# Optimal Coordination of PV Active Power Curtailment and EVs Charging among Aggregators
## 1 Introduction  
Electric vehicles and renewable sources like photovoltaic systems have dramatically increased worldwide in recent years. Electrification of the transport has enabled a sustainable energy vision for those countries that are reaching high renewable shares in their energy matrix [1]. Particularly, in residential areas, PV systems are being increasingly installed by end users to exploit the self-consumption [2, 3] and the capacity to sell their excess of energy to the distribution system operator [4]. For those users with an EV, the self-consumption results in a suitable way to reduce the cost of electricity supply by as much as 36% [5]. However, the expanding scale of the grid-connected PVs and the connection of EVs may lead to detrimental impacts on the low-voltage (LV) network operation if these devices are not properly managed, as reported in [6, 7]. This means that the network would have to face two operational scenarios. First, a significant amount of generation with a low demand condition that leads to overloading the assets of the network and consequent voltage rise due to the reverse power flow. Second, a large charging demand requirement at night, which also leads to an overloading condition with a remarkable voltage drop. Different solutions to alleviate technical problems on distribution networks with EVs and PVs have been recently proposed and studied in order to provide to the DSO a set of cost-effective tools asan alternative to traditional network reinforcement. For example, the work described in [8] proposes a hierarchical coordination scheme between the DSO and the EVs aggregators to minimise their operational cost and the peak load of the DSO under a linear programming (LP) model. As a result of the optimisation strategy, every aggregator allocates the optimal charging power dictated by the DSO to its EVs. In [9], a coordinated charging strategy based on a quadratic programming (QP) formulation for a large number of EVs is proposed. This strategy consists of three levels, i.e., from the point of view of the transmission system operator, the DSO and the charging station operator. The objective is to minimise the peak load at the transmission level, the load deviation of the DSOs and the energy purchase cost of all charging station operators while satisfying the energy and power needs of their customers. The above two works employ an energy boundary model based on the required energy level of the EVs to evaluate their charging needs. The work introduced in [10] proposes a centralised coordination strategy based on a mixed-integer linear programming formulation for EVs connected to multifamily housing. This model aims to maximise the profits of the aggregator who manages the charging ports while satisfying the power needs of its customers and the thermal capacity of the distribution transformer. In [11], the authors proposed a market framework where the aggregators of EVs interact with a transactive energy agent and the DSO to solve operational problems in the network. This was performed using a bidding model based on linear programming to minimise the total cost of the DSO for obtaining flexibility services from EVs. On the other hand, in [12], an optimal power flow (OPF) problem based on a quadratic programming formulation is proposed to minimise the energy curtailment of medium-scale PV units by finding an optimal power limit to guarantee the network will operate without thermal or voltage problems. A similar criterion for PV power curtailment in LV networks was employed in [13]. The authors extended the OPF formulation in [12] to the unbalanced three-phase case. They also analysed different PV penetration levels and export limits based on the Monte Carlo approach. In [14], a linear programming model was formulated to define an optimal power threshold to limit the excess of PV energy injected to the LV network.