Predictive Energy Management for Hybrid Powertrains

Hybrid power trains (HPT) run on multiple energy sources, often involving energy storage systems/batteries (ESS). As a result, the risk of battery degradation and the reliability of energy storage elements pose a major challenge in designing an energy-efficient hybrid power train. This paper presents an energy management strategy that adaptively splits power demand between the engine and the battery pack in a hybrid power train taking into account the battery degradation. Incorporating the battery degradation model directly into the underlying optimization problem is challenging on multiple fronts: 1) Any reasonable degradation model will, due to its complexity, result in a complicated optimization problem that is impractical for real-time implementation 2) the models contain a lot of time-varying parameters that can only be determined through destructive experimental procedures. As a result, it is essential to devise heuristics that reasonably capture the degradation per usage of the batteries. One such heuristic considered in this paper is the absolute power extracted from the battery. A distributed model predictive strategy is then developed to coordinate the power split to maximize efficiency while mitigating the failure risk due to battery degradation. The designed EM strategy is demonstrated through a realistic simulation of three different hybrid power trains: hybrid road vehicles (for example: a hybrid electric vehicle (HEV)), hybrid surface vehicles (for example: dynamically positioned hybrid ships (DPS)), and hybrid aerial vehicles (for example: hybrid electric aircraft (HEA)). The results show the effectiveness of the energy management strategy in managing battery degradation.

💡 Research Summary

The paper addresses the energy management (EM) problem for hybrid powertrains (HPTs) that combine an internal‑combustion engine (or generator) with an energy storage system (ESS), typically a battery. While many recent works have focused on minimizing fuel consumption through model predictive control (MPC) or reinforcement learning, they often neglect the degradation of the battery, which can become the limiting factor for vehicle lifetime and overall efficiency. Directly embedding sophisticated battery degradation models into the MPC formulation, however, leads to high‑dimensional, nonlinear optimization problems that are unsuitable for real‑time implementation and require parameters that are difficult to obtain experimentally.

To overcome these challenges, the authors propose a heuristic that treats the absolute power extracted from the battery (i.e., the integral of the absolute battery current, also known as Ah‑throughput) as a proxy for battery wear. This metric is simple to compute, correlates well with capacity loss in many experimental studies, and can be incorporated into the cost function without dramatically increasing computational burden.

The core of the methodology is a distributed MPC architecture built on a generalized Euler‑Lagrange vehicle dynamics model. The dynamics are expressed as

M(x) ¨x + V_m(x, ẋ) ẋ + G(x) + F(ẋ) = τ,

where x denotes the generalized coordinates, M the inertia matrix, V_m the Coriolis matrix, G the gravity vector, F the damping torque, and τ the generalized torque supplied by the powertrain. By assuming a stable reference trajectory ˙x_d = f(x_d), the authors linearize the dynamics into a regressor‑parameter form Y(x, ẋ, x_d) θ. An adaptive estimator updates the unknown parameter vector θ online, while a Lyapunov‑based control law

τ = −k₁ η − γ₁ ∫₀ᵗ Y(ν)ᵀ η(ν) dν

guarantees global asymptotic stability of the speed‑tracking error η = ẋ − ẋ_d. The resulting power split satisfies p_e + p_b = p_d, where p_e is engine power, p_b is battery power, and p_d is the demanded power derived from the tracking error dynamics.

The MPC optimization problem minimizes, over a prediction horizon h, the weighted sum

∑_{k=1}^{h}