Parameter Optimization of Droop Controllers for Microgrids in Islanded Mode by the SQP Method with Gradient Sampling

Algorithm 1

SQP-GS method.

(1)	Initialization: set ; Set sample size , sample radius , constraint violation tolerance , penalty parameter , line search constant , backtracking constant , sampling radius reduction factor , constraint violation tolerance reduction factor , penalty parameter reduction factor , infeasibility tolerance , stationarity tolerance parameter .
(2)	Termination conditions check: while , if or , and , output solution and stop.
(3)	Gradient sampling: generate sample point in (50) and obtain gradient of multiple operating condition from (56) and (57), Generate sample point from (51), and get the gradient of smooth constraint in (37)-(42).
(4)	Search direction calculation: set , solve (45)-(49) to get .
(5)	L-BFGS update: update for next iteration according to Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method [20].
(6)	Parameter update: if , go to Step 7. Otherwise, if , set ; if , set . And set and go to step 8.
(7)	Line search: set as the largest value in the sequence such that satisfies:
(8)	Iteration increment: set and go to step 2.
(9)	end do