CN108983863B - A Photovoltaic Maximum Power Tracking Method Based on Improved Firefly Algorithm - Google Patents

Abstract

The present invention relates to a photovoltaic maximum power tracking method based on an improved firefly algorithm, comprising: step S1: loading the initial vaccine database, step S2: setting the population size, and initializing the positions of all fireflies in the population based on the vaccine database, and setting the positions of each firefly The objective function value is taken as the respective maximum fluorescence brightness; Step S3: Divide the perception radius of each firefly and update the attractiveness; Step S4: Update the position of each firefly; Step S5: Perform immune supplementation operation; Step S6: Determine whether the convergence condition is met, if If yes, execute step S7; if no, return to step S4; step S7: get the maximum power point based on the current position of each firefly, and update the vaccine database. Compared with the prior art, the invention can effectively reduce algorithm failure, accelerate convergence speed and improve control effect due to the addition of vaccine library and immune supplement operation, and realize rapid response in dynamic environment. In addition, a step size function is constructed to weaken the steady-state oscillation of the algorithm.

Description

A Photovoltaic Maximum Power Tracking Method Based on Improved Firefly Algorithm

technical field

The invention relates to a photovoltaic power control technology, in particular to a photovoltaic maximum power tracking method based on an improved firefly algorithm.

Background technique

Ideally, the photovoltaic cells in the photovoltaic array work under the same temperature and solar irradiance. At this time, the P-U curve of the photovoltaic array presents a single-peak characteristic. The maximum power point can be achieved by using the incremental method and the disturbance observation method. track. However, in actual situations, aging, local shading, and dust coverage will cause inconsistent output characteristics of photovoltaic cells. At this time, there are multiple power peak points on the P-U curve of the photovoltaic array, and the traditional single-peak MPPT method may be trapped in local The peak point not only causes a large amount of energy loss, but also increases the complexity of photovoltaic array scheduling.

The swarm intelligence algorithm can realize distributed parallel search and provide solutions to problems that are difficult to deal with by traditional methods and have no precise mathematical model, so it can be used to realize multi-peak GMPPT. However, most swarm intelligence algorithms have disadvantages such as: restarting is required when external conditions change; under dynamic PSC, the algorithm does not converge or the convergence time is long; the convergence time is unstable and other shortcomings.

Contents of the invention

The purpose of the present invention is to provide a photovoltaic maximum power tracking method based on an improved firefly algorithm in order to overcome the above-mentioned defects in the prior art.

The purpose of the present invention can be achieved through the following technical solutions:

A photovoltaic maximum power tracking method based on the improved firefly algorithm, including:

Step S1: Load the initial vaccine library,

Step S2: Set the population size, and initialize the positions of all fireflies in the population based on the vaccine library, and use the objective function value of each firefly as their respective maximum fluorescence brightness;

Step S3: Divide the perception radius of each firefly and update the degree of attraction;

Step S4: update the position of each firefly;

Step S5: Based on the immune complement operation, some new fireflies are generated to replace fireflies with lower maximum fluorescence brightness;

Step S6: Judging whether the convergence condition is satisfied, if yes, execute step S7, if no, return to step S4;

Step S7: Obtain the maximum power point based on the current position of each firefly, and update the vaccine library.

The vaccine library consists of the previously found maximum power points and corresponding firefly positions.

Described step S2 specifically comprises:

Step S21: taking the objective function values of fireflies as their respective maximum fluorescence brightness;

Step S22: Calculate the spatial distance between each firefly:

r _ij =||x _i -x _j ||

Among them: r _ij is the spatial distance between firefly i and firefly j, ||·|| is the Euclidean norm, x _i is the position of firefly i, and x _j is the position of firefly j.

The objective function value of the firefly is the power obtained based on the voltage corresponding to the position of the firefly.

Described step S3 comprises:

Step S31: Calculate the perception radius according to the maximum fluorescent brightness of fireflies:

R＝φI ₀

Among them: R is the perception radius, I ₀ is the maximum fluorescence brightness of fireflies, and φ is the perception coefficient;

Step S32: Calculate the degree of attraction between fireflies according to the spatial distance between fireflies:

Among them: β is the attraction between firefly i and firefly j, β ₀ is the maximum attraction, γ is the light intensity absorption coefficient, and e is the natural base.

