## 1 Introduction  
One of the major thrust areas of demand side management (DSM) is demand response (DR) which is defined as a set of actions taken to reduce users' electricity consumptions in response to higher market prices or market incentives [1]. Moreover, system operators may apply DR programs to reduce the load temporarily in emergency grid conditions such as unit outage or unpredictable change in renewable generation [2, 3]. Therefore, the main idea of DR is to encourage customers to manage their consumption patterns in a way not only to maximize their own utility, but also to support safe operation of the power system [4]. According to the Federal Energy Regulatory Commission (FERC), DR programs can be classified into two major categories, namely, time-based rate (TBR) and incentive-based programs (IBPs) [5]. In TBR programs (also known as price-based DR programs [6]), time-varying prices are given to consumers based on the electricity price in different time periods, encouraging them to change their consumption level in response to the changing price signals. On the other hand, in IBP schemes,customers are offered fixed or time-varying incentives, to reduce their electricity consumption during periods of system stress, however they would be penalized for no participation in the program [7]. The focus of this paper is on TBR programs which are mainly divided into three categories, real-time pricing (RTP), time of use (TOU), and critical peak pricing (CPP) programs. These programs are well-suited for implementation in residential areas (e.g., residential microgrids (MGs)) where there are more possibilities for load management purposes [8; 9; 10; 11]. However, there exist a number of challenges, such as rebound peaks during low cost periods and service interruptions. Moreover, the presence of uncertain elements within an environment such as wind and photovoltaic (PV) power generation imposes development of sophisticated balancing mechanisms between supply and demand to meet the system stability. Therefore, TBR models need to be well-designed and implemented to provide efficient operating conditions for such systems in presence of uncertainties. Regarding the MG scheduling under uncertainty, much research has been done recently [12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. The effect of wind energy forecast errors on the network-constrained market-clearing problem, in which energy and reserve are simultaneously dispatched, was investigated in [12; 13] using two-stage stochastic programming models. Based on the proposed method in [12], cost of MG was minimized with regard to the uncertainty of renewable energy resources (RESs). In [13], optimal dispatch of a MG was presented with regard to emissions and fuel consumption cost minimization using heuristic optimization. Authors in [14; 15] exploited MG management as a multi-objective optimization problem to mitigate emission level as well as operation and maintenance costs. To obtain efficient energy management, artificial intelligence techniques were also used with multi-objective optimization programming [16]. However, in the reviewed literature, the procurement of the MG reserve (in terms of spinning and/or non-spinning reserve) for reliable operation of the system has been neglected. To address this issue, effective methods for providing reserve in typical MGs with high penetration of RESs are developed based on DR programs [17; 18; 19]. In [17], a day-ahead market structure was presented where DR can provide contingency reserves through a bidding procedure representing the cost of load curtailment. Also, authors in [18] introduced a price-responsive DR action for optimal regulation service reserve provision under high levels of wind penetration. The same type of study was carried out in [19], considering load uncertainty and generation unavailability as different working scenarios.