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High Power Factor Electronic Ballast for High Pressure
Sodium Lamps with Low Crest Factor
Fernando Soares dos Reis*
[email protected]
Gabriel Bartz Ceccon
[email protected]
Reinaldo Tonkoski Jr.
[email protected]
Vicente Mariano Canalli
[email protected]
Gert Bolten Maizonave
[email protected]
Julio César Marques de Lima
[email protected]
*contact author
Pontifícia Universidade Católica do Rio Grande do Sul – PUCRS
Department of Electrical Engineering
Av. Ipiranga, 6681 – 90619-900 – Porto Alegre, RS – BRASIL
Phone: (+55 51) 3320 3686 / 224 Fax: (+55 51) 3320 3540
Topic Area: Power Electronics
Subject Area: Power Electronic Devices and Systems
Keywords: Electronic Ballasts, HPS lamps and Resonant Filters.
1
High Power Factor Electronic Ballast for High Pressure
Sodium Lamps with Low Crest Factor
Pontifícia Universidade Católica do Rio Grande do Sul – PUCRS
Department of Electrical Engineering
Av. Ipiranga, 6681 – 90619-900 – Porto Alegre, RS – BRASIL
Phone: (+55 51) 3320 3686 / 224 Fax: (+55 51) 3320 3540
Abstract – In this paper will be reported the study and implementation of a single stage high
power factor (HPF) electronic ballast for high-pressure sodium (HPS) lamps using a half-bridge
boost rectifier integrated with an LCC filter electronic ballast. In the recent years, many authors
are working to obtain single stage HPF electronic ballast for fluorescent lamps [2-4]. Usually, to
obtain HPF in electronic ballast for high-pressure sodium lamps, a power factor preregulator
(PFP) is used between the mains and the electronic ballast [3]. The main idea in this work is to
present a simple and cheap electronic ballast with HPF for HPS lamps. This simple solution also
presents low crest factor. Experimental results and a comparison with a full bridge structure will
be discussed in the final version.
2
High Power Factor Electronic Ballast for High Pressure
Sodium Lamps with Low Crest Factor
F. Dos Reis, MEMBER, IEEE, R. Tonkoski Jr., STUDENT MEMBER, IEEE, G. B. Maizonave,
G. B. Ceccon, V. Canalli and J. C. M. Lima
Pontifícia Universidade Católica do Rio Grande do Sul - PUCRS
Department of Electrical Engineering
90619-900 Porto Alegre, RS - BRASIL
Email: [email protected]
Abstract – In this paper will be reported the study
and implementation of a single stage high power factor
(HPF) electronic ballast for high-pressure sodium (HPS)
lamps using a half-bridge boost rectifier integrated with
an LCC filter electronic ballast. In the recent years,
many authors are working to obtain single stage HPF
electronic ballast for fluorescent lamps [2-4]. Usually, to
obtain HPF in electronic ballast for high-pressure
sodium lamps, a power factor preregulator (PFP) is
used between the mains and the electronic ballast [3].
The main idea in this work is to present a simple and
cheap electronic ballast with HPF for HPS lamps. This
simple solution also presents low crest factor.
Experimental results and a comparison with a full
bridge structure will be discussed in the final version.
I. INTRODUCTION
Nowadays, an important topic of awareness is the
importance of environment preservation. In this direction,
important efforts have been made in the diverse areas of
knowledge. In electrical engineering field, this phenomenon
has reflected in searching for alternatives energy systems,
higher efficiency on available resources utilization, losses
reduction in equipments and to increase power quality.
In the last few years, the market was flooded by a great
number of electronic ballasts for fluorescent lamps
operating in high frequency, especially by compact
fluorescent lamps. Its utilization was widely stimulated by
Brazilian media for energy economy, due the fact that
luminous efficiency increases with the frequency for this
kind of lamp. Brazil faced a serious energy crisis in 2001.
Many corrective actions were taken to mitigate this serious
problem. One of them was the energy rationing which
consisted in overtaxing or even cutting energy supply from
consumers, which exceeds the prefixed energy quotes. Also
many electric energy concessionaires had distributed
gratuitously compact fluorescent lamps for residential
consumers, showing the importance of illumination’s
segment inside the global energy consumption, estimated to
be about thirty percent of total consumption of electrical
energy in the country. Because of these, innumerable
research groups around the world, like [1], [2], [3] and [4],
have dedicated their efforts to the development of new
topologies and new control techniques for different kinds of
discharge lamps.
Most of magnetic ballast manufacturers had to develop
electronic ballasts for discharge lamps to guarantee their
survival in business because the consumers started to
demand more and more this type of product. It also
simplifies the production line, which has expressive
physical reduction and productivity increase in relation the
line that produces the conventional ballasts. Now, the
challenges for industries are the reduction of production
costs, the reduction of converter size, unitary power factor
and null harmonic distortion, which implies in a substantial
improvement of energy quality consumed by ballasts. Here
in Brazil, a few groups of researchers are making the
development of electronic ballasts for HID lamps. However,
in a close future, these ballasts will be in the production
lines of main national manufacturers.
The porpoise of this paper is to report the development
of low cost single stage HPF electronic ballast for HPS
lamps. The design criteria will be presented in this work for
the proposed circuit. There are many kind of high-pressure
lamps; however, this work will focus only the high-pressure
sodium lamps (HPS), widely used in public illumination.
The HPS lamps radiate energy on a great part of the visible
spectrum [5]. These lamps provide a reasonable color
reproduction (it has IRC 23 color reproduction index). They
are available up to 130 lm/W of luminous efficiency and
color temperature of 2100 K, approximately.
The HPS lamps, as any other HID lamps, need ballast to
operate correctly. The ballast is additional equipment
connected between the power line and the discharge lamp.
The ballast has two main functions: to guarantee lamps
ignition through the application of a high voltage pulse
between the lamp electrodes and to limit the current that
will circulate through it. The lamp would be quickly
destroyed without current limitation, due the negative
resistance characteristic of the lamp, as can be observed in
figure 1.
The HPS lamps have many particularities when they
operate in high frequency, such as:




