LC filtering four-leg inverter adaptive control method based on Lyapunov

Abstract

The invention provides a self-adaptive control method for an LC (inductance and capacitance) filtering four-leg inverter based on Lyapunov. The method comprises the following steps: firstly, obtaining a relation between an f bridge arm and a three-phase bridge arm terminal voltage control law by using a backstepping method to realize decoupling control of the three-phase bridge arm; and then adding a linear error term of the load voltage to an inductive current initial reference value obtained through static calculation to obtain an optimized inductive current reference value, and designing a three-phase bridge arm end voltage control law and a load admittance observer in combination with a Lyapunov theory. It is guaranteed that the system has global asymptotic stability and zero-steady-state-error output voltage under various load conditions, and meanwhile the problem that when the system operates under the small-power condition, the traditional Lyapunov-based adaptive control method is low in system energy convergence speed is solved.

Description

Technical Field

[0001] The invention relates to the technical field of power electronics, and in particular to an adaptive control method for an LC filter four-bridge-arm inverter based on Lyapunov. Background Art

[0002] Four-leg inverters have been applied to microgrids, grid-connected renewable energy generation, three-phase permanent magnet synchronous motor drives, uninterruptible power supplies, and electric vehicle charging piles. They have been widely studied due to their high power density, high DC bus voltage utilization, and strong load capacity. The control process of four-leg inverters to convert DC power into AC power can mostly be described as follows: first, the reference signal and measurement signal at the output end are used to obtain the inverter reference signal through the control law; then, pulse signals are generated using methods such as carrier modulation or space vector modulation to control the inverter switching devices; finally, the desired output is obtained at the output end after filtering out high-frequency harmonics using a filter.

[0003] Common inverter control methods are divided into linear control and nonlinear control. Linear control is represented by proportional integral control and proportional resonant control. The common practice of proportional integral control is to transform the three-phase AC signal from a stationary coordinate system to a rotating coordinate system to achieve zero steady-state error control. Its structure is simple, but parameter setting is more difficult and the dynamic adjustment time is longer. Proportional resonant control based on the internal model principle can track the sinusoidal signal with zero steady-state error without coordinate transformation. The disadvantage is that multiple resonant links need to be designed to achieve the purpose of amplifying the fundamental signal and suppressing the harmonic signal, which makes the control system more complicated.

[0004] When dealing with the discrete nonlinear characteristics of the inverter system, nonlinear control has shown great advantages. Among them, model predictive control has been a hot topic in recent years. This control method discretizes the system dynamic equations, predicts the output at the next moment from the current and past states, and selects the optimal control vector based on the principle of minimum cost function. This method has good dynamic and steady-state performance, but the switching frequency is not fixed and the system calculation burden is heavy. Deadbeat control accurately models the system and uses the collected state quantity and the reference output quantity at the next moment to calculate the pulse width of the next switching cycle. This method is simple to implement and has good steady-state and dynamic effects. The disadvantage is that the parameter robustness is poor. Sliding mode control constructs the sliding surface with the error and error derivative of the state variable, and controls the inverter according to the relative position of the current state and the sliding surface. This method is often combined with repetitive control to limit the sliding surface within a limited time. It has good dynamic performance, but its inherent jitter problem needs attention.

[0005] The above control methods have their own advantages and disadvantages, but they have a common limitation, that is, they cannot strictly guarantee the global asymptotic stability of the closed-loop control system. To address this problem, some scholars have proposed a single-loop control method based on Lyapunov, which ensures the stability of the system and has been successfully applied to power electronic system control such as DC-DC converters, three-phase AC-DC rectifiers, single-phase active filters, single-phase grid-connected photovoltaic inverters, and single-phase LCL filter grid-connected inverters. The classic Lyapunov-based control method expresses the Lyapunov function as the linear sum of squares of the tracking errors of capacitor voltage and inductor current, solves the duty cycle to ensure the negative definiteness of the derivative of the energy function, and then obtains the control law. This control method belongs to single-loop control and has steady-state errors. H. Komurcugil's team proposed an extended Lyapunov-based single-phase UPS inverter control method, which first introduced the voltage loop in the Lyapunov-based control method, and the proposed voltage and current dual-loop control method eliminated the steady-state error. The Sefa team applied the Lyapunov-based dual-loop control method to single-phase and three-phase LCL grid-connected inverters. The R. Gavagsaz-Ghoachani team used the Lyapunov stability theory for the first time to simultaneously complete the design of the current observer and control law, and constructed a single-phase LC filter rectifier adaptive control law based on Lyapunov, which saved the current sensor while obtaining the global stability of the system. He Jinsong et al. combined the advantages of the control methods of the H. Komurcugil team and the R. Gavagsaz-Ghoachani team, and proposed a Lyapunov-based single-phase and three-phase three-leg inverter adaptive control method, which saved the load current sensor while ensuring the global asymptotic stability of the system and achieved zero steady-state error control.

