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First harmonic analysis (FHA) is arguably the most widely used analytical technique for wireless power transfer (WPT) circuits due to its simplicity. Although FHA can provide closed-form solutions, the existence of rectifier diode forward voltage drop and higher order harmonics, especially the second and third harmonics at variable duty cycle operation, can significantly deteriorate its accuracy. This paper presents an accurate and efficient method called enhanced multiple harmonic analysis (eMHA) for the optimal design and optimal control of WPT systems. The eMHA method considers the nature of nonlinear rectification networks under nonsinusoidal current and reexamines the concept of the equivalent load. As a result, the rectified WPT system is transformed into a series of linear systems with complex load impedances. The steady-state electric quantities can be then explicitly calculated. This enables eMHA to seamlessly work with numerical optimization algorithms to facilitate the automated design and optimization of WPT systems. An example of optimal design and optimal control of a 10 W WPT system is demonstrated. The results obtained by eMHA and FHA are also compared. A prototype of the designed circuit was constructed. The accuracy and effectiveness of eMHA are verified by experimental measurements. This paper is accompanied by a MATLAB-based analytical tool with a graphical user interface demonstrating the effects of circuit variables on electrical quantities and waveforms. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper analyzes two fault-tolerant dual-multiphase motor drives, a series-connected topology, and a standard H-bridge topology. Previous studies have shown that the series connected topology is appropriate to an aerospace application and has lower peak current in degraded mode in comparison with the H-bridge topology, which may consequently diminish the system's weight and cost. This paper extends the study to compare different control strategies of these structures under two fault conditions: short-circuit of an inverter's switch and an open-phase of the machine. The control strategies analyzed in this paper do not impact the fundamental current or the torque generation, but the amplitudes of some harmonics in degraded mode are expected to be narrowed down in order to reduce the inverter's size. Some analyses of maximum voltage and peak current in degraded mode have been used for inverter dimensioning. Experimental results are shown and compared to the simulated ones to confirm the validity of this study. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel polygonal voltage space vector structure (SVS) having 30 sides, for a star-connected induction motor drive. The SVS eliminates the presence of harmonics up to 25th order from motor phase voltage throughout the entire modulation range, providing a torque profile devoid of lower order pulsations. Linear modulation is extended till 99.63% of base speed without exceeding the motor phase voltage rating. Topology consists of a dc-link fed primary inverter and two equal low voltage modular capacitor fed secondary inverters. Here the harmonics generated by the primary inverter is canceled by the secondary inverter which acts as a switched capacitive filter. Detailed description of the SVS generation and timing calculations are provided in this paper. Effectiveness of the proposed scheme is validated using experimental results, inverter loss calculations, and harmonic analysis. [ABSTRACT FROM AUTHOR]

The main technical challenge of the medium-voltage motor drives with modular multilevel converter (MMC) is the serious low-frequency fluctuation on the capacitor voltages, and the existing suppression methods inevitably inject high-frequency circulating currents in MMC. However, the output currents are evidently distorted by the large injected components, while little research has been done to study and solve this problem. This paper analyzes and proves the essential interactions between the output current distortion and the injected components, and the specific dominant output harmonic groups are derived and summarized, revealing the nature of the problem, and it can be taken as a favorable reference for the controller designing. Based on the derivations, this paper proposes a novel suppression method for the greatly improved harmonic characteristics of the output currents during the low-frequency operation. The output harmonics can be accurately measured by the proposed control and effectively suppressed for much lower current total harmonic distortion, benefiting for the superior output control performances with improved efficiency. The simulation results on PSCAD/EMTDC and experimental verifications on a 2.2 kW MMC-based motor drive prototype prove the validity of the presented harmonic analysis and suppression method. [ABSTRACT FROM AUTHOR]

Frequency-locked loops (FLLs) create a rather large category of closed-loop synchronization techniques, which have received considerable attention in different engineering applications, particularly for synchronization, signal processing, and control purposes. Focusing on single-phase grid applications, designing FLLs is often based on a second-order generalized integrator (SOGI), and the SOGI-FLL is regarded as a standard structure. Using the linear Kalman filter (LKF), complex bandpass filter (CBF), and circular limit-cycle oscillator (CLO) are some alternative approaches. FLLs based on these filters/elements, which are briefly referred to as the LKF-FLL, $1\phi$ -CBF-FLL, and CLO-FLL, have not been well analyzed in the literature, and limited knowledge about their real advantages/disadvantages compared to the SOGI-FLL exists. Covering this gap is the objective of this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a current control of dual three-phase permanent magnet synchronous machine (PMSM) based on five-leg inverter. The five-leg inverter can be utilized to drive dual three-phase PMSM with full torque at slow speed when the conventional dual three-phase voltage source inverter (VSI) has a faulty inverter leg. Usually, the common leg in the five-leg inverter may have severe current stress. By dedicated selection of which two phases as a pair to share the common leg, its current rating is approximately half of current rating of other legs. Meanwhile, the five-leg inverter can fully fulfill the vector space decomposition control for dual three-phase PMSM, which has the same dynamical performance as the conventional dual three-phase VSI. However, due to the asymmetry of five-leg inverter non-linearity, the currents of dual three-phase PMSM are unbalanced. To mitigate this issue, the five-leg inverter non-linearity compensation is also introduced and investigated in this paper, whose effectiveness is verified by comparative experiments on a prototype dual three-phase PMSM. [ABSTRACT FROM AUTHOR]

