# Optimal Installation of Heat Pumps in Large District Heating Networks

^{*}

## Abstract

**:**

_{2}emissions of almost 4% can be obtained by installing a single heat pump of about 4 MWe (over a total thermal load of about 305 MWt), while this positive effect can be reduced by up to 63% if placing the heat pump at non-optimal locations.

## 1. Introduction

## 2. Methodology

- A thermo-fluid dynamic model of the DH network, which is used to reproduce mass-flow rates and pressures within the thermal distribution infrastructure. This step, described in Section 2.1, is essential to obtain a proper estimation of the temperature at which the HP works according to the location selected.
- A model of the HP operations. The model, as discussed in Section 2.2, is coupled to the thermo-fluid dynamic model of the DH network, since the performance and outlet temperature of the HP depend on the temperature of water.

_{2}emissions in the different cases in Section 2.5.

#### 2.1. Thermo-Fluid Dynamic Model of the District Heating Network

- At the building level, the heating load profile reproduces a typical pattern in Mediterranean regions: in these areas, the heating devices of the buildings are shut down (as in the reported case) or attenuated during the night, leading to huge thermal requests in the morning when the systems are switched back on. Thus, the thermal transient occurring in the morning is significant, but limited to few hours of the day. On the other hand, after the start-up transient, an almost steady behavior is observed for the rest of the day until the system is shut down in the late evening. To have a better understanding of this aspect, the example reported in the figure has been tested using a self-developed algorithm to identify the steady-state operating conditions. The resulting steady-state operating points are reported with green dots in the figure, and the corresponding average steady-state is represented with a dashed red line. The main outcome of this test is that steady-state conditions can be identified for the majority of the day: in the presented case, they occur for more than 80% of all the on conditions.
- A similar trend can be observed at the plant level: in this case, the total heating load can be seen as a combination of all the heating loads of the buildings connected to the network, the thermal losses, and the dynamics of the network itself. The profile reported in the figure shows also in this case a low heating load during the night (due to shut down and attenuation of the different buildings), a consequent heating peak in the morning, and an approximate steady trend immediately after the morning start-up phase. Possible deviation from average conditions (like the small valley in the afternoon) are generally managed with thermal storages, while heating plants are typically operated with a steady load. Again, steady conditions can be observed for the majority of the time.

#### 2.2. Heat Pump Model

#### 2.3. Coupling District Heating and Heat Pump Models

- At first, a simulation of the supply line of the district heating network is performed. This simulation uses as input the mass-flow rates required by all the buildings of the network ${G}_{u}$, the share of mass-flow rate supplied by each plant ${G}_{p}$, and the supply temperature of each plant of the network ${T}_{p}^{s}$. These values represent the boundary conditions of the supply-simulation thermal problem. By applying the thermo-fluid dynamic model developed in Section 2.1 to the supply network, it is possible to obtain the temperature distribution along the whole supply line${\mathbf{T}}^{\mathbf{s}}$
**,**besides the mass-flow rates and pressure distribution (for clarity, only the thermal part is discussed in this section, although the hydraulic part is also included in the simulation). - The second step consists of a simplified modeling of the thermal users’ behavior. This step allows calculating the boundary conditions of the return network thermal simulation ${T}_{u}^{r}$(that are the input of the next step) by knowing the mass-flow rates required by the users ${G}_{u}$, their heating loads ${\Phi}_{u}$, and the supply temperatures of the thermal substations ${T}_{u}^{s}$ (which are part of the solution calculated at step 1 ${\mathbf{T}}^{\mathbf{s}}$).
- Once the boundary conditions of the return network thermal problem (namely the temperatures leaving each thermal substation ${T}_{u}^{r}$) are known, it is possible to run a simulation of the return line of the network, requiring as further input the mass-flow rates injected from the buildings ${G}_{u}$ and those extracted from the plants ${G}_{p}$. This is the step including the coupling with the heat pump model (being the heat pump considered with “source-return” configuration). Indeed, the temperature distribution along the return network ${\mathbf{T}}^{\mathbf{r}}$, which is the solution of the thermal simulation of the return network, is influenced in this case also by the presence of the heat pump, which is responsible for a temperature rise in the corresponding branch and needs to be accurately included into the return network simulation. Thus, the conditions described in Section 2.2 are imposed here: in the outlet node of the heat pump, there will be a Dirichlet boundary condition to fix its temperature equal to ${T}_{ou{t}_{HP}}$, evaluated according to Equations (5) and (6); it is worth highlighting again that this system of equations is non-linear, due to the dependency of the COP on the network temperatures themselves. Thus, the coupling and the solution of this step is non-trivial. Moreover, further non-linearities arise when considering the mass-flow rate ${G}_{HP}$ as not known a priori as assessed by the solution of the hydraulic problem, but evaluated depending on the thermal solution itself, as will be shown in Section 4.4. In this last case, some iterations are also needed to obtain the correct solution. In the end, this step allows evaluating the temperature distribution along the whole return network ${\mathbf{T}}^{\mathbf{r}}$.
- The last step allows evaluating the final heating load of the plants as ${\Phi}_{p}={G}_{p}{c}_{p}\left({T}_{p}^{s}-{T}_{p}^{r}\right)$. The total heating load of the plants will be reduced with respect to the case without heat pump because of the higher value of the return temperature ${T}_{p}^{r}$, included of the solution obtained at Step 3, in at least one of the plants.

#### 2.4. Exergy Analysis

#### 2.5. CO_{2} Emissions Reduction

_{2}that can be saved through the installation of the HP. The carbon dioxide emissions can be evaluated through the following equation:

_{4}(which can be directly related to the primary energy), ${r}_{C{O}_{2}/C{H}_{4}}$ is the CO

_{2}emission factor that can be estimated around 1.956 kg

_{CO2}/Sm

^{3}

_{gas}, and ${H}_{i}$ is the lower heating value, equal to 33.96 MJ/Sm

^{3}for the natural gas. The carbon emission savings are obtained by subtracting the carbon dioxide emissions in the two cases (case without HP installation minus case with HP), which has been done for all the scenarios analyzed to compare the emissions savings in various HP locations.

#### 2.6. Cost Savings

## 3. Case Study

#### 3.1. System Description

#### 3.2. Analyzed Scenarios

- Cogeneration-based operation (Configuration 1): The thermal power is completely supplied by the two cogeneration plants CHP1 and CHP2 and by the newly installed HP. The operation selected is that CHP1 and CHP2 process 53% and 47% of the total mass-flow rate respectively.
- Cogeneration and heat-only boiler operation (Configuration 2): The thermal power is provided by cogeneration system and heat only boiler. Specifically, 63% of the total mass-flow rate is provided by cogeneration plants and 37% from boilers. This scenario refers to large demands that cannot be fully met by the cogenerators and less efficient production systems—e.g., heat-only boilers (HOB)—must be operated.
- The other configurations are characterized by off operations of the various plants (this could happen for various reasons, such as maintenance or fault). Specifically, the plants taken off in Configuration 3 to 6 are respectively CHP1 (Configuration 3), CHP2 (Configuration 4), HOB1 (Configuration 5), and HOB2 (Configuration 6).

- Base-case: The installation of the HP along the return network brings an increase in the return temperature to one or more production plants. The mass-flow rate processed by each plant is kept unchanged with respect to the case without the HP. Consequently, the heating load of the production plants with higher return temperature decreases, regardless of whether the plant is a CHP or a HOB.
- Different mass-flow rate control strategy: In this second case, when the HP preheats the flow in the return line to the production plants, the mass-flow rate of the different plants are subjected to a control strategy and modified with respect to the base-case such that the CHPs are forced to work always at the same thermal power. If the HP preheats a water flow directed to the CHP, its mass-flow rate is increased so that the CHP thermal load is constant. The increased mass-flow rate also helps keeping temperatures lower, improving the COP of the device. Instead, the HOB mass-flow rate is decreased so that its thermal load decreases. This strategy results in a further total exergy reduction even when the HP is located in the proximities of a CHP plant, (in case of combined CHP-HOB operations). The heating load of the CHP plants is reduced only in the case HOBs are not in operation (e.g., as occurs in Configuration 1). This mass-flow rate control strategy can be applied only when there are not specific constraints on the network infrastructure (e.g., mass-flow rate congestion and fluid-dynamic bottlenecks).

