3D curved surface flexible photovoltaic module / array dynamic topology optimization method and system

Abstract

The invention provides a 3D curved surface flexible photovoltaic module / array dynamic topology optimization method and system, and the method comprises the steps: S1, building a curved surface photovoltaic module geometric model, carrying out the division of curved surface photovoltaic micro-elements, and obtaining the irradiance and temperature of each micro-surface through a radiation distribution model; s2, calculating electrical performance parameters of each battery through the photovoltaic battery model; s3, constructing an m * n-dimensional photovoltaic module current matrix, and constructing a target function by taking a current mismatch index CM I as a target; and S4, based on an improved simulated annealing algorithm I SAA, performing dynamic topology reconstruction optimization on the current matrix of the 3D curved-surface photovoltaic module, and based on the optimized current matrix, establishing measurement indexes of output characteristics of the reconstructed curved-surface photovoltaic module, including output power, efficiency and daily generating capacity of the photovoltaic module. According to the method, on the basis of the irradiance equilibrium principle, the simulated annealing algorithm is combined, and the current mismatch is reduced by dynamically optimizing the circuit topological structure of the photovoltaic module, so that the curved-surface photovoltaic module obtains the maximum daily generating capacity.

Description

Technical Field

[0001] This invention relates to the field of photovoltaic technology, and in particular to a method and system for dynamic topology optimization of 3D curved flexible photovoltaic modules / arrays. Background Technology

[0002] In recent years, flexible photovoltaics (PV) has become increasingly popular due to its lightweight, flexibility, and bendability, making it suitable for various complex applications such as building-integrated photovoltaics (BIPV), mobile energy devices, transportation, and wearable devices. However, when flexible PV is combined with irregular surfaces, it often results in uneven light intensity across different areas of the PV module. This unevenness in illumination directly leads to inconsistent output current in the PV cells, and this localized difference in illumination causes power mismatch, affecting the overall system's power generation efficiency.

[0003] Optimizing the circuit topology is an important means to improve the output performance of photovoltaic systems under mismatch conditions. Reconfiguration strategies, which adapt to local shading conditions by adjusting the interconnection between photovoltaic modules, are divided into two categories: static reconfiguration and dynamic reconfiguration.

[0004] Current topology reconstruction methods are mostly applied to optimize the output power of photovoltaic arrays under localized shading. The non-uniform irradiance caused by localized shading is limited to a local area, while 3D curved photovoltaic modules exhibit dynamic, global, and continuously changing irradiance characteristics, leading to significant differences in their photoelectric response characteristics compared to traditional modules. In existing technologies, topology reconstruction methods such as TCT (Full Cross-Shading) and SDS (Partially Dispersed Shading) are widely used for photovoltaic module power optimization. These methods perform well in planar photovoltaic arrays or under conditions with only a few discrete shading elements. However, for 3D continuous curved photovoltaic modules, these methods face significant limitations:

[0005] 1. The TCT and SDS topology reconstruction methods are mainly based on fixed battery interconnection patterns, which makes it difficult to perform real-time optimization for complex three-dimensional curved surfaces and continuous non-uniform irradiation fields.

[0006] 2. Under a three-dimensional curved surface irradiation field, the amount of solar energy received by photovoltaic cells in different regions varies significantly. Existing methods cannot dynamically adjust the cell position or circuit connection mode, leading to aggravated current mismatch.

[0007] 3. Due to the inability to effectively optimize the topology of three-dimensional curved photovoltaic modules, existing methods typically result in the overall power generation efficiency of the modules being significantly lower than the theoretical maximum.

[0008] Therefore, proposing an effective method to determine the real-time solar irradiance received by 3D flexible curved photovoltaic modules, and thereby optimizing their photoelectric output power and photoelectric conversion efficiency, is of great significance to the application of 3D flexible curved photovoltaic modules. Summary of the Invention

[0009] The purpose of this invention is to provide an optimization method that can, to a certain extent, solve the mismatch loss problem in 3D flexible curved photovoltaic modules.

[0010] To achieve the above objectives, this invention proposes a dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays, comprising the following steps:

[0011] S1: Establish a geometric model of the curved photovoltaic module, divide the curved photovoltaic micro-element, calculate the geometric parameters of the curved photovoltaic module, and obtain the irradiance and temperature on each micro-surface by combining real-time horizontal irradiance and ambient temperature through the radiation distribution model.