[0006] Lyapunov-based adaptive control is an extremely attractive control method. The design of this method in the control of a four-leg inverter cannot be compared with that of a three-leg inverter, because in the control of a three-leg inverter, only one load admittance needs to be observed. After the system state equation is converted from the abc stationary coordinate system to the dq0 rotating coordinate system to decouple the system, the control target changes from a sinusoidal AC quantity to a constant, and the load admittance matrix to be observed can be separated from the state vector, which makes it very easy to construct adaptive control laws and parameter design. However, a four-leg inverter needs to deal with unbalanced load conditions and observe multiple load admittances. When performing coordinate transformation, the load admittance matrix to be observed cannot be separated from the state vector, so the Lyapunov-based four-leg inverter adaptive control law cannot be designed and implemented using a similar method; when the system operates at low power, the traditional Lyapunov-based inverter adaptive control method has the problem of slow system energy convergence. Summary of the invention

[0007] In view of the deficiencies of the above-mentioned prior art, the present invention proposes an adaptive control method for a four-bridge-arm inverter with LC filtering based on Lyapunov. First, the relationship between the voltage control law of the f-bridge-arm terminal and the voltage control law of the three-phase bridge-arm terminal is obtained by the back-stepping method to realize the decoupling control of the three-phase bridge-arm; then, the initial reference value of the inductor current obtained by static calculation is added with the linear error term of the load voltage to obtain the optimized reference value of the inductor current, and the three-phase bridge-arm terminal voltage control law and the load admittance observer are designed in combination with the Lyapunov stability theory. The proposed method does not require a load current sensor, and ensures that the system has global asymptotic stability and an output voltage with zero steady-state error under various load conditions. At the same time, it solves the problem of slow system energy convergence speed in the traditional adaptive control method based on Lyapunov when the system is running at low power.

[0008] The technical solution of the present invention is:

[0009] A Lyapunov-based LC filter four-leg inverter adaptive control method specifically includes the following steps:

[0010] Step 1: Based on Kirchhoff's voltage law, establish the voltage dynamic equations of the two-level four-leg inverter;

[0011] The expression of the voltage dynamic equation group of the two-level four-bridge-arm inverter is:

[0012]

[0013] Among them, u ao 、u bo 、u co and u fo They represent the voltages of the bridge arms of phases a, b, c and f, respectively; u no Indicates the voltage at the neutral point of the load relative to the midpoint of the DC side capacitor; i La 、i Lb 、i Lc and i Lf Respectively represent the a-phase, b-phase and c-phase inductor currents and the neutral inductor current; u Ca 、u Cb and u Cc They represent the capacitor voltages of phase a, phase b and phase c on the output side (also the load voltage); L represents the filter inductor;

[0014] Step 2: Set the voltage of the load neutral point relative to the midpoint of the DC side capacitor to zero, eliminate the common term of the voltage dynamic equation obtained in step 1, and obtain the voltage dynamic equation group of the decoupled two-level four-leg inverter;

[0015] Let u no=0, and substitute it into the voltage dynamic equation group of step 1, eliminate the common terms of the voltage dynamic equation, so that the three voltage dynamic equations representing the three-phase bridge arms are decoupled, and the voltage dynamic equation group of the decoupled two-level four-bridge-arm inverter is obtained;

[0016] The voltage dynamic equations of the decoupled two-level four-bridge-arm inverter are expressed as follows:

[0017]

[0018] Step 3: Add the four voltage dynamic equations in the decoupled voltage dynamic equation group obtained in step 2 to obtain the overall voltage dynamic equation; establish the current dynamic equation group of the two-level four-bridge arm inverter based on Kirchhoff's current law; substitute the inductor current relationship of the four bridge arms into the overall voltage dynamic equation, eliminate the inductor current term, and obtain the relationship between the voltage control law at the f bridge arm end and the voltage control law at the three-phase bridge arm end;

[0019] Step 3.1: Add the voltage dynamic equations of the four bridge arms in the equation group (2) of step 2 to obtain the overall voltage dynamic equation;

[0020] The expression of the overall voltage dynamic equation is:

[0021] u ao +u bo +u co +u fo =Ldi La / dt+Ldi Lb / dt+Ldi Lc / dt-Ldi Lf / dt+u Ca +u Cb +u Cc (3)

[0022] Step 3.2: Based on Kirchhoff's current law, establish the current dynamic equations of the two-level four-leg inverter;

[0023] The expression of the two-level four-bridge-arm inverter current dynamic equation group is:

[0024]

[0025] Among them, G a , G b and G c They represent the actual values ​​of the load admittance of phase a, phase b and phase c respectively; C represents the filter capacitor;

[0026] Step 3.3: Substitute the inductor current relationship of the four bridge arms in equation group (4) into the overall voltage dynamic equation, eliminate the inductor current term, and obtain the relationship between the voltage control law at the f bridge arm end and the voltage control law at the three-phase bridge arm end. The specific expression is:

[0027] u fo =u Ca +u Cb +u Cc -u ao -u bo -u co (5)

[0028] Step 4: Taking bridge arm a as an example, define the load voltage reference value and the load admittance estimation; define the tracking error of the load voltage and the estimation error of the virtual load admittance; substitute the load voltage reference value into the decoupled dynamic equations obtained in step 2, and obtain the initial reference value of the inductor current under the assumption that the system is in a steady state; add the linear error term of the load voltage to the initial reference value of the inductor current to obtain the optimized reference value of the inductor current; define the tracking error of the inductor current;

[0029] Step 4.1: Define the load voltage reference value as u Caref , where u Caref is a known time-varying sinusoidal alternating quantity with an amplitude of U m , the angular frequency is ω; the load admittance estimate is defined as

