A maximum power point tracking control method for photovoltaic power generation system considering time delay

Abstract

A maximum power point tracking control method for a photovoltaic power generation system taking time lag into consideration belongs to the technical field of maximum power point tracking control for photovoltaic cells. The present invention solves the problems of low tracking accuracy, slow tracking speed, and inability to cope with complex working environments, changes in the parameters of the battery array itself, and time lag in the system in traditional maximum power point tracking control methods. The present invention uses an averaging method based on time delay to average the system to obtain an equivalent system, uses a constant variation formula method based on ordinary differential equations to perform quantitative stability analysis on the equivalent system, establishes a quantitative relationship between system stability and controller parameters, and obtains the final controller form, thereby achieving true MPPT tracking control of photovoltaic cells, improving tracking accuracy and tracking speed, and effectively reducing power loss of photovoltaic cells. The method of the present invention can be applied to maximum power point tracking control of photovoltaic power generation systems with time lag.

Description

Technical Field

[0001] The present invention belongs to the technical field of photovoltaic cell maximum power point tracking control, and in particular relates to a maximum power point tracking (MPPT) control method for a photovoltaic power generation system taking time lag into consideration. Background Art

[0002] Traditional fossil energy has underpinned rapid social development since modern times. However, humanity's demand for energy has increased dramatically with explosive population growth and the booming development of industry and technology. Due to the crises and environmental pollution caused by traditional energy sources, new energy technologies such as solar energy, wind energy, hydropower, and biomass have emerged as new vistas and are being further developed and utilized. As a representative of new energy sources, solar energy boasts numerous advantages, such as being clean and sustainable, and is experiencing rapid growth. Currently, direct applications of solar energy are primarily focused on photovoltaic power generation. However, photovoltaic cells, as components that rely on solar energy, are inherently unstable. Their power generation capacity is significantly affected by sunlight conditions, resulting in significant fluctuations in power generation capacity at different times of the day and in different weather conditions. This environmentally induced instability in photovoltaic power generation poses significant challenges to the conversion efficiency and resource utilization of photovoltaic power systems. Therefore, energy management systems are needed to manage and distribute electrical energy in real time based on changes in photovoltaic cell power and system load, preventing inappropriate consumption and maximizing energy storage and utilization.

[0003] The key to photovoltaic cell energy management systems lies in maximum power point tracking (MPPT). By monitoring the current and voltage of the photovoltaic cells and energy storage batteries in a solar photovoltaic power generation system and adjusting the DC / DC converter gain in real time according to an optimization algorithm, the photovoltaic cells are consistently operating at their maximum power point. This power is then distributed through the power distributor. PV cell MPPT control technology uses a control algorithm to predict the potential maximum power output point of the photovoltaic cells under current operating conditions based on real-time output power from the photovoltaic array. The widespread adoption and application of MPPT technology enables comprehensive control of the voltage and output voltage of solar photovoltaic cells in a relatively short period of time, comprehensively improving the management of photovoltaic conversion efficiency. Traditional MPPT control algorithms include constant voltage tracking and perturbation-observation methods. The constant voltage tracking method is simple to implement and offers stable performance. However, its limitations lie in its suitability for standalone photovoltaic systems with low power, stable insolation, and minimal external fluctuations. Its control effect approximates MPPT control and does not truly achieve MPPT. The perturbation-and-observe control system has a simple structure and relatively easy-to-implement control algorithm, but the operating point of the photovoltaic cell constantly fluctuates around the maximum power point, rather than remaining stable at it. This results in low tracking accuracy and a certain amount of power loss. Furthermore, traditional maximum power point tracking algorithms suffer from slow tracking speed, model dependence, inability to cope with complex operating environments, variations in the array's own parameters, and system lag. Therefore, it is necessary to develop an intelligent MPPT control method with real-time search capabilities. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems of low tracking accuracy, slow tracking speed and inability to cope with complex working environments, changes in battery array parameters themselves and time lag in the system in traditional maximum power point tracking control methods, and to propose a maximum power point tracking control method for photovoltaic power generation systems that takes time lag into account.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a maximum power point tracking control method for a photovoltaic power generation system considering time lag, the method specifically comprising the following steps:

[0006] Step 1: Based on the current-voltage relationship of a single photovoltaic cell, an ideal mathematical model of a photovoltaic power generation system consisting of multiple photovoltaic cells connected in series is established;

[0007] Step 2: Perform Taylor expansion on the ideal mathematical model of the photovoltaic power generation system to obtain a quadratic static objective function, estimate the quadratic Hessian matrix and the duty cycle in the quadratic static objective function, and obtain the upper bound of the second norm of the quadratic Hessian matrix in the quadratic static objective function, as well as the upper and lower bounds of the duty cycle;

[0008] Step 3: Establish a control system that takes time delay into account based on the quadratic static objective function, and perform averaging on the control system to obtain a disturbance system equivalent to the control system;

[0009] Step 4: Based on the estimation results of the upper bound of the second norm of the quadratic Hessian matrix, the upper bound of the duty cycle, and the lower bound of the duty cycle, a quantitative stability analysis of the disturbance system is performed, and a quantitative relationship between the stability of the disturbance system and the controller parameters is established;

[0010] The controller parameters are selected according to the quantitative relationship between the stability of the disturbance system and the controller parameters to achieve maximum power point tracking control.

[0011] The beneficial effects of the present invention are:

[0012] The present invention takes into account the changes in environmental parameters in the actual working environment of the photovoltaic power generation system, the changes in the parameters of the battery array itself, and the time lag in the system, and establishes a photovoltaic cell MPPT control algorithm based on bounded multivariable disturbance extreme value search. The system is averaged by using an averaging method based on time delay to obtain an equivalent system. The equivalent system is quantitatively analyzed using a constant variation formula method based on ordinary differential equations, and a quantitative relationship between the system stability and the controller parameters is established to obtain the final controller form, thereby achieving true MPPT tracking control of the photovoltaic cell, improving tracking accuracy and tracking speed, and effectively reducing the power loss of the photovoltaic cell. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is the equivalent circuit diagram of a single photovoltaic cell;

[0014] Figure 2 This is a block diagram of the bounded extreme value search algorithm based on gradient estimation;

[0015] Figure 3 is a duty cycle graph;

[0016] Figure 4 is the output power curve;

[0017] Figure 5 is a graph of duty cycle error. DETAILED DESCRIPTION

[0018] Specific embodiment 1: This embodiment describes a maximum power point tracking control method for a photovoltaic power generation system considering time lag, and the method specifically includes the following steps:

[0019] Step 1: Based on the current-voltage relationship of a single photovoltaic cell, an ideal mathematical model of a photovoltaic power generation system consisting of multiple photovoltaic cells connected in series is established;

[0020] Step 2: Perform Taylor expansion on the ideal mathematical model of the photovoltaic power generation system to obtain a quadratic static objective function, estimate the quadratic Hessian matrix and the duty cycle in the quadratic static objective function, and obtain the upper bound of the second norm of the quadratic Hessian matrix in the quadratic static objective function, as well as the upper and lower bounds of the duty cycle;

[0021] Step 3: According to the quadratic static objective function and Figure 2 The bounded extreme value search algorithm based on gradient estimation is used to establish a control system considering time delay, and the control system is averaged using the averaging method based on time delay to obtain a disturbance system equivalent to the control system.

[0022] Step 4: Based on the estimated results of the upper bound of the second norm of the quadratic Hessian matrix, the upper limit of the duty cycle, and the lower limit of the duty cycle, a constant variation formula method based on ordinary differential equations is used to perform a quantitative stability analysis on the disturbance system, and a quantitative relationship between the stability of the disturbance system and the controller parameters is established;

[0023] According to the quantitative relationship between the stability of the disturbance system and the controller parameters, the controller parameters are selected (i.e., given the controller parameters k i ,α i , according to the quantitative relationship to select ε * , and then we get ε∈(0,ε * ], that is, we get ω i ) to achieve maximum power point tracking control.

