Method for distributed robust optimization configuration of microgrid reliability with electro-hydro coupling

Abstract

This invention belongs to the field of microgrid optimization technology, specifically involving a distributed robust optimization configuration method for the reliability of microgrids with electric-hydrogen coupling. The steps include: establishing a battery operation architecture and a hydrogen energy storage system operation architecture, and constructing reliability indices including the probability of power outage time and the probability of load shedding; constructing a two-stage robust optimization configuration model for the electric-hydrogen coupled microgrid, including a planning stage model and an operation stage model; solving the two-stage robust optimization configuration model for the electric-hydrogen coupled microgrid using a column and constraint generation algorithm to obtain the optimal capacity configuration scheme; and calculating the off-grid operating time of the microgrid based on the optimal capacity configuration scheme to verify its effectiveness. This invention significantly improves the off-grid power supply reliability and long-term autonomous operation time of microgrids while reducing equipment investment and operating costs, increasing photovoltaic absorption rate, and achieving synergistic optimization of economy and reliability.

Description

Technical Field

[0001] This invention belongs to the field of microgrid optimization technology, specifically relating to a distributed robust optimization configuration method for microgrid reliability including electric-hydrogen coupling. Background Technology

[0002] Under the dual-carbon goals, the continuous increase in renewable energy penetration has become one of the key characteristics of new power systems. To address the issue of large-scale renewable energy integration, microgrids, as a technological means to promote the effective integration of distributed renewable energy, have experienced rapid development.

[0003] Microgrids consist of distributed generation devices, energy storage devices, and intelligent load management systems. They can flexibly connect to or disconnect from the main grid, supporting both grid-connected and islanded operation modes. With the deepening of global energy structure transformation, the continuous development of microgrid technology places higher demands on its long-term off-grid operation capabilities to enhance the resilience of the distribution network under extreme conditions. Currently used battery energy storage has advantages in second-level response, but frequent charging and discharging accelerates its capacity decay and shortens its cycle life. In terms of long-term energy storage, batteries suffer from significant energy loss, easily leading to increased curtailment rates in microgrids and hindering long-term energy transfer, thus failing to meet the needs of long-term off-grid operation. Therefore, there is an urgent need to develop energy storage technologies with longer time scales and larger capacities. Thus, the synergistic optimization of hybrid energy storage for both short and long cycles has become one of the key aspects of microgrid construction.

[0004] "Green hydrogen," produced through the electrolysis of water using renewable energy, is a clean secondary energy source and a novel form of energy storage with high energy density. Its production process significantly reduces carbon emissions and enhances the absorption capacity of renewable energy. In hydrogen energy storage systems, the electrolyzer, hydrogen storage tank, and fuel cell can all be decoupled, allowing for independent optimization of cost and efficiency in each component. Therefore, combining long-cycle energy storage, represented by hydrogen storage, with short-cycle energy storage, represented by batteries, can provide comprehensive support for the flexibility and reliability of microgrid operation. Related research shows that electric-hydrogen coupled microgrids have significant advantages in capacity configuration, energy balance, and seasonal regulation. Considering source-load interaction, optimizing the configuration of wind, solar, and hydrogen production capacities can improve the absorption of new energy sources while ensuring system economics. For the planning of complex coupled systems, existing research has proposed phased optimization strategies, establishing optimized configuration models for the "hydrogen production-hydrogen storage" system and the hybrid hydrogen gas turbine based on the energy abundance and scarcity seasons. Furthermore, electric-hydrogen hybrid energy storage systems are also used to address the instability of solar energy, playing a crucial role in seasonal regulation while balancing economic and environmental goals.

[0005] With the rapid development of microgrids, improving their operational reliability, enhancing their off-grid autonomy, and optimizing energy allocation have become crucial issues in microgrid planning. Current research largely employs Monte Carlo time-series simulation to analyze the stochastic characteristics of renewable energy generation and assess the reliability of distribution networks containing microgrids. Some studies use fault tree diagrams to construct reliability models of microgrids in off-grid operation, calculating failure rates and evaluating continuous power supply under extreme conditions. For wind-solar-storage combined generation systems, some research establishes power generation reliability assessment models based on sequential Monte Carlo simulation and proposes corresponding coordinated dispatch strategies. In wind / diesel / energy storage systems, system planning methods based on cost-benefit analysis have been developed to maintain power supply reliability at a set level. Furthermore, some studies combine different power output probability models with stochastic power flow calculation methods to evaluate the reliability of various configuration schemes based on node voltage exceedance rates. However, most of these studies treat reliability as an evaluation index or constraint, ultimately describing it in terms of economics, and the independent measurement of reliability remains insufficient.

[0006] In independent microgrids, uncertainty modeling of renewable energy and load mainly employs two types of methods: scenario-based stochastic optimization and robust optimization. Scenario-based stochastic optimization suffers from efficiency issues due to the need to construct a large number of scenarios, while robust optimization suffers from overly conservative results. Distributed robust optimization combines the advantages of both, reducing conservatism while ensuring system robustness. Some studies have constructed distributed robust optimization models based on probability distribution sets and used data-driven methods to cluster historical data of a large number of uncertain scenarios, using norm constraints on discrete scenario probabilities to reduce solution complexity. However, existing research is prone to NP-hard problems during the solution process, and the optimization results are relatively one-sided, making them difficult to directly apply to mixed-integer programming problems. Summary of the Invention

[0007] In view of the shortcomings of the prior art, the purpose of this invention is to provide a distributed robust optimization configuration method for microgrid reliability with electric-hydrogen coupling, which can significantly improve the reliability of off-grid power supply and long-term autonomous operation of microgrids, while reducing equipment investment and operating costs, increasing photovoltaic absorption rate, and achieving synergistic optimization of economy and reliability.

