Ingineria Iluminatului - Journal of Lighting Engineering - Prof. Florin ...

COMBINED HIGH PRESSURE SODIUM LAMP MODEL REFLECTING THE
LAMP VOLT-AMPERE BAHAVIOR
1. Introduction
28
Neli Ratz, Nicolina Yaneva
TU – Sofia, Bulgaria
This paper presents a MAT LAB model for the simulation of both static and dynamic
characteristics of Sodium high intensity discharge (HID) lamps. The proposed model
was developed from the combination and modification of the classical Francis and
Mayr equations. It is helpful for a preliminary design of electronic ballasts.
Experimental results on sodium-HID lamps at different conditions are presented and
they appear to be in good agreement with the simulation results.
High-pressure sodium discharge lamps are applied
widely in the road and tunnel illumination because
of their high effectivity and long lifetime. Like
most of the discharge lamps, they have also
negative differential resistance at work. As a
consequence current limiting components called
ballasts are connected to the lamp in series. Apart
from the classical inductive ballasts, wider
application finds so called electronic ballasts. The
last provide higher luminance yields, higher
luminance indexes and longer exploitation
lifetime. Some of the ballasts allow dimming o the
lamp what leads to energy economy. In order to
design electronic ballast a simulation of the
cooperation between the ballast and the highpressure
sodium lamp is needed first. The
luminance source model that has to describe
adequate the behavior of the electrical parameters
and the luminance flux is also needed. It is very
difficult and uncomfortable for the engineer, to
analyze the chemical-physical processes in the
discharge tube when designing electronic ballasts
and thus to model the lamp as system with
distributed parameters. The paper is representing a
high pressure sodium lamp model as a two pole
with concentrated parameters, which variables are
current flowing trough the lamp and the voltage on
lamp terminals. The luminous flow is expressed
by the lamp electrical parameters.
INGINERIA ILUMINATULUI 15-2005
2. Mathematical model of the sodium lamp.
The experimental and theoretical investigations
show that for chemical-physical point of view the
current flowing process in the discharge tube of the
HID lamp is too complicated and multifarious. The
developed descriptions are observing the arc usually
with certain restrictions, mainly constant power of
the arc [1]. Mayr consider that the attitude of the arc
depend on the square of the amplitude of the current
and analytical enunciate the equation for the arc
conductance:
⎛ i ⎞
d ⎜ ⎟
u i ⎛ ui ⎞
⎝ ⎠
= ⎜ −1⎟
dt τ u ⎜ P ⎟
⎝ 0 ⎠
(1)
where:
u, i are the voltage and the current of the arc, τ -
the time constant of the arc, which Mayr defines
as ratio of the reserved energy in volume unit of
the arc and the give up power from this unit, P0
– dispersed power from the arc.
The equation (1) corresponds very well for
small values of current. For bigger current
values the Francis equation (2) is much more
suitable. Which is further developed in [4] for
work with HID lamp during dimming. This
equation can be transformed into next form: