# A Comprehensive Energy Model for an Optimal Design of a Hybrid Refrigerated Van

^{1}

^{2}

^{*}

## Abstract

**:**

_{2},e emissions could be reduced by 20% compared to a standard refrigerated van. Despite the environmental benefits provided by this sustainable solution, the payback period is still too long (above 20 years) because of the necessary investment to adapt the vehicle and considering fuel and electricity prices currently.

## 1. Introduction

_{2},e (carbon dioxide equivalent) emissions and reduce vulnerability to climate change. CO

_{2},e emissions from this sector are about 30% in developed countries of anthropogenic origin and 23% worldwide [1]. There are 4 million refrigerated road vehicles, and together with refrigerated containers and supermarkets, 45% of the electricity is consumed by refrigeration equipment [2]. Of that, 55% of the refrigerated road vehicles are vans, followed by semi-trailers and trucks (25% and 20%, respectively). CO

_{2},e emissions per kg of food and kilometer from refrigeration systems of the small vehicles are more than double the larger ones, for both chilled and frozen distribution of different products [3]. More than 98% of all foods within the UK are transported by road, and the distances traveled have increased in recent years [4]. Tertiary distribution using rigid vehicles was the most energy-intensive transportation method, while primary distribution at ambient temperature was the least.

_{2}emissions of vans with refrigeration units are 15% higher than standard vehicles, with NO

_{X}emissions estimated to rise by 18%. The weight of the additional engine in the transport refrigerated sector is significant [5]. Sovacool et al. [6] highlighted the transport and delivery sector as one of the most carbon-intensive emissions of the food and beverages industry. A significant improvement was the uptake of distributed generation and small-scale renewable energy systems. It is one of the three most significant areas with higher energy and carbon savings potential.

_{2},e emissions between 5% and 15% in a refrigerated trailer when replacing R404A with R452A. Citarella et al. [9] conducted a thermo-economic and environmental analysis in which R452A presented low set-up costs and high COP in the optimal configuration, representing a good compromise as a mid-term R404A replacement. Górny et al. [10] confirmed the suitability of a method for assessing the lubricity of POE with R404A and R452A, which is essential in the selection of oil for new refrigerants and long-life refrigeration systems with low energy consumption. Recently, Maiorino et al. [11] presented a comprehensive review about the state of the art of the technologies used in the refrigerated transport sector, identifying the main issues and possible solutions to improve the sustainability of the cold chain.

_{2},e emissions caused by the energy consumption to power the compressor and carry the refrigeration unit resulted in a large part of the total. Moreover, refrigerators driven by auxiliary engines have higher CO

_{2},e emissions than those operated by the vehicle engine or electricity.

^{2}PV integration for a cold storage facility, and the energy consumption decreased by around half, with a 5.2 years payback period. Novaes Pires Leite et al. [25] found robust techno-economic viability in integrating air-conditioning and solar PV systems, especially in tropical latitude regions. Essential variables are energy price, annual adjustment, PV cost, and solar panel efficiency.

_{2},e emissions compared to solar absorption heat pumps, and economies of scale offer opportunities to improve them.

_{2},e emissions. From energy and economic perspectives, this work aims to model and analyze an innovative hybrid refrigerated van equipped with a PV system that powers the refrigeration unit. Moreover, the renewable source is sized considering different PV technologies. The charge and discharge curves are evaluated as a function of the required cooling load, battery capacity, impact of temperature on performance, and comparison between lithium and lead-acid batteries.

## 2. Comprehensive Energy Model

_{2},e emissions (Figure 1). A photovoltaic system to provide a gross peak power of 600 W was considered for this investigation. The main characteristics of the van and the photovoltaic system can be found in Appendix A.