[0030] Step 4.2: Define e2 and e3 as the load voltage tracking error and virtual load admittance estimation error respectively. The specific expressions are:

[0031]

[0032] Step 4.3: Assuming the system is in steady state, set u Ca =u Caref Substituting into the current dynamic equation, we get the initial reference value of the inductor current i Laref ;

[0033] The expression of the initial reference value of the inductor current is:

[0034]

[0035] Step 4.4: Add the linear error term of the load voltage to the initial reference value of the inductor current to obtain the optimized reference value of the inductor current i Laref1 ;

[0036] The expression of the optimized inductor current reference value is:

[0037]

[0038] The constant τ (τ>0) is a control parameter used to adjust the relationship between the optimized inductor current reference value and the load voltage error;

[0039] Step 4.5: Define e1 as the inductor current tracking error. The specific expression is:

[0040] e1=i La -i Laref1 (9)

[0041] Step 5: Construct the Lyapunov function using the three errors defined in step 4;

[0042] Use e1, e2, and e3 defined in step 4 to construct a Lyapunov function to characterize the energy of the system;

[0043] The expression of the constructed Lyapunov function is:

[0044]

[0045] Among them, ρ, η (ρ>0, η>0) represent two control parameters, which are used to allocate the proportion of each energy;

[0046] Step 6: Derivate the Lyapunov function obtained in step 5 and the three errors defined in step 4, and substitute the derivatives of the three errors into the derivative of the Lyapunov function; on the principle of ensuring that the derivative of the Lyapunov function is always less than zero at the unstable point, construct the load admittance observer and terminal voltage control law of the a bridge arm with unknown parameters, and similarly obtain the load admittance observer and terminal voltage control law of the b and c bridge arms, and obtain the terminal voltage control law of the f bridge arm with unknown parameters according to step 3.3;

[0047] Step 6.1: Calculate the derivative of the Lyapunov function in step 5. The specific expression is:

[0048]

[0049] The derivatives of the tracking error of the load voltage, the inductor current and the estimated error of the load admittance are obtained. The specific expressions are:

[0050]

[0051] Substituting formula (12) into formula (11), we can obtain the expansion of the derivative of the Lyapunov energy function, which is expressed as follows:

[0052]

[0053] Simplifying and reorganizing formula (13), we get the block expansion of the derivative of the Lyapunov energy function, which is expressed as follows:

[0054]

[0055] The constant k (k>τL / C) is a control parameter, which is introduced to add the current error term to the voltage control law, thereby speeding up the dynamic response of the system.

[0056] Step 6.2: Let α = β = 0, and derive the bridge arm load admittance observer and terminal voltage control law with unknown parameters;

[0057] The expression of the bridge arm load admittance observer is obtained as follows:

[0058]

[0059] The expression of the voltage control law at the a bridge arm terminal is obtained as follows:

[0060]

[0061] The design process of the load admittance observer and terminal voltage control law of bridge arms b and c is similar to that of bridge arm a. Furthermore, according to step 3.3, the terminal voltage control law of bridge arm f with unknown parameters can be obtained;

[0062] Step 7: Under the condition that the system meets the requirements of fast dynamic response and appropriate damping and the output voltage of the inverter bridge arm is within the linear range, obtain the parameter value range; select any set of parameters within the above parameter value range, substitute them into the observer and control law obtained in step 6, obtain the terminal voltage control law of the four bridge arms, and generate a pulse signal for controlling the on and off of the power switch tube through carrier modulation;

[0063] Step 7.1: Perform stability analysis on the system. It can be seen that the parameters are within a larger range (ρ, τ, η>0, and k>τLC) and will not affect the global large signal stability of the system. The voltage output of each bridge arm should be within the linear range, that is, it should be ensured that the voltage control law of each bridge arm is always between -0.5E and 0.5E during the dynamic process of the system. Based on the above principles, the appropriate control parameter value range of the present invention is determined to be ρ∈(2~11), k∈(15~40), τ∈(0.001~0.03), η∈(160~500);

[0064] Step 7.2: Select a set of data in the above parameter value range as the control parameters of the present invention. The selected control parameters are specifically ρ=7, k=25.5, τ=0.15, η=300, and substitute the control parameters into the observer and control law obtained in step 6 to obtain the terminal voltage control law of the four bridge arms, and generate a pulse signal for controlling the on and off of the power switch tube through carrier modulation.

[0065] The beneficial effects of adopting the above technical solution are:

[0066] The method of the present invention improves the traditional Lyapunov-based inverter adaptive control method, realizes the Lyapunov-based four-bridge-arm inverter adaptive control method, and establishes an improved load admittance observer, saving three load current sensors. The method of the present invention not only ensures that the system has global asymptotic stability and an output voltage with zero steady-state error, but also, compared with the traditional Lyapunov-based inverter adaptive control method, ensures that the system energy convergence speed is always related to the load voltage error, and improves the dynamic response speed of the system when it operates in a low-power situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 : is a topology diagram of a two-level four-bridge-arm inverter in this embodiment;

[0068] Figure 2 This is a structural diagram of the control system of the method proposed in this embodiment;

[0069] Figure 3 is the performance of the proposed method in this embodiment under a linear load step; wherein, (a) load voltage; (b) load current; (c) load voltage in dq0 coordinate system; (d) load admittance observation value;

