With demand for increased efficiency and smaller carbon footprint, power system operators are striving to improve their modeling, down to the individual consumer device, paving the way for higher production and consumption efficiencies and increased renewable generation without sacrificing system reliability. This dissertation explores two lines of research. The first part looks at stochastic continuous-time power system scheduling, where the goal is to better capture system ramping characteristics to address increased variability and uncertainty. The second part of the dissertation starts by developing aggregate population models for residential Demand Response (DR), focusing on storage devices, Electric Vehicles (EVs), Deferrable Appliances (DAs) and Thermostatically Controlled Loads (TCLs). Further, the characteristics of such a population aggregate are explored, such as the resemblance to energy storage devices, and particular attentions is given to how such aggregate models can be considered approximately convex even if the individual resource model is not. Armed with an approximately convex aggregate model for DR, how to interface it with present day energy markets is explored, looking at directions the market could go towards to better accommodate such devices for the benefit of not only the prosumer itself but the system as a whole.