With the deregulation of electricity market and the penetration of renewable energy, microgrid system operators may encounter more difficulties in operation management when facing complex economic, technological, and political uncertainties. In this paper, a robust cost-risk tradeoff model is developed for day-ahead schedule optimization in residential microgrid system under uncertainties. This method is an integration of inexact two-stage stochastic programming and worst-case conditional value-at-risk theory, and could handle uncertainties with inexact or partly known probability distribution information. Besides, by introducing the financial risk measurement, it could also hedge against the worst-case scenario caused by multiple independent uncertainties. The proposed model was applied to a hypothetical residential microgrid system with combined heat and power generation for obtaining optimal day-ahead schedule strategies under variable conditions with respect to renewable energy generation, power demand, and electricity market price. The obtained solutions demonstrate that the proposed model could reflect better tradeoff information between economic operation and stable performance according to different risk-aversion attitudes. In general, more conservative risk attitude would be coupled with higher system cost, which implies higher system stability is at the expense of the economic costs. The developed robust cost-risk tradeoff method would be expected to have a potential for wide applications. (C) 2018 Elsevier Ltd. All rights reserved.