Multi-energy system scheduling method based on cooperation of double electrolytic cells and multiple control modes

Abstract

The invention aims to provide a multi-energy system scheduling model based on double electrolytic cells and multi-control mode collaboration. The multi-energy system scheduling model comprises the following steps: modeling for a wind power photovoltaic system, a pumped storage system and a hydrogen fuel cell system in a comprehensive energy system; carrying out comparison modeling by adopting two control strategies on the basis of the electrolytic bath with two different hydrogen production modes; two control strategies are adopted for comparison; constructing a multi-energy system comprehensive scheduling model comprising the system, wherein the system comprises a wind power photovoltaic system, a pumped storage system, a hydrogen fuel cell system and an electrolytic cell hydrogen production system; the model goal is economical and environment-friendly; solving the model in the step 3 by using an improved Hereum optimization algorithm; and the solved comprehensive energy scheduling strategy can ensure that the carbon emission is relatively small when the economic cost is lowest, so that the overall comprehensive benefit is improved.

Description

Technical Field

[0001] This invention relates to a multi-energy system dispatching method based on dual electrolyzers and multi-control mode coordination, belonging to the field of power system dispatching technology. Background Technology

[0002] Against the backdrop of global energy transition and the advancement of "dual carbon" goals, the optimal scheduling of multi-energy systems with high proportions of renewable energy has become a core research focus. Renewable energy sources such as wind and solar power are intermittent and volatile, requiring the integration of energy storage and hydrogen production equipment to achieve stable operation. Pumped hydro storage, as a mature large-scale energy storage technology, can effectively mitigate power fluctuations. Electrolyzer hydrogen production can not only absorb surplus renewable energy but also achieve energy transfer across time and space through hydrogen energy.

[0003] Existing research on multi-energy system scheduling does not adequately consider the dynamic characteristics of electrolyzers, and the optimization algorithms need to be improved in terms of accuracy and efficiency under complex constraints. At the same time, traditional scheduling models generally only use a single control method for operation optimization, without fully exploring the differentiated impact of different control methods on hydrogen production efficiency and equipment lifespan. Therefore, it is of great significance to construct a scheduling method that takes into account economic efficiency, environmental friendliness, and detailed modeling of multiple devices. Summary of the Invention

[0004] The present invention aims to provide a multi-energy system scheduling model based on dual electrolyzers and multi-control mode coordination, so as to overcome the problems of insufficient consideration of electrolyzer operating characteristics and neglect of coordinated scheduling between pumped storage power stations and electrolyzers in the existing technology, and to improve the overall system benefits.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] This invention discloses a multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination, comprising the following steps:

[0007] S1: Modeling wind power and photovoltaic systems, pumped storage systems, and hydrogen fuel cell systems in integrated energy systems;

[0008] S2: Comparative modeling was conducted using two electrolyzers with two different hydrogen production methods and two control methods; and the two control methods were compared.

[0009] S3: Construct a multi-energy system integrated scheduling model that includes the above systems. The given systems include wind power and photovoltaic, pumped storage, hydrogen fuel cells, and electrolyzer hydrogen production systems. The model objectives are economic efficiency and environmental friendliness.

[0010] S4: Solve the model from step 3 using the improved Hippo optimization algorithm.

[0011] Specifically, the integrated energy system modeling in S1 includes modeling of photovoltaic power generation systems, wind power generation systems, hydrogen fuel cells, and pumped hydro storage systems. Each model is based on the power equation:

[0012] The operating equations for the photovoltaic and wind turbines include:

[0013] Photovoltaic output power equation:

[0014]

[0015] Among them, P t PV G t T c,t and T amb,t G represents the photovoltaic output power, solar irradiance, module temperature, and ambient temperature at time t, respectively. STC and T c,STC These represent solar irradiance and module temperature under standard test conditions, respectively. NOCT T c,NOCT and T amb,NOCT These are the solar irradiance, module temperature, and ambient temperature under the nominal working cell temperature test conditions, respectively, k. T W is the temperature coefficient. PV For the design capacity of photovoltaics;

[0016] Wind turbine output power equation:

[0017]

[0018] Among them, v t and P t WT The actual wind speed and the output power of the wind turbine at time t are respectively, v R v ci and v co These are the rated wind speed, cut-in wind speed, and cut-out wind speed, respectively, W WT For the design capacity of wind power;

[0019] The operating equations and constraints of the pumped storage power station include:

[0020] Hydropower turbine output power equation:

[0021]

[0022] Among them, P t HPS Let t be the power generation of HPS. Let H be the velocity of the water flowing through the turbine for power generation at time t. e For the rated head, η HPSWhere g is the power generation efficiency, and g is the acceleration due to gravity.

[0023] Reservoir water balance constraints:

[0024]

[0025] in, and V represents the inflow and outflow velocities of the reservoir at time t. t Let Vt be the current water storage of the reservoir at time t, and V0 be the initial water storage at the start of the scheduling process, where the initial water storage is equal to the final water storage at the end of the scheduling process, i.e., V0 = Vt. end Δt is the time step of the scheduling process;

[0026] Relationship between water level and water storage:

[0027]

[0028] Among them, z t Let z be the water level of the reservoir at time t. d Let A be the dead water level of the reservoir and A be the surface area of ​​the reservoir.

[0029] Components of reservoir outflow:

[0030]

[0031] in, Let t be the flow rate discharged from the reservoir through the spillway;

[0032] Safety constraints:

[0033]

[0034] Where the subscripts min and max represent the upper and lower limits of the variable, respectively, and Δz is the maximum allowable water level fluctuation of the reservoir within a time interval;

[0035] The operating equations and constraints of hydrogen fuel cells include:

[0036] Fuel cell energy storage constraints include charge / discharge power constraints and battery state of charge constraints.

[0037] Charge and discharge power constraints:

[0038]

[0039] Fuel cell state of charge constraints:

[0040] SOC Ebat,min ≤SOC Ebat ≤SOC Ebat,max

[0041] SOCEbat,1 =SOC Ebat,T

[0042] In the formula, and These represent the charging and discharging power at that specific moment. and These represent the maximum charging and discharging power, respectively; SOC Ebat This refers to the real-time state of charge (SOC) of the fuel cell. Ebat,max and SOC Ebat,min These represent the maximum and minimum states of charge (SOC) of the fuel cell. Ebat,1 and SOC Ebat,T This refers to the initial and final states of charge of the fuel cell.

