## 3 EV Load Characterisation  
The diverse range of EVs involves a number of various approaches to modelling. In this study, voltage-dependent load (VDL) modelling is utilised to determine the active and reactive powers of the ZIP load model, a prominent form of EV load.  
A thorough understanding of the battery profile is required for modelling the EV load for steady-state analysis. Batteries are linked to the distribution system through chargers fitted with two types of bidirectional converters known as AC-DC and DC-DC converters. The detailed analysis of the charger parameters is discussed in [39]. As seen in Figure 2, the grid voltage \(V_{o}\) and grid current \(I_{o}\) are given to the battery charger from the grid side, while the terminal voltage of the battery is \(V_{B}\) and \(I_{B}\) is the current absorbed by the battery. A standard layout of an on-board EV battery charger, which features two converters: an AC-DC converter and a DC-DC converter, is also illustrated in Figure 2 where the dynamic parameters of the battery  
Figure 1: Wind speed power characteristics.  
describe the terminal voltage of the battery (\(V_{B}\)), while charging, the grid-side active \((P_{o})\) and reactive \((Q_{o})\) powers can be calculated using the following equations:  
\[\begin{split} P_{o}&=V_{o}l_{o}cos\phi\\ Q_{o}&=V_{o}l_{o}sin\phi\end{split} \tag{4}\]  
The active and reactive powers utilised on the AC side are monitored at each state of charge (SOC) and voltage level, while a set of \(I_{B}\) and \(V_{B}\) values are acquired at various nominal voltage levels for a range of \(V_{o}\) (180 V to 230 V) and SOC (10% to 100%). These acquired values are analysed to evaluate the VDL characteristics of the EV at various levels of SOC. To ascertain the EV-ZIP values, a constrained least-squares approach is employed to generate a best-fit approximation to the monitored values. Finally, the best-fit ZIP values can be used in the ZIP equations shown below:  
\[\begin{split} P_{ZIP}&=P_{o}\left[p_{3}\left(\frac{ V_{i}}{V_{o}}\right)^{2}+p_{2}\left(\frac{V_{i}}{V_{o}}\right)+p_{1}\right]\\ Q_{ZIP}&=Q_{o}\left[q_{3}\left(\frac{V_{i}}{V_{o}} \right)^{2}+q_{2}\left(\frac{V_{i}}{V_{o}}\right)+q_{1}\right]\end{split} \tag{5}\]  
where \(P_{o}\) and \(Q_{o}\) are active load power and reactive load power acquired from Equation (4). \(V_{i}\) is the bus voltage at which load is connected and \(V_{o}\) is the nominal rated voltage. \(p_{3}\), \(p_{2}\), and \(p_{1}\) are the constant impedance, constant current, and constant power parameters of the active fraction of the EV load. \(q_{3}\), \(q_{2}\), and \(q_{1}\) are the constant impedance, constant current, and constant power parameters of the reactive fraction of the EV load. The values of these various active and reactive parameters of Equation (5) are detailed in [29].  
EVs are substantial loads comparable to all other residential loads; thus, if they do not encourage and sustain the stability of the grid, the DSO will have to acquire additional units to assure power quality, which will raise the cost to customers. Consequently, the converters employed in battery chargers enable the active and reactive power regulation of the EV, allowing it to be used in the operation of the distribution network. The parking lots and parking spots of apartment buildings have access to a distribution network that can supply the necessary energy consumption of EV batteries. As illustrated in Figure 3, the charger must be operated in both charging and capacitive modes if the distribution network demands reactive power while the EV is in charging mode. Consequently, the distribution network provides active power to accommodate EV loads, while EVs introduce reactive power to support the network's reactive requirements [40; 41].  
Figure 2: On-board EV battery charger.