Steady-state Current Error Research Articles

Adaptive Hamiltonian-Based Energy Control with Built-In Integrator for PEMFC Hybrid Power Conversion Architecture

In this article, an Adaptive Hamiltonian-Based Energy Control (AHBEC) with a built-in integrator is introduced for the Proton-Exchange Membrane Fuel Cell (PEMFC) hybrid power-conversion system. The presented additional built-in integrator is based on the Lyapunov and Hamiltonian functions. Unlike previous works, the control strategy proposed in this article aims to regulate the output current of the PEMFC stack, i.e., to provide sufficient power support to the load, and the integrator is built into the control loop in order to eliminate the steady-state current error caused by external disturbances and model parameter uncertainties. The large-signal stability of the whole system is demonstrated by selecting a suitable Lyapunov-candidate function. An experimental setup is constructed in the laboratory to verify the proposed control strategy. The experimental results demonstrate the robustness and effectiveness of the designed energy-control approach.

An Improved FCS-MPC Based on Novel Sector Optimization and Capacitor Charge Balance Algorithm for T-Type 3P-3L Converters

Conventional FCS-MPC suffers from high computational burden and cumbersome weight factor design, especially for three-phase three-level (3P-3L) converters. In this paper, an improved FCS-MPC is proposed for T-type 3P-3L converters to reduce computational burden, eliminate weight factor and improve system performance. Three improvements are as follows. First, a sector optimization method based on effective vector radiation range is proposed to determine the optimal vector for current tracking without vector enumeration, and combined virtual vector is adopted to supersede basic vector and avoid affecting neutral-point (NP) potential. Second, a capacitor charge balance algorithm is proposed to determine the optimal vector for NP potential balance without weight factor, which minimizes negative effects on current tracking. Third, a hybrid vector output mode is proposed to give full consideration to current tracking and NP potential balance performance. Finally, advantages of proposed MPC are verified in simulation and experiment, where code execution time and current THD are reduced by 16.1 μs and 1.27%, steady-state current error and capacitor voltage deviation are experimentally reduced by 0.8 A and 0.6 V, and transient DC voltage recovery time and capacitor voltage deviation are experimentally reduced by 2 ms and 0.4 V compared with conventional FCS-MPC.

Sliding Mode Predictive Current Control for Single-Phase H-Bridge Converter with Parameter Robustness

As the important technology of renewable energy systems, power electronics technology is directly bound up with the prospect and development of renewable energy technology. As the output end of renewable energy systems, a single-phase H-bridge converter needs to stabilize the output current. When predictive current control (PCC) tracks the reference current, the dynamic response is the fastest, but the control delay and the changes in model parameters will cause the output current steady-state error. The sliding mode predictive current control (SMPCC) algorithm is proposed to control the output current better. The proposed SMPCC scheme uses the combination of traditional PCC and variable structure scheme, and it establishes the mathematical model according to the state equation of the converter. Taking the exponential reaching law as control law, the expression of the variable structure controller is obtained. The MATLAB experimental and simulation results show that SMPCC can not only improve its robustness to the parameter changes but also obtain better steady-state performance while enhancing the rapidity of the current changes. In conclusion, SMPCC has a better control effect in the converter.

Fault-Tolerant Current Control of Six-Phase Permanent Magnet Motor With Multifrequency Quasi-Proportional-Resonant Control and Feedforward Compensation for Aerospace Drives

To improve the current tracking performance, this article proposes a new fault-tolerant current control for the six-phase fault-tolerant permanent magnet synchronous motor (FTPMSM) system with multifrequency quasi-proportional-resonant (QPR) control and back electromotive force (EMF) feedforward compensation, which can track the time-varying sinusoidal and nonsinusoidal reference currents in the stationary reference frame (SRF) under normal and fault conditions. First, the multifrequency QPR current controller with shunt topology is proposed to track the time-varying reference current in SRF, which can guarantee the current control performance regardless of the motor speed variation and the load torque change. Second, the optimized feedforward compensation method for the back EMF is proposed to further reduce the steady-state current tracking error, which takes the time delay of the digital implementation into consideration. Finally, the effectiveness of the proposed approach is verified on a 3 kW six-phase FTPMSM platform. The resulting six-phase FTPMSM system with the proposed current control has great current tracking performance, strong robustness to various external/internal disturbance, as well as low computational burden, which can guarantee the multiphase FTPMSM system performance in normal and fault conditions.

