A Markov chain based method for probabilistic load flow with wind power

Probabilistic load flow with correlated wind power sources using a frequency and duration method

“…For example, whether a variable violation (e.g. violation of voltage or branch flow) occurs once every day (frequency information) with ten‐cycle duration (duration information) or occurs ten times a day with a one‐cycle duration is meaningful for the performance assessment of a power system even though the calculated probabilities of the violation are identical [17–19]. In addition, the direction of power flow may change when considering random input variables.…”

“…The change frequency of power flow direction and the average duration of each change are intuitively available to both system planners and operators. Although the frequency and duration information of random variables in a power system has practical value in many aspects, only a few PLF studies [17–19] have considered it. A PLF random input variable (e.g.…”

“…A method used to calculate frequency and duration quantities is generally referred to as a frequency and duration method. In addition to [17–19], various frequency and duration methods [20–28] have been proposed for the reliability evaluation of power systems and the simulation of wind speeds. These methods can also be applied to PLF with wind power sources to solve frequency and duration problems.…”

“…The other technique widely used to solve frequency and duration problems is the Markov chain [17–19, 26–28]. A Markov chain can be used to model the variations of a stochastic process as Markov state transitions in which the sequential characteristics (i.e.…”

“…the ARMA model). Based on Markov chains, various analytic methods [17–19] have been proposed to solve PLF problems with frequency and duration quantities. In [17, 18], random loads and wind power sources were modelled using Markov chains.…”