MPPT control method for photovoltaic hydrogen production system based on improved whale-conductance increment method

Abstract

The present invention discloses a photovoltaic hydrogen production system MPPT control method based on an improved whale-conductance increment method, comprising: establishing a photovoltaic hydrogen production system with a photovoltaic array, the photovoltaic array consisting of a plurality of photovoltaic panels connected in series and parallel; connecting the output circuit of the photovoltaic array to a PEM electrolyzer via a boost-type DC-DC converter, the PEM electrolyzer using direct current to decompose water molecules into hydrogen and oxygen; dynamically optimizing the generation of a duty cycle D using the improved whale-conductance increment method, and controlling the start and stop of the power switching tube IGBT in the boost-type DC-DC converter by the duty cycle D to optimize the photovoltaic array voltage regulation performance of the photovoltaic hydrogen production system. The photovoltaic hydrogen production system MPPT control method of the present invention can successfully track the maximum power point under dynamically changing light conditions by improving the whale-conductance increment method, thereby improving the electrolysis efficiency of the photovoltaic hydrogen production system.

Description

Technical Field

[0001] The present invention relates to the field of renewable energy technology and power electronics technology, and in particular to an MPPT control method for a photovoltaic hydrogen production system based on an improved whale-conductance increment method. Background Art

[0002] With climate change and energy security becoming increasingly serious, energy transition has become an urgent task. Solar energy, as a clean, safe, and renewable energy source, is attracting increasing attention. However, due to the uneven distribution of solar resources and geographical constraints, the actual utilization rate of photovoltaic power generation has not reached ideal levels. According to statistics from the National Energy Administration, as of the end of 2022, the actual utilization rate of photovoltaic power generation in several regions with abundant solar resources ranged from 80.0% to 91.1%, indicating that a large amount of photovoltaic power generation is still not being effectively utilized. The introduction of hydrogen energy storage can significantly improve the energy utilization rate of photovoltaic systems and effectively absorb wasted solar energy. Among hydrogen production technologies, proton exchange membrane (PEM) electrolyzers are highly favored due to their excellent adaptability to fluctuations and compatibility with renewable energy sources such as solar energy.

[0003] Currently, research in photovoltaic hydrogen production focuses on how to quickly and accurately find the maximum power point (MPP) to maximize energy utilization and improve system stability. Under uniform illumination, traditional maximum power point tracking (MPPT) algorithms can quickly find the global maximum power point. However, under uneven illumination, traditional MPPT algorithms, due to their relatively simple control principles, are prone to falling into local optimal states, making it difficult to quickly and accurately capture the global maximum power point.

[0004] As an emerging intelligent optimization method, the Whale Algorithm is combined with the traditional conductance increment method. Although the algorithm is simple and easy to implement, it still has the following defects:

[0005] (1) When the light intensity changes rapidly, the whale optimization algorithm may experience oscillation, resulting in system instability and slow convergence;

[0006] (2) The conductivity increment method is simple in control principle when the light intensity changes rapidly, which leads to the easy fall into local optimum under complex working conditions, resulting in power loss.

[0007] Both situations cause power loss in the system and reduce hydrogen production efficiency. Therefore, it is particularly important to conduct in-depth research and optimization on these aspects to improve the performance and stability of the system and provide more reliable and efficient solutions to solve practical problems. Summary of the Invention

[0008] The purpose of the present invention is to provide an MPPT control method for a photovoltaic hydrogen production system based on an improved whale-conductance increment method, which is used to solve the technical problems of the traditional whale-conductance increment algorithm in the background technology, such as the slow convergence speed affecting the hydrogen production efficiency and the instability of the photovoltaic hydrogen production system when the light intensity changes rapidly.

[0009] The present invention solves the above problems through the following technical solutions:

[0010] The MPPT control method of photovoltaic hydrogen production system based on the improved whale-conductance increment method includes:

[0011] Establish a photovoltaic hydrogen production system with a photovoltaic array, which consists of several photovoltaic panels connected in series and parallel;

[0012] The output circuit of the photovoltaic array is connected to the PEM electrolyzer through a step-up DC-DC converter. The PEM electrolyzer uses direct current to decompose water molecules into hydrogen and oxygen.

[0013] The duty cycle D is dynamically optimized and generated by the improved whale-conductance increment method. The duty cycle D controls the start and stop of the power switch tube IGBT in the boost DC-DC converter circuit to optimize the photovoltaic array voltage regulation performance of the photovoltaic hydrogen production system.

[0014] As a further improvement of the present invention, the improved whale-conductance increment method inputs the instantaneous output current I and instantaneous output voltage U of the photovoltaic array, and calculates the instantaneous output power P=IU, and dynamically adjusts the duty cycle D by the output power change rate ΔP=P(t)-P(t-1) of the photovoltaic array, where t is the number of iterations.

[0015] As a further improvement of the present invention, the control method further includes:

[0016] Establishing a photovoltaic cell equivalent model, thereby obtaining the instantaneous output current I, instantaneous output voltage U, and instantaneous output power P=IU of the photovoltaic array according to the established photovoltaic cell equivalent model;

[0017] The photovoltaic cell equivalent model includes at least an ideal diode, a photocurrent source, a series resistor and a parallel resistor. The photocurrent source is connected in parallel with the ideal diode and the parallel resistor respectively. Finally, the entire structure is connected in series with the series resistor and the load.

[0018] As a further improvement of the present invention, the instantaneous output current I of the photovoltaic array is obtained according to the established photovoltaic cell equivalent model, and the formula is:

[0019]

[0020] Where n is the total number of photovoltaic panels; I is the instantaneous output current of the photovoltaic array; Iph is the current of the photocurrent source; I0 is the reverse saturation current of the ideal diode; q is the electron charge; U is the instantaneous output voltage of the photovoltaic array; R s is the resistance of the series resistor of the photovoltaic cell equivalent model; m is the characteristic fitting parameter of the ideal diode; K is the Boltzmann constant; T is the working environment temperature of the photovoltaic panel; R sh is the resistance of the parallel resistor of the photovoltaic cell equivalent model;

[0021] Let the resistance R of the series resistor in the photovoltaic cell equivalent model be s =0, the resistance R of the parallel resistor of the photovoltaic cell equivalent model sh =∞; due to the resistance R of the series resistor in the photovoltaic cell equivalent model s =0, the resistance of the parallel resistor R sh =∞, It tends to 0, so it can be ignored. Then the general equation of the instantaneous output current I of the photovoltaic array is simplified to:

[0022]

[0023] As a further improvement of the present invention, the equivalent circuit of the boost DC-DC converter is specifically:

[0024] A periodically operating power switch tube IGBT is connected in series with an inductor L, and then connected in parallel with a load R and a capacitor C2. Capacitor C2 is used to smooth the output voltage. Among them, capacitor C2 realizes the smoothing of the output voltage of the photovoltaic array and the suppression of voltage ripple. The ideal diode D5 prevents current backflow. The voltage regulation performance is optimized by controlling the start and stop of the power switch tube IGBT in the boost DC-DC converter.

