Photovoltaic cell maximum power point tracking control method based on random extremum search

Abstract

The invention discloses a photovoltaic cell maximum power point tracking control method based on random extremum search, and belongs to the technical field of photovoltaic power generation system maximum power point tracking control. According to the invention, the problem that the existing control method cannot optimize the controller parameters according to the stability analysis result and does not consider random interference is solved. According to the invention, under the condition that an output channel contains measurement noise, a random extremum search control algorithm, an average value theory method based on time delay and a constant variability formula method of a stochastic differential equation are designed to carry out averaging processing and stability analysis on an averaging system in sequence; and quantitative guidance on optimization parameters is provided for maximum power point tracking control design of a plurality of photovoltaic cells. The method can be applied to photovoltaic cell maximum power point tracking control.

Description

Technical Field

[0001] The invention belongs to the technical field of maximum power point tracking control of photovoltaic power generation systems, and in particular relates to a maximum power point tracking control method for photovoltaic cells based on random extreme value search. Background Art

[0002] As the shortage of fossil energy becomes more and more serious, the status of solar energy is getting higher and higher. my country has abundant solar energy resources and great development potential. With the continuous maturity of photovoltaic power generation technology, photovoltaic power generation has been widely used in social energy supply. However, with the rapid development of the photovoltaic industry, the problem of low power generation efficiency of photovoltaic systems has become more and more prominent. Therefore, in order to improve the power generation efficiency of photovoltaic systems and achieve maximum power output, photovoltaic maximum power point tracking MPPT (Maximum Power Point Tracking) control technology has become an indispensable part of photovoltaic power generation systems.

[0003] At present, the commonly used photovoltaic maximum power point tracking MPPT algorithms include constant voltage tracking method, perturbation observation method and conductance increment method. The constant voltage tracking method has poor adaptability and cannot be adjusted in time; the selection of step size of the perturbation observation method affects the tracking, and the effect is not good when the environment changes rapidly; the conductance increment method also has the problem of step size selection, and is also affected by detection accuracy and speed. Therefore, the above methods all have certain limitations, such as insufficient tracking speed or tracking accuracy. It is necessary to find an extreme value search MPPT control method that does not rely on the model and has global search capabilities 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] Extremum search has been widely used to solve the MPPT control problem of photovoltaic systems. However, the existing research on 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 a certain extent restricts the application of extreme value search control methods in photovoltaic system MPPT control. On the other hand, the volatility and randomness of solar energy will have an impact on photovoltaic power generation systems, and the existing photovoltaic MPPT control based on extreme value search does not consider the impact of random interference. Summary of the invention

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

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

[0007] Step 1: Establish 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, perform Taylor expansion on the relationship between the duty cycle and the output power in the photovoltaic power generation system, and obtain a quadratic static objective function;

[0008] 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 * ;

[0009] Step 2: Establish a control system that takes into account the random disturbance of the output according to the quadratic static objective function and the random extremum search control algorithm, and perform averaging on the control system to obtain a disturbance system equivalent to the control system;

[0010] 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 * , stability analysis of the disturbance system;

[0011] 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.

[0012] The beneficial effects of the present invention are:

[0013] In the case where the output channel contains measurement noise, the present invention designs a random extreme value search control algorithm, and performs averaging processing and stability analysis on the averaging system in turn based on the average value theory method of time delay and the constant variation formula method of stochastic differential equations, thereby providing quantitative guidance on optimization parameters for the maximum power point tracking control design of multiple photovoltaic cells.

