Analysis And Modeling Of Indirect Field

Published Date: 02 Nov 2017

Muawia Abdel Kafi Magzoub, Nordin B. Saad, Rosdiazli B. Ibrahim

Department of Electrical and Electronic Engineering

Universiti Teknologi PETRONAS, Bandar Sri Iskandar, 31750

Tronoh, Perak, Malaysia

[email protected]

Abstract—This paper presents the development of a PI-controller for the control of induction motor speed and/or torque. An induction motor PWM drive system and its controller were modeled and analyzed. The control objective was to ensure the stability of the controller when subjected to changes in reference speed and load torque. To achieve the desired results for the whole system, in system parameters, open loop and closed loop were considered. The performance of the controller has been investigated through simulation using MATLAB/Simulink.

Keywords—PI-Controller, Indirect Field-Oriented Control (IFOC)

Introduction

In the industry, induction motor is famously known as workhorse of the industry. The advances in variable speed induction motor drives have an ample history even beyond four decades. Existing sophisticated industrial drives are derived after extensive research and refinement.. The starting era of variable speed induction motor drives can be recalled from 1960s, with the emergence of the silicon controlled rectifier (SCR). During that period the principle of speed control was based on steady state concerns of the induction machine. To date, one of the techniques is the v/f control , which is commonly used for the open-loop speed control of drives with low dynamic requirements. In addition, there is another well-known control technique, named as; the slip frequency control method that is widely known to create better dynamics. Until the field oriented control (FOC) became the industry’s standard for AC drives with dynamics close to that of DC motor [1], the above-mentioned method was adopted in all high performance induction machine drives.. Therefore, the commonly known vector control or the field-oriented control was one of the integral inventions in AC motor drives which widened the opportunities for the researchers to enhance the control performance through research and development programs.. Although, by other aspects, there are many process control benefits that might be provided by an adjustable speed drive such as, smoother operation, better acceleration control, different operating speeds for each process recipe, compensation of changing process variables, allowance of slow operation for setup purposes, adjustment to the rate of production, accurate positioning, control on torque or tension and energy saving.

There are many published control techniques and commercially available tools to provide a controller for VSD (describe the full form of VSD somewhwre in your text before) in order to ensure a high degree of reliability and performance. For instance, [2] using a PLC for controlling an inverter to drive an IM but this method is more towards monitoring and protection and control analysis aspects are not fully considered. In [3], the system was evaluated when subjected to sudden changes in the reference and the optimization of PI coefficients using Ziegler-Nichols method and Genetic-Adaptive Neuro-Fuzzy Inference System (ANFIS) model but without control analysis. In [4], the work was on the PLC based hybrid-fuzzy control for PWM-driven VSD with constant V/f ratio that depended upon s-domain transfer function mathematical model of a real plant. However, the optimizations of the controller's performance against external disturbances were not considered.

In this research study, a model of a three-phase induction motor will be derived using mathematical modeling principles. The model will be executed using MATLAB/Simulink software. Based on indirect field oriented control principles, the controller will be designed, which will be implemented on the model later.

Field-oriented control

The induction motor dynamics can be modeled in higher order mathematical equations that falls under one of the VSD control classifications as shown in Figure 1.

Steady state models of induction machines are useful in studying the performance of the machine in steady state only. This means that all electrical transients are neglected during load changes and stator frequency variations. Such variations arise in applications involving variable speed drives. The variable speed drives are converter-fed from finite sources unlike the utility sources, due to the limitations in the switch ratings and filter sizes. This results in their incapability to supply large transient power. Consequently, there is a dire need to evaluate the dynamics of converter-fed variable-speed drives. Firstly, it will substantially assess the adequacy of the converter switches for a given motor and secondly, the interaction of converter switches will help to determine the digression of current and torque in the converter and motor.

Figure 2 shows the block diagram of the indirect field oriented control model for an induction motor that would be useful for the derivation of the state-space model. The prompt effects of inconsistent voltages/currents, stator frequency, and torque disturbance will be considered in the dynamic model..