[0025] As a further improvement of the present invention, the improved whale-conductance increment method includes an improved whale algorithm and an improved conductance increment method; including:

[0026] Initialize the duty cycle D, collect the instantaneous output current I and instantaneous output voltage U of the photovoltaic array, calculate the instantaneous output power P = IU, and iterate. Enable the improved whale algorithm to use nonlinear dynamic adjustment factors for dynamic search, introduce a nonlinear adaptive weight strategy to escape the local optimum, and introduce a screening perturbation mechanism to accelerate convergence for preliminary optimization.

[0027] After the iteration is completed, the output power change rate ΔP of the photovoltaic array is determined:

[0028] When the output power change rate ΔP of the photovoltaic array is greater than or equal to the preset value Z, the improved whale algorithm is restarted;

[0029] When the output power change rate ΔP of the photovoltaic array is less than the preset value Z, the improved conductance increment method is used for precise optimization to dynamically adjust and output the duty cycle D to control the start and stop of the power switch tube IGBT;

[0030] When the output power change rate ΔP of the photovoltaic array is 0, the instantaneous output power of the photovoltaic array reaches the maximum power point. At this time, the duty cycle D is directly output to control the start and stop of the power switch tube IGBT.

[0031] As a further improvement of the present invention, the improved whale algorithm adopts a nonlinear dynamic adjustment factor to perform dynamic search; the specific method is:

[0032] The formula of the nonlinear dynamic adjustment factor is defined as follows:

[0033]

[0034] Where t is the number of iterations, t_max is the maximum number of iterations, and a1 is the nonlinear dynamic adjustment factor;

[0035] Taking the first-order and second-order derivatives of the nonlinear dynamic adjustment factor a1, we can obtain:

[0036]

[0037] The curve change trend of the nonlinear dynamic adjustment factor a1 is analyzed by first-order derivative, and the concave and convex changes of the curve of the nonlinear dynamic adjustment factor a1 are analyzed by second-order derivative to understand how the nonlinear dynamic adjustment factor a1 enhances the search capability through numerical changes.

[0038] As a further improvement of the present invention, the improved whale algorithm introduces a nonlinear adaptive weight strategy; the specific expression is:

[0039]

[0040] Where t is the number of iterations, t_max is the maximum number of iterations, and w(t) is the nonlinear adaptive weight;

[0041] The improved whale algorithm updates the contraction and spiral hunting methods, and the specific expression is:

[0042]

[0043] Where X(t+1) represents the position vector of the current solution at t+1 iterations; X(t) represents the position vector of the current solution at t iterations; A, D1, D2, and D3 represent coefficient vectors, with A∈[0,2]; l and r3 represent random numbers between 0 and 1; b represents the direction of the control spiral, which is a constant 1; X rand(t) represents the position of a random humpback whale individual.

[0044] As a further improvement of the present invention, the improved whale algorithm introduces a screening perturbation mechanism, which is specifically expressed as follows:

[0045]

[0046] Where X(t+1) represents the position vector of the current solution at t+1 iterations; X(t) represents the position vector of the current solution at t iterations; f represents the fitness value of the corresponding whale individual; f med represents the median of the fitness value; rand() represents a random number uniformly distributed between 0 and 1; X1 and X2 represent the positions of the humpback whale individuals with the smallest and largest fitness values ​​in the top 50% of the fitness values, respectively.

[0047] As a further improvement of the present invention, the improved conductance increment method is used to perform precise optimization to dynamically adjust and output the duty cycle D to control the start and stop of the power switch tube IGBT; the specific method is:

[0048] Calculate the current change rate dI and voltage change rate dU between two adjacent iterations;

[0049] The instantaneous output power of the photovoltaic cell is P=IU,

[0050] When dU≠0, the voltage and duty cycle D are adjusted by judging the relationship between dI / dU and -I / U:

[0051]

[0052] When dU=0, the voltage and duty cycle D are adjusted by judging dI;

[0053]

[0054] The duty cycle D is dynamically adjusted and output through the current change rate dI and voltage change rate dU.

[0055] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0056] (1) The MPPT control method for a photovoltaic hydrogen production system of the present invention improves the accuracy and response speed of maximum power point tracking (MPPT) by improving the whale-conductance increment method and utilizing the powerful optimization capability of the improved whale algorithm, thereby overcoming the problems of slow initial search speed and insufficient search accuracy of the linear convergence factor in the later stage, and adopts a nonlinear dynamic adjustment factor, which has a larger value in the early stage to accelerate global exploration, and is reduced to a smaller value in the later stage to deepen the accuracy of local search.

[0057] (2) The MPPT control method for a photovoltaic hydrogen production system of the present invention introduces a nonlinear adaptive weighting strategy by improving the Whale-Conductance Increment Method and utilizing the improved Whale Algorithm. This overcomes the problem of the original WOA-INC algorithm being prone to falling into local optimality in multi-objective optimization and can dynamically adjust weight values ​​to meet the optimization requirements of different stages. Furthermore, during the contraction and encirclement process, the nonlinear adaptive weighting strategy can better guide the whale group toward the optimal solution while maintaining sufficient diversity to avoid premature convergence to the local optimal solution.

[0058] (3) The MPPT control method of the photovoltaic hydrogen production system of the present invention introduces a screening disturbance mechanism by improving the whale-conductance increment method and using the improved whale algorithm. To address the problem of slow convergence in the late stage of the algorithm, the output power of photovoltaic cells is sorted by fitness at the end of the iteration, and the positions of the first 50% high-fitness humpback whales are locked unchanged. At the same time, the last 50% low-fitness individuals are randomly updated among these leading groups, thereby significantly accelerating the late optimization process, improving the overall performance and optimization efficiency of the algorithm, and ensuring that the algorithm continues to operate efficiently in the convergence stage.

[0059] (4) The MPPT control method of the photovoltaic hydrogen production system of the present invention uses the improved whale-conductance increment method to further accurately search for the optimal value. Based on the relationship between the rate of change of the output voltage and the rate of change of the current of the photovoltaic cell, the two rates of change are monitored in real time and the working point is adjusted to achieve accurate tracking of the maximum power point, ensuring that the system always operates at the highest efficiency.

