# Optimal Control of a Virtual Power Plant by Maximizing Conditional Value-at-Risk
## 1 Introduction  
Climate change due to the greenhouse effect is a major topic in studying the increasingly serious problem of global warming. Controlling greenhouse gases is an important gateway for international organizations to perform environmental protection. The use of distributed energy resources (DERs) is a popular trend for friendly energy dispatch in reducing greenhouse gases. They are generally close to the load and can improve power quality and reliability [1]. DERs refer to distributed generations (DGs), including renewable energy and energy storage systems (ESS), which require a dispatch strategy to coordinate DERs for reliable operations. However, it is difficult to manage and control a large number of small-scale DERs in a conventional power system. To integrate and control scattered DERs, the concept of a virtual power plant (VPP) is proposed in [2]. A VPP can aggregate capacities of many DERs and create a single operating profile to participate in electricity markets and provide system support. Furthermore, VPP can utilize flexible loads to perform demand management (DM); it is also attractive to power utilities in electricity markets. When selecting DERs for the aggregation of VPPs, it is necessary to understand the characteristics and correlations of various DERs. A VPP is not only a power provider, butit is also a customer who can sell or buy power from the market. It can perform a demand response to shift a demand profile and reduce peaks. However, VPP operations also inherit uncertain factors from DERs in the scheduling process [3]. Optimized operation of a VPP is needed to maximize the profits of DERs and customers [4]. Challenges come from the intermittent nature of renewables, which are not predictable and are dependent on weather and other climate factors. By a proper daily dispatch in minimizing the risks of the grid, a VPP can maximize its profit to ensure higher levels of energy security and reliability. Profit may be at risk due to uncertainties. While risk is expected in the formation and operation of VPPs, addressing uncertainties in VPP operations is a key issue when studying this topic. Previous studies were conducted to solve the VPP operation problem in relation to electricity markets. [PERSON] et al. [5] and [PERSON] et al. [6] proposed a bidding strategy for VPPs in the power market, where a bi-level program with equilibrium constraints was presented for modeling the behavior of each producer. Based on the concept of aggregators, a bidding strategy for the dispatch of a VPP was proposed to obtain maximal profit [7]. VPP architecture was proposed in [8; 9] based on a smart producer to establish an energy management platform by integrating distributed power and energy storage with demand response. By considering the optimal sizing of DGs, and the price of electricity, energy management of VPPs was proposed in order to achieve security issues and technical constraints [10]. [PERSON] et al. [11] established a multi-objective VPP construction model based on decision area division, and an improved bat algorithm was used to solve this model. Based on the demand response strategy, the demand bidding mechanism of the VPP was used in the electricity market [12; 13; 14] to help participants obtain profit. Some approaches, such as the binding scenario identification approach [15], mixed integer quadratic programming [16], deep learning-based prediction and particle swarm optimization [17], etc., were used to solve the operation and dispatch problem of VPPs. In the above studies, VPP problems were addressed by considering the risks without the related uncertainties, i.e., with the concept of a \"deterministic\" risk, regardless of the fact that uncertainties are inherent in risk. Combining the conditional value-at-risk (CVAR) method and robust stochastic optimization theory, a revenue-risk equilibrium model was constructed taking into account uncertainties [18]. Risk assessments of VPPs are considered in energy and reserve markets [19], providing valuable information to decision makers.