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• Method is independent of initial guess of allowable transaction for ATC calculation. • Accurate computation of ATC, even under stressed system condition. • Fast computation of ATC in comparison with NRPF based method. • Proposed method is tested and validated on IEEE 30, 118 and 300-bus test system. • Tested for bilateral and multilateral transactions at different operating points. Available Transfer Capability (ATC) is the additional power that can be securely and reliably transacted over and above the already committed transactions in a power network. In the electricity market, where every player (power producer and consumer) tries to earn higher profit, quick and accurate assessment of ATC of the power network is a prime concern. Holomorphic Embedding (HE) is a novel and non-iterative way of solving the Power Flow (PF) equations, which guarantees to find the operational High Voltage (HV) solution, in case it exists. Analytic continuation extends the domain of convergence of non-analytic functions to have voltage solutions. This paper, thus, proposes an extremely efficient and accurate approach for evaluation of ATC using the Holomorphic Embedded PF (HEPF) considering the intact system condition and N - 1 contingency situations. This approach is successfully tested on IEEE 30 bus, IEEE 118 bus, and IEEE 300 bus systems for various bilateral and multilateral transactions. The results, thus, obtained prove the efficacy of the proposed approach in comparison with those obtained from the repeated Newton-Raphson PF (NRPF), Fast Decoupled PF (FDPF) and Continuation PF (CPF) based methods. [ABSTRACT FROM AUTHOR]