A two-stage distribution robust stackelberg game optimization method for hydrogen energy comprehensive energy system coupled with v2g participating in energy frequency modulation market

Abstract

The application discloses a two-stage distribution robust-Stackelberg game optimization method for hydrogen energy comprehensive energy system coupling V2G participating in energy-frequency market, and belongs to the technical field of comprehensive energy system optimization scheduling. The method combines surplus renewable energy hydrogen production with local consumption of hydrogen fuel cells (HFC), hydrogen-doped combined heat and power (CHP) and hydrogen-doped gas boilers (GB) to form an electricity-hydrogen cycle. Electric vehicles (EVs) are introduced as generalized energy storage devices to construct a Stackelberg game model for HIES and EV clusters. In view of wind and light uncertainty, a two-stage distribution robust optimization (DRO) based on comprehensive norm fuzzy sets is adopted, the first stage makes decisions on frequency modulation capacity and baseline power, and the second stage adjusts the output of other units according to the worst probability distribution. The KKT condition is used to convert the double-layer problem into a single-layer, and the column and constraint generation (C&CG) algorithm is used for solving, so that flexible resources can finally participate in the energy-frequency auxiliary service market.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system optimization and scheduling technology, specifically to a two-stage sub-Stackelberg game optimization method for integrated energy systems containing hydrogen energy, coupled with electric vehicle V2G and participating in the energy and frequency regulation ancillary service market. Background Technology

[0002] With the increasing penetration rate of renewable energy sources such as wind and solar power, their inherent randomness and volatility pose severe challenges to the safe and stable operation of the power system, leading to frequent instances of wind and solar power curtailment. Hydrogen energy, as a clean and efficient secondary energy carrier, can achieve large-scale, cross-temporal and spatial storage and utilization of renewable energy through electricity-hydrogen conversion. However, current hydrogen energy utilization pathways are relatively singular, mainly focusing on external sales or further conversion into natural gas, resulting in high energy cascade losses and transportation costs, and overall low efficiency.

[0003] On the other hand, while the rapid growth in the number of electric vehicles brings potential peak-shaving and frequency regulation resources to the power grid, disorderly charging will also exacerbate the load difference between peak and valley periods and increase operational pressure on the power grid. By guiding the market appropriately and treating EVs as generalized energy storage devices, enabling them to participate in system dispatch in a V2G (Vehicle-to-Grid) model, it is of great significance for absorbing renewable energy and improving the power grid's flexible adjustment capabilities.

[0004] In terms of optimization methods, traditional stochastic programming requires precise knowledge of the probability distribution, while robust optimization relies solely on worst-case scenarios, potentially leading to overly conservative results. Partially robust optimization, however, utilizes historical data to construct fuzzy sets, seeking a decision scheme that balances economy and robustness under the worst-case probability distribution, making it more suitable for integrated energy system scheduling with a high proportion of renewable energy integration. Furthermore, the interaction of interests between HIES (High-Intensity Integrated Systems) and EVs presents a significant challenge: how to coordinate pricing and power plans through game theory, and how to reasonably reserve regulation capacity when participating in the frequency regulation market, are pressing technical issues that need to be addressed. Summary of the Invention

[0005] The technical solution adopted in this invention is: a two-stage sub-Browser-Stackelberg game optimization method for hydrogen energy integrated energy system coupled with V2G participation in the energy-frequency regulation market, specifically including the following steps:

[0006] Step 1: Construct a comprehensive hydrogen energy system structure including an electrolyzer (EL), hydrogen fuel cell (HFC), combined heat and power (CHP), gas boiler (GB), hydrogen / thermal storage device, and electric vehicle (EV). Prioritize the use of wind power and photovoltaic (WT / PV) power. Use surplus renewable energy power to produce hydrogen through water electrolysis, and then blend hydrogen in HFC, CHP, and GB for combustion in proportion to achieve localized recycling of hydrogen energy.

[0007] Step 2: Establish a Stackelberg game model with HIES as the upper-level leader and EV cluster as the lower-level follower; the upper level decides the charging and discharging prices of EVs, and the lower level optimizes the charging and discharging baseline power and frequency regulation capacity of each EV accordingly to minimize charging costs. The KKT conditions are used to transform the lower-level problem into a constraint of the upper-level problem, forming a single-layer optimization model.

[0008] Step 3: To address the uncertainties in WT and PV output, a fuzzy set of comprehensive norm probability distribution is constructed based on 1-norm and ∞-norm constraints, forming a two-stage sub-Bruker optimization model. The first stage aims to maximize the benefits of the frequency regulation market by determining the baseline power of HFC and EV and the up- and down-frequency regulation capacity. The second stage optimizes the output of CHP, GB, EL and the amount of wind and solar curtailment under the worst-case probability distribution within the fuzzy set, so as to minimize the overall system operating cost.

[0009] Step 4: The total system cost is calculated by subtracting the frequency regulation capacity revenue, frequency regulation mileage revenue, and net EV charging revenue from the sum of electricity purchase cost, gas purchase cost, and wind and solar curtailment penalty cost. The main problem and sub-problems are iteratively solved using a column and constraint generation algorithm to obtain the optimal scheduling scheme that satisfies robustness.

[0010] Step 5: Based on the optimization results, aggregate resources with rapid adjustment capabilities such as HFC and EV, and participate in the electricity market and frequency regulation ancillary service market to provide output plans for each unit, EV charging and discharging scheduling plans, and frequency regulation capacity reservation schemes. Step 4, Vulnerability Assessment: Assess and comprehensively judge the vulnerability of the metro network from both structural and functional perspectives.

