Completely-adaptive variable-step photovoltaic maximum power point tracking method

Abstract

The invention relates to the technical field of photovoltaic power generation system control, in particular to a fully-adaptive variable-step photovoltaic maximum power point tracking method. By establishing the relation between the duty ratio of the Boost circuit and the external working condition environment of the circuit, the initial duty ratio is given, and the initial adjustment time of the system is shortened. Meanwhile, attention is paid to the quality of output electric energy of the Boost circuit, a constraint function is established according to the duty ratio disturbance quantity, the optimal step length is searched by using the Hemma algorithm, and reference is output for a conductance increment method so as to be used for searching the photovoltaic maximum power point. Simulation results show that the method provided by the invention has good tracking speed under the condition that the tracking precision is not lost, and especially under the conditions of a photovoltaic environment and large load fluctuation, the system shows excellent robustness and disturbance resistance.

Description

Technical Field

[0001] The present invention relates to the technical field of photovoltaic power generation system control, and in particular to a maximum power point tracking (MPPT) control method for a photovoltaic power generation system, specifically a fully adaptive variable step size incremental conductance (INC) MPPT method that combines initial duty cycle setting with Hippopotamus Optimization (HO) step size optimization. Background Art

[0002] The output power of photovoltaic systems is directly affected by solar radiation intensity and temperature. Since photovoltaic cells are nonlinear components and can only output maximum power at a certain operating voltage, maximum power point tracking (MPPT) is often used to track the maximum power point and improve power generation efficiency. Optimizing the tracking speed and accuracy of MPPT algorithms has become a research focus for scholars worldwide.

[0003] Currently, MPPT methods fall into three main categories: traditional algorithms, algorithms combined with artificial intelligence (AI), and meta-heuristic algorithms. Traditional algorithms include the constant voltage method (CVM), the perturbation and observation method (P&O), and the incremental conductance method (INC). While these algorithms offer relatively good tracking accuracy, their fixed-step nature results in slow tracking and a lack of automatic adjustment. Some researchers have combined AI algorithms, such as artificial neural networks (ANNs), with this method, while offering good tracking performance, relying on large amounts of data. The sheer volume of data required for computation places high demands on the control chip. Meta-heuristic algorithms, such as the Harris Hawk algorithm (HHO), have become a hot topic in MPPT algorithm research due to their ability to handle complex problems. However, simply introducing algorithms to improve tracking performance can hinder power generation quality.

[0004] To address these issues, existing research has broadly focused on two approaches: segmented variable step sizes and hybrid algorithms. Some researchers divide the 2% maximum power range around the MPP into three segments, selecting a different fixed step size for perturbation tracking based on the distance from the MPP. The initial duty cycle is set by curve fitting. However, these approaches lack the fundamental nature of the fixed step size, and the curve fitting lacks theoretical support from a mathematical model, resulting in poor universality and accuracy. To address this, some researchers have combined artificial intelligence (AI) algorithms with traditional algorithms. Instead of relying solely on traditional algorithms to find the MPP through step size addition or subtraction, they employ algorithms that directly search for the MPP. For example, they employ a particle swarm algorithm for global search and, once the required error is met, employ a fuzzy algorithm to track the MPP. This method offers high tracking accuracy but is slow and lacks adaptability to extreme weather conditions. Summary of the Invention

[0005] The present invention aims to address the existing issues of inaccurate initial duty cycle determination methods and MPPT algorithms that focus solely on algorithm tracking performance while ignoring the quality of photovoltaic system output power. This invention proposes a fully adaptive variable-step-size photovoltaic maximum power point tracking method. By establishing a photovoltaic cell model, the relationship between the initial duty cycle and the external environment is derived, shortening the initial adjustment time. Based on the relationship between the photovoltaic system and the boost circuit, an objective function is established. The objective function is optimized using the Hippo algorithm to find the step size that minimizes the objective function. This step size is then used to find the photovoltaic MPP using the conductance increment method.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A fully adaptive variable step-size photovoltaic maximum power point tracking method comprises the following steps:

[0008] Step 1: Establish a mathematical model for the photovoltaic cell and analyze the relationship between the boost circuit input capacitor voltage and the photovoltaic output voltage. Establish an initial duty cycle D0 model and derive its mathematical relationship with the external environment. Establish an objective function for the photovoltaic output power quality and the step size and number of iterations of the MPPT algorithm to balance the impact of the two.

