Photovoltaic locating and sizing method based on affine particle swarm optimization

Abstract

The invention discloses a photovoltaic locating and sizing method based on an affine particle swarm algorithm, and the method comprises the steps: carrying out the modeling of the uncertainty of photovoltaic output in an affine mathematical form, and obtaining an affine expression of photovoltaic injection power; based on an affine expression of photovoltaic injection power, through affine load flow calculation, determining an affine evaluation form of at least one system operation performance index influenced by photovoltaic output uncertainty, the affine evaluation form comprising a central value part and a fluctuation radius part; an adjustable weight coefficient is introduced, the central value part and the fluctuation radius part of the affine evaluation form are subjected to weighted fusion to construct a single objective function used for optimization decision making, and different emphasis of an optimization objective is adjusted by adjusting the weight coefficient; the single objective function further comprises a fixed cost item which is not influenced by photovoltaic output uncertainty; and solving the single objective function by adopting an improved particle swarm optimization algorithm, and outputting a photovoltaic site selection and constant volume configuration scheme.

Description

Technical Field

[0001] This invention relates to the field of power system distribution network optimization technology, and in particular to a photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm. Background Technology

[0002] As a major distributed energy source, photovoltaic (PV) power generation is seeing a continuous increase in its penetration rate within power distribution networks. However, influenced by natural factors such as geographical location and weather conditions, PV output exhibits significant intermittency and volatility. Large-scale grid connection poses challenges to the safe, stable, and economical operation of power distribution networks, potentially leading to increased grid losses and voltage exceeding limits. Therefore, scientifically and rationally selecting the site and determining the capacity of PV power plants is crucial for improving the reliability of power grid operation.

[0003] Existing photovoltaic (PV) optimization methods either rely on deterministic conditions, failing to adequately consider the uncertainty of output, or employ probabilistic or fuzzy logic methods to handle uncertainty. However, when dealing with high-dimensional, strongly correlated uncertain variables, these methods often suffer from excessive computational complexity or overly conservative optimization results, making it difficult to achieve a good balance between computational efficiency, economy, and robustness. For example, while Monte Carlo simulations can handle randomness, they involve large computational loads and are inefficient. Methods based on interval arithmetic, while ensuring robustness, typically assume independent variables and fail to adequately consider the spatiotemporal correlation of PV output, potentially leading to overly conservative optimization results and poor economic performance.

[0004] In terms of model solving, existing optimization algorithms (such as the standard particle swarm optimization algorithm) rely heavily on experience for parameter settings when solving high-dimensional, nonlinear planning problems with complex constraints. Their search strategies still have room for improvement in balancing global exploration and local exploitation capabilities. Furthermore, existing methods lack an intuitive and efficient decision-making framework for effectively coordinating economic and safety objectives under the influence of uncertainty, making it difficult to meet the differentiated needs of planners in various application scenarios. Summary of the Invention

[0005] To address the shortcomings and deficiencies of existing technologies, this invention provides a photovoltaic (PV) site selection and capacity determination method based on an affine particle swarm optimization algorithm. This method aims to solve the problems of balancing economic efficiency and robustness, and insufficient optimization efficiency and accuracy in PV distribution network planning under PV output uncertainty. The method first models the uncertainty of PV output using affine mathematics, representing the injected PV power as an affine expression containing a central value and a fluctuation range. The modeling process considers the correlation between PV output variables, and the fluctuation range is determined based on historical PV output data of the target distribution network area. Next, based on the affine expression of the injected PV power, at least one affine evaluation form of the system operating performance index affected by PV output uncertainty is determined through affine power flow calculation. This affine evaluation form includes a central value component and a fluctuation radius component. Subsequently, an adjustable weighting coefficient is introduced to balance the central value component and the fluctuation radius of the affine evaluation form. The process involves weighted fusion to construct a single objective function for optimization decisions. This single objective function includes a fixed cost term unaffected by the uncertainty of photovoltaic output, and may also include penalty terms for exceeding limits on the number of installations, installation capacity, and voltage. Finally, an improved particle swarm optimization algorithm is used to solve the single objective function. The algorithm's adaptive parameter update strategy includes a non-linear decrease in inertia weight with the number of iterations, and random adjustment of the local and global learning rates within a preset range. Furthermore, the discrete variables in the particle position vector are transformed into installation decisions through a probability mapping function, ultimately outputting a photovoltaic site selection and capacity configuration scheme.

