Interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary system

Abstract

The application discloses an interval constraint high-dimensional multi-objective optimization method for a multi-energy complementary system, belongs to the technical field of multi-energy comprehensive utilization, and solves the difficulty problem of collaborative scheduling among wind power, photovoltaic, thermal power and energy storage. The method comprises the following steps: introducing interval numbers to describe the fluctuation ranges of wind power, photovoltaic output and load demand, and establishing a high-dimensional multi-objective optimization system covering seven targets of carbon emission, peak regulation cost, pollutant penalty cost, thermal power unit load balance, climbing rate, renewable energy ratio and supply-demand deviation amount, so as to comprehensively evaluate the operation state of the multi-energy complementary system from three aspects of environmental protection, economy and stability; a collaborative evolution mechanism of a leader population and a follower population is constructed, and a dynamic Stackelberg uncertainty weight adjustment method is provided; and three time windows of history, real time and prediction are integrated into a unified optimization framework. The application is suitable for collaborative scheduling of the multi-energy complementary system.

Description

Technical Field

[0001] This application relates to the field of multi-energy integrated utilization technology, and in particular to the coordinated optimization scheduling of multi-energy complementary systems. Background Technology

[0002] Multi-energy complementary systems improve renewable energy absorption capacity, system operation economy, and energy supply reliability by coordinating and optimizing the scheduling of various energy types, including wind power, photovoltaics, thermal power, and energy storage. Traditional optimization methods for multi-energy complementary systems are typically based on deterministic models, making unit output allocation and operational decisions under fixed parameter assumptions. However, in actual operation, wind power and photovoltaic output, as well as load demand, often exhibit significant fluctuations and uncertainties, leading to limitations in deterministic models. This makes it difficult to simultaneously consider system economy, environmental friendliness, and operational stability in scenarios with a high proportion of renewable energy integration. Interval constraints use interval numbers to describe the fluctuation range of renewable energy output and load demand, handling uncertainty boundaries and replacing the precise parameters in traditional deterministic models. Multi-objective optimization seeks a compromise solution that achieves overall system optimization by simultaneously optimizing multiple conflicting performance indicators, such as economy, environmental friendliness, and stability. Furthermore, as the scale of systems continues to expand and coupling constraints become increasingly complex, there is a growing demand for unified modeling and collaborative solving of multi-energy complementary systems using interval constraints and high-dimensional multi-objective optimization methods to optimize multi-dimensional performance indicators such as carbon emissions, peak-shaving costs, pollutant emissions, load balancing, ramp rate, and renewable energy consumption. This has become one of the core research directions in related fields.

[0003] A search of existing literature revealed that Chinese patent CN120784978A proposes a method for optimizing scheduling rules in a hydro-wind-solar integrated system. This method constructs a multi-energy complementary scheduling diagram to form long-term, medium-term, and short-term scheduling rules, and establishes a multi-objective optimization model to optimize system operation indicators. However, this method primarily focuses on the construction of integrated hydro-wind-solar scheduling rules, emphasizing specific energy combinations and scheduling scenarios, and does not characterize uncertainties such as wind and solar power within interval constraints. Chinese patent CN121234613A proposes a method for determining the power transmission curve of a base based on frequency analysis and multi-energy complementary simulation operation. This method establishes a simulation model of multi-energy complementary operation of a clean energy base, analyzes the original power transmission process curve, and determines the power transmission curve. However, this method mainly addresses the problem of determining the base power transmission curve, focusing on power transmission characteristic analysis and planning. It does not adequately consider the collaborative optimization of multiple devices, constraints, and objectives within the multi-energy complementary system, and it does not form a unified modeling and solution method for high-dimensional multi-objective optimization under interval constraints. Therefore, existing technologies still struggle to achieve high-dimensional, multi-objective collaborative optimization of multi-energy complementary systems under the conditions of renewable energy uncertainty and complex constraints. Summary of the Invention

[0004] The purpose of this invention is to solve the technical problems of large fluctuations in new energy output, rapid changes in load demand, and difficulties in coordinated scheduling among wind power, photovoltaic power, thermal power and energy storage in the actual operation of existing multi-energy complementary systems. It provides a high-dimensional multi-objective optimization method and system with interval constraints for multi-energy complementary systems.

[0005] The technical solution adopted by this invention to solve the above problems is: a high-dimensional multi-objective optimization method with interval constraints for multi-energy complementary systems, wherein the multi-energy complementary system includes a power supply side, a power receiving side, and a dispatch control side; the power supply side includes wind farms, photovoltaic power plants, thermal power plants, and battery energy storage systems; the power receiving side includes the demand side and the power grid; and the dispatch control side is a computing service center.

[0006] The method includes:

[0007] Step 1: Construct a high-dimensional multi-objective optimization model with interval constraints for multi-energy complementary systems, including:

[0008] Assume the number of thermal power units is , No. Taiwan thermal power units in the time window The electricity generated within is expressed as Its start / stop status is represented as ;in, ,when When, it indicates that the thermal power unit is in a shutdown state. When the time is specified, it indicates that the thermal power unit is in the startup state; the next time... Each energy storage unit within the time window The amount of discharge within is expressed as Its maximum discharge power is expressed as Its time window The remaining energy storage capacity is expressed as Users in the time window The load demand within is expressed as ;

[0009] Establish a three-rolling time window and uncertainty representation, wherein the three-rolling time window includes a historical time window. Real-time time window and prediction time window It is used to characterize the historical operating state, current scheduling state, and future trend of a multi-energy complementary system during continuous operation;

[0010] Multiple optimization objectives are established to uniformly characterize the comprehensive performance of the multi-energy complementary system during the rolling scheduling process; corresponding constraints are set based on the multiple optimization objectives.

[0011] Step 2: Construct the decision space of the optimization model and initialize the reference vector, leader population, and follower population; a real-time time window is also included in the decision variables. and prediction time window Operating status of thermal power units inside With power generation Information is used to construct the decision space for the current optimization cycle;

[0012] Step 3: Construct a comprehensive evaluation function for the leader population and execute the dynamic Stackelberg uncertainty weight adjustment method;

[0013] The comprehensive evaluation function includes: incorporating the convergence and uncertainty of an individual into a single fitness evaluation function, wherein uncertainty is used to characterize the stability and reliability of the scheme under conditions of renewable energy output and load fluctuations;

[0014] The dynamic Stackelberg uncertainty weight adjustment adaptively balances convergence and uncertainty through gradient descent, thereby generating a uniformly distributed non-dominated solution set;

[0015] Step 4: Implement a local search strategy within the follower population;

[0016] Step 5: Select the execution environment for the follower population based on regional exploration ability, constraint feasibility, and individual comprehensive fitness, so as to select the next generation of follower population from the candidate individuals;

[0017] Step 6: Perform environmental selection on the leader population to select the next generation of leaders from the candidate individuals;

[0018] Step 7: Repeat steps 3 to 6. When the termination condition is met, output the final optimized scheduling scheme.

[0019] The beneficial effects of this invention are:

[0020] This invention characterizes the uncertainties of wind power output, photovoltaic power output, and load demand through interval constraints, and coordinates and schedules wind power, photovoltaic, thermal power, and energy storage units in a unified manner. It dynamically adjusts the operating status of equipment, improves the matching degree between power generation and consumption, reduces the peak-shaving pressure of thermal power, enhances the regulation of energy storage and the absorption of renewable energy, reduces operating costs and carbon emissions and pollutant emissions, and achieves safe, stable, economical, and clean operation of multi-energy complementary systems.

[0021] First, this paper presents a high-dimensional multi-objective optimization method with interval constraints that can effectively quantify the uncertainty of renewable energy output. This method needs to overcome the limitations of traditional deterministic models by introducing interval numbers to describe the fluctuation range of wind power, photovoltaic output, and load demand. It also establishes a high-dimensional multi-objective optimization system covering seven objectives: carbon emissions, peak-shaving costs, pollutant penalty costs, thermal power unit load balancing, ramp-up rate, renewable energy share, and supply-demand deviation. This system comprehensively evaluates the operating status of the multi-energy complementary system from three aspects: environmental friendliness, economic efficiency, and stability.

