Automation metering services, load forecasting and energy feedback are among the great benefits of smart meters. These meters are usually connected using Narrowband power Line Communication (PLC) to transmit the collected waveform readings. The huge volume of these streams, the limited-bandwidth, energy and required storage space pose a unique management challenge. Compression of these streams has a significant opportunity to solve these issues. Therefore, this paper proposes a new lossless smart meter readings compression algorithm. The uniqueness is in representing smart meter streams using few parameters. This is effectively achieved using Gaussian approximation based on dynamic-nonlinear learning technique. The margin space between the approximated and the actual readings is measured. The significance is that the compression will be only for margin space limited points rather than the entire stream of readings. The margin space values are then encoded using Burrow-Wheeler Transform followed by Move-To-Front and Run-Length to eliminate the redundancy. Entropy encoding is finally applied. Both mathematical and empirical experiments have been thoroughly conducted to prove the significant enhancement of the entropy (i.e. almost reduced by half) and the resultant compression ratio (i.e. 3.8:1) which is higher than any known lossless algorithm in this domain.