[0070] Figure 4 is the performance of the proposed method in this embodiment under a nonlinear rectifier load step; wherein, (a) load voltage; (b) load current; (c) load voltage in dq0 coordinate system; (d) load admittance observation value;

[0071] Figure 5 The performance of the proposed method in this embodiment under the reference voltage step under unbalanced load; wherein, (a) load voltage; (b) load current; (c) load voltage in dq0 coordinate system; (d) load admittance observation value;

[0072] Figure 6 : The performance of the method proposed in this embodiment under the DC side power supply voltage step with a linear unbalanced load; wherein, (a) load voltage; (b) load current; (c) load voltage in dq0 coordinate system; (d) load admittance observation value;

[0073] Figure 7 : The performance of the dual-loop PI method under a linear load step in this embodiment; wherein, (a) load voltage; (b) load current; (c) load voltage in the dq0 coordinate system;

[0074] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and implementation examples.

[0075] The two-level four-leg inverter topology is as follows: Figure 1 As shown. E represents the DC side voltage; S1~S8 represent switch components; L represents filter inductor; C represents filter capacitor; i La 、i Lb 、i Lc and i Lf Respectively represent the a-phase, b-phase and c-phase inductor currents and the neutral inductor current; u Ca 、u Cb and u Cc Respectively represent the output side a phase, b phase and c phase capacitor voltage (also represents the load voltage);

[0076] The present embodiment provides an adaptive control method for a four-leg inverter with LC filter based on Lyapunov, the method comprising the following steps:

[0077] Step 1: Based on Kirchhoff's voltage law, establish the voltage dynamic equations of the two-level four-leg inverter;

[0078] The expression of the voltage dynamic equation group of the two-level four-bridge-arm inverter is:

[0079]

[0080] Among them, u ao 、u bo 、u co and u fo They represent the voltages of the bridge arms of phases a, b, c and f, respectively; u no Indicates the voltage at the neutral point of the load relative to the midpoint of the DC side capacitor;

[0081] Step 2: From equation (17), we can see that the voltage dynamic equations of each bridge arm contain a common term u no , that is, there is a coupling relationship between the bridge arms. To facilitate the design of the adaptive control law, the voltage of the load neutral point relative to the midpoint of the DC side capacitor is set to zero, that is, u no =0, and substitute it into the equation group (17), eliminate the common terms of the voltage dynamic equations, decouple the three voltage dynamic equations representing the three-phase bridge arms, and obtain the voltage dynamic equation group of the decoupled two-level four-bridge-arm inverter;

[0082] The voltage dynamic equations of the decoupled two-level four-bridge-arm inverter are expressed as follows:

[0083]

[0084] Step 3: Add the voltage dynamic equations of the four bridge arms in equation group (18) to obtain the overall voltage dynamic equation;

[0085] The expression of the overall voltage dynamic equation is:

[0086] u ao +u bo +u co +u fo =Ldi La / dt+Ldi Lb / dt+Ldi Lc / dt-Ldi Lf / dt+u Ca +u Cb +u Cc (19)

[0087] Based on Kirchhoff's current law, the current dynamic equations of the two-level four-leg inverter are established;

[0088] The expression of the two-level four-bridge-arm inverter current dynamic equation group is:

[0089]

[0090] Among them, G a , G b and G c Respectively represent the actual values ​​of the load admittance of phase a, phase b and phase c;

[0091] Substitute the inductor current relationship of the four bridge arms in equation group (20) into the overall voltage dynamic equation, eliminate the inductor current term, and obtain the relationship between the voltage control law at the f bridge arm end and the voltage control law at the three-phase bridge arm end. The specific expression is:

[0092] u fo =u Ca +u Cb +u Cc -u ao -u bo -u co (twenty one)

[0093] Using the relationship between the derived f bridge arm voltage control law and the three-phase bridge arm voltage control law, we can ensure u no =0, further, the three-phase bridge arm can be regarded as three independent half-bridge inverters;

[0094] Step 4: Taking bridge arm a as an example, define the load voltage reference value and the load admittance estimation; define the tracking error of the load voltage and the estimation error of the virtual load admittance; substitute the load voltage reference value into the decoupled dynamic equation group, and obtain the initial reference value of the inductor current through static calculation under the assumption that the system is in a steady state; add the linear error term of the load voltage to the initial reference value of the inductor current to obtain the optimized reference value of the inductor current; define the tracking error of the inductor current;

[0095] Step 4.1: Define the load voltage reference value as u Caref , the control process of load voltage is as follows:

[0096] u Ca →u Caref (twenty two)

[0097] Among them, u Caref is a known time-varying sinusoidal alternating quantity with an amplitude of U m , the angular frequency is ω;

[0098] The estimator of load admittance is defined as The load admittance estimation process can be described as follows:

[0099]

[0100] Step 4.2: Define e2 and e3 as the load voltage tracking error and virtual load admittance estimation error respectively. The specific expressions are:

[0101]

[0102] Step 4.3: Assuming the system is in steady state, set u Ca =u Caref Substituting into the current dynamic equation of equation group (20), we get the initial reference value of the inductor current i Laref ;

[0103] The expression of the initial reference value of the inductor current is:

[0104]

[0105] Step 4.4: Add the linear error term of the load voltage to the initial reference value of the inductor current to obtain the optimized reference value of the inductor current i Laref1 ;

