The introduction of a liberalised electricity market has brought a new challenge to generating companies as well as system regulators. Under this more competitive environment, generating companies are exposed to various risks that might compromise their investment return. Moreover, the various risks in the market affect each type of generation technology in a different way; hence influence the technology choice. Furthermore, it is not yet clear whether the investment cycles in a liberalised electricity market will take place in an orderly fashion or whether 'boom and bust' cycles may arise. As a consequence various market designs, investment incentives and policies have been implemented by system regulators to try to ensure the security of supply. Investment decisions under a market with incentive mechanism are even more complicated to model because the generating company needs to forecast the revenue that the new investment will make from both the energy market and the mechanism. This thesis develops some models that could be used by system regulators to study the performance of market designs and by generating companies to assess a new investment under a liberalised electricity market. Three main models have been developed to serve these purposes. A generation expansion model has been developed using Agent-based modelling approach. In this model each generating company makes investment decision taking into account their competitors' investment strategies and the interactions between them. Several incentive mechanisms are also modelled to study their impacts on the generating companies' investment decision and the dynamic of the investments. A more comprehensive investment framework for a generating company to evaluate an investment in a new power plant has also been developed. The framework consists of two stages: 1) it first models the expected future investments and retirements from all the companies in the market and 2) then calculates the market prices and revenues of the new investment against the future system expansion obtained in the first stage. Two investment models have been developed using this framework. The first model is a probabilistic valuation model to assess investment considering risks and uncertainties. The second model is developed to evaluate investment in an oligopoly electricity market taking into account various risk characteristics of different technologies. The investment framework for a generating company to evaluate an investment is also extended so that the generating company can evaluate investments in a market with an incentive mechanism.