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The DC distribution power system has drawn widespread attention and rapidly developed in recent years, however, its stability issue is one of the urgent challenges, requiring much attention. In previous stability studies, the line impedance network is often overlooked, which is convenient for geographically centralized systems, but inaccurate for the distributed systems. In this paper, the modeling and stability criteria of these two systems are simultaneously studied. For the distributed systems, firstly, the transfer functions from each input voltage or current disturbance to the bus voltage are derived. On this basis, the sufficient and necessary condition for the system stability is discussed. Subsequently, a bus node impedance criterion (BNIC) is proposed to assess the small-signal stability of the DC distribution power system. For the centralized systems, by ignoring the line impedance network, its small-signal model can be deduced by the distributed system, and the proposed BNIC is proved to be still valid. In addition, some existing impedance-based stability criteria are analyzed and compared with the proposed BNIC. Finally, the correctness and effectiveness of the proposed BNIC is verified by the cases study and experiments.

Resonant converters are periodic time-varying system, one of whose distinctive features is the sideband effect. To be specific, when a small-signal perturbation is injected into the converter, a series of sideband frequency components will occur. The two sideband frequency components around the switching frequency determine the small-signal response of the resonant tank if it has sufficient band-pass filtering. Using complex Fourier series, the relationship between different frequency components can be described with a series of gains. This paper derives all the necessary transfer functions between different frequencies for resonant converters. Combining them together forms a general small-signal model of resonant converters. There are multiple frequency components, i.e., the perturbation frequency and two sideband frequencies in this model, hence the name multi-frequency model. Two kinds of inverters, i.e., the full-bridge and half-bridge structure, and three modulation methods, i.e., the switching frequency control, the duty-cycle control, and the input voltage control are considered in this paper. The experimental results verify the validity of the proposed model.

Power electronic converter can produce massive voltage stresses on the connected transformer, with great effects on electrical ageing of the insulation. Such effects can be diverse upon different insulation components under different harmonic voltages, which have not been well clarified. This paper aims at enhancing online monitoring of converter transformers from two aspects. First, electrical ageing evaluation models are developed for different types of transformer insulation. It is the first time to clarify the effects related to the component location and the ageing severity under differential-mode and common-mode (CM) voltages. Interlayer (IL) insulation faces a serious ageing threat and the line-lead component is aged with the severest degree. Second, CM voltages are used to build transfer function (TF) measurement for IL insulation monitoring. The key is to identify the optimal monitoring frequency with the highest sensitivity. Based on the analytical case introducing typical parameters, the TF performance is analyzed in different ageing conditions. Online experiments validate that the proposed method is effective and has good application prospect. The contributions lie in that the diverse ageing effects of converter harmonic voltages on different insulation components can be distinguished and online monitoring of IL insulation can be achieved effectively.

Due to the nonlinear time-periodic nature, precise impedance modeling of power-converter-based single-phase ac systems is complex. Small-signal modeling for the systems with a fixed operating point is easy, but the extension of the same procedure to the systems with time-periodic trajectory is still challenging. In this article, a recursive single-input single-output (SISO) impedance modeling framework for single-phase rectifiers is presented, which can greatly simplify both the modeling procedure and the resulting impedance model. A general linear-time periodic modeling method is proposed by extending the linear-time invariant modeling method, where frequency-coupling effects are modeled by the transfer function vector rather than the transfer function matrix, so the modeling complexity is reduced. Furthermore, based on the idea of mathematical induction, an analytical and accurate recursive SISO impedance model is derived. The resulting recursive SISO impedance model can characterize the frequency-coupling dynamics of arbitrary order with a low computation burden. Experiments validate the accuracy of the recursive SISO impedance modeling method.

This article classifies, describes, and critically compares different modeling techniques and control methods for dual-active-bridge (DAB) dc–dc converters and provides explicit guidance about the DAB controller design to practicing engineers and researchers. First, available modeling methods for DAB including reduced-order model, generalized average model, and discrete-time model are classified and quantitatively compared using simulation results. Based on this comparison, recommendations for suitable DAB modeling method are given. Then, we comprehensively review the available control methods including feedback-only control, linearization control, feedforward plus feedback, disturbance-observer-based control, feedforward current control, model predictive current control, sliding mode control, and moving discretized control set model predictive control. Frequency responses of the closed-loop control-to-output and output impedance are selected as the metrics of the ability in voltage tracking and the load disturbance rejection performance. The frequency response plots of the closed-loop control-to-output transfer function and output impedance of each control method are theoretically derived or swept using simulation software PLECS and MATLAB. Based on these plots, remarks on each control method are drawn. Some practical control issues for DAB including dead-time effect, phase drift, and dc magnetic flux bias are also reviewed. This article is accompanied by PLECS simulation files of the reviewed control methods.

