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By taking the data-receiving energy consumption into account, we propose an extended analytical model to derive the optimal parameters-the number of clusters for wireless sensor networks. Our analyses show that the previous existing model underestimates the optimal number of clusters within a sensor network. The simulation results verify our analyses and demonstrate the modified model is more accurate in deriving the optimal number of clusters to maximize the network lifetime of the wireless sensor networks. Using our extended model, we also develop the energy-threshold-driven based clustering reconfiguration schemes with the optimal number of clusters to further improve the wireless sensor-network lifetime. The simulation experiments indicate that our clustering reconfiguration schemes outperform the existing ones in terms of sensor-network lifetime while imposing low overhead due to clustering reconfigurations.