Induction motor control strategies

Vector control

Scalar control

Sensorless

With speed sensor

With speed sensor

Open loop

Sensorless

Direct torque control

Field-oriented vector control

Air flux-oriented vector control

Rotor-oriented vector control

Stator-oriented vector control

Indirect

Indirect

Indirect

Direct

Direct

Direct

Natural field orientation

The classifications of variable speed induction motor drives

3-phase Inverter

PWM Modulator

d,q

Flux Controller

Torque Controller

Field weakening

Velocity Controller

d,q

a,b,c

M

Sensor

Measured Stator AC Currents

Clarke

Park

Rotor Angle

Rotating Reference Frame Stator Currents

Applied Stator AC Voltage

Rotating Reference Frame Stator Voltage

Target Velocity

Indirect Field Oriented Control model block diagram for induction motor drive

Mathematical formulas

The dynamic model of the induction motor is derived by using a two-phase motor in direct and quadrature axis. The description of the notations, used through out the paper, is given in Table 1. The state space model of induction motor, in a stationary reference frame, can be derived with the help of voltage and flux linkage equations of induction motor in the arbitrary reference frame [5]; as follows:

Voltage equations:

Flux linkage equations:

The final state space model of induction motor in a stationary reference frame can be written as shown in equations (7)-(12) below:

The uniqueness of this work will be the implemention of PI-controller on a state-space model. The state-space models of induction machines are useful to study the performance of the machine in steady state, to ensure the stability of the system.

Nomenclature

d- and q-axis stator current components respectively and expressed in stationary reference frame

d- and q-axis rotor current components respectively and expressed in stationary reference frame

Magnetizing inductance

Self-inductance of the stator and rotor respectively

The resistance of a stator and rotor phase winding respectively

Electromagnetic torque and Load torque reflected on the motor shaft respectively

d- and q-axis stator voltage components respectively and expressed in stationary reference frame

Leakage resistance of the stator and rotor respectively

d- and q-axis stator flux components respectively and expressed in stationary reference frame

d- and q-axis rotor flux components respectively and expressed in stationary reference frame

Mechanical and electrical angular rotor speed respectively

Synchronous speed or dominant frequency

Number of pairs of poles

Operator

The inertia of the rotor

The damping constant which represents dissipation due to windage and friction

Development of im model

The state space model of induction motor, in a stationary reference frame, can be derived with respect to the voltage and flux linkage equations. This phenomenon will provide better dynamics. The controller and the model will be developed on MATLAB/Simulink. A set of first order differential equations, describing the induction motor in a state space stationary reference frame mentioned in the problem formulation section (where is this section??), will be used to develop the model [6]. The S-function and the related IM parameters will also be used, as mentioned in Table 2.

Parameters

Figures

Figures 3 and 4 show the simulated stator currents, while the simulated rotor fluxes are depicted in Figures 5 and 6. Figures 7 illustrates the electrical angular rotor speed for a given reference speed; whereas the electromagnetic torque, as reflected on the motor shaft, is given in Figure 8.

C:\Users\user\Desktop\Figures for UTP Conf\Ids.bmp

Showing d-axis stator current components in stationary reference frame

C:\Users\user\Desktop\Figures for UTP Conf\Iqs.bmp

Showing q-axis stator current components in stationary reference frame

C:\Users\user\Desktop\Figures for UTP Conf\lamda_dr.bmp

Showing d-axis rotor flux components in stationary reference frame

C:\Users\user\Desktop\Figures for UTP Conf\lamda_qr.bmp

Showing q-axis rotor flux components in stationary reference frame

C:\Users\user\Desktop\Figures for UTP Conf\speed_r.bmp

Electrical angular rotor speed

C:\Users\user\Desktop\Figures for UTP Conf\Torqu.bmp

Electromagnetic torque reflected on the motor shaft

Up to this point, the developed model was based on the d-q equations, which portrayed some preliminary results. This could be a good moment to superimpose a PI control algorithm on the model before the start of rigorous work on much more advanced level of control strategies..