[0060] (5) The MPPT control method of the photovoltaic hydrogen production system of the present invention can successfully track the maximum power point under dynamically changing light conditions by improving the whale-conductance increment method, thereby improving the electrolysis efficiency of the photovoltaic hydrogen production system. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A circuit diagram of a photovoltaic cell equivalent model of the present invention;

[0062] Figure 2 A topological diagram showing the connection between the photovoltaic array and the boost DC-DC converter of the present invention;

[0063] Figure 3 This is a schematic diagram of the charging phase of the boost DC-DC converter of the present invention;

[0064] Figure 4 This is a schematic diagram of the freewheeling phase of the boost DC-DC converter of the present invention;

[0065] Figure 5 The output of the photovoltaic array cell of the present invention is P -U characteristic curve diagram;

[0066] Figure 6 Schematic diagram comparing the linear convergence factor and the nonlinear convergence factor of the present invention;

[0067] Figure 7 Schematic diagram of the nonlinear adaptive weight strategy curve of the present invention;

[0068] Figure 8 This is a flow chart of the MPPT control method for a photovoltaic hydrogen production system based on the improved whale-conductance increment method of the present invention;

[0069] Figure 9 Schematic diagram of the photovoltaic array output power curve under uniform illumination of the present invention;

[0070] Figure 10 Schematic diagram of the photovoltaic array output power curve under dynamically changing illumination of the present invention. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below in conjunction with the drawings in the preferred embodiments of the present application. In the drawings, the same or similar reference numerals throughout represent the same or similar parts or parts with the same or similar functions. The described embodiments are part of the embodiments of the present application, not all of the embodiments. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain the present application, and should not be understood as limitations on the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0072] The following will be combined Figure 1-10 , the MPPT control method of the photovoltaic hydrogen production system based on the improved whale-conductance increment method involved in the embodiment of the present application is described in detail. It is worth noting that the following embodiments are only used to explain the present application and do not constitute a limitation of the present application.

[0073] Example 1:

[0074] The MPPT control method of photovoltaic hydrogen production system based on the improved whale-conductance increment method includes the following steps:

[0075] Step 1: Establish a photovoltaic hydrogen production system with a photovoltaic array. The photovoltaic array is composed of K photovoltaic panels connected in series (number of series connected * number of parallel connected panels) to generate electricity. The output circuit of the photovoltaic array is connected to a PEM electrolyzer via a step-up DC-DC converter. The PEM electrolyzer uses direct current to decompose water molecules into hydrogen and oxygen.

[0076] In a preferred embodiment, the output circuit of the photovoltaic array is connected to a PEM electrolyzer via a boost DC-DC converter. The PEM electrolyzer uses direct current to decompose water molecules into hydrogen and oxygen. The specific method is as follows:

[0077] 1.1. Connect the output circuit of the photovoltaic array through a boost DC-DC converter, and optimize the voltage regulation performance of the photovoltaic array by controlling the start and stop of the switching tube IGBT of the boost DC-DC converter.

[0078] The equivalent circuit of a boost DC-DC converter is as follows: Figure 2 As shown, this can be described as an ideal cyclically operating IGBT in series with an inductor L, then in parallel with a load R and a capacitor C2. Capacitor C2 smoothes the output voltage. Capacitor C1 smoothes the output voltage of the photovoltaic array and suppresses voltage ripple, while diode D5 prevents current reverse flow. Voltage regulation performance is optimized by controlling the start and stop of the IGBT in the boost DC-DC converter.

[0079] The power switching tube IGBT controls its on and off time during a duty cycle based on logic signals. The inductor is connected to loops ① and ② at different time periods, storing and releasing energy during this conversion process, ensuring that the output voltage is stable and always higher than the input voltage. The input and output voltages of the boost DC-DC converter circuit are:

[0080] The relationship between the input and output voltage of the boost DC-DC circuit is:

[0081]

[0082] Where: D is the duty cycle, switch on time T on The ratio of the total switching cycle time T; U in The circuit input voltage of the step-up DC-DC converter; U out This is the output voltage of the boost DC-DC converter circuit.

[0083] The working process of a boost DC-DC converter in one cycle can be divided into two stages:

[0084] The first stage is the charging stage, the principle is as follows Figure 3 As shown, at this time, the logic signal is high, the power switch tube IGBT is turned on, one end of the inductor is grounded, and the voltage V at the LX node is LX The on-resistance of the IGBT is zero (ignoring the on-resistance of the power switch tube IGBT), the diode D5 is in the reverse cut-off state, and the filter capacitor C2 continues to supply power to Uout to ensure that the output voltage remains stable.

[0085] The second stage is the freewheeling stage, the principle is as follows Figure 4 As shown, at this time, the logic signal jumps from high level to low level, the power switch tube IGBT is turned off, one end of the inductor is connected to the positive end of the diode, and the diode D5 is turned on (there is a conduction voltage drop V D5 ), the voltage U at the LX node L x=Uout+U D , at this time the inductance L and the input voltage U in Together they supply power to the load and charge the filter capacitor to ensure the output voltage U out Always stable.

[0086] 1.2 The start and stop of the power switch IGBT in the boost DC-DC converter circuit is controlled by the duty cycle D. The duty cycle can be generated by the improved whale-conductance increment method.

[0087] In practical applications, power switch tubes IGBTs (insulated gate bipolar transistors) are used as switching devices to control the flow of current. The duty cycle D is controlled and adjusted through a PWM (pulse width modulation) signal. The high level duration of the PWM signal determines the on-time of the power switch tube IGBT. Therefore, the duty cycle D determines the on-time of the power switch tube IGBT within a switching cycle. Specifically:

[0088] When the duty cycle D needs to be increased, the high-level time of the PWM signal is lengthened, and the conduction time of the power switch tube IGBT is prolonged, thereby increasing the output voltage and current.

[0089] When the duty cycle D needs to be reduced, the high-level time of the PWM signal is shortened, and the conduction time of the power switch tube IGBT is shortened, thereby reducing the output voltage and current.

[0090] 1.3. The output end of the boost DC-DC converter circuit is connected to a PEM electrolyzer. The PEM electrolyzer uses direct current to decompose water molecules into hydrogen and oxygen. The anode produces oxygen and the cathode produces hydrogen.