_{in}, c

_{in}and T

_{in}are the mass, the specific heat capacity, and the air temperature inside the cold van, respectively. ${\dot{Q}}_{aux}$, ${\dot{Q}}_{defrost}$, and ${\dot{Q}}_{door}$ are the thermal loads due to the auxiliary components, the defrost cycle, and the door opening, respectively, ${\dot{Q}}_{RU}$ is the cooling power, and ${\dot{Q}}_{in-w}$ and ${\dot{Q}}_{in-c}$ are the thermal loads due to the heat exchange with the walls and the cabinet, respectively. The initial conditions are calculated for any external condition (airspeed, irradiance, temperature), considering the case in which the temperature profile in the walls follows a hysteretic cycle. This cycle oscillates around the set-point air temperature following the refrigeration ON/OFF cycle. Figure 2 represents the thermal fluxes to which the cold chamber is subjected.

_{2},e emission, together with the value of the electricity losses at the PV panels, battery (electrical connections), refrigeration unit, inverter, and relative savings in electricity over the entire month, excluding the battery charge. Fuel consumptions due to van traction and power refrigeration system depend on the specific route. The input data are the time of arrival at each checkpoint (points at which the parameters are evaluated and then kept constant until the next checkpoint), average speed of the van, distance between two successive checkpoints, and load carried.

_{r}Rolling resistance coefficient, ${\eta}_{mec}$ vehicle transmission efficiency, and ${\eta}_{g}$ overall efficiency of the internal combustion engine.

^{3}kg

^{−1}, a unit cost of methane Cu of 0.99 € per kg referred to the last quarter of 2018 in Italy [31], and an emission factor f of 56.1·10

^{−3}kgCO

_{2},e MJ

^{−}

^{1}[32], the cost and carbon footprint of the trip can be obtained from Equations (5)–(7).

## 3. Results and Discussion

#### 3.1. Single-Delivery Scenario

#### 3.1.1. Selection of PV Panels

#### 3.1.2. Selection of Batteries

_{b}), and another the available solar energy (RTE

_{tot}). Both factors are added to the energy absorbed from the grid, as shown in Equations (9) and (10).

_{b}does not vary much between months since the energy the battery provides is almost constant throughout the year. The deviations between RTE

_{b}and RTE

_{tot}are shown only during summer, since there is an increase in the available solar energy. In detail, a significant difference can be observed for the smallest lead-acid battery (50 Ah). The latter switches into charge mode very often. Therefore, it is characterized by a high state of charge, and it switches into charge mode with a constant voltage if the available solar energy is high. In this state, the current is reduced to protect the battery from an overvoltage, so RTE

_{tot}decreases. In the end, a 100 Ah lead-acid battery provides the best techno-economical compromise.

#### 3.1.3. Overall Results

_{RU}represents the energy absorbed by the refrigeration unit; E

_{PS}is the energy provided by the photovoltaic system to run the refrigeration unit or recharge the battery; and E

_{b}is the energy supplied by the battery to run the refrigeration unit. Losses are attributed to each section of the photovoltaic power supply system.

_{2},e emissions by about 150 to 250 kg per year; even in this case, the situation could improve considering longer trips and carrying out more than one trip per day.

#### 3.2. Multiple-Deliveries Scenario

_{2},e savings compared with the same van without PV panels. As seen, there is a yearly economic saving of about 138 €. Undoubtedly the savings would be of no minor importance for longer trips and carrying out more than one delivery per day. Moreover, like in the single delivery scenario, higher cost savings should be expected with an increasing unit cost of methane.

_{2},e per year is possible, which is more noticeable during the peak in the spring and summer months. Since the economic and environmental savings are caused by the increase of energy produced by the PV panels, similar trends are observed. Moreover, the results could improve considering longer trips and carrying out more than one multiple-delivery per day.

## 4. Conclusions

_{2},e emissions for any type of use. The model can be seen as an initial supporting tool aiming to design a sustainable refrigerated-transport system for food and perishable goods. The model uses the set-point temperature, battery and photovoltaic panel characteristics, and trip as input parameters. Then, the V-I characteristic curve of the photovoltaic panels and the environmental conditions are determined. The thermal model of the refrigerated cabin, and the electrical model, including batteries and photovoltaic panels, are coupled.

