Energy saving and carbon reduction schemes for families with the household PV-BES-EV system

•Regions where feed-in tariff higher than valley price should follow dual objective optimization.•The economy of the household PV-BES-EV system mainly depends on the purchase cost of EVs.•Decreasing electricity price will not undermine the effectiveness of the household PV-BES-EV system.•The energy bills and carbon emissions decrease significantly with the optimal scheduling schemes.