## 4. Results and Discussion

#### 4.1. Cogeneration-Based Operation

- If the HP is installed in the proximity of the plant, the distribution losses are lower. Oppositely, if the mass-flow rate is heated-up far from the production plant, the heat dispersion increases.
- The closer the HP to the plant, the lower is the inlet temperature ${T}_{in}$, due to the distribution losses on the return line. This results in a positive effect for the $\mathrm{COP}$.
- The mass-flow rate is higher in the branches that are closer to the plant. Therefore, given that the electric power of the LHP is fixed, and so is the thermal power, the temperature rise is lower. As a consequence, ${T}_{out}$ might be significantly reduced: this is a further and more relevant positive effect for the $\mathrm{COP}$. However, it is worth remembering that the mass-flow rate that the HP is able to process has a limit: if the branch exceeds this threshold, only a portion of the flow rate is treated by the HP and then it is mixed with the remaining part. This is the reason why comparable values of $\phi $ are obtained for all the cases with a sufficient large mass-flow rate.

#### 4.2. Cogeneration and Heat-Only Boiler Operation

_{2}emissions reduction is of $46.6{t}_{CO2}/\mathrm{d}\mathrm{a}\mathrm{y}$. This proves that reducing the thermal load of a boiler is far more effective than reducing the thermal load of a CHP plant.

#### 4.3. Average Operating Conditions

_{2}emissions that can be avoided in a whole heating season, which is extended from October 15th to April 15th in the location considered. If the HP is located in its optimal position they accounts for $4220{t}_{CO2}/y$, which represents a reduction of about $3.3\%$ with respect to the total amount of emissions in a year without the power-to-heat device (that are about $126\cdot {10}^{3}{t}_{CO2}/y$). This percentage strongly depends on the size of the HP, and it can be further enhanced by increasing its electric power. If the HP is installed close to CHP2 and to HOB2 the CO

_{2}reductions are respectively of $1560{t}_{CO2}/y$ and $4058{t}_{CO2}/y$. This would lead to a decrease in the CO

_{2}savings of −63.0% and −3.8% if placing the HP respectively close to the cogeneration and boiler plants instead of its optimal position considering the whole yearly operation.

#### 4.4. Mass-Flow Rate Control Strategy

_{2}emissions, by applying the mass-flow rate control strategies it is possible to obtain a reduction of $4823{t}_{CO2}/y$($-3.8\%$ with respect to the case without HP) by locating the HP at its best position, $4376{t}_{CO2}/y$ near the cogenerator and $4298{t}_{CO2}/y$ near the boiler. Consequently, potential CO

_{2}savings of respectively 9.3% and 10.9% risk being lost if placing the HP close to the CHP or the boiler rather than at its optimal position, which must be evaluated considering the average yearly operation. Comparing the reduction obtained in the case of mass-flow control strategy, improvements have been achieved in all the cases, but the most significant improvement is achieved in the proximities of the CHP plant, where the previous strategy performed poorly.

#### 4.5. Comparison and Discussion

_{2}emissions is given in Figure 12. To have a global view of the potential benefits, results are referred to the average yearly operation and are reported both for the base-case and for the second scenario with mass-flow rate control strategy. From this figure, it is possible to see that the CO

_{2}emission reduction that can be achieved through the installation of the HP is always greater when the mass-flow rate control strategy is applied, since in this case more positions become significant for the installation of the device. In the best position, the installation of HP using the mass-flow rate control strategy brings to a reduction in the yearly CO

_{2}emissions of 4823 ${t}_{C{O}_{2}}/y$), which represents a −3.8% reduction compared with the case without HP.

_{2}savings of 63.0% risk to be lost if misplacing the HP close to the CHP plant (corresponding to a CO

_{2}reduction of 1560 ${t}_{C{O}_{2}}/y$), despite this plant being in operation for most of the time; this potential reduction would be instead of 3.8% if placing the HP close to the boiler (corresponding to a CO2 reduction of 4058 ${t}_{C{O}_{2}}/y$).

