In this paper, the uplink performance of cell-free massivemulti-input multi-output (mMIMO) system with the zero-forcing(ZF) and conjugate beamforming (CB) receivers is investigated. Anovel tight approximate rate expression for the ZF receiver is derived,which provides us with a tool for easily quantifying the impactsof the multi-antenna access point (AP), estimation error, pilotcontamination, and power control scheme. Then, leveraging on thetrackable ZF rate expression and the pre-studied CB rate expression,two power control algorithms are proposed. In particular, thefirst algorithm elaborates on maximizing the total rate, subjectingto the quality-of-service (QoS) constraint and each user power constraint. This algorithm utilizes the sequential convex approximationmethod to solve the non-convex issues. In addition, the secondaims at maximizing the rate of one user, in which the remainingusers can meet their QoS constraints. It can be characterized as ageometry programming. Simulation results are provided to showthat the ZF receiver is superior to the CB receiver in terms of sumrate and our proposed algorithms work well in many respects.