[0011] In one embodiment, in step one, both CHP and GB adopt an adjustable thermoelectric ratio model, and the hydrogen doping ratio is maintained in the range of 0-20%; HFC has an adjustable thermoelectric ratio and has the ability to adjust the frequency upward and downward.

[0012] The adjustable thermoelectric ratio operating model of the CHP is as follows:

[0013]

[0014] Where: Pe CHP(t) is the power generation of CHP in time period t; Pt CHP(t) is the heat generation of CHP in time period t; η CHP denoted as CHP energy conversion efficiency; Pg CHP(t) and Ph CHP(t) are the amounts of natural gas and hydrogen input to CHP, respectively; Pmin CHP(t) and Pmax CHP(t) are the upper and lower limits of CHP heat production power; ΔPmin CHP and ΔPmax CH are the ramping constraints of CHP; kmin CHP(t) and kmin CHP(t) are the upper and lower limits of CHP heat-to-electricity ratio.

[0015] The hydrogen doping ratio of the CHP is subject to the following constraints:

[0016]

[0017] Where: α CHP (t) represents the hydrogen blending ratio of CHP at time t; L H2 and L CH4 These are the lower heating values ​​of hydrogen and natural gas, respectively.

[0018] The operating model of GB is as follows:

[0019]

[0020] Where: α GB (t) represents the hydrogen blending ratio of GB in time period t; Ph GB(t) and Pg GB(t) represent the amount of hydrogen and natural gas input into GB, respectively.

[0021]

[0022] Where: PGB(t) is the heat generation power of GB during time period t; η GB GB represents the energy conversion efficiency; Pmin GB and Pmax GB represent the upper and lower limits of heat production in GB; ΔPmin GB and ΔPmax GB represent the ramping constraints; kmin GB and kmmax GB represent the thermoelectric ratio limits in GB.

[0023] The energy conversion and adjustable thermoelectric ratio of the HFC are as follows:

[0024]

[0025] Where: P HFC (t) represents the total input energy of the HFC; η HFC Pi represents the HFC conversion efficiency; PeHFC(t) and PtHFC(t) represent the HFC power generation and heat generation, respectively; PgHFC(t) and PhhHFC(t) represent the input natural gas and hydrogen quantities; PminHFC and PmaxHFC represent the upper and lower limits of power generation; ΔPminHFC and ΔPmaxHFC represent the ramp-up constraints; and kmminHFC and kmmaxHFC represent the upper and lower limits of the heat-to-power ratio.

[0026] The constraint relationship between the up-modulation capacity RHFC up and the down-modulation capacity RHFC dn of the HFC is as follows:

[0027]

[0028] Where: RHFC up and RHFC dn are the up and down frequency modulation capacities of HFC, respectively; Pmax HFC,e is the maximum power output of HFC; Pbase HFC is the baseline power of HFC; l up (t), l dn (t) represents the cumulative amount of the frequency modulation signal.

[0029] In one embodiment, in step two, the EV model treats each EV as a generalized energy storage unit, whose charging and discharging power and frequency regulation capacity meet the capacity constraints and satisfy the SOC dynamic recursive relationship.

[0030] The actual charging and discharging power and adjustment ratio constraints of the EV are as follows:

[0031]

[0032] Where: Pc i(t) and Pd i(t) are the actual charging power and discharging power of the i-th EV in time period t, respectively; Pci,max(t) and Pd i,max(t) are the maximum charging and discharging power; uc(t) and ud(t) are the charging and discharging control variables.

[0033] The constraint relationship between its baseline power and charge / discharge ratio variable is as follows:

[0034]

[0035] Where: Pci,base(t) and Pdi,base(t) are the charging and discharging baseline powers, respectively; μi,base(t) c (t), μ d (t) represents the charge / discharge ratio variable; μ(t) represents the total adjustment ratio.

[0036] The constraint relationship between the upward frequency modulation capacity Rup i(t) and the downward frequency modulation capacity Rdn i(t) of the EV and the maximum / minimum charging and discharging power is as follows:

[0037]

[0038] Where Rup i(t) and Rdn i(t) are the up and down frequency modulation capacities, respectively; Pmax i,c(t) and Pmax i,d(t) are the maximum charge and discharge power limits.

[0039] The state of charge (SOC) of the EV i The dynamic recurrence relation of (t) is:

[0040]

[0041]

[0042] Where: l up (t), l dn (t) represents the cumulative amount of the frequency modulation signal; η c η d For charge / discharge efficiency; C cap This refers to the battery capacity.

[0043] Its SOC upper and lower limits and the expected SOC for off-grid operation are constrained as follows:

[0044]

[0045] Where: SOCmin i and SOC,max i are the upper and lower limits of SOC; SOCexp i is the expected SOC when leaving.

[0046] In one embodiment, in step two, the upper-level objective of the Stackelberg game is to minimize the total cost of HIES, and the lower-level objective is to minimize the net charging cost of the EV cluster. The lower-level model is transformed into an equivalent first-order optimality condition using KKT conditions, and the Big M method is used to linearize the complementary relaxation constraints.

[0047] The Lagrangian function for the lower-level EV optimization problem is constructed as follows:

[0048]

[0049]

[0050] Among them: price c (t), price d λ(t) represents the charging and discharging valence values, respectively; λ1(t) to λ4(t) are Lagrange multipliers.

[0051] Its partial derivatives with respect to the variables and the KKT conditions are set as follows:

[0052]

[0053] Where: η c1 (t), η c2 (t), η d1 (t), η d2 (t) is a KKT multiplier.

