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Modeling of a Village-Scale Multi-Energy System for the Integrated Supply of Electric and Thermal Energy^{ †}

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## Abstract

**:**

## Featured Application

## Abstract

## 1. Introduction

## 2. Case Study and Scenario Characterization

^{2}∙year).

## 3. Modeling Approach

#### 3.1. Load Profiles

#### 3.1.1. Electric Load Curves

#### 3.1.2. Thermal Load Curves

- ${T}_{gw}\left[K\right]$ is the groundwater temperature;
- ${n}_{day}[-]$ is the progressive number of the considered day of the year;
- $\overline{{T}_{amb}}\left[K\right]$ is the yearly average ambient temperature;
- ${n}_{day}^{min}[-]$ is the progressive number of the day with the lowest temperature of the year.

- ${P}_{task}\left[W\right]$ is the power required to heat the water for the operation of the task;
- $c{p}_{w}\left[\frac{kJ}{kgK}\right]$ is the water isobaric specific heat;
- ${T}_{gw}\left[K\right]$ is the groundwater temperature.

- (i)
- commercial activities,
- (ii)
- domestic,
- (iii)
- public offices,
- (iv)
- school.

#### 3.2. Multi-Energy System

_{k}user-scale subsystems (where N

_{k}is the number of users within the k-th class). Indeed, the thermal energy balance (Equation (3)) satisfies independently the thermal demand (in this case DHW only) for each thermal user class k, and for each time step t.

#### 3.2.1. Electric Components

#### 3.2.2. Thermal Components

#### Solar Thermal Collectors

#### Hot-Water Tanks

- The energy stored in the tank is constrained not to exceed the maximum capacity ${C}_{SOC}{}_{tank}$ of the tank, for each class k.$${E}_{SO{C}_{Tank}}\left(k,t\right)\le {C}_{SOC}{}_{tank}\left(k\right)\forall k,\forall t$$
- The energy stored in the tank is constrained to be kept above a minimum value (defined as depth of discharge, ${D}_{SOC}$), defined as a percentage of the nominal tank capacity.$${E}_{SO{C}_{Tank}}\left(k,t\right)\ge {C}_{SOC}{}_{tank}\left(k\right)\xb7{D}_{SOC}\forall k,\forall t$$
- The thermal energy flow out of the tank (${E}_{Tan{k}_{out}}$) is constrained to be lower than the tank maximum power of discharge (${P}_{out,max}$) multiplied by a delta time ($\u2206t$) calibrated on the time-step.$${E}_{Tan{k}_{out}}\left(k,t\right)\le {P}_{out,max}\left(k\right)\xb7{\u2206}_{t}\forall k,\forall t$$

#### Electric Resistance Heating Elements

#### LPG Boilers

#### 3.2.3. Optimization

## 4. Results and Discussion

#### 4.1. Generated Load Profiles

#### 4.2. Optimization Results

## 5. Conclusions and Future Work

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MES | Multi-Energy System |

LPG | Liquid Propane Gas |

DHW | Domestic Hot Water |

TPES | Total Primary Energy Supply |

TFC | Total Final (energy) Consumption |

NPC | Net Present Cost |

LCOE | Levelized Cost of Energy |

LP | Linear Programming |

MILP | Mixed-Integer Linear Programming |

BESS | Battery Energy Storage System |

## Nomenclature

${T}_{gw}$ | Groundwater temperature | K |

${n}_{day}$ | Progressive number of the considered day of the year | - |

$\overline{{T}_{amb}}$ | Yearly average ambient temperature | K |

${n}_{day}^{min}$ | Progressive number of the day with the lowest temperature of the year | - |

${P}_{task}$ | Power required to heat the water for the operation of the task | W |

$\dot{{m}_{w}}$ | Water mass flow required by the task | l/s |

$c{p}_{w}$ | Water isobaric specific heat | $\mathrm{kJ}/\left(\mathrm{kg}\mathrm{K}\right)$ |

${E}_{Th,classdemand}\left(k,t\right)$ | Thermal energy demand | Wh |

${E}_{boiler}\left(k,t\right)$ | Energy supplied by the boiler | Wh |

${E}_{Tan{k}_{out}}\left(k,t\right)$ | Energy exiting the hot-water tank | Wh |

${E}_{Curt}\left(k,t\right)$ | Fraction of the excess energy produced by solar collectors that cannot be stored in the tank | Wh |

${E}_{lostload,th}\left(k,t\right)$ | Allowed fraction of unmet thermal load | Wh |

${E}_{El,demand}\left(t\right)$ | Electricity demand of the study area | Wh |

${E}_{PV}\left(t\right)$ | Energy produced by the PV panels | Wh |

${E}_{Gen}\left(t\right)$ | Energy produced by the generator | Wh |

${E}_{bat,ch}\left(t\right)$ | Flow of energy into the battery | Wh |

${E}_{bat,dis}\left(t\right)$ | Flow of energy out of the battery | Wh |

${E}_{Curt}\left(t\right)$ | Electric energy that is curtailed | Wh |

${E}_{Res,class}\left(k,t\right)$ | Energy supplied to the thermal storage through electric resistance heating elements | Wh |

${E}_{Res,tot}\left(t\right)$ | Cumulative energy absorbed by the electric resistance heating elements of all n thermal classes | Wh |

${E}_{lostload}\left(t\right)$ | Allowed fraction of unmet electric load | Wh |

${E}_{S{C}_{tot}}\left(k,t\right)$ | Total thermal energy provided by the solar collectors | Wh |

${E}_{SC}\left(k,t\right)$ | Energy generated by a single solar collector | Wh |

${N}_{SC}\left(k\right)$ | Number of solar collectors in the class | - |

${E}_{SO{C}_{Tank}}\left(k,t\right)$ | Thermal energy stored in the tank at the time step t | Wh |

${E}_{SO{C}_{Tank}}\left(k,t-1\right)$ | Thermal energy stored in the tank at the timestep t–1 | Wh |

${\eta}_{tank}$ | Coefficient accounting for energy losses due to the heat transfer between thermal storage and environment | - |

${\eta}_{Res}$ | Thermal efficiency of the electric resistances | - |

${D}_{SOC}$ | Depth of discharge | - |

${P}_{out,max}\left(k\right)$ | Tank maximum power of discharge | W |

$LP{G}_{cons}$ | LPG consumption | l |

${\eta}_{boiler}$ | Boiler efficiency | - |

$LH{V}_{LPG}$ | Lower heating value of the LPG | $\mathrm{kJ}/\mathrm{kg}$ |

$Inv$ | Total investment cost | $\$$ |

$YCC$ | Yearly constant cost of the project | $\$$ |

$e$ | Discount rate | - |

$r$ | Interest rate | - |

$Cos{t}_{rep}$ | Cost of components replacement | $\$$ |

${N}_{PV}$ | Number of installed PV panels | - |

${C}_{PV}$ | Capacity of a PV unit | kW |

${U}_{PV}$ | Specific cost of PV unit | $/kW |

${C}_{bat}$ | Capacity of installed battery bank | kWh |

${U}_{bat}$ | Specific cost of battery bank | $/kWh |

${C}_{gen}$ | Capacity of installed generator | kW |

${U}_{gen}$ | Specific cost of generator | $/kW |

${N}_{SC}\left(k\right)$ | Number of solar collectors installed | - |

${C}_{SC}$ | Capacity of a solar collector | kW |

${U}_{SC}$ | Specific cost of solar collector | $/kW |

${C}_{SOC}{}_{tank}\left(k\right)$ | Capacity of the installed hot-water tank | kWh |

${U}_{Tank}$ | Specific cost of the hot-water tank | $/kWh |

${C}_{Boiler}\left(k\right)$ | Capacity of the installed boiler | kW |

${U}_{Boiler}$ | Specific cost of the boiler | $/kW |

${C}_{Res}\left(k\right)$ | Capacity of the installed electric resistance | kW |

${U}_{Res}$ | Specific cost of the electric resistance | $/kW |

$fun$ | Percentage of the investment financed by a bank | - |

$Cos{t}_{O\&M}$ | Cost of operation and maintenance of the system | $\$$ |

$Cos{t}_{finan}$ | Fixed-rate loan payment | $\$$ |

$Cos{t}_{Diesel}\left(t\right)$ | Cost of the used diesel | $\$$ |

$Cos{t}_{\mathrm{gas}}\left(t\right)$ | Cost of the used LPG | $\$$ |

$L{L}_{\mathrm{cos}\mathrm{t}}\left(t\right)$ | Cost of the actually unmet load | $\$$ |

${E}_{demand}$ | Total energy demand (electric and thermal) of the system | kWh |

${E}_{demand,net}$ | Net (i.e., after subtracting the lost load) total energy demand | kWh |

${E}_{supply}$ | Total energy supplied by each j-th energy supply technology | kWh |

${\eta}_{overall}$ | Overall system efficiency | - |

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**Figure 2.**Schematic summary of the four scenarios considered: (

**a**) traditional energy system; (

**b**) conventional micro-grid; (

**c**) multi-good micro-grid; (

**d**) integrated multi-energy system.

**Figure 3.**Schematic representation of the integrated electric and thermal energy system model. The thermal energy system is not a single centralized entity but rather the aggregate of multiple user-scale individual systems, which are modeled for each user within each user class and only connected through the electricity grid, in the absence of a heat distribution network.

**Figure 5.**Thermal load profiles for the four user classes: (

**top right**) domestic; (

**top left**) commercial activities; (

**bottom left**) public offices; and (

**bottom right**) school.

**Figure 6.**Electric energy dispatch strategy in the four modeled scenarios, namely: (

**a**) baseline; (

**b**) conventional micro-grid; (

**c**) multi-good micro-grid; (

**d**) integrated multi-energy system. The represented day is 23rd September 2017. Representative days for all the modeled seasons are reported in the Supplementary Information of this work.

**Figure 7.**Example of thermal energy dispatch for representative single users for each of the four modeled user classes. The represented day is 23rd September 2017. Representative days for all the modeled seasons are reported in the Supplementary Information of this work.

Inputs | Outputs |
---|---|

PV panel output | Optimal system size |

Solar collector output | Net Present Cost (NPC) |

Electric load profile | Levelized Cost of Energy (LCOE) |

Thermal load profile | Electric dispatch strategy |

Economic parameters | Thermal dispatch strategy |

Traditional Energy System (Baseline) | Conventional Micro-Grid | Multi-Good Micro-Grid | Integrated Multi-Energy System | |
---|---|---|---|---|

TPES [ktoe] | 467.8 | 322.2 | 362.3 | 442.9 |

Imports [%TPES] | 100% | 77.0% | 16.2% | 6.3% |

Renewables [%TPES] | 0% | 23.0% | 83.8% | 93.7% |

BESS Use [%TFC_el] | 0% | 67.8% | 61.0% | 53.8% |

LCOE [USD/kWh] | 0.259 | 0.220 | 0.198 | 0.090 |

**Table 3.**Summary of installed nominal capacities, total investment, and operations and maintenance (O&M) costs for different energy conversion and storage technologies in the four proposed scenarios.

Traditional Energy System (Baseline) | Conventional Micro-Grid | Multi-Good Micro-Grid | Integrated Multi-Energy System | |
---|---|---|---|---|

PV panels [kW] | - | 320 | 1312 | 321 |

Battery storage [kWh] | - | 1621 | 6257 | 1563 |

Diesel gensets [kW] | 181 | 19 | 159 | 42 |

Solar collectors [kW] | - | - | - | 1703 |

Hot-water tanks [kWh] | - | - | - | 8533 |

LPG boilers [kW] | 1417 | 1417 | - | 1 |

Electric heaters [kW] | - | - | 1467 | 229 |

Total investment cost [MUSD] | 0.18 | 1.68 | 6.24 | 2.56 |

Total O&M cost [MUSD] | 11.55 | 8.31 | 2.74 | 1.53 |

Net Present Cost [MUSD] | 11.73 | 9.98 | 8.98 | 4.09 |

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## Share and Cite

**MDPI and ACS Style**

Stevanato, N.; Rinaldi, L.; Pistolese, S.; Balderrama Subieta, S.L.; Quoilin, S.; Colombo, E.
Modeling of a Village-Scale Multi-Energy System for the Integrated Supply of Electric and Thermal Energy. *Appl. Sci.* **2020**, *10*, 7445.
https://doi.org/10.3390/app10217445

**AMA Style**

Stevanato N, Rinaldi L, Pistolese S, Balderrama Subieta SL, Quoilin S, Colombo E.
Modeling of a Village-Scale Multi-Energy System for the Integrated Supply of Electric and Thermal Energy. *Applied Sciences*. 2020; 10(21):7445.
https://doi.org/10.3390/app10217445

**Chicago/Turabian Style**

Stevanato, Nicolo, Lorenzo Rinaldi, Stefano Pistolese, Sergio Luis Balderrama Subieta, Sylvain Quoilin, and Emanuela Colombo.
2020. "Modeling of a Village-Scale Multi-Energy System for the Integrated Supply of Electric and Thermal Energy" *Applied Sciences* 10, no. 21: 7445.
https://doi.org/10.3390/app10217445