The thesis solves the problem of finding the local-risk minimizing strategies in an incomplete market of electricity and fuels where there is a time-change. This is done under two methodologies: in the classical sense and by aid of BSDEs. The novelty resides in the latter approach. The model is described initially by a spot price and from there the following steps are taken. Firstly, the forward prices on fuels and electricity are derived with respect to the physical measure. Then, the same is done under the minimal martingale measure. Afterwards, local-risk minimizing and mean-variance hedging strategies are found for a contingent claim written on fuel and electricity forwards, capacity of production and demand. This is done under both the classical and the BSDE way Secondly, an absolutely continuous time-change is introduced to the Brownian motion leading the dynamics of fuels. The new model is derived and the local-risk minimization problem is solved in the classical sense and in a newly adapted BSDE form. Finally, the thesis provides a new method for tackling local-risk minimization in a time-changed setting with the help of the BSDE theory.