An anti-interference backstepping control method for off-grid three-level inverter based on ESO

Abstract

The present invention discloses an anti-interference backstepping control method for an off-grid three-level inverter based on an ESO. First, a second-order mathematical model of an off-grid T-type three-level circuit with an LC filter is established, and the model is transformed into a rotating coordinate system through coordinate transformation. Secondly, for the system in the rotating coordinate system, two types of interference, parameter perturbation and load interference, are introduced, and an extended state observer is designed to estimate the interference in the system. Thirdly, a backstepping controller and an extended state observer are combined to design a feedforward-feedback composite anti-interference voltage tracking controller. Finally, by selecting appropriate observer and feedback controller gains, the off-grid T-type three-level inverter can accurately output the desired voltage value. At the same time, with the help of an SVPWM modulation algorithm with proportional-integral midpoint potential correction, balanced control of the midpoint potential is achieved. The present invention is simple in form, reduces the complexity of existing voltage control technology, and effectively improves the anti-interference performance and stability of the system.

Description

Technical Field

[0001] The present invention relates to an anti-interference backstepping control method for an off-grid three-level inverter based on an extended state observer (ESO), belonging to the technical field of power system inverter control. Background Art

[0002] Today's inverter technology is developing rapidly, and there are now various types of inverters to meet the changing needs of DC-AC. Three-level inverters have the characteristics of small harmonic components and simple structure, which are outstanding advantages. Due to these significant advantages, three-level inverters have broad application prospects in both military and civilian fields and have gradually attracted the attention of many researchers. However, the three-level inverter system needs to consider the midpoint potential stability issue, otherwise it will introduce additional harmonic interference to the output. It is a typical weak nonlinear, single-input and single-output second-order system. At the same time, it is also susceptible to internal interference such as load interference and parameter uncertainty during operation, as well as complex external environmental interference. This brings great difficulties to the tracking control design of its output voltage. The design difficulty is specifically manifested as follows:

[0003] 1) Weak nonlinearity of the system. Due to the coupling problem of dq axis parameters in the rotating coordinate system, the system has nonlinear terms, which brings challenges to establishing a system model that can accurately describe the system characteristics and is suitable for control design.

[0004] 2) The T-type three-level inverter system is significantly affected by interference, including parameter uncertainty, load interference, etc. These interference factors make it challenging to design a reliable and high-performance voltage control method.

[0005] 3) The imbalance of the midpoint potential of the T-type three-level inverter will introduce additional harmonic components into the circuit and reduce the service life of the electronic components in the circuit. Reasonable control of the midpoint potential also increases the difficulty of controlling the three-level inverter.

[0006] Due to the difficulty of the above-mentioned three-level inverter output voltage control problem, traditional linear control strategies (such as PID control, linear quadratic regulator, etc.) often cannot obtain satisfactory control performance. Therefore, some nonlinear control methods are applied to the output voltage control of T-type three-level inverter, such as sliding mode control, H ∞ However, these control methods are not satisfactory for the control of the disturbed off-grid T-type three-level inverter system: sliding mode control will produce more obvious chattering; model predictive control has a large amount of calculation and a more complex structure. Summary of the Invention

[0007] The technical problem solved by the present invention is: in view of the characteristics of an off-grid T-type three-level inverter system with an LC filter having coupling, nonlinear terms, and being affected by complex interference, an off-grid T-type three-level inverter anti-interference output voltage control method based on the backstepping method is proposed.

[0008] An anti-interference backstepping control method for an off-grid three-level inverter based on ESO, comprising the following steps:

[0009] Step 1: Establish a mathematical model of the three-phase current and voltage of an off-grid T-type three-level inverter system with an LC filter;

[0010] Step 2: The off-grid T-type three-level inverter system with an LC filter described in step 1 is processed by transforming the coordinates to a rotating coordinate system, thereby eliminating the zero-sequence voltage component therein;

[0011] Step 3: For the second-order system in the rotating coordinate system described in step 2, the load disturbance and the capacitance parameter perturbation are treated as lumped non-matching disturbances, and the inductance parameter perturbation is treated as matching disturbances. Two extended state observers are constructed to observe the matching disturbance and the non-matching disturbance respectively.

[0012] Step 4: using the interference estimation, designing an anti-interference output voltage tracking controller based on backstepping control technology to track and control the output voltage of the inverter in real time;

[0013] Step 5: Using the measured midpoint potential deviation, the midpoint potential is balanced based on the proportional-integral midpoint potential correction technology, and the midpoint potential of the T-type three-level inverter is corrected in real time. The present invention is further improved in that: the mathematical model of the three-phase voltage and current of the inverter in step 1 is as follows:

[0014]

[0015] Among them, V Lx =[V La ,V Lb ,V Lc ] T and I ix =[I ia ,I ib ,I ic ] T Respectively represent the output voltage and inductor current values of phases a, b, and c of the LC filter in the three-phase stationary coordinate system, V iox =[V ioa ,V iob ,V ioc ] T is the voltage at the midpoint of the busbar voltage divider capacitor for phases a, b, and c of the LC filter in the three-phase stationary coordinate system, I Lx =[ILa ,I Lb ,I Lc ] T It is used to describe the output current of phases a, b, and c of the LC filter in the three-phase stationary coordinate system. o'o It represents the potential difference between the neutral point and the midpoint of the busbar voltage divider capacitor, L represents the actual size of the filter inductor, and C represents the actual size of the filter capacitor.

[0016] The present invention is further improved in that the mathematical model of the system in the rotating coordinate system in step 2 is:

[0017]

[0018] Among them, V Ldq =[V Ld ,V Lq ] T , V idq =[V id ,V iq ] T It is used to describe the inverter output point to neutral point voltage of the dq axis in the two-phase rotating coordinate system of the LC filter, I idq =[I id ,I iq ] T , I Ldq =[I Ld ,I Lq ] T , w=2*f*π, f=50Hz means the output voltage frequency is 50Hz.

[0019] The mathematical model after introducing interference is:

[0020]

[0021] in, L0 represents the size of the nominal filter inductor, and C0 represents the size of the nominal filter capacitor.

[0022] The present invention is further improved in that: the unmatched aggregate interference d 1dq The extended state observer is as follows:

[0023]

[0024] Matched interference d 2dq The extended state observer is as follows:

[0025]

[0026] Among them, 1dq,ζ 2dq ,ζ 3dq ,ζ 4dq V Ldq d 1dq , I idq d 2dq The estimated value of , α1, α2, α3, and α4 are the observer gains.

[0027] The present invention is further improved in that:

[0028] In step 4, the designed feedforward-feedback composite anti-interference output voltage controller is specifically formulated as follows:

[0029]

[0030] in, The expected output voltage is [200V 0V] T , is a virtual controller; K eV , K eI is a positive controller gain.

[0031] The present invention is further improved in that:

[0032] In step 5, the designed PI midpoint potential correction algorithm is specifically formulated as follows:

[0033]

[0034] Where, ΔV c Represents the voltage difference between the two ends of the busbar voltage divider capacitor, t small_vector Represents the total time of positive and negative small vectors in a modulation cycle in the SVPWM algorithm. Positive and negative small vectors are two vector forms that appear in the SVPWM modulation cycle, corresponding to the output state of each phase in the three phases. They have the same effect in modulation, but have completely opposite effects on the midpoint potential. In an uncorrected SVPWM modulation cycle, the positive and negative small vectors have the same action time, which is Δt represents the adjustment amount of the positive and negative small vector action time within a sampling period in the SVPWM algorithm, and sat(g) is the saturation function: K P , K i They are the proportional coefficient and integral coefficient in the proportional-integral midpoint potential correction algorithm respectively.

[0035] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0036] 1) For the output of an off-grid T-type three-level inverter with an LC filter, where there is significant coupling between the d-axis and q-axis outputs, an extended state observer is used to estimate the matched interference and the mismatched lumped interference. The interference estimates are used for feedforward compensation, and a feedforward-feedback composite anti-interference output voltage controller is designed. This controller not only ensures accurate output voltage control of the off-grid T-type three-level inverter with an LC filter, but also improves the anti-interference performance of the system.

[0037] 2) The feedback controller is designed based on the backstepping control technique, which makes the proposed controller have a simpler structure, thereby increasing the practicality and reliability of the controller;

[0038] 3) Based on the extended state observer to accurately estimate the constant disturbance, the composite controller designed in this invention can ensure the accuracy of voltage control of the off-grid T-type three-level inverter system with LC filter under parameter perturbations and load disturbances;

[0039] 4) The feedforward-feedback composite anti-interference output voltage control design concept proposed in the present invention has good universality and can be applied to the output voltage control design of other types of inverters. The applicable scenarios are complex and changeable, and it has good flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The structure diagram of an off-grid T-type three-level inverter with an LC filter;

[0041] Figure 2 Design a flow chart for the present invention;

[0042] Figure 3 This is the closed-loop system block diagram of an off-grid T-type three-level inverter with an LC filter;

[0043] Figure 4 The output voltage curve of the off-grid T-type three-level inverter with LC filter according to the method of the present invention;

[0044] Figure 5 The output error curve of the off-grid T-type three-level inverter with LC filter according to the method of the present invention (where (a) is the d-axis output voltage error e Vd , (b) is the q-axis output voltage error e Vq );

[0045] Figure 6 The control quantity curve of the off-grid T-type three-level inverter with LC filter according to the present invention (where (a) is the d-axis control voltage input V id , (b) is the q-axis control voltage input V iq );

[0046] Figure 7 The mismatch interference estimation curve of the off-grid T-type three-level inverter with LC filter, where (a) is d 1d , (b) is d 1q .

[0047] Figure 8 The matching interference estimation error curve of the off-grid T-type three-level inverter with LC filter, where (a) is d 2d , (b) is d 2q .

[0048] Figure 9 This is the midpoint potential curve of an off-grid T-type three-level inverter with an LC filter. DETAILED DESCRIPTION

[0049] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are intended only to illustrate the present invention and are not intended to limit the scope of the present invention. It should be noted that the terms "front," "rear," "left," "right," "up," and "down" used in the following description refer to directions in the accompanying drawings, and the terms "inward" and "outward" refer to directions toward or away from the geometric center of a particular component, respectively.

[0050] The following describes the design steps of the embodiments of the present invention in detail with reference to the accompanying drawings.

[0051] Step 1: Establish a mathematical model of the three-phase current and voltage of the off-grid T-type three-level inverter system with LC filter

[0052] Figure 1 The structure diagram of the off-grid T-type three-level inverter is as follows:

[0053]

[0054] Among them, V Lx =[V La ,V Lb ,V Lc ] T and I ix =[I ia ,I ib ,I ic ] T Respectively represent the output voltage and inductor current values of phases a, b, and c with LC filter in the three-phase stationary coordinate system, V iox =[V ioa ,V iob ,V ioc ] T It is used to describe the voltage of the midpoint of the busbar voltage divider capacitor of phases a, b, and c in the three-phase stationary coordinate system with an LC filter. Lx =[ILa ,I Lb ,I Lc ] T It is used to describe the output current of phases a, b, and c with an LC filter in a three-phase stationary coordinate system. V o'o It represents the potential difference between the neutral point and the midpoint of the busbar voltage divider capacitor, L represents the actual size of the filter inductor, and C represents the actual size of the filter capacitor. These are system parameters that can be directly obtained.

[0055] Step 2: Change the three-phase stationary coordinate system to the two-phase rotating coordinate system

[0056] The mathematical model of the system in the two-phase rotating coordinate system is:

[0057]

[0058] Among them, V Ldq =[V Ld ,V Lq ] T , V idq =[V id ,V iq ] T It is used to describe the neutral point voltage of the dq axis of the off-grid T-type three-level inverter with LC filter in the two-phase rotating coordinate system, I idq =[I id ,I iq ] T , I Ldq =[I Ld ,I Lq ] T , w=2*f*π, f=50Hz means the output voltage frequency is 50Hz.

[0059] The mathematical model after introducing interference is:

[0060]

[0061] in, L0 represents the size of the nominal filter inductor, and C0 represents the size of the nominal filter capacitor.

[0062] Step 3: Design the Extended State Observer

[0063] Non-matching set interference d 1dq The extended state observer is as follows:

[0064]

[0065] Matched interference d 2dq The extended state observer is as follows:

[0066]

[0067] Among them, 1dq ,ζ 2dq ,ζ 3dq ,ζ 4dq V Ldq d 1dq , I idq d 2dq The estimated value of , α1, α2, α3, α4 are the observer gains;

[0068] Taking the extended state observer (4) as an example, the observation error is defined as The closed-loop observation error system is obtained as

[0069] e o =A e e o +σ e (6)

[0070] in,

[0071] By selecting appropriate observer gains α1 and α2, the observation error system matrix A can be guaranteed to be e For Hurwitz, when σ e When is bounded, the closed-loop observation error system (6) is ISS stable. Assuming that , the closed-loop observation error system (6) will converge to 0 asymptotically, and the interference estimate will asymptotically approach the actual value.

[0072] Step 4: Design a feedforward-feedback composite anti-interference output voltage controller

[0073] Combine Figure 2 It can be seen that the feedforward-feedback composite anti-interference output voltage controller designed in this invention is based on backstepping control technology and uses the disturbance estimate obtained by the extended state observer in step 3 for feedforward compensation. The specific form of the designed composite controller is as follows:

[0074]

[0075] in, The expected inverter output voltage is [200V 0V] T , is a virtual controller; K eV , K eI is a positive controller gain.

[0076] Taking controller (7) as an example, the closed-loop control error system under the d-axis can be obtained as

[0077] e c =A c e c +σ c (8)

[0078] in,

[0079] By selecting appropriate observer gain and feedback controller gain, A c is a Hurwitz matrix, when σ e When bounded, the closed-loop control error system (8) is ISS stable. As the system (6) is asymptotically stable, The closed-loop control error system is asymptotically stable, enabling the off-grid T-type three-level inverter system with an LC filter to achieve closed-loop IS stability under the proposed feedforward-feedback composite anti-interference output voltage controller. Similarly, the closed-loop control error system under the q-axis is also asymptotically stable, achieving precise output voltage control while also exhibiting good anti-interference performance.

[0080] Step 5: Design PI midpoint potential correction algorithm

[0081]

[0082] Where, ΔV c Represents the voltage difference between the two ends of the busbar voltage divider capacitor, t small_vector Represents the total time of positive and negative small vectors in a modulation cycle in the SVPWM algorithm. Positive and negative small vectors are two vector forms that appear in the SVPWM modulation cycle, corresponding to the output state of each phase in the three phases. They have the same effect in modulation, but have completely opposite effects on the midpoint potential. In an uncorrected SVPWM modulation cycle, the positive and negative small vectors have the same action time, which is Δt represents the adjustment amount of the positive and negative small vector action time within a sampling period in the SVPWM algorithm, and sat(g) is the saturation function: K P , K i They are the proportional coefficient and integral coefficient in the proportional-integral correction algorithm respectively.

[0083] In order to verify the effectiveness of the feedforward-feedback composite anti-interference output voltage controller proposed in this paper, a numerical simulation of an off-grid T-type three-level inverter with an LC filter was performed. The expected output voltage value of the off-grid T-type three-level inverter with an LC filter in a two-phase rotating coordinate system is [200V 0V] T , there are parameter perturbations of capacitance and inductance in the whole process, and load interference is introduced at 0.1s.

[0084] Figure 4 、 5 They are respectively the output voltage curve and the output error curve of the off-grid T-type three-level inverter with LC filter under the action of the composite controller designed by the present invention. Figure 5 The output voltage error curve of the off-grid T-type three-level inverter with LC filter according to the method of the present invention is shown in FIG. 1 , where (a) is the d-axis output voltage error e Vd , (b) is the q-axis output voltage error e Vq ,In the presence of matched and mismatched interference, the off-grid T-type three-level inverter system with LC ,filter can achieve high output voltage control accuracy and good ,anti-interference performance.

[0085] Figure 6 The control quantity curve of the off-grid T-type three-level inverter with LC filter, where (a) is the d-axis control voltage input V id , (b) is the q-axis control voltage input V iq .

[0086] Figure 7 The mismatch interference estimation curve of the off-grid T-type three-level inverter with LC filter, where (a) is d 1d , (b) is d 1q .

[0087] Figure 8 The matching interference estimation error curve of the off-grid T-type three-level inverter with LC filter, where (a) is d 2d , (b) is d 2q .

[0088] Figure 9 The busbar voltage divider capacitor potential curve of an off-grid T-type three-level inverter with an LC filter.

[0089] The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above-mentioned embodiment, but also include technical solutions composed of any combination of the above technical features.

Claims

1. An anti-interference backstepping control method for an off-grid three-level inverter based on ESO, characterized in that the steps include: Step 1: Establish a mathematical model of the three-phase current and voltage of an off-grid T-type three-level inverter system with an LC filter; Step 2: The off-grid T-type three-level inverter system with an LC filter described in step 1 is processed by transforming the coordinates to a rotating coordinate system, thereby eliminating the zero-sequence voltage component therein; Step 3: For the second-order system in the rotating coordinate system described in step 2, the load interference and the capacitance parameter perturbation are treated as lumped non-matching interference, and the inductance parameter perturbation is treated as matching interference. Two extended state observers are constructed to observe the matching interference and the non-matching interference respectively. The extended state observer in step 3 is in the following form: Unmatched aggregate interference d 1dq The extended state observer is as follows: Matched interference d 2dq The extended state observer is as follows: Among them, 1dq ,ζ 2dq ,ζ 3dq ,ζ 4dq V Ldq d 1dq , I idq d 2dq The estimated value of , α1, α2, α3, α4 are the observer gains; Step 4: Using the interference estimation, an anti-interference output voltage tracking controller is designed based on the backstepping control technology to track and control the output voltage of the inverter in real time. In step 4, the feedforward-feedback composite anti-interference output voltage controller is designed in the following form: in, The expected output voltage is [200V 0V] T , is a virtual controller; K eV , K eI is the positive controller gain; C0 represents the size of the nominal filter capacitor; Step 5: Using the measured mid-point potential deviation, the mid-point potential is balanced based on the proportional-integral mid-point potential correction technology, and the mid-point potential of the T-type three-level inverter is corrected in real time.

2. The anti-interference backstepping control method for an off-grid three-level inverter based on ESO according to claim 1, characterized in that: The three-phase voltage and current mathematical model of the inverter in step 1 is as follows: Among them, V Lx =[V La ,V Lb ,V Lc ] T and I ix =[I ia ,I ib ,I ic ] T Respectively represent the output voltage and inductor current values of phases a, b, and c of the LC filter in the three-phase stationary coordinate system, V iox =[V ioa ,V iob ,V ioc ] T is the voltage at the midpoint of the busbar voltage divider capacitor for phases a, b, and c of the LC filter in the three-phase stationary coordinate system, I Lx =[I La ,I Lb ,I Lc ] T It is used to describe the output current of phases a, b, and c of the LC filter in the three-phase stationary coordinate system. o'o It represents the potential difference between the neutral point and the midpoint of the busbar voltage divider capacitor, L represents the actual size of the filter inductor, and C represents the actual size of the filter capacitor.

3. The anti-interference backstepping control method for an off-grid three-level inverter based on ESO according to claim 1, characterized in that: The mathematical model of the system in the rotating coordinate system in step 2 is: Among them, V Ldq =[V Ld ,V Lq ] T , V idq =[V id ,V iq ] T It is used to describe the inverter output point to neutral point voltage of the dq axis in the two-phase rotating coordinate system of the LC filter, I idq =[I id ,I iq ] T , I Ldq =[I Ld ,I Lq ] T , w=2*f*π, f=50Hz means the output voltage frequency is 50Hz, L represents the actual size of the filter inductor, and C represents the actual size of the filter capacitor; The mathematical model after introducing interference is: in, L0 represents the size of the nominal filter inductor, and C0 represents the size of the nominal filter capacitor.

4. The anti-interference backstepping control method for an off-grid three-level inverter based on ESO according to claim 1, characterized in that: In step 5, the designed PI midpoint potential correction algorithm is specifically formulated as follows: Where, ΔV c Represents the voltage difference between the two ends of the busbar voltage divider capacitor, t small_vector Represents the total time of positive and negative small vectors in a modulation cycle in the SVPWM algorithm. Positive and negative small vectors are two vector forms that appear in the SVPWM modulation cycle, corresponding to the output state of each phase in the three phases. They have the same effect in modulation, but have completely opposite effects on the midpoint potential. In an uncorrected SVPWM modulation cycle, the positive and negative small vectors have the same action time, which is Δt represents the adjustment amount of the positive and negative small vector action time within a sampling period in the SVPWM algorithm, and sat(·) is the saturation function: K P , K i They are the proportional coefficient and integral coefficient in the proportional-integral midpoint potential correction algorithm respectively.

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