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Photovoltaic (PV) generation is increasingly popular in power systems. The nonlinear dependence associated with a large number of distributed PV sources adds the complexity to construct an accurate probability model and negatively affects confidence levels and reliability, thereby resulting in a more challenging operation of the systems. Most probability models have many restrictions when constructing multiple PV sources with complex dependence. This paper proposes a versatile probability model of PV generation on the basis of pair copula construction. In order to tackle the computational burden required to construct pair copula in high-dimensional cases, a systematic simplification technique is utilized that can significantly reduce the computational effort while preserving satisfactory precision. The proposed method can simplify the modeling procedure and provide a flexible and optimal probability model for the PV generation with complex dependence. The proposed model is tested using a set of historical data from colocated PV sites. It is then applied to the probabilistic load flow (PLF) study of the IEEE 118-bus system. The results demonstrate the effectiveness and accuracy of the proposed model.

Technology This paper presents an analysis of the evolution of the probability density function of the dynamic trajectories of a single machine infinite bus power system. The probability density function can be used to determine the impact of random (stochastic) load perturbations on system stability. The evolution of the state probability density function over time leads to several interesting observations regarding stability regions as a function of damping parameter. The Fokker-Planck equation (FPE) is used to describe the evolution of the probability density of the states. The FPE is solved numerically using PDE solvers (such as finite difference method). Based on the results, the qualitative changes of the stationary density produce peak-like, ridge-like and other complicated shapes. Lastly, the numerical FPE solution combined with SMIB equivalent techniques lay the framework extended to the multimachine system.

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