Search

This paper presents a comparative analysis involving several fault-tolerant operating strategies, applied to three-phase induction-motor drives, that intend to compensate for inverter faults. The results presented show the advantages and the inconveniences of several fault-tolerant drive structures, under different control techniques, such as the field-oriented control and the direct torque control. Experimental results concerning the performance of the three-phase induction motor, based on the analysis of some key parameters, like induction-motor efficiency, motor power factor, and harmonic distortion of both motor line currents and phase voltages, will be presented. Index Terms--AC motor drives, fault tolerance, induction-motor drives, reliability.

Optimal time trajectories, based on the Pontryagin's maximum principle, are deduced for a squirrel-cage induction motor with constant load torque. These trajectories are valid for acceleration and deceleration with or without the load torque and for a loaded or unloaded motor, and ensure the minimal time transients with the stator current limited to the previously fixed value. Moreover, the optimal trajectories place the motor at the end of the transient at the minimum current point, which is close to the one of maximum efficiency, thus combining the brevity of the transients with the saving of energy. An optimal-time control system that implements these trajectories is designed. The results of the simulation of the proposed control system and the results of the experiments on a real drive are presented. Index Terms--Constant load torque, energy saving, maximum principle, optimal control, squirrel-cage motors.

Conventional pulsewidth-modulation (PWM) schemes fully depend on a microprocessor (MPU) for extensive real-time computation, intervention, and housekeeping, and are limited to applications at low fundamental frequencies and low precision. At 20-kHz switching, the overhead of a modern 16-bit CPU increases up to 90%, making virtually no time available for regular control tasks. It also has poor cycle-to-cycle accuracy of [+ or -] 5-10 [micro]s. A novel self-managed high-frequency and precision PWM architecture and integrated circuit are developed for distributed drive control systems. This architecture permits near-zero interfacing rate with the coprocessor, thus eliminating the overhead of the MPU's intervention and housekeeping, while being capable of both asynchronous and synchronous PWM at a range of 0-1000 Hz of fundamental frequencies, expandable to several kilohertz. A cycle-to-cycle accuracy of 50 ns is achievable in precision open-loop control. Experimental results verify our new design. This effectively supports distributed ac drive systems with highly coordinated controls. Index Terms--Cycle-to-cycle accuracy, distributed ac drive systems, high-frequency and precision pulsewidth modulation (PWM), near-zero interfacing rate with main processor, precision and high-frequency synthesizer.

Low-cost motor drives are being sought for high-volume energy-efficient home appliances. Key to the realization of such low-cost motor drives is the reduction of the power electronic converter to the barest in terms of its components, particularly the active devices, finding the motor with the least complexity for manufacturing and a controller that can extract the desired performance from the machine and converter combination. These and other factors such as self-starting, speed control over a wide range, and, most of all, the crowning aspect of four-quadrant operation with a bare minimum number of controllable switches remain as formidable challenges for low-cost motor drive realization. An innovative four-quadrant switched reluctance motor (SRM) drive with only one controllable switch is realized in this paper, for the first time, in the opinion of the authors. The motor drive is realized using a two-phase machine and a single controllable switch converter. The theory and operation of the proposed four-quadrant SRM drive with the proposed control algorithm for its realization are described. The motor drive is modeled, simulated, and analyzed to verify its feasibility for self-starting, speed control, and for four-quadrant operation, and the simulation results are presented. Experimental results confirm the validity of the proposed control algorithm for four-quadrant control of the SRM drive. The focus of the paper is mainly directed toward the control algorithm for realizing the four-quadrant operation of the two-phase SRM drive with a single controllable switch converter. Index Terms--Motor drives control, power electronics, switched reluctance motor (SRM) drives.

The self-bearing or bearingless machine is an electromagnetic device that supports its own rotor by way of magnetic forces generated by windings on its stator. Various winding configurations have been used to accomplish the task of force production. This paper proposes a winding based on a bridge connection for polyphase self-bearing rotating electrical machines with advantages such as: 1) requiring only one power supply for torque production; 2) lateral forces are produced using auxiliary power supplies of relatively low current and voltage ratings; 3) relatively low power loss; and 4) preserving the flexibility for extensions to other polyphase machines. The bridge connection has been verified to exhibit the characteristics of a self-bearing motor via an electrically coupled finite-element analysis. A comparison of power loss with conventional winding schemes and general applications of such a proposed scheme are also presented. Index Terms--Bearingless machines, bridge configured winding, magnetic bearings, self-bearing machines.

