A dynamic model of hybrid photovoltaic/thermal panel

Transcription

1 November 5-7, Sousse Tunisia A dynamic model of hybrid photovoltaic/thermal panel Majed Ben Ammar, Mohsen Ben Ammar,2 and Maher Chaabene Unité de Commande de Machines et Réseaux de Puissance (CMERP, ENIS Route de Soukra Km 3.5, BP W, 3038 Sfax, Tunisia,2 aboratoire : Modélisation, Information et systèmes (MIS, UPJV-IUP 7, Rue Moulin Neuf, 8060 Amiens, France benammarmajed@yahoo.fr, mohsen.ben.ammar@u-picardie.fr maherchaabane@yahoo.com ABSTRACT In this paper a dynamic simulation model of a photovoltaic and water heating system (PV/T is developed. The model consists of a set of mathematical equations governing the main components of the system; namely: transparent cover, solar cell, absorber plate, operating fluid and storage tank. The model is based on the analysis of the energy balance which includes the photo electric conversion and the thermal conduction, convection and radiation. The model gathers all components equations so as to reflect the electrical and thermal behaviour of the PV/T system. It delivers the state equation of the system function of the climatic parameters and the fluid flow rate. The investigation of the effect of water mass flow rate through the collector on PV/T outputs have been carried out. Keywords - PV/T, modeling, state equation, simulation.. INTRODUCTION Many researchers have improved the performance of photovoltaic system. Some investigations stated that the efficiency increases when the cell temperature decreases. Hence, a new technology combining thermal and photovoltaic effects (Photovoltaic/Thermal PV/T is developed. Considered as a hybrid system, the PV/T collector can simultaneously produce thermal and electric energy. It is composed of a flat-plate water heating collector inserted within a PV module. Many technological improvements have been introduced in literature. In fact, a thermal behavior of a copolymer PV/T solar system in low flow rate condition has been investigated []. It confirms that the utilization of a copolymer for the total design of the solar collector has numerous advantages as reducing the weight, facilitating the manufacturing and reducing the cost. Similarly, a parametric study on the performance evaluation of hybrid PV/T water/air heating system confirms that the daily efficiency of Integrated photovoltaic and thermal solar (IPVTS system with water is higher than these of all configurations except glazed without tedlar (GWT [2]. Also many applications of PV/T have been implemented. Indeed, a distributed dynamic modeling and experimental study of PV evaporator in a PV/T solar-assisted heat pump is developed [3]. The study has improved the overall system efficiency. In the same way a hybrid photovoltaic-thermosyphon water heating system for residential application is investigated, a high final hot water temperature in the collector system can be achieved after a one-day exposure [4]. In this paper, an explicit dynamic model suitable for PV/T system simulation is introduced. The effectiveness of PV/T system compared to a photovoltaic panel (PV is underlined. The model provides the thermal state of various collector components and generates results for hourly and transient performance analysis (thermal/electrical gain. Nomenclature Number of tubes in the plane sensor Outlet temperature of the fluid ( C. Constant of Stefan (W/m 2.K 4 Ambient temperature ( C. ength of the tube (m. Temperature of the absorber ( C. Outdistance between the tubes (m. Temperature of the cell ( C. Internal diameter of the tube (m. Inlet temperature of the fluid ( C. Area of sensor (m 2. Conductivity of the insulator (W/mk. Average temperature of the fluid ( C. Conductivity of material of the tube (W/mk

2 Conductivity of the absorber (W/mk. Wind speed(m.s -. m Mass density (kg/s. Number of glass covers. m c Effective collector capacity (J/K. Incident solar irradiation (W/m 2. C. Flow mass (Kg/s.m 2. Reflectivity diffuses glazing. Conductance of the thermal losses (J/kg.K. The absorptance of the absorber. Volume through put (m 3 /s. Transmissivity of the glazing. Thermal conductivity (W/m. C. Emittance of absorber. Pranl number. Emittance of glass. Reynolds number. Photovoltaic voltage (V. Coefficient of heat loss (W/m 2 C. Photovoltaic current (A. Thermal coefficient (W/m. C. Current in standard conditions (A. Convection coefficient of exchange (W/m. C. 2. DESIGN OF THE PV/T SYSTEM Temperature coefficient of short-circuit (ma/ C. The hybrid photovoltaic thermal system is basically constructed by pasting photovoltaic solar cells directly over the absorber plate of the solar collector in conventional forced circulation type solar water heater. A PV/T solar collector is composed of: (i A transparent cover allowing sunlight to pass towards the absorber and to create an effect of greenhouse. It is composed by one or more panes. (ii A photovoltaic cell for the production of electricity. (iii A plate absorbing for transfers from energy collected to a coolant. (iv A box ensuring the protection of the whole of these elements. (v A heat insulator allowing limiting the losses by conduction through the walls back and side. The schematics of the PV/T collector are shown in Figure ; the upper cover is represented by a glass sandwich that includes PV cells. The cell area can cover the entire glazed surface or can be distributed in a grid where the spacing between adjacent columns and rows can allow a direct gain of solar radiation to the backward absorber plate. The glass sandwich looks like a chess board composed of squares with or without PV cells embedded. Different configurations of PV/T collector can be created changing the cell area density in order to balance electricity and thermal energy output of the system. (a Cross section (b View of the array Figure. Construction of a PV/T collector for water heating. 3. DYNAMIC MODE OF PV/T (a Exploded view The dynamic thermal model of the PVT collector is built upon the finite-difference control-volume technique. The PV/T collector is composed of four major components which represent the different nodes: Glass cover, solar

