A multi-period planning method for networked hydrogen-based microgrid based on probabilistic constraints and information gap decision theory

Abstract

The present application belongs to the technical field of comprehensive energy, and discloses a networked hydrogen-based micro-grid multi-period planning method based on probability constraint and information gap decision. A two-stage multi-period planning framework is constructed, a hybrid chance constraint-information gap decision theory (CCP-IGDT) co-modeling method and an adaptive prediction-correction Benders decomposition (APC-BD) algorithm are designed, the robustness of the system to unexpected hydrogen load growth is maximized under fixed budget constraints, and the heterogeneous characteristics of short-term random fluctuations and long-term structural uncertainties are effectively handled.

Description

Technical Field

[0001] This invention belongs to the field of integrated energy-related technology, and more specifically, relates to a multi-cycle planning method for networked hydrogen-based microgrids based on probabilistic constraints and information gap decision-making. Background Technology

[0002] Hydrogen storage, as a zero-emission, high-energy-density, and low-leakage energy carrier, can effectively alleviate seasonal power imbalances in distribution networks with high renewable energy penetration. Hydrogen-based microgrids, by integrating electrolyzers, fuel cells, hydrogen storage systems, and renewable energy, achieve flexible and coordinated conversion and utilization of electricity and hydrogen energy, and their application scenarios are rapidly expanding from distribution networks to transportation, industry, and other fields. However, current hydrogen-based microgrid planning faces the following challenges: High investment costs: Capital expenditures for electrolyzers and hydrogen storage systems are far higher than those for electrical energy storage systems, and their economic viability is significantly affected by uncertainties in technological development and demand growth; Uncertainty complexity: The system simultaneously faces short-term random fluctuations (such as renewable energy output and load changes) and long-term structural uncertainties (such as hydrogen demand growth trajectories and technology cost changes); Single planning model: Existing planning often adopts static single-stage methods, which cannot adapt to dynamic demand growth and are prone to over-investment or insufficient capacity; High computational complexity: Multi-stage, multi-uncertainty coupled planning models are typically large-scale mixed integer second-order cone programming (MISOCP) problems, which are difficult to solve.

[0003] Therefore, how to develop a multi-period planning framework that maximizes the system's robustness to unexpected hydrogen load growth under fixed budget constraints, effectively handles the heterogeneity of short-term random fluctuations and long-term structural uncertainties, and efficiently solves the resulting MISOCP problem is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a multi-period planning method for networked hydrogen-based microgrids based on probabilistic constraints and information gap decision-making. Its purpose is to maximize the system's robustness to unexpected hydrogen load growth under fixed budget constraints, while effectively handling the heterogeneous characteristics of short-term random fluctuations and long-term structural uncertainties, and to develop a multi-period planning framework.

[0005] To achieve the above objectives, this invention provides a multi-period planning method for networked hydrogen-based microgrids based on probabilistic constraints and information gap decision-making, comprising: The optimal multi-cycle planning strategy is obtained by maximizing the maximum deviation α of the hydrogen load that the system can accommodate relative to the predicted value. The hydrogen-based microgrid comprises a set of nodes and a set of directed branches. The set of nodes includes renewable energy sources, dispatchable generators, energy conversion devices, electrical energy storage systems, and hydrogen energy storage systems. These renewable energy sources, dispatchable generators, energy conversion devices, electrical energy storage systems, and hydrogen energy storage systems can share electricity. The renewable energy sources and dispatchable generators have power generation capabilities. The optimal multi-cycle planning strategy includes the hydrogen tank capacity of the hydrogen energy storage system, the energy storage capacity of the electric energy storage system, and the timing of equipment expansion.

[0006] The present invention also provides an electronic device, comprising: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the above-described method.

[0007] The present invention also provides a computer-readable storage medium storing computer instructions for causing a processor to perform the above-described method.

[0008] The present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the above-described method.

[0009] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: 1. This invention constructs a two-stage, multi-cycle planning framework. This framework discretizes the long-term planning perspective into multiple decision-making stages, optimizing the timing and capacity expansion of electrolyzers, fuel cells, hydrogen storage tanks, and batteries through phased investment. Unlike traditional expected cost minimization, this invention uses maximizing the robustness level of the gap-of-information decision theory (IGDT) (i.e., the maximum deviation of the hydrogen load the system can accommodate from the predicted value) as the objective function, and performs optimization under the hard constraint of the total investment budget, thereby achieving a trade-off between cost efficiency and demand adaptability.

