An integral terminal sliding mode control MPPT method based on GPI observer

Abstract

The application discloses an integral terminal sliding mode control MPPT method based on a GPI observer, and comprises the following steps: S10, analyzing a Boost circuit topological structure of a photovoltaic system, establishing a system mathematical model, and obtaining an output state equation of a converter; S20, introducing proportional integral control to estimate a system state, designing a terminal sliding mode function, and constructing a sliding mode controller according to the mathematical model in S10; and S30, according to the sliding mode controller in S20, verifying the existence of a sliding mode dynamic and the stability of the system by using a Lyapunov stability theorem. The application can accurately track a maximum power point of the photovoltaic, and can suppress ordinary sliding mode chattering. The application realizes smooth, stable and fast converging MPPT control, and improves the conversion efficiency of light energy.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electronic power control and new energy, and relates to an integral terminal sliding mode control MPPT method based on a GPI observer. BACKGROUND

[0002] Sliding mode control has strong robustness and stability, can adapt to uncertain system parameters and disturbances, and makes the system have good stability. It is often mentioned in the field of automatic control and is widely used in maximum power tracking of solar photovoltaic panels, can realize fast response and fast convergence, and can track the maximum power point of a photovoltaic cell array more quickly.

[0003] Maximum power point tracking (MPPT) is a commonly used control algorithm in photovoltaic power generation systems. Its working principle is to control the external equivalent load of the photovoltaic panel to be equal to the internal resistance of the photovoltaic panel, so as to maximize the output power of the photovoltaic panel. The commonly used MPPT algorithms include constant voltage method, perturbation and observation method, conductance increment method, three-point comparison method, etc. However, these algorithms have poor control accuracy, slow convergence speed, and complex algorithms that occupy a large amount of resources. However, the conventional sliding mode control algorithm often uses a large upper bound to counteract the influence of uncertain factors, resulting in severe chattering phenomenon. Moreover, it cannot quickly achieve the MPPT purpose, which easily causes power loss of the photovoltaic system. Therefore, in view of the above-mentioned defects existing in the prior art, it is necessary to conduct research to provide a solution to solve the defects existing in the prior art. SUMMARY

[0004] In view of the nonlinearity problem caused by the sliding mode, the sliding mode observer emerges as the times require. The sliding mode observer is a special state observer based on the sliding mode control theory, which uses the sliding mode control law to observe the nonlinear system to accurately estimate the state of the sliding mode system. The sliding mode observer is mainly used to process the state estimation problem of the nonlinear system, and its strong applicability lies in its ability to accurately capture the changes of the state of the nonlinear system, thereby making the state estimation more accurate. When applied to photovoltaic control, it can more accurately and efficiently track the maximum power point.

[0005] First, the photovoltaic system is mathematically modeled to obtain the state equation of the Boost circuit; a proportional integral (PI) control is introduced to estimate the system state; a terminal sliding mode function is designed, a sliding mode controller is constructed, and the stability of the system is proved by Lyapunov stability theorem.

[0006] The GPI observer is a technology for state estimation. It realizes the estimation of the system state by linearizing the state equation of the system and introducing a proportional integral (PI) controller. The role of the PI controller is to adjust the system state by using the proportional term and the integral term, so as to realize the estimation of the system state. The GPI observer has the advantages of effectively solving the problem of state estimation, and has high stability and reliability.

[0007] The introduced GPI observer can accurately estimate the system state, has high estimation accuracy of the system state, can better track the system state and control target, can effectively suppress the chattering problem caused by the sliding mode, and achieve the goal of tracking the maximum power point. The application provides an integral terminal sliding mode control MPPT method based on a GPI observer, which comprises the following steps:

[0008] S10, analyzing the equivalent Boost circuit topology of the photovoltaic system, establishing a system mathematical model, and obtaining the output state equation of the converter;

[0009] S20, introducing proportional integral control to estimate the system state, designing a terminal sliding mode function, and constructing a sliding mode controller according to the mathematical model in S10;

[0010] S30, according to the sliding mode controller in S20, the existence of the sliding mode dynamics is verified by using the Lyapunov stability theorem.

[0011] Preferably, the S10 analyzes the equivalent Boost circuit topology of the photovoltaic system, establishes a mathematical model, and comprises analyzing the Boost circuit switch working in two states, and the mathematical model is:

[0012]

[0013] Where, i L is the inductance current, V C is the capacitor voltage, V i is the input voltage, R is the load resistance value, C is the capacitor value, L is the inductance value, and μ is the control law, which is the duty ratio of the control signal in macroscopic performance.

