An Interval Probabilistic Energy Flow Calculation Method for CCHP Campus Microgrids

Probabilistic models are used to describe the uncertainty of injected power in traditional probabilistic energy flow (PEF) calculations. Owing to the difficulty of obtaining the accurate distribution parameters of the probability models, the uncertainty of the distribution parameters needs to be considered in the PEF calculation of a combined cooling, heating, and power campus microgrid (CCHP-CMG). In this article, the parameterized probability box (p-box) model is applied for describing the uncertain distribution parameters of the probability model of injected power, and the interval PEF (IPEF) calculation model of a CCHP-CMG is developed. An affine arithmetic-based interval point estimation method (AIPEM) is put forward to solve the IPEF calculation model. The location intervals of injected powers are calculated from their p-boxes, and the interval energy flow calculation is performed with each location interval to estimate the moment intervals of the output variables. Affine arithmetic is used to reduce the interval expansion in the interval calculation, and to further reduce the interval expansion caused by affine multiplication/division operation, a method of removing the accumulation of extra noise terms is proposed. In addition, based on the Nataf inverse transformation and the p-box model, an AIPEM considering the correlation of injected powers is proposed that considers the uncertain correlation coefficients. A case study on a CCHP-CMG shows that the proposed AIPEM has higher computational accuracy than the existing interval cumulant method, especially when the uncertain fluctuation range of the injected power is large, although it consumes more CPU time.