A method and system for multi-objective coordinated optimization of direct current voltage levels of a photovoltaic system

Abstract

The present application relates to a kind of photovoltaic system direct current voltage grade multi-objective collaborative optimization method and system, its method includes: the direct current bus voltage grade of photovoltaic direct current power generation system, cable cross-sectional area and transmission distance are as the optimization variable of multi-objective collaborative optimization;Multi-objective optimization function strongly coupled with direct current bus voltage grade, cable cross-sectional area and transmission distance is constructed;Set multiple constraint conditions, and multi-objective optimization function is solved based on vertical and horizontal crossing optimization algorithm.The present application breaks through the static limitation of traditional empirical formula, realizes the multi-dimensional dynamic quantification of loss, economy, environmental protection;Through voltage grade, cross-sectional area, distance three-dimensional optimization framework, improve system comprehensive performance under multiple constraints;Application vertical and horizontal crossing algorithm effectively solves the problem of low convergence precision and insufficient diversity of high-dimensional multi-objective optimization, applicable to various photovoltaic power generation system direct current transmission scene, significantly improve the scientificity and economy of system voltage grade selection.

Description

Technical Field

[0001] This invention relates to the field of DC power transmission technology for photovoltaic power generation systems, and specifically to a multi-objective collaborative optimization method and system for DC voltage levels in photovoltaic systems. Background Technology

[0002] Photovoltaic DC transmission technology has become a core development direction for large-scale grid-connected renewable energy due to its advantages such as high transmission efficiency, low loss, and simplified power conversion process. Among these advantages, the selection of the DC bus voltage level is a key design parameter affecting the overall performance of the photovoltaic DC system.

[0003] However, traditional voltage level selection methods have significant technical bottlenecks that restrict the improvement of overall system performance: First, traditional methods generally use voltage sequence standards for AC transmission systems, relying on empirical formulas and static lookup tables, which cannot adapt to complex engineering scenarios with multivariate coupling and dynamic constraints, and are difficult to accurately determine voltage levels for specific scenarios; Second, existing methods have a single evaluation dimension, neither systematically quantifying the economic costs of the entire life cycle of equipment investment, operation and maintenance, and replacement, nor ignoring the carbon emission impact throughout the entire process of equipment production, transportation, and decommissioning. Differences in voltage levels can indirectly change the total carbon emissions by affecting equipment demand and energy consumption. This separation of technical, economic, and environmental assessments makes it difficult to support low-carbon design; Third, existing optimization algorithms are prone to getting trapped in local optima in multi-objective high-dimensional spaces. Cross-cutting algorithms have significant advantages in balancing global exploration and local development, but have not yet been applied in this field.

[0004] Therefore, it is urgent to construct a multi-objective dynamic coupling model that integrates energy efficiency, economy, and low carbon emissions, and combine it with a cross-functional high-efficiency optimization algorithm to achieve the scientific selection of voltage levels for photovoltaic DC power generation systems. Summary of the Invention

[0005] This invention provides a multi-objective collaborative optimization method and system for DC voltage levels in photovoltaic systems to solve at least one of the above-mentioned technical problems.

[0006] The technical solution of this invention to solve the above-mentioned technical problems is as follows: A multi-objective collaborative optimization method for DC voltage levels of a photovoltaic system, comprising:

[0007] S1, the DC bus voltage level, cable cross-sectional area and transmission distance of the photovoltaic DC power generation system are used as optimization variables for multi-objective collaborative optimization;

[0008] S2, construct a three-dimensional model including transmission loss, full-cycle economic cost and carbon emissions based on the optimization variables, and form a multi-objective optimization function strongly coupled with the DC bus voltage level, the cable cross-sectional area and the transmission distance;

[0009] S3. Set multiple constraints, and solve the multi-objective optimization function under the multiple constraints based on the cross-cutting optimization algorithm to obtain the optimal solution of the optimization variables.

[0010] Based on the above technical solution, the present invention can be further improved as follows.

[0011] Furthermore, in S2, the three-dimensional model includes a photovoltaic system transmission loss model, a photovoltaic system full-cycle economic cost model, and a photovoltaic system full-cycle carbon emission model.

[0012] Furthermore, the photovoltaic system transmission loss model is expressed as follows:

[0013] ;

[0014] in, For the transmission loss of photovoltaic systems, For the installed capacity of photovoltaic systems, The DC bus voltage level, The resistivity of the cable. For the transmission distance, The cross-sectional area of ​​the cable is [value missing]. This is a temperature correction factor; The temperature coefficient of cable resistance. This refers to the actual operating temperature.

