Non-orthogonal multiple access (NOMA) is recognized as a promising radio access technique for the next generation wireless systems. We consider a practical downlink NOMA system with imperfect successive interference cancellation and derive bounds on the power allocation factors for a given number of users in each cluster. We propose a minimum signal-to-interference-plus-noise ratio difference criterion between two successive NOMA users in a cluster of users to achieve higher rates than an equivalent orthogonal multiple access (OMA) system. We then propose adaptive multi-user clustering and power allocation algorithms for downlink NOMA systems. Through extensive simulations, we show that the proposed algorithms achieve higher rates than the state-of-the-art algorithms.