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Journal of Green Engineering (JGE) Volume-9, Issue-1, April 2019
Investigations on Transient Behavior of an Energy Conservation Chopper Fed DC
Series Motor Subjected to a Change in Duty Cycle
Sunil Thomas1, Nithiyananthan Kannan
2, Aliakbar Eski
3
1Department of Electrical and Electronics Engineering, Birla Institute of
Technology and Science, Pilani, Dubai, UAE. E-mail: [email protected]. 2Department of Electrical Engineering, Faculty of Engineering,
King Abdulaziz University, Rabigh, Kingdom of Saudi Arabia. E-mail :[email protected]. 3Embedded Systems Designer, NanoLeaf, Toronto, Canada.
E-mail: [email protected].
Abstract This paper throws light on the transients that occur in a direct current series
motor fed through a direct current chopper which has been subjected to a
change in duty cycles. In this work it has been considered a direct current
series motor running at a constant speed powering a stable and constant
load when a sudden change in the input t006F the motor from the energy
conservation direct current chopper occurs. This sudden changes is
simulated as the changes that an operator would require to do for e.g. in a
lift or a traction motor application scenario. Various parameters such as
current, voltage and torque are simulated and plotted during the transient in
an effort to understand their variation and changes during the transient
period of change. Different loads are considered and the authors observe
the difference in the variation of the parameters. The plots are then
analyzed so as to develop an understanding and methodology of designing
motors and control systems that provide an adequate response to the
changes as required and as quickly as possible.
Keywords: DC Chopper, DC Series Motor, Duty cycle, Simulation,
Transient analysis.
Journal of Green Engineering, Vol. 9_1, 92–111. Alpha Publishers
This is an Open Access publication. © 2019 the Author(s). All rights reserved
93 Sunil Thomas et al
1 Introduction
DC Series motors are a popular type of DC motors in which the field
coil is in series with the armature. They are widely used as traction motors
due to their high starting torque capability and in washing machines, fans or
vacuum cleaners due to their high speed capability. Both these properties
are specific to the series motor due to its specific connection. The series
connection of the motor results in a large startup current. Due to this series
connection the torque has a square dependency on the armature current and
hence the startup torque is of a remarkably high magnitude. As the motor
speeds up this current quickly decays to zero. Due to the series connection
the back emf too depends on armature current and hence in an effort to
keep back emf as close to supply voltage the motor has an ideal maximum
speed of infinity. But due to the real life non ideal effects of friction the
motor draws a non zero current which keeps the speed in check, but it„s still
very high. It„s for this reason DC series motors are never run on a no-load
condition. These motors are also capable of running off AC supply and
hence are called Universal motors also. Since the torque is dependent on
the square of the current, its unaffected by the polarity of the current and
maintains its direction. The back emf depends on the current on the other
hand and hence depends on the polarity which changes every half cycle.
Large number of research work has been reported on computer
applications on Electrical Engineering. [1-31] and a significant amount of
work has been done in the field of transient analysis of power electronics
and motors. There has been work in developing an Equivalent circuit model
of a Series motor and analyzing it. Based on this research has been carried
out to improve the computation time in simulation of high frequency
switching devices interfaced with DC series motors [32-37]. Analysis have
conducted to understand the feasibility of such machines in various fields
such as hybrid and electric drives in various modes [38, 40]. There has been
research to analyze Dc series motors with choppers in regenerative braking.
The use of computers in simulation is almost ubiquitous. A significant
amount of research has gone into to trying to make computer simulations
feasible for such system„s [35]. Along with this, there have been
publications analyzing different kind of speed control techniques for
various applications of DC Series motors [37, 39, 41].
A notable work [42] has been reported in literature which describes the
operation of a Four Quadrant DC Chopper (FQDC) for Drive. Now a days
the applications of DC to DC converter is very much essential in Power
electronic related industries. Since may industries requires DC source at
different levels at different levels DC chopper plays vital role as source
device. The variable DC source voltage improves the efficiency of the
applications in the industry and it also improves the control mechanism of
the equipment‟s involved in the process. DC choppers are used in various
Energy Conservation Chopper Fed DC Series Motor 94
applications such as trolley buses, electric vehicles, process industries etc.
DC to DC chopper is a static power electronic device which provides
constant power supply with the conversion of variable power supply. DC-
DC chopper is considered as high speed switches with connects and
disconnects the load from the variable DC source according to the
requirements. A novel algorithm [43] is proposed to introduce a new
concept for identification of various system parameters to operate the motor
drive in stable condition. The operation of Chopper in DC Series motor has
been discussed say for example, to perform several modes of operation
such as driving, field weakening, regenerative braking, resistive braking,
generator, reverse and parallel mode driving. However the introduction of
power electronic converter especially chopper would also introduce noise
to the system resulting in poor dynamics of the system. A large number of
works related to above statement has been reported in literature [44-50].
