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

• Prof. B.G.Fernandes

Thu Sep 24, 2009

1/10 Lecture 21

Sub‐Topics:

• Eq. circuit(contd..)
• O.C and S.C tests
• Efficiency of Transformer
• Efficiency of Transformer

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

2/10 Lecture 21

Review

• Winding connected to the source is known as primary

g p y winding

• H.V → H.V. winding, L.V → L.V. winding

g, g

• I1 ≠ 0 when I2 = 0
• For an ideal transformer

1 1 1 2

V N E I

• For an ideal transformer,

1 1 1 2 2 2 2 1

V N E I V N E I = = = and Input VA = Output VA

• Eq. secondary ‘R’ referred to primary

2

N ⎛ ⎞

1 2 2 2

N r '=r N ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

3/10 Lecture 21

• Under normal operation, V1 ≅ V2’

If V1 = 11kV, V2’≅ 11kV or If V 440V V ’≅440V If V1 = 440V, V2’≅440V

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

4/10 Lecture 21

• eg. 100kVA, 11kV/440V, 1‐φ transformer and HV winding

is connected to the 11kV Transformer is fully loaded and is connected to the 11kV. Transformer is fully loaded and load P.F. is 0. 6lag h t d 100kVA ? what does 100kVA mean? Is it primary VA or secondary VA or both? ⇒ only in case of ideal transformer, primary VA = sec. VA when secondary winding is kept open y g p p ⇒ primary current is finite ⇒ this current has two components (core loss + magnetizing)

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

5/10 Lecture 21

⇒ since secondary is open → there is no load on the Transformer ≅ 5‐10% of full load current (?) Transformer ⇒The corresponding current is known as no‐load current ≅ 5 10% of full load current (?) ⇒ It is the rated load that the transformer can supply at rated terminal voltage rated terminal voltage ⇒ V2I2

2

VA Full load current V ∴ = VA

2 1

VA under this condtion, primary 'I' may not be , but it is V ≅

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

6/10 Lecture 21

what is V2? when primary winding is connected to 11kV, secondary ⇒ but it is ≅ 440V when primary winding is connected to 11kV, secondary terminal ‘V’ need not be 440V ∴ using VA, V1 and V2, it is possible to estimate the rated ‘I’ in the primary & secondary windings without using the

• eq. circuit

rated load current on L.V. side

3

100 10 440 x = = 227A at 0.6 lag r'1 = r2 = 0.0112 Ω 440 x'l1 = xl2 = 0.096 Ω X’M = 44 Ω & R’c=132 Ω

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

7/10 Lecture 21

( )( )

E' 440 0 227 53 0.0966 83.34 = ∠ + ∠− ∠ 459.067 1.38V E I' 10.43 88.7A = ∠ = = ∠−

m M

I 10.43 88.7A jX E I' 3 47 1 38A ∠ = = ∠

C C

I 3.47 1.38A R = = ∠

' 1 2

Total I ' = I I 237.52 54A + = ∠−

( )( )

1 2 1 O

Total I I I 237.52 54A V' 459.067 1.38 237.52 54 0.0966 83.34 9 3 + ∠ = ∠ + ∠− ∠ ∠

O

479.5 3 V = ∠

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

8/10 Lecture 21

• winding resistance << leakage flux (??)

Observations:

• winding resistance << leakage flux (??)
• Io is predominantly reactive

’

• E1 ≅ V’2 ≅ V1

⇒ can we shift the magnetizing branch to supply side ?

1 1

• c

M

V V I j R X = −

I0

' s 2

I = I I + φ θ

eq eq eq

Z R jX = +

1 2 2 eq

& V V' I' Z ∠σ = ∠ + ∠φ ∠θ ⇒ approximate eq circuit

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

⇒ approximate eq. circuit

9/10 Lecture 21

with approximate eq. circuit

M

479.5 I 10.89A % change = 3.6 44 479 5 = =

c

479.5 I 3.62A % change = 4.3 132 = =

lagging P.F. unity P.F. leading P.F.

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Thu Sep 24, 2009

10/10 Lecture 21