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

Abstract

The application 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. The application solves the problem that the existing photovoltaic system maximum power point tracking control method based on extremum search does not consider the time delay existing in the system, and leads to system oscillation and instability. The application constructs an average theory method based on time delay to average the obtained time delay control system, and utilizes a constant variable formula method based on ordinary differential equation to quantitatively analyze the stability of the obtained equivalent system, obtains a quantitative relationship between an optimal parameter and tracking control performance and an ultimate upper bound expression of an estimation error of a control algorithm, selects the optimal parameter according to the quantitative relationship, and provides a set of rules with reliable basis for accurately finding key optimal parameters. The application method can be applied to photovoltaic system maximum power point tracking control.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of photovoltaic system maximum power point tracking control, and particularly relates to a photovoltaic system maximum power point tracking control method based on time delay extremum search. BACKGROUND

[0002] Spacecraft, satellites and other spacecraft fly in space mainly rely on batteries to provide power, and the power supply comes from the photovoltaic cells in the sail wing. Due to the many nonlinear factors in the photovoltaic cell system, and the many uncertainties of the system caused by the complex environment in space, the traditional method is difficult to ensure rapid convergence at the maximum power point and real-time tracking, and to ensure the stability of the system operation. For these reasons, the extremum search algorithm based on model-free and real-time optimization is applied to the photovoltaic cell maximum power point tracking control, which can realize the search of the global maximum power point.

[0003] The existing research on the photovoltaic system maximum power point tracking control method based on the extremum search algorithm, such as the quantitative control of the photovoltaic system based on the adaptive sliding layer extremum search algorithm, is based on the existing extremum search algorithm and analysis, and can only provide qualitative analysis of the system, and cannot give quantitative guidance to the selection of key optimization parameters.

[0004] In the extremum search control, time delay is a kind of widely existing and very important characteristics. Because the measurement, calculation and transmission of the output information need to consume a certain time before the output signal is used to generate the control signal, there are inevitable measurement time delay and transmission time delay in the extremum search control. The existence of time delay often brings adverse effects on the performance of the extremum search control, and can even cause system oscillation and instability. The existing method does not consider the time delay in the system when analyzing the photovoltaic maximum power point tracking control system based on the extremum search. SUMMARY

[0005] The purpose of the present application is to solve the problem that the existing photovoltaic system maximum power point tracking control method based on the extremum search does not consider the time delay in the system, which causes system oscillation and instability, and a photovoltaic system maximum power point tracking control method based on time delay extremum search is proposed.

[0006] The technical solution adopted by the present application to solve the above technical problems is: a photovoltaic system maximum power point tracking control method based on time delay extremum search, which specifically comprises the following steps:

[0007] Step one, establish an ideal mathematical model of a photovoltaic power generation system generated by n photovoltaic cells in series, and perform Taylor expansion on the ideal mathematical model of the photovoltaic power generation system to obtain a quadratic static objective function;

[0008] and the upper bound of the maximum output power P * and the upper bound of the duty ratio corresponding to each photovoltaic cell and the lower bound of the duty ratio corresponding to each photovoltaic cell d i * ;

[0009] Step two, a control system considering time delay is established according to the quadratic static objective function, and the control system is averaged to obtain a perturbation system equivalent to the control system;

[0010] Step three, the constant variation formula method based on ordinary differential equation and the upper bound of the maximum output power P * , the upper bound of the duty ratio and the lower bound of the duty ratio d i * are used to analyze the stability of the perturbation system;

[0011] According to the stability analysis result, the controller parameters are obtained, and the photovoltaic power generation system is controlled by the controller to track the maximum power point.

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

[0013] The present application studies the maximum power point tracking control problem of the photovoltaic system based on the classical perturbation extremum search algorithm under the consideration of the time delay of the system output, the time delay control system obtained is averaged by constructing the averaging theory method based on time delay, and the equivalent system obtained is quantitatively analyzed for stability by using the constant variation formula method based on ordinary differential equation, the quantitative relationship between the optimal parameters, the tracking control performance and the final upper bound expression of the estimation error of the control algorithm is obtained, the selection of the optimal parameters is carried out according to the quantitative relationship, a set of rules with reliable basis are provided for accurately finding the key optimal parameters, and the problem that the existing method does not consider the time delay existing in the system, resulting in system oscillation and instability is solved. BRIEF DESCRIPTION OF DRAWINGS

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

[0015] Figure 2 is the equivalent circuit diagram under the condition of series generation of multiple photovoltaic cells;

[0016] Figure 3 is the I-V curve of a single photovoltaic cell under 1000W / m 2 at different temperatures;

