Photovoltaic system maximum power point tracking control method based on time delay extremum search

Abstract

The invention discloses a photovoltaic system maximum power point tracking control method based on time-delay extremum search, and belongs to the technical field of photovoltaic system maximum power point tracking control. According to the method, the problem that the system oscillates and is unstable due to the fact that an existing photovoltaic system maximum power point tracking control method based on extremum search does not consider time lag existing in the system is solved. According to the invention, the averaging theory method based on time delay is constructed to carry out averaging processing on the obtained time delay control system, and the constant variation formula method based on the ordinary differential equation is used to carry out stability quantitative analysis on the obtained equivalent system. The quantitative relation between the optimization parameters and the final upper bound expression of the tracking control performance and the control algorithm estimation error is obtained, the optimization parameters are selected according to the quantitative relation, and a set of data-followed rules is provided for accurately searching key optimization parameters. The method can be applied to photovoltaic system maximum power point tracking control.

Description

Technical Field

[0001] The invention belongs to the technical field of photovoltaic system maximum power point tracking control, and in particular relates to a photovoltaic system maximum power point tracking control method based on time-delay extreme value search. Background Art

[0002] Spacecraft such as spacecraft and satellites rely mainly on batteries to power their flight in space, and the power supply comes from the photovoltaic cells in the sails. Due to the large number of nonlinear factors in the photovoltaic cell system and the many uncertainties brought by the complex environment in space, traditional methods are difficult to ensure rapid convergence and real-time tracking of the maximum power point, as well as the stability of system operation. For these reasons, the application of model-free, real-time optimized extreme value search algorithms to photovoltaic cell maximum power point tracking control can achieve the search of the global maximum power point.

[0003] Existing research on maximum power point tracking control methods for photovoltaic systems based on extreme value search algorithms, such as quantitative control of photovoltaic systems based on adaptive sliding mode layer extreme value search algorithms, are all based on existing extreme value search algorithms and analyses, and can only provide qualitative analysis of the system, but cannot provide quantitative guidance for the selection of key optimization parameters.

[0004] In extreme value search control, time lag is a widely existing and very important characteristic. Before the output signal is used to generate the control signal, it takes a certain amount of time to measure, calculate and transmit the output information, which makes it inevitable to have measurement lag and transmission lag in extreme value search control. The existence of time lag often has an adverse effect on the performance of extreme value search control, and in severe cases, it will cause system oscillation and instability. At present, the existing methods have not yet analyzed the photovoltaic maximum power point tracking control system based on extreme value search under the condition of time lag in the system. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the existing photovoltaic system maximum power point tracking control method based on extreme value search does not take into account the time lag in the system, resulting in system oscillation and instability, and proposes a photovoltaic system maximum power point tracking control method based on time lag extreme value search.

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

[0007] Step 1: Establish an ideal mathematical model of a photovoltaic power generation system consisting of n photovoltaic cells connected in series, perform Taylor expansion on the ideal mathematical model of 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 lower bound d i * ;

[0009] Step 2: Establish a control system taking time delay into account according to the quadratic static objective function, and average 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] The present invention studies the maximum power point tracking control problem of a photovoltaic system based on a classical perturbation extreme value search algorithm under the condition of considering the system output time lag, averages the obtained time-delay control system by constructing an averaging theoretical method based on time delay, and uses a constant variation formula method based on ordinary differential equations to perform a stability quantitative analysis on the obtained equivalent system, and obtains a quantitative relationship between the optimization parameters and the tracking control performance and the final upper bound expression of the control algorithm estimation error. The optimization parameters are selected according to the quantitative relationship, and a set of well-documented rules are provided for accurately finding key optimization parameters, thereby solving the problem that the existing method does not consider the time lag in the system, resulting in system oscillation and instability. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is the equivalent circuit diagram of a single photovoltaic cell;

[0015] Figure 2 It is the equivalent circuit diagram of multiple photovoltaic cells connected in series for power generation;

[0016] Figure 3 1000W / m 2 IV variation curve of a single photovoltaic cell at different temperatures;

[0017] Figure 4 1000W / m 2PV change curve of a single photovoltaic cell at different temperatures;

[0018] Figure 5 This is the IV variation curve of a single photovoltaic cell at different temperatures at 25°C;

[0019] Figure 6 It is the PV change curve of a single photovoltaic cell at different temperatures at 25℃;

[0020] Figure 7 It is a block diagram of the overall photovoltaic power generation system consisting of photovoltaic arrays, DC / DC converters and loads;

