Proportional Integral Resonant Research Articles

A Proportional-Integral-Resonant Current Control Strategy for a Wind-Driven Brushless Doubly Fed Generator during Network Unbalance

This article proposes a proportional-integral-resonant (PIR) current control strategy for a wind-driven brushless doubly fed generator (WDBDFG) during network unbalance. Firstly, four control objectives of WDBDFG, including eliminating unbalanced currents of power winding (PW), pulsations of control winding (CW) currents, torque, and PW power, are discussed and different from current controls in which the references to PW currents were computed; the CW current references are derived here. Then, an improved CW current controller using a PIR controller is proposed to achieve different control objectives. In contrast with current controls, CW currents are not involved with sequence extraction in the proposed control and can be totally regulated only in a positive synchronous reference frame. Hence, the system control structure is greatly simplified, and dynamic characteristics are improved. Furthermore, in order to obtain completely decoupled control of current and average power, feedforward control, considering all the couplings and perturbances, is also applied in CW current loops. Simulation results for a 2 MW grid-connected WDBDFG show that the proposed control is capable of achieving four control objectives, including canceling CW current distortion, PW current unbalance, pulsations of PW active power or pulsations of reactive power, and machine torque. Its dynamic process is much more smoothly and quickly than that of current controls, and therefore the proposed control has better dynamic control characteristics during network unbalance.

A Deep Learning Based Enhancing the Power by Reducing the Harmonics in Grid Connected Inverters

The increasing use of renewable energy systems has led to a rise in the number of grid-connected inverters, which can have a detrimental effect on the superiority and constancy of grid electricity due to the injected current harmonics. In this study, the proportional integral (PI) and proportional resonant (PR) controllers have been investigated for their effectiveness in reducing harmonics in grid-connected inverters. The study also investigates the impact of harmonics compensators (HC) on the control strategies. The results of the study suggest that the implementation of PI and PR controllers in the synchronous frame can effectively reduce the injected current harmonics in grid-connected inverters. The use of harmonics compensators can further enhance the performance of the controllers by reducing the distortion and improving the stability of the grid. The efficiency of the regulator strategies be contingent on the type and level of harmonics in the grid, as well as the design and tuning of the controllers and compensators. The statement that the “PR+HC controller has a superior quality output current” is more specific and suggests that this control method may be more effective than the others in reducing harmonics and enlightening the value of the productivity current. The comparison of the IEEE 1547 standard by three viable inverters from diverse constructors is also noteworthy, as it can provide insights into the compatibility and performance of different types of inverters with the standard. The use of deep learning with the RCNN network for analyzing harmonics and providing information about power is an interesting application of machine learning in power systems research. This approach may have the probable to development the accuracy and competence of harmonics analysis as well as power monitoring in grid-connected inverters. Overall, the study highlights the importance of effective control strategies for managing harmonics in grid-connected inverters, particularly in the context of the increasing usage of renewable energy systems. The findings of the study can inform the development of more efficient and reliable grid-connected inverters, which are essential for the incorporation of renewable energy systems into the power grid.

Super-twisting resonant controller-based inverter nonlinearity compensation for permanent magnet synchronous motor drive system

In this paper, a novel super-twisting resonant controller with a fixed-time adaptive law (FTAL-STRC) is proposed to improve robustness and current smoothness of permanent magnet synchronous motor (PMSM). Firstly, the STRC controller is proposed, which incorporates the benefits of both the super-twisting controller (STC) and the quasi-resonant controller (QRC). Compared to the universal proportional integral resonant (PIR) control method, the proposed STRC can decrease the influence of inverter nonlinearity, and improve the robustness to parameters change, simultaneously. Secondly, an adaptive law based on fixed-time convergence theory (FTAL) is proposed to further compensate for the unknown disturbance, and realize fast tracking. Then, the composite control strategy is developed. Meanwhile, the stability of the proposed FTAL-STRC is proved rigorously. Finally, simulations and experiments are conducted to validate the effectiveness of the proposed method.

VSC control strategy for HVDC compensating harmonic components

This paper proposes a voltage source converter (VSC) control strategy for the high voltage direct current (HVDC) transmission systems compensating the harmonic components. For VSC-HVDC AC system accounted for a relatively large share of the 5th, 7th, 11th, 13th and other low harmonics. A selective harmonic current control strategy based on vector proportional integral (VPI) regulator in dq coordinate system is proposed on the basis of PI control. In which, PI is used to control the DC component of the current error, while VPI is used to suppress the multiplicative fluctuations of the current error. Unlike the proportional-integral resonant (PIR) regulator, the VPI contains a second-order numerator that achieves the ideal 0° phase delay of the closed-loop transfer function of the control system at the set resonant frequency point, so its control accuracy for harmonic currents is better than that of the PIR. A two-terminal VSC-HVDC system is built using Simulink software, and current compensation simulations are performed for three control methods: conventional PI, PIR and PI parallel VPI schemes. The superior harmonic suppression performance of VPI is verified by comparing the harmonic content.

