Analytical Optimal Solution to the Energy Management Problem in Series Hybrid Electric Vehicles

Abstract

Optimal solution to the energy management problem in hybrid electric vehicles has been extensively addressed in literature during last decade, especially with the application of dynamic programming, Pontryagin minimum principle or equivalent consumption minimization strategy. However, most of the works consist in finding cycle-specific optimal trajectories which are far from being general control strategies.The aim of this work is to derive an analytical expression, general and not cycle-specific, for the energy management problem that summarizes the optimal controls for a series hybrid electric vehicle. Starting from a simple definition of the powertrain, an explicit formulation is deducted to minimize fuel consumption based on an analytic analysis of Pontryagin minimum principle. Explicit expressions for control variables and costates are provided. The result is a general control strategy that specifies the optimal generator set usage for a given probability distribution of expected traction demands. This methodology is benchmarked with common methods in literature (dynamic programming and numerical Pontryagin minimum principle) showing near identical results but with strongly reduced computational time. The general form of this control strategy can also be used to analyze the optimal operation range of the engine, which could be useful for designing purposes.

Hybrid Electric Vehicle Two-Step Fuel Efficiency Optimization With Decoupled Energy Management and Speed Control

“…Analogously to the OCP-S-1 formulated in the previous section, OCP-S-2 is subject to the constraints (20), (21), (41),…”

“…The problem of EM optimization for an HEV while following a predefined speed profile is standard with a rich literature (see, for example [14], [16] and the references cited therein). The problem has also been specifically formulated in numerous prior studies as an OCP in the form of (18) (see, for example [41]).…”

Fuel cell vehicle energy management strategy based on the cost of ownership

“…A scaled version of the Mirai FC stack is modelled by modifying (6) to reflect the improved current density of the Mirai FC [7] and the resulting FC polarisation curve is given by (22) The new FC polarisation curve coefficient values and the mass flow coefficients are specified in Table 6. Offline optimisation of the new FC model shows that the optimum FC efficiency occurs at 88 A (4.87 kW).…”

“…Other studies that implement model‐based optimisation techniques include [22], where PMP is applied to a series‐HEV to minimise fuel consumption, and the computational time is reduced by utilising probability distributions for future traction demands. In [23], minimisation of the fuel consumption and battery degradation are the dual objectives which are resolved using PMP for a parallel‐HEV.…”

Analytical Solution to Equivalent Consumption Minimization Strategy for Series Hybrid Electric Vehicles

“…Stochastic dynamic programming (SDP) has been employed to tackle the prior knowledge requirement of DP for real-time implementation by estimating future power demands using probabilistic framework [7], [8]. SDP achieves near-optimal results but has high computational burden that limits its usage in real-time [6], [9].…”