PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · Energy systems, storage and demand
Energy from Physics, Ch The grid with variable renewables: power flow, inertia, adequacy and electrification
Problem
A cluster of N=25 wind sites, each of equal capacity and each with output fluctuation of standard deviation σ (per unit of its own capacity), has a pairwise correlation coefficient r=0.2 between any two sites. The standard deviation of the aggregated output, per unit of total capacity, is σN1+(N−1)r.
((a)) Find this fluctuation factor (the multiple of σ) for the 25 correlated sites.
((b)) Find the factor that would apply if the 25 sites were uncorrelated (r=0).
((c)) Find the large-N floor for r=0.2 and compare it with the answer to part (a).