# A Critical Perspective on Positive Energy Districts in Climatically Favoured Regions: An Open-Source Modelling Approach Disclosing Implications and Possibilities

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## Abstract

**:**

## 1. Introduction

#### 1.1. Positive Energy District Analysis in Literature

#### 1.2. Annual Energy Balance in Energy System Modelling

#### 1.3. Open-Source Energy Modelling

#### 1.4. Progress beyond the State of the Art

- Is a PED technically and spatially feasible under perfect climatic conditions?
- How is a PED affected by the type of settlement (urban or rural) under these conditions?
- What are the PED’s implications in terms of cost and technology portfolio if the grid impact is kept low?
- How does the renewable share of the grid mix affect the PED economically and technically, if assessed hourly?

## 2. Materials and Methods

#### 2.1. Model Overview

#### 2.2. Mathematical Model

#### 2.2.1. Objective Function

- ${I}_{0}$, the initial investment cost in year zero of the optimised technology portfolio;
- ${R}_{y}$, the annual revenues from selling excess generated electricity to the grid; specified in Equation (2);

#### 2.2.2. PED Energy Balance

#### 2.2.3. PV Constraints

^{2}] for each respective angle constellation and each time step, ${\eta}_{pv}$—efficiency of the PV module and $PR$—performance ratio of the system installation, that includes unavoidable losses of a PV plant, $A\_avai{l}_{az,\beta}$—area available according to angle constellation and $GCR$—ground coverage ration, which accounts for spacing of tilted PV installations on flat roofs to avoid shading, $ca{p}_{pv}$—installed peak capacity of PV [kW], $AZ$—vector of used azimuth angles, and $TILT$—vector of used tilt angles.

#### 2.2.4. Battery Constraints

#### 2.3. Case Study Definition

#### 2.3.1. Location

^{2}, despite the large difference in surface area. Thus, the floor space index mentioned before as a great indicator of PED feasibility lies around 3 and 0.68 for the urban and rural district, respectively. The gross floor area is derived from the Spanish open kataster data in QGIS. Table 2 and Table 3 show the available space for PV power installations for the urban and the rural district, which has been derived manually in QGIS.

#### 2.3.2. Time Series Data

#### 2.3.3. Initial Scenarios

#### 2.3.4. Sensitivity Scenarios

## 3. Results

#### 3.1. Rural vs. Urban and Variation of Roof Space Available

#### 3.2. Variation of Grid Exchange Power

#### 3.3. Variation of Local Generation Mix

#### 3.4. Variation of the Electricity Price

## 4. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$\Delta $ | Delta |

CAPEX | Capital Expenditure |

$C{O}_{2}$ | Carbon Dioxide |

EC | European Commission |

EPN | Energy Positive Neighbourhood |

EU | European Union |

ex | Export |

FSI | Floor Space Index |

GFA | Gross Floor Area |

GGS | Grid Generation Mix Scenario |

GTS | Grid Tariff Scenario |

im | Import |

KPI | Key Performance Indicator |

LP | Linear Programming |

MILP | Mixed Integer Linear Programming |

NPV | Net Present Value |

PED | Positive Energy District |

PEF | Primary Energy Factor |

PES | Power Exchange Scenario |

PV | Photovoltaic |

PVPC | Voluntary Price for Small Consumer |

REE | Red Eléctrica de España |

ts | Time step |

R | Rural |

S | Scenario |

SET | Strategic Energy Technology |

SVS | Space Variation Scenario |

U | Urban |

Units | |

° | Degree |

€ | Euro |

kW | Kilowatt |

$k{W}_{p}$ | Kilowatt peak |

kWh | Kilowatt hour |

${m}^{2}$ | Square meter |

t | Tonnes |

## Appendix A. Primary Energy Factor of Import Electricity

**Figure A1.**Battery charge and discharge power of PES lim2 scenario with wrong PEF for grid tp Battery power.

## Appendix B. Input data

Input Variable | Value | Unit |
---|---|---|

CAPEX | 1070.0 | EUR/$k{W}_{p}$ |

OPEX fix | 12.8 | EUR/a |

OPEX var | 0.0 | EUR/kWh |

${\eta}_{pv}$ | 19 | % |

PR | 0.84 | - |

GCR flat | 0.8 | - |

GCR tilt roof | 1 | - |

Input Variable | Value | Unit |
---|---|---|

CAPEX | 750.0 | EUR/kWh |

OPEX fix | 0.0 | EUR/a |

OPEX var | 0.0 | EUR/kWh |

${\eta}_{batt}$ | 95 | % |

Cap/Power ratio | 0.3 | - |

$SO{C}_{1,0}$ | 0 | kWh |

Input Variable | Value | Unit |
---|---|---|

Latitude | 28.803 | - |

Longitude | −17.774 | - |

Altitude | 288 | m |

Albedo | 0.15 | - |

Average Temperature | 17.8 | °C |

Input Variable | Value | Unit |
---|---|---|

i | 0.05 | - |

$PE{F}_{diesel}$ | 2.75 | - |

$C{O}_{2}$ Emission factor diesel | 74.1 | t/TJ |

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**Figure 2.**Static and dynamic electricity balance of a PED according to primary energy factors (PEF).

