Improving Mechanical Characteristics of Inverter-induction Motor Drive System

An inverter-three-phase squirrel-cage induction mot or drive system with improved mechanical characteristics is presented. The propos ed system provides mechanical characteristics with constant maximum torque or increased maximum torque and reduced slip speed at frequencies below the nominal frequency. The control algorithm is bas ed on the constant volts per hertz principle using two improvement techniques: keeping maximum torque constant or keeping magnetic flux constant. Performance analysis of the system under different operation conditions was provided. For this purpose, a standard state-space model of three-phas e squirrel-cage induction motor, with respect to a synchronously rotating d-q reference frame was deri ved. The correctness and validity of the derived model of induction motor was verified. The inverter was considered as a static linear element and modeled through its input-output equation based on the modulation index. Three types of controllers were modeled, simulated and experimentally tested. The results show that both suggested control methods improve the system performance. The slip sp eed has been decreased and the starting torque and maximum torque have been increased. Controller with constant maximum torque can be used in drive systems working with constant load, while con tr ller with constant flux can be used in drive systems working with constant power.


INTRODUCTION
Induction motor is the most used in industry because of its high robustness, reliability, low cost, high efficiency and good self-starting capability [1] . In spite of this popularity, the induction motor has two inherent limitations: (1) The standard motor is not a true constant-speed machine, its full-load slip varies from less than 1% (in high-horsepower motors) to more than 5% (in fractional-horsepower motors) and (2) It is not inherently capable of providing variable-speed operation [2,3] . These limitations can be solved through the use of smart motor controllers and adjustable speed controllers [4,5] . The basic control action involved in a smart motor controller is control of stator voltage at a fixed frequency to accomplish start/stop/braking control and energy efficient operation. The basic control action involved in adjustable speed control of induction motors is to apply a variable frequency variable magnitude AC voltage to the motor to achieve the aims of variable speed operation [6] . The most common AC drives today are based on sinusoidal pulse-width modulation SPWM. Both voltage source inverters and current source inverters are used in adjustable speed AC drives. However, voltage source inverters with constant Volts/Hertz (V/f) are more popular, especially for applications without position control requirements, or where the need for high accuracy of speed control is not crucial.
Ideally, by keeping a constant V/f ratio for all frequencies the nominal torque-speed characteristic of the induction motor can be reproduced at any frequency. In this case, the stator flux, stator current and torque will be constant at any frequency. The great majority of variable-speed drives in operation today are of this type. However, since the introduction of fieldoriented control theory, almost all research has been concentrated in this area and little has been published about constant V f operation. Its practical application at low frequency is still challenging, due to the influence of the stator resistance and the necessary rotor slip to produce torque [7] . In addition, the nonlinear behavior of the pulse-width modulated voltage-source inverter in the low voltage range makes it difficult to use constant V f drives at frequencies below 3Hz [8] .  [7] .
The objective of this study was to develop new techniques to improve the performance of inverterinduction motor drive system with constant V f controller. For this purpose, two improving techniques are presented. The first technique is based on keeping the maximum torque constant for all operating frequencies and equals to its value at nominal frequency. The second technique is based on maintaining the magnetic flux constant at all operating frequencies and equals to its nominal value. The proposed techniques are validated by simulation and experimental results. It is shown that large torques are obtained, even in the low frequency range, with significantly reduced steady-state error in speed.

Modeling system components:
The block diagram of inverter-three-phase squirrel cage induction motor is presented in Fig. 1. It consists of IGBT-inverter-based AC-to-AC converter, three-phase squirrel cage induction motor and controller. In order to analyze the system performance, all of these components should be modeled (mathematically described).

Modeling of the IGBT-inverter-based AC to AC converter:
The inverter-based AC-to-AC converter is considered to be an ideal system, where the DC voltage at the input of the inverter has no AC component and the output voltage of the filter at the output of the inverter has no harmonics. For sinusoidal pulse width modulation SPWM, the ratio of the amplitude of the sinusoidal waveform to the amplitude of the triangular waveform is called the modulation index m , which can be in the range of 0 to 1 [5] . The stator voltage s V can be defined as:  equations, the electrical model of the squirrel cage three-phase induction motor with respect to a synchronously rotating d q − coordinates can be expressed as [2,9] : The mechanical model of an induction motor can be represented by [2] :  The state-space model of induction motor in standard form, with respect to a synchronously rotating d-q coordinates, can be derived from Eqs. 4 and 5 as: x Ax Bu y Cx Du where the matrix quantities in Eq. 6 are as follows:    The state-space model of induction motor according to Eq. 6 is represented in Fig. 4. The validity and correctness of the derived model were checked by comparing its response to that of the embedded MATLAB model. Both models gave identical responses with relative error of 0.01% under the same conditions. The parameters of simulated induction motor are given in Table 1.
The complete model of the drive system studied using MATLAB Simulink is shown in Fig. 5.   at any frequency f.

Controller with constant maximum torque:
The maximum torque at nominal frequency max( ) n T can be determined by the following equation [6] : Under this condition and based on the induction motor steady-state equivalent circuit and phasor diagram [7] , the stator voltage V can be determined as: Eq. 11 shows that the stator voltage V in the case of controller with constant flux is always greater than that of V f =constant controller. The model of controller with constant flux is shown in Fig. 9. Simulated mechanical characteristics of the drive system with different types of controllers are represented in Fig. 10, which shows that the decrease of frequency causes significant increase of maximum torque in the case of controller with constant flux. Fig. 10 also shows that the absolute slip reduced and became less than that of other types of controllers. The obtained mechanical characteristics of the drive system with constant flux controller are similar to those of drive system operating with constant power.

RESULTS
To verify the use of the proposed controllers with constant maximum torque and with constant magnetic flux, some experiments have been carried out with the same drive system that was simulated. The mechanical characteristics were obtained for different frequencies.
Some of these characteristics are presented in Fig. 11. The experimental characteristics are similar to simulated characteristics, which means that the proposed techniques can be implemented in drive systems based on squirrel cage induction motors.

CONCLUSION
Based on the results of this study, the following conclusions can be made: * The derived state-space model of three-phase squirrel-cage induction motor can be used to analyze the performance of induction motor drive systems. * The implementation of constant maximum torque and constant flux controllers improve the mechanical characteristics of inverter-induction motor drive systems. * The mechanical characteristics of the drive system with constant flux controller are harder than that with constant maximum torque controller. * It is recommended to use constant maximum torque controller in drive systems operating with constant torque. * It is recommended to use constant flux controller in drive systems operating with constant power.