## 7 Conclusions  
This paper proposes a new energy management strategy for a hybrid electric urban bus. The proposed strategy takes profit from the route pattern of urban buses by using information from the vehicle story for energy management optimization. While this is an approach widely discussed in the literature, this paper proposes a different alternative: the strategies available in the literature are based on the estimation of future driving conditions from the vehicle story, however, the solution proposed in this paper is based on using the optimal solution of a reference driving cycle, previously recorded, to estimate a cost-to-go that can be embedded in an online optimization. The proposed strategy is evaluated with data from a bus route in Valencia consisting of a loop of 15.1 km in urban conditions that is covered between 9 and 10 times per day. The recorded data and the optimal evolution of the \(SoE\) was analyzed using the Fourier transform in space domain, showing the existence of patterns that are repeated at the characteristic length of the loop. In the same way, the singular value decomposition of the vehicle speed-acceleration probability distributions in several loops shows that there is a close relation between the operating conditions reached by the bus in the different loops of the route. The analysis suggests that a single loop can be representative of the driving cycle assuming periodicity. Following this idea, the optimal solution of a single loop is computed offline by DP; the cost-to-go generated by this solution is stored and used as an approximation for the cost-to-go from the next time-step in the online application of the HJB equation in the actual driving cycle. The proposed strategy is compared with the theoretical optimal obtained by DP and the online applicable ECMS. Simulations results show that the proposed method is able to keep the \(SoE\) within the range delimited by the EMS and reduces the fuel consumption increase in the ECMS from 11% to 1.9%. The main contributions of the paper can be summarized as follows:  
Figure 11: Impact of the look ahead on the fuel consumption obtained by the rollout strategy (**left**) and probability distribution of the deviation between the optimal \(SoE\) (DP) and that obtained by rollout with different look-ahead horizons (**right**). * It was shown that there exist patterns in the different loops covered by an urban bus that can be used for EMS optimization. * A novel EMS strategy able to exploit those patterns was proposed and simulations offer near optimum results, improving the fuel consumption obtained with other algorithms in the literature calibrated with the same information. * The proposed strategy does not require the estimation of future driving conditions. Regarding future works, authors can observe the following possible lines:
* Upgrade the objective function to include other important aspects to be addressed by the EMS, such as emissions, drivability or battery aging. * Consider other systems and actuators in the vehicle such as the thermal management to address temperature limitations in the powertrain elements and the impact of temperature on their efficiency. * Extend the energy management to other elements in the bus such as the HVAC, which can be an important energy consumer. A holistic approach to all the energy flows in the vehicle can potentially improve its efficiency. * Include other relevant aspects in the description of the driving cycle, for example the mass of the vehicle that can change substantially in the route depending on the number of passengers. One can expect a similar periodicity in the number of passengers on the bus, and the optimization can explore this information. All the previous aspects involve to some extent increasing the model complexity, but the algorithm presented in Section 5 can be generalized to consider them at the expense of computation complexity. Conceptualization, B.P. and P.B. ; methodology, B.P. and P.B. ; software, D.P. ; formal analysis, B.T. ; data curation, D.P.