DC MACHINE-Motoring and generation, Armature circuit equation

Motoring and generation
Armature circuit equation for motoring and generation,
Types of field excitations - separately excited, shunt and series.
Open circuit characteristic of separately excited DC generator,
back EMF with armature reaction,
voltage build-up in a shunt generator,
critical field resistance and critical speed.
V-I characteristics and torque-speed characteristics of separately excited shunt and series motors.
Speed control through armature voltage.
Losses, load testing and back-to-back testing of DC machines

1. DC Machines –II Motoring and generation Armature circuit equation for motoring and generation, Types of field excitations - separately excited, shunt and series. Open circuit characteristic of separately excited DC generator, back EMF with armature reaction, voltage build-up in a shunt generator, critical field resistance and critical speed. V-I characteristics and torque-speed characteristics of separately excited shunt and series motors. Speed control through armature voltage. Losses, load testing and back-to-back testing of DC machines..

2. Motoring and Generation - Motoring and generation are two fundamental concepts associated with the operation of DC (Direct Current) machines, such as DC motors and DC generators. These concepts describe how these machines function when they are either consuming electrical power to produce mechanical work (motoring) or converting mechanical work into electrical power (generation).

3. Motoring: Motoring refers to the operation of a DC machine as an electric motor. In this mode, electrical power is supplied to the machine to produce mechanical output or work . When voltage is applied to the armature of the DC motor, it generates a magnetic field due to the flow of current in the coils (windings). The magnetic field interacts with the field produced by the stator's field winding (either permanent magnets or separate field windings) to create a mechanical torque.

4. This torque causes the motor's shaft to rotate, which is used to drive a load or perform some mechanical task. The motor operates until an opposing force, such as friction or the load, is balanced by the motor's torque. The speed and direction of rotation can often be controlled by adjusting the applied voltage and the field winding current.

5. Generation: Generation refers to the operation of a DC machine as an electric generator. In this mode, mechanical work is applied to the machine, causing it to generate electrical power. When the shaft of the DC generator is mechanically rotated (e.g., by a prime mover like a steam turbine, waterwheel, or engine), it induces an electromotive force (EMF) in the armature coils. This EMF creates an electrical current, which can be used to power external electrical loads or charge batteries.

6. The generated voltage is proportional to the speed at which the machine is rotated (N) and the strength of the magnetic field (Φ) produced by the field winding or permanent magnets. DC generators are commonly used in applications where a steady and controllable DC power source is required, such as in portable generators and backup power systems.

7. In summary, the key difference between motoring and generation in DC machines is the direction of energy flow. In motoring, electrical energy is supplied to the machine to produce mechanical work, while in generation, mechanical work is applied to the machine to produce electrical energy. The operation mode (motor or generator) depends on the direction of the current flow and the relative relationship between the applied voltage and the machine's generated voltage.

8. D ifference between motoring and generation in DC machines Motor Generator Input and Output Motor has dc current as an input and mechanical energy as an output. Generator has dc current as an output and mechanical energy as an input. EMF (Electromotive Force) EMF is used to energize the coil to rotate the armature. EMF is generated around the coil and transmitted to the load or another section of the circuit. Generated EMF Motor has a generated EMF less than the voltage across the source terminal (EMF<V). Generator has a generated EMF more than the voltage across the source terminal (EMF>V). EMF Calculation Eb = V – IaRa Eg = V + IaRa

9. Motor Generator Electric current Electric current is used to energize the armature winding through the commutator. Electric current is generated from the armature winding to the commutator. Rule Fleming Left Hand Rule Fleming Right Hand Rule Work principle Operated by a current-carrying conductor in a magnetic field and generates forces. Operated by mechanical force that rotates the armature in a magnetic field and generates induced current. Armature shaft The armature is supplied by an electrical current in a magnetic field. The armature is rotated by a mechanical energy in a magnetic field.

10. Motor Generator Energy conversion The motor will rotate faster when supplied with higher power up to its maximum power rating. The generator will likely produce fixed voltage with rated rpm. Examples Robotic motors, production and manufacturing tools and machines, printers, and many more. Wind turbines, hydro power plants, dynamos, alternators, and many more.