A Robust Nonlinear Sliding Mode Controller for a Three-Phase Grid-Connected Inverter with an LCL Filter

In distributed power generation systems, grid-connected inverters are becoming an attractive means of delivering the energy generated from renewable sources into the grid. However, the performance of the current controller drastically decreases in the presence of model uncertainty, grid harmonics, filter parametric, and grid impedance variations, which can jeopardize the entire system’s stability. This paper presents a novel design of a super-twisting integral sliding mode control (ST-ISMC) strategy for the first time in the application of a three-phase voltage source grid-connected inverter. The designed controller has shown robustness and maintains a low total harmonic distortion (THD) in the presence of filter parameters drift, grid impedance variation, and grid harmonics distortion. The super-twisting action is added to remove the chattering problem associated with the conventional SMC strategy, and integral action is adopted to improve the grid’s current steady-state error. The modeling and simulation of a complete system are carried out using MATLAB/SIMULINK. Finally, a real-world hardware prototype system is fabricated to demonstrate the performance and effectiveness of the proposed controller.

Model Inaccuracy Analysis and Compensation of Stationary Frame-Based Deadbeat Predictive Current Control for High-Speed PMSM Drives

Due to explicit modeling of delay effects and fast dynamic response, the recently reported stationary frame-based deadbeat predictive current control (DBPCC) is particularly attractive for high-speed permanent magnet synchronous machine (PMSM) drives. However, its actual control performances would be heavily dependent on model accuracy. Therefore, this article presents an analytical and systematical investigation into the influences of model inaccuracy on the stationary frame-based DBPCC. Steady-state and transient performance degradations under machine parameter mismatches and inverter nonlinearity over the whole speed range have been studied. Importantly, the analyses show that the steady-state control errors will increase greatly under parameter mismatch as the speed rises; while the transient current tracking errors, only caused by inductance mismatch, can be quickly suppressed after two time-steps. To further improve the parameter robustness of the stationary frame-based DBPCC for high-speed drives, this article also proposes a simple but effective method, called adaptive reference correcting current injection (ARCCI). The proposed method can effectively eliminate all the steady-state current errors caused by model inaccuracy. It can be easily implemented and applicable at high speeds with low switching-to-fundamental frequency ratios (SFRs) as well. Both the presented analyses and compensation methods have been validated by extensive simulations and experiments.

Analysis, Design, and Implementation of Multi-Quasi-Proportional-Resonant Controller for Thyristor-ControlledLC-Coupling Hybrid Active Power Filter (TCLC-HAPF)

Compared with the conventional active power filter, the thyristor-controlled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -coupling hybrid active power filter (TC <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -HAPF) has a distinct characteristics of low dc-link operating voltage, which can lower the system and operational costs in the medium-voltage-level system. It also has a wider operational range than the conventional hybrid active power filter. Besides that, the TC <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -HAPF can provide reactive, harmonic, and unbalanced powers compensation simultaneously. In this article, the modeling of the TC <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -HAPF is investigated based on the linear control aspect. Then, the analysis, design, and implementation of a multi-quasi-proportional-resonant (MQPR) controller with gain scheduling for the TC <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -HAPF will be proposed, which can automatically change the resonant gain between the inductive and capacitive loads operation to improve its compensation performances. The proposed controller can significantly reduce the TC <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -HAPF steady-state current tracking errors and output current ripple. Finally, the simulation and experimental results are also provided to verify the effectiveness and performance of the MQPR controller for the TC <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -HAPF in comparison with the hysteresis current controller and quasi-proportional-resonant (QPR) controller, which shows superior compensating performances.

A New Control Strategy for Three-Phase Shunt Active Power Filters Based on FIR Prediction

In this article, a new discrete-time control strategy for three-phase three-wire shunt active power filters (APFs) is presented, based on a mathematical model in the stationary reference frame. It involves a feedback-linearization-type approach to control the filter currents, whereby the voltage control loop is decoupled from the current control. The voltage control loop is for controlling the dc-side voltage of the pulsewidth modulation (PWM) converter, and employs a proportional-integral (PI) controller to generate the reference amplitude for the compensated grid currents. An important feature of the proposed control strategy is the compensation of the one-sampling-period delay caused by microcontroller computation using a finite impulse response (FIR) predictor. This predictor is designed to accomplish one-step-ahead prediction of the control variable, which is the PWM converter's switching function space vector. Furthermore, the FIR predictor is optimized so that the low-order harmonics in the control variable are predicted with minimal error. The proposed control strategy is analyzed to obtain the steady-state filter current error and ranges for the PI controller gains for stability. Simulation and experimental results are presented to show the effectiveness of the proposed shunt APF.