Field-Oriented Control and PI Parameters

Filed oriented control is the most well-known control technique of AC induction motors. The formulation for the electromagnetic torque of the smooth-air-gap machine is alike the formulation for the torque of the separately excited DC machine, in particular reference frames, In the instance of induction machines, the control is usually subjugated in the reference frame (d-q), which is appended to the rotor flux space vector [7]. Due to this reason, the processing of vector control needs information on the modulus and the space angle (position) of the rotor flux space vector. Flux and torque-generating components are the major part of the stator currents of the induction machine, which are produced by the utilization of transformation to the d-q coordinate system.

The transformation matrix is mainly used to transform the physical abc variables (e.g., Voltages, flux-linkages) into the d-q variables in the synchronously rotating reference frame, in which sinusoidal variables will be seen as the DC-based quantity. The voltage, flux-linkage, torque equations in abc axis can be transformed into the d-q axis voltage equations in the arbitrary reference frame. It is noticeable here that these rotor resistance, rotor inductance, rotor current, rotor voltage and rotor flux linkage are already referred to the stator circuit by using the fictitious turn ratio (this concept is similar to the turn ratio in transformer). So, the superscript (’) will be removed for the rotor quantities referred to the stator circuit. Figure 9 illustrates the implementation of the PI-controller on the IM-model via field-oriented control approach. However, Figure 10 illustrates the speed closed loop transfer function and the process of selection of the speed PI-controller parameters.

Indirect vector control model block diagram layout IFOC and SVM

ωr +

-

Te

The Speed closed loop transfer function

For the current PI-controller parameters, the current controller in the synchronous rotating reference frame will be designed because in the synchronously rotating reference frame, sinusoidal variables will be seen as DC-based quantity. Figure 12 and Figure 13 illustrate the current; Ids and Iqs as a closed loop transfer function respectively. Therefore, the controller parameters have been chosen as a function of settling time.

i*ds +

-

The Current Ids closed loop transfer function

i*qs +

-

The Current (Iqs) closed loop transfer function

Figures

The simulation results of the PI speed controller, for indirect vector control of induction motor, were run for three seconds. While the motor started from standstill at t=0 and reached the rated speed of 200 rad/sec and the load torque of TL=0 as shown in Figure 13. Figure 14,15 and 16 shows the related torque and current profiles.

C:\Users\user\Desktop\Figures for UTP Conf\FOC\speed.bmp

Speed (ωr) response

C:\Users\user\Desktop\Figures for UTP Conf\FOC\torque.bmp

Torque (Te) response

Comparing the response of closed loop for the Te (Figure 14) with its counterpart in the open loop system (Figure 8), one can clearly see the better response in the closed loop system as well as its attachment to the pre-set value. Ids kept the rotor flux density at its rated value due to which it was maintained constantly, as shown in Figure 15.

C:\Users\user\Desktop\Figures for UTP Conf\FOC\ids.bmp

Closed loop Ids response

It can also be observed that the closed loop system response was tracking the desired value. The response of motor speed (ωr) of closed loop system reached the desired value in a smooth manner (Figure 13) and therefore, kept steady. While the open loop response shot up and delayed (Figure 7).

C:\Users\user\Desktop\Figures for UTP Conf\FOC\iqs.bmp

Closed loop Iqs current component response

Vds and Vqs were generated from Ids and Iqs and can be seen as DC while Va and Vβ that were calculated from Vds and Vqs can be observed as time varying components, that is why the controllers have been designed in the d-q synchronously reference frame, as illustrated in Figures 17,18,19 and 20.

C:\Users\user\Desktop\Figures for UTP Conf\FOC\Vds.bmp

Vds response

C:\Users\user\Desktop\Figures for UTP Conf\FOC\vqs.bmp

Vqs response

C:\Users\user\Desktop\Figures for UTP Conf\FOC\Va.bmp

Va response

C:\Users\user\Desktop\Figures for UTP Conf\FOC\Vb.bmp

Vβ response

From the above results it is concluded that the model performed according to the expectations when a set of tests was corroborated with a PI-controller.

Conclusions

The primary emphasis of the current work was put on the formulation, development and modeling of an IM PI-model and its controller for VSD modeling via field-oriented approach. The developed IM model could be used to augment more advanced controllers, which could further be studied to improve the IM VSD performance.

Acknowledgment

The authors want to acknowledge the support from the Universiti Teknologi PETRONAS through their Graduate Assistantship Scheme.