A sensorless model-free predictive control method for LCL inverter

Abstract

The application provides a kind of LCL inverter sensorless model-free predictive control method, belong to LCL inverter technical field.It solves the problem of traditional finite set model-free predictive control, such as variable switching frequency, phase lag of high-order observer, and reducing the efficiency of inverter.The LCL inverter sensorless model-free predictive control method, the control method adopts RLS-TDE decoupling design, discards the excessive dependence of traditional MFPC on full-order parameter identification, TDE performs pure algebraic operation based on one-step delayed data, eliminates the pole placement problem and phase lag problem caused by high-order observer such as LESO, significantly improves the robustness of the system under extreme mismatch of parameters and load mutation.The virtual resistance active damping technology based on voltage difference is proposed, which simulates the physical characteristics of capacitor current without any additional current sensor, avoiding the additional power loss of passive damping, saving the hardware cost and volume of sensor, and eliminating high-frequency sampling noise.

Description

Technical Field

[0001] This invention belongs to the field of LCL inverter technology, and in particular to a sensorless and model-free predictive control method for LCL inverters. Background Technology

[0002] Currently, voltage-source inverters (VSIs) widely employ LCL filters to attenuate high-frequency harmonics. In the control of LCL inverters, Model Predictive Control (MPC) is widely used due to its strong multivariable handling capability and fast dynamic response. To overcome the heavy reliance of traditional MPC on accurate system mathematical models, the industry has proposed Model-Free Predictive Control (MFPC), which utilizes hyperlocal models and extended state observers to uniformly estimate unknown nonlinear dynamics. Simultaneously, to suppress the third-order underdamped high-frequency resonance of the LCL filter, existing technologies typically employ passive damping with series resistors or add capacitors / grid current sensors to achieve active damping.

[0003] The existing technical solutions have the following drawbacks: 1. Model parameter dependence and large computational load: Traditional finite set model-free predictive control FCS-MFPC has the problem of variable switching frequency, and it needs to traverse all discrete states to find the optimal solution, resulting in a huge computational burden. 2. High-order observers have phase lag: Existing MFPCs generally use the linear extended state observer (LESO) to estimate lumped disturbances. LESO has inherent phase lag and requires complex pole configuration, which can easily overlap with the LCL resonant frequency, leading to positive feedback instability. 3. Full-order model identification is prone to divergence: Traditional continuous set model-free predictive control CCS-MFPC requires the use of recursive least squares (RLS) to identify the full-order autoregressive parameters of the system online. When the load changes abruptly or the parameters are mismatched, the identification error will be amplified sharply, leading to duty cycle saturation and system instability. 4. Active damping relies on additional sensors: Traditional active damping strategies require the addition of capacitor current sensors or grid-connected current sensors, which not only increases hardware costs and system size, but also introduces high-frequency sampling noise. Passive damping, on the other hand, will result in additional power loss and reduce inverter efficiency. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned problems in existing technologies by proposing a sensorless, model-free predictive control method for LCL inverters. The technical problem to be solved by this invention is: how to solve the problems of variable switching frequency, phase lag of higher-order observers, sharp amplification of identification errors during load changes or parameter mismatches, duty cycle saturation and system instability in traditional finite set model-free predictive control, and additional power loss and reduced inverter efficiency caused by passive damping.

[0005] The objective of this invention can be achieved through the following technical solutions: A sensorless, model-free predictive control method for LCL inverters, characterized by comprising the following steps: Step 1: The two-level voltage source inverter topology includes an LCL output filter. The LCL filter filters out high-frequency switching harmonics to provide high-quality voltage support for the AC load. The inverter-side inductor is defined as... L f With parasitic resistance R f The load-side inductance is L o With parasitic resistance R o The filter capacitor is C f The inverter-side current is i fj and load-side current are i oj The voltage across the filter capacitor is v jn The load terminal voltage is v oj The bridge arm switch status is S j DC bus voltage is v dc ; Step 2: Gain Adaptive Extraction Based on Dimensional Reduction RLS: In the traditional CCS-MFPC framework, the inverter's output dynamics are typically described by a full-order autoregressive exogenous ARX model. All autoregressive pole parameters are identified online using recursive least squares (RLS). a i With input gain parameter b m With capacitor voltage v jn,k To control the target, the ARX model of the capacitor voltage can be defined using the following pulse transfer function: choose nA =3 and nB =2 achieves the best balance between voltage tracking error requirements and simplified computational complexity. The predicted voltage difference equation for the next time step is: Unknown parameter set The ARX model described above is typically converted into a discrete state-space form through online real-time estimation and updating using recursive least squares (RLS) with a forgetting factor.