[0010] 2. To address the heterogeneous uncertainties faced by hydrogen-based microgrids, this invention designs a hybrid opportunity-constrained-information gap decision theory (CCP-IGDT) collaborative modeling method. Specifically, opportunity-constrained programming (CCP) is used to handle short-term stochastic fluctuations (such as wind and solar power output and hourly load changes), providing quantified probabilistic reliability guarantees by setting risk tolerance; information gap decision theory (IGDT) is used to handle long-term non-stochastic deep uncertainties (such as hydrogen demand growth trajectory and technology cost evolution), immune to structural prediction biases without requiring probability distribution assumptions.

[0011] 3. For the large-scale mixed-integer second-order cone programming (MISOCP) problem involving discrete investment decisions, second-order cone power flow constraints, and mixed uncertainty constraints, this invention designs an adaptive predictive-corrected Benders decomposition (APC-BD) algorithm. This algorithm introduces a unified slack subproblem (UR-SP), using penalized slack variables to uniformly handle operational feasibility and optimality, eliminating the complex infeasible cut construction process in traditional methods. Simultaneously, a cost-weighted trust region mechanism based on prediction fidelity is designed, dynamically adjusting the trust region radius and regularization weights according to the approximation quality of the linearized model. Combined with a non-monotonic multipath acceptance criterion, it effectively suppresses boundary oscillations of the main problem during iteration, achieving robust convergence. The proposed adaptive predictive-corrected Benders decomposition (APC-BD) method is built upon an adaptive trust region framework and introduces two key algorithmic innovations: a multipath acceptance criterion and score-based cut management. These three synergistic components—trust region stabilization, acceptance control, and cut pruning—balance convergence speed and robustness while maintaining approximate accuracy under the nonlinearity caused by SOCP.

[0012] 4. This invention can ensure that the system maximizes its capacity to meet future uncertain hydrogen demand while meeting a fixed budget, significantly reducing the total life cycle cost (13.46%-18.19% lower than static planning) and exhibiting superior adaptability in high-load growth scenarios. At the same time, the APC-BD algorithm significantly improves the computational efficiency and numerical stability of large-scale complex coupled problems while ensuring the quality of the solution. Attached Figure Description

[0013] Figure 1 A schematic diagram of the multi-period planning method for networked hydrogen-based microgrids based on probabilistic constraints and information gap decision-making provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of the networked hydrogen-based microgrid provided in an embodiment of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0015] This invention provides a multi-cycle planning method for networked hydrogen-based microgrids based on probabilistic constraints and information gap decision-making, such as... Figure 1 As shown, it includes: The optimal multi-cycle planning strategy is obtained by maximizing the maximum deviation α of the hydrogen load that the system can accommodate relative to the predicted value. The hydrogen-based microgrid comprises a set of nodes and a set of directed branches. The set of nodes includes renewable energy sources, dispatchable generators, energy conversion devices, electrical energy storage systems, and hydrogen energy storage systems. These renewable energy sources, dispatchable generators, energy conversion devices, electrical energy storage systems, and hydrogen energy storage systems can share electricity. The renewable energy sources and dispatchable generators have power generation capabilities. The optimal multi-cycle planning strategy includes the hydrogen tank capacity of the hydrogen energy storage system, the energy storage capacity of the electric energy storage system, and the timing of equipment expansion.

[0016] This implementation method is based on a radial distribution network (e.g., the IEEE 33-bus system) that includes multiple types of distributed energy resources (DERs), and solves the planning problem of coupling short-term stochastic fluctuations with long-term deep uncertainty through a two-stage optimization framework. Figure 2 As shown, construct a set of nodes. Set of directed branches The power distribution network model. Four types of devices can be configured: Renewable Energy (RES): Photovoltaics (PV) and wind turbines (WT) provide undispatchable green electricity; Dispatchable generator (DG): Gas turbine (GT) provides stable balanced power; Energy conversion equipment: electrolyzer (EL, responsible for E2H electro-hydrogen conversion) and fuel cell (FC, responsible for H2E hydrogen-electric conversion); Energy storage systems: Battery energy storage system (ESS) and hydrogen energy storage system (HSS).

[0017] Define the planning horizon (e.g., 10 years) can be discretized into a set of multiple decision-making stages. Introducing typical day sets To capture seasonal variations, define stage weights. and typical daily weight To reflect the operating costs for the entire year.