This article presents a new hybrid-mode pulse-frequency-modulation control method for an LLC resonant converter. In the proposed control method, the primary-side resonant current sensing signal of the current-mode control variable is combined with a ramp signal of the voltage-mode control variable to determine an operating frequency. Then, the proposed control method mainly modulates the ramp signal in accordance with the output load condition. Therefore, the control-to-output voltage transfer function has both the current - mode control and voltage-mode control characteristics that provide fast frequency response and stable output voltage regulation in a light-load condition. In addition, since the ramp signal is also used for slope compensation of the resonant current sensing signal, an external slope compensation circuit is not required. A small-signal ac modeling and loop analysis of the proposed method verify the advantages. The proposed control method is implemented into a field programmable gate array (FPGA) board with an analog front-end board. An experiment is carried out on a 288-W LLC resonant converter. The result shows that the proposed control method provides fast dynamic performance and stable operation under a light-load condition without an additional slope compensation circuit.

Duty-cycle control is a widely used control method of resonant converters. In this article, the existing model of duty-cycle controlled resonant converters is found to have discrepancy compared with the simulation and experimental results. The reason behind is investigated, showing the phase change in the output voltage of the inverter bridge caused by the duty-cycle perturbation was ignored in the existing model. The phase change law is highly dependent on the duty-cycle scheme used, which is further determined by the forms of the carriers and the switching sequences of the resonant converters. With this consideration, improved models of both full-bridge and half-bridge resonant converters with different duty-cycle control schemes are rederived. It is revealed that different duty-cycle control schemes lead to different phase curves of the duty-cycle-to-output-voltage transfer functions, therefore care should be taken when selecting the appropriate duty-cycle control scheme. In the end, a series-series compensated wireless power transfer system is built to verify the validity of the proposed models.

The proportional-integrator (PI) controller in the synchronous reference frame (dq-frame) and the proportional-resonant (PR) controller in the stationary reference frame (αβ-frame) are two typical linear current control schemes for three-phase voltage source converters. It is generally believed that the plant model is mathematically uncoupled in αβ-frame. Hence, the decoupling control required to attenuate the axis cross-coupling effect in dq-frame is regarded as not necessary in αβ-frame. However, detailed analysis with complex coefficient transfer functions reveals differences in the control performance between the fully decoupled PI control scheme in dq-frame and the PR control scheme in αβ-frame. When regulating sinusoidal currents in αβ-frame, the α-axis and β-axis current references are strongly correlated with each other, which implies a cross-coupling effect equivalent to that of dq-frame. In analogy to the dq-frame decoupling control, cross-coupling terms can be employed together with the conventional PR control scheme. It can bring the benefit of improving the transient response of current tracking and reducing the sensitivity of the resonant controller to frequency variation, especially for low-switching-frequency applications with limited current control bandwidth. Furthermore, the cross-coupling terms based on reference current feed-forward are proposed to improve the performance of both positive- and negative-sequence current control. Experimental results are shown to validate the analysis and the performance of the proposed control scheme.

Multiple second-order generalized integrators (MSOGI) has been widely used to extract the signal that contains multiple harmonics. The MSOGI needs to be implemented in the discrete-time domain for its practical applications. More critically, the discretization method can greatly affect its performance. The existing discretization methods for MSOGI can be divided into three categories: entire transfer-function discretization, SOGI-transfer-function discretization, and integrator discretization. The theoretical analysis indicates that the first method can avoid the errors caused by unit delay, but it is hard to be digitally realized for high-order transfer functions. The other two methods have nonnegligible errors in both the phase and the quadrature characteristic due to the unit delay. In this letter, we propose a novel discretization method by modifying the structure of integrator discretization. This method can enhance the performance in both the phase and the quadrature characteristic with an acceptable computation burden, which has been theoretically analyzed and experimentally verified.

Frequency responses are nonidentical between the positive and the negative frequency range for symmetric three-phase systems modeled with complex transfer functions, which shows unbalanced stability margins. The unbalanced stability margins limit the system performance, as the system dynamics are restricted by the worst one. This article extends the discussion of unbalanced stability margins to asymmetric three-phase systems, i.e., three-phase grid-tied inverters, which are described by transfer matrices. The reason for unbalanced stability margins is analytically investigated, and different impacts are analyzed. It is found that both the control delay and asymmetric control loops can lead to the unbalanced stability margins. To improve the performance limited by the worst stability margin, a margin balancing control is proposed. By implementing a phase correction term, the worst stability margin can be increased by reducing the best one. As a result, the overall stability margin of the system can be improved. The design procedure is elaborated based on a 2-MW inverter system. Verifications are presented based on a 1-kW prototype including simulations, experimental results, and Nyquist analyses. This method applies to all types of grid-tied inverters with multiple control loops.

Variable frequency control is widely used in half-bridge and full-bridge converters. Measuring the switching-frequency-to-output-voltage transfer function is critical to verify a derived model and guide the design of closed-loop parameters. The existing voltage-controlled-oscillator-based measurement method is complicated in circuit implementation and the accuracy could be affected by the bandwidth of the voltage-controlled current source. In this letter, a pulsewidth-modulator-based measurement method is proposed, which is much simpler in the circuit and more accurate. The principle of this method is analyzed in detail. Finally, the experimental results of a half-bridge and a full-bridge series–series compensated wireless power transfer systems are presented to verify the proposed method.