[0106] The expression of the optimized inductor current reference value is:

[0107]

[0108] The constant τ (τ>0) is a control parameter used to adjust the relationship between the optimized inductor current reference value and the load voltage error;

[0109] The control process of the inductor current can be described as:

[0110] i La →i Laref1 (27)

[0111] Step 4.5: Define e1 as the inductor current tracking error. The specific expression is:

[0112] e1=i La -i Laref1 (28)

[0113] Step 5: Construct the Lyapunov function using the three errors defined in step 4;

[0114] Use e1, e2, and e3 to construct the Lyapunov function to characterize the energy of the system;

[0115] The expression of the constructed Lyapunov function is:

[0116]

[0117] Among them, ρ, η (ρ>0, η>0) represent two control parameters, which are used to allocate the proportion of each energy. When each error is reduced to zero, the system energy converges to zero, indicating that the system reaches a steady state. At this time, the load voltage tracks the reference voltage, the inductor current tracks the reference current, and the load admittance estimate is equal to the actual value;

[0118] Define ξ=[e1,e2,e3] T According to Lyapunov theory, if the system is globally asymptotically stable, the following three conditions must be met:

[0119] 1) V ≥ 0, if and only if ξ = [0, 0, 0] T When V=0

[0120] 2) If any element in ξ tends to infinity, then V→∞

[0121] 3) When ξ≠0,

[0122] It can be seen from the form of equation V that conditions 1) and 2) can always be met, so as long as condition 3) is met, the system state point can be guaranteed to move to the equilibrium point in the end;

[0123] Step 6: Derivate the Lyapunov function and the three errors, and substitute the derivatives of the three errors into the derivative of the Lyapunov function; based on the principle that the derivative of the Lyapunov function is always less than zero at the unstable point, construct the load admittance observer and terminal voltage control law of the a bridge arm with unknown parameters, and similarly obtain the load admittance observer and terminal voltage control law of the b and c bridge arms, and obtain the terminal voltage control law of the f bridge arm with unknown parameters according to step 3.3;

[0124] Step 6.1: Find the derivative of the Lyapunov function. The specific expression is:

[0125]

[0126] The derivatives of the tracking error of the load voltage, the inductor current and the estimated error of the load admittance are obtained. The specific expressions are:

[0127]

[0128] Substituting formula (31) into formula (30), we can obtain the expansion of the derivative of the Lyapunov energy function, which is expressed as follows:

[0129]

[0130] Simplifying and reorganizing equation (32), we get the block expansion of the derivative of the Lyapunov energy function, which is expressed as follows:

[0131]

[0132] The constant k (k>τL / C) is a control parameter. This parameter is introduced to add the current error term to the voltage control law, thereby accelerating the dynamic response speed of the system. From formula (33), it can be seen that if α=β=0, then when ξ≠[0,0,0] T When

[0133]

[0134] Condition 3) is met, and the system is globally asymptotically stable;

[0135] Step 6.2: Let α = β = 0, and derive the bridge arm load admittance observer and terminal voltage control law with unknown parameters;

[0136] The expression of the bridge arm load admittance observer is obtained as follows:

[0137]

[0138] The expression of the voltage control law at the a bridge arm terminal is obtained as follows:

[0139]

[0140] The design process of the load admittance observer and terminal voltage control law of bridge arms b and c is similar to that of bridge arm a. Furthermore, according to step 3.3, the terminal voltage control law of bridge arm f with unknown parameters can be obtained;

[0141] Step 7: Under the condition that the system meets the requirements of fast dynamic response and appropriate damping and the output voltage of the inverter bridge arm is within the linear range, obtain the parameter value range; select any set of parameters within the above parameter value range, substitute them into the observer and control law obtained in step 6, obtain the terminal voltage control law of the four bridge arms, and generate a pulse signal for controlling the on and off of the power switch tube through carrier modulation;

[0142] Step 7.1: Since the system state matrix has unknown quantity G a and u Ca and the time variable u Caref , the system parameter tuning cannot be performed by traditional methods. The stability analysis of the system shows that the parameters are within a large range (ρ, τ, η>0, and ) value will not affect the global large signal stability of the system, and the voltage output of each bridge arm should be within the linear range, that is, it should be ensured that the voltage control law of each bridge arm is always between -0.5E and 0.5E during the dynamic process of the system. It can be seen from formula (37) that the parameters ρ, k and τ on the diagonal affect the dynamic response of the system, while the parameters τ and η on the non-diagonal affect the damping of the system. The larger η is, the greater the system damping is. The system parameters are shown in Table 1. Based on the above principles, the appropriate control parameter value ranges in the present invention are determined to be ρ∈(2~11), k∈(15~40), τ∈(0.001~0.03), η∈(160~500);

[0143] Step 7.2: Select a set of data in the above parameter value range as the control parameters of the present invention. The selected control parameters are specifically ρ=7, k=25.5, τ=0.15, η=300, and substitute the control parameters into the observer and control law obtained in step 6 to obtain the terminal voltage control law of the four bridge arms, and generate a pulse signal for controlling the on and off of the power switch tube through carrier modulation.

