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In this paper, an extended optimal power flow model (EOPF) is presented to restore the solvability of optimal power flow (OPF). In this model, slack variables to equality constraints and inequality constraints are added; meantime, penalty items corresponding to the slack variables are added to objective function. The extended model is solved by improved primal-dual interior point method. Test results of examples show that: if the original problem is solvable, optimal solution of original problem can be obtained; if the original problem is unsolvable due to the violations of constraints or control variables, it can quickly and automatically search for an approximate solution in an expanded region, as well as point out clearly the key constraints leading to insolvability of original problem. Thus the adjustive measures, including active power supplement, reactive power compensation or security constraint indices corrections, can be obtained conveniently. The improved model and algorithm prove to have a good convergent property and can be applied to several aspects.