[0006] The present invention also provides a robust optimization configuration system and computer equipment for photovoltaic distribution networks that implements the above method. By integrating affine theory with an improved particle swarm optimization algorithm, it can accurately quantify the impact of photovoltaic output uncertainty and flexibly adjust the optimization objective to emphasize economy and robustness, thereby improving the feasibility and adaptability of the planning scheme while ensuring computational efficiency.

[0007] The present invention specifically adopts the following technical solution:

[0008] A photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm includes:

[0009] The uncertainty of photovoltaic power output is modeled using affine mathematics, and an affine expression for photovoltaic injected power is obtained.

[0010] Based on the affine expression of the photovoltaic injected power, at least one affine evaluation form of the system operating performance index affected by the uncertainty of photovoltaic output is determined by affine power flow calculation. The affine evaluation form includes a central value part and a fluctuation radius part.

[0011] An adjustable weighting coefficient is introduced to weight and fuse the central value part and the fluctuation radius part of the affine evaluation form to construct a single objective function for optimization decision-making, wherein different emphases of the optimization objective are adjusted by adjusting the weighting coefficient;

[0012] The single objective function also includes a fixed cost term that is unaffected by the uncertainty of photovoltaic output;

[0013] An improved particle swarm optimization algorithm is used to solve the single objective function, and the resulting photovoltaic site selection and capacity configuration scheme is output.

[0014] Furthermore, the fluctuation range of the affine expression for the photovoltaic injected power is determined based on the historical photovoltaic power output data of the target distribution network area; the noise element in the affine expression takes a symmetrical interval.

[0015] Furthermore, the fixed cost item in the single objective function includes equipment investment indicators and operation and maintenance indicators; wherein, the equipment investment indicators are calculated based on unit quantity coefficient, unit capacity coefficient, depreciation rate and service life, and the operation and maintenance indicators are calculated based on unit capacity operation coefficient and photovoltaic installation capacity.

[0016] Furthermore, the method also includes constraints, including constraints on the number of photovoltaic installations, constraints on the photovoltaic installation capacity, and robust constraints based on the affine form of node voltage; the single objective function also includes a limit violation penalty term, which is a weighted sum of penalty terms corresponding to limit violations in the number of installations, limit violations in the installation capacity, and limit violations in the voltage, calculated using a preset penalty factor.

[0017] Furthermore, the central value portion of the affine evaluation form corresponds to the economic indicators of system operation, and the fluctuation radius portion corresponds to the robustness indicators of system operation. By adjusting the weight coefficients, the optimization process can adjust the emphasis on economy and robustness.

[0018] Furthermore, the robust constraint based on the affine form of node voltage specifically involves jointly limiting the center value and fluctuation radius of the affine form of each node voltage to ensure that the node voltage remains within the allowable upper and lower limits of the rated voltage of the distribution network under all uncertain scenarios.

[0019] Furthermore, the adaptive parameter update strategy of the improved particle swarm optimization algorithm includes: the inertia weight adopts a non-linear decreasing strategy, which is dynamically adjusted from the maximum value to the minimum value as the number of iterations increases; the learning rate includes a local learning rate and a global learning rate, which adopts a strategy of randomly adjusting within a preset range to balance the algorithm's global exploration and local development capabilities.

[0020] Furthermore, in the improved particle swarm optimization algorithm, the position vector of each particle consists of a discrete variable representing the photovoltaic installation location and a continuous variable representing the photovoltaic installation capacity; the discrete variable is transformed into a decision of installation or non-installation through a probability mapping function, and the threshold of the probability mapping function is preset according to engineering requirements; the convergence judgment condition of the algorithm is: the number of iterations reaches the preset total number of iterations, or the global optimal fitness improvement value of multiple consecutive iterations is less than the preset threshold.

[0021] Furthermore, the affine power flow calculation is based on the distribution network node admittance matrix. The specific process is as follows: the photovoltaic injection power in affine form is substituted into the power flow equation, the power flow equation is linearized and then an iterative format is established. The affine form of each node voltage and system operation performance index is updated through multiple iterations until the node voltage change is less than the preset convergence threshold.