[0018] This invention distinguishes between two types of uncertainty based on time characteristics and the availability of probabilistic information, and establishes mathematical models for the heterogeneous uncertainties faced by hydrogen-based microgrids: 1) Short-term stochastic uncertainty modeling (chance-constrained programming, CCP) For hydrogen load Electrical load ,illumination and wind speed The hourly fluctuations are assumed to follow normal distributions (load), Beta distributions (solar irradiance), and Weibull distributions (wind speed), respectively. Chance-constrained programming (CCP) is employed, requiring system operation constraints to be within a certain confidence level. The following is established to provide quantifiable reliability guarantees:

[0019] in, For a random parameter vector, Risk tolerance.

[0020] 2) Long-term non-stochastic uncertainty modeling (IGDT) To address the deep uncertainty in long-term hydrogen demand growth, the Information Gap Decision Theory (IGDT) is employed. The uncertainty set is defined. Actual hydrogen load Relative to the predicted value The relative deviation does not exceed :

[0021] The unilateral IGDT criterion based on a planning perspective only considers the worst-case scenario of upward load growth:

[0022] in, The robustness radius represents the maximum percentage increase in load that the system can withstand.

[0023] S3. Construction of Multi-Period Robust Programming Model A multi-period robust programming model is established, constructing a mixed-integer second-order cone programming (MISOCP) model, specifically including: 1. Objective function The planning objective is to maximize the system's IGDT robustness to hydrogen load growth. :

[0024] 2. Constraints The planning model is constrained by budget constraints, investment constraints, and operational constraints.

[0025] The total cost must meet the following budget constraints:

[0026] in, Due to budget constraints, For interest rates. Calculated using unit capital cost Increased incremental power and energy capacity and . Based on the representative day assessment, where the weights Extend aggregation across the entire cycle In addition, hourly operating costs It is broken down into maintenance costs for electrical and energy equipment, fuel costs, renewable energy reduction penalties, and distribution line losses.

[0027] Equipment Function Conversion: Based on the above equipment functions, the equipment energy conversion formula is as follows:

[0028] The above formulas define PV output, WT output (based on a piecewise cubic function), GT energy conversion, FC power generation, and EL hydrogen production processes, respectively.

[0029] Investment constraints: Investment decisions are subject to physical and reliability constraints. 1) Physical constraints: Investment decision variables are subject to the following physical constraints:

[0030] in, The number of newly installed units (integer). Unit capacity, cumulative capacity and It is an increment and The accumulation of history.

[0031] 2) Reliability constraints:

[0032] The first line introduces an equivalent load for the electrical load. To ensure the reliability of the system's hydrogen and electricity supply, the second line requires that renewable energy installations meet a certain proportion, and the third and fourth lines guarantee the overall system's power sufficiency (including reserve margin). ) and hydrogen supply adequacy (including reserve margin) ).

[0033] Operational constraints include power flow constraints and hydrogen flow constraints. Details are as follows: Power flow constraints: The power flow formula includes power decision constraints, energy storage system (ESS) state of charge (SoC) dynamics, and network topology constraints.

[0034] 1) Power Decision Limitations: The operating output of the equipment must meet the following capacity limits:

[0035] The first line limits the power output of all devices within their installed capacity. The second and third lines impose limits on the charging and discharging of the ESS. The fourth and fifth lines indicate that renewable energy cuts and load shedding are limited to the proportion of predicted generation and demand. and In addition, power factor constraints are imposed on wind turbines (WT) and gas turbines (GT) in lines 6 and 7.

[0036] 2) ESS State of Charge Dynamics: The update of the ESS State of Charge (SOC) is modeled across multiple time scales as follows:

[0037] Among them, leakage rate Charging efficiency and discharge efficiency The first, second, and third lines control SOC updates within the day, between days, and between cycles, respectively. The fourth line limits storage energy from exceeding the existing capacity, and the fifth line ensures that the initial and final SOCs are equal to achieve cyclic scheduling.

[0038] 3) Distribution Network Constraints: To ensure operational safety, a radial network topology was adopted. The DistFlow model is described as follows:

[0039] The first and second rows contain the active and reactive power balance constraints of the nodes. and The predicted power outputs for photovoltaic and wind turbines are respectively. , , These are the power outputs of the electrolyzer, fuel cell, and gas turbine, respectively. and This represents the net active and reactive power injection. The third and fourth lines represent branch power flow conservation. and Indicates a branch The power flow on, where and Indicates busbar The upstream and downstream neighbor sets. The fifth line is the voltage drop equation. and The first line represents the branch resistance and reactance; the sixth line represents the relationship between branch current and power flow; and the seventh line represents the safe operating limits for voltage and current.