This letter proposes a passivity-based dual-loop vector voltage and current control method for grid-forming voltage-source converters (GFM-VSCs). A passive output impedance of GFM-VSC is guaranteed in both the voltage control mode and the current-limiting mode with a wide range of time delay. The frequency-domain analysis, simulation and experimental tests validate the effectiveness of the approach.

This article presents a novel reduced order average model for dual-active-bridge converter which can be applied to all modulation methods, such as single-phase-shift modulation, dual-phase-shift modulation, extended-phase-shift modulation and triple-phase-shift modulation. This model considers conduction, inductance, and transformer power losses. Furthermore, the input–output filters are suitable for system performance analysis. Based on the large-signal average model, the small-signal model and the output transfer function are derived. The detailed model for predicting the large-signal transient is established and the small signal analysis in frequency domain is carried out. This model can accurately predict the steady-state and transient-state response of the system. The experimental results agreed well with the simulation results which proved the accuracy and correctness of the model.

The stability analysis methods of single-bus dc distribution power systems (DPSs) have been widely studied; however, the multivoltage-level dc DPSs, which have been used in data center, all-electric ship, and so on, its stability analysis methods are rarely reported. The main focus of this article is to study the stability analysis methods, especially the impedance ratio of multivoltage-level dc DPSs. From the point of view of whole system, the two-port small-signal models of multivoltage-level dc DPSs are established and the equivalent loop gains are obtained and used to judge the system stability. On the other hand, the multivoltage-level dc DPSs can be regarded as conventional single-bus dc DPSs at different interfacing locations, and the impedance-ratio type stability criteria are obtained. And it is proved that the two stability analysis methods, namely the system equivalent loop gain and impedance-ratio type stability criterion at different interfacing locations, have the same stability results, which clarifies the stability status by considering different interfacing locations. Finally, the analysis is verified with simulations and hardware-based experiments of a three-converter three-stage dc DPS.

This article explores the use of a variable inductor as a reactive element for energy transfer in a dual-active-bridge (DAB) converter. By using a controlled variable inductor, the optimal switching region in the operation of the phase-shift DAB can be extended, and thus, high efficiencies can be achieved over wider load ranges compared to the traditional solution. Moreover, the combined use of the variable inductance together with the phase shift, as two control parameters, allows for the linearization of the DAB converter transfer function, which improves the stability and the performance of the controller. And finally, due to the controlled saturation of the device, it is feasible to reduce the magnetic core size, yielding a size optimization of the full converter. This article develops a circuit-based model to simulate the converter system, aiming to study the proposed improvements. Furthermore, a 2-kW SiC-based DAB converter prototype is constructed, including a controlled variable inductor. The experimental results presented in this article validate the studies carried out for the different operation conditions.

In wireless power receiver systems, the buck converter is widely used to step down the higher rectified voltage derived from the wireless receiver coil, to a lower output voltage for the immediate battery charging process. In this work, the presence and effect of the right-half-plane (RHP) zeros found in the small-signal inductor-current-to-duty-ratio and output-voltage-to-duty ratio transfer functions of the buck converter in the wireless power receiver system on the control performance, are investigated. It is found and mathematically proved that the RHP zeros are introduced by the current source nature of the system attributed to the series-series compensation and finite DC-link capacitance. The RHP zero not only results in non-monotonic open-loop dynamic response but also complicates the design of feedback control and causes potential closed-loop instability. Theoretical and experimental results are provided to validate the presence of the RHP zeros and their effect on open-loop and closed-loop dynamic responses., 11 pages. IEEE Transactions on Power Electronics 2020 (Early access)

The interconnection stability of a grid-tied inverter system can be investigated not only based on classical control theory, e.g., Nyquist criterion, but also from the energy dissipation point of view. If a critical resonance occurs within the regions, where the system equivalent impedance behaves passively, i.e., has only nonnegative real parts, the system stability can be guaranteed. Thus, it is preferred to design systems with passive regions over a wide-frequency range. This article investigates passivity properties influenced by different control loops and operating points in the $dq$ frame, which facilitates the stability assessment in the frequency domain. Based on this, a virtual damping control method is proposed to improve the stability by enhancing the system passivity. By implementing a damping transfer function in the $d$ - and $q$ -axis individually, nonpassive regions can be accordingly reduced over a specific frequency range. Asymmetrical designs can be considered in the $d$ - and $q$ -axis according to corresponding passivity properties, which is impossible to be realized through symmetric physical filter components. The design procedure is elaborated based on a 2 MW inverter system, which is based on a combined graphical and analytical approach. Verifications are conducted based on a 1 kW prototype including both simulations and experimental results. The method applies to all types of grid-tied inverters with multiple control loops. This article is accompanied by a video demonstrating the validations.

The commonly used average model is not applicable to predict the stability performances of constant on -time (COT) controlled buck converters. It has been reported that the issues of stability can be addressed by using the control signal to output voltage transfer function of the converters, named G VC, for such class of converters. G VC can be mathematically derived using describing-function approach to include the effects of side-band harmonics of the pulsewidth modulation (PWM) modulator. This is essential for modeling the control behavior of the COT converter class. However, the actual G VC can deviate significantly from the derived ideal model. Therefore, a measured G VC transfer function is important for real-world stability predictions. G VC measurement, however, is often not feasible because the points of measurements are physically inaccessible due to integrated control circuit implementation. In this article, a realistic G VC extraction method is proposed for each of the four commonly used COT schemes. Based on the measured G VC, a procedure to predict the stability boundary is proposed and verified.