**Figure 3.**Location of case study: (

**a**) Location of La Palma in the North-West of the Canarian Archipelago (red circle). (

**b**) Location of Los Sauces in the North-East of La Palma (red circle). (

**c**) Urban buildings considered for urban PED example (labelled in yellow). (

**d**) Rural buildings considered for rural PED example (labelled in yellow).

**Figure 4.**(

**a**) Tariff 2.0 DHA and feed-in tariff during 24th and 25th of August 2019. (

**b**) Generation mix during 24th and 25th of August 2019.

**Figure 6.**Composition of the net present value by scenario in CAPEX, fixed costs, variable costs and revenue.

**Figure 8.**(

**a**) NPV composition with power exchange limitations of the rural PED. (

**b**) NPV composition with power exchange limitations of the urban PED. (

**c**) Distribution of grid exchange power observations of PES lim2 rural. (

**d**) Distribution of grid exchange power observations of PES lim2 urban.

**Figure 9.**Electricity dispatch on the 24th and 25th of August 2019 considering (

**a**) load coverage under the low RES La Palma grid mix, (

**b**) load coverage under the high RES El Hierro grid mix, (

**c**) PV power distribution under the low RES La Palma grid mix, (

**d**) PV power distribution under the high RES El Hierro grid mix, (

**e**) Battery Charge and Discharge Power under the low RES La Palma grid mix and (

**f**) Battery Charge and Discharge Power under the high RES El Hierro grid mix. Considered herein is the urban scenario with a grid exchange limit of 132 kW (PES lim2—U).

**Figure 10.**Sensitivity of the status quo (S1), the SVS3–U and the PES lim 2–U towards tariff increase.

Model Decision Variables | |
---|---|

$ca{p}_{tec}$ | Capacities of selected technologies |

$fuel\_con{s}_{y,ts}$ | Fuel consumption at each time step each year (not used in this work) |

${p}_{y,ts}^{out,in}$ | Power flow at each time step in each year depending on source (out) and target (in) |

${A}_{az,\beta}$ | Area used for PV installation for each angle pair |

${C}_{y}$ | Annual costs |

${I}_{0}$ | Investment cost at year 0 |

$NPV$ | Net Present Value - model objective |

$O\_M\_fi{x}_{y}$ | Annual fix costs |

$O\_M\_va{r}_{y}$ | Annual variable costs |

${R}_{y}$ | Annual Revenues |

$SO{C}_{y,ts}$ | State of charge of the battery at each time step each year |

Other model parameters | |

$\eta $ | Efficiency |

$\beta $ | Tilt angle |

A | Area |

$az$ | Azimuth angle |

$AZ$ | Vector of considered azimuth angles |

$feedi{n}_{y,ts}$ | Feed-in Tariff at each ts |

$Irr$ | Irradiance |

$PR$ | Performance Ratio |

$GCR$ | Ground Coverage Ratio |

$tarif{f}_{y,ts}$ | Tariff at each ts |

$tec$ | Specific technology |

$TEC$ | Vector over all selected technologies |

$TILT$ | Vector of tilt angles |

$TS$ | Number of time steps in one year |

v | Optimisation variable |

V | Vector of optimisation variables |

x | Technology with electricity output |

X | Vector over technologies with electricity output |

y | Year |

Y | Time horizon in years |

z | Technology with electricity input |

Z | Vector over technologies with electricity input |

Occupation | Area Urban [m^{2}] | Area Rural [m^{2}] |
---|---|---|

Flat roof | 678 | 3138 |

Terrace | 2150 | 2295 |

Water Storage | 0 | 2190 |

Total | 2828 | 8323 |

Azimuth Angle [°] | Area Urban [m^{2}] | Area Rural [m^{2}] |
---|---|---|

0 | 40 | 235 |

45 | 0 | 195 |

90 | 29 | 270 |

135 | 0 | 170 |

180 | 40 | 240 |

225 | 0 | 215 |

270 | 90 | 250 |

315 | 0 | 155 |

**Table 4.**Description of initial scenarios with the respective scenario number (S) and variation in available space for PV power generation with its respective space variation scenario number (SVS) for the rural (R) and urban (U) cases.