This paper proposes a two-degree-of-freedom (2DoF) interleaving scheme based on phase-disposition (PD) PWM for minimizing the high-frequency zero-sequence circulating current (ZSCC) in modular interleaved three-level converters. The method incorporates an internal interleaving by phase-shifting the carriers in each individual converter, and an external interleaving by phase-shifting the carriers of the different converters. A general harmonic distribution analysis which is valid for all types of voltage source converters is carried out to simplify the evaluation of the proposed method. A comprehensive evaluation of the proposed method shows that the PD-2DoF interleaving scheme produces the lowest ZSCC maximum value as compared to existing approaches. Moreover, it can achieve comparable performances as existing methods do in terms of output quality and common mode voltage magnitude, showing a great potential for practical implementation. Simulation and experimental results are obtained to demonstrate the performance of the proposed method. Generalization of the 2DoF interleaving scheme to high-level converter is also discussed in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates a Vienna rectifier as a charger for series-connected battery packs. Focusing on carrier-based pulsewidth modulation (CBPWM), the ripple current flowing through the neutral point (NP) results in the voltage oscillation if the loads are resistive. To reduce the ripple of average NP current with mitigated distortion under balanced and unbalanced dc-link voltages conditions, a novel CBPWM with segmented component injection scheme (SCIS) is proposed in this paper. After dc component injection, continuous intervals for optimized component injection and clamping intervals for compensation component injection are identified. Optimized components are calculated originally based on unbalanced factor to make the average NP current zero-size in one switching period. Moreover, unique compensation components generate suitable NP current to shape the sinusoidal input currents according to the circuit analysis. In consequence, the SCIS not only keeps the input current with low-harmonic distortion, but also minimizes the oscillation of dc-link voltage under balanced and unbalanced conditions. In addition, the value of the NP current during the clamping intervals is analyzed under various operating conditions. The effectiveness and the performance of the proposed SCIS are verified by simulation and experiments. [ABSTRACT FROM AUTHOR]

The capacitance of sub-module capacitor has a great impact on the cost, size, and operation of the modular multi-level converter (MMC). However, the capacitance selected by the existing methods does not always meet the requirement in practice. To find out the reasons for this improper selection, the existing selection methods are analyzed in this paper. Based on the analysis, a new capacitance-selection method is proposed. In the new method, the problems of the existing methods are solved, and the calculation of capacitor voltage is based on a proposed capacitor-voltage model whose calculation error can be smaller than 0.1%. Furthermore, the Secant Method is used in the capacitance selection to quickly calculate the required capacitance. The new capacitance-selection method can be applicable to the MMC not having a circular operating region. In addition, this paper found that the capacitor voltage and the capacitor-voltage ripple reach their maximum values when the power-factor angles of the MMC are –π/2 and π/2, respectively, and the dc component in the capacitor voltage changes according to the operating condition of the MMC. Finally, the proposed selection method and theoretical analyses are verified by both simulation and experiment. [ABSTRACT FROM AUTHOR]

Switching behavior analysis is an indispensable step for evaluating the steady-state performance of a bidirectional dc–dc converter and a prerequisite for soft-switching modulation design. For dual-bridge series resonant dc–dc converters (DBSRCs), the commonly used fundamental harmonic approximation (FHA) does not usually provide predictions accurate enough for reliable analysis and design. This paper discloses the exact closed-form solution for the zero-voltage switching (ZVS) operation conditions of DBSRCs for the most general case, in which all modulation quantities—i.e., phase shift, duty cycles, and switching frequency—are included. The proposed approach relies on a geometrical analysis of the converter state-plane trajectory, and allows us to analytically predict the ZVS or hard-switching state of any switch and for any given converter operating point. By inherently capturing the effects of all tank harmonics, the model disclosed in this paper shows higher accuracy than the conventional FHA-based approach, and translates into a practical tool for ZVS prediction and optimization at the converter design stage. Based on the derived analytical results, switching behavior of DBSRCs with minimum rms current trajectory (MCT) modulation is investigated, and an effective design choice of resonant-to-switching frequency ratio is presented, which contributes to reduced switching losses and enhanced efficiency. Furthermore, a variable frequency modulation scheme is formulated, achieving ZVS operation of all transistors over a wide input/output voltage range and efficiency improvement versus MCT technique. The analysis and conclusions are validated via extensive experimental tests on a 700 W DBSRC prototype. [ABSTRACT FROM AUTHOR]

This paper presents the first experimental validation of the stability analysis based on the online measurement of harmonic impedances exploiting the linear time-periodic (LTP) approach applied to ac networks of power converters. Previous studies have provided the theoretical framework for the method, enabling the stability assessment of an unknown system adopting a black-box approach, relying only on injected perturbations and local measurements. The experimental case study considered in this paper comprises two single-phase converters, one acting as source subsystem and the other as load subsystem. A third converter, the stability measurement unit, is controlled to inject small current perturbations at the point of common coupling (PCC). From the measured small-signal perturbations of PCC voltage, source current, and load current, the harmonic impedances of source and load subsystems are calculated. The LTP Nyquist criterion is then applied to the ratio of the two harmonic impedances in order to assess the stability of the whole system. Theoretical and experimental results from a 5-kW laboratory prototype are provided and confirm the effectiveness of the method. In addition, the measurements do not require sophisticated equipment or control boards and can be easily performed from data sampled by commercial micro-controllers. [ABSTRACT FROM AUTHOR]

This paper proposes a coordinated control strategy for the rotor-side converter (RSC) and the grid-side converter (GSC) of an LC-filtered doubly fed induction generator (DFIG) under distorted grid voltage condition, to eliminate the distortion of the total output current (including the stator current, the GSC current, and the filter capacitor current). For an LC-filtered DFIG connected to a distorted grid, the low-order current harmonics can freely flow into the filter capacitor thereby polluting the total output current, even when the stator current and the GSC current are both controlled as sinusoidal. Although this problem can be addressed by measuring the output current or the capacitor current, the extra current sensors are undesired in industrial applications. In this paper, a novel hybrid virtual impedance method is implemented in both the RSC and the GSC, to reshape the parallel impedance of the stator, the GSC and the filter capacitor to nearly infinite for low-order harmonics, thus, the freely flowing output current harmonics can be mitigated. Meanwhile, the low-order current harmonics required by the output current compensation can be flexibly distributed between the stator and the GSC according to their operating conditions, to disperse the side-effects on the drive train and the GSC, thereby better protecting the whole system. The effectiveness of the proposed strategy is theoretically analyzed and verified with both simulation and experiment. [ABSTRACT FROM AUTHOR]