Can be modeled by a resistance in steady state;
Can have luminous intensity controlled;
The spectrum color reproduction can be modified;
Presents the acoustic resonance phenomenon,
which can result in the arc extinguishing until the
lamp destruction;
2
Positive Resistance
Lamp
Current
Negative Resistance
Lamp
Voltage
Breakdown Voltage
quantitative analysis looking for a L_PFC inductor design
criteria generically. All this analysis is based on Dos Reis
[7] considering all the components ideal components. This
analysis is valid only for the DCM.
Figure 3 presents a usual boost PFP. When transistor Q
is ON, starts the first analysis stage where the input current
ig increases linearly. In Figure 4, the equivalent circuit for
this stage is presented.
Fig. 1. Typical voltage x current curve for HID lamps.
In order to obtain low cost electronic ballast for HPS
lamps with HPF a single stage converter was conceived.
The idea is to build the PFC using the half-bridge boost
rectifier working in discontinuous conducting mode (DCM)
integrated with the electronic ballast. Using this simple idea
high power factor and low crest factor can be obtained in a
single stage converter. Martin et al. in [6] proposed the
integration of a boost with a full bridge converter for using
in HID lamps. In this paper will be explored the half-bridge
integrated with a boost converter topology. Advantages and
Disadvantages of each structure will be discussed in the
final version.
Fig. 3. PFP with a boost converter.
II. STUDIED ELECTRONIC BALLAST
The studied single stage high power factor electronic
ballast for high-pressure sodium lamps structure
incorporates a bridge rectifier, a half-bridge boost rectifier
and an input LC filter to minimize the EMI generated by the
DCM input current. Figure 2 shows an electrical diagram of
the proposed circuit. Similar circuits have been proposed by
other authors using fluorescent lamps, but any paper using
the boost integrated with a half bridge converter topology
for HPS lamps was not found by the authors. The capacitor
CF in this figure is responsible by the DC bus voltage once
the voltage in this capacitor has a low ripple the crest factor
in the HPS is minimized. The inductor LPFC is the boost
inductor, this inductor must be designed to work in DCM
once the MOSFET duty cycle is constant to guarantee the
perfect operation of the electronic ballast. The resistor ESR
represents the equivalent series resistance of the capacitor
Cs, inductor Ls and MOSFETs on resistance.
Fig. 4. Equivalent circuit for the first stage.
It may be observed that the diode D is blocked and the
voltage (vd = V) is applied on it. Equation 1 presents the
input current for this stage.
d i g (t)
v g (t) = L
dt
(1)