[0054] For the complementary relaxation condition, the Big M method is used for linearization transformation, transforming the original inequality constraint 0≤Pc i(t)π. i ≥0 is converted to mixed integer linear constraints such as 0≤Pc i(t)≤M(1-ω):

[0055]

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[0075] In one embodiment, in step three, the comprehensive norm fuzzy set is defined as the set of all possible discrete probability distributions. A typical scenario involves generation via Latin hypercube sampling and obtaining the set through a synchronous back-substitution reduction method based on probability distance. The comprehensive norm fuzzy set includes the 1-norm constraint ∑Ns s=1︱p s -p0 s︱≤θ1 and ∞-norm constraint max s︱p s -p0s︱≤θ ∞ .

[0076] In one embodiment, in step four, the objective function for the total system cost is a distributed robust optimization objective function in a two-layer, two-stage form; the solution process of the column and constraint generation algorithm is as follows: first, solve the main problem to obtain the decision variables for the first stage; then, substitute these variables into the subproblem to find the worst probability distribution within the fuzzy set that maximizes the cost of the second stage, and generate the corresponding cutting plane constraints to feed back to the main problem; iterate repeatedly until convergence.

[0077] The prototype of the objective function for the two-layer, two-stage sub-Bruker optimization is:

[0078]

[0079] Where: x is the decision variable for the first stage; y is the decision variable for the second stage; p s Let Ω be the probability of scene s; Ω be the comprehensive norm fuzzy set; N be the probability of scene s; Ω ... s Number of scenes.

[0080] The frequency modulation capacity gain F1 is:

[0081]

[0082] Among them: price R Rup(t) represents the frequency modulation capacity price; Rup(t) and Rdn(t) represent the frequency modulation capacity of the EV; RupHFC(t) and RdnHFC(t) represent the frequency modulation capacity of the HFC.

[0083] The FM mileage gain F2 is:

[0084]

[0085] Among them: price l (t) represents the FM mileage price; up (t), l dn (t) represents the mileage of the frequency modulation signal.

[0086] The electricity purchase cost C1 is:

[0087]

[0088] Among them: price e (t) represents the electricity price; Pe buy(t) represents the amount of electricity purchased.

[0089] The gas purchase cost C2 is:

[0090]

[0091] Among them: price g (t) represents the gas price; Pg buy(t) represents the gas purchase volume.

[0092] The penalty cost C3 for power curtailment is:

[0093]

[0094] Where: cq is the curtailment penalty coefficient; Pf WT and Pf PV are the predicted output; Pa WT and Pa PV are the actual output.

[0095] The net EV charging revenue PEV i is:

[0096]

[0097] Among them: price e (t) represents the charging electricity price; price d (t) represents the discharge electricity price.

[0098] In one embodiment, in step five, the effectiveness of the proposed method is verified by comparing the renewable energy penetration rate, system energy purchase cost, frequency regulation market revenue, EV charging revenue, and total system cost under different scenarios; the comparison scenarios include no EV participation, disordered EV charging, hydrogen-free hydrogen co-firing utilization, and the complete scheme using the proposed game theory and decomposed bar optimization.

[0099] The beneficial effects of this invention are: (1) By producing hydrogen from surplus renewable energy and directly blending it with hydrogen for combustion in HFC, CHP and GB, the localized and efficient utilization of hydrogen energy is realized, avoiding transportation costs and energy multi-stage conversion losses, constructing a complete electric-hydrogen-heat cycle, and significantly improving the penetration rate of renewable energy and the efficiency of hydrogen energy utilization. (2) Using EV as generalized energy storage, the Stackelberg game model is adopted to coordinate the interests of the system and EV. Under the premise of meeting charging needs, the charging cost of users is reduced, while providing the system with flexible adjustment capability and frequency regulation capacity. (3) A two-stage sub-Blu-ray optimization based on the comprehensive norm is introduced to effectively handle the uncertainty of WT and PV, and make robust decisions under the worst probability distribution in the given fuzzy set. It takes into account the economy and robustness of the scheduling scheme, and avoids the dependence of traditional stochastic programming on the precise distribution and the overly conservative defects of conventional robust optimization. (4) By aggregating fast-regulating resources such as HFC and EV, and participating in the energy and frequency regulation ancillary service market, the revenue channels of the integrated energy system are broadened, and the overall economic benefits are further improved. Attached Figure Description

[0100] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0101] Figure 1 This is an overall flowchart of the present invention;

[0102] Figure 2 This is a schematic diagram of the energy flow structure of the HIES-coupled EV V2G proposed in this invention;

[0103] Figure 3 A schematic diagram showing the relationship between baseline power and frequency modulation capacity when EVs participate in frequency modulation.

[0104] Figure 4 This is a diagram of the two-layer, two-stage DRO-Stackelberg game optimization framework used in this invention.

[0105] Figure 5 This is a typical daily forecast of wind power and photovoltaic output, as well as electricity, heat, and gas load curves.

[0106] Figure 6 This is a chart showing information on time-of-use electricity pricing, frequency regulation capacity, and mileage pricing.

[0107] Figure 7 The diagram shows the power balance results of the system's electricity, heat, gas, and hydrogen after optimized scheduling;

[0108] Figure 8 The graph shows the game results between HIES and EV, where (a) is the total load curve under different scenarios, (b) is the EV charging and discharging power and frequency regulation capacity, and (c) is the charging and discharging price obtained from the game.