[0022] And, a photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm, comprising:

[0023] The affine modeling module is used to model the uncertainty of photovoltaic power output using affine mathematics to obtain the affine expression for photovoltaic injected power.

[0024] The affine power flow calculation module is used to determine, based on the affine expression of the photovoltaic injected power, at least one affine evaluation form of the system operating performance index affected by the uncertainty of photovoltaic output through affine power flow calculation. The affine evaluation form includes a central value part and a fluctuation radius part.

[0025] The objective function reconstruction module is used to introduce adjustable weight coefficients to weight and fuse the central value part and the fluctuation radius part of the affine evaluation form to construct a single objective function for optimization decision-making. The different emphases of the optimization objective are adjusted by adjusting the weight coefficients. The objective function reconstruction module is also used to add a fixed cost term that is not affected by the uncertainty of photovoltaic power output to the single objective function.

[0026] The solution module is used to solve the single objective function using an improved particle swarm optimization algorithm, and outputs the photovoltaic site selection and capacity configuration scheme.

[0027] And a computer device including a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the steps of the method described above.

[0028] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0029] Compared with the prior art, the present invention and its preferred embodiments have at least the following beneficial effects:

[0030] Effectively handles uncertainty while balancing economy and robustness: By modeling and propagating the uncertainty of photovoltaic output using affine mathematics and introducing adjustable weight coefficients to weight and integrate economic and robustness objectives, this invention can flexibly generate a series of differentiated planning schemes ranging from pursuing economic optimization to emphasizing operational robustness within a single optimization framework. This effectively overcomes the risks of traditional deterministic planning and the overly conservative results of interval optimization and other methods.

[0031] The improved particle swarm optimization algorithm enhances the balance between global exploration and local exploitation through an adaptive parameter update strategy. It also effectively handles the discrete-continuous mixed variable problem in addressing and sizing by combining a hybrid coding method. This improves the convergence speed and optimization accuracy when solving such high-dimensional, nonlinear optimization problems, and helps to obtain better configuration schemes.

[0032] It enhances the flexibility and practicality of planning decisions: It provides an intuitive decision support mechanism, allowing planners to customize optimization objectives by adjusting weighting coefficients according to specific grid operation requirements, risk preferences, or different application scenarios, thereby obtaining customized photovoltaic configuration schemes that meet actual needs and improving the engineering applicability and decision support capabilities of the method. Attached Figure Description

[0033] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0034] Figure 1 This is a flowchart illustrating the photovoltaic site selection and capacity optimization process according to an embodiment of the present invention.

[0035] Figure 2 This is an extended topology diagram of the IEEE 33-node power distribution system according to an embodiment of the present invention.

[0036] Figure 3 This is a graph showing the photovoltaic power generation curves under different weather conditions according to an embodiment of the present invention;

[0037] Figure 4 This is a daily load curve diagram for different types of loads in an embodiment of the present invention;

[0038] Figure 5 This is a comparison chart of fitness functions without considering uncertainties in the embodiments of the present invention;

[0039] Figure 6 A comparison chart of fitness functions considering uncertainties in embodiments of the present invention. Detailed Implementation

[0040] In the following, specific embodiments of this application will be described in detail with reference to the accompanying drawings. Based on these detailed descriptions, those skilled in the art will be able to clearly understand and implement this application. Without departing from the principles of this application, features from various embodiments can be combined to obtain new implementations, or certain features from some embodiments can be substituted to obtain other preferred implementations.

[0041] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in conjunction with the accompanying drawings:

[0042] To address the shortcomings of existing technologies, this invention provides a robust photovoltaic optimization configuration method based on affine theory and an improved particle swarm optimization algorithm.

[0043] (1) An affine mathematical method is used to model the uncertainty of photovoltaic power output in order to accurately characterize its fluctuation range. This method describes photovoltaic power output in an affine form and embeds the uncertainty into the original site selection and capacity optimization model, thus laying the foundation for robust optimization at the modeling level. Compared with the Monte Carlo simulation method, this method significantly improves computational efficiency; compared with the traditional interval algorithm, it effectively reduces the conservatism of the optimization results by considering the correlation of variables.