[0022] Second, a dual-population co-evolutionary solution framework capable of simultaneously handling multiple conflicting optimization objectives is provided. This method overcomes the difficulty of balancing convergence and diversity in high-dimensional objective spaces. By constructing a co-evolutionary mechanism between a leader population and a follower population, and proposing a dynamic Stackelberg uncertainty weight adjustment method, convergence and interval uncertainty are adaptively balanced through gradient descent, thereby generating a uniformly distributed non-dominated solution set, providing decision-makers with a clear basis for multi-objective trade-offs.

[0023] Third, a closed-loop dynamic scheduling mechanism based on three rolling time windows is provided. This method incorporates historical, real-time, and predictive time windows into a unified optimization framework. Historical window data are fixed values, while real-time and predictive windows are represented by interval parameters. Continuous iterative optimization is achieved through the rolling advancement of time windows. Simultaneously, temporally coupled physical constraints such as thermal power unit ramp rate constraints, start-stop state constraints, and energy storage state of charge constraints are explicitly incorporated into the model to ensure the physical executability of scheduling commands and achieve continuous optimization of the multi-energy complementary system during continuous operation.

[0024] This invention is applicable to the coordinated scheduling of multi-energy complementary systems. Attached Figure Description

[0025] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the overall process of a high-dimensional multi-objective optimization method with interval constraints for multi-energy complementary systems according to the present invention. Figure 2 This is a schematic diagram of the multi-energy complementary system architecture in this invention. Figure 3 This is a schematic diagram of the real-time time window decision space in this invention. Figure 4 and Figure 5 The graph shows the trend of objective function changes for different methods in representative implementation scenarios. Detailed Implementation

[0027] This implementation method, starting from the actual scheduling requirements of multi-energy complementary systems, first constructs an optimized scheduling model for the coordinated operation of wind power, photovoltaic, thermal power, and energy storage; then, based on this model, it constructs a decision space and forms initial candidate schemes; subsequently, iteratively evaluates, updates, and filters the candidate schemes; finally, it outputs an optimized scheduling scheme that meets the system's operational requirements. Based on this, this implementation method provides an interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems, including:

[0028] Step 1: Construct a high-dimensional multi-objective optimization model with interval constraints for multi-energy complementary systems.

[0029] The high-dimensional multi-objective optimization model with interval constraints for multi-energy complementary systems is established as follows:

[0030] 1. Basic Architecture Setup:

[0031] like Figure 2 As shown, the multi-energy complementary system involved in this invention generally includes a power supply side, a power receiving side, and a dispatch control side. The power supply side includes wind farms, photovoltaic power plants, thermal power plants, and battery energy storage systems; the power receiving side includes the demand side and the power grid; and the dispatch control side is a computing service center. These components cooperate to form a multi-energy collaborative operation architecture integrating power generation, energy storage, power transmission and distribution, and load response, providing a foundation for the establishment of subsequent optimized dispatch models.

[0032] In the above context, wind farms, photovoltaic power plants, thermal power plants, and battery energy storage systems jointly undertake the tasks of power supply and regulation. Their power output is transmitted to the power grid after unified coordination to meet the electricity demand on the demand side. The demand side includes mobile terminals, industrial production systems, and lighting systems, which are used to represent different types of electricity loads. The computing service center is used to receive short-term load forecast data, wind power generation capacity forecast data, and photovoltaic power generation capacity forecast data, and generate corresponding scheduling plans based on the data, thereby realizing unified coordination and control of the multi-energy complementary system.

[0033] Assume the number of thermal power units is , No. Taiwan thermal power units in the time window The electricity generated within is expressed as Its start / stop status is represented as .in, ,when When, it indicates that the thermal power unit is in a shutdown state. At this time, it indicates that the thermal power unit is in the startup state. Each energy storage unit within the time window The amount of discharge within is expressed as Its maximum discharge power is expressed as Its time window The remaining energy storage capacity is expressed as Users in the time window The load demand within is expressed as .

[0034] 2. Characterization of Uncertainty and Three Rolling Time Windows:

[0035] Given the randomness and volatility of wind power output and photovoltaic output, this invention preferably uses an interval form to characterize the uncertainty of wind power output and photovoltaic output, specifically expressed as follows: In the formula, Indicates time window Wind power output within the region Indicates time window Internal photovoltaic power output; and These represent time windows. Lower and upper limits of internal wind power output and These represent time windows. The lower and upper limits of internal photovoltaic power output.

[0036] The present invention preferably adopts a three-rolling time window structure consisting of a historical time window, a real-time time window, and a prediction time window, which is used to characterize the historical operating status, current scheduling status, and future trend of the multi-energy complementary system during continuous operation.

[0037] in, Indicates a historical time window, Indicates the real-time time window. This represents the prediction time window. The historical time window is used to represent the known historical operating state, the real-time time window is used to output the current scheduling decision, and the prediction time window is used to provide forward-looking information for the current decision.

[0038] The data in the historical time window are known and definite values. The wind power output and photovoltaic output in the real-time time window and the prediction time window are characterized by the above-mentioned interval parameters to reflect the uncertainty brought about by the fluctuation of renewable energy to the system operation.

[0039] 3. Establishing multiple optimization objectives:

[0040] After completing the basic architecture construction of the multi-energy complementary system and the characterization of the three rolling time windows and uncertainties, in order to ensure that the established scheduling model can simultaneously take into account environmental protection, economy and stability, this invention further establishes multiple optimization objectives to uniformly characterize the comprehensive performance of the multi-energy complementary system in the rolling scheduling process.

[0041] Specifically, environmental friendliness is used to characterize the carbon emission level, pollutant emissions, and renewable energy utilization during system operation; economic efficiency is used to characterize the overall operating cost during system scheduling; and stability is used to characterize the operating status of thermal power units and the supply-demand matching of the system. Based on the above three aspects, the following optimization objectives are further constructed:

[0042] The first optimization objective is to minimize carbon emissions. To reduce the carbon emission level of the multi-energy complementary system during the rolling dispatch cycle, the total life-cycle carbon emissions of thermal power, wind power, and photovoltaic power generation within the real-time and forecast time windows are taken as the optimization objective, and its mathematical expression is: , Wind power output and photovoltaic power output are represented using intervals, and their corresponding carbon emission contributions are also expressed as interval values. Thermal power generation is a fixed value, and its corresponding carbon emission contribution is also a fixed value. When adding the fixed value to an interval, it is added to both the upper and lower bounds of the interval, and the result is still an interval. After adding, the total carbon emissions are obtained. Let be an interval value, where This indicates the lower bound of total carbon emissions. This represents the upper limit of total carbon emissions. The carbon emission factor represents the entire life cycle of thermal power generation. The carbon emission factor represents the entire life cycle of wind power operation; This represents the carbon emission factor throughout the entire life cycle of photovoltaic power generation.

[0043] This objective involves uniformly converting the power generation contributions from thermal power, wind power, and photovoltaic (PV) into carbon emissions within the dispatch cycle and then summing them up. Wind and PV power generation are entered into the objective function in an interval format to reflect the range of carbon emission levels under fluctuating renewable energy output. The smaller this target value, the lower the overall carbon emission level of the system while meeting power supply demands.

[0044] The second optimization objective is to minimize peak-shaving costs. To balance system dispatch economy with the operational costs of thermal power units participating in peak shaving, the total cost comprised of unit startup and fuel consumption is defined as the peak-shaving cost, calculated using the following formula: .in Indicates peak shaving cost, This indicates the start-up and shutdown costs of thermal power units. This indicates the cost of fuel consumption.

[0045] The formula for calculating the start-up and shutdown costs of thermal power units is as follows: ,in: Indicates the first Start-up and shutdown cost parameters for Taiwan's thermal power units. Indicates the first The start-up and shutdown status of the thermal power unit within the previous time window. In the above formula, This is used to characterize the startup behavior of a unit transitioning from shutdown to startup between adjacent time windows. Specifically, this invention uses the startup event of a thermal power unit as the cost trigger condition when calculating startup and shutdown costs. If the unit's state remains unchanged, this part is set to 0, and no corresponding startup cost is generated.

