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Smart grid is a modern infrastructure for improving the efficiency and reliability of power grid by integrating automated control, sensing and metering technologies, modern communication infrastructure and modern energy management techniques. Security and quality-of-service (QoS) are two most critical requirements for the communications network in smart grid. Frequency hopping (FH) technology, due to its inherent security, is a promising candidate technology in the physical layer of smart gird communication infrastructure. Unfortunately, all the existing FH systems can support only a single level of QoS due to the fact that traditional FH sequence sets can provide the same level of Hamming cross-correlation. In this paper, an FH-based communication network is developed for smart grid, particularly the advanced smart metering (AMI), to address the above two key challenges. A novel type of FH sequence set which meets the multi-level QoS requirement is designed. Then, the data traffic in AMI is investigated and modeled as a general Poisson process which is validated by real measurements of power consumptions. With the proposed sequence set and data model, the analytic performance in terms of error probabilities for the proposed FH communication with M-ary frequency-shift keying (FSK) modulation is derived for a slow Rayleigh fading channel. The analytic results are validated by numerical simulation results.