[0044] (2) An optimization configuration model based on uncertainty affine transformation is established and reconstructed. A fitness function that weights and normalizes economy and robustness is defined, and corresponding weights can be set to make the result biased towards economy or robustness. This improved strategy enhances the decision-making adaptability of the algorithm in uncertain environments, enabling the optimization result to achieve the optimal balance between system performance and operational robustness. For this model, an improved particle swarm optimization algorithm embedded with affine power flow calculation is designed, which enables the direct and accurate handling of uncertain variables in each iterative evaluation, and achieves effective solution.

[0045] Compared to existing technologies, the site selection and capacity optimization method considering photovoltaic output uncertainty proposed in this embodiment of the invention, by performing affine modeling on the photovoltaic output uncertainty, can simultaneously obtain the center value and fluctuation range of state variables during calculation. While ensuring computational efficiency, it can achieve results with both superior benchmark performance and lower fluctuation risk under uncertain environments. The established economic and robustness-weighted normalized fitness function can flexibly adjust preference weights according to actual decision-making needs, generating customized configuration schemes that combine good performance and controllable risk.

[0046] The implementation process of the present invention will be further demonstrated and described below:

[0047] 1. Affine-based uncertainty analysis of photovoltaics

[0048] 1.1 Affine Modeling of Photovoltaic Uncertainty

[0049] Photovoltaic power output is affected by environmental factors such as sunlight intensity and temperature, and the resulting fluctuations often bring uncertainty to the operation of the distribution network. This invention, based on the deterministic prediction of photovoltaic power output, introduces an affine fluctuation term for modeling, thus determining the active power of the distributed generation (DG). reactive power It is expressed as follows:

[0050]

[0051] In the formula, and The center values ​​of active and reactive power output for photovoltaic power generation. and For the fluctuation range of photovoltaic power output, and This represents the noise element corresponding to active and reactive power.

[0052] 1.2 Affine Power Flow Algorithm

[0053] To analyze the propagation of photovoltaic output uncertainty in the distribution network, affine power flow calculations are required. The traditional Gaussian power flow method based on the nodal admittance matrix can be expressed as follows:

[0054]

[0055] In the formula, Here is the nodal admittance matrix. To balance the node voltage, Set the voltage value for the balancing node. Inject power into the node, Inject current into the node.

[0056] To characterize the uncertainty of photovoltaic output, equation (1) is used to represent the node-injected power of the photovoltaic system. Substituting equation (1) into equation (2), expanding and rearranging the equations, we obtain the following affine power flow equations:

[0057]

[0058] The above equation is the core of the affine power flow algorithm. It linearizes and iteratively solves the above equation using affine arithmetic, and its expansion and iterative format are as follows:

[0059]

[0060] Solving this equation yields the affine form of the voltage at each node in the power system, providing a foundation for subsequent network loss calculations and interval analysis of voltage deviations.

[0061] 2. Photovoltaic Optimization Allocation Model Considering Uncertainties

[0062] 2.1 Optimization Model

[0063] The optimization model of this invention aims to determine the optimal installation location and capacity of photovoltaic systems. This model targets the optimal overall system performance, considering the comprehensive index C and the penalty for exceeding limits P, and establishes the objective function f, expressed as follows:

[0064]

[0065] (1) Comprehensive indicators

[0066] Comprehensive indicator C covers equipment investment indicators, operation and maintenance indicators, network loss indicators, and purchased energy indicators:

[0067]

[0068] The equipment investment index C0 represents the investment level of equipment, and its expression is as follows:

[0069]

[0070] In the formula, cnum and ccap are the unit quantity coefficient and unit capacity coefficient, respectively, r is the depreciation rate, and γ is the useful life.

[0071] Operation and maintenance index C1 represents the level of operation and maintenance requirements of the solution, and its expression is as follows:

[0072]

[0073] In the formula, coper is the corresponding unit capacity operating coefficient.

[0074] The network loss index C2 represents the network loss level of the system operation, and its expression is as follows:

[0075]

[0076] In the formula, ce is the unit electricity price coefficient, n is the number of system nodes, and Gij is the conductance between node i and node j.

[0077] The purchased energy index C3 represents the amount of energy purchased from the power grid, and its expression is as follows:

[0078]

[0079] In the formula, pload,t is the total load at time t, and ppv,t,i is the output power of photovoltaic k at time t.