[0021] Figure 8 It is the duty cycle estimation value variation curve of the DC / DC converter corresponding to each photovoltaic cell in the photovoltaic power generation system;

[0022] Fig. 9 It is the output power variation curve of photovoltaic power generation system;

[0023] Fig.10 is the duty cycle estimation error variation curve of the DC / DC converter corresponding to each photovoltaic cell in the photovoltaic power generation system;

[0024] Fig.11 It is the tracking change curve of the optimal duty cycle in the photovoltaic power generation system. DETAILED DESCRIPTION

[0025] Specific implementation method 1: A photovoltaic system maximum power point tracking control method based on time-delay extreme value search described in this implementation method specifically includes the following steps:

[0026] Step 1: Establish an ideal mathematical model of a photovoltaic power generation system consisting of n photovoltaic cells connected in series, perform Taylor expansion on the ideal mathematical model of the photovoltaic power generation system, and obtain a quadratic static objective function;

[0027] 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 the lower bound d i * ;

[0028] Step 2: Establish a control system taking time delay into consideration according to the quadratic static objective function and the extreme value search algorithm based on gradient estimation, and use the averaging method based on time delay to average the control system to obtain a disturbance system equivalent to the control system;

[0029] 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;

[0030] 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.

[0031] 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. Figure 1 As shown, each photovoltaic cell can generally 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 power loss and contactor resistance are represented by R s and R p The generated current I ph Depends on solar irradiance S and temperature T, the formula is:

[0032]

[0033] 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:

[0034]

[0035] 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).

[0036] Using KCL and KVL laws:

[0037] I=I ph -I D -V D / R p (4)

[0038] V D =V+R s I(5)

[0039] Where, I is the output current of the photovoltaic cell, and V is the output voltage of the photovoltaic cell;

[0040] The IV relationship of a single photovoltaic cell can be obtained as follows:

[0041]

[0042] Specific implementation method 2: Figure 2 As shown, the present embodiment is different from the specific embodiment 1 in that in the step 1, an ideal mathematical model of a photovoltaic power generation system in which n photovoltaic cells are connected in series to generate electricity is established, specifically:

[0043] The I of the i-th photovoltaic cell in the photovoltaic power generation system i -V i The relationship is:

[0044]

[0045] 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;

[0046]

[0047] 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;

[0048] Draw the IV curve according to formula (6) (such as Figure 3 and Figure 5 As shown) and PV curve diagram (as shown Figure 4 and Figure 6 As shown in Figure 2, it can be proved that the output power peak of photovoltaic cells exists and depends on irradiance and temperature. The maximum power point tracking task is completed by using DC / DC power electronics devices, such as Figure 7 As shown, the DC / DC power electronics-level device can adjust the output DC and voltage to a nearly constant value, while forcing the photovoltaic array output voltage to be equal to the optimal voltage value to obtain maximum power output, thereby achieving impedance matching by changing the duty cycle parameters without changing the external load.

[0049] The output voltage and output current of each photovoltaic cell in the photovoltaic power generation system are passed through the DC / DC converter.

[0050]

[0051] 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;

[0052] 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:

[0053]

[0054] in, is the power efficiency of the DC / DC converter, d i is the switching duty cycle of the diode corresponding to the i-th photovoltaic cell;

[0055] For each set of duty cycles, there is a set of PV cell voltages. In addition, assuming that each PV cell has a bypass diode, this means that the overall output power has only one peak.

[0056] Then the output power P′ of the photovoltaic power generation system is:

[0057]

[0058] Among them, P i ′ is the output power of the ith photovoltaic cell after passing through the DC / DC converter.

[0059] The other steps and parameters are the same as those in the first embodiment.

[0060] When n = 2, T = T r When , the relationship between current and voltage is:

[0061]

[0062] From formula (10) and formula (11), we can get the following equations:

[0063]

[0064] 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.

[0065] Specific implementation method three: This implementation method is different from specific implementation method one or two in that the ideal mathematical model of the photovoltaic power generation system is Taylor expanded to obtain a quadratic static objective function; specifically:

[0066] 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 Right now

[0067] exist satisfy:

[0068]

[0069] in, It is the ideal mathematical model of photovoltaic power generation system in d * The first-order derivative value at d * is the maximum output power P of the photovoltaic power generation system * The corresponding DC / DC converter duty cycle vector; It is the ideal mathematical model of photovoltaic power generation system in d * The second-order derivative value at , H is the quadratic Hessian matrix, H T is the transpose of H;

[0070] The ideal mathematical model of the photovoltaic power generation system is Taylor expanded, and the expansion terms higher than the second order are ignored to obtain the quadratic static objective function:

[0071]

[0072] Where t is time, d(t) is the duty cycle vector at time t, and P′(t) is the output power of the photovoltaic power generation system at time t.

