A data-driven photovoltaic flexible power point tracking method and system
By using a data-driven photovoltaic flexible power point tracking method, voltage updates and filtering are optimized using measured data, which solves the problems of slow dynamic performance and power oscillation in flexible power point tracking control algorithms, and achieves faster tracking speed and higher accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANDONG UNIV
- Filing Date
- 2024-07-24
- Publication Date
- 2026-04-28
AI Technical Summary
Existing flexible power point tracking control algorithms suffer from slow dynamic performance and power oscillations near the stable point in photovoltaic power plants, and their performance degrades due to inaccurate reliance on photovoltaic array models.
A data-driven photovoltaic flexible power point tracking method is adopted, which updates and filters voltage using measured data. It does not rely on the photovoltaic array model at all. It optimizes voltage updates by using gradient and perturbation signals, avoids power oscillations, and improves tracking speed and accuracy.
It achieves power-free oscillations near the stable point, improves tracking speed and accuracy, reduces accumulated errors, and avoids performance degradation caused by inaccurate system models.
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Figure CN118819230B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of photovoltaic grid-connected power generation technology, and in particular to a data-driven photovoltaic flexible power point tracking method and system. Background Technology
[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.
[0003] As photovoltaic (PV) penetration increases, the proportion of synchronous generators in the power grid decreases, leading to a reduction in power system inertia and a decline in primary frequency regulation capability. To provide active power support during grid frequency fluctuations, it is crucial for PV power plants to actively participate in grid frequency regulation. By replacing Maximum Power Point Tracking (MPPT) control with Flexible Power Point Tracking (FPPT) control, PV power plants can reserve a certain amount of active power. When grid frequency fluctuates, this reserve can participate in grid frequency regulation. Although FPPT control reduces solar irradiance and sacrifices a small amount of active power, PV power plants gain frequency regulation capability. This contributes to improving grid frequency stability.
[0004] Currently, flexible power point tracking control strategies can be divided into two categories:
[0005] The first type involves modifying the control structure of the converter in a photovoltaic grid-connected system. This method requires multi-mode switching, and the controller needs to be re-initialized during the mode switching process, resulting in slow dynamic performance.
[0006] The second category involves modifying flexible power point tracking (WPPT) control algorithms. Compared to the first category, these methods do not require mode switching and are easier to implement. Traditional WPPT control algorithms are mainly based on linear search methods, with the perturbation-observation method being a typical example. It typically uses a constant voltage step size, resulting in slow convergence. To improve convergence speed, WPPT control algorithms based on two-step methods and adaptive step sizes have been proposed. However, these algorithms suffer from power oscillations near the steady-state point. Summary of the Invention
[0007] To address the aforementioned issues, this invention proposes a data-driven photovoltaic flexible power point tracking method and system. The proposed method is based on a data-driven approach, utilizing only measured data to achieve photovoltaic flexible power point tracking without relying on the photovoltaic array model. After voltage updates, filtering is applied to reduce reference voltage fluctuations. Furthermore, there are no power oscillations near the stable point, ensuring both tracking speed and accuracy.
[0008] In some implementations, the following technical solutions are adopted:
[0009] A data-driven photovoltaic flexible power point tracking method includes:
[0010] The output voltage and current of the photovoltaic array are collected, and the output power of the photovoltaic array is calculated.
[0011] Calculate the difference between the output power of the photovoltaic array and a given reference power, and determine whether the flexible power point has been tracked based on the difference;
[0012] If the flexible power point is not tracked, apply a perturbation signal to the current output voltage of the photovoltaic array and obtain the output power of the photovoltaic array after the voltage perturbation; estimate the gradient based on the output power of the photovoltaic array before and after the perturbation.
[0013] Based on the gradient, reference power, and the output voltage and output power of the photovoltaic array before the perturbation, the output voltage of the photovoltaic array is updated; the updated output voltage is filtered to obtain the voltage reference value of the photovoltaic array at the next moment.
[0014] Repeat the above process until the flexible power point is located.
[0015] As an optional approach, the difference between the output power of the photovoltaic array and a given reference power is calculated. If the absolute value of the difference is less than a set power threshold, the flexible power point is tracked; otherwise, the flexible power point is not tracked.
[0016] If the flexible power point is detected, the output voltage of the photovoltaic array is directly output, and the tracking ends.
[0017] As an optional approach, the gradient is estimated based on the photovoltaic array output power before and after the perturbation, specifically:
[0018] The gradient is the ratio of the difference between the output power value of the photovoltaic array after the voltage perturbation is applied and the output power value of the photovoltaic array before the voltage perturbation is applied, to the applied perturbation voltage value.
[0019] As an optional solution, the updated output voltage of the photovoltaic array is specifically as follows:
[0020]
[0021] in, For the updated voltage, U k The output voltage of the photovoltaic array before the perturbation is applied, a1∈[0,1] represents the learning rate, g k For the estimated gradient, P k To determine the output power of the photovoltaic array before applying the disturbance, P refGiven a reference power, P is the projection operator, and U = [U min U max ], U min and U max These are the lower and upper bounds of the output voltage of the photovoltaic array, respectively.
[0022] As an optional approach, the updated output voltage is filtered to obtain the voltage reference value of the photovoltaic array at the next moment, specifically:
[0023]
[0024] in, For the updated voltage, U k The output voltage of the photovoltaic array before the perturbation is applied, and a2∈[0,1] represents the first-order filter factor.
[0025] In other embodiments, the following technical solutions are adopted:
[0026] A data-driven photovoltaic flexible power point tracking system includes:
[0027] The power calculation module is used to collect the output voltage and output current of the photovoltaic array and calculate the output power of the photovoltaic array.
[0028] The flexible power point tracking module is used to calculate the difference between the output power of the photovoltaic array and a given reference power, and to determine whether the flexible power point has been tracked based on the difference. If the flexible power point has not been tracked, a perturbation signal is applied to the current output voltage of the photovoltaic array, and the output power of the photovoltaic array after the voltage perturbation is obtained. The gradient is estimated based on the output power of the photovoltaic array before and after the perturbation. The output voltage of the photovoltaic array is updated based on the gradient, the reference power, the output voltage and output power of the photovoltaic array before the perturbation are applied, and the updated output voltage is filtered to obtain the voltage reference value of the photovoltaic array at the next moment. Finally, the module re-determines whether the flexible power point has been tracked.
[0029] In other embodiments, the following technical solutions are adopted:
[0030] A terminal device includes a processor and a memory, the processor being used to implement instructions; the memory being used to store multiple instructions adapted to be loaded and executed by the processor in accordance with the above-described data-driven photovoltaic flexible power point tracking method.
[0031] In other embodiments, the following technical solutions are adopted:
[0032] A computer-readable storage medium storing a plurality of instructions adapted for loading and execution by a processor of a terminal device of the aforementioned data-driven photovoltaic flexible power point tracking method.
[0033] Compared with the prior art, the beneficial effects of the present invention are:
[0034] (1) This invention is based on a data-driven approach, which uses only measured data to achieve photovoltaic flexible power point tracking without relying on the photovoltaic array model. This solves the problem that the photovoltaic array model is difficult to establish accurately and can effectively avoid problems such as the degradation of algorithm performance caused by inaccurate system model establishment.
[0035] (2) The present invention updates the voltage by random approximation, which improves both the tracking speed and tracking accuracy; after the voltage update is completed, filtering is applied to reduce the reference voltage fluctuation; when the absolute value of the difference between the photovoltaic array output power and the reference power is less than the set power threshold, the algorithm stops iterating and outputs the photovoltaic array output voltage, which can ensure that there is no power oscillation near the stable point.
[0036] Other features and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0037] Figure 1 This is a flowchart of the data-driven photovoltaic flexible power point tracking method in an embodiment of the present invention;
[0038] Figure 2 This is a structural diagram of a three-phase photovoltaic grid-connected system in an embodiment of the present invention;
[0039] Figures 3(a)-3(d) The methods employed are the traditional fixed-step algorithm, the two-step algorithm, the adaptive step-size algorithm, and the method proposed in this embodiment, respectively, at an irradiance of 1000 W / m². 2 Simulation comparison of output power and output voltage of photovoltaic array when the reference power changes by a step change of 1 second and the operating point is located to the right of the maximum power point;
[0040] Figures 4(a)-4(d) The methods employed are the traditional fixed-step algorithm, the two-step algorithm, the adaptive step-size algorithm, and the method proposed in this embodiment, respectively, at an irradiance of 1000 W / m². 2 Simulation comparison of photovoltaic array output power and output voltage when the reference power changes by a step change of 1 second and the operating point is to the left of the maximum power point;
[0041] Figures 5(a)-5(d) The figures show a comparison of the output power and output voltage of the photovoltaic array when the irradiance changes linearly for 1-3 seconds and 6-8 seconds, the reference power changes stepwise for 2 seconds and 7 seconds, and the operating point is located to the right of the maximum power point, using the traditional fixed step size algorithm, the two-step size algorithm, the adaptive step size algorithm, and the method proposed in this embodiment.
[0042] Figures 6(a)-6(d) The figures show a comparison of the output power and output voltage of the photovoltaic array when using the traditional fixed-step algorithm, the two-step algorithm, the adaptive step-step algorithm, and the method proposed in this embodiment, respectively, with linear changes in irradiance of 1-3 seconds and 6-8 seconds, step changes in reference power of 2 seconds and 7 seconds, and the operating point being to the left of the maximum power point. Detailed Implementation
[0043] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0044] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0045] Example 1
[0046] In one or more embodiments, a data-driven photovoltaic flexible power point tracking method is disclosed, combining... Figure 1 Specifically, it includes the following process:
[0047] (1) Collect the output voltage and output current of the photovoltaic array and calculate the output power of the photovoltaic array.
[0048] Specifically, the output current I of the photovoltaic array is measured. k and output voltage U k Calculate the corresponding output power P k , can be represented as P k =U k *I k .
[0049] (2) Calculate the difference between the output power of the photovoltaic array and the given reference power, and determine whether the flexible power point has been tracked based on the difference.
[0050] For a given reference power P ref If |P k -P ref If |<ε (ε is the power threshold), it can be considered as tracking the flexible power point. At this time, the output voltage of the photovoltaic array is directly output as the reference voltage of the photovoltaic array at the next moment, which can satisfy the conditions for flexible power point tracking, and the tracking ends.
[0051] If |P is not satisfied k -P ref If |<ε (ε is the power threshold), then continue with the subsequent process.
[0052] (3) If the flexible power point is not tracked, apply a perturbation signal to the current output voltage of the photovoltaic array and obtain the output power of the photovoltaic array after the voltage perturbation; estimate the gradient based on the output power of the photovoltaic array before and after the perturbation.
[0053] Specifically, the output voltage U of the photovoltaic array k Apply a disturbance ΔU, according to the formula Obtain the perturbation voltage of the photovoltaic array.
[0054] Measuring the disturbance voltage of the photovoltaic array Corresponding output current Calculate the output power of the photovoltaic array corresponding to the disturbance voltage.
[0055] Based on the output power P of the photovoltaic array before the voltage perturbation was applied k and the output power of the photovoltaic array after applying voltage perturbation Estimate the corresponding gradient g k , can be represented as
[0056] (4) Based on the gradient, reference power, and the output voltage and output power of the photovoltaic array before the perturbation, update the output voltage of the photovoltaic array; the updated voltage is:
[0057]
[0058] in, For the updated voltage, U k The output voltage of the photovoltaic array before the perturbation is applied, a1∈[0,1] represents the learning rate, g k For the estimated gradient, P k To determine the output power of the photovoltaic array before applying the disturbance, P ref Given a reference power, P is the projection operator, and U = [U min U max ], U min and U max These are the lower and upper bounds of the output voltage of the photovoltaic array, respectively.
