# e4clim 1.0: The Energy for a Climate Integrated Model: Description and Application to Italy

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## Abstract

**:**

## 1. Introduction

**Specifications.**

- 1.
- Design and analyse mixes with high shares of VREs,
- 2.
- Evaluate the benefits of spatial and technological diversification,
- 3.
- Assess different optimization strategies taking the variability of both the generation and the demand into account,
- 4.
- Choose between optimal mixes representing different trade-offs,
- 5.
- Assess the impact of climate variability on energy mixes on a broad range of time scales (from hours to decades),
- 6.
- Take the impact of climate change into account,
- 7.
- Integrate new technologies for which little data is available,
- 8.
- Track uncertainties and evaluate the robustness of results to input data and modeling approaches using observations, statistical models and multiple input data sources,
- 9.
- Use a fully open-source tool available to the research, engineering and education communities, helping access and manage open-data, relying on free third-party libraries, and covering the whole chain of operations, from downloading input data to representing results,
- 10.
- Perform sensitivity analyses which are computationally tractable,
- 11.
- Easily configure and extend the model to new applications and research questions.

## 2. Methodology and Software Design

- Computing georeferenced energy time series from historic or climate data,
- Distributing capacities spatially and technologically,
- Post-processing and analyzing the resulting mixes.

## 3. A Concrete Implementation for Mean-Variance Analyses

#### 3.1. Mix Analysis

#### 3.2. Mix Optimization

#### 3.3. Energy Models

- the “wind” production is “predicted” from wind data fed to a power curve at each grid point of the climate data (Appendix A.3.1), summed over each zone, and bias corrected against wind production observations (Appendix A.3.3),
- the “PV” production is computed from surface irradiance and temperature data fed to an electric model (Appendix A.3.2), summed over each zone, and bias corrected against PV production observations (Appendix A.3.3),
- the “demand” is estimated via a linear Bayesian regression model taking as input warming and cooling degree days averaged over each zone and fitted to demand observations (Appendix A.3.4).

#### 3.4. Energy, Climate and Geographic Data

## 4. Application: Italian PV-Wind Optimal Recommissioning

#### 4.1. General Results

#### 4.2. Comparison with the 2015 Italian Mix

#### 4.3. Choice of the Climate Data and Climate Variability

#### 4.3.1. Dependence on the Climate Data

#### 4.3.2. Interannual to Decadal Variability

#### 4.3.3. Intraday Variability

## 5. Conclusions

## 6. Known Limitations of the Software and Methodology

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Data and Model Description

#### Appendix A.1. Energy Data: GME and Terna Databases

**Table A1.**Yearly electrical demand (from GME) and yearly mean PV and wind capacity factors (from Terna) averaged over 2010–2018.

Zone | Electrical Demand | Capacity Factor (%) | ||
---|---|---|---|---|

(TWh/y) | (%) | PV | Wind | |

NORD | 121 | 58 | 11.7 | 20.0 |

CNOR | 19.4 | 9.2 | 13.4 | 19.5 |

CSUD | 30.3 | 14 | 13.9 | 18.9 |

SUD | 15.0 | 7.1 | 15.0 | 21.0 |

SARD | 10.8 | 5.1 | 14.4 | 18.5 |

SICI | 13.5 | 6.4 | 15.2 | 18.6 |

#### Appendix A.2. Climate Data

#### Appendix A.2.1. CORDEX Regional Simulations

**Figure A1.**Domain of the HyMeX/MED-CORDEX simulation covering Europe and the Mediterranean region. The rectangle indicates the domain of investigation of this study.

#### Appendix A.2.2. MERRA-2 Reanalysis

#### Appendix A.3. Model Description

#### Appendix A.3.1. Wind Model

**Figure A2.**Hourly (orange) and daily mean (blue) wind capacity factor (

**a**,

**b**), PV capacity factor (

**c**,

**d**) and electricity demand (

**e**,

**f**) for the NORD zone, the first week of January (left) and of July (right) 2010. The data is predicted from the daily mean CORDEX data with the models and intra-day parametrizations described in Appendix A.3.

#### Appendix A.3.2. PV Model

^{−1}, a reference temperature of 25 ${}^{\circ}\mathrm{C}$ and a cell temperature at nominal operatning cell temperature of 46 ${}^{\circ}\mathrm{C}$ [113]. The efficiency of the overall electrical installation behind the modules is assumed to be of $86\%$. Note, however, that constant multiplicative factors such as the electrical efficiency do not play a role in this study, due to the bias correction of the capacity factors presented in Appendix A.3.3.

#### Appendix A.3.3. Aggregation and Bias Correction

**Figure A3.**Time evolution of weekly averaged PV (orange) and wind (blue) capacity factors (

**a**) and demand (

**b**). The shadings represent the standard deviation of the time series.

#### Appendix A.3.4. Electricity-Demand Model

- applications: assessments, forecasting [116],

**Figure A4.**Daily mean electricity demand versus the surface temperature for each zone. Each point is an observed realization of temperature and demand. The lines represent the functions ${f}_{i}^{\mathrm{work}\left|\mathrm{sat}\right|\mathrm{off}}$ of the demand model, while the associated shaded regions represent the variance of the prediction. Blue, orange and green data points and functions correspond to working days, Saturdays, and Sundays and holidays, respectively. The two vertical dashed lines represent the temperature thresholds ${T}_{H}=9.5$ and ${T}_{C}=13.0$.