[0006] State vector The system matrix stores historical data on voltage and input, and is defined as follows:

[0007] The online fitting of the RLS algorithm to the ARX model is retained to ensure the statistical completeness of the data, and the system matrix susceptible to disturbances is discarded during control law synthesis. A vjn Only the input matrix is ​​extracted. B vjn High-frequency control gain in the middle:

[0008] In the formula b 0 This represents the transient gain of the output voltage due to changes in duty cycle. To prevent algorithm crashes caused by singular values ​​during RLS initialization or extreme transients, [the following is added]: b 0 Apply safety baseline constraints b min :

[0009] Step 3, Hyperlocal Model and TDE Disturbance Observer: A first-order hyperlocal model was constructed for the single-phase output voltage dynamics of the inverter. (8) In the formula, u k The equivalent control input under a continuous control set; D(k) Defined as the lumped disturbance of the system, within this decoupling framework... D(k) It encompasses LCL third-order dynamics, load current surges, cross-coupling interference, and dead-time nonlinear effects, providing a basis for... D(k) To achieve fast and hysteresis-free estimation, a time delay estimation (TDE) technique is introduced, given the high sampling frequency of the inverter. T s The value is 25µs, which can be preset so that the rate of change of physical disturbance approaches zero within two adjacent discrete sampling periods, i.e. D(k) ≈ D (k-1) According to the formula of the first-order hyperlocal model above, the physical disturbance at the previous moment can be solved algebraically by using known voltage measurements and historical control inputs:

[0010] A first-order digital low-pass filter (LPF) is cascaded at the output of the TDE algorithm to smooth the perturbation of the observations.

[0011] in The filtering time constant; Step 4: Sensorless Virtual Damping Based on Discrete Voltage Differentiation: Based on the physical differential characteristics of capacitance In digital control systems, the discrete rate of change of load voltage can directly represent the transient trend of capacitor current. The discrete differential term of voltage is defined as follows:

[0012] Constructing sensorless virtual active damping components : In the formula, K d > 0 represents the introduced virtual damping gain. This damping component is injected into the voltage tracking trajectory in the form of negative feedback to form the corrected desired prediction target. : (13) When the LCL filter experiences high-frequency oscillations due to grid disturbances or sudden load changes, i.e. When the voltage increases dramatically, the corrected reference trajectory will cause the controller to output a huge reverse suppression voltage instantaneously. Step 5: Continuous set deadbeat control law and constraint handling: Under the continuous control set (CCS) predictive control framework, in order to ensure that the predicted system voltage at the next moment accurately tracks the corrected reference trajectory, a quadratic cost function based on the single-step predictive horizon is constructed: (14) Substituting the prediction model formula (8) and the corrected trajectory formula (13) into formula (14), the cost function can be reconstructed as a function of continuous control variables. u k The quadratic polynomial: (15) Based on the extremum properties of quadratic functions, the cost function formula (15) is interpreted with respect to... u k Find the partial derivative and set its first derivative to zero:

[0013] By solving this algebraic equation, the analytical solution for the unconstrained optimal control input that minimizes the cost function can be directly derived:

[0014] Utilizing DC bus voltage vdc The unconstrained optimal duty cycle required to map the equivalent voltage to sinusoidal pulse width modulation (SPWM) d unc,k :

[0015] The physical current constraint is equivalently reconstructed into a duty cycle boundary constraint. Combined with the inherent boundary of the PWM modulator Multiple limiting measures are applied to the optimal duty cycle determined by analysis:

[0016] Ultimate optimal duty cycle d opt,k Output to the PWM module to generate a drive signal with a fixed switching frequency.