The authors of this paper however have now analyzed the transients during
the changes in duty cycle of not only the motor but considering the motor-
chopper system on a whole. The duty cycle is changed first manually and
then through a control algorithm of proportional control in order to bring up
the motor to a specific set speed. This control could have been part of an
Electric Car„s rotational speed controller mechanism. Transient analyses for
power electronic circuits are more important to conduct and just as harder
to carry out.
Since power electronic circuits switch at a much higher frequency,
simulation time steps have to be much smaller and the simulation is much
more computationally intensive. Due to switching, harmonics are
introduced into the system and hence it becomes important to analyze
transients to control the harmonics. Different parameters such as ia, E a and
ω are now closely monitored to keep harmonics in check and this requires
transient analyses to be performed.
The following section will now explain in detail the transient analysis to
be performed.
2 Problem Formulation
The system consists of a DC series motor which is being fed power
through an energy conservation DC chopper. In the first analysis the motor
is initially kept at rest and the entire system is relaxed. The motor has an air
drag load with a coefficient of 0.03. The air drag load is a fan which acts as
an artificial load to limit the speed of the motor as well as to cool the motor.
The system is started to a specified duty cycle. The chopper controls the
voltage through a through time Ratio Control (TRC) in the form of PWM
specified by the duty cycle.
95 Sunil Thomas et al
The Duty cycle is controlled by an operator. Once the motor has
achieved a certain speed, the duty cycle is abruptly switched to another
Value and held at that value, allowing the system to come upto the new
value of voltage specified by the new duty cycle. The duty cycle is then
slowly ramped up to a new value and left there allowing the motor to catch
up. The duty cycle finally abruptly set to another third value allowing the
motor to attain steady state. In the second analysis, the duty cycle is
controlled by a P-D controller which attempts to bring the motor up to a set
speed as quickly as possible. The PD controller is not tuned to its most
optimum setting, but it oscillates as it tries to get the motor upto speed. This
is to show the duty cycle as a nonlinear function and observe transients of
such a change on the entire chopper – motor system. The set point for the
speed is the steady state speed at 50% duty cycle which is 24.1 rad/sec.
Figure 1indicates the circuit diagram of the entire proposed dc series motor
setup and the values of the various parameters and the initial values of the
variables used in the motor is given in Table 1 and Table 2 respectively.
Figure 1 Circuit Diagram of energy conservation DC chopper DC chopper and DC series
Energy Conservation Chopper Fed DC Series Motor 96
Motor the values of the various parameters are as follows:
Supply Voltage (Vs) 100 V
Chopper Series Resistance (Rc) 0.05 Ω
Chopper filter inductance (Lc) 1 H
Chopper filter Capacitance (Cc) 100µF
Armature Resistance, (Ra) 0.08 Ω
Armature Inductance (La) 0.12 H
Field Resistance (Rf) 0.4 Ω
Field Inductance (Lf) 0.72 H
Drag coefficient (B) 0.03 Nm/(rad/s)2
Moment of Inertia (J) 2 kgm/s2
Switching Frequency (fs) 1 kHz
Power MOSFET Current Rating 50 A
Power MOSFET Voltage Rating 200V
Table 1 Parameter Values
ia 0 A
ω 0 rad/sec
ic 0 A
vc 0 V
iL 0 A
Table 2 Initial Variable Values
The Mathematical model of the entire system is setup as follows for the
transient analysis and simulations:
When the MOSFET is ON:
Vs = iLRc + Lc diL/dt + vc (1)
ic = iL – ia (2)
ic = C dvc/dt (3)
97 Sunil Thomas et al
When the MOSFET is OFF:
iLRc + Lc diL/dt + vc = 0 (4)
ic = iL – ia (5)
ic = C dvc/dt (6)
Motor Dynamics
Vc = ia (Ra + Rf) +(La + Lf) dia/dt + kϕω (7)
Kϕ = kfia (8)
Vc = ia (Ra + Rf) +(La + Lf) dia/dt + kωkfia (9)
J dω/dt = k kf ia2 -Bω
2 (10)
For P-D control the Duty cycle calculation
function is included in the system equations:
Duty cycle = 0.5 + kp*error + kd*d(error)/dt (11)
Error = ωset – ω (12)
Where,
kp = 0.025, kd = 0.0125
The above Equations describe the system shown in Fig. 1
3 Simulation Techniques
The system consists of a switching system as well as a nonlinear torque
equation which depends on the square of the current and the square of the
angular speed. These non-linear equations make the system difficult to
solve analytically and hence numerical solutions are the solutions that are
normally looked for. However due to the switching characteristics of the
Power electronics devices, the equations incorporate discontinuous
functions which cannot be described in a finite no. of standard functions for
analytical or numerical solutions by Runge Kutta - order 4 methods. Hence
the best solution is to brute force„and time step through the differential
equation by converting it into a difference equation. In this method every
differential equation is converted into a difference equation by assuming
the infinitesimal change in time to be some extremely small quantity called
the time step. In this case dt = 10µs. This time step is chosen keeping in
mind the value of the Switching Frequency which is kept at 1 kHz. At a
sampling frequency of 100 kHz, 100 samples are taken every one cycle of
the chopper.