[0014] Preferably, the S20 comprises the following steps: first, constructing a GPI observer, constructing a GPI observer to estimate the disturbance and system state through the output voltage information; then, designing a sliding mode controller based on the estimation result; finally, generating the final PWM signal by comparing the control input and the sawtooth wave, driving the switch of the Boost converter, so that the photovoltaic system satisfies the impedance matching, and the MPPT is achieved.

[0015] Preferably, the S20 specifically comprises the following steps:

[0016] S21, introduce a terminal sliding surface, which is determined by the initial state and target state of the system, and design an integral terminal sliding function, which is as follows:

[0017]

[0018] where x ！ , x2 are state variables, λ ！ and λ2 are parameters of the integral terminal sliding function, which are both constants greater than 0, and q ！ > q2 is a positive odd number.

[0019] Set the initial value of the integral term of the system tracking error as follows:

[0020]

[0021] S22, refer to the second-order dynamic mathematical model of the Boost circuit, and expand it to a third-order state equation:

[0022]

[0023] where x ！ , x2, x3 are state variables, d represents the total disturbance of the system, represents the first derivative of x1, x2, x3, represents the first derivative of d.

[0024] S23, design the ESO observer equation of the system:

[0025]

[0026] where c ！ , c2, and c3 represent the gains of the ESO observer, w ！ , w2, w3 represent the estimated values of x ！ , x2, x3, , w2, w3 represent the first derivatives of w ！ , w2, w3.

[0027] Based on the ESO observer, the GPI observer equation of the system can be established:

[0028]

[0029] where k ！ , k2, k3, and k4 represent the gains of the GPI observer, represent the estimated values of x ！ , x2, x3, x4.

[0030] S24, the estimation error expression of the GPI observer is defined as follows:

[0031]

[0032] where θ ！ , θ2, θ3 and θ4 represent error variables;

[0033] The GPI observer is obtained as follows:

[0034]

[0035] Transformed into matrix form:

[0036]

[0037] Define the matrix:

[0038]

[0039] The characteristic equation of the matrix A is obtained:

[0040]

[0041] where E is a four-order unit matrix, and k ！ +1 / RC>0, k ！ / RC>0, k4>0, and is bounded, therefore, the poles of the system are always located in the left half plane, so the GPI observer of the Boost circuit is stable;

[0042] S25, the sliding mode function s of the system is designed:

[0043]

[0044] The control law u is designed:

[0045]

[0046] where η is a constant greater than 0, and

[0047] Preferably, S30, the existence of the sliding mode and the stability of the system are verified by using Lyapunov theorem, and the Lyapunov function is designed as follows:

[0048]

[0049] For a first-order nonlinear differential inequality:

[0050] ​

[0051] wherein m>0, 0<n<1, V(x) is a Lyapunov function with respect to state x, the function V(x) converges to the origin from any initial condition V(x(0))=V(0) in finite time t, and the finite time t is:

[0052]

[0053] Therefore, in the above formula, when η>(k2+λ·k ！ )·|θ ！ |, the condition of Lyapunov function stability is met, and the system motion point reaches the sliding mode surface s=0 at any position within the finite time t>T0.

[0054] The present application has at least the following beneficial effects: in the face of uncertain parameters in the system, the conventional sliding mode control algorithm only estimates the upper bound of the uncertain parameters, rather than observing a more accurate value, so the output gain of the controller is a large constant value. The GPI core lies in estimating the unknown state by calculating the difference between the system input and output, and synthesizing the advantages of proportional control and integral control through appropriate weighting. An important feature of the GPI observer is its good adaptability to the nonlinear characteristics of the photovoltaic system. Even with small uncertain disturbances, the controller still maintains a large gain, which can cause severe chattering phenomenon, i.e. part of the power will be lost in maximum power point tracking. Compared with the prior art, when there are external disturbances such as changing temperature, light, or the solar photovoltaic system cannot be accurately modeled, the GPI observer accurately estimates the parameter, and then brings the estimated value into the controller expression. The maximum power point of the photovoltaic system can be accurately tracked, and the ordinary sliding mode chattering can be suppressed. Smooth, stable and fast-converging MPPT control is achieved, and the conversion efficiency of light energy is improved. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 A step flowchart of the integral terminal sliding mode control MPPT method based on the GPI observer of the embodiment of the present application is shown in the figure.