_{2},e emissions are avoided. In a more realistic scenario that simulates multiple deliveries, the yearly economic saving is increased to 138 € and 464 kgCO

_{2},e reduction of carbon footprint. It is proved that the batteries and the photovoltaic production are insufficient to provide the cooling required by the refrigeration unit. However, along with higher cooling requirements, electricity production is maximized in the summer.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Symbols | |

A | amplitude of the exponential area [V] |

B | constant of time in the exponential area [Ah^{−1}] |

c | specific heat [J kg^{−1} K^{−1}] |

Cd | coefficient of aerodynamic drag [-] |

C_{inf} | infiltration coefficient [m^{1/2} s^{−1}] |

C | cost [€] |

Corr_{R} | resistance correction parameter [Ah^{−1}] |

Corr_{K} | polarization constant correction parameter [A^{−1}] |

Cr | rolling resistance coefficient [-] |

Cu | unit cost of methane [€ kg^{−1}] |

d | distance [m] |

D_{en} | engine displacement [m^{−3}] |

E | electric energy [kWh] |

Exp | exponential voltage [V] |

$f$ | emission factor [kgCO_{2},e MJ^{−1}] |

F | fuel consumption [kg] |

FR | instantaneous rate of fuel consumption [kg s^{−1}] |

g | gravity [m s^{−2}] |

G | solar radiation [W m^{−2}] |

h | convective heat transfer coefficient- [W m^{−2} K^{−1}] |

H | door’s height [m] |

i | current [A] |

$i$* | filtered current [A] |

it | actual charge of the battery [Ah] |

j | specific enthalpy [kJ kg^{−1}] |

k | engine friction value [-] |

K | polarization constant [V Ah^{−1}] |

l | transport load [kg] |

LHV | lower heating value [kJ kg^{−1} or MJ kh^{−1}] |

m | mass [kg] |

$\dot{m}$ | mass flow rate [kg s^{−1}] |

N_{en} | engine rotation speed [rps] |

P | electric power [W] |

Q | battery capacity [Ah] |

$\dot{Q}$ | heat transfer [W] |

$\dot{q}$ | heat flow rate [W m^{−2}] |

R | internal resistance of the battery [Ω] |

RTE | Round Trip Efficiency [-] |

s | width [m] |

S | surface [m^{2}] |

SOC | State Of Charge [%] |

T | temperature [°C or K] |

t | time [s] |

v | speed [m s^{−1}] |

V | voltage [V] |

$\overline{V}$ | constant voltage [V] |

Greek symbols | |

η | efficiency [-] |

η_{i} | Coulombic efficiency [-] |

σ | Stephan–Boltzmann constant [W m^{−2} K^{−4}] |

ρ | density [kg m^{−3}] |

τ | characteristic time constant of the considered battery [s] |

Subscripts | |

AG | air gap |

amb | ambient |

aux | auxiliary components |

b | battery |

B | body |

back | back side |

c | cabinet |

conv | conversion |

defrost | defrost system |

door | door |

drive | drive |

e | external |

en | engine |

front | front side |

fuel | fuel |

g | global |

in | inside |

Li | Lithium battery |

mec | mechanical |

mp | maximum power |

nom | nominal |

oc | open circuit |

Pb | lead-acid battery |

PV | photovoltaic |

rad | radiation |

real | real or indicated |

ref | reference |

Reintegrated | reintegrated from the grid |

roof | roof |

RU | refrigeration unit |

sc | short circuit |

sol | solar |

sky | sky |

w | wall |

Abbreviations | |

CO_{2},e | Carbon dioxide equivalent |

MPPT | Maximum Power Point Tracking |

PV | Photovoltaic |

## Appendix A. Refrigerated Van and PV System Features

Parameter | Characteristics |
---|---|

Engine (F1CFA401A) | Four-stroke bi-fuel spark ignition (petrol-methane) maximum power (methane): 100 kW (136 CV) @ 2730–3500 rpm maximum torque (methane): 350 N·m @ 1500–2730 rpm Displacement: 2998 cm ^{3} |

