1. SYNCHRONOUS GENERATORS
SUBMITTED BY:
Ms. JASPREET KAUR
ASST. PROFESSOR-EEE

2. SYNCHRONOUS GENERATORS Phasor Diagram of Equivalent Circuit
Voltages in Syn. Gen. are ac & expressed in phasor which have both magnitude and angle, therefore need to be presented in 2 dimensional plot.
KVL relation of one phase can be plotted in terms of phasor voltages through this 2 dimensional plot named phasor diagram
which show the relationship between different voltages and currents

3. SYNCHRONOUS GENERATORS Phasor Diagram of Equivalent Circuit
Figure below show the phasor diagram when supplying a load at unity power factor
EA differs from Vφ by resistive & inductive voltage drops, all referenced to Vφ which arbitrarily assumed at an angle of 0◦

4. SYNCHRONOUS GENERATORS Phasor Diagram of Equivalent Circuit
Phasor diagram when generators operating at lagging & leading power factors

5. SYNCHRONOUS GENERATORS Phasor Diagram of Equivalent Circuit
Note: at specific phase voltage & armature current, a larger internal voltage EA required for lagging loads than for leading loads
Therefore a larger field current required with lagging loads to get same terminal voltage
EA=Kφω
Alternatively for a given IF and load current , Vφ is lower for lagging loads & higher for leading loads
In real synchronous machines, XS normally much larger than RA & often neglected in qualitative study

6. SYNCHRONOUS GENERATORS Power and Torque
A synchronous generator is a synchronous machine used as generator
converts mechanical energy to 3 phase electrical energy
Source of mechanical energy is prime mover (a diesel engine , a steam turbine, …)
Any source employed should have an almost constant speed regardless of load
If it were not constant, the power system frequency would wander

7. SYNCHRONOUS GENERATORS Power and Torque
Not all mechanical power going to a synchronous generator becomes electrical power the difference between input & output power represent losses, Power flow Diagram

8. SYNCHRONOUS GENERATORS Power and Torque
input mechanical power is shaft power in generator
Pin=Тprime-mover ωm
(Тprime-mover ≡ Tapp in text book)
Pconv=Tgenerated ωm = 3EA IA cos γ
(γ angle between EA and IA)
(Tgenerated ≡Tind in text book)
Difference between Pin and Pconv in generator represents mechanical, core, and stray losses of machine

9. SYNCHRONOUS GENERATORS Power and Torque
Real elect. output power of syn. Gen. in line quantities:
Pout=√3 VT IL cosθ
in phase quantities:
Pout=3 Vφ IA cosθ
reactive power output:
Qout=√3 VT IL sinθ
Qout=√3 Vφ IA sinθ
ignoring armature resistance RA (XS>>RA), a useful relation can be derive to approximate output power of Gen.

10. SYNCHRONOUS GENERATORS Power and Torque
Generator Equivalent circuit for Δ connection

11. SYNCHRONOUS GENERATORS Power and Torque
To derive that useful equation, when stator resistance ignored, phasor diagram employed

12. SYNCHRONOUS GENERATORS Power and Torque
The vertical segment bc is EA sinδ or XS IA cosθ
 IA cosθ = EA sinδ / XS
Substituting this in equation of Pout 
P = 3Vφ EA sinδ / XS
since resistances assumed zero, losses not included in this equation (& it is both Pconv ,Pout)
Above equation shows power produced by a Syn. Gen. depends on angle δ (between Vφ,EA), the torque angle
Maximum power that Gen. can supply occurs when δ=90◦. At this angle sinδ=1 
Pmax=3Vφ EA / XS (1)

13. SYNCHRONOUS GENERATORS Power and Torque
Maximum power in last equation called “static stability limit” of Gen.
Real or practical Gen. never get close to this limit
Full load torque angles of 15 to 20◦ are typical angle of real machines
If Vφ assumed constant, real power output directly proportional to IA cosθ and EA sinδ
These are useful for plotting phasor diagram of Syn. Gen. as load changes