11. Motoring and generation Armature circuit equation for motoring and generation- The armature circuit equation for both motoring (electric motor operation) and generation (electric generator operation) in a direct current (DC) machine can be expressed using the following equation: Ea = V - Ia * Ra ± (Φ * N) Where: Ea is the back electromotive force (EMF) generated in the armature coil. V is the applied voltage to the armature. Ia is the armature current. Ra is the armature resistance. Φ is the magnetic flux in the machine's magnetic field. N is the speed of the machine (rotational speed in revolutions per minute, RPM).

12. In the above e quation: When the machine is operating as a motor (motoring), the armature current Ia flows in the direction of the applied voltage V, and the back EMF Ea opposes the applied voltage. Therefore, the equation becomes: Ea = V - Ia * Ra - Φ * N When the machine is operating as a generator (generation), the armature current Ia flows in the opposite direction of the applied voltage V, and the back EMF Ea aids the applied voltage. Therefore, the equation becomes: Ea = V - Ia * Ra + Φ * N Ea = V - Ia * Ra ± (Φ * N)

13. In both cases, the armature current Ia and the armature resistance Ra cause a voltage drop, and the term Φ * N represents the voltage generated due to the machine's magnetic field interacting with the armature coils as they rotate. The polarity of the generated voltage ( Ea ) depends on whether the machine is operating as a motor or a generator.ta

14. Types of field excitations – separately excited, shunt and series.

15. The magnetic flux in a d.c machine is produced by field coils carrying current.  The production of magnetic flux in the device by circulating current in the field winding  is called excitation. Excitation - What is the main purpose of excitation in dc machine ??

16. T he main purpose of excitation in a DC machine is - to establish and control the magnetic field, which is fundamental for converting electrical energy to mechanical energy (in the case of a motor) or mechanical energy to electrical energy (in the case of a generator) while providing control, stability, and adaptability to different operating conditions.

17. Creation of Magnetic Field Conversion of Electrical Energy to Mechanical Energy (Motor Mode ) Conversion of Mechanical Energy to Electrical Energy ( Generator Mode ) Control of Machine Operation Reversibility Stability and Regulation Starting

18. The types of DC Motors are -

19. There are two types of excitation in D.C machine.  Separate excitation, and Self-excitation . Self-excitation – The current flowing through the field winding is supplied by the machine itself. S eparate excitation – The field coils are energized by a separate D.C. Source .

20. Separately Excited DC Motor - In separately excited DC motors, the  supply is given to the field and armature windings separately.   The main feature of this type of DC motor is that the current through the armature doesn’t flow through the field windings because the field winding is energized by a separate DC source. This can be understood in a better way through the diagram given below. 

21. Separately excited DC machines are commonly used in applications requiring fine control of speed and torque, such as in industrial drives and some types of electric vehicles.

22. Self Excited DC Motor - As the name implies self-excited, hence, in this type of motor, the current in the windings is supplied by the machine or motor itself to establish the magnetic field in the field winding . This type of excitation is based on the feedback of the generated electromotive force (EMF) to the field winding . There are three subtypes of self-excited DC machines :

23. Shunt-Wound DC Machine : In a shunt-wound DC machine, the field winding (shunt field) is connected in parallel with the armature winding . They both receive the same supply voltage. Shunt-wound machines have relatively constant speed characteristics and are commonly used in applications where stable speed is required , such as in small generators and certain types of industrial applications.

24. The parallel connection means that the current is split between the two components. A DC shunt motor has a constant speed that doesn’t change with varying mechanical loads.

25. b . Series-Wound DC Machine : In series-wound DC motors, the field winding and the armature coil are connected in series to the power supply. This means the same current flows through the coil and armature. Since these types of motors can work both with DC and AC, they are also called universal motors. Series motors always rotate in the same direction, and their speed depends on the mechanical load .

26. Series-wound machines provide high starting torque but tend to have poor speed regulation, making them suitable for applications like electric traction (e.g., locomotives).