In the first analysis the Duty cycle is initially kept at a value of 0.36 for
25% of the total simulation time, which is for 10 seconds. For the next 25%
Energy Conservation Chopper Fed DC Series Motor 98
of total simulation time the duty cycle is ramped up to a value of 0.81. In
the next 25% of the simulation time the duty cycle is once again ramped
down to the value of 0.36. From there for the next 25% the duty cycle is
abruptly changed to 0.54 from 0.36 and kept at that value till the end of the
simulation time. During the second analysis the duty cycle of the motor is
now controlled directly by a P-D controller a given by equation (11-12).
The P-D controller changes the duty cycle in such a way that it attempts to
get the motor upto speed but it overshoots and has to reduce the duty cycle
to slow it down again. It oscillates in such a way and settles to a setpoint.
The controller is not tuned so as to show the effects of non-linear change of
duty cycle on the motor-chopper system.
The duty cycle is re-evaluated every 10 chopper cycles. In real life
systems, the duty cycle may be evaluated faster and even the switching
frequency may be well in the range of 100s of kHz. However for simulation
purposes rates has been checked. The duty cycle is reevaluated every 10
cycles so as to allow the chopper system to settle down at the voltage
specified by the duty cycle before the duty cycle is re-evaluated and a
disturbance is caused again. The motor with a higher mechanical time
constant is not able to settle as fast and hence remains in transient state.
This is seen especially in the state of ramping up/down the duty cycle.The
high accuracy required by the simulation requires the solution of about
900000 equations per second of simulation, which clearly is not possible to
solve manually.
Hence the entire system is converted to difference equations and
programmed into a C# application which steps through the entire solution
till the specified time limit and writes the value of all variables such as ia, ic,
iL, vc, ω to a data file, which is then plotted in MATLAB for interpretation
and verification.
4 Results
4.1 Analysis – I – Du0074y Cycle Changed by an Operator
Figure 2 shows the plot between duty cycle and time. The duty cycle is
started to 36% and kept at that value till 25% of the total simulation time,
i.e. 10 seconds in this case. The duty cycle is then slowly ramped up all the
way to 86% in the next 2.5 seconds and then ramped downwards back to
36% in the next 2.5 seconds. At 7.5 seconds the duty cycle is again abruptly
switched to 54% and kept at that value till end of the simulation time. It is
important to keep in mind these values and the plot since all the other plots
are affected by and are dependent on the duty cycle„s variation with respect
to time.
99 Sunil Thomas et al
Figure 2 Duty Cycle vs Time
Figure 3 shows the plot for armature current vs time. The armature
current is seen to shoot up as the duty cycle is switched to 36%, it quickly
peaks and start dropping, behaving as an under-damped system and
oscillating. However by the 2.5 seconds mark, the duty cycle begins its
ramp upwards to 86%. Due to the low electrical time constant and the
lightweight motor
With low inertia (J = 2kgm/s2) armature current can keep up with the
duty cycle. At the 5 sec mark the duty cycle starts ramping downwards
back to 36%. It takes a few ms for the armature current to track the change
in the duty cycle. At 7.5 seconds as the duty cycle switches to 54%. As the
motor is already in operation, ia doesn„t oscillate but slowly rises to steady
state value of 11 Amps
Figure 4 plots inductor current against time. The inductor current is
exactly as same as the armature current as they are in series. The only
striking point about the plot would be the thickness of the line tracing the
inductor current. This indicates the charging & discharging of the inductor
during the switching of the chopper.
Energy Conservation Chopper Fed DC Series Motor 100
Figure 3 Armature Current vs Time
Figure 4 Inductor Current vs Time
Figure 5 plots the chopper output voltage with respect to time. The
output voltage exhibits heavy oscillations due to the under-damping and the
abrupt switching of the chopper circuit. The motor due to a higher
mechanical time constant can filter out the oscillations and keep a steady
speed increase or decrease (as is shown in fig 6) it must be pointed out
101 Sunil Thomas et al
thought that as the duty cycle is ramped up, the output voltage does not
oscillate much. This is because the duty cycle is changing very gradually.
Oscillations are seen once again when the duty cycle switches from 36% to
54% which then slowly settles down to 54 V.
