A photovoltaic grid-connected inverter control method based on sliding mode control

Abstract

The application belongs to the field of power systems, and discloses a photovoltaic grid-connected inverter control method based on a sliding mode control. The method comprises the following steps: firstly, selecting an error and an integral thereof to construct a sliding mode surface, so as to ensure that the system has robustness in the whole operation process; secondly, a variable exponent reaching law is adopted in a voltage outer loop, a variable speed term is introduced to adaptively adjust the convergence speed of the system, a hyperbolic tangent function is introduced to make the switching function continuous and weaken the system chattering; the current inner loop is combined with a super-spiral algorithm to transfer the high-frequency chattering signal in the traditional sliding mode to a high-order derivative, so that the output control signal is continuous, thereby the chattering is weakened; and an active damping method is adopted to suppress the resonance peak generated by the filter. Finally, through Matlab / Simulink simulation analysis, it is shown that under the condition of system parameter change and external factor influence, the control method can make the system quickly reach a steady state, effectively reduce the grid-connected current harmonic distortion, enhance the robustness of the system, and prove the effectiveness and feasibility of the control method.

Description

Technical Field

[0001] This invention belongs to the field of power systems, specifically a control method for photovoltaic grid-connected inverters based on sliding mode control. Background Technology

[0002] As the core equipment of a photovoltaic (PV) grid-connected system, the performance of the grid-connected inverter is closely related to the overall system efficiency. To obtain high-quality grid-connected current and reduce harmonic distortion, scholars both domestically and internationally have conducted extensive research on inverter control. LCL (Limited-Low Collision Cable) filters have advantages over L-type filters, such as smaller size and better frequency suppression performance; however, as third-order filters, their inherent resonance can decrease system stability. Some studies have addressed the resonance spike problem by connecting a resistor in series with the filter capacitor, increasing system losses. Other studies have employed active damping methods, which do not add any components, saving system costs.

[0003] Grid-connected inverters typically employ PI control, quasi-PR control, and repetitive control. The paper "Simulation Study of Voltage and Current Dual Closed-Loop Control of Grid-Connected Inverter for Photovoltaic Power Generation System" uses PI control, achieving satisfactory dynamic performance, but the grid-connected current THD is relatively high. The paper "Quasi-PR Control of Three-Phase Photovoltaic Grid-Connected Inverter Using LCL Filter" uses quasi-PR control, exhibiting fast dynamic response and strong robustness; however, the system's dynamic performance is affected by its own bandwidth, decreasing with decreasing bandwidth. The paper "Research on Repetitive Control Based on Grid-Connected Current of LCL Photovoltaic Inverter" uses repetitive control, reducing the grid-connected current THD, but its dynamic performance is poor and affected by periodic delay. While these controls are simple to implement and easy to design, their robustness and stability are difficult to guarantee when influenced by external factors and uncertainties.

[0004] Sliding mode control (SMC) is minimally affected by changes in system parameters, demonstrating its strong robustness and excellent dynamic performance, thus attracting considerable attention. Its motion process includes approaching and sliding motions, but it is robust only in the sliding mode. Since SMC is constantly switching, chattering inevitably occurs, leading to system oscillations. Higher-order sliding mode control, due to its simplicity, robustness, and ability to effectively suppress chattering, is a novel control method for addressing sliding mode chattering.

[0005] In summary, this paper proposes an improved dual-loop sliding mode control (hereinafter referred to as "improved SMC") method for LCL-type photovoltaic grid-connected inverters, taking into account both robustness and stability. Summary of the Invention

[0006] To address the issue that PI control in LCL-type photovoltaic grid-connected inverters fails to achieve ideal dynamic characteristics and robustness, this invention provides a control method for photovoltaic grid-connected inverters based on sliding mode control. First, a sliding mode surface is constructed by selecting the error and its integral to eliminate steady-state errors, enabling global robustness of the system. Second, sliding mode control is designed in the voltage outer loop using a variable exponential reaching law; the current inner loop employs super-spiral sliding mode control (STC) and uses active damping to suppress resonance. Then, the stability of the photovoltaic grid-connected system is proven using Lyapunov functions. Finally, simulation analysis verifies the effectiveness of the proposed method.