[0015] Furthermore, the full-cycle economic cost model of the photovoltaic system is expressed as follows:

[0016] ;

[0017] in, For the full life cycle economic cost of photovoltaic systems, For equipment investment costs, For maintenance costs, For converter replacement cost, For land costs; For the cost of photovoltaic modules, For the cost of DC cables, For converter cost; Cost per unit capacity of photovoltaic power For the installed capacity of photovoltaic systems; Cost per unit length and unit cross-sectional area of ​​cable For the transmission distance, The cross-sectional area of ​​the cable; Cost per unit capacity converter; The annual operation and maintenance fee rate for photovoltaic power generation. The annual maintenance rate for the cable. The annual maintenance cost of the converter, For the entire project lifecycle, The discount rate is... For the rate of return on investment; For converter lifespan, The number of times the converter was replaced; As the reference distance, Baseline distance The corresponding land cost benchmark value, These are nonlinear coefficients. This is an adjustment item for installed capacity.

[0018] Furthermore, the full-cycle carbon emission model of the photovoltaic system is expressed as follows:

[0019] ;

[0020] in, For the entire life cycle carbon emissions of photovoltaic systems, This represents the total carbon emissions during the production phase. For total carbon emissions from transportation, To address total carbon emissions during decommissioning; Carbon emissions from photovoltaic module production Carbon emissions from the production of DC cables Carbon emissions are generated for the converter; For the installed capacity of photovoltaic systems, For the first The direct carbon emissions of each process. Carbon emission factor per unit of electricity For the first The power consumption per unit of each process For the first Influencing factors of each process This represents the total number of production processes. For the transmission distance, The cross-sectional area of ​​the cable is [value missing]. To produce carbon emission factors per unit mass of metallic materials. The density of metallic materials; Carbon emissions per unit power of the converter This is the voltage influence coefficient. The DC bus voltage level; For transportation distance, This refers to the total weight of the transported goods. For the first The global warming potential of these greenhouse gases For the first The conversion coefficient of a gas to CO2 equivalent, Fuel consumption intensity, Greenhouse gas emission coefficient for fuel; The total carbon content of decommissioned equipment. The carbon conversion rate in waste through incineration.

[0021] Furthermore, in step S2, the multi-objective optimization function is expressed as:

[0022] ;

[0023] in, Let the objective function be the transmission loss of the photovoltaic system. For the transmission loss of photovoltaic systems; Let the objective function be the economic cost of the photovoltaic system throughout its entire lifecycle. The economic cost of the entire lifecycle of a photovoltaic system; The objective function for the carbon emissions of the photovoltaic system throughout its entire lifecycle is... This accounts for the carbon emissions throughout the entire lifecycle of photovoltaic systems.

[0024] Furthermore, in S3, the multiple constraints include optimization variable constraints and current carrying capacity constraints;

[0025] The optimization variable constraints are expressed as follows:

[0026]

[0027] The current carrying capacity constraint condition is expressed as follows:

[0028] ;

[0029] in, The DC bus voltage level, This is a set of standard discrete values ​​for DC bus voltage levels. The cross-sectional area of ​​the cable is [value missing]. This is the set of standard discrete values ​​for cable cross-sectional area; For the transmission distance, To minimize the transmission distance, This represents the maximum transmission distance. For cable current carrying capacity, For the corresponding cross-sectional area The maximum current carrying capacity of the cable; It is the minimum value in the standard discrete value set of DC bus voltage levels. For the installed capacity of photovoltaic systems, The resistivity of the cable. For the transmission distance, To allow for voltage drop.

[0030] Furthermore, in S3, the multi-objective optimization function is solved under the multiple constraints based on the cross-cutting optimization algorithm, specifically including:

[0031] S31, by using a preset population generation rule, randomly generate N sets of feasible solutions that satisfy the multiple constraints to form the initial parent population;

[0032] S32, calculate the objective optimization function value of each particle in the parent population according to the multi-objective optimization function; perform horizontal crossover of the particles in the parent population in each dimension to generate a horizontally crossed offspring population; process the DC bus voltage level and cable cross-sectional area of ​​each particle in the horizontally crossed offspring population to map them to the nearest standard level, and calculate the objective optimization function value of each particle in the horizontally crossed offspring population according to the multi-objective optimization function;

[0033] S33, perform vertical crossover on each particle in the parent population in each dimension to generate a vertically crossed offspring population; process the DC bus voltage level and cable cross-sectional area of ​​each particle in the vertically crossed offspring population to map them to the nearest standard level, and calculate the objective optimization function value of each particle in the vertically crossed offspring population according to the multi-objective optimization function.

[0034] S34, the parent population, the horizontally crossed offspring population, and the vertically crossed offspring population are mixed to form a mixed population of size 3N;

[0035] S35, based on the Pareto dominance principle, the mixed population is divided into different levels;

[0036] S36, calculate the sparsity of the distribution of the objective optimization function values ​​within each level;

[0037] S37. Based on the sparsity of the distribution of the objective optimization function values ​​within each level, select the first N particles to form a new parent population in the order of "non-dominated levels from low to high and crowding distance in the same level from large to small", and return to S32 to iterate until the number of iterations reaches the preset maximum number of iterations, and then output the optimal solution of the optimization variable.

