Demand Response (DR) is one of the solutions that can help achieve the goals in the smart grid paradigm. One of the main challenges regarding the scheduling of demand-responsive appliances is the unpredictability of energy consumption patterns. This unpredictability in consumption could bring about unwanted discomfort for the energy consumer and inaccurate estimation of costs. This phenomenon is even more impactful when thermostatically controlled loads (TCA) are used as demand-responsive appliances. In chapter one, The Electric Water Heater (EWH) was chosen as a TCA appliance since it consumes a large portion of energy. At the same time, it has good insulation, which enables it to preserve energy for an extended period. Given the uncertainty challenge in energy consumption, in chapter one, a statistical optimization method was developed to address the unpredictable hot water usage for scheduling EWHs. On top of the stochastic optimization framework, a new cost-based treatment of discomfort (due to the use of DR that can cause underheated water) was introduced. Given these two Improvements in the appliances modeling, a new stochastic comfort-based optimization model was developed to minimize the electric and discomfort cost based on the probability of energy usage.

In Chapter two of this dissertation, a new method to increase the photovoltaic self-absorption was introduced. One of the challenges to increasing the share of solar energy in power systems is the uneven generation of solar energy, where most of the energy production happens in the middle of the day. The uneven generation causes numerous challenges for operating a grid with a large share of solar energy. In chapter two, a new approach to increase the PV self-absorption based on the aforementioned comfort- based model in chapter one was developed for EWH. Using this method, the EWH can act as a virtual battery by utilizing the thermal energy storage of the EWH. The EWH can absorb solar energy as thermal energy in the middle of the day. This self-absorption method was developed as an optimization method that aims to minimize the cost of electricity. By using this method, the daily operational cost of electricity usage is reduced, but also the capital cost for the installation of solar systems is reduced as well. This reduction happens since the EWH can act as thermal energy storage in the midday and reduce the need for large batteries in solar systems.

Chapter three of this dissertation is focused on developing a coordination mechanism for price responsive devices (PRD). In a power system with a large share of PRDs, it would be very challenging to reach a balance between generation/consumption where customers bid for energy based on the electricity price. I.e., a change in the price signal (which is supposed to be a function of the expected consumption pattern) yields a considerable change in PRDs energy bids. This phenomenon makes reaching a balance between generation and consumption very challenging. The third chapter of this dissertation proposes a distributed PRD coordination algorithm based on the Dantzig-Wolfe (DW) decomposition method. In this fashion, the self-benefiting PRDs are modeled as subproblems in the DW algorithm. The algorithm is solved iteratively while each iteration at the device level is solved simultaneously, making the algorithm reach the optimal point very rapidly. When the algorithm is solved (at the optimal point), no PRD is willing to change its consumption plan.