Refrigerated cabin | Reinforced isothermal class F (thermal transmittance of the walls between 0.29 and 0.4 W m^{−2}K^{−1}), minimum temperature inside the cabin of −20 °C |

Refrigeration unit | R-452A refrigerant, hermetic compressor with inverter (30 to 80 Hz) |

Refrigeration unit power supply | Electric mains or dedicated auxiliary alternator, directly driven by the heat engine |

Parameter | Body | Polyurethane | Glass Fiber Reinforced Polymer (GRFP) |
---|---|---|---|

Heat transfer transmittance, λ (W m^{−1} K^{−1}) | 60 | 0.024 | 0.64 |

Width, s (m) | 0.005 | 0.064 | 0.002 |

Density, ρ (kg m^{−3}) | 2700 | 40 | 1800 |

Specific heat capacity, c (J kg^{−1} K^{−1}) | 900 | 1400 | 1255 |

Parameter | Type A | Type B | Type C |
---|---|---|---|

Technology | HJT | Monocrystalline | Monocrystalline |

Peak power [W] | 120 | 108 | 52 |

V_{oc} [V] | 17.3 | 15.3 | 10.9 |

V_{mp} [V] | 14 | 12.6 | 9.1 |

i_{mp} [A] | 8.6 | 8.6 | 5.7 |

i_{sc} [A] | 9 | 9 | 6 |

Dimensions [mm] | 1046 × 683 | 1046 × 683 | 1109 × 293 |

Weight [kg] | 1.7 | 1.7 | 0.8 |

Parameter | Value |
---|---|

Nominal power [VA/W] | 3000/3000 |

Voltage [VAC] | 230 |

AC Voltage regulation (battery mode) [VAC] | 230 ± 5% 170–280 (For Personal Computers) 280 (For Home Appliances) |

Peak power [VA] | 6000 |

Efficiency peak [/] | 90% to 93% |

Transfer time [ms] | 10 (For Personal Computers) 20 (For Home Appliances) |

Waveshape | PURE WAVE |

Battery/charge voltage [VDC] | 24/27 |

Overcharge protection [VDC] | 33 |

Type of charge controller | MPPT |

Maximum capacity PV [W] | 1500 |

Maximum PV array open-circuit voltage [VDC] | 145 |

PV Array MPPT Voltage Range [VDC] | 30 to 115 |

Maximum charge current: solar and AC/rest [A] | 60/120 |

Relative humidity | 5% to 95% |

Operating/storage temperature [°C] | −10 to 50/−15 to 60 |

## Appendix B

Type of Heat Transfer | Equation |
---|---|

Convective between the walls’ external surface and the external air [34] | ${\dot{Q}}_{e-w}={h}_{e}{S}_{e}\left[{T}_{amb}-{T}_{w-e}\left(x=0\right)\right]$ |

Convective between the walls’ external surface and the air inside the driver’s cabin [34] | ${\dot{Q}}_{c-w}={h}_{c}{S}_{c}\left[{T}_{c}-{T}_{w-c}\left(x=0\right)\right]$ |

Incident solar radiation [34] | ${\dot{Q}}_{rad}={\displaystyle {\displaystyle \sum}_{i=1}^{4}}{\alpha}_{B}{G}_{i}{S}_{i}$ |

Radiative with the celestial vault (the vehicle is considered a small convex object placed inside a cavity) [34] | ${\dot{Q}}_{w-sky}=\sigma {\epsilon}_{B}{S}_{roof}\left[{T}_{sky}^{4}-{T}_{w-ext}{\left(x=0\right)}^{4}\right]$ |

Convective between the internal air and the surface of the inner wall bordering the outside | ${\dot{Q}}_{in-w}={h}_{in-w}{S}_{in-e}\left[{T}_{w-e}\left(x={s}_{wall}\right)-{T}_{in}\right]$ |

