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Engineering, Technology & Applied Science Research Vol. 12, No. 3, 2022, 8559-8566 8559 
 

www.etasr.com Said et al.: Modeling and Simulation of a UV Water Treatment System Fed by a GPV Source Using … 

 

Modeling and Simulation of a UV Water Treatment 

System Fed by a GPV Source Using the Bond Graph 

Approach 
 

Riahi Said 

UR-LAPER, Faculty of Sciences of Tunis 
University of Tunis El Manar 

Tunis, Tunisia 

riahi.said@fst.utm.tn 

Naoufel Zitouni  

UR-LAPER, Faculty of Sciences of Tunis 
University of Tunis El Manar 

Tunis, Tunisia 

naoufel_zitouni@yahoo.fr 

Viorel Minzu 

Control and Electrical Engineering Department  

Dunarea de Jos University  
Galati, Romania 

Viorel.Minzu@ugal.ro 

Abdelkader Mami 

UR-LAPER, Faculty of Sciences of Tunis 

University of Tunis El Manar 
Tunis, Tunisia 

abdelkader.mami@fst.utm 
 

Received: 15 February 2022 | Revised: 4 March 2022 | Accepted: 5 March 2022 

 

Abstract-This work presents a simulation model for a UV water 

treatment system, powered by a photovoltaic generator, which 

relates the current consumed by the lamp to the UV flux and 

water quality. The overall system also includes electronic 

converters, electronic ballast (RLC resonant circuit), a UV lamp 
(UV irradiation source), and a centrifugal pump. To optimize the 

power transfer from the PV generator to the ballast and the UV 

lamp, a Maximum Power Point Tracking (MPPT) device is used. 

The overall water treatment system presents a complex model 

due to its hybrid components. The bond graph tool with a 

multidisciplinary vocation allows precisely, by its graphic nature, 

using a unified language, to explicitly display the nature of the 
power exchanges in the system and facilitate its control. This tool 

is a solution for non-linear systems that guarantees and facilitates 
their modeling without difficulties.  

Keywords-bondbraph; UV water treatment system; complex 

model; photovoltaic generator; centrifugal pump; simulation 

I. INTRODUCTION  

Several water resources may be untreated and therefore 
they can be factors of transmission of diseases. The reuse of 
wastewater after an adequate treatment by UV radiation, 
presents a very good solution to solve the problems related to 
water pollution and constitutes a potential water resource. The 
majority of the existing UV disinfection systems use low 
pressure mercury arc lamps as a source of UV radiation that 
generates short waves in the region of 253,7nm [1-3]. The 
discharge lamp is placed in a reactor and is surrounded by a 
quartz tube immersed in a chamber in which the fluid is 
circulated. It is powered by an energy source such as a 
photovoltaic generator via an electronic ballast composed of an 
inverter, a transformer and a resonant circuit (RLC) [4, 5]. A 

centrifugal motor pump as shown in Figure 1 ensures the 
circulation of water between the two tanks. The physico-
chemical parameters (pH, temperature, etc.), the applied UV 
dose, the exposure time, as well as the number and type of 
microorganisms, are factors that can influence the final water 
quality. Many studies have been developed to improve water 
treatment systems despite their complexity, especially of the 
UV lamp model [6-8]. 

The aim of this study was to build a simulation model for 
all the components of the complex UV water treatment system 
shown in Figure 2. The bond graph approach is a modeling tool 
that facilitates the links between the different physical domains 
(mechanical, hydraulic, electrical) that represent the overall 
system. A photovoltaic (PV) generator model is presented in 
the first section along with the MPPT control in order to adapt 
the PV source and the load with a simulation result.  

 

 
Fig. 1.  Structure of the overall UV water treatment system powered by a 

PV panel. 

Corresponding author: Abdelkader Mami



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Fig. 2.  Representation of the energy exchanges in the system with 

different physical fields. 