[0014] By solving the explicit stability condition containing the optimization parameters obtained in step three, the value range of the optimization parameters under the algorithm is determined. Using MATLAB for simulation, the effectiveness of the maximum power point tracking control method for a single photovoltaic cell based on random extreme value search under random interference can be verified. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is the overall block diagram of the photovoltaic power generation system;

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

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

[0018] Figure 3 is the estimated value curve of duty cycle of two photovoltaic cells;

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

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

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

[0022] Specific implementation method 1: A photovoltaic cell maximum power point tracking control method based on random extreme value search described in this implementation method specifically includes the following steps:

[0023] Step 1: Establish 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, perform Taylor expansion on 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 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 * ;

[0025] Step 2: Establish a control system that takes into account the random disturbance of the output according to the quadratic static objective function and the random extremum search control algorithm, and use the time delay-based averaging method to average the control system to obtain a disturbance system equivalent to the control system;

[0026] 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 * , stability analysis of the disturbance system;

[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 according to ε i ), and then use the controller to track the maximum power point of the photovoltaic power generation system.

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

[0029]

[0030] in, 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 affects the model of the ideal diode:

[0031]

[0032] in, 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 battery voltage, V D is the diode terminal voltage, k is 1.38×10 -23 J / K, q is the electron charge number (the value is 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 IV relationship of a single photovoltaic cell can be obtained as follows:

[0038]

[0039] Specific implementation method 2: Combination Figure 1 The present embodiment is different from the first embodiment in that, in 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, which is specifically:

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

[0041]

[0042] 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 ith photovoltaic cell, R s,i is the power loss of the ith photovoltaic cell, I i is the output current of the ith photovoltaic cell, N is the semiconductor emission coefficient, V t is the hot battery voltage, R p is the contactor resistance;

[0043] Intermediate variables

[0044] in, is the diode reference reverse saturation current corresponding to the ith 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;

[0045] According to the IV relationship of photovoltaic cells, the PV change curve of photovoltaic cells can be drawn. It is found that there is an extreme point in the PV characteristic curve of photovoltaic cells, that is, the power reaches the maximum value at this time. At the same time, this peak value of power is related to irradiance and temperature.

[0046] The output voltage and output current of each photovoltaic cell in the photovoltaic power generation system are passed through the DC / DC converter.

[0047]

[0048] 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 ith photovoltaic cell after the DC / DC converter, I oiis 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;

[0049] When the DC / DC converter is in continuous current mode (CCM), the switching pulse width modulation (PWM) frequency f s Significantly higher than the bandwidth of the control loop, and at the same time by I i -V i Functional Relationship I i =f i (V i ), we can get the output voltage of each photovoltaic cell V=[V1 V2 …V n ] Τ The diode duty cycle corresponding to each photovoltaic cell is d = [d1 d2 … d n ] Τ The relationship is:

[0050]

[0051] 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;

[0052] For each set of duty cycles, there is a set of PV cell voltages. Furthermore, assuming that there is a bypass diode for each PV cell, this means that there is only one peak value for the overall output power.

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

[0054]

[0055] Among them, P i is the output power of the ith photovoltaic cell after passing through the DC / DC converter.

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

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

[0058]

[0059] From formula (10) and formula (11), we can get the following equations:

[0060]

[0061] In practical applications, the accuracy of the parameters in the above formulas is often difficult to meet the requirements and changes with the external environment. It is impossible to directly track the maximum power point through this ideal mathematical model, and it is necessary to use a model-free extreme value search algorithm.

[0062] Specific implementation method three: This implementation method is different from specific implementation method one or two in that 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 battery system in actual use, which is composed of multiple photovoltaic cells connected in series to generate electricity, the extreme value exists and is global. The system in a certain environment corresponds to a unique (d * ,P * ),in Existence satisfy:

[0064]

[0065] in, is the formula (12) in d * The first-order 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 1st photovoltaic cell, ..., the nth photovoltaic cell; is the formula (12) in d * The second-order derivative value at , H is the quadratic Hessian matrix, H T is the transpose of H; H<0 means that when d(t)=d * There is a maximum value P′ * ;

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

[0067]

[0068] 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.

[0069] The other steps and parameters are the same as those in the first or second embodiment.