The instantaneous output power of the two-stage single-phase grid-connected photovoltaic (PV) inverter pulsates at twice the line frequency ($2f_{{\text{o}}}$), generating second harmonic current (SHC) in the front-end dc–dc converter and PV panel, which will affect the maximum power point tracking operation and deteriorate the overall conversion efficiency. The generating mechanism of the SHC is analyzed in this paper and it is pointed that in order to eliminate the SHC in the front-end dc–dc converter and PV panel, the voltage loop gain of the front-end dc–dc converter should be high enough at $2f_{{\text{o}}}$. Since there is a −180° phase abrupt at the resonant frequency of the input side filter capacitor and the inductor, the system may be unstable. To cope with this problem, the inductor current feedback active-damping scheme (ADS) is adopted. For further improving the loop gain at $2f_{{\text{o}}}$ , proportional–integral–resonant regulator with ADS (PIR + ADS) is proposed in this paper. Besides, a step-by-step closed-loop parameters design method is presented. Finally, a 3-kW two-stage single-phase grid-connected PV inverter has been fabricated and tested, and the experimental results verify the feasibility of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper is focused on a dual-loop current control method (grid current loop and fundamental current loop) for digitally controlled LCL-type shunt active power filters (APFs). Normally, a proportional-resonant (PR) unit is used as the fundamental current controller, where the proportional part of PR unit actually serves as the proportional feedback of inverter-side current and provides a certain degree of damping for LCL resonance. However, its valid damping region is only up to one-sixth of the sampling frequency (fs/6), which leads to less robustness to the grid impedance. To address this issue, a delay-compensation control link is proposed in this paper to replace the proportional part of the PR fundamental current controller and widen the effective damping region. As a result, the system robustness is improved without adding extra sensors or introducing an extra active damping loop. Theoretical analysis proves that it can obtain a wider damping region of (0, fs/4). Moreover, a systematic controller parameter design criterion is studied. In particular, a numerical optimization algorithm is developed to optimize damping property, and a design method based on root locus plot and Bode diagram is presented to enhance harmonic compensation accuracy. Finally, experimental results implemented on a 30 kVA APF prototype have validated the feasibility of the proposed current controller and parameter design criterion. [ABSTRACT FROM AUTHOR]

Due to inherent high reliability and low maintenance cost, the brushless doubly fed induction generator (BDFIG) has become a promising candidate in offshore wind energy generation systems and dc/ac/hybrid microgrids. This paper proposes a novel BDFIG based system targeting at dc power generation (BDFIG-DC), which features interfacing the power winding (PW) and the dc grid through an uncontrolled rectifier and common dc link. Compared to conventional BDFIG systems fed by ac grid, the BDFIG-DC system offers an alternative to integrate the BDFIG into the dc transmission system with a simpler structure and lower cost. Due to the constraint imposed by the dc-side diode bridge, torque ripple reduction emerges as an urgent issue as a result of the distorted flux and current. To achieve the smooth dc-connected operation of the BDFIG, an improved vector control strategy is proposed in this paper, where the control of the system is divided into three parts: torque ripple reduction, frequency regulation, and average torque control. Based on the investigations into the electromagnetic torque reduction and small-signal model of the PW flux linkage, average torque and PW frequency are successfully controlled with torque ripple effectively suppressed. The effectiveness of the proposed system, along with the associated control strategy, is validated by the experimental results of a 10-kW 2/1 dual-stator BDFIG (DS-BDFIG) prototype. [ABSTRACT FROM AUTHOR]

One promising topology for solid state transformer (SST) is a modular multilevel cascaded converter, in which submodule is composed of dual active bridge (DAB) and H-bridge. For SST application in PV system, the efficiency could be severely affected especially for DAB due to the wide voltage and power range of PV panels. Thus, the motivation of this paper is to deal with the control strategy to improve DAB efficiency inside SST for PV application. Instead of utilizing time-domain based analysis method, which requires complex modeling process, this paper models DAB under frequency domain by fully considering the effect of both fundamental and harmonic frequency component. To achieve high efficiency operation, a multiorder reactive-current suppression (MRS) strategy is proposed by controlling phase shift angle as well as the duty cycles of primary and secondary side H-bridges. In terms of DAB controller design inside SST, the small signal model under MRS is established and a notch filter is implemented to suppress the second order line frequency fluctuation in the control loop. Finally, a 10 kV/1 MW SST prototype is introduced along with the system control structure and implementation method. The experiment of the submodule and SST confirms the effectiveness of proposed method. [ABSTRACT FROM AUTHOR]

The use of LCL filters is a well-accepted solution to attenuate the harmonics created by the pulsewidth modulation. However, inherently LCL filters have a resonance region where the unwanted harmonics are amplified, which can compromise stability. Several techniques have been developed in order to tackle this issue. At first the use of passive damping, by intentionally increasing the resistance of the LCL filter components, is a simple, robust, and straightforward solution; however, it decreases the overall efficiency of the system, and hence in general is unwanted. Alternatively, active damping strategies, where the resonance damping is provided by the current controller, are of major interest. This paper analyzes the robustness of the closed-loop dynamics when different active damping techniques are implemented. The analyzed active damping techniques, which have been selected because of their readiness and simplicity, are: 1) filtered capacitor voltage feedforward and 2) second-order filters in cascade with the main current controller. The impedance/admittance stability formulation is used to model the system, which has been proven to be very convenient for the assessment of robustness. Experimental tests are provided in order to show the accuracy of the analysis and verify the findings. This paper proves that filtered capacitor voltage feedforward is a more robust and reliable solution than implementations based on cascade notch filters. [ABSTRACT FROM AUTHOR]

