Effects of PWM Chopper Drive on the TorqueSpeed Characteristic of DC Motor Ayetül Gelen
Saffet Ayasun
Department of Electrical and Electronics Engineering, Nigde University, Nigde, 51100, TURKEY
[email protected] [email protected]
Abstract-This paper describes a MATLAB/Simulink realization of the DC motor speed control method by controlling the voltage applied to the armature circuit using a pulse width modulated (PWM) chopper drive. Torque-speed characteristics are obtained for different values of switching frequency to demonstrate its effect on the linearity of the characteristic. The proposed simulation model is developed as a part of a software laboratory to support and enhance undergraduate electric machinery courses at Nigde University, Nigde, Turkey.
I.
INTRODUCTION
Computer modeling and simulation tools have been extensively used to support and enhance electric machinery courses. MATLAB with its toolboxes such as Simulink and SimPowerSystems [1] is one of the most popular software packages used by educators to enhance teaching the transient and steady-state characteristics of electric machines [2, 3]. There is an ongoing effort to restructure and modernize electric machinery courses at Nigde University, Turkey by integrating computer simulations into both lecture and laboratory parts. For that purpose, simulation models of transformer and induction motor’s tests have already been developed using MATLAB/Simulink, and successfully integrated into a third-year electric machinery course [4, 5]. A software laboratory was designed to enable students to simulate the no-load and short circuit tests of transformers, and DC, no-load and blocked-rotor tests of induction motors. We have experienced that the simulating transformer or induction motor tests before the hardware experiments help students clearly understand the experimental procedure, and simulation models complement laboratory practices [4, 5]. In order to have a complete set of simulation tools for electric machinery experiments, simulation models of speed control experiments of DC motors, namely field resistance control, armature voltage control, and armature resistance control methods [6] need to be developed and included in previously designed software laboratory. In practice, the armature voltage control method is commonly used to control the DC motor speed. In such a case, DC motors are driven from a power electronic converter such as a controllable rectifier or PWM chopper. Therefore, nonlinear torque-speed characteristics might be observed in the motor performance [7]. This paper presents a MATLAB/Simulink model of a DC motor speed control method in which a PWM chopper drive is used to control the voltage applied to the armature. Torque-
speed characteristics are obtained for different values of switching frequency to demonstrate its effect on the linearity of the characteristic. It is observed that torque-speed curves become linear as the switching frequency increases. The simulation models of DC motors together with previously designed models [4, 5] have been integrated into electric machinery courses to enhance the teaching the steady-state and dynamic analysis of DC motors. The enhancement has been achieved by using the simulation models for various educational activities such as classroom demonstration, exercises and assignments. It is observed that with the help of simulation results they obtain, student increase their understanding of DC motor characteristics and dynamic behavior, and power electronic converters beyond the understanding they gain from classroom lectures and textbooks. II. TORQUE-SPEED CHARACTERISTIC AND SPEED CONTROL METHODS The dynamic and steady-state models are needed to examine the response of the motor speed to sudden changes using feedback control system, and to analyze the torquespeed characteristics using the equivalent circuit. The schematic representation of the model of a shunt DC motor is shown in Fig. 1. In this figure, vt is the terminal voltage applied to the motor, i f , R f , and L f are the current, resistance, and inductance of the field circuit, respectively; ia , Ra and La are the current, resistance, and inductance of the armature circuit; respectively; ea is the generated speed voltage; ωm is the angular speed of the motor; Te and Tl are the electromagnetic torque developed by the motor and the mechanical load torque opposing direction. The generated speed voltage and electromagnetic torque are given by [6, 8]:
ea = Kφωm
(1)
Te = Kφ ia
(2)
where K is the design constant depending on the construction of the motor. The dynamic performance of the motor is described by these equations together with the differential equation of the mechanical system and voltampere equations of the armature circuit. These equations are given by
IEEE International Universities Power Engineering Conference, (UPEC 2008), pp: 1068-1071, DOI: 10.1109/UPEC.2008.4651640, 1-4 September 2008, University of Padova, Italy.
