A random extreme value search-based photovoltaic cell maximum power point tracking control method

Abstract

The application discloses a photovoltaic cell maximum power point tracking control method based on random extreme value search, and belongs to the technical field of maximum power point tracking control of photovoltaic power generation systems. The application solves the problems that the existing control method cannot optimize the controller parameters according to the stability analysis result and does not consider random interference. In the case that the output channel contains measurement noise, the application designs a random extreme value search control algorithm, and sequentially carries out average processing and stability analysis on the average system based on the time delay average value theory method and the constant variable formula method of the random differential equation, so as to provide quantitative guidance for optimizing parameters for maximum power point tracking control design of multiple photovoltaic cells. The method of the application can be applied to maximum power point tracking control of photovoltaic cells.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of maximum power point tracking control of photovoltaic power generation system, and particularly relates to a photovoltaic cell maximum power point tracking control method based on random extreme value search. BACKGROUND

[0002] With the increasingly serious problem of fossil energy shortage, the status of solar energy is becoming higher and higher, and China is rich in solar energy resources and has great development potential. With the continuous maturity of photovoltaic power generation technology, photovoltaic power generation has been widely used in social energy supply. However, while the photovoltaic industry is developing rapidly, the problem of low power generation efficiency of photovoltaic system is becoming increasingly prominent. Therefore, in order to improve the power generation efficiency of photovoltaic system and achieve maximum power output, the photovoltaic maximum power point tracking (MPPT) control technology has become an indispensable part of photovoltaic power generation system.

[0003] The commonly used photovoltaic maximum power point tracking (MPPT) algorithms at present include constant voltage tracking method, perturbation and observation method and conductance increment method. The constant voltage tracking method has poor adaptability and cannot be adjusted in time. The step selection of the perturbation and observation method affects tracking, and the effect is not good when the environment changes quickly. The conductance increment method also has the problem of step selection and is affected by detection accuracy and speed. Therefore, the above methods have certain limitations and have problems such as insufficient tracking speed or tracking accuracy. It is necessary to find an extreme value search MPPT control method which is independent of model and has global search ability for extreme value search control. The extreme value search control method has the advantages of simple principle, small calculation amount, real-time optimization and model-free.

[0004] The extreme value search has been widely applied to solve the MPPT control problem of photovoltaic system. However, the existing photovoltaic MPPT control based on extreme value search algorithm has certain limitations. On the one hand, most of the existing extreme value search control methods can only provide stability analysis and cannot provide accurate quantitative guidance for the selection of optimization parameters, which to some extent restricts the application of extreme value search control method in photovoltaic system MPPT control. On the other hand, the volatility and randomness of solar energy will affect the photovoltaic power generation system, and the existing photovoltaic MPPT control based on extreme value search does not consider the influence of random disturbance. SUMMARY

[0005] The purpose of the present application is to solve the problems that the existing control method cannot optimize the controller parameters according to the stability analysis results and does not consider random disturbance, and a photovoltaic cell maximum power point tracking control method based on random extreme value search is proposed.

[0006] The technical scheme adopted by the present application to solve the above technical problems is: a photovoltaic cell maximum power point tracking control method based on random extreme value search, which specifically comprises the following steps:

[0007] Step one, a relationship between duty cycle and output power in a photovoltaic power generation system in which n photovoltaic cells are connected in series is established, the relationship between duty cycle and output power in the photovoltaic power generation system is Taylor expanded to obtain a quadratic static objective function;

[0008] and an upper limit of the maximum output power P * in the quadratic static objective function is estimated, as well as an upper limit of the duty cycle corresponding to each photovoltaic cell and a lower limit of the duty cycle d i * ;

[0009] Step two, a control system considering random disturbance of output is established according to the quadratic static objective function and a random extreme value search control algorithm, and the control system is averaged to obtain a perturbation system equivalent to the control system;

[0010] Step three, the perturbation system is analyzed for stability by using a constant variation formula method based on ordinary differential equation and the estimated upper limit of the maximum output power P * , the upper limit of the duty cycle and the lower limit of the duty cycle d i * ;

[0011] Controller parameters are obtained according to the stability analysis result, and the controller is used to perform maximum power point tracking control on the photovoltaic power generation system.