[0091] Anode: H2O-2e - →0.5O2+2H + ;

[0092] Cathode: 2H + +2e - →H2;

[0093] 1.4. The output voltage of a PEM electrolyzer is composed of open circuit voltage, activation overvoltage, diffusion overpotential, and ohmic overpotential, as shown in the following formula:

[0094] V el =V oc +V act +V diff +Vohm

[0095] The open circuit voltage can be obtained by the Nernst equation:

[0096] Where: E0 is the standard electromotive force of the PEM electrolyzer; R is the gas constant; T is the operating temperature of the electrolyzer; F is the Faraday constant; P H2 、P O2 is the partial pressure of hydrogen and oxygen; a H2O is the activity of water. The calculation formula of E0 is: E0=1.229-0.9×10 -3 (T-298);

[0097] The activation overpotential is caused by activation loss during the electrochemical reaction and is affected by many factors including operating temperature, catalyst, and reactants. The electrode surface reaction at the activation overvoltage is expressed using the Butler-Volmer equation as follows:

[0098] Where: T a 、T c is the operating temperature of the anode and cathode of the electrolytic cell; a a 、a c is the charge transfer coefficient between the anode and cathode; j is the current density; j 0,a 、j 0,c is the current density at the anode and cathode.

[0099] The diffusion overpotential is formed due to the fact that the transfer of reactants and products in the porous electrodes in the PEM electrolyzer is hindered, especially under high current density conditions. The diffusion overpotential is combined with the Nernst equation and Fick's law to form the following expression:

[0100] Where: C O2 、C H2 ——Oxygen and hydrogen concentrations at the interface between the membrane and the electrode; C O2,0 , C H2,0 ——Corresponding reference value.

[0101] The ohmic overpotential is formed by the impedance of the internal devices of the electrolytic cell, mainly the membrane resistance, and other resistances are ignored. The expression is as follows:

[0102] Where: δ m ——proton exchange membrane thickness, 200um; λ——proton exchange membrane water content, 20.

[0103] The mathematical models of the above open circuit voltage, activation overvoltage, diffusion overpotential and ohmic overpotential are combined to obtain the overall mathematical model of the output voltage of the PEM electrolyzer, thereby building a simulation model of the output voltage of the PEM electrolyzer.

[0104] 1.5. Electrolysis efficiency η of electrolytic cell el That is, the water splitting efficiency under stable temperature and pressure conditions is determined by the current efficiency η el(i) and voltage efficiency η el(v) Influence.

[0105]

[0106] Where: U tn ——The minimum voltage at which water electrolysis occurs.

[0107] Step 2: Establishing a photovoltaic cell equivalent model, thereby obtaining the instantaneous output current I, instantaneous output voltage U, and instantaneous output power P=IU of the photovoltaic array according to the established photovoltaic cell equivalent model;

[0108] like Figure 1 As shown, the photovoltaic cell equivalent model mainly consists of four main components:

[0109] An ideal diode D4, a photocurrent source Iph, a series resistor Rs and a parallel resistor Rsh, these components together constitute the working principle and electrical characteristics of the photovoltaic cell. The ideal diode represents the PN junction inside the photovoltaic cell, simulating the change of current with light intensity and temperature under the photovoltaic effect. The photocurrent source Iph is an ideal current source, which represents the maximum photocurrent under specific lighting conditions. The series resistor Rs simulates the resistance inside the cell, and the parallel resistor Rsh simulates the non-ideal current leakage path, such as tiny cracks or pollution on the surface of the cell. The equivalent model of the entire photovoltaic cell can be described as: the photocurrent source Iph is connected in parallel with the ideal diode D4 and the parallel resistor Rsh respectively, and finally the entire structure is connected in series with the series resistor Rs and the load RL, I, I d , Ish are the currents passing through the series resistor Rs, the ideal diode D4 and the parallel resistor Rsh respectively.

[0110] According to the established photovoltaic cell equivalent model, the instantaneous output current I of the photovoltaic array is obtained as follows:

[0111]

[0112] Let the resistance R of the series resistor in the photovoltaic cell equivalent model be s =0, the resistance R of the parallel resistor of the photovoltaic cell equivalent model sh =∞; due to the resistance R of the series resistor in the photovoltaic cell equivalent model s=0 and the resistance R of the parallel resistor sh =∞, It tends to 0, so it can be ignored. Then the general equation of the instantaneous output current I of the photovoltaic array is simplified to:

[0113]

[0114] Where n is the total number of photovoltaic panels; I is the instantaneous output current of the photovoltaic array; I ph is the current of the photocurrent source; I0 is the reverse saturation current of the ideal diode; q is the electron charge; U is the instantaneous output voltage of the photovoltaic array; R s is the resistance of the series resistor of the photovoltaic cell equivalent model; m is the characteristic fitting parameter of the ideal diode; K is the Boltzmann constant; T is the working environment temperature of the photovoltaic panel; R sh is the resistance of the parallel resistor of the photovoltaic cell equivalent model.

[0115] Step 3: Dynamically optimize and generate the duty cycle D using the improved whale-conductance increment method. The duty cycle D controls the start and stop of the power switch tube IGBT in the equivalent circuit of the boost DC-DC converter to optimize the photovoltaic array voltage regulation performance of the photovoltaic hydrogen production system.

[0116] By dynamically optimizing the duty cycle D through the improved whale-conductance increment method, when the instantaneous change rate of the photovoltaic array output power is 0, the maximum power point is found and the duty cycle D is kept unchanged, so that the photovoltaic array output power reaches the maximum power point.

[0117] Specifically, the improved whale-conductance increment method takes as input the instantaneous output current I, instantaneous output voltage U, and instantaneous output power P=IU of the photovoltaic array, and dynamically adjusts the duty cycle D by the output power change rate ΔP=P(t)-P(t-1) of the photovoltaic array; specifically, it includes:

[0118] Initialize the duty cycle D, collect the instantaneous output current I and voltage U of the PV array, calculate the instantaneous output power P = IU, and iterate. The improved whale algorithm uses a nonlinear dynamic adjustment factor for dynamic search, introduces a nonlinear adaptive weight strategy to escape local optima, and introduces a screening perturbation mechanism to accelerate convergence for preliminary optimization. The primary goal of the preliminary optimization stage is to quickly find the approximate maximum power point range. This stage typically uses a relatively rough method to quickly search for the maximum power point.

[0119] After the iteration is completed, the output power change rate ΔP of the photovoltaic array is determined:

[0120] When the output power change rate ΔP of the photovoltaic array is greater than or equal to the preset value Z, the improved whale algorithm is restarted, and the duty cycle D is not output during this process;

[0121] When the output power change rate ΔP of the photovoltaic array is less than the preset value Z, after completing the iterative optimization of the improved whale algorithm, the improved conductivity increment method is enabled for precise optimization to dynamically adjust and output the duty cycle D to control the start and stop of the power switch tube IGBT; this stage uses preliminary optimization to quickly find the approximate location of the maximum power point, and then starts the precise optimization stage. It will adjust the duty cycle more finely to achieve a more accurate maximum power point. This stage usually uses a more efficient algorithm.

