This paper proposes two second-order continuous-time algorithms to solve the economic power dispatch problem in smart grids. The collective aim is to minimize a sum of generation cost function subject to the power demand and individual generator constraints. First, in the framework of nonsmooth analysis and algebraic graph theory, one distributed second-order algorithm is developed and guaranteed to find an optimal solution. As a result, the power demand constraints can be kept all the time under appropriate initial condition. The second algorithm is under a centralized framework, and the optimal solution is robust in the sense that different initial power conditions do not change the convergence of the optimal solution. Finally, simulation results based on five-unit system, IEEE 30-bus system, and IEEE 300-bus system show the effectiveness and performance of the proposed continuous-time algorithms. The examples also show that the convergence rate of second-order algorithm is faster than that of first-order distributed algorithm.