v g (t) (t - t 1i )
+ i g ( t 1i )
L
Where, t1i is the start time as may be observed on
figure 5.
i g (t) =
i
i
g máx
g
v (t - t )
g 1i
2i
L
v
g
L
t
- ( V- v )g
L
t
1i
t
2i
t
cond
Fig. 2. Studied HPF Electronic Ballast.
III. ANALYSIS AND DESIGN OF THE POWER FACTOR
CORRECTOR STAGE
The analysis of the Half Bridge converter integrated
with a PFP stage may be done independently considering
two different circuits according with [6]. In this section, will
be presented the boost power factor preregulator
3i
t
4i
t
t'
apa
T
Fig. 5. Input current for a single commutation period.
When transistor Q is turned off, starts the second stage,
where the diode D is directly polarized by the current ig. On
Figure 6 is represented the equivalent circuit for this stage.
2
Table 1. Input and diode current for each stage.
Stages
1st
i g (t)=
On this stage, the output voltage V is applied to the
transistor Q (VQ = V). The input current ig and the diode
current id are the same and is presented on equation 2.
( v g (t) - V )
(t - t 2i ) + i g ( t 2i )
L
(2)
where, t2i is the time where the transistor Q is blocked, this
instant is represented on figure 6 where the value of the
current ig(t2i) is the value of ig when the transistor Q is
blocked. Manipulating equation 1with equation 2 it is
obtained equation 3.
i g (t)= i d (t)=
( v g (t) - V )
v g (t) ( t 2i - t 1i )
(t - t 2i ) +
+ i g ( t 1i )
L
L
v g (t) (t - t 1i )
L
i d (t) = 0
Fig. 6. Equivalent circuit for the second stage.
i g (t) = i d (t) =
2nd
(3)
This stage ends when the diode D is blocked. This
happens when the current id is null starting the third and last
stage, represented on figure 5.
i g (t)=
3rd
( v g (t) - V ) ( t - t 2i ) v g (t) ( t 2i - t 1i )
+
L
L
i g (t)= 0
( v g (t) - V ) ( t - t 2i ) v g (t) ( t 2i - t 1i )
+
L
L
i d (t) = 0
i d (t) =
If the input current ig is substituted on this equation by
the equation presented on table 1, the following expression
may be found:
i g med (t) =
1 t 2i v g (t) (t - t 1i )
1
dt +
T t1i
L
T
t 3i
( v g (t) - V)
v g (t)
(t - t 2i ) +
( t 2i - t 1i ) dt
L
L
t 2i

(4)

i g med (t) =
2
2
2
v g (t) t cond
v g (t)
t cond
+
2L T
2 L (V - v g ) T
Where:
t apa = t cond
v g (t)
V - v g (t)
(5)
Obtained from equation 3.
To find out the output voltage, it may be used the
following equation valid for every kind of converters,
except the buck converter.

T
R 1
V =   i d (t) dt d
 oT o
(6)
The diode current is represented on figure 8.
Fig. 7. Equivalent circuit for the third stage.
This stage stills until the transistor Q is turned ON
again. Analyzing the input current equations from the
converter, it may be concluded that its start value is null (ig
(t1i) = 0). Observing figure 7, the voltage over the transistor
Q is the input voltage vg and the voltage over the diode D,
vd, is the difference between the output and input voltage
(V-vg). Using these statements, the input and diode current
may be written as it is shown in table 1.
With table 1, it is possible to sketch the waveform of
the input current ig. This waveform is represented on figure
5. The input current average value in a single commutation
period may be obtained by your definition
i g med (t) =
1
T
t 4i
 i (t) dt
g
.
Fig. 8. Current over the diode D in a single commutation
cycle.
Using equation 3, in equation 6, it may be obtained:
t 1i
3
V=
R
T
 t3 i
 ( v g (  ) - V)
v g (  ) ( t 2i - t 1i ) 
(t - t 2i ) +
 dt d
L
L

  
o t2i

R
V=
T


o
2
2
vg ( )
t cond
d
2 L (V - v g (  ))


2
R t cond
V=
2 LT
2
2
V =
Vg

d
sen 
d
V
1 - g | sen  |
V

2
2
Vg
o V
2
RT
2L


o
sen 
d
| sen  |
1M
2

V =V g d
Fig. 9. Kboundary vs. M graphic.
y(M)
 K
(7)
v g (t) dT = (V - v g(t)) (1 - d) T
V
1
=
vg 1 - d
(8)

d= M
M - | sen( t) |
d=
M
where d is the duty cycle expressed as (d = tcond/T), M is the
static gain of the converter defined as (M = V/Vg) and y(M)


o
sen 
d
| sen  |
1M
.
2
2L
RT
(9)
When a converter is operating between the boundary
condition, the time interval (t4i – t3i), from figure 5, is null.
Therefore, if a volts-second balance in inductor L is done, it
is possible to establish certain relations. With equation 8,
we can manipulate equation 7 obtaining:
K ( t)=
(M - | sen ( t)| )2 y(M)
M

