Grid-connected inverter active disturbance rejection control method based on variable gain superhelix observer

Abstract

The invention discloses a grid-connected inverter active-disturbance-rejection control method based on a variable-gain super-spiral observer, and the method comprises the steps: firstly, building a mathematical model of a three-phase grid-connected inverter, converting the mathematical model into a d-q rotating coordinate system, converting the mathematical model into a second-order active-disturbance-rejection normal form on this basis, and then carrying out the design of a super-spiral expansion state observer. Replacing a discontinuous switching item sign function in the super-spiral expansion state observer with a hyperbola function; secondly, a variable gain function changing in real time along with observation errors is designed to replace the linear gain of ST-ESO; and then introducing the combination of backstepping control and a terminal complementary sliding mode as a feedback controller. According to the method, the problems of relatively large DC bus voltage fluctuation, overlarge output current overshoot, long transient time, coupling between a d axis and a q axis and the like when the power of the three-phase grid-connected inverter is suddenly changed in a traditional PI control method are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics, and in particular relates to an auto-disturbance rejection control method of a grid-connected inverter based on a variable gain super-helical observer. Background Art

[0002] With the increasing attention paid to renewable energy around the world, clean energy such as solar energy and wind energy has been widely used. At the same time, in response to global climate change, countries have proposed dual carbon goals, namely achieving carbon peak and carbon neutrality, in order to reduce greenhouse gas emissions and promote sustainable development.

[0003] As the core equipment for energy conversion and distribution, the three-phase grid-connected inverter is responsible for converting direct current into alternating current to meet the needs of the power grid and power-consuming equipment. The optimization of its control technology is crucial to improving energy efficiency and system stability. Although existing control strategies such as proportional integral (PI) control and vector control can achieve precise control of the inverter to a certain extent, they may have problems such as slow response speed and insufficient control accuracy when facing rapidly changing loads and power grid environments. In addition, with the development of smart grids, the requirements for the flexibility and adaptability of inverter control strategies are becoming higher and higher. Improving the conversion efficiency of the inverter and reducing the system cost are important goals of the new energy power generation system. However, the existing control technology may be limited by factors such as hardware conditions and algorithm complexity in practical applications, making it difficult to achieve high efficiency and low cost at the same time. Therefore, it is necessary to continuously explore new control strategies and technical means to balance the relationship between system efficiency and cost. Summary of the invention

[0004] The purpose of the present invention is to provide a grid-connected inverter self-disturbance rejection control method based on a variable gain super-helical observer, which solves the problem that when a power mutation occurs in a three-phase grid-connected inverter, the DC bus voltage fluctuates greatly and there is coupling between the d and q axes in the traditional PI control method.

[0005] The technical solution adopted by the present invention is an auto-disturbance rejection control method for a grid-connected inverter based on a variable gain super-helical observer. First, a mathematical model of a three-phase grid-connected inverter is established and converted into a dq rotating coordinate system. On this basis, it is converted into a second-order auto-disturbance rejection paradigm. Then, a super-helical extended state observer is designed, and the discontinuous switching term sign function in the super-helical extended state observer is replaced by a hyperbolic function. Secondly, a variable gain function that changes in real time with the observation error is designed to replace the linear gain of the ST-ESO. Then, a backstepping control combined with a terminal complementary sliding mode is introduced as a feedback controller.

[0006] The present invention is also characterized in that:

[0007] Follow the steps below to implement it:

[0008] Step 1: Establish a mathematical model of the three-phase grid-connected inverter in the dq rotating coordinate system and convert it into a second-order active disturbance rejection paradigm;

[0009] Step 2: Controller design;

[0010] Step 2.1: Design of power outer loop controller;

[0011] Step 2.2: Design of current inner loop controller;

[0012] Step 2.2.1: Design of variable gain superhelical ESO;

[0013] Step 2.2.2: Design of backstepping complementary terminal sliding mode controller;

[0014] Step 3: Obtain the control output through the controller, use SPWM modulation to get the duty cycle, and apply the duty cycle to the control of the switch tube of the three-phase grid-connected inverter, thereby realizing the signal control of the three-phase grid-connected inverter.

[0015] Step 1 is specifically as follows:

[0016] During the grid-connected operation of the grid-connected inverter, the working states of the two switches in each bridge arm are complementary. Therefore, the switching function is defined as follows:

[0017]

[0018] In formula (1), j = a, b, c, representing the three phases a, b, and c of the AC power grid;

[0019] According to Kirchhoff's law, the voltage and current relationship equation of the grid-connected inverter in the abc three-phase stationary coordinate system is:

[0020]

[0021] In formula (2), u a 、u b 、u c is the three-phase voltage on the AC side of the three-phase grid-connected inverter; i sa 、i sb 、i sc is the three-phase current on the AC side; e a 、e b 、e c is the AC grid voltage; L is the filter inductance; C dc is the DC side capacitance; R is the line equivalent resistance parameter; i r is the DC side power supply current; u dc 、i C is the DC side capacitor voltage and current; s ka 、s kb 、skc They are the switch control signals of the three-phase bridge arms a, b and c respectively;

[0022] By performing Park transformation on equation (2), the mathematical model of the inverter in the dq coordinate system can be obtained as follows:

[0023]

[0024] In formula (3), ω is the angular frequency of the grid voltage; e d 、i d 、s d They are the grid voltage, current, and switching function of the d-axis, and the e-axis q 、i q 、s q are the grid voltage, current and switch function of the q axis respectively; L is the filter inductance; u dc 、i C is the DC side capacitor voltage and current.