[0109] Figure 9 Operating parameters for the remaining major equipment in the system (such as CHP, HFC, GB, EL, and energy storage devices) Detailed Implementation

[0110] To address the problems existing in the background technology, this application proposes the following technical solution: a two-stage sub-Browser-Stackelberg game optimization method for hydrogen energy integrated energy system coupled with V2G participation in the energy-frequency regulation market, specifically including the following steps:

[0111] This invention employs a layered modeling approach for the Hydrogen Integrated Energy System (HIES) based on its multi-energy complementarity characteristics. To comprehensively consider the system's electrical, thermal, and hydrogen coupling characteristics and market regulation capabilities, this invention divides the HIES into a physical equipment layer and a game theory decision-making layer. The physical equipment layer comprises electrolyzers (EL), hydrogen fuel cells (HFC), combined heat and power (CHP) units, gas-fired boilers (GB), and energy storage devices, describing the multi-energy conversion and storage relationships of electricity, heat, and hydrogen. The game theory decision-making layer consists of HIES operators and electric vehicle (EV) clusters, describing the economic interaction behavior of the energy and frequency regulation markets. Based on this, this invention proposes a Stackelberg game theory scheduling method based on two-stage distributed bar optimization (for HIES and EV interest coordination and uncertainty handling), the overall flowchart of which is shown below. Figure 1 As shown.

[0112] Step 1: System Structure and Key Equipment Model Construction

[0113] Reference Figure 1 The hydrogen integrated energy system (HIES) constructed in this invention includes wind power generation, photovoltaic power generation, an electrolyzer (EL), a hydrogen fuel cell (HFC), a combined heat and power (CHP) unit, a gas-fired boiler (GB), hydrogen storage tanks, thermal storage tanks, and electric vehicle (EV) charging facilities. The system purchases electricity from the grid, prioritizing the use of wind and solar power. Surplus renewable electricity is used to produce hydrogen via the EL and stored in the hydrogen storage tanks. The hydrogen is then supplied to the HFC for pure combustion, and to the CHP and GB units for combustion in a proportionate blend to produce electricity and heat, meeting the electricity and heat load demands. EVs interact with the system via V2G charging stations, serving as flexible loads or distributed power sources.

[0114] In this embodiment, the mathematical models of various devices and the formulas from the original paper are as follows:

[0115] 1. CHP Model

[0116] The adjustable thermoelectric ratio model has the following operating constraints:

[0117]

[0118] Where: Pe CHP(t) is the power generation of CHP in time period t; Pt CHP(t) is the heat generation of CHP in time period t; η CHP denoted as CHP energy conversion efficiency; Pg CHP(t) and Ph CHP(t) are the amounts of natural gas and hydrogen input to CHP, respectively; Pmin CHP(t) and Pmax CHP(t) are the upper and lower limits of CHP heat production power; ΔPmin CHP and ΔPmax CH are the ramping constraints of CHP; kmin CHP(t) and kmin CHP(t) are the upper and lower limits of CHP heat-to-electricity ratio.

[0119] The hydrogen doping ratio of the CHP is subject to the following constraints:

[0120]

[0121] Where: α CHP (t) represents the hydrogen blending ratio of CHP at time t; L H2 and L CH4 These are the lower heating values ​​of hydrogen and natural gas, respectively.

[0122] 2. GB Model

[0123] GB's output power is solely thermal power, and its hydrogen doping ratio is constrained as follows:

[0124]

[0125] Where: α GB (t) represents the hydrogen blending ratio of GB in time period t; Ph GB(t) and Pg GB(t) represent the amount of hydrogen and natural gas input into GB, respectively.

[0126] Its operation and ramping constraints are:

[0127]

[0128] Where: PGB(t) is the heat generation power of GB during time period t; η GB GB represents the energy conversion efficiency; Pmin GB and Pmax GB represent the upper and lower limits of heat production in GB; ΔPmin GB and ΔPmax GB represent the ramping constraints; kmin GB and kmmax GB represent the thermoelectric ratio limits in GB.

[0129] 3. HFC Model

[0130] HFCs generate electricity and heat by consuming hydrogen gas. Their thermoelectric ratio is adjustable, and the energy conversion relationship is as follows:

[0131]

[0132] Where: P HFC (t) represents the total input energy of the HFC; η HFC Pi represents the HFC conversion efficiency; PeHFC(t) and PtHFC(t) represent the HFC power generation and heat generation, respectively; PgHFC(t) and PhhHFC(t) represent the input natural gas and hydrogen quantities; PminHFC and PmaxHFC represent the upper and lower limits of power generation; ΔPminHFC and ΔPmaxHFC represent the ramp-up constraints; and kmminHFC and kmmaxHFC represent the upper and lower limits of the heat-to-power ratio.

[0133] HFC also has frequency modulation capability, and its upward and downward frequency modulation capacity constraints are as follows:

[0134]

[0135] Where: RHFC up and RHFC dn are the up and down frequency modulation capacities of HFC, respectively; Pmax HFC,e is the maximum power output of HFC; Pbase HFC is the baseline power of HFC; l up (t), l dn (t) represents the cumulative amount of the frequency modulation signal.

[0136] Step 2, Stackelberg Game and EV Model

[0137] Reference Figure 2This invention treats EVs as generalized energy storage units and establishes a Stackelberg game model between EVs and HIES. HIES, as the upper-level leader, decides the charging and discharging prices of EVs at different times; EVs, as the lower-level followers, optimize the charging and discharging baseline power and frequency regulation capacity based on this to minimize net charging costs.

[0138] 1. Actual charging and discharging power limitations of EVs

[0139]

[0140] Where: Pc i(t) and Pd i(t) are the actual charging power and discharging power of the i-th EV in time period t, respectively; Pci,max(t) and Pd i,max(t) are the maximum charging and discharging power; uc(t) and ud(t) are the charging and discharging control variables.

[0141] 2. EV baseline power and charge / discharge ratio constraints

[0142]

[0143] Where: Pci,base(t) and Pdi,base(t) are the charging and discharging baseline powers, respectively; μi,base(t) c (t), μ d (t) represents the charge / discharge ratio variable; μ(t) represents the total adjustment ratio.