Figure 5 Energy conservation DC chopper Output Voltage vs time
Figure 6 shows the plot of speed vs time. The speed vs time plot is the
smoothes of all plots due to the high mechanical time constant of the
machine. The speed of the machine initially increases to 20 rad/sec but at
2.5 seconds as the duty cycle starts ramping up to 86%, the speed starts
increasing too. Due to the higher mechanical time constant, the speed takes
a while to react to the change and at the 5 seconds marks as the duty cycle
starts reducing, It has been seen that the speed takes a few ms to start
reducing itself. A similar case is visible as the speed cannot track the duty
cycle all the way down to 36% and even before it can settle to the 20
rad/sec speed at 36 V it settles instead directly to the 24rad/sec mark at 54
V.
Energy Conservation Chopper Fed DC Series Motor 102
Figure 6 Speed vs Time
4.2 Analysis – II – Duty Cycle Controlled by P-D Controller.
Figure 7 plots the duty cycle against time. The duty cycle is now
controlled by the P-D controller and the plot basically shows the output
variable of the PD control system. The duty cycle eventually settles down
at the duty cycle set point which has been set to 50%.
Figure 7 Duty Cycle vs Time
103 Sunil Thomas et al
Figure 8 Plots the armature current vs time. Just as in the first analysis it
has been seen that armature current can track the duty cycle due to its low
time constant. Here since the changes in the duty cycle are gradual, the
armature current can keep up with the changes and no oscillations are
noticed.
Figure 8 Armature Current vs Time
Figure 9 Inductor Current vs Time
Energy Conservation Chopper Fed DC Series Motor 104
Figure 9 plots the inductor current wrt time. The inductor current just as
in analysis 1 has to be same as armature current since they are in series.
However, the line will be thicker as this indicates the oscillations that
occur due to discharging & charging of the inductor during switching.
Figure 10 Chopper Output Voltage
Figure 10. Shows the chopper voltage against time.Just as in analysis –
1 the chopper voltage has a high amount of oscillations. The oscillations
however die out In a while and soon the output voltage smoothens out and
begins to follow the variations in duty cycle. The transient period in the
first few seconds is because the capacitor is charging up.
Figure 11 Angular Speed vs Time
105 Sunil Thomas et al
Figure11Shows the speed vs time plot. As expected by a P-D controller,
the speed initially is made to shoot up quickly, which eventually leads to an
overshoot above the set point. The speed is then brought down by adjusting
the duty cycle and finally settles down at the set point of 24.1 rad/sec. It
should be kept in mind that the P-D controller is not tuned.
5 Conclusions Based on the duty cycle the transient analysis carried out on the direct
current dc series motor fed direct chopper has been analyzed. Different
types of parameters such as current; voltage and torque are simulated and
plotted during the transient in an effort to understand their variation and
changes during the transient period of change. The performance of direct
current dc series motor fed direct chopper is compared from that direct
current dc series motor without chopper fed. In addition to this the overall
efficiency of the system gets improved with the direct current dc series
motor fed direct chopper.Different loads are considered and it has been
observed that the difference in the variation of the parameters. The plots are
then analysed are useful is the performance analysis of the dc series motor
at transient conditions which helpful in design of the chopper and dc series
motor. This analysis will helpful in increase the usage of dc series motors
in various industries.
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Energy Conservation Chopper Fed DC Series Motor 110
Biographies
Dr. Sunil Thomas is currently working as an Assistant Professor in the
Department of Electrical and Electronics Engineering, BITS Pilani, Dubai
Campus, U.A.E. He completed his PhD in Electrical Engineering from BITS
Pilani in the year 2015. His areas of interests are Electrical machines, Power
Electronics, Electric Drives and Power system engineering and have 10 years
of teaching/research experience.
Prof. Dr. Nithiyananthan Kannan is currently working as a Professor in the
Department of Electrical Engineering, King Abdulaziz University, Rabigh,
Saudi Arabia. He has 19 years of teaching/research experience. He completed
his PhD in Power System Engineering from the College of Engineering Guindy
Campus, Anna University, India in 2004. He is an active member of IET (UK)
and he received Charted Engineer title in 2016 from Engineering Council, UK.
His areas of interest are computer applications to power system engineering,
modelling of modern power systems, renewable energy, smart grid and micro
grid.
111 Sunil Thomas et al
Mr. Aliakbar Eski is currently an Embedded Systems Engineer currently
employed with Nanoleaf in Toronto, Canada. He received his B.E. in Electrical
Engineering from BITS, Pilani, Dubai Campus and M.Eng. in Electrical
Engineering with specialization in Power Electronics from the University of
Toronto. He enjoys teaching and is a tutor in the Electrical and Computer
Engineering department at the University of Toronto.