Filter networks for long cable drives have been studied in the last decade to solve the overvoltage problem at the motor terminals. However, little research has been dedicated to analyze their influence on the voltage distribution in the motor stator winding and on the circulation of the common-mode currents. In this paper, the project of dv/dt filters through simulation and analysis from previous work is extended, including the motor voltage distribution and common-mode current analysis. Simulation and experimental results are presented, demonstrating the usefulness of the filter networks on the motor overvoltage mitigation. Three filter topologies will be discussed and compared here: RLC filter at the motor terminals, RLC filter at the inverter output and reactor filter, which is extensively used in the industry. Simulation and experimental results demonstrate that the RLC filter at the inverter output is the most interesting solution among the main types of passive filter networks. Index Terms--Electrical drive systems design and applications, industrial drives, overvoltage and dv/dt filter design.

The main hurdle in achieving real-time performance for the simulation of power-electronic circuits is the large calculation effort required to update the model after a discontinuous change in switch impedance. The method presented here suggests that by separating the switch model from the rest of the circuit, only a much smaller equation set needs updating. Thus, it reduces the update effort to a level where it is no longer the bottleneck of the overall simulation loop. Unlike previous works on this issue, the method is independent on both the simulation approach and the circuit topology. The method has been tested on a variety of circuits with impressive results, two of which are presented here. First, there is a complete HVdc system, representing the higher limit in size and complexity. Second, a pulse-width-modulated motor drive with an external controller in a hardware-in-the-loop configuration represents a higher limit in performance requirements. Both test circuits are simulated in real time on a low-cost off-the-shelf personal computer, using the xPC technology from Simulink and automatic generation of optimized code, and are compared to a very precise variable step offline simulation. Index Terms--Model update, motor drives, optimization, power-electronic circuit, real-time simulation, switching.

In this paper we deduce, from analytical field solutions, the influence of leading design parameters on the performance of a radially magnetized, iron-cored, tubular permanent-magnet machine and its drive system. We derive analytical formulas for predicting the open-circuit electromotive force, the thrust force, the iron loss, and the winding resistance and inductances, as well as the converter losses. The force density, the machine and drive system efficiencies, and the power factor and converter volt-ampere (VA) rating are established as functions of a set of machine dimensional ratios, with due account of magnetic saturation and subject to a specified thermal constraint. We validate the utility and accuracy of the analytically derived formulas by finite-element calculations. Finally, we show that the design optimization of such a linear drive system must account for the losses and VA rating of the converter as well as the design parameters of the tubular machine. Index Terms--Design optimization, electric drive, linear machine, permanent-magnet machine.

This paper presents new inverse modeling for synchronous reluctance motor (SyRM). This modeling is valid when the inductances are sinusoidal or nonsinusoidal and even when the machine is saturated. This technique involves the generation of constant torque curves as a function of two-phase currents in the Concordia's reference frame when the rotor angle is fixed. We also introduce an experimental method to obtain directly the inverse modeling. This practical method takes into account the saturation of the motor. This technique allows the reduction of the low torque ripple in the case of nonsinusoidal inductances. Index Terms-Electric drive, optimal control, synchronous motors, Torque ripple.

A new battery configuration technique and accompanying control circuitry, termed a Synergetic Battery Pack (SBP), is designed to work with Lithium batteries, and can be used as both an inverter for an electric vehicle AC induction motor drive and as a battery charger. In this paper, the performance of a Synergetic Battery Pack during motor drive operation is compared via computer simulation with a conventional motor drive which uses sinusoidal pulse width modulation (SPWM) to determine its effectiveness as a motor drive. The study showed that the drive efficiency was compatible with the conventional system, and offered a significant advantage in the lower frequency operating ranges. The voltage total harmonic distortion (THD) of the SBP was significantly lower than the PWM drive output, but the current THD was slightly higher due to the shape of the harmonic spectrum. In conclusion, the SBP is an effective alternative to a conventional drive, but the real advantage lies in its battery management capabilities and charger operation.