[0012] S2: Input the irradiance and temperature of each microfacet into the photovoltaic cell model to calculate the electrical performance parameters of each cell, including voltage and current parameters;

[0013] S3: Based on the current parameters of each cell, construct an m×n dimensional photovoltaic module current matrix, and construct an objective function with the current mismatch index CMI as the target, where CMI is defined as the sum of squares of the current deviations of each parallel branch:

[0014]

[0015] Among them, I si and I sl These are the row current values ​​for the i-th and l-th rows, respectively;

[0016] S4: Based on the improved simulated annealing algorithm ISAA, dynamic topology reconstruction optimization is performed on the current matrix of 3D curved photovoltaic modules. The optimization methods include:

[0017] 1) Initial temperature T, minimum temperature T min Cooling rate α and current matrix I current ;

[0018] 2) When temperature T > T min And the number of iterations i <N max At that time, the random exchange matrix I current The value at the index position is used to obtain the new solution matrix I. new Calculate the new solution matrix I new CMI new Value, and determine: if CMI new value <CMI current Then accept the new solution matrix I. new Otherwise, a new solution is accepted with probability P, where,

[0019] 3) Update the temperature T = T*α until the termination condition is met, then output the final optimal solution matrix I. best and the optimal CMIbest value;

[0020] S5: Based on the optimized current matrix, establish metrics for the output characteristics of the reconstructed curved photovoltaic module, including the output power, efficiency, and daily power generation of the photovoltaic module.

[0021] Furthermore, in step S4, the specific methods for dynamically reconstructing and optimizing the photovoltaic module current matrix include:

[0022] S4.1: Set the initial temperature T and the minimum temperature T min and cooling rate α;

[0023] S4.2: Initialize the current solution matrix I current Given an initial i*j matrix, calculate its fitness function CMI, and use the obtained CMI value as the CMI of the initial optimal solution. best At the same time, the corresponding optimal matrix is ​​saved, where the initial solution can be represented as:

[0024]

[0025] S4.3: When temperature T > T min And the number of iterations i <N max Under the premise of:

[0026] 1) Generate a new solution I by swapping two random elements in the matrix. new Specifically:

[0027] Two random position indices (i1, j1) and (i2, j2) are generated, satisfying:

[0028] i1,i2∈{1,2,…,m}; j1,j2∈{1,2,…,n}, (i1,j1)≠(i2,j2);

[0029] to I current By swapping the values ​​at the index positions, a new solution matrix I is obtained. new The expression formula is:

[0030] I new (i1,j1)=I current (i2,j2), I new (i2,j2)=I current (i1,j1); while other elements remain unchanged, i.e.

[0031] 2) Based on the current solution matrix I current and the new solution matrix I new Calculate the CMI value, denoted as CMI. current and CMI new ;

[0032] 3) Judge whether to accept the new solution I according to the Metropolis criterion new :

[0033] If the new solution is better than the current solution, that is, CMI new <CMI current , then directly accept it, update the current solution i*j matrix and the optimal solution matrix, and update CMI at the same time best , that is, I best = I new = I current , CMI best = CMI new ;

[0034] If the new solution is not better than the current solution, then accept the new solution with probability P: Generate a random number rand() ∈ [0, 1]. If rand() < P, then accept the new solution;

[0035] 4) Update the temperature T = T * α, and reduce the temperature to gradually reduce the probability of accepting a worse solution;

[0036] 5) When the temperature T is lower than T min or reaches the maximum number of iterations, stop the algorithm;

[0037] S4.4: Output the final optimal solution matrix I best and the optimal CMI best value.

[0038] Further, in step S1, the specific method for dividing the curved surface photovoltaic micro-elements and calculating the geometric parameters of the curved surface photovoltaic module is as follows:

[0039] 1.1: Establish a two-dimensional coordinate system, set the x-axis to point to the east-west direction, the y-axis to point to the north-south direction, and the bending angle of the module is k° in the x direction and q° in the y direction;

[0040] 1.2: Differentiate the curved surface photovoltaic along the north-south direction and the east-west direction by 1° to form a number of micro-surfaces;

[0041] [[ID=�5]]1.3: Define the micro-surface number n, and calculate η n :

[0042]

[0043] where η n is the angle between the micro-surface n and the horizontal plane;

[0044] Calculate the tilt angle β of each micro-surface in the north-south direction n : <?

[0045] βn = -(q / 2+1)+n+β c ;

[0046] Where, β c Let n be the tilt angle of the component, and n be the micro-surface number (when the central angle in the y direction is q°, 1≤n≤q+1);

[0047] 1.4: The tilt angle β of each micro-surface in the north-south direction n Renamed to β b Calculate the east-west micro-surface tilt angle β n and azimuth γ n The calculation formula is:

[0048] cosβ n =cosβ b cosμ n ;

[0049]

[0050] Where, μ n Let n be the angle between the unit normal vector of microface n and the normal vector of the base plate; n is the microface number (when the central angle in the x direction is k°, 1≤n≤k+1);

[0051] At this time, the incident angle θ of the microfacet n n The calculation method is as follows:

[0052]

[0053] Where, β n It is the micro-surface tilt angle; γ n ω is the azimuth angle of the micro-surface; ω is the solar hour angle; δ is the solar declination angle. It is the local latitude.

