CRITICAL SPEED CONTROL OFA SOLAR CAR 105 solar power (W) critical speed (km/h) 92 91 90 89 88 87 86 85 1500 1000 500 0 Figure5 . The critical speed v * increases with solar power. 0 10 20 30 40 50 60 70 80 … Optimization and Engineering, 3,97-107,2002 c*2002 KluwerAcademic Publishers. Manufactured in The Netherlands. Critical Speed Control ofa Solar Car PETERPUDNEY, PHILHOWLETT Centre for Industrial and Applicable Mathematics, University of South Australia, Mawson Lakes, Australia 5095 email: peter .pudney@unisa.edu.au email: phil.howlett@unisa.edu.au

Abstract. The World Solar Challenge isa 3000 kmraceforsolar powered cars across the Australian continent from Darwin to Adelaide. Each car is powered by a panel of photovoltaic cells which convert sunlight into electrical power. The power can be used directly to drive the car or stored in a battery for later use. Previous papers (P. Howlett, P. Pudney, T. Ta rnopolskaya, and D. Gates, IMA Journal of Mathematics Applied in Business and Industry vol. 8, pp. 59-81,1997; P.G. Howlettand P.J. Pudney, Dynamics of Continuous, Discrete and Impulsive Systems vol. 4, pp. 553-567,1998) using a simplified model of the battery, have shown that the optimal strategy is essentiallyaspeedholding strategy. In this paper, with a more realistic model of the battery, we show that the optimal driving strategy is a critical speed strategy. For an optimal journey with no beginning and no ending the solar car must always travel at the critical speed. For an optimal journey of finite length the speed must be close to the critical speed for most of the journey. The critical speed depends on the solar power and will normally vary slowly with time. Keywords: solar power, optimal control, energy-efficiency 1. Introduction The WorldSolar Challenge isa 3,000 kmraceforsolar powered cars across the Australian continent from Darwin to Adelaide. The 1999 race was won by the Aurora 101 usinga driving strategy devised by the Scheduling and Control Group at the University of South Australia. Although the daily solar radiation was estimated usinga Markovmodelthe short term driving strategy was essentially the strategy described in this paper. The Aurora 101 is shown in figure 1. The main components ofasolarcararea panel of photovoltaic cells which convert sunlight into electrical power, an energy storage system which is usually a battery and a traction system with motor controllers, an electric motor and driven wheels. The driver controls the power applied to the traction system. Extra power can be drawn from the battery if required and excess solar power can be stored. The cars have a mechanical friction brake and a regenerative braking system. The mechanical brake is essentiallya safety mechanism and will be ignored. We assume that the road is level and that the solar power is known in advance1 although we do not assumea particular formula. The rules for the World Solar Challenge specify maximum dimensions for the car and the solar panels and a maximum size for the battery. Up to five kilowatt-hours of electrical energy maybe stored in the battery. This provides enough energy to travel about 250 km at 90km/h. The cars race for nine hours each day. The aim of the race is to promote the use of solar energy and to encourage the development of energy-efficient technology such

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