[0046] The formula for calculating fuel consumption costs is: ,in Indicates coal price, , and They represent the first The coal consumption coefficient of a Taiwanese thermal power unit. From this formula, we can see... This reflects the additional costs incurred by thermal power units due to frequent start-ups caused by load changes. This reflects the fuel consumption level of thermal power units at a given output level. The purpose of this target is to minimize unnecessary unit start-ups and avoid prolonged high-coal-consumption operation of thermal power units while ensuring power supply reliability. A smaller target value indicates lower economic costs for the system in fulfilling peak-shaving tasks and better economic efficiency of the dispatching scheme.

[0047] The third optimization objective is to minimize the cost of pollutant penalties. To characterize the comprehensive environmental and social burden of nitrogen oxides, sulfur dioxide, and particulate matter emissions during thermal power generation, the total cost of pollutant emissions, calculated using appropriate penalty factors, is defined as the cost of pollutant penalties. ,in , and They represent the first Taiwan thermal power units in the time window The costs of nitrogen oxides, sulfur dioxide, and particulate matter generated within the environment.

[0048] The penalty costs for each type of pollutant are defined as follows: , , }in: , and These represent the emission factors for nitrogen oxides, sulfur dioxide, and particulate matter, respectively. , and These represent the penalty factors for nitrogen oxides, sulfur dioxide, and particulate matter, respectively.

[0049] This target translates pollutant emissions into environmental costs; the higher the output of the thermal power unit, the higher the corresponding environmental cost. A smaller target value indicates that the system, while fulfilling its power supply task, has less negative impact on the air and ecological environment, and is more environmentally friendly.

[0050] The fourth optimization objective is to minimize the load balance of thermal power units. To prevent some thermal power units from bearing excessively high loads for extended periods, avoid localized overloads, and improve the coordination of output distribution among units, the deviation of the actual load borne by a thermal power unit from the average load of currently operating units is defined as the load balance objective, and its mathematical expression is: .in Indicates the first Taiwan thermal power units in the time window The actual amount of electricity generated within the area. Indicates time window The average power generation capacity of all operating thermal power units within the region. Indicates time window The total power generation capacity of all operating thermal power units within the region. Indicates time window The number of thermal power units currently in operation.

[0051] In the above formula, the absolute value term represents the deviation between the actual load of a single thermal power unit and the current average load. The sum of the deviations of all units and all time windows yields the overall load imbalance of the system. If some units operate above average load for extended periods, while others operate below average load, the target value will increase; conversely, if the load on each operating unit is relatively evenly distributed, the target value will decrease. A smaller target value indicates a more balanced power distribution among the thermal power units, which helps reduce individual unit overload, improve equipment reliability, and enhance the system's adaptability to external disturbances.

[0052] The fifth optimization objective is to minimize the ramp rate. To reduce the mechanical stress and operational shock caused by rapid changes in the output of thermal power units between adjacent time windows, the rate of change in output of each thermal power unit between consecutive time windows is defined as the ramp rate objective, and its mathematical expression is: . Indicates time window The previous moment corresponds to the historical time window or the previous scrolling window; Indicates the length of the time window.

[0053] This target is calculated by dividing the output change of thermal power units between adjacent time windows by the time window length to obtain the unit output adjustment speed. The absolute value sign indicates that regardless of whether the unit output increases or decreases, if the change is too large, it will be considered a factor detrimental to the stable operation of the system and will be penalized. The smaller this target value, the smoother the output adjustment of thermal power units over time, which can effectively reduce the impact of rapid fluctuations in net load on the power grid, reduce equipment wear, extend unit life, and improve the stability of the system regulation process.

[0054] The sixth optimization objective is to maximize the proportion of renewable energy. To increase the proportion of wind and solar power in the total system power generation and enhance the system's clean energy absorption capacity, the proportion of renewable energy power generation to total power generation is defined as the renewable energy proportion objective. Since this invention uniformly uses a minimization approach for solution, the negative of the renewable energy proportion is preferably used as the optimization objective, and its mathematical expression is: The numerator represents the sum of wind and solar power generation during the dispatch period; the denominator represents the total power generation of the system during the dispatch period, which is the sum of thermal power generation and wind and solar power generation; the negative sign before the formula is used to transform maximizing the proportion of renewable energy into minimizing the objective value under a unified solution framework.

[0055] This target reflects the contribution of wind and solar power to the overall energy supply structure. A higher proportion of renewable energy indicates a higher utilization rate of clean energy in the system and a relatively lower reliance on thermal power. Since wind and solar power generation are expressed in interval form, this proportion target also exhibits interval characteristics, more accurately reflecting the range of changes in the system's clean energy supply capacity under conditions of renewable energy fluctuations. After adopting the aforementioned negative value form, The smaller the value, the higher the proportion of renewable energy in its original sense, the stronger the system's ability to absorb new energy, and the cleaner the energy structure.

[0056] The seventh optimization objective is to minimize the deviation between power generation and electricity load demand. To ensure the best possible match between supply-side power generation capacity and demand-side load demand, the relative deviation between total power generation and load demand is defined as the supply-demand deviation objective, whose mathematical expression is: .in Indicates time window Total power generation of all thermal power units in the area. Indicates time window Internal wind power generation range Indicates time window Internal photovoltaic power generation range Indicates time window Total load demand on the internal user side.

[0057] In the above formula, the fractional term represents the ratio of total power generation to load demand. When this ratio equals 1, it indicates that supply and demand are perfectly matched within the time window; when the ratio is greater than 1, it indicates that power generation exceeds load demand; and when the ratio is less than 1, it indicates that power generation is lower than load demand. By subtracting 1 from this ratio and taking the absolute value, both insufficient and excessive power supply can be uniformly measured. The smaller this target value, the closer the total power generation of the system is to the actual load demand within each time window, indicating a higher degree of supply-demand matching. This is beneficial for improving the reliability of power supply and reducing curtailment and reserve pressure.

[0058] In summary, the seven optimization objectives mentioned above together constitute a multi-objective optimization system for the rolling scheduling of multi-energy complementary systems, used to comprehensively evaluate the system's operating status from three aspects: environmental friendliness, economy, and stability. To ensure that the optimization results meet actual operational requirements and that the resulting scheduling scheme is feasible, this invention further sets corresponding constraints based on the aforementioned optimization objectives:

[0059] 1. Upper and lower limits of power generation capacity of thermal power units: .in, Indicates the first The minimum power output of a thermal power unit in Taiwan; Indicates the first The highest power output of the thermal power unit in Taiwan.

[0060] 2. Upper and lower limits of gradient rate constraints for thermal power units: .in, Indicates the first The maximum downhill gradient of the thermal power unit; Indicates the first The maximum uphill gradient of the thermal power unit.

[0061] 3. Constraints of Energy Storage Units: .in, Indicates time window Inner The discharge amount of each energy storage unit; Indicates the first Maximum discharge power of each energy storage unit; Indicates time window Inner The remaining energy storage capacity of each energy storage unit.

[0062] 4. Electrical load constraints: .in, Indicates the first The discharge efficiency of an energy storage device.

[0063] Thus, a high-dimensional multi-objective optimization model with interval constraints for multi-energy complementary systems is constructed, providing a unified system of objective functions and constraints for subsequent solution processes. This high-dimensional multi-objective optimization model with interval constraints for multi-energy complementary systems is denoted as InTriTime-MEC (Interval-constrained Many-objective Multi-energy Complementary model with Three Rolling Time Windows).

[0064] Step 2: Construct the decision space of the optimization model and initialize the reference vector, leader population, and follower population.