[0038] Furthermore, the formula for the lateral intersection is:

[0039] ;

[0040] in, and A random number in the range [0,1]. and A random number in the range [-1, 1]. and These are respectively the first generation in the parent population. The particle and the first The first particle Dimensional optimization variables, and These are respectively the th generation in the horizontally crossed offspring population. The particle and the first The first particle Dimensional optimization variables; These correspond to the DC bus voltage level, cable cross-sectional area, and transmission distance, respectively.

[0041] The formula for the longitudinal intersection is:

[0042] ;

[0043] in, A random number in the range [0,1]. and These are respectively the first generation in the parent population. The first particle Dimensional optimization variables and Dimensional optimization variables, The first generation in the vertical crossover offspring population The first particle Dimensional optimization variables;

[0044] The formula for calculating the sparsity of the distribution is:

[0045] ;

[0046] in, This is the current solution to be evaluated. for The sparsity of the distribution, , for The preceding and following adjacent solutions after sorting the z-th objective function. and They are respectively and In the The objective function value in each objective function. and The first The maximum and minimum values ​​of the objective optimization function. The total number of functions to be optimized for the objective.

[0047] Based on the above-mentioned method for multi-objective collaborative optimization of DC voltage levels in photovoltaic systems, this invention also provides a system for multi-objective collaborative optimization of DC voltage levels in photovoltaic systems.

[0048] A multi-objective collaborative optimization system for DC voltage levels of a photovoltaic system includes: a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it implements the multi-objective collaborative optimization method for DC voltage levels of a photovoltaic system as described above.

[0049] The beneficial effects of this invention are as follows: A multi-objective collaborative optimization method and system for DC voltage levels in photovoltaic systems breaks through the limitations of traditional static parameter selection by constructing a three-dimensional optimization framework of DC bus voltage level, cable cross-sectional area, and transmission distance. It captures the correlation between multiple variables through multi-dimensional coupled modeling, adapting to complex constraints in different scenarios. Simultaneously, it establishes a multi-objective quantitative model for transmission loss, full life-cycle economic cost, and carbon emissions, achieving a comprehensive evaluation of the system's overall performance. Furthermore, it employs a cross-optimization algorithm, combining horizontal global exploration and vertical local development with Pareto non-dominated sorting and congestion distance screening, to solve the problems of low convergence accuracy and insufficient solution diversity in multi-dimensional, multi-objective optimization, outputting a collaborative optimal solution set composed of DC bus voltage level, cable cross-sectional area, and transmission distance. This invention is applicable to various photovoltaic system scenarios with different installed capacities, significantly improving the system's comprehensive performance in terms of energy efficiency, economy, and environmental protection. Attached Figure Description

[0050] Figure 1 This is a flowchart of a multi-objective collaborative optimization method for DC voltage levels in a photovoltaic system according to the present invention;

[0051] Figure 2 This is a schematic diagram of the physical structure of an exemplary photovoltaic DC power generation system;

[0052] Figure 3 This is a schematic diagram illustrating the spatial distribution of parameters for an exemplary optimal solution. Detailed Implementation

[0053] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0054] Example 1:

[0055] like Figure 1 As shown, a multi-objective collaborative optimization method for DC voltage levels in a photovoltaic system includes:

[0056] S1, the DC bus voltage level, cable cross-sectional area and transmission distance of the photovoltaic DC power generation system are used as optimization variables for multi-objective collaborative optimization;

[0057] S2, construct a three-dimensional model including transmission loss, full-cycle economic cost and carbon emissions based on the optimization variables, and form a multi-objective optimization function strongly coupled with the DC bus voltage level, the cable cross-sectional area and the transmission distance;

[0058] S3. Set multiple constraints, and solve the multi-objective optimization function under the multiple constraints based on the cross-cutting optimization algorithm to obtain the optimal solution of the optimization variables.

[0059] This invention breaks through the static limitations of traditional empirical formulas, achieving multi-dimensional dynamic quantification of losses, economy, and environmental protection; through a three-dimensional optimization framework of voltage level, cross-sectional area, and distance, it improves the overall performance of the system under multiple constraints; and by applying the cross-sectional algorithm, it effectively solves the problems of low convergence accuracy and insufficient diversity in high-dimensional multi-objective optimization, making it suitable for various photovoltaic power generation systems and DC transmission scenarios, significantly improving the scientific and economical nature of system voltage level selection.

[0060] This embodiment uses the construction of a large-scale photovoltaic medium-voltage DC power generation system with an installed capacity of P=100MW in a certain region as an application scenario. The schematic diagram of the system physical structure is as follows. Figure 2 As shown. Using this large-scale project as a platform, this invention will verify the adaptability and effectiveness of the synergistic optimization of "DC bus voltage level-cable cross-sectional area-transmission distance" in practical engineering scenarios by integrating multi-dimensional technical indicators such as transmission loss optimization, full-cycle economic cost optimization, and carbon emission optimization. The following is a detailed explanation of each step.

