## 4 Proposed Approach: Quantitative Assessment of the Flexibility
### Flexibility Providers  
Once the distribution network is modelled, several scenarios can be applied to model the flexibility provisions. For instance, typical scenarios can reproduce the existing or the expected level of distributed generation (DG), demand response and electric vehicles, which are the DERs involved in the market as flexibility providers. As well as these kinds of DERs, an important role in flexibility provision can be played by energy storage systems (ESSs). They, due to their inherent operational characteristics, may favour the transition towards more flexible and \"smarter\" distribution systems. ESSs, behaving as a four-quadrant generator, can provide several services to the DSOs related to voltage regulation, energy losses reduction, continuity and power quality improvement, etc. Indeed, if installed close to the TSO/DSO interfaces, they may offer flexibility services also to the TSO. However, the current European regulatory framework (starting from the \"Clean Energy Package\" [39]), despite giving a new role to the DSOs, considers storage operations as a competitive activity in the framework of European market design, and therefore, in principle, not allowed for monopolistic grid operators. For this reason, to avoid obstacles in market competitivity that may arise in the considered extended centralised market model, in this paper, ESSs owned and managed by the DSOs are not contemplated in the evaluation of the distribution's potential flexibility. In truth, an exception exists where under specific strict conditions, and only with the approval of the national regulatory authority, ESSs may be owned and managed by DSOs, especially if the implemented market model is the _shared balancing responsible_ model, but this possibility is not considered in this paper [39; 40; 41]. In the proposed application, only private ESSs may be included to increase the potential bids of the DER owners. In this case, the added new flexibility quantity would be comprised in their offers in the market. However, it is worth noticing that this scenario can be expected only when the flexibility market is well-consolidated, and the DER owners envisage the ESSs as a possible source of extra income. Starting from the known or estimated production of a distribution network, generators can be allocated in the representative feeders that compose the passive model of the synthetic network until it achieves the supposed real DG penetration. As well as the active customers agreeing to participate in demand response programs, a DERs scenario may include different combinations of non-programmable RES (i.e., solar or wind-based generators), programmable energy sources (i.e., CHP or biomass generators) for modelling the realistic DG penetration derived from the public data used for defining the power profiles at the TSO/DSO interface. The proposed approach starts from the defined profiles at the PCC, locates the production plants along with the feeders of a real or a model of the distribution network, and hypothesises the participation profiles of the DERs (production plants, storages and active loads) involved in offering flexibility products, to estimate the market potential of DERs connected to a distribution network. The DERs behaviour in the market is described in terms of pairs price/quantity of flexibility, and the bids are differentiated between upward and downward offers. It is assumed that such new market players behave rationally (i.e., by trying to maximise their profits), and the bid prices can be defined according to any model. For instance, a PV producer may offer in downward even reducing to zero the injection of power into the grid, and increase the injection if he has derated the production of his plant from the perspective of offering flexibility services in upward (e.g., especially if the plant is equipped by an energy storage system).