scholarly journals A Very Short-Term Probabilistic Prediction Interval Forecaster for Reducing Load Uncertainty Level in Smart Grids

2021 ◽  
Vol 11 (6) ◽  
pp. 2538
Author(s):  
Fermín Rodríguez ◽  
Najmeh Bazmohammadi ◽  
Josep M. Guerrero ◽  
Ainhoa Galarza
Keyword(s):  
Power Systems ◽  
Lower Bounds ◽  
Confidence Level ◽  
Prediction Interval ◽  
Decision Makers ◽  
Upper And Lower Bounds ◽  
Probabilistic Prediction ◽  
Short Term ◽  
Interval Algorithm ◽  
Interval Coverage

Very short-term load demand forecasters are essential for power systems’ decision makers in real-time dispatching. These tools allow traditional network operators to maintain power systems’ safety and stability and provide customers energy with high reliability. Although research has traditionally focused on developing point forecasters, these tools do not provide complete information because they do not estimate the deviation between actual and predicted values. Therefore, the aim of this paper is to develop a very short-term probabilistic prediction interval forecaster to reduce decision makers’ uncertainty by computing the predicted value’s upper and lower bounds. The proposed forecaster combines an artificial intelligence-based point forecaster with a probabilistic prediction interval algorithm. First, the point forecaster predicts energy demand in the next 15 min and then the prediction interval algorithm calculates the upper and lower bounds with the user’s chosen confidence level. To examine the reliability of proposed forecaster model and resulting interval sharpness, different error metrics, such as prediction interval coverage percentage and a skill score, are computed for 95, 90, and 85% confidence intervals. Results show that the prediction interval coverage percentage is higher than the confidence level in each analysis, which means that the proposed model is valid for practical applications.

Short Term Wind Speed Forecast Revision Method Based on Volatility Characteristics and Confidence Level

2013 ◽  
Vol 816-817 ◽  
pp. 1260-1264
Author(s):  
Shi Qian Wang ◽  
Li Di ◽  
Jing Hui Huang ◽  
Chun Zheng Tian
Keyword(s):  
Wind Speed ◽  
Power Systems ◽  
Wind Power ◽  
Confidence Level ◽  
Power Markets ◽  
Short Term ◽  
Forecasting Method ◽  
Forecast Revision ◽  
Forecasting Errors ◽  
Positive Effect

Accurately forecasting short-term wind speed can effectively reduce the adverse effects of wind power in power systems and improve the competition of wind power in power markets. Because of the wind randomness, there are huge forecasting errors existing in those commonly used forecasting methods at wind mutation points, and through improving the forecasting method itself can merely provide positive effect. From the angle of revision, a new method is going to be proposed and applied to revise the forecasted wind speed in this paper, which is based on the historical data fluctuation characteristics and confidence level. Under this method, we can turn the original forecasted wind speed into the optimized wind speed. The revision method can be applied on all short-term wind forecast methods. The validity and feasibility of this method are going to be verified through a wind speed forecasting method based on the Grey model GM(1,1).

Computation of Upper and Lower Bounds on Reliability Indices for Bulk Power Systems

1984 ◽  
Vol PER-4 (8) ◽  
pp. 71-72 ◽  
Author(s):  
K. A. Clements ◽  
B. P. Lam ◽  
D. J. Lawrence ◽  
N. D. Reppen
Keyword(s):  
Power Systems ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Reliability Indices ◽  
Bulk Power

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 164
Author(s):  
Tobias Rupp ◽  
Stefan Funke
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real World ◽  
Road Network ◽  
Upper And Lower Bounds ◽  
Bounded Degree ◽  
Shortest Path Routing ◽  
Graph Classes ◽  
Speed Up ◽  
To Come

We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.

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