[0012] The present application has the following beneficial effects:

[0013] In the case that the output channel contains measurement noise, the present application designs a random extreme value search control algorithm, and sequentially performs averaging processing and stability analysis on the averaged system by using the time delay average value theory method and the constant variation formula method of random differential equation, thereby providing quantitative guidance for optimal parameters for maximum power point tracking control design of multiple photovoltaic cells.

[0014] The value range of the optimal parameters is determined by solving the explicit stability condition obtained in step three, and the effectiveness of the single photovoltaic cell maximum power point tracking control method based on random extreme value search under random disturbance can be verified by using MATLAB for simulation. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is a whole block diagram of a photovoltaic power generation system;

[0016] Figure 2 is a photovoltaic cell MPPT control system block diagram based on random extreme value search algorithm;

[0017] In the figure, Measurement Noise represents measurement noise, Dither signals represents dither signals, and Plant represents a photovoltaic power generation system.

[0018] Figure 3 is a duty cycle estimation value curve of two photovoltaic cells;

[0019] Figure 4 is a photovoltaic system output power curve;

[0020] Figure 5 is a duty cycle estimation error value curve of two photovoltaic cells;

[0021] Figure 6 is a convergence curve of the duty cycle of two photovoltaic cells. DETAILED DESCRIPTION

[0022] Embodiment one: the photovoltaic cell maximum power point tracking control method based on random extreme value search described in the embodiment specifically includes the following steps:

[0023] Step one, establish the relationship between the duty cycle and the output power in a photovoltaic power generation system with n photovoltaic cells in series, Taylor expand the relationship between the duty cycle and the output power in the photovoltaic power generation system, and obtain a quadratic static objective function;

[0024] and estimate the upper bound of the maximum output power P * in the quadratic static objective function, and the upper bound and the lower bound d of the duty cycle corresponding to each photovoltaic cell. i * ;

[0025] Step two, establish a control system considering random disturbance of output according to the quadratic static objective function and the random extreme value search control algorithm, and perform averaging processing on the control system by using the time delay-based averaging method, to obtain a perturbation system equivalent to the control system;

[0026] Step three, perform stability analysis on the perturbation system by using the constant variation formula method based on ordinary differential equations and the estimated upper bound of the maximum output power P * , the upper bound and the lower bound d i * of the duty cycle.

[0027] According to the stability analysis results, the controller parameters (i.e., given k and a i , and ε∈(0, ε * ), and then determine ω i ) according to ε, and then use the controller to perform maximum power point tracking control on the photovoltaic power generation system.

[0028] The photovoltaic effect of the photovoltaic cell can convert solar energy into electrical energy. When the cell receives light, a voltage difference appears in the cell. Generally, an ideal current source can be used to represent each photovoltaic cell, and the current source current is I ph , and the current source is connected in parallel with an ideal diode. The electrical loss and the contact resistance are represented by R s and R p , respectively. The generated current I ph depends on the solar irradiance S and the temperature T, and the formula is:

[0029]

[0030] where, is the standard short-circuit current, T r is the standard temperature, k i is the dimensionless short-circuit temperature coefficient. At the same time, the photovoltaic cell material has an impact on the model of the ideal diode, and there is:

[0031]

[0032] where, is the diode reference reverse saturation current, E g is the semiconductor band gap energy, N is the semiconductor emission coefficient, V t is the thermal cell voltage, V D is the diode terminal voltage, k is 1.38×10 -23 J / K, q is the electronic charge number (1.6×10 - 19 C).

[0033] Using KCL and KVL laws:

[0034] I=I ph -I D -V D / R p (4)

[0035] V D =V+R s I (5)

[0036] where I is the output current of the photovoltaic cell, and V is the output voltage of the photovoltaic cell.

