With the rapid development of the electricity market and the increasingly stringent operational standards, the longstanding infeasible network-constrained unit commitment (NCUC) issue in market operations is calling for effective and systematic methods that can analyze and repair infeasible NCUC models. Studies show that a set of irreducible infeasible subsets (IISs) may lead to infeasibility in a model. The identification and repair of IISs can correct the original infeasible model, while traditional filtering algorithms for IIS location often exhibit computational inefficiency. A fast infeasibility analysis framework of NCUC and a relaxation filtering algorithm are proposed in this paper to analyze infeasible NCUC models more comprehensively and effectively. The infeasibility analysis framework employs subsystem-based IIS analysis method, generating and analyzing simplified models to repair the infeasible NCUC. The relaxation filtering algorithm can achieve greater effectiveness of IIS identification in the holistic NCUC compared with traditional general filtering algorithms. The case studies show that the proposed framework and algorithm can analyze and repair infeasible NCUC models effectively, reducing the analytical time by at least one order of magnitude compared with that of traditional general methods.