[0017] Compared with existing technologies, the sensorless and model-free predictive control method for LCL inverters of the present invention has the following advantages: Extremely robust and stable: The RLS-TDE decoupling design is adopted, which abandons the excessive reliance of traditional MFPC on full-order parameter identification. TDE performs pure algebraic operations based on data delayed by one step, eliminating the pole placement problem and phase lag problem caused by high-order observers such as LESO, and significantly improving the robustness of the system under extreme parameter mismatch and load change. Achieving active damping with zero hardware cost increase: A virtual resistance active damping technology based on voltage difference is proposed to simulate the physical characteristics of capacitor current without any additional current sensor. This avoids the additional power loss of passive damping, saves the hardware cost and size of the sensor, and eliminates high-frequency sampling noise. With low computational cost and fixed switching frequency: By directly integrating the observed values ​​and virtual damping terms into the deadbeat quadratic cost function and performing analytical differentiation, the optimal duty cycle of the continuous set is obtained directly, eliminating the huge enumeration and iteration calculation burden of traditional finite set predictive control FCS-MPC, and ensuring that the inverter operates at a fixed switching frequency, outputting a high-quality voltage with low total harmonic distortion (THD), and reducing the steady-state THD to 3.32%. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the three-phase two-level voltage source inverter of the present invention.

[0019] Figure 2 This is a block diagram of the MFPC of the present invention.

[0020] Figure 3 This is the steady-state waveform diagram of the present invention.

[0021] Figure 4This is the dynamic waveform diagram of the present invention.

[0022] Figure 5 This is the THD diagram of the present invention.

[0023] Figure 6 This is the THD diagram of the traditional FCS-MPC.

[0024] Figure 7 This is a steady-state waveform diagram under the parameter mismatch condition of the present invention.

[0025] Figure 8 This is the THD analysis chart of the present invention. Detailed Implementation

[0026] The following are specific embodiments of the present invention, which are described in conjunction with the accompanying drawings. However, the present invention is not limited to these embodiments.

[0027] A sensorless, model-free predictive control method for LCL inverters includes the following steps: Step 1, as follows Figure 1 As shown, the two-level voltage source inverter topology includes an LCL output filter. The LCL filter filters out high-frequency switching harmonics to provide high-quality voltage support for the AC load. The inverter-side inductance is defined as... L f With parasitic resistance R f The load-side inductance is L o With parasitic resistance R o The filter capacitor is C f The inverter-side current is i fj and load-side current are i oj The voltage across the filter capacitor is v jn The load terminal voltage is v oj The bridge arm switch status is S j DC bus voltage is v dc ; Step 2, Adaptive gain extraction based on dimensionality-reduced RLS: such as Figure 2 As shown, in the traditional CCS-MFPC framework, the inverter's output dynamics are typically described by a full-order autoregressive exogenous ARX model, and all autoregressive pole parameters are identified online using recursive least squares (RLS). a i With input gain parameterb m With capacitor voltage v jn,k To control the target, the ARX model of the capacitor voltage can be defined using the following pulse transfer function: Given that the LCL filter is physically a typical third-order system, the choice nA =3 and nB =2 achieves the best balance between voltage tracking error requirements and simplified computational complexity. The predicted voltage difference equation for the next time step is: Unknown parameter set The ARX model described above is typically converted into a discrete state-space form through online real-time estimation and updating using recursive least squares (RLS) with a forgetting factor.

