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Distributed energy resources (DER) systems introduce uncertainties in the electrical grid that cannot be addressed by classical deterministic methods. Power system analytic tools, such as Load Flow (LF), should be revisited to address such uncertainties. Probabilistic Load Flow (PLF) provides a solution to this problem by handling these uncertainties as random variables. Among the existing sampling...
With increasing number of electric vehicles and electric vehicle charge stations, the question that if existing infrastructure of distribution system will meet new requirements has gained great importance. Mutable load profiles of distribution system and charge stations makes engineering analyses more sophisticated. In this study, some probabilistic analyses are carried out in a local distribution...
Probabilistic Load Flow (PLF) analysis is becoming an important part of grid design, optimization and operation due to the uncertainties added to the power network from both the generation and consumption sides. A reliable, fast and robust mathematical method for such analyses is the main step in such development. The conventional deterministic Monte Carlo (MC) analysis, though simple in implementation,...
The problem of selecting a template that matches a given candidate signal is applicable across a wide variety of domains. Using the correlation coefficient as the avenue for selecting the winning template is perhaps the most common technique. The challenge lies in selecting the winning template when there is no clear separation between the correlation coefficient values of the winning template and...
We consider a newsvendor problem with stationary and temporally dependent demand in the absence of complete information about the demand process. The objective is to compute a probabilistic guarantee such that the expected cost of an inventory-target estimate is arbitrarily close to the expected cost of the optimal critical-fractile solution. We do this by sampling dependent uniform random variates...
Probabilistic load flow (PLF) calculation is the first step to evaluate the impact of the integrated wind power to the power system. The wind power is featured with stochastic and variable property and it's hard to fit its distribution characteristics to any common probability distribution function (PDF). However, the traditional methods including Monte Carlo for PLF are all based on the input variable's...
This paper considers the uncertain factors under electricity market, calculates the probabilistic distribution of the Locational Marginal Price (LMP) based on the Point Estimate Method (PEM) 2n+1 scheme. What is more, the correlated loads are considered. The method has higher efficiency than Monte Carlo Simulation (MCS), and the procedure of linearizing the power flow equation in analytical method...
The paper adopts the Latin Hypercube Sampling with Dependence (LHSD) method to solve the Probabilistic Load Flow (PLF) problem with correlated random variables for distribution networks. The proposed method is investigated using modified IEEE 34 distribution system with random loads, Wind power and Photovoltaics (PVs). Three different cases are studied and the comparison results shows that the LHSD...
The goal of this paper is to provide calculation formulas for the possibilistic correlation coefficient and ratio for two marginal possibility distributions of triangular form when their joint possibility distribution is defined by the product t-norm. We will also introduce an alternative definition for the possibilistic correlation coefficient and ratio when their joint possibility distribution is...
We present two probability inequalities. The simpler first inequality weakens both hypotheses in Hoffding-Azumaine quality. Using it, we generalize concentration results previously known for the uniform density for the TSP, MWST and Random Projections to long-tailed inhomogeneous distributions. The second more complicated inequality further weakens the moment requirements and using it, we prove the...
In this paper, we address the problem of efficient query evaluation over highly correlated probabilistic streams. We observe that although probabilistic streams tend to be strongly correlated in space and time, the correlations are usually quite structured (i.e., the same set of dependencies and independences repeat across time) and Markovian (i.e., the state at time "t+1" is independent...
In this paper, we present a probabilistic inference approach for cooperative spectrum sensing. We probabilistically model the cooperative sensing system on a representative factor graph, and approach the decision fusion problem as one of probabilistic inference on a factor graph that can be tackled by message passing algorithms like belief propagation. This approach allows for the rigorous modeling...
A schedule is said robust if it is able to absorb some degree of uncertainty in tasks duration while maintaining a stable solution. This intuitive notion of robustness has led to a lot of different interpretations and metrics. However, no comparison of these different metrics have ever been preformed. In this paper, we perform an experimental study of these different metrics and show how they are...
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