[0070] Through the modeling of the relationship between output power and duty cycle based on physical principles, it can be found that the relationship of photovoltaic cells is very complex, with many parameters and uncertainties, and also has nonlinear characteristics. The differences between individual photovoltaic cells and the aging of photovoltaic cells in actual use will make it difficult to establish a unified and accurate model for photovoltaic power generation systems composed of a large number of photovoltaic cells in series. When photovoltaic cells are in actual operation, the changes in the surrounding environment are unpredictable, and the output characteristics of photovoltaic cells will be affected by related factors, resulting in more complex and even time-varying nonlinear output characteristics. Therefore, it is more difficult to track the photovoltaic output power by establishing an accurate model in such an uncertain environment.

[0071] As a model-free real-time online adaptive optimization control method, the random extreme value search algorithm of the present invention is very suitable for the situation where it is difficult to establish an accurate model of the photovoltaic system.

[0072] Specific implementation method 4: This implementation method is different from any one of specific implementation methods 1 to 3 in that, in step 2, a control system considering random interference of output is established according to a quadratic static objective function and a random extremum search control algorithm, specifically:

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

[0074]

[0075] Where P′(t) is the output power after being 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 the noise intensity, C ≥ 0;

[0076] Defining the upper bound of the duty cycle and lower bound d i * satisfy: in, definition is the maximum output power P * The upper bound of is a known quantity; define the 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 maximum eigenvalue of the matrix H, and |·| represents the absolute value;

[0077] The block diagram of the photovoltaic cell MPPT control system based on the random extreme value search algorithm is as follows Figure 2 As shown;

[0078] Definition * The real-time estimate is The estimated error for:

[0079]

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

[0081]

[0082] Among them, the excitation signals S(t) and M(t) satisfy:

[0083]

[0084] Among them, a i is the controller parameter corresponding to the i-th 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; let

[0085]

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

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

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

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

[0090] So that KH is a Hurwitz matrix.

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

[0092]

[0093] For the initial value The solution of formula (23) satisfies the random process

[0094]

[0095] Here, s is the integration variable and the last random integral is type.

[0096] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0097] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the control system is averaged by using the averaging method based on time delay to obtain a disturbance system equivalent to the control system; specifically:

[0098] 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:

[0099]

[0100] Where s is the integral variable, 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] in, express The column vector composed of

[0109] Application of the control system of formula (23) The formula is:

[0110]

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

[0112]

[0113] in,

[0114] because Then the third term on the right side of equation (24) is expressed as:

[0115]

[0116] Where: τ is the integration variable,

[0117] The fourth term on the right side of formula (24) is expressed as:

[0118]

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

[0120] From equation (27), equation (28), equation (30), equation (31) and equation (32), we can get:

[0121]

[0122] The solution of the extreme value 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 extreme value search system (24).

[0123] Define z(t):

[0124]

[0125] The time-delay system of equation (33) is transformed into:

[0126]

[0127] Simplify formula (35) to:

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

[0129] Among them, ω(t) is the intermediate variable;

[0130]

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

[0132] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0133] Specific implementation method 6: This implementation method is different from any one of the specific implementation methods 1 to 5 in that Y1(t), Y2(t) and Y3(t) are respectively:

[0134]

[0135] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0136] Specific implementation method 7: This implementation method is different from any one of the specific implementation methods 1 to 6 in that Y4(t) and Y5(t) are respectively:

[0137]

[0138] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0139] Specific implementation eight: This implementation differs from specific implementations one to seven in that the specific process of step three is as follows:

[0140] Assumptions and Inequality, we have:

[0141]

[0142] in, represents the computational expectation;

[0143] definition:

[0144]

[0145] Among them, 0<σ<L 1 / 6 ;

[0146] Due to -βI n <H<-αI n ,but

[0147] ||H||≤β (42)

[0148] Among them, ||·|| is the L2 norm;

[0149] From formula (26), we get:

[0150]

[0151] Further:

[0152]

[0153] in:

[0154]

[0155] Depend on The isometric properties are By applying formula, Inequality, equation (41) and equation (43) give the solution of the system of equation (23) The upper bound of t∈[0,ε] in the mean square sense is:

[0156]

[0157] From equation (25) and equation (43), we can get:

[0158]

[0159] but

[0160]

[0161] From equation (26), equation (40), equation (41) and The inequality is:

[0162]

[0163] but

[0164]

[0165] in: From formula (31) and the above formula, we can get:

[0166]

[0167] application Isometric properties and Inequality, from equation (20) and equation (31), we get:

[0168]

[0169] in,

[0170]

[0171] in, From equation (43) and equation (33), we can get:

[0172]

[0173] in,

[0174]

[0175] in, According to Fubini's theorem and The nature of From equation (50), equation (52) and have to:

[0176]

[0177] From equation (47), equation (48) and equation (53), we can get:

[0178]

[0179] in, From equation (36), equation (45) and equation (46), we can get:

[0180]

[0181] Using the constant transformation formula of formula (38), we get:

[0182]

[0183] Where e is the base of natural logarithms;

[0184]

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

[0186]

[0187] Among them, h1,…,h n is a matrix The first, ..., nth elements on the diagonal have a superscript of -1, which represents the inverse of the matrix;

[0188] -βI n ≤H≤-αI n (59) Using the orthogonal matrix U∈R n×nAnd equation (58) and equation (59) we get:

[0189]

[0190] Then, through equations (55) and (60), we have

[0191]

[0192] Through equation (54), equation (60) and Inequality, we get

[0193]

[0194] From formula (60) and The isometric property is:

[0195]

[0196] Substituting equations (61) to (63) into equation (57), we obtain:

[0197]

[0198] According to formula (64), formula (36) and formula (46), we can get:

[0199]

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

[0201]

[0202] Since Φ<0, Φ<0 means According to equations (45) and (65), we can obtain * ) and C∈(0,C * )The inequality of formula (67) holds:

[0203]

[0204] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0205] Note 1: In order to achieve the convergence of the extreme value search algorithm, the present invention introduces a The condition is defined a priori by a known constant L, and the bound imposed by L 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-globally converges. The introduced boundedness assumption is realistic in practical applications. In addition, through equation (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 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 equation (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 ensures that the constraint in equation (41) holds.

[0208] (i) When t∈[0,ε], due to and 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 Therefore, equation (41) holds for t∈[0,ε].

[0213] (ii) When t ≥ ε, as shown in (i), and It is continuous in time, and Equation (41) is valid for some cases where t>ε. By the contradiction assumption, for some t>ε, Equation (41) does not hold, that is, there exists a minimum time instance t * ∈(ε,∞), such that

[0214]

[0215] Therefore, for all t∈[ε,t * ], Established. There is an upper bound, The proof of the existence of an upper bound and the actual stability of the z system is similar, and we finally get t∈[ε,t * ] is a non-rigid version of (65). In addition, the feasibility of Φ<0 in the theorem guarantees that This is similar to Therefore, for all t ≥ ε, Proof of completion;

[0217] The simulation is performed for an ideal photovoltaic cell model, and the photovoltaic cell system consisting of two photovoltaic cells connected in series is considered. The relevant parameters of the selected photovoltaic cells are shown in Table 1:

[0218] Table 1 Photovoltaic cell related parameters

[0219]

[0220] The parameters in the hypothesis can be estimated through the Pd relationship and the Taylor expansion form of dP, as shown in Table 2:

[0221] Table 2

[0222]

[0223]

[0224] According to the stability condition of Theorem 1, the parameters of the random extremum search algorithm can be obtained as shown in Table 3:

[0225] Table 3

[0226]

[0227] The simulation shows the system response curve of the closed-loop system, and the results show that the closed-loop system finally converges; for the initial conditions from Figure 3 It can be seen that the duty cycle estimate and Converges to d * (i.e. maximum power point). Figure 4 It can be clearly seen that the output power P is stable at the maximum power P * From Figure 5 The duty cycle estimation error can be obtained and All converge to 0. Figure 6 It can be seen that the curve drawn based on the duty cycle of the two photovoltaic cells as the horizontal and vertical coordinates finally converges to the point Considering random interference noise, the photovoltaic control system based on multivariable extreme value search can still track the maximum power point well. By observing the system response, it can be found that the multivariable random extreme value search control algorithm responds quickly, converges quickly, and the final error is also small.

