# PV Sizing for EV Workplace Charging Stations--An Empirical Study in France
## 3 Context and Methodology
### Collective Self-Consumption Scheme  
As explained in the introduction and visualized in Figure 1, we consider the general case where the EVCI and the PV installation are managed by two separate entities, namely the Charging Point Operator and PV Operator (CPO and PVO). The CPO has to manage the charging of a certain number of EVs while utilizing the production from the PV plant, characterized by a certain peak power, noted \(P_{PV}^{peak}\). We also consider that they agree on an exchange of PV energy. Without loss of generality, this agreement could be a partnership with a 'third party' called Legal Person (LP), or Personne Morale Organisatrice (PMO) in French, according to the scheme called \"collective self-consumption\" in France. This LP entity plays the role of a facilitator for the financial as well as power flows between the CPO and the PVO. The CPO also contracts with an energy supplier (ESEV) that provides supplementary energy to the charging stations when PV production is insufficient to the EV charging consumption. In the meantime, the PVO also establishes a contract with another energy supplier (ESPV), which extracts the surplus PV energy produced when there is more PV production than EV consumption.  
In this paper, the power \(x\) is denoted \(P_{x}\). The energy of \(P_{x}\) over a period \(\Delta\), \(E_{x}^{\Delta}\) is the integral of this power over \(\Delta\): (\(E_{x}^{\Delta}=\int^{\Delta}P_{x}dt\)). The energy of the power \(P_{x}\) calculated over a day, a month and a year are noted \(E_{x}^{d}\), \(E_{x}^{m}\) and \(E_{x}^{a}\), respectively. The energy of the power \(P_{x}\) computed on an arbitrary period is noted without a subscript, i.e., \(E_{x}\). The price per kWh that actor A pays when he buys a given amount of energy from actor B is noted \(Pr_{B-A}\). It is important to note that this price may also include other services, apart from the energy production fee itself, such as transport, taxes and contributions.  
With these notations (summarized in Table 2), the principle of this scheme, represented in Figure 2, is the following:  
* The PV power (\(P_{PV}\)) and the corresponding energy (\(E_{PV}\)), produced by the PV plant during the period, are visualized in the top left part of the figure;
* The charging power (\(P_{EV}\)) and energy (\(E_{EV}\)) consumed by the EVs are represented on the bottom left diagram;* The CPO partially charges the EVs with the power \(P_{SP}\) (SP for Self-Production) such that \(P_{SP}=min(P_{PV},~{}P_{EV})\). The CPO buys the associated energy, represented in green and noted \(E_{SP}\) to the LP at a price noted \(Pr_{LP-CPO}\);
* The PVO, for his part, sells \(E_{SP}\) to the LP at a price noted \(Pr_{PVO-LP}\);
* The CPO also charges the EVs with the power \(P_{ESEV}\) that complements \(P_{SP}\) when there is not enough solar power (i.e., such as \(P_{ESEV}=max(P_{EV}-P_{PV},~{}0)\)). The CPO buys the associated energy, represented in dark blue and noted \(\mathrm{E}_{\mathrm{ESEV}}\), to the power supplier ESEV at a price noted \(Pr_{ESEV-CPO}\);
* The PVO injects in the network the power \(P_{ESPV}\), if any, produced by the PV plant but not consumed by the EVS (i.e., such as \(P_{ESPV}=max(P_{PV}-P_{EV},~{}0)\)). The PVO sells the associated energy, represented in pink and noted \(\mathrm{E}_{\mathrm{ESPV}}\), to the power supplier ESPV at a price \(Pr_{PVO-ESPV}\).  
In such a configuration, the local DSO is responsible for the virtual dispatch (\"virtual\" because the dispatch is performed in front of the meter); the DSO measures \(E_{EV}\) and \(E_{PV}\) from the power meters of the EV charging point and the PV plants, respectively. The meters are read at a frequency that depends on the market time step whose value depends on countries. The DSO computes \(E_{ESPV},\ E_{ESEV}\), \(E_{SP}\) based on the following logics and transfers these values to the LP, ESPV and ESEV, respectively.  
* \(E_{ESPV}=max(E_{PV}-E_{EV},\ 0)\)
* \(E_{ESEV}=max(E_{EV}-E_{PV},\ 0)\)
* \(E_{SP}=min(E_{PV},\ E_{EV})\)