A Review of Load Flow Methodologies for Constrained Networks: A South African Case Study

South Africa, along with the rest of the world, is becoming increasingly dependent on variable renewable energy sources which increase the uncertainties associated with operating and planning a power system. Traditionally, deterministic load flow analysis was used for modelling power systems, but it has been shown to be unable to represent the uncertainties of network states well. Commonly, probabilistic load flow analysis is suggested as an alternative to DLF. This review paper provides a comparative analysis of probabilistic load flow analysis (PLF) and DLF at the hand of prevalent literature. The advantages and disadvantages of the respective methodologies are emphasised specifically in relation to modern power networks with a large share of renewable generators to determine which is better suited to constrained systems. This paper discusses certain commonly used PLF methodologies along with their typical applications and their suitability for capacity planning in South Africa. PLF is found to be preferable to DLF for decision-making purposes, as it provides users with probabilistic information representing risks associated with modelling outcomes. PLF, however, carries a significantly larger computational burden and requires more detailed data on various network components. The added information provided by PLF potentially allows for more economic system designs during power system planning as well as more efficient utilisation of existing infrastructure during operations, as it provides a measure of the risks associated with making these decisions. Of the PLF methodologies considered, numerical PLF methods show the greatest maturity for use in system operation and network planning purposes. Analytical and approximate methods have been shown useful for specific scenarios but seem limited in their aptness for the South African system due to the amount of input variables and the complexity of correlations that can be considered, respectively.