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 08, 2009

1/15 Lecture 18

Sub‐Topics:

• Hysteresis & Eddy current loss
• Hysteresis & Eddy current loss
• Loss representation in equivalent circuit

Loss representation in equivalent circuit

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue, Sep 08, 2009

2/15 Lecture 18

Review

1

NI φ = ℜ If μr → ∞ (core is highly permeable) AT required to establish φ in the core = 0 0, ℜ → ⇒If core gets saturated ( φ does not change with ‘i') dφ

1

d di l φ ⇒ → ⇒ →

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue, Sep 08, 2009

l ⇒ →

3/15 Lecture 18

‘v’ is input voltage ⇒ should not allow the core to saturate ⇒ ‘i' is limited by ‘r’ (winding resistance) ⇒ should not allow the core to saturate ⇒ provide an air gap φ ⇒ all the AT is used to establish φ in the air gap ⇒ Inductance reduces and leakage flux would increase

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue, Sep 08, 2009

4/15 Lecture 18

Leakage flux is negligible Fringing is negligible

Tue, Sep 08, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

g g g g

5/15 Lecture 18

Air gap = 4mm Leakage flux is more

Tue, Sep 08, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

6/15 Lecture 18

Tue, Sep 08, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

7/15 Lecture 18

Air gap 4mm

Tue, Sep 08, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

8/15 Lecture 18

Air gap 4mm

Tue, Sep 08, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

9/15 Lecture 18

e.g.

1 1

l ℜ =

1 1 1

A ℜ μ l2

2 1 2

l A ℜ = μ

3 3 2

l A ℜ = μ0

2

A μ

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue, Sep 08, 2009

10/15 Lecture 18

Magnetization Curve: Consider a ‘brand new’ core (not magnetized) ‘I’ Consider a ‘brand new’ core (not magnetized) ‘I’ = 0 ∴ H = 0 & ⇒ φ = 0 ( B = 0 ) ‘I’ ( H ) ⇒ φ also ( B ) Increase ‘H‘ further For low values of ‘I’ (& ∴ H) B linearly till point ‘C’ ⇒ φ also ( B ) Increase H further ⇒ corresponding increase in ‘B’ is non linear . ⇒ Core is saturated ⇒ ‘B’ remains ≅ constant B is non linear .

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

⇒ Core is saturated

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue, Sep 08, 2009

11/15 Lecture 18

⇒ B‐H curve (OD) is the magnetization curve ⇒ f OC i it i d(?) t b li ⇒ from OC circuit is assumed(?) to be linear , NI l A ℜ = ℜ μ μ

φ =

rA

ℜ μ μ ⇒ In this region is assumed to remain constant ℜ ∴ μr is constant ⇒ ‘C’ is point where saturation starts constant ⇒ C is point, where saturation starts ⇒ Knee point variation of ф(B) with i(H) is non‐linear CD core is saturated

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue, Sep 08, 2009

12/15 Lecture 18

⇒ is not constant ℜ i t t t It t ti ⇒ as the degree of saturation ⇒ is not constant ℜ ∴ℜ depends on the operating flux density ∴ µr is not constant. It as saturation ⇒ ‘φ’ is produced by ‘I’ flowing in a coil ⇒ change in ‘φ’ beyond ‘C’ is small ⇒ φ is produced by I flowing in a coil ⇒ this coil has its own resistance ⇒ I2R loss Where do we operate the magnetic circuit ? ⇒ I2R loss

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

• Prof. B.G.Fernandes

Tue, Sep 08, 2009

13/15 Lecture 18

Generating action: conductor is rotated in the magnetic field ‘F’ limits ‘v’

B

e lv ∝ ∴ ‘e’ can be by B conductor is rotated in the magnetic field Motoring action : ‘I’ carrying conductor placed in a magnetic field F limits v ∴ e can be by B

F BIl ∝

‘I’ carrying conductor placed in a magnetic field experiences force

F BIl ∝

∴ If ‘I’ , I2R loss , temperature rise, η F ⇒ operate the magnetic circuit at ‘C’ F A B ∴ ∝

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

⇒ operate the magnetic circuit at C

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Tue, Sep 08, 2009

14/15 Lecture 18

Hysteresis: Brand new core: A ‘i' (f A B) H & φ B ‘i' now decreases (B‐C) As ‘i' (from A‐B), H & ∴ φ or B B‐H curve will follow a different path (PQ) When i = 0 (H=0), B = Br Residual magnetism

Tue, Sep 08, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Residual magnetism

15/15 Lecture 18