[0122] When the output power change rate ΔP of the photovoltaic array is 0, the instantaneous output power of the photovoltaic array reaches the maximum power point. At this time, the duty cycle D is directly output to control the start and stop of the power switch tube IGBT.

[0123] In this embodiment, the preset value Z=0.08, which is a constant.

[0124] Example 2:

[0125] This study conducted simulation experiments on MATLAB / Simulink to verify the feasibility of the MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method. Figure 8 The parameters of the solar module used are shown in Table 1 (five 3*3 photovoltaic cells connected in series).

[0126] Table 1:

[0127] Series 3 in parallel 3 Open circuit voltage 36.3v Short-circuit current 7.84A Maximum power point voltage 29V Maximum power point current 7.35A

[0128] The Boost circuit parameter settings are shown in Table 2:

[0129] Table 2:

[0130] Components Numerical inductance 3mh Capacitor 1 10uF Capacitor 2 80uF DC load 45Ω Switching frequency 20khz

[0131] When a photovoltaic array is under uniform illumination, its output power-voltage (PU) curve displays a clear peak, making it easy for traditional maximum power point tracking (MPPT) algorithms to find this maximum power point (MPP). However, under dynamically changing illumination conditions, the PU curve may exhibit multiple peaks, increasing the difficulty of finding the global maximum power point. In this multi-peak scenario, traditional MPPT algorithms, due to their simple control mechanisms, tend to lock onto a local maximum rather than the global maximum power point. This prevents the system from achieving its maximum possible power output, resulting in power loss.

[0132] like Figure 5Figure 1 shows the PU characteristic curves of the photovoltaic array under different lighting conditions, which shows the multi-peak characteristics under non-uniform lighting conditions. To solve this problem, more advanced MPPT algorithms are needed. These algorithms can effectively track the global maximum power point under complex lighting conditions, reduce power loss and improve the overall efficiency of the system.

[0133] The traditional Whale-Conductance Incremental Method (WOA) mimics humpback whale hunting behavior, including swarming, spiraling, and random search, to approach the optimal solution. The whales alternate between shrinking swarming and spiraling paths with a 50% probability to approach the target, simulating the behavior of swarming prey.

[0134] To overcome the problems of long tracking time and large output fluctuations in the traditional whale conductance increment (WOA-INC) algorithm, this embodiment provides an improved whale-conductance increment method (PEWOA-INC), which specifically includes: an improved whale algorithm and an improved conductance increment method, wherein:

[0135] The improved whale algorithm uses a nonlinear dynamic adjustment factor for dynamic search;

[0136] And introduce nonlinear adaptive weight strategy to jump out of local optimum and introduce screening perturbation mechanism to accelerate convergence and perform preliminary optimization;

[0137] After the improved whale algorithm completes the iterative optimization, the improved conductance increment method is used for precise optimization.

[0138] The improved whale-conductance increment method introduces three key improvements:

[0139] (1) Dynamic search using nonlinear dynamic adjustment factors;

[0140] In order to optimize the ability of the traditional WOA-INC algorithm to solve nonlinear problems, the convergence factor of the traditional algorithm was upgraded to overcome the problems of slow initial search speed and insufficient search accuracy in the later stage due to the linear convergence factor. Specifically, a nonlinear dynamic adjustment factor was adopted. This factor has a large value in the early stage to accelerate global exploration, and decreases to a smaller value in the later stage to improve the accuracy of local search, such as Figure 6 The formula of the nonlinear dynamic adjustment factor is defined as follows:

[0141]

[0142] Where t is the number of iterations, t_max is the maximum number of iterations, 2, -5, and 3 are parameters that control the nonlinear decrease rate, and a1 is the nonlinear dynamic adjustment factor;

[0143] The nonlinear dynamic adjustment factor a1 is first-order and second-order derivatives taken. The first-order derivative is used to analyze the curve change trend of the nonlinear dynamic adjustment factor a1. The second-order derivative is used to analyze the concave and convex changes of the curve of the nonlinear dynamic adjustment factor a1, so as to understand how the nonlinear dynamic adjustment factor a1 can enhance the search capability through numerical changes. The first-order and second-order derivative formulas are:

[0144]

[0145] The coefficient of -30 after the first-order derivative (da1 / dt) means that as the number of iterations t increases, the search range will gradually narrow, which helps to find the optimal solution faster, and then gradually narrow the search range to find the optimal solution.

[0146] Second order derivative (da1 2 / d 2 t) we can know that: when When d 2 a1 / dt 2 =0, and Right now Therefore, within the maximum range of iterations (mid-range of iterations), the nonlinear convergence factor a1 curve has concave and convex changes:

[0147] If d is in (x,y) 2 a1 / dt 2 <0, then the nonlinear convergence factor a1 curve on (x, y) is convex, that is, When the nonlinear convergence factor a1 is The upper curve is convex;

[0148] If d is in (x,y) 2 a1 / dt 2 > 0, the nonlinear convergence factor a1 curve on (x, y) is concave, that is, When the nonlinear convergence factor a1 is The upper curve is concave.

[0149] In this way, the algorithm can use a larger a1 to quickly explore the solution space in the early stage of the search, and as a1 decreases in the later stage, it can search the potential optimal solution area more carefully, thereby significantly improving the search efficiency when solving nonlinear problems.

[0150] (2) Introducing nonlinear adaptive weight strategy;

[0151] In order to overcome the problem that the original WOA-INC algorithm is prone to falling into local optimality in multi-objective optimization, a nonlinear adaptive weight strategy is introduced:

[0152]

[0153] Where t is the number of iterations, t_max is the maximum number of iterations, and w(t) is the nonlinear adaptive weight.

[0154] The nonlinear adaptive weight strategy is as follows Figure 7 As shown in the figure, the weight values ​​can be dynamically adjusted to meet the optimization needs of different stages. In the early stages of the algorithm, the weight values ​​are large, which helps promote global search and transitions and expand the search range. In the later stages, the weight values ​​gradually decrease to ensure that the details of the search process are refined and avoid a drop in accuracy in the later stages. This strategy can adaptively adjust the search vector and span based on the characteristics of the function and the current state of the algorithm, thereby significantly improving the efficiency and accuracy of the algorithm. This dynamic weight adjustment not only facilitates macro-level exploration in complex problems, but also optimizes at the micro level, effectively preventing the algorithm from falling into a local optimal solution.