[0025] Step 2.1 is as follows:

[0026] The main function of the power outer loop is to ensure power conservation during the grid connection process of the inverter and provide a reference value for the subsequent current inner loop. According to the instantaneous power theory, in order to make the three-phase grid-connected inverter close to the unity power factor grid connection, the reactive current is always equal to 0. Under the condition of balanced three-phase grid voltage, the instantaneous values ​​of active power P and reactive power Q on the grid side of the three-phase grid-connected inverter are expressed as:

[0027]

[0028] From formula (4), we know that through i d and i q Control P and Q separately to achieve independent regulation of active power and reactive power; transform equation (4) to ref , Q ref When given, the d and q axis current reference values ​​are directly obtained by calculation; however, in order to eliminate the steady-state error, the PI regulator is introduced. After the deviation between P, Q and the P, Q command values ​​is adjusted by PI, the active current reference value i is obtained based on the instantaneous power theory and the dynamic response of the system P and Q. dref and reactive current reference value i qref , as shown below:

[0029]

[0030] In formula (5), P ref , Q ref For given active power and reactive power reference values, i dref 、i qref is the inner loop reference value of d and q axis current, kdp , k di is the d-axis PI adjustment parameter, k qp , k qi is the q-axis PI adjustment parameter.

[0031] Step 2.2.1 is as follows:

[0032] First, define the state variable d-axis current i d For x d1 , state variable q-axis current i q For x q1 , from formula (3):

[0033]

[0034] In order to simplify the difficulty of controller design, the inner loop coupling terms and unmodeled parts of the current of the d and q axes and the internal and external disturbances of the inner loop are regarded as the total disturbance of the inner loop, and are represented by f d1 , f q1 It means that the derivative of formula (3) is converted into the ADRC paradigm as follows:

[0035]

[0036] In formula (7), b d , b q are the gains of the d-axis and q-axis control quantities respectively;

[0037] Definition b do , b qo is the estimated value of the d and q axis control gain, let Transform formula (7) into:

[0038]

[0039] In formula (8), f d =(b d -b do )s d +f d1 , f q =(b q -b qo )s q +f q1 , b do , b qo is the estimated value of the d and q axis control quantity gain;

[0040] The lumped disturbance f d 、f q Expand to new state variables z d3 、z q3 , then the superhelical expansion state observer can be designed as follows:

[0041]

[0042] In formula (9), z d1 For x d1 The estimated value of z q1 For x q1 The estimated value of z d2 , z q2 is the estimated value of the derivative, x d1 For x q1 The estimated value of the derivative; e d1 is the difference between the observed value and the actual value of the d-axis, e q1 is the difference between the observed value and the actual value of the q axis; z d3 is the total disturbance f including d-axis coupling, internal disturbance and unmodeled part. d The estimated value of z q3 is the total disturbance f including the q-axis coupling term, internal disturbance and unmodeled part. q The estimated value of β d1 , β d2 , β d3 , β q1 , β q2 , β q3 is the observer gain. When the observation error e of the superhelical ESO is close to 0, the expression of the observer is consistent with that of the linear extended state observer. Therefore, the bandwidth method is used for tuning as follows:

[0043] The value conditions of β1, β2, β3 are: β1 = 3ω0, β2 = 3ω0 2 , β3=ω0 3 .

[0044] In order to reduce system chattering and improve the observation capability of the superhelical extended state observer to the total disturbance of the inner loop, a variable gain superhelical ESO is proposed, and the sign function of the discontinuous switching term in the superhelical extended state observer is replaced by a hyperbolic function; secondly, a variable gain function that changes in real time with the observation error is designed to replace the linear gain of the ST-ESO, so as to improve the observation capability of the disturbance;

[0045] The switching function sign expression is:

[0046]

[0047] It can be seen from formula (10) that the sign function is a discontinuous function. When the sign function sign is used as the switching function of the super-helical sliding mode expansion state observer, discontinuous switching control characteristics will be generated along with the observation error, resulting in chattering problems and affecting the observation accuracy of the system. Therefore, a smooth hyperbolic function F(e i) as the switching function of the observer.

[0048] Hyperbolic F(e i ) function is expressed as:

[0049]

[0050] The improved supercoil ESO expression is:

[0051]

[0052] In formula (12), z d1 For x d1 The improved estimate of the observer, z q1 For x q1 The improved estimate of the observer; d2 For x d1 The observer-improved estimate of the derivative, z q2 For x q1 The observer-improved estimate of the derivative; z d3 is the total disturbance f including coupling terms, internal disturbances and unmodeled parts. d The improved estimate of the observer, z q3 is the total disturbance f including coupling terms, internal disturbances and unmodeled parts. q The improved estimate of the observer; The improved variable gain function of the observer is as follows:

[0053]

[0054] The expression of variable gain L(t) is:

[0055]

[0056] In formula (14), η i , σ are both adjustable positive real numbers, and σ determines the observation accuracy of the improved superhelical ESO.

[0057] Step 2.2.2 is as follows:

[0058] Define the system state error d, the deviation between the actual current and the reference current of the q-axis is e:

[0059] e=xx ref (15)

[0060] According to the design idea of ​​cascade progression of the backstepping method, a virtual feedback quantity is defined:

[0061]

[0062] In formula (16), a is a constant, x is a state variable, that is, d current id Or q-axis current i q ;

[0063] Define the Lyapunov function V a for:

[0064]

[0065] Deriving equation (17), and substituting equation (8) and equation (16) into it, we get:

[0066]

[0067] make If k is a constant, then we have Formula (18) can be transformed into:

[0068]

[0069] From formula (19), we know that when ρ converges to 0, The subsystem is stable, so the control law can be designed by controlling the virtual feedback quantity ρ;

[0070] The terminal term is introduced into the complementary sliding surface and the generalized sliding surface s is designed. g and complementary sliding surface s c as follows:

[0071]

[0072] In formula (20) and formula (21), m and λ are positive constants. a and b are both positive odd numbers, corresponding to the same positive constant λ, and the sum of the sliding surface is obtained:

[0073] s(t)=s g +s c =2ρ+2λρ m (twenty two)

[0074] From equations (20), (21) and (22), the relationship between the sliding surfaces is:

[0075]

[0076] Select the Lyapunov function V for the BCTSMC system b as follows:

[0077]

[0078] V b The derivative is:

[0079]

[0080] Due to -ηs 2 ≤0, so let but It still holds, satisfies the Lyapunov stability condition, and the system can converge in a finite time; according to the equivalent control theory, the equivalent control law s eq for:

[0081]

[0082] The sliding mode switching control part is designed as follows:

[0083]

[0084] In formula (27), l1 and l2 are both constants greater than 0;

