Download simulation model of an input power factor of a single - phase ac

SIMULATION MODEL OF AN INPUT POWER FACTOR OF A SINGLE – PHASE
AC- DC DRIVE
Osunde, O.D
Department of Electrical/Electronics Engineering
Faculty of Engineering, University of Lagos.
Email: osundave2@yahoo.com; dosunde@unilag.edu.ng
ABSTRACT: The re-awakening of the
Ajaokuta Steel rolling mills and other
industrialized sectors of the Nigerian
economy where a large numbers of users of
drives exist has influenced this research. It
establishes the Input Power factor problem
by simulating a DC drive and also provides
useful information on the behaviour factors
viz; Harmonic factor, Displacement factor
and Ripple factors to users who lack
knowledge of the basic understanding of the
drive
Keywords: Power factor (PF), Harmonic
Factor (HF), Displacement Factor (DF),
Drive
I. INTRODUCTION
Power factor problem is not a new
phenomenon. It is one of the consequences
of harmonics present in ac supply. Effort to
improve it to unity has been a major concern
of power engineers from the early days of
utility systems [1]. There has been identified
research on power factor [2] – [9],
particularly, Metha [10] and Sen [11] has
established the power factor problem by
mathematical analysis for a DC drive
operating in a continuous armature current
conduction mode.
In the present study, a simulation model of
the Single – Phase AC – DC is undertaken
to establish the poor power factor of the
drive. The choice of this drive is influenced
by the fact that: it presents the worst form of
harmonics, it has a wide range of
applications and it is use in low power motor
control system. The simulation presents
results for the input current, ripples, total
harmonic distortion (THD). Also, from the
simulation, the behaviour factors can be
derived. Experimental results obtained
validate the simulation results.
II. ANALYSIS OF THE DRIVE
The circuit of a DC drive operating in a
continuous armature current conduction
mode is shown in figure (1) and its
associated voltage and current waveforms in
figure (2)
Fig 1: Circuit configuration of a
Single - Phase AC –DC Drive
where,
P = Real Power
S = Apparent Power
Vs = Rms value of the converter input phase
voltage
I s = Rms value of the converter input
current
I s = Rms fundamental component of I s
1
 s = Phase angle between Vs and I s
1
1
α = Firing angle of the Drive
m = No. of Phase
Fig. 2: Voltage and current waveforms for
Phase Angle control – (PAC)
A mathematical analysis of the asymmetric
Single – phase drive can be found in [11]
and [12]. For,
P  mVs I s1 Cos s1
(1)
S= mVs I s
(2)
The Behaviour factors are summarized as.
Input Power Factor (PFac):
PFac 
2 1  cos  
    2
1
(3)
Harmonic Factor (HF):
     

HF  
 1
 41  cos   
1
2
(4)
Displacement Factor (DF):
  
DF  Cos s1  cos

 2 
(5)
Equations (3) – (5) were simulated in a
Matlab environment and the results are
presented in Figure (3). It shows a graphical
relationship between the behaviour factors
with the firing angle of the thyristors of the
Drive.
III SIMULATION
The circuit of Figure (1) was simulated at
the Power Electronics laboratory at the
Michigan State University using SABER
simulation software with the following
machine parameters at 230Vrms and a
switching frequency of 50Hz.
Load Resistance Rs = 0.09Ω
Load Inductance Ls = 10μH
Motor parameters: Kt = 0.55
Converter gain
Ke = 0.057
Rms supply current I = 46A
Moment of Inertia J = 15m4
The complete simulation diagram is shown
in Figure (4) with appropriate thyristor
controls. The simulation results shows the
variation of harmonic content of ac supply,
ac input current and voltages and the
armature speed.
1
7
0.9
6
0.8
Power Factor In pu
0.7
4
3
0.6
0.5
0.4
0.3
2
0.2
1
0
0.1
0
0
0.5
1
1.5
2
Delay Angle In Radians
2.5
3
3.5
0
0.5
1
1.5
2
Delay Angle In Radians
(b)
(a)
1
0.9
0.8
0.7
Displacement Factor
Harmonic Factor In pu
5
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
Delay Angle In Radians
2.5
3
(C)
Figure (3): Behaviour factors of the bridge
(a) Harmonic factor
(b) Power factor
(c) Displacement factor
3.5
2.5
3
3.5
Fig. 4: Simulation layout of a Single – Phase AC – DC Drive
IV SIMULATION RESULTS
(a)
(c)
(b)
(d)
Fig 5: Simulation results of the Single – Phase Asymmetric Bridge Drive
Table 1, was constructed using the simulation results and the expressions for PF and DF of
equations (3) and (5) respectively.
V SIMULATION ANALYSIS
.
Table 1: Variation of THD, PF and DF with delay angles
Firing Angle
“α” in(Degs.)
50
Firing Angle ‘α’
in (Radians)
0.08727
Input (THD)
Input ( PF )
0.03861
0.9997
Displacement
Factor ( DF )
0.9999
100
0.17453
0.05931
0.9942
0.9960
150
0.26180
0.10160
0.9860
0.9910
200
0.34907
0.15240
0.9730
0.9848
300
0.52360
0.25520
0.9360
0.9660
400
0.69813
0.40700
0.8706
0.9400
500
0.87267
0.58480
0.7855
0.9100
600
1.04720
0.82370
0.6684
0.8660
700
1.22173
1.20400
0.5133
0.8190
800
1.39626
1.89700
0.3572
0.7660
900
1.57079
4.443600.
0.1552
0.7070
A computer programme was written in Matlab using the results of table 1 to simulate the
behavior factors. They are displayed in figure 6.
1
7
0.9
6
0.8
5
Harmonic Factor In pu
Power Factor In pu
0.7
0.6
0.5
0.4
0.3
4
3
2
0.2
1
0.1
0
0
0.5
1
1.5
2
Delay Angle In Radians
2.5
3
3.5
0
0
0.5
1
(a)
1.5
2
Delay Angle In Radians
2.5
3
(b)
1
0.9
0.8
Displacement Factor
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
Delay Angle In Radians
2.5
3
3.5
(c)
Fig. 6: Graphical display of simulated Input Power Factor, Total Harmonic Distortion and
Displacement Factor
VI. CONCLUSION
It is evident from the characterization that
the plots of the behavioural factors obtained
from simulation are in complete agreement
with that obtained from mathematical
analysis. Obviously, the input power factor
problem exists for the asymmetrical single –
phase bridge converter and it decreases with
increase in the firing angle of the Drive. The
poor input power factor is further
demonstrated by the distortions seen in the
input current waveform as a result of
harmonics in the ac supply which makes it
non – sinusoidal and out phase with the
input voltage waveform
One point to note is that a decrease in power
factor leads to an over damped output speed
oscillations, which results in instability of its
3.5
operating system. Also, increased power
factor reduces reactive load energy
efficiency and conservation.
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Ismail Daut, Rosnazri Ali and Soib
Taib. “Design of a Single-Phase
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2006, Pp. 1902-1904
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Basau, S and Bollen M.H.J. “A novel
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Osunde, O.D. “Input Power Factor
Problem
and Correction For
Industrial Drive”. Ph.D Thesis, 2010.
University of Lagos, lagos, Nigeria.