The voltage closed-loop field-weakening scheme (VCFS) is an effective method to achieve the maximum output torque for induction motor high-speed drives. However, the cross-coupling between the inner current and outer voltage loops leads to system performance deterioration. To address this problem, this article proposed a unified complex vector field-weakening control. First, the inherent coupling problem in VCFS is analyzed based on the double closed-loop structure. On this basis, a complex vector structure is designed to unify the inner current and outer voltage loops, following with a decoupled criterion for controller coefficient selection. Compared with the conventional VCFS, the studied scheme can eliminate the natural complex vector zero in the voltage loop, leading to current ripple and voltage overshoot reduction. The experimental results confirm the effectiveness of the investigated scheme.

The variable switching frequency pulsewidth modulation (VSFPWM) is varying the carrier frequency of pulsewidth modulation (PWM) based on the prediction model to reduce the switching losses and lower the electromagnetic interference (EMI). However, it may cause some deterioration in digital dq current control of voltage source converters. This article takes the L -type grid-connected converter as the research object, and first presents the generation mechanism of the varying time delay caused by VSFPWM. In the case of proportional-integral current regulator implemented with VSFPWM, the varying time delay is accompanied by the frame rotation, which causes a varying phase lag in output voltages, degrading the system performance. Subsequently, an analytical method based on complex coefficient transfer functions is developed to provide an accurate explanation of the relation between the VSFPWM and the corresponding impacts. A compensation method is then proposed to eliminate the varying phase lag of output voltages when the VSFPWM is employed, improving the steady state and dynamic performance of dq current control. Finally, the simulation and experimental results are presented to verify the analysis and the effectiveness of the proposed compensation method.

Accurate estimation of electrical parameters of voltage-source-inverter-fed induction machine (IM) drives is very important while employing high-dynamic-performance control schemes, such as vector control. Parameter estimation schemes reported in the literature can estimate only four parameters ( $R_s$ , $L_{ss}$ , $\sigma$ , and $\tau _r$ ) independently out of five electrical parameters ( $R_s$ , $R_r$ , $L_{\sigma s}$ , $L_{\sigma r}$ , and $L_m$ ), when the core loss resistance is neglected. All the five parameters are not independently identified. This article proposes a parameter estimation method that independently identifies all the six electrical parameters ( $R_s$ , $R_r$ , $R_c$ , $L_{\sigma s}$ , $L_{\sigma r}$ , and $L_m$ ) of the IM, including the core loss resistance. Besides, the variation of core loss resistance with frequency is also discussed in this article. The Kalman filter algorithm is used to estimate machine parameters in the proposed method. In the proposed method, a sine-triangle pulsewidth modulation signal is used as input excitation, instead of pseudorandom binary sequence signals. The proposed estimation method is validated using both simulation and experimental results.

This article studies the modeling of high-bandwidth buck converters under constant-frequency voltage-mode control, where the traditional small-signal averaged model fails due to two major factors in the pulsewidth modulation (PWM), i.e., the large harmonics of modulation waveform and the considerable sideband components. Several modified small-signal models have been proposed to improve the predictions of the frequency domain characteristics. However, these models are less generalized or with high complexity, and may hardly be used in the closed-loop design of real applications. To handle this issue, this article proposes a generalized multifrequency small-signal model (G-MFSSM) for high-bandwidth buck converters, which makes further progress in accuracy while maintaining simplicity in deriving the analytical transfer functions for a closed-loop design. The generalized average model is adopted to precisely describe the first-order harmonic of the modulation waveform, from which a correction factor is extracted to evaluate the influence of the ripple. Furthermore, two dominant sideband components are selected optimally for extremely accurate loop gain predictions. Finally, a closed-loop design procedure is presented for wide-input, high-bandwidth buck converters based on the proposed G-MFSSM. The validity of the proposed G-MFSSM is verified by simulations and experiments.

In dc microgrids, droop control is widely employed in power converters interfacing distributed energy resources and common dc bus for automatic power sharing. In order to limit the dc-bus voltage variations even during load transient conditions, it is necessary to shape the output impedance of droop-controlled converters to be always lower than the dc resistive value. A commonly used way is to install bulky output capacitance, which not only increases the system cost, size, and weight, but also generates higher short-circuit fault currents. In order to avoid large output capacitance, this article proposes a design approach for droop-controlled converters, including the selection criterion of the output capacitance and the design of the droop coefficient. Herein, the required output capacitance is calculated based on the dc droop coefficient and the voltage control bandwidth. The droop coefficient is designed as a frequency-dependent term instead of a constant value. As a result, resistive–capacitive output impedance can be obtained with a much smaller output capacitance. The proposed design strategy is applied to buck and boost converters and validated by experimental results performed on a buck-based and a boost-based dc microgrid prototype, respectively.

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.