Fig. 2. The torque-speed characteristic and the effect of armature voltage change on it.
Fig. 1. The equivalent circuit of a shunt DC motor.
J
d ωm + Bωm + Tl = Te dt
vt = va = ea + Ra ia + La dia dt
(3)
where J is the combined moment of inertia of the load and the rotor, B is the equivalent viscous friction constant of the load and the motor. The steady-state model of a DC motor can easily be obtained from the dynamic model represented by (1)-(4) by neglecting the armature inductance and by assuming constant speed as follows
Ea = Kφωm
(5)
Te = Kφ I a
(6)
Vt = Va = Ea + Ra I a
(7)
From these equations, we can gain an understanding of the torque-speed characteristics of a DC motor. Using (5)-(7) and equivalent circuit of Fig. 1 under the steady-state conditions, the torque-speed characteristic of a shunt DC motor is described by
ωm =
Vt Ra − Te Kφ ( Kφ )2
Scope2
Pulse Generator
(4)
(8)
Equation (8) indicates the speed of a DC motor can be varied by controlling the field flux, the armature resistance or the terminal voltage applied to the armature. The three most common speed control methods are field resistance control, armature voltage control and armature resistance control methods [6, 9]. Since this paper presents Simulink model of speed control method by controlling the terminal voltage applied to the armature using a PWM chopper drive, only the armature voltage control method is briefly described in this section.
DC Motor
Load Torque
Scope1
300
TL
m
DATA g
m
a
k
GTO
A-
Clock
+
i -
F+
Load current
FW Diode U = 350 V
dc
A+
F-
Scope3 + v -
w Scope5
240 V VF
Load voltage
0
In Mean
Display Scope4 DATA1 Clock1
0 Display1
Fig. 3. Simulink realization of armature voltage speed control method using a PWM chopper drive.
In the armature voltage control method, the voltage applied to the armature circuit, Vt is varied without changing the voltage applied to the field-circuit of the motor. As (8) indicates, the torque-speed characteristic is represented by a straight line with a negative slope when the DC motor is driven from an ideal DC source. This characteristic is illustrated in Fig. 2. In order for the speed of the motor vary linearly with torque, the terminal voltage Vt and the flux φ must remain constant as the load changes. Typically a rectifier or a motor-generator set is required to provide the controlled armature voltage for the motor whose speed is to be controlled. Observe that the no-load speed of the motor increases while the slope of the curve remains unchanged since the flux is kept constant in this method. By the armature voltage control method, it is possible to control the speed of the motor for speeds below base speed but not for speeds above base speed. In order to achieve a speed faster than the base speed, an excessive armature voltage is required, which possibly damages the armature circuit. III. SIMULINK MODEL OF THE SPEED CONTROL METHOD In this section, MATLAB/Simulink model of PWM chopper based speed control method is presented and performance of the DC motor driven from a PWM chopper
In order to investigate the effect of armature voltage on the torque-speed characteristic, three different armature voltages with average values VT = 180 , 240 and 300 V are applied while the voltage applied to the field circuit is kept constant at its nominal value 240 V. A constant 350 V DC is applied to the input of PWM chopper. The average value of the chopper output is changed by changing the duty ratio (D). A pulse generator is used to change the duty ratio, and switching frequency is initially selected as f s = 50 Hz . The following duty ratios are used to obtain 180, 240 and 300 V average output voltages applied to the armature: D = 0.514, 0.685 and 0.857 . The torque-speed characteristics are obtained for these armature voltages. Fig. 4 shows the torque-speed curves f s = 50 Hz . It is clear that torque-speed curves contain both linear and nonlinear regions. The linear region of operation for 300V approximately starts at TL = 75 Nm and a perfect linearity begins at TL = 250 Nm. For 240 V torque-speed curve is linear for TL > 125 Nm . Finally, torque-speed curve becomes linear for TL > 150 Nm for 180 V. The discontinuous armature current results in a highly non-linear torque-speed characteristic.
180 V 240 V 300 V
225 200 175
w (rad/s)
150 125 100 75 50 25 0
0
25
50
75
100
125 150 175 200 Load Torque (Nm)
225
250
275
300
Fig. 4. Torque speed characteristics for f s = 50 Hz .