[0080] (2) Penalty for exceeding the limit

[0081] To soften the constraints, a penalty term P is introduced to ensure that the solution searches near the feasible region. λ0, λ1, and λ2 are the corresponding penalty factors, which are applied when the model exceeds the limits. The expression for P is:

[0082]

[0083] The expression for the penalty P0 for exceeding the installation limit is as follows:

[0084]

[0085] The expression for the penalty P1 for exceeding the installation capacity limit is as follows:

[0086]

[0087] The expression for the voltage over-limit penalty P2 is as follows:

[0088]

[0089] 2.2 Uncertainty Model Reconstruction

[0090] The uncertainty of photovoltaic power output is modeled by affine mathematics, and the original optimization model is reconstructed into an affine optimization model.

[0091] (1) Affine constraint treatment

[0092] Under uncertainty modeling, the photovoltaic capacity and quantity constraints remain in their original form, while the constraint form for the node voltage under affine modeling is as follows:

[0093]

[0094] To ensure the robustness of the constraints, that is, to ensure that the inequality constraints are still satisfied under the influence of all possible uncertainties, it is necessary to constrain their possible minimum and maximum values, as expressed below:

[0095]

[0096] In the formula, The center value of the node voltage. For the affine variables involved in the node voltage.

[0097] (2) Affine objective function reconstruction

[0098] The network loss and purchased energy indices in the original objective function are transformed into affine numbers after affine power flow calculation. Based on the structure of affines, the original optimization model can be converted into a weighted sum of affine center values ​​and affine radii, thereby realizing the reconstruction of the affine optimization model. Its expression is as follows:

[0099]

[0100] In the formula, C2,cen and C2,r are the center value and fluctuation radius of the network loss index, respectively; C3,cen and C3,r are the center value and fluctuation radius of the purchased energy index, respectively; and ω is the optimization weight, which takes the value [0,1].

[0101] Among them, the central value of the affine number represents the expected level of the performance index and is related to economic efficiency; the fluctuation radius represents the sensitivity of the index to uncertainty and is related to robustness (conservatism).

[0102] By minimizing the reconstructed objective function, the multi-energy microgrid can be optimized in terms of both economy and conservatism. Furthermore, this affine objective function is a multi-objective function; the optimization weights ω can be used to adjust the emphasis among the multiple objectives, and the value of ω can be adjusted according to the actual needs of economy and conservatism.

[0103] 2.3 Solving the Optimization Model

[0104] For the nonlinear mixed-integer programming problem of photovoltaic site selection and capacity determination, this invention uses the Particle Swarm Optimization (PSO) algorithm as the solution framework, and embeds affine power flow calculation to characterize uncertainties. In the affine PSO algorithm process, the PSO algorithm parameters are first initialized, and then the algorithm is iterated.

[0105] (1) Particle encoding and updating

[0106] Each particle represents a planning scheme, and its position vector is composed of discrete location variables xi and continuous capacities si.

[0107] Continuous variables are updated using the standard particle swarm optimization algorithm:

[0108]

[0109] In the formula, and Let be the velocities of particle i at the previous and next time steps. Let pbest,i be the current position of the particle, pbest,i be the optimal position of the particle, and gbest be the optimal position of all particles.

[0110] Discrete variables are mapped from binary variables to probabilities using the sigmoid function, and the update formula is as follows:

[0111]

[0112] (2) Adaptive parameter update strategy

[0113] The inertia weight is updated using a non-linear decreasing strategy:

[0114]

[0115] In the formula, m is the current iteration number, M is the total iteration number, and ωmax and ωmin are the maximum and minimum values ​​of the particle swarm update weights.

[0116] Update the learning rate according to the following formula:

[0117]

[0118] In the formula, , , and These are the maximum and minimum values ​​of the corresponding learning rates.

[0119] (3) Particle Swarm Optimization Algorithm Embedded with Affine Current

[0120] In each iteration, for the position of each particle, the nodal injection power Si in affine form is first generated based on the photovoltaic capacity Si, and then the affine power flow is calculated. Based on the calculated affine nodal voltage value, the objective function f is calculated as the fitness of the particle.

