NarrowBand-Internet of Things (NB-IoT) is a new 3GPP radio access technology designed to provide better coverage for a massive number of low-throughput low-cost devices in delay-tolerant applications with low power consumption. To provide reliable connections with extended coverage, a repetition transmission scheme is introduced to NB-IoT during both Random Access CHannel (RACH) procedure and data transmission procedure. To avoid the difficulty in replacing the battery for IoT devices, the energy harvesting is considered as a promising solution to support energy sustainability in the NB-IoT network. In this work, we analyze RACH success probability in a self-powered NB-IoT network taking into account the repeated preamble transmissions and collisions, where each IoT device with data is active when its battery energy is sufficient to support the transmission. We model the temporal dynamics of the energy level as a birth-death process, derive the energy availability of each IoT device, and examine its dependence on the energy storage capacity and the repetition value. We show that in certain scenarios, the energy availability remains unchanged despite randomness in the energy harvesting. We also derive the exact expression for the RACH success probability of a {randomly chosen} IoT device under the derived energy availability, which is validated under different repetition values via simulations. We show that the repetition scheme can efficiently improve the RACH success probability in a light traffic scenario, but only slightly improves that performance with very inefficient channel resource utilization in a heavy traffic scenario.