Robust model predictive current control without dead‐zone compensation

To solve the problems of large steady-state errors, high harmonic components and poor robustness of traditional current model prediction, a novel three-vector model predictive current control for permanent magnet synchronous motor is presented in this study. The vectors operating time is calculated with the combination of current increment and the unconventional modulation method is adopted to generate duty cycle containing dead zone. Adopting the current command correction link, the current deviation caused by inaccuracy parameter is reduced. Proved by experiment, novel control system not only the current steady-state error and current harmonic component are reduced, but also the parameter robustness is enhanced.

Fast triple-parameter extremum seeking exemplified for jet control

A fast triple-parameter extremum seeking method is applied for jet control based on the pioneering work of Gelbert et al. (J Process Control 22(4):700, 2012). The simultaneous adaptation of three input parameters takes less time than the single-input adaptation of each parameter combined. The key enablers are phase-shifted sinusoids for the input each of which is evaluated by an extended Kalman filter (EKF). An acceleration of the adaption is obtained by a combined EKF coupling the output to all inputs. The method is illustrated for an analytical optimization problem and experimentally demonstrated for a turbulent jet mixing control. The considered Reynolds numbers $${\hbox {Re}}_D$$ based on the jet exit diameter and velocity are 5700, 8000 and 13,300. The main jet is manipulated by a pulsed radially injected minijet which is varied by a mass flow controller and an electromagnetic valve up to high frequencies. The mixing performance is characterized by the centerline jet decay rate and monitored by a hot-wire sensor five diameters downstream at the end of the potential core. The proposed triple-parameter extremum seeking method optimizes the actuation mass flow ratio, frequency and duty cycle. The decay rate increases 11-fold from the unforced reference value of 0.05 to the optimal actuation level of 0.56. The reproducibility is demonstrated with various initial actuation parameters. Moreover, the adaptive control robustly tracks the optimal open-loop actuation for varying $${\hbox {Re}}_D$$ ; the optimal decay rate remains unchanged given the mass flow rate, frequency and duty cycle are optimized. The unforced and actuated flow are investigated with hot wires and visualizations. The three-input ES significantly outperforms a two-parameter optimization for the same configuration in multiple respects (Wu et al. in AIAA J 56(4):1463, 2018): First, the jet decay rate is $$8\%$$ faster. Second, the convergence time for three parameters is only $$25 \%$$ of the adaptation period of two parameters when $${\hbox {Re}}_D$$ is varied. Finally, the current steady-state error is $$45\%$$ less than that of the two-parameter optimization. We expect the proposed triple-parameter extremum seeking to be applicable for a large range of flow control experiments.

Improved Model Predictive Current Control of Single-Phase Five-Level PWM Rectifier

In this paper, a single-phase five-level rectifier with coupled inductors is studied. First, a discrete mathematical model of a single-phase five-level rectifier is created in two-phase(αβ). A traditional single vector finite control set model predictive control (FCS-MPC) algorithm is improved to overcome the problems of a varying switching frequency, the large amount of time needed for calculation, and the inaccurate setpoint of current loop tracking. Then, the objective function of the system is established, and a simple objective function is used instead of an iterative optimization of the traditional FCS-MPC algorithm. At the same time, to eliminate the delay error and to reduce harmonic distortion, deadbeat control technology is introduced. Finally, the simulation and experimental results show that the improved model predictive current control algorithm not only retains the fast response of traditional model predictive control, but also has the advantages of fixed switching frequency, small calculation time, and small current steady-state error.

