Improving Solar Energy Penetration with Lagrange Multipliers
Abstract: Continued advances in technology have led to falling costs and a dramatic increase in our solar capacity worldwide. One problem for increased solar penetration is a supply-demand mismatch in the grid, due to the intermittent nature of solar generation. We argue that it is useful to explicitly control the rate of solar generation of each solar array in order to handle such mismatches.
We introduce smart solar arrays that actively modulate their solar output based on the notion of proportional fairness. We present a decentralized Langranigan optimization algorithm that enables each solar array to locally decide its fair share of solar power to insert into the grid. The evaluation on a city-scale dataset shows that our approach enables 2.6x more solar penetration, while causing smart arrays to reduce their output by as little as 12.4%. Using an adaptive gradient approach, our decentralized algorithm has 3 to 30x faster convergence than the standard algorithm.