The control of the switched-reluctance motor (SRM) is usually based on the inductance profiles as a function of position. This paper addresses the problem of obtaining optimal performance from an SRM in the presence of parameter variation, which can alter the phase inductance profiles. The operation of an SRM drive in the controlled current mode from zero to base speed is considered. New self-tuning algorithms are presented which optimize the steady-state performance of the drive as measured by torque per ampere (TPA). Computer simulations are employed to show the existence and uniqueness of a solution to the optimal TPA problem. The application of the new control strategy is explained in the content of a speed-controlled drive system. Experimental results are provided to demonstrate the validity of the self-tuning controller. Index Terms - Control, self tuning, switched-reluctance motor drive.

Preventive maintenance of electric drive systems with induction motors involves monitoring of their operation for detection of abnormal electrical and mechanical conditions that indicate, or may lead to, a failure of the system. Intensive research effort has been for sometime focused on the motor current signature analysis (MCSA). The MCSA techniques utilize the results of spectral analysis of the stator current. Reliable interpretation of the spectra is difficult, since distortions of the current waveform caused by the abnormalities in the drive system are usually minute. In this paper, an alternate medium for the motor signature analysis, namely the instantaneous power, is proposed. By theoretical analysis, computer simulations, and laboratory experiments, it is shown that the instantaneous power carries more information than the current itself. Utilization of the instantaneous power is thus enhancing the reliability of diagnostics of induction motor drives.

In this paper, a sliding-mode speed controller based on a new switching surface is proposed for induction motor systems. With this variable structure control switching surface, the exponential stability is guaranteed for the speed servo control and insensitivity to uncertainties and disturbances are obtained as well. Moreover, an adaptive variable structure speed control is studied to relax the need for the bound of disturbance in variable structure control. The insensitivity or robustness of the proposed method for general speed servo systems is maintained, and the dynamic performances are improved as well. Finally, the validity of proposed scheme is demonstrated by computer simulations and experimentations.

A new adaptive control system for dc motor drive with field weakening is proposed. The adaptation mechanism is based on the gain scheduling. A deep knowledge of the phenomena in the drive was necessary to define the scheduled variables that capture the essential nonlinearities of the process considered. However, in practice, to realize the proposed adaptive control system, the only a priori knowledge required is the experimentally determined magnetization curve. Simulation and experimental results indicating high performances of the control system proposed, are presented.

The stator winding current commutation timing is the central subject of switched reluctance motor control. The direct use of coil inductance information for current commutation is introduced in this paper. The drawbacks of position-based commutation, in the presence of drifting electrical parameters, are overcome by using the instantaneous coil inductance information. Algorithms to optimize torque using this approach are also presented in this paper.

This paper proposes a sensorless speed measurement scheme that improves the performance of transducerless induction machine drives, especially for low-frequency operation. Speed-related harmonics that arise from rotor slotting and eccentricity are analyzed using digital signal processing. These current harmonics exist at any nonzero speed and are independent of time-varying parameters, such as stator winding resistance. A spectral estimation technique combines multiple current harmonics to determine the rotor speed with more accuracy and less sensitivity to noise than analog filtering methods or the fast Fourier transform. An on-line initialization routine determines machine-specific parameters required for slot harmonic calculations. This speed detector, which has been verified at frequencies as low as 1 Hz, can provide robust, parameter-independent information for parameter tuning or as an input to a sensorless flux observer for a field-oriented drive. The performance of the algorithm is demonstrated over a wide range of inverter frequencies and load conditions.

Current-regulated brushless dc machines are used in a wide variety of applications including robotics, actuators, electric vehicles, and recently, ship propulsion systems. When conducting system analysis of this or any other type of drive, average-value reduced-order models are invaluable since they provide a means of rapidly predicting the electromechanical dynamics and are readily linearized for control system synthesis. In this paper, a highly accurate average-value reduced-order model of a hysteresis current-regulated brushless dc drive is set fourth. In so doing, it is demonstrated that the drive exhibits five distinct operating modes. The physical cause of each of these modes is explained and a mathematical model for each mode is set fourth. The mathematical models are verified both experimentally and through the use of computer simulation. It has been found that the model set fourth herein is on the order of 300 times faster than a detailed computer simulation in calculating electromechanical transients.

Permanent-magnet synchronous machines fed from current-regulated converters feature nearly ideal performance at low-to-moderate speeds. However, as rotor speed increases the back emf rises which results in loss of current regulation and decreased torque. In buried-magnet machine drives, flux weakening is often used to extend the speed range. This paper sets forth a flux-weakening control specifically designed for surface-mounted permanent-magnet machines which is simple and does not require knowledge of the machine or system parameters. The proposed method is demonstrated both experimentally and through the use of computer simulation.

