Conventional planar solar concentrators own the merit of compactness but usually with some issues, such as complicated fabrication, complex assembly, low efficiency, etc. Our previous work investigated a kind of planar solar concentrators, the concentrator of the side-absorption concentrated photovoltaic system (SCPV) which consists of the single concentrating element and is rather compact, feasible for fabrication and assembly, as well as efficient. Since the angular acceptance is essential for concentrating photovoltaics, this study proposes two schemes to increase the acceptance angle of a SCPV. The first scheme optimizes the v-groove array reflector at the bottom of the concentrator by means of tracing the angular subtense of the sun, while the second scheme replaces the v-groove array with the parabolic groove by investigating a sacrifice region. The design principles and the numerical evaluations of the two schemes are reported, while the experimental results and the causes of efficiency loss are systematically analysed and discussed. The simulated results show that the acceptance angles of the first and the second schemes are enlarged by factors of 2.2 and 3.1, respectively, while the theoretical optical-efficiency of concentrator are 85.5% and 94.2%, respectively. Experimentally, the acceptance angle for the first scheme was measured as ±4.4° equivalent to an enlargement by a factor of 2.2 and agreeing with the simulation. From comparisons between modelling and experimental results, the causes of efficiency loss are thoroughly explored, and the approaches for further efficiency enhancement are presented. Moreover, since enlarging the acceptance angle of the concentrating photovoltaics eases the maintenance and reduces the expenses of the tracker, this work highlights the potential of the reported schemes for benefitting cost reduction, maintenance, compactness and weather endurance of the concentrated photovoltaic system.