[0024] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the current-voltage relationship of a single photovoltaic cell is established as follows:

[0025] 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, such as Figure 1 As shown, a photovoltaic cell is represented by an ideal current source, and the current source is connected in parallel with an ideal diode, and the current of the current source is recorded as I ph ;

[0026] The current of the current source I ph for:

[0027]

[0028] in, is the standard short-circuit current, T r is the standard temperature, T is the actual temperature, S is the solar irradiance, and k′ is the dimensionless short-circuit temperature coefficient;

[0029] The current flowing through the diode in parallel with the current source is recorded as I D , the terminal voltage of the diode connected in parallel with the current source is recorded as V D ,but

[0030]

[0031] in, is the diode reference reverse saturation current, V D is the diode terminal voltage, E g is the semiconductor band gap energy, N is the semiconductor emission coefficient, V t is the thermoelectric cell voltage, k is a constant, and the value of k is 1.38×10 -23 J / K, q is the electron charge number, and the value of q is 1.6×10 -19 C;

[0032] Using KCL and KVL laws, we can get:

[0033]

[0034] Among them, R p is the contactor resistance, I is the current of the photovoltaic cell, V is the voltage of the photovoltaic cell, R s It is the electrical loss;

[0035] According to formula (3), the current-voltage relationship of a single photovoltaic cell is obtained:

[0036]

[0037] Other steps and parameters are the same as those in the first embodiment.

[0038] Specific embodiment three: This embodiment differs from specific embodiment one or two in that, in step one, an ideal mathematical model of a photovoltaic power generation system in which multiple photovoltaic cells are connected in series is established, specifically:

[0039] Connect n photovoltaic cells in series to form the entire photovoltaic power generation system, and express the current-voltage relationship of the i-th photovoltaic cell as follows:

[0040]

[0041] Among them, I ph,i is the current of the current source corresponding to the i-th photovoltaic cell, I 0,i is the intermediate variable, V i is the voltage of the ith photovoltaic cell, R s,i is the electrical loss in the equivalent circuit corresponding to the i-th photovoltaic cell, I i is the current of the i-th photovoltaic cell;

[0042] According to formula (5), IV curve and PV curve are drawn to prove the existence of the peak output power of photovoltaic cells and their dependence on irradiance and temperature;

[0043] The maximum power point tracking task is completed by using DC / DC power electronic devices, which can adjust the output DC voltage to a near constant value, while forcing the output voltage of the photovoltaic array to be equal to the optimal voltage value to obtain maximum power output, and realize impedance matching by changing the duty cycle parameters without changing the external load.

[0044] The DC / DC converter is used to adjust the DC voltage output by the photovoltaic power generation system to a constant value:

[0045]

[0046] Among them, V dc The photovoltaic power generation system outputs a constant DC voltage, V oi is the output voltage of the ith photovoltaic cell after passing through the DC / DC converter, I oi is the output current of the ith photovoltaic cell after passing through the DC / DC converter, I dc is the output current of the photovoltaic power generation system;

[0047] When the DC / DC converter operates 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 voltage of each photovoltaic cell in the photovoltaic power generation system V=[V1 V2 … V n ] Τ With duty cycle d=[d1 d2 … d n ] Τ The relationship is:

[0048]

[0049] in, is the power efficiency of the DC / DC converter, d i is the diode switch duty cycle corresponding to the i-th photovoltaic cell;

[0050] For each duty cycle, there is a set of photovoltaic cell voltages. In addition, each photovoltaic cell has a bypass diode, which means that the overall output power of the photovoltaic power generation system has only one peak value.

[0051] The output power of the photovoltaic power generation system is:

[0052]

[0053] Among them, P i =V oi I oi .

[0054] Other steps and parameters are the same as those in the first or second embodiment.

