Power system design issues require stochastic simulation methods in order to derivate synthetic time series for the stochastic source modelling. In this paper, essential aspects about the use Markov chain Monte Carlo (MCMC) method for wind speed activity simulation, are analyzed. Emphasis is given to simulation of multiple, spatially correlated wind speed time series. The modified MCMC simulation method is introduced, aimed to capture the stochastic dependency between the series, in conjunction with individual persistence.