We propose a nested Dantzig-Wolfe decomposition, combined with dynamic programming, for the distributed scheduling of a large heterogeneous fleet of residential appliances with nonlinear behavior. A cascaded column generation approach gives a scalable optimization strategy, provided that the problem has a suitable structure. The presented approach extends the TRIANA smart grid framework for predictive demand side management; the main goal of this framework is peak shaving. Simulations validate that the approach is effective, but also show that the performance degrades for smaller group sizes.