27. c. Compound-Wound DC Machine: Compound-wound DC machines combine elements of both shunt and series winding. They have two sets of field windings: one connected in parallel (shunt) and another in series with the armature. Compound-wound machines offer a compromise between the characteristics of shunt and series machines, providing good torque and speed regulation.

28. They are used in various industrial applications, including machine tools and rolling mills.

29. These motors are further divided into Short shunt and L ong shunt and Cumulative Compound Differential Compound motors .

30. Relation Between Back EMF and Load Current - When the armature of the DC motor rotates under the influence of the driving force, the armature of the conductors moves through the magnetic field and generates an electromotive force( emf ) in them . The induced emf is in opposite direction to the externally applied voltage and this induced voltage is known as back emf and denoted by E. Emf induced in any DC motor is given by the formula 

31. Where N = Speed of DC motor P = Number of pole φ = magnetic flux Z = Number of Conductor A = Number of Parallel Path for a dc motor Number of Pole(P), Number of conductors (Z), and Number Of Parallel Path (A) is constant hence we can replace this emf equation in a general form By Removing all Constant By a new Constant K then 

32. If this motor is connected with a DC Source of terminal voltage V and a load Current I start to flow in the motor then due to internal armature resistance(R), a voltage will drop then We can write the KVL equation for this motor like this  V = E+IR E=V - IR k𝜙N =V - IR

33. Torque Equation of Separately Excited DC motor It is a mathematical equation that provides the torque value produced by the motor at its shaft. it is given as Power Developed In armature = Mechanical Power Developed at the shaft of DC motor Above equation shows torque equation of a separately excited DC motor.

34. PARAMETER Series Wound DC Motor Shunt Wound DC Motor Compound Wound DC Motor Permanent Magnet DC(PMDC) Construction Rotor, Field windings in series Rotor, Field windings in parallel Rotor, Combined series and shunt windings Rotor with permanent magnets, Stator with windings Advantages High starting torque, Suitable for heavy loads Good speed regulation, Precise control, Stable operation Compromise between torque and speed regulation Simple construction, High efficiency, Responsive

35. PARAMETER Series Wound DC Motor Shunt Wound DC Motor Compound Wound DC Motor Permanent Magnet DC(PMDC) Disadvantages Limited speed control, Inefficient at high speeds, Prone to overheating Lower starting torque, Efficiency may not be as high Complex control, Efficiency may not be optimal Limited to low to moderate power, Limited speed control Application Electric vehicles, Winches, Elevators Conveyor belts, Printing presses Rolling mills, Industrial equipment Toys, Small appliances, Fans

36. Applications of DC Motors The applications of a dc motor depend on the requirement of the electrical equipment and the characteristics of the DC motor. DC Series Motor Applications Cranes Lifts and elevators Winching systems Hair driers Power tools

37. DC Shunt Motor Applications Windscreen wiper drives Drills Conveyers Fans Centrifugal pumps Blowers Compound DC Motor Applications Conveyers Stamping machines Compressors Heavy planners Rolling mills Presses

38. Permanent Magnet DC Motors  Toys Starter motors Disc drivers Wheels chairs Brushless DC Motor Applications   Computer cooling fans Heating and ventilation Cooling systems in aircraft and vehicles Handheld power tools Separately Excited DC Motor Applications  Actuators in industrial machinery Traction motors in trains Steel rolling mills

39. Open circuit characteristics of separately excited DC generator

40. What is open circuit characteristics of separately excited DC generator ???

41. The curve which gives the relation between field current (If) and the generated voltage (E0) in the armature on no load is called magnetic or open circuit characteristic of a DC generator. The plot of this curve is practically same for all types of generators, whether they are separately excited or self-excited

42. It is also known as magnetic characteristics or no-load saturation characteristics. It shows the relation between the induced emf E  at the no-load condition and the field current I f  at a constant speed . For separately excited DC generator, the open circuit characteristics is obtained by conducting an experiment under no-load conditions.

43. An ammeter is connected to the field winding and a voltmeter is connected to the generator to measure the induced voltage .