Fireflies with lower maximum fluorescence brightness within the perception radius of any firefly will move closer to the center of the perception radius.

In the step S4, the positions of each firefly are updated as follows:

x _i (t+1)＝ _xi (t)+β[x _j (t) _-xi (t)]+S

Among them: x _i (t+1) is the position of firefly i after the t-th iteration update, x _i (t) is the position of firefly i before the t-th iteration update, x _j (t) is the t-th iteration The updated position of firefly j, S is the step size function, the expression is as follows:

Among them: r is the horizontal spacing of fireflies, x _max and x _min represent the upper and lower limits of the firefly distribution area.

In the step S5, the number of fireflies to be replaced is μn, where: μ is the immune coefficient whose value is on [0,1], and n is the set population size.

Described step S6 comprises:

Step S61: recalculate the firefly's objective function value according to the updated position of the firefly;

Step S62: When the iteration accuracy is satisfied or the maximum number of iterations is reached, then output the global extremum point and the optimal individual value; otherwise, return to step S4 for the next iteration calculation.

The step 7 specifically includes:

Step S71: Use the voltage corresponding to the position of the firefly with the largest objective function value as the maximum power point voltage, and output the global maximum power point;

Step S72: Update and replace the closest vaccine in the vaccine library with the obtained maximum power point.

Compared with the prior art, the present invention has the following beneficial effects:

1) Due to the addition of the vaccine library and immune supplementary operations, it can effectively reduce the phenomenon of algorithm failure, speed up the convergence speed and improve the control effect, and achieve rapid response in dynamic environments. In addition, a step size function is constructed to weaken the steady-state oscillation of the algorithm.

2) On the basis of maintaining the excellent local search ability of the firefly algorithm, the vaccine library is used to obtain and narrow the distribution interval of the initial population to improve the convergence speed of the algorithm.

3) A variable step size function is constructed to weaken steady-state oscillations. Simulation results show that the algorithm can achieve good GMPPT tracking and positioning capabilities under dynamic environmental conditions.

Description of drawings

Fig. 1 is a schematic flow chart of the main steps of the inventive method;

Fig. 2 is the five-peak P-U curve;

Figure 3 is the iterative trend of the optimal value of the population;

Figure 4 is FA steady state oscillation;

Figure 5 shows the improved FA algorithm to eliminate steady-state oscillations;

Figure 6 is the failure process of the FA algorithm;

Fig. 7 is the flowchart of immune supplement operation;

Figure 8 shows the time-consuming impact of immune supplementation on the algorithm;

Fig. 9 is four peak P-U curves;

Figure 10 shows the dynamic tracking of the maximum output power iterative trend of the improved FA algorithm;

Figure 11 shows the iterative trend of the improved FA algorithm to dynamically track the fitness of the optimal value;

Figure 12 is the dynamic tracking population distribution of the FA algorithm;

Figure 13 shows the dynamic tracking population distribution of the improved FA algorithm.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is carried out on the premise of the technical solution of the present invention, and detailed implementation and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

A photovoltaic maximum power tracking method based on the improved firefly algorithm, as shown in Figure 1, including:

Step S1: Load the initial vaccine library. The vaccine library is composed of the previously found maximum power point and the corresponding firefly position. By vaccinating the population to obtain an excellent initial population, according to the previously found maximum power point, the composition The vaccine library is updated every time the algorithm converges.

Step S2: Set the population size, and initialize the positions of all fireflies in the population based on the vaccine library,

In the initialization process, the vaccine library is divided into three areas on the basis of maximizing the geometrical margin by using Support Vector Machine (SVM), and the number of vaccines contained in each area is respectively Y ₁ , Y ₂ , Y ₃ , the number of individuals in the initial population in the three areas is calculated by the following formula, where m is the population size, and θ is the vaccine coefficient on [0,1].

And the objective function value of each firefly is taken as their respective maximum fluorescence brightness, specifically including:

Step S21: The objective function value of the firefly is taken as the respective maximum fluorescence brightness, wherein the objective function value of the firefly is the power obtained based on the voltage corresponding to the position of the firefly;

Step S22: Calculate the spatial distance between each firefly:

r _ij =||x _i -x _j ||

Among them: r _ij is the spatial distance between firefly i and firefly j, ||·|| is the Euclidean norm, x _i is the position of firefly i, and x _j is the position of firefly j.

