# Sistemas de potencia

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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

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