[0043] Specifically, the modeling in S2 based on the two types of electrolyzers includes cold / hot start-up constraints, load range constraints, and the construction of hydrogen production characteristic equations; specifically, it includes the following constraints:

[0044] The operating equations and constraints of the AEL and PEMEL include:

[0045] Cold / hot start constraints:

[0046] AEL startup constraints:

[0047]

[0048] in, and These are binary variables used to determine whether AEL is in a working, warm-start, or cold-start state at time t, respectively, where ε is the idle time before a cold start. M is a sufficiently large positive number used as a binary variable to help determine whether AEL needs a cold start at time t;

[0049] PEMEL's startup constraints:

[0050]

[0051] in, and These are binary variables used to determine whether PMMEL is in a working, warm-start, or cold-start state at time t, respectively, where ε is the idle time before a cold start. M is a sufficiently large positive number used to help determine whether PEMEL needs a cold start at time t;

[0052] Load range constraints:

[0053] AEL's load range constraints:

[0054]

[0055] PEMEL's load range constraints:

[0056]

[0057] Among them, P t AEL and P t PEMEL The power of AEL and PEMEL for hydrogen production at time t are respectively. and These are the minimum and maximum load thresholds for AEL, respectively. and These are the minimum and maximum load thresholds for PEMEL, respectively.

[0058] Hydrogen production characteristic equation:

[0059] AEL's characteristic equation for hydrogen production:

[0060]

[0061] in, and The times (in minutes) consumed during the AEL cold start and warm start processes are shown below. and ξ represents the correction factors for the AEL cold start and hot start processes, respectively. AEL The electricity consumption for hydrogen production per AEL unit. The actual hydrogen production of AEL at time t;

[0062] PEMEL's hydrogen production characteristic equation:

[0063]

[0064] in, and These represent the time (in minutes) consumed during the PEMEL cold start and warm start processes, respectively. and ξ represents the correction factors for PEMEL's cold start and hot start processes, respectively. PEMEL The electricity consumption per unit of hydrogen production for PEMEL The actual hydrogen production of PEMEL at time t;

[0065] The two basic control methods include a simple start-stop algorithm and a rotation algorithm, with the following specific mechanisms:

[0066] Simple start-stop algorithm: The simple start-stop algorithm allocates power based on the electrolyzer numbering order, labeling the electrolyzers sequentially as E1, E2...E nAt each time point, if the current renewable energy power exceeds the minimum starting power, then E1 starts. If the current renewable energy power exceeds the rated power of E1 and the remaining power meets the minimum starting power of E2, then the remaining power is allocated to E2, and so on until all electrolytic cells start. When the input power of an electrolytic cell is lower than the lower limit of the operating power, it enters standby mode. If the standby time exceeds 3 hours or the current renewable energy power cannot maintain standby, it is shut down. Electrolytic cells in the shutdown or standby state are restarted when the power is sufficient. This algorithm is simple and easy to implement, but it tends to give priority to using electrolytic cells with lower numbers, resulting in significant differences in the running time of each electrolytic cell.

[0067] Rotation Algorithm: The rotation algorithm achieves balanced distribution of operating time by periodically adjusting the electrolytic cell number. The electrolytic cells are cyclically renumbered at fixed time intervals to change the start-up priority, so that the usage frequency of each electrolytic cell tends to be balanced within a specific time interval. By alternating activation and shutdown to adjust the operating status, the difference in operating time is effectively reduced.

[0068] Specifically, the integrated scheduling model in S3 aims to minimize scheduling operation costs and carbon emissions, integrating cost items such as pumped storage, electrolyzers, and grid interaction, and considering the parameters and constraints of each device; the specific cost function is as follows:

[0069] F Total =Z WT +Z PV +Z PHS +Z Grid +Z sum_PEM +Z Zbat

[0070]

[0071] Z WT =z WT P WT

[0072] Z PV =z PV P PV

[0073] In the formula, Z WT For wind power operating costs; Z PV For photovoltaic operating costs; Z PHS The operating cost of pumped storage hydroelectric power plants; Z sum_PEM For the operating cost of the electrolytic cell array; Z Zbat For battery operating costs; Z Grid For grid interaction costs; and These are the unit energy costs for charging and discharging pumped storage devices, respectively. and These are the charging and discharging power of the pumped storage device, respectively. and These are the unit energy costs for charging and discharging hydrogen fuel cell batteries, respectively. and These are the charging and discharging power of the battery, respectively. and These represent the unit cost of electricity purchased and sold during grid interconnection; and These represent the buying and selling power of the grid interaction; z PV and z WT These represent the unit cost of electricity generated by photovoltaic power generation and wind power generation, respectively; P PV and P WT These represent the power outputs of photovoltaic power generation and wind power generation, respectively.

[0074] The carbon emission function is as follows:

[0075] CE = CE WV +CE chou +CE Ebat +CE PEM +CE Grid

[0076] CE indicates the total carbon emissions of a system over its entire life cycle; CE WV CE chou CE Ebat CE PEM CE Grid These represent the total carbon emissions throughout the entire lifecycle of a combined wind and solar power system, a pumped storage unit, a fuel cell, an electrolyzer, and electricity purchased from the grid.

[0077] Specifically, the improved hippo optimization algorithm in S4 achieves efficient solution of multi-objective optimization models by simulating the exploration and development behavior of a hippo, balancing global search and local optimization capabilities; its steps include:

[0078] Circle chaotic mapping initializes the population: To improve the ergodicity and diversity of the initial population, a maximum number of iterations is set, and the Circle chaotic mapping is introduced to initialize the decision variables, generating a set of hippo individuals, each representing a potential optimal scheduling method; firstly, a chaotic sequence in the interval [0,1] is generated iteratively through the Circle mapping:

[0079]

[0080] In the formula, x kis the chaotic variable value of the k-th iteration, x0 is a random initial value in (0,1); a and b are control parameters; mod is the operation of taking the decimal part to ensure that the result is always in the range [0,1];

[0081] Mapped to the search space:

[0082] Then, the generated chaotic sequence is mapped to the actual search space of the decision variables:

[0083] X i,j =Lb j +x j ·(Ub j -Lb j )

[0084] In the formula, X i,j It is the initial position of the i-th hippopotamus in the j-th dimension; Lb j and Ub j Let x represent the lower and upper bounds of the j-th dimension decision variable, respectively; j It is the corresponding chaotic variable value generated by mapping Circle to this dimension;

[0085] Fitness assessment:

[0086] Calculate the multi-objective fitness value vector for each individual hippopotamus:

[0087] F(x) = [f1(x), f2(x), ..., f k (x)]

[0088] The quality of a solution is judged by the Pareto dominance relation: solution x a Dominant solution x b If and only if:

[0089]

[0090] Non-dominated sorting and external archive set management:

[0091] Sort the current population according to Pareto dominance, identify and label all non-dominated solutions, and store them in an external archive set; after each iteration, compare the newly generated non-dominated solutions with the original solutions in the archive set, and retain all solutions that are not mutually dominant.

