It is known that compound parabolic concentrators (CPCs) can improve electrical performance of a photovoltaic (PV) flat-plate system. However, a lumped electrical model of a PV cell/module with CPC for assessing performance under different operating conditions is unavailable. In this paper, a six parameter based model is developed and applied to a PV cell, two PV models with CPC, and a PV module with 2D asymmetric CPC (trough). For validation, CPC with a single PV cell and two CPC modules with 2 x 2 and 9 x 9 PV cells are fabricated and measured in an indoor laboratory under standard test conditions. Results show that the optimised algorithm precisely predicts the six model parameters. A sensitivity analysis is performed to identify the importance of each parameter in the model. Ideality factor, circuit current and reverse saturation current are found to be the most dominant factor, while shunt resistance is the least important with CPC gain coefficient and series resistance are in between. Transient performance of a PV cell with CPC under variable outdoor climate conditions is also examined by coupling optical, thermal and electrical effects. (C) 2016 The Authors. Published by Elsevier Ltd.