Trading activity in intraday (ID) electricity markets has increased significantly over the last few years. We study the problem of a financial agent wishing to maximize a constant relative risk-aversion expected utility of their terminal wealth while operating in an ID market. Assuming that the price of traded hours follows an additive Ornstein– Uhlenbeck process, we derive the optimal strategy via the Hamilton–Jacobi–Bellman equation. The optimal portfolio in the log case is totally myopic with respect to time to maturity, while in the power case it becomes more and more risky as final maturity approaches. In order to implement our strategy, it is necessary to estimate the model parameters. One cannot resort to known results, as it is typical for time series to be unevenly time spaced, with more and more transactions as maturity approaches. Thus, we present an estimation procedure for unevenly spaced observations, based on maximum likelihood estimation and a bootstrap bias correction, in order to compensate for having few observations at the beginning of the observation frame. Finally, we backtest our method and conclude.