[0085] Combining equations (26) and (27), we can obtain the BCTSMC control law S BCT , which is expressed as follows:

[0086] S BCT =s eq +s v (28)

[0087] Substituting the observed values ​​of the d and q axis variables in ESO in equation (12), we can obtain the final control law S of the inverter system: d , S q for:

[0088]

[0089] The beneficial effects of the present invention are:

[0090] The present invention is an improved sliding mode auto-disturbance rejection control method for a three-phase grid-connected inverter based on a variable gain super-helical ESO. First, the grid-connected inverter is modeled and converted into a second-order auto-disturbance rejection paradigm, and on this basis, the observer and controller are designed. The specific effects are as follows:

[0091] 1) The sign function is a discontinuous function. When the sign function sign is used as the switching function of the super-helical sliding mode expansion state observer, discontinuous switching control characteristics will be generated along with the observation error, resulting in chattering problems and affecting the observation accuracy of the system. Therefore, a smooth hyperbolic function F(e i ) is used as the switching function of the observer to reduce system chattering and keep the system stable.

[0092] 2) A variable gain function that can change in real time with the observation accuracy is designed to replace the fixed-value gain of ST-ESO, so as to improve the observer's ability to observe disturbances and increase the convergence speed of the system.

[0093] 3) The terminal complementary sliding mode control (TCSMC) in the present invention combines the characteristics of terminal sliding mode and complementary sliding mode control. By introducing the terminal term in the control strategy, the system can converge to the equilibrium point in a finite time, thereby achieving rapid response. TCSMC has strong robustness to external disturbances and uncertainties. Due to the introduction of the terminal term and the complementary term, the system can maintain stable performance in the presence of disturbances and uncertainties, and quickly recover to the desired state.

[0094] 4) In order to better improve the robustness of the system, simplify the design process and improve efficiency, backstepping control is introduced in combination with sliding mode control. The backstepping method adopts the recursive idea for design, and can effectively handle systems with mismatched uncertainties. By recursively constructing the Lyapunov function of the closed-loop system, the feedback controller is obtained, making the controller design process systematic and structured. This method can greatly improve the quality of the system transition process, ensure the global stability of the closed-loop system, and at the same time ensure that the motion quality of each subsystem reaches the desired performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 It is a control block diagram of the grid-connected inverter auto-disturbance rejection control method based on the variable gain super-helical observer of the present invention;

[0096] Figure 2 It is the structural diagram of three-phase grid-connected inverter;

[0097] Figure 3 is the hyperbolic function F(e i ) and sign(x) comparison chart;

[0098] Figure 4 It is a control diagram of the grid-connected inverter auto-disturbance rejection control method based on the variable gain super-helical observer of the present invention;

[0099] Figure 5 This is the transient waveform of the three-phase current on the grid side under PI control;

[0100] Figure 6 It is a transient waveform diagram of three-phase current on the grid side under the control method of the present invention;

[0101] Figure 7 This is the bus voltage transient response diagram when P jumps from 30kW to 80kW under PI control;

[0102] Figure 8 This is the bus voltage transient response diagram when P jumps from 80kW to 30kW under PI control;

[0103] Fig. 9 This is a bus voltage transient response diagram when P jumps from 30kW to 80kW under the control method of the present invention;

[0104] Fig.10 This is a bus voltage transient response diagram when P jumps from 80kW to 30kW under the control method of the present invention;

[0105] Fig.11 This is the transient response diagram when the active power direction switches from 30kW to -30kW under PI control;

[0106] Fig.12 This is the transient response diagram when the active power direction switches from -30kW to 30kW under PI control;

[0107] Fig.13 It is a transient response diagram when the active power direction is switched when P jumps from 30kW to -30kW under the control method of the present invention;

[0108] Fig.14 It is a transient response diagram when the active power direction is switched when P jumps from -30kW to 30kW under the control method of the present invention;

[0109] Fig.15 This is the current harmonic analysis diagram under PI control;

[0110] Fig.16 This is a current harmonic analysis diagram when the control method of the present invention is used for control. DETAILED DESCRIPTION

[0111] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0112] Example 1

[0113] This embodiment provides a grid-connected inverter auto-disturbance rejection control method based on a variable gain super spiral observer. Figure 1 As shown in the figure, firstly, the mathematical model of the three-phase grid-connected inverter is established and converted into the dq rotating coordinate system. On this basis, it is converted into the second-order anti-disturbance paradigm form, and then the super-helical extended state observer is designed, and the discontinuous switching term sign function in the super-helical extended state observer is replaced by a hyperbolic function; secondly, a variable gain function that changes in real time with the observation error is designed to replace the linear gain of the ST-ESO; then the backstepping control combined with the terminal complementary sliding mode is introduced as a feedback controller.

[0114] Follow the steps below to implement it:

[0115] Step 1: Establish a mathematical model of the three-phase grid-connected inverter in the dq rotating coordinate system and convert it into a second-order active disturbance rejection paradigm;

[0116] The three-phase grid-connected inverter converts direct current into alternating current that is synchronized with the power grid, and realizes the effective grid connection of the renewable energy system. The high-performance control strategy of the three-phase grid-connected inverter is the core of determining the quality of the power grid and the reliability of the system. In the inverter system, a dual closed-loop control structure of the voltage outer loop and the current inner loop is often used, which has high control accuracy, but the proportional integral (PI) control is sensitive to parameter settings, has poor dynamic response, and is prone to overshoot and overcurrent. PQ control (constant power control) is used for the inverter part. PQ control is an important control strategy in the power system, mainly used to maintain the stability and reliability of the power system; the PQ control principle of the three-phase inverter is to accurately control the output current of the inverter to achieve the regulation of active power and reactive power, and ensure that the output power reaches the preset value, thereby ensuring the output quality of the inverter and the stable operation of the power grid. This control strategy has broad application prospects in practical applications, especially in the fields of renewable energy grid-connected power generation and microgrids;

[0117] Three-phase grid-connected inverter Figure 2 As shown, u in is the DC side power supply voltage of the inverter; s1~s6 are the six switch tubes on the inverter bridge arm respectively; it is assumed that the three-phase waveform of the grid voltage is symmetrical and there is no distortion; during the grid-connected operation of the grid-connected inverter, the working states of the two switch tubes on each bridge arm are complementary, so the switching function is defined as follows:

[0118]

[0119] In formula (1), j = a, b, c, representing the three phases a, b, and c of the AC power grid;

[0120] Depend on Figure 2 According to Kirchhoff's law, the voltage and current relationship equation of the grid-connected inverter in the abc three-phase stationary coordinate system is:

[0121]

[0122] In formula (2), u a 、u b 、u c is the three-phase voltage on the AC side of the three-phase grid-connected inverter; i sa 、i sb 、i sc is the three-phase current on the AC side; e a 、e b 、e c is the AC grid voltage; L is the filter inductance; C dc is the DC side capacitance; R is the line equivalent resistance parameter; i ris the DC side power supply current; u dc 、i C is the DC side capacitor voltage and current; s ka 、s kb 、s kc They are the switch control signals of the three-phase bridge arms a, b and c respectively;

[0123] By performing Park transformation on equation (2), the mathematical model of the inverter in the dq coordinate system can be obtained as follows:

[0124]

[0125] In formula (3), ω is the angular frequency of the grid voltage; e d 、i d 、s d They are the grid voltage, current, and switching function of the d-axis, and the e-axis q 、i q 、s q are the grid voltage, current and switching function of the q axis respectively; u dc is the DC side capacitor voltage.

[0126] Step 2: Controller design;

[0127] The PQ control strategy is used for inverter control. PQ control usually involves two key control loops: the power outer loop and the current inner loop. The outer loop determines the active power and reactive power that the inverter should provide according to the system operation requirements, and calculates the corresponding dq axis current reference value i according to the set P and Q values. dref 、i qref The current inner loop monitors the inverter output current component i in real time. d and i q , compared with the current reference value generated by the outer loop, it is used to guide the inverter to output specific active and reactive power. The core of PQ control is to decouple active power and reactive power so that they can be adjusted independently;

[0128] Step 2.1: Design of power outer loop controller;

[0129] Step 2.2: Design of current inner loop controller;

[0130] Step 2.2.1: Design of variable gain superhelical ESO;

[0131] Step 2.2.2: Design of backstepping complementary terminal sliding mode controller;

[0132] Step 3: Obtain the control output through the controller, use SPWM modulation to get the duty cycle, and apply the duty cycle to the control of the switch tube of the three-phase grid-connected inverter, thereby realizing the signal control of the three-phase grid-connected inverter.

[0133] Example 2

[0134] This embodiment provides an active disturbance rejection control method for a grid-connected inverter based on a variable gain super spiral observer. Based on Embodiment 1, step 2.1 is specifically as follows:

[0135] The main function of the power outer loop is to ensure power conservation during the grid connection process of the inverter and provide a reference value for the subsequent current inner loop. According to the instantaneous power theory, in order to make the three-phase grid-connected inverter close to the unity power factor grid connection, the reactive current is always equal to 0. Under the condition of balanced three-phase grid voltage, the instantaneous values ​​of active power P and reactive power Q on the grid side of the three-phase grid-connected inverter are expressed as:

[0136]

[0137] From formula (4), we know that through i d and i q Control P and Q separately to achieve independent regulation of active power and reactive power; transform equation (4) to ref , Q ref When given, the d and q axis current reference values ​​are directly obtained by calculation; however, in order to eliminate the steady-state error, the PI regulator is introduced. After the deviation between P, Q and the P, Q command values ​​is adjusted by PI, the active current reference value i is obtained based on the instantaneous power theory and the dynamic response of the system P and Q. dref and reactive current reference value i qref , as shown below:

[0138]

[0139] In formula (5), P ref , Q ref For given active power and reactive power reference values, i dref 、i qref is the inner loop reference value of d and q axis current, k dp , k di is the d-axis PI adjustment parameter, k qp , k qi is the q-axis PI adjustment parameter.

[0140] Example 3

[0141] This embodiment provides a grid-connected inverter active disturbance rejection control method based on a variable gain super spiral observer. Based on Embodiment 1-2, step 2.2 is as follows:

[0142] Step 2.2.1 is as follows:

[0143] First, define the state variable d, q axis current i d 、i qFor x d1 、x q1 , from formula (3):

[0144]

[0145] In order to simplify the difficulty of controller design, the inner loop coupling terms and unmodeled parts of the current of the d and q axes and the internal and external disturbances of the inner loop are regarded as the total disturbance of the inner loop, and are represented by f d1 , f q1 It means that the derivative of formula (3) is converted into the ADRC paradigm as follows:

[0146]

[0147] In formula (7), b d 、b q are the gains of the d-axis and q-axis control quantities respectively;

[0148] Since the value of b is generally unknown in actual engineering operations and cannot be accurately determined, b is defined as do 、b qo are the estimated values ​​of the d-axis and q-axis control quantity gains respectively, let Transform formula (7) into:

[0149]

[0150] In formula (8), f d =(b d -b do )s d +f d1 , f q =(b q -b qo )s q +f q1 ,b do 、b qo is the estimated value of the d and q axis control quantity gain;

[0151] f d , f q Expand to a new state variable z d3 , z q3 , the superhelical expansion state observer is designed as follows:

[0152]

[0153] In formula (9), z d1 For x d1 The estimated value of z q1 For x q1 The estimated value of z d2 , zq2 is the estimated value of the derivative, x d1 For x q1 The estimated value of the derivative; e d1 is the difference between the observed value and the actual value of the d-axis, e q1 is the difference between the observed value and the actual value of the q axis; z d3 is the total disturbance f including d-axis coupling, internal disturbance and unmodeled part. d The estimated value of z q3 is the total disturbance f including the q-axis coupling term, internal disturbance and unmodeled part. q The estimated value of β d1 , β d2 , β d3 , β q1 , β q2 , β q3 is the observer gain. When the observation error e of the superhelical ESO is close to 0, the expression of the observer is consistent with that of the linear extended state observer. Therefore, the bandwidth method is used for tuning as follows:

[0154] The value conditions of β1, β2, β3 are: β1 = 3ω0, β2 = 3ω0 2 , β3=ω0 3 .

[0155] In order to reduce system jitter and improve the observation capability of the super-twisting expanded state observer to the total disturbance of the inner loop, a variable gain super-twisting ESO (VGST-ESO) is proposed. In order to reduce system jitter, the sign function of the discontinuous switching term in the super-twisting expanded state observer is replaced by a hyperbolic function; secondly, a variable gain function that can change in real time with the observation error is designed to replace the linear gain of the super-twisting expanded state observer, so as to improve the observation capability of the disturbance;

[0156] In order to reduce system chattering and improve the observation capability of the superhelical extended state observer to the total disturbance of the inner loop, a variable gain superhelical ESO is proposed, and the sign function of the discontinuous switching term in the superhelical extended state observer is replaced by a hyperbolic function; secondly, a variable gain function that changes in real time with the observation error is designed to replace the linear gain of the ST-ESO, so as to improve the observation capability of the disturbance;

[0157] The switching function sign expression is:

[0158]

[0159] It can be seen from formula (10) that the sign function is a discontinuous function. When the sign function sign is used as the switching function of the super-helical sliding mode expansion state observer, discontinuous switching control characteristics will be generated along with the observation error, resulting in chattering problems and affecting the observation accuracy of the system. Therefore, a smooth hyperbolic function F(e i ) as the switching function of the observer.

[0160] Hyperbolic F(e i ) function is expressed as:

[0161]

[0162] Hyperbolic function F(e i ) and the image of the symbolic function sign(x) are compared as Figure 3 As shown, by formula (11) and Figure 2 It can be seen that the switching function F(e i ) is continuous and smooth, with no discontinuities, which can theoretically reduce the system chattering problem and improve the observation capability of generalized superhelical ESO to disturbances;

[0163] In order to improve the observer's ability to observe disturbances and increase the convergence speed of the system, a variable gain function that can change in real time with the observation accuracy is designed to replace the fixed value gain of ST-ESO;

[0164] The improved supercoil ESO expression is:

[0165]

[0166] In formula (12), z d1 For x d1 The improved estimate of the observer, z q1 For x q1 The improved estimate of the observer; d2 For x d1 The observer-improved estimate of the derivative, z q2 For x q1 The observer-improved estimate of the derivative; z d3 is the total disturbance f including coupling terms, internal disturbances and unmodeled parts. d The improved estimate of the observer, z q3 is the total disturbance f including coupling terms, internal disturbances and unmodeled parts. q The improved estimate of the observer; The improved variable gain function of the observer is as follows:

[0167]

[0168] The expression of variable gain L(t) is:

[0169]

[0170] In formula (14), η i , σ are both adjustable positive real numbers, and σ determines the observation accuracy of the improved superhelical ESO.

[0171] In order to meet the high-precision control design requirements of the inverter, a terminal complementary sliding mode controller is introduced to replace the traditional sliding mode control. Compared with the traditional sliding mode control, the complementary sliding mode control (CSMC) has significant advantages and can effectively reduce the system tracking error, thereby improving the overall performance of the system tracking. However, it is slightly insufficient in speed, especially when compared with the terminal sliding mode control (TSMC) system. The TSMC system can achieve t r +Δt time period, it can quickly return to the origin from any state. In contrast, the convergence speed of CSMC is slower. In order to overcome this limitation, the CSMC is combined with the TSMC idea, and a complementary terminal sliding mode controller (CTSMC) is designed to further improve the control performance of the system. At the same time, in order to better improve the robustness of the system, simplify the design process and improve efficiency, backstepping control is combined with sliding mode control. The design of the backstepping complementary terminal sliding mode controller (BCTSMC), that is, step 2.2.2, is as follows:

[0172] Define the system state error d, the deviation between the actual current and the reference current of the q-axis is e:

[0173] e=xx ref (15)

[0174] According to the design idea of ​​cascade progression of the backstepping method, a virtual feedback quantity is defined:

[0175]

[0176] In formula (16), a is a constant, x is a state variable, that is, d current i d Or q-axis current i q ;

[0177] Define the Lyapunov function V a for:

[0178]

[0179] Deriving equation (17), and substituting equation (8) and equation (16) into it, we get:

[0180]

[0181] make If k is a constant, then we have Formula (18) becomes:

[0182]

[0183] From formula (19), we know that when ρ converges to 0, The subsystem is stable, so the control law can be designed by controlling the virtual feedback quantity ρ;

[0184] In the design of BCTSMC, the sliding surface is established in the backstepping control. The complementary sliding surface is composed of the generalized sliding surface and the complementary sliding surface. The terminal term is introduced into the complementary sliding surface to design the generalized sliding surface s g and complementary sliding surface s c as follows:

[0185]

[0186] In formula (20) and formula (21), m and λ are positive constants. a and b are both positive odd numbers, corresponding to the same positive constant λ, and the sum of the sliding surface can be obtained:

[0187] s(t)=s g +s c =2ρ+2λρ m (twenty two)

[0188] From equations (20), (21) and (22), the relationship between the sliding surfaces is:

[0189]

[0190] Select the Lyapunov function V for the BCTSMC system b as follows:

[0191]

[0192] V b The derivative is:

[0193]

[0194] Due to -ηs 2 ≤0, so let but It still holds, satisfies the Lyapunov stability condition, and the system can converge in a finite time; according to the equivalent control theory, the equivalent control law s eq for:

[0195]

[0196] The sliding mode switching control part is designed as follows:

[0197]

[0198] In formula (27), l1 and l2 are both constants greater than 0;

[0199] Combining equations (26) and (27), we can obtain the BCTSMC control law S BCT , which is expressed as follows:

[0200] S BCT =s eq +s v (28)

[0201] Substituting the observed values ​​of the ESO d and q axis variables into equation (12), we can obtain the final inverter control law S d , S q for:

[0202]

[0203] Step 3 uses SPWM (Sine Pulse Width Modulation), that is, sinusoidal pulse width modulation, to modulate the inverter signal. Its basic working principle is as follows:

[0204] According to the controller designed by the control part, the obtained control signal is used as the modulation wave, and a high-frequency triangle wave is selected as the carrier. By comparing the size of the modulation wave and the carrier, the on-off state of the switch tube in the inverter is determined. When the modulation wave is higher than the carrier, the switch tube is turned on; when the modulation wave is lower than the carrier, the switch tube is turned off. In this way, at the output end of the inverter circuit, a pulse sequence with a width that changes according to the sine law is obtained, that is, an SPWM wave.

[0205] Therefore, the inverter control block diagram can be obtained as follows: Figure 4 shown.

[0206] The grid-connected inverter auto-disturbance rejection control method based on variable gain super-helical observer of the present invention has the following advantages:

[0207] 1) The sign function is a discontinuous function. When the sign function sign is used as the switching function of the super-helical sliding mode expansion state observer, discontinuous switching control characteristics will be generated along with the observation error, resulting in chattering problems and affecting the observation accuracy of the system. Therefore, a smooth hyperbolic function F(e i ) is used as the switching function of the observer to reduce system chattering and keep the system stable.

[0208] 2) The present invention designs a variable gain function that can change in real time with the observation accuracy to replace the fixed value gain of ST-ESO, so as to improve the observer's observation ability of disturbances and improve the convergence speed of the system.

[0209] 3) In the present invention, the terminal complementary sliding mode control (TCSMC) combines the characteristics of terminal sliding mode and complementary sliding mode control. By introducing the terminal term in the control strategy, the system can converge to the equilibrium point in a finite time, thereby achieving rapid response. TCSMC has strong robustness to external disturbances and uncertainties. Due to the introduction of the terminal term and the complementary term, the system can maintain stable performance in the presence of disturbances and uncertainties, and quickly recover to the desired state.

[0210] 4) In order to better improve the robustness of the system, simplify the design process and improve efficiency, the present invention introduces a combination of backstepping control and sliding mode control. The backstepping method adopts a recursive idea for design, and can effectively handle systems containing mismatched uncertainties. By recursively constructing the Lyapunov function of the closed-loop system, a feedback controller is obtained, so that the design process of the controller has the advantages of being systematic and structured. This method can greatly improve the quality of the system transition process, ensure the global stability of the closed-loop system, and at the same time ensure that the motion quality of each subsystem reaches the desired performance.

[0211] Simulation and Experimental Analysis

[0212] In order to verify the effectiveness of the grid-connected inverter auto-disturbance rejection control method based on the variable gain super-helical observer of the present invention, a corresponding simulation circuit is constructed in the MATLAB / Simulink simulation software, and it is compared and analyzed with the traditional PI control strategy. For simulation parameter settings, see Table 1. In the entire simulation process, a unified simulation environment and parameter configuration are used to ensure the fairness and accuracy of the comparison results.

[0213] Table 1 Circuit parameters

[0214] parameter Numeric Grid voltage amplitude e 311V <![CDATA[DC power supply voltage u dc > 800V Filter inductor L 0.5mH Filter capacitor C 50μF Inductor parasitic resistance R 0.01Ω <![CDATA[DC regulated capacitor C dc > 1mF <![CDATA[DC-side inductor L dc > 1mH Load power 30kW-80kW

[0215] In order to verify the advantages of the control strategy proposed in this paper compared with the traditional PI control strategy, the corresponding active power mutation is set in the simulation to intuitively compare the three-phase current response under different control during dynamic changes. The simulation results are shown in Figure 2. Figure 5-6 shown.

[0216] Figure 5-6 The figure shows the transient waveform of the three-phase current on the grid side when facing power jump under different control conditions. Two active power jumps are set at 0.25s (P jumps from 30kW to 80kW) and 0.35s (P jumps from 80kW to 30kW). Figure 5 Data analysis shows that under the PI control strategy, when the three-phase inverter output active power jumps from 30kW to 80kW, the three-phase current i a 、i b 、i c The amplitude of the three-phase current i jumps from 64.9A to 172.3A, and after a transient process of 18.5ms, it returns to steady-state operation. When the output power jumps from 80kW to 30kW, the three-phase current i a 、i b 、i c The amplitude jumps from 172.3A to 64.9A, and after a transient process of 14.5ms, it returns to steady-state operation. Figure 6 It can be seen that in the two transient processes under the control strategy of this paper, the three-phase current i a 、i b 、i c The transition time is 5.5ms and 6.5ms respectively, which is significantly lower than that of PI control. Therefore, in the process of active power jump, the method of the present invention shows a faster response characteristic and better transient performance.

[0217] In order to further verify the superiority of the method of the present invention over the existing control strategy, a hardware-in-the-loop (HIL) experimental platform was used. During the experiment, the corresponding active power mutation was set, and the performance differences of the two control strategies in dealing with dynamic changes were intuitively compared. The sampling frequency of the experiment was set to 20kHz to ensure the accuracy of data acquisition. First, a simulation circuit was constructed using Simulink to simulate the circuit control logic in the actual system; secondly, the constructed simulation circuit was imported into MT6020 and RCP1050 through the host computer to simulate the operating behavior and response of the actual hardware; finally, the real-time signal generated by the experimental platform was connected to the oscilloscope through the adapter board, and the oscilloscope was used to monitor and record the key data in the experimental process in real time, so as to facilitate subsequent data analysis and verification.

[0218] In the figure below, i d 、i a 、i b 、i cRespectively represent the d-axis current of the inverter AC side and the a, b, c three-phase currents in the three-phase stationary coordinate system. To verify the performance of the method of the present invention, it is compared with the PI control strategy. When the inverter outputs active power of 30kW and reactive power of 0, i d is 64.3A, i q When the output active power is 80kW and the reactive power is 0, i d is 171.5A, i q The calculation result can be used as a reference value for the experiment. The experiment sets the DC bus voltage to 800V in steady state. d 、i a 、i b 、i c The accuracy is 100A / grid. The comparison results of power jump experiment under two control strategies are as follows: Figure 7-14 shown.

[0219] according to Figure 7-8 The data shows that under the PI control strategy, when the output active power of the three-phase inverter jumps from 30kW to 80kW, i d The current fluctuation caused by the jump from 65.3A to 172.4A produces an overshoot of 26A. After 22ms, the three-phase current i a 、i b 、i c The amplitude jumps from 65A to 172A, and after a 12ms transient process, it returns to steady-state operation. When the output power jumps from 80kW to 30kW, i d The overshoot caused by the current fluctuation is 22A, and the three-phase current i a 、i b 、i c The amplitude jumps from 172A to 65A, and recovers to steady-state operation after a transient process of 21ms.

[0220] according to Figure 9-10 It can be seen that under the method of the present invention, the i d The overshoot is almost 0. At the same time, the method of the present invention has two transient processes, i d The transition time is 11ms, and the three-phase current i a 、i b 、i c The transition time of PI control is 7ms and 9ms respectively, which is significantly reduced compared with PI control. Therefore, in the process of active power jump, the method of the present invention has better transient performance and the switching process is smoother. d And three-phase current i a 、ib 、i c The waveform has obvious chattering and high harmonic content, and the method of the present invention can better suppress the chattering and enable the system to have better steady-state performance.

[0221] according to Figure 11-12 It can be seen that under the PI control strategy, when the output active power of the three-phase inverter jumps from 30kW to -30kW, the current direction switches, i d The three-phase current i jumps from 65.3A to -65.3A and returns to steady state after 12ms. a 、i b 、i c After a 21ms transient process, it returns to steady-state operation. When the output power jumps from -30kW to 30kW, i d From -65.3A to 65.3A, i d The transition time is 11ms, and the three-phase current i a 、i b 、i c After a transient process of 19ms, it returns to steady-state operation.

[0222] according to Figure 13-14 It can be seen that under the method of the present invention, during the transient process of two active power direction switching, i d The transition time to restore steady state is 11ms, and the three-phase current i a 、i b 、i c The transition time is 10ms and 12ms respectively. Compared with PI control, the system recovers steady-state operation under the method of the present invention, and the transient time is shorter. Therefore, in the process of power direction switching, the method of the present invention has excellent transient performance, faster transient response speed, and better vibration suppression effect on the current waveform.

[0223] During the simulation, the grid-connected current of the inverter was analyzed when the output active power was 30kW. The analysis showed that when the method of the present invention was adopted, the inverter output current waveform was smoother and the waveform fluctuation range was significantly suppressed. In order to further verify the influence of the control strategy on the power quality, the Fourier analysis tool in Simulink was used to perform spectrum analysis of the grid-connected current in two steady-state cycles.

[0224] Depend on Figure 15-16 The results of spectrum analysis show that the harmonic distortion rate under the PI control strategy is 4.54%, and when the method of the present invention is used, the harmonic distortion rate is reduced to 1.21%. The data show that the method of the present invention effectively suppresses the harmonic components that interfere with the power grid, and the high-frequency harmonic components of the current are significantly reduced. Therefore, higher quality electric energy can be provided under the control of the method of the present invention.

Claims

1. A grid-connected inverter auto-disturbance rejection control method based on a variable gain super-helical observer, characterized in that: Firstly, the mathematical model of the three-phase grid-connected inverter is established and converted into the dq rotating coordinate system. On this basis, it is converted into the second-order anti-disturbance paradigm. Then, the super-helical extended state observer is designed, and the discontinuous switching term sign function in the super-helical extended state observer is replaced by a hyperbolic function. Secondly, a variable gain function that changes in real time with the observation error is designed to replace the linear gain of the ST-ESO. Then, the backstepping control combined with the terminal complementary sliding mode is introduced as a feedback controller.

2. The grid-connected inverter active disturbance rejection control method based on variable gain super helical observer according to claim 1, characterized in that: Follow the steps below to implement it: Step 1: Establish a mathematical model of the three-phase grid-connected inverter in the dq rotating coordinate system and convert it into a second-order active disturbance rejection paradigm; Step 2: Controller design; Step 2.1: Design of power outer loop controller; Step 2.2: Design of current inner loop controller; Step 2.2.1: Design of variable gain superhelical ESO; Step 2.2.2: Design of backstepping complementary terminal sliding mode controller; Step 3: Obtain the control output through the controller, use SPWM modulation to get the duty cycle, and apply the duty cycle to the control of the switch tube of the three-phase grid-connected inverter, thereby realizing the signal control of the three-phase grid-connected inverter.

3. The grid-connected inverter active disturbance rejection control method based on variable gain super spiral observer according to claim 2, characterized in that: The step 1 specifically comprises: During the grid-connected operation of the grid-connected inverter, the working states of the two switches in each bridge arm are complementary. Therefore, the switching function is defined as follows: In formula (1), j = a, b, c, representing the three phases a, b, and c of the AC power grid; According to Kirchhoff's law, the voltage and current relationship equation of the grid-connected inverter in the abc three-phase stationary coordinate system is: In formula (2), u a 、u b 、u c is the three-phase voltage on the AC side of the three-phase grid-connected inverter; i sa 、i sb 、i sc is the three-phase current on the AC side; e a 、e b 、e c is the AC grid voltage; L is the filter inductance; C dc is the DC side capacitance; R is the line equivalent resistance parameter; i r is the DC power supply current; u dc 、i C is the DC side capacitor voltage and current; s ka 、s kb 、s kc They are the switch control signals of the three-phase bridge arms a, b and c respectively; Perform Park transformation on equation (2) to obtain the mathematical model of the inverter in the dq coordinate system: In formula (3), ω is the angular frequency of the grid voltage; e d 、i d 、s d They are the grid voltage, current, and switching function of the d-axis, and the e-axis q 、i q 、s q are the grid voltage, current and switch function of the q axis respectively; L is the filter inductance; u dc 、i C is the DC side capacitor voltage and current.

4. The grid-connected inverter active disturbance rejection control method based on variable gain super helical observer according to claim 3, characterized in that: The step 2.1 is specifically as follows: According to the instantaneous power theory, in order to make the three-phase grid-connected inverter close to unity power factor grid-connected, the reactive current is always equal to 0. Under the condition of balanced three-phase grid voltage, the instantaneous values ​​of active power P and reactive power Q on the grid side of the three-phase grid-connected inverter are expressed as: From formula (4), we know that through i d and i q Control P and Q separately to achieve independent regulation of active power and reactive power; Transform equation (4) and when P ref , Q ref When given, the d and q axis current reference values ​​are directly obtained by calculation; however, in order to eliminate the steady-state error, the PI regulator is introduced. After the deviation between P, Q and the P, Q command values ​​is adjusted by PI, the active current reference value i is obtained based on the instantaneous power theory and the dynamic response of the system P and Q. dref and reactive current reference value i qref , as shown below: In formula (5), P ref , Q ref For given active power and reactive power reference values, i dref 、i qref is the inner loop reference value of d and q axis current, k dp , k di is the d-axis PI adjustment parameter, k qp , k qi is the q-axis PI adjustment parameter.

5. The method for grid-connected inverter auto-disturbance rejection control based on variable gain super-helical observer according to claim 4, characterized in that: The step 2.2.1 is specifically as follows: First, define the state variable d, q axis current i d 、i q For x d1 、x q1 , from formula (3): In order to simplify the controller design difficulty, the inner loop coupling terms and unmodeled parts of the current of the d and q axes as well as the internal and external disturbances of the inner loop are regarded as the total disturbance of the inner loop, and are represented by f d1 、f q1 It means that the derivative of formula (3) is converted into the ADRC paradigm as follows: In formula (7), b d 、b q are the gains of the d-axis and q-axis control quantities respectively; Definition b do 、b qo is the estimated value of the d and q axis control gain, let Transform formula (7) into: In formula (8), f d =(b d -b do )s d +f d1 , f q =(b q -b qo )s q +f q1 , bdo and bqo are the estimated values ​​of the control quantity gains of the d and q axes; The lumped disturbance f d 、f q Expand to new state variables z d3 、z q3 , then the superhelical expansion state observer is designed as follows: In formula (9), z d1 For x d1 The estimated value of z q1 For x q1 The estimated value of z d2 , z q2 is the estimated value of the derivative, x d1 For x q1 The estimated value of the derivative; e d1 is the difference between the observed value and the actual value of the d-axis, e q1 is the difference between the observed value and the actual value of the q axis; z d3 is the total disturbance f including d-axis coupling, internal disturbance and unmodeled part. d The estimated value of z q3 is the total disturbance f including the q-axis coupling term, internal disturbance and unmodeled part. q The estimated value of β d1 , β d2 , β d3 , β q1 , β q2 , β q3 is the observer gain. When the observation error e of the superhelical ESO is close to 0, the expression of the observer is consistent with that of the linear extended state observer. Therefore, the bandwidth method is used for tuning as follows: The value conditions of β1, β2, and β3 are: β1 = 3ω0, β2 = 3ω0 2 , β3 = ω0 3 ; In order to reduce system chattering and improve the observation capability of the superhelical extended state observer to the total disturbance of the inner loop, a variable gain superhelical ESO is proposed, and the sign function of the discontinuous switching term in the superhelical extended state observer is replaced by a hyperbolic function; secondly, a variable gain function that changes in real time with the observation error is designed to replace the linear gain of the ST-ESO, so as to improve the observation capability of the disturbance; The switching function sign expression is: From formula (10), we know that the sign function is a discontinuous function. When the sign function sign is used as the switching function of the super-helical sliding mode expansion state observer, discontinuous switching control characteristics will be generated along with the observation error, resulting in chattering problems and affecting the observation accuracy of the system. Therefore, a smooth hyperbolic function F(e i ) as the switching function of the observer; Hyperbolic F(e i ) function is expressed as: The improved supercoil ESO expression is: In formula (12), z d1 For x d1 The improved estimate of the observer, z q1 For x q1 The improved estimate of the observer; d2 For x d1 The observer-improved estimate of the derivative, z q2 For x q1 The observer-improved estimate of the derivative; z d3 is the total disturbance f including coupling terms, internal disturbances and unmodeled parts. d The improved estimate of the observer, z q3 is the total disturbance f including coupling terms, internal disturbances and unmodeled parts. q The improved estimate of the observer ; The improved variable gain function of the observer is as follows: The expression of variable gain L(t) is: In formula (14), η i , σ are both adjustable positive real numbers, and σ determines the observation accuracy of the improved superhelical ESO.

6. The grid-connected inverter active disturbance rejection control method based on variable gain super spiral observer according to claim 5, characterized in that: The step 2.2.2 is specifically as follows: Define the system state error d, the deviation between the actual current and the reference current of the q-axis is e: e=x-x ref (15) According to the design idea of ​​cascade progression of the backstepping method, a virtual feedback quantity is defined: In formula (16), a is a constant, x is a state variable, that is, d current i d Or q-axis current i q ; Define the Lyapunov function V a for: Deriving equation (17), and substituting equation (8) and equation (16) into it, we get: make If k is a constant, then we have Formula (18) becomes: From formula (19), we know that when ρ converges to 0, The subsystem is stable, so the control law is designed by controlling the virtual feedback quantity ρ; The terminal term is introduced into the complementary sliding surface and the generalized sliding surface s is designed. g and complementary sliding surface s c as follows: In formula (20) and formula (21), m and λ are positive constants. a and b are both positive odd numbers, corresponding to the same positive constant λ, and the sum of the sliding surface is obtained: s(t)=s g +s c =2ρ+2λρ m (22) From equations (20), (21) and (22), the relationship between the sliding surfaces is: Select the Lyapunov function V for the BCTSMC system b as follows: V b The derivative is: Due to -ηs 2 ≤0, so let but It still holds, satisfies the Lyapunov stability condition, and the system converges in a finite time; according to the equivalent control theory, the equivalent control law s eq for: The sliding mode switching control part is designed as follows: In formula (27), l1 and l2 are both constants greater than 0; Combining equations (26) and (27), we can obtain the BCTSMC control law S BCT , which is expressed as follows: S BCT =s eq +s v (28) Substituting the observed values ​​of the d-axis and q-axis variables of ESO into equation (12), we can obtain the final control law S of the inverter system: d , S q for:

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