[0121] The convergence conditions are set as follows:

[0122]

[0123] In the formula, and The global optimal fitness is the fitness before and after each iteration. The threshold is set, and k is the upper limit of the number of consecutive iterations without improvement. When the number of iterations reaches the upper limit or the fitness improvement is insufficient after k consecutive iterations, the iteration stops and the optimized solution is output.

[0124] Based on the above design, the entire process of optimizing photovoltaic site selection and capacity determination is as follows: Figure 1 As shown:

[0125] The process begins with the initial stage, where the first step is to import the distribution network structure and operating parameters. The network structure includes basic topology information such as node admittance matrix and node connection relationships, while the operating parameters cover key data such as node load characteristics, baseline power and rated voltage, photovoltaic candidate site locations and capacity constraints, laying the data foundation for subsequent optimization calculations.

[0126] The second step is to initialize the parameters of the particle swarm optimization algorithm. Core parameters such as population size, maximum and minimum values ​​of inertia weight, upper and lower limits of learning rate, penalty factor, upper limit of iterations, convergence threshold, and upper limit of iterations without improvement need to be set. At the same time, the particle position vector (including discrete location variables and continuous capacity variables) and velocity are initialized. Each particle corresponds to a set of photovoltaic location and capacity candidate schemes.

[0127] The third step is to perform affine power flow calculations. For each photovoltaic configuration scheme corresponding to a particle, the photovoltaic output is first converted into nodal injection power in affine form, and then substituted into the affine power flow equation for linearization and iterative solution to obtain the affine expression of the voltage of each node (including the center value and fluctuation radius), which provides support for the uncertainty analysis of subsequent network loss, voltage deviation and other indicators.

[0128] The fourth step involves implementing a fitness function evaluation that takes into account uncertainties. Based on the affine power flow calculation results, comprehensive indicators such as equipment investment, operation and maintenance, network loss, and purchased energy are calculated, as well as penalty terms corresponding to the number of installations, capacity, and voltage exceeding limits. Then, the particle fitness is calculated through the reconstructed affine objective function (including economic and robustness weighted terms) to evaluate the comprehensive performance of the candidate scheme.

[0129] The fifth step is to adaptively update the particle velocity and position. The continuous fixed-capacity variable adopts the standard particle swarm velocity-position update formula, and the discrete location variable is updated by mapping it to probability through the sigmoid function. At the same time, the inertia weight is adjusted according to the non-linear decreasing strategy, and the learning rate is updated adaptively in sync. Then, the particle perturbation mutation operation is performed to avoid the algorithm from getting stuck in local optima.

[0130] Finally, the convergence condition is checked. If the number of iterations reaches the preset upper limit, or the improvement of the global optimal fitness after k consecutive iterations is less than the threshold T, the iteration stops and the optimal photovoltaic site selection and capacity setting scheme is output, and the process ends. If the convergence condition is not met, the process returns to the affine power flow calculation stage and enters the next iteration cycle.

[0131] The effectiveness of the solution provided in the embodiments of the present invention is further verified through a specific simulation example below:

[0132] 1. Case Setup

[0133] (1) Simulation platform and parameters

[0134] To verify the effectiveness of the method proposed in this invention, an extended IEEE 33-bus distribution system was selected as a test case, the topology of which is as follows: Figure 2 As shown.

[0135] The system has a base power of 10MVA and a rated voltage of 12.66kV. Nodes 8, 13, 30, 31, and 32 are selected as candidate sites for photovoltaic (PV) installations. The maximum number of PV installations is set at 5, the maximum capacity of a single PV unit is 1MW, and the maximum total installed PV capacity is 2MW.

[0136] The algorithm parameters are set as follows: unit quantity coefficient cnum = 20, unit capacity coefficient ccap = 300, unit capacity operation coefficient coper = 6, depreciation rate r = 0.08, service life γ = 25 years, and unit electricity price coefficient ce = 0.05. The population size of the particle swarm optimization algorithm is set to 80, and the penalty coefficients λ0, λ1 are set to 106, and λ2 is set to 105.

[0137] (2) Photovoltaic and load model

[0138] By clustering photovoltaic (PV) output data under three typical weather conditions—sunny, cloudy, and rainy—in a certain region, daily PV output curves were obtained, as shown below. Figure 3 As shown, the power fluctuation ranges for the three weather types are set to ±10%, ±25%, and ±10%, respectively.