- The exergy parameter $\phi $ defined in Equation (7) and representing the ratio between the exergy of the fossil fuel that can be saved thanks to the HP and the electric power required.
- The CO
_{2}reduction which can be obtained as the difference between the CO_{2}emissions obtained in the scenario without the installation of the HP and the CO_{2}emissions achieved using the HP in the different cases, i.e.,: ${m}_{C{O}_{2}}^{withoutHP}-{m}_{C{O}_{2}}^{withHP},$ calculated according to Equation (12). No emissions are considered for the electricity needed by the HP, since it is supposed to be driven by renewable sources in this scenario. - The cost savings that can be achieved through the installation of the HP. This is calculated as $\frac{{c}^{withoutHP}-{c}^{withHP}}{{c}^{withoutHP}}$, where the specific operating costs are evaluated using Equation (13). In this case, both costs for natural gas needed by HOBs and CHPs and the cost for electricity from renewables are considered. The investment cost is not included in the computation since it has been found to be negligible: considering the investment costs reported in [42,43] and the expected lifetime [43], it impacts cost savings of less than 0.1%.

_{2}reduction decreases to 1006 ${t}_{CO2}/y$ in the base-case and 1607 ${t}_{CO2}/y$if applying the mass-flow rate control strategy; concerning cost savings, these are of 0.5% and 1.0% in the two different scenarios.

## 5. Conclusions

_{2}emissions and production costs are proposed as further KPIs.

_{2}emission reduction; (c) the unit production cost.

_{2}emissions reduction of about $4220{t}_{CO2}/y$ ($-3.3\%)$if a HP of $4\mathrm{MWe}$ is used. Potential CO

_{2}savings of 63.0% can potentially be lost if misplacing the HP close to the cogeneration plant (corresponding to a CO

_{2}reduction of $1560{t}_{CO2}/y$), despite it is the plant that works for the majority of the time; this reduction would be 3.8% if placing the HP close to the boiler (corresponding to a CO

_{2}reduction of $4058{t}_{CO2}/y$).

_{2}savings reduce by 9.3% and 10.9% respectively.

_{2}emissions monitoring could be performed under variable excess of electric power. Furthermore, the model could be extended to also take into account the distribution losses in the electric grid.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$c$ | Specific cost (€/kWh) | Acronyms | |

