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’s Name: B G Fernandes Instructor s 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

Lecture 14 1/12

Mon, Aug 31, 2009

Sub‐Topic:

• Measurement of Power

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 14 2/12

Mon, Aug 31, 2009

REVIEW

• Balanced system: 3 Voltage sources have same

magnitude & ‘f’, but phase displaced by 120o

• Balanced load: |Z| & θ are same in all 3 phases
• In Y connected system, |VL| = |Vph| &

leads by 30o 3

L

V

Ph

V y

L

• In Δ connected system, |VL| = |Vph| & |IL| =

|Iph| & 3

p p

lags by 30o

L

I

Ph

I

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 14 3/12

Mon, Aug 31, 2009

• Phase sequence & reference vector should be known to

it ‘V’ ti f ll 3 h write ‘V’ equations for all 3 phases 3 Ø, 440V, 50Hz ⇒ 440 V is L‐L Voltage (R.M.S value) g ( )

• In 3 phase 4 wire system
• In 3‐phase 4‐wire system,

( )

= + +

N A B C

I I I I

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 14 4/12

Mon, Aug 31, 2009

Power in 3‐Ф circuits: ⇒ Recall ‘p’ in 1Ф circuits pulsates at 2f ⇒ Recall p in 1Ф circuits pulsates at 2f

2 4 π π ⎛ ⎞ ⎛ ⎞

∴ 1‐Ф motors require special resilient mountings

2 4 2 sin 2 sin 2 sin 3 3 , &

a b c

v V t v V t v V t π π ω ω ω ⎛ ⎞ ⎛ ⎞ = = − = − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠

Let

( ) 2 4 2 i 2 i 2 i i I t i I t i I t π π θ θ θ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟

and ∴Instantaneous power

( ) 2 sin , 2 sin , 2 sin 3 3

a b c

i I t i I t i I t ω θ ω θ ω θ ⎛ ⎞ ⎛ ⎞ = − = − − = − − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠

and

( )

cos cos 2

a a a

p v i VI t θ ω θ ⎡ ⎤ = = − − ⎣ ⎦

( )

2 240 i VI t θ θ ⎡ ⎤

( )

cos cos 2 240

b b b

p v i VI t θ ω θ ⎡ ⎤ = = − − − ⎣ ⎦

( )

cos cos 2 480

c c c

p v i VI t θ ω θ ⎡ ⎤ = = − − − ⎣ ⎦

EE 111: Introduction to Electrical Systems B.G.Fernandes

( )

⎣ ⎦

Lecture 14 5/12

Mon, Aug 31, 2009

∴Total instantaneous 3‐Ф power = 3VI cosθ = 3VphIphcosθ 3VphIphcosθ

ph ph

I V

θ =∠

= Average power = Constant If system is ‘Y’ connected ,

L ph ph L

v v I I = = 3 cos

L L

P V I θ ∴ = , 3

ph ph L

3 cos

L L

P V I θ ∴ If Load is delta connected

3

L Ph L Ph

V V I I = =

, L Ph L Ph

P = 3 cosθ W

L L

V I ∴ Independent of type of connection

*

Q = 3 sinθ VAr S = 3 VA

L L L L

V I V I ∴

EE 111: Introduction to Electrical Systems B.G.Fernandes

Q

L L L L

Lecture 14 6/12

Mon, Aug 31, 2009

Measurement of Power: ‘W’ di

I

How many wattmeters to use? ‘W’ reading

Flowing Applied

I Flowing Applied V

= I V cos∠

How many wattmeters to use? Incase of 3‐phase 4 wire system, if the load is balanced ⇒ One meter is sufficient Total power = W * 3 Total power W 3 If the load is unbalanced, 3 Total power = W1+W2+W3 ⇒ use 3 meters

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 14 7/12

Mon, Aug 31, 2009

In case of 3‐phase 3 wire load: T tt t th d Two wattmeter method:

A

I

cos W V I = ∠ A

AB

1 V

cos

AB A

W V I = ∠

A AB Ac

I I I = +

Let

A

I

α ∠ =

Let

A AB

V

α ∠ = cos = I cos cos I I α θ θ +

AB 1

cos I cos cos

A AC

I I α θ θ +

EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 14 8/12

Mon, Aug 31, 2009

1

cos

AB A

W V I α ∴ =

AB AB

V I

cos cos(60+ )

AB AB AB AC

V I V I θ = ∠ +

= Power in phase AB

cos(60+ )

L AC

V I θ +

Power in phase AB

cos(60 )

L AC

V I θ +

Similarly

C

I

cos W V I = ∠

Similarly

C CB

2 V

cos

CB C

W V I = ∠

C CB CA

I I I = +

2

cos

CB CB

I CB CB V I

W V I = ∠ cos

CA CB

I CB CA V

V I + ∠ (60 )

CA

I V

θ ∠ = −

EE 111: Introduction to Electrical Systems B.G.Fernandes

(60 )

CB

V

θ ∠

Lecture 14 9/12

Mon, Aug 31, 2009

( ) ( )

cos 60 cos 60

L AC L AC

V I V I θ θ + + −

Power in 3rd phase

cosθ =

L AC

V I

⇒ Observations: If load is balanced

h

I

1

2

3 cosθ = +

⇒

L L

V I W W

ph ph

I V

θ =∠

If load is unbalanced

3 θ W W P P P V I

1 2

3 cosθ + = + + ≠

A B C L L

W W P P P V I

Power in phase A

EE 111: Introduction to Electrical Systems B.G.Fernandes EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 14 10/12

Mon, Aug 31, 2009

1

cos = ∠ A

AB

I AB A V

W V I cos(30 ) θ + V I cos(30 ) θ = +

L L

V I

2

cos = ∠ C

CB

I CB C V

W V I cos(30 ) θ = −

L L

V I

If θ = 0 ⇒ Load is ‘R’, W1 = W2 If θ = π/3, one of the Wattmeter would read zero ⇒ If θ > π/3, read ‐ve ( h & ) (interchange M & L)

1

2 1

tan 3 θ

−

⎛ ⎞ − = ⎜ ⎟ ⎝ ⎠ W W W W

EE 111: Introduction to Electrical Systems B.G.Fernandes EE 111: Introduction to Electrical Systems B.G.Fernandes

1 2

⎜ ⎟ + ⎝ ⎠ W W

Lecture 14 11/12

Mon, Aug 31, 2009

Note: Phase sequence & lines in which they are connected should be known to determine whether connected should be known to determine whether θ is +ve or ‐ve

EE 111: Introduction to Electrical Systems B.G.Fernandes EE 111: Introduction to Electrical Systems B.G.Fernandes

Lecture 14 12/12

Mon, Aug 31, 2009