[0061] S1, Define the optimization variables:

[0062] This invention relates to the DC bus voltage level of a photovoltaic DC power generation system. Cable cross-sectional area and transmission distance As an optimization variable in multi-objective collaborative optimization; among them, the DC bus voltage level of the photovoltaic DC power generation system. and cable cross-sectional area It should be selected from the standard discrete values ​​within the medium voltage range; transmission distance This represents the distance from the DC bus to the grid connection point, and its value is continuous.

[0063] S2, Construct a multi-objective optimization function:

[0064] In S2, the three-dimensional model includes a photovoltaic system transmission loss model, a photovoltaic system full-cycle economic cost model, and a photovoltaic system full-cycle carbon emission model.

[0065] The magnitude of transmission losses directly impacts energy transmission efficiency, requiring sophisticated modeling to capture this dynamic relationship. Lifecycle economic costs encompass expenditures throughout the entire lifecycle, from equipment investment to operation, maintenance, and replacement, as well as land costs. Different voltage levels and equipment selection and scale lead to significant differences in cost structures, necessitating a systematic analysis of cost composition at each stage. Lifecycle carbon emissions span the entire process of equipment production, transportation, and decommissioning; differences in voltage levels indirectly alter total carbon emissions by influencing energy consumption and equipment demand. Therefore, quantitative models for these three dimensions need to be constructed separately to provide a scientific basis for the optimal selection of voltage levels.

[0066] (1) Constructing a photovoltaic system transmission loss model:

[0067] Transmission losses mainly originate from cable resistance losses, which are affected by DC bus voltage, cable cross-sectional area, transmission distance, and installed capacity. The temperature correction effect on resistance must be considered. The photovoltaic system transmission loss model is expressed as follows:

[0068] ;

[0069] in, This refers to the transmission loss of a photovoltaic system (which takes temperature correction into account, and is therefore also called the temperature-corrected transmission loss of a photovoltaic system). For the installed capacity of photovoltaic systems, The DC bus voltage level, The resistivity of the cable. For the transmission distance, The cross-sectional area of ​​the cable is [value missing]. This is a temperature correction factor, and Represented as:

[0070] ;

[0071] in, The temperature coefficient of cable resistance. This refers to the actual operating temperature.

[0072] The objective optimization function derived from the photovoltaic system transmission loss model is the photovoltaic system transmission loss objective function, which is expressed as:

[0073] .

[0074] (2) Constructing a full-cycle economic cost model for photovoltaic systems:

[0075] The total lifecycle economic cost includes equipment investment cost, operation and maintenance cost, and replacement cost. This model is calculated based on the present value of all components. The cost components are calculated as follows:

[0076] Equipment investment cost:

[0077] Equipment investment costs mainly include the cost of photovoltaic modules, DC cables, and converters. The cost of photovoltaic modules is mainly related to the installed capacity, the cost of DC cables is related to the length and cross-sectional area of ​​the DC cables, and the cost of converters is mainly related to the installed capacity, as detailed below:

[0078] ;

[0079] in, For equipment investment costs; For the cost of photovoltaic modules, For the cost of DC cables, For converter cost; Cost per unit capacity of photovoltaic power For the installed capacity of photovoltaic systems; Cost per unit length and unit cross-sectional area of ​​cable For the transmission distance, The cross-sectional area of ​​the cable; Cost per unit capacity converter.

[0080] Operation and maintenance costs:

[0081] Operation and maintenance costs are the expenses incurred throughout the entire lifecycle of operation and maintenance. They are calculated as a fixed percentage of the initial investment and discounted to present value. The specific formula is as follows:

[0082] ;

[0083] in, For maintenance costs, The annual operation and maintenance fee rate for photovoltaic power generation. The annual maintenance rate for the cable. The annual maintenance cost of the converter, For the entire project lifecycle, The discount rate is... This refers to the rate of return on investment.

[0084] Replacement cost:

[0085] When the equipment lifespan is shorter than the project cycle, replacement costs need to be calculated. Photovoltaic modules and DC cables typically have a lifespan consistent with the project cycle and do not require replacement. Therefore, during their service life, the primary consideration is the replacement cost of the converter, as detailed below:

[0086] The full-cycle economic cost model of the photovoltaic system is expressed as follows:

[0087] ;

[0088] in, Cost of replacing the converter; For converter lifespan, For the number of converter replacements, and Represented as:

[0089] ;

[0090] Land costs:

[0091] In addition to the three costs mentioned above, land costs must also be considered. Land resources are scarce in short-distance areas, and the costs of land acquisition and leasing increase non-linearly as distance decreases, as detailed below:

[0092] ;

[0093] in, For land costs, As the reference distance, Baseline distance The corresponding land cost benchmark value, These are nonlinear coefficients. This is an adjustment item for installed capacity.