[0054] Furthermore, in step S1, the specific method for calculating the irradiance is as follows:

[0055] 1) Calculate the direct radiation S reaching the micro-surface n bm,tl :

[0056] S bm,tl =S bm,h r bm,n ,

[0057] Among them, S bm,h r represents the direct irradiance on a horizontal plane. bm,n This is the ratio of the direct irradiance on the microsurface n to the direct irradiance on the horizontal plane. α is the solar altitude angle;

[0058] 2) Calculate the diffuse radiation S reaching the micro-surface ndf,tl :

[0059]

[0060] C = max{0,cosθ n}, B = max{cos85°, cosZ}

[0061] Among them, S df,h and S df,tl These represent diffuse radiation on the horizontal and inclined planes, respectively; F1 and F2 represent the anisotropy coefficients of the surrounding sun and the zenith, respectively; Z is the solar zenith angle.

[0062] 3) Calculate the total radiation on the micro-surface: S n =S bm,tl +S df,tl .

[0063] Furthermore, in step S2, the photovoltaic cell model is as follows:

[0064]

[0065] Where V is the output voltage of the photovoltaic cell; V oc I m I sc V m These are the open-circuit voltage under reference operating conditions, the operating current at maximum power, the short-circuit current, and the operating voltage at maximum power, respectively.

[0066] Photovoltaic modules mostly adopt a fully cross-connected (TCT) structure. Photovoltaic cells are first connected in series to form cell strings, and these cell strings are then connected in parallel to form a TCT structure. For a photovoltaic module with dimensions of m×n, the current in any row of its TCT structure can be calculated as:

[0067]

[0068] Where i and j correspond to the row number and column number respectively, I rowi This represents the current output current in the i-th row, where Im is the battery's output current under the current irradiation, and k... ij This represents the position of the battery in the matrix.

[0069] According to Kirchhoff's voltage law, the voltage of each battery in the same row is the same. The formula for calculating the voltage of any row in TCT is:

[0070] V m,i =V m ;

[0071] Among them, V m,i V represents the current output voltage of the i-th row. mThis refers to the output voltage produced by the battery under standard irradiance. The maximum output voltage V of the battery described in this paper is... m All values ​​are taken as 0.598V.

[0072] Furthermore, in step S3, a current matrix of size m*n is formed by obtaining the current parameters of each cell in the photovoltaic module, and this matrix is ​​initialized and fixed to the current matrix before optimization.

[0073]

[0074] The non-uniform irradiation on 3D curved photovoltaic modules causes significant differences in the solar energy received by photovoltaic cells at different locations, resulting in substantial variations in the current and voltage output characteristics of the cells and ultimately leading to energy mismatch and loss. Therefore, an objective function is constructed with the current change exponent of the photovoltaic module as the target:

[0075]

[0076] The current mismatch index (CMI) is defined as the sum of squares of the deviations between row current levels, and is used to assess the degree of current mismatch between different strings in a photovoltaic module; si and I sl These are the row current values ​​for the i-th and l-th rows, respectively.

[0077] Furthermore, in step S5, the formulas for calculating output power and efficiency are as follows:

[0078] P mpp =I mpp V mpp ,

[0079] Among them, I mpp V mpp These represent the maximum output current and maximum output voltage of the component under the current operating conditions; S n To determine the total solar radiation reaching the base plate, A pv This represents the actual area of ​​the photovoltaic cell.

[0080] This invention also proposes a dynamic topology optimization system for implementing the above-mentioned dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays. The system includes:

[0081] Irradiation distribution modeling module: used to perform micro-surface partitioning and irradiance calculation in step S1;

[0082] Battery parameter calculation module: used to generate photovoltaic cell electrical parameters in step S2;

[0083] Optimize the algorithm execution module: Configure an improved simulated annealing algorithm for dynamic reconstruction of the current matrix;

[0084] Performance evaluation module: Used to output the power, efficiency and power generation indicators of the reconfigured components.

