Decision evaluation with interval mathematics: a power distribution system case study (original) (raw)
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International Journal of Global Energy Issues, 2007
This paper presents new concepts and methodological tools to decide the investments that electric distribution utilities must perform under regulatory frameworks based on performance (Performance Based Regulation or PBR). The proposal is focused on short-term investments. In this work, the subject of hierarchical expansion planning and the basis for an investment decision methodology are presented. Furthermore, the uncertainties to be considered in the problem are indicated and uncertainty representation by means of Type-2 Fuzzy Numbers (T2-FN) is proposed due to the fact that T2-FN, besides modelling the uncertainties in quantitative form, can model uncertainties associated to expert knowledge of qualitative characteristics. System diagnosis and identification of problem areas are considered and it is proposed to classify these areas by using performance indices, then the possible short-term investments are analysed. Finally, a profit-cost and risk analysis for a high-priority investment classification are proposed.
Towards interval analysis of the load uncertainty in power electric systems
2004
The aim of this paper is to present a methodology based on interval mathematics to deal with load uncertainty in power electric systems. The approach is suitable to model two types of uncertainty in power flow analysis, namely: (i) the influence of the load measurement errors at all system buses on the voltage profile; (ii) the voltage profile behavior under a load variation during a specific period of time. This methodology entails an interval power flow model and the resulting interval non-linear system is solved using Krawczyk's method. We implemented the algorithm in the Matlab environment using the IntLab toolbox. Results for IEEE test-systems and a comparison with related work are presented.
A Comparative Study on Decision Making Methods with Interval Data
Journal of Computational Engineering, 2014
Multiple Criteria Decision Making (MCDM) models are used to solve a number of decision making problems universally. Most of these methods require the use of integers as input data. However, there are problems which have indeterminate values or data intervals which need to be analysed. In order to solve problems with interval data, many methods have been reported. Through this study an attempt has been made to compare and analyse the popular decision making tools for interval data problems. Namely, I-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), DI-TOPSIS, cross entropy, and interval VIKOR (VlseKriterijumska Optimiza-cija I Kompromisno Resenje) have been compared and a novel algorithm has been proposed. The new algorithm makes use of basic TOPSIS technique to overcome the limitations of known methods. To compare the effectiveness of the various methods, an example problem has been used where selection of best material family for the capacitor application ha...
Interval analysis to address uncertainty in multicriteria energy market clearance
MedPower 2014, 2014
A serious problem in every complex decision making process is how to deal with uncertainty. In complex systems the uncertainty is usually addressed with the use of probabilistic models where information about the distribution of the uncertain parameters is available or derived. However, in many engineering problems such information is unknown. Evermore, quite often the decision is made once, rendering irrelevant the probabilistic framework. In this study a multicriteria methodology is used in order to model the clearance of the energy market. The proposed model deals with uncertainty as far as the desired energy policy and restrictions are concerned with use of interval analysis. This way, the robustness of the optimal solution for different energy policies, which is necessary in order to evaluate them, is studied, thus creating a decision support system for the market operator.
2006
Prioritizing shortterm investments and risk assessment have become a necessity for utilities due to new regulatory frameworks based on performance and uncertainties in the planning parameters. In this paper, uncertainty modeled by means of fuzzy numbers is proposed since they take into account the possibility of occurrence of different future values of the planning parameters. System performance evaluation and economic evaluation are described. These evaluations are applied to different short-term investment alternatives that compete to improve distribution network areas with problems, taking into consideration the data uncertainty. Then, an investment hierarchy according to a confidence level, which is based on the economic profit and the associated risk, is achieved using a method for ranking fuzzy numbers. A numerical example is given to illustrate the applications and results.
