Abstract-A probabilistic power flow (PPF) study is an essential tool for the analysis and planning of a power system when specific variables are considered as random variables with particular probability distributions. The most widely used method for solving the PPF problem is Monte Carlo simulation (MCS). Although MCS is accurate for obtaining the uncertainty of the state variables, it is also computationally expensive, since it relies on repetitive deterministic power flow solutions. In this paper, we introduce a different perspective for the PPF problem. We frame the PPF as a probabilistic inference problem, and instead of repetitively solving optimization problems, we use Bayesian inference for computing posterior distributions over state variables. Additionally, we provide a likelihood-free method based on the Approximate Bayesian Computation philosophy, that incorporates the Jacobian computed from the power flow equations. Results in three different test systems show that the proposed methodologies are competitive alternatives for solving the PPF problem, and in some cases, they allow for reduction in computation time when compared to MCS.
Current power systems are undergoing an energy transition, where technological elements such as distributed generation and electric vehicles through AC or DC microgrids are important elements to face this transition. This paper presents a methodology for quantifying distributed resource-based generation and the number of electric vehicles that can be connected to isolated DC grids without impacting the safe operation of these networks. The methodology evaluates the maximum capacity of distributed generation considering the uncertainty present in the electric vehicle charging of fleets composed of five types of electric vehicles. Specifically, the uncertainty is associated with the following variables: the home arrival time, home departure time, traveled distance, and battery efficiency. The methodology was applied to a 21-bus DC microgrid and a 33-bus DC network under different test conditions. The results show that higher penetrations of EVs and distributed resource-based generation can be introduced while guaranteeing a secure operation of the DC networks.
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