[0144] 3. Coupling constraints between EV frequency modulation capacity and charging / discharging power

[0145]

[0146] Where Rup i(t) and Rdn i(t) are the up and down frequency modulation capacities, respectively; Pmax i,c(t) and Pmax i,d(t) are the maximum charge and discharge power limits.

[0147] 4. Dynamic recursion and boundary constraints of EV's SOC

[0148]

[0149]

[0150] Where: l up (t), l dn (t) represents the cumulative amount of the frequency modulation signal; η c η d For charge / discharge efficiency; C cap This refers to the battery capacity.

[0151]

[0152] Where: SOCmin i and SOC,max i are the upper and lower limits of SOC; SOCexp i is the expected SOC when leaving.

[0153] 5. KKT condition transformation in Stackelberg games

[0154] In this embodiment, the lower-level EV optimization problem is transformed into equivalent first-order optimality conditions using the KKT conditions, and the Big M method is used to linearize the complementary relaxation constraints. Specifically, the Lagrangian function is:

[0155]

[0156]

[0157] Among them: price c (t), price d λ(t) represents the charging and discharging valence values, respectively; λ1(t) to λ4(t) are Lagrange multipliers.

[0158] Its partial derivatives with respect to the variables and the KKT conditions are set as follows:

[0159]

[0160] Where: η c1 (t), η c2 (t), η d1 (t), η d2 (t) is a KKT multiplier.

[0161] For the complementary relaxation condition, the Big M method is used for linearization transformation, transforming the original inequality constraint 0≤Pc i(t)π. i ≥0 is converted to mixed integer linear constraints such as 0≤Pc i(t)≤M(1-ω).

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[0182] Step 3: Two-stage sub-Bruker optimization based on comprehensive norm fuzzy sets

[0183] Reference Figure 3 To address the inherent uncertainties in the output of WT and PV, this invention employs a two-stage sub-Bruker optimization model based on a fuzzy set of comprehensive norm probability distribution.

[0184] First, several typical scenarios and their initial probability distributions are generated through Latin hypercube sampling and probabilistic distance reduction. Then, a comprehensive norm fuzzy set is constructed based on 1-norm and ∞-norm constraints, specifically ∑Ns s=1︱p s -p0 s︱≤θ1 and ∞-norm constraint max s︱p s -p0 s︱≤θ ∞ .

[0185] In the first phase, with the goal of maximizing the benefits of the frequency modulation market, the baseline power and up / down frequency modulation capacity of HFC and EV are determined. The frequency modulation capacity benefits and mileage benefits are as follows:

[0186] The prototype of the objective function for the two-layer, two-stage sub-Bruker optimization is:

[0187]

[0188] Where: x is the decision variable for the first stage; y is the decision variable for the second stage; p sLet Ω be the probability of scene s; Ω be the comprehensive norm fuzzy set; N be the probability of scene s; Ω ... s Number of scenes.

[0189] The frequency modulation capacity gain F1 is:

[0190]

[0191] Among them: price R Rup(t) represents the frequency modulation capacity price; Rup(t) and Rdn(t) represent the frequency modulation capacity of the EV; RupHFC(t) and RdnHFC(t) represent the frequency modulation capacity of the HFC.

[0192] The FM mileage gain F2 is:

[0193]

[0194] Among them: price l (t) represents the FM mileage price; up (t), l dn (t) represents the mileage of the frequency modulation signal.

[0195] The electricity purchase cost C1 is:

[0196]

[0197] Among them: price e (t) represents the electricity price; Pe buy(t) represents the amount of electricity purchased.

[0198] The gas purchase cost C2 is:

[0199]

[0200] Among them: price g (t) represents the gas price; Pg buy(t) represents the gas purchase volume.

[0201] The penalty cost C3 for power curtailment is:

[0202]

[0203] Where: cq is the curtailment penalty coefficient; Pf WT and Pf PV are the predicted output; Pa WT and Pa PV are the actual output.

[0204] The net EV charging revenue PEV i is:

[0205]

[0206] Among them: price e (t) represents the charging electricity price; price d (t) represents the discharge electricity price.

[0207] In this embodiment, the Column and Constraint Generation (C&CG) algorithm is used to iteratively solve the two-stage problem. The main problem is responsible for obtaining the decision variables for the first stage, while the subproblems search for the worst-case probability distribution that maximizes the total cost of the second stage within the fuzzy set and generate corresponding cutting plane constraints to feed back to the main problem. This iterative process is as described at the end of Section III of the original paper, until the upper and lower bounds converge.

[0208] Step 4: Analysis of Calculation Examples and Implementation Results

[0209] This embodiment uses a typical 24-hour day as the scheduling cycle, with a time step of 1 hour and a scheduling cycle of 24 hours. A computational example is performed based on the method described above to verify the joint optimization effect of the proposed Hydrogen Integrated Energy System (HIES) coupled with V2G participation in the Frequency Regulation Ancillary Services Market (FRASM). The system includes 50 electric vehicles, divided into three categories based on actual charging behavior. The charging pile power is set based on real charging station data, and the predicted data for wind power, photovoltaic, and electricity, heat, and gas loads are as follows: Figure 4 As shown. Market transaction prices, frequency regulation capacity prices, and mileage prices are all derived from actual transaction data in the PJM frequency regulation market, such as... Figure 5 As shown. The operating parameters of the remaining major system equipment (such as CHP, HFC, GB, EL, and energy storage devices) are detailed below. Figure 9 .

[0210] 1. Multi-energy flow balance analysis after optimized scheduling

[0211] First, a multi-energy flow coupling analysis was performed on the system's scheduling results during a typical day to verify whether the method of this invention can achieve efficient consumption of renewable energy and localized recycling of hydrogen energy while meeting load demand. The results are as follows: Figure 6 As shown.