Step S3: Divide the perception radius of each firefly and update the degree of attraction, including:

Step S31: Calculate the perception radius according to the maximum fluorescent brightness of fireflies:

R＝φI ₀

Among them: R is the perception radius, I ₀ is the maximum fluorescence brightness of fireflies, and φ is the perception coefficient;

Fireflies with larger objective function values have larger perception radius, and fireflies with lower maximum fluorescence brightness within the perception radius will approach the center of the perception radius;

Step S32: Calculate the attraction between fireflies according to the spatial distance between fireflies. Since the fluorescence emitted by fireflies will weaken with distance when propagating in the medium, it is defined as a monotonically decreasing function related to distance:

Among them: β is the attraction between firefly i and firefly j, β ₀ is the maximum attraction, γ is the light intensity absorption coefficient, and e is the natural base.

Step S4: Update the position of each firefly, wherein, update the position of each firefly as:

x _i (t+1)＝ _xi (t)+β[x _j (t) _-xi (t)]+S

Among them: x _i (t+1) is the position of firefly i after the t-th iteration update, x _i (t) is the position of firefly i before the t-th iteration update, x _j (t) is the t-th iteration The updated position of firefly j, S is the step size function, the expression is as follows:

Among them: r is the horizontal spacing of fireflies, x _max and x _min represent the upper and lower limits of the firefly distribution area.

The iterative formula of the traditional FA algorithm is:

x _i (t+1)＝ _xi (t)+β[x _j (t) _-xi (t)]+α(rand-1/2)

In the formula, α is a step factor, and rand is a random factor that obeys a uniform distribution on [0,1].

In the step S5, the number of fireflies to be replaced is μn, where: μ is the immune coefficient whose value is on [0,1], and n is the set population size.

Within the perception radius of firefly j, firefly i is attracted by firefly j with higher maximum fluorescence brightness and moves its position.

Step S5: Generate some new fireflies based on the immune supplementation operation to replace fireflies with lower maximum fluorescence brightness to help jump out of the local optimal solution and maintain the diversity of the population, where the number of replaced fireflies is μn, where: μ is the value The immune coefficient on [0,1], n is the set population size,

In this process, new fireflies are randomly generated instead of based on the vaccine library, which can improve diversity, and more effectively solve algorithm failures, and achieve rapid response in dynamic environments.

Step S6: Judging whether the convergence condition is satisfied, if yes, execute step S7, if no, return to step S4, including:

Step S61: recalculate the firefly's objective function value according to the updated position of the firefly;

Step S62: When the difference before and after the iteration is less than the threshold or reaches the maximum number of iterations, output the global extremum point and the optimal individual value; otherwise, return to step S4 for the next iteration calculation.

Step S7: Obtain the maximum power point based on the current position of each firefly, and update the vaccine library, specifically including:

Step S71: Use the voltage corresponding to the position of the firefly with the largest objective function value as the maximum power point voltage, and output the global maximum power point;

Step S72: Update and replace the closest vaccine in the vaccine library with the obtained maximum power point.

The following is a simulation verification of the effect of the application method. Specifically, the solar cell model that comes with matlab is used, and the S-Function module is used as the core of the GMPPT controller to build a simulation model. The simulation verification is divided into two parts: one is to verify the impact of immune supplementation on the algorithm . The second is the power tracking comparison between the traditional firefly algorithm and the improved algorithm under dynamic PSC.

The algorithm parameter settings are shown in Table 1:

Table 1 FA algorithm parameter settings

Initialize the immune library M=[94.962, 84.305, 76.081, 61.964, 74.650, 82.905, 81.630, 85.610, 77.106, 77.879], set the vaccine coefficient θ to 0.6, and the immune coefficient μ to 0.3.

The flow chart of the algorithm is shown in Figure 1.

The first part of simulation verification:

The multi-peak P-U curve obtained by simulation is shown in Figure 2. The five power peak points are 35.619, 62.662, 84.164, 102.175, and 116.200V. GMPP is the third peak point, and its global maximum output power is 1.8240kW.

Firstly, the immune supplement operation in the improved FA algorithm is temporarily deleted, where FA (Firefly Algorithm, FA) is the firefly algorithm, and the improved FA algorithm is the improved firefly algorithm.