[0085] Compared with the prior art, the advantages of the present invention are:

[0086] 1. This invention deeply integrates curved surface geometric modeling, irradiance distribution modeling, and circuit topology optimization (ISAA algorithm) to form a closed-loop optimization system of "irradiance-electrical parameters-topology". Based on the principle of irradiance balance, combined with simulated annealing algorithm, the circuit topology of photovoltaic modules is dynamically optimized to improve the maximum power output and daily power generation of photovoltaic modules. This provides a theoretical basis and technical support for the subsequent optimization design and practical application of curved photovoltaic systems, and promotes the development and application of 3D flexible curved photovoltaic modules in complex application scenarios.

[0087] 2. This invention addresses the dynamic reconstruction of continuous non-uniform irradiation fields on 3D curved surfaces. By improving the simulated annealing algorithm (ISAA) to optimize the current matrix in real time, it significantly reduces current mismatch of components under non-uniform irradiation conditions, achieving maximum power output. It solves the unique global and dynamic irradiation mismatch problem of curved components. The algorithm effectively avoids getting trapped in local optima in continuously changing irradiation environments by combining a probabilistic acceptance of inferior solutions (Metropolis criterion) with a dynamic cooling strategy, significantly improving global search efficiency. This not only improves system stability and reduces computational burden, but also allows the system to escape local optima and find global optima in continuously changing irradiation. Compared with traditional intelligent algorithms, it achieves smaller mismatch losses and a larger power increase percentage.

[0088] 3. In the process of generating a new solution during the topology reconstruction of a 3D curved photovoltaic module, this invention limits the exchange operation to only two random elements of the current matrix, which greatly reduces the computational complexity and achieves real-time performance in engineering.

[0089] 4. Based on real-time irradiance data, this invention dynamically adjusts the battery position mapping relationship through current matrix exchange, thereby adapting to the continuous irradiance gradient of curved modules as the solar angle changes. The current mismatch index (CMI) is used as the optimization target. This index quantifies the current deviation of parallel branches, thereby directly relating to the mismatch loss. Topology optimization is achieved through virtual current matrix exchange (non-physical reconfiguration circuit), avoiding the high cost problem of dynamic switching circuits and providing a feasible solution for flexible curved photovoltaics. Attached Figure Description

[0090] Figure 1 This is a flowchart of the dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays based on an improved simulated annealing algorithm proposed in Embodiment 1 of the present invention.

[0091] Figure 2This is a schematic diagram of the 3D flexible curved surface component in Embodiment 1 of the present invention;

[0092] Figure 3 This is a schematic diagram of the photovoltaic cell array reconfiguration configuration in Embodiment 1 of the present invention;

[0093] Figure 4 This is a flowchart of the improved simulated annealing algorithm in Embodiment 1 of the present invention;

[0094] Figure 5 This is a diagram showing the initial irradiance of the x120°, y120° curved photovoltaic module at 12 o'clock and the position matrix analysis results under different topological configurations in Embodiment 1 of the present invention.

[0095] Figure 6 The results of the comparative analysis of the IV characteristic curve and PV characteristic curve of the x120°, y120° curved photovoltaic module in Embodiment 1 of the present invention at time 12:00.

[0096] Figure 7 This is a comparative analysis of the dynamic performance of the electrical output of the 6*6 photovoltaic array before and after reconstruction under sunny and cloudy conditions in Embodiment 1 of the present invention.

[0097] Figure 8 This is a comparative analysis of the performance of the 6*6 photovoltaic array before and after reconstruction under sunny and cloudy conditions in Embodiment 1 of the present invention.

[0098] Figure 9 This is a pseudocode description of the optimization method based on the simulated annealing algorithm in the present invention. Detailed Implementation

[0099] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be further described below.

[0100] Example 1

[0101] Example 1 proposes a dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays, such as... Figure 1 As shown, the method includes the following steps:

[0102] S1: Establish a geometric model of the curved photovoltaic module, divide the curved photovoltaic micro-element, calculate the geometric parameters of the curved photovoltaic module, and then import the geometric parameters of the curved photovoltaic module, real-time horizontal irradiance and ambient temperature into the radiation distribution model to obtain the irradiance and temperature on each micro-surface.

[0103] In this embodiment, the specific method for dividing the curved photovoltaic micro-element and calculating the geometric parameters of the curved photovoltaic module is as follows:

[0104] 1.1: Establish as follows Figure 2The two-dimensional coordinate system of the curved photovoltaic module shown is set with the x-axis pointing east-west and the y-axis pointing north-south, and the bending angle of the module is assumed to be 120° in the x-direction and 120° in the y-direction.

[0105] 1.2: Divide the curved photovoltaic surface by 1° along the north-south and east-west directions to form several micro-facets, and calculate the geometric parameters of different micro-facets on the curved photovoltaic module;

[0106] 1.3: The tilt angle β of each micro-surface in the north-south direction is calculated using the following formula 1. n :

[0107] β n = -(q / 2+1)+n+β c Formula 1;

[0108] Where, β c Let n be the tilt angle of the component, and n be the micro-surface number (when the central angle in the y direction is q°, 1≤n≤q+1);

[0109] 1.4: The tilt angle β of each micro-surface in the north-south direction n Renamed to β b The east-west micro-surface tilt angle β is calculated using the following formulas 2 and 3. n and azimuth γ n The calculation formula is:

[0110] cosβ n =cosβ b cosμ n Formula 2;

[0111]

[0112] Where, μ n Let n be the angle between the unit normal vector of microface n and the normal vector of the base plate; n is the microface number (when the central angle in the x direction is k°, 1≤n≤k+1);

[0113] At this time, the incident angle θ of the microfacet n n The calculation method is as follows: Formula 4:

[0114]

[0115] Where, β n It is the micro-surface tilt angle; γ n ω is the azimuth angle of the micro-surface; ω is the solar hour angle; δ is the solar declination angle. It is the local latitude.

[0116] Furthermore, in step S1, the specific method for calculating the irradiance is as follows:

[0117] 1) Calculate the direct radiation S reaching the micro-surface n using Formula 5. bm,tl :

[0118] S bm,tl =S bm,h r bm,n Formula 5;

[0119] Among them, S bm,h r represents the direct irradiance on a horizontal plane. bm,n α is the ratio of the direct irradiance on the microsurface n to the direct irradiance on the horizontal plane, and α is the solar altitude angle.

[0120] 2) Calculate the diffuse radiation S reaching the micro-surface n using Formula 6. df,tl :

[0121]

[0122] Among them, S df,h and S df,tl These represent diffuse radiation on the horizontal and inclined planes, respectively; F1 and F2 represent the anisotropy coefficients of the surrounding sun and the zenith, respectively; Z is the solar zenith angle.

[0123] 3) Calculate the total radiation on the micro-surface using Formula 7:

[0124] S n =S bm,tl +S df,tl Formula 7;

[0125] S2: Input the irradiance and temperature of each microface obtained in step S1 into the photovoltaic cell model, and calculate the electrical performance parameters of each cell, including voltage parameters and current parameters.

[0126] In this embodiment, the photovoltaic cell model is as follows:

[0127]

[0128] Where V is the output voltage of the photovoltaic cell; V oc I m I sc V m These are the open-circuit voltage under reference operating conditions, the operating current at maximum power, the short-circuit current, and the operating voltage at maximum power, respectively.

[0129] In this embodiment, a 6*6 curved photovoltaic module array is established, and the electrical performance parameters of the 6×6 photovoltaic cells in the module are obtained.

[0130] S3: Based on the current parameters of each cell in the photovoltaic module obtained in step S2, construct a photovoltaic module current matrix with size m*n, initialize and fix the matrix to the current matrix before optimization; and construct an objective function with the current mismatch index CMI as the target.

[0131] In this embodiment, a 6*6 initial current matrix is ​​constructed:

[0132]

[0133] The current mismatch index (CMI) is used as an indicator to evaluate the power loss of 3D curved photovoltaic modules. CMI is defined as the sum of squares of the current deviations in each parallel branch, used to assess the degree of current mismatch between different strings in the photovoltaic module.

[0134]

[0135] Among them, I si and I sl These are the row current values ​​for the i-th and l-th rows, respectively;

[0136] S4: Based on the improved simulated annealing algorithm ISAA, dynamic topology reconstruction optimization is performed on the current matrix of 3D curved photovoltaic modules. The optimization process is as follows: Figure 4 As shown, the method specifically includes:

[0137] S4.1: Input matrix I current (In this embodiment, it is also referred to as M) ij And initialize the simulated annealing parameters, that is, set the initial temperature T = 1000 and the minimum temperature T min =1e -3 And the cooling (temperature reduction) rate α = 0.9;

[0138] S4.2: Initialize the current solution matrix I current Given an initial i*j matrix, calculate its fitness function CMI, and use the obtained CMI value as the CMI of the initial optimal solution. best At the same time, the corresponding optimal matrix is ​​saved, where the initial solution can be represented as:

[0139]

[0140] S4.3: When temperature T > T min And the number of iterations i <N max Under the premise of:

[0141] 1) to I current By swapping the values ​​at the index positions, a new solution matrix I is obtained. new (In this embodiment, it is also referred to as M) ij The formula is as follows:

[0142] I new (i1, j1) = I current (i2, j2), I new (i2, j2) = I current (i1, j1); while other elements remain unchanged, that is

[0143] 2) Based on the current solution matrix I current and the new solution matrix I new , calculate the CMI value, denoted as CMI current and CMI new ;

