Nineteenth Mathematical and Statistical Modeling Workshop for Graduate Students

Concentrating solar energy and transforming it into electricity is clean, economical and renewable. One design of solar power plants consists of an array of heliostats which redirects sunlight to a central receiver tower and the generated heat is converted into electricity. Currently, the angles of elevation of heliostats are controlled by motors and drives that are costly and require diverting power that can otherwise be used for producing electricity. Photosensitive smart materials exist which change their shape due to light. The light causes their molecular structure to kink and in turn the entire material deforms. We present an application of how such a material may be beneficial for replacing the motor mechanism in small heliostats. In particular, a mathematical model is derived which shows the dependence of the angle of elevation on the required photostrain, composition of the photosensitive smart material, intensity and temperature of light and angle of light polarization. For example, a photomechanical rod structure can provide 60◦ elevation for temperatures of about 40◦C and "kink" compositions greater than 90%. Photostrains of about 1% to 10% are desired for both implementations to provide sufficient tilt under most conditions. With the same composition, the beam structure can generate more tilt at lower temperatures.