[0059] (5) Filter the updated output voltage to obtain the voltage reference value of the photovoltaic array at the next moment.
[0060] The specific voltage reference value for the photovoltaic array at the next moment is as follows:
[0061]
[0062] Among them, U k+1 Let a2 be the reference voltage of the photovoltaic array at the next moment, and let a2∈[0,1] represent the first-order filter factor.
[0063] (6) Return to step (1) and re-determine whether the flexible power point has been tracked. If yes, the tracking ends; otherwise, repeat steps (3)-(6) until the flexible power point is tracked.
[0064] In this embodiment, Figure 2 Taking the three-phase photovoltaic grid-connected system shown as an example, it includes a photovoltaic array PV and a DC capacitor C. dc Filter capacitor C f , filter inductors L1 and L2, AC power grid and grid-connected inverter.
[0065] The data-driven photovoltaic flexible power point tracking control method in this embodiment is executed to output a DC bus voltage reference value U. dc,ref The difference between the reference value and the measured value of the DC bus voltage is sent to the proportional-integral controller, which outputs the d-axis current reference value I in a two-phase rotating coordinate system. d,ref To achieve unity power factor grid connection, the reference value of the q-axis current in the two-phase rotating coordinate system is 0. The three-phase voltage and current on the AC side are transformed to obtain the d- and q-axis components I in the two-phase rotating coordinate system. dq and U dq Combining the d-axis and q-axis current reference values, and after current inner loop control, the output is the d-axis and q-axis voltage reference values U in a two-phase rotating coordinate system. dq,ref The output U of the voltage and current dual closed-loop control module dq,ref After coordinate transformation, the input quantity U of the inverter switching signal generation module is obtained. abc,ref .
[0066] Figures 3(a)-3(d) The methods employed are the traditional fixed-step algorithm, the two-step algorithm, the adaptive step-size algorithm, and the method proposed in this embodiment, respectively, at an irradiance of 1000 W / m². 2 Simulation comparison of output power and output voltage of photovoltaic array when the reference power changes by a step change of 1 second and the operating point is located to the right of the maximum power point;
[0067] Figures 4(a)-4(d) The methods employed are the traditional fixed-step algorithm, the two-step algorithm, the adaptive step-size algorithm, and the method proposed in this embodiment, respectively, at an irradiance of 1000 W / m². 2 The simulation comparison of the output power and output voltage of the photovoltaic array when the reference power changes by a step change of 1 second and the operating point is to the left of the maximum power point.
[0068] It can be seen that one second ago, the photovoltaic system was operating at the flexible power point, and the power emitted by the photovoltaic system was equal to the reference power. One second later, the reference power changed from 9000W to 10000W. The photovoltaic system should then track the new reference power to achieve flexible power point tracking. Both the traditional method and the proposed method can achieve flexible power point tracking when the reference power changes abruptly, but some differences remain. When the operating point is to the right of the maximum power point, the proposed method only takes 0.4 seconds to track the new reference power, with a cumulative error of approximately 0.75% within 0-4 seconds. When the operating point is to the left of the maximum power point, it only takes 0.3 seconds, with a cumulative error of approximately 0.51% within 0-4 seconds. Compared with the traditional method, the proposed method shows improved tracking speed and significantly reduced cumulative error during tracking. Furthermore, the proposed method does not exhibit power oscillations when reaching steady state, while the traditional method exhibits power oscillations near the steady point.
[0069] Figures 5(a)-5(d) The figures show a comparison of the output power and output voltage of the photovoltaic array when the irradiance changes linearly for 1-3 seconds and 6-8 seconds, the reference power changes stepwise for 2 seconds and 7 seconds, and the operating point is located to the right of the maximum power point, using the traditional fixed step size algorithm, the two-step size algorithm, the adaptive step size algorithm, and the method proposed in this embodiment. Figures 6(a)-6(d) The figures show a comparison of the output power and output voltage of the photovoltaic array when using the traditional fixed-step algorithm, the two-step algorithm, the adaptive step-step algorithm, and the method proposed in this embodiment, respectively, with linear changes in irradiance of 1-3 seconds and 6-8 seconds, step changes in reference power of 2 seconds and 7 seconds, and the operating point being to the left of the maximum power point.
