This article investigates the age of information (AoI) performance in a wireless powered communication network (WPCN), where a sensor node (SN) harvests energy from an energy transmitter (ET) and then transmits status information to its data receiver (DR) by using the harvested and accumulated energy. The AoI penalty is used as a performance metric to characterize the nonlinear feature of dissatisfaction with data obsolescence at the DR. We derive the closed-form expressions of the average AoI penalty and the average peak AoI (PAoI) penalty with the Rician fading model. To further explore the system performance limit in terms of AoI penalty, we formulate two optimization problems to minimize the average AoI penalty and the average PAoI penalty with respect to the battery discharge threshold. Particularly, we reveal the conditions for the existence of the average AoI penalty and average PAoI penalty. Simulation results show that there exists a unique optimal battery discharge threshold that minimizes the system’s average AoI penalty and a unique optimal battery discharge threshold that minimizes the system’s average PAoI penalty. Moreover, as expected, the average AoI penalty and the average PAoI penalty decrease with the increment of the Rician $K$ -factor, and increase with the increment of the distance between ET and SN. Besides, the average AoI penalty and the average PAoI penalty first decrease with the increment of transmit power of ET and then tend to be flat. Additionally, a smaller data size of SN yields better system performance.