Solar powered cars may never be practical. Nevertheless, in the 1996 World Solar Challenge the Honda Dream carried two people 3000km across Australia at an average speed of 90km/h, powered only by sunlight. You clearly don?t need a 2500kg machine powered by polluting fuels to get you to work and back each day. The Australian Aurora 101 solar powered car requires less than 2000W of power to travel at 100km/h. To achieve such high performance the car has high aerodynamic efficiency, motor efficiency greater than 98%, low rolling resistance tyres, and weighs less than 280kg with the driver in it. The energy used to propel the car is generated by high-efficiency photovoltaic cells Another key to achieving high performance is efficient energy management. The car has a small battery that can store enough energy to drive the car about 250km at 100km/h. Energy stored in the battery can be used when extra power is required for climbing hills or for driving under clouds. More importantly, energy stored while the car is not racing can be used to increase the average speed of the car. How should the battery be used? The motivation for this problem was to develop an energy management strategy for the Aurora solar racing team to use in the World Solar Challenge, a triennial race across Australia from Darwin to Adelaide. The real problem? with weather prediction, detailed models of the car and numerous race constraints?is intractable. But by studying several simplified problems it is possible to discover simple rules for an efficient energy management strategy. The simplest problem is to find a strategy that minimises the energy required to drive a car with a perfectly efficient battery and a constant drive efficiency. The optimal strategy is to drive at a constant speed. This is just the beginning of the solar car problem, however. More general problems, with more general models for the battery, drive system and solar power, can be formulated as optimal control problems, where the control is (usually) the flow of power from or to the battery. By forming a Hamiltonian function we can use Pontryagin?s Maximum Principle to derive necessary conditions for an optimal strategy. We then use these conditions to construct an optimal strategy. The strategies for the various simplified problems are similar: ? On a level road, with solar power a known function of time, and with a perfectly efficient drive system and battery, the optimal strategy has three driving modes: maximum power, speed holding, and maximum regenerative braking. ? If the perfectly efficient battery is replaced by a battery with constant energy efficiency then the single holding speed is replaced by two critical speeds. The lower speed is held when solar power is low, and the upper speed is held when solar power is high. The battery discharges at the lower speed and charges at the higher speed. The difference between the upper and lower critical speeds is about 10km/h. There are precise conditions for switching from one mode to another, but small switching errors do not have a significant effect on the journey. ? If we now change from a level road to an undulating road, the optimal strategy still has two critical speeds. With hills, however, the conditions for switching between driving modes are more complex. Steep gradients must be anticipated. For steep inclines the control should be switched to power before the incline so that speed increases before the incline and drops while the car is on the incline. Similarly, for steep declines the speed of the car should be allowed to drop before the decline and increase on the decline. ? With more realistic battery models the optimal control is continuous rather than discrete. The optimal strategy is found by following an optimal trajectory in the phase space of the state and adjoint equations. This optimal trajectory is very close to a critical point of the phase space for most of the journey. Speed increases slightly with solar power. As before, the optimal speed lies within a narrow range for most of the journey. ? Power losses in the drive system affect the initial power phase, the final regenerative braking phase, and the speed profile over hills. The optimal speed still lies within a narrow range for most of the journey. ? With spatial variations in solar power it is possible to vary the speed of the car in such a way that the extra energy collected more than compensates for the extra energy used. Speed should be increased under clouds, and decreased in bright sunlight. The benefits of ?sun-chasing? are small, however. ? Solar power is not known in advance. By modelling solar power as a Markov process we can use dynamic programming to determine the target distance for each remaining day of the race. Alternatively, we can calculate the probability of completing the race at any given speed. These principles of efficient control have been used successfully since 1993 to develop practical strategy calculations for the Aurora solar racing team, winner of the 1999 World Solar Challenge. / Thesis (PhD)--University of South Australia, 2000
| Identifer | oai:union.ndltd.org:ADTP/284168 |
| Date | January 2000 |
| Creators | Pudney, Peter |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Copyright 2000 Peter Pudney |
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