[0056] Figure 2 A structure schematic diagram of the integral terminal sliding mode controller based on the GPI observer of the embodiment of the present application is shown in the figure.

[0057] Figure 3 A sliding mode control structure diagram of the GPI observer of the integral terminal sliding mode control MPPT method based on the GPI observer of the embodiment of the present application is shown in the figure.

[0058] Figure 4 ​A system diagram for tracking a maximum power point of photovoltaic power generation by the integral terminal sliding mode control MPPT method based on a GPI observer of an embodiment of the present application;

[0059] Figure 5 A circuit schematic diagram of an embodiment of the present application Figure 4 ;

[0060] Figure 6 A photovoltaic output voltage and output power waveform diagram of an MPPT controller based on a common SMC in the prior art;

[0061] Figure 7 A photovoltaic output voltage and output power waveform diagram of an integral terminal sliding mode control MPPT method based on a GPI observer of an embodiment of the present application;

[0062] Figure 8 A load voltage diagram of an MPPT controller based on a common SMC in the prior art and an integral terminal sliding mode control MPPT controller based on a GPI observer of an embodiment of the present application;

[0063] Figure 9 A load power diagram of an MPPT controller based on a common SMC in the prior art and an integral terminal sliding mode control MPPT controller based on a GPI observer of an embodiment of the present application. DETAILED DESCRIPTION

[0064] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0065] On the contrary, the present application covers any substitution, modification, equivalent method and solution defined by the claims on the essence and scope of the present application. Further, in order to make the public have a better understanding of the present application, some specific details are described in detail in the following detailed description of the present application. The present application can also be completely understood without the description of these details by those skilled in the art.

[0066] Referring to Figure 1 , a method flowchart of the present application includes the following steps:

[0067] S10, analyzing a Boost circuit topology equivalent to a photovoltaic system, establishing a system mathematical model, and obtaining an output state equation of the converter;

[0068] S20, introducing a proportional integral control to estimate the system state, designing a terminal sliding mode function, and constructing a sliding mode controller according to the mathematical model in S10;

[0069] S30, according to the sliding mode controller in S20, the existence of sliding mode dynamics is verified by Lyapunov stability theorem.

[0070] In S10, the equivalent Boost circuit topology of photovoltaic system is analyzed, and a mathematical model is established, including the analysis of the Boost circuit switch working in two states, and the mathematical model is:

[0071]

[0072] Where, i L is the inductance current, V C is the capacitor voltage, V i is the input voltage, R is the load resistance value, C is the capacitor value, L is the inductance value, μ is the control law, which is the duty ratio of the control signal in macro performance.

[0073] Referring to Figure 2 , it is the structure diagram of integral terminal sliding mode controller based on GPI observer. V ref is the reference output voltage, and the difference between it and the system output voltage V O is the tracking error e. The tracking error e is input into the GPI-ITSMC controller to obtain the equivalent control law u eq and the switching control law u sw . The sum of the two is the total control law u of the system. Through the total control rate u, a specific duty ratio PWM wave is output to control the state of the power switch tube in the boost type DC-DC converter, so as to control V O .

[0074] Referring to Figure 3 , it is the sliding mode control structure of GPI observer. The GPI observer estimates the disturbance and system state (x1, x2, x3, x4) by outputting the voltage information V O . Then, based on the estimation result , the sliding mode controller is designed. Finally, by comparing the control input and the sawtooth wave, the final PWM signal is generated to drive the switch of the DC-DC boost converter. S20 includes: first, constructing the GPI observer, constructing the GPI observer to estimate the disturbance and system state by outputting the voltage information; then, based on the estimation result, designing the sliding mode controller; finally, by comparing the control input and the sawtooth wave, the final PWM signal is generated to drive the switch of the Boost boost converter, so that the photovoltaic system meets the impedance matching, to achieve MPPT.