[0009] Step 2: Leveraging the novel metaheuristic capabilities of the Hippo algorithm (HO) and its advantages in multivariable optimization problems, we search for the step size and number of iterations that minimize the objective function of the PV output power quality and the MPPT algorithm step size and number of iterations under different duty cycle disturbances. We then use the incremental conductance method (INC) to find the PV maximum power point (MPP).

[0010] Preferably, in step 1, the following method is specifically included: the simulation model parameters of the photovoltaic cell adopt the AdvancePower API-M350 photovoltaic panel, and its relevant parameters under standard conditions are shown in Table 1.

[0011] Table 1. Related parameters of Advance Power API-M350 photovoltaic panels under standard conditions

[0012] parameter Numerical <![CDATA[P m (W)]]> 350.35 <![CDATA[U m (V)]]> 38.5 <![CDATA[I m (A)]]> 9.1 <![CDATA[U oc (V)]]> 47.4 <![CDATA[I sc (A)]]> 9.81

[0013] Based on the mathematical model of photovoltaic modules derived in formula (1.1), a photovoltaic module model is built in MTALAB / Simulink. Its PU characteristic curves under different environments are as follows: Figure 2 shown.

[0014] To describe the output characteristics of photovoltaic cells, it is often necessary to consider the coupled relationship between the photogenerated current, the diode current, and the parallel leakage current. Based on the equivalent circuit characteristics of photovoltaic devices, there is a certain nonlinear relationship between the output current and the voltage. The diode conduction characteristics are closely related to parameters such as temperature, charge, and emission coefficient. Furthermore, the presence of series and parallel resistances also affects the current distribution. Under ideal approximations, the photogenerated current can be approximated as the short-circuit current, simplifying the overall model.

[0015] However, the aforementioned model is primarily a classic photovoltaic modeling approach widely used in existing research. Its core framework has been adopted by numerous publications and constitutes background content. To better reveal the relationship between photovoltaic output characteristics and their critical operating points, this paper builds on this foundation and innovatively establishes an explicit expression for the output current based on typical operating point parameters. This expression is as follows:

[0016]

[0017] The above formula is when the photovoltaic panel is in standard condition (T ref =25℃, S ref =1000lx) to derive an expression for the photovoltaic cell output characteristic. Compared with traditional modeling methods, this expression offers advantages such as a simple structure and the ability to directly calculate the output current without solving a set of nonlinear equations. This facilitates rapid estimation of the operating status of photovoltaic modules in practical applications. Furthermore, considering the dynamic changes in light intensity and temperature in real applications, this paper modifies the aforementioned model by introducing temperature and light correction coefficients, extending the model from standard conditions to arbitrary operating conditions. The specific correction method is as follows:

[0018]

[0019] Where α is I sc The temperature coefficient is taken as 0.04 in this paper, β and γ are U oc The light and temperature coefficients are taken as 0.5 and 0.3 respectively in this paper. are the short-circuit current and open-circuit voltage of photovoltaic cells under any environment, where is the current and voltage at the maximum power point of the photovoltaic cell under any given environment, T and S are the temperature and light intensity, respectively. e is a natural constant. As can be seen from the above equations, the output of a photovoltaic module is determined by solar irradiance and temperature.

[0020] Preferably, in step 2, the method specifically includes the following: the voltage U across the input capacitor C1 of the Boost circuit C1 and the Boost circuit output voltage U O Satisfies the relationship:

[0021]

[0022] Where D is the duty cycle of the Boost circuit. The input capacitor C1 acts as a medium between the photovoltaic module and the Boost circuit, and is responsible for stabilizing the photovoltaic output voltage U PV Input capacitor voltage U C1 and U PV Should meet

[0023]

[0024] The purpose of the MPPT algorithm is to make Substituting equation (1.1) into equation (2.2) we get

[0025]

