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Physical layer security is known as a promising paradigm to ensure security for the beyond 5G (B5G) networks in the presence of eavesdroppers. In this paper, we elaborate on a tractable analysis framework to evaluate the reliability and security of wireless-powered decode-and-forward (DF) multi-relay networks. The nonlinear energy harvesters, in-phase and quadrature-phase imbalance (IQI) and channel estimation errors (CEEs) are taken into account in the considered system. To further improve the secure performance, two relay selection strategies are presented: 1) suboptimal relay selection (SRS); 2) optimal relay selection (ORS). Specifically, exact analytical expressions for the outage probability (OP) and the intercept probability (IP) are derived in closed-form. For the IP, we consider that the eavesdropper can wiretap the signal from the source or the relay. In order to obtain more useful insights, we carry out the asymptotic analysis and diversity orders for the OP in the high signal-to-noise ratio (SNR) regime under non-ideal and ideal conditions. Numerical results show that: 1) Although the mismatches of amplitude/phase of transmitter (TX)/receiver (RX) limit the OP performance, it can enhance IP performance; 2) Large number of relays yields better OP performance; 3) There are error floors for the OP because of the CEEs; 4) There is a trade-off for the OP and IO to obtain the balance between reliability and security.