Search

In order to overcome the limitations of the existing classical and solid-state Marx pulse generators, this paper proposes a new modular multilevel voltage-boosting Marx pulse generator (BMPG). The proposed BMPG has hardware features that allow modularity, redundancy, and scalability as well as operational features that alleviate the need of series-connected switches and allows generation of a wide range of pulse waveforms. In the BMPG, a controllable, low-voltage input boost converter supplies, via directing/blocking (D/B) diodes, two arms of a series modular multilevel converter half-bridge sub-modules (HB-SMs). At start up, all the arm's SM capacitors are resonantly charged in parallel from 0 V, simultaneously via directing diodes, to a voltage in excess of the source voltage. After the first pulse delivery, the energy of the SM capacitors decreases due to the generated pulse. Then, for continuous operation without fully discharging the SM capacitors or having a large voltage droop as in the available Marx generators, the SM capacitors are continuously recharged in parallel, to the desired boosted voltage level. Because all SMs are parallelly connected, the boost converter duty ratio is controlled by a single voltage measurement at the output terminals of the boost converter. Due to the proposed SMs structure and the utilization of D/B diodes, each SM capacitor is effectively controlled individually without requiring a voltage sensor across each SM capacitor. Generation of the commonly used pulse waveforms in electroporation applications is possible, while assuring balanced capacitors, hence SM voltages. The proposed BMPG has several topological variations such as utilizing a buck-boost converter at the input stage and replacing the HB-SM with full-bridge SMs. The proposed BMPG topology is assessed by simulation and scaled-down proof-of-concept experimentation to explore its viability for electroporation applications. - 1986-2012 IEEE. Manuscript received June 12, 2018; revised October 23, 2018 and December 29, 2018; accepted February 5, 2019. Date of publication February 18, 2019; date of current version August 29, 2019. This work was supported by the Qatar National Research Fund (a member of the Qatar Foundation) under NPRP Grant 7-203-2-097. Recommended for publication by Associate Editor J. Clare. (Corresponding author: Mohamed A. Elgenedy.) M. A. Elgenedy is with the Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1RD, U.K., and also with the Department of Electrical Engineering, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt (e-mail:,mohamed.elgenedy@strath.ac.uk). Scopus

High-voltage (HV) pulses are used in electroporation to subject pulsed electric field (PEF) onto a sample under treatment. Pulse-waveform shape, voltage magnitude, pulse duration, and pulse repetition rate are the basic controllable variables required for particular PEF application. In practice, a custom-made pulse generator is dedicated for each PEF application with limited flexibility in changing these variables. In this paper, a universal pulse-waveform generator (UPG) is proposed, where the controller software algorithm can manipulate a basic generated multilevel pulse waveform to emulate many different PEF pulse waveforms. The commonly used PEF HV pulse waveforms can be generated as bipolar or monopolar with controllable pulse durations, repetition times, and voltage magnitudes. The UPG has the ability to generate multilevel pulses that have controllable $dv/dt$ , which allows reduction of the electromagnetic interference generated by the converter. The UPG topology is based on half-bridge modular multilevel converter (HB-MMC) cells forming two transition arms in conjunction with two bistate arms, together creating an H-bridge. The HB-MMC cell capacitors provide a controllable energy source which charge from the dc input supply and discharge across the load, while the two bistate arms allow charging the HB-MMC cell capacitors. Hence, the UPG topology offers modularity, redundancy, and scalability. The HB-MMC individual cell capacitance is low and the cell voltages are balanced by employing the sorting and rotating algorithm used in conventional HB-MMC topologies for HV dc transmission applications. The viability of the proposed UPG converter is validated by MATLAB/Simulink simulation and scaled-down experimentation.

This paper proposes a controlled transition full-bridge (CTFB) hybrid multilevel converter (HMC) for medium and high voltage applications. It employs a full-bridge cell chain-link (FB-CL) between the two legs in each phase to generate multilevel bipolar output voltage. The CTFB-HMC has twice dc voltage utilization or power density of conventional converters due to the bipolar capability of its full-bridge configuration. Hence, for the same power rating and same voltage level number, its total cells per phase are quarter that in modular multilevel converter (MMC), which reduces the hardware installation volume. Also, in the proposed converter, the total device number in the conduction paths is the same as in the half-bridge MMC, leading to low conduction losses. The FB-CL current of the CTFB converter has no dc component, which offers the potential to enhance the transient response. Comparative studies between the CTFB and other multilevel topologies are carried out to clarify its main features. The modulation strategies and parameter sizing of the proposed converter are investigated using a generic case. Simulation and experimental results are used to verify the effectiveness of the proposed approach.