[0075] S20 specifically includes the following steps:

[0076] S21, introduce a terminal sliding surface, which is determined by the initial state and target state of the system, and design an integral terminal sliding function, which is as follows:

[0077]

[0078] Where x1, x2 are state variables, λ ！ and λ2 are parameters of the integral terminal sliding function, both are constants greater than 0, and q ！ >q2 is a positive odd number;

[0079] Set the initial value of the system tracking error integral term as follows:

[0080]

[0081] S22, refer to the second-order dynamic mathematical model of the Boost circuit, and expand it to a third-order state equation:

[0082]

[0083] Where d represents the total disturbance of the system, respectively represent the first derivative of x1, x2, x3, and d! represents the first derivative of d;

[0084] S23, design the ESO observer equation of the system:

[0085]

[0086] Where c ！ , c2 and c3 represent the gain of the ESO observer, w ！ , w2, w3 represent the estimated value of state variables x ！ , x2, x3, respectively represent the first derivative of w ！ , w2, w3;

[0087] And on the basis of the ESO observer, the GPI observer equation of the system can be established:

[0088]

[0089] Where k ！ , k2, k3 and k4 represent the gain of the GPI observer, respectively represent the estimated value of state variables x ！ , x2, x3, x4;

[0090] S24, define the estimated error expression of the GPI observer as follows:

[0091]

[0092] where θ ！ , θ2, θ3 and θ4 represent error variables;

[0093] The GPI observer is obtained as follows:

[0094]

[0095] where represent the first order derivatives of θ ！ , θ2, θ3, θ4, respectively;

[0096] Transformed into matrix form:

[0097]

[0098] Define the matrix:

[0099]

[0100] The characteristic equation of matrix A is obtained as follows:

[0101]

[0102] where E is a four-order unit matrix, and k ！ +1 / RC>0, k ！ / RC>0, k4>0, and is bounded, therefore, the poles of the system are always located in the left half plane, so the GPI observer of the Boost circuit is stable;

[0103] S25, design the sliding mode function s of the system:

[0104]

[0105] Design the control law u:

[0106]

[0107] where η is a constant greater than 0. Wherein,

[0108] S30, use Lyapunov theorem to verify the existence of sliding mode and the stability of the system, and the Lyapunov function is designed as follows:

[0109]

[0110] For a first-order nonlinear differential inequality:

[0111] ​

[0112] where m>0, 0<n<1, V(x) is a Lyapunov function about state x, the function V(x) converges to the origin from any initial condition V(x(0))=V(0) in finite time t, and the finite time t is:

[0113]

[0114] Therefore, in the above formula, when η>(k2+λ·k ！ )·|θ ！ |, the condition of Lyapunov function stability is met, and the system motion point reaches the sliding mode surface s=0 at any position within the finite time t>T0.

[0115] Through the above mathematical derivation, it can be concluded that the integral terminal sliding mode controller of the GPI observer based on the Boost circuit model meets the stability requirement, can realize stable voltage output, and further realizes the purpose of maximum power point tracking.

[0116] The integral terminal sliding mode control method based on the GPI observer is applied to the maximum power point tracking of a photovoltaic system. Uncertain parameters in the photovoltaic system are estimated, replacing the classical sliding mode function.

[0117] After the introduction of the nonlinear term in the terminal sliding mode function, the singularity problem of the terminal sliding mode function can be solved, and the integral term can eliminate the steady-state error when the system is subjected to external disturbance.

[0118] Referring to Figure 4 and Figure 5 The system diagram and the circuit principle diagram for the application of the present application to track the maximum power point of photovoltaic power generation include a 100W solar photovoltaic panel 40, a 1000W iodine tungsten lamp 50, a sampling panel 30, a DSP 10 as a 28069 minimum system panel, a 100-ohm variable resistor 60, and a Boost power panel 20. In terms of function, the 1000W iodine tungsten lamp 50 simulates sunlight, the 100W solar photovoltaic panel 40 outputs current and voltage as a photovoltaic component, the sampling panel 30 can collect the voltage and current output by the photovoltaic cell, the DSP 10 can complete the MPPT method and adjust the pulse modulation of the Boost power panel 20, in order to ensure that the photovoltaic panel has a better use in power generation efficiency, the Boost circuit is selected to realize the maximum power point tracking, and the 100-ohm variable resistor 60 can be directly connected with the photovoltaic panel 40, and the maximum power point at the time can be estimated by changing the resistance value. Figure 5 In (a), the Boost circuit is selected as the conversion circuit of the MPPT controller, R is a load resistor, C is a capacitor, L is an inductor, i L is an inductor current, V Cis the capacitor voltage, V i is the input voltage, V O is the output voltage. When the switch is closed, Figure 5 In (b), the inductor L will pass V i Energy is stored, and the capacitor C discharges to the load R. As time goes by, the voltage across the capacitor decreases. Figure 5 In (c), the inductor L discharges, releasing energy to supply power to the load. The current i L As time goes by, the voltage across capacitor C increases.