[0092] Calculate congestion:

[0093] When the archive exceeds capacity or a leader selection is required, crowding distance is used to evaluate the diversity of solutions; solutions with larger crowding distances will be prioritized for retention or selection; the calculation formula is as follows:

[0094]

[0095] In the formula:

[0096] CD(i) is the crowding distance of solution i; k is the number of objective functions; f m (i+1) and f m (i-1) are the function values ​​of the two adjacent solutions of solution i after sorting according to the m-th objective function value; and These are the maximum and minimum values ​​of the m-th objective in the current non-dominated solution set;

[0097] Differential mutation leader generation:

[0098] To enhance the algorithm's global exploration capability and avoid getting trapped in local optima, a differential evolution approach is introduced to dynamically generate a leader; three distinct non-dominated solutions are randomly selected from an external archive set. A mutation vector is generated using the differential mutation method, and this vector will serve as the dominant leader position to guide population renewal.

[0099]

[0100] In the formula, F is a scaling factor, a constant that controls the amplitude of the disturbance; this newly generated It will serve as the leader guiding population updates in this iteration;

[0101] Hippo location update:

[0102] Male hippopotamus position updates: The positions of male hippos in the population are adjusted based on the positions of dominant individuals, using the following formula:

[0103] x Mtippo,ij =x i,j +y1·(D hippo,j -I1x ij )

[0104] In the formula: x Mtippo,ij Indicates the location of the male hippopotamus; D hippo,j The position of the dominant male hippopotamus is indicated; y1 is a random number between 0 and 1; I1 is a random number between 1 and 2; x represents each individual hippopotamus.

[0105] Female and juvenile hippopotamus position updates: The positions of female and juvenile hippos are dynamically adjusted based on selection probabilities, using the following formula:

[0106]

[0107] In the formula: τ is the selection probability; M j b is the average number of randomly selected hippos; min,j and b max,j Let α represent the lower and upper bounds of the j-th variable, respectively;j and β j Let θj represent the j-th element of the random vector; θ1 and θ2 are random numbers between 0 and 1; I2 is a random number between 1 and 2; t is the current iteration number; T is the maximum iteration number; Defensive behavior mechanism: When a predator is detected, the hippopotamus defends itself by adjusting its position, as shown in the following formula:

[0108]

[0109] D j =|P Predator,j -x ij |

[0110] In the formula: x HippoR,ij Indicates the hippopotamus's position facing the predator; L j Let represent the i-th element of the Levi flight random vector; ω represents a 1×m random vector; f is a random number between 2 and 4; c is a random number between 1 and 1.5; d is a random number between 2 and 3; g is a random number between -1 and 1; D j Let be the distance between the i-th hippopotamus and the predator;

[0111] Escape Location Update: This stage simulates the hippo's behavior when escaping predators. Optimal solution convergence is achieved through a local fine-grained search. The formula for updating the hippo's safe location is as follows:

[0112]

[0113] In the formula: x Hippos,jj The algorithm finds a safe location for the hippopotamus; λ is a random number between 0 and 1, and a is a normally distributed random number; through the synergistic effect of the above exploration and development stages, the hippopotamus optimization algorithm can achieve a balance between global search and local optimization, effectively avoid local optimum traps, and improve solution accuracy and efficiency.

[0114] This invention aims to address the shortcomings of existing multi-energy system scheduling research, which fails to adequately consider the dynamic characteristics of electrolyzers, such as cold / hot start-up and load range, leading to model distortion. Furthermore, it neglects the differentiated impact of different control methods on hydrogen production efficiency and equipment operation. Additionally, existing optimization algorithms suffer from limitations in optimization accuracy and convergence efficiency when solving multi-objective scheduling problems with complex constraints. The beneficial effects of this invention are: it provides a multi-energy system scheduling method based on dual electrolyzers and multi-control mode collaboration. This method constructs refined dynamic models of two types of electrolyzers, AEL and PEMEL, and compares and analyzes two different control methods, simple start-stop and rotary start-stop, making the scheduling model closer to actual operating conditions. Simultaneously, it employs an improved multi-objective hippopotamus optimization algorithm that introduces Circle chaotic mapping to initialize the population and differential mutation leader generation to solve the model, significantly improving the algorithm's global exploration capability and solution efficiency. This invention enables collaborative optimization scheduling of multi-energy systems including wind and solar power, pumped storage, hydrogen fuel cells, and dual electrolyzers, effectively improving the overall operational efficiency of the system while balancing multiple objectives such as minimum operating cost and minimum carbon emissions. Attached Figure Description

[0115] Figure 1 This is a flowchart of a multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination as described in this invention;

[0116] Figure 2 This is a diagram showing the switching between two electrolyzer hydrogen production operating states under actual conditions involved in this invention;

[0117] Figure 3 This is a flowchart of the working process of the hippo optimization algorithm described in this invention; Specific implementation methods

[0118] With reference to the accompanying drawings of the embodiments of the present invention, the relevant technical solutions will be systematically and comprehensively described below; Figure 1 This paper introduces the overall process of a multi-energy system based on dual electrolyzers and multi-control mode coordination, and builds an overall framework for the optimization scheduling problem of the multi-energy system based on the process. Figure 2 This is a flowchart for selecting two hydrogen production methods using electrolyzers under actual conditions. Based on the method selection, the hydrogen production characteristics of the electrolyzer are modeled, which is more in line with the actual situation. Figure 3The flowchart of the Hippo Optimization Algorithm is introduced, and the algorithm flow is reasonably designed to better solve the multi-energy system optimization scheduling problem constructed in this paper. It should be noted that the embodiments only represent some implementation cases of the present invention and do not cover all possible technical forms. The specific implementation cases listed in this paper are only used as explanations of the present invention and should not be regarded as limiting definitions of the present invention. Based on the content of the embodiments disclosed in this invention, all technical solutions derived by those skilled in the art without creative effort are within the scope of protection of this invention.