[0065] After constructing the interval-constrained high-dimensional multi-objective optimization model for the multi-energy complementary system in step one, a decision space corresponding to the optimization model is further constructed, and a reference vector, a leader population, and a follower population are initialized. The decision space represents the range of values ​​for all candidate scheduling schemes within the current optimization cycle; the reference vector is used to partition the multi-objective space into regions; the leader population guides candidate schemes to converge towards a better direction; the follower population enhances the search capability for boundary regions, low-density regions, and unexplored regions, thus providing a foundation for subsequent dual-population co-evolutionary solutions; and each individual represents a specific candidate scheduling scheme in the decision space, with subsequent population evolution, fitness evaluation, and environment selection all taking individuals as the basic processing object.

[0066] First, considering that the InTriTime-MEC constructed in this invention comprehensively considers three types of time windows: historical time windows, real-time time windows, and prediction time windows, the information corresponding to historical time windows is known and certain, and therefore is not used as an optimization decision variable for the current period; real-time time... The window reflects the actual scheduling needs at the current moment, and the prediction time window. This reflects the predicted scheduling information for the next time period. Therefore, this invention incorporates real-time time windows into the decision variables. and prediction time window Operating status of thermal power units inside With power generation Information is used to construct the decision space for the current optimization cycle.

[0067] Based on the above three-rolling time window setting method, the decision space of the optimization model is represented as a combination of the real-time time window decision subspace and the prediction time window decision subspace: .in: This represents the overall decision vector for the current optimization cycle; This represents the real-time time window decision subspace; This represents the decision subspace for the prediction time window. The real-time time window decision subspace is represented as: The prediction time window decision subspace is represented as: .in Indicates the number of thermal power units. Indicates the first Taiwan thermal power units in real-time time window The start / stop status within the system. Indicates the first Taiwan thermal power units in real-time time window Electricity generation within the region Indicates the first Taiwan thermal power units in the predicted time window The start / stop status within the system. Indicates the first Taiwan thermal power units in the predicted time window The amount of electricity generated within the region.

[0068] It should be noted that the decision variables in the real-time time window are used to form the actual dispatch output at the current moment and are output to the corresponding power generation unit; the decision variables in the predictive time window only serve as auxiliary supporting information for real-time time window optimization and are not directly used as the execution output at the current moment. As the time window rolls forward, in the next optimization cycle, the original predictive time window... This will be transformed into a new real-time time window, allowing for further real-time optimization. Its rolling relationship can be represented as follows: .in Indicates the first Predictive time window decision information in each optimization cycle Indicates the first Real-time time window decision information within each optimization cycle.

[0069] Furthermore, to ensure that the decision space matches the constraint system established in step one, all decision vectors satisfying all constraints constitute the feasible decision space, denoted as . .in, any decision vector All satisfy the upper and lower limits of thermal power unit generating capacity, upper and lower limits of ramp rate, energy storage unit constraints, and electricity load constraints established in step one. Based on this, any decision vector After mapping through the seven optimization objective functions in step one, the corresponding interval objective vector is obtained. .in Represents the decision vector The corresponding interval target vector, Indicates the number of objective functions. Indicates the first The lower bound of the interval for each objective function. Indicates the first The upper bound of the interval for each objective function.

[0070] To accommodate the subsequent high-dimensional multi-objective optimization solution process with interval constraints, this invention further initializes a set of reference vectors for dividing the target space into regions, providing a foundation for subsequent individual region attribution determination, boundary region identification, unexplored region marking, and environment selection processes. The reference vectors are preferably uniformly distributed in... In the target space, its expression is: , , .in, Represents the set of reference vectors; Indicates the first One reference vector; Indicates the first The reference vector at the th reference vector in the th ... Components in each target dimension.

[0071] After the reference vector is initialized, further initialization is performed on all vectors of the same size. The leader population and follower population. The leader population is represented as... The follower population is represented as... . Represents the first leader in the initial leader population. Individual, Represents the first in the initial follower population Each individual variable is initialized using a random initialization method on the decision variables.

[0072] For any given individual generated, it is essentially a candidate scheduling scheme containing decision information from both the real-time time window and the prediction time window, which can be uniformly represented as: .in Indicates the first One candidate individual, This represents the decision sub-vector corresponding to the candidate individual within the real-time time window. This represents the decision sub-vector corresponding to the candidate individual within the prediction time window.

[0073] After initializing the reference vector, leader population, and follower population, the relevant operating parameters are further set. These parameters include the learning rate. and the maximum number of evaluations Since both the leader and follower populations have already undergone one initialization generation, the current evaluation count is initialized to: Through the above steps, the construction of the decision space of the optimization model and the initialization of the reference vector, leader population, and follower population are completed. This enables subsequent steps to carry out dynamic Stackelberg uncertainty weight adjustment and dual-population co-evolution solutions based on a unified decision expression, unified target mapping, and unified population structure.

[0074] Step 3: Construct a comprehensive evaluation function for the leader population and perform dynamic Stackelberg uncertainty weight adjustment.

[0075] After initializing the reference vector, leader population, and follower population in step two, this invention constructs a comprehensive evaluation function for the leader population to dynamically balance convergence and uncertainty at different evolutionary stages. Based on this function, a dynamic Stackelberg uncertainty weight adjustment method is proposed, specifically including the following two points:

[0076] 1. Constructing a comprehensive evaluation function for the leader population

[0077] Since the objective function in interval-constrained high-dimensional multi-objective optimization problems has interval characteristics, it is necessary to integrate the convergence and uncertainty of individual components into a single fitness evaluation function. Convergence characterizes how closely the candidate scheduling scheme approximates the overall optimal result, while uncertainty characterizes the stability and reliability of the scheme under conditions of renewable energy output and load fluctuations. Let the individual... The The target for each interval is represented as: , .in, Indicates the number of objective functions; and They represent the first The lower and upper bounds of the interval for each target.

[0078] To eliminate the influence of differences in the dimensions of different objectives, each objective is first normalized. Let the normalized objective be... One goal is , No. The normalized upper and lower bounds of the intervals are respectively: , ;in, and They represent the first and second digits in the current population, respectively. The minimum and maximum values ​​of each target.

[0079] Based on this, define the individual The convergence evaluation term is Uncertainty evaluation item is ; respectively represented as: and ;in: Indicates the first The weighting coefficients of each objective. Indicates the first The normalized center value of each interval target Indicates the first The normalized interval width of each interval target.

[0080] Furthermore, a fitness function incorporating dynamic Stackelberg uncertainty weights is constructed: The fitness function is used to comprehensively evaluate the quality of individuals. Its function value reflects the overall performance of an individual in terms of convergence, uncertainty, and constraint satisfaction. Subsequently, better individuals are selected based on the fitness function value to enter the next stage of the evolutionary process. Represents an individual Given weight parameters The mating fitness function under the following conditions, when When the size is small, the method focuses more on convergence; when... When the value is large, the method focuses more on reducing uncertainty. The degree of constraint violation for each individual is then calculated. Let there be a total of [number missing] constraints in step one. Inequality constraints ,as well as Equality constraints Then the individual The The degree of violation of class constraints can be expressed as: .in This represents the constraint relaxation factor. Therefore, the individual... The total degree of constraint violation is It also indicates the feasibility of an individual, when When this occurs, it indicates that the individual is a feasible individual. When this occurs, it indicates that the individual is an infeasible individual.

[0081] Through the above steps, the comprehensive evaluation function of the leader population is constructed, providing an evaluation basis for subsequent dynamic Stackelberg uncertainty weight adjustment.

[0082] 2. Dynamic Stackelberg Uncertainty Weight Adjustment

[0083] After constructing the leader population comprehensive evaluation function, two candidate mating pools are initialized, denoted as follows: , Simultaneously, two candidate Stackelberg uncertainty weight parameters are set: , .in: This represents the current generation of dynamic Stackelberg uncertainty weight parameters. The parameter represents the uncertainty weight fluctuation value. and They are used to store the candidate individual sets obtained under different weight parameters.

[0084] Then, for each individual in the leader population, based on and Calculate the fitness function value and construct two candidate mating pools according to the principles of feasibility priority and fitness priority. For any two individuals... and If and only if one of the following conditions is met: , or , or , , Then it is defined as: Using the above rules, we can obtain the following: , .in, This indicates a candidate mating pool selection operation based on weight parameters.