## Appendix B. Mean-Variance Analysis

#### Appendix B.1. Mean-Variance Optimization Problem

#### Appendix B.2. Method to Find an Approximation of the Optimal Frontier

#### Appendix B.2.1. The Biobjective Algorithm

#### Appendix B.2.2. How to Find the Bound on the RHS of (A9) and (A13)

#### Appendix B.2.3. Algorithm to Solve the Single-Objective Problems

## References

- International Energy Agency (IEA). World Energy Outlook 2018; Technical Report; IEA: Paris, France, 2018. [Google Scholar]
- Labussière, O.; Nadaï, A. (Eds.) Energy Transitions: A Socio-Technical Inquiry; Palgrave Macmillan: London, UK, 2018. [Google Scholar] [CrossRef]
- Ueckerdt, F.; Brecha, R.; Luderer, G. Analyzing Major Challenges of Wind and Solar Variability in Power Systems. Renew. Energy
**2015**, 81, 1–10. [Google Scholar] [CrossRef] - Hirth, L.; Ueckerdt, F.; Edenhofer, O. Integration Costs Revisited—An Economic Framework for Wind and Solar Variability. Renew. Energy
**2015**, 74, 925–939. [Google Scholar] [CrossRef] - Giebel, G. Wind Power Has a Capacity Credit. A Catalogue of 50+ Supporting Studies. e-WINDENG J.
**2005**, 1, 13. [Google Scholar] - Stoft, S. Power System Economics: Designing Markets for Electricity; Wiley-IEEE Press: Hoboken, NJ, USA, 2002. [Google Scholar]
- Apt, J. The Spectrum of Power from Wind Turbines. J. Power Sources
**2007**, 169, 369–374. [Google Scholar] [CrossRef] - Frunt, J.; Kling, W.L.; van den Bosch, P.P.J. Classification and Quantification of Reserve Requirements for Balancing. Electr. Power Syst. Res.
**2010**, 80, 1528–1534. [Google Scholar] [CrossRef] - Huber, M.; Dimkova, D.; Hamacher, T. Integration of Wind and Solar Power in Europe: Assessment of Flexibility Requirements. Energy
**2014**, 69, 236–246. [Google Scholar] [CrossRef] - Van Stiphout, A.; Vos, K.D.; Deconinck, G. The Impact of Operating Reserves on Investment Planning of Renewable Power Systems. IEEE Trans. Power Syst.
**2017**, 32, 378–388. [Google Scholar] [CrossRef] - Spiecker, S.; Weber, C. The Future of the European Electricity System and the Impact of Fluctuating Renewable Energy—A Scenario Analysis. Energy Policy
**2014**, 65, 185–197. [Google Scholar] [CrossRef] - Heard, B.P.; Brook, B.W.; Wigley, T.M.L.; Bradshaw, C.J.A. Burden of Proof: A Comprehensive Review of the Feasibility of 100% Renewable-Electricity Systems. Renew. Sustain. Energy Rev.
**2017**, 76, 1122–1133. [Google Scholar] [CrossRef] - Hansen, K.; Breyer, C.; Lund, H. Status and Perspectives on 100% Renewable Energy Systems. Energy
**2019**, 175, 471–480. [Google Scholar] [CrossRef] - Widén, J.; Carpman, N.; Castellucci, V.; Lingfors, D.; Olauson, J.; Remouit, F.; Bergkvist, M.; Grabbe, M.; Waters, R. Variability Assessment and Forecasting of Renewables: A Review for Solar, Wind, Wave and Tidal Resources. Renew. Sustain. Energy Rev.
**2015**, 44, 356–375. [Google Scholar] [CrossRef] - Graabak, I.; Korpås, M. Variability Characteristics of European Wind and Solar Power Resources—A Review. Energies
**2016**, 9, 449. [Google Scholar] [CrossRef] - James, I.N. Introduction to Circulating Atmospheres; Cambridge University Press: Cambridge, UK, 1994. [Google Scholar]
- Holton, J.R. An Introduction to Dynamic Meteorology, 4th ed.; Elsevier: Amsterdam, The Netherlands, 2004. [Google Scholar]
- Duffie, J.; Beckman, W. Solar Engineering of Thermal Processes, 4th ed.; John Wiley & Sons: Hoboken, NJ, USA, 2013. [Google Scholar]
- Holttinen, H. Hourly Wind Power Variations in the Nordic Countries. Wind Energy
**2005**, 8, 173–195. [Google Scholar] [CrossRef] - Katzenstein, W.; Fertig, E.; Apt, J. The Variability of Interconnected Wind Plants. Energy Policy
**2010**, 38, 4400–4410. [Google Scholar] [CrossRef] - Tarroja, B.; Mueller, F.; Eichman, J.D.; Brouwer, J.; Samuelsen, S. Spatial and Temporal Analysis of Electric Wind Generation Intermittency and Dynamics. Renew. Energy
**2011**, 36, 3424–3432. [Google Scholar] [CrossRef] - Giebel, G. A Variance Analysis of the Capacity Displaced by Wind Energy in Europe. Wind Energy
**2007**, 10, 69–79. [Google Scholar] [CrossRef] - Kempton, W.; Pimenta, F.M.; Veron, D.E.; Colle, B.A. Electric Power from Offshore Wind via Synoptic-Scale Interconnection. Proc. Natl. Acad. Sci. USA
**2010**, 107, 7240–7245. [Google Scholar] [CrossRef] [PubMed] - Gueymard, C.A.; Wilcox, S.M. Assessment of Spatial and Temporal Variability in the US Solar Resource from Radiometric Measurements and Predictions from Models Using Ground-Based or Satellite Data. Sol. Energy
**2011**, 85, 1068–1084. [Google Scholar] [CrossRef] - Marcos, J.; Marroyo, L.; Lorenzo, E.; García, M. Smoothing of PV Power Fluctuations by Geographical Dispersion. Prog. Photovolt. Res. Appl.
