New European energy policies have set a goal of a high share of renewable energy in electricity markets. In the presence of high levels of renewable generation, and especially wind, there is more uncertainty in the supply. It is natural, that volatility in energy production induces the volatility in energy prices. This can create incentives for the generators to exercise market power by traditional means: withholding the output by conventional generators, bidding not the true marginal costs, or using locational market power. In addition, a new type of market power has been recently observed: exercise of market power on ramp rate. This dissertation focuses on modeling the exercise of market power in power systems with high penetration of wind power. The models consider a single, or multiple profit-maximizing generators. Flexibility is identified as one of the major issues in wind-integrated power systems. Therefore, part of the research studies the behavior of strategic hydropower producers as main providers of flexibility in systems, where hydropower is available.Developed models are formulated as mathematical and equilibrium problems with equilibrium constraints (MPECs and EPECs). The models are recast as mixed-integer linear programs (MILPs) using discretization. Resulting MILPs can be solved directly by commercially-available MILP solvers, or by applying decomposition. Proposed Modified Benders Decomposition Algorithm (MBDA) significantly improves the computational efficiency.