An economic prediction model of hydrogen production from renewable energy complemented with off-peak electricity is developed, and the cost of carbon emission for the off-peak electricity from grid is also considered. The variation of hydrogen cost with the utilization hours of off-peak electricity and the allowable range of off-peak electricity utilization hours under different carbon prices and grid average emission factors are investigated. The results show that it is influenced by the multiplication product of the carbon price and the average carbon emission factor of the grid electricity. The use of off-peak electricity reduces the cost of hydrogen when the multiplication product is less than a critical value, while it causes an increase in the cost of hydrogen when larger than the critical value. Off-peak electricity utilization hours are also constrained by the emission intensity requirement of low-carbon or clean hydrogen. In addition, a generalized multivariate coupled analysis method is developed by investigating single variable sensitivities and decision needs at different stages of the project. The results show that the key coupling variables in the site selection stage are hydrogen price, renewable energy utilization hours and integrated tariff, which is determined by both renewable energy and off-peak grid electricity. In the scheme design stage the key coupling variables are electrolysis energy consumption and unit installed cost. When project parameters are determined along with site specific hydrogen price and renewable energy tariffs, further scheme optimization can be undertaken. (C) 2022 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.