**2012**, 20, 226–237. [Google Scholar] [CrossRef] - Buttler, A.; Dinkel, F.; Franz, S.; Spliethoff, H. Variability of Wind and Solar Power—An Assessment of the Current Situation in the European Union Based on the Year 2014. Energy
**2016**, 106, 147–161. [Google Scholar] [CrossRef] - Heide, D.; von Bremen, L.; Greiner, M.; Hoffmann, C.; Speckmann, M.; Bofinger, S. Seasonal Optimal Mix of Wind and Solar Power in a Future, Highly Renewable Europe. Renew. Energy
**2010**, 35, 2483–2489. [Google Scholar] [CrossRef] - Holttinen, H. Impact of Hourly Wind Power Variations on the System Operation in the Nordic Countries. Wind Energy
**2005**, 8, 197–218. [Google Scholar] [CrossRef] - Sinden, G. Characteristics of the UK Wind Resource: Long-Term Patterns and Relationship to Electricity Demand. Energy Policy
**2007**, 35, 112–127. [Google Scholar] [CrossRef] - Bett, P.E.; Thornton, H.E. The Climatological Relationships between Wind and Solar Energy Supply in Britain. Renew. Energy
**2016**, 87, 96–110. [Google Scholar] [CrossRef] - Coker, P.; Barlow, J.; Cockerill, T.; Shipworth, D. Measuring Significant Variability Characteristics: An Assessment of Three UK Renewables. Renew. Energy
**2013**, 53, 111–120. [Google Scholar] [CrossRef] - Widén, J. Correlations between Large-Scale Solar and Wind Power in a Future Scenario for Sweden. IEEE Trans. Sustain. Energy
**2011**, 2, 177–184. [Google Scholar] [CrossRef] - Miglietta, M.M.; Huld, T.; Monforti-Ferrario, F. Local Complementarity of Wind and Solar Energy Resources over Europe: An Assessment Study from a Meteorological Perspective. J. Appl. Meteorol. Climatol.
**2016**, 56, 217–234. [Google Scholar] [CrossRef] - Santos-Alamillos, F.J.; Pozo-Vázquez, D.; Ruiz-Arias, J.A.; Lara-Fanego, V.; Tovar-Pescador, J. Analysis of Spatiotemporal Balancing between Wind and Solar Energy Resources in the Southern Iberian Peninsula. J. Appl. Meteorol. Climatol.
**2012**, 51, 2005–2024. [Google Scholar] [CrossRef] - Hirth, L. The Market Value of Variable Renewables. The Effect of Solar Wind Power Variability on Their Relative Price. Energy Econ.
**2013**, 38, 218–236. [Google Scholar] [CrossRef] - Hirth, L. The Optimal Share of Variable Renewables: How the Variability of Wind and Solar Power Affects Their Welfare-Optimal Deployment. Energy J.
**2015**, 36, 149–184. [Google Scholar] [CrossRef] - Shirizadeh, B.; Perrier, Q.; Quirion, P. How Sensitive Are Optimal Fully Renewable Power Systems to Technology Cost Uncertainty? FAERE Policy Paper; CIRED: Paris, France, 2019. [Google Scholar]
- Heide, D.; Greiner, M.; von Bremen, L.; Hoffmann, C. Reduced Storage and Balancing Needs in a Fully Renewable European Power System with Excess Wind and Solar Power Generation. Renew. Energy
**2011**, 36, 2515–2523. [Google Scholar] [CrossRef][Green Version] - Rodríguez, R.A.; Becker, S.; Andresen, G.B.; Heide, D.; Greiner, M. Transmission Needs across a Fully Renewable European Power System. Renew. Energy
**2014**, 63, 467–476. [Google Scholar] [CrossRef][Green Version] - Becker, S.; Rodriguez, R.A.; Andresen, G.B.; Schramm, S.; Greiner, M. Transmission Grid Extensions during the Build-up of a Fully Renewable Pan-European Electricity Supply. Energy
**2014**, 64, 404–418. [Google Scholar] [CrossRef][Green Version] - Becker, S.; Frew, B.A.; Andresen, G.B.; Zeyer, T.; Schramm, S.; Greiner, M.; Jacobson, M.Z. Features of a Fully Renewable US Electricity System: Optimized Mixes of Wind and Solar PV and Transmission Grid Extensions. Energy
**2014**, 72, 443–458. [Google Scholar] [CrossRef][Green Version] - Nelson, J.; Johnston, J.; Mileva, A.; Fripp, M.; Hoffman, I.; Petros-Good, A.; Blanco, C.; Kammen, D.M. High-Resolution Modeling of the Western North American Power System Demonstrates Low-Cost and Low-Carbon Futures. Energy Policy
**2012**, 43, 436–447. [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] - François, B.; Borga, M.; Creutin, J.D.; Hingray, B.; Raynaud, D.; Sauterleute, J.F. Complementarity between Solar and Hydro Power: Sensitivity Study to Climate Characteristics in Northern-Italy. Renew. Energy
**2016**, 86, 543–553. [Google Scholar] [CrossRef] - Raynaud, D.; Hingray, B.; François, B.; Creutin, J.D. Energy Droughts from Variable Renewable Energy Sources in European Climates. Renew. Energy
**2018**, 125, 578–589. [Google Scholar] [CrossRef] - Perera, A.T.D.; Nik, V.M.; Wickramasinghe, P.U.; Scartezzini, J.L. Redefining Energy System Flexibility for Distributed Energy System Design. Appl. Energy
**2019**, 253, 113572. [Google Scholar] [CrossRef] - Siraganyan, K.; Perera, A.T.D.; Scartezzini, J.L.; Mauree, D. Eco-Sim: A Parametric Tool to Evaluate the Environmental and Economic Feasibility of Decentralized Energy Systems. Energies
**2019**, 12, 776. [Google Scholar] [CrossRef][Green Version] - Del Río, P.; Calvo Silvosa, A.; Iglesias Gómez, G. Policies and Design Elements for the Repowering of Wind Farms: A Qualitative Analysis of Different Options. Energy Policy
**2011**, 39, 1897–1908. [Google Scholar] [CrossRef] - Markowitz, H. Portfolio Selection. J. Financ.