[0085] After constructing the two candidate mating pools, the uncertainty weight parameters are further updated using gradient descent. Let the evaluation index function be... Here As an independent variable, it is used to characterize the changes in the evaluation index under different weight parameter values. Among them, This represents the inverse generational distance within the interval, used to evaluate the proximity between the current candidate non-dominated solution set and the ideal Pareto front sample point set; the smaller the value, the better the current weight setting. The weight update rule can then be expressed as: .in: Indicates the learning rate. This represents the gradient of the evaluation metric with respect to the current weight parameters.

[0086] Finally, the updated dynamic Stackelberg uncertainty weights are... The results are passed on to the next generation of leader populations and simultaneously to follower populations for subsequent local search and environment selection processes. Through these steps, dynamic Stackelberg uncertainty weights are adjusted, causing the leader population to prioritize convergence in the early stages of optimization and to prioritize reducing interval uncertainty in the later stages, thus providing dynamic guidance for the co-evolution of the two populations.

[0087] Step 4: Implement a local search strategy within the follower population.

[0088] After completing the dynamic Stackelberg uncertainty weight adjustment in step three, a local search strategy is further implemented in the follower population to increase the probability of boundary individuals being selected as parents and enhance the search capability for unexplored areas, as follows. First, let the current generation of follower population be: Furthermore, the local search pool, global search pool, and unexplored region set are initialized, denoted as follows: , , .in: Indicates a local search pool. Represents the global search pool. This represents the set of unexplored regions. Combined with the reference vector set obtained during initialization in step two above, this gives... Therefore, it can be known that for any individual follower The region to which a target vector belongs is determined based on the angle or cosine distance between its target vector and each reference vector: ,in: Represents an individual The target vector, Represents the individual target vector and the first The angle or cosine distance between the reference vectors Represents an individual The region code to which it belongs.

[0089] After determining the region affiliation, the number of individuals within each region is counted, and the first [individual] is defined. The regional density of each region is: .when When, explain the first The region currently has no individuals assigned to it, which means it is an unexplored region. Therefore: .

[0090] Furthermore, for any individual ,like If the density is small, the corresponding area is considered an unexplored or low-density area, and its priority for entering the local search pool should be increased. The lower the density of the area to which an individual belongs, the greater the probability of it being selected into the local search pool; when an individual is located near a boundary area or an unexplored area, its probability of being selected also increases due to the low density of the corresponding area. This is to increase the probability of boundary individuals being selected, thereby strengthening the exploration of unknown areas. Accordingly, two reference variables are randomly selected from the follower population. and ,like , and then from Two individuals are randomly selected from their neighborhood and added to the local search pool. As the parent generation; in addition, two individuals are randomly selected from the global pool and added to the global search pool. Repeat the above selection process until the sizes of the local and global search pools reach the preset requirements. Then, the search pool with the better IIGD value will be selected as the new follower population search pool. Then As a new pool for searching follower populations, the opposite will... As a new follower population search pool.

[0091] Through the above steps, a local search strategy is executed within the follower population. This allows the follower population to prioritize localized enhanced searches around boundary individuals, individuals in low-density areas, and individuals near unexplored areas. This enhances the population's coverage and diversity within the target space and provides a basis for candidate individuals in the environmental selection process of the follower population in step five.

[0092] Step 5: Perform follower population environment selection.

[0093] After completing the local search strategy in step four, environmental selection is further performed on the follower population to select the next generation of follower individuals from the candidate individuals. The environmental selection of the follower population focuses on balancing regional exploration ability, constraint feasibility, and overall individual fitness, as detailed below:

[0094] 1. Constructing a candidate set of follower populations:

[0095] First, the parent generation of the follower population, the offspring generation of the follower population, and the offspring generation of the leader population are mixed to construct a candidate set of the follower population, represented as: ;in: This indicates the current generation of follower population. This represents the offspring of the follower population obtained through the local search and mating operation in step 4. Indicates the offspring of the leader population. This represents the set of candidate followers used for environmental selection;

[0096] 2. Divide the set of individuals into feasible and infeasible sets:

[0097] Furthermore, for the candidate set any individual Calculate the degree of constraint violation. Assume there are a total of [number missing] constraints in step one. Inequality constraints ,as well as Equality constraints The candidate set can be... Divide into a set of feasible individuals and a set of infeasible individuals. , ,in, Represents the set of feasible individuals. This represents the set of infeasible individuals. Based on this, and according to the partitioning results of the reference vector in step four, the region to which each individual belongs is determined.

[0098] 3. Determine the region to which an individual belongs and calculate the region density:

[0099] Let the set of reference vectors be Then the individual The region can be represented as: .in: Represents an individual The reference vector region to which it belongs Represents an individual The corresponding target vector, Represents the target vector With reference vector The angle or cosine distance between them.

[0100] Furthermore, the number of individuals in each region is counted, and the first [individual] is defined. The regional density of each region is ,in, Indicates the first The number of individuals within a region. If If so, it means that the area is an unexplored area; if A smaller value indicates a low-density region. Let the set of unexplored regions be: Let the set of low-density regions be: ,in, This represents the threshold for identifying low-density areas. Subsequently, environmental selection is performed on candidate individuals. The selection principles are as follows.

[0101] 4. Implement the four-layer environment selection principle:

[0102] Candidate individuals are screened in descending order of priority, as follows: feasibility priority > greater than unexplored areas priority > low-density areas priority > dynamic fitness determination, any two individuals and The selection rules are as follows.

[0103] Feasibility priority principle: For any two candidate individuals and If satisfied Individuals will be given priority in preservation. If neither of these two options is feasible, then the individual with the lesser constraint violation will be retained first. In the formula, Represents an individual Prioritizing the individual in environmental choices .

[0104] Unexplored Area Priority Principle: If two candidate individuals are indistinguishable in terms of feasibility, their respective areas are further compared. Let... and Individuals located in unexplored areas will be given priority for preservation. ,Right now: , This rule is used to improve the population's coverage of underdeveloped areas of the target space.

[0105] Low-density area priority principle: If neither of the two candidate individuals belongs to an unexplored area, and their feasibility cannot be distinguished, then the density of their respective areas is further compared. If there are... Individuals located in lower-density areas will be preferentially retained. ,Right now This rule is used to mitigate the problem of excessive aggregation of individuals in localized high-density areas and to maintain the diversity of follower populations.

[0106] Dynamic fitness discrimination principle: When two individuals are difficult to distinguish in terms of feasibility, regional exploration status and regional density, a fitness function constructed using dynamic Stackelberg uncertainty weights passed from the leader population is used to further distinguish the superiority or inferiority of individuals.

[0107] Let the dynamic Stackelberg uncertainty weights obtained in step three be... Then the individual The overall fitness function can be expressed as: .in Represents an individual The overall fitness value, Represents an individual Convergence evaluation terms, Represents an individual Uncertainty evaluation item, This represents the dynamic Stackelberg uncertainty weights in the current iteration phase. If it satisfies... Then the individual is preserved. ,Right now

[0108] 5. Follower Population Update:

[0109] According to the selection rules described above, from the candidate set Individuals are selected sequentially until a preset size is obtained. The new generation of follower population: , This refers to a new generation of follower populations formed through environmental selection.

[0110] Through the above steps, the follower population's environmental selection can not only prioritize the retention of individuals with less constraint violation, but also prioritize the retention of individuals located in unexplored and low-density areas. When necessary, it can further complete the individual discrimination by using the comprehensive fitness function formed by the dynamic Stackelberg uncertainty weights, so that the follower population can maintain good diversity and the ability to explore unknown areas in the subsequent evolution process.

[0111] Step Six: Execute Leader Population Environment Selection.

[0112] After completing the follower population environment selection in step five, further environment selection is performed on the leader population to select the next generation of leaders from the candidate individuals, so that the leader population can retain better individuals while taking into account the evenness of distribution, as follows.