The three-phase two-level voltage source converter (VSC) is widely employed in power conversions between AC and DC for its four-quadrant operation and control flexibility. However, it suffers from the low output voltage range with a peak value of half DC-link per phase, which necessitates the use of either high DC-link voltage or bulky step-up transformer to enable the medium voltage operation. Additionally, the high common mode (CM) voltage between AC loads neutral points and ground may reduce the service life and reliability of electric machinery. In this paper, a three-phase AC side voltage-doubling VSC topology with intrinsic Buck-Boost cell is analyzed. By this configuration, the AC side voltage is doubled with the phase peak value equal to DC-link. That is, only half of the DC side capacitor bank is needed to generate the same output voltage. The proposed converter uses its buck-boost cell as a virtual voltage source to synthesize negative half of the output voltage by modulating its output AC phase voltage around the negative bus (which is the real zero when grounded). This permits the average CM voltage to be suppressed to zero, and loads connected to converter AC side not to withstand any DC voltage stress (reducing the insulation requirement). Modeling and control design for both rectifier and inverter modes of this converter in synchronous reference frame have been investigated to ensure a four-quadrant three-phase back-to-back system. Experimental results have verified the feasibility and the effectiveness of the proposed configuration and the designed control strategies.

DC fault protection is one challenge impeding the development of multi-terminal DC grids. The absence of manufacturing and operational standards has led to many point-to-point HVDC links built at different voltage levels, which creates another challenge. Therefore, the issues of voltage matching and DC fault isolation are undergoing extensive research and are addressed in this paper. A quasi two-level operating mode of the modular multilevel converter is proposed, where the converter generates a square wave with controllable dv/dt by employing the cell voltages to create transient intermediate voltage levels. Cell capacitance requirements diminish and the footprint of the converter is reduced. The common-mode DC component in the arm currents is not present in the proposed operating mode. The converter is proposed as the core of a DC to DC transformer where two converters operating in the proposed mode are coupled by an AC transformer for voltage matching and galvanic isolation. The proposed DC transformer is shown to be suitable for high-voltage high-power applications due to the low switching frequency, high efficiency, modularity, and reliability. The DC transformer facilitates DC voltage regulation and near instant isolation of DC faults within its protection zone. Analysis and simulations confirm these capabilities in a system-oriented approach.

Tapped-inductor variations of single-switch, single-diode, dc-to-dc converters are categorized based on a new unified sequential circuit topology and mathematical transformation approach, all seeded from a basic buck–boost converter and its transfer function. Classification focuses on identifying two different ac circuit coupled inductor arrangements of the basic buck–boost dc-to-dc converter. Subsequent dc circuit sequential manipulation yields all 11 known, documented, in theory, in simulation and practically, tapped-inductor dc-to-dc converter topologies. The procedure not only generates sequences of topologies, but also generates the voltage transfer functions without recourse to analysis of the circuit internal operating mechanisms. Consequently, two converter classes group the 11 known tapped-inductor topologies, which is at least one fewer topology classes than universally accepted. The methodology yields two new classes of three and ten coupled inductor converter topologies, all with new transfer functions. The new analysis approach is adaptable to the analysis of all single-switch, single-diode, (noncoupled inductor), dc-to-dc converters (single and two inductor topologies), formulated from the basic buck–boost converter.

This paper proposes a linearized large signal state-space model for the fixed-frequency phase-controlled series-parallel resonant converter. The proposed model utilizes state feedback of the output filter inductor current to perform linearization. The model combines multiple-frequency and average state-space modeling techniques to generate an aggregate model with dc state variables that are relatively easier to control and slower than the fast resonant tank dynamics. The main objective of the linearized model is to provide a linear representation of the converter behavior under large signal variation which is suitable for faster simulation and large signal estimation/calculation of the converter state variables. The model also provides insight into converter dynamics as well as a simplified reduced order transfer function for PI closed-loop design. Experimental and simulation results from a detailed switched converter model are compared with the proposed state-space model output to verify its accuracy and robustness.

With series insulated-gate bipolar transistor (IGBT) operation, well-matched gate drives will not ensure balanced dynamic voltage sharing between the switching devices. Rather, it is IGBT parasitic capacitances, mainly gate-to-collector capacitance Cgc, that dominate transient voltage sharing. As Cgc is collector voltage dependant and is significantly larger during the initial turn-off transition, it dominates IGBT dynamic voltage sharing. This paper presents an active control technique for series-connected IGBTs that allows their dynamic voltage transition dVce/dt to adaptively vary. Both switch ON and OFF transitions are controlled to follow a predefined dVce/dt. Switching losses associated with this technique are minimized by the adaptive dv/dt control technique incorporated into the design. A detailed description of the control circuits is presented in this paper. Experimental results with up to three series devices in a single-ended dc chopper circuit, operating at various low voltage and current levels, are used to illustrate the performance of the proposed technique.

Various applications, like in underground mines and oil and gas industries, require remote operation of vector-controlled medium-voltage variable speed drives via a long motor feeder. The use of voltage source inverters in such cases leads to motor overvoltage and harmonic quality problems. The current source inverter (CSI) is ideally matched to these applications because of its motor-friendly voltage output. Speed sensorless operation is mandatory due to the long motor feeder. Although the model reference adaptive system (MRAS) is a powerful and proven speed estimation tool, its implementation in long motor feeder drives faces many challenges. Among them, and addressed in this paper, are inherent dc offset in its stator model, the need for actual motor voltage and current values, and oscillations in the estimated speed due to errors in the motor current measurement signals. In this paper, a sensorless CSI vector-controlled drive, suitable for long motor feeder applications, is studied. Improved speed estimation is achieved by proposing 1) a modified dc-offset eliminator for an MRAS speed estimation and 2) a compensation technique for motor current's measurement errors. Intensive experimental results, for a low-voltage scaled model, along with simulations validate the effectiveness of the proposed technique.

In this paper, a single-phase, single-stage current source inverter-based photovoltaic system for grid connection is proposed. The system utilizes transformer-less single-stage conversion for tracking the maximum power point and interfacing the photovoltaic arrays to the grid. The maximum power point is maintained with a fuzzy logic controller. A proportional-resonant controller is used to control the current injected into the grid. To improve the power quality and system efficiency, a double-tuned parallel resonant circuit is proposed to attenuate the second- and fourth- order harmonics at the inverter dc side. A modified carrier-based modulation technique for the current source inverter is proposed to magnetize the dc-link inductor by shorting one of the bridge converter legs after every active switching cycle. Simulation and practical results validate and confirm the dynamic performance and power quality of the proposed system.

This paper presents three topological classes of dc-to-dc converters, totaling nine converters (each class with three buck, boost, and buck-boost voltage transfer function topologies), which offer continuous input and output energy flow, applicable and mandatory for renewable energy source, maximum power point tracking and maximum source energy extraction. A current sourcing output caters for converter module output parallel connection. The first class of three topologies employs both series input and output inductance, while anomalously the other two classes of six related topologies employ only either series input (three topologies) or series output (three topologies) inductance. All nine converter topologies employ the same elements, while additional load shunting capacitance creates a voltage sourcing output. Converter time-domain simulations and experimental results for the converters support and extol the concepts and analysis presented.

This paper presents an indirect vector control scheme with an improved flux pattern using third harmonic injection. The control objective is to independently control both flux and torque and to generate a nearly rectangular air-gap flux, resulting in improved machine power density. If there is a proportional relation between the third harmonic and fundamental plane currents, variable misalignment between fundamental and third air-gap flux components occurs with varying mechanical loading. Due to this misalignment, saturation may take place. Accordingly, the total flux is saturated and iron loss increases. Hence, coupling results between different sequence planes. Instead of a proportional relation between the current components, direct and quadrature current components of the injected third harmonic current reference are a function of the fundamental direct and quadrature reference current components, respectively. These functions ensure that the air-gap flux is near rectangular with a maximum value of 1 p.u. from no load to full load. Moreover, this controller guarantees complete decoupling between the sequence planes. An eleven-phase induction machine is used to validate the proposed controller experimentally, while supporting simulation results and theoretical analysis use both MATLAB and finite element platforms.

This paper presents a novel active snubber recovery circuit for series-connected insulated gate bipolar transistors (IGBTs). The proposed technique allows turnon and turnoff switching of the series IGBTs to be controlled and balanced through conventional snubber effects, but the configuration includes active circuitry to recover into the dc supply, the stored snubber energy. Detailed waveform analysis and associated mathematical equations are presented, supported by PSpice simulations. The proposed technique is practically demonstrated, at a scaled power level, on a single IGBT to illustrate the control concept and on three series-connected IGBTs to demonstrate dynamic voltage sharing.

A new fuzzy-logic controller for maximum power point tracking of photovoltaic (PV) systems is proposed. PV modeling is discussed. Conventional hill-climbing maximum power-point tracker structures and features are investigated. The new controller improves the hill-climbing search method by fuzzifying the rules of such techniques and eliminates their drawbacks. Fuzzy-logic-based hill climbing offers fast and accurate converging to the maximum operating point during steady-state and varying weather conditions compared to conventional hill climbing. Simulation and experimentation results are provided to demonstrate the validity of the proposed fuzzy-logic-based controller.

A new control scheme for parallel-connected inverters taking into account the effect of line impedance is presented. The system presented here consists of two single-phase inverters connected in parallel. The control technique is based on instantaneous average current-sharing control that requires interconnections among inverters for information sharing. A generalized model of a single-phase parallel-connected inverter system is derived. The model incorporates the detail of the control loops that use a proportional-resonant controller, but not the switching action. The voltage- and current-controller design and parameters selection process are discussed. Adaptive gain scheduling is introduced to the controller to improve the current and power sharing for a condition, where the line impedance is different among the inverters. The simulation results show that the adaptive gain-scheduling approaches introduced improve the performance of conventional controller in terms of current and power sharing between inverters under difference line impedance condition. The experiments validate the proposed system performance.

This paper presents a predictive direct power control strategy for doubly fed induction generators (DFIGs). The method predicts the DFIG's stator active and reactive power variations within a fixed sampling period, which is used to directly calculate the required rotor voltage to eliminate the power errors at the end of the following sampling period. Space vector modulation is then used to generate the required switching pulses within the fixed sampling period that results in a constant switching frequency. The impact of sampling delay on the accuracy of the sampled active and reactive powers is analyzed, and detailed compensation methods are proposed to improve the power control accuracy and system stability. Experimental results for a 1.5-kW DFIG system demonstrate the effectiveness and robustness of the proposed control strategy during power steps, and variations of rotating speed and machine parameters. System performance for tracking varying stator power references further illustrates the dynamic performance of the proposed method.

This paper proposes new direct power control (DPC) strategies for three-phase DC/AC converters with improved dynamic response and steady-state performance. As with an electrical machine, source and converter flux, which equal the integration of the respective source and converter voltage, are used to define active and reactive power flow. Optimization of the lookup table used in conventional DPC is outlined first so as to improve power control and reduce current distortion. Then, constant switching frequency DPC is developed where the required converter voltage vector within a fixed half switching period is calculated directly from the active and reactive power errors. Detailed angle compensation due to the finite sampling frequency and the use of an integral controller to further improve the power control accuracy are described. Both simulation and experimental results are used to compare conventional DPC and vector control, and to demonstrate the effectiveness and robustness of the proposed control strategies during active and reactive power steps, and line inductance variations.

A transformerless single-phase inverter topology is proposed that can operate over a wide dc input voltage range and has the ability to track reference signals with fast dynamics, making it suitable for harmonic elimination and distributed generation applications. The necessary capacitor and inductor are easier to design than those for filtering the output of traditional inverters. Unlike traditional inverters, no output filter stage is required. Analysis of inverter operating mechanisms is carried out for two control schemes, which are confirmed by simulation and practical results.

A requirement of the three-level neutral-point-clamped voltage source inverter, with or without a separately supporting dc link, is to maintain the balance of the two dc-link capacitor voltages. In this paper, balancing of the capacitor voltages for these two dc-link voltage source possibilities is analyzed and an algorithm is proposed to independently balance the capacitor voltages. The algorithm considers the average energy effect of each vector on capacitor voltage and the necessary optimal vector state sequence in each modulation cycle. The algorithm minimizes the voltage rating overheads of the hardware, reduces the voltage ripple, and attenuates the negative effects associated with dc-link voltage oscillations.

This paper generically classifies and unifies basic single-switch, single-inductor, DC-TO-DC converters. The boost and buck/boost flyback converters are shown to be supplementary, each being part of the same three-port terminal transfer function. Realizing one of these converters inherently results in the other as a fully functional composite output port. Three-port examination of the forward converter reveals it too combines two different converter voltage/current transfer functions. Generalized three-port analysis is used to specify the requirements of a realizable universal DC-TO-DC converter theoretically capable of producing isolated output DC and AC voltage and current in the range plusmninfin.