**1952**, 7, 77–91. [Google Scholar] - Brazilian, M.; Roques, F. Analytical Methods for Energy Diversity and Security: Portfolio Optimization in the Energy Sector: A Tribute to the Work of Dr. Shimon Awerbuch; Elsevier: Amsterdam, The Netherlands, 2008. [Google Scholar]
- Beltran, H. Modern Portfolio Theory Applied To Electricity Generation Planning. Ph.D. Thesis, University of Illinois at Urbana-Champaign, Champaign County, IL, USA, 2009. [Google Scholar]
- Roques, F.; Hiroux, C.; Saguan, M. Optimal Wind Power Deployment in Europe-A Portfolio Approach. Energy Policy
**2010**, 38, 3245–3256. [Google Scholar] [CrossRef][Green Version] - Thomaidis, N.S.; Santos-Alamillos, F.J.; Pozo-Vázquez, D.; Usaola-García, J. Optimal Management of Wind and Solar Energy Resources. Comput. Oper. Res.
**2016**, 66, 284–291. [Google Scholar] [CrossRef][Green Version] - Santos-Alamillos, F.J.; Thomaidis, N.S.; Usaola-García, J.; Ruiz-Arias, J.A.; Pozo-Vázquez, D. Exploring the Mean-Variance Portfolio Optimization Approach for Planning Wind Repowering Actions in Spain. Renew. Energy
**2017**, 106, 335–342. [Google Scholar] [CrossRef] - Pryor, S.C.; Barthelmie, R.J.; Schoof, J.T. Inter-Annual Variability of Wind Indices across Europe. Wind Energy
**2006**, 9, 27–38. [Google Scholar] [CrossRef] - Papadimas, C.D.; Fotiadi, A.K.; Hatzianastassiou, N.; Vardavas, I.; Bartzokas, A. Regional Co-Variability and Teleconnection Patterns in Surface Solar Radiation on a Planetary Scale. Int. J. Climatol.
**2010**, 30, 2314–2329. [Google Scholar] [CrossRef] - Andresen, G.B.; Søndergaard, A.A.; Greiner, M. Validation of Danish Wind Time Series from a New Global Renewable Energy Atlas for Energy System Analysis. Energy
**2015**, 93, 1074–1088. [Google Scholar] [CrossRef][Green Version] - Zeyringer, M.; Price, J.; Fais, B.; Li, P.H.; Sharp, E. Designing Low-Carbon Power Systems for Great Britain in 2050 That Are Robust to the Spatiotemporal and Inter-Annual Variability of Weather. Nat. Energy
**2018**, 3, 395–403. [Google Scholar] [CrossRef] - Pozo-Vazquez, D.; Santos-Alamillos, F.J.; Lara-Fanego, V.; Ruiz-Arias, J.A.; Tovar-Pescador, J. The Impact of the NAO on the Solar and Wind Energy Resources in the Mediterranean Area. In Hydrological, Socioeconomic and Ecological Impacts of the North Atlantic Oscillation in the Mediterranean Region; Vicente-Serrano, S.M., Trigo, R.M., Eds.; Advances in Global Change Research; Springer: Dordrecht, The Netherlands, 2011; pp. 213–231. [Google Scholar] [CrossRef]
- Hurrell, J.W.; Kushnir, Y.; Ottersen, G.; Visbeck, M. The North Atlantic Oscillation Climatic Significance and Environmental Impact; American Geophysical Union: Washington, DC, USA, 2003. [Google Scholar]
- Thornton, H.E.; Scaife, A.A.; Hoskins, B.J.; Brayshaw, D.J. The Relationship between Wind Power, Electricity Demand and Winter Weather Patterns in Great Britain. Environ. Res. Lett.
**2017**, 12, 064017. [Google Scholar] [CrossRef] - Collins, S.; Deane, P.; Gallachóir, B.Ó.; Pfenninger, S.; Staffell, I. Impacts of Inter-Annual Wind and Solar Variations on the European Power System. Joule
**2018**, 2, 2076–2090. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bett, P.E.; Thornton, H.E.; Clark, R.T. European Wind Variability over 140 Yr. Adv. Sci. Res.
**2013**, 10, 51–58. [Google Scholar] [CrossRef][Green Version] - Vautard, R.; Cattiaux, J.; Yiou, P.; Thépaut, J.N.; Ciais, P. Northern Hemisphere Atmospheric Stilling Partly Attributed to an Increase in Surface Roughness. Nat. Geosci.
**2010**, 3, 756–761. [Google Scholar] [CrossRef] - Bakker, A.M.R.; den Hurk, B.J.J.M.V.; Coelingh, J.P. Decomposition of the Windiness Index in the Netherlands for the Assessment of Future Long-Term Wind Supply. Wind Energy
**2013**, 16, 927–938. [Google Scholar] [CrossRef] - Tobin, I.; Vautard, R.; Balog, I.; Bréon, F.M.; Jerez, S.; Ruti, P.M.; Thais, F.; Vrac, M.; Yiou, P. Assessing Climate Change Impacts on European Wind Energy from ENSEMBLES High-Resolution Climate Projections. Clim. Chang.
**2015**, 128, 99–112. [Google Scholar] [CrossRef] - Barstad, I.; Sorteberg, A.; dos Santos Mesquita, M. Present and Future Offshore Wind Power Potential in Northern Europe Based on Downscaled Global Climate Runs with Adjusted SST and Sea Ice Cover. Renew. Energy
**2012**, 44, 398–405. [Google Scholar] [CrossRef] - Jerez, S.; Tobin, I.; Vautard, R.; Montávez, J.P.; López-Romero, J.M.; Thais, F.; Bartok, B.; Christensen, O.B.; Colette, A.; Déqué, M.; et al. The Impact of Climate Change on Photovoltaic Power Generation in Europe. Nat. Commun.
