Effects of Synchronous Generator Load Change

Effect of Generator Loads Lagging Power Factor

If lagging loads (+Q or inductive reactive power loads) are added to a generator, the phase voltage V and the terminal voltage VT decrease.

Keep field excitation the same 'A AE E

A s AjX E V I

Effect of Generator Loads Unity Power Factor

A s AjX E V I

If unity-power-factor loads (no reactive power) are added to a generator, the phase voltage V and the terminal voltage VT slightly decrease.

Keep field excitation the same 'A AE E

Effect of Generator Loads Leading Power Factor

A s AjX E V I

If leading loads (-Q or capacitive reactive power loads) are added to a generator, the phase voltage V and the terminal voltage VT may increase.

Keep field excitation the same 'A AE E

Generator Voltage Regulation

100%nl flfl

V VVR

V

Lagging Load -> large positive voltage regulationUnit Power Factor Load -> small positive voltage regulationLeading load -> may be negative voltage regulation

Generator V Curves

The shape is like the letter V For each fixed real power, plot

armature current vs. field current.

Example 1 (1) A 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 0.015 . At full load, the machine supplies 1200 A 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 A 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 machines overall efficiency?(e) If the generators 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 A at 0.8 PF leading, how

much field current would be required to keep VT at 480 V?

Example 1 (2)

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Example 2 (1)

After the MatLab program can work, please change the load current to be 60 A at 1.0 PF, and 60 A at 0.8 PF leading and redo the above.

A 480V, 60 Hz, Y connected, six pole synchronous generator has a synchronous reactance of 1 and an armature resistance of 0.1 . At full load, the machine supplies 60 A 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 ?

sg2.m

Example 2 (2)

s A s A AR jX V I I E

0 sin cos sinA As A s A A

R I X I E I I

Imaginary part of

Let the angle of : =0. VV

becomes:

cos sinsin A As A s A

A

X I R IE

I INote: is negative when current is lagging.

cos cos sinA AA s A s A

V E R I X I I I

AI

A V I

Synchronous Generator Capability Curve

Generator Capability Curves (1)

(1) Stator Copper Loss (stator heating):

(2) Rotor Copper Loss (rotor heating):

(3) Prime-movers Power Limit.

23SCL A sP I R

2RCL F FP I R

The maximum allowable heating of the rotor sets a maximum field current IF for the machine. Its equivalent to set a maximum EA for the machine.

The maximum allowable heating of the rotor sets a maximum phase current IA for the machine. Its equivalent to set a maximum apparent power for the machine. (power factor is irrelevant)

Generator Capability Curves (2)

rotor field current sets the rated power factor

(rotor heating)

(stator heating)

A s AjX E V I

Generator Capability Curves (3)

A s AjX E V I

Assume V keeps rated value. Multiply the above figure by 3

S

VX

P

Q

Generator Capability Curves (4)

P

Q

capability curve

Q

Pflip

Generator Capability Curves (5)

Q

P

Add prime movers power limit (real power)

Example 3

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A 480V, 50 Hz, Y connected, six pole synchronous generator is rated at 50 kVA at 0.8 PF lagging. It has a synchronous reactance of 1.0 per phase. Assume 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 A 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?