Improving performance of droop-controlled microgrids through distributed   PI-control
  This paper investigates transient performance of inverter-based microgrids in terms of the resistive power losses incurred in regulating frequency under persistent stochastic disturbances. We model the inverters as second-order oscillators and compare two algorithms for frequency regulation: the standard frequency droop controller and a distributed proportional-integral (PI) controller. The transient power losses can be quantified using an input-output H2 norm. We show that the distributed PI-controller, which has previously been proposed for secondary frequency control (the elimination of static errors), also has the potential to significantly improve performance by reducing transient power losses. This loss reduction is shown to be larger in a loosely interconnected network than in a highly interconnected one, whereas losses do not depend on connectivity if standard droop control is employed. Moreover, our results indicate that there is an optimal tuning of the distributed PI-controller for loss reduction. Overall, our results provide an additional argument in favor of distributed algorithms for secondary frequency control in microgrids. 
Emma Tegling, Martin Andreasson, John W. Simpson-Porco and Henrik   Sandberg
math.OC