**2015**, 6, 1–8. [Google Scholar] [CrossRef] [PubMed][Green Version] - Isaac, M.; van Vuuren, D.P. Modeling Global Residential Sector Energy Demand for Heating and Air Conditioning in the Context of Climate Change. Energy Policy
**2009**, 37, 507–521. [Google Scholar] [CrossRef] - Eskeland, G.S.; Mideksa, T.K. Electricity Demand in a Changing Climate. Mitig. Adapt. Strategies Glob. Chang.
**2010**, 15, 877–897. [Google Scholar] [CrossRef] - Jourdier, B. Wind Resource in Metropolitan France: Assessment Methods, Variability and Trends. Ph.D. Thesis, Ecole Polytechnique, Palaiseau, France, 2015. [Google Scholar]
- Bremen, L.V. Large-Scale Variability of Weather Dependent Renewable Energy Sources. In Management of Weather and Climate Risk in the Energy Industry; Troccoli, A., Ed.; NATO Science for Peace and Security Series C: Environmental Security; Springer: Dordrecht, The Netherlands, 2010; pp. 189–206. [Google Scholar]
- Staffell, I.; Pfenninger, S. Using Bias-Corrected Reanalysis to Simulate Current and Future Wind Power Output. Energy
**2016**, 114, 1224–1239. [Google Scholar] [CrossRef][Green Version] - Pfenninger, S.; Staffell, I. Long-Term Patterns of European PV Output Using 30 Years of Validated Hourly Reanalysis and Satellite Data. Energy
**2016**, 114, 1251–1265. [Google Scholar] [CrossRef][Green Version] - Moraes, L.; Bussar, C.; Stoecker, P.; Jacqué, K.; Chang, M.; Sauer, D.U. Comparison of Long-Term Wind and Photovoltaic Power Capacity Factor Datasets with Open-License. Appl. Energy
**2018**, 225, 209–220. [Google Scholar] [CrossRef] - Schlachtberger, D.P.; Brown, T.; Schäfer, M.; Schramm, S.; Greiner, M. Cost Optimal Scenarios of a Future Highly Renewable European Electricity System: Exploring the Influence of Weather Data, Cost Parameters and Policy Constraints. Energy
**2018**, 163, 100–114. [Google Scholar] [CrossRef][Green Version] - Weijermars, R.; Taylor, P.; Bahn, O.; Das, S.R.; Wei, Y.M. Review of Models and Actors in Energy Mix Optimization—Can Leader Visions and Decisions Align with Optimum Model Strategies for Our Future Energy Systems? Energy Strategy Rev.
**2012**, 1, 5–18. [Google Scholar] [CrossRef][Green Version] - Ringkjøb, H.K.; Haugan, P.M.; Solbrekke, I.M. A Review of Modelling Tools for Energy and Electricity Systems with Large Shares of Variable Renewables. Renew. Sustain. Energy Rev.
**2018**, 96, 440–459. [Google Scholar] [CrossRef] - Pfenninger, S.; DeCarolis, J.; Hirth, L.; Quoilin, S.; Staffell, I. The Importance of Open Data and Software: Is Energy Research Lagging Behind? Energy Policy
**2017**, 101, 211–215. [Google Scholar] [CrossRef] - Feser, F.; Rockel, B.; von Storch, H.; Winterfeldt, J.; Zahn, M. Regional Climate Models Add Value to Global Model Data: A Review and Selected Examples. Bull. Am. Meteorol. Soc.
**2011**, 92, 1181–1192. [Google Scholar] [CrossRef][Green Version] - Monforti, F.; Huld, T.; Bódis, K.; Vitali, L.; D’Isidoro, M.; Lacal-Arántegui, R. Assessing Complementarity of Wind and Solar Resources for Energy Production in Italy. A Monte Carlo Approach. Renew. Energy
**2014**, 63, 576–586. [Google Scholar] [CrossRef] - Von Storch, H.; Zwiers, F.W. Statistical Analysis in Climate Research; Cambridge University Press: Cambridge, UK, 1999. [Google Scholar]
- Miettinen, K.M. Nonlinear Multiobjective Optimization; Springer: New York, NY, USA, 1999. [Google Scholar]
- Hartmann, D.L. Global Physical Climatology; Academic Press: San Diego, CA, USA, 1994. [Google Scholar] [CrossRef]
- Boccard, N. Capacity Factor of Wind Power Realized Values vs. Estimates. Energy Policy
**2009**, 37, 2679–2688. [Google Scholar] [CrossRef] - GSE. Rapporto Statistico 2015: Energia Da Fonti Rinnovabili in Italia; Technical Report; GSE: Roma, Italy, 2015. [Google Scholar]
- Ruti, P.M.; Somot, S.; Giorgi, F.; Dubois, C.; Flaounas, E.; Obermann, A.; Dell’Aquila, A.; Pisacane, G.; Harzallah, A.; Lombardi, E.; et al. Med-CORDEX Initiative for Mediterranean Climate Studies. Bull. Am. Meteorol. Soc.
**2016**, 97, 1187–1208. [Google Scholar] [CrossRef][Green Version] - Long, C.S.; Fujiwara, M.; Davis, S.; Mitchell, D.M.; Wright, C.J. Climatology and Interannual Variability of Dynamic Variables in Multiple Reanalyses Evaluated by the SPARC Reanalysis Intercomparison Project (S-RIP). Atmos. Chem. Phys.
**2017**, 17, 14593–14629. [Google Scholar] [CrossRef][Green Version] - Skamarock, W.C.; Klemp, J.B.; Dudhia, J.; Gill, D.O.; Barker, D.M.; Wang, W.; Powers, J.G. A Description of the Advanced Research WRF Version 2; Technical Report NCAR/TN-468+STR; NCAR: Boulder, CO, USA, 2005. [Google Scholar]
- Drobinski, P.; Ducrocq, V.; Alpert, P.; Anagnostou, E.; Béranger, K.; Borga, M.; Braud, I.; Chanzy, A.; Davolio, S.; Delrieu, G.; et al. HyMeX A 10-Year Multidisciplinary Program on the Mediterranean Water Cycle. Bull. Am. Meteorol. Soc.