The influence of a filter inductor on the steady-state performance of a parallel-type resonant converter is elaborated and analyzed in this paper. By steady-state operation analysis, it is shown that the ripple current of the filter inductor results in an inaccurate prediction of fundamental harmonic approximation (FHA), and such problem would become serious when the filter inductance is small. In order to portray such feature, an improved fundamental harmonic approximation (IFHA) is proposed. Unlike an FHA equivalent circuit, an equivalent inductor is added to the ac resistance parallelly in an IFHA equivalent circuit. Due to that, the equivalent inductor branch takes account of the ripple current of the filter inductor, and the IFHA is expected to own higher accuracy and can be used in a parameter design procedure. In this paper, the equivalent inductor expressions of full-bridge rectifier and current-doubler rectifier are derived as examples. In order to verify the theoretical analysis, a 500 W LCC resonant converter is built as a prototype. The close-loop experiment results show that small filter inductance would lead to the failure of output voltage regulation and hard-switching operation of power switches. And open-loop experiment results show the IFHA gives more accurate predictions than those of FHA. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for treating the harmonic torque in permanent magnet motors at selected harmonic orders. The method is based on the online estimation of the motor harmonic flux. For this purpose, a novel minimal parameter harmonic flux estimator (MPHFE) is developed. The MPHFE is formulated such that the inductance, resistance, and stator current and its derivative are not necessary for the estimation of the harmonic flux. This was achieved by forcing the harmonic current to zero through the combined action of a field-oriented controller (FOC) and a feedforward controller. Subsequently, the harmonic flux can be obtained directly from the estimated harmonic back EMF without the involvement of other motor parameters. Finally, the estimated flux is used in conjunction with a comprehensive model of the motor harmonic torque to determine the stator current compensation for eliminating the torque harmonic. Experimental results presented from a permanent magnet motor confirm the theoretical claims in this paper as well as demonstrate the effectiveness of the proposed method to reduce the magnitude of the harmonic torque significantly. [ABSTRACT FROM AUTHOR]

Compared with the conventional power systems, large-scale power electronics based power systems present a more complex situation, where harmonic instability may be induced by the mutual interactions between the inner control loops of the converters. This paper presents an approach to locate which power converters and buses are more sensitive and have a significant contribution to the harmonic instability. In the approach, a power electronics based system is introduced as a multi-input multi-output (MIMO) dynamic system by means of a dynamic admittance matrix. Bus participation factors (PFs) are calculated by the oscillatory mode sensitivity analysis versus the elements of the MIMO transfer function matrix. The PF analysis detects which power electronic converters or buses have a higher participation in harmonic instability excitation than others or at which buses such instability problems have a higher impact. In order to confirm the effectiveness of the presented approach, time-domain simulation results are provided for a 400-MW wind farm in PSCAD software environment. [ABSTRACT FROM AUTHOR]

In a hybrid ac/dc grid, the ac-side unbalance voltage introduces adverse effects on dc grids and interfacing converters (IFC) (active power oscillations, dc-link voltage oscillations, and IFC peak current increase at the same average power production). For parallel IFCs, these adverse effects can be easily aggregated. In this paper, two new control strategies are proposed for parallel IFCs to improve both ac and dc subgrids power quality. The proposed control strategies focus on canceling active power oscillations of parallel IFCs that provide oscillation-free dc link and sharing collective peak current of parallel IFCs. In the first proposed control strategy, IFCs’ power coefficients are controlled by solving a set of nonlinear equations, and this method is called as coefficient-based strategy, whereas, in the second proposed control strategy, peak currents of IFCs are controlled directly through the derived relationship of IFCs' peak currents under zero power oscillation in this paper, and this method is named as peak current based strategy. This peak current based strategy features much simplified calculation and could be easy to implement. To achieve control objectives, thorough study on parallel IFCs' peak currents is conducted. Based on the study, it is shown that the collective peak current of all IFCs is a constant under zero total active power oscillation, and therefore, keeping all IFCs' peak currents in the same phase and in-phase with collective peak current optimizes the utilization range of parallel IFCs. The numerical examples and experimental results are provided to verify the validity of the proposed control strategies under different operating conditions. [ABSTRACT FROM AUTHOR]

This paper proposes a new fault-tolerant strategy to revamp performance of three-phase multilevel converters with a single faulty switch. The proposed fault-tolerant strategy is based on the application of a modified selective harmonic elimination (SHE) technique in conjunction with the fundamental phase-shift compensation method. The proposed fault-tolerant strategy makes the most use of the converter capacity in the faulty condition, generates balanced line voltages, and eliminates a wide range of lower order harmonics to limit the total harmonic distribution of the converter voltages in the faulty condition. In this paper, first, a brief background about cascaded H-bridge multilevel converters and SHE technique is provided. Then, the proposed fault-tolerant strategy and the modified SHE technique are presented. Finally, several experimental results are provided to validate the operation of the proposed strategy. [ABSTRACT FROM PUBLISHER]

Paralleling is the development tendency of the auxiliary inverter. This paper analyzes the problems of the parallel process in detail. First, for inherent contraction between voltage regulation performance and current sharing performance, the paper adopts the resistive droop method. Second, the paper improves dynamic performance and reliability of the droop method by improving power calculation and introducing the whole cycle adaptive droop method. Third, in order to solve the unshared current problem caused by inconsistent parameters, the paper increases active power proportion droop coefficient, and introduces voltage compensation strategy to compensate voltage drop caused by increased proportion droop coefficient. Fourth, the auxiliary parallel system has complicated load characteristics; the paper proposes voltage compensation strategy to compensate voltage drop caused by the pump load. This paper utilizes three-phase total reactive power to droop frequency and active power of each phase to droop amplitude, unbalanced current can be shared. This paper introduces special virtual impedance technology to solve the harmonic current sharing problem caused by the nonlinear load. Finally, the effectiveness of above theory is fully verified by simulation and experiment. [ABSTRACT FROM PUBLISHER]

Low-frequency oscillation (LFO), harmonic resonance, and harmonic instability phenomena in high-speed railways (HSRs) result from the interactions between multiple electric trains and the traction network. A train–network interaction system and a unified impedance-based model are therefore presented to reveal the mechanism of these three phenomena in Part I of the two-part paper. Part II of the paper presents and compares the detailed simulation and experiment results to investigate the available possible influential factors, verifications, and discussions of the three phenomena. The influential factors include the following: 1) four-quadrant converter (4QC) parameters involving the control parameters of the current controller (CC), the voltage controller (VC), and the phase-locked loop (PLL); 2) network parameters involving the utility power system, traction transformer, primary/secondary supply lines, catenary lines, and autotransformers (ATs); and 3) different numbers and positions of trains and railway lines will also be considered and discussed. In order to validate the theoretical results, the time-domain simulation and experiment system have been conducted. Finally, the differences and the relations among the three phenomena are discussed. [ABSTRACT FROM AUTHOR]

This paper presents an impedance-based model to systematically investigate the interaction performance of multiple trains and traction network interaction system, aiming to evaluate the serious phenomena, including low-frequency oscillation (LFO), harmonic resonance, and harmonic instability. The train–network interaction mechanism is therefore studied, and one presents a detailed coupling model for investigating the three interactive phenomena and their characteristics, influential factors, analysis methods, and possible mitigation schemes. In Part I of the two-part paper, the measured waveforms of such three phenomena are first characterized to indicate their features and principles. A unified framework of the train–traction network system for investigating the three problems is then presented. In order to reveal the interaction mechanism, all-frequency impedance behaviors of the electric trains and traction network are equally modeled. In which, an impedance-based input behavior of the train is fully investigated with considering available controllers and their parameters in DQ-domain. The entire traction network, including traction transformer, catenary, supply lines, is represented in a frequency-domain nodal matrix. Furthermore, the impedance–frequency responses of both electric train and traction network are measured and validated through frequency scan method. Finally, a generalized train–network simulation and experimental system are conducted for verifying the theoretical results of the two-part paper. [ABSTRACT FROM AUTHOR]

This paper presents the study of an offline flyback-based light-emitting diode (LED) driver with reduced storage capacitance. An approach called active ripple compensation was used for minimizing the converter bulk capacitance. This technique is oriented to voltage-controlled pulse width modulation converters and is based on the modulation of the duty cycle, which allows for the reduction of the filtering capacitance by increasing the harmonic content of the input current up to the limits established by the standards. By means of the design procedure presented in this paper, the amount of capacitance reduction and input current distortion can be fully controlled and theoretically predicted. In addition, no extra sensors are required to implement the proposed technique, apart from the LED current sensor already available in most LED drivers. Experimental results from a 50-W laboratory prototype supplied from a 220-V 60-Hz grid were carried out. The results were compared with the conventional approach, attesting the superior performance of the proposed methodology. [ABSTRACT FROM AUTHOR]

An analytical steady-state model of the modular multilevel converter (MMC) can be used for component sizing and assessment of the impact of different parameters on the MMC performance. Thus, this paper proposes an enhanced steady-state model for the MMC, which enables one to calculate the amplitudes of the harmonic components of MMC arm currents, submodule capacitor voltages, and arm voltages. In addition, the proposed model allows for the calculation of the amplitude and phase angle of the modulating signal, and it also presents a criterion for resonance of the arm currents. This is achieved by means of a polynomial function of the modulation index, and through checking the stability criteria established by the proposed model. The capability of formulating the modulating signal enables a more accurate calculation of the steady-state amplitudes of the variables, as compared to the previously published models. This paper also presents an accurate method of submodule capacitor sizing, based on the proposed steady-state model. The proposed method gives the exact value of the submodule capacitance (i.e., the capacitance that results in dc voltage fluctuations within a desired range) for a prespecified submodule capacitor voltage variation and a given circulating current amplitude. The stability criterion given by the proposed steady-state model, used for sizing the arm inductance, and the submodule capacitor voltage variation given by the proposed capacitor sizing method, used for sizing the submodule capacitor, allows for the determining of the operating limits of the MMC in terms of its parameters. Extensive simulation results are presented to demonstrate the efficacy of the proposed steady-state model and the capacitor sizing method. Further, the results obtained from the proposed capacitor sizing method are compared with experimental results from the literature. [ABSTRACT FROM AUTHOR]

This paper proposes an active switching harmonic current reduction method within the dc-link capacitor of two-level, three-phase, back-to-back converters. This method is based on the derived analytical solution for switching harmonic currents in the dc-link. It is shown that by controlling the pulse width modulation carrier waveform's phase angles, the harmonics in the second carrier band of the rectifier and the inverter can be synchronized such that cancellation occurs in the dc-link capacitor. This synchronization is provided by harmonic phase feedback control. The feasibility of the proposed approach has been verified experimentally and results are presented in this paper. [ABSTRACT FROM PUBLISHER]

This paper presents a new feed-forward strategy for suppressing low-order harmonic circulating currents in pulsewidth-modulated (PWM) based modular multilevel converters (MMCs). The approach is based on the new average model approach established in this paper, which identifies cross-coupling interactions between the system-level and submodule elements using decomposed dependent sources. As well as improving the damping of the system, the major advantage of this approach is that it maintains the natural DC bus balance property of a PWM modulated MMC by considering the upper and lower arms together (unlike existing feed-forward schemes which treat each MMC arm independently). Moreover, unlike existing direct control resonant strategies, which require careful gain tuning and are highly dependent on the ac system frequency, the proposed approach achieves wideband circulating current ripple suppression without requiring knowledge of the circulating current harmonic frequencies and needs only a simple proportional–integral (PI) controller to regulate the circulating current dc component for power balance. This makes it particularly suitable for use in multifrequency or variable-frequency ac systems. Extensive simulation and matching experimental results, including steady-state and transient responses compared against existing circulating current suppression approaches, validate the effectiveness and benefits of this new feed-forward compensation technique. [ABSTRACT FROM PUBLISHER]

This paper presents a new system for reactive power compensation and suppression of negative-sequence current for power quality improvement in electrical railways and the feeding three-phase utility grid, based on YNvd-connected balance transformer. Different from the conventional railway static power conditioner based compensation systems, this system integrates multiplex back-to-back converters (MBTBC) into phase-β side flexible taps through a cascade connection instead of into phase-β side feeder via a coupling transformer, thus the installation space and initial costs are reduced significantly. In addition, a new power distribution strategy with simple implementation is adopted in this paper, by which the compensation capacity of MBTBC can be decreased by 25%, compared with the commonly used full compensation scheme. As the first part of this topic, this paper focuses on the theoretical analysis, including the system topology, basic and partial compensation principles and its implementation method. While, the controller design on converter-level, stability analysis, and simulation and experimental verification are the main tasks of the second part of this topic. [ABSTRACT FROM PUBLISHER]