The estimation of the disturbance torque in a sensorless dc drive is carried out by extending the classical observer theory. Three estimation schemes are formulated according to the representation of the disturbance torque and the processing of the observer states. In addition to the disturbance torque, all the schemes deliver an estimation of the motor speed. Steady-state accuracy and dynamics of the schemes are first determined in nominal conditions, identifying the scheme with the best performance. The effects of variations in the motor parameters are then analyzed, with the finding that a proper modeling of the motor makes the steady-state estimation of the disturbance torque insensitive to any variation. As a test, the schemes are applied to a sensorless dc drive for both compensating for the disturbance torque and closing the speed loop. The responses obtained with the best-performance scheme are reported.

In this paper, a direct torque and stator flux vector control system is presented. The principle of this method was proposed by Takahashi and Noguchi in 1985. In contrast to the field oriented control, no coordinate transformation and current control loop is required. In practical application, however, problems occur with start and operation at zero speed region. This paper shows how by introducing an additional carrier signal to the torque controller input, the robust start and improved operation at low speed region can be achieved. The simulation and experimental results which illustrate the performances of the proposed system are presented. Also, nomograms for controller design are given.

The problem of modeling multiconverter systems in presence of harmonic and interharmonic distortion is considered. Specifically, current source rectifiers are considered as distortion sources some supplying d.c. motors and the remaining supplying inverters feeding a.c. machines. The classical analogue, frequency domain and time domain models proposed in the literature to study harmonic distortion in a multiconverter system are considered and for each model suitable extensions to include the interharmonic distortion are presented and critically analysed. The results of several experiments are reported to show the usefulness and to compare the accuracy of the different extensions considered. Keywords - Multiconverter Systems, Harmonic and Interharmonic Distortion, DC Motor Drive, Synchronous Motor Drive.

Current source a.c. drives draw a current waveform from the supply which is both distorted and unsteady. The frequency spectrum of the supply current contains harmonic components and interharmonic components which change frequency with the speed of the output motor. The increasing number of large current source variable frequency a.c. motor drives in use on power systems is causing concern over the interharmonic current distortion produced by the drives. If the interharmonic currents are excessive and compensation is required, it is difficult to achieve attenuation of these components with conventional passive filters. This paper describes how a single phase p.w.m. current source inverter connected in the d.c. link of a current source drive may be used to filter out a.c. side current interharmonic components. A prototype filter has been built and tested on a low power model of a variable speed synchronous motor drive system. Results show clearly that a significant reduction in the interharmonic current magnitude can be achieved using the d.c. side active filter. The results of computer simulations show that the rating of the active filter should be approximately 1% of the drive rating. Hence, the active filter may be realised using commonly available power semiconductor devices.

Current source inverter drives are sources of harmonic and non-harmonic distortion in supply systems. The non-harmonic components have frequencies that change with motor speed, so conventional filters might not be effective in reducing their amplitude. The distortion calculation at the design stage allows preventive actions to minimise the distortion at source by varying d.c. link and/or a.c. motor parameters. The aim of the paper is to discuss the modeling of the supply side current distortion and to analyse the effects of non-ideal supply conditions. The main utilizable models, both analogue and numerical, are discussed and analysed Several laboratory and numerical experiments are reported to compare the different model characteristics and to analyse the current distortion sensitivity to the supply voltage distortion and unbalance. Keywords - Power System, Harmonic and Interharmonic Distortion, Inverter Drive.

The design of a superconducting linear motor for driving a positive displacement bellows pump used in two-phase helium cooling of superconducting magnets is discussed. The motor consists of superconducting loudspeaker voice coil for the armature and a stator made of samarium and cobalt. Its design is such that its demagnetization current influences the peak pressure of the pump.

This paper proposes the use of Artificial Neural Networks (ANN's) to identify and control an induction machine. Two systems are presented: a system to adaptively control the stator currents via identification of the electrical dynamics, and a system to adaptively control the rotor speed via identification of the mechanical and current-fed system dynamics. Various advantages of these control schemes over other conventional schemes are cited and the performance of the combined speed and current control scheme is compared with that of the standard vector control scheme.