[0040] Hydrogen flow constraints: Hydrogen network modeling takes into account hydrogen decision constraints, hydrogen storage system (HSS) dynamics, and hydrogen network mass flow balance.

[0041] 1) Hydrogen decision-making constraints: Hydrogen equipment variables are subject to the following constraints:

[0042] The first and second lines limit the hydrogen charging and discharging rate of the HSS to no more than the rated capacity of the HSS. The product of the multiplier; the third line limits the hydrogen load cut-off to no more than the maximum proportion of the predicted hydrogen load. .

[0043] 2) HSS State of Charge Dynamics: HSS SoC updates follow multi-scale logic:

[0044] in, and The hydrogen charging and decharging rates and leakage rate of the HSS are respectively. Hydrogen charging efficiency and hydrogen release efficiency The first, second, and third lines control the SOC updates of the HSS within the day, between days, and between periods, respectively. The fourth line limits the storage energy from exceeding the existing HSS capacity, and the fifth line ensures that the initial and final SOCs are equal to achieve cyclic scheduling.

[0045] 3) Hydrogen Network Constraints: Without loss of generality, the hydrogen flow network adopts the same network topology as the electrical network:

[0046] The first row contains the node hydrogen mass balance equation, including hydrogen production from electrolyzers. Fuel cells consume hydrogen HSS hydrogen charging and discharging Hydrogen load and amount of resection , It is a busbar The net hydrogen injection. The second line is the branch hydrogen flow conservation equation. and These are the downstream branches and downstream branches The hydrogen flow rate is defined as follows: the third line represents the capacity limit of the branch hydrogen flow rate.

[0047] 3. Model Convexification The above model contains nonlinear and nonconvex constraints. It is made convex through the following transformation to achieve efficient computation: 1) Variable substitution for bilinear terms: Auxiliary variable and Introduced to eliminate the explicit bilinear product in the running cost function, we get:

[0048] The DistFlow equation can be transformed into:

[0049] 2) Linear Approximation: The non-convex power factor coupling constraint can be approximated by the following linear inequality:

[0050] 3) Second-order cone relaxation: The non-convex branch current constraint (11f) is relaxed to a second-order cone (SOC) constraint by convexity:

[0051] 4. Compact System Model Based on the above convex relaxation, the multi-period programming model is expressed in compact form as follows:

[0052] in, For planning decision variables (such as installed equipment capacity), To run decision variables, The variables representing the SOC of a second-order cone are: Uncertainty bias parameters in the IGDT model This is an uncertainty vector. , , , , , The coefficient matrix, to This is a constant vector. The first row is the objective function, maximizing the system's robustness to hydrogen load uncertainty; the second row is the deterministic constraint for planning decisions; the third row is the uncertainty-related constraint for planning decisions; the fourth row is the constraint for operational decisions; the fifth row is the coupling constraint between planning and operational decisions; the sixth and seventh rows are second-order cone constraints, relaxations from the DistFlow model; the eighth and ninth rows are the definition of the IGDT uncertainty set; the tenth and eleventh rows are joint chance constraints, ensuring probabilistic guarantees for budget and operational feasibility.

[0053] 5. Model Transformation To facilitate the solution, the compact form applies the following mathematical transformations: 1) IGDT Linearization: Since the worst-case scenario occurs when hydrogen load demand deviates upward, the IGDT uncertainty set is restricted to a one-sided upper envelope. Therefore, (19f) is linearized as follows:

[0054] 2) Scene-based CCP approximation: using a finite set of scenes Approximate CCP constraints are applied, and a representative scene set is generated using Monte Carlo sampling. Introducing binary variables Indicates the scene selection. The constraints are restated as follows:

[0055] Among them, among them, Choose a variable vector for a binary scenario. Representing a scene The probability weights are then assigned. Similarly, the constraints are transformed into a scenario-based equivalent:

[0056] Based on the above restatement, the multi-period programming model under mixed uncertainties is restated as the MINLSOC problem, as shown below:

[0057] Given that the MINLSOC problem mentioned above also includes discrete integer decision variables Boolean variables Furthermore, the non-convex second-order cone constraint makes the calculation very difficult and requires a specialized decomposition algorithm to solve.