Due to the phase delay caused by low-pass filter, device retarding, and software retarding, the extracted sensorless motor commutation signal deviation occurs. Unfortunately, the relationship between the phase shift and inactive phase freewheeling has been scarcely referred to through the published papers, and most of the commutation instant shift compensation methods present slow convergence rate. Therefore, a fast commutation instant shift correction method based on analyzing the back-electromotive force (EMF) harmonic information is proposed in this paper. The method is effective both in the steady-speed control and in variable-speed control. Considering that commutation instant shift may induce inactive phase freewheeling and negative torque in motor windings, the freewheeling condition and motor electric operation condition are analyzed as well. Furthermore, to exactly delay the zero-crossing points (ZCPs) of EMF by 30° and compensate the commutation instant shift, the speed detection accuracy and feedback frequency are enhanced by measuring and summing up the 2 × P consecutive half-period of the ZCPs signal. Finally, the validity of the proposed commutation instant shift correction method is verified through experimental results. [ABSTRACT FROM AUTHOR]

A matrix converter (MC) with model predictive control based on the source reactive power control usually fails to show sinusoidal source currents. The analysis presented in this paper shows that this common combination of a converter and control has the inherent inability to suppress some harmonics in the source currents, even with additional passive or active damping control. Direct source current control can be implemented to give sinusoidal source currents and intrinsic active damping. However, the issue of steady-state error in output currents then arises, as the MC topology does not allow of the independent control of source and output currents. Therefore, feedback control of load active power is proposed to address this issue without degrading the fast dynamic performance. Benefiting from the direct source current control, a simplified implementation is also proposed to decrease the number of candidate switching states from 27 to 5, which significantly reduces the computational burden. Experimental results have verified the theoretical analysis and the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Harmonic resonances in traction power supply systems (TPSSs) have attracted great attention due to their potentially destructive impact on the safe and stable operation of railways. Based on operation data acquired from Chinese railways, this paper presents a comprehensive review of this issue considering both academic and engineering requirements. Analyzing actual incidents, the general patterns and effects of TPSS resonances are derived. The relation between the TPSS and the locomotive is illustrated by circuit models. Relevant methods for modeling locomotives and TPSSs are discussed. Both advanced resonance analysis methods giving general influence factors and a simplified resonance analysis explaining resonance features in a practical manner are discussed. Multiple ground-based and on-board solutions for resonance elimination are presented. At last, preidentifying resonances in actual systems is investigated for addressing the open topic of resonance prevention. [ABSTRACT FROM AUTHOR]

This paper proposes a dc-link voltage shaping method for a cascaded H-bridge (CHB) static synchronous compensator (STATCOM). A recently proposed low capacitance-STATCOM system, which intentionally operates with large voltage ripples on the dc-link capacitors, offers the advantage of superior harmonic performance. However, the capacitor voltage ripples decrease when operating at below-rated reactive current, which removes the aforementioned harmonic performance benefit of this system. In addition, such harmonic performance benefit is only achieved in capacitive operation mode. In order to expand the operating region where advantageous voltage ripples are present, a new voltage shaping method is proposed. The proposed method uses a CHB multilevel converter coupled with simple dc–dc converters to shape voltage ripples on the dc-link capacitor regardless of its operating point. This is achieved by controlling the average current of the dc–dc converter using model predictive control. The concept is best applied to an enhanced STATCOM, or E-STATCOM, application in which the STATCOM is integrated with either a renewable energy source or energy storage system. The operational principle of the proposed approach is validated via simulation and experimental results on a five-level single-phase CHB STATCOM. [ABSTRACT FROM AUTHOR]

In this paper, a novel current solution is proposed to suppress the electromagnetic torque ripple of brushless dc motor (BLDCM), and simultaneously minimize the rotor eddy-current loss to prevent thermal demagnetization of the permanent magnets. To determine the current solution, an optimizing problem of the rotor loss is developed, subjecting to the constraints of average torque and the sixth harmonic torque. Finite dc supply is also considered. In addition, an improved model of the rotor loss is proposed with a simpler expression of quadratic form, so that the problem can be solved analytically. A comparison with the square-wave and minimal-copper-loss current solutions is studied based on a 3.77 kW, 12000 r/min BLDCM, which indicates that the proposed solution performs as well as the two solutions in suppressing the torque ripple and producing stator losses, but the rotor loss can be significantly reduced by at least 86% and 35%, respectively. Precision of the rotor loss model and performance of the proposed solution are validated experimentally on the 3.77 kW BLDCM setup. [ABSTRACT FROM AUTHOR]

This paper presents a new harmonic compensation system along with a hybrid load observer used for micro-grids in the islanded mode. The proposed control system includes an online hybrid load observer, which is able to precisely estimate the harmonic contents of the load as well as the equivalent load impedance in the islanded mode. One of the main features of the proposed control system is its capability to deal with unknown load harmonics, which is a big challenge in micro-grids. Basically, the proposed control system is able to detect, estimate, and compensate various load disturbances and harmonics (e.g., synchronous and asynchronous harmonics, and dc components). Theoretical analysis, simulation results, and experimental results verify the feasibility and performance of the proposed control system. [ABSTRACT FROM AUTHOR]

For stable and efficient drives of interior permanent-magnet synchronous machines (IPMSMs), stator flux should be observed across a wide speed range. However, distortions such as a dc offset and low-order harmonics are contained in the estimated flux due to various reasons. In this paper, a distortion-minimizing flux observer is proposed to suppress the effects of dc offset and harmonics by implementing frequency-adaptive observers. The proposed frequency-adaptive flux observer is designed to extract a fundamental flux while keeping a simple structure even if the rotating speed of the IPMSM varies. The fundamental flux could be estimated by the proposed current- and voltage-model based flux observer, which is implemented with the frequency-adaptive observer and harmonic extractors. Moreover, parameter sensitivity and model transition are discussed to improve the performance of the proposed observers. The validity and effectiveness of the proposed methods are verified with simulation and experimental results. [ABSTRACT FROM AUTHOR]

