# Modeling and Solving Method for Supporting Vehicle-to-Anything' EV Charging Mode
## 5 Conclusions  
A generic model that can fit the various activities of V2A application has been presented in this paper. With the proposed model, the decisions of charging/discharging statuses including charging, V2H, V2B, V2V, and V2G of EVs under the guidance of power price signals for different parking places can be supported. The battery degradation issue has also been considered. As demonstrated by the simulation results, the proposed model can be utilized to help minimize the power energy cost of the power consumption entity or community involved with V2A applications in response to the price signals released by the grid operator. For instance, a reduction of 4.37% in energy expenses can be achieved in a case study with EV discharging enabled for a household. This also reflects that EVs are prone to perform less discharging when the demand for the lifecycle of EV batteries is higher. Since power prices can induce different charging/discharging behaviors in EVs, future work should be focused on price tuning for regulating EV charging/discharging behaviors. The constraints of power grids can also be studied to fit the proposed model into more practical applications.  
Figure 15: Details of the aggregated EV charging/discharging profiles for the charging station with different \(\lambda_{i}\): (**a–e**): \(\lambda_{i}\) = 0, 0.1, 0.2, 0.3 and 0.5 respectively; with the increase of \(\lambda_{i}\), EVs choose to perform less discharging.  
**Author Contributions:** [PERSON] conducted the investigation, designed the methodology and completed the original draft; [PERSON] and [PERSON] gave suggestions on the proposed idea and simulation cases; [PERSON] and [PERSON] revised the paper based on comments from the reviewers; [PERSON] checked the proofreading.  
**Acknowledgments:** This paper was supported by the project \"Research on power system planning theory with high proportion of intermittent renewable energy resources\" of the China Southern Power Grid (CSGTRC-K163007).  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
\begin{tabular}{l l} \(t\) & Time index \\ \(i\) & EV index \\ \(ST\) & Time interval set \\ \(SE\) & EV set at a power consumption unit \\ \(Soc^{i}_{EV,min}\) & Lower SOC limit for the \(i\)th EV \\ \(Soc^{i}_{EV,max}\) & Upper SOC limit for the \(i\)th EV \\ \(Soc^{i}_{EV,t}\) & SOC state of the \(i\)th EV at time \(t\) \\ \(Soc^{i}_{EV,t_{start}}\) & SOC value at plugging-in time of \(i\)th EV \\ \(Soc^{i}_{EV,t_{start}}\) & SOC value at plugging-out time of \(i\)th EV \\ \(Soc^{i}_{EV,exp}\) & Expected SOC value of \(i\)th EV from the car owner \\ \(Soc^{i}_{EV}\) & Nominal battery SOC of the \(i\)th EV \\ \(P^{i}_{EV}\) & Nominal charging power of the \(i\)th EV \\ \(C_{EV}\) & Battery capacity of the \(i\)th EV \\ \(\eta^{i}_{d}\) & Charging efficiency of the \(i\)th EV \\ \(\eta^{i}_{d}\) & Discharging efficiency of the \(i\)th EV \\ \(S_{EV,t}^{i}\) & Charging status (0 or 1) at time \(t\) of the \(i\)th EV \\ \(S_{EV,t}^{i}\) & V2H status (0 or 1) at time \(t\) of the \(i\)th EV \\ \(S_{EV,t}^{i}\) & V2B status (0 or 1) at time \(t\) of the \(i\)th EV \\ \(S_{EV,t}^{i}\) & V2V status (0 or 1) at time \(t\) of the \(i\)th EV \\ \(S_{EV,t}^{i}\) & V2V status (0 or 1) at time \(t\) of the \(i\)th EV \\ \(S_{EV,t}^{i}\) & V2G status (0 or 1) at time \(t\) of the \(i\)th EV \\ \(t_{start}\) & Charging start time \\ \(t_{end}\) & Charging end time \\ \(T^{i}_{EV}\) & Working period of the \(i\)th EV \\ \(T_{B}\) & Time period of basic load for a power consumption unit \\ \(P^{t}_{b}\) & Basic power load at time \(t\) for a power consumption unit \\ \(\phi_{V2G,t}\) & V2G power price at time \(t\) \\ \(\phi_{L,t}\) & Power load price at time \(t\) \\ \(\rho_{i}\) & Penalty coefficient for energy desire of the \(i\)th EV \\ \(\lambda_{i}\) & Penalty coefficient for charging cycles of the \(i\)th EV \\ \end{tabular}