Improved Power Control of DFIGs Driven by Wind Turbine under Unbalanced Grid Voltage

AbstractUndesired oscillation components appear in active and reactive powers, electromagnetic torque and DC-link voltage of doubly fed induction generators (DFIGs) connected to unbalanced grid voltage. These components oscillate at double source frequency as a result of negative sequence components in voltage and current. Different direct power control (DPC) techniques were studied in literatures to damp these oscillations. However, these techniques require sequence decomposition process, axes transformation of stator voltage/current and estimation of different power components which complicate the overall control system. This paper presents a simplified DPC of DFIGs in stationary reference frame under normal and unbalanced grid voltage. Decomposition process, axes transformation and compensation power terms are totally eliminated. Vector proportional- integral (VPI) controllers are designed to regulate stator active and reactive powers. The performance of the proposed DPC scheme using VPI and proportional-integral-resonant (PIR) controllers is analyzed and compared under different operating conditions. Bode diagram of open loop and closed loop control using VPI and PIR are studied to illustrate stability, steady state and transient response of the two controllers. Also, the performance of proposed technique and previous DPCs designed in synchronous reference frame is compared to prove the validity of proposed one. The results show that proposed DPC using VPI has superior performance in steady state and transient conditions with simple implementation.

Single-phase transformerless inverter topologies at different levels for a photovoltaic system, with proportional resonant controller

<span lang="EN-US">In this paper, we have studied the topologies of single-phase transformerless inverters with different levels using a <a name="_Hlk115945664"></a>proportional-integral-resonant (PIR) AC controller, and the multi-level cascade inverter topology with sinusoidal pulse with modulation (SPWM) control in an open and closed loop. To ensure that these photovoltaic inverters can inject a defined amount of reactive power into the grid according to international regulations. Therefore, precise monitoring of the mains voltage vector by a phase-locked loop (PLL) system is applied to ensure the proper functioning of this system. For inverter topologies with less than three levels, the simulation results show that the highly efficient and reliable inverter concept (HERIC) topology performance is better than that of H5 and H6. On the other hand, the performance of the topology H6 ameliorate is superior to those of H4, H5, and HERIC in currents of leakage. On the other hand, for the control of cascaded multi-level closed-loop inverters, we notice that there is an improvement in the spectra and the elimination of all frequency harmonics, close to that of the fundamental, and a reduction in the rate of harmonic current distortion.</span>

The Suppression of Modular Multi-Level Converter Circulation Based on the PIR Virtual Impedance Strategy

In recent years, with the rise of the electric vehicle industry, there has been significant research on charging and power supply vehicle technologies for electric vehicles. In terms of the corresponding converter usage, modular multi-level converters (MMCs) are also increasingly used in the field of electric vehicle power supply research because of their unique advantages. However, the circulating current problem of MMCs has not been effectively addressed in existing domestic and international studies. In this paper, we propose a proportional-integral resonant (PIR) control method combined with virtual impedance for the optimal suppression of the MMC internal circulating current problem based on the comparison and generalization of the existing methods. Based on the analysis of the working principle of MMCs, this paper proposes and adopts the control strategy of combining virtual impedance and proportional-integral resonance to suppress the circulating current and builds a simulation model in MATLAB to verify that the control strategy proposed in this paper is feasible.

Proportional Integral Resonant and Proportional Derivative Controllers Applied to Zero Sequence Harmonic Compensation in Four-Wire Microgeneration Systems

Proportional Integral Resonant and Proportional Derivative Controllers Applied to Zero Sequence Harmonic Compensation in Four-Wire Microgeneration Systems

Control Strategy for Resonant Inverter in High Frequency AC Power Distribution System with Harmonic Suppression and Transient Performance Improvement