[0155] Corresponding updates have also been made to the contraction hunting and spiral hunting methods. In the contraction hunting process, the nonlinear adaptive weighting strategy can better guide the whale group toward the optimal solution while maintaining sufficient diversity to avoid premature convergence to a local optimum. In the spiral hunting method, this strategy can help whales approach the optimal solution more efficiently, especially in the later stages of the algorithm, by reducing the weight value to enhance local search capabilities, thereby ensuring search accuracy.

[0156] The improved whale algorithm has been updated for the shrinking encirclement and spiral attack methods. The specific expressions are:

[0157]

[0158] Where X(t+1) represents the position vector of the current solution at t+1 iterations; X(t) represents the position vector of the current solution at t iterations; A, D1, D2, and D3 represent coefficient vectors, with A∈[0,2]; l and r3 represent random numbers between 0 and 1; b represents the direction of the control spiral, which is a constant 1; X rand (t) represents the position of a random humpback whale individual.

[0159] By introducing a nonlinear adaptive weight strategy, not only can the performance of the original WOA-INC algorithm in multi-objective optimization be improved, but the search efficiency and accuracy of the shrinking encirclement and spiral hunting methods can also be effectively improved, making the algorithm more robust and efficient in solving complex problems.

[0160] (3) Introducing a screening perturbation mechanism;

[0161] To address the problem of slowing convergence in the late stages of the algorithm, the output power of photovoltaic cells is sorted by fitness at the end of the iteration. The positions of the top 50% of humpback whales with high fitness remain unchanged, while the bottom 50% of individuals with low fitness are randomly updated among these leading groups. This significantly accelerates the optimization process in the late stages, improves the overall performance and optimization efficiency of the algorithm, and ensures that the algorithm continues to operate efficiently during the convergence stage. The specific expression is:

[0162]

[0163] Where X(t+1) represents the position vector of the current solution at t+1 iterations; X(t) represents the position vector of the current solution at t iterations; f represents the fitness value of the corresponding whale individual; f med represents the median of the fitness value; rand() represents a random number uniformly distributed between 0 and 1; X1 and X2 represent the positions of the humpback whale individuals with the smallest and largest fitness values ​​in the top 50% of the fitness values, respectively.

[0164] The improved whale algorithm has shown significant advantages in the field of complex multi-objective optimization. It is not only fast but also stable, providing strong support for solving complex problems in practical engineering and scientific research.

[0165] (4) After the improved whale algorithm completes the iterative optimization, the improved conductance increment method is used to further accurately optimize;

[0166] Compared to the perturbation-and-observe method and the constant voltage method, the conductance increment method demonstrates higher tracking accuracy. This method is based on the relationship between the rate of change of the photovoltaic cell's output voltage and current. By monitoring these two rates in real time and adjusting the operating point, it accurately tracks the maximum power point, ensuring the system always operates at peak efficiency.

[0167] The specific method is:

[0168] Calculate the current change rate dI and voltage change rate dU between two adjacent iterations;

[0169] dI=I(t)-I(t-1);

[0170] dU=U(t)-U(t-1);

[0171] The instantaneous output power of the photovoltaic cell is P = IU. Differentiating the voltage on both sides of the equation yields dP / dU = I + U * dI / dU, where dP is the power change rate ΔP between two adjacent iterations. When dP / dU = 0, the photovoltaic cell operates at its maximum power point.

[0172] That is, when dU≠0, dP=0, dI / dU=-I / U, at which time the photovoltaic cell operates at the maximum power point;

[0173] The voltage and duty cycle D can be adjusted by determining the relationship between dI / dU and -I / U:

[0174]

[0175] Where I(t) represents the current at iteration t; I(t-1) represents the current at iteration t-1; U(t) represents the voltage at iteration t; U(t-1) represents the voltage at iteration t-1; I represents the current; and dP represents the rate of change of power between two adjacent iterations.

[0176] When dU=0, the duty cycle D is adjusted and output by judging dI;

[0177]

[0178] The duty cycle D is dynamically adjusted and outputted through the current change rate dI or voltage change rate dU.

[0179] In this embodiment, specifically, the MPPT control method of the photovoltaic hydrogen production system based on the improved whale-conductance increment method is as follows: Figure 8 As shown, the specific steps include:

[0180] Step A: Initialize the duty cycle D, calculate the whale fitness and the whale optimal solution, and record the individual position of the optimal solution to generate the nonlinear dynamic adjustment factor a1, A, the coefficient vector C, and randomly generate three random numbers r1, r2 and r3, where r1, r2 and r3 are all ∈ [0, 1];

[0181] The coefficient calculation formula is as follows:

[0182]

[0183] Where a1 represents the nonlinear dynamic adjustment factor; r1 and r2 represent random numbers between 0 and 1; t represents the number of iterations; t_max is the maximum number of iterations; A, C, D1, D2, and D3 represent the coefficient vectors, A∈[0,2]; X * represents the position vector of the current optimal solution; X represents the position vector of the current solution; X rand (t) represents the position of a random humpback whale individual.

[0184] Step B: collecting the instantaneous output current I and instantaneous output voltage U of the photovoltaic array, and calculating the instantaneous output power P=IU;

[0185] Step C, iterative start, using the improved whale algorithm to perform preliminary optimization: determine the value of the random number r3; use the following formula to achieve:

[0186]

[0187] Where X(t+1) represents the position vector of the current solution at t+1 iterations; X(t) represents the position vector of the current solution at t iterations; A, D1, D2, and D3 represent coefficient vectors, with A∈[0,2]; l and r3 represent random numbers between 0 and 1; b represents the direction of the control spiral, with a value of constant 1, and X rand (t) represents the position of a random humpback whale individual.

[0188] If the random number r3 ≥ 0.5, the spiral attack of the improved whale algorithm is used;

[0189] If the random number r3 is less than 0.5, the value of |A| is determined; if |A| ≥ 1, the random search of the improved whale algorithm is used; if -1 < A < 1, the contraction and round-up of the improved whale algorithm is used;

[0190] Step D: At the end of the iteration, enable the improved whale algorithm’s screening perturbation mechanism to speed up convergence. This is achieved using the following formula:

[0191]

[0192] Where X(t+1) represents the position vector of the current solution at t+1 iterations; X(t) represents the position vector of the current solution at t iterations; f represents the fitness value of the corresponding whale individual; f med represents the median of the fitness value; rand() represents a random number uniformly distributed between 0 and 1; X1 and X2 represent the positions of the humpback whale individuals with the smallest and largest fitness values ​​in the top 50% of the fitness values, respectively.

