Contingency constrained economic dispatch has been an extensively studied research topic. However, most existing works assume that the load demands at all buses are given. Such an assumption works well for conventional power grids, where the load demands are relatively easy to predict. We can select a few representative demand profiles and perform economic dispatch over them. However, such a practice will no longer work in smart grids, where the load demands fluctuate dramatically. We will need a huge number of demand profiles to cover all possible scenarios, which is computationally expensive. To address the problem, we propose a parameterized stochastic model through independent component analysis to capture both the spatial and temporal correlation of the load demands. Although this stochastic version of the contingency constrained economic dispatch problem is more difficult to solve, we show that it can be cast as a Semi-Infinite Programming problem, a solution to which can be established by adopting the Multivariate Remes Exchange framework. Our experiments based on IEEE power system testcases and data from Electric Reliability Council of Texas (ERCOT) have shown that our approach can achieve over 30x speedup with a similar generation cost when compared to the conventional practice of considering a number of demand profile samples and when the dispatch solutions from both methods satisfy the contingency constraints over all possible profiles. © 2011 IEEE.