[0026] The tracking speed is unified as the number of steps μ, the tracking accuracy is unified as the step length η, and the duty cycle disturbance that changes with solar irradiance and temperature is ΔD. The relationship can be obtained:

[0027] ΔD=μ*η (2.3)

[0028] Combining the effects of step size and number of steps, the approximate relationship between output voltage ripple and regulation time can be modeled as:

[0029]

[0030] Where k1 is the linear coefficient of voltage ripple, which refers to the direct gain of η to ΔU. k2 is the noise suppression coefficient of the number of steps to the ripple, which is set to 0.1. k3 is the delay coefficient of system inertia on initial convergence, but the initial duty cycle has been set above, so k3 is taken as 0 here. k4 is the time cost coefficient of a single iteration, which is taken as 0.00001. k1 is mainly determined by the circuit, including the parameters of the energy storage component and the maximum voltage ripple. Assuming the voltage ripple range is ±0.02%U m ,but

[0031]

[0032] Where, T c The capacitor charge and discharge time constant is 0.001, C is the output capacitance value is 1mF, L is the inductance value is 0.5mH, and k1=0.4 is obtained by substituting them into the calculation.

[0033] To balance the voltage ripple ΔU and the system regulation time tr, the objective function is established

[0034] F(ΔU,tr)=λ1·ΔU+λ2·tr (2.5)

[0035] Substituting equation (2.4) into equation (2.5) yields:

[0036]

[0037] According to formula (2.3), the objective function can be written as:

[0038]

[0039] Where λ1 represents the weight of output voltage stability and quality in the objective function, and λ2 represents the weight of regulation time in the objective function. To balance the impact of these two factors on the objective function, λ1 = 0.4 and λ2 = 0.6 are used. The optimization goal of the HO algorithm is to minimize F(ΔU,tr).

[0040] Preferably, in step 2, the following method is specifically adopted: the natural state of the hippo population can be represented by the initial matrix constituting the step length, which is represented by the X matrix

[0041]

[0042] Each hippopotamus can be represented as x i =[x i, 1······x i,m ].

[0043] During position updating (exploration phase), hippos tend to gather close to each other, with dominant male hippos protecting the herd and territory from potential threats. The following equation expresses the position of male hippos:

[0044] X i Mhippo :x ij Mhippo =x ij +y1·(D hippo -I 1,2 x ij ) (2.7)

[0045] Where x ij Mhippo Indicates the position of the male hippopotamus, D hippo Indicates the position of the dominant hippopotamus, that is, the optimal number of steps in the current iteration, y1 is a random number between 0 and 1, I 1,2 is a random number between 1 and 2.

[0046]

[0047] Calculate the position of the female or immature hippopotamus in the herd (X i FBhippo ). Among them, the selection probability τ=exp(-ξ i / ξ),ξ iis the current iteration number, ξ is the total iteration number. i is the mean of a randomly selected sample. b j max and b j min represents the upper and lower bounds of the j-th decision variable, is a random vector, θ 1,2 is a random number between 0 and 1.

[0048] During the hippopotamus's defense (exploration) phase, when attacked by a predator, the hippopotamus may exhibit behaviors that approach the predator and threaten its retreat. Equation (2.9) represents the predator's position. The calculated position of the predator's population in the current iteration is combined with Equation (2.10) to simulate the scenario of a hippopotamus encountering a predator.

[0049]

[0050]

[0051] In formula (2.10), X i HippoR It is the hippopotamus' strategy when facing predators. is a random vector with Levy distribution that represents the sudden change in the predator's position when attacking the hippopotamus. F represents the distance from the i-th hippopotamus to the predator. j predator Represents the hippopotamus's defense against predators. f is a random number between 2 and 4, c is a random number between 1 and 1.5, d is a random number between 2 and 3, and g is a random number between -1 and 1. is a random vector of dimension 1×m.

[0052] During the hippopotamus's escape from the predator (exploitation) phase, when the hippopotamus is unable to fight the predator, it will attempt to escape to the nearest lake or pond. The hippopotamus's new position is calculated using Equation (2.7).

[0053] X i Hippoε :x ij Hippoε =x ij +λ·(b j min +δ·(b j max -b j min )) (2.11)

[0054] X i HippoεThe hippopotamus is searched for the nearest safe location and its current location is updated. λ represents a random number between 0 and 1, and δ is a normally distributed random number. The algorithm ends after ξ iterations of the three phases to find the optimal solution to the objective function under the current circumstances.

[0055] In the algorithm description above, the hippopotamus position represents a candidate MPPT step size (i.e., the independent variable to be optimized, with each position representing a possible step size). The male hippopotamus position represents the optimal step size within the current population, and the predator position represents the worst step size within the current population. During the exploration phase, the hippopotamus's defense / escape behaviors against predators represent two search strategies: avoiding poor solutions and meticulously searching for the optimal region. The optimal step size found by the hippopotamus algorithm is input into the conductance increment method to find the photovoltaic MPP.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. The present invention establishes the relationship between the duty cycle D, temperature T and light intensity S to find the initial duty cycle, thereby greatly shortening the time required for the initial adjustment.

[0058] 2. The present invention takes into account the tracking speed and accuracy of the MPPT algorithm, the adjustment time of the rectifier circuit output voltage, and the voltage ripple. Based on their inverse proportional relationship, a function of power quality with respect to step size and number of steps is established, and the Hippo algorithm is used for optimization.

[0059] 3. The present invention outputs the optimal step size found by the Hippo algorithm to the conductance increment method, and finally completes the search and tracking of the maximum power point of the photovoltaic system. The superiority of HO-INC is verified through comparative experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is the equivalent circuit model of photovoltaic cells;

[0061] Figure 2 This is the PU characteristic curve of the Advance PowerAPI-M350 photovoltaic panel under different environments;

[0062] Figure 3 It is a simulation model for photovoltaic power generation system;

[0063] Figure 4 Comparison of the INC algorithm performance with and without given D0;

[0064] Figure 5 This is the flow chart of the HO-INC algorithm;

[0065] Figure 6 The figure shows the comparison of algorithm effects, where (a) is the change of R, (a) is the change of S, and (a) is the change of T. DETAILED DESCRIPTION

[0066] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings so that those skilled in the art can better understand the advantages and features of the present invention and thus more clearly define the scope of protection of the present invention. The embodiments described in the present invention are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making any creative work shall fall within the scope of protection of the present invention.

[0067] A fully adaptive variable step-size photovoltaic maximum power point tracking method includes the following steps:

[0068] (1) Photovoltaic modules use the photovoltaic effect to convert light energy into electrical energy. Its equivalent circuit model is as follows: Figure 1 As shown. Figure 1 The equivalent circuit can be obtained according to KCL: the output current of the photovoltaic module

[0069] I PV =I ph -I d -I sh (1.1)

[0070] Where I ph is the photocurrent, I sh is the leakage current of the parallel branch, the diode conduction current

[0071]

[0072] I0 is the reverse saturation current of the diode, in A; q is the charge, which is 1.6×10 -19 (C); A is the diode emission coefficient, which is generally 1-2; K is the Boltzmann constant, which is 1.38×10 -23 (J / K); T is Kelvin temperature, unit K. Figure 1 Diode voltage according to KVL

[0073] U d =U PV +I PV R s (1.3)

[0074] Then the parallel circuit leakage current can be obtained

[0075]

[0076] Where U PV is the PV module output voltage, R s is the equivalent resistance of the photovoltaic cell in series, Rsh is the equivalent resistance of the photovoltaic cell in parallel. Substituting equations (1.2) to (1.4) into equation (1.1), we get:

[0077]

[0078] Since R sh Very big, R s The diode on-state resistance is very small, and the photovoltaic cell parallel equivalent resistance is much larger than the diode on-state resistance and R s , so ignoring the influence of the two, we can get I ph ≈I sc The simplified formula (1.5) is

[0079]

[0080] I sc is the photovoltaic cell short-circuit current, U oc is the open circuit voltage of the photovoltaic cell. When the photovoltaic cell is open circuit, U PV =U oc , I PV =0, substitute into the above formula and we get:

[0081]

[0082] At the maximum power point, U PV =U m ,I PV =I m , substituting into the above formula, we get:

[0083]

[0084] Combining the above three formulas, we get

[0085]

[0086] The above formula is when the photovoltaic panel is in standard condition (T ref =25℃, S ref =1000lx) to derive the output characteristic expression of the photovoltaic cell. The actual situation requires the above formula to be modified:

[0087]

[0088] Where α is I sc The temperature coefficient is taken as 0.04 in this paper, β and γ are U oc The light and temperature coefficients are taken as 0.5 and 0.3 respectively in this paper. are the short-circuit current and open-circuit voltage of photovoltaic cells under any environment, The values ​​of T and S are the current and voltage at the maximum power point of the photovoltaic cell under any environment, respectively. The above equations show that the output of a photovoltaic module is determined by solar irradiance and temperature.

[0089] The simulation model parameters of the photovoltaic cell adopt the Advance Power API-M350 photovoltaic panel. Based on the relevant parameters under standard conditions, the photovoltaic module mathematical model is derived. The photovoltaic module model is built in MTALAB / Simulink, and its PU characteristic curve is obtained as follows: Figure 2 shown.

[0090] (2) Photovoltaic MPPT relies on the Boost circuit and input capacitor. Traditional algorithms such as the constant voltage method, the perturbation observation method, and the conductance increment method ultimately determine whether the maximum power point has been reached by checking whether dP / dU is 0 based on the PU characteristic curve. If the MPP has been reached, the perturbation or increment (step length) is set to 0; if the MPP has not been reached or has been exceeded, the step length is increased or decreased until the MPP is reached. The step length mentioned in the method is the voltage, and the increase or decrease of the voltage is controlled by the post-stage Boost circuit, so the increase or decrease of the step length is essentially the change of the duty cycle of the Boost circuit. Traditional algorithms will encounter two problems during the search process: 1. The initial duty cycle is not given, and the tracking speed of the MPPT algorithm is slow in the initial operation; 2. The step length accuracy is insufficient, and the MPPT algorithm cannot be completely stable and continues to oscillate on both sides of the MPP. To solve the above problems, this paper constructs an initial duty cycle model, finds the relationship between environmental changes and duty cycle changes, and uses the HO algorithm to improve the fixed step length in the conductance increment method, so as to achieve adaptive variable step length tracking of the MPP according to the duty cycle disturbance.

[0091] Photovoltaic power generation system simulation model Figure 3 As shown in Figure 1, the photovoltaic power generation system model consists of a photovoltaic model and a Boost circuit. The voltage across the input capacitor C1 of the Boost circuit is U C1 and the Boost circuit output voltage U O satisfy

[0092]

[0093] Where D is the duty cycle of the Boost circuit. The input capacitor C1 acts as a medium between the photovoltaic module and the Boost circuit, and is responsible for stabilizing the photovoltaic output voltage U PV Input capacitor voltage and U PV Should meet

[0094]

[0095] The purpose of the MPPT algorithm is to make Substituting equation (1.10) into equation (2.2) we get

[0096]

[0097] The tracking speed is unified as the number of steps μ, the tracking accuracy is unified as the step length η, and the duty cycle disturbance that changes with solar irradiance and temperature is ΔD. The relationship can be obtained:

[0098] ΔD=μ*η (2.3)

[0099] Combining the effects of step size and number of steps, the approximate relationship between output voltage ripple and regulation time can be modeled as:

[0100]

[0101] Where k1 is the linear coefficient of voltage ripple, which refers to the direct gain of η to ΔU. k2 is the noise suppression coefficient of the number of steps to the ripple, which is set to 0.1. k3 is the delay coefficient of system inertia on initial convergence, but the initial duty cycle has been set above, so k3 is taken as 0 here. k4 is the time cost coefficient of a single iteration, which is taken as 0.00001. k1 is mainly determined by the circuit, including the parameters of the energy storage component and the maximum voltage ripple. Assuming the voltage ripple range is ±0.02%U m ,but

[0102]

[0103] Where Tc is the capacitor charge and discharge time constant, which is 0.001, C is the output capacitance, which is 1mF, and L is the inductance, which is 0.5mH. Substituting these into the equation, we get k1 = 0.4.