[0017] Figure 4 is the I-V curve of a single photovoltaic cell under 1000W / m 2Fig. 1 is a P-V curve of a single photovoltaic cell at different temperatures;

[0018] Figure 5 Fig. 2 is an I-V curve of a single photovoltaic cell at different temperatures;

[0019] Figure 6 Fig. 3 is a P-V curve of a single photovoltaic cell at different temperatures;

[0020] Figure 7 Fig. 4 is a block diagram of a photovoltaic power generation system composed of a photovoltaic array, a DC / DC converter and a load, etc.;

[0021] Figure 8 Fig. 5 is a curve of the duty cycle estimation error of a DC / DC converter corresponding to each photovoltaic cell in a photovoltaic power generation system;

[0022] Figure 9 Fig. 6 is a curve of the output power of a photovoltaic power generation system;

[0023] Figure 10 Fig. 7 is a curve of the duty cycle estimation error of a DC / DC converter corresponding to each photovoltaic cell in a photovoltaic power generation system;

[0024] Figure 11 Fig. 8 is a curve of the tracking of the optimal duty cycle in a photovoltaic power generation system. DETAILED DESCRIPTION

[0025] Embodiment 1: A photovoltaic system maximum power point tracking control method based on time delay extremum search, which specifically comprises the following steps:

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

[0027] and estimate the upper bound of the maximum output power P * in the quadratic static objective function, as well as the upper bound and the lower bound d of the duty cycle corresponding to each photovoltaic cell; i * ;

[0028] Step 2: Establish a control system considering time delay according to the quadratic static objective function and the extremum search algorithm based on gradient estimation, 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;

[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 lower bound d i * Stability analysis of the perturbed system is performed;

[0030] 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.

[0031] The photovoltaic effect of a photovoltaic cell can convert solar energy into electrical energy. When the cell receives light, a voltage difference appears in the cell. As shown in Figure 1 , each photovoltaic cell can generally be represented by an ideal current source with a current of 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:

[0032]

[0033] 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:

[0034]

[0035] 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, and q is the electronic charge number (1.6×10 - 19 C).

[0036] Using the 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 I-V relationship of a single photovoltaic cell is:

[0041]

[0042] Specific embodiment two: as shown in the embodiment, different from the first embodiment is that, in step one, the ideal mathematical model of the photovoltaic power generation system generated by n photovoltaic cells in series is established, specifically: Figure 2

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

[0044]

[0045] where 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;

[0046]

[0047] where, 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;

[0048] According to formula (6), the I-V curve (as shown in Figure 3 and Figure 5 ) and the P-V curve (as shown in Figure 4 and Figure 6 ) can be drawn, which can prove the existence of the output power peak of the photovoltaic cell, and it depends on the irradiance and temperature. The DC / DC power electronic stage device is used to complete the maximum power point tracking task, as shown in Figure 7 , the DC / DC power electronic stage device can adjust the output DC voltage to a constant value, and at the same time force the photovoltaic array output voltage to be equal to the optimal voltage value to obtain the maximum power output, so as to realize impedance matching by changing the duty cycle parameter without changing the external load.

[0049] ​The output voltage and output current of each photovoltaic cell in a photovoltaic power generation system are converted by a DC / DC converter, and then

[0050]

[0051] 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 conversion by the DC / DC converter, I oi is the output current of the i th photovoltaic cell after conversion by the DC / DC converter, I dc is a constant value of the output DC current of 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 is significantly higher than the bandwidth of the control loop, and the relationship between I i and V i is a function, I i = f i (V i ), so that 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 satisfy the following relationship:

[0053]

[0054] wherein, 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 photovoltaic cell voltages. In addition, assuming that there is a bypass diode for each photovoltaic cell means that the overall output power has only one peak value.

[0056] The output power P' of the photovoltaic power generation system is:

[0057]

[0058] wherein P i ' is the output power of the i th photovoltaic cell after conversion by the DC / DC converter.

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

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

[0061]

[0062] Equations can be obtained from formula (10) and formula (11):

[0063]

[0064] In practical application, the parameters in the above formula are often difficult to meet the requirements, and change with the external environment, so it is impossible to directly track the maximum power point by using the ideal mathematical model, and a model-free extremum search algorithm is needed.

[0065] Specific implementation three: the difference between this embodiment and specific implementation one or two is 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 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

[0067] There exists satisfying:

[0068]

[0069] wherein, is the first-order derivative value of the ideal mathematical model of the photovoltaic power generation system at d * , d * is the maximum output power P * of the photovoltaic power generation system corresponding to the DC / DC converter duty cycle vector; is the second-order derivative value of the ideal mathematical model of the photovoltaic power generation system at d * , H is a 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 items higher than the quadratic are ignored to obtain a quadratic static objective function:

[0071]

[0072] wherein, t is time, d(t) is the duty cycle vector at t, and P'(t) is the output power of the photovoltaic power generation system at t.

