EEE454 High Voltage Techniques – 2013 Prof.Dr.Aydoğan ÖZDEMİR Department of Electrical Engineering Istanbul Technical University 34469 Maslak, ISTANBUL Tel: 212 – 285 6758 High Voltage Laboratory-ITU Gümüşsuyu Campus Tel 212 – 252 2220 Email :
[email protected] Website : http://www.elk.itu.edu.tr/~ozdemir Grading Policy Midterm test : 25 % 2 Homeworks : 5% + 5% 1 group project : 15% Final test : 50% Week Date Subject 1 06.02.2013 Introduction and Timelines of Electricity 2 13.02.2013 Basic concepts of electrostatic field, Laplace's and Poisson's equations in different coordinate systems. Basic equations of electrostatic fields. Planar electrode systems. 3 20.02.2013 Concentric spherical electrode systems. 4 27.02.2013 High Voltage Laboratory Visit 5 06.03.2013 Coaxial cylindrical electrode systems. 6 13.03.2013 Non-coaxial cylindrical electrode systems: eccentric and parallel cylindrical electrode systems. 7 20.03.2013 Approximate calculation of maximum electric field strength for different electrode systems. 8 27.03.2013 Electrode systems with multi-dielectrics: Electrode systems with multi- dielectrics: planar electrode systems of two dielectrics. 9 03.04.2013 Electrode systems with multi-dielectrics: coaxial cylindrical systems with multi-dielectrics, uniformly stressed cylindrical electrode systems 10 10.04.2013 Midterm test 11 17.04.2013 Numerical methods for electrostatic field calculations. 12 24.04.2013 Numerical methods for electrostatic field calculations. Conduction and breakdown in gases. 13 01.05.2013 Conduction and breakdown in gases (cont.). Corona discharges, surface discharges and lightning discharges. Breakdown in liquid and solid dielectrics 14 08.05.2013 Project presentation There may small revisions in the program. Please check it every week. References 1. Prof.Dr.Muzaffer ÖZKAYA, Yüksek Gerilim Tekniği : Cilt 1, Birsen Yayınevi, İstanbul 1996. 2. Akpınar S., Yüksek Gerilim Tekniği, Karadeniz Teknik Üniv., Trabzon, 1997. 3. Gönenç İ.., Yüksek Gerilim Tekniği, Cilt 1: Statik Elektrik Alanı ve Basit Elektrot Sistemleri, İ.T.Ü. Kütüphanesi, Sayı:1085, İstanbul, 1977. 4. E. Kuffel, W. S. Zaengl, J. Kuffel , Yüksek Gerilim Mühendisliği Temelleri, Tercüme yayın EMO Yayınları, 2008. 5. E. Kuffel, W. S. Zaengl, J. Kuffel, High Voltage Engineering Fundamentals, Pergamon Press, Oxford, 2000. 6. M. S. Naidu, V. Kamaraju, High Voltage Engineering, Tata McGraw-Hill, New Delhi, 1997. 7. M. Abdel-Salam, H. Anis, A. El Morshedy, R. Radwan, High Voltage Engineering: Theory and Practice, Marcel Dekker, New York, 2000. 8. Kind, D., Feser, K., High-Voltage Test Techniques, SBA Publ./Vieweg, 2. Ed. 1999. 9. M. Khalifa, High Voltage Engineering, Theory and Practice, Marcel Dekker, New York, 1990. 10. H. M. Ryan, High Voltage Engineering and Testing, Peter Peregrinus Ltd., London, 2001. 11. C. L. Wadhwa, High Voltage Engineering, New Age Int. Ltd., 2 nd Edition, New Delhi, 2007. 12. Subir Ray, An Introduction to High Voltage Engineering, Printice Hall of India, New Delhi 2004 March 6, 2013 HOMEWORK #1 1. Potential distribution of an electrode system for a voltage of U=200 kV is given as follows, | | | | cm y cm x y x kV y x b a y x v , , 9 4 ; 1 . ) , ( 2 2 2 2 s + s | | | . | \ | ÷ + = a) Determine the constants ( a and b) if v(0 , 2 cm)=200 kV and v(3 cm , 0)=0 kV. b) Determine and sketch the equipotential curves of v 1 =0 kV, v 2 =200 kV and v 3 =100 kV . c) Determine the field strength vector E and min max , E E . da 2. a) Outer sphere radius of a concentric spherical