For high performance induction machine control, the technique of indirect rotor flux oriented vector control is commonly utilized. The torque performance of this technique is significantly affected by the performance of the current control loops. In this paper a new adaptive high bandwidth current controller for induction machines is presented. The technique is derived and validated through simulation and experimental results. The new architecture is shown to achieve a dead-beat response, with a rise time of one sample period and no overshoot, when the inverter voltage limit is not exceeded. When the voltage limit is exceeded the current response is achieved in a minimum time with no overshoot. It is shown that the new control technique achieves similar dynamic response to the conventional dead-beat control scheme while eliminating parameter sensitivity issues. It is demonstrated that the new algorithm offers higher bandwidth than the commonly used synchronous frame proportional plus integral control technique while maintaining good steady state performance.

This paper proposes a novel rotor resistance identification method for an indirect rotor flux-orientated controlled induction machine drive. The method is effectively integrated with the intermediate current control loop of the system. A decoupled synchronous voltage control scheme is used to achieve a fast, accurate current control response and indicates the relative thermal change of the rotor resistance. A model reference adaptive control scheme is then used to track the variation of the rotor resistance. Other issues, such as the nonideal characteristics of the power devices, stator resistance variation and comparison with two other parameter identification methods, are included. This method is less complex and more effective than others, and this is supported by theoretical analysis, and verified by simulation and experimental results.

A new soft-switching PWM scheme for a three-phase, AC-DC, step-down unity power factor converter is described. The main advantage of the scheme is that it requires no additional hardware components to achieve a combination of zero current and voltage turn-off and zero and reduced voltage turn-on. The scheme relies on the repositioning of the PWM pulses within the carrier period to obtain natural commutation from one switching device to the next. The theoretical reduction in the total switching losses is mathematically shown to be 42% compared with the standard center-aligned PWM scheme used with the converter. A PSpice/sup TM/ simulation of the new scheme reveals soft-switching waveforms. Practical results are given to support the simulation results and heat-sink temperature rise results show a reduction in heat-sink temperature rise for the new scheme compared to the old.

In this paper, insulated gate bipolar transistor (IGBT) models published in the literature are reviewed, analyzed, compared and classified into different categories according to mathematical type, objectives, complexity, accuracy and speed. Features of the different models are listed. Different modeling criteria are discussed according to various circuit conditions, structures, thermal considerations and accuracies. Some problems and trends in IGBT modeling are discussed.

This paper presents the implementation of Slotine's approach of sliding mode control for position control of a vector-controlled synchronous reluctance machine. A comparison is undertaken between the performance of a fixed gain controller and two sliding mode controllers for both the regulator and servo cases. Invariant performance is obtained using Slotine's approach of sliding mode control compared to a fixed gain controller. Robustness to parameter variation is an important feature of this technique. This can be achieved through the control law design, assuming parameter variation bounds are known. These improvements are demonstrated for variations in the load inertia. Machine inductance ripple affects the quality of achievable position control. A state-space model for the machine to incorporate this effect yields drive simulation results that agree with presented experimental results.

The turn-on loss of high-speed insulated gate bipolar transistors (IGBTs) accounts for a significant proportion of the total switching energy. In many applications, this loss is increased by the energy associated with diode reverse recovery of current. Such energy is absorbed by the IGBT switch at high voltage. Linear turn-on snubber inductors may be used to control the turn-on loss, diode reverse recovery, and electromagnetic compatibility (EMC). These snubbers have the disadvantage of involving substantial stored energy that must be reset, normally by dissipation. An alternative is to use a saturable turn-on snubber inductor, which stores substantially less energy than a linear inductor. In this paper, the suitability of saturable turn-on snubber inductors for use with IGBTs is investigated, and possible circuit topologies for single-ended and bridge-leg applications are proposed. Mathematical analysis, simulation, and practical results are presented for the saturable inductor turn-on snubber circuit topologies.

A new analytical insulated gate bipolar transistor (IGBT) model for improved on-state characteristics prediction is proposed. Two-dimensional (2-D) effects in the forward conduction of an IGBT are studied analytically. These effects significantly in8uence the on-state characteristics of the device and must be accounted for when IGBT modeling. Dynamic characteristics and temperature effects are included in the model. Both three-dimensional (3-D) numerical simulation and experimental results support the theoretical analysis.

