This paper presents a new technique to lower the computational cost of the electrothermal (ET) analysis of a large on-chip power distribution network. It is based on a node reduction strategy following a preliminary efficient steady-state solution of the ET problem. After a proper classification of nodes according to temperature and voltage drop ranges, a reduced network is then produced by means of clustering and topological network transformations, and is available for any static/dynamic analysis. Due to the achievable reduction ratios, it possible to lower by order of magnitudes the computational cost at very good accuracies. A case-study is provided where a power grid of 4 millions of nodes is reduced by a factor of 180 (electrical network) and 500 (thermal network).