[0055] When n = 2, T = T r When , the relationship between current and voltage is:

[0056]

[0057] From formula (7) and formula (8), we can get the following equations:

[0058]

[0059] In actual applications, the parameter accuracy in the formula 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.

[0060] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that, in step 2, Taylor expansion is performed on the ideal mathematical model of the photovoltaic power generation system to obtain a quadratic static objective function; specifically:

[0061] The ideal mathematical model of the photovoltaic power generation system (i.e., formula (9)) is Taylor expanded, and the expansion terms higher than quadratic in the expansion result are ignored. The quadratic static objective function is obtained as follows:

[0062]

[0063] Among them, P * is the maximum output power of the photovoltaic power generation system; P(t) is the power output of the photovoltaic power generation system at time t; d * is the maximum output power P * The duty cycle vector composed of the diode switching duty cycles corresponding to each photovoltaic cell is: is the maximum output power P * is the diode switching duty cycle corresponding to the first, second, …, nth photovoltaic cell at output power P(t), d(t) is the duty cycle vector composed of the diode switching duty cycles corresponding to each photovoltaic cell at output power P(t), the superscript T represents the transpose of the matrix, and H(·) is the quadratic Hessian matrix.

[0064]

[0065] The other steps and parameters are the same as those in the first to third embodiments.

[0066] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the quadratic Hessian matrix satisfies in, is a known matrix, and ||ΔH||≤κ, κ is a known scalar, ||·|| is the L2 norm;

[0067] The duty cycle vector d * satisfy Among them, d i * is the maximum output power P * The duty cycle corresponding to the i-th photovoltaic cell is, It is d i * The lower limit of It is d i * The upper limit of

[0068] The other steps and parameters are the same as those in the first to fourth embodiments.

[0069] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the specific process of step 3 is as follows:

[0070] Step 3: Consider an uncertain static quadratic mapping with a small constant output time lag and express the quadratic static objective function as:

[0071]

[0072] Where D is the time lag, and d(tD) is the duty cycle vector composed of the diode switching duty cycles corresponding to each photovoltaic cell after considering the time lag D;

[0073] In order to further design the algorithm and analyze the control system, the quadratic Hessian matrix is orthogonally transformed:

[0074]

[0075] Among them, U Τ is the transpose of U, which is an orthogonal matrix, is the orthogonal transformation result of H, yes The orthogonal transformation result of is the orthogonal transformation result of ΔH, and is an intermediate variable;

[0076] Then there is yes The first, ..., nth diagonal elements in , Equation (14) can be rewritten as:

[0077]

[0078] The error is defined as:

[0079]

[0080] in, is the duty cycle vector error, is the time lag error;

[0081] make According to formula (15), Then there is

[0082] Let the gain matrix be K=diag{k1,K,k n},i=1,K,n, where k1,K,k n are the controller gains of the 1st, ..., nth photovoltaic cells respectively; let the control system considering time delay be:

[0083]

[0084] in, yes The first derivative of yes The i-th element in ω i is the frequency parameter of the controller of the i-th photovoltaic cell, α i is the controller parameter of the i-th photovoltaic cell;

[0085] Then there is

[0086]

[0087] make

[0088]

[0089] Among them, ε is the parameter to be designed, l i is a rational number, N + is a set of positive integers;

[0090] Integrate both sides of equation (19) from t-ε to t, and then divide by ε. When t≥2D+ε, we have

[0091]

[0092] Where τ is the integration variable;

[0093] The first term on the right side of formula (21) is:

[0094]

[0095] in, represent The column vector composed of

[0096] Since formula (23) holds:

[0097]

[0098] Then the first term on the right side of formula (22) is:

[0099]

[0100]

[0101] because

[0102]

[0103] Then the second term on the right side of formula (22) is:

[0104]

[0105]

[0106] Among them, h i is the i-th element in H, yes The jth element in ; the second term on the right side of formula (21) is:

[0107]

[0108] Among them, sin(k i P(τ))±sin(k i P(t))=sin(k i P(τ))+sin(k i P(t))-sin(k i P(t)), due to

[0109]

