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In this paper, we consider the problem of power control and load balancing in the uplink of the cell-free (CF) multi-user (MU) massive multiple-input multiple-output system. The power control problem is solved using three different criteria: 1) power minimization; 2) maximize min quality of service (QoS); and 3) maximize sum spectral efficiency (SE) under imperfect channel state information. While power minimization and min-QoS maximization problems can be solved in polynomial time, sum SE maximization is NP-hard. Hence, we apply a successive approach to convert it into a geometric program and achieve near optimum solution. As the number of connections in CF-MU system is large, we minimize the number of base stations (BSs) serving each user while maintaining the optimized power consumption and QoS from the previous stage. We propose an iterative elimination (IE) algorithm to remove ineffective BSs …