[0058] The proposed MINLSOC model is characterized by: (i) discrete investment decision-making, (ii) bilinear chance constraint formula, and (iii) second-order conical power flow constraint. It is computationally very difficult. To address this complexity, this invention proposes an Adaptive Predictive Correction Benders Decomposition (APC-BD) algorithm. This algorithm dynamically adjusts the trust region radius and regularization penalty through rigorous prediction fidelity evaluation, effectively mitigating boundary oscillations and accelerating convergence. The process is as follows: 1. Decomposition Framework: Following the standard Benders decomposition paradigm, the problem is decomposed into: Main Problem (MP): Determining the optimal investment decision Robustness margin and scene selection .

[0059] Sub-problems (SP): For each scenario Calculate the optimal operating decision And generate Benders cut.

[0060] 2. Main Problem Model To facilitate decomposition, auxiliary variables are introduced. To approximate the operating costs under different scenarios, the coupled budget constraint is then decoupled into a logical form:

[0061] Because only Depends on the scenario (and) (Coupling), the constraint can be restated as:

[0062] The resulting bilinear term By introducing auxiliary variables Linearization is performed using the McCormick envelope, and it can be restated as follows:

[0063] in, yes The upper limit.

[0064] 1) Standard Master Problem: The standard master problem is then constructed as a mixed-integer linear programming (MILP) problem and linearly approximated using Benders cut as follows:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] . The first row maximizes the robustness radius. ,and As an auxiliary objective function, it has sufficiently small weights. To avoid Symmetric solutions on, and by producing the same in multiple solutions The unique optimal solution is chosen to achieve cost efficiency. The third line represents the set of Benders cuts accumulated from the solutions to the subproblems (see the section on Benders cut generation later). These linear constraints provide cost compensation. The external approximation of the subproblem is derived from the explicit coefficients of the subproblem dual variables introduced in subsequent chapters.

[0074] Limitations: However, due to the lack of regularization, the standard principal problem often suffers from oscillation effects, resulting in slow convergence or even divergence in the early iterations.

[0075] 2) Stabilization Master Problem: To alleviate oscillatory behavior and accelerate convergence, this invention proposes a stabilization master problem by combining a proximal regularization term and a trust region constraint. The stabilization master problem of the next iteration is formulated as follows:

[0076]

[0077]

[0078]

[0079] Among them, the adjacent items in the first row Punishment and Current Stability Center The deviation is used to suppress oscillations. The upper bound of the forced component is set in the second row. This is to prevent unrealistic one-step changes. It's worth noting that the third line introduces a cost-weighted trust region, limiting economic deviations to a radius. Traditional trust region methods typically employ uniform metrics (such as the Euclidean norm), failing to account for the heterogeneous economies of scale of energy equipment. This is achieved by using their unit cost of capital. Adjustment amount of capacity By applying weights, the constraint projects the deviation onto a uniform economic dimension, ensuring that the total economic disturbance remains within the adaptive radius.

[0080] Linearization: The proximal regularization term involves The -norm introduces nonlinearity. To maintain the MILP structure of the stable master problem, auxiliary continuous variables are introduced. The stabilization master problem is linearized as follows:

[0081] 3. Subproblem Formulation and Cut Generation For a given trial solution Provided by the stabilization master problem, the running subproblems ( The subproblem is solved to determine the optimal strategy. However, the feasibility of the subproblem cannot be guaranteed during the iteration process. Unlike traditional methods where the optimal cut (OC) and feasible cut (FC) rely on binary feasibility checks, we introduce a unified relaxed subproblem (UR-SP) to uniformly handle potential infeasibility. For each scenario... Introducing slack variables And with a large penalty coefficient. To relax the constraints:

[0082] in, and As an auxiliary variable, These are the dual variables associated with the coupling constraints.

[0083] Note 2 (Simplified Duality Extraction). Introducing auxiliary variables with fixed constraints significantly simplifies duality extraction in the presence of complex hydrogen-electric coupling, eliminating the derivation process of the explicit duality problem. Based on dual solution ( This generates a uniform Benders cut, as shown below.

[0084]

[0085] Unlike traditional methods, the last item A conditional activation mechanism has been introduced: Active state ( =0): When scenario n is selected, the penalty term disappears and the cut constraint becomes a tight constraint; hibernation state ( =1): When not selected, the cut constraint is relaxed, but the dual information is still encoded and preserved for possible future activation.