Three‐vector‐based low‐complexity model predictive current control with reduced steady‐state current error for permanent magnet synchronous motor

The three-vector-based model predictive current control has the advantages of fast dynamic response, low current ripple and no weight factor, but there are also problems of large computational efforts and steady-state current error under parameter mismatch. To solve the fore-mentioned drawbacks, a three-vector-based low-complexity model predictive current control with reduced steady-state current error for the permanent magnet synchronous motor drive system is proposed in this study. Firstly, the selection process of optimal voltage vector combination is simplified to reduce the computational burden of three-vector-based model predictive current control. Moreover, the sensitivity of parameters is analysed, respectively. In order to reduce the steady-state current error caused by parameter mismatch, a Luenberger observer is introduced to estimate the lump disturbance caused by parameter mismatch and unmodelled dynamics. The estimated lump disturbance is considered as compensation to the model. Finally, the validity of the proposed method is verified by experiments.

An Improved Deadbeat Predictive Current Control With Online Parameter Identification for Surface-Mounted PMSMs

In this article, an improved deadbeat predictive current control (DPCC) method with parameters identification for surface-mounted permanent magnet synchronous machines (SPMSMs) is proposed. With the proposed DPCC method, zero steady-state current error and deadbeat dynamic current response could be achieved, even with inaccurate initial motor parameters. On basis of the conventional DPCC method, a novel parameters identification for the stator resistance and inductance is developed, which is the main contribution of this article. The proposed parameters identification method works based on a reconstructed characteristic vector from the disturbance observer with current injection. Compared with traditional recursive-least-square methods, the proposed method can be implemented with greatly reduced computation burden. Additionally, since the design is established based on the fully discretized model, the effectiveness will be guaranteed on both low-frequency and high-frequency motors, which is a significant advantage of the proposed method.

Robust predictive current control for IPMSM without rotor flux information based on a discrete‐time disturbance observer

This study proposes a novel robust predictive current control that is based on a discrete-time disturbance observer for an interior permanent magnet synchronous motor (IPMSM), does not require rotor flux information. To confirm the effects of the current control response on a parameter mismatch, the parameter sensitivity for the current prediction of a conventional deadbeat predictive current control (DPCC) is analysed. With the proposed method, disturbances owing to a parameter mismatch, rotor flux term, and unmodelled dynamics are estimated using a Luenberger observer in the discrete-time domain. The estimated disturbances are compensated with the predicted reference voltage model considering a digital delay. The stability of the proposed disturbance observer owing to a parameter mismatch of the stator resistance and d–q inductance is also analysed. The proposed method is robust against the stator resistance and an inductance variation, and an accurate predicted current control can be obtained without an offline or online estimation of the rotor flux. Compared with the conventional DPCC, the proposed method can eliminate a steady-state current and transient state error caused by disturbances of the system. Experimental results are presented to verify the proposed control scheme even with mismatched parameters of the IPMSM.

Deadbeat Predictive Current Control for Permanent Magnet Synchronous Machines With Closed-Form Error Compensation

Deadbeat predictive current regulator features fast dynamic responses. However, it suffers from the steady-state current tracking error in a practical system due to the plant uncertainties, particularly the inductances. Instead of using observer-based disturbance voltage feedforward methods, this article proposes a new closed-form method to directly compensate the current tracking errors with a simple feedforward term added to the voltage commands. Zero steady-state error is achieved with negligible computation compared to the observer-based methods. The new method is first derived to tackle the inductance mismatch in the surface-mount permanent magnet synchronous motor, then the system close-loop transfer function is established to prove that the proposed method guarantees the zero steady-state error even with mismatches of the stator resistance and rotor flux linkage. Furthermore, based on the proposed compensation method, noise suppression schemes are added and designed to reduce high-frequency noise sensitivities in practical systems. Finally, the proposed method is extended to the interior permanent magnet synchronous motor (IPMSM). IPMSM system simulation and 68.5-kW experimental results are provided to validate the proposed method.

Robust three‐vector‐based low‐complexity model predictive current control with supertwisting‐algorithm‐based second‐order sliding‐mode observer for permanent magnet synchronous motor

This study presents a robust three-vector-based low-complexity model predictive current control with supertwisting-algorithm-based second-order sliding-mode observer for permanent magnet synchronous motor (PMSM). First, to reduce the computational complexity of the three-vector-based model predictive current control, the optimal voltage vector combination is directly determined by the sector of desired voltage vector. Second, a supertwisting-algorithm-based second-order sliding-mode observer is designed to observe the lump disturbance caused by model mismatch and unmodelled dynamics. The estimated lump disturbance is considered as the compensation to the original PMSM model to reduce steady-state current error, which improves the robustness of the three-vector-based model predictive current control. Finally, the effectiveness of the proposed method is verified by experiments on a two-level-inverter-fed PMSM drive platform. Experimental results prove that, compared with three-vector-based model predictive current control, the proposed method can reduce the computational complexity and enhance robustness against motor parameters variation.