[0144] Taking bridge arm a as an example, the stability analysis of the control system constructed by the proposed control method is carried out:

[0145] Substituting equations (35) and (36) into equation (31), we can obtain the following first-order differential equations for the error:

[0146]

[0147] The above formula can be expressed as Expand the matrix A(t), the specific expression is as follows:

[0148]

[0149] If the matrix A(t) is a non-singular matrix with time-varying elements, then the system is a linear time-varying continuous system with one and only one equilibrium point. The necessary and sufficient condition for the system to be asymptotically stable over a large range at the equilibrium point is that for any given continuous symmetric negative definite matrix Q(t), there exists a continuous symmetric positive definite matrix P(t) that satisfies:

[0150]

[0151] The Lyapunov function of the system is:

[0152] V(ξ)=ξ T P(t)ξ (40)

[0153] The matrix P(t) can be expressed as:

[0154]

[0155] Substituting P(t) and A(t) into equation (39), we can obtain the matrix Q(t):

[0156]

[0157] From equation (42), we can see that the system has negative eigenvalues ​​in both e1 and e2 dimensions, which means that as t→∞, e1, e2→0, and Substituting it into equation (31), we have e3→0. Therefore, although Q(t) is a symmetric semi-negative definite matrix, the system is still asymptotically stable over a large range, indicating that the voltage control law at the a bridge arm end has global asymptotic stability. Similarly, the stability of the voltage control law at the b and c bridge arm ends can be analyzed.

[0158] Reasons for optimizing the initial reference value of the inductor current:

[0159] The derivative of the energy function indicates the rate of change of the system energy. A negative derivative indicates energy decay. The smaller the derivative, the faster the decay rate. The derivative of the energy function constructed by the traditional Lyapunov-based adaptive control method is: The energy function derivative of the proposed method is The energy function derivatives of both are composed of the square of the inductor current tracking error and the square of the load voltage tracking error. Each parameter represents the correlation between the system energy change speed and each item. Although the larger the parameter, the faster the system energy decays, the output voltage u ao It varies between -E / 2 and E / 2. Inappropriate control parameters will make equation (36) invalid at a certain moment, which will lead to system instability. Assume that the energy derivative is When , the system performance is optimal, λ1 and λ2 are positive constants, which can ensure the convergence of system energy from two dimensions. In order to make the system built by the traditional Lyapunov adaptive control method achieve optimal performance, it is necessary to ensure that the following formula holds;

[0160] k=λ1,ρG a =λ2 (43)

[0161] From formula (36), we can see that if ρ is too large, the system will be unstable at a certain moment. When the system operates at low power, that is, the load gradually decreases, ρG a→0, from a certain moment on, equation (43) is no longer valid, the energy derivative is independent of the load voltage error, and the system control performance deteriorates. In the control system constructed by the proposed method, in order to optimize the system performance, the following equation must be guaranteed to hold;

[0162]

[0163] It can be seen that even if ρG a →0, we can also find the appropriate parameter ρτ to satisfy equation (44), optimize the system performance, and ensure that the system energy can converge from the two dimensions of load voltage error and inductor current error under various load conditions.

[0164] In order to verify the feasibility and superiority of the adaptive control method of the four-leg inverter with LC filter based on Lyapunov proposed in this invention, a four-leg inverter simulation control system was built based on the Matlab / Simulink software platform. The system parameters are shown in Table 1. The three loads are: three-phase balanced load (Load1, R a =R b =R c =10Ω), three-phase unbalanced load (Load2, R a =10Ω, phase b is unloaded, R c =100Ω), nonlinear load (bridge rectifier circuit with variable resistor R). The simulation system verifies the dynamic and steady-state performance of the proposed control method under balanced, unbalanced and nonlinear load conditions, as well as the system's ability to cope with changes in the reference voltage and DC side voltage under unbalanced load conditions, and compares the performance with the dual-loop PI control method under load step conditions.

[0165] Table 1 System nominal parameters

[0166]

[0167] Performance analysis of the proposed control method:

[0168] like Figure 3 As shown in FIG. 1 , the load switches from balanced load Load1 to unbalanced load Load2 at 0.04 seconds, and returns to balanced load Load1 after 40 milliseconds. The load voltage returns to a steady state after a short dynamic process starting from the load switching. Figure 4 As shown in the figure, R in the nonlinear load switches from 60Ω to no-load in 0.05 seconds, and the system reaches a new steady state after a short dynamic process. The total harmonic distortion (THD) of the load voltage is reduced from 3.11% to 0.27%. The simulation results verify that the proposed control method can respond quickly to linear load switching and nonlinear load switching.

[0169] like Figure 5 As shown, the load voltage reference switches from 162.6V to 100V in 0.04 seconds and recovers to 162.6V after 40 milliseconds. The load voltage can always quickly track the reference voltage and maintain stability, which verifies that the proposed control method has a strong tracking ability for different load reference voltages.

[0170] like Figure 6 As shown in the figure, under the unbalanced load condition, the DC side power supply voltage switches from 400 V to 300 V in 0.04 seconds and recovers to 400 V after 40 ms. The load voltage and current are almost unaffected by this disturbance, which verifies that the proposed control method is robust to DC side load voltage disturbances.

