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To address the security and performance challenges, a novel smart grid communication system based on the frequency-hopping (FH) technology is investigated in this paper. A new FH sequence set with various levels of Hamming cross-correlation values is proposed for this system in order to endow the power users various qualities of services (QoSs). By using the real measurement, we propose a statistic model of the data collected from power grid. Based on the proposed FH sequence set and the data model, the analytic expression of the bit error rate (BER) of such a system with binary frequency shift keying (BFSK) modulation is derived under slow Rayleigh fading channel model. This expression firstly reveals the general relation among the BER, the properties of deterministic FH sequence and other system parameters and provides the guidance for the sequence design in the view of the system performance. The simulation results which are performed by using the real measurement data coincide with the analytical conclusions.