The result of a single operation of the algorithm is shown in Figure 3. P is the optimal value of the population after each iterative operation, and S ₁ and S ₂ are the convergence points of the improved FA and traditional FA algorithms respectively. It can be seen from the figure that the improved FA The algorithm converges faster than traditional FA, and FA converges to the local optimal solution, that is, the second peak point, and the final output power is 1.7865kW. After the algorithm converges, the vaccine library is updated, and the third peak power point 84.164V is used to replace the closest vaccine 85.610V in the vaccine library.

Taking the voltage of the optimal individual representative after each iteration as the observation object, the improved FA algorithm and the running results of the FA algorithm are obtained, as shown in Figure 4 and Figure 5, respectively. It can be seen that the FA algorithm will lead to steady-state oscillations. Although the amplitude is small, the algorithm will not converge when the convergence conditions are stricter. The improved FA algorithm solves the problem of steady state oscillation well through the step size function

Due to the randomness of the operation of the algorithm, 30 simulations were performed under the improved FA and FA environments respectively, and the simulation results are shown in Table 2. Improved FA is obviously better than FA, not only with higher average output power and faster convergence, but also never converges to the local optimum. In comparison, the probability of FA to converge to the local optimum is almost 50%. In addition, when the FA and the improved FA are running, the algorithm fails, and if such a situation occurs, the algorithm is re-run.

Table 2 Algorithm running results for multiple times

The initial distribution of the firefly population at the time of failure is shown in Figure 6. The positions of the 10 individuals are 97.766, 110.612, 15.238, 111.470, 73.933, 11.704, 33.419, 65.625, 114.593, and 115.786V. After the population position is updated, individuals with lower objective function values in area 1 and area 2 will move closer to fireflies with better positions and gather at one point. For other individuals in the population, point K ₁ is outside the perception radius of K ₂ , so the position will not be updated, and K ₃ and K ₄ are also not within the perception range of individuals with higher objective functions. Therefore, K ₃ and K ₄ also do not change positions as the number of iterations increases. After each iteration is completed, the algorithm outputs the objective function value of the optimal individual. At this time, the output P will not change each time. In this case, the algorithm neither converges to the global optimum nor converges to Local optimum, so it is called algorithm failure.

Figure 7 is the specific flow of the immune supplementation operation.

At this point, the immune supplementation operation is added.

The improved FA algorithm with or without the immune complement operation is simulated 30 times under the P-U characteristic shown in Figure 2, and the results are shown in Table 3. The immune supplement operation can not only further shorten the time required for algorithm convergence, but also further reduce the algorithm risk of failure.

Table 3 Effect of immune supplementation on algorithm operation

When there is no immune supplement operation, the time required for the algorithm to run 30 times is shown in Figure 8. It can be seen from the figure that after the immune supplement is added, the time-consuming algorithm is more stable. Calculate the variance of the time-consuming in the two cases respectively, and get When there is no immune supplement operation, the time-consuming variances are 0.0125 and 0.0819, respectively.

The second part of simulation verification:

Take Figure 2 as the P-U curve corresponding to the first static PSC, and Figure 9 as the P-U curve corresponding to the second static PSC. The peak power points in Figure 9 are 26.819, 67.660, 73.554, and 108.301V respectively. The algorithm switches to the second PSC when the number of iterations under the first PSC reaches 10. The distribution positions of the maximum power peak points of the two P-U curves are quite different, and it is difficult to realize dynamic tracking, which makes the simulation results convincing.

The specific tracking process of the improved FA algorithm under dynamic PSC is shown in Figure 10 and Figure 11. P and J are the output power and fitness corresponding to the optimal individual in the population after the iteration is completed, respectively. After PSC switching, the improved FA algorithm only iterates 17 times to successfully track the global maximum power point.

Figure 12 and Figure 13 respectively show the trend of individual position changes over time of FA and improved FA algorithms in a dynamic PSC environment. It can be clearly seen from the figure that FA is in failure state before and after dynamic PSC switching. Before 0.266sPSC switching, FA has achieved local convergence in a small area, which increases the probability of algorithm failure under dynamic PSC. The distribution of population positions in Figure 12 It can be clearly seen that the population position does not change after PSC switching, the diversity is lost, and the algorithm fails.