${c}_{p}$ | Specific heat (J/kg/K) | COP | Coefficient of Performance |

$E$ | Exergy (W) | DH | District Heating |

$G$ | Mass-flow rate | DHN | District Heating Network |

${H}_{i}$ | Lower heating value (MJ/m^{3}) | HP | Heat Pump |

$p$ | Percentage of time (–) | LHP | Large-scale Heat Pump |

$Q$ | Useful heat (W) | ||

$r$ | Emission factor (kg/m^{3}) | Matrix/Vectors | |

$T$ | Temperature (K) | $A$ | Incidence matrix (–) |

$W$ | Input work (W) | $G$ | Mass-flow rate vector (kg/s) |

$g$ | Known terms vector (W/K) | ||

Greek letters | $K$ | Stiffness matrix (W/K) | |

${\eta}_{I}$ | First-law efficiency (–) | $P$ | Pressure vector (Pa) |

${\eta}_{II}$ | Second-law efficiency (–) | $T$ | Temperature vector (K) |

$\phi $ | Exergy KPI (–) | $Y$ | Fluid-dynamic conductance matrix (Pa) |

$\mathsf{\Phi}$ | Heating power (W) | ||

$\psi $ | HP second-law efficiency (–) | $\tau $ | Pressure rise vector (Pa) |

## References

- Persson, U.; Werner, S. Heat distribution and the future competitiveness of district heating. Appl. Energy
**2011**, 88, 568–576. [Google Scholar] [CrossRef] - Westner, G.; Madlener, G. The impact of modified EU ETS allocation principles on the economics of CHP-based district heating systems. J. Clean. Prod.
**2012**, 20, 47–60. [Google Scholar] [CrossRef] - Werner, S. International review of DH and cooling. Energy
**2017**, 137, 617–631. [Google Scholar] [CrossRef] - Münster, M.; Morthorst, P.E.; Larsen, H.V.; Bregnbæk, L.; Weling, J.; Lindboe, H.H.; Ravn, H. The role of district heating in the future Danish energy system. Energy
**2012**, 48, 47–55. [Google Scholar] [CrossRef] - European Commission. An Energy Policy for Europe; European Commission: Brussels, Belgium, 2007. [Google Scholar]
- Lund., H.; Werner, S.; Wiltshire, R.; Svendsen, S.; Thorsen, J.E.; Hvelplund, F.; Mathiesen, B.V. 4th Generation District Heating (4GDH)—Integrating smart thermal grids into future sustainable energy systems. Energy
**2014**, 68, 1–11. [Google Scholar] - Lund, H.; Østergaard, P.A.; Connolly, D.; Mathiesen, B.V. Smart energy and smart energy systems. Energy
**2017**, 137, 556–565. [Google Scholar] [CrossRef] - Lauka, D.; Guska, J.; Blumberga, D. Heat pump integration in district heating networks of the Baltic states. Procedia Comput. Sci.
**2015**, 52, 835–842. [Google Scholar] [CrossRef] - Lund, R.; Ilic, D.D.; Trygg, L. Socioeconomic potential for introducing large-scale heat pumps in district heating in Denmark. J. Clean Prod.
**2016**, 139, 219–229. [Google Scholar] [CrossRef] - Coss., S.; Verda, V.; Le-Corre, O. Multi-objective optimization of district heating network model and assessment of demand side measures using the load deviation index. J. Clean. Prod.
**2018**, 182, 338–351. [Google Scholar] [CrossRef] - Sarbu, I.; Mirza, M.; Muntean, D. Integration of Renewable Energy Sources into Low-Temperature District Heating Sys-tems: A Review. Energies
**2022**, 15, 6523. [Google Scholar] [CrossRef] - Averfalk, H.; Ingvarsson, P.; Persson, U.; Gong, M.; Werner, S. Large heat pumps in Swedish district heating systems. Renew. Sustain. Energy Rev.
**2017**, 79, 1275–1284. [Google Scholar] [CrossRef] - Lund, H.; Mathiesen, B.V. Energy system analysis of 100% renewable energy systems—The case of Denmark in years 2030 and 2050. Energy
**2009**, 34, 524–531. [Google Scholar] [CrossRef] - Østergaard, P.A.; Smith, K.M.; Tunzi, M.; Svendsen, S. Low-temperature operation of heating systems to enable 4th generation district heating: A review. Energy
**2022**, 248, 123529. [Google Scholar] [CrossRef] - Mancarella, P. MES (multi-energy systems): An overview of concepts and evaluation models. Energy
**2014**, 65, 1–17. [Google Scholar] [CrossRef] - Capone, M.; Guelpa, E.; Mancò, G.; Verda, V. Integration of storage and thermal demand response to unlock flexibility in district multi-energy systems. Energy
**2021**, 237, 121601. [Google Scholar] [CrossRef] - Guelpa, E.; Capone, M.; Sciacovelli, A.; Vasset, N.; Baviere, R.; Verda, V. Reduction of supply temperature in existing district heating: A review of strategies and implementations. Energy
**2023**, 262, 125363. [Google Scholar] [CrossRef] - Østergaard, D.S.; Svendsen, S. Costs and benefits of preparing existing Danish buildings for low-temperature district heating. Energy
**2019**, 176, 718–727. [Google Scholar] [CrossRef] - Blarke, M.B. Towards an intermittency-friendly energy systems: Comparing electric boilers and heat pumps in distributed cogeneration. Appl. Energy
**2012**, 91, 349–365. [Google Scholar] [CrossRef] - Frederiksen, S.; Werner, S. District Heating and Cooling; Studentlitteratur AB: Lund, Sweden, 2013. [Google Scholar]
- Bach, B.; Weling, J.; Ommen, T.; Münster, M.; Morales, J.M.; Elmegaard, B. Integration of large-scale hat pumps in the district heating systems of Greater Copenhagen. Energy
**2016**, 107, 321–334. [Google Scholar] [CrossRef] - Østergaard, P.A.; Andersen, A.N. Booster heat pumps and central heat pumps in district heating. Appl. Energy
**2016**, 184, 1374–1388. [Google Scholar] [CrossRef] - David, A.; Mathiesen, B.V.; Averfalk, H.; Werner, S.; Lund, H. Heat Roadmap Europe: Large-Scale Electric Heat Pumps in District Heating Systems. Energies
**2017**, 10, 578. [Google Scholar] [CrossRef] [Green Version] - Abokersh, M.H.; Saikia, K.; Cabeza, L.F.; Boer, D.; Vallès, M. Flexible heat pump integration to improve sustainable transition toward 4th generation district heating. Energy Convers. Manag.
**2020**, 225, 113379. [Google Scholar] [CrossRef] - Lygnerud, K.; Ottosson, J.; Kensby, J.; Johansson, L. Business models combining heat pumps and district heating in buildings generate cost and emission savings. Energy
**2021**, 234, 121202. [Google Scholar] [CrossRef] - Wei, Z.; Ren, F.; Yue, B.; Ding, Y.; Zheng, C.; Li, B.; Zhai, X.; Wang, R. Data-driven application on the optimization of a heat pump system for district heating load supply: A validation based on onsite test. Energy Convers. Manag.
**2022**, 266, 115851. [Google Scholar] [CrossRef] - Barco-Burgos, J.; Bruno, J.C.; Eicker, U.; Saldana-Robles, A.L.; Alcantar-Camarena, V. Review on the integration of high-temperature heat pumps in district heating and cooling networks. Energy
**2022**, 239, 122378. [Google Scholar] [CrossRef] - Ommen, T.; Markussen, W.B.; Elmegaard, B. Heat pumps in combined heat and power systems. Energy
**2014**, 76, 989–1000. [Google Scholar] [CrossRef] - Pieper, H.; Ommen, T.; Elmegaard, B.; Markussen, W.B. Assessment of a combination of three heat sources for heat pumps to supply district heating. Energy
**2009**, 176, 156–170. [Google Scholar] [CrossRef] - Sayegh, M.A.; Jadwiszczak, P.; Axcell, B.P.; Niemierka, E.; Bryś, K.; Jouhara, H. Heat pump placement, connection and operational modes in European district heating. Energy Build.
**2018**, 166, 122–144. [Google Scholar] [CrossRef] - Kontu, K.; Rinne, S.; Junnila, S. Introducing modern heat pumps to existing district heating systems—Global lessons from viable decarbonizing of district heating in Finland. Energy
**2019**, 166, 862–870. [Google Scholar] [CrossRef] - Ayele, G.T.; Mabrouk, M.T.; Haurant, P.; Laumert, B.; Lacarrière, B. Optimal placement and sizing of heat pumps and heat only boilers in a coupled electricity and heating networks. Energy
**2019**, 182, 122–134. [Google Scholar] [CrossRef] - Bahlawan, H.; Ferraro, N.; Gambarotta, A.; Losi, E.; Manservigi, L.; Morini, M.; Saletti, C.; Spina, P.R.; Venturini, M. Detection and identification of faults in a District Heating Network. Energy Convers. Manag.
**2022**, 266, 115837. [Google Scholar] [CrossRef] - Jakubek, D.; Ocłon, P.; Nowak-Ocłon, M.; Sułowicz, M.; Varbanov, P.S.; Klemes, J.J. Mathematical modelling and model validation of the heat losses in district heating networks. Energy
**2023**, 267, 126460. [Google Scholar] [CrossRef] - Harary, F. Graph Theory; Narosa Publishing House: New Delhi, Indian, 1995. [Google Scholar]
- Versteeg, H.K.; Malalasekera, W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method; Pearson Education Limited: London, UK, 2017. [Google Scholar]
- Capone, M.; Guelpa, E.; Verda, V. Accounting for pipeline thermal capacity in district heating simulations. Energy
**2021**, 219, 119663. [Google Scholar] [CrossRef] - Capone, M.; Guelpa, E.; Verda, V. Optimal operation of district heating networks through demand response. Int. J. Thermodyn.
**2019**, 22, 35–43. [Google Scholar] - Sciacovelli, A.; Verda, V.; Borchiellini, R. Numerical Design of Thermal Systems; CLUT Editrice: Turin, Italy, 2015. [Google Scholar]
- Guelpa, E.; Sciacovelli, A.; Verda, V. Thermo-fluid dynamic model of large district heating networks for the analysis of primary energy savings. Energy
**2019**, 184, 34–44. [Google Scholar] [CrossRef] - IRENA. Renewable Power Generation Costs in 2021. Available online: https://www.irena.org/-/media/Files/IRENA/Agency/Publication/2022/Jul/IRENA_Power_Generation_Costs_2021_Summary.pdf?la=en&hash=C0C810E72185BB4132AC5EA07FA26C669D3AFBFC (accessed on 4 January 2023).
- Pieper, A.; Ommen, T.; Buhler, F.; Paaske, B.L.; Elmegaard, B.; Markussen, W.B. Allocation of investment costs for large-scale heat pumps supplying district heating. Energy Procedia
**2018**, 147, 358–367. [Google Scholar] [CrossRef] - CRAVEzero Project. Available online: https://www.cravezero.eu/pboard/CostDB/CostDB.htm (accessed on 4 January 2023).