[0144] 3) According to the Metropolis criterion, determine whether to accept the new solution I new :

[0145] If the new solution is better than the current solution, that is CMI new < CMI current , then directly accept it, and update the current solution i*j matrix and the optimal solution matrix, and at the same time update CMI best [[ID=B6]] best = I new = I current , CMI best = CMI new ;

[0146] If the new solution is not better than the current solution, then accept the new solution with probability P: Generate a random number rand() ∈ [0, 1], if rand() < P, then accept the new solution;

[0147] 4) Update the temperature T = T * α, lower the temperature to gradually reduce the probability of accepting a worse solution;

[0148] 5) When the temperature T is lower than T min or reaches the maximum number of iterations, stop the algorithm; where the maximum number of iterations is determined according to the influence of the code running speed and accuracy. In this embodiment, when setting three iteration numbers of 10,000, 100,000, and 1,000,000, it is found that the accuracy influence of 100,000 compared to 1,000,000 is not significant, but the code running speed is greatly improved. Therefore, the maximum number of iterations is set to 100,000.

[0149] By dynamically adjusting the cooling rate and limiting the exchange of 2 matrix elements at a time, the computational complexity is reduced, and the computational timeliness problem of the traditional SA algorithm in the curved surface photovoltaic scenario is solved.

[0150] S4.4: Output the final optimal solution matrix I best and the optimal CMI​best value.

[0151] In step S4, the pseudocode description of the dynamic topology reconstruction optimization of the current matrix of the 3D curved photovoltaic module based on the improved simulated annealing algorithm I SAA is as follows: Figure 9 As shown.

[0152] S5: Based on the optimized current matrix, establish metrics for the output characteristics of the reconstructed curved photovoltaic module, including the output power, efficiency, and daily power generation of the photovoltaic module.

[0153] In this embodiment, the formulas for calculating output power and efficiency are as follows:

[0154]

[0155] Among them, I mpp V mpp These represent the maximum output current and maximum output voltage of the component under the current operating conditions; S n To determine the total solar radiation reaching the base plate, A pv This represents the actual area of ​​the photovoltaic cell.

[0156] Using TCT (Fully Cross-Connected) and SDS (Partially Shaded Dispersion) topologies as comparative examples, such as Figure 5 As shown, it displays the initial irradiance of x120° and y120° curved photovoltaic modules at 12 o'clock and the position matrices under different topologies. In each column, the upper matrix represents the irradiance matrix on a 6x6 module; the lower matrix represents the position number of the corresponding irradiance matrix. Figure 5 It can be seen that, under the TCT topology, the maximum and minimum row irradiance difference of the module reaches 3658.30 W / m. 2 After reconstruction, the difference between the maximum and minimum row irradiance of the modules under SDS and ISAA was reduced to 711.62 W / m². 2 and 28.44W / m 2 Further calculations show that the CMI of the component under TCT, SDS, and ISAA are 11629.64, 709.87, and 0.05, respectively.

[0157] Using TCT (Fully Cross-Connected) and SDS (Partially Shaded Dispersion) topologies as comparative examples, such as Figure 6 As shown, it presents a comparative analysis of the IV and PV characteristic curves of x120° and y120° curved photovoltaic modules at 12 time points under three different topologies: ISAA, TCT, and SDS. Figure 6It can be seen that the IV characteristic curves under TCT and SDS have multiple steps, and the PV characteristic curves have multiple local maximum power points. In contrast, the characteristic curves under ISAA are relatively smooth and have higher power output. At this time, the maximum output power of the module is 163.53W and the electrical efficiency is 24.12%, which is significantly better than other topologies.

[0158] Using TCT (Fully Cross-Connected) and SDS (Partial Shading Dispersion) topologies as comparative examples, the performance of 6×6 photovoltaic modules under sunny and cloudy conditions was analyzed using MATLAB simulation software. The results were compared with those of the TCT and SDS schemes to evaluate the algorithm's adaptability to dynamic irradiance environments. Figure 7 The attached diagram illustrates the dynamic performance analysis results of the 3D curved photovoltaic module before and after TCT, SDS, and ISAA reconstruction. Figure 7 This demonstrates the dynamic changes in power and efficiency of the component under three different topology reconfiguration methods: TCT, SDS, and ISAA. Figure 7 It can be seen that under both sunny and cloudy conditions, the power output trends of the three topology reconfiguration methods, TCT, SDS, and ISAA, are generally consistent. ISAA consistently exhibits higher power output and efficiency advantages at all times, consistently outperforming SDS and TCT. Under sunny conditions, the electrical efficiency of ISAA remains above 24%, with an average daily efficiency of approximately 24.37%, significantly better than SDS's 21.95% and TCT's 16.89%. Under cloudy conditions, ISAA's power output is also consistently higher than SDS and TCT, with an average daily efficiency of approximately 23.77%, significantly better than SDS's 22.26% and TCT's 16.83%.

