DC Machines

Chapter-4DC MachinesTerm-151

1Direct Current (DC) Machines FundamentalsGenerator action: An emf (voltage) is induced in a conductor if it moves through a magnetic field.Motor action: A force is induced in a conductor that has a current going through it and placed in a magnetic field.Any DC machine can act either as a generator or as a motor.2DC Machines- Direction of Power Flow and Losses

33DC Machines- Direction of Power Flow and Losses

4DC Machines AnalysisSymbols that will be used.

= flux per pole p = no. of poles z = total number of active conductors on the armature a = no. of parallel paths in the armature winding

n = speed of rotation of the armature in rpmwm = speed in radians per second

55The Internal Generated Voltage Equations Of Real MachinesThe induced voltage in any given machine depends on three factors:The flux in the machineThe speed of the machine's rotorA constant depending on the construction of the machineThe voltage out of a real machine = the number of conductors per current path x the voltage on each conductor6EMF EquationWhen the rotor rotates in the field a voltage is developed in the armature.

The flux cut by one conductor in one rotationTherefore in n rotations, the flux cut by one conductor

The flux cut per second by one conductor

The number of conductors in series

77EMF Equation

EMF induced in the armature windings

8The Induce Torque Equations Of Real MachinesThe torque in any dc machine depends on three factors:The flux in the machineThe armature (or rotor) current IA in the machine A constant depending on the construction of the machineThe torque on the armature of a real machine =the number of conductors Z x the torque on each conductor9TORQUE EQUATIONEaIa=Tem

- In the DC machine losses areexpressed as rotational losses due to friction and windage (F&W).

- The torque equation can then be rewritten as:-

SHAFT OUTPUT TORQUE = (Te - TF&W)

10Construction of DC Machines

11Features of DC Machine

Field Winding12Construction of DC Machines13 Construction of DC Machines Field system Armature core Armature winding CommutatorBrushes

14 Field System

15Field systemIt is for uniform magnetic field within which the armature rotates.Electromagnets are preferred in comparison with permanent magnets They are cheap , smaller in size , produce greater magnetic effect and field strength can be varied 16Field system consists of the following partsYoke Pole coresPole shoes Field coils

17Armature core The armature core is cylindrical. High permeability silicon steel stampings.Lamination is to reduce the eddy current. loss

18

Armature winding 19 Armature winding There are 2 types of windingLap and Wave windingA = P

It is meant for high current and low voltages.

The armature windings are divided into number of sections equal to the number of poles.A = 2

It is meant for low current output and high voltages.

2 brushes20

Commutator Connect with external circuit. Converts ac into unidirectional current. Cylindrical in shape .Made of wedge shaped copper segments.Segments are insulated from each other.Each commutator segment is connected to armature conductors by means of a copper strip called riser.Number of segments equal to number of coils.21Carbon brush Carbon brushes are used in DC machines because they are soft materials.It does not generate spikes when they contact commutator.To deliver the current through armature. Carbon is used for brushes because it has negative temperature coefficient of resistance.

22DC Machine Equivalent CircuitsMagnetic equivalent circuitElectrical equivalent circuit

23Magnetic equivalent circuit

DC machine Cross-sectional view

DC machine Magnetic equivalent circuit

Flux-mmf relation in a dc machine24Electrical equivalent circuit

DC Generator25DC Generator Equivalent circuitThe magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated. This induced voltage is represented by a voltage source. The stator coil has resistance, which is connected in series.The pole flux is produced by the DC excitation/field current, which is magnetically coupled to the rotorThe field circuit has resistance and a sourceThe voltage drop on the brushes represented by a battery26DC Generator Equivalent circuitEquivalent circuit of a separately excited dc generator.

27DC Generator Equivalent circuitThe magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated. The dc field current of the poles generates a magnetic flux The flux is proportional with the field current if the iron core is not saturated:

The rotor conductors cut the field lines that generate voltage in the coils.

