# Optimal Coordination of PV Active Power Curtailment and EVs Charging among Aggregators
## 1 Introduction
Another unbalanced three-phase case is studied in [15] using a multiobjective OPF problem to minimise network losses and PV power curtailment cost, along with the improvement of voltage magnitude and balance profiles. By employing the weighted sum method, the optimisation problem is handled as a single-objective problem, which is solved by applying the sequential quadratic programming (SQP) technique. It should be clarified that the above works define the maximum PV power injection as a percentage of the inverter capacity. However, such a limit can also be expressed through a reference signal--for instance, when the actual voltage is right over the set upper voltage limit, as in [16; 17]. Some research studies [7; 18; 19] assess these devices for small applications in commercial buildings, residential microgrids and charging stations in parking decks. A smart charging scheme to improve PV self-consumption in commercial facilities using particle swarm optimisation was proposed in [18]. In [7], the authors present a model that maximises the self-consumption of PV and reduces the peak demand of a small microgrid in the Netherlands using bidirectional charging technologies. In [19], a multi-objective optimisation model subject to several constraints imposed by the utility at the point of connection is used to maximise the profits of an EV station with PV units while minimising the capacity loss of a battery energy storage system (BESS) connected to the same facility. Further control techniques based on BESSs and EVs to increase PV generation amount on the network are widely reviewed in [20]. Most of these studies have in common that both the EVs and PVs in sizable quantities are separately analysed, and hence, their combined effect on the network is not considered, especially in LV grids. In this context, this paper proposes a centralised control strategy for managing the aggregation of both the excess of PV power injected to the LV network and the charging of EVs in multiple aggregators under a unique DSO. With this control strategy, the computational effort of the proposed optimisation problem is highly reduced, as well as the amount of data exchange between the aggregators and DSO. The loading level of the DSO's assets, i.e., main cables and distribution transformers, is adopted as a key parameter to evaluate their performance when introducing a high penetration level of EVs and PVs. The proposed methodology was designed to be applicable for the context where the DSO manages the LV network by means of the aggregators at the LV side of the distribution transformers, i.e., each aggregator supervises and controls a particular feeder. Note that with the introduction of the advance metering infrastructure in residential housing, this coordination schema can be expanded to dynamically responding to a time-of-use price mechanism for each aggregator. Additionally, an energy boundary model to evaluate the charging requirements of the EVs controlled by each aggregator was proposed. This model differs a unique aspect from the one formulated in [8; 9]; the proposed model here is based on the arrival energy level of the EVs instead of their required energy state. This article is organised as follows: Section 2 describes the individual and aggregated mathematical model of EVs and PVs. The optimisation model of the centralised control strategy by the DSO is formulated in Section 3. In Section 4, a numerical case study is introduced, and Section 5 discusses the results and the effectiveness of the proposed coordination strategy. Finally, conclusions and hints on future works are presented in Section 6.