Sistemas de potencia

A Short Course on Synchronous Machines and Synchronous Condensers
G. Heydt S. Kalsi E. Kyriakides
Arizona State University American Superconductor
© 2003 G. Heydt, S. Kalsi and E. Kyriakides

Session Introductions 1 Fundamentals of synchronous machines

Time 8:30 – 8:40 8:40 – 9:50

Topics • Energy conversion • Synchronous machine construction • Energy transfer in a synchronous machine• Motor and generator action • Phasor diagram for synchronous machines • Losses • Superconducting designs • Power factor and torque angle • Example of calculations • Transients and damper windings • Saturation and the magnetization curve

Instructor Bradshaw Heydt

BREAK

9:50 – 10:00

2 Synchronous condensers

10:00 10:30

–

3 Superconducting 10:30 synchronous 12:00 condensers

–• What is a synchronous condenser? • Applications of synchronous condensers • Analysis • Superconductivity • The superconducting synchronous condenser (SSC) • Performance benefits of SSC in a grid

Kalsi

Kalsi

LUNCH

12:00 – 1:30

4 Synchronous machine models

1:30 – 2:30

5 State estimation applied to synchronous generators

2:30 – 3:30

• Park’s transformation • Transientand subtransient reactances, formulas for calculation • Machine transients • Basics of state estimation • application to synchronous generators • demonstration of software to identify synchronous generator parameters

Heydt

Kyriakides

BREAK 6 Machine instrumentation Question and answer session

3:30 – 3:40 3:40 – 4:30

4:30 – 5:00

• DFRs • Calculation of torque angle • Usualmachine instrumentation

Heydt, Kyriakides, and Kalsi All participants

SESSION 1

Fundamentals of synchronous machines

Synchronous Machines
• Example of a rotating electric machine • DC field winding on the rotor, AC armature winding on the stator • May function as a generator (MECHANICAL ELECTRICAL) or a motor (ELECTRICAL MECHANICAL) • Origin of name: syn = equal, chronos = timeSynchronous Machines

ROTATION

• FIELD WINDING • ARMATURE WINDING

Synchronous Machines
The concept of air gap flux
STATOR

ROTOR

Synchronous Machines
• The inductance of the stator winding depends on the rotor position • Energy is stored in the inductance • As the rotor moves, there is a change in the energy stored • Either energy is extracted from the magnetic field (and becomesmechanical energy – that is, its is a motor) • Or energy is stored in the magnetic field and eventually flows into the electrical circuit that powers the stator – this is a generator

Synchronous Machines
The basic relationships are POWER = ( TORQUE ) (SPEED)
2) ENERGY = (1/2) ( L I

POWER = d(ENERGY) / d(TIME)

Synchronous Machines
Consider the case that the rotor (field) is energized byDC and the stator is energized by AC of frequency f hertz. There will be average torque produced only when the machine rotates at the same speed as the rotating magnetic field produced by the stator. RPM = ( 120 f ) / (Poles) Example: f = 60 Hz, two poles, RPM = 3600 rev/min

Synchronous Machines
d
The axis of the field winding in the direction of the DC field is called the rotor direct axisor the d-axis. 90 degrees later than the d-axis is the quadrature axis (q-axis).

ROTATION

q
The basic expression for the voltage in the stator (armature) is v = r i + dλ/dt Where v is the stator voltage, r is the stator resistance, and λ is the flux linkage to the field produced by the field winding

Synchronous Machines
Basic AC power flow

jx
SEND
Vsend

RECEIVE

VreceiveSynchronous Machines
Vinternal

Vterminal
The internal voltage, often labeled E, is produced by the field interacting with the stator winding, and this is the open circuit voltage

GENERATOR ACTION – POWER FLOWS FROM MACHINE TO EXTERNAL CIRCUIT, E LEADS Vt

Synchronous Machines
Vterminal
Vinternal

The internal voltage, often labeled E, is produced by the field interacting with the...