**2014**, 95, 1063–1082. [Google Scholar] [CrossRef] - Dee, D.; Uppala, S.M.; Simmons, A.J.; Berrisford, P.; Poli, P.; Kobayashi, S.; Andrae, U.; Balmaseda, M.; Balsamo, G.; Bauer, P.; et al. The ERA-Interim Reanalysis: Configuration and Performance of the Data Assimilation System. Q. J. R. Meteorol. Soc.
**2011**, 137, 553–597. [Google Scholar] [CrossRef] - Salameh, T.; Drobinski, P.; Dubos, T. The Effect of Indiscriminate Nudging Time on Large and Small Scales in Regional Climate Modelling: Application to the Mediterranean Basin. Q. J. R. Meteorol. Soc.
**2010**, 136, 170–182. [Google Scholar] [CrossRef] - Omrani, H.; Drobinski, P.; Dubos, T. Optimal Nudging Strategies in Regional Climate Modelling: Investigation in a Big-Brother Experiment over the European and Mediterranean Regions. Clim. Dyn.
**2013**, 41, 2451–2470. [Google Scholar] [CrossRef] - Omrani, H.; Drobinski, P.; Dubos, T. Using Nudging to Improve Global-Regional Dynamic Consistency in Limited-Area Climate Modeling: What Should We Nudge? Clim. Dyn.
**2015**, 44, 1627–1644. [Google Scholar] [CrossRef] - Flaounas, E.; Drobinski, P.; Vrac, M.; Bastin, S.; Lebeaupin-Brossier, C.; Stéfanon, M.; Borga, M.; Calvet, J.C. Precipitation and Temperature Space–Time Variability and Extremes in the Mediterranean Region: Evaluation of Dynamical and Statistical Downscaling Methods. Clim. Dyn.
**2013**, 40, 2687–2705. [Google Scholar] [CrossRef] - Stéfanon, M.; Drobinski, P.; D’Andrea, F.; Lebeaupin-Brossier, C.; Bastin, S. Soil Moisture-Temperature Feedbacks at Meso-Scale during Summer Heat Waves over Western Europe. Clim. Dyn.
**2014**, 42, 1309–1324. [Google Scholar] [CrossRef] - Chiriaco, M.; Bastin, S.; Yiou, P.; Haeffelin, M.; Dupont, J.C.; Stéfanon, M. European Heatwave in July 2006: Observations and Modeling Showing How Local Processes Amplify Conducive Large-Scale Conditions. Geophys. Res. Lett.
**2014**, 41, 5644–5652. [Google Scholar] [CrossRef][Green Version] - Lebeaupin Brossier, C.L.; Drobinski, P.; Béranger, K.; Bastin, S.; Orain, F. Ocean Memory Effect on the Dynamics of Coastal Heavy Precipitation Preceded by a Mistral Event in the Northwestern Mediterranean. Q. J. R. Meteorol. Soc.
**2013**, 139, 1583–1597. [Google Scholar] [CrossRef] - Lebeaupin Brossier, C.L.; Bastin, S.; Béranger, K.; Drobinski, P. Regional Mesoscale Air–Sea Coupling Impacts and Extreme Meteorological Events Role on the Mediterranean Sea Water Budget. Clim. Dyn.
**2015**, 44, 1029–1051. [Google Scholar] [CrossRef] - Berthou, S.; Mailler, S.; Drobinski, P.; Arsouze, T.; Bastin, S.; Béranger, K.; Lebeaupin-Brossier, C. Prior History of Mistral and Tramontane Winds Modulates Heavy Precipitation Events in Southern France. Tellus A Dyn. Meteorol. Oceanogr.
**2014**, 66, 24064. [Google Scholar] [CrossRef][Green Version] - Berthou, S.; Mailler, S.; Drobinski, P.; Arsouze, T.; Bastin, S.; Béranger, K.; Lebeaupin-Brossier, C. Sensitivity of an Intense Rain Event between Atmosphere-Only and Atmosphere–Ocean Regional Coupled Models: 19 September 1996. Q. J. R. Meteorol. Soc.
**2015**, 141, 258–271. [Google Scholar] [CrossRef] - Berthou, S.; Mailler, S.; Drobinski, P.; Arsouze, T.; Bastin, S.; Béranger, K.; Flaounas, E.; Brossier, C.L.; Somot, S.; Stéfanon, M. Influence of Submonthly Air–Sea Coupling on Heavy Precipitation Events in the Western Mediterranean Basin. Q. J. R. Meteorol. Soc.
**2016**, 142, 453–471. [Google Scholar] [CrossRef][Green Version] - Omrani, H.; Drobinski, P.; Arsouze, T.; Bastin, S.; Lebeaupin-Brossier, C.; Mailler, S. Spatial and Temporal Variability of Wind Energy Resource and Production over the North Western Mediterranean Sea: Sensitivity to Air-Sea Interactions. Renew. Energy
**2017**, 101, 680–689. [Google Scholar] [CrossRef] - Drobinski, P.; Anav, A.; Lebeaupin Brossier, C.; Samson, G.; Stéfanon, M.; Bastin, S.; Baklouti, M.; Béranger, K.; Beuvier, J.; Bourdallé-Badie, R.; et al. Model of the Regional Coupled Earth System (MORCE): Application to Process and Climate Studies in Vulnerable Regions. Environ. Model. Softw.
**2012**, 35, 1–18. [Google Scholar] [CrossRef] - Gelaro, R.; McCarty, W.; Suárez, M.J.; Todling, R.; Molod, A.; Takacs, L.; Randles, C.A.; Darmenov, A.; Bosilovich, M.G.; Reichle, R.; et al. The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). J. Clim.