[0037] The I-V relationship of a single photovoltaic cell is:

[0038]

[0039] Specific implementation two: combined Figure 1 This embodiment is described. This embodiment is different from the first embodiment in that, in step one, the relationship between the duty cycle and the output power in the photovoltaic power generation system formed by n photovoltaic cells in series is established, specifically:

[0040] The I-V relationship of the i-th photovoltaic cell in the photovoltaic power generation system is: i -V i relationship is:

[0041]

[0042] wherein, I ph,i is the current of the current source corresponding to the i-th photovoltaic cell, V i is the output voltage of the i-th photovoltaic cell, R s,i is the electrical loss of the i-th photovoltaic cell, I i is the output current of the i-th photovoltaic cell, N is the semiconductor emission coefficient, V t is the thermal cell voltage, R p is the contact resistance;

[0043] Intermediate variable

[0044] wherein, is the reference reverse saturation current of the diode corresponding to the i-th photovoltaic cell, T r is the standard temperature, T is the actual temperature, E g is the semiconductor band gap energy, k is a constant, and q is the electronic charge number;

[0045] According to the I-V relationship of the photovoltaic cell, the P-V variation curve of the photovoltaic cell can be drawn, and it is found that the P-V characteristic curve of the photovoltaic cell has an extreme point, i.e., the power reaches the maximum value at this time, and the peak value of the power is related to the irradiance and the temperature;

[0046] The output voltage and the output current of each photovoltaic cell in the photovoltaic power generation system are converted through a DC / DC converter, and then

[0047]

[0048] wherein, V dc is a constant value of the output DC voltage of the photovoltaic power generation system, V oi is the output voltage of the i-th photovoltaic cell after the DC / DC converter, and I oiIi is the output current of the ith photovoltaic cell after the DC / DC converter dc is a constant value of the output DC current of the photovoltaic power generation system;

[0049] When the DC / DC converter is in continuous current mode (CCM), the switching pulse width modulation (PWM) frequency f s is significantly higher than the bandwidth of the control loop, while I i -V i is the function relationship of I i = f i (V i ), the output voltage of each photovoltaic cell V = [V1 V2 … V n ] Τ and the duty cycle d = [d1 d2 … d n ] Τ of the diode corresponding to each photovoltaic cell are as follows:

[0050]

[0051] wherein, is the power efficiency of the converter, d i is the switching duty cycle of the diode corresponding to the ith photovoltaic cell;

[0052] For each set of duty cycles, there is a set of photovoltaic cell voltages. In addition, assuming that there is a bypass diode for each photovoltaic cell, it means that the overall output power has only one peak value.

[0053] The output power P of the photovoltaic power generation system is:

[0054]

[0055] wherein, P i is the output power of the ith photovoltaic cell after the DC / DC converter.

[0056] The other steps and parameters are the same as in the first embodiment.

[0057] When n = 2, T = T r , the relationship between the current and the voltage is as follows:

[0058]

[0059] The equation group can be obtained from formula (10) and formula (11):

[0060]

[0061] In practical application, the parameters in the above formula are often difficult to meet the requirements, and change with the external environment, so the maximum power point tracking cannot be directly performed through the ideal mathematical model, and a model-free extremum search algorithm needs to be used.

[0062] Specific embodiment three: different from the specific embodiment one or two, the relationship between the duty cycle and the output power in the photovoltaic power generation system is Taylor expanded to obtain a quadratic static objective function; specifically:

[0063] For the photovoltaic cell system in actual use, the extremum exists and is global, and the system under a certain environment corresponds to a unique (d * ,P * ), wherein that is, there is satisfying:

[0064]

[0065] wherein, is the first-order derivative value of formula (12) at d * , d * is the maximum output power P * of the photovoltaic power generation system, and d is the duty cycle of the first photovoltaic cell, …, and the duty cycle of the nth photovoltaic cell when the maximum output power P * ; is the second-order derivative value of formula (12) at d * , H is a quadratic Hessian matrix, H T is the transpose of H; H < 0 means that there is a maximum value P′ * at d(t)=d * ;

[0066] The relationship between the duty cycle and the output power in the photovoltaic power generation system is Taylor expanded, and the expansion items higher than the second order are ignored to obtain a quadratic static objective function:

[0067]

[0068] wherein, t is time, d(t) is the duty cycle vector at t, d(t)=[d1(t)…d n (t)] T , and P(t) is the output power of the photovoltaic power generation system at t.

[0069] The other steps and parameters are the same as those in the specific embodiment one or two.

