## 1 Introduction
A CM method based on OPF, presented in [16], relieved congested transmission lines by using both power generation rescheduling and load curtailment. In [17], the authors analyzed both the enhancement of voltage loadability and the transmission mechanisms of line outage contingencies in a smart power network and found that if a few lines were able to be fully loaded, some voltages could be adjusted to their lower restrictions. Although no violation occurred, even a small disturbance, such as a load change, could cause the system to deteriorate into an unstable condition. As the penetration of wind energy into a power network increases, the influence of wind turbines on the voltage stability becomes more significant. Following a large incorporation of wind power into a grid, severe problems may arise due to both the characteristics of the wind generators and the random nature of wind. Hence, when wind power systems are connected to weak networks, the voltage stability should be considered in addition to the uncertainties of the wind power in their CM frameworks. Voltage stability refers to the ability of a power system to sustain steady levels of voltage for all of the network buses after being subjected to a disturbance [18]. Voltage instability can lead to load shedding, branch trips, or even cascading outages caused by acting protective relays. Voltage collapse is a phenomenon in which a sequence of voltage instability events leads to a blackout. Generally, the closeness to voltage collapse can be used to measure the voltage stability of a power system. In systems with weak connections among areas, congestion problems frequently occur due to either overloading or voltage security requirements. Several techniques have been proposed to solve voltage security problems in CM. In [19], a multi-objective method was presented to maximize both the social benefits of the power market and the distance to the maximum loading point. In this method, which employed a loading margin, the ISO paid more for security enhancement. In [20], a method for ensuring voltage security after the implementation of CM was proposed. However, it did not consider the diverse effects of different loads on the voltage security. In addition, due to the complexities of power-system stability problems, both the solution spaces resulting from inter-area power transfer problems and the system stability boundaries may become complicated. As such, traditional optimization techniques can occasionally fail or encounter numerical difficulties with objective functions. In contrast, both particle swarm optimization (PSO) and differential evolution are powerful population-based searching algorithms [21]. However, transforming a typical single-objective PSO into a multi-objective PSO requires reestablishing both the best local and global individuals to seek a front of optimal solutions. In this paper, we propose an approach to solving CM problems, focusing in particular on both voltage stability and wind farms in the electricity market. The problem is modeled as a probabilistic voltage-stability constrained optimal power flow (P-VSCOPF) to maximize both the social welfare and the voltage stability margin. A multi-objective particle swarm optimization (MOPSO) algorithm is used to determine the P-VSCOPF solution for mitigating the transmission congestion problem. Since wind speed is a random variable and load forecasting contains uncertainties as well, we apply a probabilistic approach based on Monte Carlo simulations (MCSs). The contingency analysis for line outages is also considered by using the voltage stability index (VSI). The optimal sites of wind farms are determined based on the congestion distribution factor (CDF), and the voltage stability margin (VSM) is considered within the CM framework. Simultaneously, optimal pricing expressions for relieving congestion are derived with linear programming (LP).