This research aims to develop solutions to relieve system stress conditions in electric grids. The approach adopted in this research is based on a new concept in the Smart Grid, namely, demand response optimization. A number of demand response programs with energy storage systems are designed to enable a community to achieve optimal demand side energy management. The proposed models aim to improve the utilization of the demand side energy through load management programs including peak shaving, load shifting, and valley lling. First, a model is proposed to nd the optimal capacity of the battery energy storage system (BESS) to be installed in a power system. This model also aims to design optimal switchable loads programs for a community. The penetration of the switchable loads versus the size of the BESS is investigated. Another model is developed to design an optimal load operation scheduling of a residential heating ventilation and air-conditioning system (HVACs). This model investigates the ability of HVACs to provide optimal demand response. The model also proposes a comfort/cost trade-os formulation for end users. A third model is proposed to incorporate the uncertainty of the photovoltaic power in a residential model. The model would nd the optimal utilization of the PV-output to supply the residential loads. In the first part of this research, mixed integer programming (MIP) formulations are proposed to obtain the optimal capacity of the (BESS) in a power system. Two optimization problems are investigated: (i) When the BESS is owned by a utility, the operation cost of generators and cost of battery will be minimized. Generator on/o states, dispatch level and battery power dispatch level will be determined for a 24-hour period. (ii) When the BESS is owned by a community for peak shaving, the objective function will have a penalty component for the deviation of the importing power from the scheduled power. MIP problems are formulated and solved by CPLEX.The simulation results present the effect of switchable load penetration level on battery sizing parameters. In the second part, a mixed integer programming (MIP) based operation is proposed in this part for residential HVACs. The objective is to minimize the total cost of the HVAC energy consumption under varying electricity prices. A simplied model of a space cooling system considering thermal dynamics is adopted. The optimization problems consider 24-hour operation of HVAC. Comfort/cost trade-o is modeled by introducing a binary variable. The big-M technique is adopted to obtain linear constraints while considering this binary variable. The MIP problems are solved by CPLEX. Simulation results demonstrate the effectiveness of HVAC's ability to respond to varying electricity price. Then, in the final part of this research, two Benders Decomposition strategies are applied to solve a stochastic mixed integer programming (MIP) formulation to obtain the optimal sizing of a photovoltaic system (PV) and battery energy storage system (BESS) to power a residential HVACs. The uncertainty of PV output is modeled using stochastic scenarios with the probability of their occurrence. Total cost including HVAC energy consumption cost and PV/battery installation cost is to be minimized with the system at grid-connected mode over eight hours subject to a varying electricity price. The optimization problem will nd the optimal battery energy capacity, power limit, a number of PV to be installed, and expected HVAC on/o states and BESS charging/discharging states for the next eight hours. This optimization problem is a large-scale MIP problem with expensive computing cost.