II. MODELING OF THE PV SOURCE BY THE BOND GRAPH 

APPROACH 

A. The PV Generator Model 

In order to power UV water disinfection systems with solar 
energy in a simple and inexhaustible way, we need to use PV 
generators. PV panels are characterized by the non-linearity of 
their output which is influenced by environmental factors 
(temperature and irradiation). The PV model used has two 
resistors in series and in shunt as shown in the equivalent 
electrical diagram in Figure 3. 

 

 
Fig. 3.  Equivalent electrical circuit of a single diode PV generator. 

The simplified equation of the PV current is: 

0

( )
exp 1

s
pv ph sh

s

q V I R
I I I I

n K N T

× + ×
= − − −

× × ×

  
  

   
    (1) 

where Ipv is the the output current, I0 the diode inverse 
saturation current, and Rs the series resistor. K is the 
Boltzmann's constant, q is the electronic charge, n is the ideal 
diode factor (1<n<2) for a unique junction, and T is the 
functioning temperature. The current through the shunt resistor 
is given by: 

( ) /sh pv pv s shI V I R R= + ×     (2) 

The photocurrent generated by the cell depends on the 
ambient temperature (T) and the solar irradiation (G) and is 
represented by: 

( 298) /1000ph sc II I K T= + ⋅ − ⋅G     (3) 

B. Bond Graph Model of the Photovoltaic Generator 

A simplified model that does not take into account the 
losses was adopted. This model is called mono-diode coupled 
to a starting capacitor that is placed in parallel with the 

photovoltaic generator. The added capacitance represents the 
capacitance of the PN junction and it depends on the voltage 
Vd. 

 

 
Fig. 4.  Electrical diagram of the PV generator with starting capacity. 

The bond graph model for the equivalent circuit is 
presented in Figure 5. It contains an element of capacitance, 
and the element noted as RD is the resistance of the diode. It 
contains the non-linear characteristic. This allowed us to 
replace the generator by a modulated flux source Sf which 
plays the role of the modulating signal representing the 
photovoltaic current Iph. This model was simulated by the 
software 20-sim [6, 9-11]. 

 

 
Fig. 5.  Bond graph of the PV model. 

To simulate the characteristics of the photovoltaic panel 
I=f(V) and P=f(V) [18-19], we use the BG model shown in 
Figure 5. In this simulation, the receiver is an initially 
discharged capacitor. The simulation results are represented in 
Figure 6. 

 

 
Fig. 6.  Simulation of the characteristic curves of the PV system. 

III. CONVERTERS USED 

Static converters are mainly made up of semiconductor 
components that work in switching mode (thyristors, power 

MSfIph 0:Vpv

C:Cp

R:RD

Puissance

R1

1:Ipv



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transistors, etc.). In our UV system, the converters are placed as 
follows: a first chopper booster is inserted between the UV 
lamp and the PV generator, a second chopper devolver is 
inserted between the motor pump and the PV panel, and a 
single-phase inverter generates a square voltage. 

A. Dynamic Boost Converter 

As the name suggests, this type of static converter amplifies 
the output voltage relative to the input voltage. In electronic 
structure, a boost chopper generally has a switch controlled on 
opening and closing (transistor, IGBT) and a diode [14, 15]. 

 

 
(a) 

 
(b) 

Fig. 7.  Boost converter: (a) equivalent model, (b) its bond graph model. 

B. Dynamic Buck Converter 

The static converter (DC/DC) used, is most frequently used 
as a devolving converter, its basic schematic is that of Figure 8. 
A buck converter converts a DC voltage into another DC 
voltage of lower value [11, 16-18]. 

 

 
(a) 

 
(b) 

Fig. 8.  Buck converter: (a) equivalent model, (b) its bond graph model. 

C. Single Inverter 

The resonant circuit (electronic ballast) requires a square 
voltage, which is obtained with an inverter, which is a static 
converter that converts electrical energy from DC to AC. It 
allows obtaining an alternating voltage adjustable in frequency 
and in RMS value, thus using an appropriate control sequence. 