[0028] State vector The system matrix stores historical data on voltage and input, and is defined as follows:

[0029] However, as a third-order system, the LCL filter has a complete discrete state space matrix. A vjn Severe oscillations are easily generated during load changes or grid disturbances. Directly using incompletely converged identification results in control law calculations can lead to significant amplification of calculation errors, resulting in duty cycle saturation and system instability. To address this, this paper proposes a dimensionality-reduced RLS extraction strategy. This strategy preserves the online fitting of the RLS algorithm to the ARX model to ensure statistical completeness of the data, while discarding the system matrix susceptible to disturbances during control law synthesis. A vjn Only the input matrix is ​​extracted. B vjn High-frequency control gain in the middle:

[0030] In the formula b 0 This represents the transient gain of the output voltage due to changes in duty cycle. To prevent algorithm crashes caused by singular values ​​during RLS initialization or extreme transients, [the following is added]: b 0 Apply safety baseline constraints b min :

[0031] The advantage of this decoupled design lies in the clear division of labor among the algorithms: the RLS algorithm is mainly used to identify the basic control gain of the system to adapt to the slow drift of the inductor parameters; while the nonlinear dynamic process, which is difficult to model accurately, is handled by the TDE observer with fast response capability, thereby greatly reducing the computational burden and divergence risk of multi-parameter identification.

[0032] Step 3, Hyperlocal Model and TDE Disturbance Observer: A first-order hyperlocal model was constructed for the single-phase output voltage dynamics of the inverter. (8) In the formula, u k The equivalent control input under a continuous control set; D(k) Defined as the lumped disturbance of the system, within this decoupling framework... D(k) It encompasses LCL third-order dynamics, load current surges, cross-coupling interference, and dead-time nonlinear effects, providing a basis for... D(k) To achieve fast and hysteresis-free estimation, a time delay estimation (TDE) technique is introduced, given the high sampling frequency of the inverter. T s The value is 25µs, which can be preset so that the rate of change of physical disturbance approaches zero within two adjacent discrete sampling periods, i.e. D(k) ≈ D (k-1) According to the formula of the first-order hyperlocal model above, the physical disturbance at the previous moment can be solved algebraically by using known voltage measurements and historical control inputs:

[0033] Considering that pure derivative operations easily amplify high-frequency sampling noise, a first-order digital low-pass filter (LPF) is cascaded at the output of the TDE algorithm to smooth the perturbation of the observations.

[0034] in With a filtering time constant, the TDE observer only needs one step of delayed data to reconstruct the disturbance, compared to higher-order observers that require complex pole configurations, such as the Linear Extended State Observer (LESO). This algebraic operation characteristic eliminates the risk of positive feedback instability caused by the bandwidth limitations of higher-order observers or overlap with the LCL resonant frequency, significantly improving the system's immunity to nonlinear transient disturbances.

[0035] Step 4: Sensorless Virtual Damping Based on Discrete Voltage Differentiation: Since the hyperlocal model removes the pole regression term from the full-order ARX model, the model itself no longer contains a mathematical description characterizing the inherent damping properties of the LCL filter. If deadbeat predictive control is directly implemented on this basis, the high-frequency resonant mode of the system will inevitably be excited. To reduce costs, this paper proposes a virtual active damping scheme that does not rely on an additional current sensor. Based on the physical differential characteristics of capacitance... In digital control systems, the discrete rate of change of load voltage can directly represent the transient trend of capacitor current. The discrete differential term of voltage is defined as follows:

[0036] Constructing sensorless virtual active damping components : In the formula, K d > 0 represents the introduced virtual damping gain. This damping component is injected into the voltage tracking trajectory in the form of negative feedback to form the corrected desired prediction target. : (13) When the LCL filter experiences high-frequency oscillations due to grid disturbances or sudden load changes, i.e. When the voltage spikes, the corrected reference trajectory will cause the controller to output a huge reverse suppression voltage instantaneously; this is mathematically equivalent to the voltage applied to the filter capacitor. C f A resistor with a value of is connected in parallel at both ends. K d The virtual resistance is inversely proportional, thus achieving strong active suppression of LCL resonance without adding any hardware sensors.