The ripple-based constant on-time (COT) control with ripple compensation has been widely adopted in buck converters in the recent years because of its simplicity, fast transient response, and high light-load efficiency. However, this control has the potential issues of instability and excessive load transient response with wide input/output voltage range conditions in the power management integrated circuit (PMIC) applications. In this article, an accurate adaptive COT control scheme is proposed to solve these problems. The control scheme achieves accurate output voltage, and nearly constant quality factor and well transient response over a wide-range operation with simple circuit. The small-signal model is also derived based on the describing function (DF) technique for design optimization. Finally, the simulations and experimental verifications were conducted to verify the proposed concepts.

Converter-grid interactions tend to bring in frequency-coupled oscillations that deteriorate the grid stability and power quality. The frequency-coupled oscillations are generally characterized by means of multiple-input multiple-output (MIMO) impedance models, which requires using the multivariable control theory to analyze resonances. In this article, instead of the MIMO modeling and analysis, the two-port network theory is employed to integrate the MIMO impedance models into a single-input single-output (SISO) open-loop gain, which is composed by a ratio of two SISO impedances. Thus, the system resonance frequency can be readily identified with Bode plots and the classical Nyquist stability criterion. Case studies in both simulations and experimental tests corroborate the theoretical stability analysis.

Linear vernier permanent-magnet (LVPM) motors have a bright future in long stroke applications, because of their merits of high efficiency, high force capability, and low cost. However, the position sensor for the LVPM motor costs huge. In this article, a sensorless control based on an improved mover flux observer is proposed. The proposed mover flux observer combines a disturbance observer and a feedback controller. It can be easily implemented, which results in low computation burden. Due to simple tuning parameters of this observer, the mover flux observer can have strong robustness to the dc bias and the initialization errors of integrators that are main weakness of flux model. This proposed observer also does not introduce error in either the estimated mover flux amplitude or phase. Then, a phase-locked loop is used to detected position information from the mover fluxes. Finally, the LVPM motor operates by using the estimated position and speed signals. Simulation and experimental results of the LVPM motor demonstrate the accuracy and dynamic performance of the proposed sensorless operation.

Inductive power transfer (IPT) systems with front-side and load-side converters are generally developed for better overall system efficiency than a single IPT converter by providing maximum efficiency tracking and output regulation against variations of coupling coefficient ( $k$ ) and load. The optimum efficiency point of an IPT converter is at a particular loading resistance, which varies with $k$ and is hard to measure directly for the purpose of control. Perturb and observe control is normally implemented to iteratively track the optimum efficiency point. However, this heuristic algorithm results in slow response to the variations of $k$ and load. Recently, a much faster linear control for optimum efficiency tracking has been developed for the series-series (SS) IPT system only. This paper proposes a general linear control scheme for all four basic IPT systems to track the optimum efficiency point. Unlike the SS IPT converter, it is found that additional control of either frequency or adaptive compensation is needed for the other three basic IPT converters to operate against the variation of $k$ . Different input to output transfer functions and their $k$ - and load-independent properties at optimum efficiency are identified for all four basic IPT systems. Thus, a general fast linear control can be applied in the front-side converter to achieve optimum efficiency, while the load-side converter regulates the output power independently. Furthermore, the maximum efficiencies of the IPT converters with these four basic compensations for an identical loosely-coupled transformer are compared theoretically and verified experimentally. The parallel–parallel IPT converter gives the best efficiency. Its additional frequency control in conjunction with the optimum efficiency tracking and the output power regulation is also experimentally validated.

This article demonstrates all-digital tuning and dynamic control of feedback compensator in digital low drop out regulators to enhance the transient performance under process and passive variations, aging, and load changes. The measured results from a 130-nm CMOS test-chip shows 2.1× improvement in transient performance under process variations and 30% improvement for aging-induced degradations. We demonstrate 55-ns setting time for a 5 to 45 mA load step in 100 ps, with 97.8% peak current efficiency.

The traditional pulsewidth modulation predictive control (PPC) has poor steady-state performance when used for fault-tolerant control of multi-phase machine drives, because this paper finds that PPC theoretically has a large steady-state error when tracking ac signals. Thus, an improved PPC regulator is proposed, which can rapidly and accurately track ac current references and realize decoupling control among phase currents. The proposed method is developed by redesigning the transfer function of the conventional PPC to a resonant form, reducing the amplitude and phase error in the conventional approach. By making the resonant frequency of the resonant term track the machine frequency, the amplitude and phase response of the system at the working frequency are close to zero. Thus, the proposed R-PPC features fast-response-performance and high-ac-tracking-accuracy. The effectiveness of the proposed method has been verified on a surface-mounted permanent magnet synchronous machine by experiments.

The main standard for avionic equipment DO-160G defines a set of tests that require compliance before the employment of a device in aircraft. An important test involves the generator voltage and consequential current distortion of the three-phase load in the variable 360–800 Hz frequency grid. The main purpose of this paper is to present and analyze a systematic design methodology for three-phase boost and buck rectifiers in order to meet with the voltage distortion test requirement. For a given voltage harmonic profile, the current harmonic limits that have to be satisfied are translated into equivalent per-harmonic admittances and a profile of maximum rectifier input admittance versus frequency is obtained. The defined profile, due to normalization, is applicable to arbitrary power level with simple shifting by the base admittance governed by the converter nominal power. It is shown that for boost-type rectifiers there is a tradeoff between current controller bandwidth and input inductor size, while for the buck-type rectifiers main limitation lies in the input LC filter design used for differential electromagnetic interference filtering. The experimental results conducted on an SiC three-phase 10 kW VIENNA rectifier are tightly backing up the proposed theoretical analysis. This paper is accompanied by three videos demonstrating experimental measurement of d -axis open-loop duty cycle to inductor current transfer function, loop-gain of d -axis current controller with 3.8 kHz bandwidth and variable grid frequency 360–800 Hz operation of the converter under 0% and 10% input three-phase voltage total harmonic distortion.

LCL resonance complicates the design of a current control loop and can even threaten its stability. Extensive approaches have been proposed to deal with this resonance, among which active damping (AD) schemes based on the feedback of a single filter variable have been shown to be effective and cost-efficient. This paper presents a study of such AD techniques, where a generalized approach to developing an AD controller by relating a control diagram to an equivalent circuit is proposed. Based on this approach, AD controller forms with any one of four commonly used filter variables to realize virtual resistors (VRs) in six different connections to the LCL filter are derived. Comparisons are then made between these 24 AD controller alternatives by considering the implementation complexity of the AD controller, the number of measuring sensors, and the effect of the AD controller on the power stage. Consequently, grid-side current feedback AD to realize a VR in parallel with the filter capacitor is selected as a considered alternative. Next, two issues associated with the practical implementation of the selected grid-side current feedback AD, caused by the second-order differential expression and the digital time delay, are discussed and solved. Finally, the selected AD method is analyzed in the discrete z -domain, and its effectiveness is experimentally verified.

Digital peak current mode (DPCM) control is widely used for dc–dc converters operating in continuous current mode. However, current tracking delay (CTD) in the system is normally neglected in the modeling stage, which leads to poor compensator design and degraded performance. This paper investigates CTD effect in boost converter with different DPCM controls. Based on dynamic relationship between the reference current and actual inductor current, the CTD transfer functions are derived, which improves the accuracy of small signal model. Since CTD degrades the phase margin of the system, equivalent migration of right half plane zero is proposed to model CTD effect. This method is very simple and straightforward, which facilitates the compensator design. Furthermore, two novel DPCM control strategies with minimized CTD are proposed, and they are based on duty cycle restriction and duty cycle extension, respectively. Both controls greatly reduce the CTD effect and improve the response speed. Besides, the duty cycle extension benefits from an extended pulsewidth modulation (ExPWM). This optimizes the calculation algorithm and speed, while improving the time margin for digital calculations. Combined with the proposed models and controls, the CTD effect is greatly reduced. The effectiveness is verified through detailed simulations and experiments.

Conventionally, a proportional-integral (PI)-based dual-loop control strategy, in which both the dc-bus voltage and the inductor current are regulated, is utilized to control ac/dc converters with power factor correction (PFC). Due to the characteristics of the PI controller, converters experience poor control performance such as current distortion and slow dynamic response. This paper proposes a novel cascaded proportional control in conjunction with algebraic estimation method for PFC ac/dc converters. Different from the conventional control system, the average dc-bus energy and the instantaneous input power of the converter are regulated. Moreover, system nonlinearity, load power and uncertainties are estimated by incorporating algebraic estimators. A holistic design of controller parameters and stability analysis are presented based on the z -domain transfer functions. A 1 kW PFC ac/dc prototype is designed and experimental results demonstrate the effectiveness of the proposed control scheme.

Operating in the high-speed range is necessary for high-performance permanent-magnet synchronous motor (PMSM) drives. However, due to the back electromotive force effect, the PMSM is approaching the voltage limit at field decreasing scope. This paper presents a new flux-weakening scheme along with an improved vector control strategy to alleviate the influence of this problem. Control parameters of the anti-windup proportional and integral (AWPI) controller are optimized off-line in relying on an adaptive velocity particle swarm optimization (AVPSO) algorithm. The AVPSO algorithm considers the summation of AWPI measurement error which is the objective function of the optimization problem without knowing the transfer function of the plant. Hence, the tuned flux-weakening controller with a filter is used to set the flux level without saturating the current controllers. Meanwhile, the other controllers of inner and outer loops award a great dynamic and steady-state performance for the PMSM. In the proposed scheme, the flux-weakening control is not dependent on machine parameters that adapts the flux level automatically and provide a fast transition between the constant torque region and the field-weakening region. Effectiveness and advantages of the proposed scheme are presented in this paper through both simulation and experimental results.

