transient analysis of separately excited dc motor and braking of

National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &

Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and

Technology, Pg.117-131

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Transient Analysis of Separately Excited DC Motor and Braking of DC Motor Using Numerical

Technique

Pavan R Patil, Javeed Kittur, Pavankumar M Pattar, Prajwal Reddy, Poornanand

Chittal

Department of Electrical and Electronics

B.V.B College of Engineering and Technology

Hubli, India

e-mail:[email protected], [email protected]

Abstract: This paper deals with transient analysis of separately excited DC motor and

braking of DC motor where transient equations are worked out using numerical technique.

The code is written for both transient analysis of separately excited DC motor and braking

and thus verified using the GNU plot and also the results are verified using MATLAB /

Simulink model.

Keywords- Regenerative Braking; Plugging; Dynamic Braking.

I. INTRODUCTION

Transient Analysis is done to know the performance of motors. Basically, it tells us how one

parameter is varied with respect to the other. In this paper, it tells us how current is varied

with respect to time and how speed is varied with respect to time, without and with load

torque of separately excited DC motor.

Brakes are used to reduce or cease the speed of motors. We know that there are various

types of motors available (DC motors, induction motors, synchronous motors, single phase

motors, etc.) and the specialty and properties of these motors are different from each other,

hence this braking method also differs from each other [1]. Breaking can be attained either

mechanically or electrically. Under electrical breaking, there are three types, namely

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Regenerative Braking

Plugging type Braking

Dynamic Braking.

II. NUMERICAL TECHNIQUE

Numerical analysis involves the study of methods of computing numerical data. In many

problems this implies producing a sequence of approximations by repeating the procedure

again and again [2]. People who employ numerical methods for solving problems have to

worry about the following issues: the rate of convergence (how long does it take for the

method to end the answer), the accuracy (or even validity) of the answer and the

completeness of the response (do other solutions, in addition to the one found, exist).

Numerical methods provide approximations to the problems in question. No matter how

accurate, they are, they do not, in most cases, provide the exact answer. In some instances

working out the exact answer by a different approach may not be possible or may be too

time consuming and it is in these cases where numerical methods are most often used [3].

Euler’s method:

Euler’s method provides us with approximation for the solution of the differential equations.

The idea behind Euler’s method is to use the concept of linearity to join multiple small line

segments so that they make up an approximation of the actual curve.

Note: Generally, the approximation gets less accurate the further you get away from the

initial point [4].

Three things needed in order to use Euler’s method:

1) Initial point –Starting point must be given.

2) Delta- The change in step size must be given directly or information to find it.

3) The differential equation-The slope of each individual line segment should be known so

that delta is found.

Let us take as an example an initial value problem in ODE

(1)

The forward Euler’s method is one such numerical method and is explicit. Explicit methods

calculate the state of the system at a later time from the state of the system at the current

time without the need to solve algebraic equations. For the forward (from this point on




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forward Euler’s method will be known as forward) method, we begin by choosing a step size

or ∆t the size of ∆t determines the accuracy of the approximate solutions as well as the

number of computations. Graphically, this method produces a series of line segments, which

thereby approximates the solution curve.

Fig. 1 Graphical illustration of Euler’s method

Let = 0, 1, 2… be a sequence in time with (2)

Let , and , be the exact and the approximate solution at , respectively. To obtain

from , we use the differential equation. Since the slope of the solution to the equation

at the point is , the Euler method determines the point (), by

assuming that it lies on the line through with the slope , Hence the formula

for the slope of a line gives

Or (4)

As the step size or ∆t decreases, then the error between the actual and approximation is

reduced. Roughly speaking, we halve the error by halving the step size in this case.

However, halving the ∆t doubles the amount of computation.

Backward Euler’s method:

The backward Euler’s method is an implicit one which, contrary to explicit methods finds the

solution by solving an equation involving the current state of the system and the later one.

More precisely, we have

(5)




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This disadvantage to using this method is the time it takes to solve this equation. However,

advantages to this method include that they are usually more numerically stable for solving a

stiff equation a larger step size ∆t can be used.

Let us take following initial value problem

(6)

We will use forward and the backward Euler’s method to approximate the solution to this

problem and these approximations to the exact solution

(7)

In both methods we let ∆t = 0.1 and the final time t = 0.5.

(T)

(FEA)

(BEA)

Exact

(FE)

(BE)

0 1 1 1 0 0

0.1 0.9 0.9441 0.925795 0.025795 0.018305

0.2 0.853 0.916 0.889504 0.036504 0.026496

0.3 0.8374 0.9049 0.876191 0.03791 0.028709

0.4 0.8398 0.9039 0.876191 0.036391 0.027709

0.5 0.8517 0.9086 0.883728 0.032028 0.024872

Where T-time, FEA- forward Euler’s approximation, BEA-backward Euler’s approximation,

FE- forward error, BE- backward error [5].

Forward and Backward Euler’s Method Compared to Exact Solution

The |ei| error averages were also computed for both methods and the result was for the

average error for forward Euler’s method was 0.028105 and the average error for the

backward Euler’s method was 0.021015. As it can be seen in both the chart above and the

|ei| error averages that the backward Euler’s method seems to be the more accurate

between the methods [5].




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III. TRANSIENT ANALYSIS OF SEPARATELY EXCITED DC MOTOR

Fig.2 Separately Excited DC Motor (Saber Model)

Where V: applied voltage, : motor current, : induced back emf voltage, : armature

winding inductance, : Armature Resistance, T: motor output torque, : motor output

speed.

Solution of Transient equations of the DC motor drive using Backward Euler’s method




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Using equations (12) and (16) we can carry out the simulation in C-language. Here open

source software ‘Code blocks’ is used for programming.

GNU PLOT:

GNU PLOT is a command line program that can generate two and three dimensional plots of

functions, data and data fits. It is a frequently used for publication-quality graphics as well as

education.

Pseudo Code:

Start of Program

Initialize the value

Open a file to store

current and speed

values

Start of loop execution

continue till the specified

time is encountered

End of execution




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Flow Chart:

Fig. 3 Waveform showing Open loop operation of separately excited DC motor without load

torque.

Fig. 3 shows current and speed waveforms during open loop operation of DC motor drive. In

this case, the motor is operating under no load conditions. The motor current increases

START

Initialize values

For(i=0;i<n,t<=n;i++,t=t+h)

Displaying speed,

current w.r.t time

END

DDD

D




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initially, and reaches its maximum peak. The initial motor current is high as the back emf is

negligible during starting. When the speed of the motor increases and tends towards steady

speed, the value of back emf becomes considerable and thus opposes the supply voltage.

This causes the motor current to decrease and tend towards zero.

Fig. 4 Waveform showing the Open loop operation of separately excited DC motor with load

torque.

Fig. 4 shows the current and speed waveforms during open loop operation of DC motor with

applied torque T= 3 N-m. It is observed that the motor takes more time to attain its steady

speed as compared to that of no load condition. This is because, when the motor is

connected to the supply, the initial value of the current is zero and due to the armature circuit

inductance, it takes some time to reach the load current. And the armature current value

remains finite.

MATLAB (Simulink) model of separately excited DC Motor (without load torque):




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Fig. 5 Matlab(Simulink) model of separately excited DC Motor(without load torque)

Simulink Plots:

Fig. 6 Variation of speed with respect to time




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Fig. 7 Variation of current with respect to time

IV. BRAKING

The term braking comes from the term brake. The brake is an equipment to reduce the

speed of any moving or rotating equipment, like vehicles, locomotives. The process of

applying the brakes can be termed as braking. In braking, the motor works as a generator

developing a negative torque, which opposes the motion [1].

Where, Ia = Armature current

V= Supply voltage

E= Back emf

Ra= Armature resistance

There are three types of braking

Plugging type Braking

Dynamic Braking

Regenerative Braking




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Using GNU Plots for these 3 breaking operations:

Plugging type Braking:

For plugging, the supply voltage of a separately excited motor is reversed so that it assists

the back emf in forcing armature current in the reverse direction. A resistance Ra is also

connected in series with the armature to limit the current. Plugging gives fast braking due to

higher average torque, even with one section of barking resistance Ra. Plugging is highly

inefficient because in addition to the generated power, the power supplied by the source is

also wasted in resistances.

Fig. 8 Plugging Circuit (Saber Model)

Speed and current waveforms of DC motor during plugging is shown in Fig.9. Here motoring

operation is same as that of regenerative braking. In plugging, the voltage applied to the

armature is reversed so that the armature current flows in the reverse direction, therefore the

torque produced is opposite to the earlier torque direction. Hence opposite torque braking is

achieved.




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Fig. 9 Waveform showing motoring and plugging operations

Dynamic Braking:

Shows the current and speed waveform for dynamic braking. When the motor attains the

desired speed, supply voltage to the armature circuit is cut off and an external resistance RB

(10Ω) is connected across the armature. In this case, the motor acts as a generator and

converts kinetic energy stored in moving parts into electrical energy and this energy is

dissipated in the form of heat in the resistor RB. The braking time depends upon the value of

the external resistance connected in parallel to the armature circuit. As shown in Fig.10,

braking with RB= 50Ω is faster compared to that with RB= 10Ω, shown in Fig.11.

Fig. 10 Waveform showing motoring and dynamic braking with RB =50 Ω




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Fig. 11 Waveform showing motoring and dynamic braking with RB =10 Ω

Regenerative Braking:

Regenerative braking operation of the DC motor drive is depicted in Fig.12.When the motor

attains its constant speed, the supply voltage is cut off and switching pulses are reversed.

Thus, the direction of the current will reverse. Later, the motor speed decreases to reach

zero value. In this case, the motor act as a generator and the current stored in the armature

inductance is fed back to the source.




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Fig. 12 Waveform showing motoring and regenerative braking

V. CONCLUSION

Transient behaviour: Plot of current and speed with respect to time is verified both

using GNU plots (both with and without load torque) and MATLAB (Simulink) model (without

load torque) of separately excited DC motor. All 3 types of braking are verified using GNU

plots. In dynamic braking, braking time depends on the value of the resistance, higher the

value of resistance less is the braking time.

Appendix:

Separately excited DC Motor specification:

Sl. No Motor Parameters Values

01. Rated Power (P) 15 hp

02. Rated Voltage ( V) 230V

03. Armature resistance (Ra) 0.5 Ω

04. Armature inductance( La) 0.05H

05. Coefficient of Viscous friction (B) 0.02Nm/rad/sec

06. Moment of inertia (J) 2kg-m2

ACKNOWLEDGEMENTS

We wish to place on record our profound and deep sense of gratitude to our guide

Asst Prof. Javeed Kittur, for his wholehearted guidance without which this endeavour

would not have been possible. Our diction falls short of words to gratify our guide for being

the primary source of inspiration and strength for the project study.

We are grateful to Dr. A. B. Raju, our Head of the Department for their valuable

guidance and encouragement with suggestions and permitting me to carry out my project

work and also for their co-operation throughout the project.




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We are grateful to Dr. Ashok Shettar, our respected principal for having provided us

the academic environment which nurtured our practical skills contributing to the success of

our project.

VI. REFERENCES [1] Types of Braking - Electrical4u.com

[2] Steven C. Chapra & Raymond P. Canale, “Numerical methods for Engineers”, Fourth Edition.

[3] Numeicalanalysis-www.math.niu.edu/~rusin/known-math/index/65.

[4] What is NumericalMethod.

www3.ul.ie/~mlc/support/CompMaths2/files/

[5] Euler'sMethod_www.mathscoop.com(euler)

[6] Gopal K. Dubey, “Fundamentals of Electrical Drives”, Second edition 2002.

[7] Explicit and Implicit Methods In Solving Differential Equations

digitalcommons.uconn.edu/cgi/viewcontent.cgi.

[8] Balaguruswamy, “Programming in ANSI C”.

transient analysis of separately excited dc motor and braking of

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