Motivated by the strategic participation of electricity producers in electricity day-ahead market, we study the problem of online learning in repeated multi-unit uniform price auctions. The main contribution of this paper is the introduction of a new modelling of the action space. Indeed, we prove that a learning algorithm leveraging the structure of this problem achieves a regret of O(K^{4/3}T^{2/3}) under bandit feedback, improving over the bound previously obtained in the literature. This improved regret rate is tight up to logarithmic terms. Inspired by electricity reserve markets, we further introduce a different feedback model under which all winning bids are revealed. This feedback interpolate between the full-information and bandit scenario depending on the auctions' result. We prove that, under this feedback, the algorithm that we propose achieves regret O(K^{5/2}T^{1/2}).