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 Mon Oct 1/13 Prof. B.G.Fernandes Lecture 32 26, 2009

Sub ‐ Topics: • Effect of variation of load P.F. on synchronous machine • Expression for power EE 111: Introduction to Electrical Systems Mon Oct 2/13 Prof. B.G.Fernandes Lecture 32 26, 2009

Review Synchronous generator → Alternator Synchronous generator → Alternator used for high power (MW) applications ⇒ Invariably stator has 3 ‐ φ distributed winding ⇒ 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 ∴ℜ → reluctance) ℜ ( ⇒ ‘L’ is independent of rotor position ‘L’ i i d d f i i EE 111: Introduction to Electrical Systems Mon Oct 3/13 Prof. B.G.Fernandes Lecture 32 26, 2009

⇒ Salient pole construction is suitable for low speed applications (no. of poles could be 24) pp p Salient pole → air gap is non ‐ uniform & ∴ℜ ⇒ ℜ is minimum along field axis (direct axis) ⇒ ℜ is maximum along q ‐ axis (quadrature axis) ∴ ‘L’ depends on rotor position p p If is min → ‘L’ would be max ℜ If is max, → L would be min is max → ‘L’ would be min ℜ ℜ If ∴ ‘L’ varies between L min (= L q ) & L max (= L d ) ⇒ so what? ⇒ later ⇒ apart from field winding there is cage winding as well EE 111: Introduction to Electrical Systems Mon Oct 4/13 Prof. B.G.Fernandes Lecture 32 26, 2009

i) variation of E 0 (open circuit voltage) with I F at constant N is OCC N r is OCC φ f In phasor form E f ii) when I s is flowing in the stator winding, it produces its own flux ⇒ air gap flux → vector sum of φ F & φ A ⇒ 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. ⇒ this effect depends on load P.F. EE 111: Introduction to Electrical Systems Mon Oct 5/13 Prof. B.G.Fernandes Lecture 32 26, 2009

⇒ In eq. ckt this effect could be represented by a reactance X reactance, X a X sl → leakage reactance R s → stator resistance/ph R i / h In high power m/c → R << (X l + X ) In high power m/c → R s << (X sl + X a ) x s → synchronous reactance ⇒ Z S = (R S + jX S ) → synchronous impedance, neglecting R s , Z s ≅ X s l i R Z X EE 111: Introduction to Electrical Systems Mon Oct 6/13 Prof. B.G.Fernandes Lecture 32 26, 2009

Lagging power factor: π π ∠ ∠ Eo Eo = ∠ ∠ Ea Ea = φ F φ R 2 2 < | φ | | φ | | φ | | φ | R R F F ⇒ lagging ‘I’ tries to oppose the field flux ⇒ demagnetizing effect ⇒ demagnetizing effect Leading power factor: | φ R | could be greater than | φ F | ⇒ leading current tries to aid ⇒ leading current tries to aid the field flux ⇒ magnetizing effect ⇒ magnetizing effect EE 111: Introduction to Electrical Systems Mon Oct 7/13 Prof. B.G.Fernandes Lecture 32 26, 2009

Unity power factor: ⇒ difference between| φ R | & | φ F | in UPF case < difference between | φ R | & | φ F | in lagging P.F. case difference between | φ R | & | φ F | in lagging P.F. case ⇒ though in phase component of current does not directly oppose the field flux, it tries to distort the field ⇒ cross magnetization EE 111: Introduction to Electrical Systems Mon Oct 8/13 Prof. B.G.Fernandes Lecture 32 26, 2009

If V t = V ∠ 0 = ∠ δ is +ve for generator action E E δ 0 0 Expression for power: Expression for power: ∠δ − ∠ E V 0 = 0 I Z ∠θ S S S ∠ δ − θ ∠ − θ E V ( ) = = − 0 Z Z S S ⎡ ⎤ ⎡ ⎤ E V E V = δ − θ − δ θ θ + θ + δ − θ + δ θ + θ θ 0 0 0 0 ⎢ ⎢ ⎥ ⎥ j j ⎢ ⎢ ⎥ ⎥ cos( cos( ) ) cos cos sin( sin( ) ) sin sin Z Z Z Z ⎣ ⎦ ⎣ ⎦ S S S S EE 111: Introduction to Electrical Systems Mon Oct 9/13 Prof. B.G.Fernandes Lecture 32 26, 2009

power/phase = V I s cos φ V E V [ ] = δ − θ − θ V cos( ) cos 0 Z S In synchronous machine |R S |<< |X S | π θ ≅ 2 |Z S | ≅ |X S | & 2 3E V = δ 0 Total power sin X X S ⇒ synchronous generator (rating in MVA) is always connected in parallel with other generators ⇒ connected to grid EE 111: Introduction to Electrical Systems Mon Oct 10/13 Prof. B.G.Fernandes Lecture 32 26, 2009

δ → angle between F s and F R From Newton’s law, (rate of change of ’ l ( f h f angular momentum is the net torque) d ω dt ∝ − (T T ) m e dt T e → electrical torque T m → mechanical torque d δ dt = ω at steady state, T m = T e & ∴ ω = ω st = synchronous speed EE 111: Introduction to Electrical Systems Mon Oct 11/13 Prof. B.G.Fernandes Lecture 32 26, 2009

Operation at δ 1 : assume that for some reason, δ 1 has ↑ slightly assume that for some reason, δ 1 has ↑ slightly ⇒ no change in mechanical input ⇒ (T m ‐ T e ) (or (P m ‐ P e )) 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 δ 2 : Operation at δ 2 : if for some reason δ 2 has ↑ ⇒ (T ⇒ (T m ‐ T e ) is + ve T ) is + ve try to accelerate the rotor further ⇒ δ 2 ↑ further δ ↑ f ∴ unstable h bl EE 111: Introduction to Electrical Systems Mon Oct 12/13 Prof. B.G.Fernandes Lecture 32 26, 2009

π ∴ stable operating range is < < 2 0 δ 2 ⇒ generally δ is around 30 0 ⇒ If δ is high and big disturbance is given, δ may ↑ above π /2 and the system may become unstable EE 111: Introduction to Electrical Systems Mon Oct 13/13 Prof. B.G.Fernandes Lecture 32 26, 2009