450 Load Voltage 400 Load Current (A) and Load Voltage (V)
IV. SIMULATION RESULTS
250
350 300 250 200 150 Load Current 100 50 0 -50 0.32
0.33
0.34
0.35
0.36 Time (s)
0.37
0.38
0.39
0.4
Fig. 5. Armature current and voltage for 180 V and 50 Hz at 50 Nm.
350 300 Load Current (A) and Load Voltage (V)
drive is analyzed. A 5-HP DC motor of 240-V rating 1220 r/min is used in the simulation model. The equivalent circuit parameters of DC motor used in the simulation are R f = 240 Ω , L f = 120 H , Ra = 0.6 Ω , La = 12 mH . Fig. 3 shows the Simulink realization of this method. The armature circuit is supplied from a PWM chopper in which a Gate Turn-off (GTO) thyristor is used as an electronic switch and a freewheeling diode is used to solve the stored inductive energy problem in the circuit. The field circuit is separately excited from an ideal DC voltage source as 240 V. A DC motor block of SimPowerSystems toolbox is used. An access is provided to the field connections (F+, F-) so that the motor model can be used as a shunt-connected. The field circuit is represented by an RL circuit, ( R f and L f in series) and is connected between the ports (F+, F-). The armature circuit consists of an inductor La and resistor Ra in series with an electromotive force EA and is connected between the ports (A+, A-). The load torque is specified by the input port TL . The electrical and mechanical parameters of the motor could be specified using its dialog box. The output port (port m) allows for the measurement of several variables, such as rotor speed, armature and field currents, and electromechanical torque developed by the motor. Through the scope and display block, the waveform and steady-state value of the rotor speed can be easily measured in radian per second (rad/s).
250 200 150 100 50 0 Load Current
Load Voltage -50 0.32
0.33
0.34
0.35
0.36 Time (s)
0.37
0.38
0.39
Fig. 6. Armature current and voltage for 180 V and 50 Hz at 250 Nm.
0.4
Fig. 5 and Fig. 6 show the armature voltage and current obtained at 50 Nm (in the non-linear region) and 250 Nm (in the linear region) for average value of 180 V. These figures clearly illustrate the discontinuous and continuous operation of the PWM chopper drive in non-linear and linear regions, respectively. Fig. 7 shows torque-speed curves for f s = 150 Hz . When it is compared with Fig. 4, it is clearly seen that for all voltage values linear region of operation extends when the switching frequency is increased. For example, the region between 0 and 150 Nm was nonlinear for 180 V armature voltage for f s = 50 Hz . For f s = 150 Hz , the size of nonlinear region is shrunk to the region between 0 and 50 Nm. This is because of the fact that armature current becomes continuous and smoother when the switching frequency is increased. Fig. 8 shows armature voltage and current obtained at 50 Nm (in the linear region) for average value of 180, clearly illustrating the continuous operation of the PWM chopper drive.
V. CONCLUSIONS A Simulink model of DC motor speed control method which is realized using a PWM chopper is presented. Torquespeed curves for two different switching frequencies are obtained for a wide-range of loading conditions. It is shown that torque-speed curves become nonlinear due to the discontinuity in armature current. Moreover, linearity of curves could be improved by increasing the switching frequency of the PWM chopper drive. REFERENCES [1] [2]
[3] [4]
250 180 V 240 V 300 V
225 200
[5]
175
w (rad/s)
150
[6] 125
[7]
100 75
[8] 50
[9]
25 0
0
25
50
75
100
125 150 175 200 Load Torque (Nm)
225
250
275
300
0.37 0.372 0.374 0.376 0.378 Time (s)
0.38
Fig. 7. Torque speed characteristics for f s = 150 Hz .
400 Load Voltage
Load Current (A) and Load Voltage (V)
350 300 250 200 150 100 50 0 Load Current -50 0.36
0.362 0.364 0.366 0.368
Fig. 8. Armature current and voltage for 180 V and 150 Hz at 50 Nm.
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