module g1 electric power generation and machine controls james d. mccalley
TRANSCRIPT
Module G1
Electric Power Generation and Machine Controls
James D. McCalley
Overview• Energy transformation into electrical form• Generation operation
– Revolving magnetic field– Phasor diagram– Equivalent Circuit– Power relationships– Generator pull-out power
• Excitation control• Turbine speed control
Energy Transformation
• Transformation processes:– Chemical– photovoltaic– electromechanical
• Electromechanical: conversion of energy from coal, petroleum, natural gas, uranium, water flow, geothermal, and wind into electrical energy
• Turbine-synchronous AC generator conversion process most common in industry today
http://powerlearn.ee.iastate.edu/library/html/isupp39.html
Click on the below for some pictures of power plantsand synchronous generators
http://powerlearn.ee.iastate.edu/library/html/amespp1.html
http://powerlearn.ee.iastate.edu/library/html/amespp34.html
http://powerlearn.ee.iastate.edu/library/html/isupp1.html
ISU Power Plant
ISU Power Plant synchronous generator
Ames Power Plant
Ames Power Plant synchronous generator
Feedback Control Systems for Synchronous Generators
• Turbine-generator basic form
• Governor and excitation systems are known as feedback control systems; they control the speed and voltage respectively
A Two Pole Machine (p=2)Salient Pole Structure
Synchronous Machine Structure
N
S
+
+
DCVoltage
Phase A
Phase B
Phase C
STATOR(armaturewinding)
ROTOR(field winding)
The negative terminalfor each phase is180 degrees fromthe correspondingpositive terminal.
+
Salient PoleConstruction
Smooth rotorConstruction
A Four Pole Machine (p=4)(Salient Pole Structure)
Synchronous Machine Structure
N
S
N
S
Generation Operation
• The generator is classified as a synchronous machine because it is only at synchronous speed that it can develop electromagnetic torque
• • = frequency in rad/sec
• = machine speed in RPM
• p = number of poles on the rotor of the machine
m ep2
e f2
Np
fs 120
For 60 Hz operation (f=60)
• Synchronous generator
Rotor construction
Round Rotor Salient Pole
Two pole s = 3600 rpm
Four Poles = 1800 rpm
Eight Poles = 900 rpm
No. of Poles (p) Synchronous speed (Ns)------------------- ----------------------------- 2 3600 4 1800 6 1200 8 900 10 720 12 600 14 514 16 450 18 400 20 360
For 60 Hz operation (f=60)
Fact: hydro turbines are slow speed, steam turbines are high speed.
Do hydro-turbine generators have few poles or many?
Do steam-turbine generators have few poles or many?
Fact: salient pole incurs significant mechanical stress at high speed.
Do steam-turbine generators have salient poles or smooth?
Fact: Salient pole rotors are cheaper to build than smooth.
Do hydro-turbine generators have salient poles or smooth?
Generation Operation• A magnetic field is provided by the DC-current
carrying field winding which induces the desired AC voltage in the armature winding
• Field winding is always located on the rotor where it is connected to an external DC source via slip rings and brushes or to a revolving DC source via a special brushless configuration
• Armature winding is located on the stator where there is no rotation
• The armature consists of three windings all of which are wound on the stator, physically displaced from each other by 120 degrees
Synchronous Machine Structure
N
S
+
+
DCVoltage
Phase A
Phase B
Phase C+
• voltage induced in phase wdgs by flux from field wdg• current in phase wdgs produces flux that also induces voltage in phase wdgs.
Stator
Statorwinding Slip
rings
Brushes
Rotorwinding
+-
Generation Operation: The revolving magnetic field
• = flux associated with the revolving magnetic field which links the armature windings. It will have a flux density of B.
• At any given time t, the B-field will be constant along the coil.
• By Faraday’s Law of Induction, the rotating magnetic field will induce voltages phase displaced in time by 120 degrees (for a two pole machine) in the three armature windings
• Let’s consider just the A-phase.
f
dlBuec
A )(
B
u
eB field
Direction of rotation+
_
Voltage induced in the conductor = Blu
Magneticfield lines
Stator
RotorAirgap
0
2
B, flux densityin the air gap
Voltage induced in one turn ( 2 conductors)is e = 2Blu.
