This study presents a biogeography-based optimisation (BBO) algorithm to solve optimal power flow (OPF) problems of a power system with generators that may have either convex or non-convex fuel cost characteristics. Different operational constraints, such as generator capacity limits, power balance constraints, line flow and bus voltages limits and so on, have been considered. Settings of transformer tap ratio and reactive power compensating devices have also been included as the control variables in the problem formulation. Biogeography describes how a species arises, migrates from one habitat to another and eventually gets wiped out. The algorithm developed using this concept is known as BBO, which searches for the global optimum mainly through two steps: migration and mutation. BBO has been implemented for three different objectives that reflect fuel cost minimisation, voltage profile and voltage stability improvement with the OPF embedded on IEEE 30-bus system. The superiority of the proposed method over other methods has been demonstrated for these three different objectives. Considering the quality of the solution obtained by the proposed method seems to be a promising alternative approach for solving the OPF problems.