Abstract: Light robust（LR） model was originally developed to reduce the conservatism of classic linear robust models. However, some of its limitations impede the application in practice, such as unable being independently solved, significant calculation burden, no guaranteed conservatism improvement, violations of boundless constraints. In this paper, an improved light robust（ILR） model with right hand-side uncertain polynomial is proposed, which could overcome aforementioned shortcomings. The effectiveness of the conservatism improvement through the ILR is justified by a proposition which is strictly proved. Then, its tractable linear counterpart with budgeted uncertain set is further deduced and then its equivalence to the original constraints is justified by a proven proposition. The derived linear counterpart can be efficiently solved by linear programming algorithms because of the preserved linearity characteristics. The results from the examples demonstrate the validity of the proposed model. The research promotes the development of robust optimization theory and meantime it also builds a strong basis for solving other similar optimization problems in power systems such as unit commitment.