Optimal Sizing of a Series PHEV: Comparison between Convex Optimization and Particle Swarm Optimization

Abstract

Building a plug-in hybrid electric vehicle that has a low fuel consumption at low hybridization cost requires detailed design optimization studies. This paper investigates optimization of a PHEV with a series powertrain configuration, where plant and control parameters are found concurrently. In this work two often used methods are implemented to find optimal energy management with component sizes. In the first method, the optimal energy management is found simultaneously with the optimal design of the vehicle by using convex optimization to minimize the sum of operational and component costs over a given driving cycle. To find the integer variable, i.e., engine on-off, dynamic programming and heuristics are used. In the second method, particle swarm optimization is used to find the optimal component sizing, together with dynamic programming to find the optimal energy management. The results show that both methods converge to the same optimal design, achieving a 10.4% fuel reduction from the initial powertrain design. Additionally, it is highlighted that the usage of each of the method poses challenges, such as computational time (where convex optimization outperforms particle swarm optimization by a factor of 20) and the tuning effort for the particle swarm optimization and the ability to handle integer variables of convex optimization.

Synthesis of Realistic Driving Cycles With High Accuracy and Computational Speed, Including Slope Information

“…Each candidate cycle can be used in assessing the vehicle's performance, for which a vehicle model is necessary, as used in [25]. It can occur that the power demanded by a synthesized cycle is larger then what the vehicle can deliver.…”

Joint Design and Control of Electric Vehicle Propulsion Systems

“…They have the advantage that the solution can be computed in polynomial time and is guaranteed to be globally optimal. These approaches have been extensively applied to compute the fuel-optimal control strategies for hybrid electric vehicles [12]- [14], sometimes also optimizing the size of the battery, the engine and the motor [15]- [17]. Nevertheless, they consider the transmission design to be fixed and treat its operation as a pre-computed exogenous signal (which sometimes is separately optimized in an iterative, multi-level fashion).…”

Cyber-Physical Energy-Saving Control for Hybrid Aircraft-Towing Tractor Based on Online Swarm Intelligent Programming

“…Particle swarm optimization (PSO) algorithm is a potential candidate for real-time NMPC solving [22], since it works with fewer tuning parameters and less computational effort. PSO also has the capability of dealing with integer variables and it has been successfully applied in hybrid electric vehicle offline optimization [23]- [26]. Furthermore, the PSO's convergence speed and the capability of finding the real global optima can be further optimized by upgrading the standard PSO into Chaos-enhanced Accelerated Particle Swarm Optimization (CAPSO) algorithm [27].…”