[0212] Depend on Figure 6 (a) The power balance results show that power supply and demand are strictly balanced throughout the daily dispatch cycle. During the daytime period from 08:00 to 16:00, when sunlight is abundant, the system prioritizes the full utilization of photovoltaic power, while a small amount of wind power is also utilized as a priority power source. Due to the low load and surplus power during this period, the electrolyzer (EL) starts producing hydrogen, consuming some of the excess power and effectively avoiding wind and solar curtailment. During the peak load period from 17:00 to 20:00, when renewable energy output is insufficient, the system prioritizes the use of hydrogen fuel cells (HFC) and combined heat and power (CHP) units to fill the gap. At the same time, electric vehicles (EVs) discharge a small amount during peak electricity price periods, greatly reducing the need to purchase electricity from the grid at high prices.

[0213] Depend on Figure 6(b) The heat balance results show that the gas-fired boiler (GB) bears most of the system's basic heat load throughout the day. This "gas-for-heat" approach effectively reduces the excess power output of the CHP due to its "heat-driven power generation" principle. During the peak output period of the cogeneration unit from 16:00 to 18:00, the CHP and HFC, as heat and power sources, not only provide power support but also supply heat simultaneously, achieving synergistic heat and power generation.

[0214] Depend on Figure 6 (c) The hydrogen balance results show that the hydrogen production of the electrolyzer is mainly concentrated during the period of peak renewable energy generation from 08:00 to 16:00, and the produced hydrogen is temporarily stored in the hydrogen storage tank; while during the peak electricity load period from 17:00 to 20:00, the hydrogen released from the hydrogen storage tank is mainly used to supply HFC power generation and CHP hydrogen blending, forming a closed-loop electricity-hydrogen cycle of "curtailment of wind and solar power - electrolysis hydrogen production - hydrogen storage - peak power generation".

[0215] Depend on Figure 6 (d) The natural gas balance results show that the natural gas purchased is mainly used to meet the GB heating and CHP co-combustion (the remaining part is mixed with hydrogen). In actual dispatching, the reduction of natural gas consumption mainly depends on the increase of hydrogen blending ratio, which effectively reduces the cost of purchased natural gas in the system.

[0216] 2. Game Theory Analysis between HIES and EV Clusters

[0217] The Stackelberg game model used in this invention achieves the coordination of interests between the system operator and the electric vehicle cluster. The specific game results are as follows: Figure 7 As shown.

[0218] Depend on Figure 7 (a) A comparison of load curves shows that the black solid line represents the load curve when electric vehicles are charging haphazardly, forming an extremely high electricity consumption peak around 17:00; the blue line represents the original load curve without considering charging; and the red line represents the load curve under the orderly charging and discharging scheme of this invention. It can be seen that this invention guides electric vehicle charging through pricing, avoiding the load peaks caused by haphazard charging. While meeting the charging needs of all electric vehicles, it achieves peak shaving and valley filling of the load curve, significantly reducing grid pressure.

[0219] Depend on Figure 7(b) The results of the charging and discharging power and frequency regulation capacity allocation of electric vehicles show that during the off-peak electricity price period from 00:00 to 08:00, the charging power of the 50 electric vehicles is relatively concentrated; while during the evening peak electricity price period from 17:00 to 21:00, some electric vehicles participate in V2G discharge. At the same time, the system reserves approximately 0~6kW of real-time up and down frequency regulation capacity for each electric vehicle to ensure that it can provide sufficient rapid response capability for FRASM while participating in the energy market.

[0220] Depend on Figure 7 (c) The price curve obtained from the game theory shows that the discharge price is consistently higher than the charging price during the same period, and the discharge price increases significantly (approximately $0.07 / MWh) during the peak load period from 16:00 to 19:00, thereby incentivizing electric vehicles to actively discharge. The charging price, on the other hand, consistently matches the price at which the system purchases electricity from the grid and is lower than the discharge price, ensuring that the system operator profits from buying low and selling high, while also reducing the charging costs for car owners, achieving a "win-win" situation for both parties.

[0221] 3. Comparison of overall benefits in different scenarios

[0222] To quantitatively verify the comprehensive advantages of the method of the present invention in terms of economic benefits and renewable energy absorption capacity, this embodiment sets up four comparative scenarios: Scenario 1 is that the system has no electric vehicles involved; Scenario 2 is that the system has electric vehicles involved in charging, but no Stackelberg game is performed (disorderly charging); Scenario 3 is that the system has no hydrogen energy co-processing (hydrogen is only sold externally or directly emitted); Scenario 4 is the electric vehicle Stackelberg game participation and local hydrogen recycling scheme proposed in this invention.

[0223] The data comparison results across the four scenarios show significant differences. Scenario 1, lacking V2G and frequency regulation capacity, has the highest total cost, reaching approximately $1070.10, with a renewable energy penetration rate of 98.74%. Although Scenario 2 incorporates uncontrolled charging, generating approximately $22.83 in revenue from EV charging, the increased cost of electricity purchases makes its total cost reduction insignificant, amounting to only $1061.67.

[0224] Scenario 3 introduces the hydrogen fuel cell and frequency regulation market (frequency regulation capacity revenue reaches approximately US$573.24), significantly reducing the total system cost to US$617.24. However, it fails to fully utilize local hydrogen recycling, resulting in a renewable energy penetration rate of only 96.97%. In contrast, Scenario 4 proposed in this invention achieves the best overall benefits, with the lowest total system cost of only US$598.88, representing reductions of approximately 78.68%, 77.27%, and 3.07% compared to Scenario 1, Scenario 2, and Scenario 3, respectively. Simultaneously, Scenario 4 achieves the highest renewable energy penetration rate of 98.82%.