[0104] To balance the voltage ripple ΔU and the system regulation time tr, the objective function is established

[0105] F(ΔU,tr)=λ1·ΔU+λ2·tr (2.5)

[0106] Substituting equation (2.4) into equation (2.5) yields:

[0107]

[0108] According to formula (2.3), the objective function can be written as:

[0109]

[0110] Where λ1 represents the weight of output voltage stability and quality in the objective function, and λ2 represents the weight of regulation time in the objective function. To balance the impact of these two factors on the objective function, λ1 = 0.4 and λ2 = 0.6 are used. The optimization goal of the HO algorithm is to minimize F(ΔU,tr).

[0111] The above analysis is based on the circuit modal analysis and model establishment, and the duty cycle D and U PV , T and S. In addition, the objective function of voltage ripple ΔU, tr with respect to step size and number of steps is established.

[0112] (3) The Hippopotamus Optimization Algorithm is a meta-heuristic optimization algorithm inspired by the group behavior of hippos, which is mainly used to solve multivariable complex optimization problems. Its core is a three-stage optimization mechanism: the first stage: the hippopotamus updates its position in the river (exploration stage); the second stage: the hippopotamus defends against predators (exploration stage); the third stage: the hippopotamus escapes from predators (exploitation stage);

[0113] The natural state of the hippo population can be represented by the initial matrix that constitutes the step length, represented by the X matrix

[0114]

[0115] Each hippopotamus can be represented as x i =[x i, 1······x i,m ].

[0116] During position updating (exploration phase), hippos tend to gather close to each other, with dominant male hippos protecting the herd and territory from potential threats. The following equation expresses the position of male hippos:

[0117] X i Mhippo :x ij Mhippo =x ij +y1·(D hippo -I 1,2 x ij ) (2.7)

[0118] Where x ij Mhippo Indicates the position of the male hippopotamus, D hippo Indicates the position of the dominant hippopotamus, that is, the optimal number of steps in the current iteration, y1 is a random number between 0 and 1, I 1,2 is a random number between 1 and 2.

[0119]

[0120] Calculate the position of the female or immature hippopotamus in the herd (X i FBhippo ). Among them, the selection probability τ=exp(-ξ i / ξ),ξ i is the current iteration number, ξ is the total iteration number. iis the mean of a randomly selected sample. b j max and b j min represents the upper and lower bounds of the j-th decision variable, is a random vector, θ 1,2 is a random number between 0 and 1.

[0121] During the hippopotamus's defense (exploration) phase, when attacked by a predator, the hippopotamus may exhibit behaviors that approach the predator and threaten its retreat. Equation (2.9) represents the predator's position. The calculated position of the predator's population in the current iteration is combined with Equation (2.10) to simulate the scenario of a hippopotamus encountering a predator.

[0122]

[0123]

[0124] In formula (2.10), X i HippoR It is the hippopotamus' strategy when facing predators. is a random vector with Levy distribution that represents the sudden change in the predator's position when attacking the hippopotamus. F represents the distance from the i-th hippopotamus to the predator. j predator Represents the hippopotamus's defense against predators. f is a random number between 2 and 4, c is a random number between 1 and 1.5, d is a random number between 2 and 3, and g is a random number between -1 and 1. is a random vector of dimension 1×m.

[0125] During the hippopotamus's escape from the predator (exploitation) phase, when the hippopotamus is unable to fight the predator, it will attempt to escape to the nearest lake or pond. The hippopotamus's new position is calculated using Equation (2.7).

[0126] X i Hippoε :x ij Hippoε =x ij +λ·(b j min +δ·(b j max -b j min )) (2.11)

[0127] X i HippoεThe location of the hippopotamus is searched to find the nearest safe place, and the current location is updated. λ represents a random number in the range of 0 to 1, and δ is a random number with a normal distribution. The three stages are iterated ξ times, and the optimal solution of the objective function is found in the current situation. The algorithm ends. The flowchart of the HO-INC algorithm is as follows Figure 4 As shown in the figure, the hippopotamus position represents the candidate MPPT step number value (i.e., the independent variable to be optimized, each position represents a possible step value), the male hippopotamus position represents the better step value in the current population, and the predator position represents the worst step value in the current population. During the exploration phase, the two behaviors of the hippopotamus in defending / escaping from the predator represent the two search strategies of staying away from the worse solution and carefully searching the optimal area.