[0110] Then the first term on the right side of formula (27) is:

[0111]

[0112]

[0113]

[0114] Among them, v is the integral variable; due to

[0115]

[0116] The second term on the right side of formula (27) is:

[0117]

[0118]

[0119] make

[0120]

[0121] Then there is

[0122]

[0123] When t≥2D+ε, let

[0124]

[0125] Among them, v and s are integral variables, then we have

[0126]

[0127] make

[0128]

[0129] Then Equation (18) is equivalently expressed as a perturbation system:

[0130]

[0131] in, It is z i The first derivative of (t), w i (t) is an intermediate variable.

[0132] The other steps and parameters are the same as those in the first to fifth embodiments.

[0133] Specific embodiment 7: This embodiment differs from any one of specific embodiments 1 to 6 in that the specific process of step 4 is as follows:

[0134] Satisfy the initial conditions yes The i-th element in , given the controller parameter k i ,α i , given Let ε * >0 satisfies:

[0135]

[0136] Among them, W i (ε * ) is an intermediate variable, δ i is the convergence rate of the i-th photovoltaic cell;

[0137] Then ε∈(0,ε * ], the solution of formula (18) satisfies:

[0138]

[0139] Where, e is the base of natural logarithms;

[0140] When ε∈(0,ε * ] and there are initial conditions When the solution of Equation (18) converges at a rate δ i The exponential converges to the sphere of Equation (40):

[0141]

[0142] Where, formula (40) represents and Converge to

[0143] The other steps and parameters are the same as those in the first to sixth embodiments.

[0144] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the intermediate variable W i (ε * )for:

[0145]

[0146] Among them, Δ1, Δ2, Δ3, Δ4, Δ5 and Δ6 are intermediate variables, H M is the upper bound of the two-norm of the matrix H.

[0147] The other steps and parameters are the same as those in the first to seventh embodiments.

[0148] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the intermediate variable δ i for:

[0149]

[0150] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0151] Specific embodiment ten: This embodiment differs from any one of specific embodiments one to nine in that the intermediate variables Δ1, Δ2, Δ3, Δ4, Δ5 and Δ6 are:

[0152]

[0153] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0154] Simulation verification:

[0155] Build a virtual photovoltaic battery system and select the photovoltaic battery parameters as shown in Table 1 and Table 2;

[0156] Table 1 Parameters of photovoltaic cell 1 selected for simulation

[0157]

[0158]

[0159] Table 2 Parameters of photovoltaic cell 2 selected for simulation

[0160]

[0161] According to the model of formula (11) and the environments given in Tables 1 and 2 above, the maximum power point of a theoretical single photovoltaic cell can be calculated, as shown in Table 3.

[0162] Table 3 Theoretical maximum power point of simulated photovoltaic array

[0163]

[0164] The quadratic form parameters and parameter selection are shown in Table 4.

[0165] Table 4 Simulation parameter selection of bounded multivariable extreme value search algorithm

[0166]

[0167]

[0168] A virtual single photovoltaic cell maximum power tracking control system was built in Matlab for simulation. The simulation results are as follows: Figures 3 to 5 shown.

[0169] Figure 3 The red curve in the figure represents the optimal duty cycle d1(t) of the first photovoltaic cell, and the blue curve represents the optimal duty cycle d2(t) of the second photovoltaic cell. Figure 4 The green curve in the figure is the simulated output power P(t) of two photovoltaic cells. Figure 5The red curve in the figure shows the error between the optimal duty cycle of the first photovoltaic cell and the theoretical optimal duty cycle. The blue curve represents the error between the optimal duty cycle of the second photovoltaic cell and the theoretical optimal duty cycle.

[0170] according to Figure 3 、 Figure 4 and Figure 5 As shown in the figure, in the simulation environment, the algorithm basically completes the search in 2 seconds, and the estimation error does not exceed 4%, achieving the tracking of the maximum power point of the photovoltaic battery system.

