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F. Calise, et al. Energy Conversion and Management 220 (2020) 113043
than 13 °C and they are switched off when the temperature reaches The user-developed models by other tools and then included into
11 °C. For DHW production, two water-to-water heat pumps the TRNSYS environment by the authors are:
(DHW_HP), operating in parallel, are designed to supply DHW at 45 °C
•
to the users. The electricity produced by PV panels is used to supply first the heat exchangers HE1 and a flat-fin compact heat exchanger for
the RO unit and then the heat pumps. A variable level water storage DHW production are developed using a modified version of the well-
basin, aiming at storing the produced freshwater, is also included. In known ɛ-NTU method [34]; details are reported in reference [29];
particular, if the production of the RO unit is higher than the district • the MED model is reported in reference [25]. The model consists of a
water demand, the surplus is supplied to the basin, which stores the stationary model based on mass and energy balances and heat
produced freshwater. Conversely, when the solar radiation availability transfer equations applied to i) the first effect, supplied by solar
is scarce and/or if the district water demand is higher than the RO energy; ii) the second to the last effect, and iii) the condenser;
production, the stored desalted water is supplied to the user. In this • the triple-junction concentrating PVT collector model, based on
way, the dependency of the island on the freshwater supplied by ships is zero-dimensional energy balances, reported in reference [30];
reduced. Details regarding the layout and some special control strate- • the RO unit model based on the Solution-Diffusion model [31–33],
gies adopted to allow the proper operation of the RO unit are reported that is one of the most widely accepted description for the RO
in reference [8]. Note that such a plant is not equipped with water or process. The detailed model of the RO unit (in-house developed by a
electric storage systems. Therefore, when the PV panels production is zero-dimensional approach) and its validation are reported in re-
scarce, with respect to the energy demand of RO unit and heat pumps, ference [8];
the necessary electricity is supplied from the grid. Conversely, the • the energy and economic model developed to evaluate the energy
electric excess is delivered to the grid. and economic performance of the plants.

3. System model In the following the energy, economic and environmental model, as
well as the CPVT and RO models are described.
All the components included in the investigated plants are modelled
by adopting models provided in the dynamic simulation tool TRNSYS 3.1. CPVT collector model
17 [26]. This is a well-known software in the academic community and
is successfully used to carry out dynamic analyses of several types of This collector consists of a parabolic trough concentrator and a
solar systems [27]. Note that the studied layouts do not exist yet, so, a linear triangular receiver, located at the focus of the parabola, with the
validation against a real system is not possible. Nevertheless, the lower surface equipped with a triple-junction InGaP/InGaAs/Ge,
models of TRNSYS are based on unsteady algorithms and they are va- whereas the upper surface is equipped with an absorber surface. By
lidated using experimental data or based on manufacturers’ data. The energy balances developed in EES (Engineering Equation Solver), the
achieved results are, therefore, considered highly reliable and it can be temperatures and energy flows of the main components of the collectors
assumed that the plants are validated. For the sake of brevity, the are calculated. Therefore, the overall energy balance on a control vo-
complete models of the incorporated components (pumps, diverters, lume including the entire receiver (from PVT to the insulation) is:
mixers, diverters, heat exchangers, auxiliary heaters, etc.) are not re-
η
I α top
in
̇ f
rec b
rec b opt PV
ported here, since they were presented in a recent works developed by A I C PVT opt + A top tot = m h( out − h ) + C PVT A I η η
4
4
η ρ
some of the authors [8]. In the following, some brief details about these + AI C PVT opt PVT + A top R top σ T( top − T )
rec b
ε ,
sky
components is provided. 4 4
,
+ A PVT σε R PVT T ( PVT − T conc )
• Type 94, modelling the performance of photovoltaic panels, by + A PVT h c PVT, T ( PVT − T ) + A top c top, T ( top − T ) (1)
h
a
a
considering the electric performance of the poly-crystalline/crys- A second energy balance considers the control volume that includes
talline silicon cells. The so-called “four parameters” model, de- the metallic substrate and the fluid channel, assumed as a heat ex-
scribed in reference [26] is used. Type 94 calculates the four para- changer, and it is:
meters values from manufacturers’ data in order to generate an IV
− h ) − T )
̇ f
̇ f f
curve at each time step. mh( out in = εm c T( sub in (2)
• Type 4, simulating the energy storage tanks providing thermal en- in which T sub is the temperature of the metallic substrate.
ergy for space heating, DHW, cooling, and the energy for seawater For the given boundary conditions (beam and total radiations and
desalination. They consist of fluid-filled sensible vertically stratified relative angle of incidence, inlet temperature and mass flow rate, en-
tank, modelled by dividing the tank in n fully-mixed nodes with vironment and sky temperature, ambient pressure and wind velocity),
equal volumes [26]; the unknown variables are five, namely: PVT temperature, substrate
• Type 107, using a map catalogue approach to simulate the perfor- temperature, fluid outlet temperature, temperature of top receiver
mance of the LiBr-H 2 O single effect absorption chiller at any time surface (facing the sky), and temperature of the concentrator.
step of the simulation [26]; Therefore, three more – a total of five – equations must be considered.
• Type 927, modeling a single-stage water-to-water reversible heat The third required equation is derived from an energy balance on a
pump. This model is based on user-supplied catalog data file con- control volume including the PVT layer and the metallic substrate.
taining the normalized capacity and power draw, based on the en-
tering load and source temperatures and the normalized source and T PVT − T sub − h ) T sub − T top
̇ f
A rec = mh( out in + A top
load flowrates [26]; r PVT −sub r top (3)
• Type 56, simulating the dynamic energy performance of the district The fourth energy balance can be considered with respect to the
buildings in terms of heating and cooling loads. In particular, Type control volume that includes the top side of the substrate and the top
56 takes into account the 3D geometry (by means the the Google
surface of the triangular receiver:
SketchUp TRNSYS3d plug-in [28]), envelope thermophysical pro-
prieties, and indoor (i.e. lighting, machineries heat gains schedule as T sub − T top
I
A top + A top top
well as the buildings users’ occupation and activity) and environ- r top
mental conditions of the buildings (i.e. solar radiation, ambient 4 4
I ρ
h
ε ,
sky
a
= A top top top + A top R top σ T( top − T ) + A top c top, T ( top − T ) (4)
temperature, humidity) etc. For further details see reference [2].
Finally, the last energy balance considers the control volume that
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