[0073] The other steps and parameters are the same as those in the first or second embodiment.

[0074] Specific implementation method 4: This implementation method is different from the specific implementation methods 1 to 3 in that the specific process of step 2 is as follows:

[0075] Consider a quadratic static objective function with a small constant output delay:

[0076]

[0077] Where D is the time lag, and P(t) is the output power of the photovoltaic power generation system at time t after considering the time lag;

[0078] d * The i-th element in satisfies definition Definition | * |≤P M * , P M * is the maximum output power P * The upper bound of P M * is a known quantity; define the matrix H to satisfy βI n ≤H≤αI n <0, where α, β are known negative scalars, I n is the identity matrix;

[0079] make

[0080]

[0081] in, For d * The estimated value of for The derivative with respect to time, S(t) is the excitation signal, M(t) is the intermediate vector, and K is the gain matrix;

[0082]

[0083] Among them, ω i is the frequency of the controller, i=1,...,n, a i is the parameter that controls the amplitude of the excitation signal;

[0084] The gain matrix is ​​defined as:

[0085] K=kI n (20)

[0086] Where k is the gain of the controller;

[0087] The estimation error is defined as:

[0088]

[0089] in, is the estimation error;

[0090] According to equations (18) and (19), the control system considering time delay is obtained:

[0091]

[0092] The superscript T represents the transpose of the matrix. yes The first-order derivative of

[0093]

[0094] Among them, ε is the intermediate variable (the quantity to be optimized of the controller);

[0095] The system of equation (22) is averaged using the time delay-based averaging method, that is, both sides of equation (22) are integrated from t-ε to t, and then the integral result is divided by ε. When t≥D+ε, we have:

[0096]

[0097] Among them, τ is the integration variable;

[0098] because

[0099]

[0100] but

[0101]

[0102] because

[0103]

[0104] Then the second term on the right side of formula (24) is:

[0105]

[0106] Among them, (H) ij is the element in the i-th row and j-th column of the matrix H;

[0107] Define x±y=x+yy, the third term on the right side of equation (24) is:

[0108]

[0109] Among them, s is the integration variable; due to

[0110]

[0111] Then the fourth term on the right side of formula (24) is:

[0112]

[0113] make:

[0114]

[0115] Then we have:

[0116]

[0117] Let the intermediate variables Y1(t) and Y2(t) be:

[0118]

[0119] The system of formula (22) can be expressed as:

[0120]

[0121] make:

[0122]

[0123] Then the system of formula (22) is finally expressed as the perturbation system of formula (37):

[0124]

[0125] in, is the first derivative of z(t).

[0126] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0127] Compare the system of formula (37) with the system It can be seen that the system of equation (22) has additional G(t), Y1(t) and Y2(t) terms, and they are all of order O(ε), so d(t), and z(t) is of order O(1). For sufficiently small ε>0, the system of equation (22) is considered to be a system The disturbance system finally The upper bound of is determined by the upper bound of |z|, which can be obtained by the constant variation formula method.

[0128] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that 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 is performed; specifically:

[0129] Assume that:

[0130]

[0131] Among them, σ>σ0, |·| means taking the absolute value;

[0132] When t∈[0,D), we have According to formula (17) and βI n ≤H≤αI n <0 equals:

[0133]

[0134] in:

[0135]

[0136] When t≥D+ε, the constant transformation of equation (36) yields:

[0137]

[0138] Where e is the base of natural logarithms;

[0139] From formula (39), we get:

[0140]

[0141] Then there is

[0142]

[0143] Among them, ||·|| represents the L2 norm, and Δ1 is the intermediate variable;

[0144]

[0145] From formula (34), we get:

[0146]

[0147] According to formula (45), we get:

[0148]

[0149] Among them, Δ2 and Δ3 are intermediate variables;

[0150]

[0151] According to formula (41) to formula (46), we can get:

[0152]

[0153] Since H>0, there exists an orthogonal matrix U∈R n×n , then:

[0154]

[0155] in, is a diagonal matrix, h1,…,h n is a diagonal matrix The elements on the diagonal of ;

[0156] By βI n ≤H≤αI n <0 equals:

[0157]

[0158] Then we have:

[0159]

[0160] By performing constant transformation on formula (37), we can obtain:

[0161] z(t)=e kHt z(0), t≥0 (52)

[0162] From equation (48) and equation (51), we can get:

[0163]

[0164] From formula (36), we get:

[0165]

[0166] Then we have:

[0167]

[0168] Then we have:

[0169]

[0170] This means:

[0171]

[0172] Among them, ε * is the upper bound of ε, that is:

[0173]

[0174] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0175] Using the proof-by-contradiction approach, we can prove that the validity of equation (58) leads to the validity of equation (38).