[0128] Figure 5 Taking a 20×15 photovoltaic array as an example, the positive effect of the initial duty cycle on the adjustment time based on the mathematical model is tested. The main parameters of the photovoltaic control system are set to input capacitance C1 = 1×10 -3 F, output capacitor C2 = 1 × 10 -4 F, inductance L = 3 × 10 -5 The experiment was conducted under non-standard conditions at T = 25 ° C, S = 700 lx. Under this environment, the voltage at the maximum power point of the photovoltaic array group is 582.5V. The simulation results are as follows Figure 4 The simulation results show that the adjustment time tr of the INC algorithm under given D0 is about 0.07s, which is 75% shorter than the 0.28s under the condition of no given D0.

[0129] In order to better conduct comparative experiments and highlight the speed and stability of the HO-INC algorithm, the INC, PSO-INC and HO-INC algorithms are experimentally compared under three conditions: load change, light intensity change and temperature change. The simulation results are shown in the figure below. Figure 6 shown.

[0130] The data are organized into a table as shown in Table 2.

[0131] Table 2. Regulation time tr and voltage ripple ΔU of the three algorithms under different working conditions

[0132] algorithm R change tr / s S change tr / s T change tr / s R change ΔU / % S change ΔU / % T change ΔU / % INC 0.1 0.16 0.01 0.034 0.034 0.034 PSO-INC 0.05 0.12 0.004 0.017 0.017 0.017 HO-INC 0.03 0.07 0.002 0.021 0.021 0.023

[0133] Analysis of the data in the table shows that, due to the direct impact of photovoltaic cell temperature on voltage, all three algorithms respond quickly to temperature changes. However, illumination directly affects the photovoltaic cell output current, resulting in a slightly slower response for both the INC and PSO-INC algorithms. The PSO-INC algorithm also exhibits small fluctuations in tracking accuracy. The proposed algorithm maintains tracking speed while also balancing tracking accuracy. When the load changes, both the INC and PSO-INC algorithms experience significant overshoot. Furthermore, due to the PSO algorithm's susceptibility to local optima and poor noise immunity, the initial settling time is long and subject to significant fluctuations. The proposed method not only shortens this initial settling time by using the initial duty cycle, but also maintains optimal tracking quality and output power quality even when disturbances are introduced later.

[0134] In summary, this paper addresses the shortcomings of curve-fitting methods, which suffer from poor performance and limited universality, by establishing a mathematical model to derive the relationship between the initial duty cycle and the external environment, and then developing a function. This method is more accurate and applicable to any photovoltaic panel under any operating conditions, making it more universal. Furthermore, existing methods often make trade-offs regarding the two key metrics of tracking accuracy and tracking speed, as well as power quality, in photovoltaic MPPT algorithms, lacking a single, definitive evaluation function. This paper constructs an evaluation function and uses the Hippo algorithm to search for the minimum step size that minimizes the evaluation function when duty cycle variables are present, using the conductance increment method to track the MPP. Simulation results demonstrate that this algorithm achieves high step accuracy, low voltage ripple, and strong noise immunity.

[0135] The descriptions and practices disclosed in this invention are easy to understand and comprehend for those skilled in the art, and modifications and refinements may be made without departing from the principles of the invention. Therefore, modifications and improvements made without departing from the spirit of the invention should also be considered within the scope of protection of this invention.

Claims

1. A fully adaptive variable step-size photovoltaic maximum power point tracking method, characterized in that: The steps include: Step 1: Establish a mathematical model for the photovoltaic cell and analyze the relationship between the boost circuit input capacitor voltage and the photovoltaic output voltage. Establish a model for the initial duty cycle D0 and derive its mathematical relationship with the external ambient temperature and light intensity. Establish an objective function F(ΔU, tr) that reflects the relationship between the boost circuit output voltage ripple ΔU and the system regulation time tr, as well as the MPPT algorithm step size η and number of iterations μ. This objective function is used to balance output voltage quality and tracking speed. Step 2: Optimize the objective function F(ΔU, tr) using the Hippo algorithm to find the optimal step size η and number of iterations μ that minimize the objective function under different duty cycle disturbances ΔD; input the optimal step size μ found by the Hippo algorithm into the conductance increment method, calculate the duty cycle adjustment amount using the optimal step size η through the conductance increment method, and output the corresponding PWM control signal to the Boost circuit switch tube to drive the photovoltaic system to operate at the maximum power point.

