ECE320_Formula_Sheet - ECE 320 Energy Conversion and Power...

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ECE 320 Energy Conversion and Power Electronics Formula Sheet Transmission Lines () [] 2 cos 1 max 2 max V dt t V T V T o v = + = φ ω 2 cos 1 max 2 max I dt t I T I T o i = + = ( ) ( ) v t V t v + = cos max Æ V V = ˆ / v ( ) ( ) i t I t i + = cos max Æ I I = ˆ / i Instantaneous power: () () () ( ) ( )( ) ( ) i v i v t t I V t I t V t i t v t p + + = + + = = cos cos cos cos max max max max Average power phasor: i v VI P = cos Real Imaginary V I P Q S V P Q Equation Units Real Power ( ) pf S pf VI VI P i v = = = cos Watts Reactive Power ( ) leading) (for 1 lagging) (for 1 sin 2 2 pf S pf S VI Q i v = = = Volt-Amperes-Reactive Apparent Power VI S = = = * ˆ ˆ ˆ I V S V / v I / i jQ P S + = ˆ 2 2 2 Q P S + = Volt-Amperes
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n V 12 1 3 2 + + + + V 1n V 3n V 2n V V V -V V V 31 V 23 V V V V n n 3 ˆ ˆ ˆ 2 1 12 = = / φ + π /6 I 1 2 1 3 I 2 I 3 I I I I I I -I I 1 I 3 I 2 I I I I 3 ˆ ˆ ˆ 31 12 1 = = / - π /6 () i v l l l i v l l l n n I V j I V I V jQ P S + = = + = sin 3 cos 3 ˆ ˆ 3 ˆ * 1 1 3 3 3 For a balanced 3 system: Δ = Z Z Y 3 1
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Magnetic Circuits and Materials 1Wb = 1 V·s 1T = 1 (Wb/m 2 ) 1H = 1 (Wb/A) = 1 (J/A 2 ) μ o = 400 π (nH/m) Name Point Form Integral Form Faraday’s Law t B = × E ∫∫ = CS ds n B dt d dl ˆ E Ampere’s Law Modified by Maxwell t D J H + = × + = S C ds n t D J dl H ˆ Gauss’s Law ρ = D = V S ˆ dv ds n D Gauss’s Law for Magnetism 0 = B 0 ˆ S = ds n B Electric Circuit Magnetic Circuit V r I I a b c Electrically Conductive Material V r φ I a b c High Permeability Driving Force applied battery voltage = V applied ampere-turns = F Response resistance electric force driving current = or R V I = reluctance magnetic force driving flux = or R F = Impedance Impedance is used to indicate the impediment to the driving force in establishing a response. A l R σ = = resistance where l = 2 π r , σ = electrical conductivity, A = cross-sectional area A l μ = = R reluctance where l = 2 π r , = permeability, A = cross- sectional area
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Electric Circuit Magnetic Circuit Equivalent Circuit V I R V = IR F φ R F = R Fields Electric Field Intensity r V l V π 2 = E (V/m) or = V dl E Magnetic Field Intensity r l H 2 F F = (A-t/m) or = F dl H Potential Electric Potential Difference ab ab ab b a b a ab IR l A l l I l l IR dl l V dl V = = = =
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ECE320_Formula_Sheet - ECE 320 Energy Conversion and Power...

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