Stochastic AC Optimal Power Flow Considering the Probabilistic Behavior of the Wind, Loads and Line Parameters

Abstract

As is known, the insertion of new generation technologies, whether it is on transmission or distribution, has several effects on the traditional electric network, from technical changes to its regulation. There is a global interest on finding the best way to take advantage of those emerging technologies and the best way they can interact with the traditional power system. This paper proposes a methodology to exploit the maximum potential of the traditional electric network and the integration of a well-known generation technology such as the wind generation. To do so, we present a Probabilistic AC Optimal Power Flow (POPF) that takes into account load variation, wind's stochastic behavior and variable line's thermal rating which is usually used as a deterministic value in several studies. A validation of two proposed schemes of the Point Estimate Method (PEM) is made, not only for normal distributions but for different kinds of probability distributions, such as Weibull and generalized extreme value. Obtained results are compared with the Monte Carlo (MC) simulation indicating that the proposed method significantly reduces the computational burden while maintaining a high level of accuracy.

Robust linear model for multi‐period AC optimal power flow

“…The IEEE 118-bus test system is used in this study. [24]. Prediction errors for the second and third intervals are 3 and 4.5% of the forecasted active power for each wind plant, respectively.…”

Affine arithmetic for efficient and reliable resolution of weather-based uncertainties in optimal power flow problems

“…Such a formulation allows identifying the central values and the partial deviations of both the state and the control variables, satisfying the optimality conditions defined by the following Theorem: Theorem 1 (AA-Optimality Conditions). 33 Given an AA-based Optimization Problem as (17),x * is said to be an optimal solution if the quantity…”

“…To face this issue, several class of methods can be adopted, including those based on the probability theory 13,14,15 , approximation techniques 16,17,18,19,20,21,22 and sample based methodologies. Experimental results obtained on several case studies demonstrated that the performances of these solution algorithms mainly depend on the consistency and the statistical proprieties of the input data, which, unfortunately, can be rarely assumed in solving W-OPF problems in a real operating scenario.…”

Optimal Power Flow Techniques under Characterization of Conventional and Renewable Energy Sources: A Comprehensive Analysis

“…The objective function involves the monetary factors, such as investment, operation, and reliability costs, as well as the technical penalty factor. In 2014, Sebastián et al [97] presented a probabilistic AC optimal power flow (POPF) that takes into account load variation, wind's stochastic behaviour, and variable line's thermal rating which is usually used as a deterministic value in several studies. In 2015, Aien et al [98] reviewed the probabilistic techniques used for probabilistic optimal power flow (POPF) and proposed a method by using the unscented transformation (UT) technique.…”

“…In 2014, Panda and Tripathy [104] presented an OPF solution for modified power system in which three conventional generators are replaced by wind-energy conversion systems (WECS). To justify the limitation of reactive power generation capability of WECS, genetic algorithm (GA) and a modified bacteria [92][93][94][95][96][97][98][99][100][101][102][103][104][105][106] foraging algorithm are employed independently, for determining the optimal schedule. In 2015, Panda and Tripathy [105] presented a modified bacteria foraging algorithm, which is capable of handling multiobjective optimization problems.…”