In many countries, electricity prices on day-ahead auction markets result from a market clearing designed to maximize social welfare. For each hour of the day, the market price can be represented as the intersection of a supply and demand curve. Structural market models reflect this price formation mechanism and are widely used in prospective studies guiding long-term decisions (e.g. investments and market design). However, simulating the supply curve in these models proves challenging since estimating the sell orders it comprises (i.e. offer prices and corresponding quantities) typically requires formulating numerous techno-economic hypotheses about power system assets and the behaviors of market participants. Due to imperfect competition, real market prices differ from the theoretical optimum, but modeling this difference is not straightforward. The objective of this work is to propose a model to simulate prices on day-ahead markets that account for the optimal economic dispatch of generation units, while also making use of historical day-ahead market prices. Inferring from historical data is especially important when not all information is made public (e.g. bidding strategies) or due to difficulty in accurately accounting for qualitative notions in quantitative models (e.g. market power). In this paper we propose a method for the parametrization of sell orders associated with production units. The estimation algorithm for this parametrization makes it possible to mitigate the requirement for analytic formulation of all of the above-mentioned aspects and to take advantage of the ever-increasing volume of available data on power systems (e.g. technical and market data). Parametrized orders also offer the possibility to account for various factors in a modular fashion, such as the strategic behavior of market participants. The proposed approach is validated using data related to the French day-ahead market and power system, for the period from 2015 to 2018.