44. The circuit is connected as shown in the above diagram. The field current is varied by connecting an additional resistance(Rheostat) and is measured by an ammeter .

45. At a constant speed, when the field current is increased from zero, the flux and hence the induced emf increases. The values of induced emf corresponding to the field current is measured and tabulated. From the tabulation, a graph is drawn with field current as the x-axis and generated emf as the y-axis . The graph shows the open circuit characteristics of a separately excited DC generator

46. From the above graph, it is observed that the increase in field current increases the emf induced. When the poles get saturated, the increase in field current does not increase the flux and thus the emf induced also remains constant . Different curves can be obtained for different speeds . From graph it is observed that, for higher speeds, the emf induced will be more.

47. voltage build-up in a shunt generator, critical field resistance and critical speed.

48. Conditions to build up voltage in shunt generator: The shunt winding should have residual magnetic field. The direction of shunt winding and armature winding should be in such a way that flux generated by them should aid together. The shunt winding should have critical winding resistance .

49. Process of voltage build up : When the armature is rotated, the residual flux in field winding will induce small voltage in armature. The induced voltage in armature generates a flux and it will aid(add) with field flux and the net flux will increase further. This process will be repeating until the actual treminal voltage is reached. Once the terminal voltage is reached then the winding will get saturated and hence there won't be any further increase in flux, also the voltage gets constant.

50. Consider a DC Shunt Generator at no load as shown in figure below. The switch in the field circuit is supposed open and the armature of DC Shunt Generator is driven at rated speed . Because of presence of small residual flux in the field poles, DC Shunt Generator will have a small voltage at its terminal even though the switch S is open when driven at rated speed. Now suppose the switch S is closed.

51. As there is small voltage is there across the terminals of DC Shunt Generator and Switch S is closed, therefore a small current will start flowing through the field circuit of DC Shunt Generator which in turn will produce magnetic flux and if the produced magnetic flux adds the residual magnetic flux then net flux will increase and the generated voltage ( E a  = K a Øω m ) will increase corresponding to point J on the Magnetization curve as shown in figure below.

52. Since the generated voltage has increased, therefore the field current will also increase to OK corresponding to which the Generated Voltage across the Terminals of DC Shunt Generator will increase to point L. In the same manner the voltage will continue to build up till the point of intersection of Field Resistance Line and Magnetization curve / Open Circuit Characteristics of DC Shunt Generator.

53. Beyond point of intersection of Field Resistance Line and Magnetization curve / Open Circuit Characteristics the voltage won’t build up as in that case the generated voltage Ea will not be able to drive the required field current. Thus the stable point at which the voltage will remain fix is the voltage Ea corresponding to point of intersection of Field Resistance Line and Magnetization curve / Open Circuit Characteristics.

54. Effect of variation of field resistance of DC Shunt Generator in its Voltage Build up:

55. If the field resistance is increased to OA, then Field Resistance line intersect the OCC curve at point p, and hence there will not be voltage build up beyond point p . Now , if shunt field resistance is such that OB represents the Field resistance line then as clear from the figure above, the lone is intersecting the OCC curve at many points between q and r, therefore the field current will fluctuate between s and t and hence the voltage generated at the terminals of DC Shunt Generator will vary from qs to rt resulting in unstable condition.

56. If we find the slope ( tanƟ ) of the Field Resistance Line then we will get Field Resistance value which is known as  Critical Filed Resistance .

57. What is the significance of Critical Field Resistance? As clear from the figure above, if the field resistance is more than the Critical Field Resistance then there will not be voltage build up in DC Shunt Generator.  See in the figure OA is shunt field resistance which is more than Critical Field Resistance OB (check by slope, slope of OA is more than slope of OB), hence there is no voltage build up in DC Shunt Generator.

58. Effect of variation of speed of rotation of DC Shunt Generator in its Voltage Build up:

59. Suppose the field resistance is OC and DC Shunt Generator is running at a speed of n1 for which the stable point of its terminal voltage is C. Now the speed of DC Shunt Generator is reduced to n2 therefore the OCC curev will also move downward as shown in figure. It should be noted here that the same field resistance line OC is now tangent to the new OCC curve and therefore will create an unstable condition of operaton of DC Shunt Generator.

