# Improving Thermoeconomic and Environmental Performance of District Heating via Demand Pooling and Upscaling

^{*}

## Abstract

**:**

_{2}mitigations. In conclusion, upscaling and demand pooling tend to improve specific efficiencies, reduce specific costs, reduce total investment through the peak power sizing method, and mitigate temporal mismatch in solar-driven systems. Possible drawbacks are additional heat losses due to the distribution network and reduced performance in heat pumps due to the higher temperatures required. Nevertheless, the advantages outweigh the drawbacks in most cases.

## 1. Introduction

_{2}emissions have increased considerably since 1900, with a rise of approximately 90% from 1970 to 2011, wherein the combustion of fossil fuels and industrial processes accounted for 78% of the total greenhouse gas emissions [1]. As a result, several countries have established objectives to reduce greenhouse gas emissions and have introduced policies to promote the implementation of low-carbon technologies such as renewable energy [2,3,4]. Zappa et al. [5] examined the feasibility of a 100% renewable energy-based European power system and compared the economic gains with respect to a non-renewable energy-driven system. The results from their study indicate that a 100% renewable European power system could potentially provide similar system sufficiency to the present power system, even when utilizing the European sources alone. However, the total annual cost of a 100% renewable system was found to be at least 30% higher than for a system including nuclear technologies or carbon fuels. In France, space heating and water heating accounted for a major share (about 77%) of the energy consumption in the building sector in 2017 [6]. Therefore, the energy practices and strategies pertaining to space heating and hot water production play a significant role in controlling environmental impacts.

## 2. Materials and Methods

#### 2.1. Case Study

^{2}[19]. The collective residential and commercial sectors are spread over surface areas of 17,580 m

^{2}and 5200 m

^{2}, respectively. The surface areas of the different types of buildings (belonging to each sector) are listed in Table A1 (Appendix A).

^{2}, and 20% additional surface for the bathroom, office equipment, etc. [20] with the temperature difference set at 55 °C (i.e., 65–10 °C). Therefore, the average annual DHW demand per employee was calculated to be 46.6 kWh/employee, and the average annual DHW demand per square meter was estimated as 3.2 kWh/m

^{2}for office buildings. In order to obtain the hourly DHW profiles for offices, the annual DHW demand was assumed to be equally distributed between office working hours from 08:00 h to 18:00 h, while the hourly DHW demands from 19:00 h to 07:00 h were assumed to be null. The annual DHW needs for offices and collective residential sectors were evaluated to be 320 MWh and 804 MWh, respectively (Figure 1).

#### 2.2. Systems for Heat Production

#### 2.3. Simulation Model

_{0}= −11 °C was used, as this is the typical design temperature suggested by the French RT2012 legislation on building energetics in the H1 climatic zone of France [24].

_{el}at building scale and 130 EUR/MWh

_{el}at sector or district scales. In the framework of our study, the electric grid was considered to be completely amortized. Its operating expenses are implicit in the price of electricity. Fuel prices of the grid, both energy and exergy, were deduced from the selling price of electricity, via the grid energy and exergy efficiencies, respectively:

_{2}emissions (${\phi}_{{\mathrm{CO}}_{2}}$), in kilograms, from each of the heat production systems. The CO

_{2}emissions from ST and PV panels were assumed to be zero (disregarding the embodied energy). Further, the CO

_{2}emissions from the heat pump (HP) and electric boiler (EBOIL) depend on the source of electrical energy used to drive each of the systems. Thus, in the case of the HP driven by PV (or PV-driven EBOIL), there are no CO

_{2}emissions from the system. However, whenever the grid is used to drive the HP or EBOIL, CO

_{2}is released:

_{td}and L

_{a}denote the transmission and distribution losses and the appliance losses, respectively. The losses L

_{td}and L

_{a}are assumed to be 40% and 20%, respectively [35]. The term ${x}_{{\mathrm{CO}}_{2}}$ (in kg/kWh) represents the amount of CO

_{2}emitted per kWh of energy produced [36].

#### 2.4. Performance Criteria

_{2}mitigation ($Ne{t}_{{\mathrm{CO}}_{2}}$) was used as the environmental indicator to compare the different heat production solutions. Among the heat production systems considered, the gas-fired boiler produces the highest CO

_{2}emissions. The net CO

_{2}mitigation, in kilograms, represents the amount of CO

_{2}emitted by the system in comparison with the gas boiler (GBOIL).

_{2}emissions from the natural gas boiler and the system being assessed, respectively.

## 3. Results and Discussion

_{th}). This solution benefits from both low prices in investment (90 EUR/kW) and in fuel (30 EUR/MWh

_{th}). In comparison, the biomass boiler has even lower fuel costs (24 EUR/kW) but much higher investment costs (558 EUR/kW), resulting in a higher LCOE (52.2 EUR/MWh

_{th}). Nevertheless, these LCOE may be sensitive to some factors not considered in this study, such as the availability of biomass or environmental regulations on emissions from gas-driven processes. Thus, readers should consider costs in the current French context and re-assess them when considering a very different context.

_{el}) and especially at building scale (176 EUR/MWh

_{el}). Heat pumps are subject to the same fuel costs as electric boilers and to even higher investment costs (750 EUR/kW

_{th}). Yet, they lead to lower LCOE than electric boilers, thanks to their COP (2.08 to 2.44). PV-powered solutions have generally lower LCOE than their grid-driven counterparts, thanks to solar irradiation being cost-free. Still, the investment costs for PV panels are much higher (1092–1349 EUR/kW

_{el}) than for the boilers, preventing them from reaching lower LCOE.

_{th}), and ideally zero fuel costs. However, temporal mismatch forces the use of the GRID + EBOIL backup (LCOE of 152–190 EUR/MW

_{th}depending on the scale). As a result, the overall LCOE is close to that of the backup system (137–196 EUR/MW

_{th}). In fact, at building scale it is even higher, i.e., running on GRID + EBOIL alone would yield better payoffs. This is coherent with the fact that overall efficiencies are almost as low as those of the GRID + EBOIL backup (see Figure 3). This indicates that a temporal mismatch has a severe impact on the efficiency and especially the LCOE of this solution, even with heat storage. At this point, the reader should recall two hypotheses. First, the sizing of solar panels followed the peak power method, which may not be optimal, especially at building scale. Second, heat storage may be oversized. With cost-optimal sizing on both units, ST collectors should be economically viable at any scale, as demonstrated in [45]. It should also be noted that the calculation of the LCOE for ST collectors does not account for the heat dissipated due to overproduction. Only the useful heat that is actually utilized counts. Consequently, a strong temporal mismatch can increase the LCOE of ST collectors exponentially. The same tendency may occur with PV panels, and by extension with any PV-powered solution, with the difference that the surplus electricity is sold to the grid, leading to additional revenues. Optimization of storage sizes for minimizing the LCOE of solar-driven systems is out of the scope of this study.

_{el}, versus 615 EUR/kW

_{th}). Moreover, they tend to require greater surfaces than ST collectors for the same demand, due to their lower efficiency (19–21% versus 60–70%). This is especially true if they are connected to an electric boiler instead of a heat pump. For all these reasons, one would expect that PV-powered solutions would require higher LCOE than their grid-driven counterparts and even ST collectors. However, this did not occur in the present study, since excess electricity from PV panels can be sold unlimitedly to the grid at a constant price of 100 EUR/MWh

_{el}. As a result, PV-powered solutions have lower LCOE than their grid-driven counterparts. This shows that PV-powered solutions may have better tools to compensate for mismatch, economically speaking. This tendency was already observed and discussed for one dwelling by the authors in a previous study [17].

_{2}mitigation of each solution at each sizing scale. From the standpoint of this indicator, the PV-powered heat pump (PV + HP) is the most promising solution at any scale. It mitigates 1895 tCO

_{2}/year, 1965 tCO

_{2}/year, and 1956 tCO

_{2}/year at the building, sector, and district scales, respectively. Nevertheless, the implementation of biomass boilers (BBOIL) results in an almost equivalent solution at every scale (1856 tCO

_{2}/year, 1955 tCO

_{2}/year, and 1955 tCO

_{2}/year, respectively). The GRID + HP solution loses the advantages of the free CO

_{2}energy source of solar panels (1790 tCO

_{2}/year, 1835 tCO

_{2}/year, and 1835 tCO

_{2}/year), and the PV + EBOIL solution loses the advantages of the high efficiency of the heat pump (1666, 1757, and 1738 tCO

_{2}/year). The ST (+ backup) solution is close to the PV + EBOIL solution (1595 tCO

_{2}/year, 1682 tCO

_{2}/year, and 1669 tCO

_{2}/year), due to mismatch issues already analyzed for the previous indicators (Figure 4 and Figure 5). Lastly, the GRID + EBOIL solution has the lowest mitigation (1411 tCO

_{2}/year, 1484 tCO

_{2}/year, and 1484 tCO

_{2}/year) but is nevertheless better than gas boilers, which have the highest emissions and were taken as the baseline for this environmental assessment.

_{2}mitigation by up to 5%. Likely, the beneficial effects of upscaling would be even more noticeable if embodied energy was taken into account. With this statement, the authors assumed that the specific CO

_{2}emissions of constructing a unit tend to decrease with size, just as specific costs decrease.

_{2}mitigation overall. However, a life cycle analysis might change this conclusion in favor of biomass-fired boilers, for two reasons. First, embodied energy: A PV-powered heat pump involves the installation of two units, while a biomass boiler requires only one. Second, if biomass comes from trees, some sources, such as the French ADEME, consider that trees capture and neutralize, during their life, nearly as much CO

_{2}as their biomass releases upon combustion. This hypothesis assumes that the specific operating emissions of a biomass boiler would be null, instead of the 0.035 kg CO

_{2}/kWh

_{th}that we considered in this study. Nevertheless, biomass boilers may have the operational limitations that we mentioned in the energy analysis (Figure 3), which would necessitate a backup. On the other hand, both the PV panels and the ground-source heat pumps may have practical limitations such as the space available or the ability to exploit ground-source heat. It was concluded that biomass boilers and PV-powered heat pumps are theoretically almost equivalent here, but selecting one of the two is a very context-specific decision [17].

_{ex}/year). Both the biomass- and the gas-fired boilers are the best solutions at the sector and district scales (4.75 GWh

_{ex}/year) and the second-best solutions at building scale (5.12 GWh

_{ex}/year). These three technologies distinguish themselves from the rest by a considerable margin. The main reason that the GRID + HP system is outperformed at larger scales is the drop in COP (refer to the analysis in Figure 3).

_{th}of heat produced). At building scale, PV-powered heat pumps perform almost as well (325 kEUR/year), thanks to the heat pump COP and to solar irradiation being a costless fuel. In fact, with better temporal matching they could outperform biomass boilers. At the larger scales, gas-fired boilers are second best (227 kEUR/year and 168 kEUR/year). Any solution involving the electric grid falls behind, as grid-based electricity is costlier than gas, biomass, and solar irradiation (cf. Table 2). In fact, grid costs have a strong impact downstream, increasing the exergy destruction costs of heat pumps, electric boilers, and even the district network.

## 4. Conclusions

- Overall, upscaling has clear economic and environmental benefits, mostly advantageous exergoeconomic effects, and mixed effects on energy efficiency and exergy efficiency. These combined advantages would favor the implementation of centralized units for heat production, especially for mixed residential, commercial, and office districts.
- From the viewpoint of energy efficiency, upscaling has mixed effects. On the one hand, specific efficiency increases for certain units, such as boilers or solar panels. On the other hand, large-scale implementation requires a district network that introduces additional losses, and in the case of heat pumps, a drop in performance due to higher temperature lifts. In solar-driven systems, upscaling enables demand pooling, with beneficial effects on overall performance. This pooling effect compensates for the drawbacks of upscaling at least partially and may even outweigh them in some instances. The pooling effect seems to be stronger between sectors than between buildings, due to the complementarity of residential and office demand profiles. In this specific study, upscaling led to relative increases of up to +11% in overall efficiency for some systems, but relative decreases of up to −11% for other systems, especially those involving a heat pump. The most efficient solutions were the biomass- and gas-fired boilers at large scales, with overall efficiencies of 90% (85% at building scale).
- From the viewpoint of exergy efficiency, the most efficient solution overall does not involve upscaling (grid-powered heat pumps at building scale, for 21.5% exergy efficiency). Biomass and gas boilers are the second-best solutions after upscaling (20.3%). The effects of upscaling on exergy efficiency are less promising than on energy efficiency: up to a +10% relative increase for certain systems, but up to a -20% relative decrease for other systems, especially those involving a heat pump. Nevertheless, maximizing the pooling effect can compensate for these drawbacks.
- From an economics viewpoint, upscaling and demand pooling lead to lower specific investment costs and fuel costs, reducing the LCOE of heat. In this study, the reduction was up to –54% with gas-fired boilers, −45% with biomass boilers, −35% with PV-powered electric boilers, −31% with PV-powered heat pumps, −30% with solar thermal collectors, −21% with grid-driven heat pumps, and −20% with grid-powered boilers. Upscaling yields more cost-efficient systems, even when accounting for some uncertainty in investment and fuel costs. Furthermore, upscaling hardly increases the sensitivity of the LCOE, and in some cases it even reduces it. Out of 21 systems evaluated in this study, the six most cost-efficient ones involved upscaling. The most promising system was a gas boiler plant at district scale.
- From an exergoeconomic viewpoint, upscaling reduced exergy destruction costs for most of the systems, except those involving a heat pump. The reduction was up to −55% for biomass and gas boilers, −23% for PV-powered boilers, −14% for grid-powered boilers, and −10% for solar thermal collectors. On the other hand, exergy destruction costs increased by up to +13% and +6% for the grid-powered and PV-powered heat pumps, respectively. Out of 21 solutions, the best four involved upscaling. The most promising approach was a biomass-fueled boiler at district scale. Upscaling did not increase the sensitivity of exergy destruction costs, and in some instances, it even reduced it.
- From an environmental viewpoint, upscaling improved CO
_{2}mitigation by up to 5% in the current study. The improvement could be more substantial if embodied energy was taken into account. In this study, the systems with fewer emissions were biomass boilers and PV-powered heat pumps, and they were almost equivalent. The most promising approach consisted of PV-powered heat pumps at sector scale. The best four out of 21 solutions involved upscaling.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Nomenclature | |

CAPEX | Capital expenditure (EUR) |

${\dot{C}}^{D}$ | Cost of exergy destruction (EUR) |

${c}^{F}$ | Specific energy cost of fuel (EUR/kWh) |

${c}^{F,ex}$ | Specific exergy cost of fuel (EUR/kWh) |

${\dot{C}}^{F}$ | Total fuel cost (EUR) |

COP | Coefficient Of Performance (kW_{th}/kW_{el}) |

CRF | Capital Recovery Factor (-) |

$\dot{E}{n}^{F}$ | Total energy input in fuel(s) (kWh) |

$\dot{E}{n}^{in}$ | Total input of energy (kWh) |

$\dot{E}{n}^{out}$ | Total output of energy (kWh) |

$\dot{E}{n}^{P}$ | Total energy output in product(s) (kWh) |

$\dot{E}{x}^{F}$ | Total exergy input in fuel(s) (kWh) |

$\dot{E}{x}^{in}$ | Total input exergy (kWh) |

$E{x}^{out}$ | Total output exergy (kWh) |

$\dot{E}{x}^{P}$ | Total exergy output in product(s) (kWh) |

$i$ | Effective rate of economic return |

LCOE | Levelized cost of energy (EUR/kWh) |

n | System’s economic lifespan (years) |

OPEX | Operating expenses (EUR) |

${T}_{0}$ | Dead state temperature for exergy analysis (K) |

${T}^{out}$ | Output temperature of the unit under analysis (K) |

${T}_{s}$ | Surface temperature of the sun (K) |

${x}^{{\mathrm{CO}}_{2}}$ | Specific CO_{2} emission (kg/kWh) |

${z}^{CI}$ | Specific investment cost (EUR/kW_{peak}) |

Greek Symbols | |

${\Delta}^{{\mathrm{CO}}_{2}}$ | CO_{2} mitigation (tCO_{2}/year) |

ε | Exergy efficiency (-) |

η | Energy efficiency (-) |

φ | Maintenance cost factor (-) |

${\phi}^{{\mathrm{CO}}_{2}}$ | CO_{2} emissions (tCO_{2}/year) |

Superscripts | |

F | Fuel, as in payed input of energy to a unit |

grid | French national electric grid |

P | Product, as in priced output of energy from a unit |

ProdSyst | Heat production system |

Abbreviations | |

HP | Heat pump |

BBOIL | Biomass-fired boiler |

DHN | District heating Network |

EBOIL | Electric boiler |

GBOIL | Gas-fired boiler |

Grid | French national electric grid |

PV | Solar photovoltaic panels |

ST | Solar Thermal collectors |

## Appendix A

Sector | Building Surface Area | Total Surface Area [m ^{2}] | Space Heating Consumption [kWh/m^{2}] | DHW Consumption [kWh/m ^{2}] |
---|---|---|---|---|

Residential | 70 m^{2} or less | 8064 | 20.0 | 28.0 |

Between 70–100 m^{2} | 5757 | 19.9 | 16.1 | |

Between 100–150 m^{2} | 1584 | 20.8 | 11.1 | |

Greater than 150 m^{2} | 2173 | 20.6 | 6.9 | |

Office | 1000 m^{2} or less | 0 m^{2} | 35.7 | 3.2 |

Between 1000–5000 m^{2} | 31,000 m^{2} | 34.9 | 3.2 | |

Greater than 5000 m^{2} | 69,000 m^{2} | 34.1 | 3.2 | |

Commerce | 125 m^{2} or less | 2600 m^{2} | 82.5 | – |

Greater than 125 m^{2} | 2600 m^{2} | 98.3 |

**Table A2.**Percentage distribution coefficients for space heating and domestic hot water consumption in residential (R), office (O), and commerce (C) sectors.

Hour | R | O | C | Day | R | O | C | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

SH | DHW | SH | DHW | SH | SH | DHW | SH | DHW | SH | ||||

Sat | Sun | Others | |||||||||||

00:00 | 2.2% | 1.8% | 1.5% | 1.7% | 2.8% | 0% | 2.8% | Mon | 13.6% | 13.7% | 17.4% | 20% | 18.5% |

01:00 | 2.2% | 1.0% | 1.0% | 0.9% | 2.8% | 0% | 3.4% | Tue | 13.6% | 13.4% | 17.5% | 20% | 16.0% |

02:00 | 2.5% | 0.6% | 0.6% | 0.5% | 2.9% | 0% | 3.1% | Wed | 13.6% | 14.0% | 17.3% | 20% | 15.0% |

03:00 | 2.5% | 0.5% | 0.4% | 0.4% | 3.0% | 0% | 3.2% | Thu | 13.6% | 13.7% | 17.5% | 20% | 15.3% |

04:00 | 2.8% | 0.5% | 0.4% | 0.7% | 3.1% | 0% | 3.0% | Fri | 13.6% | 13.9% | 16.0% | 20% | 15.0% |

05:00 | 4.0% | 0.8% | 0.6% | 1.4% | 4.8% | 0% | 3.2% | Sat | 16.0% | 14.0% | 7.3% | 0% | 13.2% |

06:00 | 4.9% | 1.3% | 0.8% | 2.8% | 8.1% | 0% | 3.3% | Sun | 16.0% | 17.3% | 7.0% | 0% | 7.0% |

07:00 | 5.0% | 2.6% | 1.3% | 3.9% | 7.4% | 0% | 3.2% | ||||||

08:00 | 5.0% | 4.1% | 2.6% | 4.3% | 6.5% | 9.09% | 3.5% | ||||||

09:00 | 5.1% | 5.9% | 4.5% | 5.0% | 5.5% | 9.09% | 5.7% | ||||||

10:00 | 5.0% | 6.4% | 6.0% | 5.2% | 5.1% | 9.09% | 7.2% | Month | R | O | C | ||

11:00 | 4.8% | 7.1% | 7.1% | 5.7% | 4.5% | 9.09% | 6.4% | SH | DHW | SH | DHW | SH | |

12:00 | 4.5% | 7.5% | 7.6% | 7.0% | 4.5% | 9.09% | 6.4% | Jan | 15.5% | 8.9% | 15.0% | 8.33% | 15.3% |

13:00 | 4.4% | 7.5% | 7.4% | 6.4% | 4.2% | 9.09% | 6.0% | Feb | 14.0% | 8.8% | 14.0% | 8.33% | 14.0% |

14:00 | 4.3% | 6.6% | 6.0% | 4.5% | 4.0% | 9.09% | 5.7% | Mar | 12.5% | 8.9% | 12.2% | 8.33% | 12.3% |

15:00 | 4.2% | 5.0% | 5.3% | 4.0% | 4.0% | 9.09% | 5.1% | Apr | 9.5% | 8.4% | 9.0% | 8.33% | 8.5% |

16:00 | 4.2% | 4.9% | 5.0% | 4.7% | 3.9% | 9.09% | 4.6% | May | 5.0% | 8.4% | 5.0% | 8.33% | 5.1% |

17:00 | 4.3% | 5.5% | 6.0% | 5.9% | 3.6% | 9.09% | 4.8% | Jun | 2.5% | 8.1% | 3.0% | 8.33% | 3.0% |

18:00 | 4.6% | 6.2% | 7.6% | 6.9% | 3.7% | 9.09% | 5.1% | Jul | 1.5% | 7.2% | 2.0% | 8.33% | 2.0% |

19:00 | 4.8% | 6.4% | 8.2% | 7.7% | 4.2% | 0% | 4.3% | Aug | 1.5% | 6.5% | 2.0% | 8.33% | 2.0% |

20:00 | 4.8% | 6.2% | 7.8% | 7.6% | 3.5% | 0% | 3.0% | Sep | 3.5% | 8.0% | 3.5% | 8.33% | 3.5% |

21:00 | 5.0% | 4.9% | 5.7% | 5.7% | 2.5% | 0% | 2.5% | Oct | 7.0% | 8.6% | 7.5% | 8.33% | 7.5% |

22:00 | 4.8% | 3.9% | 4.0% | 4.1% | 2.7% | 0% | 2.5% | Nov | 12.5% | 9.0% | 12.0% | 8.33% | 12.0% |

23:00 | 4.3% | 2.8% | 2.6% | 3.0% | 2.7% | 0% | 2.4% | Dec | 15.0% | 9.2% | 14.8% | 8.33% | 14.8% |

**Figure A1.**Graphical representation of the nodal model used in the OMEGAlpes tool. The dashed red arrow applies only at building scale. CU = conversion unit; FCU = fixed-profile consumption unit; FPU = fixed-profile production unit; VCU = variable-profile consumption unit; VPU = variable-profile production unit. The optimization tool is authorized to alter only variable profiles for optimization purposes. The rest of the units have a fixed hourly profile, predetermined by the users.

Unit | Energy and Exergy Balances | Auxiliary Equations |
---|---|---|

GBOIL | $\dot{E}{n}_{GBOIL}^{in}={\dot{Q}}_{GBOIL}^{out}+\dot{E}{n}_{GBOIL}^{L}$ | ${\dot{Q}}_{GBOIL}^{out}={\eta}_{GBOIL}\xb7\dot{E}{n}_{GBOIL}^{in}$ |

$\dot{E}{x}_{GBOIL}^{in}=\dot{E}{x}_{GBOIL}^{Q,out}+\dot{E}{x}_{GBOIL}^{L}+\dot{E}{x}_{GBOIL}^{D}$ | $\dot{E}{x}_{GBOIL}^{Q,out}={\dot{Q}}_{GBOIL}^{out}\xb7\left(1-{T}_{0}/{T}_{GBOIL}^{out}\right)$ | |

BBOIL | $\dot{E}{n}_{BBOIL}^{in}={\dot{Q}}_{BBOIL}^{out}+\dot{E}{n}_{BBOIL}^{L}$ | ${\dot{Q}}_{BBOIL}^{out}={\eta}_{BBOIL}\xb7\dot{E}{n}_{BBOIL}^{in}$ |

$\dot{E}{x}_{BBOIL}^{in}=\dot{E}{x}_{BBOIL}^{out}+\dot{E}{x}_{BBOIL}^{L}+\dot{E}{x}_{BBOIL}^{D}$ | $\dot{E}{x}_{BBOIL}^{Q,out}={\dot{Q}}_{BBOIL}^{out}\xb7\left(1-{T}_{0}/{T}_{BBOIL}^{out}\right)$ | |

Grid | $\dot{E}{n}_{Grid}^{in}={\dot{W}}_{Grid}^{out}+\dot{E}{n}_{Grid}^{L}$ | ${\dot{W}}_{Grid}^{out}={\eta}_{Grid}\xb7\dot{E}{n}_{Grid}^{in}$ |

$\dot{E}{x}_{Grid}^{in}={\dot{W}}_{Grid}^{out}+\dot{E}{x}_{Grid}^{L}+\dot{E}{x}_{Grid}^{D}$ | $\dot{E}{x}_{Grid}^{in}=\dot{E}{n}_{Grid}^{in};\dot{E}{x}_{Grid}^{L}=\dot{E}{n}_{Grid}^{L}$ | |

EBOIL | ${\dot{W}}_{EBOIL}^{in}={\dot{Q}}_{EBOIL}^{out}$ | ${\dot{W}}_{EBOIL}^{in}={\dot{W}}_{Grid}^{out,EBOIL}+{\dot{W}}_{PV}^{out,EBOIL}$ |

$\dot{E}{x}_{EBOIL}^{in}=\dot{E}{x}_{EBOIL}^{Q,out}+\dot{E}{x}_{EBOIL}^{D}$ | $\dot{E}{x}_{EBOIL}^{in}={\dot{W}}_{EBOIL}^{in}$; $\dot{E}{x}_{EBOIL}^{Q,out}={\dot{Q}}_{EBOIL}^{out}\xb7\left(1-{T}_{0}/{T}_{EBOIL}^{out}\right)$ | |

ST | $\dot{E}{n}_{ST}^{in}={\dot{Q}}_{ST}^{out}+\dot{E}{n}_{ST}^{L}$ | ${\dot{Q}}_{ST}^{out}={\eta}_{ST}\xb7\dot{E}{n}_{ST}^{in}$ |

$\dot{E}{x}_{ST}^{in}=\dot{E}{x}_{ST}^{Q,out}+\dot{E}{x}_{ST}^{L}+\dot{E}{x}_{ST}^{D}$ | $\dot{E}{x}_{ST}^{Q,out}={\dot{Q}}_{ST}^{out}\xb7\left(1-{T}_{0}/{T}_{ST}^{out}\right)$; $\dot{E}{x}_{ST}^{in}=\dot{E}{n}_{ST}^{in}\xb7\left(1-{T}_{0}/{T}_{s}\right)$ | |

HP | ${\dot{Q}}_{HP}^{in}+{\dot{W}}_{HP}^{in}={\dot{Q}}_{HP}^{out}$ | ${\dot{W}}_{HP}^{in}={\dot{W}}_{Grid}^{out,HP}+{\dot{W}}_{PV}^{out,HP}$; $CO{P}_{HP}={\dot{Q}}_{HP}^{out}/{\dot{W}}_{HP}^{in}$ |

$\dot{E}{x}_{HP}^{Q,in}+{\dot{W}}_{HP}^{in}=\dot{E}{x}_{HP}^{Q,out}$ | $\dot{E}{x}_{HP}^{Q,out}={\dot{Q}}_{HP}^{out}\xb7\left(1-{T}_{0}/{T}_{HP}^{out}\right)$ | |

PV | $\dot{E}{n}_{PV}^{in}={\dot{W}}_{PV}^{out}+\dot{E}{n}_{PV}^{L}$ | ${\dot{W}}_{PV}^{out}={\eta}_{PV}\xb7\dot{E}{n}_{PV}^{in}$ |

$\dot{E}{x}_{PV}^{in}={\dot{W}}_{PV}^{out}+\dot{E}{x}_{PV}^{L}$ | $\dot{E}{x}_{PV}^{in}=\dot{E}{n}_{PV}^{in}\xb7\left(1-{T}_{0}/{T}_{S}\right)$ | |

DHN | ${\dot{Q}}_{\mathrm{DHN}}^{in}={\dot{Q}}_{\mathrm{DHN}}^{out}+{\dot{Q}}_{\mathrm{DHN}}^{L}$ | ${\dot{Q}}_{\mathrm{DHN}}^{L}={\varphi}_{\mathrm{DHN}}^{L}\xb7{\dot{Q}}_{\mathrm{DHN}}^{in}$ |

$\dot{E}{x}_{\mathrm{DHN}}^{Q,in}=\dot{E}{x}_{\mathrm{DHN}}^{Q,out}+\dot{E}{x}_{\mathrm{DHN}}^{L}+\dot{E}{x}_{\mathrm{DHN}}^{D}$ | $\dot{E}{x}_{\mathrm{DHN}}^{Q}={\dot{Q}}_{\mathrm{DHN}}\xb7\left(1-{T}_{0}/T\right)$ |

**Table A4.**Unit-by-unit formulation of technoeconomic and exergoeconomic balances and auxiliary equations.

Unit | Techno- and Exergoeconomic Balances | Auxiliary Equations |
---|---|---|

GBOIL | ${c}_{GBOIL}^{F}\xb7\dot{E}{n}_{GBOIL}^{in}+{\dot{Z}}_{GBOIL}^{CI}+{\dot{Z}}_{GBOIL}^{OM}={c}_{GBOIL}^{P}\xb7\dot{E}{n}_{GBOIL}^{out}$ | ${\dot{Z}}_{GBOIL}^{CI}={z}_{GBOIL}^{CI}\xb7{\wp}_{GBOIL}\xb7CR{F}_{GBOIL}$ |

${c}_{GBOIL}^{F,ex}\xb7\dot{E}{x}_{GBOIL}^{in}+{\dot{Z}}_{GBOIL}^{CI}+{\dot{Z}}_{GBOIL}^{OM}={c}_{GBOIL}^{P,ex}\xb7\dot{E}{x}_{GBOIL}^{out}$ | ${\dot{Z}}_{GBOIL}^{OM}={\varphi}_{GBOIL}^{OM}\xb7{\dot{Z}}_{GBOIL}^{CI}$ | |

BBOIL | ${c}_{BBOIL}^{F}\xb7\dot{E}{n}_{BBOIL}^{in}+{\dot{Z}}_{BBOIL}^{CI}+{\dot{Z}}_{BBOIL}^{OM}={c}_{BBOIL}^{P}\xb7\dot{E}{n}_{BBOIL}^{out}$ | ${\dot{Z}}_{BBOIL}^{CI}={z}_{BBOIL}^{CI}\xb7{\wp}_{BBOIL}\xb7CR{F}_{BBOIL}$ |

${c}_{BBOIL}^{F,ex}\xb7\dot{E}{x}_{BBOIL}^{in}+{\dot{Z}}_{BBOIL}^{CI}+{\dot{Z}}_{BBOIL}^{OM}={c}_{BBOIL}^{P,ex}\xb7\dot{E}{x}_{BBOIL}^{out}$ | ${\dot{Z}}_{BBOIL}^{OM}={\varphi}_{BBOIL}^{OM}\xb7{\dot{Z}}_{BBOIL}^{CI}$ | |

Grid | ${c}_{Grid}^{P}={c}_{Grid}^{F}/{\eta}_{Grid}$ | ${\dot{Z}}_{Grid}^{CI}=0$ ${\dot{Z}}_{Grid}^{OM}=Implicitinelectricityprice$ |

${c}_{Grid}^{P,ex}={c}_{Grid}^{F,ex}/{\eta}_{Grid}^{ex}$ | ||

EBOIL | ${c}_{EBOIL}^{F}\xb7\dot{E}{n}_{EBOIL}^{in}+{\dot{Z}}_{EBOIL}^{CI}+{\dot{Z}}_{EBOIL}^{OM}={c}_{EBOIL}^{P}\xb7\dot{E}{n}_{EBOIL}^{out}$ ${c}_{EBOIL}^{F,ex}\xb7\dot{E}{x}_{EBOIL}^{in}+{\dot{Z}}_{EBOIL}^{CI}+{\dot{Z}}_{EBOIL}^{OM}={c}_{EBOIL}^{P,ex}\xb7\dot{E}{x}_{EBOIL}^{out}$ | ${c}_{EBOIL}^{F}=\frac{\left({c}_{Grid}^{P}\xb7\dot{E}{n}_{Grid}^{out,EBOIL}+{c}_{PV}^{P}\xb7\dot{E}{n}_{PV}^{out,EBOIL}\right)}{\dot{E}{n}_{EBOIL}^{in}}$ |

$\left({\dot{Z}}_{EBOIL}^{CI}={z}_{EBOIL}^{CI}\xb7{\wp}_{EBOIL}\xb7CR{F}_{EBOIL}\right)$ $\left({\dot{Z}}_{EBOIL}^{OM}={\varphi}_{EBOIL}^{OM}\xb7{\dot{Z}}_{EBOIL}^{CI}\right)$ | ${c}_{EBOIL}^{F,ex}=\frac{\left({c}_{Grid}^{P,ex}\xb7\dot{E}{x}_{Grid}^{out,EBOIL}+{c}_{PV}^{P,ex}\xb7\dot{E}{x}_{PV}^{out,EBOIL}\right)}{\dot{E}{x}_{EBOIL}^{in}}$ | |

ST | ${c}_{ST}^{F}\xb7\dot{E}{n}_{ST}^{in}+{\dot{Z}}_{ST}^{CI}+{\dot{Z}}_{ST}^{OM}={c}_{ST}^{P}\xb7\dot{E}{n}_{ST}^{out}$ | ${\dot{Z}}_{ST}^{CI}={z}_{ST}^{CI}\xb7{\wp}_{ST}\xb7CR{F}_{ST}$ |

${c}_{ST}^{F,ex}\xb7\dot{E}{x}_{ST}^{in}+{\dot{Z}}_{ST}^{CI}+{\dot{Z}}_{ST}^{OM}={c}_{ST}^{P,ex}\xb7\dot{E}{x}_{ST}^{out}$ | ${\dot{Z}}_{ST}^{OM}={\varphi}_{ST}^{OM}\xb7{\dot{Z}}_{ST}^{CI}$ | |

HP | ${c}_{HP}^{F}\xb7\dot{E}{n}_{HP}^{in}+{\dot{Z}}_{HP}^{CI}+{\dot{Z}}_{HP}^{OM}={c}_{HP}^{P}\xb7\dot{E}{n}_{HP}^{out}$ ${c}_{HP}^{F,ex}\xb7\dot{E}{x}_{HP}^{in}+{\dot{Z}}_{HP}^{CI}+{\dot{Z}}_{HP}^{OM}={c}_{HP}^{P,ex}\xb7\dot{E}{x}_{HP}^{out}$ | ${c}_{HP}^{F}=\frac{\left({c}_{Grid}^{P}\xb7\dot{E}{n}_{Grid}^{out,HP}+{c}_{PV}^{P}\xb7\dot{E}{n}_{PV}^{out,HP}\right)}{\dot{E}{n}_{HP}^{in}}$ |

$\left({\dot{Z}}_{HP}^{CI}={z}_{HP}^{CI}\xb7{\wp}_{HP}\xb7CR{F}_{HP}\right)$ $\left({\dot{Z}}_{HP}^{OM}={\varphi}_{HP}^{OM}\xb7{\dot{Z}}_{HP}^{CI}\right)$ | ${c}_{HP}^{F,ex}=\frac{\left({c}_{Grid}^{P,ex}\xb7\dot{E}{x}_{Grid}^{out,EBOIL}+{c}_{PV}^{P,ex}\xb7\dot{E}{x}_{PV}^{out,EBOIL}\right)}{\dot{E}{x}_{EBOIL}^{in}}$ | |

PV | ${c}_{PV}^{F}\xb7\dot{E}{n}_{PV}^{in}+{\dot{Z}}_{PV}^{CI}+{\dot{Z}}_{PV}^{OM}={c}_{PV}^{P}\xb7\dot{E}{n}_{PV}^{out}$ | ${\dot{Z}}_{PV}^{CI}={z}_{PV}^{CI}\xb7{\wp}_{PV}\xb7CR{F}_{PV}$ |

${c}_{PV}^{F,ex}\xb7\dot{E}{x}_{PV}^{in}+{\dot{Z}}_{PV}^{CI}+{\dot{Z}}_{PV}^{OM}={c}_{PV}^{P,ex}\xb7\dot{E}{x}_{PV}^{out}$ | ${\dot{Z}}_{PV}^{OM}={\varphi}_{PV}^{OM}\xb7{\dot{Z}}_{PV}^{CI}$ | |

DHN | ${c}_{\mathrm{DHN}}^{F}\xb7\dot{E}{n}_{\mathrm{DHN}}^{in}+{\dot{Z}}_{\mathrm{DHN}}^{CI}+{\dot{Z}}_{\mathrm{DHN}}^{OM}={c}_{\mathrm{DHN}}^{P}\xb7\dot{E}{n}_{\mathrm{DHN}}^{out}$ ${c}_{\mathrm{DHN}}^{F,ex}\xb7\dot{E}{x}_{\mathrm{DHN}}^{in}+{\dot{Z}}_{\mathrm{DHN}}^{CI}+{\dot{Z}}_{\mathrm{DHN}}^{OM}={c}_{\mathrm{DHN}}^{P,ex}\xb7\dot{E}{x}_{\mathrm{DHN}}^{out}$ | ${c}_{\mathrm{DHN}}^{F}=\sum {c}_{ProdSyst}^{P}\xb7{\dot{Q}}_{ProdSyst}^{out}/{\dot{Q}}_{\mathrm{DHN}}^{in}$ |

$\left({\dot{Z}}_{\mathrm{DHN}}^{CI}={z}_{\mathrm{DHN}}^{CI}\xb7{\wp}_{\mathrm{DHN}}\xb7CR{F}_{\mathrm{DHN}}\right)$ $\left({\dot{Z}}_{\mathrm{DHN}}^{OM}={\varphi}_{\mathrm{DHN}}^{OM}\xb7{\dot{Z}}_{\mathrm{DHN}}^{CI}\right)$ | ${c}_{\mathrm{DHN}}^{F,ex}=\sum {c}_{ProdSyst}^{P,ex}\xb7\dot{E}{x}_{ProdSyst}^{out}/\dot{E}{x}_{\mathrm{DHN}}^{in}$ |

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**Figure 1.**Boundary mapping (© OpenStreetMap contributors - licensed under the Open Data Commons Open Database License–OdbL-by the OpenStreetMap Foundation-OSMF)and distribution of annual space heating and DHW demands of the Cassine district located in Chambéry, France.

**Figure 2.**Schematic representation of the three approaches considered for sizing the heat production units.

**Figure 3.**Overall energy and exergy efficiencies for each solution, at each scale size. D = District-scale sizing; S = Sector-scale sizing; B = Building-scale sizing.

**Figure 4.**Overall LCOE of heat for every solution at every scale. D = district-scale sizing; S = sector-scale sizing; B = building-scale sizing.

System | Scale of Sizing | Energy Unit(s) | Backup Unit(s) |
---|---|---|---|

GBOIL | Building | Gas boiler (GBOIL) | Not needed |

Sector or District | GBOIL + DHN | ||

BBOIL | Building | Biomass boiler (BBOIL) | Not needed |

Sector or District | BBOIL + 80 °C/60 °C network (DHN) | ||

Grid + EBOIL | Building | Grid-driven electric boiler (EBOIL) | Not needed |

Sector or District | EBOIL + DHN | ||

PV + EBOIL | Building | Photovoltaic panels (PV) | Grid + EBOIL |

Sector or District | PV + EBOIL + DHN | ||

ST | Building | Solar thermal collectors (ST) | Grid + EBOIL |

Sector or District | ST + DHN | ||

Grid + HP | Building | Air-source heat pump (ASHP) | Not needed |

Sector or District | Geothermal HP (GHP) + DHN | ||

PV + HP | Building | ASHP (PV-driven) | Grid + HP |

Sector or District | GHP (PV-driven) + DHN |

**Table 2.**Unit-by-unit performance, economic and environmental parameters, at each scale size. Whenever a range of values is shown, the nominal case refers to the arithmetic average. Lower and upper bounds were used for sensitivity analyses.

η | T^{out} | θ^{out} | θ^{in} | η^{ex} | z^{CI} | c^{F} | φ^{OM} | n | x_{CO2} | ||
---|---|---|---|---|---|---|---|---|---|---|---|

Unit | Scale | [%] | [°C] | [-] | [-] | [%] | [EUR/kW] | [EUR/MWh] | [%_{CAPEX}] | [yr] | [kg/kWh] |

GBOIL | D | 95 | 80 | 0.26 | 1.00 | 27.0 | 60–120 | 30.0 | 3.5 | 20 | 0.380 |

S | 95 | 80 | 0.26 | 1.00 | 27.0 | 60–120 | 40.0 | 3.5 | 20 | 0.380 | |

B | 85 | 65 | 0.22 | 1.00 | 22.7 | 344 | 73.7 | 3.5 | 15 | 0.380 | |

BBOIL | D | 95 | 80 | 0.26 | 1.00 | 29.6 | 470–645 | 24.0 | 1.8 | 25 | 0.035 |

S | 95 | 80 | 0.26 | 1.00 | 29.6 | 550–665 | 24.0 | 1.7 | 25 | 0.035 | |

B | 85 | 65 | 0.22 | 1.00 | 17.5 | 350–950 | 63.0 | 2.7 | 25 | 0.035 | |

ST | D | 70 | 80 | 0.26 | 0.95 | 20.3 | 530–700 | 0.0 | 1.0 | 30 | 0.000 |

S | 70 | 80 | 0.26 | 0.95 | 20.3 | 530–700 | 0.0 | 1.0 | 30 | 0.000 | |

B | 60 | 65 | 0.22 | 0.95 | 14.1 | 940–1180 | 0.0 | 1.4 | 25 | 0.000 | |

TES | D | 95 | 80 | 0.26 | 0.26 | 90.3 | 4–6 | =c^{P,solar-driven} | 2.0 | 30 | 0.000 |

S | 95 | 80 | 0.26 | 0.26 | 90.3 | 10–20 | =c^{P,solar-driven} | 2.0 | 30 | 0.000 | |

B | 90 | 65 | 0.22 | 0.22 | 90.3 | 20–40 | =c^{P,solar-driven} | 2.0 | 30 | 0.000 | |

PV | D | 21 | N/A | 1.00 | 0.95 | 22.1 | 1092–1349 | 0.0 | 2.4 | 25 | 0.000 |

S | 21 | N/A | 1.00 | 0.95 | 22.1 | 1092–1349 | 0.0 | 2.4 | 25 | 0.000 | |

B | 19 | N/A | 1.00 | 0.95 | 20.0 | 2630–2640 | 0.0 | 2.6 | 25 | 0.000 | |

EBOIL | D | 99 | 80 | 0.26 | 1.00 | 25.5 | 60–120 | 130.0 | 3.5 | 20 | 0.056 |

S | 99 | 80 | 0.26 | 1.00 | 25.5 | 60–120 | 130.0 | 3.5 | 20 | 0.056 | |

B | 99 | 65 | 0.22 | 1.00 | 22.5 | 338 | 176.5 | 3.5 | 20 | 0.056 | |

HP | D | 208 | 80 | 0.26 | 0.52 | 49.2 | 600–900 | 130.0 | 3.5 | 30 | 0.056 |

S | 208 | 80 | 0.26 | 0.52 | 49.2 | 600–900 | 130.0 | 3.5 | 20 | 0.056 | |

B | 244 | 65 | 0.22 | 0.45 | 50.3 | 1100–1400 | 176.5 | 2.1 | 17 | 0.056 | |

NETW | D | 95 | 65 | 0.22 | 0.26 | 82.9 | 416–732 | (Equations (11) and (12)) | 7.5 | 20 | 0.000 |

S | 95 | 65 | 0.22 | 0.26 | 82.9 | 416–732 | (Equations (11) and (12)) | 7.5 | 20 | 0.000 |

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**MDPI and ACS Style**

Fitó, J.; Dimri, N.; Ramousse, J.
Improving Thermoeconomic and Environmental Performance of District Heating via Demand Pooling and Upscaling. *Energies* **2021**, *14*, 8546.
https://doi.org/10.3390/en14248546

**AMA Style**

Fitó J, Dimri N, Ramousse J.
Improving Thermoeconomic and Environmental Performance of District Heating via Demand Pooling and Upscaling. *Energies*. 2021; 14(24):8546.
https://doi.org/10.3390/en14248546

**Chicago/Turabian Style**

Fitó, Jaume, Neha Dimri, and Julien Ramousse.
2021. "Improving Thermoeconomic and Environmental Performance of District Heating via Demand Pooling and Upscaling" *Energies* 14, no. 24: 8546.
https://doi.org/10.3390/en14248546