[0113] 1. Constructing the candidate set of leaders for the population:

[0114] First, let the current generation of leaders be: Let the set of leader offspring obtained through mating, mutation, or co-evolution be: Then the candidate set corresponding to the leader population environment selection is represented as: In the formula: This refers to the offspring of the current generation of leaders. This represents the set of offspring individuals from the current generation of the follower population. Since the follower population can discover potential high-quality individuals in areas not yet covered by the leader population, the offspring of the follower population are included in the candidate set during the leader population's environmental selection process to enhance the synergy between the two populations and the retention of high-quality individuals.

[0115] Furthermore, for the candidate set any individual in Calculate its interval target vector ,in Indicates the number of objective functions. Indicates the index of the objective function. and Each represents an individual In the The lower bound and upper bound of the interval for each target.

[0116] 2. Determining the dominance relationship between intervals and defining the non-dominant frontier:

[0117] Since the leader population environment selection needs to both prioritize the retention of better individuals and maintain a uniform distribution of individuals, it is necessary to first identify non-dominant individuals in the candidate set, and then further screen them based on the degree of crowding or density distribution among individuals.

[0118] For any two candidate individuals and The interval dominance relationship is defined as follows:

[0119] If for any target All satisfy: and And there is at least one target. satisfy and Then it is considered that the individual Interval Dominant Individuals , denoted as: In the formula, This represents the interval dominance relationship. Based on the above interval dominance relationship, the candidate set can be... Divided into several layers of non-dominated frontier: .in, Indicates the first layer of non-dominated frontier. Indicates removal The second layer of non-dominated frontier is then obtained, and so on.

[0120] 3. Feasibility assessment, dividing the individual sets into feasible and infeasible categories:

[0121] Furthermore, combining the constraints from step one, the total constraint violation degree is calculated for each individual in the candidate set, dividing the set into feasible / infeasible sets. Let the individual... The total degree of constraint violation is: .in: Indicates the first Inequality constraints Indicates the first Equality constraints, This represents the relaxation factor of the equality constraint. Therefore, the set of leader candidates can be divided into a set of feasible individuals and a set of infeasible individuals: and During the environmental selection process, feasible individuals are given priority; if the number of feasible individuals is insufficient, then individuals are added from the infeasible individuals according to the degree of constraint violation, from smallest to largest. Represents the set of feasible individuals. This represents a set of infeasible individuals.

[0122] 4. Evaluation of individual distribution based on interval density estimation:

[0123] When the number of individuals in a certain layer of the non-dominated front exceeds the current number of remaining retainable individuals, further screening based on the distribution of individuals in the target space is required. Therefore, displacement-based interval density estimation is performed on the individuals in the non-dominated front. Let the individuals... In the The center value of the interval on each target is: Then the individual The interval center vector is represented as: Furthermore, define any two individuals and The displacement distance between them is: Based on this, we define an individual. The local density estimate is ,in: Represents an individual The set of neighboring individuals This indicates the prevention of small positive numbers with a denominator of zero. Represents an individual The local density estimate.

[0124] From the above formula, it can be seen that if an individual If there are many nearby individuals, then A larger size indicates that it is located in a high-density area; if an individual If there are few individuals in the surrounding neighborhood, then A smaller density indicates that the individual is located in a sparse region. Therefore, within the same non-dominant front, prioritizing the retention of individuals with lower densities is beneficial for improving the evenness of the leader population's distribution in the target space.

[0125] 5. Leader selection rules based on population environment:

[0126] The selection of the leader population is carried out according to the following rules. First, individuals are added to the new generation of leaders in descending order of strength according to the Pareto non-dominant front hierarchy. Let the new generation of leaders be: If the following conditions are met: Then the first All individuals in the non-dominated frontier join the new generation of leader population, that is: If the following conditions are met: This indicates that the number of individuals in the current non-dominated frontier exceeds the remaining retainable capacity, and in this case, it is necessary to... The individuals are sorted according to their local density estimates, with priority given to retaining individuals with lower densities. Let the sorted sequence of individuals be: And it satisfies: Then select the first one from them in sequence. Individuals are added to the new generation of leader population, that is: This approach allows for the maintenance of population uniformity near the Pareto front while prioritizing the convergence of the leader population.

[0127] 6. Output of Leader Population Environment Selection Results:

[0128] When the new generation of leaders meets: At this point, the current generation of leader population environment selection ends, and the resulting new generation of leader population is output to the next generation of iterations. Through the above steps, the leader population environment selection is completed, enabling the leader population to preferentially retain individuals with better interval non-dominance, higher constraint satisfaction, and more even distribution in the target space during subsequent evolution. This provides a guiding population with better convergence and distribution for the entire dual-population co-evolutionary process.

[0129] Step 7: Repeat steps 3 to 6. When the termination condition is met, output the final optimized scheduling scheme.

[0130] After completing the leader population environment selection in step six, determine whether the current method meets the preset termination condition. If the termination condition is not met, return to step three and continue to execute dynamic Stackelberg uncertainty weight adjustment, follower population local search, follower population environment selection, and leader population environment selection; if the termination condition is met, end the iteration process.

[0131] After the operation terminates, the set of non-dominated solutions in the leader population is output, and this set is used as the result of interval-constrained high-dimensional multi-objective optimization for multi-energy complementary systems. Decision-makers can select the corresponding optimized scheduling scheme from the set of non-dominated solutions based on system operational requirements, serving as the basis for actual scheduling in the current rolling cycle.

[0132] The interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems proposed in this invention uses the interval inverse generation distance (IIGD) and the distribution uniformity (SP) as performance evaluation indicators in simulation experiments to compare the solution performance of the proposed method with comparative methods. IIGD characterizes the closeness between the obtained non-dominated solution set and the ideal Pareto front; a smaller IIGD value indicates better convergence performance. SP characterizes the uniformity of the distribution of the obtained non-dominated solutions in the objective space; a smaller SP value indicates better distribution uniformity. In addition to the above indicators, the objective functions of carbon emissions, peak-shaving costs, pollutant penalty costs, thermal power unit load balancing, ramp-up rate, renewable energy share, and the deviation between power generation and electricity load demand are further compared and analyzed to verify the comprehensive optimization effect of the proposed method.

[0133] Figure 1The overall process of the method of this invention is demonstrated. First, a high-dimensional multi-objective optimization model with interval constraints for multi-energy complementary systems is constructed, and a decision space under three rolling time windows is established. Then, the reference vector, leader population, and follower population are initialized. Next, dynamic Stackelberg uncertainty weight adjustment is performed in the leader population, and a local search strategy is performed in the follower population, and the environment selection of the follower population and the leader population are completed respectively. Finally, the iteration is repeated until the termination condition is met, and a set of non-dominated optimal scheduling schemes is output.

[0134] Figure 2 This invention demonstrates the multi-energy complementary system architecture addressed by this invention. The system includes a wind farm, a photovoltaic power plant, a thermal power plant, a battery energy storage system, a demand side, a power grid, and a computing service center. The computing service center receives load forecasting information and renewable energy output forecasting information, and coordinates the operational decisions of each energy unit and energy storage unit, thereby achieving collaborative and optimized scheduling of the multi-energy complementary system.

[0135] Figure 3 This invention demonstrates the configuration of the three-rolling-window decision space. The historical time window records known operational information, the real-time time window outputs the current scheduling decision, and the predictive time window provides forward-looking information for the current scheduling. As the time windows roll forward, the original predictive time window transforms into a new real-time time window, thus achieving dynamic rolling optimization.

[0136] Figure 4 and Figure 5 This figure compares the optimization results of different methods on various objective functions in this embodiment. As shown in the figure, the method of the present invention exhibits good comprehensive optimization effects on multiple objectives, including carbon emissions, peak-shaving costs, pollutant penalty costs, thermal power unit load balancing, ramp-up rate, renewable energy ratio, and deviation between power generation and electricity load demand, and can provide a better scheduling scheme for multi-energy complementary systems.

[0137] Table 1: Statistical results of IIGD on the ZXH-CF1-7 test set for SBREA and five comparative methods.