[0070] It can be seen that one second ago, the photovoltaic system was operating at the flexible power point, and the power emitted by the photovoltaic system was equal to the reference power. From 1 to 3 seconds, the irradiance increased from 1000 W / m². 2 Linear variation to 1280W / m 2 Simultaneously, the reference power changed from 9000W to 11000W in a step within 2 seconds. The irradiance increased from 1280W / m² in 6-8 seconds. 2 Linear variation up to 1000W / m 2 Simultaneously, the reference power changes stepwise from 11000W to 9000W within 7 seconds. The photovoltaic system should also track the reference power to achieve flexible power point tracking when irradiance changes. When the operating point is to the right of the maximum power point, the proposed method requires 4.5 seconds to track the new reference power, with a cumulative error of approximately 2.26% within 0-12 seconds. When the operating point is to the left of the maximum power point, it requires 4.6 seconds, with a cumulative error of approximately 1.81% within 0-12 seconds. Compared to traditional methods, the proposed method improves tracking speed and reduces cumulative error during tracking. Furthermore, the proposed method does not exhibit power oscillations when reaching steady state, while traditional methods exhibit power oscillations near the steady point.
[0071] Example 2
[0072] In one or more embodiments, a data-driven photovoltaic flexible power point tracking system is disclosed, comprising:
[0073] The power calculation module is used to collect the output voltage and output current of the photovoltaic array and calculate the output power of the photovoltaic array.
[0074] The flexible power point tracking module is used to calculate the difference between the output power of the photovoltaic array and a given reference power, and to determine whether the flexible power point has been tracked based on the difference. If the flexible power point has not been tracked, a perturbation signal is applied to the current output voltage of the photovoltaic array, and the output power of the photovoltaic array after the voltage perturbation is obtained. The gradient is estimated based on the output power of the photovoltaic array before and after the perturbation. The output voltage of the photovoltaic array is updated based on the gradient, the reference power, the output voltage and output power of the photovoltaic array before the perturbation are applied, and the updated output voltage is filtered to obtain the voltage reference value of the photovoltaic array at the next moment. Finally, the module re-determines whether the flexible power point has been tracked.
[0075] The specific implementation process of each of the above modules is the same as that in Example 1, and will not be described in detail again.
[0076] Example 3
[0077] In one or more embodiments, a terminal device is disclosed, including a server. The server includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the data-driven photovoltaic flexible power point tracking method of Embodiment 1. For simplicity, further details are omitted here.
[0078] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.
[0079] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.
[0080] In the implementation process, each step of the above method can be completed by the integrated logic circuits in the processor hardware or by software instructions.
[0081] Example 4
[0082] In one or more embodiments, a computer-readable storage medium is disclosed, wherein a plurality of instructions are stored, the instructions being adapted to be loaded by a processor of a terminal device and executed by the data-driven photovoltaic flexible power point tracking method described in Embodiment 1.
[0083] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.