[0225] The above data analysis shows that by introducing local hydrogen recycling and HFC participation in the frequency regulation market, the system's operating costs have achieved a dramatic decrease. Furthermore, by introducing orderly V2G game theory with electric vehicles, the proportion of renewable energy consumption has been further increased while maintaining extremely low operating costs. Scenario 4 achieves the highest level of renewable energy consumption at the lowest cost, fully validating the outstanding advantages of this invention in achieving synergistic optimization of system economy and environmental friendliness.

[0226] 4. Application Prospects and Benefit Evaluation

[0227] The above examples demonstrate that the system using the method of this invention excels in balancing economic efficiency and renewable energy consumption. At the operational level, the system can effectively absorb previously abandoned wind and solar power through water electrolysis to produce hydrogen. The produced hydrogen can be supplied to CHP, GB, and HFC for local consumption, avoiding the high costs of hydrogen transportation and recompression. In conjunction with the V2G frequency regulation service market, the profit model of HIES shifts from a single energy sale to a composite revenue stream of "energy + ancillary services." Against the backdrop of improved microgrid flexibility and the low-carbon transformation of urban energy systems, this invention provides a practical and feasible optimized scheduling scheme for comprehensive hydrogen energy utilization and distributed renewable energy frequency regulation, with broad application prospects.

Claims

1. A two-stage sub-Browser-Stackelberg game optimization method for a hydrogen energy integrated system coupled with V2G participation in the energy-frequency regulation market, characterized in that, The method specifically includes the following steps: Step 1: Construct a comprehensive hydrogen energy system structure including an electrolyzer (EL), hydrogen fuel cell (HFC), combined heat and power (CHP), gas boiler (GB), hydrogen / thermal storage device, and electric vehicle (EV). Prioritize the use of wind power and photovoltaic (WT / PV), and use surplus renewable energy power to produce hydrogen through water electrolysis. Then, blend hydrogen in HFC, CHP, and GB in proportion for combustion to achieve localized recycling of hydrogen energy. Step 2: Establish a Stackelberg game model with HIES as the upper-level leader and EV cluster as the lower-level follower; the upper level decides the charging and discharging prices of EVs, and the lower level optimizes the charging and discharging baseline power and frequency regulation capacity of each EV accordingly to minimize charging costs, and uses KKT conditions to transform the lower-level problem into the upper-level problem constraint to form a single-layer optimization model. Step 3: To address the uncertainties in WT and PV output, a fuzzy set of comprehensive norm probability distribution is constructed based on 1-norm and ∞-norm constraints, forming a two-stage sub-Bruker optimization model. The first stage aims to maximize the benefits of the frequency regulation market by determining the baseline power of HFC and EV and the up- and down-frequency regulation capacity. The second stage optimizes the output of CHP, GB, EL and the amount of wind and solar curtailment under the worst probability distribution within the fuzzy set, so as to minimize the overall system operating cost. Step 4: The total system cost is calculated by subtracting the frequency regulation capacity revenue, frequency regulation mileage revenue, and net EV charging revenue from the sum of electricity purchase cost, gas purchase cost, and wind and solar curtailment penalty cost. The main problem and sub-problems are iteratively solved using a column and constraint generation algorithm to obtain the optimal scheduling scheme that satisfies robustness. Step 5: Based on the optimization results, aggregate resources with rapid adjustment capabilities such as HFC and EV, and participate in the power energy market and frequency regulation ancillary service market to provide output plans for each unit, EV charging and discharging scheduling plans, and frequency regulation capacity reservation schemes.

2. The method according to claim 1, characterized in that, In step one, both CHP and GB adopt an adjustable thermoelectric ratio model, and the hydrogen doping ratio is maintained in the range of 0-20%; HFC has an adjustable thermoelectric ratio and has the ability to adjust the frequency upward and downward. The adjustable thermoelectric ratio operating model of the CHP is as follows: Where: Pe CHP(t) is the power generation of CHP in time period t; Pt CHP(t) is the heat generation of CHP in time period t; η CHP denoted as CHP energy conversion efficiency; Pg CHP(t) and Ph CHP(t) are the amounts of natural gas and hydrogen input to CHP, respectively; PminCHP(t) and Pmax CHP(t) are the upper and lower limits of CHP heat production power; ΔPmin CHP and ΔPmax CH are the ramp-up constraints of CHP; kmin CHP(t) and kmin CHP(t) are the upper and lower limits of CHP heat-to-electricity ratio. The hydrogen doping ratio of the CHP is subject to the following constraints: Where: α CHP (t) represents the hydrogen blending ratio of CHP at time t; L H2 and L CH4 These are the lower heating values ​​of hydrogen and natural gas, respectively. The operating model of GB is as follows: Where: α GB (t) represents the hydrogen blending ratio of GB in time period t; Ph GB(t) and Pg GB(t) represent the amount of hydrogen and natural gas input into GB, respectively; Where: PGB(t) is the heat generation power of GB during time period t; η GB GB represents the energy conversion efficiency; Pmin GB and Pmax GB represent the upper and lower limits of heat production in GB; ΔPmin GB and ΔPmax GB represent the ramping constraints; kmin GB and kmat GB represent the thermoelectric ratio limits in GB. The energy conversion and adjustable thermoelectric ratio of the HFC are as follows: Where: P HFC (t) represents the total input energy of the HFC; η HFC Pe represents the HFC conversion efficiency; PeHFC(t) and PtHFC(t) represent the HFC power generation and heat generation, respectively; PgHFC(t) and PhhHFC(t) represent the input natural gas and hydrogen quantities; PminHFC and PmaxHFC represent the upper and lower limits of power generation; ΔPminHFC and ΔPmaxHFC represent the ramp-up constraints; and kmminHFC and kmmaxHFC represent the upper and lower limits of the heat-to-power ratio. The constraint relationship between the up-modulation capacity RHFC up and the down-modulation capacity RHFC dn of the HFC is as follows: Where: RHFC up and RHFC dn are the up and down frequency modulation capacities of HFC, respectively; Pmax HFC,e is the maximum power output of HFC; Pbase HFC is the baseline power of HFC; l up (t), l dn (t) represents the cumulative amount of the frequency modulation signal.

