Accurate, efficient and reliable parameter extraction of solar photovoltaic (PV) models from the measured current-voltage (I-V) characteristic curves is important for evaluation, modelling, and diagnosis of the actual operating state of in-situ PV arrays. In recent years, numerical heuristic optimization algorithms based parameter extraction methods have been proposed. However, the efficiency and reliability of these methods are limited due to heuristic or stochastic searching strategies. In this paper, by combining the trust-region reflective (TRR) deterministic algorithm with the artificial bee colony (ABC) metaheuristic algorithm, a new hybrid algorithm ABC-TRR is proposed to improve the parameter extraction of PV models. The ABC-TRR algorithm combines the global exploration capability of the ABC and the local exploitation of the TRR, which achieves a good tradeoff among accuracy, convergence and reliability. The proposed ABC-TRR hybrid algorithm is evaluated and compared with other state-of-the-art algorithms using the standard I-V curves of the benchmark Photowatt-PWP201 PV module and RTC France solar cell as well as the measured I-V curves of a laboratory PV module/string/array. Comprehensive experimental analysis and comparison results demonstrate that the proposed ABC-TRR algorithm achieves the same level of accuracy as the best reported algorithms with the highest overall reliability. More importantly, the ABC-TRR algorithm converges 4.69 times faster than the best-reported algorithms on average. In view of these advantages, the proposed ABC-TRR algorithm is a promising altemative for accurately, efficiently and reliably extracting the parameters of PV models from measured I-V curves. In addition, it was experimentally demonstrated that the parameter extraction result can be used to indicate the partial shading and abnormal degradation conditions.