[0119] Reference Figure 1 Establish a general process for a multi-energy system based on dual electrolyzers and multi-control mode coordination; based on Figure 2 The content constructs constraint models for two types of electrolyzers in hydrogen production operation; based on Figure 3 As shown, the working principle of the improved hippo optimization algorithm is explained; a multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination includes the following steps:

[0120] S1: Modeling of wind power and photovoltaic systems, pumped storage systems, and hydrogen fuel cell systems in integrated energy systems;

[0121] In this embodiment of the invention, modeling is included for the power output of wind and solar power systems, the operating characteristics of pumped hydro storage systems, and the power output of hydrogen fuel cell systems.

[0122] S2: Comparative modeling was conducted using two electrolyzers with two different hydrogen production methods and two control methods; and the two control methods were compared.

[0123] In this embodiment of the invention, the operating states of both types of electrolyzers are affected by the multi-condition switching process. Their state transitions need to meet physical constraints such as start-up and shutdown times and load ranges. The modeling accuracy is optimized by comparing two control methods. By defining the start-up and shutdown state variables of the two types of electrolyzers and the operating parameters under different conditions, a state transition timing constraint model is established, including mutual exclusion constraints of working states and start-up and shutdown transition time intervals. This enables a mathematical representation of the dynamic characteristics of the electrolyzers under multiple operating conditions, providing a basis for optimized scheduling.

[0124] S3: Construct a comprehensive scheduling model for a multi-energy system that includes the above systems. The given systems include wind power and solar power, pumped storage, hydrogen fuel cells, and electrolyzer hydrogen production systems. The model objectives are economic efficiency and environmental friendliness.

[0125] In this embodiment of the invention, the constructed multi-energy system integrated scheduling model covers wind power and photovoltaic, pumped storage, hydrogen fuel cells, and electrolyzer hydrogen production systems, with the goal of optimal economic efficiency and minimum carbon emissions; the constraints include power balance constraints, output constraints of each unit, energy storage system constraints, and hydrogen system constraints.

[0126] S4: Solve the model in step 3 using an optimization method based on the improved hippo optimization algorithm;

[0127] In this embodiment of the invention, an improved hippo optimization algorithm is used to solve the constructed multi-energy system integrated scheduling model. This algorithm achieves optimization by simulating the natural behavior of a hippo, including two core processes: an exploration phase and a development phase. It can effectively balance global search and local optimization capabilities, providing an efficient solution for multi-objective optimization problems.

[0128] Specifically, step S1 includes the following steps:

[0129] S11: Photovoltaic output power equation:

[0130]

[0131] Among them, P t PV G t T c,t and T amb,t G represents the photovoltaic output power, solar irradiance, module temperature, and ambient temperature at time t, respectively. STC and T c,STC These represent solar irradiance and module temperature under standard test conditions, respectively. NOCT T c,NOCT and T amb,NOCT These represent solar irradiance, module temperature, and ambient temperature under nominal operating cell temperature test conditions, respectively, k T W is the temperature coefficient. PV For the design capacity of photovoltaics;

[0132] S12: Wind turbine output power equation:

[0133]

[0134] Among them, v t and P t WT The actual wind speed and the output power of the wind turbine at time t are respectively, v R v ci and v co These are the rated wind speed, cut-in wind speed, and cut-out wind speed, respectively, W WT For the design capacity of wind power;

[0135] S13: The operating equations and constraints of pumped storage power stations include:

[0136] S131: Equation for the output power of the water turbine:

[0137]

[0138] Among them, P t HPS Let t be the power generation of HPS. Let H be the velocity of the water flowing through the turbine for power generation at time t. e For the rated head, η HPS Where g is the power generation efficiency, and g is the acceleration due to gravity.

[0139] S132: Reservoir water balance constraint:

[0140]

[0141] in, and V represents the inflow and outflow velocities of the reservoir at time t. t Let Vt be the current water storage of the reservoir at time t, and V0 be the initial water storage at the start of the scheduling process, where the initial water storage is equal to the final water storage at the end of the scheduling process, i.e., V0 = Vt. end Δt is the time step of the scheduling process;

[0142] S133: Relationship between water level and water storage:

[0143]

[0144] Among them, z t Let z be the water level of the reservoir at time t. d Let A be the dead water level of the reservoir and A be the surface area of ​​the reservoir.

[0145] S134: Composition of reservoir outflow:

[0146]

[0147] in, Let t be the flow rate discharged from the reservoir through the spillway;

[0148] S135: Safety Constraints

[0149]

[0150] Where the subscripts min and max represent the upper and lower limits of the variable, respectively, and Δz is the maximum allowable water level fluctuation of the reservoir within a time interval;

[0151] S14: The operating equations and constraints for hydrogen fuel cells include:

[0152] Fuel cell energy storage constraints include charge / discharge power constraints and battery state of charge constraints.

[0153] S141: Charge / discharge power constraint:

[0154]

[0155] S142: Fuel cell state of charge constraint:

[0156] SOC Ebat,min ≤SOC Ebat ≤SOC Ebat,max

[0157] SOC Ebat,1 =SOC Ebat,T

[0158] In the formula, SOC Ebat This refers to the real-time state of charge (SOC) of the fuel cell. Ebat,max and SOC Ebat,min These represent the maximum and minimum states of charge (SOC) of the fuel cell. Ebat,1 and SOC Ebat,T This refers to the initial and final states of charge of the fuel cell.

[0159] S21: The operating equations and constraints of the AEL and PEMEL include:

[0160] S211: Cold / Hot Start Constraints

[0161] S2111: AEL startup constraints:

[0162]

[0163] in, and These are binary variables used to determine whether AEL is in a working, warm-start, or cold-start state at time t, respectively, where ε is the idle time before a cold start. M is a sufficiently large positive number used as a binary variable to help determine whether AEL needs a cold start at time t;

[0164] S2112: PEMEL's startup constraints:

[0165]

[0166] in, and These are binary variables used to determine whether PMMEL is in a working, warm-start, or cold-start state at time t, respectively, where ε is the idle time before a cold start. M is a sufficiently large positive number used to help determine whether PEMEL needs a cold start at time t;

[0167] S212: Load range constraint:

[0168] S2121: AEL load range constraint:

[0169]

[0170] S2122: PEMEL's load range constraint:

[0171]

[0172] Among them, P t AEL and P t PEMEL The power of AEL and PEMEL for hydrogen production at time t are respectively.

