In the near future power systems, efficient management of uncertainties with considering the system constraints without any simplification will be a challenge for system operators. Considering AC constraints leads to providing more accurate schedule of generating units, which can have a significant impact on the reduction of operating costs. Although numerous studies have been done to convexify AC optimal power flow constraints, most of the models are non-linear, which can be intractable for large-scale systems. In this study, a novel linear robust AC model is introduced using a combination of the quadratic convex relaxation (QCR) and the Frank-Wolfe algorithm for linearising the AC constraints. The uncertainties are modelled by applying the robust optimisation with recourse to obtain an optimal schedule for the conventional units in multiperiod real-time markets. The Benders-dual algorithm is implemented to solve the optimisation problem. The proposed model was applied to the IEEE 3-bus, 118-bus, and 300-bus systems. The results indicate that the proposed algorithm obtains more precise approximation than the QCR method. In addition, the costs and losses of the proposed model are less than those of the conventional robust DC and stochastic models. Furthermore, because the proposed model is linear, its runtime is rational. NomenclatureIndices i, j index of buses, 1 to N b t index of time intervals, 1 to T k index of generating units, 1 to N g w index of wind power plants, 1 to N w Decision variablest active/reactive power outputs of generating unit k in time interval t V i, t voltage magnitude of bus i in time interval t θ i, t the voltage phase angle of bus i in time interval t κ i, j, t auxiliary complex variable replacing the product of V i, t ∠θ i, t and V j, t ∠ − θ j, t ϑ i, t auxiliary variable replacing V i, t 2 cs i, j, t /sn i, j, t auxiliary variable replacing cos θ i, t − θ j, t /sin θ i, t − θ j, t . σ i, j, t /ψ i, j, t auxiliary variable replacing the real/imaginary parts of κ i, j, t Λ i, j, t auxiliary variable replacing the product of V i, t