutes, respectively. Day-ahead scheduling mainly predicts energy price fluctuations based on load changes, and determines the scheduling strategy for the integrated energy system based on the predicted price fluctuations, using a 24-hour cycle and a 1-hour timescale. Mid-day scheduling, based on day-ahead scheduling and considering the uncertainty of non-renewable energy, schedules energy flows between the three regions, using a 1-hour cycle and a 15-minute timescale.

[0148] Step 3: Improve the existing multi-objective particle swarm optimization method.

[0149] Multi-objective particle swarm optimization (MOPSO) is a metaheuristic algorithm for solving multi-objective optimization problems, which is an extension of the standard particle swarm optimization (PSO). PSO is a swarm intelligence-based optimization algorithm that simulates the behavior of bird or fish swarms, searching for optimal solutions in the solution space through cooperation and information sharing.

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

[0151] x i = x i + v i (21)

[0152] where i = 1, 2,..., N, N is the total number of particles in the swarm; v i is the velocity 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 has a maximum value of v max (greater than 0), if v i is greater than v max , then equation 20, equation 21 are the standard form of PSO.

[0153] MOPSO introduces the concept of multi-objective optimization problems, enabling 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 set of Pareto optimal solutions, which are a set of solutions that cannot be improved. This set is characterized by being the optimal solution in the absence of other solutions that are better in all objectives. To achieve this, MOPSO introduces a fitness function to evaluate the quality of solutions and measures the superiority of solutions through the Pareto dominance relationship. This relationship refers to a solution that is superior to another solution in one objective and inferior to it in another objective.

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

[0155] Fitness = w1 x f1(x) + w2 x (1 - f2(x)) (22)

[0156] To maintain the diversity of the solution set, MOPSO can also employ techniques such as a diversity preservation mechanism and a solution clustering technique. These techniques help ensure that as many high-quality solutions as possible are found across the entire Pareto front, rather than just local optima.

[0157] In the improved MOPSO algorithm, a local search mechanism is introduced to enhance the combination of global and local search capabilities. Specifically, by dynamically adjusting the mutation rate, the algorithm gradually transitions from global search to local search during the iteration process. The improved method of the invention is a sinusoidal periodic convergence factor adaptive mutation rate adjustment; first, according to the current iteration number and the total iteration number, the mutation rate pmu is calculated, and then 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 as the iteration number increases, so that a more extensive search is performed in the early iterations, while a more local search is performed in the later iterations. Next, for each particle, it is determined whether to perform a mutation operation based on the mutation rate; if the random number is greater than the mutation rate, mutation is performed. For the selected particles that are subjected to mutation, a dimension is randomly selected, and the value of that dimension is adjusted according to the mutation rate. The adjusted value is randomly generated within the upper and lower bounds of that dimension. Finally, the mutation rate is gradually reduced 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 being performed.

[0160] To increase the diversity of solutions, the improved multi-objective particle swarm optimization algorithm optimizes the archive by calculating the crowding degree of the solutions and replacing the solutions in the grid with higher crowding degrees. This preserves a more dispersed set of solutions, improving the search ability of the particles and helping to optimize the quality and diversity of the solutions.

[0161] Inertia Weight is a parameter in Particle Swarm Optimization (PSO) algorithm, usually denoted by ω. It controls the proportion of the current velocity of particles to be retained in the update, thus affecting the behavior of particles in the search space. The traditional method generally fixes it, and the application adopts a unique nonlinear adaptive periodic strategy to make the inertia weight increase or decrease with the actual situation of the particle swarm.

[0162]

[0163] Where ω new And ω old New and old inertia weight respectively, ΔG is the change rate of the current non-dominated solution quantity, when it is less than T, it is no significant change, when it is greater than T, it is significant change. By the change degree of the population number of the optimal solution of the particle swarm, the size of the inertia weight is adapted to control, the global search and local search are combined.

[0164] As Figure 4 , Figure 5 Indicated, this paper adopts the standard test function Sphere to compare the basic PSO algorithm and the improved PSO algorithm respectively, and tests the convergence and stability of the algorithm in this section.

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

[0166]

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

[0168] Step four, determine the optimal compromise solution in the Pareto solution.