[0176] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that 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; specifically:

[0177] Consider the system of equation (22) with initial conditions Given parameters k, a i , i=1,2,Λ,n, given σ>σ0>0, let ε * >0Satisfaction:

[0178]

[0179] Since the intermediate variable Φ1<0, we have The system of formula (22) satisfies (the third inequality of formula (39) satisfies the first inequality of formula (60)):

[0180]

[0181] Where, δ is the convergence rate;

[0182] When ε∈(0,ε * ] and satisfy the initial conditions When , the solution of the system of equation (22) converges to the following sphere Θ at a convergence rate δ exponentially:

[0183]

[0184] According to ε∈(0,ε * ]Get the controller frequency ω i ,ω i And given parameters k, a i is the controller parameter. The parameters on both sides of the colon in formula (61) are restrictions.

[0185] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5. Specific embodiments

[0187] Assume that the photovoltaic array is composed of two photovoltaic cells connected in series, that is, n=2, and the two cells are photovoltaic cell 1 and photovoltaic cell 2, and a set of reasonable photovoltaic cell parameters are given according to the existing photovoltaic cell parameters. The specific parameters are shown in Table 1 and Table 2.

[0188] Table 1 Parameters of photovoltaic cell 1

[0189]

[0190]

[0191] Table 2 Parameters of photovoltaic cell 2

[0192]

[0193] According to formula (14) and the environments given in Tables 1 and 2, the maximum power points of multiple photovoltaic cells can be calculated theoretically, as shown in Table 3.

[0194] Table 3 Theoretical maximum power point of photovoltaic array

[0195]

[0196] According to the quantitative relationship between the optimization parameters, time delay size, control system stability and algorithm performance given in step 3, the parameters are selected as shown in Table 4.

[0197] Table 4 Parameter selection of time lag extreme value search algorithm

[0198]

[0199] The environment was set up to simulate the maximum power point tracking control of two photovoltaic cells in series. The simulation results show that in the simulation environment, the algorithm basically completes the search in 3500s, and the estimation error does not exceed 5.6%. Figure 8 It can be seen that the photovoltaic cell maximum power point tracking control method based on time-delay extreme value search makes each photovoltaic cell in the photovoltaic system work at the theoretical maximum power point; Fig. 9 It can be seen that the final output power of the designed photovoltaic power generation system is basically equal to the theoretical maximum output power. The comparison between the simulated output power and the theoretical maximum power is shown in Table 5. Fig.10 It can be seen that the duty cycle estimation error obtained by the photovoltaic cell maximum power point tracking control method based on time-delay extreme value search is small, and the extreme value search task is completed; Fig.11 It can be seen that the two components search for the tracking path of the maximum power point; it can be seen from Table 6 that the estimated error of the system output is smaller than the final upper bound of the theoretical estimated error, indicating that the theory has a certain degree of conservatism; since the quadratic model used in control system design and analysis is significantly different from the real nonlinear model used in simulation, the simulation results also show that the optimization parameter scheme selected by the method of the present invention has good robustness.

[0200] Table 5 Comparison of simulation results and theoretical results of time-delay extreme value search

[0201]

[0202] Table 6 Comparison between simulated UB and theoretical UB for time-delay extreme value search

[0203]

