Electromobility Studies Based on Convex Optimization: Design and Control Issues Regarding Vehicle Electrification

Egardt, Bo; Murgovski, Nikolce; Pourabdollah, Mitra; Mårdh, Lars Johannesson · 2014 · OpenAlex-citations

DOI: 10.1109/mcs.2013.2295709

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Summary

This paper addresses the coupled challenges of component sizing and energy management in electrified vehicle powertrains, specifically hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), and pure electric vehicles (EVs). The authors identify that traditional design methods often decouple these tasks, optimizing component sizes and control strategies sequentially or iteratively. This decoupling fails to achieve global optimality because the optimal energy management strategy depends on component properties, while optimal sizing depends on the control strategy. Furthermore, existing nested optimization approaches that do achieve global optimality suffer from high computational burdens or require significant modeling approximations. The paper proposes a unified design approach based on convex optimization to simultaneously optimize both the energy management strategy and the sizing of driveline components, facilitating efficient early-stage design studies. The methodology involves modeling powertrain components—such as combustion engines, electric machines, transmissions, and energy buffers (batteries or supercapacitors)—using a unified framework based on power flows and stored energy. The authors derive convex approximations for component dissipation (losses) and linear scaling laws for component cost, weight, and power capabilities. By representing the powertrain as a network of these convex component models, the combined problem of minimizing operational costs (fuel and electricity) and capital costs (component sizing) is formulated as a convex optimization problem. The approach handles non-affine equality constraints arising from dissipation terms by relaxing them into convex inequalities, which does not alter the optimal solution due to the physical nature of energy conservation. The method assumes a known driving mission and predetermined switching signals for components like the engine. The paper illustrates the approach through case studies, including the sizing of an energy buffer for a series-configuration PHEV city bus. In this example, the optimization determines the optimal trade-off between the cost of a larger battery/supercapacitor and the savings from increased electric energy usage, subject to constraints on charging time and operational efficiency. The convex formulation allows for the efficient computation of optimal power flows and component sizes over long driving cycles. The results demonstrate that this method provides a computationally efficient tool for global optimization of electrified powertrains, overcoming the limitations of sequential design methods and the computational intensity of traditional nested optimization techniques. The significance of this work lies in providing a rigorous, computationally tractable framework for the simultaneous design and control of electrified vehicles. By leveraging convex optimization, the approach enables comprehensive feasibility studies and early-phase design iterations that were previously impractical due to computational constraints. This facilitates more efficient development of electrified powertrains by ensuring that component sizing and energy management strategies are co-optimized, leading to globally optimal designs that minimize total cost of ownership. The paper also discusses extensions, such as handling switching decisions and integrating charging infrastructure, highlighting the potential for broader application in electromobility research and industry.

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• v2x connected vehicle