[0037] Step 5: Continuous set deadbeat control law and constraint handling: Under the continuous control set (CCS) predictive control framework, in order to ensure that the predicted system voltage at the next moment accurately tracks the corrected reference trajectory, a quadratic cost function based on the single-step predictive horizon is constructed: (14) Substituting the prediction model formula (8) and the corrected trajectory formula (13) into formula (14), the cost function can be reconstructed as a function of continuous control variables. u k The quadratic polynomial: (15) Unlike the finite control set (FCS), which requires exhaustive optimization by traversing discrete switch combinations, this paper adopts a deadbeat-free optimization criterion. Based on the extremum characteristics of quadratic functions, the cost function formula (15) is applied to... u k Find the partial derivative and set its first derivative to zero:

[0038] By solving this algebraic equation, the analytical solution for the unconstrained optimal control input that minimizes the cost function can be directly derived:

[0039] Utilizing DC bus voltage v dc The unconstrained optimal duty cycle required to map the equivalent voltage to sinusoidal pulse width modulation (SPWM) d unc,k :

[0040] To ensure the hardware safety of the inverter under various extreme operating conditions, the inverter-side filter current must be controlled. i fj,k+1 Strictly limited to the maximum allowable range This paper introduces the Effective Set Method (ASM), which utilizes the extrapolation relationship of the discrete model to equivalently reconstruct the physical current constraint into a duty cycle boundary constraint. Combined with the inherent boundary of the PWM modulator Multiple limiting measures are applied to the optimal duty cycle determined by analysis:

[0041] Final optimal duty cycle d opt,k The output is sent to the PWM module to generate a drive signal with a fixed switching frequency. This strategy replaces the complex numerical iterative optimization process with extremely low algebraic computation cost, and theoretically solves the instability problem of LCL inverters under data-driven control under completely sensorless conditions.

[0042] To verify the effectiveness and superiority of the proposed strategy, a simulation model of a three-phase LCL filter grid-connected inverter was built on the MATLAB / Simulink platform. The simulation parameters are set as shown in the table below.

[0043] Table 1. Simulation Parameters <![CDATA[Load-side inductor L o > 2.4mH <![CDATA[Inverter-side inductor L f > 2.4mH <![CDATA[filter capacitor C f > 25μF <![CDATA[Parasitic resistance R f ,R o > 1mΩ <![CDATA[Sampling time T s > 25μs <![CDATA[Input DC voltage V s > 650V <![CDATA[reference voltage v ref > 200V Forgetting factor 0.99 Steady-state performance and dynamic performance Figure 3 The steady-state voltage waveform of the proposed method is shown. Figure 4The study demonstrated the tracking performance of the actual three-phase voltage when the reference voltage jumped from 200V to 100V and the load changed from 20Ω to 10Ω, showing that its dynamic response was very fast. Figure 5 and Figure 6 The proposed method is compared with the traditional model predictive control (MPC) method in terms of spectral analysis. When the reference voltage is 200V, the total harmonic distortion (THD) of the proposed method is 2.77%, which is comparable to the 3.21% of the traditional FCS-MPC method. The results show that the proposed method has good steady-state and dynamic performance.

[0044] Robustness analysis under extreme mismatch of LCL parameters Figure 7 and Figure 8 The output voltage waveform and harmonic distortion rate are shown in the model mismatch scenario, C. f L f The THD was reduced by 20%, with a reduction of 4.39%. The results show that the proposed method demonstrates the superiority of model-free predictive control under model mismatch conditions, i.e., it has good robustness.