[0169] As Figure 6 Indicated, it is the Pareto frontier of the multi-time and space multi-objective comprehensive energy system. In which figure (1) is the process solution, and the red dot in it is the current optimal solution, and the blue dot is the dominated solution, that is, the solution set optimized out. In which 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 operation law of the system, the optimal compromise solution of the system is solved, and the sensitivity analysis is carried out. The concept of optimal compromise solution is Pareto optimal, and the formula is as follows.

[0171]

[0172] wherein w1 and w2 are the weights of the two targets respectively, the entropy weight method is adopted to determine the weight parameter, the entropy weight method as an objective weighting method mainly determines the weight of each index in the multi-index evaluation system based on the principle of information entropy. As shown in the following formula (1), it is the flow of determining the weight of the entropy weight method. Figure 7

[0173] Step five, sensitivity analysis is performed on the results.

[0174] As shown in the following formula (1), (2) and (3), they are respectively the energy supply and demand balance diagram of the industrial area in the day-ahead scheduling. Figure 8 、 Figure 9 、 Figure 10 、 Figure 11 As shown in the following formula (1), (2) and (3), they are respectively the energy supply and demand balance diagram of the industrial area in the day-ahead scheduling.

[0175] As shown in the following formula (1), (2) and (3), they are respectively the energy supply and demand balance diagram of the industrial area in the day-ahead scheduling. Figure 8 From the power supply and demand diagram, it can be seen that the photovoltaic output is concentrated between 6 am and 6 pm, at which time solar energy can be converted into electric energy. Since it is an industrial area, pressure energy can be generated and converted into electric energy by expanding the natural gas. 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 electric load, the electric demand is also used for electrolytic hydrogen and electric refrigerator, and the gas turbine can provide part of the electric energy for the supply side. Since there is pressure energy, which is a stable power supply, it can reduce the pressure between other areas.

[0176] As shown in the following formula (1), (2) and (3), they are respectively the energy supply and demand balance diagram of the industrial area in the day-ahead scheduling. Figure 9 The industrial area has no heat load demand, and the main heat supply is the absorption refrigerator. From 6:00 to 22:00, the absorption refrigerator needs more heat energy, which is related to the increase of temperature at noon and the high work load of the factory during the day. Since the night gas turbine has small work power and the night heat network price is low, the gas turbine output is small.

[0177] As shown in the following formula (1), (2) and (3), they are respectively the energy supply and demand balance diagram of the industrial area in the day-ahead scheduling. Figure 10 The demand for natural gas is mainly composed of gas load and gas turbine. Since natural gas is basically purchased from the gas network, it is not a small cost. According to the production requirements during the day, the gas load from 6:00 to 21:00 is relatively large, and the gas load at night is relatively low.

[0178] As shown in the following formula (1), (2) and (3), they are respectively the energy supply and demand balance diagram of the industrial area in the day-ahead scheduling. Figure 11 According to the production requirements, the cold load covers the whole day, but since the daytime environment temperature is high, the daytime cold load is also improved, reaching the peak at 13 o'clock. The supply side is mainly composed of electric refrigerator and absorption refrigerator. Since the electric refrigerator produces high carbon emissions, the proportion of absorption refrigerator in the refrigeration is larger.

[0179] ​Figure 12 For 24 hours, the carbon emission trends of the three zones, the carbon emission data of the industrial zone, commercial zone, and residential zone showed different characteristics and trends. The carbon emission of the industrial zone was the highest overall and fluctuated greatly, with a peak emission coinciding with the peak of industrial production activities. Although it decreased at night, it still maintained a relatively high emission level. The carbon emission of the commercial zone was relatively stable, with higher emissions during the daytime work hours and evening business hours, and significantly lower emissions at night. The carbon emission of the residential zone varied with the residents' activities, with the lowest emission from night to early morning and a peak from evening to night due to the increase in residents' daily activities. Overall, the carbon emission peak of the industrial zone was significantly higher than that of the commercial zone and residential zone, while the difference between the commercial zone and the residential zone was relatively small. To reduce carbon emissions, each region should take measures such as optimizing production processes, reasonably planning business activities, and encouraging energy-saving and low-carbon lifestyles, while the government should also strengthen supervision and management to promote low-carbon economic development. The implementation of these measures will help reduce carbon emissions, protect the environment, and promote sustainable development.

[0180] Figure 13 For the industrial zone, the carbon emission distribution of different components is diverse, with electricity, gas, and heat purchases occupying a dominant position, accounting for 28.13%, 30.14%, and 24.15% respectively. Gas turbines, as important equipment for industrial production, account for 14.80% of carbon emissions. In contrast, clean energy such as electric refrigerators, photovoltaics, and wind power have very low carbon emission ratios, accounting for 2.67%, 0.06%, and 0.06% respectively. This indicates that traditional energy consumption is still the main source of carbon emissions in the industrial zone, and the use of clean energy needs to be strengthened. To reduce carbon emissions, the energy structure should be further optimized to increase the proportion of clean energy.

[0181] Figure 14 For the 24-hour cost and carbon emission surface plot, the carbon emission and cost data in this study both exhibit significant fluctuations over a 24-hour period. Carbon emissions experienced multiple fluctuations throughout the day, with peaks occurring at hours 8 and 19, which likely coincide with periods of high production activity and energy consumption, such as concentrated industrial production or busy commercial activity. The valleys of carbon emissions occurred at hours 23 and 2, reflecting periods of reduced production activity or energy use, such as factory shutdowns at night and reduced residential electricity consumption.

[0182] The cost data also fluctuated significantly, but its peak period was mainly concentrated in the middle of the day, the evening to night, which is related to the peak of energy consumption, electricity price fluctuations (such as peak valley price difference) or specific changes in production efficiency, due to the increase of evening electricity in residential areas, the cost is higher, but compared to the heavy production task in the afternoon, there is still a gap. It is worth noting that although there is a certain positive correlation between carbon emissions and cost, the fluctuations of the two are not completely synchronized, and this difference may be caused by the combined effects of many factors, including energy types (such as the use of natural gas and renewable energy), fluctuations in production efficiency, and electricity price policies.

[0183] The above description is only the preferred specific implementation of the present application, but the protection scope of the present application is not limited to this. Any skilled person in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims. The unmentioned part of the present application is applicable to the prior art.

