In this paper, a new voltage stability constrained optimal power flow (VSC-OPF) model is developed using semidefinite programming (SDP), which optimally calculates the cost of increasing stability margins. The main advantages of the proposed method are, it a) incorporates voltage stability constraints in a convex optimal power flow (OPF) formulation, b) always finds the optimal solution in comparison with probable local optimum solutions while using other non-convex methods, and c) can compare the cost of increasing loading margin using convex relaxation. The effectiveness of this method is evaluated using the IEEE 14-bus and IEEE 118-bus test systems with various network constraints. The results show that the proposed convex formulation find the optimal operating schedule and critical loading point. The effect of incorporating voltage stability margin can also be examined using the proposed method.