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 Tue Sep Lecture 20 Prof. B.G.Fernandes 1/17 22, 2009

Sub ‐ Topics: • Transformers • Ideal and practical Transformers • Equivalent circuit representation • Equivalent circuit representation EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 2/17 22, 2009

Review Case i: ‘r’, leakage flux & core loss are neglected core loss = 0 ⇒ Air core d φ φ d = φ = φ ω = = φ e N dt t V E f N ⇒ , sin , 4.44 m m N → No. of turns ‘ φ ’ in the core is determined by supply ‘V’ alone ∠ = ∠ I I 0 0 90 90 V Case ii: Core loss is taken, V = E ∠ < I 0 90 V � � I I I I ∠ � ∠ � I cos cos 0 2 0.2 But But c m V EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 3/17 22, 2009

= = E v E v = = I I & c m R R X X c m = E 2 R C = core loss where I C I → I M → produces the ф → magnetizes the core ф → d th ti th L M (X M ) → Magnetizing inductance (reactance) (X ) → Magnetizing inductance (reactance) L � ∵ � R R I I c m c m ⇒ 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 Tue Sep Lecture 20 Prof. B.G.Fernandes 4/17 22, 2009

Case iii: ‘r’, leakage φ & core loss are taken into account V ≠ E but r & X l are small ∴ = φ � V E f N 4.44 m → Flux is determined by ‘V’ alone EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 5/17 22, 2009

TRANSFORMERS An important device used in power transmission, d d electronic circuits & communication systems. ⇒ consists of a magnetic circuit in which a time varying ‘ ф ’ lines link two or more coils ⇒ coupling can be air → air core transformer li b i i t f Iron → iron core transformer core is made up of laminations to ↓ core loss core is made up of laminations to ↓ core loss Purpose : Transfer electric energy from one circuit to another another Magnetic Electrical Electrical Energy gy Energy gy Energy Energy EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 6/17 22, 2009

No electrical connection between two circuits. ⇒ Electrically isolated ⇒ Electrically isolated 1 Principle of Operation: ⇒ magnetic circuit in which time 1 varying flux links two or more coils coils winding connected to source → Primary → Secondary → Secondary winding connected to load winding connected to load (?) Primary when connected to alternating source & secondary is open ⇒ no current in secondary ⇒ AT produced by secondary = 0 AT d d b d 0 EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 7/17 22, 2009

⇒ 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 N 1 turns & voltage (e 1 /E 1 ) is 1 1 1 induced = φ φ φ m φ m → peak value of ‘ φ ’ φ E f N 4.44 m m 1 1 1 1 � E V 1 1 ⇒ same ‘ ф ’ links the secondary ⇒ same ф links the secondary EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 8/17 22, 2009

⇒ e E / is the voltage induced in N 2 2 2 = φ E f N 4.44 m 2 2 ⇒ E 2 & E 1 are in phase ⇒ E & E are in phase E N ∴ = 2 2 E N 1 1 If N 2 > N 1 ⇒ Step up transformer N 2 < N 1 ⇒ Step down transformer Connect the load to secondary i 2 will flow ⇒ which sets up its own flux, φ 2 EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 9/17 22, 2009

⇒ This φ 2 opposes the parent ‘ φ ’ ⇒ fl ⇒ flux in the core tends to ↓ d t ↓ i th t ⇒ E 1 tends to ↓ ∵ V 1 is held constant V 1 = E 1 & ∴ ‘ ф ’ in the core should remain constant E 1 & ∴ ф in the core should remain constant V 1 ⇒ can happen when i 1 ↑ such that − = ℜφ N I N I 1 1 2 2 ⇒ ‘ ф ’ in the core is determined by V 1 alone ⇒ ф in the core is determined by V 1 alone EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 10/17 22, 2009

