## 2 Problem Description  
### Coordination between the VPP and the Power Market  
With the high penetration of RESs in the power system, the grid's operational framework changes. References [33; 34] show that installing and connecting the ESS in the power system to support RESs provides ancillary services, and leverage energy arbitrage opportunities are increasingly interested. Some electricity markets, such as AEMO, have changed their rules to allow privately owned ESSs and RESs to participate in the electricity market. Accordingly, the VPP model is getting more and more attention. This paper considers a CVPP consisting of RESs, ESSs, and demand, as shown in Figure 1. The VPP can participate in the DA market, both as supplier and consumer, i.e., the VPP either sells or purchases electricity from the main grid, depending on whether RESs available power output is higher or less than the local demand. The ESS also allows VPs to trade in the BC market. While the ESS has a high investment cost, it has very low operating costs and the ability to change power output very quickly. Therefore, ESS can serve as an efficient reserve source compared to other alternatives, such as demand response or RES curtailment [34]. The BC market, in which supplier and demand trade their reserve capacity, plays an essential role in worldwide power systems. It can be seen that the transmission system operators (TSOs) should match the supply and demand to maintain frequency and achieve system stability. However, events such as prediction errors and power outages are unpredictable, and TSOs, therefore, need to be able to adjust for such unexpected power fluctuations. On the other hand, the power generation company shuts down unnecessary generators when there is no buyer, and restarting these units requires at least a few hours. The BC market helps the TSOs secure the number of generators (or the amount of capacity) that can be adjusted in advance. The BC market has regulations on contract duration, minimum bid amount, and continuous operation time corresponding to each BC product in all countries. For example, the Japan electricity market requires that the BC market should be cleared before the operating day, at least one day for tertiary reserve-2, and at least one week for the other four types of reserve (Table 1). Moreover, each generation plant with a BC contract must supply a reserve capacity of at least 5 MW and maintain it for the required duration. Although the classification of reserve services may vary from country to country, they generally have similar requirements [24; 35], and a VPP should satisfy these requirements to participate in the BC market. If a VPP joins the BC market, the VPP operator must solve the problem of determining its BC trading to maximize the total profit in both BC and DA markets. It should be noted that the profit obtained from the BC market consists of two parts: profit from the provision of reserve capacity and profit from the activation of reserve service. The VPP operator does not know whether its reserve service will be called and how much electric power will be generated for the reserve. It can be seen that if the VPP is not called to provide reserve service, its total profit may be lower than in the case that its full available capacity is sold to the energy market. Thus, the probability of reserve activation should be considered in the profit maximization problem from the BC market. It is assumed that the VPP has a contract to provide reserve capacity, as described in Figure 2. In each hour of this period, the VPP is faced with two possibilities of either being called or not being called to provide reserve service. Considering ESSs integrated into the VPP, it can be seen that whether reserve capacity is fully/partly activated or not will affect the energy stored in the VPP. In addition, unlike the conventional power plants that commonly maintain a certain ramp magnitude, the maximum available power output of