## 1 Introduction  
Congestion management (CM) is one of the most critical transmission problems of open access environments [1]. Congestion occurs in a power market if the transmission system is incapable of adjusting all of the desired transactions because of the existence of system violations [2]. System congestion may also threaten the reliability of the power system by making it more vulnerable to sudden disturbances. It may also impede market efficiency, forcing consumers to reduce their electric power consumptions because of the rises in market prices. As the organizations responsible for maintaining power system security efficiently, independent system operators (ISOs) have to mitigate congestion problems by using market-based tools and/or effective operating facilities [3]. Market-based techniques using both locational marginal prices (LMPs) and nodal congestion prices (NCPs) have been proposed to manage and relieve transmission congestion [4]. The LMP is the generation marginal cost of meeting both the power demands and the transmission losses at a specific node, and the NCP is the cost of satisfying network security parameter limits. Consequently, the market price structure both provides the marginal cost of generating units and indicates the system security cost of the power network. Thus, it is currently used by ISOs as well as many researchers as CM pricing [5; 6]. In addition, the influence of CM can be analyzed through the results obtained from LMPs and NCPs. Recently, wind energy has emerged as a critical candidate for bridging the gap between global power supply and demand [7]. Wind energy is primarily considered as a sustainable method of mitigating severe problems that result from the use of fossil fuels, such as market volatility, social conflict, and global warming [8; 9]. Hence, special attention should be paid to wind energy sources in the CM of the electricity market. CM is essential to the efficient operation of any electricity market, with a special emphasis on wind energy. Assume that several buses in a power system each have strong potential for wind installation. An ISO should consider several factors in determining the optimal placements for wind farms in order to alleviate transmission congestion via additional power injection. CM that uses proper power injection reduces both the component of the LMP associated with the congestion price and reduces transmission losses. Several CM problems involving renewable energy sources have been analyzed in the literature [10; 11; 12]. In [10], the authors proposed a new optimal model of congestion management with an emphasis on the promotion of renewable energy sources in a competitive electricity market. In [11], the CM problem incorporated a wind farm based on the sensitivity factor. In [12], the authors addressed transmission congestion relief by considering both the sizes and the sites of new renewable energy sources. However, the impact of renewable energy congestion relief on the probabilistic approach was not considered. Wind behavior is often unpredictable, as it is a stochastic phenomenon. In particular, wind speed is highly dependent upon the weather conditions, geographical region, and season. Wind farms, which deploy many wind turbine generators to harness wind energy for electricity production, have a variable power outputs due to variations in wind speed [13]. Therefore, the rapid global growth of wind power capacity may increase the uncertainties for congestion problems. A reliable probabilistic method that can consider random wind speeds must be found to solve congestion problems. CM is essentially an optimization problem with an exponential number of constraints that can be generally described as an optimal power flow (OPF) problem whose objective function is the maximization of social welfare and whose constraints are the load flow equations and the operation limitations [14]. In [15], the authors applied CM to the adjustments of power transfers in transmission lines based on a transmission congestion penalty-factor.