[0070] By modeling the relationship between the output power and the duty cycle based on physical principles, it is found that the relationship of the photovoltaic cell is very complex, has many parameters and uncertainties, and has a nonlinear characteristic. Differences between various photovoltaic cells and aging of the photovoltaic cells in actual use will lead to difficulty in establishing a unified and accurate model for a photovoltaic power generation system composed of a large number of photovoltaic cells in series. When the photovoltaic cells are in an actual operating state, the surrounding environment changes cannot be predicted, and the output characteristics of the photovoltaic cells will be affected by related factors, and more complex or even time-varying nonlinear output characteristics will appear, so it is more difficult to track the output power of the photovoltaic cells by establishing an accurate model in such an uncertain environment.

[0071] The random extreme value search algorithm of the application is very suitable for the case that it is difficult to establish an accurate model for the photovoltaic system as a model-free real-time online adaptive optimization control method.

[0072] Specific implementation four: different from one of the specific implementations one to three, in step two, a control system considering random disturbance of the output is established according to the quadratic static objective function and the random extreme value search control algorithm, and specifically:

[0073] After considering the random disturbance of the output, the quadratic static objective function is statically mapped as:

[0074]

[0075] Wherein, P'(t) is the output power destroyed by the Brownian motion B(t), P'(t)∈R, B(t)∈R, d(0)∈R n , P * ∈R,d * ∈R n , R is a real number, C is a noise intensity, C≥0;

[0076] The upper limit of the duty cycle is defined as And the lower limit is defined as d i * Satisfies: Wherein, The definition is The upper limit of the maximum output power P * is defined as Is a known quantity; the Hessian matrix H satisfies: -βI n ≤H≤-αI n <0, wherein, α and β are known positive scalars, I n ∈R n×n is a unit matrix, and |β|≥|λ max (H)|, λ max(H) is the maximum eigenvalue of the matrix H, |·| represents taking absolute value;

[0077] The block diagram of the photovoltaic cell MPPT control system based on the random extremum search algorithm is shown in Figure 2

[0078] The real-time estimate of d * is defined as The estimation error is:

[0079]

[0080] The random extremum search control algorithm is designed as:

[0081]

[0082] wherein the excitation signal S(t) and M(t) satisfy:

[0083]

[0084] wherein a i is the controller parameter corresponding to the ith photovoltaic cell, ω i is the controller frequency corresponding to the ith photovoltaic cell, ω i ≠ ω j ≠ 0, i ≠ j, ω i / ω j is a rational number; it is assumed that

[0085]

[0086] wherein ε is a parameter to be designed, l i is a rational number, and N + is a set of positive integers;

[0087] The adaptive gain matrix K is selected as:

[0088] K = kI n , k > 0, (22)

[0089] wherein k is the controller gain corresponding to each photovoltaic cell;

[0090] so that KH is Hurwitz.

[0091] The control system considering the random disturbance of the output is obtained from equation (17), equation (18) and equation (19):

[0092]

[0093] For the initial value the solution of equation (23) satisfies the random process​

[0094]

[0095] where s is the integration variable, and the last stochastic integral is of the form

[0096] The other steps and parameters are the same as one of the first three embodiments.

[0097] Embodiment five: The difference between this embodiment and one of the first four embodiments is that the control system is averaged using a time-delay based averaging method to obtain a disturbance system equivalent to the control system. Specifically, the control system of equation (23) is averaged by integrating both sides of equation (23) from t-ε to t+ε and dividing the result by ε, for t≥ε:

[0098]

[0099]

[0100] where s is the integration variable, and let

[0101]

[0102] where f is defined as:

[0103]

[0104] The left side of equation (24) is expressed as:

[0105]

[0106] The first term on the right side of equation (24) is expressed as:

[0107]

[0108] where is a column vector composed of

[0109] The control system of equation (23) is applied to formula to obtain:

[0110]

[0111] The second term on the right side of equation (24) is expressed as:

[0112]

[0113] where ​​

[0114] Since The third term on the right-hand side of equation (24) is expressed as

[0115]

[0116] where τ is an integral variable,

[0117] The fourth term on the right-hand side of equation (24) is expressed as

[0118]

[0119] where h ij is the element in the i-th row and j-th column of matrix H,

[0120] From equations (27), (28), (30), (31) and (32), we have

[0121]

[0122] The solution of the extremum search system (24) is also the solution of the time-delay system (33). Therefore, the stability of the time-delay system (33) can guarantee the stability of the extremum search system (24).

[0123] Define z(t) as

[0124]

[0125] Convert the time-delay system of equation (33) into

[0126]

[0127] Simplify equation (35) into

[0128] dz(t) = KHz(t)dt + ω(t)dt + CKM(t)dB(t), t ≥ ε, (36)

[0129] where ω(t) is an intermediate variable;

[0130]

[0131] If in the mean square sense (z(t)) is O(1) order, the terms G(t), Y j (t) (j = 1, 3, 4) are O(ε 2 ) order, and the terms Y j (t) (j = 2, 5) are O(C 2 ) order. Therefore, in the mean square sense, ω(t) is O(max{ε 2 , C2 Thus, when ε > 0, κ > 0, C > 0 are small, the system of (36) can be viewed as a perturbation of the linear system dz(t) = KHz(t)dt which is exponentially stable since KH is Hurwitz. By (34), the resulting bound on |z| will lead to a bound on z. The bound on z can be obtained by the constant variation formula of (36).

[0132] The other steps and parameters are the same as one of the first to fourth embodiments.

[0133] The sixth embodiment is different from the first to fifth embodiments in that Yl(t), Y2(t) and Y3(t) are respectively:

[0134]

[0135] The other steps and parameters are the same as one of the first to fifth embodiments.

[0136] The seventh embodiment is different from the first to sixth embodiments in that Y4(t) and Y5(t) are respectively:

[0137]

[0138] The other steps and parameters are the same as one of the first to sixth embodiments.

[0139] The eighth embodiment is different from the first to seventh embodiments in that the specific process of step three is:

[0140] Assume and inequality, we have:

[0141]

[0142] where, represents the calculation of expectation;

[0143] Definition:

[0144]

[0145] where, 0 < σ < L 1 / 6 ;

[0146] Since -βI n < αI n , we have

[0147] ||H||≤β (42)

[0148] where || · || is the L2 norm;

[0149] From equation (26) we have:

[0150]

[0151] Further we have:

[0152]

[0153] where:

[0154]

[0155] From equation (25) and equation (43) we have: the equidistance property of then by applying equations, inequality, equation (41) and equation (43) we have the solution of the system of equation (23) an upper bound in the mean square sense of t e [0, ε]:

[0156]

[0157] From equation (25) and equation (43) we have:

[0158]

[0159] then

[0160]

[0161] From equation (26), equation (40), equation (41) and inequality we have:

[0162]

[0163] then

[0164]

[0165] where: From equation (31) and the above equation we have:

[0166]

[0167] By applying the equidistance property and inequality, from equation (20) and equation (31) we have:

[0168]

[0169] where,

[0170]

[0171] where, From equation (43) and equation (33), we have

[0172]

[0173] where,

[0174]

[0175] where, According to Fubini theorem and the property of , we have From equation (50), equation (52) and we have

[0176]

[0177] From equation (47), equation (48) and equation (53), we have

[0178]

[0179] where, From equation (36), equation (45) and equation (46), we have

[0180]

[0181] Using the constant variation formula of equation (38), we have

[0182]

[0183] where, e is the base of natural logarithm;

[0184]

[0185] Since H < 0, there exists an orthogonal matrix U ∈ R n×n (obviously, ||U|| = 1) such that:

[0186]

[0187] where, h1,...,h n are the first,...,nth elements on the diagonal of the matrix -1represent the inverse of the matrix; since

[0188] -βI n ≤H≤-αI n (59)Using the orthogonal matrix U ∈ R n×nand formula (58) and formula (59) are obtained:

[0189]

[0190] Then by formula (55) and formula (60), there are

[0191]

[0192] By formula (54), formula (60) and Inequality, it is obtained that

[0193]

[0194] By formula (60) and The equidistance property is obtained:

[0195]

[0196] Substituting formula (61) to formula (63) into formula (57) obtains:

[0197]

[0198] According to formula (64), formula (36) and formula (46), it is obtained that

[0199]

[0200] Theorem 1: Assuming that the system of formula (24) has a unique solution on [0, ∞), and Wherein, L is an arbitrary large known constant, and σ satisfies: ω i Given by formula (21), the initial condition is Given k and a i , given ε * > 0, C * > 0, let inequality (66) be established:

[0201]

[0202] Since Φ < 0, Φ < 0 means And according to formula (45) and formula (65), it is obtained that for ε ∈ (0, ε * ) and C ∈ (0, C * ), the inequality of formula (67) is established:

[0203]

[0204] The other steps and parameters are the same as one of the first to seventh embodiments.

