With a wide range of design choices and the high cost of prototype vehicles, design characteristics of the battery pack that maximize the net present value (NPV) of a plug-in hybrid-electric vehicle (PHEV) need to be determined quickly and systematically.
Vehicle control and battery design parameters need to be optimized simultaneously to achieve a realistic result, since interactions between controls and hardware design have a significant impact on vehicles’ performance. In a study of development process improvements, Argonne National Laboratory and MathWorks integrated optimization and parallel computing methods with the system level simulation model of a midsize passenger PHEV with a 120-kW (peak power) permanent-magnet motor and a 110-kW gasoline engine. Four independent variables related to vehicle control and battery design—including battery storage capacity, maximum battery discharge power, gasoline engine turn-on, and turn-off thresholds—were tuned by the numerical optimizer to maximize the NPV over 30 real-world drive cycles.
The fuel and electrical energy consumptions of the PHEV were obtained from simulation using Autonomie (Figure 2), a modeling tool developed by Argonne based on MathWorks’ Simulink. Fuel savings were calculated for each battery size and energy management strategy. A direct-search optimization algorithm was used to generate an initial set of eight normalized variation coordinates in the four dimensions being searched. The initial eight-point grid was scaled to cover the entire range of the four design parameters so that local minima could be avoided.
At each of the eight initial points, all drive cycles were simulated in parallel computing rapid-accelerator operating mode to determine the NPV for each point. The four-dimensional coordinate with the highest NPV was then chosen as the new center-point of the optimization, and the span of subsequent variations was reduced until a 1% normalized parameter variation tolerance was met.
The optimization approach was chosen to avoid the problem of local minima and to provide a simple, robust approach to finding the global maximum NPV value. The four-variable optimization using 30 drive cycles per simulation required approximately 1000 simulations in total. The process was completed in approximately 4 h on a single quad-core PC.
Two optimization tests were conducted with long-term battery costs and short-term battery costs.
For the short-term estimates, the higher battery costs forced the optimizer to reduce the battery size as far as possible. The reduction in fuel consumption was enough to offset the battery cost, but it was not enough to justify the investment on a larger battery. A 2-kW·h battery with an 8-kW power discharge capacity would still result in higher PHEV fuel efficiency than a conventional vehicle. With the short-term battery cost estimates, the optimization algorithm did not find any increase in the benefit by increasing the battery size.
For the long-term cost estimates, when the battery is expected to be significantly cheaper than the current scenario, the algorithm chose a large 18-kW·h battery with a medium-power discharge capability of 40 kW. The optimum engine ON threshold was found to be 80 kW, and the OFF threshold was found at 10 kW. The 80-kW maximum power result suggested that the vehicle control algorithm did not find any incentive to use the engine while the battery was capable of providing the power for propulsion. The 80-kW result may have been different if emissions and penalties for frequent engine starts had been factored in.
This article is based on SAE technical paper 2010-01-2310 by P. Maloney of MathWorks and R. Vijayagopal, J. Kwon, and A. Rousseau of Argonne National Laboratory.