Abstarct: Nowadays, the power grid is experiencing new challenges and opportunities. One of them is the presence of enormous electric vehicles in the power grid, which can play an important role. In addition, it has been the opportunities in the power grid, including ancillary services. In this thesis study a virtual power plant that includes a category of plug-in hybrid electric vehicles (PHEVs), which includes a maximum of 20,000 fleets of this type of vehicle, as well as other assets such as conventional power plants, wind farm, and electric load demand as a Virtual Power Plant (VPP), The VPP takes part in the day-ahead (DA) energy markets and regard up and down reserves regulation and the balancing market (BM) also called real-time market (RT) as an ancillary services markets, to compete with other producers and consumers which are also known as rivals. Some data are used in this study includes wind production, positive and negative imbalance power prices, demand of load are related to the Nord Pool power market in the DK1 area in Denmark country, which is on March 13, 2020, the first day of quarantine or lockdown because of COVID-19 pandemic in Denmark Country. In this thesis a stochastic bi-level optimization problem that considers the uncertainties related to the virtual power plant, including the behavior of PHEV owners, it means when the PHEV arrives/ departures at/from the workplace, and the proportion of the initial state of charge of the battery when the PHEV arrives at the workplace, as well as other uncertainty parameters like wind generation and load demand using ARIMA model to implements the scenarios for handle the uncertainties in this study. Also to implement the problem mathematically, using a bi-level problem. The upper level of problem is from the point of view of the virtual power plant that aims to maximize the profit of the virtual power plant itself, where the virtual power plant is assumed to be a strategic plaxyer in the power market it works as a price maker, In the other hand lower level problem is from the aspect of Independent System Operator (ISO), and it deals with the purpose of maximization of social welfare. afterward transformed to a single level problem called Mathematical program with equilibrium constraints (MPEC) by using Karush–Kuhn–Tucker conditions (KKT). The MPEC problem is transformed into a Mixed-Integer Linear Programming (MILP) by using the strong duality theorem and Big-M. Finally, it’s optimized by using a Cplex solver in GAMS software, which is commercial software.