[0007] To achieve the above objectives, the present invention employs the following technical solutions:

[0008] A control method for a photovoltaic grid-connected inverter based on sliding mode control includes the following steps:

[0009] Step 1: Select the error and its integral to construct the sliding mode surfaces of the voltage outer loop and the current inner loop, and eliminate the steady-state error by selecting appropriate initial values ​​for the integral, so that the system can achieve global robustness;

[0010] Step 2: The voltage outer loop adopts a variable exponential reaching law, introduces a variable speed term, adaptively adjusts the convergence speed of the photovoltaic grid-connected system, and introduces a hyperbolic tangent function to make the switching function continuous and reduce system chattering; the current inner loop combines a super-spiral algorithm to transfer the high-frequency chattering signal in the traditional sliding mode to the higher-order derivative, making the output control signal continuous, thereby reducing chattering; and an active damping method is used to suppress the resonance spikes generated by the filter.

[0011] Step 3: Use the Lyapunov function to prove the stability of the photovoltaic grid-connected system.

[0012] Furthermore, the specific process of selecting the error and its integral to construct the voltage outer ring sliding mode surface in step 1, and eliminating the steady-state error by selecting a suitable initial value for the integral, is as follows:

[0013] The voltage tracking error is defined as:

[0014]

[0015] In the formula, u dc The voltage across the DC-side capacitor is... This is a reference value for the voltage across the DC-side capacitor;

[0016] The sliding surface is constructed by selecting the error and its integral, and its expression is as follows:

[0017]

[0018] In the formula, λ is the control gain, which is greater than zero, and t is the running time;

[0019] The initial value for integration is chosen as:

[0020]

[0021] In the formula: e(0) represents the value of the voltage error at zero time.

[0022] Furthermore, the specific process of selecting the error and its integral to construct the inner current sliding mode surface in step 1, and eliminating the steady-state error by selecting a suitable initial value for the integral, is as follows:

[0023] Define the current error as:

[0024]

[0025] In the formula, e1 and e2 are the d-axis and q-axis current errors, respectively, i d and i q These are the three-phase grid-connected currents i a i b i c The current components on the d and q axes are obtained by Clark and Park transforms. This is the reference value for the d-axis current. This is the reference value for the q-axis current;

[0026] The sliding surface is constructed by selecting the error and its integral as follows:

[0027]

[0028] In the formula: s1 and s2 are the sliding surfaces constructed by the d-axis and q-axis current errors, respectively; λ1 is the control gain, which is greater than zero; and t is the running time.

[0029] The initial value for integration is chosen as:

[0030]

[0031] In the formula: e1(0) and e2(0) represent the values ​​of the d-axis and q-axis current errors at time zero.

[0032] Furthermore, in step 2, the voltage outer loop adopts a variable exponential reaching law, introduces a variable speed term, adaptively adjusts the convergence speed of the system, and introduces a hyperbolic tangent function to make the switching function continuous, thereby reducing system chattering. The specific process is as follows:

[0033] Step 2.1 proposes a variable exponential reaching law, the expression of which is:

[0034]

[0035] In the formula: ||X|| PLet be the p-order norm of variable X; s be the sliding surface function; ε and q be gain parameters, both greater than zero; the reaching law consists of two terms, -ε||X|| P sgn(s) is the variable term, and -qs is the exponential term; initially, the state variable is far from the sliding surface, i.e., approaching motion, and the system moves at both variable and exponential rates. The system velocity changes with ||X|| P As |X|| increases, the time for the system to reach the sliding surface decreases; the state variable approaches the sliding surface, i.e., sliding motion, and -qs gradually decreases until it becomes zero. At this point, the variable term dominates, and the system velocity increases with ||X||. P The coefficient of sgn(s) is reduced until it becomes zero, thus suppressing chattering.

[0036] Step 2.2 To further suppress chattering, sgn(s) is smoothed by replacing it with the hyperbolic tangent function; its expression is:

[0037]

[0038] Compared to sgn(s), it is a continuous function that varies between -1 and 1, and its slope can vary with the constant ε. The larger ε is, the smaller the slope and the smoother the curve; the larger ε is, the closer the curve is to sgn(s); where e is the voltage tracking error.

