Thesis submitted in fulfilment of the requirements for the degree Doctor of Technology: Electrical Engineering in the Faculty of Engineering at the Cape Peninsula University of Technology 2013 / The objective of the economic dispatch problem of electrical power generation is to schedule the committed generating unit outputs to meet the required load demand while satisfying the system equality and inequality constraints. The thesis formulates single area and multi-area Combined Economic Emission Dispatch (CEED) problem as single criterion, bi-criterion and multi-criteria optimisation problems based on fuel cost and emission criterion functions, constraints over the operational limits of the generator and the tie-lines, and requirements for a balance between the produced power and the system demand and power loss. Various methods, algorithms and softwares are developed to find solution of the formulated problems in single area and multi-area power systems. The developed methods are based on the classical Lagrange's and on the meta-heuristic Particle Swarm Optimisation (PSO) techniques for a single criterion function. Transformation of the bi-criteria or multi-criteria dispatch problem to a single criterion one is done by some existing and two proposed in the thesis penalty factors. The solution of the CEED problems is obtained through implementation of the developed software in a sequential way using a single computer, or in a data-parallel way in a Matlab Cluster of Computers (CC). The capabilities of the developed Lagrange's and PSO algorithms are compared on the basis of the obtained results. The conclusion is that the Lagrange's method and algorithm allows to receive better solution for less computation time. Data-parallel implementation of the developed software allows a lot of results to be obtained for the same problem using different values of some of the problem parameters. According to the literature papers, there are many algorithms available to solve the CEED problem for the single area power systems using sequential methods of optimisation, but they consume more computation time to solve this problem. The thesis aim is to develop a decomposition-coordinating algorithm for solution of the Multi Area Economic Emission Dispatch (MAEED) problem of power systems. The MAEED problem deals with the optimal power dispatch inside and between the multiple areas and addresses the environmental issue during the economic dispatch. To ensure the system security, tie-line transfer limits between different areas are incorporated as a set of constraints in the optimisation problem. A decomposition coordinating method based on the Lagrange's algorithm is developed to derive a set of optimal solutions to minimize the fuel cost and emissions of the multi-area power systems. An augmented function of Lagrange is applied and its decomposition in interconnected sub problems is done using a new coordinating-vector. Task-parallel computing in a Matlab Cluster is used to solve the multi-area dispatch problem. The calculations and tasks allocation to the Cluster workers are based on a shared memory architecture. Implementation of the calculation algorithm using a Cluster of Computers allows quick and simpler solutions to the multi-area CEED problem. The thesis applied the developed algorithms for the various problem formulation scenarios, i.e. fuel cost and emission function with and without valve point loading effect, quadratic and cubic fuel cost and emission functions. The various IEEE benchmark models are used to test the developed Lagrange's and PSO algorithms in the sequential, data-parallel, and task-parallel implementations. Developed methods, algorithms and software programmes can be applied for solution of various energy management problems in the regional and national control centres, smart grid applications, and in education and research institutions.