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Hitting control limits changes the behavior of the control systems and invalidates commonly adopted assumptions made when calculating the operating point of doubly fed induction generator (DFIG)-based wind turbines (WTs). The current computing methods rely on trials and errors and iterations. This paper proposes an optimization-based algorithm with control limits integrated into the problem formulation. Hitting or not hitting a control limit is modeled as a binary variable. Both rotor-side converter (RSC) current order limits and grid-side converter (GSC) current order limits are modeled in the proposed mixed-integer programming (MIP) formulation. For a WT with given terminal voltage and wind speed, the electrical and mechanical variables of the system can be computed directly from the optimization problem. The proposed formulation has included losses in the back-to-back converters and nonzero reactive power support through GSC. The computing results have been validated with the electromagnetic transient (EMT) simulation results. This formulation can help accurately detect whether control limits are hit for low voltage conditions and facilitate Type-III wind turbine fault ride through analysis.