[0119] Next, two experimental examples will be used to illustrate the superiority of the present invention over existing control algorithms in photovoltaic system maximum power point tracking. In the experiment, we choose the conventional sliding mode control algorithm SMC as the control group. Figure 6 The MPPT controller shown is based on a common SMC. Figure 7 The figure shows an MPPT controller based on GPI-ITSMC (integrated terminal sliding mode control). Taking the ordinary SMC controller as the control group, it can be seen that the output voltage and output power jitter of the MPPT controller with GPI-ITSMC are reduced, indicating that the MPPT controller based on GPI-ITSMC can better suppress output jitter; Figure 8 and Figure 9 As shown in the figure, when the maximum power point of the photovoltaic panel changes, the MPPT controller based on GPI-ITSMC converges faster and has smaller voltage and power overshoot values ​​than the MPPT controller based on ordinary SMC, indicating that the MPPT controller based on GPI-ITSMC can better adapt to changes in input conditions.

[0120] In summary, the MPPT controller based on GPI-ITSMC is capable of achieving smooth, stable, and fast-converging MPPT control and improving the conversion efficiency of light energy.

[0121] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A GPI observer-based integral terminal sliding mode control MPPT method, characterized in that, The method comprises the following steps: S10, analyzing the equivalent Boost circuit topology of a photovoltaic system, establishing a mathematical model of the system, and obtaining the output state equation of the converter; S20, introducing proportional integral control to estimate the system state, designing a terminal sliding mode function, and constructing a sliding mode controller according to the mathematical model in S10; S30, verifying the existence of the sliding mode dynamics and the stability of the system according to the sliding mode controller in S20 by using the Lyapunov stability theorem; In S10, the equivalent Boost circuit topology of a photovoltaic system is analyzed, and a mathematical model is established, including analyzing the working state of the Boost circuit switch in two states, and the mathematical model is as follows: Wherein, i L is the inductance current, V C is the capacitance voltage, V i is the input voltage, R is the load resistance value, C is the capacitance value, L is the inductance value, μ is the control law, which is macroscopically expressed as the duty cycle of the control signal; S20 comprises the following steps: S21, introducing a terminal sliding surface, which is determined by the initial state and the target state of the system, and designing an integral terminal sliding mode function, which is as follows: Wherein, x1 and x2 are state variables, λ1 and λ2 are parameters of the integral terminal sliding mode function, and are both constants greater than 0, and q1>q2 are positive odd numbers; The initial value of the system tracking error integral term is set as follows: S22, referring to the second-order dynamic mathematical model of the Boost circuit, expanding it into a third-order state equation: S23, designing the ESO observer equation of the system: wherein x1, x2, x3 are state variables, d represents the total disturbance of the system, respectively represent the first derivative of x1, x2, x3, represents the first derivative of d; And on the basis of the ESO observer, the GPI observer equation of the system can be established: wherein c1, c2 and c3 represent gains of the ESO observer, w1, w2, w3 represent the estimated values of the state variables x1, x2, x3, respectively, represent the first order derivatives of w1, w2, w3, respectively; S24, the estimation error expression of the GPI observer is defined as follows: where k1, k2, k3, and k4 represent the gain of the GPI observer, respectively represent the estimated values of the state variables x1, x2, x3, x4. Wherein, θ1, θ2, θ3 and θ4 represent error variables; The GPI observer is as follows: Converted into matrix form: Define the matrix as follows: The characteristic equation of the matrix A is as follows: S25, designing the sliding mode function s of the system: where E is a fourth-order identity matrix, and it is known that k1+1 / RC>0, k1 / RC>0, k4>0, and is bounded, thus the poles of the system are always in the left half plane, so the GPI observer of the Boost circuit is stable; Design the control law u as follows: For a first-order nonlinear differential inequality: wherein η is a constant greater than 0, wherein The S30, using Lyapunov theorem verifies the existence of sliding mode and stability of the system, and designs Lyapunov function formula as follows: Obtained Wherein, m>0, 0<n<1, for x∈R, V(x) is a Lyapunov function about the state x, and the function V(x) converges to the origin from any initial condition V(x(0))=V(0) in a finite time, and this finite time t is as follows: ​ Therefore, in the above equation, when η > (k2+ λ·k1)·|θ1|, the system is stable. The condition of Lyapunov function stability is met, and the system motion point reaches the sliding mode surface s = 0 at any position within a finite time t > T0.

Images