[0039] Step 2.3 Controller Design

[0040] Combining equation (9), differentiating equation (2) yields equation (10):

[0041]

[0042]

[0043]

[0044] In the formula, u dc C is the voltage across the DC-side capacitor. dc For DC side capacitor, i PV For the output current of the photovoltaic cell, u gd i represents the grid-side voltage component on the d-axis. gd The d-axis component of the grid-side current. The sliding surface function s constructed for the voltage error, the voltage error e, and the voltage u across the DC-side capacitor are respectively. dc The derivative of λ, where λ is the control gain and is greater than zero;

[0045] Combine equations (7), (8), and (10), and let... The control equations for the outer voltage loop can be obtained as follows:

[0046]

[0047] Furthermore, in step 2, the current inner loop combined with the superspiral algorithm transfers the high-frequency chattering signal in traditional sliding mode to higher-order derivatives, making the output control signal continuous and thus reducing chattering; and the specific process of using active damping to suppress the resonant spikes generated by the filter is as follows:

[0048] Superspiral sliding mode control is a second-order sliding mode control designed using a superspiral algorithm. Compared to the traditional exponential reaching law, the superspiral algorithm places the switching term sgn(s) in a higher-order derivative, thereby making the control signal continuous and achieving the effect of suppressing chattering. Its expression is:

[0049]

[0050] In the formula: α and β are adjustable control parameters, and α and β > 0; s is the sliding surface function. From the above formula, it can be seen that the superspiral algorithm consists of two parts, the first part being u... s1 It is a continuous sliding surface function, the second part u s2 This involves integrating the sliding mode surface over time, transferring sgn(s) into the first derivative of the control law, thus no longer directly affecting the control law. This makes the output control signal continuous, thereby suppressing chattering.

[0051] The control law is selected as equivalent control combined with the superspiral algorithm. Therefore, the S in the state equation of the photovoltaic grid-connected inverter in the dq coordinate system is... d S q It can be represented as:

[0052]

[0053] In the formula: u eq1 u eq2 The equivalent control laws for the d-axis and q-axis are respectively, u st1 u st2 Superspiral algorithms for the d-axis and q-axis respectively;

[0054] The state equation of a photovoltaic grid-connected inverter in the dq coordinate system is:

[0055]

[0056] In the formula: L = L1 + L2, where L1 is the inverter-side inductance and L2 is the grid-side inductance; R = R1 + R2, where R1 and R2 are the parasitic resistances of inductors L1 and L2, respectively; u dc i is the voltage across the DC-side capacitor. d i q u gd u gq S dS q The components of the grid-side current, grid-side voltage, and switching function on the d and q axes are given, where ω is the angular frequency.

[0057] Combining equation (14) and differentiating equation (5), we obtain equation (15):

[0058]

[0059]

[0060] In the formula, The derivatives of the sliding surface functions s1 and s2, constructed from the errors of the d-axis current and q-axis current, are respectively. These are the derivatives of the d-axis current and q-axis current errors, respectively. These are the derivatives of the d-axis current and the q-axis current, respectively.

[0061] make The equivalent control law can be obtained as follows:

[0062]

[0063] Combining equations (12), (13), and (16), the governing equation for the inner current loop can be obtained as follows:

[0064]

[0065] Furthermore, in step 3, proving the effectiveness of the photovoltaic grid-connected system using the Lyapunov function specifically involves:

[0066] For the voltage outer loop: define the Lyapunov function as V = 0.5s 2 Differentiating it, we get:

[0067]

[0068] In the formula: ε>0, q>0, therefore This proves that the system is operating stably.

[0069] For the inner current loop: define the Lyapunov function as V = 0.5s T Taking the derivative of s, we get:

[0070]

[0071] In the formula: α and β take positive values. Therefore, the system is stable.

[0072] Compared with the prior art, the present invention has the following advantages:

[0073] 1) This invention constructs a sliding mode surface by selecting the error and its integral, and eliminates steady-state error by selecting appropriate initial integral values. This overcomes the limitation of traditional SMCs, which are only robust in the sliding mode, making the system robust throughout the entire process. The voltage outer loop control uses a variable exponential reaching law to reduce chattering and allow the system's convergence speed to be adaptively adjusted. The current inner loop control combines a super-spiral algorithm to integrate discontinuous switching terms, making the output control quantity continuous and reducing chattering.