Convective between the internal air and the walls’ inner surface bordering the driver’s cabin | ${\dot{Q}}_{i-c}={h}_{in-c}{S}_{in-c}\left[{T}_{w-c}\left(x={s}_{wall}\right)-{T}_{in}\right]$ |

Internal due to the auxiliaries | ${\dot{Q}}_{aux}$ |

Door opening (≠0 only in the goods loading/unloading phases, known duration) [35] | ${\dot{Q}}_{door}={\dot{m}}_{a}\left({j}_{a,0}-{j}_{a,in}\right)$ where, ${\dot{m}}_{a}=\left[{C}_{inf}{S}_{door}\sqrt{H}{\left(\frac{{\rho}_{in}-{\rho}_{e}}{2}\right)}^{0.5}{\left[\frac{2}{1+{\left(\raisebox{1ex}{${\rho}_{in}$}\!\left/ \!\raisebox{-1ex}{${\rho}_{e}$}\right.\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\right]}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right]\left(\frac{{\rho}_{in}+{\rho}_{e}}{2}\right)$ |

Defrost system, given by electrical resistances (≠0 only during activation, known duration) | ${\dot{Q}}_{defrost}=867W$ |

Cooling capacity of the refrigeration system | ${\dot{Q}}_{RU}$ |

Condition | Equation |
---|---|

With the ambient | $-\lambda {\frac{\partial {T}_{w-e}}{\partial x}}_{x=0}={h}_{e}\left[{T}_{amb}-{T}_{w-e}\left(x=0\right)\right]+\frac{{\dot{Q}}_{rad}+{\dot{Q}}_{w-sky}}{{S}_{e}}$ |

With the cabin | $-\lambda {\frac{\partial {T}_{w-c}}{\partial x}}_{x=0}={h}_{c}\left[{T}_{c}-{T}_{w-c}\left(x=0\right)\right]$ |

With the internal air (wall that exchanges with the ambient) | $-\lambda {\frac{\partial {T}_{w-e}}{\partial x}}_{x={s}_{wall}}={h}_{in}\left[{T}_{w-e}\left(x={s}_{wall}\right)-{T}_{in}\right]$ |

With the internal air (wall that exchanges with the driver’s cabin) | $-\lambda {\frac{\partial {T}_{w-c}}{\partial x}}_{x={s}_{wall}}={h}_{in}\left[{T}_{w-c}\left(x={s}_{wall}\right)-{T}_{in}\right]$ |

Between two adjacent layers of the stratigraphy (i and j) | $-{\lambda}_{i}{\frac{\partial {T}_{w}}{\partial x}}_{x={s}_{i}^{-}}=-{\lambda}_{j}{\frac{\partial {T}_{w}}{\partial x}}_{x={s}_{i}^{+}}$ |

Density $\left({\mathit{\rho}}_{\mathit{P}\mathit{V}}\right)$ | Width $\left({\mathit{s}}_{\mathit{P}\mathit{V}}\right)$ | Specific Heat Capacity $\left({\mathit{c}}_{\mathit{P}\mathit{V}}\right)$ | Absorptivity (Front Side) $\left({\mathit{\alpha}}_{\mathit{f}\mathit{r}\mathit{o}\mathit{n}\mathit{t}}\right)$ | Absorptivity (Back Side) $\left({\mathit{\alpha}}_{\mathit{b}\mathit{a}\mathit{c}\mathit{k}}\right)$ | Emissivity $\left(\mathit{\epsilon}\right)$ |
---|---|---|---|---|---|

2700 kg m^{−3} | 0.003 m | 900 J kg^{−1} K^{−1} | 0.72 | 0.2 | 0.91 |

## Appendix C

#### Appendix C.1. Lithium Battery

_{R}and Corr

_{K}, have been introduced, which allow considering a variation of the internal resistance as the battery charge varies (it) and the variation of the bias constant as the discharge current varies (i). These parameters are calculated using an optimization function that minimizes the mean square error between the two curves (simulated and real) at a given current value. An average and a maximum error of 0.4% and 1% are obtained.

