Bounds on the smoothing of renewable sources

We consider the problem of smoothing the output of renewable sources such as PV and wind using energy storage. Two measures for smoothness are considered - worst case ramp rate and variability. We provide tight bounds for the size of storage required to control worst case ramping both when forecasts are available and without forecasts. It is shown that having future forecasts reduces the amount of storage required by a factor of 1 over 2. When the increments in the renewable source are uncorrelated, a moving average filter of length N reduces the variability of the output by a factor of √N. Similarly geographic diversity with R diverse locations for renewable plants reduces the variability in the total output by √R when the increments in the output between locations are uncorrelated. Results are also presented comparing the moving average filter with the optimal control formulation using a simple persistent forecast.