[0074] 2) The improved SMC proposed in this invention greatly improves the grid-connected current quality of the system; it can quickly recover stability with small fluctuations under the conditions of changes in system parameters and light intensity, demonstrating strong robustness. Attached Figure Description

[0075] Figure 1 This is a structural diagram of an LCL-type three-phase photovoltaic inverter grid-connected system.

[0076] Figure 2 This is a control block diagram for a photovoltaic grid-connected system.

[0077] Figure 3 This paper compares the traditional exponential reaching law with the variable exponential reaching law and the superspiral algorithm control law of this invention.

[0078] Figure 4 The waveforms of phase A grid-connected voltage and current under the improved SMC.

[0079] Figure 5 Harmonic analysis of grid-connected current under three control methods: (a) PI control; (b) traditional SMC; (c) improved SMC.

[0080] Figure 6 To change the grid-connected current of phase A and the reactive power of the system after changing the grid-side inductance; (a) is PI control; (b) is traditional SMC; (c) is improved SMC.

[0081] Figure 7 (a) is for grid-connected current harmonic analysis; (b) is for PI control; (c) is for traditional SMC; (d) is for improved SMC.

[0082] Figure 8 This is the DC bus voltage waveform. Detailed Implementation

[0083] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings. It should be noted that those skilled in the art can make several modifications and improvements without departing from the principle of the present invention, and these should also be considered to fall within the protection scope of the present invention.

[0084] 1. Topology and Mathematical Model of Three-Phase Photovoltaic Grid-Connected Inverter

[0085] The photovoltaic grid-connected system is a two-pole type. The Boost circuit uses MPPT control, and the DC / AC inverter circuit uses a modified SMC; an LCL filter is used for filtering. Its topology is as follows: Figure 1 As shown. Figure 1 In the diagram, D represents a diode; i PV For photovoltaic output current; i C i is the capacitor current; inv C is the current flowing into the inverter. dc V0 to V6 are the DC-side capacitors; V0 to V6 are the IGBT switching transistors; L1 is the inverter-side inductor; C is the filter capacitor; L2 is the grid-side inductor; R1 and R2 are the parasitic resistances of inductors L1 and L2, respectively; u g This is the grid-side voltage.

[0086] The state equation of the photovoltaic grid-connected inverter in the dq coordinate system is shown in equation (1):

[0087]

[0088] In the formula: L = L1 + L2; R = R1 + R2; u dc i is the voltage across the DC-side capacitor. d i q u gd u gq S d S q These represent the components of grid-side current, grid-side voltage, and switching function on the d and q axes.

[0089] The active and reactive power on the grid side are as follows:

[0090]

[0091] In the formula: P g Q represents active power. g This refers to reactive power.

[0092] Considering the inverter in ideal dq coordinates, the grid voltage u gq =0, then the d-axis component i of the current gd P can be adjusted g The q-axis component of the current i gq Q can be adjusted g Ignoring inverter energy losses, the power balance equation is as follows:

[0093]

[0094] According to equation (3), Kirchhoff's current law (KCL) provides its mathematical model as follows:

[0095]

[0096] 2. Improve the design of the reaching law

[0097] 2.1 Traditional Exponential Approach Law

[0098] Academician Gao and others proposed the concept of the reaching law and designed an exponential reaching law, which has been widely used. Its expression is:

[0099] u'=-αsgn(s)-βs (5)

[0100] In the formula: s is the sliding surface function; α and β are gain parameters, and are greater than zero.

[0101] As can be seen from equation (5), the traditional exponential approach law contains a high-frequency switching discontinuity term αsgn(s). The presence of αsgn(s) leads to discontinuous control input, which is the main reason for chattering.

[0102] 2.2 Variable Exponential Approach Law

[0103] This invention proposes a variable exponential reaching law to reduce the chattering present in exponential reaching laws. Its expression is:

[0104] u=-ε||X|| p sgn(s)-qs (6)

[0105] In the formula: ||X|| P Let be the p-order norm of variable X; ε and q are gain parameters, and are greater than zero.