[0008] To achieve the above objectives, this invention provides a distributed robust optimization configuration method for microgrid reliability including electric-hydrogen coupling, comprising the following steps: S1. Establish the battery operation architecture and the hydrogen energy storage system operation architecture, and construct reliability indicators including the probability of power shortage time and the probability of load failure. S2. Construct a two-stage robust optimization configuration model for a microgrid with electricity-hydrogen coupling, including a planning stage model and an operation stage model. The planning stage model takes minimizing the total operating cost and investment cost within the microgrid as the objective function, and the capacity configuration of the electrolyzer, hydrogen fuel cell, photovoltaic cell, battery, and hydrogen storage tank as optimization variables. The operation stage model takes minimizing the loss cost and the probability of power outage and load loss within one operating cycle of the microgrid as the optimization objective. The optimal installed capacity calculated by the planning stage model is incorporated into the off-grid operation scenario of the operation stage model, and the operation data of the microgrid is obtained through calculation. S3. The column and constraint generation algorithm is used to solve the two-stage robust optimization configuration model of microgrid with electric-hydrogen coupling to obtain the optimal capacity configuration scheme. S4. Based on the optimal capacity configuration scheme, calculate the off-grid runtime and verify the effectiveness of the optimal capacity configuration scheme.

[0009] As a preferred embodiment of the present invention, the process of establishing the battery operating architecture in S1 is as follows: The battery's capacity at time t Charging power at time t Discharge power at time t Related, represented as: ; In the formula, This indicates the battery's capacity at time t-1; The charge / discharge rate of the battery; Indicates the power loss rate; State of charge of the battery at time t From reserves and battery capacity Represented as: .

[0010] As a preferred embodiment of the present invention, the process of establishing the hydrogen energy storage system operation architecture in S1 is as follows: The output power of the electrolytic cell is expressed as: ; In the formula, Let be the power consumption of the electrolytic cell at time t; The output efficiency of the electrolytic cell; Let t be the output power of hydrogen converted by the electrolyzer at time t; When a proton exchange membrane fuel cell is used as a hydrogen fuel cell, its output power is expressed as: ; In the formula, Let t be the output electrical power of the hydrogen fuel cell at time t; For the output efficiency of hydrogen fuel cells; Let t be the hydrogen consumption power of the hydrogen fuel cell at time t; The hydrogen storage capacity of the hydrogen storage tank is expressed as follows: ; In the formula, , The hydrogen storage capacity of the hydrogen storage tank at times t and t-1 are respectively. Energy loss rate of hydrogen storage tank; The hydrogen filling and discharging efficiency of the hydrogen storage tank.

[0011] As a preferred embodiment of the present invention, in S1, the power outage time probability Defined as: ; In the formula, is the system power outage time counter at time t, with a value of 1 indicating a system power outage and 0 indicating that the system can meet all load demands; T is the total power supply time of the operating cycle. Probability of load loss Defined as: ; In the formula, Let be the function for determining the power loss during load shedding at time t; Let t be the load power demand at time t.

[0012] As a preferred embodiment of the present invention, in S2, the objective function of the planning stage model for: ; In the formula, The investment cost of a microgrid; The operating cost of the microgrid; Cost of curtailment of solar power in microgrids; For microgrid loss costs; in: ; ; ; ; ; In the formula, This is the capital recovery coefficient; Let k be the unit power investment cost of equipment k; A collection of devices; Let k be the capacity of the device; The discount rate; Let k be the number of years the equipment has been in operation. To maintain the scaling factor; Let k be the maintenance cost coefficient for equipment k. Let k be the operating power of device k; For time intervals; The predicted photovoltaic output at time t is the curtailment penalty coefficient. Let be the predicted photovoltaic power output at time t; Let t be the operating value of the photovoltaic power output at time t; Cost per unit of power loss.

[0013] As a preferred embodiment of the present invention, in S2, the objective function of the running phase model for: ; In the formula, Let n be the probability of an offline scenario occurring. Let N be the confidence set of the scenario probability; N is the set of typical off-grid operation scenarios. , Weighting coefficients for adjusting the reliability ratio; Let n be the full-cycle load failure probability in the off-grid scenario n; Let n be the probability of power outage throughout the entire off-grid scenario. The constraints of the operational phase model include upper and lower bound constraints, comprehensive norm constraints, power balance constraints, and reliability constraints.

[0014] As a preferred embodiment of the present invention, the solution process in S3 is as follows: Boolean variables are introduced to linearize the comprehensive norm constraint, transforming the original nonlinear probability deviation constraint into a linear constraint that can be directly solved. At the same time, operational constraints including mutual exclusion of battery charging and discharging, consistency of hydrogen storage charging and discharging, daily SOC balance and weekly hydrogen storage balance are embedded to construct the main problem and sub-problem framework of the two-stage optimization model. The main problem aims to minimize the investment and operating costs of the microgrid throughout its entire lifecycle, determining the optimal capacity configuration of photovoltaic cells, batteries, electrolyzers, hydrogen fuel cells, and hydrogen storage tanks, and outputting a lower bound for the target value. The subproblems, based on the capacity configuration given by the main problem, seek the worst-case probability distribution under probabilistic fuzzy set constraints, calculate the minimum operating cost and load failure probability under this scenario, output an upper bound for the target value, and feed back the constraints and variables corresponding to the new scenario to the main problem. By iterating between the main problem and the subproblems, the algorithm gradually converges to the optimal solution of the original problem. When the difference between the upper and lower bounds meets the preset convergence threshold, the algorithm terminates and finally obtains the optimal capacity configuration scheme that balances robustness and economy.

[0015] As a preferred embodiment of the present invention, in S4, based on the optimal capacity configuration scheme obtained by solving, the rated parameters of each device are used as fixed inputs, the initial energy storage state and operating constraints are set, and hourly off-grid operation simulation is carried out. The power balance and power shortage state of the microgrid system are determined at each time step, and the cumulative duration of continuous power shortage of the microgrid system is counted to obtain the longest off-grid operation time of the microgrid. By comparing with the traditional scheme, the effectiveness of the optimal capacity configuration scheme is verified.

[0016] As a preferred embodiment of the present invention, if the verification result of the off-grid operation time of the microgrid does not meet the preset reliability requirements, the current optimal capacity configuration scheme is determined to be invalid; the root cause of power shortage is located by backtracking the hourly simulation data, the upper limit of equipment capacity configuration, operating constraints or probabilistic fuzzy set parameters are adjusted, and the optimization model is solved again by column and constraint generation algorithm to obtain the updated capacity configuration scheme; the off-grid operation time verification is carried out again, and the optimization is iteratively performed until the output optimal capacity configuration scheme meets the preset reliability requirements.