[0205] Note 1: In order to achieve the convergence of the extreme value search algorithm, the present invention introduces a The conditions defined a priori by a known constant L impose a limit L that is only required to be finite and can be arbitrarily large. In this sense, when t∈[0,ε] There is an upper bound and when t≥ε The existence of an upper bound guarantees that ε * and C * Small enough semi-global convergence. The introduced boundedness assumption is realistic in practical applications. In addition, by formula (66), although ε * and C * It decreases with the increase of L, but when L is large enough, it can still be achieved by choosing a suitable i and k to achieve not too small ε * and C * .

[0206] Note 2: The effect of the optimization parameters on ε is discussed. * 、C * , the influence of the decay rate δ. Let k be given L (large enough), a i and σ>σ0>0, it is obvious that Φ in (66) is a * and C * is an increasing function of . Therefore ε * and C * As k increases, it decreases. On the other hand, the attenuation rate δ = kα increases as k increases. Therefore, the gain K can be adjusted to balance δ, ε * and C * .

[0207] It is proved that the condition Φ<0 in the theorem guarantees that the constraint in formula (41) holds.

[0208] (i) When t∈[0,ε], due to and It is continuous in t, so Equation (41) holds when t>0 is small enough. By contradiction, for some t∈[0,ε], Equation (41) does not hold, that is, there exists a minimum t * (0<t * ≤ε), so that

[0209]

[0210] Then use the same method to process equation (43) and so on, and we get equation (45) for t∈[0,t * ] is a non-rigorous version of the theorem. In addition, the feasibility of Φ < 0 in the theorem guarantees that

[0211]

[0212] this which contradicts. Thus, (41) holds for t ∈ [0, ε].

[0213] (ii) When t ≥ ε, since and are continuous in time, (41) holds for some t > ε. By contradiction assumption, for some t > ε, (41) does not hold, i.e., there exists a minimal time instance t * ∈ (ε, ∞) such that

[0214]

[0215] Thus, for all t ∈ [ε, t * ], holds. With there exists an upper bound, there exists an upper bound, and the proof of the practical stability of the z-system, we finally obtain the non-strict version of (65) for t ∈ [ε, t * ]. Moreover, the feasibility of Φ < 0 in the theorem guarantees which contradicts Thus, for all t ≥ ε, the proof is complete.

[0216] Simulations are performed for the ideal photovoltaic cell model and the case of a photovoltaic cell system consisting of two photovoltaic cells in series. The selected photovoltaic cell-related parameters are shown in Table 1:

[0217] Table 1. Photovoltaic cell-related parameters

[0218]

[0219] The parameters in the assumptions can be estimated by the P-d relationship and the Taylor expansion form of d-P, as shown in Table 2:

[0220] Table 2

[0221]

[0222]

[0223] According to the stability condition of Theorem 1, the random extreme value search algorithm parameters can be obtained as shown in Table 3:

[0224] Table 3

[0225]

[0226] The simulation shows the system response curve of the closed-loop system, and the results show that the closed-loop system converges eventually; for the initial condition From Figure 3 it can be seen that the duty ratio estimation value and converge to d * (i.e. the maximum power point). From Figure 4 it can be clearly seen that the output power P stabilizes at the maximum power P * . From Figure 5 it can be obtained that the duty ratio estimation error value and both converge to 0. From Figure 6 it can be seen that the curve drawn according to the duty ratios of the two photovoltaic cells as horizontal and vertical coordinates eventually converges to the point In the case of considering random interference noise, the photovoltaic control system based on multivariable extremum search can still track the maximum power point well. By observing the system response, it can be found that the multivariable random extremum search control algorithm responds fast, converges rapidly, and the final error is also small.

[0227] The above examples of the present application are only for illustrating the calculation model and calculation process of the present application, and are not intended to limit the embodiments of the present application. For those skilled in the art, other different forms of changes or variations can be made on the basis of the above description, and it is impossible to enumerate all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present application are still within the protection scope of the present application.

