Predictive Torque Control of an Induction Motor Fed by Five-to-Three Direct Matrix Converter Omar Abdel-Rahim1, IEEE Student Member, Omar Ellabban2, 3, IEEE Senior Member, Haitham Abu-Rub2, IEEE Senior Member 1 Electrical Engineering Department, Aswan Faculty of Engineering, Aswan University, Aswan, Egypt, 81542. 2 Electrical and Computer Engineering Department, Texas A&M University at Qatar, Doha, Qatar. 3 Electrical Machines and Power Engineering Department, Helwan University, Cairo, Egypt.
[email protected] multiphase machines need to be converted into three phase to enable connection with the utility grid or to feed a load. There are too many techniques to do that, one of them is convert the output of multiphase generator into DC voltage and then a three phase inverter is used to convert DC voltage into ac three phase voltages and another direct conversion technique is the use of a matrix converter. Direct matrix converter is able to convert ac voltage into ac voltage with different amplitude, frequency and different number of phases. It is also considered as a powerful tool for AC to AC power conversions, so that they receive considerable attentions nowadays. This is due to inherent advantages such as bi-directional power flow, which is very important in regeneration process, nearly sinusoidal input and output waveform, controlled input power factor, output current amplitude and frequency are also controlled, compact design and lack of dc-link capacitors for energy storage. There are many configurations that have been developed for matrix converter in the literature [11]-[12]. A five to three matrix converter is able to convert a five phase input into a three phase output voltages. It has fifteen switches as each output phase is connected to all the input phases through a bidirectional switches, and hence, there are approximately are 2 expected switching states. But with taking into account the two constraints: input phases should not be short circuited together and output phases should not interrupt under any condition, due to the presence of inductive loads. Accordingly, the switching states are limited to 125. This paper proposes a Predictive Torque Control (PTC) for a three-phase IM using a five-to-three direct matrix converter. The idea of using a five-to-three direct matrix converter is to enable using multiphase generation units without changing the existing loads or the three-phase grid. This paper provides: the three-phase induction motor model, analysis for the five-tothree direct matrix converter and the PTC algorithm description.
Abstract—Direct matrix Converter is considered as a powerful tool for AC/AC power conversion providing AC output voltage and frequency control. It also has many features such as a bidirectional power flow, a compact size and a direct conversion capability. In this paper, matrix converter is used to convert a five phase input voltage into three phase output voltage with controlling output current amplitude and frequency. Five-to-three phase matrix converter is used to control a three phase induction motor. Using a five-to-three phase matrix converter enables using multiphase generation units and at the same times there is no need to change existing three phase loads. Predictive Torque Control (PTC) algorithm is used to control the induction motor fed by a matrix converter. The performance of the proposed speed control system is verified by a MATLAB simulation of a 4 kW induction motor fed by a five-to-three phase matrix. The simulation results during different operation modes verify the validity of the proposed closed loop speed control method. Keywords— Direct Matrix Converter, Predictive Torque Control.
I.
INTRODUCTION
For a long period, Field Oriented Control (FOC) Direct Torque Control (DTC) were the two control strategies that dominate the electrical drives for high performance applications [1]-[4]. Predictive control is considered a very promising control for the power converters and electric drives, due to its inherent advantages. Predictive control has many advantages that make it a real option if high dynamic control of electrical drives is required: The concept is easy to understand and implement, constraints and nonlinearities can be included and multivariable case can be considered [5]-[8]. The main idea of the predictive control is based on the calculation of the future system behavior and then uses this calculation to determine the optimal values for the actuating variables. The predictive control algorithm used for an induction motor (IM), could be divided into three main steps: estimation of the variables that cannot be measured, like stator and rotor fluxes, prediction of the future plant behavior and finally optimization of outputs according to reference conditions. Inherent advantages of multiphase generators such as higher output power, reduced phases losses, reduced sized for the same amount of output power compared to three phase generator make it challenging and a suitable solution for Wind Energy Conversion System (WECS). But as all the available grid and loads all over the world are three phase , the output of
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II.
DYNAMIC EQUATIONS OF THE THREE-PHASE INDUCTION MOTOR
By utilizing the definitions of the fluxes, currents and voltages space vectors, the dynamic equations of the threephase IM in stationary reference frame can be written into the following mathematical form [13]. (1)
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S S S S S 1 (7) Matrix converter, depicted in Fig. 1, uses a set of bidirectional switches to connect five-phase input supply to a three-phase load and enables bidirectional power flow. The relation between input and output voltage of the five-to-three phase matrix converter is as follow: .
IV.
(3) (4)
A. Flux Estimation
(2)
is the stator voltage space vector, and are the where stator and rotor current space vectors, respectively, and is are the stator and rotor flux space vectors, respectively, the rotor angular speed, and are the stator and rotor and are the stator, rotor resistances, respectively, , and mutual inductance, respectively. The electromagnetic torque is expressed in terms of the cross product of the stator and the rotor flux space vectors as: sin
Estimations of the stator flux and the rotor flux , at the present sampling step k, are required. Stator and rotor flux estimation could be calculated using the following equations: 1 . . . (9) . . . (10) B. Stator Flux and Electric Torque Prediction Prediction of the stator flux and the electromagnetic torque at the sampling step k + 1 is a necessity as they represent the 1 control variables in PTC. The stator flux prediction is obtained by means of the stator voltage equation (1) and by using the Euler formula to discretize (1) and shifting the result to a single time step, the stator flux prediction is obtained, as: 1 . . . (11) The electromagnetic torque prediction depends on the stator flux and stator current predictions according to, 1 (12) . . 1 . 1 1 is The prediction expression of the stator current obtained using the equivalent equation of the stator dynamics of a squirrel-cage induction motor, as [15]:
(5)
where γ is the load angle between stator and rotor flux space vectors, is the number of pole pairs of the motor and ⁄ is the dispersion factor. The motion 1 equation is as follows: (6) Where is the motor’s inertia and is motor’s friction constant. III.
PREDICTIVE TORQUE CONTROL
The schematic of the proposed system is depicted in Fig. 2, the proposed system consists of five-phase generator, five-tothree phase direct matrix converter, IM and the control system is PTC [14]. As shown in the schematic, a PI controller is used to generate the required reference torque to achieve the required speed. IM’s stator voltages, currents and its speed are feed to the PTC algorithm then the PTC does the following steps: estimate stator and rotor fluxes, then, predict all possible states for the machine’s torque and flux, finally, according to the cost function, PTC chose the switching state that gives the optimum torque and flux. These steps and equations for the PTC are described in the following sections and represented in Fig. 3.
Fig. 1: A five-to-three direct matrix converter topology
0
(8)
FIVE-TO-THREE DIRECT MATRIX CONVERTER
A five-to-three phase direct matrix converter is able to convert five-phase input voltages into three-phase output voltages with the required voltage amplitude and frequency. General topology of the five-to-three matrix converter is depicted in Fig. 1. There are fifteen bidirectional power switches, five switches for every output phase. The Switching pattern is defined as follow: S 1 for closed switch and 0 for open switch, with , , , , and , , . The constrains for switching operation is defined as follows:
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.
.
.
(13)
is the sampling time used in the PTC algorithm, . corresponds to the equivalent resistance, is the leakage inductance of the machine. Thus, replacing the derivatives with the Euler formula in (13), the
Where
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prediction equation of the stator current is at the instant k + 1 is obtained 1 .
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1
.
.
.
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(14)
C. Cost Function Optimization The final step in Predictive Control is the optimization using the cost function. Cost function determines the control parameter. In this paper the control parameter are stator flux and electromagnetic torque so the structure of the cost function will be as follow: 1 . 1 (15) Where denotes the index of the stator voltage vector used to 1 , calculate the predictions 1 and respectively. In (15), the torque reference is externally generated by a PI speed controller. The factor denotes a weight factor, which increases or decreases the relative importance of the torque versus flux control. If the same importance is assigned to both control objectives, this factor would correspond to the ratio between the nominal magnitudes of the torque and stator flux [14] as:
Fig. 2: Schematic of the proposed system
(16) Finally, the optimization step is carried out, and the inverter voltage vector that minimizes (16) is selected as the optimal switching state for the next sampling period k + 1. V.
RESULTS AND DISCUSSION
In this section simulation results are presented in order to verify the performance of the proposed system, MATLAB/SIMULINK platform was used as a simulation tools for a 4 kW induction motor using the parameters in Table I. Figs. 4-7 show the five-to-three direct matrix converter fed induction motor response during the motoring and regenerative braking operation modes. The system is operated in different operation modes, as shown in Fig. 4: the acceleration mode with no load during the time interval 0-0.5 sec; no load operation with rated speed during the time interval 0.5-1 sec; the steady state operation mode with half the rated torque and the rated speed during the time interval 12 sec, then from 2-3 sec, the motor was loaded with its nominal load with rated speed, from 3-4 sec the motor is reversing it speed with the rated torque; finally, during the time interval, the motor is running with rated torque with negative rated speed. Fig. 5 shows, load torque and generated electromagnetic torque. Stator current and voltage are depicted in Fig. 7 and Fig. 6, respectively.
Fig. 3: PTC Algorithm
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TABLE I.
Parameter Input Filter parameters Cf Rf Lf Machine parameters Output power RMS line voltage No. of poles Stator resistance, Rs Rotor resistance, Rr Stator inductance, Ls Rotor inductance, Lr Mutual inductance, Lm Inertia, J Fraction factor, F
MACHINE PARAMETER
Value 21µF 0.5 Ω 500 µH 4 KW 400 V 4 1.2 Ω 1 Ω 175e-3 mH 175e-3 mH 170e-3 mH 0.062 Kg m^2 0.002985 N.m.s
Fig. 6: steady state output voltage of the five-to-three matrix converter
Fig. 4: Reference and measured speed during different operation modes
Fig. 7: Stator current of induction motor during different operation modes
VI.
CONCLUSION
This paper presents a five-to-three direct matrix converter based IM drive. Using a five-to-three gives the opportunity to use multiphase generation without affecting the existing threephase loads. The predictive control strategy presented in this paper provides simple and effective control method of an induction motor. With the proposed algorithm, there is no need for modulation techniques or adjustment of linear current controllers. The control strategy is tested during different operation modes (acceleration, steady state, regenerative braking). MATLAB simulations results verify the validity of the proposed control strategy. Fig. 5: Load and electromagnetic torque during different operation modes
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ACKNOWLEDGMENT This publication was made possible by an NPRP (NPRP 4 077 - 2 - 028) grant from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.
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