Análise intervalar do fluxo de potência em microrredes com distorções harmônicas: uma abordagem usando série de Taylor

Abstract

The constant growth in electricity consumption, combined with the use of alternative sources, results in a greater number of issues related to power quality. In addition, uncertainty about load, generation data makes it difficult to analyze electrical networks in real time. The importance of dealing with uncertainties in methods for evaluating power systems is directly related with decision-making in a control center, ensuring a panoramic and systemic view which strives for greater reliability and security for planning and operation. Within this context, this work aims to propose tools for interval analysis based on the calculation of Power Flow (PF) and Harmonic Power Flow (HPF) considering microgrids operating connected to the main grid and in islanded mode assuming uncertainties associated with the load and generation values. Due to the scarcity of related works that evaluate the introduction of uncertainties in microgrids, this work proposes the development of an interval power flow in voltage polar coordinates (magnitudes and angles) to evaluate the operation of these networks and their harmonic propagation. Based on the expansion to the second order terms of the Taylor series in which the derivatives of the algebraic equations of the PF are calculated with respect to a parameter of percentage uncertainty, the impact of uncertain data on the possible solutions of the PF is determined. The reason for using the Taylor series is related with the ease of manipulation of the equations to be implemented. Thus, the method uses, in addition to the Jacobian matrix containing the first order derivatives, the Hessian matrix referring to the PF and HPF equations, containing all the second order partial derivatives. In order to connect Distributed Generation units (DGs) to microgrids, voltage source inverters (VSIs) with their frequency control characteristics (Voltage Source Inverters) are considered with the purpose of evaluating not only the network operating state variables but also the impact of uncertainties on the frequency value, in Hz, of the microgrids. For the computational simulations, IEEE systems of 33 and 69 buses are used, modified by the inclusion of DGs and non-linear loads, modeled as harmonic current sources. The results demonstrate how the developed method allows calculating intervals associated with the magnitudes and voltage angles of a microgrid, as well as its frequency and harmonic distortions for each bus. To validate the proposed methodology, Monte Carlo (MC) simulations are conducted, attesting the compatibility between the solutions provided by them. As a main contribution, the proposed methodology determines the solution with less computational time and presents similar results since the calculations are performed directly without iterative characteristics.