[0193] Step E: After the iteration is completed, the output power change rate △P is determined;

[0194] If the output power change rate ΔP ≥ Z, in this embodiment, Z = 0.08, and return to step A to restart the improved whale algorithm;

[0195] If the output power change rate △P<Z, the improved conductivity increment method is used and the process goes to step F;

[0196] If the output power change rate △P=0, go directly to step G;

[0197] Step F: After the improved conductance increment method is activated, the rate of change of the voltage and current is checked, and the duty cycle D is outputted accordingly;

[0198] Calculate the current change rate dI and voltage change rate dU between two adjacent iterations;

[0199] dI=I(t)-I(t-1);

[0200] dU=U(t)-U(t-1);

[0201] The instantaneous output power of the photovoltaic cell is P = IU. Differentiating the voltage on both sides of the equation yields dP / dU = I + U * dI / dU, where dP is the power change rate △P between two adjacent iterations and U is the photovoltaic output voltage monitored in real time. When dP / dU = 0, the photovoltaic cell operates at its maximum power point.

[0202] When dU≠0, dP=0, dI / dU=-I / U;

[0203] The voltage and duty cycle can be adjusted by determining the relationship between dI / dU and -I / U:

[0204]

[0205] Where I(t) represents the current at iteration t; I(t-1) represents the current at iteration t-1; U(t) represents the voltage at iteration t; U(t-1) represents the voltage at iteration t-1; I represents the current; and dP represents the rate of change of power between two adjacent iterations.

[0206] When dU=0, the duty cycle D is adjusted and output by judging dI;

[0207] If dI = 0, it means that the photovoltaic cell is operating at the maximum power point and directly outputs the duty cycle D;

[0208] If dI>0, increase the duty cycle D;

[0209] If dI<0, reduce the duty cycle D;

[0210] Step G: Output duty cycle D to control the start and stop of the power switch tube IGBT switch tube.

[0211] Simulation Results

[0212] In order to verify the performance of the proposed control algorithm, tests were carried out under static lighting conditions and dynamically changing conditions.

[0213] 1) Performance test of the proposed algorithm under static uniform illumination

[0214] The uniform illumination condition is set to: 1000W·m -2 、1000W·m -2 、1000W·m -2 、1000W·m -2 、1000W·m -2 The simulation results are as follows. Figure 9 and shown in Table 3.

[0215] Table 3 Comparison of algorithm performance under uniform illumination

[0216]

[0217] according to Figure 9 As shown in Table 3, under uniform illumination conditions, the INC algorithm can find the maximum power point within 0.01 seconds, achieving a tracking accuracy of 99.92% and an error of only 0.08%. The electrolysis efficiency is also 93.33%. In comparison, the WOA-INC algorithm, while also achieving the same tracking accuracy and error, takes longer to 0.19 seconds, and achieves a slightly improved electrolysis efficiency of 94.62%. The PEWOA-INC algorithm stands out, not only finding the maximum power point within 0.08 seconds but also achieving a higher tracking accuracy of 99.97%, reducing the error to 0.03%, and achieving the highest electrolysis efficiency of 94.92%, with minimal fluctuation in the output curve.

[0218] These results show that under uniform illumination conditions, the INC algorithm excels with its fast convergence speed and high stability. However, compared to the WOA-INC algorithm, the PEWOA-INC algorithm exhibits faster tracking speed, higher stability, and better electrolysis efficiency. Therefore, the PEWOA-INC algorithm effectively tracks the maximum power point of photovoltaic cells under uniform illumination conditions, demonstrating its effectiveness in finding the maximum power point under static uniform illumination conditions.

[0219] 2) Performance test of the proposed algorithm under dynamically changing lighting

[0220] Dynamically changing light conditions are set to: 1000W·m -2 、1000W·m -2 , 800W·m -2 , 700W·m -2 , 700W·m -2 , and suddenly changes to: 1000W·m at 0.3s -2 、1000W·m -2 , 900W·m -2 , 800W·m -2 , 800W·m -2 The simulation results are as follows. Figure 10 and as shown in Table 4.

[0221] Table 4 Comparison of algorithm performance under dynamic changes

[0222]

[0223]

[0224] The simulation results show that under dynamic conditions, the INC algorithm fell into a local optimum and failed to successfully track the maximum power point. Its electrolysis efficiency before and after the step was 64.61% and 80.43%, respectively. In contrast, the WOA-INC algorithm was able to find the maximum power point within 0.16 seconds, with tracking accuracies of 99.88% and 99.90%, respectively, and errors of 0.12% and 0.10%, respectively. The electrolysis efficiency was 76.42% and 83.86%, respectively. The PEWOA-INC algorithm performed even better, finding the maximum power point within 0.08 seconds and 0.10 seconds, with tracking accuracies of 99.94% and 99.95%, respectively, with errors reduced to 0.06% and 0.05%, respectively. The electrolysis efficiency was also 76.42% and 83.86%.

[0225] A comparative analysis revealed that the INC algorithm failed to effectively track the maximum power point under dynamically changing conditions. However, the PEWOA-INC algorithm, compared to the WOA-INC algorithm, not only tracked the maximum power point faster and more stably, but also achieved higher electrolysis efficiency. Therefore, under dynamically changing conditions, the PEWOA-INC algorithm can effectively track the maximum power point of photovoltaic cells and improve electrolysis efficiency, thus validating the effectiveness of the PEWOA-INC algorithm in finding the maximum power point under dynamic illumination conditions.

[0226] Although the present invention is described herein with reference to illustrative embodiments of the present invention, the above embodiments are merely preferred embodiments of the present invention, and the embodiments of the present invention are not limited to the above embodiments. It should be understood that those skilled in the art can design many other modifications and implementations, which will fall within the scope and spirit of the principles disclosed in this application.

Claims

1. The MPPT control method of photovoltaic hydrogen production system based on the improved whale-conductance increment method is characterized by: include: Establish a photovoltaic hydrogen production system with a photovoltaic array, which consists of several photovoltaic panels connected in series and parallel; The output circuit of the photovoltaic array is connected to the PEM electrolyzer through a step-up DC-DC converter. The PEM electrolyzer uses direct current to decompose water molecules into hydrogen and oxygen. The duty cycle D is dynamically optimized and generated by the improved whale-conductance increment method. Duty cycle D controls the start and stop of the power switch tube IGBT in the boost DC-DC converter circuit to optimize the photovoltaic array voltage regulation performance of the photovoltaic hydrogen production system. The improved whale-conductance increment method includes an improved whale algorithm and an improved conductance increment method; including: Initialize the duty cycle D, collect the instantaneous output current I and instantaneous output voltage U of the photovoltaic array, calculate the instantaneous output power P = IU, and iterate. Enable the improved whale algorithm to use nonlinear dynamic adjustment factors for dynamic search, introduce a nonlinear adaptive weight strategy to escape the local optimum, and introduce a screening perturbation mechanism to accelerate convergence for preliminary optimization. After the iteration is completed, the output power change rate ΔP of the photovoltaic array is determined: When the output power change rate ΔP of the photovoltaic array is greater than or equal to the preset value Z, the improved whale algorithm is restarted; When the output power change rate ΔP of the photovoltaic array is less than the preset value Z, the improved conductance increment method is used for precise optimization to dynamically adjust and output the duty cycle D to control the start and stop of the power switch tube IGBT; The improved conductivity increment method calculates the current change rate dI and the voltage change rate dU between two adjacent iterations to dynamically adjust the duty cycle D. When dU≠0, the voltage and duty cycle D are adjusted by judging the relationship between dI / dU and -I / U. When dU=0, the voltage and duty cycle D are adjusted by judging dI. When the output power change rate ΔP of the photovoltaic array is 0, the instantaneous output power of the photovoltaic array reaches the maximum power point. At this time, the duty cycle D is directly output to control the start and stop of the power switch tube IGBT.

2. The MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method according to claim 1 is characterized in that: The improved whale-conductance increment method takes the instantaneous output current I and instantaneous output voltage U of the photovoltaic array as input, calculates the instantaneous output power P=IU, and dynamically adjusts the duty cycle D by the output power change rate ΔP=P(t)-P(t-1) of the photovoltaic array, where t is the number of iterations.

3. The MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method according to claim 2 is characterized in that: The control method further includes: Establishing a photovoltaic cell equivalent model, thereby obtaining the instantaneous output current I, instantaneous output voltage U, and instantaneous output power P=IU of the photovoltaic array according to the established photovoltaic cell equivalent model; The photovoltaic cell equivalent model includes at least an ideal diode, a photocurrent source, a series resistor and a parallel resistor. The photocurrent source is connected in parallel with the ideal diode and the parallel resistor respectively. Finally, the entire structure is connected in series with the series resistor and the load.

4. The MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method according to claim 3 is characterized in that: According to the established photovoltaic cell equivalent model, the instantaneous output current I of the photovoltaic array is obtained as follows: Where n is the total number of photovoltaic panels; I is the instantaneous output current of the photovoltaic array; I ph is the current of the photocurrent source; I0 is the reverse saturation current of the ideal diode; q is the electron charge; U is the instantaneous output voltage of the photovoltaic array; R s is the resistance of the series resistor of the photovoltaic cell equivalent model; m is the characteristic fitting parameter of the ideal diode; K is the Boltzmann constant; T is the working environment temperature of the photovoltaic panel; R sh is the resistance of the parallel resistor of the photovoltaic cell equivalent model; Let the resistance R of the series resistor in the photovoltaic cell equivalent model be s =0, the resistance R of the parallel resistor of the photovoltaic cell equivalent model sh =∞; due to the resistance R of the series resistor in the photovoltaic cell equivalent model s =0, the resistance of the parallel resistor R sh =∞, It tends to 0, so it can be ignored. Then the general equation of the instantaneous output current I of the photovoltaic array is simplified to:

5. The MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method according to claim 3 is characterized in that: The equivalent circuit of the boost DC-DC converter is specifically: A periodically operating power switch tube IGBT is connected in series with an inductor L, and then connected in parallel with a load R and a capacitor C2. Capacitor C2 is used to smooth the output voltage. Among them, capacitor C2 realizes the smoothing of the output voltage of the photovoltaic array and the voltage ripple. The ideal diode prevents current backflow. The voltage regulation performance is optimized by controlling the start and stop of the power switch tube IGBT in the boost DC-DC converter.

6. The MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method according to any one of claims 1 to 5, characterized in that: The improved whale algorithm uses a nonlinear dynamic adjustment factor for dynamic search; the specific method is: The formula of the nonlinear dynamic adjustment factor is defined as follows: Where t is the number of iterations, t_max is the maximum number of iterations, and a1 is the nonlinear dynamic adjustment factor; Taking the first-order and second-order derivatives of the nonlinear dynamic adjustment factor a1, we can obtain: The curve change trend of the nonlinear dynamic adjustment factor a1 is analyzed by first-order derivative, and the concave and convex changes of the curve of the nonlinear dynamic adjustment factor a1 are analyzed by second-order derivative to understand how the nonlinear dynamic adjustment factor a1 enhances the search capability through numerical changes.

7. The MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method according to any one of claims 1 to 5, characterized in that: The improved whale algorithm introduces a nonlinear adaptive weight strategy; the specific expression is: Where t is the number of iterations, t_max is the maximum number of iterations, and w(t) is the nonlinear adaptive weight; The improved whale algorithm updates the contraction and spiral hunting methods, and the specific expression is: Where X(t+1) represents the position vector of the current solution at t+1 iterations; X(t) represents the position vector of the current solution at t iterations; A, D1, D2, and D3 represent coefficient vectors, with A∈[0,2]; l and r3 represent random numbers between 0 and 1; b represents the direction of the control spiral, which is a constant 1; X rand (t) represents the position of a random humpback whale individual.

8. The MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method according to any one of claims 1 to 5, characterized in that: The improved whale algorithm introduces a screening perturbation mechanism, which is specifically expressed as follows: Among them, X(t+1) represents the position vector of the current solution at t+1 iterations; X(t) represents the position vector of the current solution at t iterations; f represents the fitness value of the corresponding whale individual; f med represents the median of the fitness value; rand() represents a random number uniformly distributed between 0 and 1; X1 and X2 represent the positions of the whale individuals with the smallest and largest fitness values ​​in the top 50% of the fitness values, respectively.

9. The MPPT control method for photovoltaic hydrogen production system based on the improved whale-conductance increment method according to any one of claims 1 to 5, characterized in that: The improved conductance increment method is used to perform precise optimization to dynamically adjust and output the duty cycle D to control the start and stop of the power switch tube IGBT; the specific method is: Calculate the current change rate dI and voltage change rate dU between two adjacent iterations; The instantaneous output power of the photovoltaic cell is P=IU, When dU≠0, the voltage and duty cycle D are adjusted by judging the relationship between dI / dU and -I / U: When dU=0, the voltage and duty cycle D are adjusted by judging dI; The duty cycle D is dynamically adjusted and output through the current change rate dI and voltage change rate dU.

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