**5. Conclusions and Further Works**

BESS, among the distributed energy resources, can be considered the most flexible ones, and they can be suitably exploited for selling system services to the TSO and for solving temporary critical contingencies in distribution networks. The use of BESS will allow providing the services necessary for the management of RES in both distribution and transmission network, during the transition from the demonstration phase to the actual use of the flexibility product market. The paper presents an MO approach for optimizing the installation of BESS in distribution networks. The proposed process is a suitable instrument for the identification of the amount of flexibility (in terms of energy and power) that could be shared between DSO and TSO, without causing constraints violations on the distribution networks. The main novelty proposed in this paper is the optimization of both the objectives of maximizing the BESS owner profits and reducing the operation risk for the DSO. The proposed methodology is capable of producing a set of possible combination of BESS that are capable of offering valuable services to DSO for network operation while system services can be provided to the TSO. Further works will be devoted to the investigation of different remunerative schemes and/or regulatory frameworks regarding the DSO exploitation of the BESS owners. Because the formulation of the optimization problem is quite innovative and the results of different approaches are not available in the current scientific literature, in future research, the authors intend to apply different optimization techniques in order to identify which is more suitable for this kind of problem.

**Author Contributions:** Conceptualization, G.C. and F.P.; methodology, G.C., G.G.S., S.R.; software, G.G.S. and S.R.; validation, S.R., G.P. and F.P.; visualization, G.C.; data curation, S.R. and G.G.S.; writing—original draft preparation, S.R. and G.G.S.; writing—review and editing, F.P., G.C., G.P., S.R.; supervision, F.P.; funding acquisition, F.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research has been supported by the project "Planning and flexible operation of micro-grids with generation, storage and demand control as a support to sustainable and efficient electrical power systems: regulatory aspects, modelling and experimental validation", funded by the Italian Ministry of Education, University and Research (MIUR) Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2017—grant 2017K4JZEE, and by the project "BERLIN—Cost-effective rehabilitation of public buildings into smart and resilient nano-grids using storage", funded by the European Union under the ENI CBC Mediterranea Sea Basin Programme 2014–2020, priority B.4.3—grant A\_B.4.3\_0034.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The network test data used in this study are presented in the Appendix A. **Acknowledgments:** The authors would like to thank the colleagues from EDF R&D (H. Baraffe, J. Fournel, G.

Malarange, J. Morin) for the interesting discussion on this subject.

**Conflicts of Interest:** The authors declare no conflict of interests.

#### **Appendix A**

In the following the main parameters of the test network shown in Figure 6 are provided. Table A1 reports the main information of the lines (starting end and finish end, line length and line type) and the conductor parameters (cross section, resistance, reactance, capacitance, rated current). In Table A2 e in Table A3, respectively, the data about loads and generators are listed (node location, rated power, power factor (P.F.), and load/generator type). Loads are characterized by the daily load profiles shown in Figure 7. Generation is represented with representative production profiles according to the type of source.


**Table A1.** Main parameters of the line of the studied network.

BC: buried cable; OHL: overhead line.


**Table A2.** Loads main characteristics.

RES: residential; AGR: agriculture.


