Pearson’s random walk approach to evaluating interference generated by a group of converters Jacek Bojarski a , Robert Smolenski b,⇑ , Adam Kempski b , Piotr Lezynski b a Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora, ul. Licealna 9, 65-417 Zielona Gora, Poland b Faculty of Electrical Engineering, Computer Science and Telecommunications, University of Zielona Gora, ul. Licealna 9, 65-417 Zielona Gora, Poland article info Keywords: Electromagnetic compatibility Interference Converters Pearson’s random walk abstract According to the EMC Directive 2004/108/EC requirements: ‘‘where an apparatus is capable of taking different configurations, the electromagnetic compatibility assessment should confirm whether the apparatus meets the protection requirements in the configurations foreseeable by the manufacturer as representative of normal use in the intended applica- tions’’. However there are no precise descriptions of how to evaluate the electromagnetic compatibility of a system consisting of many interference sources, neither in the EMC Directive nor in the harmonized standards. The aim of this paper is to evaluate the aggre- gated interference caused by a group of power electronic converters [1] using a simplified model of DC/DC converters and Pearson’s random walk approach. Ó 2013 Elsevier Inc. All rights reserved. 1. Introduction Power electronic converters are increasingly being used in smart grid systems [2], as interfaces between power grid and renewable energy sources, due to high performance and elasticity of energy conversion [3–6]. However, on the other hand, power electronic interfaces produce a substantial level of electromagnetic interference (EMI), mainly in the conducted emis- sion frequency range. Such high level interference can cause problems with both internal and external electromagnetic com- patibility. This is why power electronic converters are often treated as the main reasons for industrial system malfunctions by their designers. The steep slopes of the voltage waveforms produced by power electronic converters excite parasitic capacitive couplings, forcing EMI currents to flow [7,6,8]. The currents spread over the system in common mode (CM) and differential mode (DM) circuits [9]. The slope shapes and residual parameters of the current’s paths determine the cur- rent’s shape. There are usually multi-resonant circuits, however, practically, it is possible to distinguish one dominant mode of oscillation in an investigated frequency range. Frequency domain analyzes are the preferred international standard, thus for that purpose the simplified frequency domain model of aggregated interferences generated by a group of identical DC/DC converters connected to the same supply terminals is proposed in the paper. 2. EMI currents generated by DC/DC converters The DC/DC converters allow the control of the output DC voltage by means of the duty cycle changes in the rectangle waveform [10–12]. This can be done by comparison of the triangle function with the reference level (A m ) proportional to the required output voltage. Fig. 1 shows the waveforms that depict the typical Pulse Width Modulation (PWM) technique applied in DC/DC converters. 0096-3003/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.amc.2012.12.088 ⇑ Corresponding author. E-mail address: r.smolenski@iee.uz.zgora.pl (R. Smolenski). Applied Mathematics and Computation 219 (2013) 6437–6444 Contents lists available at SciVerse ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc