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**3. ARMATURE VOLTAGE AND GOVERING EQUATIONS**

The induced voltage in a conductor is Then the induced voltage across armature terminal is Let Bp express average flux density under one pole.

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

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**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.

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**2). Governing Equations of steady-state operation**

Generator : Example: Separately excited generator Features : (1). (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. Governing equation of armature circuit where --- resistant of armature winding --- voltage drop caused by brush contact resistant

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**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.

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**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

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**4. POWER FLOW AND EFFICIENCY**

1). Losses 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

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**2). Power Flowing diagram**

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

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**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.

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(3). Efficiency DEVELOPED TORQUE (ELECTROMAGNETIC TORQUE) 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

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**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

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**Substituting Eqs. (1), (3), (4), (5) and (6) into Eqs**

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 ?

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**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 ? Useful Expression --- calculating T from power

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**Governing Equation for torque**

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

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