# Charge Management of Electric Vehicles from Undesired Dynamics in Solar Photovoltaic Generation
## 3 Methodology  
This section introduces the methodological approach and data sources that form the basis of this analysis. First, a brief description of the components of the energy management system (EMS) is presented. This system is used to test the control technique. Next, the power ramp-rate algorithm is presented. The starting point of the EMS in Figure 2 corresponds to the database of the historical information of the PV solar power system, which is obtained from the records of the supervisory control and data acquisition (SCADA) system of the microgrid laboratory of the University of Cuenca [15]. This PV system, also available in this laboratory, has four strings of 15 panels of the poly-Si type connected in series. Each one has a nominal power of 250 Wp, reaching a total of 15 kWp. The array is managed by a two-level three-phase DC/AC converter with Pulse Wide Modulation [2]. The system is connected directly to the distribution grid and is operated by an MPPT algorithm. The dynamic behavior of PV systems presents a wide range of power fluctuations over short periods. An increasing insertion of these systems can lead to instability in the grid [1]. Therefore, the study applies the method of control of ramp-rate power and uses the storage system of the EV battery bank to manage these power fluctuations. According to the EMS diagram (Figure 2), the charging system has the function of modifying the supply power to the batteries according to the dynamic behavior of the PV generation. The range of the charging power variation (PEV) must be within the established limits, which come from the electrical characteristics of the vehicle model and what SAE J1772 norm states [19]. The maximum P\({}_{\text{EV}}\) follows the standard of the single-phase slow charge of some EV models. The minimum P\({}_{\text{EV}}\) considers the power obtained with the lowest current level necessary to start the charging process. Hence, the variation range goes from 7.2 kW to 1.32 kW, due to the restrictions of the J1772 standard. Finally, 50% of the power range sets a reference level for this variation; for example, if an EV has a maximum charging power of 6.5 kW, the set power is 3.91 kW. Changes in the PEV may not be immediately reflected in the EV battery system, as was the case in the study that developed some tests with two different models of EVs. The goal was to assess their battery system response time [20]. With a 30% to 50% variation of the duty cycle, this system reacted in 2 and 0.68 s, respectively. Therefore, to observe the reaction of this parameter in the case of the study will take different values. The method developed for the ramp-rate algorithm calculates the PV power ramp rate (Equation (1)) (R\({}_{\text{PV}}\)) and constrains its value to the PV power ramp limit for this case study  
Figure 2: Energy management system. (Equation (2)) (R\({}_{\rm LIM}\)). The condition of R\({}_{\rm LIM}\) is to keep the active power variation below 10% of the nominal power per minute. This condition considers the regulations accepted by PREPA since the Republic of Ecuador has no statutes in this regard. The algorithm of ramp-rate control applied for the study is presented in Figure 3.  
\[\rm R_{PV}=\frac{\Delta P_{PV}}{\Delta_{t}}=\frac{P_{PV}\left[n\right]-P_{PV} \left[n-1\right]}{t[n]-t[n-1]}\ \left[\frac{W}{min}\right] \tag{1}\]  
\[\rm R_{Lim}=10\%\frac{P_{PV\;nom}}{min}=10\%\frac{15\,kW}{min}=1500\ \frac{W}{min}\ (25\ W/s) \tag{2}\]  
In Equation (1), n represents the discrete sampling time. This paper considers a discrete sampling time of 1 s, which means that every second a value of PV power is read. Following the operation process of the ramp-rate (RR) algorithm shown in Figure 3, it starts by reading the PV output power. Then, it sets R\({}_{\rm LIM}\). Therefore, according to Equation (2), with a solar generation capacity of 15 kWp, the maximum supported rate of change in this study reaches \(\rm\mid\)RR\(\rm\mid\) < 1.5 kW/min.