Advances in Electrical and Computer Engineering Volume xx, Number x, 20xx [622654]

Advances in Electrical and Computer Engineering Volume xx, Number x, 20xx
1
1Abstract— Nowadays, the m ost challenging issue for
power supplies designers is to build circuits capable of feeding
the latest generation of microprocessors and D SPs, since
they require a high current density while maintaining a low
output voltage. A similar situation can be found when a high
power circuit i s necessary to supply a continuous wave
infrared laser diode array. This article follows the heuristic
optimization and the de sign of a synchronous DC/DC closed
loop step -down converter in Matlab/Simulink having
adjustable parameters for loop coefficients and reactive
components, which also allows for using this converter in many
other applications.

Index Terms — Laser, power sup ply, optimization algorithm ,
mathematical modeling.
I. INTRODUCTION
Recently, there are many power supply applications for
which manual parameter optimization isn’t a good solution.
There are solutions for manual optimization, and the
solution which will be f urther discussed is a heuristic
optimization algorithm, the ‘Particle Swarm Optimization’.
The ‘Particle Swarm Optimization’ algorithm is a
heuristic optimization algorithm, for which finding a global
minimum is not guaranteed, but through the interaction of
particles yields a value close to the global. This algorithm
can be used to solve a wide variety of optimization
problems, such as common optimization problems or more
specific optimization problems w hich include certain
constraints, nonlinear programmi ng, multi -objective
optimization, stochastics, programming problems and
combinatorial optimization.
In this case, the synchronous converter outputs a constant
current, and the mathematical model which describes a
scenario where a laser diode acts as load has been
developed.
Laser diodes are sensitive components and should be
handled with great care. A laser diode shouldn’t be driven
by any fixed voltage source without the possibility of
limiting the output current, otherwise the device will suffer
thermal runaway. Also, measures should be taken in order to
avoid any possible electrostatic discharge through the
semiconductor [ 1].
II. THEORETICAL FUNDAMENT ALS
For a better understanding of this algorithm, it can be
made an analogy between these particles and a sw arm of
bees passing through an open field in which several groups

1 of flowers can be found. The swarm tends to locate the
position with the highest density of flowers inside a certain
area in this field. The group of particles which, in this case,
is repres ented by bees, has no previous knowledge of the
field. Therefore, the bees will start the search and spread to
random locations. Each bee can remember the locations that
have the most flowers, called the most favorable personal
locations, and this informat ion can be communicat ed to the
rest of the swarm. At a certain point in time, the bees whose
result is weaker than the previous one, will be directed to its
previous successful position to find a group of flowers with
higher density. Another favorable loca tion is the location
reported by the entire swarm of bees, called the global
minimum or maximum, which contributes to making a
decision on the next location where a certain bee will be
guided. That bee will move in a direction composed of both
results in s uch a way that the flight path will result
somewhere between the se two points, depending on the
influence of the best personal point and the best global
point. Occasionally, a bee may fly over the position reported
by the group, where the field may have mo re flowers than
the location discovered by any swarm. In this case, the
whole group will be di rected to that position [2].
A mathematical approach for this algorithm is presented
below in Figure 1.

Figure 1. Vectorial Components for Particles [2]

From t he previously presented figure the following
components can be distinguished:
– Inertia factor, represented by the result obtained in the
previous iteration;
– The memory factor, for which the component is Implementation of Parallel PSO for
Synchronous Constant Current Converter
Mihnea -Antoniu COVACI1, Lorant Andras SZOLGA1
1Technical University of Cluj -Napoca ,
Faculty of Electronics, Telecommunications and Information Technology, 400114, Romania
covaci.a. mihnea@utcluj.didatec.ro , lorant.szolga@bel.utcluj.ro

Advances in Electrical and Computer Engineering Volume xx, Number x, 20xx
2 calculated according to the best result correspon ding to that
particle, called the personal optimum;
– The cooperation factor, the value which is calculated
using the most favorable point determined by the whole
group, a point called the global optimum.
This algorithm allows the optimization of processe s with
‘n’ variables, the search space being thus constituted by
these dimensions. At a certain point in time described by
index ‘k’, the position of the particle will be calculated using
equation (1). Before using this equation, the speed should be
calcul ated using several random constants, as function of
previous speed and previous global minimum.
i
ki
ki
k vx x1 1  
(1)
A further improvement for this algorithm is the parallel
processing, allowing for a Simulink model to b e optimized
much faster, depending on the number of physical CPU
cores. The principle is illustrated in Figure 2.

Figure 2. Parallel Implementation of Algorithm

Moreover, a dynamic or static topology can be used
because it has been shown to improve per formance b y
adding components in equation (1) represented by the
connections in Figure 3. There are several types of
interactio ns between particles, namely [3]:
– Global topology;
– Local topology;
– Von Neumann topology;
– Wheel topology
– Multiple cluster topology .

Figure 3. Particle Topologies [3]

The synchronous DC/DC step -down converter has a
similar structure to a standard step -down converter. Several
elements have been modified, the feedback is given as a
function of current and not depending on the output voltage
and a logical circuit has been built in such way that all
transistors are synchronized. The block diagram is presented in Figure 4.

