## 1 Introduction  
In recent years, governments have provided many incentives to increase the proportion of renewable energy sources (RES) in the power system, such as wind or solar power. As a result, not only is the ever-increasing electricity demand satisfied but also the consumption of fossil fuel sources and greenhouse gas emissions, which are the main causes of climate change, are reduced. However, due to the inherent uncertainty in wind speed and solar radiation, it is impossible to predict the RES' maximum available power output accurately. Therefore, preparing the operating plan and maintaining the power balance become more challenging. In addition, RESs often have a typically small rated capacity, especially rooftop PV systems whose sizing can be less than 10 kW. From the system operator's viewpoint, it is almost impossible to control such small-scale distributed RESs; consequently, small-scale distributed RESs are not allowed to participate directly in the electricity market [1; 2; 3; 4]. The virtual power plant (VPP) concept seems to be an appropriate solution to these issues. According to this concept, VPP can integrate many dispersed small-scale RESs and consumers and then participate in the electricity market on their behalf. From the system operator's viewpoint, these RESs and consumers can be treated as a unified market agent acting as a supplier or a consumer (named \"prosumer\") depending on the difference between RES' available power output and actual local demand each hour. A significant advantage of this model is the ability to manage and control many resources without being limited by geographical location [5; 6; 7; 8]. In addition, VPP can integrate flexible load and energy storage systems (ESS) and coordinate them with the operation of RES; as a result,the surplus or lack of power due to the uncertainty in RES can be eliminated. Depending on whether the technical constraints of the network connecting internal sources are considered, a VPP can be a commercial VPP (CVPP) or a technical VPP (TVPP) [8]. So far, the VPP model has been developed in several countries, such as Australia, Germany, and Canada, and the potential of this model can be shown in [9; 10; 11; 12]. The report [9] also indicates that VPP can participate in both energy and ancillary services markets, such as providing frequency regulation or reserve power. In the literature, many studies focus on the VPP's optimal trading strategy in different markets, aiming to maximize the VPP's profit [13]. Depending on the type of market the VPP participates in, different optimal scheduling models have been launched to optimally coordinate the VPP's components and maximize the VPP's profits. For instance, studies [14; 15; 16] only consider the role of VPP in the day-ahead (DA) market, while in studies [17; 18], the authors assume that their VPPs participate in the joint DA and intraday (ID) markets. Some more recent studies [19; 20; 21; 22; 23; 24] consider the VPP's trading strategy in both DA and balancing markets. Note that the balancing market includes the balancing capacity (BC) market and the balancing energy (BE) market and plays an essential role in maintaining the system frequency and stabilizing power system operation. The BC market is cleared at least one day before the operating day. In this market, the reserve providers, called active agents, trade their reserve capacity. The BE market operates closer to real-time, in which the active providers' reserve capacity is activated. Some power plants/customers can sell/buy their surplus/shortage of energy at that time in the BE market, and they are called passive agents. To participate in the BC market, the reserve providers must satisfy several requirements, such as response time or minimum bid volume [25; 26; 27]. Therefore, small and uncertain sources often do not participate in the BC market but only act as passive agents in the BE market.