3. The method according to claim 1, characterized in that, In step two, the EV model treats each EV as a generalized energy storage unit, whose charging and discharging power and frequency regulation capacity meet the capacity constraints and satisfy the SOC dynamic recursive relationship. The actual charging and discharging power and adjustment ratio constraints of the EV are as follows: Where: Pc i(t) and Pd i(t) are the actual charging power and discharging power of the i-th EV in time period t, respectively; Pc i,max(t) and Pd i,max(t) are the maximum charging and discharging power; uc(t) and ud(t) are the charging and discharging control variables; The constraint relationship between its baseline power and charge / discharge ratio variable is as follows: Where: Pci,base(t) and Pdi,base(t) are the charging and discharging baseline powers, respectively; μi,base(t) c (t), μ d (t) represents the charge / discharge ratio variable; μ(t) represents the total adjustment ratio; The constraint relationship between the upward frequency modulation capacity Rup i(t) and the downward frequency modulation capacity Rdn i(t) of the EV and the maximum / minimum charging and discharging power is as follows: Where Rup i(t) and Rdn i(t) are the up and down frequency modulation capacities, respectively; Pmax i,c(t) and Pmax i,d(t) are the maximum charge and discharge power limits; The state of charge (SOC) of the EV i The dynamic recurrence relation of (t) is: Where: l up (t), l dn (t) represents the cumulative amount of the frequency modulation signal; η c η d For charge / discharge efficiency; C cap Battery capacity; Its SOC upper and lower limits and the expected SOC for off-grid operation are constrained as follows: Where: SOCmin i and SOC,max i are the upper and lower limits of SOC; SOCexp i is the expected SOC when leaving.

4. The method according to claim 1, characterized in that, In step two, the upper-level objective of the Stackelberg game is to minimize the total cost of HIES, and the lower-level objective is to minimize the net charging cost of the EV cluster. The lower-level model is transformed into an equivalent first-order optimality condition using KKT conditions, and the Big M method is used to linearize the complementary relaxation constraints. The Lagrangian function for the lower-level EV optimization problem is constructed as follows: Among them: price c (t), price d (t) represent the charging and discharging valence values, respectively; λ1(t) to λ4(t) are Lagrange multipliers; Its partial derivatives with respect to the variables and the KKT conditions are set as follows: Where: η c1 (t), η c2 (t), η d1 (t), η d2 (t) is a KKT multiplier; For the complementary relaxation condition, the Big M method is used for linearization transformation, transforming the original inequality constraint 0≤Pc i(t)π. i ≥0 is converted into mixed integer linear constraints such as 0≤Pc i(t)≤M(1-ω).

5. The method according to claim 1, characterized in that, In step three, the comprehensive norm fuzzy set is defined as the set of all possible discrete probability distributions. A typical scenario involves generation via Latin hypercube sampling, obtained through a synchronous back-substitution reduction method based on probability distance. The comprehensive norm fuzzy set includes the 1-norm constraint ∑Ns s=1︱p s -p0 s︱≤θ1 and ∞-norm constraint max s︱p s -p0 s︱≤θ ∞ .

6. The method according to claim 1, characterized in that, In step four, the objective function for the total system cost is a distributed robust optimization objective function in a two-layer, two-stage form. The solution process of the column and constraint generation algorithm is as follows: First, solve the main problem to obtain the decision variables for the first stage; then, substitute these variables into the subproblem to find the worst probability distribution within the fuzzy set that maximizes the cost of the second stage, and generate the corresponding cutting plane constraints to feed back to the main problem; iterate repeatedly until convergence. The prototype of the objective function for the two-layer, two-stage sub-Bruker optimization is: Where: x is the decision variable for the first stage; y is the decision variable for the second stage; p s Let Ω be the probability of scene s; Ω be the comprehensive norm fuzzy set; N be the probability of scene s; Ω ... s Number of scenes; The frequency modulation capacity gain F1 is: Among them: price R (t) represents the frequency modulation capacity price; Rup i(t) and Rdn i(t) represent the frequency modulation capacity of EV; Rup HFC(t) and Rdn HFC(t) represent the frequency modulation capacity of HFC. The FM mileage gain F2 is: Among them: price l (t) represents the FM mileage price; up (t), l dn (t) represents the FM signal mileage; The electricity purchase cost C1 is: Among them: price e (t) represents the electricity price; Pe buy(t) represents the amount of electricity purchased; The gas purchase cost C2 is: Among them: price g (t) represents the gas price; Pg buy(t) represents the gas purchase volume; The penalty cost C3 for power curtailment is: Where: cq is the curtailment penalty coefficient; PfWT and PfPV are the predicted output; PaWT and PaPV are the actual output; The net EV charging revenue PEV i is: Among them: price e (t) represents the charging electricity price; price d (t) represents the discharge electricity price.

7. The method according to claim 1, characterized in that, In step five, the effectiveness of the proposed method is verified by comparing the renewable energy penetration rate, system energy purchase cost, frequency regulation market revenue, EV charging revenue, and total system cost under different scenarios. The comparison scenarios include no EV participation, disordered EV charging, hydrogen-free hydrogen co-firing utilization, and a complete scheme using the proposed game theory and decomposed bar optimization.

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