The current energy transition needed to meet the world climate objectives is causing stability challenges in all the power systems. As a consequence, finding solutions that allow dealing with those frequency stability issues is critical to achieving the sustainability objectives. In this context, batteries can find new revenue opportunities by being part of the solution to this problem. This paper develops a mathematical model that provides the optimal bidding strategy and the most convenient operational planning for batteries participating in balancing markets. More specifically, this project is focused on the Swedish frequency markets whose minimum bid size is smaller than 5 MW. The proposed optimization problem is a two-stage stochastic mixed-integer and linear optimization from the battery operator's point of view that includes a novel step-by-step process for properly selecting the bid prices by the quantification of the risks, control costs and amortization of the battery. The originality of the work resides in the aforementioned process that allows risk assessment together with the linear modelling of paid-as-bid markets, commonly solved through non-linear problems. As a result, not only the profitability of this application for batteries is demonstrated, but it is also possible to observe the seasonal differences when it comes to revenue and power requirements. The model is tested with data from Sweden, but it is designed to be adjustable to other balancing markets. INDEX TERMSFrequency control; Balancing markets; Stochastic optimisation; Battery energy storage Nomenclature Economic penalization paid due to breach of FCR-N awarded bids in hour h and scenario ω[C]