Figure 4. Block Diagram for Synchronous Converter
III. COMPONENTS OF THE MODEL
Moreover, the optimization algorithm nee ds to be used
because, as the current through the laser diode is a
logarithmic function of voltage, a small voltage overshoot
may cause the current rise too high and the diode will suffer
thermal runaway. For a better understanding of this
phenomenon, anot her Simulink model has been developed
which illustrates a similar situation, presented in Figure 5. In
this case, it can be said that the DC/DC converter operates at
constant voltage. All simulation parameters are presented
below in Figure 5 and the juncti on temperature is presented
in Figure 6 .

Figure 5. Thermal Circuit

Figure 6. Junction Temperature During Runaway

Advances in Electrical and Computer Engineering Volume xx, Number x, 20xx
3 The used diode model has a similar characteristic to
NUMB07E, which is a 465 nm 2.9 W light blue laser diode,
presented in Figure 7.

Figure 7. Diode Output Current

The parallel ‘Particle Swarm Optimization’ algorithm has
been tested using the following function, presented in
equation (2). In this case, the global minimum coordinates
are 1, respectively 3.
2 2)5 2()7 2(),(  yx y x yxf
(2)
There are two variables which must be optimized and for
the DC/DC converter the situation is similar. In both cases,
it can be imagined that the particles move along two
dimensions searching for the global optimal value.
In Figure 8 is prese nted the overall global minimum as
function of current iteration . It can be observed that the
global minimum has been reached at the 14-th iteration.

Figure 8. Global Minimum

As for the closed loop regulator, the model presented in
Figure 9 has been us ed. Having the derivative component
equal to zero, the model will act as a PI regulator for which
the two parameters will be optimized using the algorithm
presented earlier.

Figure 9. PID regulator
The model was build using only integrator operation,
because when switching to other solver there will be an
insignificant difference compared to the situation where a
derivative operation is used.
Also, this circuit includes a slow start -up for the reference
used at the feedback pin. By eliminating the deriva tive
component, a lower voltage spike has been achieved but due
to the wind -up phenomenon of a PI regulator a similar
circuit should be used when at the out put is connected a
laser diode.
The circuit presented below slowly rises the current limit
towards t he steady state. At one point, the voltage begins to
follow a wind -up pattern and the diode opens, resulting in a
current spike smaller than the nominal current. The circuit is
presented below in Figure 1 0.

Figure 1 0. Slow Start Circuit

A complete layou t for the synchronous converter is
presented below in Figure 1 1. For the reactive components
also the heat transfer modeling has been developed, the
inductor uses the standard heat transfer equation and the
capacitor uses the Ohm’s thermal law.
Also, in th is case, real components were used (ideal
components with non -idealities) and all equations were
found in such way that there will be no derivative operation
in order to ensure the consistency of the result.

Figure 1 1. Converter Layout

Advances in Electrical and Computer Engineering Volume xx, Number x, 20xx
4 The parameters used in this model are presented below in
Table I.

TABLE I. SIMULATION AND MODEL PARAMETERS
Name Value
Input Voltage Range 6.5 … 10 [V]
Dimensions 35×14 [mm]
Shutdown and Turn On
Voltage 6 [V], 6.5 [V] respectively
Current Setting 3 … 5.5 [A]
Transient Response Time 100 [ms]
Controller Type PI
Kp (after optimization) 98.38
Kp (implemented) 100
Ki (after optimization) 931.7
Ki (implemented) 1000
Overall Efficiency 88.4 – 93.5 [%]
Frequency 100 [kHz]
Inductor Internal
Resistance 100 [m Ω]
Capacitor ESR 15 [m Ω]

The complete mathematical model is presented below in
Figure 12.

IV. EXPERIMENTAL RESULTS
After running the parallel ‘Particle Swarm Optimization’, another test has been run in order to ensure the stability of
the system. In hypothesis, t he regulator must be fast enough
to maintain the current at around three amperes , which is
confirmed by the result presented below in Figure 13. The
optimization was run in such way that the parameters must
be found for the following test case; during 0.01 seconds in
steady state, th e current becomes 1.4 times higher at the
same temperature . During the optimization the mathematical
model estimates the error as being the area of a triangle
described by three points : before perturbation , at maximum
current and after stabilization. Before the optimization, the
maximum current through the laser diode was 3.5 amperes.

Figure 13. Current Spike During Start -up

Also, the worst case result is presented in Figure 14,
which shows that several important parameters are within
normal limits.

Figure 14. Worst Case Result
V. CONCLUSION
Within this application we aimed to implement a
prototype mathematical model of a constant current
synchronous step -down converter used for laser diodes and
a parallel version of ‘Particle Swarm Optimization’. The
purpose of this convert er is to increase the efficiency of such
constant current circuits, compared to the standard LM317
constant current circuit.
In conclusion, following the specialized studies for each
block component of the project " Implementation of Parallel
PSO for Synch ronous Constant Current Converter " and the
simulations of electrical circuits, the theoretical and
functional implementation of the project was successful.

REFERENCES
[1] P. K. Basu, 'Semiconductor Laser Theory', University of Calcutta,
2015
[2] El-Shorbagy, M. & Hassanien, Aboul Ella. (2018). Particle Swarm
Optimization from Theory to Applications. International Journal of
Rough Sets and Data Analysis. 5. 10.4018/IJRSDA.2018040101.
[3] Elliackin M. N. Figueiredo, Teresa Bernarda Ludermir, 2012
Brazilian Symposium on Neural Networks