**Figure 1.**Representation of the heating load of a building (

**left**) and of the plants (

**right**) during a typical winter day for a large-scale DHN located in Italy.

**Figure 2.**Comparison of experimental measurements and model results for the supply and return temperature of four different substations belonging to different buildings of a small-scale DH network located in Italy. Shaded areas refer to off-conditions in which experimental measurements are not significant.

**Figure 4.**Flow chart of the model including thermo-fluid dynamic simulation of DHN and a model of the heat pump. For clarity, just single elements are represented (thermal plant, supply line, return line, thermal users, heat pumps).

**Figure 6.**φ coefficient throughout the analyzed DH network in a cogeneration-based operation (the star indicates the best position) −Configuration 1, base case.

**Figure 7.**φ coefficient throughout the analyzed DH network when supplied by both cogeneration plants and heat-only boilers (the star indicates the best position) −Configuration 2, base case.

**Figure 8.**φ coefficient throughout the analyzed DH network with different configurations (the star indicates the best position for each configuration) −Configurations 1 to 6, base case.

**Figure 9.**$\overline{\phi}$ coefficient throughout the selected DH system, averaged on the annual operation (the star indicates the best position) −Average yearly operation, base case.

**Figure 10.**$\phi $ coefficient throughout the analyzed DH network with different configurations, using the mass-flow rate control strategy (the star indicates the best position for each configuration) −Configurations 1 to 6, mass-flow rate control strategy.

**Figure 11.**$\overline{\phi}$ coefficient throughout the analyzed DH network, using the mass-flow rate control strategy (the star indicates the best position) −Average yearly operation, mass-flow rate control strategy.

**Figure 12.**Comparison of the CO

_{2}emissions avoided with and without the control strategy proposed. Three HP locations are considered: (1) the best location, (2) near CHP2, and (3) near HOB1.

**Figure 13.**$\overline{\phi}$ coefficient throughout the selected DH system, averaged on the annual operation (the star indicates the best position) −Average yearly operation with increased heating load (600 MW), base case.

**Figure 14.**Steady-state load duration curve of the large-scale DH network analyzed (

**left**) and values of $\overline{\phi}$ corresponding to each steady load (

**right**).

**Table 1.**Summary of the values assumed by the different parameters adopted in the analysis in different locations of the network.

Average Yearly Value | KPI | |||
---|---|---|---|---|

$\mathit{\phi}$ | CO_{2} Reduction | Cost Savings | ||

Base-case | Near CHP2 | 43% | $1560{t}_{CO2}/y$ | 0.8% |

Near HOB1 | 112% | $4065{t}_{CO2}/y$ | 2.7% | |

Best position | 117% | $4222{t}_{CO2}/y$ | 2.8% | |

With flow control | Near CHP2 | 121% | $4376{t}_{CO2}/y$ | 2.9% |

Near HOB1 | 118% | $4298{t}_{CO2}/y$ | 3.0% | |

Best position | 133% | $4823{t}_{CO2}/y$ | 3.2% |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Capone, M.; Guelpa, E.; Verda, V.
Optimal Installation of Heat Pumps in Large District Heating Networks. *Energies* **2023**, *16*, 1448.
https://doi.org/10.3390/en16031448

**AMA Style**

Capone M, Guelpa E, Verda V.
Optimal Installation of Heat Pumps in Large District Heating Networks. *Energies*. 2023; 16(3):1448.
https://doi.org/10.3390/en16031448

**Chicago/Turabian Style**

Capone, Martina, Elisa Guelpa, and Vittorio Verda.
2023. "Optimal Installation of Heat Pumps in Large District Heating Networks" *Energies* 16, no. 3: 1448.
https://doi.org/10.3390/en16031448