An ADMM Algorithm for MPC-based Energy Management in Hybrid Electric Vehicles with Nonlinear Losses

Abstract

In this paper we present a convex formulation of the Model Predictive Control (MPC) optimisation for energy management in hybrid electric vehicles, and an Alternating Direction Method of Multipliers (ADMM) algorithm for its solution. We develop a new proof of convexity for the problem that allows the nonlinear dynamics to be modelled as a linear system, then demonstrate the performance of ADMM in comparison with Dynamic Programming (DP) through simulation. The results demonstrate up to two orders of magnitude improvement in solution time for comparable accuracy against DP.

Fast Optimal Energy Management With Engine On/Off Decisions for Plug-in Hybrid Electric Vehicles

“…For the work presented here, we extend the model previously described in [14] to include engine switching, and in places we refer the reader to that paper for more details. Figure 1 shows a simplified diagram of a parallel PHEV powertrain and is used to define the power transfers, P .…”

“…The angular speed of the drivetrain input, ω d , is given at all times by a simple gear switching heuristic function based on vehicle velocity e.g. ω d,k = f (v k ) (see [14]). It is assumed that when the drivetrain speed is below the minimum engine speed the clutch is disengaged and the engine is off, and that a negative demand power is delivered from the motor only.…”

“…where it is assumed that the open circuit voltage, V , and resistance, R, are constant. Limits are introduced on both motor and engine power for k ∈ P to ensure that their respective torque limits are not exceeded, and to ensure that g k and f k are all non-decreasing (this is reasonable as it would be expected that an increase in output power would require an increase in input power) and real-valued (see [14]). These can then be consolidated into upper and lower limits on motor power, P em,k and P em,k , so that limits on battery power can be given ∀ k as…”

“…In [14] we proved that a formulation including general state of charge limits is convex when stated as a function of the battery power, and proposed an ADMM algorithm for its solution, but still did not consider engine switching. In [15] we proved that the algorithm of [14] is…”

“…Powertrain Model (see [14] for full interpretation of each variable) convergent even in the presence of nonconvexity, but only to a point that satisfies the first order (neccessary) conditions. ADMM was previously used in [16] as a heuristic for energy management with engine switching, but all losses in the electric system were ignored and the algorithm was not necessarily convergent.…”