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The paper introduces a robust methodology for evaluating complex electricity system efficiency, making several contributions. It systematically decomposes the electric power system into various processes, including power generation, transmission, distribution, and power consumption, with parallel sub-processes for production and domestic power consumption. Employing data envelopment analysis (DEA), the paper develops a network directional slacks-based (DSB) model to evaluate the whole system and the internal processes. The model is theoretically proven to be feasible, providing efficiency scores and identifying inefficiencies in the system and its processes. A noteworthy addition is the introduction of the DSB green Luenberger productivity index and its decomposition, offering an analysis of productivity changes in electricity systems. Empirical analysis covering 30 Chinese provinces from 2013 to 2019 uncovers the performance variations among provinces and processes, pointing out inefficiencies and changes in technology and efficiency over time. The empirical findings aim to support efforts in enhancing the overall efficiency of China's interprovincial power system. • We decompose the complex electric power system into four processes with dependence. • We build a network directional slacks-based (DSB) model for the complex power system. • We give a DSB green Luenberger productivity index (DPI) for our network model. • The efficiency score and DPI of the system are decomposed into those of processes. • We apply the model and indexes to electric power systems in Chinese provinces. [ABSTRACT FROM AUTHOR]