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The paper proposes a methodology that determines control strategies of load shedding for restoring power-flow solvability in unsolvable cases using a new tool of outage-continuation power flow (OCPF). A specified outage from a set of multiple contingencies is modelled with a homotopy function, including a parameter representing the outage. The new tool traces the path of solutions satisfying the power-flow equations with respect to variations of the parameter. At the nose point, it performs a sensitivity analysis with a normal vector to identify the most effective control variables. With the sensitivity information, location of load shedding is determined; then, an adequate amount of control is decided by applying a searching method. In numerical simulation, an illustrative example of the proposed framework is shown applied to the New England 39-bus system.