[0173] and These are the minimum and maximum load thresholds for AEL, respectively. and These are the minimum and maximum load thresholds for PEMEL, respectively.

[0174] S213: Hydrogen production characteristic equation:

[0175] S2131: Hydrogen production characteristic equation of AEL:

[0176]

[0177] in, and The times (in minutes) consumed during the AEL cold start and warm start processes are shown below. and ξ represents the correction factors for the AEL cold start and hot start processes, respectively. AEL The electricity consumption for hydrogen production per AEL unit. The actual hydrogen production of AEL at time t;

[0178] S2132: PEMEL's hydrogen production characteristic equation:

[0179]

[0180] in, and These represent the time (in minutes) consumed during the PEMEL cold start and warm start processes, respectively. and ξ represents the correction factors for PEMEL's cold start and hot start processes, respectively. PEMEL The electricity consumption per unit of hydrogen production for PEMEL The actual hydrogen production of PEMEL at time t;

[0181] S22: Two basic control methods include a simple start-stop algorithm and a rotation algorithm, with the specific mechanisms as follows:

[0182] S221: Simple Start-Stop Algorithm: The simple start-stop algorithm allocates power based on the electrolytic cell numbering order, labeling the electrolytic cells sequentially as E1, E2...E n At each time point, if the current renewable energy power exceeds the minimum starting power, then E1 starts. If the renewable energy power exceeds the rated power of E1 and the remaining power meets the minimum starting power of E2, then the remaining power is allocated to E2, and so on until all electrolytic cells start. When the input power of an electrolytic cell is lower than the lower limit of the operating power, it enters standby mode. If the standby time exceeds 3 hours or the renewable energy power cannot maintain standby, it is shut down. Electrolytic cells in the shutdown or standby state are restarted when the power is sufficient. This algorithm is simple and easy to implement, but it tends to give priority to using electrolytic cells with lower numbers, resulting in significant differences in the running time of each electrolytic cell.

[0183] S222: Rotation Algorithm: The rotation algorithm achieves balanced distribution of operating time by periodically adjusting the electrolytic cell number. The electrolytic cells are cyclically renumbered at fixed time intervals to change the start-up priority, so that the usage frequency of each electrolytic cell tends to be balanced within a specific time interval. By alternating activation and shutdown to adjust the operating status, the difference in operating time is effectively reduced.

[0184] Specifically, step S3 includes the following steps:

[0185] S31: The mass balance equations for electricity and hydrogen include:

[0186] S311: Electricity Balance Equation:

[0187]

[0188] Among them, P t WT P t PV P t HPS The output power P of the wind turbine, photovoltaic power station, and hydropower station at time t are respectively. t G Let P be the power sold to the main grid at time t. t AEL and P t PEMEL The power of AEL and PEMEL for hydrogen production at time t are respectively.

[0189] S312: Hydrogen mass balance equation for hydrogen storage tank:

[0190]

[0191] Among them, S t Let be the mass of hydrogen stored in the hydrogen storage tank at time t. and Let St represent the hydrogen inlet and outlet mass flow rates of the hydrogen storage tank at time t, and S0 be the initial hydrogen mass at the start of scheduling, where the initial hydrogen mass is equal to the final hydrogen mass at the end of scheduling, i.e., S0 = St. end ;

[0192] S32: With the objectives of minimizing the economic cost of dispatching and operation and minimizing carbon emissions in the constructed integrated energy system model, a comprehensive multi-objective hierarchical optimization function is constructed, where the economic cost of dispatching and operation is expressed by the following formula:

[0193] F Total =Z WT +Z PV +Z PHS +Z Grid +Z sum_PEM +Z Zbat

[0194]

[0195]

[0196] Z WT =z WT P WT

[0197] Z PV =z PV P PV

[0198] In the formula, Z WT For wind power operating costs; Z PV For photovoltaic operating costs; Z PHS The operating cost of pumped storage hydroelectric power plants; Z sum_PEM For the operating cost of the electrolytic cell array; Z Zbat For battery operating costs; Z Grid For grid interaction costs; and These are the unit energy costs for charging and discharging pumped storage devices, respectively. and These are the charging and discharging power of the pumped storage device, respectively. and These are the unit energy costs for charging and discharging hydrogen fuel cell batteries, respectively. and These are the charging and discharging power of the battery, respectively. and These represent the unit cost of electricity purchased and sold during grid interconnection; and These represent the buying and selling power of the grid interaction; z PV and zWT These represent the unit cost of electricity generated by photovoltaic power generation and wind power generation, respectively; P PV and P WT These represent the power outputs of photovoltaic power generation and wind power generation, respectively.

[0199] S33: Carbon emissions over the entire life cycle are expressed using the following formula:

[0200] CE = CE WV +CE chou +CE Ebat +CE PEM +CE Grid

[0201] CE indicates the total carbon emissions of a system over its entire life cycle; CE WV CE chou CE Ebat CE PEM CE Grid These represent the total carbon emissions throughout the entire lifecycle of a combined wind and solar power system, a pumped storage unit, a fuel cell, an electrolyzer, and electricity purchased from the grid.

[0202] Specifically, step S4 includes the following steps:

[0203] S41: An optimization method based on the hippo optimization algorithm, characterized in that: the improved adaptive multi-objective hippo optimization algorithm mainly includes several aspects such as initializing the hippo population, fitness evaluation, non-dominated sorting and external archive management, calculating crowding, differential mutation leader generation, hippo position update, and population and archive update.

