Probabilistic power flow computation using collocation method and including correlation modeling

In this paper, based on the probabilistic collocation method (PCM), multivariable probability density functions (PDFs) are constructed to model the dependence of power system uncertainties. In addition, paper explains how to reduce the total number of uncertainties and to achieve higher computation efficiency in the probability power flow (PPF) calculation. Large scale integration of unpredictable renewable generation and uncertain load behaviors in power systems, necessitate move from the traditional deterministic power flow (DPF) computation to the PPF analysis, which takes those uncertainties into account in power system operation and planning. High dimensionality and dependences among the uncertainties pose computation challenges in PPF analysis. The commonly used Monte Carlo simulation (MCS) method has high accuracy in handling the PPF computation but with extreme computation time for large size systems. To overcome this drawback, stochastic collocation methods, such as PCM based on the sparse grid interpolation (SGI), are applied for the PPF analysis. Nonetheless, even with the state of the art dimension-adaptive sparse grid interpolation (DASGI) algorithm, computation is inefficient for large-size power systems. In this paper, combined with the DASGI, a special multivariate PDFs modeling method is introduced to represent the dependent uncertainties and to accomplish improved PPF analysis with higher computation efficiency. Case study results obtained using historic data of transmission network of South Australia distinctly show the practicability and effectiveness of this novel PPF computation method. Performance of the proposed PPF method is compared with both the MCS-based PPF and with the DASGI-only PPF.