14. SYNCHRONOUS GENERATORS Power and Torque
From chapter 4, torque developed in a Gen. can be expressed as:
Тind= k BR X BS
Tind=k BR X Bnet
Magnitude of torque in this equation is:
Тind=kBRBnet Sinδ
δ: angle between rotor and net magnetic fields
Since BR produces voltage EA, and Bnet produces voltage Vφ, angle δ between EA and Vφ is same as angle between BR and Bnet

15. SYNCHRONOUS GENERATORS Power and Torque
Alternative expression for this torque in syn. Gen. is derived (employing Pconv= Tind ωm) and Equation (1):
Tind=3Vφ EA sinδ/(ωm XS) (2)
This equation gives torque in terms of circuit parameters, while the equation in last chapter expressed it in terms of magnetic quantities

16. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
Equivalent circuit of synchronous generator contains 3 quantities that must be determined to describe behavior of a real Syn. Gen.
1- relation between field current & flux (IF & EA)
2- Synchronous reactance
3- Armature resistance
To determine these parameters, the first step is to do open-circuit test
1- Generator is turned at rated speed, and terminals disconnected from loads, field current set to zero
2- Field current gradually increased in steps, and terminal voltage measured at each step along the way

17. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
Leave terminals open IA=0, Vφ= EA and thus construct a plot of EA or VT versus IF
This plot is open circuit characteristic (OCC) of Gen.
With this characteristic, internal generated voltage of Gen. for any given IF can be determined
typical characteristic shown 

18. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
Note : in this characteristic, as If increases first curve is almost perfectly linear until some saturation observed at high field current
Unsaturated iron in frame of synchronous machine has a reluctance several thousand times lower than air-gap reluctance
 at first all mmf is across air gap and resulting flux increase is linear
When iron saturate reluctance of iron increase profoundly and flux increases more slowly with a similar increase in mmf
Linear section of OCC called air-gap line

19. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
Second step is to perform a short circuit test
1- adjust field current to zero
2- short circuit terminals of generator through a set of ammeter
3- armature current IA or line current IL measured as IF increased
4- such a plot named short
circuit characteristic (SCC)
It is a straight line

20. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
It is a straight line, since employing the equivalent circuit developed in this section:
IA= EA/(RA+jXS)
Phasor diagram shown:
Flux density vectors shown:

21. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
Bnet is very small since almost BR and BS cancels
The machine is unsaturated and SCC is linear
The magnitude of current:
IA= EA / √[RA ^2+jXS ^2]
internal Impedance of machine ZS=√RA^2+XS^2=EA/IA
Since XS>>RA above relation reduces:
XS≈ EA/IA =Vφ,OC/ IA (3)
if EA and IA known for given situation, synchronous reactance XS can be found

22. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
Approximate method for determining synchronous reactance XS :
1- measure internal voltage EA open circuit test
at the specific field current (OCC)
2- measure short circuit current flow IA,SC at the
same field current (SCC)
3- Find XS using the approximate equation (3)

23. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
Concern:
the EA is determined from OCC where machine is partially saturated for large field currents
While IA is determined form SCC , where machine is unsaturated at all field currents
Therefore at high field currents (that core is saturated in OC) EA measured from OCC at a specific If ≠ EA measured at same If under short-circuit conditions
This makes resulting value of XS only approximate

24. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
However, answer found by this method is accurate up to the saturation point
So, unsaturated synchronous reactance XS,u can be found at any If in linear portion of OCC
Approximate Xs varies with degree of saturation of OCC, so it should be calculated at approximate load on machine
Plot of approximate XS as function of If shown 

25. SYNCHRONOUS GENERATORS MEASUREMENT of MODEL PARAMETERS
It is important to know winding resistance as well as synchronous reactance
Resistance can be approximated by applying dc voltage to winding while machine is stationary & measuring the resultant current flow
use of dc voltage means reactance of windings will be zero in measurement
However, this is not perfect since ac resistance is larger than dc resistance due to skin effect
Measured value of resistance can be inserted in impedance equation to improve determination of synchronous reactance, however this doesn’t help since the error due to saturation has much larger effect in Xs