A Maximum Power Point Tracking Method for Complex Photovoltaic Arrays

Abstract

The invention discloses a maximum power point tracking method for a complex photovoltaic array, comprising the following steps: obtaining an I-V characteristic curve of a photovoltaic cell under the condition of shadow shielding, decomposing the curve into multiple parabolas to simulate multi-point horizontal projection motion; establishing each parabolic curve and the horizontal projection motion trajectory of a particle in the same coordinate system, dividing the parabolic curve into three sections, regarding the horizontal coordinate voltage V as the motion time of the particle, and the vertical coordinate current I as its displacement in the vertical direction; regarding the I-V characteristic curve of the photovoltaic cell as a trajectory diagram of the particle performing horizontal projection motion from the position of a point (0, Isc), wherein the initial velocity is set as Vo; assuming that there are three different gravity fields g0=0, g1, and g2 in the horizontal projection motion trajectory of the particle, wherein the dividing points of the three gravity fields are the same as the I-V characteristic curve; obtaining a ball motion trajectory equation by deriving formulas of g1 and g2, namely, the I-V characteristic equation of each section of a photovoltaic array model, and finally superimposing the formulas obtained in each section; performing maximum power point tracking on the multi-point horizontal projection model in combination with a particle swarm algorithm, thereby obtaining the maximum power point.

Description

Technical Field

[0001] The invention relates to the technical field of photovoltaic arrays, in particular to a maximum power point tracking method for a complex photovoltaic array. Background Art

[0002] In recent years, solar power generation has achieved rapid development as an emerging green energy and has become the most promising alternative energy in the 21st century. In practical applications, photovoltaic power generation systems usually require the use of photovoltaic arrays to output the most electricity on a safe and stable basis. Therefore, the operating voltage of the system must be adjusted in real time so that the array can operate at the maximum power point at any time. This requires the use of maximum power tracking technology to enable the array to operate at the maximum power point at any time.

[0003] At present, domestic and foreign research on the maximum power point tracking technology has been conducted in-depth theoretical, experimental and simulation research. The mathematical model method establishes an equivalent circuit model based on the mathematical model of the photovoltaic array, and studies its output characteristic curve to obtain the maximum power point voltage in the interval [0.75Voc, 0.85Voc]. The perturbation observation method changes the output voltage by periodically applying a certain step of perturbation to the output voltage of the photovoltaic array, and observes the change in output power after the perturbation to adjust the direction of the next period of perturbation until the array outputs the maximum power. The conductance increment method determines whether the photovoltaic array is working at the maximum power point by comparing the instantaneous conductance of the photovoltaic array and its change. With the development of science and technology, some intelligent algorithms (such as fuzzy control algorithms and neural network algorithms) are combined with traditional MPPT algorithms to improve the tracking progress and tracking speed. However, these methods are only applicable to the output characteristic curve of the photovoltaic array with a single peak value. In practical applications, due to environmental factors, the illumination of the photovoltaic array is not uniform, and some parts may even be blocked, which will produce photovoltaic hot spots, thereby affecting the output characteristics of the photovoltaic system. At this time, the output volt-ampere characteristic surface of the component is stepped, and the corresponding power-voltage curve contains multiple local maximum peaks. At the same time, in the photovoltaic power generation system, in order to improve the voltage and power output of the photovoltaic power source, photovoltaic cells are connected in series and parallel to form photovoltaic arrays of various topological structures. For this reason, it is necessary to study a maximum power point tracking algorithm suitable for complex photovoltaic arrays. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a mathematical model of hot spots of photovoltaic arrays based on multi-point horizontal projection motion, which can be applied to modeling photovoltaic arrays with complex structures under hot spot conditions, and combines the model with a particle swarm algorithm to achieve a maximum power point tracking method for complex photovoltaic arrays that achieves maximum power point tracking.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] A maximum power point tracking method for a complex photovoltaic array, comprising the steps of:

[0007] 1) Obtain the IV characteristic curve of the photovoltaic cell under the condition of shadow. The existence of shadow makes the output volt-ampere characteristic curve of the photovoltaic array present multiple steps. Decompose the curve into multiple parabolas to simulate multi-point horizontal projection motion, and derive the corresponding equation according to the following steps;

[0008] 2) Each parabolic curve and particle horizontal projection motion trajectory are established in the same coordinate system, which is divided into three sections: (0, xVm), (xVm, Vm), (Vm, Voc). The horizontal axis voltage V is regarded as the motion time of the particle, and the vertical axis current I is its displacement in the vertical direction. The IV characteristic curve of the photovoltaic cell is regarded as the trajectory diagram of the particle doing horizontal projection motion from the point (0, Isc), and its initial velocity is set to Vo. In the particle's horizontal projection motion trajectory, it is assumed that there are three different gravitational fields g0=0, that is, the particle does uniform linear motion, g1, g2, and the dividing points of the three gravitational fields are the same as the IV characteristic curve;

[0009] 3) By deriving the formulas for g1 and g2, we obtain the equation for the trajectory of the ball, which is the IV characteristic equation for each section of the photovoltaic array model. Finally, we superimpose the formulas for each section.