[0106] This convergence law consists of two terms, -ε||X|| P sgn(s) is the variable term, and -qs is the exponential term. Initially, the state variable is far from the sliding surface (i.e., approaching motion), and the system moves at both variable and exponential rates. The system velocity changes with ||X||. P As ||X|| increases, the time for the system to reach the sliding surface decreases; as the state variable approaches the sliding surface (i.e., sliding motion), -qs gradually decreases until it becomes zero. At this point, the variable term dominates, and the system velocity increases with ||X||. P The coefficient of sgn(s) decreases until it becomes zero, i.e., the coefficient of sgn(s) is zero, and chattering is suppressed.

[0107] To further suppress chattering, sgn(s) is smoothed by replacing it with the hyperbolic tangent function. Its expression is:

[0108]

[0109] Compared to sgn(s), it is a continuous function that varies between -1 and 1, and its slope can vary with the constant ε. The larger ε is, the smaller the slope and the smoother the curve; the larger ε is, the closer the curve is to sgn(s).

[0110] 2.3 Superspiral Algorithm

[0111] STC is a second-order sliding mode control designed using a super-twisting algorithm. Compared to the traditional exponential reaching law, super-twisting places the switching term sgn(s) in a higher-order derivative, thereby making the control signal continuous and suppressing chattering. Its expression is:

[0112]

[0113] In the formula: α and β are adjustable control parameters, and α and β > 0. As can be seen from equation (8), super-twisting includes two parts, the first part u s1 It is a continuous sliding surface function, the second part u s2 It is a sliding mode surface integral over time, which transfers sgn(s) from u to the first derivative of u, so that it no longer directly affects the control law u, making the output control signal continuous, thereby suppressing chattering.

[0114] 3. Control Strategy Analysis

[0115] SMC is essentially a type of variable structure control. First, a sliding surface is constructed. Then, a reaching law is designed to define the system's trajectory, allowing the system to move along the trajectory to and from the sliding surface. The sliding surface is designed based on the system's final state and is unaffected by system parameters or external factors.

[0116] The control method proposed in this invention employs sliding mode control based on a variable exponential reaching law in the outer voltage loop to maintain DC bus voltage stability; the inner current loop uses STC to ensure power quality of the grid-connected current. The control model is as follows: Figure 2 As shown.

[0117] Figure 2 In the middle, the detected three-phase grid-connected current i a i b i c The current components i on the d and q axes are obtained after Clark and Park transforms. d and i q d-axis reference value Let the voltage outer loop be the output signal through the SMC, and let the reference value of the q-axis be... Setting it to 0 ensures a power factor of 1 during grid connection. The current error is converted to a voltage signal u via the STC of the inner current loop. d uq The voltage components u on the α and β axes are obtained by inverse Park and Clark transforms. α u β Simultaneously, feedback of the filter capacitor current is introduced, and SVPWM modulation is adopted.

[0118] 3.1 Design of Voltage Outer Loop Sliding Mode Controller

[0119] The voltage tracking error is defined as:

[0120]

[0121] In the formula, u dc The voltage across the DC-side capacitor is... This is a reference value for the voltage across the DC-side capacitor;

[0122] The sliding surface is constructed by selecting the error and its integral, and its expression is as follows:

[0123]

[0124] In the formula, λ is the control gain, which is greater than zero, and t is the running time;

[0125] By selecting an appropriate initial value for the integral, the system can move directly during the sliding phase, exhibiting global robustness. The initial value for the integral is:

[0126]

[0127] In the formula: λ is the gain coefficient, and λ>0; e(0) represents the value of the error at time zero.

[0128] Combining equation (4), taking the derivative of equation (10) yields:

[0129]

[0130] Combine equations (6), (7), and (12), and let... The control equations for the outer voltage loop can be obtained as follows:

[0131]

[0132] Define the Lyapunov function as V = 0.5s 2 Differentiating it, we get:

[0133]

[0134] In the formula: ε>0, q>0, therefore This proves that the system is operating stably.