[0073] The other steps and parameters are the same as those in specific implementation one or two.

[0074] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the specific process of step two is as follows:

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

[0076]

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

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

[0079] make

[0080]

[0081] in, For d * The estimated value, 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] Where, ω i It is the frequency of the controller, i = 1,...,n, a i These are parameters that control the amplitude of the excitation signal;

[0084] Define the gain matrix as follows:

[0085] K = kI n (20)

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

[0087] Define the estimation error as:

[0088]

[0089] wherein, is the estimation error;

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

[0091]

[0092] wherein, the upper index T represents the transpose of a matrix, is the first derivative of , let

[0093]

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

[0095] The system of formula (22) is averaged using the time delay based averaging method, that is, integrating both sides of formula (22) from t-ε to t, and then dividing the integral result by ε, when t≥D+ε, there is:

[0096]

[0097] wherein, τ is an integral variable;

[0098] Since

[0099]

[0100] then

[0101]

[0102] Since

[0103]

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

[0105]

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

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

[0108]

[0109] wherein, s is an integral variable; since

[0110]

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

[0112]

[0113] Let:

[0114]

[0115] Then:

[0116]

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

[0118]

[0119] Express the system of equation (22) as:

[0120]

[0121] Let:

[0122]

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

[0124]

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

[0126] The other steps and parameters are the same as one of the first to third embodiments.

[0127] Compare the system of equation (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 all are of order O(ε), so d(t), and z(t) are of order O(1). For a sufficiently small ε>0, the system of equation (22) is regarded as a perturbed system of the system Finally the upper bound of is determined by the upper bound of |z|, and the upper bound of |z| can be obtained by the constant variation formula method based on ordinary differential equations.

[0128] The fifth embodiment is different from one of the first to fourth embodiments in that the constant variation formula method based on ordinary differential equations is used to estimate the maximum output power P * upper bound, duty cycle upper bound and lower bound d i * and perform stability analysis on the perturbed system; specifically:

[0129] Assume that:

[0130]

[0131] where σ>σ0, |·| represents taking absolute value;

[0132] When t∈[0,D), there is According to formula (17) and βI n ≤H≤αI n <0 get:

[0133]

[0134] where:

[0135]

[0136] When t≥D+ε, constant variation is performed on formula (36) to obtain:

[0137]

[0138] where e is the base of natural logarithm;

[0139] According to formula (39):

[0140]

[0141] Then there is

[0142]

[0143] where ||·|| represents L2 norm, and Δ1 is an intermediate variable;

[0144]

[0145] According to formula (34):

[0146]

[0147] According to formula (45):

[0148]

[0149] where Δ2 and Δ3 are intermediate variables;

[0150]

[0151] According to formula (41) to formula (46):

[0152]

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

[0154]

[0155] where, is a diagonal matrix, h1,…,h n is a diagonal matrix on the diagonal of UH;

[0156] By βI n ≤ H ≤ αI n < 0, we have:

[0157]

[0158] Then we have:

[0159]

[0160] Taking the constant variation of equation (37), we have:

[0161] z(t) = e kHt z(0), t ≥ 0 (52)

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

[0163]

[0164] From equation (36), we have:

[0165]

[0166] Then we have:

[0167]

[0168] Then we have:

[0169]

[0170] Then we have:

[0171]

[0172] where, ε * is an upper bound of ε, that is, we have:

[0173]

[0174] The other steps and parameters are the same as one of the first four embodiments.

[0175] Using the proof idea based on the proof by contradiction, it can be proved that the establishment of equation (58) can lead to the establishment of equation (38).

[0176] Sixth embodiment: Different from one of the first to fifth embodiments, 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 formula (22) with initial conditions Given parameters k, a i , i = 1, 2,..., n, given σ > σ0> 0, let ε * > 0 satisfy:

[0178]

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

[0180]

[0181] Where δ is the convergence speed;

[0182] When ε ∈ (0, ε * ] and satisfies the initial conditions The solution of the system of formula (22) converges exponentially to the following spherical domain Θ with a convergence speed δ:

[0183]

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

[0185] The other steps and parameters are the same as one of the first to fifth embodiments. Specific embodiments

[0187] Assume that the photovoltaic array is composed of two photovoltaic cells in series, i.e. n = 2, and the two cells are photovoltaic cell 1 and photovoltaic cell 2, respectively. A set of reasonable photovoltaic cell parameters is given according to the existing photovoltaic cell parameters, and the specific parameters are shown in Tables 1 and 2.

