In this thesis, we focus on linear online power control policies for the energy harvesting communications. In the first part of the thesis, greedy policy is investigated as a special case of linear policies. The tight upper and lower bounds on the greedy threshold (c*) are provided in semi-universal settings where few parameters are known from the actual arrival distribution and clipped arrival distribution. Then the optimality region of the greedy policy is discussed. In the second part, various notions of optimal slope (s*) linear policy are discussed. The numerical results show the existence of optimal linear policy with strictly better performance than the conventional fixed fraction policy in terms of the multiplicative ratio. / Thesis / Master of Applied Science (MASc)