[0171] Performance comparison between the classic dual-loop PI control method and the proposed control method:

[0172] The dynamic and steady-state performances of the classic dual-loop PI control method and the proposed control method under linear load step conditions are compared using a simulation system. Figure 7 The waveform diagram of the classic dual-loop PI control method under load switching is shown in Table 2. The dynamic and steady-state performance indicators of the two control methods are compared. The simulation results show that the PI control method has better dynamic performance and worse steady-state performance. Its average steady-state error is 0.8%, the phase voltage unbalance rate (PVUR) is 1.97%, and the three-phase load voltage THD is 0.82%, 0.46% and 0.33% respectively; the proposed control method has a slightly longer dynamic response time than PI control, but omits the load current sensor, the average steady-state error is 0.02%, the PVUR is 0.06%, the three-phase load voltage THD is 0.25%, 0.28% and 0.26% respectively, and the three-phase load voltage steady-state error and phase voltage unbalance rate are almost zero.

[0173] Table 2 Comparison between the proposed control method and the dual-loop PI control method

[0174]

[0175] In summary, the present invention proposes a Lyapunov-based LC filter four-bridge arm inverter adaptive control method, which fills the gap in the application of Lyapunov-based adaptive control methods in four-bridge arm inverter control, and solves the problem of slow system energy convergence speed in the traditional Lyapunov-based inverter adaptive control method when the system runs in a low power situation. First, the relationship between the f-bridge arm terminal voltage control law and the three-phase bridge arm terminal voltage control law is obtained by the backstepping method, and the three-phase bridge arm decoupling control is realized; then the initial reference value of the inductor current obtained by static calculation is added to the linear error term of the load voltage to obtain the optimized inductor current reference value, and the three-phase bridge arm terminal voltage control law and load admittance observer are designed in combination with the Lyapunov stability theory, without the need for a load current sensor, to ensure that the system has global asymptotic stability under various load conditions and that the system output voltage has no steady-state error, and solves the problem of slow system energy convergence speed in the traditional Lyapunov-based adaptive control method when the system runs in a low power situation. The simulation results show that the proposed adaptive control method for the four-leg inverter with LC filter based on Lyapunov does not require a load current sensor. It can ensure load voltage balance, small steady-state error and low harmonic content under balanced, unbalanced and nonlinear load conditions. When the system operates at low power, it ensures that the system has a fast dynamic response speed and low THD.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A Lyapunov-based LC filter four-leg inverter adaptive control method, characterized in that: The method comprises the following steps: Step 1: Based on Kirchhoff's voltage law, establish the voltage dynamic equations of the two-level four-leg inverter; Step 2: Set the voltage of the load neutral point relative to the midpoint of the DC side capacitor to zero, eliminate the common term of the voltage dynamic equation obtained in step 1, and obtain the voltage dynamic equation group of the decoupled two-level four-leg inverter; Step 3: Add the four voltage dynamic equations in the decoupled voltage dynamic equation group obtained in step 2 to obtain the overall voltage dynamic equation; establish the current dynamic equation group of the two-level four-bridge arm inverter based on Kirchhoff's current law; substitute the inductor current relationship of the four bridge arms into the overall voltage dynamic equation, eliminate the inductor current term, and obtain the relationship between the voltage control law at the f bridge arm end and the voltage control law at the three-phase bridge arm end; Step 4: Define the load voltage reference value and the load admittance estimation; define the tracking error of the load voltage and the estimation error of the load admittance; substitute the load voltage reference value into the decoupled dynamic equations obtained in step 2, and obtain the initial reference value of the inductor current under the assumption that the system is in a steady state; The initial reference value of the inductor current is added with the linear error term of the load voltage to obtain the optimized reference value of the inductor current; Define the tracking error of the inductor current; Step 5: Construct the Lyapunov function using the three errors defined in step 4; Step 6: Derivative the Lyapunov function and the three errors obtained in step 5, and substitute the derivatives of the three errors into the derivative of the Lyapunov function; Based on the principle of ensuring that its derivative is always less than zero at the unstable point, the load admittance observer and terminal voltage control law of bridge arm a with unknown parameters are constructed. Similarly, the load admittance observer and terminal voltage control law of bridge arms b and c are obtained, and the terminal voltage control law of bridge arm f with unknown parameters is obtained according to step 3. Step 7: Under the condition that the system meets the requirements of fast dynamic response and appropriate damping and the output voltage of the inverter bridge arm is within the linear range, obtain the parameter value range; select any set of parameters within the above parameter value range, substitute them into the observer and control law obtained in step 6, and obtain the terminal voltage control law of the four bridge arms, and generate a pulse signal for controlling the on and off of the power switch tube through carrier modulation.

2. According to the Lyapunov-based LC filter four-leg inverter adaptive control method of claim 1, it is characterized in that: The expression of the voltage dynamic equation group of the two-level four-bridge-arm inverter is: Among them, u ao 、u bo 、u co and u fo They represent the voltages of the bridge arms of phases a, b, c and f, respectively; u no Indicates the voltage at the neutral point of the load relative to the midpoint of the DC side capacitor; i La 、i Lb 、i Lc and i Lf Respectively represent the a-phase, b-phase and c-phase inductor currents and the neutral inductor current; u Ca 、u Cb and u Cc They respectively represent the capacitor voltages of phase a, phase b and phase c on the output side (also representing the load voltage); L represents the filter inductor.

