# 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

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**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