[0135] 3.2 Design of the Inner Loop Sliding Mode Controller

[0136] Define the current error as:

[0137]

[0138] In the formula, e1 and e2 are the d-axis and q-axis current errors, respectively, i d and i q These are the three-phase grid-connected currents i a i b i c The current components on the d and q axes are obtained by Clark and Park transforms. This is the reference value for the d-axis current. This is the reference value for the q-axis current;

[0139] The integral sliding surface is designed as follows:

[0140]

[0141] In the formula: s1 and s2 are the sliding surfaces constructed by the d-axis and q-axis current errors, respectively; λ1 is the control gain, which is greater than zero; and t is the running time.

[0142] The initial value for integration is chosen as:

[0143]

[0144] In the formula: e1(0) and e2(0) represent the values ​​of the d-axis and q-axis current errors at time zero.

[0145] The control law is selected as equivalent control combined with the superspiral algorithm, therefore S in equation (1) d S q It can be represented as:

[0146]

[0147] Combining equation (1) and differentiating equation (16), we get:

[0148]

[0149] make The equivalent control law can be obtained as follows:

[0150]

[0151] Combining equations (8), (18), and (20), the governing equation for the inner current loop can be obtained as follows:

[0152]

[0153] Among them, u d =u dc Sd u q =u dc S q The two control variables u d and u q The voltage components u on the α and β axes are obtained by inverse Park and Clark transforms. α u β Simultaneously, feedback from the filter capacitor current is introduced, and the control pulse signal of the inverter is finally obtained through SVPWM.

[0154] Define the Lyapunov function as V = 0.5s T Taking the derivative of s, we get:

[0155]

[0156] α and β take positive values. Therefore, the system is stable.

[0157] 4. Simulation Analysis

[0158] Based on the voltage and current loop sliding mode controllers designed in step 3, models were built on the Matlab / Simulink simulation platform. The inverters employed PI control, sliding mode control based on the traditional exponential reaching law (hereinafter referred to as "traditional SMC"), and an improved SMC, respectively. Key system parameters: DC side reference voltage. The effective value of the three-phase grid voltage is 220V; the inverter-side inductance L1 = 2mH; the filter capacitor C = 50μF; and the grid-side inductance L2 = 0.01mH.

[0159] 4.1 Booming Simulation Comparison Experiment

[0160] Figure 3 This is a comparison chart of the traditional exponential reaching law and the variable exponential reaching law and STC control law of this invention.

[0161] from Figure 3 It can be seen that the traditional exponential control law exhibits chattering due to the presence of sgn(s). However, in the variable exponential approaching law, the gain parameter of sgn(s) is zero, thus suppressing chattering. The STC control law places sgn(s) in the first derivative, so it no longer directly affects the control law u, making the output control signal continuous, thereby suppressing chattering.

[0162] 4.2 System Control Performance Comparison Experiment

[0163] Operating Condition 1: Ideal power grid conditions. Harmonic analysis is performed on the A-phase grid-connected current under three control conditions. Figure 4 To illustrate the grid-connected voltage and current waveforms of phase A under the improved SMC, Figure 5 The graph shows the harmonic analysis of the grid-connected current, and Table 1 shows the comparison of the current harmonic distortion rate.

[0164] Table 1 Comparison of Harmonic Distortion Rates of Grid-Connected Current

[0165]

[0166] Depend on Figure 4 It can be seen that under the improved SMC, the grid-connected current reaches a steady state within half a cycle, maintaining consistency with the grid voltage frequency and phase, thus meeting the grid connection requirements; Figure 5 As shown in Table 1, the grid-connected current harmonic distortion rate is significantly reduced under the improved SMC, the output quality is greatly improved, and it is more conducive to the stable operation of the system.

[0167] Operating Condition 2: Change in system parameters (grid-side inductance value). The grid-side inductance value is changed from 0.01mH to 0.005mH at 0.3s. Figure 6 The waveforms of the grid-connected current and system reactive power of phase A under three control conditions are shown. Figure 7 The grid-connected current harmonic analysis diagram is shown in Table 2, which compares the current harmonic distortion rates.

[0168] Table 2 Comparison of harmonic distortion rates of grid-connected current (with changes in grid-side inductance)

[0169]

[0170] Depend on Figure 6 , Figure 7 As shown in Table 2, when the grid-side inductance value changes, the grid current under PI control exhibits significant distortion, reactive power fluctuates greatly, and the current THD exceeds 5%, failing to meet standard requirements. Under both traditional and improved SMCs, the grid current and reactive power show almost no fluctuation, but the improved SMC exhibits lower current harmonic distortion and a smoother waveform. This demonstrates that the improved SMC is less sensitive to changes in system parameters and possesses strong robustness.

