Understanding power prices dynamics is crucial for valuing flexibility assets such as storage or flexible consumption facilities that accommodate fluctuations in power supply from variable renewables. Owners of such assets need to know how extreme power prices can become in order to optimally manage (dis)charging or adjusting consumption volumes. We examine how to predict those high and low prices, being the different quantiles of the power price probability distribution function, and question how supply from variable renewable sources affect different quantile prices. The first contribution of our paper is that we apply quantile regressions in a panel data framework. This methodology acknowledges that day-ahead power markets’ data is structured as cross-sectional data and, as opposed to previous quantile regression techniques introduced in power markets, allows for simultaneous predictions for all hours during a delivery day. Day-ahead power prices for all 24 h in the next day are determined at the same moment, one day before delivery. The hourly data is therefore not a time-series, but a cross section. The second contribution is that we examine the interaction between demand and supply from variable renewable sources, instead of linear dependencies only. We find that lower and higher quantile prices are more heavily affected by variations in supply from variable renewable sources than centre quantile prices. This enables owners of flexibility assets to better manage their assets in anticipation of excess or scarce supply from renewable sources. By doing so, they increase the flexibility of power systems that face increasing installed capacity of variable renewable energy sources.