Since the stations (STAs) are usually powered by batteries in the wireless local area network (WLAN), the energy consumption of STAs is of great importance. The target wake time (TWT) mechanism is designed to save energy in the WLAN. Besides, the multi-link operation (MLO) technology is proposed recently to achieve the extremely high throughput transmissions in the WLAN. In this paper, we study the TWT with the newly proposed MLO. We analyze the impact of TWT and MLO both on the energy consumption of STAs. We optimize the TWT and MLO jointly with the goal of energy minimization for STAs. Through adjusting the LI parameter in TWT and the traffic allocation in MLO, we balance the tradeoff among energy consumption, transmission delay, queueing stability, as well as multi-link scheduling in WLANs. We formulate this energy optimization problem as a mixed-integer non-convex problem, and design a multi-link optimal algorithm to optimally solve it. Simulation results show that the proposed scheme has a great advantages in terms of energy consumption.