[0138]

[0139] Table 2: Objective function values ​​of SBREA and five comparative methods on InTriTime-MEC

[0140]

[0141] The comparative experiment selected IMOEA / D and InMaOEA as comparison objects, and compared them with the SBREA method proposed in this invention. Table 1 shows that SBREA outperforms the comparative methods in most test problems on the ZXH-CF1-7 test set in terms of IIGD index, demonstrating better convergence performance. Table 2 shows that SBREA performs better in multiple objective functions of the InTriTime-MEC model in Scenario 1, especially in terms of carbon emissions, peak-shaving costs, pollutant penalty costs, renewable energy share, and the deviation between power generation and electricity load demand. In conclusion, the method proposed in this invention has good feasibility and effectiveness.

Claims

1. A high-dimensional multi-objective optimization method with interval constraints for multi-energy complementary systems, characterized in that, The multi-energy complementary system includes a power supply side, a power receiving side, and a dispatch control side; the power supply side includes wind farms, photovoltaic power plants, thermal power plants, and battery energy storage systems; the power receiving side includes the demand side and the power grid; and the dispatch control side is a computing service center. The method includes: Step 1: Construct a high-dimensional multi-objective optimization model with interval constraints for multi-energy complementary systems, including: Assume the number of thermal power units is , No. Taiwan thermal power units in the time window The electricity generated within is expressed as Its start / stop status is represented as ;in, ,when When, it indicates that the thermal power unit is in a shutdown state. When the time is specified, it indicates that the thermal power unit is in the startup state; the next time... Each energy storage unit within the time window The amount of discharge within is expressed as Its maximum discharge power is expressed as Its time window The remaining energy storage capacity is expressed as Users in the time window The load demand within is expressed as ; Establish a three-rolling time window and uncertainty representation, wherein the three-rolling time window includes a historical time window. Real-time time window and prediction time window It is used to characterize the historical operating state, current scheduling state, and future trend of a multi-energy complementary system during continuous operation; Multiple optimization objectives are established to uniformly characterize the comprehensive performance of the multi-energy complementary system during the rolling scheduling process; corresponding constraints are set based on the multiple optimization objectives. Step 2: Construct the decision space of the optimization model and initialize the reference vector, leader population, and follower population; wherein, the real-time time window is simultaneously included in the decision variables. and prediction time window Operating status of thermal power units inside With power generation Information is used to construct the decision space for the current optimization cycle; Step 3: Construct a comprehensive evaluation function for the leader population and execute the dynamic Stackelberg uncertainty weight adjustment method; The comprehensive evaluation function includes: incorporating the convergence and uncertainty of an individual into a single fitness evaluation function, wherein uncertainty is used to characterize the stability and reliability of the scheme under conditions of renewable energy output and load fluctuations; The dynamic Stackelberg uncertainty weight adjustment adaptively balances convergence and uncertainty through gradient descent, thereby generating a uniformly distributed non-dominated solution set; Step 4: Implement a local search strategy within the follower population; Step 5: Select the execution environment for the follower population based on regional exploration ability, constraint feasibility, and individual comprehensive fitness, so as to select the next generation of follower population from the candidate individuals; Step 6: Perform environmental selection on the leader population to select the next generation of leaders from the candidate individuals; Step 7: Repeat steps 3 to 6. When the termination condition is met, output the final optimized scheduling scheme.

2. The interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems according to claim 1, characterized in that: Step 1 includes: The uncertainty of wind power output and photovoltaic output is characterized using an interval form, specifically expressed as follows: In the formula, Indicates time window Wind power output within the region Indicates time window Internal photovoltaic power output; and These represent time windows. Lower and upper limits of internal wind power output and These represent time windows. Lower and upper limits of internal photovoltaic power output; The multiple optimization objectives specifically include: Minimize carbon emissions: , The total carbon emissions obtained Let be an interval value, where This indicates the lower bound of total carbon emissions. This indicates the upper limit of total carbon emissions; The carbon emission factor represents the entire life cycle of thermal power generation. The carbon emission factor represents the entire life cycle of wind power operation; This represents the carbon emission factor throughout the entire life cycle of photovoltaic power generation. Indicates the number of thermal power units; Minimize peak shaving costs: ;in Indicates peak shaving cost, This indicates the start-up and shutdown costs of thermal power units. Indicates fuel consumption cost; ,in: Indicates the first Start-up and shutdown cost parameters for Taiwan's thermal power units. Indicates the first The start-up and shutdown status of the thermal power units in the previous time window. Used to characterize the startup behavior of a unit transitioning from shutdown to startup between adjacent time windows; ,in Indicates coal price, , and They represent the first Coal consumption coefficient of a thermal power unit; Minimize the cost of pollutant penalties: ,in , and They represent the first Taiwan thermal power units in the time window The costs of nitrogen oxide emissions, sulfur dioxide emissions, and particulate matter emissions generated within the environment; Minimize load balancing of thermal power units: ;in Indicates the first Taiwan thermal power units in the time window The actual amount of electricity generated within the area. Indicates time window The average power generation capacity of all operating thermal power units within the region. Indicates time window The total power generation capacity of all operating thermal power units within the region. Indicates time window The number of thermal power units currently in operation; Minimize the rate of ascent: ; Indicates time window The previous moment corresponds to the historical time window or the previous scrolling window; Indicates the length of the time window; Maximizing the proportion of renewable energy: The numerator represents the sum of wind and solar power generation during the dispatch period; the denominator represents the total power generation of the system during the dispatch period; the negative sign before the formula is used to transform maximizing the proportion of renewable energy into minimizing the objective value under a unified solution framework. Minimize the deviation between power generation and electricity load demand: ;in Indicates time window Total power generation of all thermal power units in the area. Indicates time window Internal wind power generation range Indicates time window Internal photovoltaic power generation range Indicates time window Total load demand on the internal user side; The constraints include: upper and lower limits of power generation capacity of thermal power units, upper and lower limits of ramp rate of thermal power units, constraints of energy storage units, and constraints of electricity load; among which, constraints of energy storage units include constraints of discharge power of energy storage units and constraints of remaining energy storage capacity of energy storage units.

3. The interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems according to claim 1, characterized in that: In step 2, the method for constructing the decision space includes: The decision space of the optimization model is represented as a combination of the real-time time window decision subspace and the prediction time window decision subspace: ;in, This represents the overall decision vector for the current optimization cycle; This represents the real-time time window decision subspace; The prediction time window decision subspace is represented as: The real-time time window decision subspace is represented as: The prediction time window decision subspace is represented as: ;in, Indicates the number of thermal power units. Indicates the first Taiwan thermal power units in real-time time window The start / stop status within the system. Indicates the first Taiwan thermal power units in real-time time window Electricity generation within the region Indicates the first Taiwan thermal power units in the predicted time window The start / stop status within the system. Indicates the first Taiwan thermal power units in the predicted time window The amount of electricity generated within the region.

