## 4 Energy Management Strategies in Residential BESS without RES
### Energy Management Strategy at Spring/Summer ToU Tariff  
During spring and summer, the energy price is 0.078 \(\xi\)/kWh from 11 p.m. to 7 a.m. and 0.11 \(\xi\)/kWh from 7 a.m. to 11 p.m. (Figure 1a). Consequently, at the EMS in spring/summer ToU tariff the day is segregated into one charging zone (11 p.m.-7 a.m.) and one discharging zone (7 a.m.-11 p.m.). This implies that during spring and summer one full charge/discharge cycle per day is permitted. The discharging zone is further divided into \(N\) slots. The number of time slots is selected by the end user according to the uncertainty of the forecasted energy consumption profile in the household. For instance, if the BESS is installed in a household where the residents' habits are not changing frequently, the discharging zone could be divided into few timeslots. However, if a statistic analysis proves high alterability of the inhabitant's energy consumption habits the number of timeslots \(N\) should be higher. A normal sampling time for updating the optimal discharge schedule at a BESS in a household is between the range of five minutes to one hour. This implies that the discharging zone (16 h) is divided into minimum sixteen timeslots and maximum one hundred ninety-two time slots.  
The EMS is displayed in Figure 6 and described as follows. Initially, the end user sets a desirable ageing trajectory for the BESS by utilizing the battery degradation model. Thereupon, the needed data such as the BESS's parameters present values and the day-ahead power demand profile are retrieved. Moreover, the discharging zone is segregated in a desirable number of slots \(N\) which is set by the end user. Thereafter, the dynamic optimization algorithm is called in order to define the optimal discharging schedule for the BESS. The optimizer determines the maximum permitted energy supply at the household for each one of the slots. This energy limitation is used also as an instantaneous power limitation at each slot. In that context, the optimizer determines the maximum permitted \(DOD\) at each slot and the maximum permissible discharging current as well. At the end of the present time slot, the KiBaM model is called in order to update the status of the BESS based on the actual energy supply and the mean discharge current during the time slot. By taking into account the updated parameters  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \(\xi_{1}\) & \(\xi_{2}\) & \(\xi_{3}\) & \(\xi_{4}\) & \(\xi_{5}\) & \(\xi_{6}\) & \(\xi_{7}\) & \(\xi_{8}\) & \(\xi_{9}\) & \(\xi_{10}\) & \(\xi_{11}\) & \(\xi_{12}\) & \(\xi_{13}\) \\ \hline
2330 & 1337 &of the KiBaM model and any possible updates at the forecasted power demand profile the optimizer is recalled so as to define the optimal discharge schedule for the remaining slots of the discharging zone. Once the discharging zone is passed (11 p.m.), the constant charging current is calculated by taking into account the time duration of the charging zone and the SOC of the BESS which is calculated by the KiBaM model. Then, the economic profit for the consumer according to the optimal operation of the BESS through all the day is calculated. The last step of the EMS is to estimate the daily capacity loss of the BESS based on the occurred optimal charging/discharging schedule and the current number of cycle of the BESS.