electrode system is given to be r 2 = 15 cm. Determine the maximum voltage that can safely be applied to the system if the dielectric strength of the insulation is E d = 30 kV/cm. b) Determine the inner radius of the system in order to apply U=100 kV. c) Evaluate the system from the point of discharge phenomena (will there be a discharge, if so the type) for the inner radiuses of r 1 ’= 2 cm , r 1 ’’= 7 cm and r 1 ’’’= 14 cm. 3. a) Given that the maximum voltage that can safely be applied to an air-insulated (E d = 30 kV/cm) coaxial cylindrical system is 300 kV. Determine the inner radius of the system in order to apply U=250 kV. b) Evaluate the maximum field strengths for an inner radius of r 1 and for an increased outer radiuses of r 2 ’= 1.5* r 2 , r 2 ’’= 2.0* r 2 , r 2 ’’’= 3.0* r 2 and r 2 ’’’’= 4.0* r 2 ; where r 1 and r 2 are the inner and outer radiuses calculated in b). What can you say about the maximum field strength versus outer radius of the system? Due date : March 13, 2013 HOMEWORK #1 SOLUTIONS 1. a) cm 3 b and kV 400 a solved if 0 3 1 3 . ) 0 , 3 ( 200 2 1 2 . ) 2 , 0 ( = = ¦ ¦ ) ¦ ¦ ` ¹ = ÷ = | . | \ | ÷ = = ÷ = | . | \ | ÷ = a ab b a v kV a ab b a v b) cm 3 of radius a with Circle 3 1 3 . 400 0 2 2 2 2 2 1 = + ¬ | | | . | \ | ÷ + = = y x y x kV v cm 2 of radius a with Circle 2 1 3 . 400 200 2 2 2 2 2 2 = + ¬ | | | . | \ | ÷ + = = y x y x kV v cm 2.4 of radius a with Circle 4 . 2 1 3 . 400 100 2 2 2 2 2 3 = + ¬ | | | . | \ | ÷ + = = y x y x kV v c) | | | | j y x y i y x x j y v i x v v grad E y x v 2 / 3 2 / 3 2 2 2 2 2 2 1200 1200 1 3 . 400 + + + = ( ¸ ( ¸ c c + c c ÷ = ÷ = ¬ | | | . | \ | ÷ + = | | cm kV E E cm kV E E y x y x y x y x y x E y x y x / 3 . 133 , / 300 3 2 1200 * 1200 ) , ( 9 4 3 2 2 2 2 min max 2 2 2 2 2 2 2 2 = = = = s + s + = + + = = + = + 2. a) Maximum voltage can be applied when cm r r 5 . 7 2 2 1 = = kV E U E r r r r U E d d m r m r 5 . 112 5 . 7 / 15 5 . 7 15 / max 5 . 7 1 15 2 1 2 1 2 max = ÷ = ¬ s ÷ = = = b) 10 , 5 30 15 / 15 100 / 12 11 1 1 15 1 2 1 2 max 2 cm r cm r r r E r r r r U E d cm r = = ¬ s ÷ ¬ s ÷ = = 12 1 11 r r r < < v 2 = 200 kV v 1 = 0 kV v 3 = 100 kV c) 2 since discharge partial a be will There 7 . 57 / 15 2 2 1 1 2 1 2 max 2 1 r r E cm kV r r r r U E cm r cm r d < ¬ > = ÷ = ) ` ¹ = = discharge be t won' There 8 . 26 / 15 7 1 2 1 2 max 2 1 ¬ < = ÷ = ) ` ¹ = = d E cm kV r r r r U E cm r cm r 2 since breakdown total a be will There 0 . 107 / 15 14 2 1 1 2 1 2 max 2 1 r r E cm kV r r r r U E cm r cm r d > ¬ > = ÷ = ) ` ¹ = = 3. a) Maximum voltage can be applied when e r r 2 1 = cm r e r cm r cm kV E r U r r Ln r U E d e r r 18 . 27 * , 10 30 300 30 1 2 1 1 max 2 1 1 2 1 max max > = = > ¬ = s = ( ¸ ( ¸ = = cm r cm r solved if E r Ln r E kV U For d 8 . 4 , 3 . 16 ) / 18 . 27 ( 250 250 12 11 1 1 max = = ¬ s = = 12 1 11 r r r < < b) ) / ( , 250 , 8 . 4 1 2 1 max 1 r r Ln r U E kV U cm r = = = cm kV E cm r cm kV E cm r cm kV E cm r cm kV E cm r / 7 . 16 7 . 108 18 . 27 * 0 . 4 / 3 . 18 5 . 81 18 . 27 * 0 . 3 / 4 . 21 4 . 54 18 . 27 * 0 . 2 / 3 . 24 8 . 40 18 . 27 * 5 . 1 4 max 2 3 max 2 2 max 2 1 max 2 = ¬ = = = ¬ = = = ¬ = = = ¬ = = ÷ ÷ ÷ ÷ Increasing r 2 decreases E max . However decreasing rate decreases as r 2 increases and therefore r 2 is not an effective means of reducing E max , especially after a certain value. Hw#1 M.Kemal GÜNAY 81 Ali KÖSE 62 Ali YAMAN 47 Sercan TUNCER 59 S.Tabu Ongwaya 92 Tayfun MERAL 39 Recepşan GÜNAY 60 M.Serdar DİLAVER 42 Simge TÜRKKAN 87 Harun KEÇİCİ 48 R.Anıl OKTAY 84 Samet ÖZENİR 57 Kemal GÜZEL 42