[0045] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A sensorless, model-free predictive control method for an LCL inverter, characterized in that, Includes the following steps, Step 1: The two-level voltage source inverter topology includes an LCL output filter. The LCL filter filters out high-frequency switching harmonics to provide high-quality voltage support for the AC load. The inverter-side inductor is defined as... L f With parasitic resistance R f The load-side inductance is L o With parasitic resistance R o The filter capacitor is C f The inverter-side current is i fj and load-side current are i oj The voltage across the filter capacitor is v jn The load terminal voltage is v oj The bridge arm switch status is S j DC bus voltage is v dc ; Step 2: Gain Adaptive Extraction Based on Dimensional Reduction RLS: In the traditional CCS-MFPC framework, the inverter's output dynamics are typically described by a full-order autoregressive exogenous ARX model. All autoregressive pole parameters are identified online using recursive least squares (RLS). a i With input gain parameter b m With capacitor voltage v jn,k To control the target, the ARX model of the capacitor voltage can be defined using the following pulse transfer function: choose nA =3 and nB =2 achieves the best balance between voltage tracking error requirements and simplified computational complexity. The predicted voltage difference equation for the next time step is: Unknown parameter set θ = - a 1 ， - a 2 ， - a 3 ， b 1 ， b 2 The ARX model described above is typically converted into a discrete state-space form through online real-time estimation and updating using recursive least squares (RLS) with a forgetting factor. State vector The system matrix stores historical data on voltage and input, and is defined as follows: The online fitting of the RLS algorithm to the ARX model is retained to ensure the statistical completeness of the data, and the system matrix susceptible to disturbances is discarded during control law synthesis. A vjn Only the input matrix is ​​extracted. B vjn High-frequency control gain in the middle: In the formula b 0 This represents the transient gain of the output voltage due to changes in duty cycle. To prevent algorithm crashes caused by singular values ​​during RLS initialization or extreme transients, [the following is added]: b 0 Apply safety baseline constraints b min : Step 3, Hyperlocal Model and TDE Disturbance Observer: A first-order hyperlocal model was constructed for the single-phase output voltage dynamics of the inverter. （8） In the formula, u k The equivalent control input under a continuous control set; D(k) Defined as the lumped disturbance of the system, within this decoupling framework... D(k) It encompasses LCL third-order dynamics, load current surges, cross-coupling interference, and dead-time nonlinear effects, providing a basis for... D (k) To achieve fast and hysteresis-free estimation, a time delay estimation (TDE) technique is introduced, given the high sampling frequency of the inverter. T s The value is 25µs, which can be preset so that the rate of change of physical disturbance approaches zero within two adjacent discrete sampling periods, i.e. D(k) ≈ D(k- 1) According to the formula of the first-order hyperlocal model above, the physical disturbance at the previous moment can be solved algebraically by using known voltage measurements and historical control inputs: A first-order digital low-pass filter (LPF) is cascaded at the output of the TDE algorithm to smooth the perturbation of the observations. in The filtering time constant; Step 4: Sensorless Virtual Damping Based on Discrete Voltage Differentiation: Based on the physical differential characteristics of capacitance In digital control systems, the discrete rate of change of load voltage can directly represent the transient trend of capacitor current. The discrete differential term of voltage is defined as follows: Constructing sensorless virtual active damping components : In the formula, K d > 0 represents the introduced virtual damping gain. This damping component is injected into the voltage tracking trajectory in the form of negative feedback to form the corrected desired prediction target. : （13） When the LCL filter experiences high-frequency oscillations due to grid disturbances or sudden load changes, i.e. When the voltage increases dramatically, the corrected reference trajectory will cause the controller to output a huge reverse suppression voltage instantaneously. Step 5: Continuous set deadbeat control law and constraint handling: Under the continuous control set (CCS) predictive control framework, in order to ensure that the predicted system voltage at the next moment accurately tracks the corrected reference trajectory, a quadratic cost function based on the single-step predictive horizon is constructed: （14） Substituting the prediction model formula (8) and the corrected trajectory formula (13) into formula (14), the cost function can be reconstructed as a function of continuous control variables. u k The quadratic polynomial: （15） Based on the extremum properties of quadratic functions, the cost function formula (15) is interpreted with respect to... u k Find the partial derivative and set its first derivative to zero: By solving this algebraic equation, the analytical solution for the unconstrained optimal control input that minimizes the cost function can be directly derived: Utilizing DC bus voltage v dc The unconstrained optimal duty cycle required to map the equivalent voltage to sinusoidal pulse width modulation (SPWM) d unc,k : The physical current constraint is equivalently reconstructed into a duty cycle boundary constraint. d I f m i n ， d I f m a x Combined with the inherent boundary of the PWM modulator d f m i n ， d f m a x Multiple limiting measures are applied to the optimal duty cycle determined by analysis: Final optimal duty cycle d opt,k Output to the PWM module to generate a drive signal with a fixed switching frequency.

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