Electric Machinery PowerPoint Slides Chapter 5 Synchronous Machines to accompany Electric Machinery Sixth Edition A.E. Fitzgerald Charles Kingsley, Jr. Stephen D. Umans Chapter 5 Synchronous Machines

5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES Two types: 1-Cylindirical rotor: High speed, fuel or gas fired power plants To produce 50 Hz electricity p=2, n=3000 rpm p=4, n=1500 rpm 2-Salient-pole rotor: Low speed, hydroelectric power plants To produce 50 Hz electricity p=12, n=500 rpm p=24, n=250 rpm

5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES How does a synchronous generator work? 1- Apply DC current to rotor winding (field winding) 2- Rotate the shaft (rotor) with constant speed. 3- Rotor magnetic field will create flux linkages in stator coils and as a result voltage will be produced because of Faraday’s Law. Why is impossible to rotate a synchronous motor when it is connected to 50 Hz electric power? Because before connecting to supply, the shaft speed of rotor is zero. If the motor is two-pole, when it is connected to 50 Hz supply it suddenly needs to rotate 3000 rpm. This is impossible for large synchronous motors.

5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES How is DC current applied to the rotor? 1- Slip Rings Note: Magnetic field of rotor can also be produced by permanent magnets for small machine applications 2- Brushless Excitation System: Excitation supplied from ac exciter and solid rectifiers. The alternator of the ac exciter and the rectification system are on the rotor. The current is supplied directly to the field-winding without the need to slip rings.

Torque-angle characteristic. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES Steady-state torque equation Torque-angle characteristic. 5-4

5.1 INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES Synchronous generators work in parallel with the interconnected system. Frequency and voltage are constant. The behivor is examined based on a generator connected to an INFINITE BUS. Infinite bus Generator f : constant V : constant

Fundamental component 5.2 SYNCHRONOUS-MACHINE INDUCTANCES; EQUIVALENT CIRCUTS Self inductances: Fundamental component Leakage flux component

5.2 SYNCHRONOUS-MACHINE INDUCTANCES; EQUIVALENT CIRCUTS Mutual inductances:

5.2 SYNCHRONOUS-MACHINE INDUCTANCES; EQUIVALENT CIRCUTS For balanced system Ls : Defined as synchronous inductance. It is the effective inductance seen by phase a under steady state balanced conditions.

Terminal voltage for phase a 5.2.4 EQUIVALENT CIRCUTS Terminal voltage for phase a In complex form:

Synchronous Reactance 5.2.4 EQUIVALENT CIRCUTS Motor: Generator: Synchronous Reactance

Synchronous-machine equivalent circuit showing air-gap and leakage components of synchronous reactance and air-gap voltage. Figure 5.4

Open-circuit characteristic of a synchronous machine. Figure 5.5

Typical form of an open-circuit core-loss curve. Figure 5.6

Open- and short-circuit characteristics of a synchronous machine. Figure 5.7

Phasor diagram for short-circuit conditions. Figure 5.8

Open- and short-circuit characteristics showing equivalent magnetization line for saturated operating conditions. Figure 5.9

Typical form of short-circuit load loss and stray load-loss curves. Figure 5.10

(a) Impedance interconnecting two voltages; (b) phasor diagram. Figure 5.11

Equivalent-circuit representation of a synchronous machine connected to an external system. Figure 5.12

Example 5. 6. (a) MATLAB plot of terminal voltage vs.  for part (b) Example 5.6. (a) MATLAB plot of terminal voltage vs.  for part (b). (b) MATLAB plot of Eaf vs. power for part (c). Figure 5.13

Equivalent circuits and phasor diagrams for Example 5.7. Figure 5.14

Characteristic form of synchronous-generator compounding curves. Figure 5.15

Capability curves of an 0. 85 power factor, 0 Capability curves of an 0.85 power factor, 0.80 short-circuit ratio, hydrogen-cooled turbine generator. Base MVA is rated MVA at 0.5 psig hydrogen. Figure 5.16

Construction used for the derivation of a synchronous generator capability curve. Figure 5.17

Typical form of synchronous-generator V curves. Figure 5.18

Losses in a three-phase, 45-kVA, Y-connected, 220-V, 60-Hz, six-pole synchronous machine (Example 5.8). Figure 5.19

Direct-axis air-gap fluxes in a salient-pole synchronous machine. Figure 5.20

Quadrature-axis air-gap fluxes in a salient-pole synchronous machine. Figure 5.21

Phasor diagram of a salient-pole synchronous generator. Figure 5.22

Phasor diagram for a synchronous generator showing the relationship between the voltages and the currents. Figure 5.23

Relationships between component voltages in a phasor diagram. Figure 5.24

Generator phasor diagram for Example 5.9. Figure 5.25

Salient-pole synchronous machine and series impedance: (a) single-line diagram and (b) phasor diagram. Figure 5.26

Power-angle characteristic of a salient-pole synchronous machine showing the fundamental component due to field excitation and the second-harmonic component due to reluctance torque. Figure 5.27

(a) Single-line diagram and (b) phasor diagram for motor of Example 5 Figure 5.28

Schematic diagram of a three-phase permanent-magnet ac machine Schematic diagram of a three-phase permanent-magnet ac machine. The arrow indicates the direction of rotor magnetization. Figure 5.29