Presentation on theme: "3. ARMATURE VOLTAGE AND GOVERING EQUATIONS"— Presentation transcript:
1 3. ARMATURE VOLTAGE AND GOVERING EQUATIONS The induced voltage in a conductor isThen the induced voltage across armature terminal isLet Bp express average flux density under one pole.
2 From Eqs. (2) and (4),LetSubstituting 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 2). Governing Equations of steady-state operation Generator :Example: Separately excited generatorFeatures : (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 circuitwhere--- resistant of armature winding--- voltage drop caused by brush contact resistant
5 The total equations are MotorExample: Separately excited motorFeatures : (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 equationsSummaryBefore 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 4. POWER FLOW AND EFFICIENCY 1). LossesCopper loss: armature circuit lossfield circuit lossbrush lossCore LossMechanical loss against windage and frictionAdditional loss (stray loss)--- cannot be computed accurately
8 2). Power Flowing diagram Example: compound dc machineCompound generatorMechanical power electrical powerDeveloped power (electromagnetic power):--- It is the total electrical power developed by or converted from the mechanical energy.
9 Power equations from power flow diagram: electrical power Mechanical powerCompound motorIn motors, PM is the total mechanical power converted from input electrical power.
10 (3). EfficiencyDEVELOPED TORQUE(ELECTROMAGNETIC TORQUE)The electromagnetic force acting on a conductor iswhere ic is the current of conductor.The force on the total conductors under each pole is
11 The force on all conductors of armature winding is The developed torque produced by armature winding iswhere D is the outer diameter of rotor.Let
12 Substituting Eqs. (1), (3), (4), (5) and (6) into Eqs Substituting Eqs. (1), (3), (4), (5) and (6) into Eqs. (2) and simplifying, we obtainWhere is a constant.Questions1. What is the affect of armature reaction to T if core involves in saturation ?
13 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
14 Governing Equation for torque In generator,--- torque under no-load operation--- input mechanical torqueT is called an opposed torque. T1 has to overcome T to make prime mover deliver its mechanical energy into generator.In motor,whereT is called an active torque. It drives motor and load to rotate.