[0086] Note 3 (Equivalence with traditional optimal and feasible cuts). The proposed unified cut formula naturally incorporates two types of cuts through a penalty mechanism: Feasibility The objective reduces to , representing the precise operating cost. Therefore, as the standard optimal cut, it provides a tight lower bound.

[0087] Infeasible situations ( ): Activation of slack variables The penalty term dominates, effectively transforming it into a feasible cut and guiding the stabilization master problem toward the feasible region.

[0088] 4. Adaptive Trust Region Strategy with Prediction Correction The coupling of integer investment decisions with scenario selection can lead to non-smooth target changes and oscillating behavior, as different integer configurations may generate conflicting dual information. To achieve stable convergence, an adaptive trust region strategy with prediction correction is proposed, based on Benders cut-based dynamic calibration of prediction fidelity parameters. This strategy integrates: Dynamic proximal regularization suppresses oscillations by penalizing deviations from the current solution; Adjustable trust region constraints, limiting the integer search space based on local approximation quality; The non-monotonic acceptance criterion evaluates trial solutions and adaptively adjusts penalty weights and trust region radius based on prediction accuracy.

[0089] 1) Prediction Fidelity Evaluation: The existence of second-order cone programming constraints leads to a nonlinearity in the value function, resulting in linearization errors in the Benders cut. To quantify the approximation quality, we define the prediction fidelity ratio. As a diagnostic indicator:

[0090] Among them, the The actual and predicted improvements of each iteration are defined as follows:

[0091] in, and Let these represent the total costs of the stable center and the trial solution, respectively:

[0092] Describes the lower bound of the linearized stable principal problem S-MP:

[0093] In particular, ratio As a key diagnostic indicator: High fidelity indicates accurate linearization.

[0094] Poor approximate quality indicates excessive deviation.

[0095] The model deteriorates, indicating that the results are worse than predicted.

[0096] 2) Multi-path triple acceptance criterion: To balance approximation fidelity, convergence speed, and global exploration, we propose a disjunctive acceptance framework, in which trial solutions... It is accepted if any one of the following three complementarity criteria is met: Criterion A (Model Reliability): Maintain model fidelity to prevent oscillating behavior; Criterion B (non-monotonic decline) ensures sufficient progress while tolerating temporary increases; Criterion C (breaking records) promotes global exploration to escape local optima.

[0097] Criterion A (Model Fidelity with Noise Tolerance): If the model exhibits sufficient fidelity and the solution quality does not deteriorate beyond an acceptable noise level, then it is accepted.

[0098] in, This is the minimum fidelity threshold that enforces model reliability. The second condition allows a controlled relative deterioration of up to a maximum of [value missing]. To accommodate numerical noise and prevent rejection of solutions close to the optimum. Note that, Indicates improvement, and Slight deterioration within the tolerance range is permissible.

[0099] Criterion B (Non-monotonic decline): Accept if a sufficient decline has been achieved relative to recent history.

[0100] in, It is a non-monotonic reference value, defined as:

[0101] The backtracking window size is ,in Balance memory retention and adaptability.

[0102] Adaptive tolerance Decays exponentially with iteration:

[0103] in, and Limit tolerance, Controlling the transition from exploration to development.

[0104] Note 4 (Non-monotonic strategy). Using historical reference values. It adapts to local fluctuations arising from discrete decision-making. Comparison with the nearest worst solution rather than its direct predecessor allows for the addition of temporary objectives while ensuring sufficient descent. The adaptive tolerance enforces increasingly stringent criteria as the algorithm matures, transitioning from global exploration to local convergence.

[0105] Criterion C (Record Breaking): Accept if a significant improvement over the historical best is achieved.

[0106] in, , It is the record-breaking threshold.

[0107] Note 5 (Global Exploration). This criterion encourages aggressive global exploration by accepting solutions that significantly improve upon historical optima, regardless of model fidelity or monotonicity, thus preventing the model from getting trapped in discrete local optima.

[0108] Therefore, the final decision is given as follows:

[0109] in, , These represent the Boolean results of the criteria.

[0110] 3) Parameter update and restart strategy: based on accepted results and fidelity ratio The algorithm parameters are updated dynamically.

[0111] a) Trust domain radius update

[0112] in, It is the high-fidelity threshold for triggering radius expansion, and and Control the aggressiveness of trust region growth and reduction separately.

[0113] b) Near-end weight update:

[0114] in, and Define a guard bound for the proximal weights to prevent numerical instability, while and The rates of regularization relaxation and reinforcement are controlled separately.