In this paper, diagnosis and tolerant control schemes have been studied for common electrical faults in T-type three-level inverter fed dual-three phase permanent magnet synchronous motor (PMSM) drives for safety-critical applications. Based on vector space decomposition and double three-phase space vector modulation, diagnostic and tolerant control methods have been developed comprehensively for open-phase faults, open-switch faults, and short-switch faults in T-type three-level inverter fed dual-three-phase PMSM drives, in such way that misdiagnosis of different faults sharing similar faulty features can be avoided. In particular, a two-step diagnostic scheme is proposed in order to simplify the diagnostic process. The first step is to identify the faulty phase and fault category by analyzing current trajectories on harmonic subspace, and the second step is to determine the specific fault type in a small fault-searching area obtained from the first step. In the aspect of fault-tolerant control, a novel current compensation method is proposed for open-phase fault without changing the machine model, space vector diagram, and control framework. Open-switch faults and short-switch faults are tolerated by making full use of the remaining vectors after faults. The validity of the proposed fault diagnosis and tolerance schemes has been verified by experiments. [ABSTRACT FROM AUTHOR]

In voltage-source converter systems, utilization of filter inductors with deep saturation characteristics is often advantageous because of the improved size, cost, and efficiency. However, with the use of conventional current regulation methods, the inductor saturation results in significant dynamic performance loss and poor steady-state current waveform quality. This paper proposes the saturation compensation with resistive decoupling (SCRD) method to overcome these performance issues. The method converts the nonlinear inductor of the plant to a fictitious linear inductor such that linear current regulators can perform satisfactorily. The steady-state and dynamic performances of SCRD are investigated in detail in comparison with other methods and advantageous performance attributes of SCRD are demonstrated on a 1.5-kW grid-connected system via simulations and laboratory experiments. In addition, identification of L–R parameters is performed, parameter sensitivity issues are addressed, and satisfactory performance is demonstrated. [ABSTRACT FROM AUTHOR]

This paper presents a load commutated silicon controlled rectifier (SCR) based multilevel current source inverter (CSI) fed open-end winding induction motor (IM) drive with regeneration capability. Multilevel current waveform is realized using two isolated load commutated SCR-based CSIs connected in shunt configuration, but operated with a phase shift of 30 $^\circ$ thereby attaining significant reduction in harmonic distortion of the motor current. The multilevel CSI connected to one side of the stator windings supplies real power to the motor. The other end of the stator winding is directly interfaced with a capacitor-fed voltage source inverter (VSI). The control scheme of the VSI facilitates load commutation of the multilevel CSI under all conditions of operation, including regenerative braking. The proposed scheme is experimentally verified on an IM with open-end stator winding, with the help of a digital signal processor TMS320F28335. [ABSTRACT FROM AUTHOR]

This paper presents the circuit design and magnetic integration of push–pull class-E inverters for wireless power transfer (WPT) up to megahertz. The design criterion for achieving zero-voltage switching (ZVS) of a class-E inverter with coupled windings is derived mathematically. The approaches of magnetic integration for push–pull class-E inverters are analyzed and compared. Then, a new magnetic structure with hybrid magnetic materials is proposed to build the integrated inductors with either coupled windings or uncoupled windings. A 3-MHz WPT system is built to verify the analysis. The detailed comparison of the class-E inverters with magnetic integration is presented in terms of switch voltage, efficiency, harmonic currents, and thermal distribution. In the optimized design example, the switches keep ZVS over the entire load range without using any closed-loop control. The system efficiency reaches 87.1% at 350-W output power. [ABSTRACT FROM AUTHOR]

Small grid-tied wind turbines based on permanent magnet generators often use a cost-effective power converter topology consisting of a passive rectifier, a boost converter, and an H-bridge inverter. Speed or position sensors are rarely used due to cost issues. Model-based estimators relying on electrical magnitudes are used instead. However, such estimators are parameter sensitive, which limit their accuracy. Further concerns arise if these parameters change with the operating condition of the machine, mainly due to temperature. Speed sensorless control using the rectifier voltage ripple is analyzed in this paper. This technique provides good dynamic response and does not depend on machine parameters. Simulations are provided for speed and power tracking comparison with an accurate model-based speed estimation method operating at non-rated parameters. They show the speed accuracy and power tracking capability of the proposed method are similar to that provided by a speed sensor. This is translated into a 0.9% power increase when the model-based speed estimator shows 9% of error. Experimental results are carried out to test the effect of current and temperature in the estimation, showing temperature insensitivity and some distortion due to fast current transients. A speed estimation accuracy of zero mean error and 1.7% standard error is experimentally obtained in the regular operation of the wind turbine. [ABSTRACT FROM AUTHOR]

In this paper, a novel filter structure to suppress circulating currents is proposed based on the sequence of pulsewidth modulation voltage harmonics for high-power interleaved motor-drive systems. The sideband harmonics can be divided into positive-, negative-, and zero-sequence components. Through 120° interleaving among three paralleled inverters, a majority of positive- and negative-sequence harmonics are phase shifted. By these phase shifts, the differential-mode circulating currents between the paralleled ac–dc converters can be suppressed with the proposed filters, which have an identical structure to the three-phase common-mode chokes. Such a structure highly benefits the design and manufacturability for high-power applications where a choice of magnetic-core shapes is limited. Compared to coupled inductors (CIs) with cyclic-cascade or monolithic configurations, the number of magnetic cores can be reduced by one-third. Peak flux-linkages of the proposed filters and the conventional CIs were compared to estimate the size reduction in case of flux-limited designs. Considering the whole modulation index range, which may be required in the motor-drive systems, the maximum flux-linkage can be reduced by 50%. Prototype filters are built and showed a 33% reduction in weight and size compared to the conventional CIs. The validity of the proposed filter is verified through the simulation and a small-scale experiment. [ABSTRACT FROM AUTHOR]

In the back electromotive force (EMF)-based sensorless control of interior permanent magnet synchronous motor (IPMSM), the inverter nonlinearity and flux linkage spatial harmonics will possibly give rise to (6k ± 1)th harmonics in the estimated back EMF, especially the fifth and seventh harmonics. Those harmonics will consequently introduce (6k)th harmonic ripples to the estimated rotor position, especially the sixth harmonic component. In order to solve this problem, a bilinear recursive least squares (BRLS) adaptive filter is proposed and integrated into a sliding-mode position observer to suppress the dominant harmonic components in the estimated back EMF and as a result, the accuracy of the estimated rotor position can be greatly improved. A unique feature of the BRLS adaptive filter is its ability to track and suppress the specified harmonic components in different steady state and dynamic operational conditions. The proposed method can compensate for harmonic ripples caused by the inverter nonlinearity and machine spatial harmonics at the same time; this method is also robust to machine parameter variation, and the BRLS algorithm itself is machine parameter independent. The implementation of the proposed BRLS filter in the sensorless control of IPMSM is explained in details in this paper. The enhanced drive performances using the BRLS filter have been thoroughly validated in different steady state and dynamic operational conditions on a 1.5-kW IPMSM sensorless drive. [ABSTRACT FROM AUTHOR]