Neural networks are recently showing good promise for application in power electronics and motion control systems. So far, they have been applied for a few cases, mainly in the control of converters and drives, but their application in estimation is practically new. The purpose of this paper is to demonstrate that such a technology can be applied for estimation of feedback signals in an induction motor drive with some distinct advantages when compared to DSP based implementation. A feedforward neural network receives the machine terminal signals at the input and calculates flux, torque, and unit vectors (cos[[Theta].sub.e] and sin [[Theta].sub.e]) at the output which are then used in the control of a direct vector-controlled drive system. The three-layer network has been trained extensively by Neural Works Professional II/Plus program to emulate the DSP-based computational characteristics. The performance of the estimator is good and is comparable to that of DSP-based estimation. The system has been operated in the wide torque and speed regions independently with a DSP-based estimator and a neural network-based estimator, and are shown to have comparable performance. The neural network estimator has the advantages of faster execution speed, harmonic ripple immunity, and fault tolerance characteristics compared to DSP-based estimator.

A novel control strategy to realize decoupled control of torque and reactive power for a doubly excited induction machine using position sensorless scheme is proposed. The critical issues related to the torque angle estimation and control for a doubly excited induction machine are discussed. Compared to the other position sensorless schemes for doubly fed machine, the proposed control method uses only the rotor voltages and currents as the feedback signals, which substantially reduces the costs and enhances the reliability of the position sensorless control of a doubly fed ac machine. Computer simulation and experimental results are given to verify the position sensorless control scheme.

The Bureau of Reclamation has developed new equipment and procedures for testing mechanical-hydraulic governors for hydroelectric generators. The test equipment generates a three-phase voltage that will drive the governor ballhead motor at variable speed. Most traditional governor tests can be completed with the generating unit unwatered using this equipment. In addition, frequency responsetesting and other detailed analytical tests can be performed to validate governor models using this equipment. KEYWORDS: Speed Governing, Power System Dynamic Performance, Transient Stability Models, Field Test.

In this paper, a new DC-link converter is proposed for induction motor drives. It consists of a three-phase adjustable AC/DC converter as a pre-stage, a three-active-switch converter to simplify the conventional six-active-switch inverter and eliminate the lock-out time circuit, and an adaptive DC-link voltage controller to achieve the optimal DC voltage and minimize the switching frequency of the three-active-switch converter. The simple rotor-flux-oriented control can also be implemented easily using the proposed converter to achieve high performance. Finally, a prototype circuit is constructed and some experimental results are presented for demonstration. Keywords: DC-link, converter, inverter, induction motor drives

Since torque in harmonic drives is transmitted by a pure couple, harmonic drives do not generate radial forces and therefore can be instrumented with torque sensors without interference from radial forces. The installation of torque sensors on the stationary component of harmonic drives (the Flexipline cup in this research work) produce backdrivability needed for robotic and telerobotic compliant maneuvers [3, 4, 6]. Backdrivability of a harmonic drive, when used as torque increaser, means that the output shaft can be rotated via finite amount of torque. A high ratio harmonic drive is non-backdrivable because its output shaft cannot be turned by applying a torque on it. This article first develops the dynamic behavior of a harmonic drive, in particular the non-backdrivability, in terms of a sensitivity transfer function. The instrumentation of the harmonic drive with torque sensor is then described. This leads to a description of the control architecture which allows modulation of the sensitivity transfer function within the limits established by the closed-loop stability. A set of experiments on an active hand controller, powered by a DC motor coupled to an instrumented harmonic drive, is given to exhibit this method's limitations.

Recent advances in electric drive components has made integrated electric drivetrains a reality in various military and commercial vehicles. These components promise not only propulsion system benefits but offer unique opportunities for advanced pulse power systems such as electric guns and launchers. Heretofore, the bulk of development attention has been paid to the actual pulse power and electric gun components. However, their successful integration into a viable tactical vehicle mandates a synergistic approach to combining the propulsion system requirements with those of the pulse power system. To this end high performance electric drivetrain components perform an essential part of this integration. This paper describes the rationale of power train management and the current demonstrated state of the art of various drivetrain components.

