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This paper presents an adaptive approach for modelling residential load profiles based on Markov chains that inherently accounts for seasonality. This approach is compared to a traditional approach where short-term seasonality is explicitly modelled in the transition matrix. A detailed evaluation of over 250 days of smart meter data from a few hundred households shows how the proposed approach outperforms the traditional approach in preserving the statistical properties of individual loads while minimizing the error between the aggregated load and the actual aggregated load data. Substantial improvements are achieved by means of a logistic regression model that learns the Markov transition probabilities and better captures seasonality on a medium-to long-term basis. Furthermore, a method based on least squares regression is proposed for allocating synthetic profiles to households without smart meters. Combined with aggregate power matching, the adaptive approach for load profile generation allows for a precise distribution grid state estimation based on partial smart meter data.