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Engineering 43. Prob 5.80 Solution Dual-Source Complex-Power Balance. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. BackGround EE (§5.5). Consider Sinusoidal Sources of the form Alternatively Recall for a Sinusoid Complex Power Where
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Engineering 43 Prob 5.80SolutionDual-SourceComplex-PowerBalance Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu
BackGround EE (§5.5) • Consider Sinusoidal Sources of the form • Alternatively • Recall for a Sinusoid • Complex Power • Where • S ≡ Complex Power in V∙A • P ≡ Real Power in Watts • Q ≡ ReActive Power in VAR
BackGround EE (§5.5) • Each Passive Component (R, C, L, Vsrc, Isrc) Generates it’s own Complex Power in an operating Circuit • Furthermore Complex Power is Conserved, just a real power was conserved in purely resistive Circuits; i.e.: • Equating Real & Imag Parts
R, C, L vs. P&Q • Note that the passive sign Convention Applies to Complex Power a well • Positive Pwr → ABSORBED or DISSIPATED • Negative Pwr → SUPPLIED or GENERATED • RESISTORS can only DISSIPATE Real Power per Text Eqns (5.69) & (5.71) • IRrms ≡ Current thru R • VRrms ≡ Voltage across R
R, C, L vs. P&Q • INDUCTORS create POSITIVEReActive (imaginary) Power per Text Eqns (5.70) & (5.72) • Where • ILrms ≡ Current thru L • VLrms ≡ Voltage across L • XL ≡ Inductive ReActance, ωL
R, C, L vs. P&Q • CAPACITORS create NEGATIVEReActive (imaginary) Power per Text Eqns (5.70) & (5.72) • Where • ICrms ≡ Current thru C • VCrms ≡ Voltage across C • XC ≡ Capacitive ReActance, −1/(ωC)
S by ShortHand Calc • Alternatively Calculate S for any Component using the COMPLEX CONJUGATE of the CURRENT Thru the device • Recall Conjugation for Imaginary of Phasor Values
S by ShortHand Calc • If • Then • Also For Sources the Apparent Power:
Apparent Power • Apparent Power Calculations are usually used with SOURCES, but the concept also applies to Impedance Loads • Given an Impedance with Current IZ, and Voltage-Drop VZ then
Problem 5.80 • Given Circuit • Find The Power Condition for each element, the Quantity, Nature, and if the element is Absorbing/Supplying Power • Note that this is SINGLE LOOP Circuit which thus has ONE Current
Confirm: ∑Pavg = 0 • Note that the Average Powers Add to ZERO as they must by conservation of Energy