S # | Description |
---|---|

1 | R & U: status quo |

2 | R: no PED |

3 | U: no PED |

4 | R: PED |

5 | U: PED |

SVS # | Description |

1 | R: PED; no terrace or water storage for PV generation |

2 | U: PED; no terrace for PV generation |

3 | U/R: PED; 25% of terrace allowed if no PED possible in SVS 1/2 |

**Table 5.**NPV, optimised technology portfolio, electricity export/import ratio and $C{O}_{2}$ emissions of respective scenarios.

Scenario | NPV [€Mio] | PV_flat [kW${}_{\mathit{p}}$] | PV_tilt roof [kW${}_{\mathit{p}}$] | Battery [kWh] | Export/ Import | $C{O}_{2}$ Emissions [t] |
---|---|---|---|---|---|---|

S 1 | −0.483 | 0 | 0 | 0 | - | 1971 |

S 2 & S 4 | −0.332 | 1265 | 86 | 0 | 12.60 | 978 |

S 3 & S 5 | −0.346 | 430 | 17 | 0 | 3.29 | 1047 |

SVS 1 | −0.342 | 477 | 86 | 0 | 4.47 | 1025 |

SVS 2 | - | - | - | - | - | - |

SVS 3—urban | −0.357 | 185 | 25 | 0 | 1.04 | 1134 |

**Table 6.**NPV, optimised technology portfolio, electricity export/import ratio and $C{O}_{2}$ emissions of respective PES.

Scenario | NPV [€Mio] | PV_flat [kW${}_{\mathit{p}}$] | PV_tilt roof [kW${}_{\mathit{p}}$] | Battery [kWh] | Export/ Import | $C{O}_{2}$ Emissions [t] |
---|---|---|---|---|---|---|

PES lim 2—R | −0.385 | 38 | 185 | 0 | 0.942 | 1110 |

PES lim 1.5—R | −0.445 | 34 | 192 | 148 | 0.937 | 944 |

PES lim 1—R | −0.631 | 29 | 200 | 424 | 0.928 | 867 |

PES lim 2—U | −0.514 | 175 | 29 | 301 | 0.932 | 1014 |

PES lim 1.5—U | −0.698 | 175 | 29 | 551 | 0.930 | 976 |

PES lim 1—U | −0.907 | 176 | 29 | 842 | 0.926 | 894 |

**Table 7.**NPV and optimised technology portfolio of S1&3 as well as all PE scenarios within a high RES penetrated grid mix.

Scenario | NPV [€Mio] | PV_flat [kW${}_{\mathit{p}}$] | PV_tilt roof [kW${}_{\mathit{p}}$] | Battery [kWh] | Export/ Import | $C{O}_{2}$ Emissions [t] |
---|---|---|---|---|---|---|

SVS1—R | −0.342 | 477 | 86 | 0 | 4.467 | 476 |

PES lim 2—R | −0.370 | 74 | 108 | 0 | 0.727 | 536 |

PES lim 1.5—R | −0.393 | 19 | 172 | 15 | 0.714 | 567 |

PES lim 1—R | −0.493 | 8 | 180 | 178 | 0.671 | 529 |

SVS3—U | −0.357 | 185 | 25 | 0 | 1.036 | 530 |

PES lim 2—U | −0.392 | 159 | 11 | 61 | 0.696 | 563 |

PES lim 1.5—U | −0.495 | 132 | 29 | 183 | 0.646 | 586 |

PES lim 1—U | −0.667 | 130 | 29 | 407 | 0.626 | 592 |

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**MDPI and ACS Style**

Bruck, A.; Díaz Ruano, S.; Auer, H. A Critical Perspective on Positive Energy Districts in Climatically Favoured Regions: An Open-Source Modelling Approach Disclosing Implications and Possibilities. *Energies* **2021**, *14*, 4864.
https://doi.org/10.3390/en14164864

**AMA Style**

Bruck A, Díaz Ruano S, Auer H. A Critical Perspective on Positive Energy Districts in Climatically Favoured Regions: An Open-Source Modelling Approach Disclosing Implications and Possibilities. *Energies*. 2021; 14(16):4864.
https://doi.org/10.3390/en14164864

**Chicago/Turabian Style**

Bruck, Axel, Santiago Díaz Ruano, and Hans Auer. 2021. "A Critical Perspective on Positive Energy Districts in Climatically Favoured Regions: An Open-Source Modelling Approach Disclosing Implications and Possibilities" *Energies* 14, no. 16: 4864.
https://doi.org/10.3390/en14164864