However, the population distribution of the improved FA algorithm changed significantly before and after the 0.266sPSC switch, indicating that the algorithm remained effective after the PSC switch, and the immune complement operation ensured the diversity of the population.

Claims (10)

1. A photovoltaic maximum power tracking method based on improved firefly algorithm, characterized in that, comprising: Step S1: Load the initial vaccine library, Step S2: Set the population size, and initialize the positions of all fireflies in the population based on the vaccine library, and use the objective function value of each firefly as their respective maximum fluorescence brightness; Step S3: Divide the perception radius of each firefly and update the degree of attraction; Step S4: update the position of each firefly; Step S5: Based on the immune complement operation, some new fireflies are generated to replace fireflies with lower maximum fluorescence brightness; Step S6: Judging whether the convergence condition is satisfied, if yes, execute step S7, if no, return to step S4; Step S7: Obtain the maximum power point based on the current position of each firefly, and update the vaccine library. 2 . The photovoltaic maximum power tracking method based on the improved firefly algorithm according to claim 1 , wherein the vaccine library consists of previously found maximum power points and corresponding firefly positions. 3 . 3. A photovoltaic maximum power tracking method based on the improved firefly algorithm according to claim 1, wherein said step S2 specifically comprises: Step S21: taking the objective function values of fireflies as their respective maximum fluorescence brightness; Step S22: Calculate the spatial distance between each firefly: r _ij =||x _i -x _j || Among them: r _ij is the spatial distance between firefly i and firefly j, ||·|| is the Euclidean norm, x _i is the position of firefly i, and x _j is the position of firefly j. 4. A photovoltaic maximum power tracking method based on the improved firefly algorithm according to claim 1 or 3, wherein the objective function value of the firefly is the power obtained based on the voltage corresponding to the position of the firefly. 5. A kind of photovoltaic maximum power tracking method based on improved firefly algorithm according to claim 3, is characterized in that, described step S3 comprises: Step S31: Calculate the perception radius according to the maximum fluorescent brightness of fireflies: R＝φI ₀ Among them: R is the perception radius, I ₀ is the maximum fluorescence brightness of fireflies, and φ is the perception coefficient; Step S32: Calculate the degree of attraction between fireflies according to the spatial distance between fireflies: Among them: β is the attraction between firefly i and firefly j, β ₀ is the maximum attraction, γ is the light intensity absorption coefficient, and e is the natural base. 6. A photovoltaic maximum power tracking method based on the improved firefly algorithm according to claim 5, characterized in that fireflies with lower maximum fluorescence brightness within the perception radius of any firefly will approach the center of the perception radius. 7. A kind of photovoltaic maximum power tracking method based on improved firefly algorithm according to claim 5, is characterized in that, in the described step S4, the position of updating each firefly is: x _i (t+1)＝ _xi (t)+β[x _j (t) _-xi (t)]+S Among them: x _i (t+1) is the position of firefly i after the t-th iteration update, x _i (t) is the position of firefly i before the t-th iteration update, x _j (t) is the t-th iteration The updated position of firefly j, S is the step size function, the expression is as follows: Among them: r is the horizontal spacing of fireflies, x _max and x _min represent the upper and lower limits of the firefly distribution area. 8. A photovoltaic maximum power tracking method based on the improved firefly algorithm according to claim 1, characterized in that, in the step S5, the number of replaced fireflies is μn, wherein: μ is a value in [0, 1] on the immune coefficient, n is the set population size. 9. A photovoltaic maximum power tracking method based on the improved firefly algorithm according to claim 1, wherein said step S6 comprises: Step S61: recalculate the firefly's objective function value according to the updated position of the firefly; Step S62: When the iteration accuracy is satisfied or the maximum number of iterations is reached, then output the global extremum point and the optimal individual value; otherwise, return to step S4 for the next iteration calculation. 10. A photovoltaic maximum power tracking method based on the improved firefly algorithm according to claim 1, wherein the step S7 specifically includes: Step S71: Use the voltage corresponding to the position of the firefly with the largest objective function value as the maximum power point voltage, and output the global maximum power point; Step S72: Update and replace the closest vaccine in the vaccine library with the obtained maximum power point.