Model-Predictive-Control-Based Flexible Arc-Suppression Method for Earth Fault in Distribution Networks

Traditional arc-suppression devices have a weak effect on the arc-extinguishing result of earth fault because of increased active and harmonic components of fault current. To solve the problem, in this paper, a flexible arc-suppression device based on a three-phase cascaded H-bridge (CHB) converter with auxiliary sources is further developed; on this basis, an arc-suppression method based on the improved finite control set model predictive control is proposed. The proposed approach, which uses a combination of two voltage levels in a sampling period to reduce the steady-state current error, controls the CHB converter to inject compensation current into the distribution network. Taking into account the reduction of switching losses and balancing heat in each H-bridge cell, a novel method that causes the switching transitions to be distributed evenly among the H-bridge cells is proposed to select the optimal switching combination. The tracking capability of the improved control method is analyzed, and the parameters affecting the arc-suppression performance are obtained. The simulation and experimental results show that the proposed method achieves an excellent performance of suppressing fault current and extinguishing arc. Moreover, the balance of switching transitions is also achieved.

A Modified Multifrequency Passivity-Based Control for Shunt Active Power Filter With Model-Parameter-Adaptive Capability

The passivity-based control (PBC) has a better control performance using an accurate mathematical model of the control object. It can offer an alternative tracking control scheme for the shunt active power filter (SAPF). However, the conventional PBC-based SAPF cannot achieve zero steady-state current error with the inaccurate model. In order to handle the steady-state current error of the conventional PBC-based SAPF, a modified PBC scheme is proposed, where an error proportional-integral regulator is inserted into the coupling loop. The design of the modified PBC is implemented in the dc model, transferred from the ac model by using a fast Fourier transform. A comparative performance analysis is carried out between the conventional and modified PBC-based SAPFs. A 380-V/75-A prototype is developed, where the results demonstrate that by using the modified PBC, the zero steady-state current error of SAPF can be achieved at the selected frequency or frequencies, even though the model used is not so accurate.

An internal model control for enhanced grid-connection of direct-driven PMSG-based wind generators

For Wind Energy Conversion Systems (WECS) based on Permanent Magnet Synchronous Generators (PMSG) with back-to-back converters, some strategies have been employed aiming safe and reliable grid-connection, among them the grid-side control in coordination with the braking chopper. Conventionally, the grid-side control is of the Proportional-Integral (PI) type, however, due to the presence of cross-coupling terms between the dq currents delivered to the grid, PI does not ensure null steady-state error resulting in an inappropriate power delivery. Moreover, during voltage sags at the connection point, the chopper turning on is often commanded based on the DC-link voltage increase, however, a more suitable trigger signal should be based on the current delivered to the grid. Seeking to improve the grid-connection issue, in this work a new control is presented, which is based on Internal Model State Feedback Control (IMSFC) in order to eliminate dq current steady-state error and whose the control design is achieved through Linear Quadratic Regulator (LQR). Besides, the chopper trigger signal is based on the current delivered to the grid, ensuring safe Low-Voltage Ride-Through (LVRT). The proposed control and the conventional PI have been discretized and implemented to interact with a suitable model of grid-connected PMSG WECS in MatLab/Simulink. The proposed control performance has overcome the conventional both for steady-state and low-voltage conditions.

Robust Predictive Current Control With Online Disturbance Estimation for Induction Machine Drives

This paper presents robust predictive current control (RPCC) with online disturbance estimation to achieve high- performance current loop for induction machine (IM) drives. The disturbance caused by parameter variations and other unmodeled dynamics is considered in modeling of IM. Based on this model, the control law of the proposed scheme is derived, where a discrete Luenberger observer is designed to estimate the future values of stator current and disturbance. The selection of the designed observer gain is a compromise between the system control bandwidth and robustness. Compared with the conventional RPCC, the proposed scheme removes the steady-state current error caused by the system disturbance. Experimental results on an industrial induction machine drive show that the proposed scheme provides fast and static-errorless current tracking even with mismatched machine parameters.