Synchronous Generator Introduction

Transcription

1 Synchronous Generator Introduction

2 Synchronous Generator or lternator two-pole round rotor generator and exciter.

3 Cross Section of a Large Turbo Generator (Courtesy Westinghouse)

4 Round Rotor of a Large Generator (Courtesy Westinghouse)

5 Round Rotor with Conductor Placed

6 Four Pole Salient Pole Rotor

7 Large Salient Pole Hydro Generator (1) rotor

8 Large Salient Pole Hydro Generator (2) stator

9 Two Methods to Provide DC Field Current 1. Supply the DC power from an external DC source to the rotor by means of slip rings and brushes. - used in small synchronous generators, cost effective - brushes need to be checked for wear regularly - brush voltage drop can be significant power loss 2. Supply the DC power from a special DC power source (exciter) mounted on the shaft of the synchronous generator.

10 Rotor with Slip Rings

11 2 Stack Synchronous Generator System

12 3-Stack Synchronous Generator System (1) (completely independent of any external power source)

13 3-Stack Synchronous Generator System (2)

14 ircraft Synchronous Generator J. F. Gieras, dvancements in Electric Machines, Springer, 2008.

15 Synchronous Generator Phasor Diagram and Power Flow

16 Generator Phasor Diagram Lagging Power Factor E V R I jx I s s Over excited ( E ) V

17 Generator Phasor Diagram Unity Power Factor E V R I jx I s s Slightly over excited ( E ) V

18 Generator Phasor Diagram Leading Power Factor E V R I jx I s s Maybe under excited ( E ) V

19 Generator Power Flow P P P conv out Cu P T 3E I cos conv ind m E V R I jx I E I s s

20 Output Power P out 3V I cos I cos E sin X s E V R I jx I V jx I, since R X s s s s s P out P conv 3V E sin X S

21 Induced Torque P 3VE sin T conv ind m X S T ind 3V E sin m X S T kb B sin ind net R

22 Synchronous Generator Model Parameter Measurement

23 Measurement of Model Parameters 1. The relationship between field current and E 2. The synchronous reactance 3. The armature resistance

24 Open Circuit Characteristics (1) (or E T ) Saturation for large field current Dl NN ˆ ˆ E 8 2f I a f, rms e 0 2 f g eff P

25 Open Circuit Characteristics (2) Measurement Procedure: 1. Drive rotor at rated synchronous speed. 2. Increase field current I f upward from 0 3. Take data of V oc and plot V oc (or E ) vs I f

26 Short Circuit Characteristics (1) (or I L ) V 0 I I R s E jx R E s X 2 2 s s B B net V R B S 0 0 No saturation

27 Short Circuit Characteristics (2) Take three rms values in average and get 1 I sc, Ia Ib Ic 3 Measurement Procedure: 1. When = 0 and I f = 0, short the machine through three ammeters 2. When I f = 0, drive the machine to rated synchronous speed 3. Increase I f, take data (rms values) from three ammeters and plot I, sc vs I f

28 Measurement of Synchronous Reactance I sc, R E X 2 2 s s E X s X s E I sc, (1) Therefore, an approximate method for determining the synchronous reactance X s at a given field current is: 1. Get the internal voltage E from the OCC at that field current. 2. Get the short-circuit current flow I,SC at that field current from the SCC. 3. Find X s by applying (1).

29 Unsaturated Synchronous Reactance Saturation for large field current E I, sc No saturation X S, u Follow equation X s E I, sc The unsaturated synchronous reactance X s,u can be found simply by applying X E / I s, sc at any field current in the linear portion (on the airgap line) of the OCC curve.

30 Short-Circuit Ratio Short Circuit Ratio: The ratio of the field current required for the rated voltage at open circuit to the field current required for the rated armature current at short circuit. I fv rated voltage at OC SCR I fi rated current at SC E V,rated SCR I I I V 1 I I V I X fv x x, rated fi, rated, rated, rated s, I fv Z b SCR is inversely proportional to Xs Z b V I, rated rated, base impedance

31 Measurement of rmature Resistance The armature resistance R s can be approximately measured by applying a DC voltage to the windings while the machine is in stationary and measuring the resulting current flow. Using DC voltage means that the reactance of the windings will be zero during the measurement process. This technique is not perfectly accurate, since the C resistance will be slightly larger than the DC resistance (as a results of the skin effect at higher frequencies).

32 E versus I f under Load Round rotor generator rated at MV and 0.8 power factor lagging under two load conditions. Note: E is not quite proportional to I f under load since the extrapolation results in an intercept not at origin. For many practical applications, people Develop a useful approximate proportional relationship between E and I f.

33 Synchronous Generator Operation

34 Effect of Generator Loads Lagging Power Factor Keep field excitation the same E E ' E V jx I s If lagging loads (+Q or inductive reactive power loads) are added to a generator, the phase voltage V and the terminal voltage V T decrease.

35 Effect of Generator Loads Unity Power Factor Keep field excitation the same E E ' E V jx I s If unity-power-factor loads (no reactive power) are added to a generator, the phase voltage V and the terminal voltage V T slightly decrease.

36 Effect of Generator Loads Leading Power Factor Keep field excitation the same E E ' E V jx I s If leading loads (-Q or capacitive reactive power loads) are added to a generator, the phase voltage V and the terminal voltage V T may increase.