In high frequency AC (HFAC) distribution system, the resonant inverter is used to improve power quality and keep the stability of the output AC voltage. Aiming at the problems of poor output power quality and slow transient performance caused by unreasonable filter parameter design and load change during inverter operation, a single-phase H-bridge LCLC resonant inverter based on analog circuit controller implement is introduced in this paper for HFAC power distribution system (PDS). In this study, to design harmonic compensator and analyze the responsiveness of the inverter, it is necessary to analyze the output voltage total harmonic distortion (THD) of LCLC resonant inverter and the performance of the open loop system in detail. On the one hand, a proportional-integral-resonant (PIR) controller is designed to maintain the zero static error of the voltage output and suppress the output voltage THD of LCLC resonant inverter. On the other hand, an integral controller combines with phase-shift modulation (PSM) method is presented to effectively improve the transient performance of resonant inverter and provide the fixed frequency of the output voltage. On the basis of the above, the experimental prototype is implemented with the output AC voltage root mean square of 28 V, and the output voltage frequency for resonant inverter is equal to switching frequency. A rated output power of 130 W experimental platform is built to verify the effectiveness of the theoretical analysis, control strategy, and modulation method.

Comparing Different Resonant Control Approaches for Torque Ripple Minimisation in Electric Machines

Electric machines are highly efficient and highly controllable actuators, but they do still suffer from a number of imperfections. One of them is torque ripple, which introduces high frequency harmonics into the motion. One (cost- and performance-neutral) countermeasure is to apply control that counters the torque ripple. This paper compares several single-input single-output (SISO) control approaches for feedback control of torque ripple of a Permanent Magnet Synchronous Machine (PMSM). The baseline is PI (proportional-integral) control, which does not suppress torque ripple, and the most popular control approach is proportional-integral resonant (PIR) control. Both are compared to an advanced PIR controller (PIRA), frequency modulation, a mixed sensitivity design, and an iterative learning controller (ILC). The analysis demonstrates that PIR control, mixed sensitivity state feedback, and the modulating controller achieve identical behaviour. The choice between these three options is therefore dependent on preferences for the design methodology, or on implementation factors. The PIRA and the ILC on the other hand show more sophisticated behaviour that may be advantageous for certain applications, at the expense of higher complexity.

Active torsional vibration suppression of integrated electric drive system based on optimal harmonic current instruction analytic calculation method

Torque fluctuation caused by flux harmonics in a permanent magnet synchronous motor (PMSM) leads to torsional vibrations in vehicle-integrated electric drive systems. To resolve this fluctuation, the coupling relationship between the torque fluctuation and harmonic current of the PMSM was analyzed by establishing an analytical model of the instantaneous torque of the PMSM. The analysis was performed considering the harmonic and saturation characteristics of the flux chain. An analytical calculation method for the reference harmonic-current instruction was proposed to suppress torque fluctuation. The proportional integral resonant (PIR) controller was designed to accurately control the actual current to follow the reference harmonic-current command. Thus, an active torsional vibration suppression method was developed. Simulation and experimental results showed that the proposed method can effectively reduce the amplitude of the 6th and 12th harmonic torque of the PMSM. The amplitude of each axis torque and gear-meshing force, corresponding to the harmonic frequency of the transmission system, is considerably reduced. The transmission stability is also significantly improved.

Fault‐tolerant control technology of symmetrical six‐phase permanent magnet synchronous motor

In comparison with three-phase motors, multiphase motors have garnered increasing attention owing to their high fault-tolerant ability. When the motor has an open-circuit fault, the stator combined magnetomotive force (MMF) changes, αβ and z1z2 subspaces are no longer decoupled, and the conventional vector control causes phase current distortion, harmonic current increase, and torque fluctuation of the motor. To address the aforementioned problems, first, the mathematical model of the common neutral symmetric six-phase permanent magnet synchronous motor in the static coordinate system is presented in this paper. Second, the transformation matrix of αβ and z1z2 subspace decoupling is proposed, and the corresponding mathematical model of decreasing order is constructed. Third, considering the orthogonal vector of the remaining dimension after the phase fault, the reduced-order transformation matrix expression of the general single-phase fault is obtained, which is further extended to the double-phase fault. Fourth, the harmonic current of the z1z2 subspace was tracked and controlled by the proportional integral resonant (PIR) regulator. Finally, simulation and experimental verification are performed, and the results demonstrate that the fault-tolerant control algorithm proposed in this paper can effectively reduce the torque ripple and it has good dynamic performance after an open-circuit fault.