Recently, low-frequency oscillation (LFO) occurs in electrified railways, which exhibits a synchronous periodic oscillation of about 2–7 Hz in the traction network and electric multiple units (EMUs). To suppress the LFO, an improved model predictive control (MPC) combining with extended state observer (ESO) is proposed. First, for the design of ESO, the changes of system parameters and the unmodeled item in vehicle mathematical model are extended to a new variable and then estimated to compensate the calculated control voltage in real time. Second, the observer stability is analyzed by obtaining the transfer function, and the appropriate gains of observer are chosen through the pole assignment technique. At last, by the combination of the predictive currents, the optimal control voltages can be obtained. The control performance among MPC, dq decoupling control, passivity-based control, and the proposed method is compared. In addition, the system robustness when system parameters change is discussed. At last, to further verify the effectiveness of the proposed method for suppressing LFO, an integrated dSPACE semi-physical experimental platform including eight simulated EMUs and an equivalent traction network is constructed. Simulation and experimental results show that the proposed method not only effectively suppresses LFO but also accelerates the response speed of traction line-side converter, reduces the distortion of grid-side and vehicle-side currents, and overcomes the disadvantages of MPC and dq decoupling control under the mismatching of system parameters.

The interaction of a grid-connected voltage-source converter with a weak grid is of significant interest. In this paper, the converter together with the grid impedance is modeled as a single-input single-output (SISO) system. Provided that certain assumptions hold, this allows us to apply the standard SISO Nyquist stability criterion for stability analysis and controller design. The derived model is verified against time-domain simulations and experiments. The method facilitates the design of the converter control system with adequate stability margins.

Two measurement schemes, namely, the modulation signal perturbation scheme and the pulse perturbation scheme, have been used for evaluating the loop gain of dc–dc converters. However, the two measured loop gains do not give consistent results due to the use of different forms of the injected small perturbation signal, and the difference in the two schemes cannot be distinguished by the usual averaged model. In this paper, the two loop gain measurement schemes are analyzed based on an extended-frequency-range small-signal model. Expressions of the loop gain are derived and their use in stability assessment and derivation of closed loop transfer functions is demonstrated. A sample-and-hold scheme is proposed as a simple alternative implementation of the pulse perturbation scheme. Finally, experimental prototypes of buck, boost, and buck–boost converters are tested for verification of the analytical results and the effectiveness of the sample-and-hold scheme.

Multiple loops have been used extensively to enhance the system performance in various applications. However, the increasing complexity of multi-loop systems also makes them much more difficult to analyze and implement. In this paper, a new methodology to analyze multi-loop system is proposed. In the proposed framework, multi-loop systems are regarded to be built upon of sub-modules of cascade, parallel adding, and feedback units, and then, they are simplified following a certain procedure based on the correlation of the Bode characteristics of the segmented sub-modules. Applying this methodology, the Bode plot and the transfer function of the system can be easily obtained with the system properties of gains, zeros, and poles. Two examples are provided as demonstrators, including a multi-loop low-dropout regulator (LDO) from literature, and a newly designed multi-loop LDO aiming at enhancing the stability over a wide load range, which show that the Bode plot and the transfer function can be obtained more intuitively and rapidly. Excellent agreements among theory, simulations, and measurements are confirmed, which verify the proposed method. It can help designers to gain more intuitions and insights on multi-loop systems from both circuit and device perspectives, which is also an effective tool for both stability analysis and circuit design.

Instability problem is an important issue for dc/dc conversion cascaded systems (Cascaded system in short). Though most of the existing stabilization methods can stabilize the whole system very well, they may ignore their impacts on the dynamic performance of the original cascaded system. Unfortunately, these impacts are negative to some extent. Recently, an adaptive-series-virtual-impedance (ASVI) control strategy has been reported to address the above problem. It not only can stabilize the cascaded system via shaping the load input impedance, but also can reduce its impact on the original load converter. However, though the ASVI control strategy has already greatly reduced its impact on the load converter, its remaining impact is negative. To solve this problem, this paper moves the ASVI from the load side to the source side via a proposed source-side series-virtual-impedance (SSVI) control strategy for the source converter. This SSVI control strategy not only has the same stabilization function and adaptive characteristics as the ASVI control strategy, but also improves the performance of the source converter. In addition, since the SSVI control strategy is realized by changing the control block of the source converter, the performance of the load converter is not affected. Therefore, the SSVI control strategy can be treated as a supplement and expansion of the ASVI control strategy. Moreover, depending on the method of realization, the SSVI control strategy can be divided into the source stabilization methods of the cascaded system. Finally, a 100 W 48 V–32 V–24 V cascaded system has been fabricated to validate the proposed control strategy.

Flyback converters with universal serial bus power delivery (USB-PD) specification are widely used in low-power adapter application. The wide output voltage range operation of USB-PD makes the loop gain vary under different working conditions. To ensure stability in all working conditions, the loop gain has to be compensated based on the worst case of control-to-output transfer function. However, in other conditions, the crossover frequencies of loop gain are sacrificed, resulting in poor transient responses. This paper proposes an adaptive variable-frequency peak current mode control with constant crossover frequency to mitigate the tradeoff between stability and transient response while possessing the variable frequency characteristic to improve light load efficiency. The adaptive control law is derived from the proposed small-signal model. Experimental and simulation results verify the analysis. The proposed control reduces the output voltage variation at load transient by 43% and 34% at 5 and 20 V output voltage, respectively.