[0010] 4) Combine the particle swarm algorithm to track the maximum power point of the multi-point horizontal projection model to obtain the maximum power point.

[0011] Step 3) The motion trajectory equation of the ball is derived from the kinematic theory:

[0012]

[0013] The values ​​of gi1 and gi2 are as follows:

[0014]

[0015] Where Isc, Voc, Im, and Vm are the short-circuit current, open-circuit voltage, current at the maximum power point, and voltage at the maximum power point of the photovoltaic module when the light intensity is S, respectively; (n-1) is the number of modules blocked by shadows; and x=0.00027S+0.5492.

[0016] Step 4) In the particle swarm algorithm, it is assumed that there are n particles randomly distributed in n-dimensional space, and the position of each particle is X i (i=1,2,3,……,n), speed is v i , the particle iteration formula is as follows:

[0017]

[0018] In the formula, K is the current iteration number, w is the inertia weight, c 1 and c 2 is the learning factor, r 1 and r 2 is a random number between (0,1), P m is the optimal solution for an individual, G m is the global optimal solution.

[0019] Combined with the mathematical model method, the particle selection position is reduced to [0.75V oc ,0.85V oc ], the specific implementation steps are as follows: initialize the parameters of the particle swarm; calculate the fitness value of each particle according to the fitness function; find the individual best fitness value: compare the fitness value of each particle at the current position with its historical best position (P m ) corresponding to the fitness value. If the fitness value of the current position is higher, the current position is used to update the historical best position. Find the best fitness value of the group: compare the fitness value of the current position of each example with its global best position (G m ) corresponding fitness value, if the fitness value of the current position is higher, then use the current position to update the global best position; update the speed and position of each particle according to the formula; determine whether the algorithm ends, if the end condition is not met, return to calculate the fitness value of each particle, if the end condition is met, the algorithm ends, and the global best position (G m ) is the global optimal solution.

[0020] The various parameters of the particle swarm include the number of particles, learning factor, and particle speed.

[0021] Compared with the prior art, the advantages of the present invention are: the present invention constructs a multi-point flat-throw model of a photovoltaic array, which can model complex photovoltaic arrays under local shadow conditions. The error of the model is within the engineering accuracy requirements, and the calculation amount of the model solution process is small compared with the traditional engineering model.

[0022] The present invention introduces the multi-point horizontal projection model into the particle swarm algorithm, and accurately finds the maximum power point of the photovoltaic array without changing the convergence. ;

[0023] The present invention can track the maximum power point of a complex photovoltaic array under partial shadow conditions, thereby reducing photovoltaic power generation losses compared with traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is the IV curve of the photovoltaic array output under shadow.

[0025] Figure 2 The IV output curve of the photovoltaic array without shadow.

[0026] Figure 3 Particle swarm algorithm flow chart.

[0027] Figure 4 Comparison chart without shadow.

[0028] Figure 5 Optimization curve diagram.

[0029] Figure 6 Comparison chart under shadow conditions.

[0030] Figure 7 Optimization curve diagram. DETAILED DESCRIPTION

[0031] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0032] A maximum power point tracking method for a complex photovoltaic array, comprising the steps of:

[0033] Step 1: The IV characteristic curve of the photovoltaic cell under shadow is as follows Figure 1 As shown, the existence of shadows makes the output volt-ampere characteristic curve of the photovoltaic array present multiple steps. At this time, the curve can be decomposed into multiple parabolas to simulate multi-point horizontal projection motion, and the corresponding equation can be derived according to the following steps.

[0034] Step 2: Each parabolic curve can be established in the same coordinate system as the particle's horizontal projection trajectory, and divided into three segments: (0, xVm), (xVm, Vm), and (Vm, Voc). Figure 2 As shown, the horizontal axis voltage V is regarded as the movement time of the particle, and the vertical axis current I is its displacement in the vertical direction. Then the IV characteristic curve of the photovoltaic cell can be regarded as the trajectory of the particle moving horizontally from the point (0, Isc), and its initial velocity is set to Vo. In the trajectory of the particle's horizontal motion, it is assumed that there are three different gravitational fields g0 = 0 (the particle moves in a uniform straight line), g1, and g2. The dividing points of the three gravitational fields are the same as the IV characteristic curve.