[0204] The specific steps are as follows:

[0205] Circle chaotic mapping initializes the population: To improve the ergodicity and diversity of the initial population, a maximum number of iterations is set, and a Circle chaotic mapping is introduced to initialize the decision variables, generating a set of hippo individuals, each representing a potential optimal scheduling method; firstly, a chaotic sequence in the interval between 0 and 1 is generated iteratively through the Circle mapping:

[0206]

[0207] In the formula, x k is the chaotic variable value of the k-th iteration, x0 is a random initial value between 0 and 1; a and b are control parameters; mod is the operation of taking the decimal part to ensure that the result is always within the range of 0 to 1;

[0208] Mapped to the search space:

[0209] Then, the generated chaotic sequence is mapped to the actual search space of the decision variables:

[0210] X i,j =Lb j +x j ·(Ub j -Lb j )

[0211] In the formula, X i,j It is the initial position of the i-th hippopotamus in the j-th dimension; Lb j and Ub j Let x represent the lower and upper bounds of the j-th dimension decision variable, respectively; j It is the corresponding chaotic variable value generated by mapping Circle to this dimension;

[0212] Fitness assessment:

[0213] Calculate the multi-objective fitness value vector for each individual hippopotamus:

[0214] F(x) = [f1(x), f2(x), ..., f k (x)]

[0215] The quality of a solution is judged by the Pareto Dominance relation: solution x a Dominant solution x b If and only if:

[0216]

[0217] Non-dominated sorting and external archive set management:

[0218] Sort the current population according to Pareto dominance, identify and label all non-dominated solutions, and store them in an external archive set; after each iteration, compare the newly generated non-dominated solutions with the original solutions in the archive set, and retain all solutions that are not mutually dominant.

[0219] Calculate congestion:

[0220] When the archive exceeds capacity or a leader selection is required, crowding distance is used to evaluate the diversity of solutions; solutions with larger crowding distances will be prioritized for retention or selection; the calculation formula is as follows:

[0221]

[0222] In the formula,

[0223] CD(i) is the crowding distance of solution i; k is the number of objective functions; f m (i+1) and f m (i-1) are the function values ​​of the two adjacent solutions of solution i after sorting according to the m-th objective function value; and These are the maximum and minimum values ​​of the m-th objective in the current non-dominated solution set;

[0224] Differential mutation leader generation:

[0225] To enhance the algorithm's global exploration capability and avoid getting trapped in local optima, a differential evolution approach is introduced to dynamically generate a leader; three distinct non-dominated solutions are randomly selected from an external archive set. A mutation vector is generated using the differential mutation method, and this vector will serve as the dominant leader position to guide population renewal.

[0226]

[0227] In the formula, F is a scaling factor, a constant that controls the amplitude of the disturbance; this newly generated It will serve as the leader guiding population updates in this iteration;

[0228] Hippo location update:

[0229] Male hippopotamus position updates: The positions of male hippos in the population are adjusted based on the positions of dominant individuals, using the following formula:

[0230] x Mtippo,ij =x i,j +y1·(D hippo,j -I1x ij )

[0231] In the formula: x Mtippo,ij Indicates the location of the male hippopotamus; D hippo,j The position of the dominant male hippopotamus is indicated; y1 is a random number between 0 and 1; I1 is a random number between 1 and 2; x represents each individual hippopotamus.

[0232] Female and juvenile hippopotamus position updates: The positions of female and juvenile hippos are dynamically adjusted based on selection probabilities, using the following formula:

[0233]

[0234]

[0235] In the formula: τ is the selection probability; M j b is the average number of randomly selected hippos; min,j and b max,j Let α represent the lower and upper bounds of the j-th variable, respectively; j and β jLet θj represent the j-th element of the random vector; θ1 and θ2 are random numbers between 0 and 1; I2 is a random number between 1 and 2; t is the current iteration number; T is the maximum iteration number; Defensive behavior mechanism: When a predator is detected, the hippopotamus defends itself by adjusting its position, as shown in the following formula:

[0236]

[0237] D j =|P Predator,j -x ij |

[0238] In the formula: x HippoR,ij Indicates the hippopotamus's position facing the predator; L j Let represent the i-th element of the Levi flight random vector; ω represents a 1×m random vector; f is a random number between 2 and 4; c is a random number between 1 and 1.5; d is a random number between 2 and 3; g is a random number between -1 and 1; D j Let be the distance between the i-th hippopotamus and the predator;

[0239] Escape Location Update: This stage simulates the hippo's behavior when escaping predators. Optimal solution convergence is achieved through a local fine-grained search. The formula for updating the hippo's safe location is as follows:

[0240]

[0241] In the formula: x Hippos,jj The algorithm finds a safe location for the hippopotamus; λ is a random number between 0 and 1, and a is a normally distributed random number; through the synergistic effect of the above exploration and development stages, the hippopotamus optimization algorithm can achieve a balance between global search and local optimization, effectively avoid local optimum traps, and improve solution accuracy and efficiency.

[0242] Obviously, for those skilled in the art, this invention is not limited to the specific details involved in the above exemplary embodiments. Other specific forms may be derived without departing from the spirit or essential characteristics of the invention. These embodiments are illustrative only and not limiting. The scope of the invention is defined by the appended claims and is intended to cover all variations within the meaning and scope of the equivalents of the claims. Reference numerals in the claims do not affect the scope of the claims. The specification describes embodiments, but the technical solutions of the various embodiments can be combined to form other embodiments that will be understood by those skilled in the art.

Claims

1. A multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination, characterized in that, Includes the following steps: S1: Modeling of wind power and photovoltaic systems, pumped storage systems, and hydrogen fuel cell systems in integrated energy systems; S2: Comparative modeling was conducted using two electrolyzers with two different hydrogen production methods and two control methods; and the two control methods were compared. S3: Construct a multi-energy system integrated scheduling model that includes the above systems. The given systems include wind power and photovoltaic, pumped storage, hydrogen fuel cells, and electrolyzer hydrogen production systems. The model objectives are economic efficiency and environmental friendliness. S4: Solve the model in step 3 using the improved multi-objective hippo optimization algorithm.

2. The multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination according to claim 1, characterized in that: The integrated energy system modeling covers photovoltaic power generation systems, wind power generation systems, pumped storage systems, and fuel cell systems, and the output characteristics of each of these four types of systems are modeled and analyzed.

3. The multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination according to claim 1, characterized in that: Electrolyzers with two different hydrogen production methods have different start-up and shutdown constraints, load range constraints, and hydrogen production characteristics. Modeling and analysis are performed on these three characteristics respectively.

