3. ARMATURE VOLTAGE AND GOVERING EQUATIONS

1. The induced voltage in a conductor is Then the induced voltage across armature terminal is Let Bp express average flux density under one pole. 3. ARMATURE VOLTAGE AND GOVERING EQUATIONS 1). Armature Voltage（电枢中的感应电势）

2. From Eqs. (2) and (4), Let Substituting Eqs. (6) and (7) into Eqs. (5) and simplifying, where --- constant

3. Question : If saturation appears in magnetic field, will Ea become larger or smaller? Note: Ea exists both in generator and in motor. In generator, Ea produces armature current. It is called generated emf or positive voltage. In motor, supply voltage U produces armature current and Ea opposes current to flow into armature winding. In this case it is called back emf or negative voltage.

4. Features : (1). • Governing equation of armature circuit where --- resistant of armature winding --- voltage drop caused by brush contact resistant 2). Governing Equations of steady-state operation • Generator : Example: Separately excited generator (2). Ia is produced by Ea and has the same direction as Ea. Ea is positive voltage. (3). Torque T is called negative torque because it oppose n.

5. The total equations are • Motor Example: Separately excited motor • Features : (1). (2). Ia is produced by U and has the opposite direction from Ea. Ea is negative voltage. (3). Torque T is called positive torque because it produces n.

6. Governing equation of armature circuit • Total equations • Summary Before writing governing equations, please draw schematic diagram according to excitation modes and then give correct reference direction in terms of operation modes. Example: Shunt generator and shunt motor

7. Copper loss: armature circuit loss • field circuit loss • brush loss • Core Loss • Mechanical loss --- against windage and friction • Additional loss (stray loss) • --- cannot be computed accurately 4. POWER FLOW AND EFFICIENCY 1). Losses

8. Mechanical power electrical power Developed power (electromagnetic power): --- It is the total electrical power developed by or converted from the mechanical energy. 2). Power Flowing diagram Example: compound dc machine • Compound generator

9. Power equations from power flow diagram: electrical power Mechanical power • Compound motor In motors, PM is the total mechanical power converted from input electrical power.

10. (3). Efficiency The electromagnetic force acting on a conductor is where ic is the current of conductor. The force on the total conductors under each pole is • DEVELOPED TORQUE • (ELECTROMAGNETIC TORQUE)

11. The force on all conductors of armature winding is The developed torque produced by armature winding is where D is the outer diameter of rotor. Let

12. Substituting Eqs. (1), (3), (4), (5) and (6) into Eqs. (2) and simplifying, we obtain Where is a constant. Questions 1. What is the affect of armature reaction to T if core involves in saturation ?

13. Useful Expression --- calculating T from power 2. If load torque becomes larger, how about Ia under constant external voltage in shunt motor? 3. In shunt motor, if external voltage and load torque are all kept constant, when we put an external resistance into armature circuit, how will Ia change ?

14. In generator, --- input mechanical torque --- torque under no-load operation • In motor, where T is called an active torque. It drives motor and load to rotate. Governing Equation for torque T is called an opposed torque. T1 has to overcome T to make prime mover deliver its mechanical energy into generator.