[0171] Operating Condition 3: Maintaining a constant temperature of 25℃, the light intensity increases from 800W / m² in 0.5 seconds. 2 Increased to 1000W / m 2 . Figure 8 Table 3 shows the DC bus voltage waveforms under three different control conditions, and compares the dynamic performance of the DC bus voltage.

[0172] Table 3 Comparison of DC bus voltage dynamic performance

[0173]

[0174]

[0175] Depend on Figure 8As shown in Table 3, the improved SMC has the shortest settling time and the smallest overshoot. When there are sudden changes in light intensity, using the improved SMC can effectively reduce DC bus voltage overshoot while improving dynamic response.

Claims

1. A control method for a photovoltaic grid-connected inverter based on sliding mode control, characterized in that: Includes the following steps: Step 1: Select the error and its integral to construct the sliding mode surfaces of the voltage outer loop and the current inner loop, and eliminate the steady-state error by selecting appropriate initial values ​​for the integral, so that the system can achieve global robustness; Step 2: The voltage outer loop adopts a variable exponential reaching law, introduces a variable speed term, adaptively adjusts the convergence speed of the photovoltaic grid-connected system, and introduces a hyperbolic tangent function to make the switching function continuous and reduce system chattering; the current inner loop combines a super-spiral algorithm to transfer the high-frequency chattering signal in the traditional sliding mode to the higher-order derivative, making the output control signal continuous, thereby reducing chattering; and an active damping method is used to suppress the resonance spikes generated by the filter. Step 3: Use Lyapunov functions to prove the stability of the photovoltaic grid-connected system; In step 2, the voltage outer loop adopts a variable exponential reaching law, introduces a variable speed term, adaptively adjusts the convergence speed of the system, and introduces a hyperbolic tangent function to make the switching function continuous, thereby reducing system chattering. The specific process is as follows: Step 2.1 proposes a variable exponential reaching law, the expression of which is: (7) In the formula: ||X|| P Let be the p-order norm of variable X; s be the sliding surface function; ε and q are gain parameters, and are greater than zero; the reaching law consists of two terms, -ε||X|| P sgn(s) is the variable term, and -qs is the exponential term; initially, the state variable is far from the sliding surface, i.e., approaching motion, and the system moves at both variable and exponential rates. The system velocity changes with ||X|| P As |X|| increases, the time for the system to reach the sliding surface decreases; the state variable approaches the sliding surface, i.e., sliding motion, and -qs gradually decreases until it becomes zero. At this point, the variable term dominates, and the system velocity increases with ||X||. P The coefficient of sgn(s) is reduced until it becomes zero, thus suppressing chattering. Step 2.2 To further suppress chattering, sgn(s) is smoothed by replacing it with the hyperbolic tangent function; Its expression is: (8) Compared to sgn(s), it is a continuous function varying between -1 and 1, and its slope can vary with the constant ε. The larger ε is, the smaller the slope and the smoother the curve; the larger ε is, the closer the curve is to sgn(s); where, For voltage tracking error; Step 2.3 Controller Design Combining equation (9), and differentiating equation (2), we obtain equation (10): （9） (2) (10) In the formula, The voltage across the DC-side capacitor is... For DC side capacitors, For the output current of photovoltaic cells, This represents the d-axis component of the grid-side voltage. The d-axis component of the grid-side current. , , The sliding surface function s, voltage error e, and voltage across the DC-side capacitor are respectively constructed for the voltage error. The derivative of To control the gain, it must be greater than zero; Combine equations (7), (8), and (10), and let... The governing equations for the outer voltage loop can be obtained as follows: (11)。 2. The photovoltaic grid-connected inverter control method based on sliding mode control according to claim 1, characterized in that, The specific process of selecting the error and its integral to construct the voltage outer ring sliding mode surface in step 1, and eliminating the steady-state error by selecting a suitable initial value for the integral, is as follows: The voltage tracking error is defined as: (1) In the formula, The voltage across the DC-side capacitor is... This is a reference value for the voltage across the DC-side capacitor; The sliding surface is constructed by selecting the error and its integral, and its expression is as follows: (2) In the formula, To control the gain, it must be greater than zero, and t is the running time; The initial value for integration is chosen as: (3) In the formula: e(0) represents the value of the voltage error at zero time.

3. The photovoltaic grid-connected inverter control method based on sliding mode control according to claim 1, characterized in that, The specific process of selecting the error and its integral to construct the inner current sliding mode surface in step 1, and eliminating the steady-state error by selecting a suitable initial value for the integral, is as follows: Define the current error as: (4) In the formula, and These represent the d-axis and q-axis current errors, respectively. and These are the three-phase grid-connected currents i a i b i c The current components on the d and q axes are obtained by Clark and Park transforms. This is the reference value for the d-axis current. This is the reference value for the q-axis current; The sliding surface is constructed by selecting the error and its integral as follows: (5) In the formula: , The sliding surfaces are constructed for the d-axis and q-axis current errors, respectively, where λ1 is the control gain and is greater than zero, and t is the running time. The initial value for integration is chosen as: (6) In the formula: , This represents the values ​​of the d-axis and q-axis current errors at time zero.

4. The photovoltaic grid-connected inverter control method based on sliding mode control according to claim 1, characterized in that, In step 2, the current inner loop combined with the super-spiral algorithm transfers the high-frequency chattering signal in traditional sliding mode to higher-order derivatives, making the output control signal continuous and thus reducing chattering; and the specific process of using active damping to suppress the resonant spikes generated by the filter is as follows: Superspiral sliding mode control is a second-order sliding mode control designed using a superspiral algorithm. Compared to the traditional exponential reaching law, the superspiral algorithm places the switching term sgn(s) in a higher-order derivative, thereby making the control signal continuous and achieving the effect of suppressing chattering. Its expression is: (12) In the formula: , It is an adjustable control parameter, and , , As shown in the equation above, the superspiral algorithm consists of two parts, the first part being u. s1 It is a continuous sliding surface function, the second part u s2 This involves integrating the sliding mode surface over time, transferring sgn(s) into the first derivative of the control law, thus no longer directly affecting the control law. This makes the output control signal continuous, thereby suppressing chattering. The control law is selected as equivalent control combined with the superspiral algorithm. Therefore, the S in the state equation of the photovoltaic grid-connected inverter in the dq coordinate system is... d S q It can be represented as: (13) In the formula: u eq1 u eq2 The equivalent control laws for the d-axis and q-axis are respectively, u st1 u st2 Superspiral algorithms for the d-axis and q-axis respectively; The state equation of a photovoltaic grid-connected inverter in the dq coordinate system is: (14) In the formula: L = L1 + L2, where L1 is the inverter-side inductance and L2 is the grid-side inductance; R = R1 + R2, where R1 and R2 are the parasitic resistances of inductors L1 and L2, respectively; u dc i is the voltage across the DC-side capacitor. d i q u gd u gq S d S q These represent the components of grid-side current, grid-side voltage, and switching function on the d and q axes. Angular frequency, Combining equation (14) and differentiating equation (5), we obtain equation (15): （5） (15) In the formula, , Sliding surface functions constructed for d-axis current and q-axis current errors, respectively. , The derivative of , These are the derivatives of the d-axis current and q-axis current errors, respectively. , These are the derivatives of the d-axis current and the q-axis current, respectively. make , The equivalent control law can be obtained as follows: (16) Combining equations (12), (13), and (16), the governing equation for the inner current loop can be obtained as follows: (17)。 5. The photovoltaic grid-connected inverter control method based on sliding mode control according to claim 1, characterized in that, Step 3, which uses the Lyapunov function to prove the effectiveness of the photovoltaic grid-connected system, specifically involves: For the outer voltage loop: define the Lyapunov function as V = 0.5s 2 Differentiating it, we get: (18) In the formula: ε>0, q>0, therefore A value less than 0 indicates that the system is in a stable operating state. For the inner current loop: define the Lyapunov function as V = 0.5s T Taking the derivative of s, we get: (19) In the formula: α and β take positive values. The value is less than 0, therefore the system is stable.

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