[0139] The load model is designed for three types of users: industrial, commercial, and residential, with corresponding daily load curves set for each. Figure 4 As shown.

[0140] (3) Comparison of scene design

[0141] To fully verify the effectiveness of the method of the present invention, the following three comparison scenarios were designed:

[0142] Scenario 1: Baseline scenario, without distributed photovoltaic access.

[0143] Scenario 2: Optimization is performed using a standard particle swarm optimization algorithm that does not consider fluctuations in photovoltaic power output.

[0144] Scenario 3: Optimization is performed using the affine optimization model that considers photovoltaic power output fluctuations and the improved particle swarm optimization algorithm that incorporates affine power flow, as proposed in this invention.

[0145] 2. Comparative Analysis of Optimization Results

[0146] The optimization solutions obtained for scenarios 2 and 3 are as follows:

[0147] Table 1 Comparison of Optimized Photovoltaic Configuration Schemes

[0148]

[0149] A comprehensive analysis of photovoltaic configuration schemes under three scenarios is conducted. Firstly, the fitness function evaluation results under the deterministic environment are as follows: Figure 5 As shown.

[0150] Under deterministic evaluation criteria, Scenario 2, based on ordinary particle swarm optimization, tends to incorporate more photovoltaic capacity to improve system power flow, thereby reducing grid losses and improving power quality. In contrast, Scenario 3 shows relatively limited improvement under this evaluation system.

[0151] However, considering the actual operating environment of distributed photovoltaic power output fluctuations, the fitness functions for the three scenarios are as follows: Figure 6 As shown, a detailed comparison of the various indicators is shown in Table 2.

[0152] Table 2 Comparison of Optimization Results

[0153]

[0154] Combination Figure 6 As shown in Table 2, under the comprehensive evaluation system that takes uncertainty into account, Scenario 2 (traditional method) suffers from the highest grid loss fluctuation, power purchase fluctuation, and voltage limit violation penalty due to its configuration scheme being extremely sensitive to photovoltaic fluctuations. This indicates insufficient robustness and high operational risk. In contrast, Scenario 3 (the method of this invention) achieves a more robust configuration scheme by actively considering and quantifying uncertainty in the optimization model: its fluctuation amplitude indicators and voltage limit violation are significantly lower than those of Scenario 2. Although some deterministic performance indicators (such as purchased energy indicators) are higher than those of Scenario 2, it achieves optimal overall performance and successfully achieves a better balance between system performance and operational robustness.

[0155] The simulation results demonstrate that the method proposed in this invention can effectively generate photovoltaic configuration schemes that adapt to power output fluctuations, improve the voltage safety and stability of the system operation, and reduce the risk of performance fluctuations caused by uncertainties.

[0156] Based on the same inventive concept, this invention also provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the programs include program instructions, and the processor executes the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, used to implement one or more instructions, specifically for loading and executing one or more instructions stored in a computer storage medium to implement the above-described method.

[0157] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, performs the above-described method. This storage medium can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0158] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0159] The foregoing has shown and described the basic principles, main features, and advantages of this disclosure. Those skilled in the art should understand that this disclosure is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this disclosure. Various changes and modifications can be made to this disclosure without departing from its spirit and scope, and all such changes and modifications fall within the scope of this disclosure as claimed.

[0160] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive other forms of photovoltaic site selection and capacity determination methods based on affine particle swarm optimization. All equivalent variations and modifications made within the scope of the claims of this invention shall fall within the scope of this invention.

Claims

1. A photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm, characterized in that, include: The uncertainty of photovoltaic power output is modeled using affine mathematics, and an affine expression for photovoltaic injected power is obtained. Based on the affine expression of the photovoltaic injected power, at least one affine evaluation form of the system operating performance index affected by the uncertainty of photovoltaic output is determined by affine power flow calculation. The affine evaluation form includes a central value part and a fluctuation radius part. An adjustable weighting coefficient is introduced to weight and fuse the central value part and the fluctuation radius part of the affine evaluation form to construct a single objective function for optimization decision-making, wherein different emphases of the optimization objective are adjusted by adjusting the weighting coefficient; The single objective function also includes a fixed cost term that is unaffected by the uncertainty of photovoltaic output; An improved particle swarm optimization algorithm is used to solve the single objective function, and the resulting photovoltaic site selection and capacity configuration scheme is output.