If there are N turns per winding, the voltageinduced is e = 2NBlu.
If the speed of rotation of the rotor is , andthe radius of the rotor is r, u = rand e = 2NBlr
If the flux density changes sinusoidally in the airgap, B = Bmax sin t, and the induced voltage is
e = 2BmaxNlrsin t = Emax sin t
Generation Operation: The revolving magnetic field (cont’d)
• = resultant field with associated flux obtained as the sum of the three component fluxes is the field of armature reaction
• The two fields represented by and are stationary with respect to each other
• The armature field has “locked in” with the rotor field and the two fields are said to be rotating in synchronism
• The total resultant field = +
ar
f ar
r ar f
a cb
If each of the three armature windings are connected across equal impedances, balanced three phase currents will flow in themproducing their own magnetic fields = =
Generation Operation:The phasor diagram
• From Faraday’s Law of Induction, a voltage is induced in each of the three armature windings:
where N = number of winding turns
• All voltages, ,lag their corresponding fluxes, ,by 90 degrees
• The current winding a, denoted by , is in phase with the flux it produces
dt
dNe r
Ia
ar
E E Er ar f, ,
r ar f, ,
Generation Operation: The phasor diagram (cont’d)
• Note: E E Er f ar
Generation Operation: The equivalent circuit model
• Develop equivalent model for winding a only; same applies to winding b and c with appropriate 120 degree phase shifts in currents and voltages given a balanced load
E Nddtar
ar ( )X Iar a90 jX Iar a
E E jX Ir f ar a
V E jX I E j X X It r l a f l ar a ( ) E jX If s a
Generation Operation: The equivalent circuit model (cont’d)
Generation Operation: The equivalent circuit model (cont’d)
Ef
jXs
ZloadVt
Ia
Generation Operation: The equivalent circuit model (cont’d)
In per-phase, Ef and Vt are both line to neutral voltages,Ia is the line current, and Z is the impedance of theequivalent Y-connected load.
In per-unit, Ef and Vt are per-unit voltages,Ia is the per unit current, and Z is the per unit load impedance.
You can perform per-phase equivalent analysisor you can perform per-unit analysis.
Leading and Lagging Generator Operation
LetVtt VVZZ || ,||
From the equivalent circuit,
)(||||
||||
V
tVtta Z
VZ
VZV
I
So here we see thatiVVi
Leading and Lagging Generator Operation
Assign Vt as the reference: 0V
Then,
)(||||
)(||||
ZV
ZV
ZV
I tV
tta
So here we see that i
This gives an easy way to remember the relation between load, sign of current angle, leading/lagging, and sign of power angle.
Leading and Lagging Generator Operation
Inductive load Capacitive load----------------------------------------------------------------
ggingleading/la iscurrent
0?
0?
0?
Q ppliesabsorbs/sugen
Q ppliesabsorbs/su load
i
X
ggingleading/la iscurrent
0?
0?
0?
Q bsorbssupplies/agen
Q ppliesabsorbs/su load
i
X
Circle the correct answer in each column
Phasor Diagram for Equivalent Circuit
Ef
jXs
ZloadVt
Ia
From KVL: astf IjXVE
Phasor Diagram for Equivalent Circuitastf IjXVE
This equation gives directions for constructing the phasor diagram.1. Draw Vt phasor2. Draw Ia phasor3. Scale Ia phasor magnitude by Xs and rotate it by 90 degrees.4. Add scaled and rotated vector to Vt Vt
Try it for lagging case. Ia
XsIa
jXsIa
jXsIa
Ef
Phasor Diagram for Equivalent Circuit
astf IjXVE
This equation gives directions for constructing the phasor diagram.1. Draw Vt phasor2. Draw Ia phasor3. Scale Ia phasor magnitude by Xs and rotate it by 90 degrees.4. Add scaled and rotated vector to Vt
You do it for leading case.
Phasor Diagram for Equivalent Circuit
astf IjXVE
Let’s define the angle that Ef makes with Vt as
|| ff EE
For generator operation (power supplied by machine),this angle is always positive.
For motor operation, this angle is negative.