Interval Arithmetic Power Flow Analysis of Radial Distribution System with Probabilistic Load Model and Distributed Generation

The variations in load and generation result in higher degree of uncertainty in power flow calculation and create new challenge for the system operator to develop new tools to assess the current and future state of the system. Therefore, the incorporation of the system uncertainties plays a vital role for sustainable planning of the power system. This paper demonstrates the combined application of the probabilistic and possibilistic approach to address line, load and distributed generation (DG) uncertainties in a radial distribution system. The uncertainty in load demand is represented as a Gaussian distribution function, whereas line and DG uncertainty are varied at a fixed proportion. The load is modelled as composite. Type I (penetrates real power), Type II (penetrates reactive power) and Type IV (penetrates both real and reactive power) DG are considered depending upon the type of power injected. The efficacy of improved power flow techniques with the inclusion of various types of DG and its effect on power losses is verified by four test cases on three IEEE test systems: 33-bus, 34-bus and 69-bus. The obtained results are compared to the possibilistic-only approach and found out to be superior. The convergence characteristic is also analysed at various degree of belongingness. The technique converges in smaller number of iterations as compared to other methods. The lower interval width signifies the numerical stability. The statistical analysis of power losses reduction with DG penetration is also carried out.