A novel distributed approach to treat the wind farm (WF) power maximization problem accounting for the wake interaction among the wind turbines (WTs) is presented. Power constraints are also considered within the optimization problem. These are either the WTs nominal power or a maximum allowed power injection, typically imposed by the grid operator. The approach is model-based. Coupled with a distributed architecture it allows fast convergence to a solution, which makes it exploitable for real-time operations. The WF optimization problem is solved in a cooperative way among the WTs by introducing a new distributed particle swarm optimization algorithm, based on cooperative co-evolution techniques. The algorithm is first analyzed for the unconstrained case, where we show how the WF problem can be distributed by exploiting the knowledge of the aerodynamic couplings among the WTs. The algorithm is extended to the constrained case employing Deb's rule. Simulations are carried out on different WFs and wind conditions, showing good power gains and fast convergence of the algorithm.