## 4 Results
### Operations and Approaches
#### 4.2.2 Refined Approach  
While the event-driven approach effectively captures the functional aspects of the control framework, certain refinements can optimize its practical implementation.  
* Real-time state measurements: To minimize transmission delays and ensure data availability, EV states should be measured continuously at each sampling time instant. This proactive approach (continuous monitoring) allows the CSCC to have the necessary information when an event triggers.
* Batch processing of charging requests (CRs): (i) Queued CRs: to avoid synchronization issues and delays in cost notifications, CRs can be queued and processed in batches; (ii) computational constraints: due to computational limitations, a single optimization problem can be solved per sampling period. Therefore, CRs can be collected and addressed in a unified optimization.
* Optimized sampling frequency, balancing speed and efficiency: (i) The sampling period should be carefully chosen to balance system responsiveness with computational efficiency. A smaller sampling period increases the number of optimization variables, while a larger one may lead to longer waiting times; (ii) multiple control updates: To reduce waiting times and avoid excessive computational burden while handling multiple CRs, the control signals can be computed more than once (within a finite number) during the sampling period. This approach offers a trade-off between responsiveness and computational efficiency.  
To conclude, the refined approach aims to optimize efficiency by avoiding unnecessary control re-computations for each CR. Instead, CRs are collected and processed in batches at specific scheduled time instants within the sampling interval. This reduces computational overhead, especially during periods of high CR activity.  
Similarly, the states of all charging EVs are retrieved at the beginning of the sampling interval, rather than after each CR. This minimizes data exchange and ensures that data are available for control calculations at the scheduled time instants. Figure 2 illustrates the flow of operations based on this refined approach.  
The following notation is introduced: (i) the primary sampling interval (T), i.e., the sampling time of the discrete-time optimal control problem; (ii) the secondary sampling interval (T*), i.e., the temporal distance of two consecutive points of computation within the primary sampling interval. The UML time sequence diagram resulting from the above-mentioned consideration is depicted in Figure 3.  
The steps of the sequence can be summarized as follows:  
1. Each active CS provides CSCC with the current level of battery.
2. The user makes a CR specifying UPs and CSCC collects it for the next computation.
3. CSCC asks DSO for grid constraints (optional).
4. DSO provides CSCC with the required data (optional).
5. CSCC provides the pending CSs with the estimated cost, as output of the computation.
6. CSCC provides all the pending CSs with the charging profile and updates all the other ones under its contractual control.
7. CSCC provides DSO with the aggregated planned power (optional).
8. All CSs apply the received control signals.  
Depending on the size of the LA, the number of CSs the CSCC has to manage simultaneously and the related computational burdens, the event-driven approach, the refined one or an intermediate version between them can be chosen for a practical implementation of the control system, following the methodology detailed in the previous point.  
Figure 2: Flow of operations according to the refined version of the control approach.