energies Article Modeling Stray Capacitances of High-Voltage Capacitive Dividers for Conventional Measurement Setups Alessandro Mingotti 1, * , Federica Costa 1 , Lorenzo Peretto 1 , Roberto Tinarelli 1 and Paolo Mazza 2   Citation: Mingotti, A.; Costa, F.; Peretto, L.; Tinarelli, R.; Mazza, P. Modeling Stray Capacitances of High-Voltage Capacitive Dividers for Conventional Measurement Setups. Energies 2021, 14, 1262. https://doi.org/10.3390/ en14051262 Academic Editor: Julio Barros Received: 19 January 2021 Accepted: 20 February 2021 Published: 25 February 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Electrical, Electronic and Information Engineering, Guglielmo Marconi, Alma Mater Studiorum, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy; federica.costa13@unibo.it (F.C.); lorenzo.peretto@unibo.it (L.P.); roberto.tinarelli3@unibo.it (R.T.) 2 Ricerca sul Sistema Energetico–RSE S.p.A, Via R. Rubattino, 54-20134 Milan, Italy; paolo.mazza@rse-web.it * Correspondence: alessandro.mingotti2@unibo.it Abstract: Stray capacitances (SCs) are a serious issue in high-voltage (HV) applications. Their presence can alter the circuit or the operation of a device, resulting in wrong or even disastrous consequences. To this purpose, in this work, we describe the modeling of SCs in HV capacitive dividers. Such modeling does not rely on finite element analysis or complicated geometries; instead, it starts from an equivalent circuit of a conventional measurement setup described by the standard IEC 61869-11. Once the equivalent model including the SCs is found, closed expressions of the SCs are derived starting from the ratio error definition. Afterwards, they are validated in a simulation environment by implementing various circuit configurations. The results demonstrate the expressions applicability and effectiveness; hence, thanks to their simplicity, they can be implemented by system operators, researchers, and manufacturers avoiding the use of complicated methods and technologies. Keywords: stray capacitance; high voltage; capacitive divider; modeling; voltage divider; capacitor; expressions 1. Introduction The power network has undergone a significant revolution in the last few decades, due to the spread of distributed energy resources (DER) (e.g., almost 35% of the total amount of production in Italy [1]) by intelligent electronic devices (IED), such as energy meters, phasor measurement units (PMUs), etc., and most recently, the introduction of electric vehicles (EVs), with their sales increasing daily. These changes have forced utilities and distribution system operators (DSOs) to rethink ways to manage and control the grid, for all the considered voltage levels, i.e., low, medium, and high (LV, MV, and HV, respectively), to avoid serious complications due to the presence of such new actors within the grid. In this scenario, instrument transformers (ITs) play a significant role [2–4]. In fact, despite the aforementioned changes and modifications of the grid, they must continue, in a reliable way, to operate, scaling voltages (voltage transformers, VTs) and currents (current transformers, CTs) in order to be suitable for the typical acquisition systems, and then to be evaluated by the operators. ITs rely upon a solid backbone of standards, the IEC 61869 series, comprised of fifteen documents which cover all kind of transformers and their different features and capabilities. For example, Standards IEC 61869-1 and -6 deal with general requirements [5,6] that apply to conventional ITs and low-power ITs (LPITs), respectively; Standards IEC 61869-2 to -5 describe inductive instrument transformers; regarding the new generation of electronic devices, they are standardized in Standards IEC 61869-7 to -15 (including direct current (DC) devices and merging units) [7,8]. In addition to the standards for ITs, there is also extensive related literature with available documents that try to address most of the issues that may affect their correct operation. For example, in [9–13], the effects of temperature on ITs are described; in [14–20], Energies 2021, 14, 1262. https://doi.org/10.3390/en14051262 https://www.mdpi.com/journal/energies