[0228] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

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 the output power in a photovoltaic power generation system in which n photovoltaic cells are connected in series, perform Taylor expansion on the relationship between the duty cycle and the 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: Establish a control system that takes into account the random disturbance of the output according to the quadratic static objective function and the random extremum search control algorithm, and perform averaging on the control system to obtain a disturbance system equivalent to the control system; 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 * , stability analysis of 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. A 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: The 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 ith photovoltaic cell, R s,i is the power loss of the ith photovoltaic cell, I i is the output current of the ith photovoltaic cell, N is the semiconductor emission coefficient, V t is the hot battery voltage, R p is the contactor resistance; Intermediate variables in, is the diode reference reverse saturation current corresponding to the ith 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 ith photovoltaic cell after 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; Each photovoltaic cell output voltage V = [V1 V2 ... V n ] Τ The diode duty cycle d corresponding to each photovoltaic cell is [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; 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. A 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 the output power in the photovoltaic power generation system is Taylor expanded to obtain a quadratic static objective function; specifically: exist satisfy: in, is the formula (12) in d * The first-order 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 1st photovoltaic cell, ..., the nth photovoltaic cell; is the formula (12) in d * The second-order derivative value at , H is the quadratic Hessian matrix, H T is the transpose of H; The relationship between duty cycle and output power in the photovoltaic power generation system is Taylor expanded, and the expansion terms higher than quadratic are ignored to obtain a 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. A photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 3, characterized in that: In the step 2, a control system considering random disturbance of output is established according to a quadratic static objective function and a random extremum 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 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 the noise intensity, C ≥ 0; Defining the upper bound of the duty cycle and the lower bound d i * satisfy: i=1,...,n,where, definition is the maximum output power P * The upper bound of is a known quantity; define the 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 maximum eigenvalue of the matrix H, and |·| represents the absolute value; Definition * The real-time estimate is The estimated error for: The random extremum search control algorithm is designed as: 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 ith 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 the random disturbance of the output is obtained by equations (17), (18) and (19): For the initial value The solution of formula (23) satisfies the random process Here, s is the integration variable.

5. A photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 4, 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 integral variable, let Where f is defined as: The left side of equation (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 equation (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 equation (27), equation (28), equation (30), equation (31) and equation (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; 6. A photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 5, characterized in that: The Y1(t), Y2(t) and Y3(t) are respectively:

7. A photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 6, characterized in that: The Y4(t) and Y5(t) are respectively:

8. A photovoltaic cell maximum power point tracking control method based on random extreme value search according to claim 7, characterized in that: The specific process of step three is: Assumptions t ≥ 0 and Inequality, we have: in, represents the computational expectation; definition: Among them, 0<σ<L 1 / 6 ; Due to -βI n <H<-αI n ,but ||H||≤β (42) Among them, ||·|| is the L2 norm; From formula (26), we get: Further: in: Depend on The isometric properties are By applying formula, Inequality, equation (41) and equation (43) give the solution of the system of equation (23) Upper bound in the mean square sense: From equation (25) and equation (43), we can get: but From equation (26), equation (40), equation (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 equation (50), equation (52) and have to: From equation (47), equation (48) and equation (53), we can get: in, From equation (36), equation (45) and equation (46), we can get: Using the constant transformation 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 , so that: Among them, h1,…,h n is a matrix The first, ..., nth elements on the diagonal, the superscript -1 represents the inverse of the matrix; because -βI n ≤H≤-αI n (59) Using the orthogonal matrix U∈R n×n And equation (58) and equation (59) we get: Then, through equations (55) and (60), we have Through equation (54), equation (60) and Inequality, we get From formula (60) and The isometric property is: 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 (24) has a unique solution on [0, ∞), and Where L is an arbitrarily large known constant, and σ satisfies: 0<σ0 2 <σ 2 <L 1 / 3 ,ω i Given by equation (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 obtain * ) and C∈(0,C * )The inequality of formula (67) holds:

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