28DC Generator Equivalent circuitWhen the generator is loaded, the load current produces a voltage drop on the rotor winding resistance. In addition, there is a more or less constant 1 to 3 V voltage drop on the brushes. These two voltage drops reduce the terminal voltage of the generator. The terminal voltage is;

29Electrical equivalent circuit

DC Motor30DC Motor Equivalent circuitEquivalent circuit of a separately excited dc motorEquivalent circuit is similar to the generator only the current directions are different

31DC Motor Equivalent circuitThe operation equations are:Armature voltage equation

The induced voltage and motor speed vs angular frequency

The output power and torque are:

32Classification of DC Machines33

34Separately Excited DC Machine

35Series & Shunt DC Machine

36Cumulative & Differential DC machine

37Long Shunt & Short Shunt DC Machine

38Exercise Problems39Exercise-1A four-pole dc machine has an armature of radius 12.5 cm and an effective length of 25cm. The poles cover 75 % of the armature periphery. The armature winding consists of 33 coils, each having seven turns. The coils are accommodated in 33 slots. The average flux density under each pole is 0.75 T.

If the armature is lap wound, thenDetermine the armature constant Ka.Determine the induced armature voltage when the armature rotates at 1000 rpm.Determine the current in the coil and the electromagnetic torque developed when the armature current is 400 A.Determine the power developed by the armature.

If the armature is wave-wound, repeat parts (a) to (d) above. The current rating of the coils remains the same as in the lap-wound.

40Exercise-2A 12-pole dc generator has a simplex wave-wound armature containing 144 coils of 10 turns each. The resistance of each turn is 0.011 . Its flux per pole is 0.05 Wb, and the machine is running at a speed of 200 r/min.How many current/parallel paths are there in this machine?What is the induced armature voltage of this machine?What is the effective armature resistance of this machine?If a 1 k resistor is connected to the terminals of this generator, Determine the power output and the induced counter-torque on the shaft of this generator.

414.3 DC GeneratorsEquivalent CircuitsVoltage, current & power relationsCharacteristics42Separately excited DC generator43Separately Excited DC Generator

The operation equations are:Stator or field side:

Armature voltage equation:

Load or terminal equation:

Current equation:

Power developed in the armature:

Load or terminal equation:

Current equation:

Power delivered to the load:

Load or terminal equation:

Current equation:

44CharacteristicsPerformance of the DC generators are determined by terminal output parameter IL and VTBy Kirchhoff's voltage law, the terminal voltage is,

Since the internal generated voltage is independent of armature current, the generator terminal characteristics is a straight line.Due to the armature voltage drop, the characteristics show drooping nature.

Terminal characteristics of separately excited DC generator

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Shunt DC generator46Shunt (Self-Excited) DC GeneratorThe operation equations are:Stator or field side:

Armature voltage equation:

Load or terminal equation:

Current equation:

Power developed in the armature:

Load or terminal equation:

Current equation:

Power delivered to the load:

Load or terminal equation:

Current equation:

47CharacteristicsBy Kirchhoff's voltage law, the terminal voltage is,

Since the internal generated voltage is independent of armature current, the generator terminal characteristics is a straight line.Due to the armature voltage drop, the characteristics show drooping nature.

Terminal characteristics of shunt DC generator

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Series DC generator49Series (Self-Excited) DC GeneratorThe operation equations are:Stator or field side:

Armature voltage equation:

Load or terminal equation:

Current equation:

Power developed in the armature:

Load or terminal equation:

Current equation:

Power delivered to the load:

Load or terminal equation:

Current equation:

50CharacteristicsBy Kirchhoff's voltage law, the terminal voltage is,

As the load increases, the field current rises, so EA rises rapidly The IA (RA+Rs) drop goes up too, but at first the increase in EA goes up more rapidly than the IA(RA+Rs) drop rises, so Vr increases.

Terminal characteristics of series DC generatorAfter a while, the machine approaches saturation, and EA becomes almost constant. At that point, the resistive drop is the predominant effect, and VT starts to fall.