This paper addresses the need for off-state negative gate bias with insulated gate bipolar transistor (IGBT) devices that experience a dv/dt when in the off state. Factors considered include off-state gate bias voltage, gate impedance, reapplied dv/dt, and temperature. Theoretical calculation and experimental results for a high-voltage high-current IGBT supports the assessment of these factors.

This paper shows that it is possible to use available commercial software to model and simulate a vector-controlled induction machine system. The components of a typical vector control system are introduced and methods given for incorporating these in the MATLAB/SIMULINK software package. The identification of rotor resistance is important in vector control, if high-performance torque control is needed, and modeling of the extended Kalman filter (EKF) algorithm for parameter identification is discussed. It is certainly advisable, when feasible, to precede implementation of new algorithms, whether for control or identification purposes, with an extensive simulation phase. Additionally, a technique for generating pulse-width modulation (PWM) phase commands to extend machine operation to higher speeds before field weakening occurs is simulated in a vector-controlled induction machine, driven by a PWM inverter. This demonstrates the versatility of the vector-controlled induction machine system model.

A novel passive lossless turn-on snubber with a soft-clamped turn-off snubber circuit for voltage source inverters is proposed. The energy trapped in the snubber is recovered into the DC supply and load without any active devices, associated control circuitry, or resistors. The overshoot voltage on the switches is clamped, and the peak switch current is low, making this snubber suitable for use in high-power insulated gate bipolar transistor (IGBT) inverters.

Differential-mode buck-boost inverters have merits such as reduced switch number, ability to provide voltages higher or lower than the input voltage magnitude, improved efficiency, reduced cost and size, and increased power density, especially in low-power applications. There are five buck-boost inverters that can provide flexible output voltage without the need of a large electrolytic input side capacitor, which degrades the reliability of inverters. The continuous input current of these inverters is appropriate for maximum power point tracking operation in photovoltaic and fuel cells applications. Three of the five inverters can be isolated with high-frequency-link transformers where the common-mode leakage current can be mitigated. However, the performance and control of such converters have not been discussed in detail. In this paper, the five possible single-stage three-phase differential-mode buck-boost inverters with continuous input current are investigated and compared in terms of total losses, maximum ripple current, total harmonic distortion, and device and passive element ratings. In addition, the possible methods are presented for eliminating the input third-order harmonic current, resulting from the stored energy in the passive elements, as well as the output second-order harmonic currents. The ability for isolating the input and output sides of the inverters with a small-high frequency transformers is discussed. A changeable-terminal 2.5-kW bidirectional inverter is used to validate the design flexibility of the inverter topologies, when digital signal processor-controlled. NPRP Grant NPRP 4-250-2-080 from the Qatar National Research Fund (a member of Qatar Foundation). Scopus

The limitations on the operating frequency of hard-switched and resonant-link inverters are studied. The maximum operating frequency of a hard-switched inverter is found to be well defined by the allowed power dissipation and the switching losses. For resonant link inverters the upper limit is not so well defined and depends on a trade-off between a number of different factors. For a system using high-power bipolar transistors is it seen that a hard switched inverter is limited to switching frequencies of below 2 kHz, while a comparable resonant link inverter is restricted to frequencies below 20 kHz. The frequency spectrum of the resonant link configuration has been compared with pulse width modulation (PWM). It was shown that the improvement in harmonic distortion associated with a delta-modulated resonant link is not as great as could be expected from the increase in operating frequency that may be obtained. This is a result of constraints placed on switching instants and the need to use integral pulse modulation. The simulations presented show that high-frequency resonant link systems generate more low-frequency components than those using low-frequency PWM. >

Analytic expressions for the output voltage spectrum of an asynchronous delta (or delta-sigma) modulated inverter are reported and supported by experimental data. The analysis yields three functions that give the frequency, phase, and amplitude of each component of the spectrum. These functions are in terms of the sinusoidal reference waveform and the properties of the modulator. The method provides greater accuracy and computational efficiency than the numerical methods reported to date. The spectral components form pairs of sidebands around multiples of the average switching frequency. The functions detail the relationship between the number of significant sideband components and the depth of modulation and illustrate the spread-spectrum nature of delta modulation. Extensions to nonsinusoidal reference waveforms and to hysteresis current controllers are considered. >