- $\overline{V}$ is the constant voltage of the battery [V];
- K is the Polarization constant [V A
^{−1}h^{−1}] or Polarization resistance [Ω]; - Q is the battery capacity [Ah];
- it is the actual charge of the battery [Ah];
- A is the width of the exponential area [V];
- B is the constant of time in the exponential area [Ah
^{−1}]; - R is the internal resistance of the battery [Ω];
- i is the current [A];
- i
^{*}is the filtered current [A].

#### Appendix C.2. Lead-Acid Battery

- Q(i) is the battery capacity, in Ah, at the discharge current i;
- Q
_{nom}is the nominal battery capacity at a reference discharge current i_{0}; - Q(i
_{2}) and Q(i_{1}) are two different battery capacities at different discharge rates i_{2}and i_{1}; - Exp (t) is the exponential voltage [V], given by:

_{i}is the Coulombic efficiency, with a unitary value in the case of discharge and less than one in the case of charge (variable according to the type of battery).

#### Appendix C.3. Generalization of the Model

_{conv}is a conversion parameter obtained as the ratio between the reference capacity (in this case, 100 Ah) and the nominal capacity of the battery that we want to adopt.

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**Figure 4.**Monthly distribution of energy in the system: energy required to move the compressor of the refrigeration unit, energy produced by the PV panels and sent to the battery, battery losses, and total energy produced by the PV panels.

**Figure 6.**Comparison of electrical and thermal behavior between lead-acid and lithium batteries: (

**a**) Current, (

**b**) voltage, (

**c**) SOC, (

**d**) power, and (

**e**) temperature.

**Figure 7.**Behavior of the payback period of the lithium and lead-acid batteries according to different capacities.

**Figure 8.**Comparison of RTE values among several battery solutions for both lead-acid and lithium types.

**Figure 9.**Monthly electricity absorbed by the refrigeration unit, produced by the PV system, and reintegration from the grid.

**Figure 10.**Monthly economic and CO

_{2}emissions savings provided considering single-delivery trips. The refrigerated van represents the reference solution without the PV panels installed.

**Figure 11.**Monthly electricity absorbed by the refrigeration unit, produced by the PV system and reintegration from the grid (

**a**) and monthly infiltration losses during the unloading operations of the products in each delivery (

**b**).

**Figure 12.**Monthly economic and CO

_{2},e emissions savings provided considering the multiple-deliveries scenario. The refrigerated van represents the reference solution without the PV panels installed.

Parameter | Model | Test |
---|---|---|

Total distance (km) | 90.2 | |

Total time (min) | 63 | |

Departure | 11.10 | |

Drive (kg) | 10.02 | Not applicable |

Refrigeration (kg) | 0.46 | Not applicable |

Total consumption (kg) | 10.5 | 10.1 |

Total cost (€) | 9.96 | 10.0 |

Total CO_{2} emissions (kg) | 28.1 | 28.2 |

Code | Address | Coordinates |
---|---|---|

O | Via Santa Maria La Neve, Tramonti (SA) | 40.70, 14.66 |

D1 | Via Benedetto Croce 63, Avellino (AV) | 40.92, 14.78 |

D2 | Corso Giuseppe Garibaldi 12, Castellammare di Stabia (NA) | 40.70, 14.48 |

D3 | Via Salvatore D’Alessandro 42, Nocera Inferiore (SA) | 40.75, 14.63 |

Component | Unit Cost [€] | Units | Total Cost [€] |
---|---|---|---|

MC4 connectors | 4.80 | 1 | 4.80 |

Extension cable | 1.20 | 14 | 16.80 |

Double-sided adhesive | 18.00 | 5 | 90.00 |

Inverter-MPPT | 473.72 | 1 | 473.72 |

24 V 100 Ah battery | 480.00 | 1 | 480.00 |

Total | 1065.32 |

PV Panel | Unit Cost [€] | Units | Cost PV Panels [€] | Total Cost [€] |
---|---|---|---|---|