3 cell, absorber plate, water in channels and in storage tank. 3.. PV/T modeling The energy and fluid flow equations are developed on the bass of the four nodes. All sub-parts in each node are considered lumping together in proportion to give the average properties of the representing major component, (Figure 2. Figure 2. Modeling of PV/T system. Where T g, T c, T p, T f, T a are respectively the temperature of glazing, the solar cell, the absorber plate, the water circulation and the ambient temperature. W is the wind speed, G incident solar irradiation, m the mass flow rate of fluid, P the electric power output and Q the thermal profit. Glass cover sub model The glass cover temperature is computed by equation. dtg m C GA A ( h h ( T T g g g g g Wind r, ga a g A ( h h ( T T g cg r, cg C g ( Where m g and C g are respectively the mass and the specific heat capacity of the glass cover, α g the effective absorptivity of glass. h wind, h c-g the convective heat transfer coefficients at the outer and inner glass surfaces respectively and h r,g-a, h r,c-g the radiation heat transfer coefficients at the outer and inner glass surfaces respectively. The convective heat transfer coefficient under is given by (Watmuff at al., 977 hwind 2.8 3v wind (2 The radiation heat transfer coefficient between the front cover and the ambient environment is h 2 2 r, ga g( T g T a ( T g Ta (3 And that between the front cover and the collector plate is 2 2 ( Tg Ta.( Tg Ta h r, c g (4 g c Where ε g and ε p are the emissivity of the glazing and the collector plate respectively, and σ is the Stefan- Boltzmann constant. Solar cell sub model Similarly, the temperature of the PV solar cell depends of the glass cover temperature as dt m c c Cc c cgac Achr, gctc ( Tg Achconvgc, ( Tc Tg A S hconcp, ( Tc T p c c c GA c (5 where m c, C c are correspondingly the mass and the specific heat of the solar cell, h conv,gc, h r,gc are respectively the convective and the radiation heat transfer coefficients between glass cover and solar cell, h con,cp the conduction heat transfer between cell and absorber plate. The electric power output depends on the instantaneous operating temperature T c of the PV module, and can be expressed as a function of the electrical current of the PV module: I pv np I ph V pvrs. Ipv Vpv RS. Ipv I 0 exp VT R (6 sh K B. T a. n Where V T (7 q At the level of the PV panel the solar cell temperature is expressed as: Ut.( Tp Ta Tc Tp. (8 hc, pc hr, pc The photoelectric current is given by : G I I T T (9 SC, STC STC ( a, ref 000 ph 23 where KB J, the Boltzmann K 9 constant q.6 0 C, I 0 is the opposite current of saturation of the diode, n is the factor of nonideality (n=,62 of the diode and V T is the thermodynamic potential. In the same way, the photovoltaic module voltage with N S serial is : I SC, STC I pv V N. V ln (0 pv S T I 0 The electrical power is given by: P Vpv I ( pv pv Absorber plate sub model The temperature of the absorber plate is : - 2 -