2. The photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm according to claim 1, characterized in that: The fluctuation range of the affine expression for photovoltaic injected power is determined based on historical photovoltaic power output data of the target distribution network area; the noise element in the affine expression takes values ​​within a symmetrical interval.

3. The photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm according to claim 1, characterized in that: The fixed cost item in the single objective function includes equipment investment indicators and operation and maintenance indicators; wherein, the equipment investment indicators are calculated based on the unit quantity coefficient, unit capacity coefficient, depreciation rate and service life, and the operation and maintenance indicators are calculated based on the unit capacity operation coefficient and photovoltaic installation capacity.

4. The photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm according to claim 1, characterized in that: The method also includes constraints, including constraints on the number of photovoltaic installations, constraints on the capacity of photovoltaic installations, and robust constraints based on the affine form of node voltage; the single objective function also includes a limit violation penalty term, which is a weighted sum of the penalty terms corresponding to limit violations in the number of installations, limit violations in the capacity of installations, and limit violations in the voltage, according to a preset penalty factor.

5. The photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm according to claim 1, characterized in that: The central value portion of the affine evaluation form corresponds to the economic indicators of system operation, and the fluctuation radius portion corresponds to the robustness indicators of system operation. By adjusting the weight coefficients, the optimization process can adjust the emphasis on economy and robustness.

6. The photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm according to claim 4, characterized in that: The robust constraint based on the affine form of node voltage is specifically defined as follows: the center value and fluctuation radius of the affine form of each node voltage are jointly limited to ensure that the node voltage is always within the allowable upper and lower limits of the rated voltage of the distribution network under all uncertain scenarios.

7. The photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm according to claim 1, characterized in that: The improved particle swarm optimization algorithm's adaptive parameter update strategy includes: the inertia weight adopts a non-linear decreasing strategy, dynamically adjusting from the maximum value to the minimum value as the number of iterations increases; the learning rate includes a local learning rate and a global learning rate, which adopt a strategy of randomly adjusting within a preset range to balance the algorithm's global exploration and local development capabilities.

8. The photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm according to claim 1, characterized in that: In the improved particle swarm optimization algorithm, the position vector of each particle consists of a discrete variable representing the photovoltaic installation location and a continuous variable representing the photovoltaic installation capacity; the discrete variable is transformed into a decision of installation or non-installation through a probability mapping function, and the threshold of the probability mapping function is preset according to engineering requirements; the convergence judgment condition of the algorithm is: the number of iterations reaches the preset total number of iterations, or the global optimal fitness improvement value of multiple consecutive iterations is less than the preset threshold.

9. The photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm according to claim 1, characterized in that: The affine power flow calculation is based on the distribution network node admittance matrix. The specific process is as follows: the photovoltaic injection power in affine form is substituted into the power flow equation, the power flow equation is linearized and then an iterative format is established. The affine form of each node voltage and system operation performance index is updated through multiple iterations until the node voltage change is less than the preset convergence threshold.

10. A photovoltaic site selection and capacity determination method based on affine particle swarm optimization algorithm, characterized in that, include: The affine modeling module is used to model the uncertainty of photovoltaic power output using affine mathematics to obtain the affine expression for photovoltaic injected power. The affine power flow calculation module is used to determine, based on the affine expression of the photovoltaic injected power, at least one affine evaluation form of the system operating performance index affected by the uncertainty of photovoltaic output through affine power flow calculation. The affine evaluation form includes a central value part and a fluctuation radius part. The objective function reconstruction module is used to introduce adjustable weight coefficients to weight and fuse the central value part and the fluctuation radius part of the affine evaluation form to construct a single objective function for optimization decision-making. The different emphases of the optimization objective are adjusted by adjusting the weight coefficients. The objective function reconstruction module is also used to add a fixed cost term that is not affected by the uncertainty of photovoltaic power output to the single objective function. The solution module is used to solve the single objective function using an improved particle swarm optimization algorithm, and outputs the photovoltaic site selection and capacity configuration scheme.

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