Claims
1. A data-driven photovoltaic flexible power point tracking method, characterized in that, include: The output voltage and current of the photovoltaic array are collected, and the output power of the photovoltaic array is calculated. Calculate the difference between the output power of the photovoltaic array and a given reference power, and determine whether the flexible power point has been tracked based on the difference; If the flexible power point is not tracked, a perturbation signal is applied to the current output voltage of the photovoltaic array, and the output power of the photovoltaic array after the voltage perturbation is obtained; based on the output power of the photovoltaic array before and after the perturbation, the gradient is estimated, specifically as follows: By applying a perturbation signal to the current output voltage of the photovoltaic array, the perturbation voltage is obtained. Measure the output current corresponding to the disturbance voltage. Based on disturbance voltage and output current Calculate the output power of the photovoltaic array corresponding to the disturbance voltage. ; The gradient is the ratio of the difference between the output power value of the photovoltaic array after the voltage perturbation is applied and the output power value of the photovoltaic array before the voltage perturbation is applied to the applied perturbation voltage value. Based on the gradient, reference power, and the output voltage and output power of the photovoltaic array before the perturbation, the output voltage of the photovoltaic array is updated; the updated output voltage is filtered to obtain the voltage reference value of the photovoltaic array at the next moment. The updated output voltage of the photovoltaic array is specifically as follows: ; in, For the updated voltage, To the output voltage of the photovoltaic array before applying the disturbance, Indicates the learning rate. For the estimated gradient, To determine the output power of the photovoltaic array before applying the disturbance, Given a reference power, For projection operators, , and These are the lower and upper bounds of the photovoltaic array output voltage, respectively. Repeat the above process until the flexible power point is located.
2. The data-driven photovoltaic flexible power point tracking method as described in claim 1, characterized in that, Calculate the difference between the output power of the photovoltaic array and a given reference power. If the absolute value of the difference is less than a set power threshold, the flexible power point is tracked; otherwise, the flexible power point is not tracked.
3. A data-driven photovoltaic flexible power point tracking method as described in claim 1 or 2, characterized in that, If the flexible power point is detected, the output voltage of the photovoltaic array is directly output, and the tracking ends.
4. The data-driven photovoltaic flexible power point tracking method as described in claim 1, characterized in that, The updated output voltage is filtered to obtain the voltage reference value of the photovoltaic array at the next moment, specifically: in, For the updated voltage, To the output voltage of the photovoltaic array before applying the disturbance, This represents the first-order filter factor.
5. A data-driven photovoltaic flexible power point tracking system, characterized in that, include: The power calculation module is used to collect the output voltage and output current of the photovoltaic array and calculate the output power of the photovoltaic array. The flexible power point tracking module is used to calculate the difference between the output power of the photovoltaic array and a given reference power, and to determine whether the flexible power point has been tracked based on the difference. If the flexible power point has not been tracked, a perturbation signal is applied to the current output voltage of the photovoltaic array, and the output power of the photovoltaic array after the voltage perturbation is obtained. Based on the output power of the photovoltaic array before and after the perturbation, the gradient is estimated, specifically as follows: By applying a perturbation signal to the current output voltage of the photovoltaic array, the perturbation voltage is obtained. Measure the output current corresponding to the disturbance voltage. Based on disturbance voltage and output current Calculate the output power of the photovoltaic array corresponding to the disturbance voltage. ; The gradient is the ratio of the difference between the output power value of the photovoltaic array after the voltage perturbation is applied and the output power value of the photovoltaic array before the voltage perturbation is applied to the applied perturbation voltage value. Based on the gradient, reference power, and the output voltage and output power of the photovoltaic array before the perturbation, the output voltage of the photovoltaic array is updated; the updated output voltage is filtered to obtain the voltage reference value of the photovoltaic array at the next moment; and it is then re-determined whether the flexible power point has been tracked. The updated output voltage of the photovoltaic array is specifically as follows: in, For the updated voltage, To the output voltage of the photovoltaic array before applying the disturbance, Indicates the learning rate. For the estimated gradient, To determine the output power of the photovoltaic array before applying the disturbance, Given a reference power, For projection operators, , and These are the lower and upper bounds of the output voltage of the photovoltaic array, respectively.
6. A terminal device comprising a processor and a memory, the processor for implementing instructions; the memory for storing multiple instructions, characterized in that, The instructions are adapted to be loaded by a processor and executed by the data-driven photovoltaic flexible power point tracking method according to any one of claims 1-4.
7. A computer-readable storage medium storing a plurality of instructions, characterized in that, The instructions are adapted to be loaded by the processor of the terminal device and executed as described in any one of claims 1-4, which is a data-driven photovoltaic flexible power point tracking method.
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