An adaptive proportional-integral-resonant controller for speed ripple suppression of PMSM drive due to current measurement error

An adaptive proportional-integral-resonant (PIR) controller with piecewise phase compensation is proposed to suppress the steady-state speed ripple of permanent magnet synchronous motor (PMSM) drive due to current measurement error. The frequency-varying characteristic of PMSM drive makes the parameters determination of the resonant controller more complicated when considering frequency adaptation. In this paper, after theoretical analysis on the current measurement error, the resonant controller is added in the speed PI loop of the PMSM vector control system, which makes the system more prone to instability. In order to ensure the stability of the system at different speeds, the resonant gain is firstly restricted by root locus method to get a stable system in the full speed range. Then, the resonant gain and the phase angel are further designed to obtain a robust vector margin by Nyquist diagram in different speed ranges. Such piecewise phase compensation method can achieve good stability margin and harmonic suppression ability by making a trade-off between them, avoiding the complicated calculation of the trigonometric functions for compensation in real time. Both steady and transient experiment results indicate that the proposed PIR controller can well restrain the frequency-varying speed ripples caused by current measurement error.

Cost-Effective DC Current Suppression for Single-Phase Grid-Connected PV Inverter

Due to the disparity of power modules, asymmetry of driving pulses and measurement errors of sensors, dc currents may be injected to grid-connected photovoltaic (PV) inverters. The dc current injection may cause magnetic saturation of the power transformers. To solve this issue, this article thus proposes an effective current control strategy and compensation method, which does not require any extra sensor and hardware circuit. First, the root-cause of dc current injection is comprehensively analyzed. Subsequently, a proportional-integral-resonant (PIR) controller is proposed to eliminate the dc component caused by disparity of power modules, asymmetry of driving pulses and measurement errors of grid voltage. The injected dc current caused by grid current measurement error is estimated from the line-frequency ripple of the dc-link voltage, and then it is suppressed by a feedback compensation controller. In addition, the dc current rejection capability is evaluated, and the proposed method is benchmarked with the virtual capacitor-based method. Finally, experimental tests are performed on a 1.2-kW single-phase PV inverter to verify the effectiveness of the proposal.

A High-Speed Microturbine PMa-SynRG Emulation Using Power Hardware-in-the-Loop for Wind Energy Conversion Systems

In this paper, a high-speed microturbine (MT) permanent magnet assisted synchronous reluctance generator (PMa-SynRG) real-time emulation based on linear impedance regulator (LIR) using power hardware-in-the-loop (PHIL) for wind energy generation tests is presented. The LIR is designed without any feedback control loop for reshaping the $s$ -domain performances of the current filter along with the converter inside the PMa-SynRG emulated system. The PHIL platform not only provides a method for eliminating the high cost of using real renewable energy hardware but also it enables the developers to create new, rapid, and reliable controllers for renewable energy testing. This platform can be used in investigating the performance of energy system under various conditions even if the generator prototype is not yet developed or unavailable. PMa-SynRG mathematical model is emulated in the real-time using PHIL platform while the output voltage of the proposed emulator imitates the generated voltage through the simulated model. In addition, a voltage source converter is employed as a voltage amplifier for imitating the PMa-SynRG performance when supplying nonlinear/linear loads. In this paper, the proportional-integral resonant (PIR) controller is utilized at the voltage control loop for tracking the distorted output reference signal voltage. In order to investigate the performance of the proposed PMa-SynRG emulator, it has been simulated and compared with MATLAB/SIMULINK environment.

Comparative Study of Discrete PI and PR Controls for Single-Phase UPS Inverter

This paper presents a comparative study of discrete proportional integral (PI) and proportional resonant (PR) current control for single-phase uninterruptible power supply (UPS) inverters. There is an increasing requirement for current and voltage-controlled UPS inverters with very low or zero steady-state error, improved transient response and lower total harmonic distortion (THD). The most promising type of current regulator for single-phase inverters is PR control because it can introduce an infinite gain at a selected resonance frequency such as the fundamental frequency to eliminate the steady-state error, which cannot be achieved by well-known proportional integral (PI) control. Note that PI control has limitations in terms of the steady-state magnitude and phase errors. In addition, PI control also has limited harmonic rejection capability, unlike the PR control, also can compensate for low-order harmonics. Imperfections in the current and voltage control scheme results in higher harmonic distortion of the output current and voltage. In this paper, performance of PR control parameters ($K_{p}$ , $K_{i}$ , and $\omega _{c}$ ) and filter parameters ($L_{f}$ and $C_{f}$ ) are optimally tuned to obtain a very low THD current with reduced output voltage ripple and steady-state error. The analysis, design and implementation of both PI and PR current control in single-phase UPS inverter applications through simulations and experiments are also presented in this paper. The performance of both of these control schemes are analyzed in terms of steady-state response, transient response, and level of current harmonics.