[0188] Table 1: Photovoltaic cell 1 parameters

[0189]

[0190]

[0191] Table 2 Parameters of Photovoltaic Cells

[0192]

[0193] Based on equation (14) and the environments given in Tables 1 and 2, the theoretical maximum power points of multiple photovoltaic cells can be calculated, as shown in Table 3.

[0194] Table 3 Theoretical Maximum Power Point of Photovoltaic Array

[0195]

[0196] Based on the quantitative relationship between the optimization parameters given in step three, the time delay, the stability of the control system, and the algorithm performance, the parameters are selected as shown in Table 4.

[0197] Table 4. Parameter Selection for the Time Delay Extreme Value Search Algorithm

[0198]

[0199] A simulation of maximum power point tracking (MPPT) control for two photovoltaic cells connected in series was conducted. The simulation results show that, under the simulated conditions, the algorithm completes the search within approximately 3500 seconds, 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 extremum search ensures that each photovoltaic cell in the photovoltaic system operates at its theoretical maximum power point; from Figure 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. A comparison of the simulated output power and the theoretical maximum power is shown in Table 5. Figure 10 It can be seen that the photovoltaic cell maximum power point tracking control method based on time-delay extremum search has a small duty cycle estimation error and has successfully completed the extremum search task; from Figure 11 It can be seen that the tracking path for the maximum power point is searched by two components; Table 6 shows that the estimated error of the system output is smaller than the upper bound of the theoretical estimated error, indicating that the theory has a certain degree of conservatism; Since the quadratic model used in the design and analysis of the control system is significantly different from the real nonlinear model used in the simulation, the simulation results also show that the optimization parameter scheme selected by the method of this invention has good robustness.

[0200] Table 5 Comparison of Simulation Results and Theoretical Results for Time Delay Extremum Search

[0201]

[0202] Table 6 Comparison of Simulated UB and Theoretical UB for Time Delay Extreme Value Search Table 6 Comparison of Simulated UB and Theoretical UB

[0203]

[0204] The above examples of the present application are only to illustrate the calculation model and calculation process of the present application, and are not intended to limit the embodiments of the present application. Based on the above description, other different forms of changes or variations can be made by those of ordinary skill in the art, 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 system maximum power point tracking control method based on time-delay extremum search, characterized in that, The method specifically comprises the following steps: Step one, establishing an ideal mathematical model of a photovoltaic power generation system with n photovoltaic cells connected in series, Taylor expanding the ideal mathematical model of the photovoltaic power generation system, and obtaining a quadratic static objective function; In the step one, the ideal mathematical model of the photovoltaic power generation system with n photovoltaic cells connected in series is established, specifically as follows: Ii is the current of the ith photovoltaic cell in the photovoltaic power generation system i -V i The relationship is: where 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; intermediate variable wherein, is the diode reference reverse saturation current 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; The output voltage and output current of each photovoltaic cell in the photovoltaic power generation system are converted through a DC / DC converter, and then 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 passing through the DC / DC converter, I oi is the output current of the i-th photovoltaic cell after passing through the DC / DC converter, I dc is a constant value of the output DC current of the photovoltaic power generation system; The output voltage of each photovoltaic cell V = [V1 V2...V n ] Τ The duty cycle of the diode corresponding to each photovoltaic cell d = [d1 d2...d n ] Τ The relationship is: wherein, d is the power efficiency of the DC / DC converter, 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 P' = V dc I dc (12) and estimating the upper bound of the maximum output power P * in the quadratic static objective function, and the upper and lower bounds of the duty cycle corresponding to each photovoltaic cell Step two, establishing a control system considering time delay according to the quadratic static objective function, and performing averaging processing on the control system to obtain a perturbation system equivalent to the control system; Step three, using the method of constant variation formula based on ordinary differential equation and the estimated maximum output power P * upper bound, duty cycle upper bound and lower bound d i * Stability analysis of the perturbed system; According to the stability analysis result, the controller parameters are obtained, and the controller is used to perform maximum power point tracking control on the photovoltaic power generation system.

