Convex Optimization of Charging Infrastructure Design and Component Sizing of a Plug-in Series HEV Powertrain

Abstract

With the topic of plug-in HEV city buses, this paper studies the highly coupled optimization problem of finding the most cost efficient compromise between investing in onboard electric powertrain components and installing a charging infrastructure along the bus line. The paper describes how convex optimization can be used to find the optimal battery sizing for a series HEV with fixed engine and generator unit and a fixed charging infrastructure along the bus line. The novelty of the proposed optimization approach is that both the battery sizing and the energy management strategy are optimized simultaneously by solving a convex problem. In the optimization approach the power characteristics of the engine-generator unit are approximated by a convex, second order polynomial, and the convex battery model assumes quadratic losses. The paper also presents an example for a specific bus line, showing the dependence between the optimal battery sizing and the number of charging stations on the bus line.

Convex relaxations in the optimal control of electrified vehicles

“…Similar convex relaxations have been undertaken in [12], [13], [24], [6], [15], [16], [17], [18] for problems of combined sizing and control of electrified powertrains. Common in these studies is that braking power is removed from the problem.…”

“…It has been logically reasoned in [12], [13] that the optimal solution of the relaxed convex problem (10) yields the optimal solution of the original non-convex problem, as any other solution wastes energy, and therefore, cannot be optimal. A more rigorous proof has been provided by [16] for slightly different problem formulation and stricter monotonicity conditions.…”

“…More details on the convexity of these functions can be found in [12], [23], [24], [4], [13], [15]. A convex and nondecreasing EGU model has been proposed by [12], based on the EGU models of [25].…”

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

“…It is seen as an alternative method for the optimization of the power flows in HEVs with the advantage of being computationally more efficient than for example DP or indirect methods such as PMP are. Convex optimization has already been employed for dimensioning of powertrains [28][29][30], energy efficiency analysis [31] and online control of HEVs [32,33]. However, inherently discrete decision variables, such as the engine on/off decision or the gear decision, are typically determined using heuristic approximations.…”

Conceptual Design of Complex Hydromechanical Transmissions

“…Methods for simultaneous optimisation have also been developed, the most common ones using a rule-based strategy where a few control parameters can easily be integrated with the hardware design parameters [111,112,113]. Murgovski et al [114] propose a useful method where the objective function is formulated as a convex problem and solved using convex optimisation. This method can guarantee global optimum, but is limited to problems where convex approximations of the component models are acceptable.…”