[0115] c) Stability Center Update:

[0116] d) Stagnation Handling: To prevent the algorithm from getting stuck, if continuous... If no improvement is achieved in subsequent iterations, the program will be restarted. i) Parameter reset: Reinitialize trust region and penalty weights: ; ii) Solution backtracking: Backtracking to the currently known optimal solution:

[0117] iii) Counter Reset: Reset the stalled counter: . 5. Segmentation Management Based on Scoring To maintain the computational tractability of cumulative data during cutting, this invention employs a dynamic scoring mechanism to control the bundle size. Let... Indicates the first The active cut set of the next iteration. For each cut... Define priority scoring Recursively update based on its activity level:

[0118] in, It is the maximum score of the active constraint. This is the initial rating for the newly harvested fruit. It is a decay factor that gradually reduces the importance of inactive cuts.

[0119] To enforce maximum bundle size Only the cut with the highest score is retained. Updated bundle Selected as the subset that maximizes cumulative scores:

[0120] In practice, this is achieved by sorting the data in descending order of scores and retaining the top-scoring data. This mechanism utilizes a decay factor to achieve efficient implementation. It automatically eliminates persistently inactive cuts while retaining the most recent tight constraints, effectively balancing approximate accuracy and computational efficiency.

[0121] The core idea of ​​the algorithm is to suppress oscillations through trust region constraints and proximal regularization terms, flexibly handle model errors and discrete decisions through a triple acceptance criterion, and manage the cut set size through a dynamic scoring mechanism. The main steps include: solving the stabilization master problem to obtain trial solutions, solving sub-problems for each scenario to generate Benders cuts, evaluating prediction fidelity and acceptance criteria, adaptively updating the trust region radius and proximal weights, and dynamically managing the cut pool until convergence.

[0122] This invention provides a networked hydrogen-based microgrid multi-cycle planning system based on probabilistic constraints and information gap decision-making, comprising: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any of the above embodiments.

[0123] This invention provides a computer-readable storage medium storing computer instructions that cause a processor to perform the method described in any of the above embodiments.

[0124] The technical features of the embodiments described above can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. It should be noted that the terms "in one embodiment," "for example," and "again" in this invention are intended to illustrate the invention and are not intended to limit the invention.

[0125] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A multi-period planning method for networked hydrogen-based microgrids based on probabilistic constraints and information gap decision-making, characterized in that, include: The optimal multi-cycle planning strategy is obtained by maximizing the maximum deviation α of the hydrogen load that the system can accommodate relative to the predicted value. The hydrogen-based microgrid comprises a set of nodes and a set of directed branches. The set of nodes includes renewable energy sources, dispatchable generators, energy conversion devices, electrical energy storage systems, and hydrogen energy storage systems. These renewable energy sources, dispatchable generators, energy conversion devices, electrical energy storage systems, and hydrogen energy storage systems can share electricity. The renewable energy sources and dispatchable generators have power generation capabilities. The optimal multi-cycle planning strategy includes the hydrogen tank capacity of the hydrogen energy storage system, the energy storage capacity of the electric energy storage system, and the timing of equipment expansion.

2. The multi-cycle planning method for networked hydrogen-based microgrids according to claim 1, characterized in that, The operating constraints of the hydrogen-based microgrid are at a confidence level Down: ,in For uncertainty vectors, For hydrogen load, For electrical load, For light, Wind speed; and It is a coefficient matrix; For running the decision variable set.

3. The multi-cycle planning method for networked hydrogen-based microgrids as described in claim 2, characterized in that, Define a long-term non-random uncertainty set: ,in This represents the actual hydrogen load.