Claims

1. A photovoltaic cell maximum power point tracking control method based on random extreme value search, characterized in that: The method specifically comprises the following steps: Step 1: Establish a relationship between the duty cycle and output power in a photovoltaic power generation system composed of n photovoltaic cells connected in series, perform Taylor expansion on the relationship between the duty cycle and output power in the photovoltaic power generation system, and obtain a quadratic static objective function; And estimate the maximum output power P in the quadratic static objective function * The upper bound of the duty cycle of each photovoltaic cell and duty cycle lower bound d i * ; Step 2: Based on the quadratic static objective function and the random extreme value search control algorithm, a control system is established that takes into account the random disturbance of the output, and the control system is averaged to obtain a disturbance system equivalent to the control system; In the second step, a control system considering random disturbance of the output is established according to the quadratic static objective function and the random extreme value search control algorithm, specifically: After considering the random interference of the output, the quadratic static objective function is statically mapped to: Where P′(t) is the output power after being destroyed by Brownian motion B(t), d(t) is the duty cycle vector at time t, H is the quadratic Hessian matrix, P′(t)∈R, B(t)∈R, d(0)∈R n , P * ∈R,d * ∈R n , R is a real number, C is the noise intensity, C ≥ 0; Define the upper bound of the duty cycle and the lower bound d i * satisfy: in, definition is the maximum output power P * The upper bound of is a known quantity; define the quadratic Hessian matrix H to satisfy: -βI n ≤H≤-αI n <0, where α and β are known positive scalars, I n ∈R n×n is the identity matrix, and |β|≥|λ max (H)|,λ max (H) is the largest eigenvalue of the matrix H, and |·| represents the absolute value; Definition d * The real-time estimate of The estimated error for: The random extreme value search control algorithm is designed as follows: Among them, the excitation signals S(t) and M(t) satisfy: Among them, a i is the controller parameter corresponding to the i-th photovoltaic cell, ω i is the controller frequency corresponding to the i-th photovoltaic cell, ω i ≠ω j ≠0, i≠j, ω i / ω j is a rational number; let Among them, ε is the parameter to be designed, l i is a rational number, N + is a set of positive integers; The adaptive gain matrix K is selected as: K=kI n ,k>0, (22) Where k is the controller gain corresponding to each photovoltaic cell; The control system considering random disturbance of output is obtained from equations (17), (18) and (19): For the initial value The solution of formula (23) satisfies the random process Where s is the integration variable; Step 3: Use the constant variation formula method based on ordinary differential equations and the estimated maximum output power P * Upper bound, duty cycle upper bound and the lower bound d i * , perform stability analysis on the disturbance system; The controller parameters are obtained according to the stability analysis results, and then the controller is used to perform maximum power point tracking control on the photovoltaic power generation system.

2. The photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 1, characterized in that: In the step 1, a relationship between the duty cycle and the output power in a photovoltaic power generation system in which n photovoltaic cells are connected in series is established, specifically: I of the i-th photovoltaic cell in the photovoltaic power generation system i -V i The relationship is: Among them, I ph,i is the current of the current source corresponding to the i-th photovoltaic cell, V i is the output voltage of the i-th photovoltaic cell, R s,i is the power loss of the i-th photovoltaic cell, I i is the output current of the i-th photovoltaic cell, N is the semiconductor emission coefficient, V t is the thermal battery voltage, R p is the contactor resistance; Intermediate variables in, is the reference reverse saturation current of the diode corresponding to the i-th photovoltaic cell, T r is the standard temperature, T is the actual temperature, E g is the semiconductor band gap energy, k is a constant, and q is the electron charge number; The output voltage and output current of each photovoltaic cell in the photovoltaic power generation system are passed through the DC / DC converter. Among them, V dc is the constant value of the DC voltage output by the photovoltaic power generation system, V oi The output voltage of the i-th photovoltaic cell after passing through the DC / DC converter, I oi is the output current of the ith photovoltaic cell after passing through the DC / DC converter, I dc It is the constant value of DC current output by the photovoltaic power generation system; The output voltage of each photovoltaic cell V=[V1 V2…V n ] Τ The diode duty cycle corresponding to each photovoltaic cell is d=[d1d2…d n ] Τ The relationship is: in, is the power efficiency of the converter, d i is the switching duty cycle of the diode corresponding to the i-th photovoltaic cell; Then the output power P of the photovoltaic power generation system is: Among them, P i is the output power of the ith photovoltaic cell after passing through the DC / DC converter.

