Building-integrated photovoltaics (BIPV) makes it possible to utilize building surfaces for power generation. However, BIPV is facing challenges of high material costs, difficulty of scaling, and inefficient collection of indirect solar radiation. Therefore, solar concentrators collecting non-normal-incidence sunlight while maintaining concentration factors are promising for economic non-active-tracking photovoltaic systems. Here, we demonstrate a new design for dielectric total internal reflection concentrators (DTIRCs) that increase both the acceptance angle and the concentration ratio with tunable side and top profiles, and calculate the annual collectible sun power to prove that our new design receives more power compared to traditional concentrator designs.