Recent works have addressed the ancillary services provided by multifunctional photovoltaic inverters. This concept is based on the addition of extra functions to the conventional photovoltaic systems, such as harmonic current compensation of nonlinear loads and reactive power support. However, it is important to ensure that photovoltaic inverters work below the rated current peak. Therefore, this paper proposes two current dynamic saturation techniques to limit the current peak of multifunctional photovoltaic inverters during harmonic current compensation of nonlinear loads. One technique is based on a closed loop and other on an open loop. With this approach, the photovoltaic inverters are able to perform partial harmonic current compensation, i.e., it will only be allowed to compensate harmonic currents within their maximum current capacity. Mathematical models are developed to determine the parameters of the techniques. Comparisons in simulation and experimental environments show that both techniques provide improvements in the grid power quality at the same time as the inverter rated current capacity is respected. [ABSTRACT FROM AUTHOR]

In the conventional direct power control (DPC) methods, the grid currents are highly distorted, and substantial ripple is present in the dc-bus voltage under unbalanced and distorted grid conditions. Various improved DPC methods have been proposed to address these problems, but these methods are generally complicated and not easy to use because of the complex controlling structures, need for considerable tuning, and so on. This paper proposes an improved DPC method obtained by simply adding a compensation term to the original power references. The compensation power is obtained by analyzing the power ripple in the input line inductance based on extended power theory. The reference voltage vector is subsequently calculated from the new power reference and synthesized by space vector modulation. To improve the robustness of the proposed DPC against inductance variations, an online inductance identification technique based on the gradient correction method is proposed and combined with the proposed DPC. The presented simulation and experimental results demonstrate that the proposed method can achieve sinusoidal grid currents and significantly reduce the dc-voltage ripple even with mismatched inductance under unbalanced and distorted grid conditions. [ABSTRACT FROM AUTHOR]

The pole-phase modulated induction motor (PPMIM) drives facilitate the extended range of speed-torque characteristics, which is an essential requirement for traction and electric vehicle applications. For getting the wider speed-torque variations, $15-\Phi $ PPMIM drive is analyzed, which is capable to operate at 2-pole 15-phase, 6-pole 5-phase, and 10-pole 3-phase modes. In these pole-phase operations, in high-phase and low-pole mode of operation, the increment in the linear modulation range with space vector pulsewidth modulation (SVPWM) is not significant. In the low-phase and high-pole mode of operation, there will be higher torque ripples due to the higher magnitude of space harmonics. In this paper, these issues are addressed by using carrier phase-shifted SVPWM (CPS-SVPWM) and phase grouping concepts. In low-pole operation, the linear modulation is enriched by using conventional $3-\Phi $ SVPWM to drive 15-phase machine by appropriately reorganizing the phase winding connections. Similarly, in 6-pole 5-phase mode of operation, the linear modulation range of PPMIM drive is enriched by using $5-\Phi $ SVPWM. It is known that in high-pole mode of PPMIM drive operation, each effective phase is formed by the multiple number of equal voltage potential coils (EVPCs), which are electrically in phase. The carriers of these EVPCs per phase are phase shifted by an appropriate angle to minimize the harmonics in the effective phase voltage, which results in better torque ripple profile. In addition, the detailed comparison of three possible different CPS-SVPWMs is presented, with their pros and cons for selecting the proper carrier phase shift angle. The performance of the proposed scheme has been validated by ANSYS Maxwell two-dimensional as well as laboratory prototype on 5-hp, $15-\Phi $ PPMIM drive. [ABSTRACT FROM AUTHOR]

The semicontrolled open-winding permanent magnet synchronous generators (OW-PMSGs) with a common dc bus system have received more attention in recent years due to its advantages of reduced cost and simpler power supply. Good control performances could be achieved under the zero power factor angle (PFA). However, current clamping problem is normally presented under non-zero PFA condition, resulting in unexpected torque pulsations and voltage pulse disturbances. Meanwhile, misjudgment of voltage vectors and subsequent deteriorations in steady-state performances can be observed at current zero-crossing points. In order to improve the control performances of semicontrolled OW-PMSGs, a virtual zero-crossing detection method is proposed in this paper to effectively suppress the oscillation of voltage vectors at current zero-crossing points. In addition, a segment injection strategy of third-order harmonic current is proposed. With the proposed strategy adopted, the current clamping problem can be successfully solved, and more importantly, the torque ripple and third-order harmonic current could be simultaneously suppressed. Relevant experimental validations and performance comparisons based on a 2.3-kW semicontrolled OW-PMSG system are presented to verify the proposed control strategies. [ABSTRACT FROM AUTHOR]

Optimal currents with appropriate harmonic components injected into the motor windings can effectively mitigate torque ripple for interior permanent magnet (IPM) type brushless dc motors (BLDCMs). However, existing approaches may fail to accurately inject the optimal currents into motors due to the limited current loop bandwidth. This paper proposes a simple enhanced generalized vector control strategy to mitigate the torque ripple for IPM-type BLDCMs. With the proposed vector control strategy, the control block diagram for IPM-type BLDCMs is as simple as that with traditional vector control for sinusoidal permanent magnet synchronous motors. First, an electromechanical energy conversion voltage (EECV), considering the effects of the non-sinusoidal back-EMF and the rotor salience property, is proposed in αβ-axis. Then, a novel coordinate frame is constructed with the proposed EECV, which is based on the arbitrary reference frame theory. As a result, the currents of IPM-type BLDCMs can be decomposed into two constant components, one being linked to the torque and the other one to the flux linkage. Thus, the bandwidth of current loop with simple proportional integral regulator can be equivalently expanded in the proposed coordinate frame. Finally, comprehensive experiments are conducted in different operation conditions to validate the effectiveness of the proposed vector control strategy. [ABSTRACT FROM AUTHOR]