3. According to the Lyapunov-based LC filter four-leg inverter adaptive control method of claim 1, it is characterized in that: The step 2 further comprises: Let u no =0, and substitute it into the voltage dynamic equation group of claim 2, eliminate the common terms of the voltage dynamic equations, so that the three voltage dynamic equations representing the three-phase bridge arms are decoupled, and the voltage dynamic equation group of the decoupled two-level four-bridge-arm inverter is obtained; The voltage dynamic equations of the decoupled two-level four-bridge-arm inverter are expressed as follows:

4. According to the Lyapunov-based LC filter four-leg inverter adaptive control method of claim 1, it is characterized in that: The step 3 further comprises: Step 3.1: Add the voltage dynamic equations of the four bridge arms in the equation group (2) of claim 3 to obtain the overall voltage dynamic equation; The expression of the overall voltage dynamic equation is: in ao +in bo +in co +in fo =Go La / dt+Ldi Lb / dt+Ldi Lc / dt-Ldi Lf / dt+u Ca +in Cb +in Cc (3) Step 3.2: Based on Kirchhoff's current law, establish the current dynamic equations of the two-level four-leg inverter; The expression of the two-level four-bridge-arm inverter current dynamic equation group is: Among them, G a , G b and G c They represent the actual values ​​of the load admittance of phase a, phase b and phase c respectively; C represents the filter capacitor; Step 3.3: Substitute the inductor current relationship of the four bridge arms in equation group (4) into the overall voltage dynamic equation, eliminate the inductor current term, and obtain the relationship between the voltage control law at the f bridge arm end and the voltage control law at the three-phase bridge arm end. The specific expression is: in fo =in Ca +in Cb +in Cc -in ao -in bo -in co (5).

5. According to the Lyapunov-based LC filter four-leg inverter adaptive control method of claim 1, it is characterized in that: The step 4 further comprises: Step 4.1: Taking bridge arm a as an example, define the load voltage reference value as u Caref , where u Caref is a known time-varying sinusoidal alternating quantity with an amplitude of U m , the angular frequency is ω; the load admittance estimate is defined as Step 4.2: Define e2 and e3 as the load voltage tracking error and virtual load admittance tracking error respectively. The specific expressions are: Step 4.3: Assuming the system is in steady state, set u Ca =u Caref Substituting into the current dynamic equation, we get the initial reference value of the inductor current i Laref ; The expression of the initial reference value of the inductor current is: Step 4.4: Add the linear error term of the load voltage to the initial reference value of the inductor current to obtain the optimized reference value of the inductor current i Laref1 ; The expression of the optimized inductor current reference value is: The constant τ (τ>0) is a control parameter used to adjust the relationship between the optimized inductor current reference value and the load voltage error; Step 4.5: Define e1 as the inductor current tracking error. The specific expression is: e1=i La -i Laref1 (9).

6. According to the Lyapunov-based LC filter four-leg inverter adaptive control method of claim 1, it is characterized in that: The step 5 is specifically as follows: Using e1, e2, e3 defined in claim 5 to construct a Lyapunov function for characterizing the energy of the system; The expression of the constructed Lyapunov function is: Among them, ρ, η (ρ>0, η>0) represent two control parameters, which are used to allocate the proportion of each energy.

7. The adaptive control method of a four-leg inverter with LC filter based on Lyapunov according to claim 1, characterized in that: The step 6 further comprises: Step 6.1: Calculate the derivative of the Lyapunov function in claim 6. The specific expression is: The derivatives of the load voltage, the tracking error of the inductor current and the estimated error of the load admittance are obtained. The specific expressions are: Substituting formula (12) into formula (11), we can obtain the expansion of the derivative of the Lyapunov energy function, which is expressed as follows: Simplifying and reorganizing formula (13), we get the block expansion of the derivative of the Lyapunov energy function, which is expressed as follows: The constant k (k>τL / C) is a control parameter, which is introduced to add the current error term to the voltage control law, thereby speeding up the dynamic response of the system. Step 6.2: Let α = β = 0, and derive the bridge arm load admittance observer and terminal voltage control law with unknown parameters; The expression of the bridge arm load admittance observer is obtained as follows: The expression of the voltage control law at the a bridge arm terminal is obtained as follows: The design process of the load admittance observer and the terminal voltage control law of the b and c bridge arms is similar to that of the a bridge arm. Furthermore, according to step 3.3 in claim 4, the terminal voltage control law of the f bridge arm containing unknown parameters can be obtained.

8. According to the Lyapunov-based LC filter four-leg inverter adaptive control method of claim 1, it is characterized in that: Step 7 further includes: Step 7.1: Perform stability analysis on the system. It can be seen that the parameters are within a larger range (ρ, τ, η>0, and k>τLC) and will not affect the global large signal stability of the system. The voltage output of each bridge arm should be within the linear range, that is, it should be ensured that the voltage control law of each bridge arm is always between -0.5E and 0.5E during the dynamic process of the system. Based on the above principles, the appropriate control parameter value range of the present invention is determined to be ρ∈(2~11), k∈(15~40), τ∈(0.001~0.03), η∈(160~500); Step 7.2: Select a set of data in the above parameter value range as the control parameters of the present invention. The selected control parameters are specifically ρ=7, k=25.5, τ=0.15, η=300, and substitute the control parameters into the observer and control law obtained in claim 7 to obtain the terminal voltage control law of the four bridge arms, and generate a pulse signal for controlling the on and off of the power switch tube through carrier modulation.

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