 

 
Fig. 9.  Equivalent electrical diagram of a single-phase inverter. 

D. Bond Graph MPPT: Perturbation and Observation 
Algorithm 

The Perturbation and Observation (P&O) method is a 
widely used approach in MPPT research, because it is a simple 
iterative method. It can track the Maximum Power Point (MPP) 
even during sudden changes in irradiance and temperature [2, 
9, 11, 17, 20]. Using the P&O algorithm, a link graph MPPT 
model was developed (Figures 11-12). 

 
Fig. 10.  Bond graph model of a single inverter. 

 
Fig. 11.  Adaptation model of an MPPT converter with a PV panel by bond 

graph. 

 
Fig. 12.  Simulation of the P&O control algorithm for different 

illuminations. 

IV. BOND GRAPH MODELING OF THE ELECTRONIC BALLAST 

AND THE UV LAMP  

The electronic power supply (electronic ballast) of a UV 
lamp can be broken down into three parts: The DC/AC 
converter, which is described above, the transformer, and the 
resonant circuit. 

A. The Resonant Circuit (Electronic Ballast) 

A discharge lamp needs sufficient voltage to light up. This 
lamp uses an electronic ballast capable of creating a high 
frequency voltage and an increase in the voltage value on the 
UV lamp for a short time. This overvoltage is obtained by a 
resonant circuit (RLC). The voltage delivered by the DC/AC 
converter, feeds a transformer to a resonant system formed by a 
resistor Rr in series with an inductance Lr and two capacitors 
Cr1 and Cr2 (Figure 13) The receiver is a discharge lamp (UV) 
which is compared to an infinite impedance before start-up and 
to a low value impedance after start-up [4, 5]. The 
corresponding bong-raph model is shown in Figure 14. 

1 2

3

4

5

6

7

8Se: Ve 1

R:RL

I: L

TF

C

R:RC

R: R Load0



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Fig. 13.  Equivalent electrical diagram of a UV lamp power supply. 

 
Fig. 14.  Bond-graph model of the irradiation system. 

B. The UV lamp 

The UV water treatment system consists of a high pressure 
lamp placed vertically in a quartz sheath to be thermally 
isolated from the water. This lamp is assembled in a closed 
reactor. The water circulates in thin layers in the vicinity of the 
lamp because the UV rays are rapidly absorbed by the water. 
The disinfection efficiency obtained varies between 90% and 
99.99%, depending on the duration of exposure of the water to 
radiation and the characteristics of the water to be treated. 
Certain electrical circuits generated by electronic ballasts are 
required to start the discharge lamp, to regulate the lamp cycle, 
and to control the electrical current. 

 

 
Fig. 15.  Schema of the UV reactor. 

There are several models based on the current-voltage 
characteristics of the high-frequency discharge when trying to 
find a function that describes the relationship between current, 
voltage, and power consumed by the lamp. The UV lamp has a 
complicated model, it is in conjunction with an electronic 
ballast as described in (1): 

( )
( ) ( ) ( )

e Ballast Ballast Lamp

di t
U t R i t L U t

dt
= + +     (1) 

The universal lamp model is defined by: 

( )
( )

( )

Lamp

Lamp

I t
U t

G t
=     (2) 

The literature describes the conductance of a discharge 
lamp by a first-order differential equation, named G-model [1, 
21, 22], which is presented as follows: 

2

2

n

n

dG
a i b G

dt
= −∑     (3) 

where the coefficients α2 and bn
 
can be determined 

experimentally from the voltage-current characteristics or by 
physical evaluation. The physical evaluation is possible when n 
is equal to 2 or 3. In this case, the coefficients have a physical 
meaning: 

2 2

2 2 1
( ) ( )

dG
a i b G t b G t

dt
= − −     (4) 

The determination of the parameters α2, b1, and b2 is done 
using an identification approach. According to (4), we 
developed the bond graph model of the UV lamp. Figure 16 
exhibits the established model of the UV lamp. 