3. The photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 2, characterized in that: The relationship between the duty cycle and output power in the photovoltaic power generation system is Taylor expanded to obtain a quadratic static objective function; specifically: exist satisfy: in, is the equation (12) in d * The first derivative value at d * is the maximum output power P of the photovoltaic power generation system * The corresponding converter duty cycle vector, is the maximum output power P * The duty cycle of the first photovoltaic cell, ..., the nth photovoltaic cell; is the equation (12) in d * The second-order derivative value at , H is the quadratic Hessian matrix, H T is the transpose of H; Perform Taylor expansion on the relationship between duty cycle and output power in the photovoltaic power generation system and ignore the expansion terms higher than quadratic to obtain the quadratic static objective function: Where t is time, d(t) is the duty cycle vector at time t, d(t) = [d1(t)…d n (t)] T , P(t) is the output power of the photovoltaic power generation system at time t.

4. The photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 3, characterized in that: The control system is averaged to obtain a disturbance system equivalent to the control system; specifically: The control system of Equation (23) is averaged, that is, the time delay method is used to integrate both sides of Equation (23) from t-ε to ε, and then the integral result is divided by ε. For t≥ε, we have: Where s is the integration variable, let Where f is defined as: The left side of formula (24) is expressed as: The first term on the right side of equation (24) is expressed as: in, express The column vector composed of Application of the control system of formula (23) The formula is: The second term on the right side of equation (24) is expressed as: in, because Then the third term on the right side of formula (24) is expressed as: Where: τ is the integration variable, The fourth term on the right side of formula (24) is expressed as: Among them, h ij is the element in the i-th row and j-th column of the matrix H, From equations (27), (28), (30), (31) and (32), we can get: Define z(t): The time-delay system of equation (33) is transformed into: Simplify formula (35) to: dz(t)=KHz(t)dt+ω(t)dt+CKM(t)dB(t), t≥ε, (36) Among them, ω(t) is the intermediate variable; The Y1(t), Y2(t) and Y3(t) are respectively: The Y4(t) and Y5(t) are respectively:

5. The photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 4, characterized in that: The specific process of step three is: Assumptions and Inequality, we have: in, stands for Computational Expectation; definition: Among them, 0<σ<L 1 / 6 ; Due to -βI n <H<-αI n ,but ||H||≤β (42) Where ||·|| is the L2 norm; From formula (26), we can get: Further: in: Depend on The isometric properties are By applying formula, The inequality, equation (41) and equation (43) give the solution of the system of equation (23) Upper bound in the mean square sense: From formula (25) and formula (43), we can get: but From formula (26), formula (40), formula (41) and The inequality is: but in: From formula (31) and the above formula, we can get: application Isometric properties and Inequality, from equation (20) and equation (31) we get: in, in, From equation (43) and equation (33), we can get: in, in, According to Fubini's theorem and The nature of From formula (50), formula (52) and have to: From equations (47), (48) and (53), we can get: in, From equations (36), (45) and (46), we can get: Using the constant variation formula of formula (38), we get: Where, e is the base of natural logarithms; Since H < 0, there exists an orthogonal matrix U∈R n×n , such that: Among them, h1,...,h n is a matrix The first, ..., nth elements on the diagonal, with a superscript of -1, represent the inverse of the matrix; since -βI n ≤H≤-αI n (59) Using the orthogonal matrix U∈R n×n And formula (58) and formula (59) get: Then, through equations (55) and (60), we have Through formula (54), formula (60) and Inequality, we get From formula (60) and The isometric property yields: Substituting equations (61) to (63) into equation (57), we obtain: According to formula (64), formula (36) and formula (46), we can get: Theorem 1: Assume that the system of Equation (24) has a unique solution on [0,∞), and Where L is an arbitrarily large known constant and σ satisfies: ω i Given by formula (21), the initial condition is Given k and a i , given ε * >0,C * >0, let inequality (66) hold: Since Φ<0, and according to equations (45) and (65), we can get * ) and C∈(0,C * )The inequality of formula (67) holds:

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