[0035] Step 3: By deriving the formulas for g1 and g2, we can get the equation for the trajectory of the ball, which is the IV characteristic equation for each section of the photovoltaic array model. Finally, we can superimpose the formulas for each section.

[0036] The motion trajectory equation of the ball can be deduced from the kinematic theory:

[0037]

[0038] The values ​​of gi1 and gi2 are as follows:

[0039]

[0040] In the formula, Isc, Voc, Im, and Vm are the short-circuit current, open-circuit voltage, current at the maximum power point, and voltage at the maximum power point of the photovoltaic module when the light intensity is S, respectively, and (n-1) is the number of modules blocked by shadows. Fu Wang et al. compared and analyzed a large amount of measured data in a digital photovoltaic array simulator based on a horizontal motion model and concluded that: whether it is a single-crystal silicon or polycrystalline silicon solar cell, under the general land light and temperature environmental conditions, the value of x is positively correlated with the light intensity and has little to do with the battery temperature, so the formula for fitting the optimal value of x is: x = 0.00027S + 0.5492. This formula is universal for models based on horizontal motion, and the model proposed in the present invention is also based on horizontal motion, so the value of x in the model of the present invention can also be calculated in this way.

[0041] Step 4: Combine the particle swarm algorithm to track the maximum power point of the multi-point horizontal projection model to obtain the maximum power point.

[0042] In the particle swarm algorithm, it is assumed that there are n particles randomly distributed in n-dimensional space, and the position of each particle is X i (i=1,2,3,……,n), speed is v i , the particle iteration formula is as follows:

[0043]

[0044] In the formula, K is the current iteration number, w is the inertia weight, c 1 and c 2 is the learning factor, r 1 and r 2 is a random number between (0,1), P m is the optimal solution for an individual, G m is the global optimal solution. Combined with the mathematical model method, the particle selection position is reduced to [0.75V oc ,0.85V oc ] to reduce the amount of calculation. The flow chart is as follows Figure 3 As shown, the specific implementation steps are as follows:

[0045] 1. Initialize various parameters of the particle swarm (number of particles, learning factor, particle speed, etc.)

[0046] 2. According to the fitness function, calculate the fitness value of each particle

[0047] 3. Find the best individual fitness value: Compare the fitness value of each particle at its current position with its best historical position (P m ) and the corresponding fitness value. If the fitness value of the current position is higher, the current position is used to update the historical best position.

[0048] 4. Find the best fitness value of the group: Compare the fitness value of each example's current position with its global best position (G m ) and the corresponding fitness value. If the fitness value of the current position is higher, the current position is used to update the global best position.

[0049] 5. Update the speed and position of each particle according to the formula

[0050] 6. Determine whether the algorithm is finished. If the end condition is not met, return to step 2. If the end condition is met, the algorithm ends and the global best position (G m ) is the global optimal solution.

[0051] Example

[0052] The array of 8 photovoltaic engineering models built in CTCT structure was simulated by MATLAB and compared with the output characteristics of the multi-point horizontal motion model.

[0053] The parameters for simulating normal lighting conditions are:

[0054] V oc =87.7V, I sc =41.8A, V m =72.4V, I m =38.4A.

[0055] The reference temperature is 25°C. The reference light intensity is 1000W / m 2 .

[0056] Based on the above parameters, the IV characteristic equation is derived as follows:

[0057]

[0058] The comparison between mathematical model and simulation output curve is shown in the figure below: Figure 4 shown.

[0059] The multi-point horizontal throwing model and the engineering model are respectively introduced into the particle swarm algorithm for solution, and the obtained optimization curve is shown in the figure below: Figure 5 shown.

[0060] The Vm obtained by substituting the engineering model into the particle swarm algorithm is 75.0846V, and the Vm obtained by substituting the multi-point horizontal throwing model into the particle swarm algorithm is 75.0742V, and the two values ​​are almost the same. Figure 5 It can be seen that the convergence of the optimization curves of the two models is consistent.

[0061] The parameters for simulating shadow occlusion are:

[0062] The reference temperature is 25°C and the reference light intensity is 1000W / m 2 The light intensity of the blocked part is 500W / m 2 .

[0063] Based on the above parameters, the IV characteristic equation is derived as follows:

[0064]

[0065]

[0066] The comparison of the output curves of the mathematical model and the simulation is shown in the figure below. Figure 6 shown.

