A downlink cell-free massive Multipleinput multiple-output (mMIMO) system is explored. To investigate the impact of hardware distortion on downlink cell-free mMIMO, this paper recalls a well-established model of hardware impairment and derives a new closedform downlink per-user Spectral efficiency (SE) expression for distributed conjugate beamforming precoding. Based on this trackable expression, two power control algorithms, namely max-total-SE and mixed Quality-of-service (QoS) algorithms, are proposed. Numerical results indicate that the downlink per-user SE is primarily limited by the hardware quality of the receiver, especially when the user corresponds to the receiver. In addition, the proposed max-total-SE algorithm has a fast convergence rate and can significantly improve the total SE compared to the Equal power control (EPC) scheme. What's more, our mixed QoS algorithm also performs well in many respects.