4. The multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination according to claim 2, characterized in that: Modeling the characteristics of each component in an integrated energy system: Photovoltaic output power equation: Among them, P t PV G t T c,t and T amb,t The photovoltaic output power, solar irradiance, module temperature, and ambient temperature at time t are respectively, W PV For the design capacity of photovoltaics, G STC and T c,STC These represent solar irradiance and module temperature under standard test conditions, respectively. NOCT T c,NOCT and T amb,NOCT These represent solar irradiance, module temperature, and ambient temperature under nominal operating cell temperature test conditions, respectively, k T W is the temperature coefficient. PV For the design capacity of photovoltaics; Wind turbine output power equation: Among them, v t and P t WT The actual wind speed and the output power of the wind turbine at time t are respectively, W. WT For the design capacity of wind power, v R v ci and v co These are the rated wind speed, cut-in wind speed, and cut-out wind speed, respectively. Hydropower turbine output power equation: Among them, P t HPS Let t be the power generation of HPS. Let H be the velocity of the water flowing through the turbine for power generation at time t. e For the rated head, η HPS Where g is the power generation efficiency, and g is the acceleration due to gravity. Reservoir water balance constraints: in, and V represents the inflow and outflow velocities of the reservoir at time t. t Let Vt be the current water storage of the reservoir at time t, and V0 be the initial water storage at the start of the scheduling process, where the initial water storage is equal to the final water storage at the end of the scheduling process, i.e., V0 = Vt. end Δt is the time step of the scheduling process; Relationship between water level and water storage: Among them, z t Let z be the water level of the reservoir at time t. d Let A be the dead water level of the reservoir and A be the surface area of ​​the reservoir. Components of reservoir outflow: in, Let t be the flow rate discharged from the reservoir through the spillway; Safety constraints: Where the subscripts min and max represent the upper and lower limits of the variable, respectively, and Δz is the maximum allowable water level fluctuation of the reservoir within a time interval; The operating equations and constraints of the hydrogen fuel cell include: Fuel cell energy storage constraints include charge / discharge power constraints and battery state of charge constraints. Charge and discharge power constraints: Fuel cell state of charge constraints: SOC Ebat,min ≤SOC Ebat ≤SOC Ebat,max SOCIETY Ebat,1 =SOC Ebat,T In the formula, and These represent the charging and discharging power at that specific moment. and These represent the maximum charging and discharging power, respectively; SOC Ebat This refers to the real-time state of charge (SOC) of the fuel cell. Ebat,max and SOC Ebat,min These represent the maximum and minimum states of charge (SOC) of the fuel cell. Ebat,1 and SOC Ebat,T This refers to the initial and final states of charge of the fuel cell.

5. The multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination according to claim 3, characterized in that: The two types of electrolyzers include AEL and PEMEL electrolyzers; the operating equations and constraints for AEL and PEMEL include: Cold / hot start constraints: AEL startup constraints: in, and These are binary variables used to determine whether AEL is in a working, warm-start, or cold-start state at time t, respectively, where ε is the idle time before a cold start. M is a sufficiently large positive number used as a binary variable to help determine whether AEL needs a cold start at time t; PEMEL's startup constraints: in, and These are binary variables used to determine whether PMMEL is in a working, warm-start, or cold-start state at time t, respectively, where ε is the idle time before a cold start. M is a sufficiently large positive number used to help determine whether PEMEL needs a cold start at time t; Load range constraints: AEL's load range constraints: PEMEL's load range constraints: Among them, P t AEL and P t PEMEL The power of AEL and PEMEL for hydrogen production at time t are respectively. and These are the minimum and maximum load thresholds for AEL, respectively. and These are the minimum and maximum load thresholds for PEMEL, respectively; W AEL and W PEMEL The design capacities for AEL and PEMEL are respectively; Hydrogen production characteristic equation: AEL's characteristic equation for hydrogen production: in, and These represent the time consumed during the AEL cold start and warm start processes, respectively. and ξ represents the correction factors for the AEL cold start and hot start processes, respectively. AEL The electricity consumption for hydrogen production per AEL unit. The actual hydrogen production of AEL at time t; PEMEL's hydrogen production characteristic equation: in, and These represent the time consumed during the PEMEL cold start and warm start processes, respectively. and ξ represents the correction factors for PEMEL's cold start and hot start processes, respectively. PEMEL The electricity consumption per unit of hydrogen production for PEMEL The actual hydrogen production of PEMEL at time t.

6. The multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination according to claim 1, characterized in that: The control methods include two different approaches: simple start-stop and rotary start-stop. Simple start-stop algorithm: The simple start-stop algorithm allocates power based on the electrolyzer numbering order, labeling the electrolyzers sequentially as E1, E2...E n At each time point, if the current renewable energy power exceeds the minimum starting power, then E1 starts. If the renewable energy power exceeds the rated power of E1 and the remaining power meets the minimum starting power of E2, then the remaining power is allocated to E2, and so on until all electrolytic cells start. When the input power of an electrolytic cell is lower than the lower limit of the operating power, it enters standby mode. If the standby time exceeds 3 hours or the renewable energy power cannot maintain standby, it is shut down. Electrolytic cells in the shutdown or standby state are restarted when the power is sufficient. This algorithm is simple and easy to implement, but it tends to give priority to using electrolytic cells with lower numbers, resulting in significant differences in the running time of each electrolytic cell. Rotary start-stop algorithm: The rotation algorithm achieves balanced distribution of running time by periodically adjusting the electrolytic cell number. The electrolytic cells are cyclically renumbered at fixed time intervals to change the start priority, so that the usage frequency of each electrolytic cell tends to be balanced within a specific time interval. By alternating activation and shutdown to adjust the operating status, the difference in running time is effectively reduced.

7. The multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination according to claim 1, characterized in that: Achieving total energy balance specifically includes: Electricity balance equation: Among them, P t WT P t PV P t HPS The output power P of the wind turbine, photovoltaic power station, and hydropower station at time t are respectively. t G Let P be the power sold to the main grid at time t. t AEL and P t PEMEL The power of AEL and PEMEL for hydrogen production at time t are respectively. Hydrogen mass balance equation for hydrogen storage tank: Among them, S t Let be the mass of hydrogen stored in the hydrogen storage tank at time t. and Let St represent the hydrogen inlet and outlet mass flow rates of the hydrogen storage tank at time t, and S0 be the initial hydrogen mass at the start of scheduling, where the initial hydrogen mass is equal to the final hydrogen mass at the end of scheduling, i.e., S0 = St. end Δt is the time step of the scheduling process.

