Comprehensive energy system optimization method considering refined modeling of electrolytic cell

Abstract

The invention discloses a comprehensive energy system optimization method considering electrolytic cell refined modeling, and aims to solve the problems of inflexible electrolytic cell operation, low hydrogen energy utilization efficiency, limited wind power consumption, extensive carbon emission management and the like in the existing system. The method comprises the following steps: constructing a comprehensive energy system comprising electricity-to-gas, wind power, combined heat and power generation, a gas-fired boiler, load energy storage and a proton exchange membrane electrolytic cell; a proton exchange membrane electrolytic cell model is established, and multiple working states and cold start hydrogen energy loss quantification are covered; constructing a stepped carbon transaction model in combination with system load characteristics; constructing a multi-objective optimization model, and comprehensively considering system operation flexibility, electrolytic cell start-stop cost, wind power consumption, energy purchase cost, carbon transaction cost and wind curtailment cost; and a multi-target grey wolf optimization algorithm is adopted for solving, the optimal strategy of the electrolytic cell is obtained, the hydrogen energy utilization efficiency is improved, the starting and stopping cost is reduced, wind power consumption is promoted, carbon emission fine management is achieved, and technical support is provided for low-carbon and efficient operation of the comprehensive energy system.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated energy system optimization, and in particular to an integrated energy system optimization method taking into account refined modeling of electrolyzers. Background Art

[0002] As a new type of energy infrastructure, integrated energy systems achieve efficient energy utilization and flexible management by integrating multiple energy forms. However, with the widespread access to renewable energy, the spatiotemporal decoupling of sources and loads in integrated energy systems poses significant challenges to renewable energy consumption.

[0003] Existing research has focused on solutions centered around power-to-gas technology and hydrogen storage systems. By improving water electrolysis hydrogen production processes and developing new hydrogen storage materials, the efficiency of renewable energy conversion has been significantly increased. Despite this, the cascade utilization of hydrogen energy systems remains constrained by efficiency bottlenecks in the energy conversion process. The issue of idle capacity in the coordinated scheduling of hydrogen storage equipment clusters has not been fundamentally resolved, limiting the potential of hydrogen energy as a secondary energy source for spatiotemporal regulation.

[0004] Furthermore, while the development of carbon capture technology features a diverse and parallel pipeline of technologies, such as pre-combustion and post-combustion capture, each suffers from inherent drawbacks such as high energy consumption or excessive regenerative heat consumption. While the emerging oxyfuel combustion coupled with hydrogen storage for peak-shaving improves the operating economics of carbon capture systems, the dynamic synergy between carbon emission flows and hydrogen energy flows remains incomplete.

[0005] In the field of integrated energy system optimization technology, existing optimization models suffer from two methodological limitations: On the economic dimension, traditional models overemphasize the goal of minimizing operating costs and fail to effectively couple the dynamic relationship between price fluctuations in the carbon trading market and equipment operation strategies. On the low-carbon dimension, while existing carbon flow tracking methods can increase renewable energy penetration, they lack a closed-loop material flow design that connects hydrogen production, methanation reactions, and carbon storage. Furthermore, a dynamic matching mechanism between the economic operating range of power-to-gas equipment and the volatility of renewable energy has not yet been established, leading to a significant cost surge under low-load conditions. There is a lack of quantitative guidance for the timing coordination of carbon capture systems and hydrogen storage equipment, resulting in significant fluctuations in the system's carbon emission intensity. Traditional two-stage scheduling models struggle to adapt to the uncertainty of renewable energy output, resulting in the inability to fully utilize the regulatory capacity of hydrogen energy storage systems.

[0006] For example, CN116111592B discloses an optimization scheduling method that considers the operational characteristics of large-scale hydrogen production. This method effectively improves the operating efficiency of the hydrogen production system by constructing a start-stop characteristic model and an efficiency model for the electrolyzer. However, this method still focuses primarily on the hydrogen production system itself and fails to fully consider the coordinated optimization of other energy sources in the integrated energy system.

[0007] In addition, CN117254502A discloses a multi-objective optimization scheduling method for an integrated energy system based on electric-hydrogen hybrid energy storage. This method comprehensively considers the operating efficiency of electric-hydrogen hybrid energy storage, economic scheduling, graded hydrogen prices, and user-side electric-hydrogen-thermal flexible loads, and achieves a coordinated improvement in the economic and environmental benefits of the system through a multi-objective optimization model. Although this method has made significant progress in the optimization of integrated energy systems, it still has some shortcomings. For example, the modeling of key equipment such as electrolyzers may be overly simplified and fail to fully consider the complex characteristics and dynamic changes in their actual operation; at the same time, in the multi-objective optimization process, the trade-offs and compromise strategies between the various objectives may still need to be further optimized.

[0008] To sum up, the existing technology still has many shortcomings in terms of multi-energy flow coupling efficiency, equipment coordinated control capabilities and system low-carbon economy. There are still many shortcomings and challenges in the optimization and scheduling of integrated energy systems. It is urgent to develop a more advanced, comprehensive and refined optimization and scheduling method to break through the existing technological bottlenecks and realize efficient, low-carbon and economical operation of the integrated energy system. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to provide an integrated energy system optimization method that takes into account the refined modeling of electrolyzers, so as to solve the core problems of insufficient electrolyzer operation flexibility, inefficient hydrogen energy utilization, limited wind power absorption and extensive carbon emission management in the integrated energy system.

[0010] To solve the above technical problems, the technical solution adopted by the present invention is a comprehensive energy system optimization method taking into account the refined modeling of the electrolyzer, comprising the following steps: Step 1: Build an integrated energy system that includes two-stage power-to-gas equipment, wind power generation equipment, CHP (Combined Heat and Power) equipment, GB (Gas Boiler), load ES (Energy Storage) equipment, and a proton exchange membrane electrolyzer with variable load start-stop characteristics; Step 2: Establish the proton exchange membrane (PEM) electrolyzer (hereinafter referred to as PEM) model, covering five operating states: shutdown, cold standby, low load, variable load, and overload, and quantify the hydrogen energy loss during the cold start process; Step 3: Combine the energy load coupling characteristics and regulation rules of the IES (Integrated Energy System) to build a stepped carbon trading model to quantify the system's carbon quota and actual emissions; Step 4: Construct a multi-objective optimization model that includes equipment operation constraints, power balance, and demand response. The multi-objective optimization model takes system operation flexibility, electrolyzer start-up and shutdown costs, wind power consumption, energy purchase costs, tiered carbon trading costs, and wind curtailment costs as optimization objectives. Step 5: Use the multi-objective grey wolf optimization algorithm to solve the multi-objective optimization model and obtain the optimal start-stop strategy and power allocation plan of the electrolyzer.

[0011] In the preferred solution, the PEM model in Step 2 is specifically expressed as: (1); Where, For the PEM electrolyzers in Hydrogen production power at each moment; For the PEM in Electricity consumption at each moment; is the electricity-to-hydrogen conversion efficiency of PEM; is the standby power of the PEM in cold standby state; is the penalty coefficient of hydrogen production power during cold start, which is used to represent the hydrogen energy loss caused by inconsistent time scales; Indicates the PEM at time Binary variable when in cold standby state; Indicates the PEM at time Binary variables when in working state (variable load, overload or underload state); When the PEM switches from the cold standby state to the working state, its state transition variable The following nonlinear inequality constraints are satisfied: (2); Where, Indicates the PEM at time Binary variable when in cold standby state; 、 、 Respectively represent PEM in A binary variable that is always in the state of underload, overload, and variable load.

[0012] In the preferred solution, the step-by-step carbon trading model in Step 3 is specifically expressed as follows: (3); Where, is the IES carbon emission rights trading amount, For tiered carbon trading costs; It is the base price for carbon trading; is the length of the carbon emission interval; is the price growth rate.

[0013] In a preferred solution, the optimization objective of the multi-objective optimization model in Step 4 also includes minimizing the total system cost, and the total system cost includes energy purchase cost, tiered carbon trading cost and wind curtailment cost.

[0014] In the preferred solution, the demand response in Step 4 includes demand response for transferable loads and replaceable loads, wherein the transferable load allows power transfer within the scheduling cycle, and the replaceable load allows substitution of electricity and heat demand while ensuring that the energy demand remains unchanged.

[0015] In a preferred solution, the multi-objective grey wolf optimization algorithm in Step 5 adopts a hybrid coding method when solving the multi-objective optimization model, including real number coding of continuous variables and binary coding of discrete variables.

[0016] In a preferred solution, the method further includes making a multi-objective compromise decision on the solution results of the multi-objective optimization model, quantifying the satisfaction of each optimization objective based on a fuzzy membership function, and selecting the solution with the highest comprehensive membership as the final operation plan.

[0017] In a preferred solution, the working state of the PEM is represented by a binary variable and satisfies the start-stop constraint, the start interval constraint, the operating state mutual exclusion constraint, and the overload and underload maximum time limit constraint.

[0018] In a preferred solution, the integrated energy system further includes a cogeneration unit model, a methane reactor model, a gas boiler model and a general energy storage unit model, and the models are collaboratively optimized through power balance constraints.

[0019] In the preferred solution, the solution process of the multi-objective optimization model is implemented in the MATLAB environment. By reading the current operating parameters of the system, wind and solar power forecast data, real-time electricity prices and carbon price information of the power grid, the gray wolf population is initialized, and the Pareto optimal solution set is obtained through steps such as fast non-dominated sorting, gray wolf group position update, and external archive management.

[0020] The comprehensive energy system optimization method provided by the present invention, which takes into account the refined modeling of electrolytic cells, has the following beneficial effects: 1. The present invention effectively solves the core problems of insufficient electrolyzer operation flexibility, inefficient hydrogen energy utilization, limited wind power consumption, and extensive carbon emission management in the integrated energy system, significantly improving the overall performance and operating efficiency of the system.

[0021] 2. By fine-tuning the modeling of the complex operating characteristics of the PEM, including various operating states such as shutdown, cold standby, low load, variable load and overload, and quantifying the hydrogen energy loss during the cold start process, the present invention can more accurately describe the operating state of the electrolyzer and improve the accuracy of the description of the electrolyzer's operating characteristics.

[0022] 3. The present invention constructs a multi-objective optimization model that comprehensively considers the economic efficiency, environmental protection and flexibility of system operation. The model not only covers key economic indicators such as energy purchase cost, tiered carbon trading cost and wind curtailment cost, but also incorporates operating conditions such as electric, thermal and gas power balance, system capacity constraints and electrolyzer variable load start and stop constraints, ensuring that the system is fully optimized while meeting various constraints.

[0023] 4. Combining the energy load coupling characteristics and regulation rules, the present invention constructs a stepped carbon trading model to quantify the system carbon quota and actual emissions; by modeling the stepped electricity price-carbon price linkage mechanism, it realizes the refined management of carbon emissions, solves the problem of extensive carbon emission management, reduces the carbon emission intensity of the system, and provides strong support for the low-carbon operation of the system.

[0024] 5. The present invention adopts a multi-objective grey wolf optimization algorithm to solve the constructed multi-objective optimization model. These algorithms can quickly and accurately find the optimal operation plan of the system under complex constraints, thereby improving the ability to find the optimal operation plan under complex constraints.

[0025] 6. Through refined modeling and multi-objective optimization, the present invention optimizes the operation strategy of the electrolyzer, improves the utilization efficiency of hydrogen energy, promotes the consumption of renewable energy such as wind power, reduces wind power abandonment, increases the consumption ratio of renewable energy such as wind power, and promotes the development of renewable energy.

[0026] 7. The present invention effectively reduces the operating cost of the system and improves the economic benefits of the system by optimizing the energy purchase cost and carbon trading cost.

[0027] 8. This invention provides an integrated energy system optimization method that incorporates refined electrolyzer modeling. Through refined modeling, multi-objective optimization, the application of a stepped carbon trading model, and the adoption of advanced solution algorithms, it achieves comprehensive optimization and refined management of system operations. This approach not only overcomes the limitations of existing technologies but also significantly improves the overall performance and operational efficiency of the system, providing new ideas and methods for the efficient, low-carbon, and economical operation of integrated energy systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 A flow chart of the optimization method of the present invention; Figure 2 It is a schematic diagram of the organizational structure of the present invention; Figure 3 This is a schematic diagram of the PEM operating state transition of the present invention; Figure 4 This is the variable start-stop electrolytic cell operating condition of the present invention. DETAILED DESCRIPTION

[0029] The technical solutions of the present invention are further described below with reference to the embodiments and accompanying drawings: like Figure 1 As shown, this embodiment describes in detail the specific implementation steps of the integrated energy system optimization method considering the variable load start-stop characteristics of the electrolytic cell of the present invention, which specifically includes the following steps: Step 1: Build an integrated energy system that includes two-stage power-to-gas equipment, wind power generation equipment, cogeneration equipment, gas boilers, load energy storage equipment, and proton exchange membrane electrolyzers with variable load start-stop characteristics.

[0030] Step 2: Establish the PEM model, covering five working states: shutdown, cold standby, low load, variable load and overload, and quantify the hydrogen energy loss during the cold start process.

[0031] Specifically, the mathematical models of each part are established through the following steps: An electrolyzer model that considers variable load start-stop characteristics is established. Taking into account the operating characteristics of the PEM, the operating state can be subdivided into low load, variable load, and overload states. To illustrate the operating characteristics of the PEM, five operating states are represented by binary variables: shutdown I, cold standby S, variable load L, overload R, and low load V. The time it takes for the PEM to fully start is used as the optimized time scale. Since the cold start time is less than one time scale, the loss of output hydrogen energy caused by the cold start process needs to be taken into account. The relationship between the PEM power consumption and hydrogen production power can be expressed as: (1) Where, For the PEM electrolyzers in Hydrogen production power at each moment; For the PEM in Electricity consumption at each moment; is the electricity-to-hydrogen conversion efficiency of PEM; is the standby power of the PEM in cold standby state; is the penalty coefficient of hydrogen production power during cold start, which is used to represent the hydrogen energy loss caused by inconsistent time scales; Indicates the PEM at time Binary variable when in cold standby state; Indicates the PEM at time Binary variables when in working state (variable load, overload or underload state); When the PEM switches from the cold standby state to the working state, its state transition variable The following nonlinear inequality constraints are satisfied: (2); Where, Indicates the PEM at time Binary variable when in cold standby state; 、 、 Respectively represent PEM in Binary variables when the PEM is in low load, overload, or variable load state at all times; Always in cold standby state ( ),and Enter any working mode at any time ( ), then the cold start flag is forced to be triggered ( ); This is to eliminate the possibility of missing labels during cold start operation.

[0032] The power consumption of the PEM satisfies the following inequality relationship. The coordinated control between different working states of the electrolyzer can be achieved by taking the value of the binary variable: (4) Where, is the rated operating power of the PEM.

[0033] When the binary variable is 1, it indicates that the state is in this state. At the same time, PEM ensures that the electrolyzer operates in a safe and stable working condition by limiting the switching logic and duration of states such as startup, shutdown, and cold standby, and avoids equipment loss or efficiency reduction caused by frequent switching or short start and stop. The following are the logical constraints: (5) (6) (7) (8) (9) Where, Indicates the PEM electrolyzer at time Binary variable when in shutdown state; Indicates the PEM electrolyzer at time Binary variable when in shutdown state; Indicates the PEM electrolyzer at time Binary variable when in shutdown state; and The maximum time that PEM is allowed to continuously operate in overload and underload states respectively; represents the binary variable when the PEM changes from the shutdown state to the working state; the above formulas are the start-stop constraint, the start interval constraint, the operating state mutual exclusion constraint, and the overload and underload maximum time limit constraint.

[0034] To avoid frequent starts and stops of the PEM in a short period of time, it is necessary to limit the minimum downtime and cold standby time: (10) (11) Where, 、 They are the shortest time that PEM can run continuously in shutdown and cold standby states respectively.

[0035] A cogeneration unit model with adjustable heat-to-electricity ratio is established. The specific formula is as follows: (12) Where, for t Hydrogen power consumption at all times; and They are t The power and heat generated at each moment; is the energy conversion efficiency of the fuel cell; and are the upper and lower limits of hydrogen power respectively; is the maximum climbing power; and The upper and lower limits of the adjustable range of the fuel cell's electric-to-heat ratio.

[0036] The CHP unit burns natural gas for combined heat and power generation. By controlling the turbine extraction ratio and the inlet guide vane angle, the heat-to-power ratio can be adjusted according to the real-time electric and thermal load conditions. The model is: (13) Where, For CHP units Gas power consumption at each moment; For CHP units Gas power consumption at each moment; and They are CHP units in The power and heat generated at each moment; is the energy conversion efficiency of the cogeneration unit; and They are the upper and lower limits of gas power consumption of CHP units respectively; is the maximum climbing power of the CHP unit; and They are respectively the upper and lower limits of the adjustable range of the power-to-heat ratio of the cogeneration unit.

[0037] Establish the MR (Methane generator, methane reactor) model. The specific formula is as follows: (14) Where, For MR Hydrogen power consumption at all times; For MR Hydrogen power consumption at all times; is the hydrogen conversion efficiency of MR; for Gas production power at each moment; and are the upper and lower limits of hydrogen power respectively; is the maximum climbing power.

[0038] GB and general energy storage unit models are established, and the specific formulas are as follows: (15) Where, For GB Gas power consumption at each moment; For GB Gas power consumption at each moment; is the gas-to-heat conversion efficiency of GB; for Heat production power at each moment; and are the upper and lower limits of gas power respectively; is the maximum climbing power.

[0039] Considering the similarities among electricity storage, hydrogen storage and heat storage models, a general modeling of ES is performed: (16) Where, and Respectively Energy storage units Charging and discharging power at all times; For the The maximum charge and discharge power of each energy storage unit; For the Energy storage units The charging and discharging status mark at all times, =1 means charging, =0 means energy release; and Respectively The charging and discharging efficiency and self-consumption rate of the energy storage unit; For the Energy storage units Charging and discharging power at all times; For the Energy storage units The energy of the moment; For the Energy storage units The energy of the moment; and For the The upper and lower limits of the energy storage unit capacity.

[0040] Step 3: Combine the energy load coupling characteristics and regulation rules of the integrated energy system to construct a stepped carbon trading model to quantify the system's carbon quota and actual emissions.

[0041] Specifically, step 3 includes: The specific formula for calculating the carbon emission quota model is as follows: (17) Where, 、 、 、 They are the carbon emission quotas of IES, upper-level power purchase, CHP, and GB; 、 They are the carbon emission quotas per unit electricity consumption of coal-fired units and per unit natural gas consumption of natural gas-fired units; for The amount of electricity purchased by the superior during the period; for Thermal energy output by GB during the period; The scheduling period.

[0042] To calculate actual carbon emissions, the specific formula is as follows: MR's hydrogen-to-natural gas process can absorb part of , so it needs to be taken into account. The actual carbon emission model is as follows: (18) Where, 、 They are the actual carbon emissions from IES and electricity purchased from higher authorities; is the total actual carbon emissions of CHP, GB, and MR; is the actual absorption of MR quantity; for Equivalent output power of CHP, GB and MR during the time period; 、 、 and 、 、 These are the carbon emission calculation parameters for coal-fired units and natural gas-consuming energy supply equipment; Absorbing hydrogen energy into natural gas in MR equipment Parameters.

[0043] Construct a tiered carbon emissions trading model. The specific formula is as follows: (19) Where, is the carbon emission rights trading amount of IES; By obtaining the IES carbon emission quota and actual carbon emissions, we can calculate the actual carbon emission rights trading amount in the carbon trading market.

[0044] The mathematical model of the tiered carbon trading is as follows: (3) Where, For tiered carbon trading costs; It is the base price for carbon trading; is the length of the carbon emission interval; is the price growth rate.

[0045] Step 4: Construct a multi-objective optimization model that includes equipment operation constraints, power balance, and demand response. The multi-objective optimization model takes system operation flexibility, electrolyzer start-up and shutdown costs, wind power absorption, energy purchase costs, tiered carbon trading costs, and wind power curtailment costs as optimization objectives.

[0046] The low-carbon economic dispatching goal of constructing the minimum total operating cost F is as follows: (20) Where, The cost of purchasing energy for the system; Tiered carbon trading costs for the system; is the system wind curtailment cost.

[0047] The specific formula for purchased energy cost is as follows: (twenty one) Where, and They are The amount of electricity and gas purchased by the system at any given moment; 、 They are Electricity and gas prices during the time period; The specific formula for curtailment cost is as follows: (twenty two) Where: Penalty cost for unit wind curtailment; for t Actual dispatch output of wind power at every moment; for Maximum wind power output at that moment.

[0048] Establish a power and gas purchase constraint model. The specific formula is as follows: (twenty three) Where, and They are Actual power of electrical load and thermal load at every moment; and They are Reference power of electrical load and thermal load at every moment; and They are The power of electrical load and thermal load transferred in / out at any moment; and They are The upper and lower limits of power transfer in / out at any time; for The replacement state at the moment, when it is 1, it means that replacement has occurred; for The replacement status at the moment. When it is 1, it means that replacement has occurred.

[0049] A wind power output and wind curtailment constraint model is established. The specific formula is as follows: (twenty four) Where, for Wind power at each moment; Maximum wind power at the moment; for Maximum wind curtailment rate at any given moment.

[0050] Establish a power balance constraint model. The specific formula is as follows: (25) (26) (27) (28).

[0051] Without considering the flexibility of gas load, part of the electric heating load can be transferred in the time dimension and space dimension, that is, it has the ability to respond to demand horizontally and vertically. The electric heating load is divided into fixed load, replaceable load, and transferable load. The specific formula is as follows: (29) Where, is the load type, indicating electrical / thermal load; For Moment Class load power; For Moment Fixed load power; For Moment Types of transferable load power; For Moment Class replaceable load power.

[0052] Transferable loads allow power transfer within the dispatch cycle. When performing demand response, the adjustment of electricity / heating plans is affected by electricity / heating demand. The specific formula is as follows: (30) Where, is the total electricity / heat demand of the transferable load during the dispatch period; for The power output / input at the moment; for Electricity / heat demand at each moment; and They are The upper and lower limits of power transfer in / out at any time; for The transfer status at the moment, when it is 1, it means the transfer has occurred; for The replacement state at the moment, when it is 1, it means that replacement has occurred; Minimum continuous operation time is required to avoid load transfer to multiple single periods and frequent start and stop of equipment. Alternative loads allow the substitution of electricity and heat demand while ensuring that energy demand remains unchanged, thereby alleviating the pressure of peak loads on the power grid and heat network. Alternative loads can be expressed as: (31) In the formula, in the formula, and They are Actual power of electrical load and thermal load at every moment; and The replaceable electrical load and thermal load are Baseline electricity / heat demand at the time; and They are The power of electrical load and thermal load transferred in / out at any moment; and They are The upper and lower limits of power transfer in / out at any time; for The replacement state at the moment, when it is 1, it means that replacement has occurred; for The replacement state at the moment, when it is 1, it means that replacement has occurred; The minimum continuous operating time is set to avoid frequent load replacement that affects user comfort.

[0053] Step 5: Use the multi-objective grey wolf optimization algorithm to solve the multi-objective optimization model and obtain the optimal start-stop strategy and power allocation plan of the electrolyzer.

[0054] Based on the Multi-Objective Grey Wolf Optimizer (MOGWO) algorithm, the objective function is solved in MATLAB by comprehensively considering the system's economic, environmental, and flexibility constraints through hybrid coding and adaptive search strategies. Ultimately, a Pareto optimal solution set is generated that takes into account low carbon, low operating costs, and high wind power absorption rate.

[0055] Specifically, step 5 includes: System information is initialized and a population is constructed. Current system operating parameters are read, including equipment status (such as generator start and stop signals and energy storage charge and discharge status), wind and solar power forecast data, and real-time grid electricity and carbon pricing information. The gray wolf population is initialized, with the population size and maximum number of iterations set. A hybrid encoding scheme (real number encoding for continuous variables and binary encoding for discrete variables) is used to generate an initial feasible solution.

[0056] Social hierarchy division and leader selection: Fast non-dominated sorting is used to divide the population into multiple non-dominated frontier hierarchies. The crowding degree of each solution is calculated to assess the distribution sparsity. The three solutions with the highest crowding degrees from the frontier hierarchy are selected as the leaders of the gray wolf population (α wolf, β wolf, and δ wolf) to guide the group's search direction.

