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This paper develops and presents the steady-state, fundamental-frequency model of the single-phase distributed energy resource (DER) unit which utilizes a single-phase voltage-sourced converter (VSC) as the interface medium. The model represents: 1) different operating and control modes and 2) the operational constraints and limits of the VSC and the host grid. The model is included in a sequential power-flow analysis method using: 1) a backward-forward sweep algorithm for single-phase laterals and 2) a sequence-components frame solver for three-phase networks. The interface-VSC operating limits are accommodated in the power-flow algorithm as an interleaved step to increase computational efficiency of the power-flow analysis tool. Case studies are conducted to evaluate and verify 1) the accuracy of the proposed model and 2) the computational efficiency of the power-flow algorithm.