In recent years, there has been an increasing focus on real-time mobile applications, such as news updates and weather forecast. In these applications, data freshness is of significant importance, which can be measured by age-of-synchronization (AoS). At the same time, the reduction of carbon emission is increasingly required by the communication operators. Thus, how to reduce energy consumption while keeping the data fresh becomes a matter of concern. In this paper, we study the age-energy trade-off in a multi-source single-server system, where the server can turn to sleep mode to save energy. We adopt the stochastic hybrid system (SHS) method to analyze the average AoS and power consumption with three wake-up policies including N-policy, single-sleep policy and multi-sleep policy, and three packet preemption strategies, including Last-Come-First-Serve with preemption-in-Service (LCFS-S), LCFS with preemption-only-in-Waiting (LCFS-W), and LCFS with preemption-and-Queueing (LCFS-Q). The trade-off performance is analyzed via both closed-form expressions and numerical simulations. It is found that N-policy attains the best trade-off performance among all three sleep policies. Among packet management strategies, LCFS-S is suitable for scenarios with high requirements on energy saving and small arrival rate difference between sources. LCFS-Q is suitable for scenarios with high requirements on information freshness and large arrival rate difference between sources.