[0067] Substitute it into the particle swarm algorithm to obtain the optimization curve diagram as shown below Figure 7 As shown, the obtained Vm is 75.0742V.

[0068] It can be seen from the comparison chart that the multi-point flat-throw model value of the present invention and the output characteristic value of the engineering model are slightly different, but the error is within the accuracy allowed by the engineering, and the output curves basically overlap and have the same peak. Since the engineering model involves exponential operations, the calculation is cumbersome and complicated. However, the model proposed in this article has a significantly reduced calculation time (from 4s to 0.2s) compared to the engineering model under the premise of achieving engineering accuracy, and the solution is relatively simple. At the same time, when the particle swarm algorithm is introduced for maximum power point tracking, if the engineering model encounters the situation where the photovoltaic array is shaded and hot spots are generated, it will appear powerless. The model of the present invention has strong applicability and can be used in the case of hot spots generated by shadows or not, and the model of the present invention has a wide range of applications. At the same time, the model of the present invention can be used to describe complex photovoltaic arrays, not just limited to simple structures such as series-parallel, SP, and TCT. The combination of the multi-point flat-throw model and the particle swarm algorithm can realize the maximum power point tracking of complex photovoltaic arrays under shadow occlusion, and accurately converge to the global maximum power point without improving its convergence, thereby improving the efficiency of photovoltaic power generation.

Claims

1. A maximum power point tracking method for a complex photovoltaic array, characterized by the steps include: 1) Obtain the IV characteristic curve of the photovoltaic cell under the condition of shadow. The existence of shadow makes the output volt-ampere characteristic curve of the photovoltaic array present multiple steps. Decompose the curve into multiple parabolas to simulate multi-point horizontal projection motion, and derive the corresponding equation according to the following steps; 2) Each parabolic curve and particle horizontal projection motion trajectory are established in the same coordinate system, which is divided into three sections: (0, xVm), (xVm, Vm), (Vm, Voc). The horizontal axis voltage V is regarded as the motion time of the particle, and the vertical axis current I is its displacement in the vertical direction. The IV characteristic curve of the photovoltaic cell is regarded as the trajectory diagram of the particle doing horizontal projection motion from the point (0, Isc), and its initial velocity is set to Vo. In the particle's horizontal projection motion trajectory, it is assumed that there are three different gravitational fields g0=0, that is, the particle does uniform linear motion, g1, g2, and the dividing points of the three gravitational fields are the same as the IV characteristic curve; 3) By deriving the formulas for g1 and g2, we obtain the equation for the trajectory of the ball, which is the IV characteristic equation for each section of the photovoltaic array model. Finally, we superimpose the formulas for each section. 4) Combine the particle swarm algorithm to track the maximum power point of the multi-point horizontal throwing model to obtain the maximum power point; Step 3) The motion trajectory equation of the ball is derived from the kinematic theory: The values ​​of gi1 and gi2 are as follows: Where Isc, Voc, Im, and Vm are the short-circuit current, open-circuit voltage, current at the maximum power point, and voltage at the maximum power point of the photovoltaic module when the light intensity is S, respectively; (n-1) is the number of modules blocked by shadows; x=0.00027S+0.5492; Step 4) In the particle swarm algorithm, it is assumed that there are n particles randomly distributed in n-dimensional space, and the position of each particle is X i (i=1,2,3,……,n), speed is v i， The particle iteration formula is as follows: Where K is the current iteration number, w is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers between (0,1), and P m is the optimal solution for an individual, G m is the global optimal solution; Combined with the mathematical model method, the particle selection position is reduced to [0.75V oc ,0.85V oc ], the specific implementation steps are as follows: Initialize the parameters of the particle swarm; calculate the fitness value of each particle according to the fitness function; find the best individual fitness value: compare the fitness value of each particle at its current position with its best historical position (P m ) corresponding to the fitness value. If the fitness value of the current position is higher, the current position is used to update the historical best position. To find the best fitness value of the group: compare the fitness value of each particle's current position with its global best position (G m ) and the corresponding fitness values ​​are compared. If the fitness value of the current position is higher, the current position is used to update the global best position. Update the speed and position of each particle according to the formula; determine whether the algorithm ends. If the end condition is not met, return to calculate the fitness value of each particle. If the end condition is met, the algorithm ends and the global optimal position (G m ) is the global optimal solution.

2. A maximum power point tracking method for a complex photovoltaic array according to claim 1, characterized in that The various parameters of the particle swarm include the number of particles, learning factor, and particle speed.

Images