2008 IEEE/PES Transmission and Distribution Conference and Exposition: Latin America, 2008
Prioritizing short-term investments and risk assessment have become a necessity for utilities due to the new regulatory frameworks based on performance and the uncertainties in the planning parameters. In this paper a probabilistic methodology is proposed in order to take into account these uncertainties. First, a software is used to generate aleatory scenarios and subsequently both the system performance evaluation and economic evaluation are calculated. These evaluations are applied to different short-term investment alternatives that compete to improve the distribution network. Then, an investment hierarchy is achieved using a statistical analysis. A numerical example is given to illustrate the applications and results. Additionally, a comparison with a fuzzy methodology previously proposed in other papers by the authors is also presented.
A Range Arithmetic-Based Optimization Model for Power Flow Analysis Under Interval Uncertainty
IEEE Transactions on Power Systems, 2013
This paper presents a novel framework based on Range Arithmetic for solving power flow problems whose input data are specified within real compact intervals. Reliable interval bounds are computed for the power flow problem, which is represented as an optimization model with complementary constraints to properly represent generator bus voltage controls, including reactive power limits and voltage recovery processes. It is demonstrated that the lower and upper bounds of the power flow solutions can be obtained by solving two determinate optimization problems. Several numerical results are presented and discussed, demonstrating the effectiveness of the proposed methodology and comparing it to a previously proposed Affine Arithmetic based solution approach.
Economic Dispatch: Applying Interval-Based Dependency Analysis to an Electric Power Problem
A common way to model uncertainty in the value of a quantity is to use a probability density function (PDF) or its integral, a probability distribution function (CDF). When two such values are combined to form a new value equal to their sum, product, max, etc., the new value is termed a derived distribution . It is well-known that derived distributions may be obtained by numerical convolution, Monte Carlo simulation, and analytically for specific classes of input distributions, under the assumption that the input distributions are independent. It is also possible to obtain derived distributions for specified dependency relationships other than independence. However, it is not always the case that the dependency relationship is known. Thus there is a need for obtaining solutions without assuming independence or any other specific dependency relationship. There are two numerical algorithms that have been implemented in software for this. Numerical approaches have the advantage of applicability to a very wide class of distributions. Probabilistic Arithmetic [6] is implemented in the commercially available software tool RiskCalc . Interval-Based Dependency Analysis (IBDA) [2], which extends our previous tool [1] by eliminating the independence assumption, is implemented in the software tool Statool and is available upon request from the authors. While the two tools have fundamental similarities [4], a significant difference with respect to the present problem is that IBDA supports, and Statool implements, excess width removal in the underlying interval calculations, from some expressions. In this paper we apply IBDA to generalize a solution to the well-known economic dispatch problem in electric power generation to the case where the dependency relationship between the fuel costs of two generators is unspecified.
Sensitivity Studies on Parameter Uncertainties in Distribution Network Performance Analysis
Errors in network performance assessment calculations (voltage drop and technical losses) arise due to simplifications made in the calculations and uncertainty in the magnitudes and statistical properties of assumed loads, including uncertainty in the load voltage dependency. A representative Southern African rural electrification network is analysed to provide guidance on the acceptability of certain simplifications/assumptions used in voltage drop and loss calculations, the likely error ranges associated with these simplification/assumptions and the sensitivity of voltage drop and loss calculations to load voltage dependency. The results and conclusions are valid for rural electrification networks in Southern Africa, and can be applied to other networks with similar characteristics.
Residential energy management using a novel interval optimization method
2017 4th International Conference on Control, Decision and Information Technologies (CoDIT), 2017
In this paper, a new interval optimization method is proposed to manage the uncertainty of stochastic variables to the problem of Residential Energy Management (REM). This new method is called Stochastic Predicted Bands (SPB) and it considers the uncertainty of decision making variables without knowledge of the Probability Density Function (PDF). The modeling of uncertainty is done by bands based on the prediction of stochastic variables. Besides, an auxiliary parameter is defined to provide flexibility to the decision-maker to be optimistic or conservative. Hence, applying the optimistic coefficient to the SPB method results in the enhancement of its performance. This new method is called Modified Stochastic Predicted Bands (MSPB). The simulation results of the test system show the performance of the proposed model in solving energy management problems via SPB method. Index Terms-Residential energy management, interval optimization, decision-making under uncertainty, stochastic predicted bands, power scheduling.