[0159] At the same time, such as Figure 8 As shown, it displays the average CMI of photovoltaic modules over a day under sunny and cloudy conditions using three different topology reconstruction methods: TCT, SDS, and ISAA. Figure 8 It can be seen that the daily average CMI of the modules under TCT were 6592.77 and 1896.54, respectively, while the daily average CMI of the modules under SDS were 401.24 and 110.11, respectively. I SAA dynamically adjusted the cell cell positions based on the real-time irradiance field, further optimizing the current distribution of the cells and making energy transfer between cell strings more efficient, significantly reducing the daily average CMI to 0.57 and 0.17; (See attached image) Figure 8In both sunny and cloudy conditions, the daily power generation of the ISAA modules was higher than that of SDS and TCT, at 1163.43Wh and 697.99Wh respectively. Specifically, under sunny conditions, SDS increased daily power generation by 29.80% compared to TCT, and under cloudy conditions, the increase was 32.51%; while ISAA increased daily power generation by 44.27% and 42.25% compared to TCT under sunny and cloudy conditions, respectively.

[0160] Therefore, it can be seen that the dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays based on the improved simulated annealing algorithm proposed in this invention can accurately calculate the irradiance field distribution of three-dimensional curved photovoltaic modules. At the same time, the proposed improved simulated annealing algorithm can exhibit excellent dynamic adaptability and stability under dynamic irradiation conditions.

[0161] Example 2

[0162] Example 2 proposes a dynamic topology optimization system to implement the dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays described in Example 1 above. The system includes:

[0163] Irradiation distribution modeling module: used to perform micro-surface partitioning and irradiance calculation in step S1;

[0164] Battery parameter calculation module: used to generate photovoltaic cell electrical parameters in step S2;

[0165] Optimize the algorithm execution module: Configure an improved simulated annealing algorithm for dynamic reconstruction of the current matrix;

[0166] Performance evaluation module: used to output the power, efficiency and power generation indicators of the reconfigured components;

[0167] Physical Reconstruction Interface Module: This module converts the optimized current matrix I... best Converted into a switch control signal, driving the programmable relay array to perform circuit topology switching.

[0168] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays, characterized in that, Includes the following steps: S1: Establish a geometric model of the curved photovoltaic module, divide the curved photovoltaic micro-element, calculate the geometric parameters of the curved photovoltaic module, and obtain the irradiance and temperature on each micro-surface by combining real-time horizontal irradiance and ambient temperature through the radiation distribution model. S2: Input the irradiance and temperature of each microfacet into the photovoltaic cell model to calculate the electrical performance parameters of each cell, including voltage and current parameters; S3: Based on the current parameters of each cell, construct an m×n dimensional photovoltaic module current matrix, and construct an objective function with the current mismatch index CMI as the target, where CMI is defined as the sum of squares of the current deviations of each parallel branch: Among them, I si and I sl These are the row current values ​​for the i-th and l-th rows, respectively; S4: Based on the improved simulated annealing algorithm ISAA, dynamic topology reconstruction optimization is performed on the current matrix of 3D curved photovoltaic modules. The optimization methods include: 1) Initial temperature T, minimum temperature T min Cooling rate α and current matrix I current ; 2) When temperature T > T min And the number of iterations i <N max At that time, the random exchange matrix I current The value at the index position is used to obtain the new solution matrix I. new Calculate the new solution matrix I new CMI new Value, and determine: if CMI new value <CMI current Then accept the new solution matrix I. new Otherwise, a new solution is accepted with probability P, where, 3) Update the temperature T = T*α until the termination condition is met, then output the final optimal solution matrix I. best and the optimal CMI best value; S5: Based on the optimized current matrix, establish metrics for the output characteristics of the reconstructed curved photovoltaic module, including the output power, efficiency, and daily power generation of the photovoltaic module.

