The full utilization of broadband solar irradiance is becoming increasingly useful for applications such as long-term space missions, wherein power generation from external sources and regenerative life support systems are essential. Luminescent solar concentrators (LSCs) can be designed to separate sunlight into photosynthetically active radiation (PAR) and non-PAR to simultaneously provide for algae cultivation and electric power generation. However, the efficiency of LSCs suffers from high emission losses. In this work, we show that by shaping the LSC in the form of an elliptic array, rather than the conventional planar configuration, emission losses can be drastically reduced to the point that they are almost eliminated. Numerical results, considering the combined effects of emission, transmission and surface scattering losses show the optical efficiency of the elliptic array LSC is 63%, whereas, in comparison, the optical efficiency for conventional planar LSCs is 47.2%. Further, results from numerical simulations show that elliptic array luminescent solar concentrators can convert non-PAR and green-PAR to electric power with a conversion efficiency of ~17% for AM1.5 and 17.6% for AM0, while transmitting PAR to an underlying photobioreactor to support algae cultivation.