 

 
Fig. 16.  Bond graph model of the UV lamp. 

V. BOND-GRAPH MODELING OF THE HYDRAULIC SYSTEM 

The hydraulic system is a very important part of the water 
treatment system. It consists of a direct current motor 
connected to a centrifugal pump. 

A. Modeling of the DC motor 

The water treatment system has a motor pump to draw 
contaminated water from the inlet tank as shown in Figure 17. 
The motor pump subsystem must be able to control the flow 
rate of the contaminated water, which will determine the UV 
exposure time. Equation (5) expresses the latter: 

exposure /t V Q=     (5) 

The values V and Q are the volume of the reactor and the 
flow rate of water respectively. The variation of Q determines 
the possibility to control the exposure time and consequently 
the UV dose received by the water [6, 10, 11, 23].  

The dynamics of the engine [5, 10], are described by: 

a
a a a a b

dI
U R I L K w

dt
= + +     (6) 



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m m r
dw

C J Fw C
dt

= + +     (7) 

The DC motor is modeled in bond-graph by inertial 
elements I:La and resistive elements R:ra, representing 
respectively the inductance and the resistance of the armature. 
A gyrator models the transfer of energy from the electrical part 

to the mechanical part bK  ( a bE K w= ). The mechanical 
losses are modeled in bond graph by an inductive element I:J 
and a resistive element R:f which indicate respectively the 
coefficients of inertia and viscous friction of the DC machine. 
The DC motor drives a centrifugal pump characterized by a 
rotor shaft Γ proportional to the square of speed w  

(
2

TK wΓ = ). Figure 18 presents the bond graph model of a 
DC motor. 

 

 
Fig. 17.  Schematic representation of the location of a DC motor in the UV 

water treatment system. 

 
Fig. 18.  Bond graph model of a DC motor. 

B. Modeling of the Centrifugal Pump 

The water disinfection operation consists of water 
circulating through a UV reactor. Once the pump is running, 
the rotation of the impeller produces pressure and a speed that 
determines the flow of the fluid in the hydraulic system [5, 10, 
14]. The theoretical head He developed by a centrifugal pump 
is given by: 

2 2
2

2
e

w r
H

g
=     (8) 

The pressure developed by the wheel is directly 
proportional to the angular velocity w. The shaft speed is 
proportional to the flow rate Q. The developed pressure and the 
transmitted torque have the following expressions: 

22

2

2
e eP gH

wrρρ= =     (9) 

2

2

2
eT Q

wrρ
=     (10) 

The relationship between the pressure supplied by the pump 
and the rotation speed, can be modeled in bond-graph by a 
modulated gyrator element, MGY. The latter transforms the 
mechanical flow (speed) into hydraulic force (pressure). The 
pressure losses in the pump are due to the friction between the 
liquid threads and against the walls of the machine: 

fp mpT f w=     (11) 

This friction is modeled in bond-graph by a resistive 
element R:fmp and the moment of inertia of the rotating parts of 
the pump has the following expression: 

ip pt
dw

T J
dt

=     (12) 

This moment of inertia is modeled in bond-graph by an 
inertial element I:Jpt.The pressure losses in the hydraulic circuit 
are due to the friction of the flow lines against the walls of the 
machine. They are modeled by a resistive element R:fξd. The 
height difference between the two tanks is modeled by a 
negative force source: 

eSe gHδ= −     (13) 

The associated bond graph model of the centrifugal pump is 
shown in Figure 20. 

 

 
Fig. 19.  Synoptic diagram of a centrifugal pump. 

 
Fig. 20.  Bond graph model of the centrifugal pump. 