4
4
y(M)
=
(M - 1)
M
R T K crÍtico
2

(12)
(13)
To verify the performance of the proposed system, a
LCC electronic ballast (figure 10) for a 250 W HPS lamp
was designed. The nominal lamp voltage (Vlamp) was
obtained from the lamp’s manufacturer datasheet and its
value is 100 VRMS. To design the LCC ballast it was added
10 % to consider loses effect. The electronic ballast input
power voltage comes from the output of an input bridge
rectifier; consequently, this input voltage is mains
dependent. In the present design example the mains voltage
adopted was Vmains= 127 VRMS. The switching frequency
chosen was 68 kHz. Assuming the resistive comportment of
the lamp, we can estimate the value of its resistance (R)
after ignition using equation 14.

R
Vlamp 2
P
 40
(14)
Where P is the lamps power.
(M - 1 )2 y(M)
M

(10)
To have the converter operating in the boundary
conduction condition with every input voltage, K must be:
K  K crÍtico =
L=

K crÍtico
IV. BALLAST DESIGN CRITERIA
is the solution for the integral
Finally, K is the discontinuity constant defined as:
K=
From equation 7, it may be taken the duty cycle and
using the definition of a discontinuity constant represented by
, d and L may be found. equations 12 and 13 shows its
values.
(11)
Figure 9 represents the (Kboundary vs. M) curve. The
determination of the limits between the DCM and the
continuous conduction mode was described by Dos Reis in
[7] and is represented in figure 9.
As it was indicated in [2], the best relationship between
the switching frequency and the resonance frequency before
the lamp turn on is ω0/ ωs = 3, guaranteeing the high voltage
generation for the lamp ignition and limiting the peak
current at the MOSFET to acceptable levels. If it was
adopted to work at resonance ω0 = ωs in theory we would
have the possibility of an infinite voltage generation over
the lamp which could be good for a quickly lamp turn on.
On the other hand, current would also rise to infinite
because the impedance of the circuit formed by L, Cs and Cp
is null just before the lamp is turned on. This operation
mode will result in the MOSFETs and driver’s destruction.
4
Gráfico da Variação da Impedância em função de Ql variando-se o parâmetro A
L
Cs
4


10 


15 


20 




25 


30 
Z  Ql 
Ve
Cp
R
Z  Ql 
Z  Ql 
Fig. 10. LCC Ballast.
Z  Ql 
The reference [2] and our experimental results allow us
to consider that after lamps ignition, the lamp resistance is
bigger than the Cp reactance. Therefore, it can be deduced
the equation 15:
Z  Ql 
1
1
1




3


2
1
1


1
GS( Ql)
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Ql
1
  CP
// R  R
Fig. 12. Impedance graphic varying Ql for different
values of A.
(15)
Consequently, we can say that, after lamp ignition, the
equivalent circuit is showed in figure 11.
L
Ql   o RC 
R
o L
(19)
,
Cs
Ve
Where,
C
R
CS CP
CS  CP
(20)
CP
CS
(21)
and,
Fig. 11. Ballast equivalent circuit after ignition.
A
For the circuit showed in figure 11, considering the
voltage Ve an asymmetrical square wave (from E to 0 V). It
is easy to obtain the peak value Vm of the first harmonic
from Fourier series. The equation 16 has shown this value:
Vm 
2E

(16)
After lamp ignition the ballast must guaranty that RMS
voltage over the lamp, do not overcome the nominal value.
The peak lamp voltage Vl can be obtained using the wellknown voltage divider for the circuit shown in figure 4, the
equation 17 presents this result:
Vl 
R
 Vm
Z
(17)
The impedance of the circuit can be calculated with
equation 18. To facilitate the design of the LCC filter an
impedance abacus was elaborated and the result is shown in
figure 12. This abacus presents the relationship between the
Z/R for a fixed operation frequency ω0/ωs = 3, having the
quality factor Ql and the capacitor relationship factor
defined as A=Cp/Cs as design parameters.
As it could be seen in the abacus of figure 12, if it is used
a capacitor’s relationship factor value lower then 1/20, there
is no significative change in the abacus curve. Considering
this, the adopted A factor was A=1/20. In the present design
the relationship between Z/R could be obtained from
equation 4. Remember that the most important thing is to
maintain the nominal RMS voltage in the HPS lamp, so a
new equation can be write to solve the problem the equation
22 presents this relation, for the present design results:
Z
R

