An analytical solution to the economic dispatch problem (original) (raw)
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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.
Energies
In the context of the growing penetration of renewable power sources in power systems causing probabilistic contingency conditions, a suitable economic dispatch model is decisively needed. There is a lack of research in the field of probabilistic mathematical formulation considering the uncertainties due to the stochastic nature of renewables and contingency occurrence, as it is a very complex problem to be solved. The most appropriate model is the stochastic security-constrained economic dispatch (SSCED) model for optimized economic dispatch decisions during uncertainty. However, because of its complexity, it is rarely employed. This paper attempts to solve the complex SSCED problem in the presence of the uncertainty of resources and probabilistic contingency conditions, which is a novel effort in this regard. The SSCED is carried out over multiple periods to provide the load-following or contingency reserves. In the proposed SSCED, the uncertainty problem is addressed by modeling ...