In addition to renewable energy sources and market prices uncertainties

the regulation commands issued by the superior market operator are unpredictable factors within the virtual power plant (VPP) bidding range. To avoid branch power flow outage and voltage violation under uncertain regulation commands

a tri-level robust optimization-based day-ahead energy and regulation service bidding strategy for a generalized VPP

considering various distributed energy resources is proposed

in which the VPP bidding strategy

worst scenario estimation approach and regulation service scheduling method are formulated at three optimization layers

respectively. Then

the proposed tri-level model is transformed into an equivalent

single-level

mixed integer

second-order cone programming problem with rigid proof. Numerical simulations illustrate the effectiveness and superiority of the proposed approach by comparison with other prevailing methods in recent literature.