[0094] In summary, considering the four types of costs, the full-cycle economic cost model for a photovoltaic system is expressed as follows:

[0095] ;

[0096] in, The economic cost of the entire lifecycle of a photovoltaic system.

[0097] The objective function derived from the full-cycle economic cost model of a photovoltaic system is the objective function for the full-cycle economic cost of a photovoltaic system, which is expressed as follows:

[0098] .

[0099] (3) Construct a full-cycle economic cost model for photovoltaic systems:

[0100] The production process of photovoltaic (PV) power generation systems is highly complex, with a complete system comprising numerous components and equipment such as PV modules, DC cables, and converters. Therefore, in the PV supply chain, carbon emissions are primarily concentrated in activities related to the extraction of resources for production materials, fuel transportation, and waste disposal.

[0101] Carbon emissions during the production phase:

[0102] The production phase encompasses the manufacturing processes of photovoltaic modules, DC cables, and converters, as detailed below:

[0103] ;

[0104] in, This represents the total carbon emissions during the production phase. Carbon emissions from photovoltaic module production Carbon emissions from the production of DC cables Carbon emissions are generated for the converter.

[0105] The production process of photovoltaic modules is very complex, requiring more than a dozen steps. The specific formula is as follows:

[0106] ;

[0107] in, For the installed capacity of photovoltaic systems, For the first The direct carbon emissions of each process. Carbon emission factor per unit of electricity For the first The power consumption per unit of each process For the first Influencing factors of each process This represents the total number of production processes.

[0108] The carbon emissions from the production of DC cables are directly related to the amount of materials used, as shown in the following formula:

[0109] ;

[0110] in, For the transmission distance, The cross-sectional area of ​​the cable is [value missing]. To produce carbon emission factors per unit mass of metallic materials. The density of the metallic material.

[0111] The carbon emissions from converter production are related to the installed capacity and voltage level of the photovoltaic system, as shown in the following formula:

[0112] ;

[0113] in, Carbon emissions per unit power of the converter This is the voltage influence coefficient. The DC bus voltage level is specified.

[0114] Carbon emissions during transportation:

[0115] The transport vehicles use gasoline and diesel fuel, and calculating their carbon emissions requires calculating the emissions of CO2, CH4, and N2O. CH4 and N2O can be converted into CO2 equivalents for carbon emission calculations, using the following formulas:

[0116] ;

[0117] in, For total carbon emissions from transportation, For transportation distance, This refers to the total weight of the transported goods. For the first The global warming potential of these greenhouse gases For the first The conversion coefficient of a gas to CO2 equivalent, Fuel consumption intensity, The greenhouse gas emission factor for fuel.

[0118] Carbon emissions during the decommissioning phase:

[0119] The carbon emissions from decommissioning here mainly refer to those generated by incineration, as shown in the following formula:

[0120] ;

[0121] in, To address the total carbon emissions from decommissioning, The total carbon content of decommissioned equipment. 44 / 12 represents the carbon incineration conversion rate in the waste, and 44 / 12 is the molar mass ratio of carbon dioxide to carbon.

[0122] Based on the three stages of carbon emissions, the full-cycle carbon emission model for photovoltaic systems can be expressed as follows:

[0123] ;

[0124] in, For the entire life cycle carbon emissions of photovoltaic systems

[0125] The objective optimization function derived from the full-cycle carbon emission model of the photovoltaic system is the objective function for the full-cycle carbon emission of the photovoltaic system, which is expressed as:

[0126] .

[0127] S3, setting multiple constraints and multi-objective optimization based on the cross-sectional optimization algorithm:

[0128] (1) Set multiple constraints:

[0129] The multiple constraints include optimization variable constraints and current carrying capacity constraints.

[0130] The optimization variable constraints are expressed as follows:

[0131]

[0132] The current carrying capacity constraint condition is expressed as follows:

[0133] ;

[0134] in, The DC bus voltage level, This is a set of standard discrete values ​​for DC bus voltage levels. The cross-sectional area of ​​the cable is [value missing]. This is the set of standard discrete values ​​for cable cross-sectional area; For the transmission distance, To minimize the transmission distance, This represents the maximum transmission distance. For cable current carrying capacity, For the corresponding cross-sectional area The maximum current carrying capacity of the cable; It is the minimum value in the standard discrete value set of DC bus voltage levels. For the installed capacity of photovoltaic systems, The resistivity of the cable. For the transmission distance, To allow for voltage drop.

