Representation of Time-Current Characteristic of Expulsion Fuse Links for Computer-aided Simulations

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1 Representation of Time-Current Characteristic of Expulsion Fuse Links for Computer-aided Simulations Code: G. B. Costa, A. C. Marchesan, A. Z. Bertoletti, A. P. Morais, G. Cardoso Jr e L. Zapata. Universidade Federal de Santa Maria - UFSM 17/11/2017 1

2 Objectives Model the Time-Current Characteristics (TCC) of expulsion fuse links. To achieve this, the Last Square Method has been used and the Residual Sum of Squares (RSS) as a comparative parameter. Four equations were selected to evaluate the method. 17/11/2017 2

3 Introduction Expulsion fuse links are widely used in the protection of overhead distribution systems, specifically in branches and equipment such as transformers and capacitor banks due to their simplicity and low cost in relation to other protection devices. Due to the popularization of expulsion fuse links, a great number of studies focus on the distribution protection schemes considering the presence of these devices. When research involves computational simulations, it is necessary to represent the fuse element using digital models. Generally, the data used in these models are obtained through Time-Current Curves (TCC). From the data obtained from the TCC curves, there are several approaches proposed in the literature for fuse links modeling. In this work, the aim is to evaluate the methodologies that employ analytical equations to represent the mathematical behavior of these devices in computational simulations. 17/11/2017 3

4 Methodology START STEP 1 Obtaining the MM and TC curve from the manufacturer STEP 2 Collecting at least 60 points from the MM and TC curves STEP 3 Process the curve fitting of selected function STEP 4 Evaluate the goodness of function fit END 17/11/2017 4

5 A A n B K I log( C) n I A 1 1 A2 A2 t At 0 A0 1 b. 2I q 2 2 (( II h 1) log( ( I) ) 1) log ( I) 50 Methodology Formula Equation t = p 0 + p 1. I + p 2. I 2 + (2) t = a. exp b. I + c. exp(d. I) (3) t = A I n 1 + B (5) t = A 0 + A 1 I 1 + A 2 I (8) 17/11/2017 5

6 RSS Experimental results Fuse Link type H x RSS of TC curve using Equation (5) Delmar Hubbell Power Systems Eletrofusi Power System Indel Bauru 10,58 9,5 8 7,34 6 5,24 5,03 5,13 4 3,56 3,54 2,71 2 1,47 1,2 0,76 0 1H 2H 3H 5H Elo Fusível tipo "H" 17/11/2017 6

7 RSS Experimental results Fuse Link type H x RSS of MM curve using Double Exponential. 4,0 3,5 Delmar Hubbell Power Systems Eletrofusi Power System Indel Bauru 3,91 3,5 3,0 2,87 2,5 2,0 1,5 1,66 1,0 0,58 0,5 0,0 0,94 0,71 0,79 0,86 0,57 0,6 0,15 1H 2H 3H 5H Elo Fusível tipo "H" 17/11/2017 7

8 RSS Experimental results Fuse Link type H x RSS of TC curse using Polynomial Function. 1,2 1,0 Delmar Hubbell Power Systems Eletrofusi Power System Indel Bauru 0,94 0,8 0,82 0,84 0,6 0,62 0,4 0,35 0,2 0,13 0,19 0,16 0,07 0,27 0,25 0,19 0,0 1H 2H 3H 5H Elo Fusível tipo "H" 17/11/2017 8

9 RSS Experimental results Fuse Link type K x RSS of MM curse using Equation (5). 6 4,98 4,74 4,34 4,3 4,15 4 3,96 3,7 3,56 3,25 S&C Positrol Eletrofusi Power System Cooper Power Systems Kearney 3,39 3,41 3,08 2,6 2 1,55 1,46 1,44 2 1,77 1,62 1,64 1,62 0 6K 10K 15K 25K 40K 65K 100K Elo Fusível tipo "K" 17/11/2017 9

10 RSS Experimental results Fuse Link type K x RSS of TC curse using Equation (8). 3 2,26 S&C Positrol Eletrofusi Power System Cooper Power Systems Kearney 2 1,58 1,82 1,72 1, ,12 0,78 0,66 0,48 0,42 0,3 0,29 0,23 0,12 0,12 0,17 0,1 0,09 0,11 0,2 0,07 6K 10K 15K 25K 40K 65K 100K Elo Fusível tipo "K" 17/11/

11 Conclusions Expulsion fuse links are widely used in the protection of overhead distribution systems as a result of their simplicity and low cost in relation to other devices. Hence, this study evaluated four different analytical functions proposed in the literature to model the MM and TC characteristics of expulsion fuse links, using the adjustment of the Least Squares Method. Three major manufacturers were considered. As a criterion for evaluating the quality of the analyzed adjustments, the Residual Sum of Squares (RSS) was adopted. The Polynomial function presented the best results among the selected functions. The average RSS values were the lowest considering the four functions. The disadvantage of the method, according to the study criteria selected by the authors, is that there is no single polynomial order that fits for all the full range of fuse links nominal values. 17/11/

12 Acknowledgments The authors are thankful to Brazilian government through Capes (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior). This work was supported by Capes. 17/11/

S (13) Reference: FLUID 9791

S (13) Reference: FLUID 9791 Title: A Deduction of the MulticriticalityConditionsof, Mixturesfrom the Gibbs Tangent Plane Criterion Author: Nélio Henderson Wagner.F. Sacco Raimundo A. Rodrigues Jr PII: S0378-3812(13)00550-5 DOI: http://dx.doi.org/doi:10.1016/j.fluid.2013.09.043