[0017] The beneficial effects of this invention are: To address the problems of insufficient power supply reliability and high operating costs in small and micro parks over long time scales due to the rapid physical decay and short storage cycle of traditional electrochemical energy storage, this invention introduces an electro-hydrogen coupling system. This system utilizes hydrogen energy storage, which has a much lower physical decay and capacity decay coefficient than electrochemical energy storage, to achieve energy transfer across long time scales. This significantly reduces the probability of load loss and the expected energy shortage during off-grid operation of the park, not only enhancing power supply reliability but also effectively reducing operating costs caused by power shortages.

[0018] To address the contradiction between rapid response and long-term regulation in a single energy storage form, this invention constructs a hybrid energy storage mode that complements the advantages of hydrogen energy storage (long-term) and batteries (short-term) under an electric-hydrogen coupling architecture. This solves the problem of flexible regulation of small and micro parks across multiple time scales, significantly extends the autonomous operation time of the parks in off-grid conditions, and enhances their tolerance to extreme operating conditions. At the same time, this mode also provides buffer resilience for the upper-level power grid under faults or extreme weather, supporting the overall stability of the regional energy system.

[0019] To address the limitations of traditional uncertainty modeling methods, which often fall into NP-hard problems or produce overly simplistic results when characterizing source-load fluctuations, this invention employs a distributed robust optimization method integrating 1-norm and ∞-norm to precisely constrain the probability distribution of uncertain scenarios. Combined with iterative solutions using the C&CG algorithm, the two-layer solution of the mixed-integer linear programming model becomes more efficient and comprehensive, successfully avoiding computational explosion. Numerical examples demonstrate that the optimization configuration method of this invention can effectively mitigate intraday and multi-day energy imbalances caused by photovoltaic and load uncertainties, significantly improving the operational resilience and scheduling flexibility of microgrid systems. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the principle of this invention; Figure 2 This is a diagram of the two-stage model solution in Example 1; Figure 3 This is a flowchart for calculating the longest off-grid operation time of a microgrid in Example 1; Figure 4 This is a schematic diagram of the microgrid architecture with electro-hydrogen coupling in Example 1; Figure 5 This is a comparison chart of predicted and actual photovoltaic power output in Example 1; Figure 6 This is a schematic diagram of the hydrogen storage tank filling and discharging operation in scenario 3 of Example 1; Figure 7 This is a comparison chart of hydrogen energy charge and discharge rates in scenario 3 of Example 1; Figure 8 This is a schematic diagram of the power balance in scenario 3 of Example 1 for a small industrial park; Figure 9 This is a comparison chart of the load shedding power in the park in Example 1; Figure 10 This is a schematic diagram of the net power during the longest off-grid operation in Example 1; Figure 11 This is a schematic diagram of the off-grid operation and charging / discharging of energy storage in the park in Example 1; Figure 12 This is a schematic diagram of the hydrogen storage tank charging and discharging operation mode in Example 1. Detailed Implementation

[0021] The embodiments of the present invention will be further described below with reference to the accompanying drawings: Example 1: As Figure 1 As shown, a distributed robust optimization configuration method for the reliability of microgrids with electric-hydrogen coupling includes the following steps: S1. Establish the battery operation architecture and the hydrogen energy storage system operation architecture, and construct reliability indicators including the probability of power shortage time and the probability of load failure. S2. Construct a two-stage robust optimization configuration model for a microgrid with electricity-hydrogen coupling, including a planning stage model and an operation stage model. The planning stage model takes minimizing the total operating cost and investment cost within the microgrid as the objective function, and the capacity configuration of electrolyzers, hydrogen fuel cells, photovoltaic cells, batteries, and hydrogen storage tanks as optimization variables. The operation stage model takes minimizing the loss cost and the probability of power outage and load loss within one operating cycle of the microgrid as the optimization objective. The optimal installed capacity calculated by the planning stage model is incorporated into the off-grid operation scenario of the operation stage model, and the operation data of the microgrid is obtained through calculation. S3. The column and constraint generation algorithm is used to solve the two-stage robust optimization configuration model of microgrid with electric-hydrogen coupling to obtain the optimal capacity configuration scheme. S4. Based on the optimal capacity configuration scheme, calculate the off-grid runtime and verify the effectiveness of the optimal capacity configuration scheme.

[0022] In S1, the process of establishing the battery operating architecture is as follows: The battery's capacity at time t Charging power at time t Discharge power at time t Related, represented as: ; In the formula, This indicates the battery's capacity at time t-1; The charge / discharge rate of the battery; Indicates the power loss rate; State of charge of the battery at time t From reserves and battery capacity Represented as: ; The operating constraints of the battery are: ; In the formula, , These are the minimum and maximum values ​​of the battery's state of charge, respectively. , The battery state of charge at the end and beginning of a day (with a scheduling cycle of one day) are respectively. Let t be the state variable of the battery charging and discharging at time t, where 1 represents charging and 0 represents discharging. The maximum charge and discharge power that a battery can achieve is linearly related to its capacity. It is a fixed proportional coefficient for the upper limit of energy storage power and capacity.

[0023] The process of establishing the operating architecture of a hydrogen energy storage system is as follows: An electrolyzer can electrolyze water into hydrogen and oxygen. It is a device that can convert electrical energy into hydrogen energy, and its output power is expressed as: ; In the formula, Let be the power consumption of the electrolytic cell at time t; The output power of hydrogen converted by the electrolyzer; Let be the output efficiency of the electrolytic cell at time t; A proton exchange membrane fuel cell is used as a hydrogen fuel cell, using hydrogen and oxygen as fuel to convert chemical energy into electrical energy for storage. Its output power is expressed as: ; In the formula, Let t be the output electrical power of the hydrogen fuel cell at time t; For the output efficiency of hydrogen fuel cells; Let t be the hydrogen consumption power of the hydrogen fuel cell at time t; Compared to battery storage, hydrogen storage tanks have lower energy loss, better safety performance, and are suitable for long-term hydrogen storage. Their hydrogen storage capacity is expressed as follows: ; In the formula, , The hydrogen storage capacity of the hydrogen storage tank at times t and t-1 are respectively. Energy loss rate of hydrogen storage tank; The hydrogen filling and discharging efficiency of the hydrogen storage tank; The operating constraints of hydrogen energy storage systems are: ; In the formula, Let be the hydrogen filling and discharging state variable of the hydrogen storage tank at time t, and be... Maintain consistency; The maximum achievable power for charging and discharging hydrogen from the hydrogen storage tank has a linear relationship with the tank's capacity. This refers to the installed capacity of the hydrogen storage tank; A fixed ratio coefficient between the upper limit of hydrogen charging and discharging power and the capacity of the hydrogen storage tank; For the first The state variables of hydrogen charging and discharging in the first hour of the day. For the hydrogen storage tank The state variables of hydrogen charging and discharging in the second hour of the day; Let be the hydrogen charging / discharging state variable for day v, where 1 represents hydrogen charging and 0 represents hydrogen discharging. A collection of data for each day of the week; , Hydrogen storage capacity in the hydrogen storage tank at the end of 168 hours and at the beginning of the hour.