[0135] (2) Multi-objective optimization based on the cross-sectional optimization algorithm:

[0136] Before performing multi-objective optimization based on the cross-sectional crossover optimization algorithm, it is necessary to set the algorithm parameters, including: population size N, total number of objective functions M, maximum number of iterations Maxgen, and lateral crossover rate. and vertical cross rate In this embodiment, the population size N is 100, the total number of objective functions M is 3, the maximum number of iterations Maxgen is 200, and the lateral crossover rate is... The vertical crossover rate is 1. It is 0.8.

[0137] The multi-objective optimization function is solved under the multi-constraint conditions based on the cross-sectional optimization algorithm, specifically including the following steps S31~S37:

[0138] S31, By using a preset population generation rule, randomly generate N sets of feasible solutions that satisfy the multiple constraints. To form the initial parent population. .

[0139] S32, calculate the objective optimization function value for each particle in the parent population based on the multi-objective optimization function;

[0140] The particles in the parent population are horizontally intersected in each dimension to generate a horizontally intersected offspring population. The formula for the horizontal intersection is:

[0141] ;

[0142] In the formula, and A random number in the range [0,1]. and A random number in the range [-1, 1]. and These are respectively the first generation in the parent population. Particles and the Particles The Dimensional optimization variables, and These are respectively the th generation in the horizontally crossed offspring population. The particle and the first The first particle Dimensional optimization variables; These correspond to the DC bus voltage level, cable cross-sectional area, and transmission distance, respectively.

[0143] The DC bus voltage level and cable cross-sectional area of ​​each particle in the transverse crossover offspring population are processed and mapped to the nearest standard level; wherein, the formula for mapping each particle in the transverse crossover offspring population to the nearest standard level is:

[0144] ;

[0145] in, These are the candidate values ​​obtained after horizontal crossover. For standard discrete values, The minimum difference between the candidate value and the discrete standard value; the value with the smallest difference. This is the mapping result; =1,2, which correspond to the DC bus voltage level and cable cross-sectional area, respectively;

[0146] The objective optimization function value of each particle in the horizontally crossed offspring population is calculated based on the multi-objective optimization function.

[0147] S33, Perform vertical crossover on each dimension of each particle in the parent population to generate a vertically crossover offspring population. The formula for the longitudinal intersection is:

[0148] ;

[0149] In the formula, A random number in the range [0,1]. and These are respectively the first generation in the parent population. The first particle Dimensional optimization variables and Dimensional optimization variables, The first generation in the vertical crossover offspring population The first particle Dimensional optimization variables;

[0150] The DC bus voltage level and cable cross-sectional area of ​​each particle in the longitudinal crossover offspring population are processed to map them to the nearest standard level, and the objective optimization function value of each particle in the longitudinal crossover offspring population is calculated according to the multi-objective optimization function.

[0151] Specifically, in the process of vertically crossing each particle in the parent population along each dimension, every particle in the current parent population is traversed, and each dimension U, S, L of the particle is normalized. After updating the particle with the vertical crossover algorithm, inverse normalization is performed to generate the vertically crossed offspring population. .

[0152] S34, the parent population, the horizontally crossed offspring population, and the vertically crossed offspring population are mixed to form a mixed population of size 3N.

[0153] S35. Based on the Pareto dominance principle, the mixed population is divided into different levels; where the lower the level, the better the solution.

[0154] S36, calculate the sparsity of the distribution of the objective optimization function values ​​within each level; where, the greater the distance, the better the diversity; the formula for calculating the distribution sparsity is:

[0155] ;

[0156] In the formula, The solution to be evaluated is the current solution (where "solution" refers to a particle in the mixed population). for The sparsity of the distribution, , for After sorting the z-th objective function, the preceding and following adjacent solutions (i.e., in the current iteration step, all particles in the mixed population are substituted into the z-th objective function) The objective optimization function values ​​are calculated for each objective optimization function, and then these objective optimization function values ​​are sorted. , The objective optimization function value is related to (the objective function value before and after the objective function value) and They are respectively and In the The objective function value in each objective function. and The first The maximum and minimum values ​​of the objective function (where the maximum and minimum values ​​specifically refer to: in the current iteration step, each particle in the mixed population is substituted into the x-th objective function). The objective function values ​​are calculated for each objective function, and then the maximum value is selected from these objective function values. and minimum value ), The total number of functions to be optimized for the objective.

[0157] S37. Based on the sparsity of the distribution of the objective optimization function values ​​within each level, select the first N particles to form a new parent population in the order of "non-dominated levels from low to high and crowding distance in the same level from large to small", and return to S32 to iterate until the number of iterations reaches the preset maximum number of iterations, and then output the optimal solution of the optimization variable.

[0158] Specifically, in this embodiment, when the number of iterations reaches 200, the iteration stops, and the Pareto optimal front, i.e., the set of all non-dominated solutions, is output as follows: Figure 3 As shown, based on the actual project focus, a suitable optimal solution (U*, S*, L*) can be selected from the Pareto front, and the corresponding three objective optimization function values ​​(f1*, f2*, f3*) can be calculated. Project decision-makers can then select the most suitable implementation scheme from this Pareto optimal solution set based on the specific project focus. In this embodiment, a representative optimal combination of parameters is (±50KV, 300mm). 2 (50km).

[0159] Example 2:

[0160] Based on the above-mentioned method for multi-objective collaborative optimization of DC voltage levels in photovoltaic systems, this invention also provides a system for multi-objective collaborative optimization of DC voltage levels in photovoltaic systems.

[0161] A multi-objective collaborative optimization system for DC voltage levels of a photovoltaic system includes: a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it implements the multi-objective collaborative optimization method for DC voltage levels of a photovoltaic system as described above.

[0162] A multi-objective collaborative optimization method and system for DC voltage levels in photovoltaic systems breaks through the limitations of traditional static parameter selection by constructing a three-dimensional optimization framework of DC bus voltage level, cable cross-sectional area, and transmission distance. It captures the correlation between multiple variables through multi-dimensional coupled modeling, adapting to complex constraints in different scenarios. Simultaneously, it establishes a multi-objective quantitative model for transmission loss, life-cycle economic cost, and carbon emissions, enabling a comprehensive evaluation of the system's overall performance. Furthermore, it employs a cross-optimization algorithm, combining horizontal global exploration and vertical local development with Pareto non-dominated sorting and congestion distance filtering, to address the problems of low convergence accuracy and insufficient solution diversity in multi-dimensional, multi-objective optimization. The resulting solution outputs a collaborative optimal solution set composed of DC bus voltage level, cable cross-sectional area, and transmission distance. This invention is applicable to various photovoltaic system scenarios with different installed capacities, significantly improving the system's overall performance in terms of energy efficiency, economy, and environmental protection.

[0163] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-objective collaborative optimization method for DC voltage levels in a photovoltaic system, characterized in that, include: S1, the DC bus voltage level, cable cross-sectional area and transmission distance of the photovoltaic DC power generation system are used as optimization variables for multi-objective collaborative optimization; S2, construct a three-dimensional model including transmission loss, full-cycle economic cost and carbon emissions based on the optimization variables, and form a multi-objective optimization function strongly coupled with the DC bus voltage level, the cable cross-sectional area and the transmission distance; S3, Set multiple constraints, and solve the multi-objective optimization function under the multiple constraints based on the cross-cutting optimization algorithm to obtain the optimal solution of the optimization variables; In S2, the three-dimensional model includes a photovoltaic system transmission loss model, a photovoltaic system full-cycle economic cost model, and a photovoltaic system full-cycle carbon emission model; The photovoltaic system transmission loss model is expressed as follows: ； in, For the transmission loss of photovoltaic systems, For the installed capacity of photovoltaic systems, The DC bus voltage level, The resistivity of the cable. For the transmission distance, The cross-sectional area of ​​the cable is [value missing]. This is a temperature correction factor; The temperature coefficient of cable resistance. This refers to the actual operating temperature. The full-cycle economic cost model of the photovoltaic system is expressed as follows: ； in, For the full life cycle economic cost of photovoltaic systems, For equipment investment costs, For maintenance costs, For converter replacement cost, For land costs; For the cost of photovoltaic modules, For the cost of DC cables, For converter cost; Cost per unit capacity of photovoltaic power For the installed capacity of photovoltaic systems; Cost per unit length and unit cross-sectional area of ​​cable For the transmission distance, The cross-sectional area of ​​the cable; Cost per unit capacity converter; The annual operation and maintenance fee rate for photovoltaic power generation. The annual maintenance rate for the cable. The annual maintenance cost of the converter, For the entire project lifecycle, The discount rate is... For the rate of return on investment; For converter lifespan, The number of times the converter was replaced; As the reference distance, Reference distance The corresponding land cost benchmark value, These are nonlinear coefficients. This is an adjustment item for installed capacity; The full-cycle carbon emission model of the photovoltaic system is expressed as follows: ； in, For the entire life cycle carbon emissions of photovoltaic systems, This represents the total carbon emissions during the production phase. For total carbon emissions from transportation, To address total carbon emissions during decommissioning; Carbon emissions from photovoltaic module production Carbon emissions from the production of DC cables Carbon emissions are generated for the converter; For the installed capacity of photovoltaic systems, For the first The direct carbon emissions of each process. Carbon emission factor per unit of electricity For the first The power consumption per unit of each process For the first Influencing factors of each process This represents the total number of production processes. For the transmission distance, The cross-sectional area of ​​the cable is [value missing]. To produce carbon emission factors per unit mass of metallic materials. The density of metallic materials; Carbon emissions per unit power of the converter This is the voltage influence coefficient. The DC bus voltage level; For transportation distance, This refers to the total weight of the transported goods. For the first The global warming potential of these greenhouse gases For the first The conversion coefficient of a gas to CO2 equivalent, Fuel consumption intensity, Greenhouse gas emission coefficient for fuel; The total carbon content of decommissioned equipment. The carbon conversion rate in waste through incineration.

