Mathematical models for the construction of a renewable energy hybrid plant

In order to develop renewable energy sources technology in power supply plants, it is necessary to provide designers with tools capable of recognizing at short notice any areas of convenience in its utilization, either as a stand-alone or as a hybrid (with generator back-up) project. Typical renewable sources considered are solar and wind energy, but the results are applicable to any other energy source. The block diagram of the plant includes renewable generator(s), storage battery, and standby diesel engine generator. At first, the authors developed an analysis based on a mathematical model that included only one renewable random source. This model related environmental statistical factors to the sizing parameters and consequently to the costs of each block. However, since the sizing is not univocally defined, the model takes the battery autonomy as ´variable´ and executes on it an optimization process finalized to minimum overall cost. In conclusion, the resulting output gives either the optimized sizing parameters or the costs of each block. A step-by-step optimization procedure is described including: annual cost vs battery autonomy function consideration; mathematical approach to the environmental influence; sizing criteria of the renewable generator; the database utilized and its analysis; model algorithms; comparison between experimental and theoretical results; and the two renewable generators model.<>