4. The interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems according to claim 1, characterized in that: Step 3 includes: Step 3.1: Construct a comprehensive evaluation function for the leader population, specifically including: Let individuals The The target for each interval is represented as: , ;in, Indicates the number of objective functions; and They represent the first The lower and upper bounds of the interval for each target; Let the normalized i One goal is , No. The normalized upper and lower bounds of the intervals are respectively: , ;in, and They represent the first and second digits in the current population, respectively. The minimum and maximum values ​​of each objective; Define individual The convergence evaluation term is Uncertainty evaluation item is ; respectively represented as: and ;in: Indicates the first The weighting coefficients of each objective. Indicates the first The normalized center value of each interval target Indicates the first The normalized interval width of each interval target; Construct a fitness function that includes dynamic Stackelberg uncertainty weights: ; Represents an individual Given weight parameters The mating fitness function under the following conditions, when When the size is small, the method focuses more on convergence; when... When the value is large, the method focuses more on reducing uncertainty; Assume there is a total Inequality constraints ,as well as Equality constraints Then the individual The The degree of violation of class constraints is: ;in This represents the constraint relaxation factor; thus, the individual The total degree of constraint violation is It also indicates the feasibility of an individual, when When, it indicates that the individual is a feasible individual; when When this occurs, it indicates that the individual is an infeasible individual; Step 3.2: Execute the dynamic Stackelberg uncertainty weight adjustment method, which specifically includes: Initialize two candidate mating pools, denoted as follows: , Simultaneously, two candidate Stackelberg uncertainty weight parameters are set: , ;in: This represents the current generation of dynamic Stackelberg uncertainty weight parameters. The parameter represents the uncertainty weight fluctuation value. and These are used to store the candidate individual sets obtained under different weight parameters; Then, for each individual in the leader population, based on and Calculate the fitness function value and construct two candidate mating pools according to the principles of feasibility priority and fitness priority; for any two individuals and If and only if one of the following conditions is met: , or , or , , Then it is defined as: ;get: , ;in, This indicates a candidate mating pool selection operation based on weight parameters. Indicates the current generation of leaders; The uncertainty weight parameters are updated using gradient descent; let the evaluation index function be... , As an independent variable, it is used to characterize the changes in the evaluation index under different weight parameter values; among them... The weight update rule is expressed as follows: (This represents the distance between generations in reverse order within the interval.) ;in: Indicates the learning rate. This represents the gradient of the evaluation metric with respect to the current weight parameters; Finally, the updated dynamic Stackelberg uncertainty weights are... It is passed on to the next generation of leader population and simultaneously transmitted to follower population for subsequent local search and environmental selection processes.

5. The interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems according to claim 1, characterized in that: Step 4 includes: First, let the current generation of follower population be: Initialize the local search pool, global search pool, and unexplored region set, denoted as follows: , , ;in: Indicates a local search pool. Represents the global search pool. Represents the set of unexplored regions; For any individual follower The region to which a target vector belongs is determined based on the angle or cosine distance between its target vector and each reference vector: ,in: Represents an individual The target vector, Represents the individual target vector and the first The angle or cosine distance between the reference vectors Represents an individual The area code to which it belongs; Count the number of individuals in each region, and define the first... The regional density of each region is: ;when When, explain the first The region currently has no individuals assigned to it, which means it is an unexplored region. Therefore: ; Two reference variables were randomly selected from the follower population. and ,like , and then from Two individuals are randomly selected from their neighborhood and added to the local search pool. As the parent generation; in addition, two individuals are randomly selected from the global pool and added to the global search pool. ; like Then As a new pool for searching follower populations, the opposite will... As a new follower population search pool.

6. The interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems according to claim 1, characterized in that: Step 5 includes: First, the parent generation of the follower population, the offspring generation of the follower population, and the offspring generation of the leader population are mixed to construct a candidate set of the follower population, represented as: ;in: This indicates the current generation of follower population. This represents the offspring of the follower population obtained through the local search and mating operation in step 4. Indicates the offspring of the leader population. This represents the set of candidate followers used for environmental selection; For candidate set any individual Calculate the degree of constraint violation; assume there are a total of [number] constraints in step 1. Inequality constraints ,as well as Equality constraints ; the candidate set Divide into a set of feasible individuals and a set of infeasible individuals. , ,in, Represents the set of feasible individuals. This represents the set of infeasible individuals; based on this, and according to the partitioning results of the reference vector in step 4, the region to which each individual belongs is determined; Let the set of reference vectors be Then the individual The region is represented as: ;in: Represents an individual The reference vector region to which it belongs Represents an individual The corresponding target vector, Represents the target vector With reference vector The angle or cosine distance between them; Count the number of individuals in each region, and define the first... The regional density of each region is ,in, Indicates the first The number of individuals within a region; if If so, it means that the area is an unexplored area; if A smaller value indicates that the region is a low-density region; let the set of unexplored regions be: Let the set of low-density regions be: ,in, This indicates the threshold for identifying low-density areas. The selection of the execution environment for candidate individuals specifically includes: For any two candidate individuals and If satisfied Individuals will be given priority in preservation. If neither of these options is feasible, then individuals with less constraint violation should be retained. If two candidate individuals are indistinguishable in terms of feasibility, then their respective regions are further compared; let... and Individuals located in unexplored areas will be given priority for preservation. ; If neither candidate belongs to an unexplored area and their feasibility cannot be distinguished, then further compare the density of their respective areas; if there are... Individuals located in lower-density areas will be preferentially retained. ; When two individuals are indistinguishable in terms of feasibility, region exploration status, and region density, a fitness function constructed using dynamic Stackelberg uncertainty weights passed down from the leader population is used to further differentiate the quality of individuals. Specifically, this includes: Let the dynamic Stackelberg uncertainty weights obtained in step 3 be... Then the individual The overall fitness function is expressed as: ;in Represents an individual The overall fitness value, Represents an individual Convergence evaluation terms, Represents an individual Uncertainty evaluation item, This represents the dynamic Stackelberg uncertainty weights in the current iteration phase; if it satisfies Then the individual is preserved. ; From the candidate set Individuals are selected sequentially until a preset size is obtained. The new generation of follower population: , This refers to a new generation of follower populations formed through environmental selection.

7. The interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems according to claim 1, characterized in that: Step 6 includes: Let the current generation of leaders be: Let the set of leader offspring obtained through mating, mutation, or co-evolution be: Then the candidate set corresponding to the leader population environment selection is represented as: In the formula: This refers to the offspring of the current generation of leaders. Represents the set of offspring individuals in the current generation of the follower population; for the candidate set any individual in Calculate its interval target vector ,in Indicates the number of objective functions. Indicates the index of the objective function. and Each represents an individual In the The lower and upper bounds of the interval for each target; For any two candidate individuals and Define the interval dominance relation: if for any target All satisfy: and And there is at least one target. satisfy and Then it is considered that the individual Interval Dominant Individuals , denoted as: In the formula, Represent the interval dominance relationship; based on the above interval dominance relationship, the candidate set is... Divided into several layers of non-dominated frontier: ;in, Indicates the first layer of non-dominated frontier. Indicates removal The second layer of nondominated frontier is then obtained, and so on; Based on the constraints in step 1, let the individual... The total degree of constraint violation is: ;in: Indicates the first Inequality constraints Indicates the first Equality constraints, This represents the relaxation factor of the equality constraint; thus, the set of leader candidates can be divided into a set of feasible individuals and a set of infeasible individuals. and During the environmental selection process, feasible individuals are given priority; if the number of feasible individuals is insufficient, then individuals are added from the infeasible individuals according to the degree of constraint violation, from smallest to largest. When the number of individuals in a certain non-dominated frontier exceeds the current number of remaining retainable individuals, let the number of individuals... In the The center value of the interval on each target is: Then the individual The interval center vector is represented as: Define any two individuals and The displacement distance between them is: Based on this, we define an individual. The local density estimate is ,in, Represents an individual The set of neighboring individuals This indicates a small positive number that prevents the denominator from being zero; Leader population environment selection specifically includes: First, individuals are introduced into the new generation of leader population in descending order of strength according to the Pareto non-dominant frontier hierarchy; let the new generation of leader population be: If the following conditions are met: Then the first All individuals in the non-dominated frontier join the new generation of leader population, that is: If the following conditions are met: Then for The individuals in the sequence are sorted according to their local density estimates, with priority given to retaining individuals with lower densities; let the sorted sequence of individuals be: And it satisfies: Then select the first one from them in sequence. Individuals are added to the new generation of leader population, that is: ; When the new generation of leaders meets: At that time, the current generation of leader population environment selection ends, and the resulting new generation of leader population is output to the next generation iteration process.

8. A high-dimensional multi-objective optimization system with interval constraints for multi-energy complementary systems, characterized in that: The system has a program module corresponding to the steps of any one of claims 1-7, and executes the steps in the interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems when running.

9. A computer device, characterized in that: It includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, it performs the steps of the interval-constrained high-dimensional multi-objective optimization method for multi-energy complementary systems according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that: The storage medium is used to store a computer program that executes a high-dimensional multi-objective optimization method with interval constraints for multi-energy complementary systems according to any one of claims 1-7.

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