37 Generator Voltage Regulation VR V nl V V fl fl 100% Lagging Load -> large positive voltage regulation Unit Power Factor Load -> small positive voltage regulation Leading load -> may be negative voltage regulation

38 Generator V Curves The shape is like the letter V For each fixed real power, plot armature current vs. field current.

39 Example 1 (1) 480 V, 60 Hz, connected, four pole synchronous generator has the OCC curve shown in the figure. This generator has a synchronous reactance of 0.1 and an armature resistance of t full load, the machine supplies 1200 at 0.8 PF lagging. Under full load conditions, the friction and windage losses are 40 kw, and the core losses are 30 kw. Ignore any field circuit losses. (a) What is the speed of rotation of this generator? (b) How much field current must be supplied to the generator to make the terminal voltage 480 V at no load? (c) If the generator is now connected to a load and the load draws 1200 at 0.8 PF lagging, how much field current is required to keep the terminal voltage equal to 480 V? (d) How much power is the generator now supplying? How much power is supplied to the generator by the prime mover? What is the machine s overall efficiency? (e) If the generator s load were suddenly disconnected from the line, what would happen to its terminal voltage? (f) Finally, suppose that the generator is connected to a load drawing 1200 at 0.8 PF leading, how much field current would be required to keep V T at 480 V?

40 Example 1 (2) sg1.m

41 Example 2 (1) 480V, 60 Hz, Y connected, six pole synchronous generator has a synchronous reactance of 1 and an armature resistance of 0.1. t full load, the machine supplies 60 at 0.8 PF lagging. Under full load conditions, the friction and windage losses are 1.5 kw, and the core losses are 1.0 kw. Ignore any field circuit losses. (a) What is the speed of rotation of this generator? (b) What is the terminal voltage of this generator at full load assuming the field excitation current keeps the same as no load? (c) What is the efficiency of this generator at full load? (d) How much shaft torque must be supplied by the prime mover at full load? How large is the induced counter torque? (e) What is the voltage regulation of this generator? fter the MatLab program can work, please change the load current to be 60 at 1.0 PF, and 60 at 0.8 PF leading and redo the above. sg2.m

42 Example 2 (2) Let the angle of V : V =0. Imaginary part of V R I jx I E becomes: s s 0 RI sin X I cos E sin s I s I X si cos I R sin si I sin E Note: I is negative when current is lagging. V I V E cos R I cos X I sin s I s I

43 Synchronous Generator Capability Curve

44 Generator Capability Curves (1) (1) Stator Copper Loss (stator heating): P 3I R 2 SCL s The maximum allowable heating of the stator sets a maximum phase current I for the machine. It s equivalent to set a maximum apparent power for the machine. (power factor is irrelevant) (2) Rotor Copper Loss (rotor heating): P I R 2 RCL F F The maximum allowable heating of the rotor sets a maximum field current I F for the machine. It s equivalent to set a maximum E for the machine. (3) Prime-mover s Power Limit.

45 Generator Capability Curves (2) E V jx I s (rotor heating) (stator heating) rotor field current sets the rated power factor

46 Generator Capability Curves (3) E V jx I s ssume V keeps rated value. Multiply the above figure by P 3V X S Q

47 Generator Capability Curves (4) P Q Q flip P capability curve

48 Generator Capability Curves (5) Q P dd prime mover s power limit (real power)

49 Example 3 480V, 50 Hz, Y connected, six pole synchronous generator is rated at 50 kv at 0.8 PF lagging. It has a synchronous reactance of 1.0 per phase. ssume that this generator is connected to a steam turbine capable of supplying up to 45 kw. The friction and windage losses are 1.5 kw, and the core losses are 1.0 kw. (a) Sketch the capability curve for this generator, including the prime-mover power limit. (b) Can this generator supply a line current of 56 at 0.7 PF lagging? Why or why not? (c) What is the maximum amount of reactive power this generator can produce? (d) If the generator supplies 30 kw of real power, what is the maximum amount of reactive power that can be simultaneously supplied? sg3.m

50 Synchronous Motor Operation

51 UCF Synchronous Motor and Generator (1) motor generator T ind kb R B net T ind kb R B net sin

52 UCF Synchronous Motor and Generator (2) Motor Generator V R I jx I E s s V R I jx I E s s

53 UCF Torque of Synchronous Motor V E R I jx I P T 3V I V E 3 X ind s P m s s cos sin (for m s R V E 3 sin X X s ) T ind kb R B net sin Pull-out torque: when sin=1, the maximum torque the machine can get. T max V E 3 X m s T max kb R B net o Typically take Tmax 3 Tfullload (or sin 1 / 3, ) in the design (leave margin).

54 UCF P V E 3V I cos : fixed (when I Effect of Load Change V E 3 X sin : fixed (from electrical course) s fixed or using permanent magnets) F 2 (load increases) sin more heat (3 s) P I I R (leading lagging) t full load, typically pick up cos 1 in the design. E V Xs sin, E I cos

55 UCF Example 1 Details in sm1.m

56 UCF Effects of Field Current Change V E R I jx I E s s jx I s

57 UCF Underexcited Synchronous Motor

58 UCF Overexcited Synchronous Motor Behaves like a capacitor: can be used for power factor correction. Called synchronous capacitor or synchronous condenser.

59 UCF Synchronous Motor V Curves

60 UCF Example 2 sm2.m

61 UCF Power factor Correction Using Overexcited Synchronous Motor - Example 3 sm3.m