Modeling and Simulation of a UV Water Treatment System Fed by a GPV Source Using the Bond Graph Approach

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

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][2][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 physicochemical 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][7][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. Structure of the overall UV water treatment system powered by a PV panel.

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.
where I pv is the the output current, I 0 the diode inverse saturation current, and R s 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: The photocurrent generated by the cell depends on the ambient temperature (T) and the solar irradiation (G) and is represented by:

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. The bond graph model for the equivalent circuit is presented in Figure 5. It contains an element of capacitance, and the element noted as R D is the resistance of the diode. It contains the non-linear characteristic. This allowed us to replace the generator by a modulated flux source S f which plays the role of the modulating signal representing the photovoltaic current I ph . This model was simulated by the software 20-sim [6,[9][10][11]. 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. 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].

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][17][18].

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. 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).

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.

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. 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): The universal lamp model is defined by: 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: where the coefficients α 2 and b n 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: The determination of the parameters α 2 , b 1 , and b 2 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.

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: 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] 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 b . 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 Figure 18 presents the 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 H e developed by a centrifugal pump is given by: 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: 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 mp T f w = (11) This friction is modeled in bond-graph by a resistive element R:f mp and the moment of inertia of the rotating parts of the pump has the following expression: This moment of inertia is modeled in bond-graph by an inertial element I:J pt .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:f ξd . The height difference between the two tanks is modeled by a negative force source: The associated bond graph model of the centrifugal pump is shown in Figure 20.   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. 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: a 2 =93.33, b 2 =582036.5, b 1 =994.7, R=0.9Ω, C=2.8µF, L=0.16mA. Figure 26 describes the evolution of the conductivity G 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 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 nonlinear obtained I-V characteristic after these simulations. 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. 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.