For a stationary regime (constant speed), the characteristic 
of the theoretical head of a pure centrifugal pump in vacuum 
(isolated from the hydraulic network) can be seen in Figure 21. 

 



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Fig. 21.  He (Q) simulation characteristic of a centrifugal pump. 

VI. GLOBAL MODEL OF A WATER TREATMENT SYSTEM BY 
BOND GRAPH 

After having modeled the different elements of the water 
treatment system and simulated the obtained models, we can 
deduce the global model (BG) by combining the different 
models obtained, which is presented in Figure 22.  

 

 
Fig. 22.  Global model of the global UV water treatment unit 

VII. SIMULATION RESULTS 

The UV water treatment system consists of a closed 
cylindrical stainless steel reactor with an annular cross-section, 
70cm in length, 6cm in internal diameter and 2L of useful 
volume. It is equipped with a single low-pressure mercury 
discharge lamp with the following characteristics: power 70W, 
nominal current 0.65A, length 400mm, diameter 15mm, placed 
in the axis of the irradiation room and protected by a clean 
quartz sleeve. The lamp is powered by an electronic ballast 
consisting of a single-phase inverter with transistors producing 
25-100kHz at its output and a resonant circuit to realize the 
ignition of the lamp. The disinfection system is also equipped 
with a motor pump for the suction of contaminated water, a 
pump to draw contaminated water from the inlet tank, a flow 
control valve to obtain different flow rates, and a filter to 
improve the transmittance of the contaminated water. The 
treated water in this system could be recycled through a 
recirculation circuit that could allow multiple passes through 
the irradiation chamber. 

According to the global model simulation, we obtained the 
following results: Figure 23 shows the output voltage of the 
single-phase inverter, which converts DC voltage to AC 
voltage to power the ballast and UV lamp, as they require AC 

voltage. The voltage and current curves of the UV lamp 
(discharge lamp) are shown in Figures 24 and 25 with the 
following values: the voltage is approximately 150V and the 
current 1.42A. The parameters of the UV lamp and the 
electronic ballast are: a2=93.33, b2=582036.5, b1=994.7, 
R=0.9Ω, C=2.8µF, L=0.16mA. Figure 26 describes the 
evolution of the conductivity G of the UV lamp. 

 

 
Fig. 23.  Simulation of the output voltage of the inverter. 

 
Fig. 24.  The voltage of the UV lamp. 

 
Fig. 25.  The current of the UV lamp. 

 
Fig. 26.  The conductivity of the UV lamp. 

Due to the negative impedance of discharge lamps and the 
complexity of the analysis, it is difficult to obtain models for 
the discharge lamps due to their negative impedance and the 



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complexity of the physical phenomena that occur inside the 
discharge tube. Discharge lamps can be operated at different 
frequencies with electronic ballasts. These different operating 
conditions can affect the behavior of the lamp. Generally, the 
non-linear I-V characteristic of the discharge lamps changes 
with frequency. Figure 27 represents the evolution of the non-
linear obtained I-V characteristic after these simulations. 

 

 
Fig. 27.  I-V characteristic curve of the UV lamp. 

The simulation of the continuous motor pump was 
performed using the buck converter. The motor voltage Ua is 
24V. Figure 28 shows the evolution of the induced current, the 
motor torque, the rotation speed and the water flow. One can 
see a normal evolution of the four parameters. 

 
Fig. 28.  Evolution of the motor pump's parameters. 

VIII. CONCLUSION 

This paper proposes link graph models for each subsystem 
of a UV water treatment unit. The different elements were 
connected to produce a dynamic model, which was used as the 
basis for building the simulation model. Using the 20-Sim 
software, a general simulation model was proposed. The series 
of simulations performed proved that the models were realistic 
and produced useful data. The link graph approach facilitates 
the connections between the different components of the 
overall model given the complexity of this unit. Future work 
could use this global model to determine the optimal 
parameters for all subsystems under given circumstances. The 
performance index could be the quality of water disinfection. 

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