[0024] Introducing power outage time probability The ratio of power outage time to total power supply time during the operating cycle of a microgrid system is used to evaluate its performance. It is defined as: ; In the formula, is the system power outage time counter at time t, with a value of 1 indicating a system power outage and 0 indicating that the system can meet all load demands; T is the total power supply time of the operating cycle. Introducing the probability of load failure The ratio of power shortage load to total load in the evaluation system is defined as: ; ; In the formula, This represents the function for determining the power loss during load shedding at time t. Let t be the load demand power. Let t be the operating value of the photovoltaic power output at time t; Let t be the power loss due to load shedding in the microgrid.

[0025] In S2, the objective function of the microgrid planning stage model for: ; In the formula, The investment cost of a microgrid; The operating cost of the microgrid; Cost of curtailment of solar power in microgrids; For microgrid loss costs; in: ; ; ; ; ; In the formula, This is the capital recovery coefficient; The unit power investment cost of device k includes the unit capacity investment cost of energy storage. Investment cost per unit power of photovoltaic power generation Investment cost per unit power of electrolytic cells Investment cost per unit capacity of hydrogen storage tank Investment cost per unit power of fuel cells ; A collection of devices; Let k be the capacity of the kth microgrid device (equipment k); The discount rate; Let k be the number of years the equipment has been in operation. To maintain the scaling factor; Let k be the maintenance cost coefficient for equipment k. Let k be the operating power of device k; For time intervals; The predicted photovoltaic output at time t is the curtailment penalty coefficient. Let be the predicted photovoltaic power output at time t; Let t be the operating value of the photovoltaic power output at time t; Cost per unit of power loss; The constraints of the microgrid planning stage model are as follows: due to site and economic factors, the constraints of each device should satisfy the following formula: ; In the formula, , , , , These represent the maximum values ​​of installed capacity / operating power obtained after calculation in the lower-level model for the microgrid's batteries, photovoltaic cells, electrolyzers, hydrogen fuel cells, and hydrogen storage tanks. , , , , These are the maximum values ​​that can be achieved by the installed capacity / operating power of batteries, photovoltaic cells, electrolyzers, hydrogen fuel cells, and hydrogen storage tanks, respectively. , , , , These represent the installed capacity / rated output power of batteries, photovoltaic cells, electrolyzers, hydrogen fuel cells, and hydrogen storage tanks, respectively; P on the left corresponds to power, and E corresponds to capacity.

[0026] In S2, the operation phase model employs a distributed robust optimization model to characterize the uncertainties of off-grid operation, taking into account the uncertainties of microgrid photovoltaic power generation, load output, and off-grid operation. The objective function of the microgrid operation phase model is... for: ; In the formula, Let n be the probability of an offline scenario occurring. is the confidence set of scenario probabilities, constrained by the 1-norm and ∞-norm; N is the set of typical off-grid operation scenarios; , To adjust the weighting coefficient of the reliability ratio, ; Let n be the full-cycle load failure probability in the off-grid scenario n; Let n be the probability of power outage throughout the entire off-grid scenario. The constraints of the model during the runtime phase include: Operating upper and lower limit constraints: ; In the formula, This represents the minimum capacity of the hydrogen storage tank; in this embodiment, , ; The maximum output power of the electrolyzer and hydrogen fuel cell is limited by their capacity and the remaining energy storage capacity of the hydrogen storage tank, which can be expressed as follows: ; ; In the formula, This represents the maximum output power of the electrolytic cell at time t; This represents the maximum output power of the hydrogen fuel cell at time t; Comprehensive norm constraint; under the comprehensive norm, the feasible region (the confidence set of scenario probabilities). for: ; In the formula, This represents the initial probability of the off-network scenario n determined by scenario clustering; and These are the allowable deviation limits for probability under 1-norm and ∞-norm constraints; Among them, the probability set of off-network scenarios The following confidence levels are satisfied: ; In the formula, Here, is the norm constraint adjustment coefficient; e is the natural constant; It is a probability symbol; Let the right sides of the above inequality represent the confidence levels of the probability distribution values. , Then we can get: ; ; Power balance constraints are expressed as: ; Reliability constraints are expressed as: ; In the formula, , These represent the full-cycle load failure probability and the maximum full-cycle power failure probability for off-grid scenario n, respectively.

[0027] In S3, the solution process is as follows: Boolean variables are introduced to linearize the comprehensive norm constraint, transforming the original nonlinear probability deviation constraint into a linear constraint that can be directly solved. At the same time, operational constraints including mutual exclusion of battery charging and discharging, consistency of hydrogen storage charging and discharging, daily SOC balance and weekly hydrogen storage balance are embedded to construct the main problem and sub-problem framework of the two-stage optimization model. The main problem aims to minimize the investment and operating costs of the microgrid throughout its entire lifecycle, determining the optimal capacity configuration of photovoltaic cells, batteries, electrolyzers, hydrogen fuel cells, and hydrogen storage tanks, and outputting a lower bound for the target value. The subproblems, based on the capacity configuration given by the main problem, seek the worst-case probability distribution under probabilistic fuzzy set constraints, calculate the minimum operating cost and load shedding probability under this scenario, output an upper bound for the target value, and feed back the constraints and variables corresponding to the new scenario to the main problem. The probabilistic fuzzy set is a set of probability distributions of all scenarios that are "possible and allowed".

[0028] By iterating between the main problem and the subproblems, the algorithm gradually converges to the optimal solution of the original problem. When the difference between the upper and lower bounds meets the preset convergence threshold, the algorithm terminates and finally obtains the optimal capacity configuration scheme that balances robustness and economy.

[0029] The specific solution process is as follows: Linearization of the comprehensive norm constraint: Introducing Boolean variables , ,for The synthesis norm constraint is equivalent to a linear constraint: ; In the formula, , They are respectively relatively The positive and negative offsets.

[0030] This transforms the original absolute value constraint into: ; Similarly, To process this, we also introduce 0-1 auxiliary variables. , : ; ; ; Perform constraint linearization: The operating constraints of batteries and hydrogen energy storage systems contain non-convex nonlinear constraints, which can be linearized using the Big-M method to obtain: ; ; In the formula, M is a maximum number; , , , For microgrid linear variables; Let t be the maximum value that the battery can achieve during charging and discharging. Let t be the maximum value that the hydrogen storage tank can achieve when charging or discharging hydrogen. like Figure 2 As shown, the solution to the two-stage distributed robust optimization model is as follows: Let x represent the variables in the first stage, which include investment plans for photovoltaic, electrochemical energy storage, and hydrogen energy storage systems, as well as microgrid operation variables; let x represent the variables in the second stage. The compact form of the two-stage distributed robust optimization configuration model for microgrids is shown below: ; , which are the constraints associated with the variables in the first stage; , , which are the relevant constraints for the variables in the second stage; In the formula, A represents the cost coefficient corresponding to the investment cost and operating cost of off-grid microgrid operation; For investment costs and microgrid operating costs; X represents the set of decision variables for the first stage; B represents the reliability operating coefficient for off-grid scenarios; This represents the operating cost of microgrid operation scenario n; Represents the second-stage constraint set; C, D, E, F, e and c represent the matrices or vectors corresponding to the variables in the constraints of the optimization model, respectively. This is a three-level, two-stage optimization problem in the form of min-max-min. Based on the column and constraint generation (C&CG) algorithm, the problem is decomposed into a master problem (MP) and sub-problems (SP) and iterated repeatedly until the difference between the optimization values ​​of the master problem and the sub-problems satisfies the convergence criterion, at which point the iteration stops.

[0031] MP seeks the optimal solution that satisfies the system's economic efficiency, given the known scenario p. The main problem is expressed as: ; ; In the formula, L represents the optimal solution to the main problem; The given threshold is given; W is the number of model iterations. express The optimal solution at the w-th iteration; Represents the value at the w-th iteration. ; The variables are obtained by solving. (The optimal solution for x) and the lower bound LB of the model.

[0032] The subproblem is represented as: ; The subproblem is represented as a known main problem, and the solution result is... At that time, the solution to the main problem is used as a constraint to find the worst-case scenario probability distribution within the confidence interval. Provides the upper bound UB.

[0033] Due to the confidence set of scene probabilities in SP and the second-stage constraint set in each scenario Since there is no intersection, we first solve the inner-layer minimization problem, and then solve the outer-layer max problem based on the inner-layer results, defining it as H. n Solve the problem step by step using the two functions U: ; ; The solution is obtained by the solver. optimal solution Substitute the problem into the main problem for the next optimization iteration and obtain the upper bound UB.

[0034] In S4, based on the optimal capacity configuration scheme obtained by the solution, the rated parameters of each device are used as fixed inputs. The initial energy storage state and operating constraints are set, and the off-grid operation simulation is carried out hourly. The power balance and power shortage state of the microgrid system are determined at each time. The cumulative duration of the microgrid system without power shortage is counted, and the longest off-grid operation time of the microgrid is obtained. By comparing with the traditional scheme, the effectiveness of the optimal capacity configuration scheme is verified.

[0035] This embodiment's method is based on the proposed two-stage robust optimization configuration model for microgrids with electro-hydrogen coupling. First, it solves for the optimal equipment capacity configuration combination of the microgrid system within a set operating period T. Then, it uses this configuration result as a fixed parameter and substitutes it into the hourly operation simulation model of a small microgrid park. By simulating its energy balance state during a continuous and stable off-grid operation, it calculates the maximum operating time that the microgrid system can continuously maintain power supply under a given configuration.

[0036] like Figure 3 As shown, in order to verify the effectiveness and superiority of the configuration scheme obtained by the two-stage robust optimization configuration model, the longest running time obtained by the above simulation is compared and analyzed with the maximum running time under the configuration obtained by traditional deterministic programming or stochastic programming methods.

[0037] To ensure fairness and computational efficiency in the comparative analysis, and to focus on evaluating the effectiveness of the configuration method itself in improving the system's long-term autonomy, this part of the simulation temporarily disregards the random fluctuations of photovoltaic power and load when calculating runtime. Specifically, it sets up a typical, periodic daily operating scenario using identical photovoltaic power generation and load demand curves. This simplification aims to eliminate random interference, allowing the performance comparison of the two configuration methods under identical, repeatable boundary conditions, thus more clearly and directly highlighting the differences between different optimization methods in capacity planning.

[0038] Net power of microgrid off-grid operation: Define the net power of the microgrid at time t. The difference between photovoltaic power output and load demand: ; like At this moment, the microgrid has an energy surplus, which is prioritized for charging the batteries, with the remainder used for hydrogen production. If... If the energy is insufficient, the battery will be discharged first, and the fuel cell will be activated if the energy is still insufficient.

[0039] Microgrid off-grid operation energy allocation logic: When there is a surplus of photovoltaic power ( When operating off-grid, the microgrid prioritizes charging the battery. If energy remains, the electrolyzer converts the electrical energy into hydrogen energy, which is then stored in the hydrogen storage tank. The battery charging power and the electrolyzer hydrogen production power at time t in off-grid operation mode can be expressed as: ; ; ; ; In the formula, The charging power of the battery in the off-grid operation mode of the microgrid at time t; , These represent the battery capacity at times t and t-1, respectively. , These represent the hydrogen storage capacity of the hydrogen storage tank at times t and t-1 during off-grid operation of the microgrid. The hydrogen production power of the electrolyzer at time t in off-grid operation mode; the subscript d does not represent a variable, but is used to distinguish between off-grid and grid-connected operation modes.