2. The dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays according to claim 1, characterized in that, In step S4, the specific methods for dynamically reconstructing and optimizing the photovoltaic module current matrix include: S4.1: Set the initial temperature T and the minimum temperature T min and cooling rate α; S4.2: Initialize the current solution matrix I current Given an initial i*j matrix, calculate its fitness function CMI, and use the obtained CMI value as the CMI of the initial optimal solution. best At the same time, the corresponding optimal matrix is ​​saved, where the initial solution can be represented as: S4.3: When temperature T > T min And the number of iterations i <N max Under the premise of: 1) to I current By swapping the values ​​at the index positions, a new solution matrix I is obtained. new The formula is: I new (i1,j1)=I current (i2,j2), I new (i2,j2)=I current (i1,j1); while other elements remain unchanged, i.e., I new (i,j)=I current (i,j), 2) Based on the current solution matrix I current and the new solution matrix I new Calculate the CMI value, denoted as CMI. current and CMI new ; 3) Based on the Metropol criterion, determine whether to accept the new solution I. new : If the new solution is better than the current solution, i.e., CMI new <CMI current If so, accept the result directly, update the current solution i*j matrix and the optimal solution matrix, and update the CMI. best , that is I best =I new =I current CMI best =CMI new ; If the new solution is not better than the current solution, accept the new solution with probability P: Generate a random number rand() ∈ [0, 1]. If rand() < P, accept the new solution; 4) Update the temperature T = T*α, and lower the temperature to gradually reduce the probability of accepting a worse solution; 5) When the temperature T is lower than T min Alternatively, stop the algorithm when the maximum number of iterations is reached; S4.4: Output the final optimal solution matrix I best and the optimal CMI best value.

3. The dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays according to claim 1, characterized in that, In step S1, the specific method for dividing the curved photovoltaic micro-element and calculating the geometric parameters of the curved photovoltaic module is as follows: 1.1: Establish a two-dimensional coordinate system, setting the x-axis to point east-west and the y-axis to point north-south, and the bending angle of the component to be k° in the x-direction and q° in the y-direction; 1.2: Photovoltaic displays with 1° differential surfaces along the north-south and east-west directions are formed into several microfacets; 1.3: Calculate the tilt angle β of each micro-surface in the north-south direction. n : b n =-(q / 2+1)+n+β c ; Where, β c Let n be the tilt angle of the component, and n be the micro-surface number (when the central angle in the y direction is q°, 1≤n≤q+1); 1.4: The tilt angle β of each micro-surface in the north-south direction n Renamed to β b Calculate the east-west micro-surface tilt angle β n and azimuth γ n The calculation formula is: cosβ n =cosβ b cosμ n ; Where, μ n Let n be the angle between the unit normal vector of microface n and the normal vector of the base plate; n is the microface number (when the central angle in the x direction is k°, 1≤n≤k+1); At this time, the incident angle θ of the microfacet n n The calculation method is as follows: Where, β n It is the micro-surface tilt angle; γ n ω is the azimuth angle of the micro-surface; ω is the solar hour angle; δ is the solar declination angle. It is the local latitude.

4. The dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays according to claim 1, characterized in that, In step S1, the specific method for calculating the irradiance is as follows: 1) Calculate the direct radiation S reaching the micro-surface n bm,tl : S bm,tl =S bm,h r bm,n , Among them, S bm,h r represents the direct irradiance on a horizontal plane. bm,n α is the ratio of the direct irradiance on the microsurface n to the direct irradiance on the horizontal plane, and α is the solar altitude angle. 2) Calculate the diffuse radiation S reaching the micro-surface n df,tl : Among them, S df,h and S df,tl These represent diffuse radiation on the horizontal and inclined planes, respectively; F1 and F2 represent the anisotropy coefficients of the surrounding sun and the zenith, respectively; Z is the solar zenith angle. 3) Calculate the total radiation on the micro-surface: S n =S bm,tl +S df,tl .

5. The dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays according to claim 1, characterized in that, In step S2, the photovoltaic cell model is as follows: Where V is the output voltage of the photovoltaic cell; V oc I m I sc V m These are the open-circuit voltage under reference operating conditions, the operating current at maximum power, the short-circuit current, and the operating voltage at maximum power, respectively.

6. The dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays according to claim 1, characterized in that... In step S5, the formulas for calculating output power and efficiency are as follows: Among them, I mpp V mpp These represent the maximum output current and maximum output voltage of the component under the current operating conditions; S n To determine the total solar radiation reaching the base plate, A pv This represents the actual area of ​​the photovoltaic cell.

7. A dynamic topology optimization system for implementing the dynamic topology optimization method for 3D curved flexible photovoltaic modules / arrays as described in any one of claims 1-6, characterized in that, include: Irradiation distribution modeling module: used to perform micro-surface partitioning and irradiance calculation in step S1; Battery parameter calculation module: used to generate photovoltaic cell electrical parameters in step S2; Optimize the algorithm execution module: Configure an improved simulated annealing algorithm for dynamic reconstruction of the current matrix; Performance evaluation module: Used to output the power, efficiency and power generation indicators of the reconfigured components.

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