4 dt m C P A h ( T T A h ( T T P P S concp, C P C conpa, P a (2 A h ( T T m C T F confa, f a F F f Where m p, C p are the mass and the specific heat of absorber, h cond,cp is the heat transfer coefficient between absorber and solar cells ; h cond,pa the conduction heat transfer coefficient between the absorber and the ambient environment, h con,fa the convective heat transfer coefficient of water flow in channel. The mean plate temperature is used to calculate the useful gain of a collector (Q u : Qu Ac [ S U( Tpm Ta ] (3 where S is the absorbed solar radiation. The heat loss coefficient (U is: Where U N g A C T p T a T p N g f B ( T 2 T 2 p a ( T B U t (4 A D 0, 33 p T h w C 2N g f D N N g p 0,05 g ( p p ( f h h N 2 ( 0.04 w w( 0.09 g The mean plate temperature is given by: Q ( u A T c pm T fi.( F R (5 F R. U Where the collector heat removal factor is: GCp U. F' F ( exp ( R (6 U GCp The collector efficiency factor U F' (7 lai( U ( d ( lai d F Cb dihf The effectiveness coefficient is: tanh(( lai d / 2 F (8 m ( lai d / 2 Water in channels and in storage tank sub model The fluid temperature is computed by : a dt f Tf m C f A f hc f ( TC T f C f m (9 y Where C f is the specific heat of fluid, A f the inner surface area of the flow channels per unit surface area of the collector and y is the length of channel. The convective heat transfer coefficient is given by: Nuf k f hc f D (20 h Where D h is the hydraulic diameter of the channel and k f is the thermal conductivity of fluid. The mean fluid temperature is: ( Q A T T u c fm fi.( F. U F (2 R Where F is the collector flow factor: mc p AcU F F ( exp( AcU F mc (22 p The storage tank temperature is given by : dtr mr CR mc F( TfoTfi AR hrta, ( TR Ta (23 where m R and A R are respectively the lumped mass and the outside surface area of the water tank.t fo, T fi water temperature at the inlet and outlet of the tank, h R,Ta heat loss coefficient at the outside surface of the tank, including the thermal resistance of the tank insulation STATE EQUATION OF PV/T SYSTEM By gathering the system components sub-models, the global energy balance can be written as a state equation: T ( t AT ( t B m CE (20 y ( t DT ( t T(t is a vector containing the temperatures at the 3 nodes of the PV/T system, A is the state matrix which contain the heat exchange coefficients between the system elements, B is the control matrix which encloses commands applied on the mass flow rate ( m in the PV/T system, C is the perturbation matrix acting on the perturbation inputs vector (E=[G, Ta], y(t is a vector of exit containing the electrical power, the temperature of exit of fluid and the temperature of storage tank. The detailed form of the state equation is expressed by: T c A A2 A3 T c B C C G T 2 f A 2 A22 A23 Tf B2 m C2 C22 Ta T R A3 A32 A33 TR B3 P D D2 TfoD2 D22 Tro D3 D32 D3 T c D23 Tf D33 TR (2-22 -

5 4. SIMUATION RESUTS Differential equations were converted to numerical format through finite difference scheme. The collector segments were interacted through the glass nodes, the solar cell nodes, the thermal absorber nodes and water nodes. It can simulate the transient performance of the system at a time interval of one minute. Its inputs require total solar irradiance and ambient temperature while its outputs contain the current and voltage generated by the solar cells, the temperatures of the transparent cover, solar cells, absorber plate, water inside the collector and the storage tank. The output data are analyzed and used to estimate the electrical power output, the amount of heat that can be drawn from the system. A constant wind speed of 5m/s and any hourly total solar irradiance and a daily ambient temperature are used in the simulation shown in Figure 3. The temperature of the photovoltaic modules decreases while water circulates which increases the electrical output power. Fur there, heated water may be either used as is or converted to electric energy

6 Figure 3. Simulation of the PV/T system at constant mass flow. 5. CONCUSION A PV/T dynamic model is established. Electric and thermal equations are formulated as a state equation system. The model simulation evaluates the system performances such as T fo, T p, T pvt and electric power for a considered weather conditions (G and T a and a constant operating condition ( m. It is observed that the thermal and electrical performances of PV/T system are improved when compared to separated solar thermal panel and photovoltaic panel. The developed model will be used to establish a sizing algorithm for a PV/T plant then to control the mass flow so as to bring optimum function for the system. 6. REFERENCES [] Christian Cristofori, Gilles Notton, Jean ouis Canaletti, Thermal behaviour of a copolymer PV/Th solar system in low flow rate conditions, solar energy 83 ( [2] Arvind Tiwari, M.S. Sodha, Performance evaluation of hybrid PV/thermal water/air heating system a parametric study, Renewable energy 3 ( [3] Jie Ji, Hanfeng He, Tintai Chow, Gang Pei, Wei He, Keliang iu, Distributed dynamic modeling and experimental study of PV evaporator in PV/T solar assisted heat pump, International Journal of Heat and Mass Transfer 52 ( [4] T.T. Chow, W. He, J. Ji, hybrid photovoltaicthermosyphon water heating system for residential application 80 ( [5] T.T. Chow, W. He, A..S. Chan, K.F. Fong, Z. in, J. Ji, Computer modeling and experimental validation of a building-integrated photovoltaic and water heating system, Applied Thermal Engineering 28 ( [6] Jie Ji, Jian-Ping u, Tin-Tai Chow, Wei He, Gang Pei, A sensitivity study of a hybrid photovoltaic/thermal water-heating system with natural circulation, Applied Energy 84 ( [7] Jie Jia, Tin-Tai Chow, Wei He, A dynamic performance of hybrid photovoltaic/thermal collector wall in Hong Kong, Building and Environment 38 ( [8] Y. Sukamongkol, S. Chungpaibulpatana, B. immeechokchai, and P. Sripadungtham, Simulation of Transient Performance of a Hybrid PV/T Solar Water Heating System, Technical digest of the international PVSEC-4 Tailand (2004. [9] Duffie JA, Beckman WA. Solar engineering of thermal processes, 2nd ed. New York: Wiley,