**2017**, 30, 5419–5454. [Google Scholar] [CrossRef] - Fujiwara, M.; Wright, J.S.; Manney, G.L.; Gray, L.J.; Anstey, J.; Birner, T.; Davis, S.; Gerber, E.P.; Harvey, V.L.; Hegglin, M.I.; et al. Introduction to the SPARC Reanalysis Intercomparison Project (S-RIP) and Overview of the Reanalysis Systems. Atmos. Chem. Phys.
**2017**, 17, 1417–1452. [Google Scholar] [CrossRef][Green Version] - Jurado, M.; Caridad, J.M.; Ruiz, V. Statistical Distribution of the Clearness Index with Radiation Data Integrated over Five Minute Intervals. Sol. Energy
**1995**, 55, 469–473. [Google Scholar] [CrossRef] - Tovar, J.; Olmo, F.J.; Alados-Arboledas, L. One-Minute Global Irradiance Probability Density Distributions Conditioned to the Optical Air Mass. Sol. Energy
**1998**, 62, 387–393. [Google Scholar] [CrossRef] - Holttinen, H.; Meibom, P.; Orths, A.; Lange, B.; O’Malley, M.; Tande, J.O.; Estanqueiro, A.; Gomez, E.; Söder, L.; Strbac, G.; et al. Impacts of Large Amounts of Wind Power on Design and Operation of Power Systems, Results of IEA Collaboration. Wind Energy
**2011**, 14, 179–192. [Google Scholar] [CrossRef] - Justus, C.G.; Mikhail, A. Height Variation of Wind Speed and Wind Distributions Statistics. Geophys. Res. Lett.
**1976**, 3, 261–264. [Google Scholar] [CrossRef] - Villanueva, D.; Feijóo, A.; Pazos, J.L. Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment. Resources
**2013**, 2, 370–384. [Google Scholar] [CrossRef][Green Version] - Hosenuzzaman, M.; Rahim, N.A.; Selvaraj, J.; Hasanuzzaman, M.; Malek, A.B.M.A.; Nahar, A. Global Prospects, Progress, Policies, and Environmental Impact of Solar Photovoltaic Power Generation. Renew. Sustain. Energy Rev.
**2015**, 41, 284–297. [Google Scholar] [CrossRef] - Skoplaki, E.; Palyvos, J.A. On the Temperature Dependence of Photovoltaic Module Electrical Performance: A Review of Efficiency/Power Correlations. Sol. Energy
**2009**, 83, 614–624. [Google Scholar] [CrossRef] - Reindl, D.T.; Beckman, W.A.; Duffie, J.A. Diffuse Fraction Correlations. Sol. Energy
**1990**, 45, 1–7. [Google Scholar] [CrossRef] - Reindl, D.T.; Beckman, W.A.; Duffie, J.A. Evaluation of Hourly Tilted Surface Radiation Models. Sol. Energy
**1990**, 45, 9–17. [Google Scholar] [CrossRef] - Weron, R. Modeling and Forecasting Electricity Loads and Prices; John Wiley & Sons: Chichester, UK, 2006. [Google Scholar]
- Bessec, M.; Fouquau, J. The Non-Linear Link between Electricity Consumption and Temperature in Europe: A Threshold Panel Approach. Energy Econ.
**2008**, 30, 2705–2721. [Google Scholar] [CrossRef][Green Version] - Damm, A.; Köberl, J.; Prettenthaler, F.; Rogler, N.; Töglhofer, C. Impacts of +2 Degree C Global Warming on Electricity Demand in Europe. Clim. Services
**2017**, 7, 12–30. [Google Scholar] [CrossRef][Green Version] - Bianco, V.; Manca, O.; Nardini, S. Electricity Consumption Forecasting in Italy Using Linear Regression Models. Energy
**2009**, 34, 1413–1421. [Google Scholar] [CrossRef] - Apadula, F.; Bassini, A.; Elli, A.; Scapin, S. Relationships between Meteorological Variables and Monthly Electricity Demand. Appl. Energy
**2012**, 98, 346–356. [Google Scholar] [CrossRef] - Bianco, V.; Manca, O.; Nardini, S. Linear Regression Models to Forecast Electricity Consumption in Italy. Energy Sources Part B Econ. Plan. Policy
**2013**, 8, 86–93. [Google Scholar] [CrossRef] - De Felice, M.; Alessandri, A.; Ruti, P.M. Electricity Demand Forecasting over Italy: Potential Benefits Using Numerical Weather Prediction Models. Electr. Power Syst. Res.
**2013**, 104, 71–79. [Google Scholar] [CrossRef] - Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning, 2nd ed.; Springer: New York, NY, USA, 2009. [Google Scholar] [CrossRef]
- Terna. Sustainability Report 2016; Technical Report; Terna: Rome, Italy, 2016. [Google Scholar]
- MacKay, D.J.C. Bayesian Interpolation. Neural Comput.
**1992**, 4, 415–447. [Google Scholar] [CrossRef] - Buitinck, L.; Louppe, G.; Blondel, M.; Pedregosa, F.; Müller, A.C.; Grisel, O.; Niculae, V.; Prettenhofer, P.; Gramfort, A.; Grobler, J.; et al. API Design for Machine Learning Software: Experiences from the Scikit-Learn Project. arXiv
**2013**, arXiv:1309.0238. [Google Scholar] - Mencarelli, L.; D’Ambrosio, C. Complex Portfolio Selection via Convex Mixed-Integer Quadratic Programming: A Survey. Int. Trans. Oper. Res.
**2018**, 26, 389–414. [Google Scholar] [CrossRef] - Nocedal, J.; Wright, S. Numerical Optimization, 2nd ed.; Springer: New York, NY, USA, 2006. [Google Scholar]
- Goldfarb, D.; Idnani, A. A Numerically Stable Dual Method for Solving Strictly Convex Quadratic Programs. Math. Programm.
**1983**, 27, 1–33. [Google Scholar] [CrossRef]

