Control algorithms based on the active and non-active currents for a UPQC without series transformers

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Luís Fernando Correa Monteiro, Maurício Aredes, José Gabriel Pinto, Bruno Exposto, João Luiz Afonso

“Control algorithms based on the active and non-active currents for a UPQC without series

transformers”

IET Power Electronics, July 2016, vol. 9, issue 9, 27 july 2016, pp 1985-1994.

http://digital-library.theiet.org/content/journals/10.1049/iet-pel.2015.0642

ISSN: 1755-4543

DOI 10.1049/iet-pel.2015.0642

This material is posted here with permission of the IET. This paper is a preprint of a paper accepted by IET

Power Electronics and is subject to Institution of Engineering and Technology Copyright. When the final

version is published, the copy of record will be available at the IET Digital Library.

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L. F. C. Monteiro, M. Aredes, J. G. Pinto, Bruno F. Exposto, João L. Afonso, “Control Algorithms Based on the Active and Non-Active Currents for a UPQC without Series Transformers”, IET Power Electronics, vol. 9, issue 9, 27 july 2016, pp 1985-1994, ISSN:1755_4535 (Print), 1755_4543 (Online), DOI: 10.1049/iet-pel.2015.0642.

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ൣݒൣൣൣൣൣൣݒൣൣൣൣൣൣൣݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒݒ ɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘ ήήήήήή ൫ήήήή ൫ήή ൫ήήή൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫൫݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅ ɘ݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅ ɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘ ൅ ൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅݅݅݅݅݅݅݅݅ ɘ݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅݅ ɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘ ൯ ൯൯൯൯൯൯൯൯൯൯൯൯൧ ൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧൧ሺሺሺሺሺሺሺሺሺሺሺሺሺɘሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘɘሻሻሻሻሻሻሻሻሻሻሻሻሻሻൌ െൌൌൌൌൌൌൌൌൌെെሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸ_ʹʹଵሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻቈቈቈቈቈቈቈቈቈቆቈቈቈቈቈቆቈቈቈቈቈቆቈቈቈቈቆቈቈቈቆቈቆቈቆቈቆቈቆቈቆቈቆቈቈቈቈቈቈቈቆቈቈቈቆቈቈቈቆቈቈቆቈቆቈቆቈቈቈቆቈቆቈቆቈቈቈቆቈቈቈቈቆቈቈቈቈቈቆቈቈቈቆቈቈቆቈቈቆቈቆቈቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆቆܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴቇቇቇቇቇቇቇቇቇቇቇቇቇ ൅ቇ ൅ቇ ൅ቇ ൅ቇ ൅ቇቇቇ൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅ܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫ ቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉ ʹሺʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨ ͵ߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨ ͵ ௌ஼̴ ௌ஼ ௌ஼ ௌ஼஼஼஼஼஼஼ ௌ ௌ ௌ ௌ஼஼஼஼஼̴ ௌ ௌ ௌ஼஼஼஼஼஼ ௌ஼ ௌ ௌ ௌ ௌ ௌ஼஼஼஼஼஼஼஼ ௌ ௌ ௌ ௌ஼஼஼஼஼஼஼̴ ௌ ௌ஼ ௌ஼஼̴௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔ ௉௉௉஼௉௉௉௉஼௉஼௉஼௉௉௉௉஼௉஼௉஼௉௉௉௉௉௉஼௉௉௉௉௉௉௉஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼̴௔̴̴௔̴௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔ ௗௗௗௗௗௗௗௗௗௗୡௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗୡ ୟୡ ୟୡୡୡୡୡୡୡ ୟୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡ ୟୡୡ ୟୡୡୡୡ̴ୟୡୡୡ̴̴̴ୟ̴ୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟ ାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାା ିିିିିିି ܲ ൌ ܲ ܲ ܲ ܲ ൌൌ ܲ ܲ ൌൌ ܲ ൌൌൌൌൌ ܲ ܲ ܲ ܲ ܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲ ׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵ ܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫ ൌൌൌൌൌൌൌൌൌൌൌൌൌെെെെെെെെെ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲௌௌ஼ௌௌௌௌௌௌ஼ௌௌௌ஼ௌௌ஼ௌௌ஼ௌௌ஼ௌ஼ௌௌ஼ௌ஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔ ௉஼௉஼௉௉஼௉௉஼௉௉஼௉௉௉௉஼௉௉௉௉஼௉஼௉௉஼௉஼௉௉௉஼௉஼௉௉௉௉஼௉஼௉஼௉஼௉஼௉௉௉஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔௔ ௗௗௗୡௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗௗୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡ ୟୡୡୡୡୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟୟ ା ା ା ା ା ା ା ା ା ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ܴ ൤൤൤൤൤൤൤൤൤൤൤൤൤൤൤൤൤ሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺܸሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺܸሺܸሺܸሺሺሺሺܸሺሺሺሺሺሺሺሺሺܸሺሺሺሺሺሺܸሺሺሺሺܸሺሺܸሺሺܸሺሺሺሺሺሺሺሺܸሺሺሺሺሺሺሺሺܸሺሺܸሺሺሺܸሺܸሺܸሺሺܸሺܸሺሺሺܸሺሺሺሺܸሺܸሺܸሺሺሺሺሺሺሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵሻሻ ൅ሻሻሻሻሻሻ ൅ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ൅ሻ ൅ሻሻ ൅ሻሻ ൅ሻ ൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅ሺሺሺሺሺሺܸሺሺሺܸሺሺሺሺሺሺሺܸሺሺሺܸሺሺሺܸሺሺሺሺሺܸሺሺሺܸሺܸሺሺሺܸሺሺሺܸሺܸሺܸሺܸሺሺሺܸሺܸሺሺሺሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ൨൨൨൨൨൨൨൨൨൨൨൨൨൨൨൨൨൨൨൨൨൨ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲௌௌௌௌௌௌௌ஼ௌௌௌ஼ௌௌௌௌௌௌௌௌௌௌௌௌ஼ௌௌௌ஼ௌௌ஼ௌ஼̴ௌ஼ௌ஼ௌௌௌ஼ௌ஼ௌௌ஼ௌ஼ௌௌௌ஼ௌ஼ௌ஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼̴̴̴௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕ ܲܲ ൌൌ ܲൌ ܲൌൌൌൌൌൌ ܲൌൌൌ ܲൌൌൌൌ ܲൌ ܲൌ ܲൌ ܲൌൌܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲ௉௉஼௉௉௉௉஼௉஼௉௉௉஼௉௉௉௉௉஼௉஼௉௉௉௉௉௉஼̴௉௉௉௉௉௉௉஼௉௉௉௉஼௉஼௉஼̴௉஼௉஼௉஼௉஼௉஼௉௉௉஼௉஼௉௉௉஼௉஼௉஼௉௉஼௉஼௉஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼̴௕̴̴̴௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕௕׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵ ܫ׵׵׵ ܫ׵ ܫ׵׵ ܫ׵׵׵׵ ܫ׵ ܫ׵׵׵׵׵׵׵ ܫܫܫܫܫܫܫௗୡܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫௗௗௗௗௗௗୡௗୡௗௗௗௗୡௗௗௗୡௗௗௗௗௗௗௗୡௗௗௗௗௗୡௗௗௗௗௗௗௗୡௗௗௗୡௗௗௗௗௗୡௗୡௗௗௗௗୡ̴ௗୡௗௗୡ̴ௗୡௗௗୡ̴ௗୡௗୡௗௗௗௗௗୡ̴ௗௗௗୡௗௗୡௗୡୡୡୡୡୡ̴ୠୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡ̴ୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠୠൌൌൌൌൌൌൌൌൌൌൌ െൌൌെെെെെሺሺሺሺሺሺሺܸሺܸሺሺሺܸሺܸሺሺሺሺܸሺܸሺܸሺܸሺܸሺܸሺܸሺሺሺሺܸሺܸሺሺሺܸሺሺሺሺሺሺሺܸሺሺܸሺሺܸሺሺܸሺܸሺܸሺሺሺሺܸሺܸሺܸሺሺሺሺܸሺܸሺܸሺܸሺܸሺሺሺܸሺܸሺሺሺܸሺሺሺܸሺሺሺܸሺܸሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵ ାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺ ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ_ሻ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ ቈ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺሺܸ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺܸ_ሺ_ሺܸ_ሺܸ_ሺ_ሺܸ_ሺܸ_ሺ_ሺ_ሺܸ_ሺܸ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺܸ_ሺܸ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺܸ_ሺܸ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ ܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵିିିିିିିିିሻሻሻሻ ሻሻሻሻሻሻሻ ሻሻሻሻሻሻ ሻሻሻ ሻሻሻሻሻሻሻሻሻ ሻሻሻሻ ሻሻሻሻሻሻሻሻሻሻሻሻ ሻሻሻሻ ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ሻሻሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺʹʹʹʹʹʹʹߨʹʹʹߨʹߨʹʹʹʹߨʹߨʹʹʹʹߨʹʹʹʹʹʹʹʹߨʹߨʹߨʹʹʹʹߨʹʹʹߨʹʹߨʹʹʹߨʹߨʹߨʹʹʹߨʹߨʹʹʹʹʹʹߨʹʹʹߨʹʹʹʹʹʹʹʹߨʹߨʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹߨʹʹʹʹߨʹߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤ͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵ሻ͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ൅ሻ ൅ሻሻሻሻሻ ൅ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ൅ሻ ൅ሻሻሻሻሻሻሻ ൅ሻሻሻሻሻ ൅ሻ ൅ሻ ൅ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅ሺሺሺሺሺሺሺሺܸሺሺሺܸሺሺሺሺሺሺሺሺܸሺܸሺܸሺሺሺሺܸሺܸሺሺሺܸሺܸሺሺሺܸሺሺሺሺሺሺሺሺܸሺሺܸሺܸሺܸሺܸሺܸሺܸሺሺሺሺܸሺሺܸሺܸሺܸሺܸሺܸሺܸሺܸሺܸሺሺܸሺܸሺሺሺሺሺሺܸሺሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵିିିିିିିିିሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ሻሻሻ ሻ ሻሻ ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ሻሻ ሻ ሻሻሻሻሻሻሻሻሻሻ ሻሻሻሻሻ ሻሻ ሻ ሻ ሻሻሻሻሻሻሻ ሻ ሻሻ ሻሻሻሻሻሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺʹሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺʹʹʹʹʹʹʹʹʹߨʹߨʹʹʹʹߨʹʹʹʹʹߨʹʹߨʹߨʹʹʹʹʹʹߨʹʹʹʹߨʹߨʹʹʹʹʹʹʹߨʹߨʹʹߨʹߨʹߨʹߨʹʹߨʹʹʹʹʹʹʹʹʹʹʹʹʹʹʹߨʹʹʹʹߨʹߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤ͵ΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤ͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲ ܲௌௌௌ஼ௌௌௌௌௌௌௌ஼ௌௌௌௌ஼ௌௌ஼ௌௌ஼̴ௌௌௌௌௌௌௌௌௌ஼ௌ஼ௌ஼ௌௌௌௌ஼ௌ஼ௌ஼̴ௌௌௌ஼ௌ஼ௌௌ஼ௌ஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼̴௖஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼̴̴̴௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖௖ ܲܲ ൌൌൌൌൌൌൌൌൌ ܲൌ ܲൌ ܲൌ ܲൌܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲܲ௉௉௉௉௉஼௉௉௉௉௉஼௉஼௉஼̴௉௉௉௉௉௉஼௉௉௉஼௉௉௉௉௉௉஼௉௉௉஼௉஼௉௉௉௉௉௉௉஼௉௉஼௉஼௉஼௉஼௉஼௉௉௉௉௉௉஼̴௉஼஼஼஼஼஼஼஼஼஼஼஼̴஼̴஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼஼̴̴ ׵׵׵׵׵׵׵׵׵׵׵׵׵׵׵ ܫ׵׵ ܫ׵׵׵ ܫ׵׵׵׵ܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫ ା ା ା ା ା ା ା ା ௖ ௗୡ ௖ ௗୡ ௖ ௗୡ ௖ ௗୡ ௖ ௗୡ ௖ ௗୡ ௖ ௗ ௖ ௗௗௗୡௗௗ ௖ ௗୡௗ ௖ ௗୡௗௗ ௖ ௗୡௗௗௗୡௗௗୡௗௗௗ ௖ ௗ ௖ ௗ ௖ ௗ ௖ ௖ ௗୡௗௗௗௗୡ ௖ ௗୡ ௖ ௗୡୡୡୡୡ ௖ ௗ ௖ ௗ ௖ ௗ ௖ ௗௗௗୡୡୡୡୡୡୡ ௖ ௗ ௖ ௗ ௖ ௗ ௖ ௗௗୡୡୡୡୡୡ ௖ ௗ ௖ ௖ ௗௗௗௗୡୡୡୡୡୡ ௖ ௖ ௖ ௗୡ ௖ ௗௗୡௗௗௗୡୡୡୡୡୡୡୡୡୡ ௖ ௖ ௖ ௖ ௖ ௗௗௗௗௗୡୡୡୡୡୡୡ ௖ ௖ ௖׵׵׵׵׵׵ ܫ׵׵׵׵׵ ܫ׵׵׵׵ ܫ׵ ܫ׵ ܫ׵׵׵׵׵ܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫܫௗୡௗௗௗௗௗୡୡୡୡୡୡୡ̴ୡ̴ୡ̴ୡ̴ୡ̴ୡ̴ୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡୡ ሺܸሺሺሺሺሺሺሺܸሺܸሺܸሺሺܸሺܸሺሺሺሺሺሺܸሺሺܸሺሺሺሺܸሺܸሺܸሺሺܸሺሺܸሺሺሺሺܸሺܸሺሺሺሺሺሺܸሺሺሺሺሺሺሺܸሺሺܸሺሺܸሺܸሺܸሺሺܸሺሺሺሺሺܸሺሺܸሺሺܸሺሺሺሺܸሺሺܸሺܸሺሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵ ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ା ሺܸ ሺܸ ሺܸ ሺܸ ሺܸ ሺ ሺ ሺܸܸ ሺܸܸܸܸܸܸ ሺ ሺ ሺ ሺܸܸܸ ሺܸ ሺܸܸܸܸ ሺܸ ሺ ሺ ሺ ሺܸܸܸ ሺܸܸܸ ሺ ሺ ሺ ሺܸ ሺܸ ሺܸ ሺܸ ሺܸ ሺܸܸ ሺܸ ሺ ሺ ሺ ሺܸܸܸ ሺ ሺ ሺ ሺ ሺܸܸܸܸܸܸ ሺ ሺ ሺܸܸܸܸܸܸ ሺܸ ሺ ሺܸܸܸܸ ሺ ሺ ሺܸܸܸܸܸ ሺ ሺܸ ሺܸܸܸܸܸܸܸܸ ሺܸܸܸܸܸܸܸ ሺ ሺܸܸܸܸܸ ሺ ሺܸܸܸܸ ሺ ሺܸܸܸܸ ሺ ሺ ሺ ሺܸܸܸ ሺ ሺ ሺܸ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ିିିିିିିିିሻሻ ሻሻ ሻሻሻሻሻሻሻሻሻሻሻሻሻ ሻሻሻሻሻሻሻሻሻሻሻ ሻሻሻ ሻ ሻሻሻሻሻሻሻሻ ሻሻሻሻ ሻሻሻሻሻሻሻ ሻሻሻሻሻ ሻሻሻሻ ሻሻ ሻሻሻ ሻ ሻ ሻሻሻ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ି ି ି ି ି ି ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺʹʹߨʹʹʹߨʹߨʹʹʹʹʹʹʹʹʹߨʹʹߨʹʹʹʹʹߨʹʹߨʹʹʹߨʹʹʹʹʹʹʹʹߨʹߨʹʹߨʹߨʹʹߨʹߨʹʹߨʹʹʹߨʹʹʹʹʹʹߨʹʹʹʹߨʹʹʹʹߨʹʹߨʹʹʹߨʹʹʹʹߨʹʹߨʹߨʹߨʹߨʹʹʹʹʹʹʹߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤ͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ൌ ൌ ൌ ൌ ൌ ൌ ൌ ൌ ൌ ൌ ൌ ൌ ൌ ൌ ൌെെെെെെ _ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ_ܴ ቈቈቈቈቈቈቈቈቈቈቈቈቈቈቈቈቈቈቈቈ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺܸ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ሺܸ_ሺܸ_ሺ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺ_ሺܸ_ሺܸ_ሺ_ሺ_ሺܸ_ሺܸ_ሺ_ሺ_ሺ_ሺ_ሺ_ሺܸ_ሺܸ_ሺ_ሺ_ሺܸ_ሺ_ሺ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ_ܸ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ଵ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ܸ ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅൅ሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵሻሻ ሻሻሻሻሻሻሻ ሻሻሻሻሻ ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ሻሻሻሻ ሻ ሻሻሻሻ ሻሻሻሻሻ ሻ ሻሻሻሻሻሻ ሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺʹߨʹߨʹʹʹʹߨʹʹߨʹʹʹʹߨʹʹʹߨʹʹʹʹʹʹʹʹʹʹʹʹߨʹʹʹߨʹʹʹʹʹʹʹʹʹʹʹʹߨʹʹߨʹߨʹʹʹߨʹߨʹߨʹߨʹʹߨʹʹʹʹʹߨʹʹʹʹߨʹߨʹߨʹʹʹʹʹʹʹʹʹʹʹߨʹߨʹߨʹߨʹʹʹߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨߨΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤΤ͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵ሻሻ͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵͵ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉቉ ሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵሻሻሻሻሻሻ ሺሺܸܸ ሻܸܸܸܸ ሻܸܸܸܸܸܸܸܸܸଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵଵ ሻሻሻ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺ ሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାାሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺሺܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸܸ ሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻሻ ൤ ൤ ൤ ൤ ൤ ൤ ൤ ൤ ൤ ൤ ൤ ିିିିିିିିିି

Control algorithms based on the active and non-active currents for a UPQC without series transformers

Luís Fernando Correa Monteiro, Maurício Aredes, José Gabriel Pinto, Bruno Exposto, João Luiz Afonso