[0040] When photovoltaic power is insufficient ( When the battery is in a priority discharge state, if the electrical energy is still insufficient to meet the load demand, the fuel cell is activated to burn hydrogen from the hydrogen storage tank to meet the load demand. If the load demand is still not met, load shedding is triggered. The battery discharge power and fuel cell hydrogen consumption power at time t in off-grid operation mode are expressed as follows: ; ; ; In the formula, The battery discharge power of the microgrid at time t in off-grid operation mode; This represents the minimum installed capacity of the battery in off-grid operation mode. This represents the minimum installed capacity of the hydrogen storage tank. The hydrogen consumption power of the fuel cell in the microgrid at time t is the value of the fuel cell in off-grid operation mode. When the load shedding exceeds the maximum value allowed for normal microgrid operation Or the battery charge is lower than the minimum allowable value for the battery. When the system terminates, the microgrid runtime T is recorded.

[0041] The coefficients in this embodiment can be set based on experience or existing methods such as expert methods.

[0042] If the verification results of the off-grid operation time of the microgrid do not meet the preset reliability requirements, the current optimal capacity configuration scheme is deemed invalid. The root cause of the power shortage is located by backtracking the hourly simulation data, adjusting the upper limit of equipment capacity configuration, operating constraints or probabilistic fuzzy set parameters, and resolving the optimization model through the column and constraint generation algorithm to obtain the updated capacity configuration scheme. The off-grid operation time verification is carried out again, and the optimization is iterated until the output optimal capacity configuration scheme meets the preset reliability requirements.

[0043] Figure 4 This is an electro-hydrogen coupled microgrid architecture. The power generation component includes distributed photovoltaics, the energy storage component includes electrochemical energy storage composed of batteries, a hydrogen energy storage system composed of an electrolyzer, hydrogen storage tank, and fuel cell, and the load component. This embodiment considers the microgrid to operate in an off-grid mode, i.e., disconnected from the external power grid, providing independent power supply through photovoltaics and energy storage. The microgrid is designed to have at least one week (one operating cycle T) of off-grid autonomous operation capability. Different types of energy storage have different response speeds, cycle lives, and self-loss characteristics. Short-cycle energy storage, such as electrochemical energy storage, can be frequently charged and discharged, returning to its initial load state within a short equilibrium cycle. Long-cycle energy storage, represented by hydrogen energy storage, can operate in different modes to absorb, convert, and release energy, depending on storage conditions and methods, and complete the charge-discharge cycle within a longer equilibrium cycle.

[0044] To explore the mechanism by which hydrogen energy storage systems improve the reliability of microgrid power supply and ensure safe off-grid operation, four typical technical scenarios were constructed for comparative research. Scenario 1 and Scenario 2 simulate the operation of microgrids with and without hydrogen energy storage systems under deterministic operating conditions. Scenario 3 and Scenario 4 further consider the uncertainties in system operation, evaluating the differentiated impact of configuring hydrogen energy storage systems on the reliability and resilience of microgrid power supply under uncertain environments. Through the cross-comparison of the two dimensions of "determinism and uncertainty" and "configuration and non-configuration," this study aims to systematically reveal the comprehensive contribution of hydrogen energy storage systems to the safe, stable, and economical operation of microgrid energy systems under different risk environments, thereby providing a more comprehensive and detailed theoretical basis and practical reference for relevant planning and decision-making.

[0045] Analysis of optimized configuration results: Table 1 Configuration Results As shown in Table 1, under deterministic conditions, the installed capacity of photovoltaics and batteries in Scenario 1, equipped with a hydrogen energy storage system, is significantly lower than in Scenario 2, where it is not equipped. This indicates that the hydrogen energy storage system, through multi-stage conversion and storage of electricity, hydrogen, and electricity, significantly reduces the reliance on photovoltaics and electrochemical energy storage, improving the flexibility and economy of system configuration. Furthermore, for uncertain scenarios, the comparison between Scenario 3 and Scenario 4 further demonstrates that with hydrogen energy storage, only a small increase in the capacity of photovoltaics and batteries is needed to cope with the volatility, while systems without hydrogen energy storage require further increases in photovoltaic capacity and battery storage. This indicates that hydrogen energy storage has a significant resilience-enhancing effect in mitigating the intermittency of renewable energy and the randomness of load.

[0046] Table 2 Reliability Index Analysis As shown in Table 2, under deterministic conditions, the load shedding rate and power outage rate are significantly lower in Scenario 1 (with hydrogen energy storage system) compared to Scenario 2 (without hydrogen energy storage system). This indicates that the hydrogen energy storage system significantly improves the system's power supply continuity and load guarantee capability through multi-energy conversion and storage. Under uncertain scenarios, the load shedding rate and power outage rate of the microgrid increase in both Scenario 3 and Scenario 4, but the increase rate in Scenario 4 is significantly higher than that in Scenario 3. This demonstrates that the hydrogen energy storage system exhibits strong operational resilience under fluctuating photovoltaic output and load output, significantly reducing the risk of load shedding and the probability of power outages. In summary, regardless of whether uncertainty is considered, the introduction of the hydrogen energy storage system can significantly improve the power supply reliability of the microgrid, verifying its important role in enhancing the system's ability to cope with multiple operational risks.

[0047] Table 3 Economic Analysis As shown in Table 3, comparing scenarios 1 and 2, the operating costs of scenario 2 are higher than those of scenario 1. This indicates that hydrogen energy storage systems can reduce initial investment pressure and equipment operating costs. Hydrogen energy storage systems increase energy diversification and enable energy transport across time and space, significantly reducing the initial capacity of each device and the operating costs, thus increasing the flexibility and economy of system configuration. Analysis of uncertain scenarios shows that the configuration and operating costs of microgrids equipped with hydrogen energy storage systems increase only slightly, while the operating costs of scenario 4 without hydrogen energy storage systems increase significantly. This demonstrates the good economic robustness of hydrogen energy storage systems. Therefore, hydrogen energy storage systems not only improve the reliability of microgrid power supply but also optimize the economics throughout the entire lifecycle, providing crucial support for the safe and efficient operation of microgrids with a high proportion of renewable energy.

[0048] Analysis of execution results: according to Figure 5 Analysis shows that when dealing with uncertainties, microgrids equipped with hydrogen energy storage significantly reduce their reliance on photovoltaic (PV) output, resulting in a substantial decrease in curtailment rates. Specifically, data indicates that the curtailment cost for microgrids equipped with hydrogen energy storage over their operating cycle is 32,582.7 yuan, while the curtailment cost for those without is as high as 61,136.7 yuan, representing a 46.7% reduction. This is primarily due to the large-scale, long-term energy storage capabilities of hydrogen energy storage systems. These systems effectively store excess electricity generated during peak PV periods and release energy when PV output is insufficient or load demand increases, thus significantly improving PV grid integration. In uncertain environments, the flexible adjustment function of hydrogen energy storage reduces the randomness and intermittency of PV output, optimizes energy supply and demand matching, and not only lowers curtailment costs but also enhances the operational stability and economic efficiency of the microgrid.

[0049] like Figure 6 The figure shows the hydrogen charging and discharging state changes of the hydrogen energy storage system in scenario 3. Among them, 1 represents the hydrogen production mode, which is used to absorb the redundant electrical energy generated by the excess of new energy power generation; 0 represents the hydrogen discharging mode, which indicates that there is a power shortage in the system at this time, and the stored hydrogen energy needs to be converted into electrical energy through fuel cells to meet the current load demand. Figure 7The comparison between hydrogen input and output in Scenario 3 is further presented. Analysis of the data in the figure shows that, under the uncertainty scenario, the first, third, fifth, and seventh days of the park's operation are primarily hydrogen production days, while the remaining days are dedicated to hydrogen power generation. Under the uncertainty scenario, the hydrogen energy system generally has higher power generation capacity on hydrogen production days. Surplus electricity is stored in hydrogen storage tanks through hydrogen production and released on subsequent power generation days to meet load demand. Simultaneously, the difference between hydrogen input and output capacity in the storage tanks is significantly reduced in this scenario, resulting in more stable system operation. The above analysis indicates that, to effectively address the impact of uncertainties, the hydrogen energy storage system adopts an alternating operation mode of power generation and hydrogen production days. This mode can alleviate the intraday and interday energy imbalance caused by the uncertainty of small-scale park operations to the greatest extent.

[0050] like Figure 8 The figure shows typical operating data for a small industrial park over a single cycle. Through comprehensive analysis of the output curves and load changes of each device, it is clear that the hydrogen energy storage system strictly adheres to a single charge / discharge mode operation strategy each day, while also demonstrating its outstanding ability to schedule and transfer energy across time and space. During periods of abundant photovoltaic power generation, the system can efficiently convert surplus electricity into hydrogen energy for long-term storage; while during periods of insufficient or complete photovoltaic output, the system can convert the stored hydrogen energy back into electricity output through fuel cells. The curves in the figure clearly show that during a specific period, the electrolyzer operates continuously at high power for hydrogen production and storage, while in a subsequent period, the fuel cell generates electricity stably at a similar power level. This achieves effective energy transfer and reuse from periods of ample time but surplus power to periods of tight time and power shortage. This type of energy transfer can not only cover the peak and valley differences in daily electricity consumption, but also achieve energy regulation and balance across multiple natural days or even several weeks, fully demonstrating the unique performance advantages of hydrogen energy storage technology in long-term energy storage applications.

[0051] according to Figure 9It is known that, under the hydrogen energy storage system model, the period of load shedding in small and micro parks equipped with hydrogen energy storage is 7 hours, while that in small and micro parks without hydrogen energy storage is 35 hours, more than five times longer. This demonstrates that, compared to traditional optimized configuration schemes for small and micro parks, the hydrogen energy storage system in small and micro parks with electricity-hydrogen coupling, through multi-energy conversion (electricity-hydrogen-electricity) and long-term storage, can convert excess electricity during periods of abundant photovoltaic power into hydrogen energy for storage, and stably generate electricity through fuel cells during periods of power shortage, thereby effectively suppressing load shedding events. This operating mechanism not only enhances the system's ability to cope with intraday peak-valley differences but also achieves energy balance across days and even weeks, significantly improving the power supply continuity and load guarantee capacity of small and micro parks, providing key support for improving the reliability of park power supply in scenarios with a high proportion of renewable energy.

[0052] like Figure 10 To determine the net power consumption for off-grid operation of small industrial parks equipped with hydrogen energy storage, simulation results show that the off-grid operating time for such parks is approximately 529 hours, while that for those without hydrogen energy storage is approximately 302 hours. This comparison demonstrates that configuring a hydrogen energy storage system significantly increases the off-grid operating time, thereby substantially enhancing the reliability of the park's power supply. Combined with... Figure 11 and Figure 12 Analysis of the energy storage charge / discharge and hydrogen storage tank operation curves clearly reveals its internal operating mechanism. The electro-hydrogen coupling system uses an electrolyzer to convert electrical energy into hydrogen for storage during periods of surplus power, achieving energy transfer over time. When power generation is insufficient, the fuel cell utilizes the stored hydrogen to generate electricity stably. This "electricity-hydrogen-electricity" conversion mode not only effectively integrates long- and short-cycle energy storage and improves the absorption capacity of fluctuating renewable energy sources, but also significantly reduces... Figure 11 This reduces the number of frequent charge-discharge cycles of the storage battery. On the one hand, this helps extend the battery's lifespan and reduce system maintenance costs; on the other hand, through the daily and weekly regulation of hydrogen energy storage, it fundamentally enhances the long-term energy autonomy and operational reliability of small and micro parks in off-grid conditions.

[0053] Example 2: A distributed robust optimization configuration device for microgrid reliability with electro-hydrogen coupling, comprising: One or more processors; Memory, used to store one or more computer programs; When one or more programs are executed by one or more processors, the one or more processors execute the method in Example 1.

[0054] Example 3: A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to perform the method in Example 1.

Claims

1. A distributed robust optimization configuration method for the reliability of microgrids with electric-hydrogen coupling, characterized in that... Includes the following steps: S1. Establish the battery operation architecture and the hydrogen energy storage system operation architecture, and construct reliability indicators including the probability of power shortage time and the probability of load failure. S2. Construct a two-stage robust optimization configuration model for a microgrid with electricity-hydrogen coupling, including a planning stage model and an operation stage model. The planning stage model takes the minimization of the total operating cost and investment cost within the microgrid as the objective function, and the capacity configuration of the electrolyzer, hydrogen fuel cell, photovoltaic cell, battery, and hydrogen storage tank as optimization variables. The operation phase model aims to minimize the loss cost and the probability of power outage and load loss within one operating cycle of the microgrid. The optimal installed capacity calculated by the planning phase model is incorporated into the off-grid operation scenario of the operation phase model, and the operation data of the microgrid is obtained through calculation. S3. The column and constraint generation algorithm is used to solve the two-stage robust optimization configuration model of microgrid with electric-hydrogen coupling to obtain the optimal capacity configuration scheme. S4. Based on the optimal capacity configuration scheme, calculate the off-grid runtime and verify the effectiveness of the optimal capacity configuration scheme.