[0204] 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 system maximum power point tracking control method based on time-delay extreme value search, characterized in that: The method specifically comprises the following steps: Step 1: Establish an ideal mathematical model of a photovoltaic power generation system consisting of n photovoltaic cells connected in series, perform Taylor expansion on the ideal mathematical model of 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 the lower bound d i * ; Step 2: Establish a control system taking time delay into account according to the quadratic static objective function, and average 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 system maximum power point tracking control method based on time-delay extreme value search according to claim 1, characterized in that: In the step 1, an ideal mathematical model of a photovoltaic power generation system in which n photovoltaic cells are connected in series to generate electricity 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 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 DC / DC 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: P′=V dc I dc (12)。 3. A photovoltaic system maximum power point tracking control method based on time-delay extreme value search according to claim 2, characterized in that: The ideal mathematical model of the photovoltaic power generation system is Taylor expanded to obtain a quadratic static objective function; specifically: exist satisfy: in, It is the ideal mathematical model of photovoltaic power generation system in d * The first-order derivative value at d * is the maximum output power P of the photovoltaic power generation system * The corresponding DC / DC converter duty cycle vector; It is the ideal mathematical model of photovoltaic power generation system in d * The second-order derivative value at , H is the quadratic Hessian matrix, H T is the transpose of H; The ideal mathematical model of the photovoltaic power generation system is Taylor expanded, and the expansion terms higher than the second order are ignored to obtain the quadratic static objective function: Where t is time, d(t) is the duty cycle vector at time t, and P′(t) is the output power of the photovoltaic power generation system at time t.

4. A photovoltaic system maximum power point tracking control method based on time-delay extreme value search according to claim 3, characterized in that: The specific process of step 2 is as follows: The quadratic static objective function considering time lag is: Where D is the time lag, and P(t) is the output power of the photovoltaic power generation system at time t after considering the time lag; d * The i-th element in satisfies definition Definition | * |≤P M * , P M * is the maximum output power P * The upper bound of P M * is a known quantity; define the matrix H to satisfy βI n ≤H≤αI n <0, where α, β are known negative scalars, I n is the identity matrix; make in, For d * The estimated value of for The derivative with respect to time, S(t) is the excitation signal, M(t) is the intermediate vector, and K is the gain matrix; Among them, ω i is the frequency of the controller, i=1,...,n, a i is the parameter that controls the amplitude of the excitation signal; The gain matrix is ​​defined as: K=kI n (20) Where k is the gain of the controller; The estimation error is defined as: in, is the estimation error; According to equations (18) and (19), the control system considering time delay is obtained: The superscript T represents the transpose of the matrix. yes The first-order derivative of Among them, ε is an intermediate variable; The system of equation (22) is averaged, that is, both sides of equation (22) are integrated from t-ε to t, and then the integral result is divided by ε. When t≥D+ε, we have: Among them, τ is the integration variable; because but because Then the second term on the right side of formula (24) is: Among them, (H) ij is the element in the i-th row and j-th column of the matrix H; Define x±y=x+yy, the third term on the right side of equation (24) is: Where s is the integration variable; because Then the fourth term on the right side of formula (24) is: make: Then we have: Let the intermediate variables Y1(t) and Y2(t) be: The system of formula (22) can be expressed as: make: Then the system of formula (22) is finally expressed as the perturbation system of formula (37): in, is the first derivative of z(t).

5. A photovoltaic system maximum power point tracking control method based on time-delay extreme value search according to claim 4, characterized in that: 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 is performed; specifically: Among them, σ>σ0, |·| means taking the absolute value; When t∈[0,D), we have According to formula (17) and βI n ≤H≤αI n <0 equals: in: When t≥D+ε, the constant transformation of equation (36) yields: Where e is the base of natural logarithms; From formula (39), we get: Then there is Among them, ||·|| represents the L2 norm, and Δ1 is the intermediate variable; From formula (34), we get: According to formula (45), we get: Among them, Δ2 and Δ3 are intermediate variables; According to formula (41) to formula (46), we can get: Since H>0, there exists an orthogonal matrix U∈R n×n , then: in, is a diagonal matrix, h1,…,h n is a diagonal matrix The elements on the diagonal of ; By βI n ≤H≤αI n <0 equals: Then we have: By performing constant transformation on formula (37), we can obtain: z(t)=e kHt z(0),t≥0 (52) From equation (48) and equation (51), we can get: From formula (36), we get: Then we have: Then we have: This means: Among them, ε * is the upper bound of ε, that is:

6. A photovoltaic system maximum power point tracking control method based on time-delay extreme value search according to claim 5, characterized in that: 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; specifically: Consider the system of equation (22) with initial conditions Given parameters k, a i , i=1,2,Λ,n, given σ>σ0>0, let ε * >0Satisfaction: Since the intermediate variable Φ1<0, we have The system of formula (22) satisfies: Where, δ is the convergence rate; When ε∈(0,ε * ] and satisfy the initial conditions When , the solution of the system of equation (22) converges to the following sphere Θ at a convergence rate δ exponentially: According to ε∈(0,ε * ]Get the controller frequency ω i ,ω i And given parameters k, a i These are the controller parameters.

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