Probabilistic methods for renewable energy sources and associated electrical loads for Southern African distribution systems

Significant socio-political pressure is being exerted on utilities throughout the world to expand their production and delivery of electrical energy by including renewable energy sources. To conduct meaningful analyses so that decisions may be taken in the procedures of planning, design, economics and technology, appropriate models must be derived for both loads and energy sources. The most difficult and the most important aspect in this type of modeling is the inclusion of uncertainty. In a practical hybrid solar/wind power system (HSWPS) uncertainty not only exists in the energy sources and loads but also in the manner in which the system is managed, operated and accepted by the customers. Issues relating to the second group of uncertainties have been addressed in. This paper, however, focuses on the problem of including uncertainty in analyzing the adequacy of an autonomous solar/wind installation to meet the expected load demand of a typical South African, rural community. Several authors have contributed to understanding and modeling the uncertainty associated with wind and solar power sources. Karaki describes the uncertainty in the availability of solar irradiance with the use of the beta probability distribution function (pdf) and that of the wind resource using the Weibull pdf. A discretized approach is then used to evaluate the renewable energy source in time segments. Tina et al uses a closed form solution to improve the approach. In South Africa extensive load measurements and research have produced load models for various classes of customer. The Beta pdf is most appropriate for electrification design for small groups of customers. In this paper we explore an approach to answering the question: 'How many customers of a given statistical type can be adequately supplied from an autonomous HSWPS in South Africa?' For this purpose a general model of a power system with renewable energy is proposed. Simulations are performed to match the variable outputs of the combined wind and solar renewable energy sources with the uncertainty in the expected loads, as derived from South African load research data, and with various sizes of storage battery. The results are affected by the choice of the load model and the confidence level of the simulation.