8. The multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination according to claim 1, characterized in that: Considering the costs of pumped storage devices, hydrogen fuel cells and their maintenance costs, the system's electricity purchase costs from the grid, and the parameters and constraints of each device, a comprehensive energy system model is constructed. A comprehensive multi-objective hierarchical optimization function is constructed, with the objectives of minimizing the economic cost of dispatching and operation and minimizing carbon emissions of the constructed integrated energy system model, respectively. The economic cost of dispatching and operation is expressed by the following formula: F Total =Z WT +Z PV +Z PHS +Z Grid +Z sum_PEM +Z Zbat WITH WT =z WT P WT WITH PV =z PV P PV In the formula, Z WT For wind power operating costs; Z PV For photovoltaic operating costs; Z PHS The operating cost of pumped storage hydroelectric power plants; Z sum_PEM For the operating cost of the electrolytic cell array; Z Zbat For battery operating costs; Z Grid For grid interaction costs; and These are the unit energy costs for charging and discharging pumped storage devices, respectively. and These are the charging and discharging power of the pumped storage device, respectively. and These are the unit energy costs for charging and discharging hydrogen fuel cell batteries, respectively. and These are the charging and discharging power of the battery, respectively. and These represent the unit cost of electricity purchased and sold during grid interconnection; and These represent the buying and selling power of the grid interaction; z PV and z WT These represent the unit cost of electricity generated by photovoltaic power generation and wind power generation, respectively; P PV and P WT These represent the power outputs of photovoltaic power generation and wind power generation, respectively. Carbon emissions over the entire life cycle are expressed using the following formula: WHAT=WHAT WV +CE chou +CE Ebat +CE PEM +CE Grid CE indicates the total carbon emissions of a system over its entire life cycle; CE WV CE chou CE Ebat CE PEM CE Grid These represent the total carbon emissions throughout the entire lifecycle of a combined wind and solar power system, a pumped storage unit, a fuel cell, an electrolyzer, and electricity purchased from the grid.

9. A multi-energy system scheduling method based on dual electrolyzers and multi-control mode coordination according to claim 1, characterized in that: The improved adaptive multi-objective hippo optimization algorithm mainly includes several aspects: initializing the hippo population, fitness evaluation, non-dominated sorting and external archive management, calculating crowding, differential mutation leader generation, hippo position update, and population and archive update. The specific steps are as follows: Circle chaotic mapping initializes the population: To improve the ergodicity and diversity of the initial population, a maximum number of iterations is set, and a Circle chaotic mapping is introduced to initialize the decision variables, generating a set of hippo individuals, each representing a potential optimal scheduling method; firstly, a chaotic sequence in the interval between 0 and 1 is generated iteratively through the Circle mapping: In the formula, x k is the chaotic variable value of the k-th iteration, x0 is a random initial value in the range of 0 to 1; a and b are control parameters; mod is the operation of taking the decimal part to ensure that the result is always in the range of 0 to 1; Mapped to the search space: Then, the generated chaotic sequence is mapped to the actual search space of the decision variables: X i,j =Lb j +x j ·(Ub j -Lb j ) In the formula, X i,j It is the initial position of the i-th hippopotamus in the j-th dimension; Lb j and Ub j Let x represent the lower and upper bounds of the j-th dimension decision variable, respectively; j It is the corresponding chaotic variable value generated by mapping Circle to this dimension; Fitness assessment: Calculate the multi-objective fitness value vector for each individual hippopotamus: F(x)=[f1(x),f2(x),...,f k (x)] The quality of a solution is judged by the Pareto dominance relation: solution x a Dominant solution x b If and only if: Non-dominated sorting and external archive set management: Sort the current population according to Pareto dominance, identify and label all non-dominated solutions, and store them in an external archive set; after each iteration, compare the newly generated non-dominated solutions with the original solutions in the archive set, and retain all solutions that are not mutually dominant. Calculate congestion: When the archive exceeds capacity or a leader selection is required, crowding distance is used to evaluate the diversity of solutions; solutions with larger crowding distances will be prioritized for retention or selection; the calculation formula is as follows: In the formula, CD(i) is the crowding distance of solution i; k is the number of objective functions; f m (i+1) and f m (i-1) are the function values ​​of the two adjacent solutions of solution i after sorting according to the m-th objective function value; and These are the maximum and minimum values ​​of the m-th objective in the current non-dominated solution set; Differential mutation leader generation: To enhance the algorithm's global exploration capability and avoid getting trapped in local optima, a differential evolution approach is introduced to dynamically generate a leader; three distinct non-dominated solutions are randomly selected from an external archive set. A mutation vector is generated using the differential mutation method, and this vector will serve as the dominant leader position to guide population renewal. In the formula, F is a scaling factor, a constant that controls the amplitude of the disturbance; this newly generated It will serve as the leader guiding population updates in this iteration; Hippo location update: Male hippopotamus position updates: The positions of male hippos in the population are adjusted based on the positions of dominant individuals, using the following formula: x Mtippo,ij =x i,j +y1·(D hippo,j -I1x ij ) In the formula: x Mtippo,ij Indicates the location of the male hippopotamus; D hippo,j The position of the dominant male hippopotamus is indicated; y1 is a random number between 0 and 1; I1 is a random number between 1 and 2; x represents each individual hippopotamus. Female and juvenile hippopotamus position updates: The positions of female and juvenile hippos are dynamically adjusted based on selection probabilities, using the following formula: In the formula: τ is the selection probability; M j b is the average number of randomly selected hippos; min,j and b max,j Let α represent the lower and upper bounds of the j-th variable, respectively; j and β j Let θj represent the j-th element of the random vector; θ1 and θ2 are random numbers between 0 and 1; I2 is a random number between 1 and 2; t is the current iteration number; T is the maximum iteration number; Defensive behavior mechanism: When a predator is detected, the hippopotamus defends itself by adjusting its position, as shown in the following formula: D j =|P Predator,j -x ij | In the formula: x HippoR,ij Indicates the hippopotamus's position facing the predator; L j Let represent the i-th element of the Levi flight random vector; ω represents a 1×m random vector; f is a random number between 2 and 4; c is a random number between 1 and 1.5; d is a random number between 2 and 3; g is a random number between -1 and 1; D j Let be the distance between the i-th hippopotamus and the predator; Escape Location Update: This stage simulates the hippo's behavior when escaping predators. Optimal solution convergence is achieved through a local fine-grained search. The formula for updating the hippo's safe location is as follows: In the formula: x Hippos,jj The algorithm finds a safe location for the hippopotamus; λ is a random number between 0 and 1, and a is a normally distributed random number; through the synergistic effect of the above exploration and development stages, the hippopotamus optimization algorithm can achieve a balance between global search and local optimization, effectively avoid local optimum traps, and improve solution accuracy and efficiency.

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