Type A | 430.00 | 5 | 2150.00 € | 3215.32 |

Type B | 290.00 | 5 | 1450.00 € | 2515.32 |

Type C | 260.00 | 12 | 3120.00 € | 4185.32 |

Parameter | Baseline | Type A | Type B | Type C |
---|---|---|---|---|

Investment cost [€] | NA | 3215.32 | 2515.32 | 4185.32 |

Power grid cost [€] | NA | 19.97 | 20.82 | 19.79 |

Annual costs [€] | 1606.46 | 1488.46 | 1492.68 | 1488.06 |

Net Present Value [€] | NA | 118.00 | 113.78 | 118.40 |

Payback period [years] | NA | 27 | 22 | 36 |

Parameter | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Distance [km] | 72.10 | |||||||||||

Time [min] | 77.00 | |||||||||||

E_{RU} [kWh] | 33.7 | 29.1 | 32.4 | 35.5 | 34.0 | 38.0 | 43.3 | 39.6 | 39.1 | 37.7 | 33.0 | 33.8 |

E_{PS} [kWh] | 5.2 | 5.3 | 7.4 | 10.4 | 10.4 | 11.6 | 13.4 | 11.6 | 9.0 | 7.4 | 5.2 | 5.8 |

E_{bat} [kWh] | 0.9 | 0.8 | 0.8 | 0.7 | 0.6 | 0.7 | 0.7 | 0.7 | 0.8 | 0.9 | 1.0 | 1.0 |

E_{Reintegrated} [kWh] | 30.4 | 24.0 | 26.4 | 23.9 | 21.9 | 24.7 | 24.8 | 24.9 | 26.6 | 30.6 | 29.1 | 31.8 |

Losses_{PV} [kWh] | 0.6 | 0.6 | 0.8 | 1.1 | 1.1 | 1.2 | 1.5 | 1.3 | 1.0 | 0.8 | 0.6 | 0.6 |

Losses_{bat} [kWh] | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |

Losses_{RU} [kWh] | 9.7 | 8.4 | 9.3 | 10.1 | 9.7 | 10.7 | 12.2 | 11.2 | 11.2 | 10.7 | 9.5 | 9.7 |

Losses inverter [kWh] | 3.2 | 2.8 | 3.2 | 3.6 | 3.4 | 3.8 | 4.2 | 3.9 | 3.6 | 3.6 | 3.1 | 3.4 |

Losses tot [kWh] | 13.6 | 11.8 | 13.4 | 14.9 | 14.3 | 15.9 | 18.0 | 16.4 | 15.7 | 15.5 | 13.2 | 13.8 |

Savings [%] | 4.0% | 12.1% | 18.4% | 32.8% | 35.6% | 34.9% | 39.2% | 30.4% | 22.7% | 12.9% | 5.2% | 5.7% |

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## Share and Cite

**MDPI and ACS Style**

Maiorino, A.; Mota-Babiloni, A.; Petruzziello, F.; Del Duca, M.G.; Ariano, A.; Aprea, C.
A Comprehensive Energy Model for an Optimal Design of a Hybrid Refrigerated Van. *Energies* **2022**, *15*, 4864.
https://doi.org/10.3390/en15134864

**AMA Style**

Maiorino A, Mota-Babiloni A, Petruzziello F, Del Duca MG, Ariano A, Aprea C.
A Comprehensive Energy Model for an Optimal Design of a Hybrid Refrigerated Van. *Energies*. 2022; 15(13):4864.
https://doi.org/10.3390/en15134864

**Chicago/Turabian Style**

Maiorino, Angelo, Adrián Mota-Babiloni, Fabio Petruzziello, Manuel Gesù Del Duca, Andrea Ariano, and Ciro Aprea.
2022. "A Comprehensive Energy Model for an Optimal Design of a Hybrid Refrigerated Van" *Energies* 15, no. 13: 4864.
https://doi.org/10.3390/en15134864