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A cell-free massive multiple input multiple output (MIMO) system is an attractive network model that is in the spotlight in 5G and future communication systems. Despite numerous advantages, the cell-free massive MIMO system has a problem in that it is difficult to operate in reality due to its vast amount of calculation. The user-centric cell-free massive MIMO model has a more feasible and scalable benefit than the cell-free massive MIMO model. However, this model has the disadvantage that as the number of users in the area increases, there are users who do not receive the service. In this paper, the proposed scheme creates connections for unserved users under a user-centric scheme without additional access point (AP) installation and disconnection for existing users. A downlink user-centric cell-free massive MIMO system model in which the APs are connected to the central processing unit (CPU) and the APs and users are geographically distributed is considered. First, the downlink spectral efficiency formula is derived and applied to the user-centric cell-free massive MIMO system. Then, the proposed scheme and power control algorithm are applied to the derived formula. The simulation results show that the unserved users within the area disappear by using the proposed scheme, while the bit error rate (BER) performance and sum rate improve compared to the existing scheme. In addition, it is shown that the proposed scheme works well even with a very large number of users in the area, and a significant service performance improvement for the worst 10% of users and the overall improvement of per-user throughput for the bottom 70% of users are ensured. [ABSTRACT FROM AUTHOR]