60. This speed n2 is hence called  Critical Speed .  Thus Critical Speed is that speed at which the DC Shunt Generator just fails to built up voltage with no external resistance in the field circuit.

61. V-I characteristics and torque-speed characteristics of separately excited shunt and series motors.

62. V-I characteristics of separately excited shunt motors .

63. There are generally three most important characteristic of DC motor Magnetic or Open Circuit Characteristic of Separately Excited DC Motor. Internal or Total Characteristic of Separately Excited DC Motor. External Characteristic of Separately Excited DC Motor.

64. The curve which gives the relation between field current (I f ) and the generated voltage (E ) in the armature on no load is called magnetic or open circuit characteristic of a DC Motor . The plot of this curve is practically same for all types of motors, whether they are separately excited or self-excited. This curve is also known as no load saturation characteristic curve of DC motor. Magnetic or Open Circuit Characteristic of Separately Excited DC motor

65. From the above graph, we can see the variation of generated emf on no load with field current for different fixed speeds of the armature. For higher value of constant speed, the steepness of the curve is more. When the field current is zero, for the effect residual magnetism in the poles, there will be a small initial emf (OA) as show in figure.

66. Let us consider a separately excited DC motor giving its no load voltage E for a constant field current. If there is no armature reaction and armature voltage drop in the machine then the voltage will remain constant. Therefore , if we plot the rated voltage on the Y axis and load current on the X axis then the curve will be a straight line and parallel to X-axis as shown in figure below.

67. Here , AB line indicating the no load voltage (E ). When the motor is loaded then the voltage drops due to two main reasons- Due to armature reaction, Due to ohmic drop ( I a R a ).

68. Internal or Total Characteristic of Separately Excited DC motor The internal characteristic of the separately excited DC motor is obtained by subtracting the drops due to armature reaction from no load voltage. This curve of actually generated voltage ( E g ) will be slightly dropping. Here , AC line in the diagram indicating the actually generated voltage ( E g ) with respect to load current. This curve is also called total characteristic of separately excited DC motor.

69. External Characteristic of Separately Excited DC motor The external characteristic of the separately excited DC motor is obtained by subtracting the drops due to ohmic loss ( Ia Ra ) in the armature from generated voltage ( Eg ). Terminal voltage(V) ( V) = Eg – Ia Ra . This curve gives the relation between the terminal voltage (V) and load current. The external characteristic curve lies below the internal characteristic curve.

70. Here , AD line in the diagram is indicating the change in terminal voltage(V) with increasing load current. It can be seen from figure that when load current increases then the terminal voltage decreases slightly. This decrease in terminal voltage can be maintained easily by increasing the field current and thus increasing the generated voltage. Therefore , we can get constant terminal voltage.

71. Torque-speed characteristics of separately excited dc shunt motor

72. The speed-torque characteristics of a dc motor is a graph of torque on X-axis versus the speed which is plotted on Y-axis. As the torque is proportional to the armature current , the nature of this characteristics is same as that of the speed-armature current characteristic shown in graph. From graph, at no load the torque produced by the motor is T a0 & the motor rotates at the no load speed N 0. As the load is increased, the torque requirement also increase.

73. To generate the required amount of torque, the motor has to draw more armature current & motor armature current can be drawn if the more speed decreases, because I a = Therefore, as the load increases, torque will also increase & the speed decreases. However the reduction in speed is not significant as the load is increased from no load to full load. In dc shunt motor, the torque is directly proportional to armature current. Therefore dc shunt motor is practically called as constant speed motor.  

74. V-I characteristics of separately excited series motors.

75. Open Circuit Characteristics (O.C.C) The curve (A) in the plot shows the O.C.C of a series DC motor. It is the graph plotted between the generated EMF at no-load and field current. The O.C.C can be obtained by disconnecting the field winding from the machine and is excited separately.