An optimal pulsewidth modulation method is described in which the durations of switching subcycles are considered as optimization variables, a subcycle being the time sequence of three consecutive switching state vectors. Operation at variable subcycle duration entails a prediction of the controlling reference voltage vector. It is a special advantage that the optimization and prediction can be carried out off line. The optimal technique exhibits high dynamic performance. It can be used for synchronized and asynchronous modulation in a wide range of switching frequencies. The optimization reduces the harmonic currents at a given switching frequency. The Fourier spectrum lacks dominant carrier frequencies. Hardware implementation cost compares with existing nonoptimal modulation methods.

Feedforward pulsewidth modulators generate volt [centered dot] second differences between the controlling reference signal and the switched output waveform during transient operation. This dynamic modulation error is particularly pronounced at low switching frequency, e.g., with modern high-power GTO inverters. The compensation of this error is a key requirement when designing an optimal pulsewidth modulator for these applications. The trajectory tracking approach uses the steady-state trajectories of the current vector, computed from the optimal switching sequences, as templates. A tracking controller counteracts if the actual current vector deviates from this given path at transient operation. A decomposition of the current vector trajectory into its components enables, in addition, the identification of the instantaneous fundamental current, permitting the implementation of a fast current control system. Oscillograms from a 30-kW model drive demonstrate the high quality in terms of dynamic performance and minimum harmonic distortion obtained with a three-level inverter at only 200 Hz switching frequency.

A method for the deadbeat flux level control of direct-field-oriented high-power induction servo motor drives has been developed that employs an adaptive rotor flux observer. The observer is a full-order type and is used not only in the direct-field-oriented controller, but also to determine the stator and rotor resistances of the servo motor. The observer reduces the sensitivity of a deadbeat controller to fluctuations in the motor parameters. The main advantage of this method is that it improves the efficiency of an induction servo motor without sacrificing dynamic performance. This paper describes the method as well as the fundamental characteristics of the system derived from experimental and simulation results.

The development of large induction motor drives with low torque ripple and fast dynamic response for new or retrofit applications has been limited by the device ratings and problems of series connections. This paper investigates the use of a five-level GTO voltage-sourced inverter for large induction motor drives. The advantages of such a drive are that single GTO thyristors may be used at each level, thereby avoiding the need for series connection of the thyristors. The thyristors are well protected from overvoltages by the clamping action of the dc supply capacitors. The disadvantages are that each dc level requires a separate supply, four in the case of the five-level inverter, and that the devices are not equally loaded. This paper will review the basic operation of the five-level inverter and possible PWM voltage/frequency control techniques for the specific application of induction motor drives. The simulation results will clearly show the unequal loading of the devices and the need for independent voltage supplies for the five levels. It is shown that a combination of several PWM techniques offers the best solution for the drives application. The conclusions indicate that large induction motors with ratings up to 22 MVA, 7.46 kV may be supplied by the five-level inverter using presently available 4.5 kV, 3.0 kA GTO thyristors. The recommended supply for such an inverter with full regenerative operation over the complete speed range is four, four-quadrant converters in a quasi-24-pulse configuration.

Interior permanent magnet synchronous motors can be applied to applications requiring wide-speed operation. The current vector control algorithm of an interior permanent magnet synchronous (IPM) motor for constant power operation over the base speed is proposed. As the available voltage controlling the armature current vector is small in the flux-weakening constant power region, the current vector sometimes becomes uncontrollable in transient operations because of the current regulator saturation. The high-performance current regulator is also proposed to improve the current responses in the flux-weakening region, which includes the decoupling current controller and the voltage command compensator. The control performances are confirmed by several drive tests with respect to the prototype IPM motor.

An adaptive model following speed controller for induction motor drives is proposed and successfully implemented. This adaptive controller is easy to be implemented, since for the controlled plant, only the output signal is needed to feedback. In order to choose a proper reference model, which possesses the desired drive dynamic behavior, a two-degree-of-freedom (2-DOF) controller is designed based on a systematic procedure according to the prescribed drive specifications. The reference model of the adaptive system is chosen as the transfer function of the controlled drive system by the 2-DOF controller in the nominal case. An adaptation signal is augmented to let the prescribed specifications be maintained under wide operating conditions.

In this paper, a closed-form expression to estimate the overlap angle in a slip energy recovery system is presented. The prediction of the overlap angle is important in the case of doubly-fed induction motor drives, because of its influence on speed and torque. A closed-form expression is derived using a hybrid model of the induction motor and a dynamic model of the rotor rectifier. The ripple content of the dc link current and the inverter input voltage are neglected. The predicted results obtained using the closed form expression are verified experimentally.