## 1 Introduction  
Unit commitment (UC) for the power utility determines the states (on/off) of each thermal generator over the scheduled time horizon. Recently, the problem of the high penetration of renewables in power systems has become important. [PERSON] et al. proposed a two-stage adaptive robust UC model for the security-constrained UC problem in the presence of nodal net injection uncertainty using Benders decomposition algorithm [1]. [PERSON] et al. projected all feasible generation and demand vectors onto the demand space and reformulated the UC within this loadability set [2]. Ignoring the uncertainty, [PERSON] et al. used a mixed integer linear programming based on different time-resolutions to study the UC problem, considering renewables [3]. On the other hand, demand response (DR) is the change in electric usage by end-use customers from their normal consumption patterns in response to changes in the electricity price associated with the retail market or incentive policies [4; 5; 6]. Customer participation in the DR program is a key factor to enhance the reliability in a modern smart grid. Traditionally, DR has been addressed in the scheduling of household appliances for their energy consumption in response to retail prices [7; 8] or the electricity prices in the day ahead power market [9]. [PERSON] et al. proposed a dynamic demand response controller that changed the set-point temperature to control HVAC loads, depending on electricity retail price, which was published each 15 min,and partially shifted some of this load away from the peak [10]. [PERSON] and [PERSON] developed a versatile DR optimization framework that used convex programming for the automatic load management of various household appliances in a smart home [11]. [PERSON] et al. proposed an algorithm to manage household loads according to their preset priorities and to guarantee that total household power consumption was below certain levels [12]. [PERSON] et al. proposed an approximate greedy iterative algorithm to schedule the energy usages of appliances of end-use customers. Each customer in the system will find the optimal start time and operating mode of each appliance in response to varying electricity prices [13]. DR can also be achieved by alternative approaches, such as aggregated load control [14; 15], plug-in electric vehicles [16] and frequency-related control [17]. [PERSON] et al. evaluated the thermostat setpoint control of aggregate electric water heaters for load shifting, and for providing a desired balancing reserve for the utility. This work also assessed the economic benefits of DR for customers considering time-of-use pricing [14]. [PERSON] et al. considered a third-party's management of the energy consumption of a group of users, and formulated the corresponding load scheduling problem as a constrained multi-objective optimization problem. The optimization objectives were to minimize the cost of consumed energy and to maximize a certain utility, which can be conflicting and non-commensurable [15]. [PERSON] et al. investigated a market in which users have the flexibility to sell back the energy generated by their distributed generators or the energy stored in their plug-in electric vehicles, using a distributed optimization algorithm [16]. [PERSON] et al. proposed an overall frequency restoration plan that considered the DR and spinning reserve. The DR program was used first to restore declining frequency caused by a large disturbance. The scheduled spinning reserve was then used to raise frequency back to the pre-disturbance level [17]. The concepts of DR, UC and renewable energy as they pertain to a power utility were recently integrated [18; 19; 20]. [PERSON] et al. investigated the economically driven and environmentally driven measures of DR programs and proposed a new linearized formulation of the cost-emission-based UC problem that was associated with DR program solved by mixed-integer programming [18]. [PERSON] et al.