2. The distributed robust optimization configuration method for microgrid reliability including electro-hydrogen coupling as described in claim 1, characterized in that, In S1, the process of establishing the battery operating architecture is as follows: Battery capacity at time t Charging power at time t Discharge power at time t Related, represented as: ； In the formula, This indicates the battery's capacity at time t-1; The charge / discharge rate of the battery; Indicates the power loss rate; State of charge of the battery at time t From reserves and battery capacity Represented as: 。 3. The distributed robust optimization configuration method for microgrid reliability including electro-hydrogen coupling as described in claim 2, characterized in that, In S1, the process of establishing the hydrogen energy storage system operation architecture is as follows: The output power of the electrolytic cell is expressed as: ； In the formula, Let be the power consumption of the electrolytic cell at time t; The output efficiency of the electrolytic cell; Let t be the output power of hydrogen converted by the electrolyzer at time t; When a proton exchange membrane fuel cell is used as a hydrogen fuel cell, its output power is expressed as: ； In the formula, Let t be the output electrical power of the hydrogen fuel cell at time t; For the output efficiency of hydrogen fuel cells; Let t be the hydrogen consumption power of the hydrogen fuel cell at time t; The hydrogen storage capacity of the hydrogen storage tank is expressed as follows: ； In the formula, , The hydrogen storage capacity of the hydrogen storage tank at times t and t-1 are respectively. Energy loss rate of hydrogen storage tank; The hydrogen filling and discharging efficiency of the hydrogen storage tank.

4. The distributed robust optimization configuration method for microgrid reliability including electro-hydrogen coupling as described in claim 3, characterized in that, In S1, the probability of power outage time Defined as: ； In the formula, is the system power outage time counter at time t, with a value of 1 indicating a system power outage and 0 indicating that the system can meet all load demands; T is the total power supply time of the operating cycle. Probability of load loss Defined as: ； In the formula, Let be the function for determining the power loss during load shedding at time t; Let t be the load power demand at time t.

5. The distributed robust optimization configuration method for microgrid reliability including electro-hydrogen coupling as described in claim 1, characterized in that, In S2, the objective function of the planning phase model is... for: ； In the formula, The investment cost of a microgrid; The operating cost of the microgrid; Cost of curtailment of solar power in microgrids; For microgrid loss costs; in: ； ； ； ； ； In the formula, This is the capital recovery coefficient; Let k be the unit power investment cost of equipment k; A collection of devices; Let k be the capacity of the device; The discount rate; Let k be the number of years the equipment has been in operation. To maintain the scaling factor; Let k be the maintenance cost coefficient for equipment k. Let k be the operating power of device k; For time intervals; The predicted photovoltaic output at time t is the curtailment penalty coefficient. Let be the predicted photovoltaic power output at time t; Let t be the operating value of the photovoltaic power output at time t; Cost per unit of power loss.

6. The distributed robust optimization configuration method for microgrid reliability including electro-hydrogen coupling as described in claim 5, characterized in that, In S2, the objective function of the running phase model for: ； In the formula, Let n be the probability of an offline scenario occurring. Let N be the confidence set of the scenario probability; N is the set of typical off-grid operation scenarios. , Weighting coefficients for adjusting the reliability ratio; Let n be the full-cycle load failure probability in the off-grid scenario. Let n be the probability of power outage throughout the entire off-grid scenario. The constraints of the operational phase model include upper and lower bound constraints, comprehensive norm constraints, power balance constraints, and reliability constraints.

7. The distributed robust optimization configuration method for microgrid reliability including electro-hydrogen coupling as described in claim 6, characterized in that, In S3, the solution process is as follows: Boolean variables are introduced to linearize the comprehensive norm constraint, transforming the original nonlinear probability deviation constraint into a linear constraint that can be directly solved. At the same time, operational constraints including mutual exclusion of battery charging and discharging, consistency of hydrogen storage charging and discharging, daily SOC balance and weekly hydrogen storage balance are embedded to construct the main problem and sub-problem framework of the two-stage optimization model. The main problem aims to minimize the investment and operating costs of the microgrid throughout its entire lifecycle, determining the optimal capacity configuration of photovoltaic cells, batteries, electrolyzers, hydrogen fuel cells, and hydrogen storage tanks, and outputting a lower bound for the target value. The subproblems, based on the capacity configuration given by the main problem, seek the worst-case probability distribution under probabilistic fuzzy set constraints, calculate the minimum operating cost and load failure probability under this scenario, output an upper bound for the target value, and feed back the constraints and variables corresponding to the new scenario to the main problem. By iterating between the main problem and the subproblems, the algorithm gradually converges to the optimal solution of the original problem. When the difference between the upper and lower bounds meets the preset convergence threshold, the algorithm terminates and finally obtains the optimal capacity configuration scheme that balances robustness and economy.

8. The distributed robust optimization configuration method for microgrid reliability including electro-hydrogen coupling as described in claim 1, characterized in that, In S4, based on the optimal capacity configuration scheme obtained by the solution, the rated parameters of each device are used as fixed inputs, the initial energy storage state and operating constraints are set, and the off-grid operation simulation is carried out hourly. The power balance and power shortage state of the microgrid system are determined hourly, the cumulative duration of continuous power shortage of the microgrid system is counted, and the longest off-grid operation time of the microgrid is obtained. By comparing with the traditional scheme, the effectiveness of the optimal capacity configuration scheme is verified.

9. The distributed robust optimization configuration method for microgrid reliability including electro-hydrogen coupling as described in claim 8, characterized in that, If the verification results of the off-grid operation time of the microgrid do not meet the preset reliability requirements, the current optimal capacity configuration scheme is deemed invalid. The root cause of the power shortage is located by backtracking the hourly simulation data, adjusting the upper limit of equipment capacity configuration, operating constraints or probabilistic fuzzy set parameters, and resolving the optimization model through the column and constraint generation algorithm to obtain the updated capacity configuration scheme. The off-grid operation time verification is carried out again, and the optimization is iterated until the output optimal capacity configuration scheme meets the preset reliability requirements.

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