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 B.G.Fernandes Mon, Aug 10, 2009

Lecture 8 1/11

Sub‐Topics:

• Power in 1‐ φ circuit
• Measurement of Power
• Power factor improvement

EE 111: Introduction to Electrical Systems B.G.Fernandes Mon, Aug 10, 2009

Lecture 8 2/11

Review

V IZ, Z R jX = = +

2 2 L C

Z R X , X X X ∴ = + = −

d ( / / h ( ))

L C

Z R X , X X X ∴ +

P.F. cos

I V

= ∠

In an inductive circuit (R‐L/ L /series R‐L‐C with (XL>XC)), P.F. is LAGGING In a capacitive circuit (R‐C/C/ series R‐L‐C with (XC>XL)), P.F. is LEADING

1 2

100 36 53 Z Z ( ) = +

∠

1

8 6 10 36 Z j = + = ∠

2

6 8 10 53 Z j = + = ∠

& If

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 8 3/11

Power in 1‐φ circuit: Let

2 v V sin t ω =

Let

2 v V sin t ω =

V V = ∠ is the applied voltage &

V

Z=Z∠θ

2

j

v V i I sin( t ), I Ie Z Z

θ

ω θ θ

−

= = − = ∠ − =

Instantaneous power delivered to the load, p

vi =

Instantaneous power delivered to the load, p

vi 2VI sin t sin( t ) ω ω θ = −

constant term alternating at twice the supply F

[ ]

2 VI cos cos( t ) θ ω θ = − −

constant term

2 2 VI cos VI cos cos t VI sin sin t θ θ ω θ ω = − −

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 8 4/11

∴Average power,

W P VI cosθ =

P cos VI θ =

⇒ 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

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 8 5/11

⇒ θ = ± π/2, Load is either ‘C’ or ‘L’. ⇒ p = ± VI sin2(ωt) 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 cos2ωt – Q sin2ωt, VI sinθ VI sinθ Observations: P & Q have the same dimensions

Watts ‘Var’ reactive ampere volt

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

ampere

Lecture 8 6/11

⇒ =

P VI cos , Z R jX θ = = +

2

R ( IZ )I I R ⎛ ⎞ = = ⎜ ⎟ ( IZ )I I R Z = = ⎜ ⎟ ⎝ ⎠

2

Similarly, Q I X = Complex power: Dimensions same as P & Q

S P jQ = +

VA (Volt‐Ampere) ⇒

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 8 7/11

S VI cos jVI sin θ θ = +

=

j *

VI e VI

θ

= Inductive circuit: Source supplies ‘Q’ Capacitive circuit: Source receives ‘Q’ Capacitive circuit: Source receives Q

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 8 8/11

Measurement of Power

⇒ Using wattmeter Current coil ⇒ Has 2 coils: Current coil Voltage coil M → Mains L → Load C → Common V → Voltage

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 8 9/11

Power factor improvement:

Assume that ⇒ Load is scattered (Rural areas) P i di t ib t d th h h d t i i ⇒ M t f th l d i d ti ⇒ Power is distributed through overhead transmission lines ⇒ Most of the loads are inductive ⇒ Load p.f. is lagging (

)

L L

I V

∠

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

L

Lecture 8 10/11

s L

|V | |V | >

Source P.F.= cos

s L S

I I V =

∠

S

If the P.F. is unity If P.F. is leading

s L

|V | |V | >

• r

L L

|V | |V | |V | |V | ≥ ≤

Mon, Aug 10, 2009 EE 111: Introduction to Electrical Systems B.G.Fernandes

s L

• r

s L s L

|V | |V | |V | |V | ≥ ≤

Lecture 8 11/11