[0057] The position of the gray wolf pack is updated by using a prey encirclement mechanism based on the positions of α, β, and δ wolves. An adaptive coefficient vector is used to dynamically balance global exploration and local exploitation capabilities. Discrete variables (such as the start and stop status of equipment) are updated using binary coding through probabilistic mapping, ensuring the coordinated optimization of mixed variables.

[0058] External archive management and termination judgment: Each generation of non-dominated solutions is stored in an external archive. When the archive capacity is exceeded, the dense area solution set is eliminated based on the congestion distance. If the maximum number of iterations is reached or the Pareto front hypervolume index is continuously stable, the iteration is terminated and the non-dominated solution set in the archive is output.

[0059] Multi-objective compromise decision-making: quantify the satisfaction of economic, environmental, and flexibility goals based on fuzzy membership functions, and calculate the comprehensive membership of each non-dominated solution. The solution with the highest membership is selected as the final operation plan, achieving multi-objective collaborative optimization and dynamic balance.

[0060] Figure 2 The operating structure of the present invention, the Electric Heating Hydrogen Integrated Energy System (EHH-IES), consists of four components: an energy supply unit, an energy coupling unit, an energy storage unit, and an energy consumption unit. Wind turbines (WTs) provide clean electricity, and the IES can compensate for system energy shortages by purchasing energy from upstream power and gas grids. The electricity-hydrogen coupling unit, primarily composed of an electrolyzer and a hydrogen fuel cell, effectively reduces energy losses and improves overall utilization. Furthermore, the integrated demand response of the electric heating hydrogen multi-element energy storage device and loads ensures the flexible operation of the EHH-IES.

[0061] Figure 3 This is the electrolytic cell operating state conversion principle of the present invention: 1) Shutdown state (no hydrogen production); PEM can be shut down quickly in any state and is considered an interruptible load, regardless of downtime. In this state, it usually takes 30 minutes to 1 hour to fully start up; 2) Cold standby state (no hydrogen production): PEM is shut down but does not stop, and maintains the operation of control and antifreeze units at low power standby

[10] . In this state, PEM takes 5 to 10 minutes to complete cold start; 3) Working state (hydrogen production): To ensure the safety of hydrogen production in the electrolyzer, that is, hydrogen has an upper and lower limit of explosion volume, the PEM operates in a variable load state (30% to 100% of the rated power) most of the time; at the same time, the PEM can operate in an overload state (100% to 150% of the rated power) and a low load state (10% to 30% of the rated power) for a short period of time, which makes the PEM have excellent operating flexibility.

[0062] Figure 4The PEM units exhibit a two-stage regulation during the day-ahead scheduling phase, representing the operating conditions of an electrolyzer array. During the 1:00 AM to 10:00 AM and 8:00 PM to 12:00 AM periods, to absorb excess wind power and respond to time-of-use electricity prices, the electrolyzers dynamically switch between a variable-load maximum output (approximately 120 kW) and an overload state (150 kW), resulting in power fluctuations of up to 25%. During the peak grid load period of 10:00 AM to 8:00 PM, some PEMs are switched to a cold standby state (maintaining a base power of 10 kW). This mitigates the risk of exceeding hydrogen / electricity storage capacity limits and reduces restart energy consumption by 60% compared to conventional shutdown strategies. By coupling the PEM start-up and shutdown cost constraint (a cold start requires a two-hour warm-up period) with multi-timescale power commands, this scheduling strategy limits the number of electrolyzer starts and stops to less than three per day, a 75% reduction compared to conventional models. This demonstrates the critical role of refined state modeling in maintaining the operational stability of hydrogen energy systems.

[0063] The present invention proposes a comprehensive energy system optimization method that takes into account the refined modeling of electrolyzers. By establishing a PEM model, it subdivides the five operating states of shutdown, cold standby, low load, variable load and overload, quantifies the hydrogen energy loss during the cold start process, and combines the coordinated control strategy of the electricity-hydrogen coupling unit to construct a multi-energy optimization framework with the goals of reducing equipment start-up and shutdown costs, improving wind power absorption and system economy. This method integrates a stepped carbon trading mechanism, quantifies the difference between carbon emission quotas and actual emissions, couples transferable / alternative load demand response constraints, and solves through a multi-objective gray wolf optimization algorithm to achieve dynamic adjustment of the electrolyzer operating state and hydrogen-electricity complementary coordinated optimization. The examples show that this method can effectively reduce the frequent start-up and shutdown losses of the electrolyzer, improve the wind power absorption capacity, and at the same time take into account the low-carbon economy and operational flexibility of the system, providing technical support for the coordination of multiple energy flows and low-carbon transformation of the comprehensive energy system.

[0064] In the preferred solution, the optimization objective of the multi-objective optimization model in Step 4 also includes minimizing the total system cost, and the total system cost includes energy purchase cost, tiered carbon trading cost and wind curtailment cost; the above settings enable the optimization model to more comprehensively consider economic and environmental protection. The energy purchase cost reflects the direct cost of energy purchase, the tiered carbon trading cost encourages the reduction of carbon emissions, and the wind curtailment cost promotes the improvement of wind energy utilization, which together promote the efficient operation of the system.

[0065] In the preferred solution, the demand response in Step 4 includes both transferable and replaceable loads. Transferable loads allow for power transfer within the dispatch cycle, while replaceable loads allow for the substitution of electricity and heat demand while maintaining energy demand. This configuration enhances the flexibility and reliability of the power system, optimizes resource allocation, and reduces operating costs. Furthermore, the solution considers environmental factors, promoting clean energy consumption and reducing carbon emissions through intelligent dispatch, achieving a win-win situation for both economic and environmental benefits.

[0066] In the preferred solution, the multi-objective grey wolf optimization algorithm in Step 5 adopts a hybrid coding method when solving the multi-objective optimization model, including real number coding of continuous variables and binary coding of discrete variables; the above settings not only improve the flexibility of the algorithm in dealing with complex multi-objective optimization problems, but also ensure the accuracy and efficiency of the solution process, making the optimization results more in line with actual application needs, and improving the feasibility and practicality of the overall solution.

[0067] In the preferred scheme, the method also includes making a multi-objective compromise decision on the solution results of the multi-objective optimization model, quantifying the satisfaction of each optimization objective based on the fuzzy membership function, and selecting the solution with the highest comprehensive membership as the final operation plan; the above settings can achieve an effective trade-off between multiple optimization objectives, ensuring that the obtained plan not only meets various performance indicators, but also achieves the optimal state as a whole, thereby improving the accuracy and practicality of the decision, and providing strong support for practical applications.

[0068] In the preferred scheme, the working state of the proton exchange membrane electrolyzer is represented by a binary variable and satisfies the start-stop constraints, start interval constraints, operating state mutual exclusion constraints, and overload and underload maximum time limit constraints; the above settings ensure that the electrolyzer operates under safe and efficient conditions, effectively avoids the impact of frequent start and stop on equipment life, and at the same time ensures the system's stable operation capability under different load conditions.

[0069] In the preferred scheme, the integrated energy system also includes a cogeneration unit model, a methane reactor model, a gas boiler model and a general energy storage unit model, and the models are collaboratively optimized through power balance constraints; the above settings can realize the integration and optimal utilization of different types of energy, improve energy utilization efficiency, and reduce environmental pollution, ensuring the economy and environmental protection of the system, and providing strong support for the sustainable development of the integrated energy system.

[0070] In the preferred scheme, the solution process of the multi-objective optimization model is implemented in the MATLAB environment. By reading the current operating parameters of the system, wind and solar power forecast data, real-time electricity prices and carbon price information of the power grid, the gray wolf population is initialized, and the Pareto optimal solution set is obtained through steps such as fast non-dominated sorting, gray wolf group position update and external archive management. The above settings can comprehensively consider multiple objectives such as economic costs, environmental benefits and system stability to achieve optimized scheduling decisions. Finally, the obtained solution set is imported into the decision support system to assist dispatchers in making optimal decisions and ensure the safe and efficient operation of the power system.

[0071] In summary, the comprehensive energy system optimization method provided by the present invention, which takes into account the refined modeling of electrolyzers, has demonstrated significant advantages in terms of technological innovation and problem solving, as summarized as follows: This invention effectively solves the core problems existing in integrated energy systems, such as insufficient electrolyzer operational flexibility, inefficient hydrogen energy utilization, limited wind power consumption, and extensive carbon emission management. By introducing refined electrolyzer modeling technology, the present invention can more accurately describe the operating characteristics of the electrolyzer under different operating conditions, thereby optimizing its operating strategy and improving the overall efficiency of the system. For the first time, the present invention incorporates multiple operating conditions of the PEM, such as shutdown, cold standby, low load, variable load, and overload, into the optimization model of the integrated energy system, and quantifies the hydrogen energy loss during the cold start process, achieving more precise control of the electrolyzer's operating status.

[0072] The present invention constructs a multi-objective optimization model that comprehensively considers economy, environmental protection, and flexibility. This model not only covers key economic indicators such as energy purchase cost, tiered carbon trading cost, and wind curtailment cost, but also incorporates operating conditions such as electricity, heat, and gas power balance, system capacity constraints, and electrolyzer variable load start-stop constraints, ensuring that the system achieves comprehensive optimization while meeting various constraints. Combining the energy load coupling characteristics and regulation laws, the present invention constructs a tiered carbon trading model to quantify the system's carbon quota and actual emissions; by modeling the tiered electricity price-carbon price linkage mechanism, it achieves refined management of carbon emissions, providing a new perspective and powerful tool for system optimization.

[0073] The present invention adopts the multi-objective grey wolf optimization algorithm to solve the constructed multi-objective optimization model; these algorithms can quickly and accurately find the optimal operation plan of the system under complex constraints, significantly improving the solution efficiency and accuracy.

[0074] The present invention organically integrates multiple technical means such as electrolyzer refined modeling, multi-objective optimization model, step-by-step carbon trading model and advanced solution algorithm to form a new integrated energy system optimization method; this method not only overcomes the limitations of existing technologies, but also significantly improves the overall performance and operating efficiency of the system; by implementing the method proposed in the present invention, the efficiency of hydrogen energy utilization can be significantly improved, the start-up and shutdown costs of electrolyzers can be reduced, the consumption of renewable energy such as wind power can be promoted, and the refined management of carbon emissions can be achieved. It not only has significant economic and environmental benefits, but also provides new ideas and methods for the efficient, low-carbon and economical operation of integrated energy systems.

[0075] The present invention demonstrates significant superiority in electrolytic cell refined modeling, multi-objective optimization model construction, step-by-step carbon trading model application, and solution algorithm selection, providing a new and efficient solution for the optimization of integrated energy systems.

Claims

1. A comprehensive energy system optimization method taking into account refined electrolyzer modeling, characterized in that: The following steps are involved: Step 1: Build an integrated energy system that includes a two-stage power-to-gas device, wind power generation equipment, cogeneration equipment, gas boilers, load energy storage equipment, and a proton exchange membrane electrolyzer with variable load start-stop characteristics; Step 2: Establish the PEM electrolyzer model, covering five operating states: shutdown, cold standby, low load, variable load, and overload, and quantify the hydrogen energy loss during the cold start process; Step 3: Combine the energy load coupling characteristics and regulation rules of the integrated energy system to build a stepped carbon trading model to quantify the system's carbon quota and actual emissions; Step 4: Construct a multi-objective optimization model that includes equipment operation constraints, power balance, and demand response. The multi-objective optimization model takes system operation flexibility, electrolyzer start-up and shutdown costs, wind power consumption, energy purchase costs, tiered carbon trading costs, and wind curtailment costs as optimization objectives. Step 5: Use the multi-objective grey wolf optimization algorithm to solve the multi-objective optimization model and obtain the optimal start-stop strategy and power allocation plan of the electrolyzer.

2. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 1 is characterized in that: The proton exchange membrane electrolyzer model in Step 2 is specifically expressed as follows: （1）； Where, For the PEM electrolyzers in Hydrogen production power at each moment; For the PEM in Electricity consumption at each moment; is the electricity-to-hydrogen conversion efficiency of PEM; is the standby power of the PEM in cold standby state; is the penalty coefficient of hydrogen production power during cold start; Indicates the PEM at time Binary variable when in cold standby state; Indicates the PEM at time Binary variable when in working state; When the PEM switches from the cold standby state to the working state, its state transition variable The following nonlinear inequality constraints are satisfied: （2）； Where, Indicates the PEM at time Binary variable when in cold standby state; 、 、 Respectively represent PEM in A binary variable that is always in the state of underload, overload, and variable load.

3. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 2 is characterized in that: The step-by-step carbon trading model in Step 3 is specifically expressed as follows: （3）； Where, is the IES carbon emission rights trading amount, For tiered carbon trading costs; It is the base price for carbon trading; is the length of the carbon emission interval; is the price growth rate.

4. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 3 is characterized by: The optimization objective of the multi-objective optimization model in Step 4 also includes minimizing the total system cost, and the total system cost includes energy purchase cost, tiered carbon trading cost and wind curtailment cost.

5. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 4 is characterized in that: The demand response in Step 4 includes the demand response of transferable loads and replaceable loads, wherein the transferable loads allow power transfer within the scheduling cycle, and the replaceable loads allow the substitution of electricity and heat demand while ensuring that the energy demand remains unchanged.

6. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 5 is characterized by: The multi-objective grey wolf optimization algorithm in Step 5 adopts a hybrid coding method when solving the multi-objective optimization model, including real number coding of continuous variables and binary coding of discrete variables.

7. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 6 is characterized by: The method also includes making a multi-objective compromise decision on the solution results of the multi-objective optimization model, quantifying the satisfaction of each optimization objective based on a fuzzy membership function, and selecting the solution with the highest comprehensive membership as the final operation plan.

8. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 7 is characterized in that: The working state of the proton exchange membrane electrolyzer is represented by a binary variable and satisfies the start-stop constraint, the start interval constraint, the operating state mutual exclusion constraint, and the overload and underload maximum time limit constraint.

9. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 8 is characterized by: The integrated energy system also includes a cogeneration unit model, a methane reactor model, a gas boiler model and a general energy storage unit model, and the models are collaboratively optimized through power balance constraints.

10. The comprehensive energy system optimization method taking into account the refined modeling of electrolytic cells according to claim 9 is characterized in that: The solution process of the multi-objective optimization model is implemented in the MATLAB environment. By reading the current operating parameters of the system, wind and solar power forecast data, real-time grid electricity prices and carbon price information, the gray wolf population is initialized, and the Pareto optimal solution set is obtained through steps such as fast non-dominated sorting, gray wolf group position update, and external archive management.

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