This work originates from the observation of the frequency distribution of the Irish system as obtained from a Frequency Disturbance Recorder lent to the last author by the University of Tennessee. The probability density function of such a distribution appears to be bimodal. The paper first investigates how stochastic sources, in particular, load and wind power estimation errors, impact on the distribution of the frequency of a high-voltage transmission system. Then, possible routes to obtain a bimodal distribution of the frequency are explored and the most likely cause that leads to the observed behaviour of the Irish system is identified. Finally, the paper presents a comparison of different frequency regulation strategies and their impact on the distribution of the frequency. A sensitivity analysis of wind speed and load parameters is presented and discussed based on the IEEE-14 bus system.