[0171] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A maximum power point tracking control method for a photovoltaic power generation system considering time lag, characterized in that: The method specifically comprises the following steps: Step 1: Based on the current-voltage relationship of a single photovoltaic cell, an ideal mathematical model of a photovoltaic power generation system consisting of multiple photovoltaic cells connected in series is established; Step 2: Perform Taylor expansion on the ideal mathematical model of the photovoltaic power generation system to obtain a quadratic static objective function, estimate the quadratic Hessian matrix and the duty cycle in the quadratic static objective function, and obtain the upper bound of the second norm of the quadratic Hessian matrix in the quadratic static objective function, as well as the upper and lower bounds of the duty cycle; In the second step, Taylor expansion is performed on the ideal mathematical model of the photovoltaic power generation system to obtain a quadratic static objective function; specifically, Performing Taylor expansion on the ideal mathematical model of the photovoltaic power generation system and ignoring the expansion terms higher than quadratic in the expansion result, the quadratic static objective function is obtained as follows: Among them, P * is the maximum output power of the photovoltaic power generation system; P(t) is the power output of the photovoltaic power generation system at time t; d * is the maximum output power P * The duty cycle vector composed of the diode switching duty cycles corresponding to each photovoltaic cell is: is the maximum output power P * is the diode switching duty cycle corresponding to the first, second, …, nth photovoltaic cell at t, d(t) is the duty cycle vector composed of the diode switching duty cycles corresponding to each photovoltaic cell at output power P(t), the superscript T represents the transpose of the matrix, and H(·) is the quadratic Hessian matrix; The quadratic Hessian matrix satisfies in, is a known matrix, and ||ΔH||≤κ, κ is a known scalar, ||·|| is the L2 norm; The duty cycle vector d * satisfy i=1,2,...,n,where d i * is the maximum output power P * The duty cycle corresponding to the i-th photovoltaic cell is, It is d i * The lower limit of It is d i * The upper limit of Step 3: Establish a control system that takes time delay into account based on the quadratic static objective function, and perform averaging on the control system to obtain a disturbance system equivalent to the control system; Step 4: Based on the estimation results of the upper bound of the second norm of the quadratic Hessian matrix, the upper bound of the duty cycle, and the lower bound of the duty cycle, a quantitative stability analysis of the disturbance system is performed, and a quantitative relationship between the stability of the disturbance system and the controller parameters is established; The controller parameters are selected according to the quantitative relationship between the stability of the disturbance system and the controller parameters to achieve maximum power point tracking control.

2. The maximum power point tracking control method for a photovoltaic power generation system considering time lag according to claim 1, characterized in that: The current-voltage relationship of a single photovoltaic cell is established as follows: A photovoltaic cell is represented by a current source, which is connected in parallel with a diode, and the current of the current source is recorded as I ph ; The current of the current source I ph for: in, is the standard short-circuit current, T r is the standard temperature, T is the actual temperature, S is the solar irradiance, and k′ is the dimensionless short-circuit temperature coefficient; The current flowing through the diode in parallel with the current source is recorded as I D , the terminal voltage of the diode connected in parallel with the current source is recorded as V D ,but in, is the diode reference reverse saturation current, V D is the diode terminal voltage, E g is the semiconductor band gap energy, N is the semiconductor emission coefficient, V t is the thermoelectric cell voltage, k is a constant, and q is the number of electron charges; Using KCL and KVL laws, we can get: Among them, R p is the contactor resistance, I is the current of the photovoltaic cell, V is the voltage of the photovoltaic cell, R s It is the electrical loss; According to formula (3), the current-voltage relationship of a single photovoltaic cell is obtained:

3. The maximum power point tracking control method for a photovoltaic power generation system considering time lag according to claim 2, characterized in that: In the first step, an ideal mathematical model of a photovoltaic power generation system in which multiple photovoltaic cells are connected in series to generate electricity is established, specifically: Connect n photovoltaic cells in series to form the entire photovoltaic power generation system, and express the current-voltage relationship of the i-th photovoltaic cell as follows: Among them, I ph,i is the current of the current source corresponding to the i-th photovoltaic cell, I 0,i is the intermediate variable, V i is the voltage of the ith photovoltaic cell, R s,i is the electrical loss in the equivalent circuit corresponding to the i-th photovoltaic cell, I i is the current of the i-th photovoltaic cell; The DC / DC converter is used to adjust the DC voltage output by the photovoltaic power generation system to a constant value: Among them, V dc The photovoltaic power generation system outputs a constant DC voltage, V oi is the output voltage of the ith photovoltaic cell after passing through the DC / DC converter, I oi is the output current of the ith photovoltaic cell after passing through the DC / DC converter, I dc is the output current of the photovoltaic power generation system; The voltage of each photovoltaic cell in the photovoltaic power generation system is V=[V1 V2…V n ] Τ With duty cycle d=[d1 d2…d n ] Τ The relationship is: in, is the power efficiency of the DC / DC converter, d i is the diode switch duty cycle corresponding to the i-th photovoltaic cell; The output power of the photovoltaic power generation system is: Among them, P i =V oi I oi .

4. The maximum power point tracking control method for a photovoltaic power generation system considering time lag according to claim 3, characterized in that: The specific process of step three is: Step 3.

1. Consider an uncertain static quadratic mapping with constant output time lag, and express the quadratic static objective function as: Where D is the time lag, and d(tD) is the duty cycle vector composed of the diode switching duty cycles corresponding to each photovoltaic cell after considering the time lag D; Perform an orthogonal transformation on the quadratic Hessian matrix: Among them, U Τ is the transpose of U, which is an orthogonal matrix, is the orthogonal transformation result of H, yes The orthogonal transformation result of is the orthogonal transformation result of ΔH, and is an intermediate variable; Then there is yes The first, ..., nth diagonal elements in , Equation (14) can be rewritten as: The error is defined as: in, is the duty cycle vector error, is the time lag error; make According to formula (15), Then there is Let the gain matrix be K=diag{k1,K,k n }, i=1,…,n, where k1,…,k n are the controller gains of the 1st, ..., nth photovoltaic cells respectively; let the control system considering time delay be: in, yes The first derivative of yes The i-th element in ω i is the frequency parameter of the controller of the i-th photovoltaic cell, α i is the controller parameter of the i-th photovoltaic cell; Then there is make Among them, ε is the parameter to be designed, l i is a rational number, N + is a set of positive integers; Integrate both sides of equation (19) from t-ε to t, and then divide by ε. When t≥2D+ε, we have Where τ is the integration variable; make Then there is When t≥2D+ε, let Among them, v and s are integral variables, then we have make Then Equation (18) is equivalently expressed as a perturbation system: in, It is z i The first derivative of (t), w i (t) is an intermediate variable.

5. The maximum power point tracking control method for a photovoltaic power generation system considering time lag according to claim 4, characterized in that: The specific process of step 4 is as follows: Satisfy the initial conditions is the i-th element in σ0, given the controller parameter k i ,α i , given Let ε * >0 satisfies: Among them, W i (ε * ) is an intermediate variable, δ i is the convergence rate of the i-th photovoltaic cell; The intermediate variable W i (ε * )for: Among them, Δ1, Δ2, Δ3, Δ4, Δ5 and Δ6 are intermediate variables, H M is the upper bound of the 2-norm of the matrix H; Then ε∈(0,ε * ], the solution of formula (18) satisfies: Where, e is the base of natural logarithms; When ε∈(0,ε * ] and there are initial conditions When the solution of Equation (18) converges at a rate δ i The exponential converges to the sphere of Equation (40):

6. The maximum power point tracking control method for a photovoltaic power generation system considering time lag according to claim 5, characterized in that: The intermediate variable δ i for:

7. The maximum power point tracking control method for a photovoltaic power generation system considering time lag according to claim 6, characterized in that: The intermediate variables Δ1, Δ2, Δ3, Δ4, Δ5 and Δ6 are respectively:

Images