Theory of Ideal Transformer: winding ‘r ‘& leakage ‘ ф ’ are neglected i di ‘ ‘& l k ‘ ф ’ l t d = = V E & V E 1 1 2 2 ∴ AT required to establish ф = 0 μ r = ∞ ∴ℜ = 0 E V N I ∴ ∴ − = = ∴ ∴ = = = = = = = = N I N I N I N I 0 0 1 1 1 2 a a 1 1 2 2 E V N I 2 2 2 1 ∴ = 2 2 ⇒ ⇒ Input VA = Output VA p p VI VI 1 1 1 1 2 2 V V aV = = = 1 2 2 Z Z 1 I I 2 I I I I 2 2 1 2 a V = = 2 2 2 a a Z 2 I I 2 EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 11/17 22, 2009

∴ Equivalent ‘Z’ on the primary side = a 2 Z 2 ∴ An impedance Z 2 connected in the secondary can be transferred to the primary ' ' ∴ Eq. Secondary Z referred to the primary, = 2 Z a Z 2 2 ⇒ If ‘Z 1 ’ is the primary impedance, the equivalent 1 primary ‘Z’ referred to the secondary, Z ' Z = 1 1 1 2 2 a ⇒ In an ideal transformer ‘V’ are transformed in the direct ratio ‘I’ in the inverse ratio & Z/R/X in the direct ratio, I in the inverse ratio & Z/R/X in the square of the ratio ⇒ ‘P/ S (VI) remain the same ⇒ P/ S (VI) remain the same EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 12/17 22, 2009

Practical Transformer: ⇒ winding ‘r’ leakage ф & core loss are present ⇒ winding r , leakage ф & core loss are present μ ≠ ∞ ∴ℜ ≠ of the core 0 r ⇒ Source has to supply AT to establish ‘ ф ’ in the core Eq. Circuit Representation: e 1 ≠ v 1 & e 2 ≠ v 2 r 1 & r 2 are primary & secondary resistances respectively ⇒ Total flux in the primary winding = ф l1 + ф ⇒ Total flux in the secondary winding = ф l2 + ф ⇒ Total flux in the secondary winding = ф l2 + ф EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 13/17 22, 2009

∵ � iron core is used ф l1 ф ⇒ represent leakage flux by leakage inductance/reactance ⇒ represent leakage flux by leakage inductance/reactance X l1 in the primary (2 π fL 1 ) , L 1 → corresponds to leakage flux in primary flux in primary X l2 in the secondary (2 π fL 2 ), L 2 → corresponds to leakage flux in secondary flux in secondary ⇒ we need to account for only mutual flux or flux in the core ⇒ This flux links primary tightly coupled coils, K=1 and secondary coils EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 14/17 22, 2009

⇒ core has finite permeability ⇒ finite ATs are required to establish ‘ ф ’ in the core ⇒ finite ATs are req ired to establish ‘ ф ’ in the core ⇒ can be represented by magnetizing reactance, X M = 2 π fL ⇒ since φ in the core is alternating, there would be core φ i i h i l i h ld b 2 R C loss, I C = + I I I 0 C m ⇒ EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 15/17 22, 2009

∴ Equivalent Circuit: ⇒ In the ideal transformer V, I & Z can be transformed , from one side to another EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 16/17 22, 2009

⇒ In ideal transformer, if E 2 = 0 , E 1 = 0 should be zero 2 ⎛ ⎛ ⎞ ⎞ 2 ⎛ ⎛ ⎞ ⎞ N N N N = ' ' = 1 r r ⎜ ⎟ ' X X 1 ⎜ ⎟ 2 2 l l ⎝ N ⎠ 2 2 ⎝ N ⎠ 2 2 ⎛ ⎞ ⎛ ⎞ N N = = ' ' V V 1 I I 2 ⎜ ⎟ ⎜ ⎟ 2 2 2 2 ⎝ ⎝ N ⎠ ⎠ ⎝ ⎝ N ⎠ ⎠ 2 2 1 1 EE 111: Introduction to Electrical Systems Tue Sep Lecture 20 Prof. B.G.Fernandes 17/17 22, 2009