2. The photovoltaic system maximum power point tracking control method based on time delay extremum search according to claim 1, characterized in that, The Taylor expansion is performed on the ideal mathematical model of the photovoltaic power generation system to obtain the quadratic static objective function, specifically as follows: There is satisfied: wherein, is the first derivative value of the ideal mathematical model of the photovoltaic power generation system at d * is the second derivative value of the ideal mathematical model of the photovoltaic power generation system at d * is the maximum output power P * of the photovoltaic power generation system, and D is the duty ratio vector of the corresponding DC / DC converter; is the first derivative value of the ideal mathematical model of the photovoltaic power generation system at d * is the second derivative value of the ideal mathematical model of the photovoltaic power generation system at d T is the transpose of H. The Taylor expansion is performed on the ideal mathematical model of the photovoltaic power generation system, and the expansion items higher than the quadratic expansion items are ignored to obtain the quadratic static objective function: Wherein, t is time, d(t) is a duty cycle vector at t, and P'(t) is the output power of the photovoltaic power generation system at t.

3. The photovoltaic system maximum power point tracking control method based on time delay extremum search according to claim 2, characterized in that, The specific process of the step two is as follows: The quadratic static objective function considering time delay is: Wherein, D is time delay, and P(t) is the output power of the photovoltaic power generation system at t considering time delay; d * the ith element in satisfies define define |P * |≤P M * , P M * is an upper bound of the maximum output power P * , P M * is a known quantity; the definition matrix H satisfies βI n ≤H≤αI n <0, where α, β are known negative scalars, I n is the identity matrix; Let wherein is an estimate of d * , wherein is a derivative with respect to time, S(t) is the excitation signal, M(t) is the intermediate vector, and K is a gain matrix. where ω i is the frequency of the controller, i = 1,..., n, a i is a parameter that controls the amplitude of the excitation signal; The gain matrix is defined as: K = kI n (20) Wherein, k is the gain of the controller; The estimation error is defined as: wherein is the estimated error; According to the formula (18) and the formula (19), the control system considering time delay is obtained: where the upper index T denotes the transpose of a matrix, is the first derivative of , and let Wherein, ε is an intermediate variable; The averaging processing is performed on the system of the formula (22), that is, the integral of both sides of the formula (22) from t-ε to t is performed, and then the integral result is divided by ε, and when t≥D+ε, the following formula is obtained: Wherein, τ is an integral variable; Since Then Since The second item on the right side of the formula (24) is: wherein (H) ij is the element in the i-th row and j-th column of matrix H; The third item on the right side of the formula (24) is defined as x±y=x+y-y, and the third item on the right side of the formula (24) is: Wherein, s is an integral variable; Since The fourth item on the right side of the formula (24) is: Let: Then The intermediate variables Y1(t) and Y2(t) are defined as: The system of the formula (22) is expressed as: Let: Then the system of the formula (22) is finally expressed as the perturbation system of the formula (37): wherein is the first derivative of z(t).

4. The photovoltaic system maximum power point tracking control method based on time delay extremum search according to claim 3, characterized in that, The constant variation formula method based on ordinary differential equation and the estimated maximum output power P * Upper bound, duty cycle upper bound And lower bound d i * Stability analysis is performed on the perturbed system; specifically: Wherein, σ>σ0, and |·| represents taking absolute value; When t ∈ [0, D), there is According to formula (17) and βI n ≤H≤αI n <0 get: Wherein: When t≥D+ε, the constant variation is performed on the formula (36) to obtain: Wherein, e is the base of natural logarithm; From the formula (39), the following formula is obtained: Then Wherein, ||·|| represents L2 norm, and Δ1 is an intermediate variable; From the formula (34), the following formula is obtained: From the formula (45), the following formula is obtained: Wherein, Δ2 and Δ3 are intermediate variables; According to equations (41) to (46): Since H > 0, there exists an orthogonal matrix U e R n×n Then, we have: wherein is a diagonal matrix, h1,..., h n is a diagonal matrix the elements on the diagonal of by βI n ≤ H ≤ αI n < 0 gives: Then The constant variation is performed on the formula (37) to obtain: z(t) = e kHt z(0), t ≥ 0 (52) From the formula (48) and the formula (51), the following formula is obtained: From the formula (36), the following formula is obtained: Then Then Then it is proved that: where ε * is an upper bound of ε, i.e. there is:

5. The photovoltaic system maximum power point tracking control method based on time delay extremum search according to claim 4, characterized in that, According to the stability analysis result, the controller parameters are obtained, and the controller is used to perform maximum power point tracking control on the photovoltaic power generation system; specifically as follows: 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 * > 0 satisfy: Since the intermediate variable Φ1< 0, then The system of equation (22) satisfies: Wherein, δ is convergence speed; when ε ∈ (0, ε * ] and satisfies the initial condition The solution of the system of equations (22) converges exponentially with the convergence rate δ into the following spherical domain Θ: According to ε∈(0,ε * ] get the controller frequency ω i ,ω i and given parameters k,a i , that is, the controller parameters.

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