51

Compound DC generatorsShort-Shunt generator Long-Shunt generator52Short Shunt DC GeneratorThe operation equations are:Series field side:

Shunt field current

Armature voltage equation:

Load or terminal equation:

Current equation:

Power developed in the armature:

Load or terminal equation:

Current equation:

Power delivered to the load:

Load or terminal equation:

Current equation:

53Long Shunt DC GeneratorThe operation equations are:Series field side:

Shunt field current

Armature voltage equation:

Load or terminal equation:

Current equation:

Power developed in the armature:

Load or terminal equation:

Current equation:

Power delivered to the load:

Load or terminal equation:

Current equation:

54Characteristics55

4.4 DC Motors56HW-3Draw the equivalent circuits of various DC motors & derive their voltage, current and power equations. Draw their performance characteristics.Due Date: Monday, November 16, 201557Performance of DC Machines58DC GeneratorA DC generator is a machine that takes in mechanical input power to produce electrical power output.The performance of a dc generator is assessed by means of the following:Generator Efficiency:

Voltage Regulation:

59DC Motor:A DC motor is a machine that produces mechanical output power from the applied electrical input.The performance of a dc motor is assessed by means of the following:Motor Efficiency:

Speed Regulation:

60Power Flow & Losses in a DC Machine61Efficiency CalculationsLosses in DC Machines62

All these losses appear as heat and thus raise the temperature of the machine. They also lower the efficiency of the machine.Constant LossesVariable LossesElectrical or Copper Losses (I2R Losses)Armature copper loss:

63These losses occur due to currents in the armature and field windings of the dc machine.

Brush Losses: There is also brush contact loss due to brush contact resistance (i.e., resistance between the surface of brush and surface of commutator). This loss is generally included in armature copper loss.It can also be calculated explicitly by the following relation.

Shunt field copper loss:

Series field copper loss:

Core or Iron Losses64As iron core of the armature is continuouslyrotating in a magnetic field, there are some losses taking place in the core. This loss consists ofHysteresis loss and Eddy current loss.

When the armature core rotates in the magnetic field, an emf is also induced in the core (just like it induces in armature conductors), according to theFaraday's law of electromagnetic induction. Though this induced emf is small, it causes a large current to flow in the body due to low resistance of the core. This current is known as eddy current. The power loss due to this current is known as eddy current loss.Hysteresis loss is due to reversal of magnetization of the armature core. When the core passes under one pair of poles, it undergoes one complete cycle of magnetic reversal. The frequency of magnetic reversal if given by, f=PN/120. The loss that takes place due to repeated magnetization & demagnetization of the iron core contributes to the hysteresis loss.Hysteresis loss: Eddy current loss: Mechanical Losses65The mechanical losses in a dc machine are the losses associated with mechanical effects. These losses are due to friction and windage. (i) friction loss e.g., bearing friction, brush friction etc.(ii) windage loss i.e., air friction of rotating armature.

These losses depend upon the speed of the machine. But for a given speed, they are practically constant.Mechanical and core losses are together considered as rotational losses .

The Power-Flow Diagram of DC Generator66

The Power-Flow Diagram of DC Motor67

Exercise Problems68Exercise-1A separately excited dc generator running at 1200 rpm & delivers 12kW at 240 V as terminal voltage. The armature resistance is 0.3 ohms. Each brush takes 1 V drop. Pmech=600 W, Pcore=300 W and Pstray=200 W. The field circuit resistance is 200 ohms and DC field voltage is 250 V.

69Draw the equivalent circuit and the corresponding power flow diagram.Find the induced voltage.Determine the converted or developed power and the induced torque.Find the efficiency of the machine.

Exercise-2A 220 V shunt DC motor has an armature resistance of 0.2 ohms and a field resistance of 110 ohms. At no-load the motor runs at 1000 rpm and it draws a line current of 7 A. At full-load, the input to the motor is 11 kW.

70Draw the equivalent circuit.Find the rotational losses.Find the speed, speed regulation and developed torque at full load.Find the efficiency of the motor.

HW-471Questions #:4.2, 4.16, 4.17, 4.18, 4.25, 4.26,4.39, 4.40 found on pages 192-198 of the text book.

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