Introduction to Electrical Systems Course Code: EE 111 Course Code: - PowerPoint PPT Presentation

Introduction to Electrical Systems Course Code: EE 111 Course Code: EE 111 Department: Electrical Engineering Department: Electrical Engineering Instructor Name: B G Fernandes Instructor Name: B.G. Fernandes E ‐ mail id: bgf @ee iitb ac in E ‐ mail id: bgf @ee.iitb.ac.in EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 1/11 10, 2009

Sub ‐ Topics: • Power in 1 ‐ φ circuit • Measurement of Power • Power factor improvement EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 2/11 10, 2009

Review = = + V IZ, Z R jX ∴ ∴ = + + = − 2 2 Z Z R R X , X X , X X X X X L L C C = ∠ I P.F. cos V In an inductive circuit (R ‐ L/ L /series R ‐ L ‐ C with (X L >X C )) , d ( / / h ( )) P.F. is LAGGING In a capacitive circuit (R ‐ C/C/ series R ‐ L ‐ C with (X C >X L )) , P.F. is LEADING = + = ∠ = + = ∠ If & Z j Z j 8 6 10 36 6 8 10 53 1 2 ∠ = + Z Z ( ) 100 36 53 1 2 EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 3/11 10, 2009

Power in 1 ‐ φ circuit: = = ω ω v v V sin t V sin t Let Let 2 2 Z= Z ∠θ = ∠ is the applied voltage & V V 0 v V V = = ω − θ = ∠ − θ = − θ j i I sin( t ), I Ie 2 Z Z = Instantaneous power delivered to the load, p Instantaneous power delivered to the load, p vi vi = ω ω − θ 2 VI sin t sin( t ) [ ] = θ − ω − θ VI cos cos( t ) 2 alternating at twice the supply F constant term constant term = θ − θ ω − θ ω VI cos VI cos cos t VI sin sin t 2 2 EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 4/11 10, 2009

∴ Average power, = VI cos θ P W P θ = cos VI ⇒ θ = 0, load = R, ‘p’ is always +ve ⇒ θ ≠ 0, instantaneous power is negative, even though load is passive ⇒ Energy stored in L/C is returned back to source ⇒ p pulsates at 2f. Load may experience vibration p p y p ⇒ Requires resilient mountings EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 5/11 10, 2009

⇒ θ = ± π /2, Load is either ‘C’ or ‘L’. ⇒ p = ± VI sin2( ω t) Average P = 0 Average P = 0 ⇒ Power associated with pure L or C (reactive elements) referred to as reactive power ‘Q’ referred to as reactive power Q ⇒ In general, p = P – P cos2 ω t – Q sin2 ω t, VI sin θ VI sin θ Observations: P & Q have the same dimensions ‘Var’ reactive Watts volt ampere ampere EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 6/11 10, 2009

⇒ = = θ = + P VI cos , Z R jX ⎛ ⎞ R = = = = 2 ( IZ )I ( IZ )I I R I R ⎜ ⎜ ⎟ ⎟ ⎝ ⎠ Z = 2 Similarly, Q I X = + Complex power: S P jQ Dimensions same as P & Q ⇒ VA (Volt ‐ Ampere) EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 7/11 10, 2009

= θ + θ S VI cos jVI sin θ = j * VI e VI = Inductive circuit: Source supplies ‘Q’ Capacitive circuit: Source receives ‘Q’ Capacitive circuit: Source receives Q EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 8/11 10, 2009

Measurement of Power ⇒ Using wattmeter Current coil Current coil ⇒ Has 2 coils: Voltage coil M → Mains L → Load C → Common V → Voltage EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 9/11 10, 2009

Power factor improvement: Assume that ⇒ Load is scattered (Rural areas) ⇒ Power is distributed through overhead transmission P i di t ib t d th h h d t i i lines ⇒ M ⇒ Most of the loads are inductive t f th l d i d ti ∠ I ⇒ Load p.f. is lagging ( ) L V L L EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 10/11 10, 2009

= ∠ > I I |V | |V | Source P.F.= cos s L s L V S S If P.F. is leading If the P.F. is unity > |V | |V | ≥ ≥ ≤ ≤ |V | |V | |V | |V | |V | |V | |V | |V | or or s s L L s L L s L L EE 111: Introduction to Electrical Systems Mon, Aug Lecture 8 B.G.Fernandes 11/11 10, 2009