Engine On/Off Control for Dimensioning Hybrid Electric Powertrains via Convex Optimization

Abstract

This paper presents a novel heuristic method for optimal control of mixed-integer problems which for given feasible values of the integer variables are convex in the rest of the variables. The method is based on the Pontryagin's maximum principle and allows the problem to be solved using convex optimization techniques. The advantage of this approach is the short computation time for obtaining a solution near the global optimum, which may otherwise need very long computation time when solved by algorithms guaranteeing global optimum, such as Dynamic Programming.In this study the method is applied to the problem of battery dimensioning and power split control of a plug-in hybrid electric vehicle where the only integer variable is the engine on/off control, but the method can be extended to problems with more integer variables. The studied vehicle is a city bus which is driven along a perfectly known bus line with a fixed charging infrastructure. The bus can charge either at standstill, or while driving along a tram line (slide-in).The problem is approached in two different scenarios: first, only the optimal power split control is obtained for several fixed battery sizes; second, both battery size and power split control are optimized simultaneously. Optimizations are performed over four different bus lines and two different battery types, giving solutions that are very close to the global optimum obtained by Dynamic Programming.Index Terms-plug-in/slide-in hybrid electric vehicle, battery sizing, power management, convex optimization, Pontryagin's maximum principle

Convex relaxations in the optimal control of electrified vehicles

“…The engine on/off state σ G is regarded as an external signal, since obtaining its optimal value is not in the context of this study. Interested readers are referred to [26], [27] for optimization of σ G by iteratively solving convex problems.…”

Convex Optimization for the Energy Management of Hybrid Electric Vehicles Considering Engine Start and Gearshift Costs

“…The symbol stands for optimal, and ≡ stands for identity of the trajectory. On the other hand, solving the convex problem for the optimal values of u g and u e yields the optimal value of s out ≡ s [30,34]. Therefore, if s in ≡ s , then s out ≡ s in ≡ s .…”

“…One approach to optimize discrete decision problems is to solve a mixed-integer problem [32], but its drawback is the large computational burden for optimizations on typical driving missions. A more efficient approach consists of splitting up the problem into two parts, where the discrete decision variables are optimized prior to the convex optimization [33] with the possibility to iterate between the two steps [34]. Based on this methodology, the authors of [30] showed that the optimal engine on/off strategy can be calculated for a serial HEV.…”

An Optimized Energy Management Strategy of 48V Mild Hybrid Electrical Vehicle to Reduce Fuel Consumption

“…HEV has the advantages of low emission and fuel consumption. Mild Hybrid Vehicle is one of HEV which equips with low power traction motor [1] . In 2011, five German car makers announced that they will introduce 48V system into their cars.…”