This paper is motivated by the open questions concerning the ability to compute the global optimum of nonlinear state estimators (SE). The major cause of these problems comes from the highly nonlinear functions relating measurements and voltages defined by the AC power flow models. Conventional approaches in today's AC electric power system SE are prone to sub-optimal solutions, which, in turn, creates unacceptably large differences between the true and estimated voltages. In this paper, we first formulate the problem as an equivalent convex optimization problem. We then account for the specific structure of the problem, and arrive at an efficient algorithm for finding the global optimum, namely the most accurate estimate of the state. Notably, under the no noise assumption this approach for the first time solved the problem exactly. Further, we show that our estimate is close to the global optimum even when measurement noise is present, while currently used SE only finds a local optimum. Simulations are shown to illustrate improved results obtained using the SE formulation proposed in this paper over the results obtained using today's SE.