2. A fully adaptive variable step-size photovoltaic maximum power point tracking method according to claim 1, characterized in that: In step 1, the photovoltaic cell mathematical model is established including: Based on the key operating point parameters of photovoltaic cells, standard conditions are established, namely temperature T ref =25℃, light intensity S ref =1000lx, the explicit expression of the photovoltaic cell output current is: Where, I PV is the photocurrent, I sc is the short-circuit current, I m is the maximum power point current under standard conditions, U oc is the open circuit voltage, U m is the maximum power point voltage under standard conditions; Introducing the temperature correction coefficient α, the light correction coefficient β and the temperature correction coefficient γ, the explicit expression is corrected to obtain the photovoltaic cell short-circuit current under any working condition Open circuit voltage Maximum power point current and maximum power point voltage Among them, e is a natural constant.

3. A fully adaptive variable step-size photovoltaic maximum power point tracking algorithm according to claim 1 or 2, characterized in that: In step 1, establishing an initial duty cycle D0 model and deriving its relationship with the external environment includes: Establish the voltage U across the Boost circuit input capacitor C1 C1 and the Boost circuit output voltage U O Relationship: Where D is the duty cycle of the Boost circuit; Establish input capacitor voltage U C1 and photovoltaic output voltage U PV Relationship: Combined with MPPT target, The corrected maximum power point voltage Substituting in, we get the relationship between the initial duty cycle D0 and the environmental parameters: The initial duty cycle D0 is used as the initial value of the PWM control signal of the Boost circuit when the system is started or the environment changes suddenly, thereby shortening the adjustment time.

4. A fully adaptive variable step-size photovoltaic maximum power point tracking algorithm according to claim 1, characterized in that: In step 1, establishing the objective function F(ΔU,tr) includes: Define the relationship between the duty cycle disturbance ΔD, the number of tracking speed steps μ, and the tracking accuracy step length η: ΔD=μ*η (2.3) Establish an approximate relationship between the output voltage ripple ΔU and the step size η and the number of steps η, and establish an approximate relationship between the system adjustment time tr and the step size η and the number of steps η: Among them, k1 is the voltage ripple linear coefficient, k2 is the noise suppression coefficient of the number of steps to the ripple, k3 is the delay coefficient of the system inertia to the initial convergence, and k4 is the time cost coefficient of a single iteration; Based on the output voltage ripple ΔU and the system regulation time tr, an objective function is constructed: F(ΔU,tr)=λ1·ΔU+λ2·tr (2.5) Among them, λ1 represents the weight of output voltage stability and quality in the objective function, and λ2 represents the weight of adjustment time in the objective function; Substituting the approximate relationship between ΔU and tr into the objective function, and using the relationship ΔD = μ*η, we can finally obtain the objective function represented by the step size η and the duty cycle disturbance ΔD: The objective function F(ΔU, tr) is used to quantitatively evaluate the comprehensive impact of the MPPT process on the output power quality and dynamic response speed of the Boost circuit.

5. The fully adaptive variable step-size photovoltaic maximum power point tracking algorithm according to claim 1, characterized in that: In step 2, the optimization of the objective function using the Hippo algorithm specifically includes: The candidate MPPT step value is expressed as the hippo population position matrix X; During the exploration phase, the positions of other hippos were updated based on the position of the dominant male hippopotamus; In the exploration phase, the hippopotamus's defense behavior against predators is simulated, and the hippopotamus's position is updated according to the predator's position and the distance from the hippopotamus to the predator. The predator's position represents the worst step value in the current population. During the development phase, the behavior of hippos escaping from predators was simulated and the hippos’ positions were updated to find safe areas; After multiple iterations, the optimal step size that minimizes the objective function F(ΔU,tr) is found.

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