Solar concentrators offer good promise for reducing the cost of solar power. Planar waveguides equipped with a microlens slab have already been proposed as an excellent approach to produce medium to high concentration levels. Instead, we suggest the use of a cylindrical microlens array to get useful concentration without tracking during the day. To use only a seasonal tracking system and get the highest possible concentration, cylindrical microlenses are placed in the east–west orientation. Our new design has an acceptance angle in the north–south direction of $\pm 9°$ and $\pm 54°$ in the east–west axis. Simulation of our optimized system achieves a $4.6\times$ average concentration level from 8:30 to 16:30 with a maximum of $8.1\times$ and 80% optical efficiency. The low-cost advantage of waveguide-based solar concentrators could support their use in roof-mounted solar panels and eliminate the need for an expensive and heavy active tracker.