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

Tue Sep 22, 2009

Lecture 20 1/17

Sub‐Topics:

• Transformers
• Ideal and practical Transformers
• Equivalent circuit representation
• Equivalent circuit representation

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 2/17

Review Case i: ‘r’, leakage flux & core loss core loss = 0 ⇒ Air core dφ are neglected N → No. of turns sin ,

m

t φ = φ ω , d e N dt φ = 4.44

m

V E f N = = φ ⇒

90 ∠I

‘φ’ in the core is determined by supply ‘V’ alone

90 ∠ =

I V

Case ii: Core loss is taken, V = E

90

I V

∠ <

I I

• cos

0 2

I

∠

But

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

c m

I I

• cos

0.2

V

∠

But

Tue Sep 22, 2009

Lecture 20 3/17

&

c m

E v E v I I R X = = = =

c m

R X where IC

2RC = core loss

I → d th ф → ti th

= E

IM → produces the ф → magnetizes the core L (X ) → Magnetizing inductance (reactance)

c m

I I ∵

LM (XM) → Magnetizing inductance (reactance)

c m

R R

• ⇒ Since core loss (hysteresis loss + eddy ‘I’ loss) are taken

into account ‘I’ would be non‐sinusoidal (due to hysteresis loop) ⇒ Distortion in ‘I’ ↑ as the saturation ↑

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 4/17

Case iii: ‘r’, leakage φ & core loss are taken into account V ≠ E but r & Xl are small 4.44

m

V E f N ∴ = φ

• → Flux is determined by ‘V’ alone

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 5/17

TRANSFORMERS

d d An important device used in power transmission, electronic circuits & communication systems. ⇒ consists of a magnetic circuit in which a time varying ‘ф’ lines link two or more coils li b i i t f ⇒ coupling can be air → air core transformer Iron → iron core transformer core is made up of laminations to ↓ core loss Purpose : Transfer electric energy from one circuit to another core is made up of laminations to ↓ core loss another Electrical Energy Magnetic Energy Electrical Energy

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Energy gy gy

Tue Sep 22, 2009

Lecture 20 6/17

No electrical connection between two circuits. ⇒ Electrically isolated ⇒ Electrically isolated Principle of Operation:

1

⇒ magnetic circuit in which time varying flux links two or more coils

1

coils winding connected to source → Primary winding connected to load → Secondary Primary when connected to alternating winding connected to load → Secondary

(?)

source & secondary is open ⇒ no current in secondary AT d d b d

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

⇒ AT produced by secondary = 0

Tue Sep 22, 2009

Lecture 20 7/17

⇒ AT supplied is just sufficient to establish ‘φ’ in the core ⇒ If core is highly permeable, this AT is small

( how small is this small?)

⇒ since ‘φ’ is alternating ⇒ core loss ⇒ source has to supply some power ⇒ for the present we will neglect ⇒ Time varying ‘φ’ links N1 turns & voltage (e1 /E1 ) is

1 1 1

induced

1 1

4.44

m

E f N = φ φm → peak value of ‘φ’

1 1 m

φ φm φ

1 1

E V

• ⇒ same ‘ф’ links the secondary

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 8/17

⇒ same ф links the secondary

⇒ is the voltage induced in N2

/

2 2

e E

⇒ E & E are in phase

2 2

4.44

m

E f N = φ ⇒ E2 & E1 are in phase

2 2

E N ∴ =

1 1

E N If N2 > N1 ⇒ Step up transformer N2 < N1 ⇒ Step down transformer Connect the load to secondary i2 will flow ⇒ which sets up its own flux, φ2

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 9/17

⇒ This φ2 opposes the parent ‘φ’ ⇒ fl i th t d t ↓ ⇒ flux in the core tends to ↓ ⇒ E1 tends to ↓ ∵ V1 is held constant V1 = E1 & ∴‘ф’ in the core should remain constant V1 E1 & ∴ ф in the core should remain constant ⇒ can happen when i1 ↑ such that

1 1 2 2

N I N I − = ℜφ

⇒ ‘ф’ in the core is determined by V1 alone ⇒ ф in the core is determined by V1 alone

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 10/17

Theory of Ideal Transformer: i di ‘ ‘& l k ‘ф’ l t d winding ‘r ‘& leakage ‘ф’ are neglected

1 1 2 2

V E & V E = =

μr = ∞ ∴ℜ = N I N I ∴ − =

1 1 1 2

E V N I a ∴ = = = = ∴AT required to establish ф = 0

1 1 2 2

N I N I ∴ =

2 2 2 1

a E V N I ∴ = = = =

1 1 2 2

VI VI ∴ = ⇒ Input VA = Output VA

1 1 2 2 ⇒

p p

2 2

V Z I =

1 2 1 2

V aV Z I I = =

2

I

2 1

I I a

2 2 2 2

V a a Z I = =

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

2

I

Tue Sep 22, 2009

Lecture 20 11/17

∴ Equivalent ‘Z’ on the primary side = a2 Z2 ∴ An impedance Z2 connected in the secondary can be transferred to the primary

'

∴ Eq. Secondary Z referred to the primary,

'

2 2 2

Z a Z = ⇒ If ‘Z1’ is the primary impedance, the equivalent

1

primary ‘Z’ referred to the secondary,

'

1 1 2

Z Z =

⇒ In an ideal transformer ‘V’ are transformed in the direct ratio ‘I’ in the inverse ratio & Z/R/X in the

1 2

a

direct ratio, I in the inverse ratio & Z/R/X in the square of the ratio ⇒ ‘P/ S (VI) remain the same

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

⇒ P/ S (VI) remain the same

Tue Sep 22, 2009

Lecture 20 12/17

Practical Transformer: ⇒ winding ‘r’ leakage ф & core loss are present ⇒ winding r , leakage ф & core loss are present

μ ≠ ∞

r

• f the core

∴ℜ ≠ ⇒ Source has to supply AT to establish ‘ф’ in the core

• Eq. Circuit Representation:

e1≠ v1 & e2≠ v2 r1 & r2 are primary & secondary resistances respectively ⇒ Total flux in the primary winding = фl1 + ф ⇒ Total flux in the secondary winding = фl2 + ф

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

⇒ Total flux in the secondary winding = фl2 + ф

Tue Sep 22, 2009

Lecture 20 13/17

⇒ represent leakage flux by leakage inductance/reactance iron core is used фl1 ф

• ∵

⇒ represent leakage flux by leakage inductance/reactance Xl1 in the primary (2πfL1) , L1→corresponds to leakage flux in primary flux in primary Xl2 in the secondary (2πfL2), L2 → corresponds to leakage flux in secondary ⇒ we need to account flux in secondary for only mutual flux

• r flux in the core

⇒This flux links primary and secondary coils

tightly coupled coils, K=1

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 14/17

⇒ core has finite permeability ⇒ finite ATs are req ired to establish ‘ф’ in the core ⇒ finite ATs are required to establish ‘ф’ in the core ⇒ can be represented by magnetizing reactance, XM= 2πfL i φ i h i l i h ld b ⇒ since φ in the core is alternating, there would be core loss, IC

2RC

C m

I I I = + ⇒

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 15/17

∴ Equivalent Circuit: ⇒ In the ideal transformer V, I & Z can be transformed , from one side to another

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue Sep 22, 2009

Lecture 20 16/17

⇒ In ideal transformer, if E2= 0, E1= 0 should be zero

'

2

N ⎛ ⎞

2

N ⎛ ⎞

' 1 2 2 2

N r r N ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

' 1 2 2 2 l l

N X X N ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

' 1 2 2 2

⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ N V V N

' 2 2 2 1

⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ N I I N

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

2

⎝ ⎠

1

⎝ ⎠

Tue Sep 22, 2009

Lecture 20 17/17