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: sunil.thomasp@gmail.com. 2Department of Electrical Engineering, Faculty of Engineering,

King Abdulaziz University, Rabigh, Kingdom of Saudi Arabia. E-mail :nmajaknap@kau.edu.sa. 3Embedded Systems Designer, NanoLeaf, Toronto, Canada.

E-mail: theeskis@gmail.com.

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.