2. The multi-objective collaborative optimization method for DC voltage levels of photovoltaic systems according to claim 1, characterized in that, In S2, the multi-objective optimization function is expressed as: ； in, Let the objective function be the transmission loss of the photovoltaic system. For the transmission loss of photovoltaic systems; Let the objective function be the economic cost of the photovoltaic system throughout its entire lifecycle. The economic cost of the entire lifecycle of a photovoltaic system; The objective function for the carbon emissions of the photovoltaic system throughout its entire lifecycle is... This accounts for the carbon emissions throughout the entire lifecycle of photovoltaic systems.

3. The multi-objective collaborative optimization method for DC voltage levels of photovoltaic systems according to claim 1, characterized in that, In S3, the multiple constraints include optimization variable constraints and current carrying capacity constraints; The optimization variable constraints are expressed as follows: The current carrying capacity constraint condition is expressed as follows: ； in, The DC bus voltage level, This is a set of standard discrete values ​​for DC bus voltage levels. The cross-sectional area of ​​the cable is [value missing]. This is the set of standard discrete values ​​for cable cross-sectional area; For the transmission distance, To minimize the transmission distance, This represents the maximum transmission distance. For cable current carrying capacity, For the corresponding cross-sectional area The maximum current carrying capacity of the cable; To meet the theoretical minimum cable cross-sectional area requirement of the allowable voltage drop constraint, For the installed capacity of photovoltaic systems, The resistivity of the cable. For the transmission distance, To allow for voltage drop.

4. The multi-objective collaborative optimization method for DC voltage levels of photovoltaic systems according to claim 1, characterized in that, In step S3, the multi-objective optimization function is solved under the multiple constraints based on the cross-cutting optimization algorithm, specifically including: S31, randomly generated according to preset population generation rules. N A group of feasible solutions that satisfy the multiple constraints is used to form the initial parent population; S32, calculate the objective optimization function value of each particle in the parent population according to the multi-objective optimization function; perform horizontal crossover of the particles in the parent population in each dimension to generate a horizontally crossed offspring population; process the DC bus voltage level and cable cross-sectional area of ​​each particle in the horizontally crossed offspring population to map them to the nearest standard level, and calculate the objective optimization function value of each particle in the horizontally crossed offspring population according to the multi-objective optimization function; S33, perform vertical crossover on each particle in the parent population in each dimension to generate a vertically crossed offspring population; process the DC bus voltage level and cable cross-sectional area of ​​each particle in the vertically crossed offspring population to map them to the nearest standard level, and calculate the objective optimization function value of each particle in the vertically crossed offspring population according to the multi-objective optimization function. S34, the parent population, the horizontally crossed offspring population, and the vertically crossed offspring population are mixed to form a population of size 3. N A mixed population; S35, based on the Pareto dominance principle, the mixed population is divided into different levels; S36, calculate the sparsity of the distribution of the objective optimization function values ​​within each level; S37, based on the sparsity of the distribution of the objective optimization function values ​​within each level, select the top levels in order of "non-dominated levels from low to high, and crowding distance within the same level from large to small". N The particles form a new parent population and return to the S32 loop for iterative execution until the number of iterations reaches the preset maximum number of iterations, at which point the optimal solution of the optimization variable is output.

5. The multi-objective collaborative optimization method for DC voltage levels of photovoltaic systems according to claim 4, characterized in that, The formula for the horizontal intersection is: ； in, and A random number in the range [0,1]. and A random number in the range [-1, 1]. and These are respectively the first generation in the parent population. The particle and the first The first particle Dimensional optimization variables, and These are respectively the th generation in the horizontally crossed offspring population. The particle and the first The first particle Dimensional optimization variables; These correspond to the DC bus voltage level, cable cross-sectional area, and transmission distance, respectively. The formula for the longitudinal intersection is: ； in, A random number in the range [0,1]. and These are respectively the first generation in the parent population. The first particle Dimensional optimization variables and Dimensional optimization variables, The first generation in the vertical crossover offspring population The first particle Dimensional optimization variables; The formula for calculating the sparsity of the distribution is: ； in, This is the current solution to be evaluated. for The sparsity of the distribution, , for The preceding and following adjacent solutions after sorting the z-th objective function. and They are respectively and In the The objective function value in each objective function. and The first The maximum and minimum values ​​of the objective optimization function. The total number of functions to be optimized for the objective.

6. A multi-objective collaborative optimization system for DC voltage levels in a photovoltaic system, characterized in that, include: A processor, a memory, and a computer program stored in the memory, wherein the computer program, when executed by the processor, implements the multi-objective collaborative optimization method for DC voltage levels of a photovoltaic system as described in any one of claims 1 to 5.

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