A Neutral-Point Voltage Controller With Hybrid Parameters for NPC Three-Level Grid-Connected Inverters Under Unbalanced Grid Conditions

To solve the neutral-point (NP) voltage unbalancing problem, a conventional proportional integral (PI) controller is used for NP clamped (NPC) three-level grid-connected inverters under balanced grid conditions. However, when the three-phase grid voltage is unbalanced, the NP voltage unbalancing problem becomes more serious and complex, which cannot be solved by a conventional PI controller with the variation of the unbalanced grid. Based on the transfer function of the injected zero-sequence component to the NP voltage, the NP voltage module has different characteristic performances in frequency-domain, which is a leading or lagging system with the variation of the unbalanced grid and output power factor. Besides, being appropriate for this NP voltage module in two cases, a PI controller with hybrid parameters (HP-PI controller) is proposed to balance the NP voltage in this paper. According to varied unbalanced grid and output power factor, hybrid parameters are designed for this controller in two cases by the Lagrange multiplier method appropriately. Furthermore, frequency-domain characteristics and the balancing time of the proposed HP-PI control method are analyzed. Experimental and simulation results show that, compared with conventional PI and quasi-proportional resonant (PR) control methods, the proposed HP-PI controller has a strong ability to balance NP voltage with a good dynamic and steady-state performance under varied unbalanced grid conditions, which also improves the quality of grid currents.

Impedance-Based Stability Analysis of Voltage-Controlled MMCs Feeding Linear AC Systems

This paper addresses the small-signal stability of voltage-controlled modular multilevel converters (MMCs) feeding linear ac systems. By using the harmonic state-space (HSS) modeling method, the ac-side impedance matrices (IMs) of the MMC with the open-loop and closed-loop voltage control are derived and their relationship is also explicitly given. It is revealed that the ac voltage regulator has the same effect on the centered diagonal element of the IM of the MMC as that of two-level voltage-source converters (VSCs). Moreover, when the MMC is feeding linear ac loads, the return-ratio matrix of the cascaded system has an eigenvalue that is equal to the ratio between the centered diagonal element of the IM of the MMC and the load impedance, which, consequently, facilitates the stability evaluation by checking that single-input single-output impedance ratio as a necessary condition. These findings also provide physical insights into the subsynchronous oscillation (SSO) of the voltage-controlled MMC with the proportional-resonant (PR) regulator, and a proportional-integral-resonant (PIR) regulator is further introduced to mitigate the SSO. Finally, time-domain simulations verify the effectiveness of the theoretical analysis.

Analysis of the performance characteristics and arm current control for modular multilevel converter with asymmetric arm parameters

In this paper, the performance characteristics analysis and an improved arm current control of modular multilevel converter (MMC) with asymmetric arm parameters are presented. The performance characteristics analysis of MMC is conducted based on the average switching function current model, which demonstrates that fundamental and double frequency ripples exist in the arm circulating current under asymmetric arm parameter conditions. Besides, there will be dc and double frequency components in the ac side current, while fundamental and double frequency ripples also appear in the dc side current. According to the analysis results, the arm current control based on an improved PIR (Proportional Integral-Resonant) controller via the FAC (feedback adjustment control) method is proposed to suppress the asymmetric components with significantly enhanced dynamic response. Theoretical analysis shows that by introducing the integration and feedback loops of the FAC method to the conventional PIR controller, the inertia and damping effects are emerged in the system, which can help to enhance the system dynamic response during transient and achieve better suppression performance of the asymmetric components. Simulation cases verify the correctness of the theoretical analysis and the validity of the proposed control.

Proportional Integral Control Realized in Stationary and Synchronous Reference Frames for a Single-Phase UPS Inverter System: A Comparative Study

ABSTRACTVoltage regulation of the single-phase UPS inverter has design challenges in terms of dynamic performances and control complexity. Widely used conventional integral controllers, such as proportional integral and proportional resonant in stationary frame (SF) of reference have limitations of either steady state error or implementation difficulties. Although a mature technique in three-phase applications, the synchronous reference frame (SRF) control scheme has not been exhaustively investigated for single-phase UPS inverters due to complex multiple transformations. This paper suggests a voltage control scheme which can be alternatively used in both stationary and synchronous reference frames. Three integral controllers namely, SF-proportional integral (SF-PI), SF-proportional resonant (SF-PR) and SRF-proportional integral (SRF-PI) are comparatively evaluated for steady state and transient performances. A systematic procedure for the design of control parameters with stability analysis in the frequency domain for the closed loop control system is also presented. Respective controllers are simulated in discrete time frame using MATLAB/Simulink and experimentally implemented using the TMS320F2812 Digital Signal Processor based laboratory prototype.