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

Mon Oct 26, 2009

1/13 Lecture 32

Sub‐Topics:

• Effect of variation of load P.F. on synchronous machine
• Expression for power

EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

Mon Oct 26, 2009

2/13 Lecture 32

Review Synchronous generator → Alternator Synchronous generator → Alternator ⇒ Invariably stator has 3‐φ distributed winding used for high power (MW) applications ⇒ Invariably stator has 3 φ distributed winding & rotor → field winding → connected to dc can be replaced by PM ⇒ Doubly fed machine → fed from stator as well as from rotor Rotor → cylindrical/ non‐salient pole → suitable for high speed (3000 rpm) ⇒air gap is uniform is constant ( →reluctance) ∴ℜ ℜ ‘L’ i i d d f i i

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

⇒ ‘L’ is independent of rotor position

3/13 Lecture 32

⇒Salient pole construction is suitable for low speed applications (no. of poles could be 24) Salient pole → air gap is non‐uniform & ∴ℜ ⇒ is minimum along field axis (direct axis) ℜ pp p ∴ ‘L’ depends on rotor position ⇒ is maximum along q‐axis (quadrature axis) ℜ p p If is max → ‘L’ would be min ℜ If is min →‘L’ would be max ℜ ∴ ‘L’ varies between Lmin(= Lq) & Lmax(= Ld) If is max,→ L would be min ℜ ⇒ so what? ⇒ later ⇒ apart from field winding there is cage winding as well

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

4/13 Lecture 32

i) variation of E0 (open circuit voltage) with IF at constant N is OCC Nr is OCC In phasor form

φf Ef

ii) when Is is flowing in the stator winding, it produces its

• wn flux

⇒ air gap flux → vector sum of φF & φA ⇒ effect of stator flux on rotor flux is known as armature ⇒ effect of stator flux on rotor flux is known as armature reaction ⇒ this effect depends on load P.F.

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

⇒ this effect depends on load P.F.

5/13 Lecture 32

⇒ In eq. ckt this effect could be represented by a reactance X Xsl → leakage reactance R i / h reactance, Xa Rs→ stator resistance/ph In high power m/c → R << (X l+ X ) In high power m/c → Rs<< (Xsl+ Xa) xs → synchronous reactance ⇒ ZS= (RS + jXS)→ synchronous impedance, l i R Z X neglecting Rs, Zs ≅ Xs

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

6/13 Lecture 32

Eo

π ∠

Ea

π ∠ Lagging power factor:

Eo φF

2 ∠ =

Ea φR

2 ∠ =

R F

|φ | |φ | < ⇒ lagging ‘I’ tries to oppose the field flux ⇒ demagnetizing effect

R F

|φ | |φ | ⇒ demagnetizing effect Leading power factor: |φR| could be greater than |φF| ⇒ leading current tries to aid ⇒ leading current tries to aid the field flux ⇒ magnetizing effect

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

⇒ magnetizing effect

7/13 Lecture 32

Unity power factor: ⇒ difference between|φR| & |φF| in UPF case < difference between |φR| & |φF| in lagging P.F. case ⇒ though in phase component of current does not difference between |φR| & |φF| in lagging P.F. case directly oppose the field flux, it tries to distort the field ⇒ cross magnetization

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

8/13 Lecture 32

If Vt = V∠0 E E δ = ∠ Expression for power: δ is +ve for generator action

S

E V 0 I ∠δ − ∠ = Expression for power:

S S

Z ∠θ ( ) E V ∠ δ − θ ∠ − θ = −

S S

Z Z = cos( ) cos sin( ) sin E V E V j ⎡ ⎤ ⎡ ⎤ δ θ θ + δ θ + θ ⎢ ⎥ ⎢ ⎥ cos( ) cos sin( ) sin

S S S S

j Z Z Z Z = δ − θ − θ + δ − θ + θ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

9/13 Lecture 32

V power/phase = V Iscosφ

[ ]

cos( ) cos

S

V E V Z = δ − θ − θ In synchronous machine |RS|<< |XS| |ZS| ≅|XS| & 2 π θ ≅ 2 sin 3E V X = δ Total power

S

X ⇒ synchronous generator (rating in MVA) is always connected in parallel with other generators ⇒ connected to grid

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

10/13 Lecture 32

δ → angle between Fs and FR ’ l ( f h f From Newton’s law, (rate of change of angular momentum is the net torque)

m e

dω (T T ) dt ∝ − dt Tm → mechanical torque Te → electrical torque dδ ω dt = at steady state, Tm = Te & ∴ ω = ωst = synchronous speed

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

11/13 Lecture 32

assume that for some reason, δ1 has ↑ slightly Operation at δ1: assume that for some reason, δ1 has ↑ slightly ⇒ no change in mechanical input ⇒ (Tm ‐ Te) (or (Pm‐ Pe)) is negative ( m

e) (

( m

e))

g ⇒ generator would decelerate and come back to its original place come back to its original place ⇒ stable Operation at δ2: if for some reason δ2 has ↑ Operation at δ2: ⇒ (T T ) is + ve ⇒ (Tm ‐ Te) is + ve try to accelerate the rotor further δ ↑ f h bl

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

⇒ δ2 ↑ further ∴ unstable

12/13 Lecture 32

∴ stable operating range is π δ 2 < < 2 ⇒ generally δ is around 300 ⇒ If δ is high and big disturbance is given, δ may ↑ above π/2 and the system may become unstable

Mon Oct 26, 2009 EE 111: Introduction to Electrical Systems

• Prof. B.G.Fernandes

13/13 Lecture 32