**Figure 1.**Flow chart of the concrete implementation of the mean-variance analysis for the Italian PV-wind mix.

**Figure 2.**Example of the optimal frontier of a mean-variance biobjective optimization problem. The optimal frontier is one-dimensional and represented by a plain blue line. Mixes in the white region to the right of the frontier are suboptimal. Points in the gray region to the left of the frontier are not feasible. In this example, the optimal frontier is bounded below by a minimum-variance optimal mix (blue dot) below which the variance may only increase. The optimal frontier is bounded above by a maximum-penetration optimal mix above which higher penetration mixes are not feasible due to the constraints of the problem. The point B is an example of suboptimal mix, since a higher mean penetration is achievable for the same variance (point A) and a lower variance is achievable for the same mean penetration (point D). The dashed blue line is obtained by minimizing the variance for a range of target mean penetration values. These solutions are, however, not Pareto optimal. For instance, point C yields the same variance as point A but achieves a lower mean penetration. Thus, A “dominates” C.

**Figure 3.**(

**a**) Italian bidding zones. (

**b**) PV and wind capacities installed by the end of 2015 in Italy (from Terna, see Appendix A.1). Capacities are graphically represented by the size of the disks and the corresponding legend and explicitly given in megawatts by the text boxes to the left and to the right of the disks.

**Figure 4.**(

**a**) Approximations of the optimal frontiers from the CORDEX hourly data with the global standard deviation σ

_{global}(2) in abscissa and the mean penetration μ (1) in ordinate. The thick plain curves represent numerical approximations of the frontiers for the global strategy with (plain blue line) and without (plain black curve) the total-capacity constraint (5c). The dashed and point-dashed black lines represent the optimal frontier for the technology and the base strategies without the total-capacity constraint. The black dot, blue dot and blue diamond represent the maximum-ratio mix, the minimum-variance mix and the high-penetration mix, respectively. (

**b**) Fraction of PV capacity in the mix (plain orange line); shortage frequency (plain green line); saturation frequency (dashed green line) (x axis); versus the mean penetration, for the global strategy with the total-capacity constraint (y axis). The blue and black dashed horizontal lines mark the mean-penetration values corresponding to the blue and black dots and the blue diamond on the left panels. The orange dot represents the PV ratio for the actual capacities installed in Italy in 2015.

**Figure 5.**PV-wind capacity distributions obtained from the CORDEX hourly data for the global strategy with the total-capacity constraint. The left, middle and right panels represent the optimal mixes for the minimum-variance (

**a**), maximum mean-standard deviation-ratio (

**b**) and high-penetration mixes (

**c**), respectively (blue dot, black dot and blue diamond in Figure 4a).

**Figure 7.**Decomposition of the variance over 1989–2011 of the demand (

**a**), PV capacity factors (

**b**) and wind capacity factors (

**c**) into intraday (blue), seasonal (orange) and interannual (green) frequency bands for CORDEX (left bars), MERRA-2 with 10 m winds (middle bars) and MERRA-2 with 50 m winds (right bars).

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tantet, A.; Stéfanon, M.; Drobinski, P.; Badosa, J.; Concettini, S.; Cretì, A.; D’Ambrosio, C.; Thomopulos, D.; Tankov, P. e4clim 1.0: The Energy for a Climate Integrated Model: Description and Application to Italy. *Energies* **2019**, *12*, 4299.
https://doi.org/10.3390/en12224299

**AMA Style**

Tantet A, Stéfanon M, Drobinski P, Badosa J, Concettini S, Cretì A, D’Ambrosio C, Thomopulos D, Tankov P. e4clim 1.0: The Energy for a Climate Integrated Model: Description and Application to Italy. *Energies*. 2019; 12(22):4299.
https://doi.org/10.3390/en12224299

**Chicago/Turabian Style**

Tantet, Alexis, Marc Stéfanon, Philippe Drobinski, Jordi Badosa, Silvia Concettini, Anna Cretì, Claudia D’Ambrosio, Dimitri Thomopulos, and Peter Tankov. 2019. "e4clim 1.0: The Energy for a Climate Integrated Model: Description and Application to Italy" *Energies* 12, no. 22: 4299.
https://doi.org/10.3390/en12224299