Analysis of Semi-Markov Reward Processes Motivated by Ramp Rate Limitation in Wind Farms

Ramp rate limitation, coupled with storage systems, is one of the most frequently used control strategies for the intermittent nature of wind power. This strategy, together with a penalty regime in a wind farm, is considered to develop this work, which juxtaposes a new semi-Markov reward modeling of battery operations with the mathematical methodology to compute the moments of the accumulated penalty process. The primary innovation is in how the rewards for each state of the chain are modelled. In particular, they are considered a non-linear function of independent but not identically distributed random variables that are influenced by the sojourn time length distributions. This aspect represents a further advancement in the theory of semi-Markov reward processes and generalizes previous contributions in this field. The study is aimed at showing the calculation procedure for the penalty process moments, which consists of two main steps: finding the recurrence equations of the moments and solving them through a discretization-based algorithm. Furthermore, we validate the methodology presented on real data.