Claims

1. An improved multi-objective particle swarm optimization method for solving multi-time and space integrated energy system dispatching, comprising the following steps: A multi-objective multi-time-space comprehensive energy system scheduling optimization mathematical model is established, and a structure of expander is proposed for the unused natural gas pressure energy to convert the pressure energy into electric energy to participate in energy supply and demand balance. After the model is established, the optimal scheduling scheme is solved by using the improved multi-objective particle swarm optimization algorithm, and the sensitivity analysis is performed. The basic components of the mathematical programming model include photovoltaic power generation, wind power generation, gas turbine, electrolytic cell, expander, electric refrigerator, absorption refrigerator, battery, thermal storage tank, cold storage tank, gas storage tank; the supply side is power grid, gas network, heat network; the load side is electric load, heat load, gas load, 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 of output and effort under the condition of meeting the demand of the load side; The objective function is to minimize the scheduling cost and the carbon emission under the condition of meeting the load; In the process of constructing the mathematical model, the natural gas pressure energy generation system is added, which converts the previously unused natural gas pressure energy into electric energy to participate in the overall energy supply and demand balance of the comprehensive energy system. The photovoltaic power generation model is: （1） （2） wherein G(t) is the light intensity; is the photovoltaic panel temperature; is the ambient temperature; NOCT is the set temperature; is the photovoltaic power generation; is the rated power; is the temperature coefficient; is the conversion efficiency; The wind power generation model is: （3） In the formula, is the fan output power, , , , are the cut-in wind speed, the cut-out wind speed and the rated wind speed, respectively; is the rated output power; , is the wind speed correlation coefficient; The electrolytic cell model is: （4） wherein is the hydrogen production power of the electrolyzer; is the hydrogen flow rate per unit time of the electrolyzer; is the current density of the electrolyzer; is the molar volume of the gas; , , , is a coefficient related to the Faraday efficiency, taken as = 50, = 1, = 2.5, = 6.25 x 10-6; is the conversion constant, taken as = 0.08988 kg / m2; z is the number of electrons transferred in the reaction; is the Faraday constant, taken as = 96485 C mol; is the operating voltage of the electrolyzer; is the area of the diaphragm of the electrolyzer; The absorption refrigerator model is: （5） In the formula represents t the refrigeration power of the absorption chiller at the moment; represents t the output power of the waste heat boiler for refrigeration at the moment; represents the refrigeration efficiency of the absorption chiller; The electric refrigerator model is: （6） In the formula, represents t the refrigeration power of the electric refrigerator at the moment; represents t the electric power consumed by the electric refrigerator at the moment; the refrigeration coefficient of the electric refrigerator; The expander model is: （7） wherein, Q is the natural gas flow rate; is the specific heat capacity of the gas; is the inlet temperature; are the inlet and outlet pressures, respectively; is the inlet temperature; is the natural gas index; there is an energy loss in the process of converting the pressure energy into electrical energy, which is reflected in the expander efficiency and the generator efficiency . （8） Formula 6 represents the cost of the expander under different operating conditions, which is determined by the import and export pressure of natural gas and the flow factor of natural gas. The gas turbine model is: （9） wherein the power generation of the gas turbine, the lower calorific value of the natural gas, the power generation efficiency of the gas turbine, the volume of the natural gas consumed by the gas turbine; The energy storage model is: （10） （11） （12） （13） （14） In the above formula, is the energy storage type, including electric energy storage ESS, thermal energy storage TES , cold energy storage CSS , gas energy storage GSS ; is the ratio of the initial energy storage capacity to the energy storage capacity; is the node The installation capacity of the energy storage type is; is the energy storage capacity at time t ; , indicates the charging and discharging power of the energy storage device; , respectively, the charging efficiency and discharging efficiency of the energy storage; is the self-loss factor of the energy storage; , respectively, the ratio of the minimum energy storage capacity to the maximum energy storage capacity and the energy storage capacity; The carbon emission model is: The traditional carbon emission calculation method considers two carbon sources: external grid electricity purchase and external grid gas purchase. However, new energy generation and energy storage devices are ignored because they do not produce carbon emissions during operation. However, these devices will produce carbon emissions during product production, transportation, installation, and dismantling and recycling. From the perspective of life cycle carbon emissions, they are converted into the system to further restrict carbon emissions. （15） （16） In the formula: and are carbon emissions of the scene s at different times and the total amount of natural gas consumed by each device; t , , , and are carbon emission factors of external electricity purchase, external gas purchase, photovoltaic power generation, and energy storage operation, respectively. The cost model is: （17） （18） （19） wherein is the purchase cost; Com is the maintenance cost; is the wear cost; is the maintenance factor; is the wear factor; m is each component; wherein the cost is a periodic cost, the full life cycle cost needs to be calculated; In the improved MOPSO algorithm, a local search mechanism is introduced to enhance the combination of global search ability and local search ability of the algorithm. The improvement method is to adjust the mutation rate of the sine periodic convergence factor adaptively. First, according to the current iteration number and the total iteration number, the mutation rate pmu is calculated, and then an initial mutation rate pmuinit and a final mutation rate pmufinal are defined. Then, the initial mutation rate is linearly reduced to the final mutation rate in the iteration process, as shown in formula (20). The mutation rate decreases with the increase of the iteration number, so that a more extensive search is performed in the early iteration, while a more local search is performed in the later iteration. Then, for each particle, it is determined whether to perform mutation operation according to the mutation rate. If the random number is greater than the mutation rate, mutation is performed. For the selected particles 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, the mutation rate is gradually reduced to control the amplitude of the mutation operation. pmu=pmuinit （20） wherein is a parameter factor, is the total number of iterations, is the ongoing iteration number, is the ongoing iteration number, To increase the diversity of solutions, the improved multi-objective particle swarm optimization algorithm optimizes the archive by calculating the crowding distance of solutions, and replaces the solutions in the grid with higher crowding distance; thus, the set of more scattered solutions is retained to improve the search ability of particles, which helps to improve the quality and diversity of solutions; the nonlinear adaptive period strategy is used to make the inertia weight increase or decrease according to the actual situation of the particle swarm; （21） wherein and are the new and old inertia weights, respectively, is the rate of change of the current number of inescapable solutions, which is insignificant when it is less than and significant when it is greater than .

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