2 E
  2 Vl
From the abacus of figure 12, the obtained Ql value is
0,141 as we can see in the intersection of the horizontal axis
Ql and vertical axis Z(Ql,1/20), allowing the calculus of the
resonance elements.
The inductor value can be obtained from equation 19 and
yields in equation 23:
R
(23)
L
0  Ql
In the case of the capacitors, we have that:
C
Z
Ql , A 
R

 
1  A1  


   o


1    o A 


.
  j 
Ql   o  1  A 


 
1  jQl  1  A
 o 
(18)



(22)
2
Cs 
Ql
0  R ,
C  1  A
(24)
(25)
A
and
CP  A  Cs
(26)
5
V. SIMULATION RESULTS
To validate the proposed system, a half-bridge electronic
ballast with the following specification: 250 W HPS lamp,
input voltage (127 VAC), DC bus voltage (360 VDC) and
operation frequency of (68 kHz), was simulated using the
software PSIM® 6.0. Figure 13 shows the current and
voltage in the mains without the EMI filter. The voltage in
the lamp is showed in figure 14. The crest factor was
measured. Tests indicate that ballasts with higher crest
factors may result in depreciation of lumen output or
reduced lamp life. It was found a crest factor of 1.37 using
this ballast. HID lamp recommendations suggest a
maximum crest factor of 1.8 for HPS lamps.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Dos Reis, F.S., Canalli, V.M, Lima, J. C., Tonkoski, R. Jr.,
Sarmanho, U, Edar, F., Santos, Toss, M, Ramos, F.M., Garcia, L.L.,
Callai, P., Da Silva, N. B.R, Godinho, L.A., Líbano, F.B., Low Cost
High Power Factor Electronic Ballast For High Pressure Sodium
Lamps, VI Induscon, Joinville, 2004.
Bum Suk Kang; Hee Jun Kim; High Power Factor Electronic Ballast
for High Pressure Sodium Lamp, TENCON 99. Proceedings of the
IEEE Region 10 Conference, Volume: 2, Dec 1999, Page(s): 887 890 vol.2.
Ben-Yaakov, S.; Gulko, M.; “Design and performance of an
electronic ballast for high-pressure sodium (HPS) lamps, Industrial
Electronics”, IEEE Transactions on Volume: 44 Issue: 4, Aug 1997,
Page(s): 486 -491.
Co, M.A.; Resende, C.Z.; Simonetti, D.S.L.; Vieira, J.L.F.; Almeida,
P.C.A.; Microcontrolled electronic gear for low wattage metal halide
(MH) and high-pressure sodium (HPS) lamps, Industry Applications
Conference, 2002. 37th IAS Annual Meeting. Conference Record of
the, Volume: 3, 2002, Page(s): 1863 -1868 vol.3
J.R. Coaton, Lamps and Lighting, fourth edition, Arnold 1997.
Martin, F.J.F.; Viejo, C.B.; Anton, J.C.A.; Garcia, M.A.P.; RicoSecades, M.; Alonso, J.M., Analysis and design of a high power
factor, single-stage electronic ballast for high-intensity discharge
lamps, Power Electronics, IEEE Transactions on, Volume 18, Issue
2, March 2003 Page(s):558 – 569
Dos Reis, F., Estudio y Criterios de Minimizacion y Evaluacion de
las Interferencias Electromagneticas Conducidas en los
Convertidores Ca – Cc, Tesis Doctoral, Universidad Politecnica de
Madrid, 1995.
Fig. 13. –Above, voltage and current in the mains, and
voltage in the lamp with 250 W below.
Fig. 14. –Voltage in the lamp.
VI. CONCLUSION
This paper described a single stage high power factor
electronic ballast for high-pressure sodium lamps. This
ballast presents a very low cost because it avoids an
external PFP. A high power factor was obtained. The crest
factor found was very low because the Electronic Ballast
works with low DC bus ripple. The main drawback of this
topology is to work in DCM, but for this power level is
possible to use this solution with an input EMI filter.
Experimental Results and a comparison with a full bridge
structure will be discussed in the final version.
6