It is generally known that averaged models are inadequate in describing the effects of leading-edge and trailing-edge pulsewidth modulation (PWM) on the stability of dc–dc converters. In this paper, using discrete-time models of the buck, boost, and buck–boost converters and considering the effects of leading-edge and trailing-edge PWM, the general expressions of the duty-cycle-to-output-voltage transfer function, G vd( z ), in the discrete-time domain are derived. Based on the low-pass characteristics of the dc-dc converters and related properties of the matrix functions, approximate expressions of G vd in the frequency domain are derived, which are simple and accurate up to half the switching frequency. Using the approximate G vd, the stability of the three basic dc–dc converters under leading-edge and trailing-edge PWM is analyzed. It is shown that the stability of the buck converter is unaffected by the type of PWM, while the leading-edge modulated boost and buck–boost converters have better stability than the trailing-edge modulated ones. Since the trailing-edge modulation is commonly available in PWM controller integrated circuits, the modulation signal zero-order holding (ZOH) method and the inductor current feedback control method are proposed for use in the trailing-edge modulated boost and buck–boost converters to achieve the same effect of leading-edge modulated converters. Experimental buck and boost converters were constructed for verification of the accuracy of the proposed model and the validity of the proposed control schemes.

A new controller for a grid-connected inverter with an LCL filter is proposed in this paper. The system is described by its complex representation, and the controller is designed using the complex root locus method. The complex representation allows a considerable reduction in the order of the system, simplifying the design task and making it possible to use advanced techniques, such as the complex root locus. The new complex controller adds an extra degree of freedom that makes it possible to move the poles of the systems and to improve the stability and speed of response compared with the conventional controls. This paper includes a detailed discussion of the effect of the gains of the controller on the root locus. The proposal is validated with simulation and experimental results.

This paper presents an adaptive repetitive control method for torque ripple suppression of the doubly fed induction generator (DFIG) system connected to a dc grid considering the stator frequency variation. Since the stator of DFIG is connected to the the diode bridge directly, the stator frequency should be controlled additionally. A novel frequency-locked loop (FLL) based on a second-order generalized integrator (SOGI) is proposed for acquiring stator frequency. The stator fundamental voltage is obtained by the adaptive multi-SOGI. Thus, the low-pass filter can be avoided, which can improve the bandwidth of the control loop. Furthermore, the orientation angle can be acquired by the stator fundamental voltage vector directly, which can avoid the parameter dependence on stator and rotor inductances. Since the stator frequency will be controlled to change in a certain range for efficiency optimization, an adaptive repetitive controller (RC) is added to the rotor current control loop for torque ripple suppression considering the stator frequency variation. Based on a mathematical model of the DFIG control system, the transfer function of the frequency control loop and the torque control loop are derived for analyzing the control performance and parameter design. Finally, the proposed control method is validated through the experiment results.

The stability and small-signal analyses of the dual series-resonant dc–dc converter are investigated in this paper. The small-signal model of the converter is derived from the extended describing function analysis. Frequency-domain analysis is then employed to derive the small-signal transfer functions of the converter. This procedure establishes an insightful understanding about the effects of the converter parameters and operating conditions on the stability and transient behavior of the converter. The results are used to illustrate the development of the single-loop, voltage-feedback control scheme for the dual series-resonant dc–dc converter. It is demonstrated that the proposed control method enables the converter to regulate its output voltage in the case of abrupt changes in input voltage and output load, and it provides improvement in the transient response. An experimental prototype of the dual series-resonant dc–dc converter is built and the performance of the control scheme is experimentally evaluated by applying abrupt changes in the operating condition of the converter. Based on the experimental results, it is shown that the single-loop, voltage-feedback control scheme is effective in regulating the output voltage of the converter.

In the paper by Patra et al. , a single-inductor multiple-output switcher was presented to produce buck, boost, and inverted outputs simultaneously. Unfortunately, this study showed some unexpected mistakes, especially in state-space equations and in the calculation of output voltages. The objective of this note was to provide correct analysis and rectify the errors in this paper. Some tables and equations have been modified that were present in the initial draft of this paper. The obtained parameters in this work could be an effective supplement and extension for the original work in the paper by Patra et al.

This paper proposes a generalized design procedure for repetitive current controllers in distorted distribution grids to obtain good disturbance rejection properties and well behaved and robust system dynamics. Different implementation options for repetitive controllers (RCs) are discussed based on an accurate discrete time model. A simple control design is derived, which allows any desirable dynamics to be adjusted by one single parameter. Even a deadbeat design is possible. The impact of model inaccuracies and numerical errors on the dynamic and stability of the system is investigated. It is shown that the RC leads to low damping or even instability at high switching frequencies caused by modeling errors or numerical inaccuracies. Based on the stability analysis, it is discussed how to handle these design challenges, which exist especially for RCs of high order. The proposed control structure and control design concept is verified by simulations and experiments.

Flyback converter with variable-frequency peak-current-mode (VFPCM) control is widely used in low-power adaptor and recently proposed universal serial bus power delivery application. The control scheme achieves high efficiency for the entire load range by reducing the switching frequency at light load. In the present study, an accurate unified small-signal model for VFPCM control in continuous conduction mode (CCM) and discontinuous conduction mode (DCM) is proposed. Based on the model, a compensation strategy is proposed to overcome the unstable problem in a wide range of operations and give engineers insight. Experimental and simulation results verify the proposed model and compensation strategy.