4. The multi-cycle planning method for networked hydrogen-based microgrids as described in claim 1, characterized in that, Constraints include budget constraints, investment constraints, and operational constraints: Budget constraints are: in, Due to budget constraints, For interest rates, Represented by unit cost of capital Increased incremental power and energy capacity and , Representative day assessment, For stage weights, Typical daily weighting, For a period of time, Represents the hourly operating cost. For the unit operation and maintenance fee rate of power equipment, To contribute practically, For the unit operation and maintenance rate of energy equipment, This represents the actual hydrogen flow rate. This refers to the unit price of natural gas. The amount of natural gas consumed by the gas turbine. The unit price for line loss. This refers to line loss power; Investment constraints are: in, The number of newly installed units, Unit capacity, cumulative capacity and It is an increment and Historical accumulation; and It is an increment and The rated value; in, For electrical load equivalent load, As basic electrical load, For electrolysis efficiency, This is a conversion factor for electrolysis units. As a reserve margin, To ensure adequate hydrogen supply; The operational constraints are: in, For installation capacity, For the installed energy capacity of ESS, and The charge / discharge rate of the ESS. and Renewable energy cuts and load shedding are limited to a ratio of projected power generation to demand. This is the lower limit of the power factor for wind turbine generators. and These are the upper and lower limits of the gas turbine power factor. in, For leakage rate, For charging efficiency, For discharge efficiency; in, For node active power, For node reactive power, and The predicted power outputs for photovoltaic and wind turbines are respectively. , , These are the power outputs of the electrolyzer, fuel cell, and gas turbine, respectively. and Indicates net active and reactive power injection. and Indicates a branch Power flow on, and Indicates busbar The upstream and downstream neighbor sets, and For branch resistance and reactance; in, and The hydrogen charging and discharging rate of the hydrogen storage system, The rated capacity of the hydrogen storage system, and This refers to the hydrogen charge / discharge rate. This refers to the amount of hydrogen load removed. To predict the maximum proportion of hydrogen load; in, For leakage rate, For hydrogen charging efficiency, For hydrogen release efficiency; in, For the hydrogen production capacity of the electrolyzer, For fuel cell hydrogen consumption, The amount of hydrogen charged and discharged for the hydrogen storage system, Hydrogen loading, For the amount of tissue removed, It is a busbar Net hydrogen injection, and These are the downstream branches and downstream branches The hydrogen flow.

5. The multi-period planning method for networked hydrogen-based microgrids as described in claim 4, characterized in that, By making the nonlinear and nonconvex constraints in the above constraints convex, we obtain: in, and .

6. The multi-cycle planning method for networked hydrogen-based microgrids as described in claim 5, characterized in that, The compact form based on the aforementioned convex relaxation is expressed as: in, For planning decision variables, To run decision variables, The variables representing the SOC of a second-order cone are: , , , , , The coefficient matrix, to It is a constant vector.

7. The multi-cycle planning of networked hydrogen-based microgrids as described in claim 6, characterized in that, Based on linearization of decision theory that maximizes information gaps and approximation of opportunity-constrained programming based on scenarios, the compact form is expressed as a MINLSOC problem: 。 8. The multi-cycle planning of networked hydrogen-based microgrids as described in claim 7, characterized in that, Solve the MINLSOC problem as follows: Break the problem down into: Main Problem (MP): Determining the optimal investment decision Robustness margin and scene selection ; Sub-problem SP: For each scenario Calculate the optimal operating decision And generate Benders cut; Introducing auxiliary variables Using approximate operating costs under different scenarios, the coupling budget constraints are decoupled into: ; The generated bilinear terms By introducing auxiliary variables Linearization using the McCormick envelope: in, yes The upper limit; The main problem MP was then constructed as a mixed-integer linear programming problem MILP, and linearly approximated by Benders cut as follows: . Combining the proximal regularization term and the trust region constraint, the first The stabilization master problem of the next iteration is formulated as follows: in The radius of the trust region; Introducing auxiliary continuous variables The stabilization master problem is linearized as follows: Pair problem SP in each scenario Introducing slack variables Combined with a penalty coefficient To relax the constraints: in, and As an auxiliary variable, For dual variables associated with coupling constraints; Based on dual solution ( Generate a unified Benders cut: Define prediction fidelity ratio As a diagnostic indicator: Among them, the The actual and predicted improvements of each iteration are defined as follows: in, and Let these represent the total costs of the stable center and the trial solution, respectively: Trial solution It is accepted if any one of the following three complementarity criteria is met: Criterion A: in, It is the minimum fidelity threshold for mandating model reliability; Criterion B: in, It is a non-monotonic reference value; Criterion C: in, , It is the record-breaking threshold; Based on the accepted results and fidelity ratio The algorithm parameters are updated dynamically. A dynamic scoring mechanism is adopted, and a score is set. Indicates the first The active cut set of the next iteration, for each cut Define priority scoring Recursively update based on its activity level: in, It is the maximum score of the active constraint. This is the initial rating for the newly harvested fruit. It is the attenuation factor; Only retain the highest-scoring cut, and update the bundle. Selected as the subset that maximizes cumulative scores: 。 9. A multi-period planning system for a networked hydrogen-based microgrid based on probabilistic constraints and information gap decision-making, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method as described in any one of claims 1 to 8.

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