76. Internal Characteristics The internal characteristics of a DC series motor is the graph plotted between generated EMF ( Eg ) on-load and the armature current. Because of the effect of armature reaction, the magnetic flux on-load will be less than the flux at no-load. Therefore , the generated EMF (E) under loaded condition will be less than the EMF generated (E ) at no-load. As a result of this, the internal characteristics curve lies just below the open circuit characteristics [See the curve (B)].

77. External Characteristics or Load Characteristics The external characteristics or load characteristics is the plot between the terminal voltage (V) and load current (I L }). Since , the terminal voltage is less than the generated voltage due to armature and series field copper losses, which is given by, V = E − Ia ( Ra + Rse ) Therefore, the external characteristics curve will lie below the internal characteristics curve by an equal amount to voltage drop due to copper losses in the machine [see the curve (C)].

78. Torque-speed characteristics of separately excited series motor

79. The speed –torque characteristics of a dc series motor is shown in above graph. We know that, T ∝ . & N ∝ & N ∝   This shows that the speed decreases with increase in the value of torque that is with increase in load.

80. Comparison of DC shunt & DC series Motors S.N. parameter DC shunt motor DC series motor 01 Connection of field winding with armature Field is in parallel with armature Field is in series with armature 02 Type of starter Three point Four point 03 Torque developed Low High 04 Applications Machine tool, printing, pumps, paper machine Electric trains, crains , Hoists, Conveyers

81. Comparison of Speed- Torque characteristics of DC shunt & DC series Motors S.N parameter DC shunt motor DC series motor 01 Nature of characteristics 02 Relation between speed & torque As load increases, T increases & Speed reduces slightly As load increases, torque increases & speed reduces exponentially. 03 Reduction in speed with increased load Slightly reduction in Speed takes place. Drastic reduction in speed takes place 04 Starting torque Moderately high Very high

82. Speed control through armature voltage The relationship given below gives the speed of a D.C. motor The above equation shows that the speed depends upon the supply voltage V, the armature circuit resistance R a , and the field flux Ф, which is produced by the field current.  Thus, there are three general methods of speed control of D.C. Motors.

83. Thus , there are three general methods of speed control of D.C. Motors . Resistance variation in the armature circuit: This method is called armature resistance control or Rheostat control . Variation of field flux Ф: This method is called field flux control. Variation of the applied voltage.: This method is also called armature voltage control.

84. The speed is directly proportional to the voltage applied across the armature. As the supply voltage is normally constant, the voltage across the armature can be controlled by adding a variable resistance in series with the armature as shown in the Fig.

85. Speed control of a DC shunt motor through armature voltage involves adjusting the armature voltage to vary the motor's speed while keeping the field current (field winding voltage) constant. This method is commonly used in applications where precise speed control is required. Here's how you can control the speed of a DC shunt motor using armature voltage:

86. Basic Principle: The speed of a DC shunt motor is directly proportional to the armature voltage and inversely proportional to the field current. By increasing or decreasing the armature voltage, you can increase or decrease the motor's speed while maintaining a constant field current.

87. Method of Control: Increasing Speed: To increase the motor's speed, we need to increase the armature voltage. We can achieve this by adjusting the output voltage of an adjustable power supply connected to the motor's armature terminals. As the armature voltage increases, the motor speeds up. Decreasing Speed: To decrease the motor's speed, you reduce the armature voltage . This can be done by lowering the output voltage of the power supply. As the armature voltage decreases, the motor slows down.

88. The field winding is excited by the normal voltage hence I sh  is rated and constant in this method. Initially the rheostat position is minimum and rated voltage gets applied across the armature. So speed is also rated. For a given load, armature current is fixed. So when extra resistance is added in the armature circuit, I a  remains same and there is voltage drop across the resistance added ( I a  R).

89. Hence voltage across the armature decreases, decreasing the speed below normal value. By varying this extra resistance, various speeds below rated value can be obtained . So far a constant load torque, the speed is directly proportional to the voltage across the armature. The relationship between speed and voltage across the armature is shown in the following graph.

90. Advantages : Disadvantages: Precise Speed Control . 1) Reduced Torque at Lower Speeds Energy Efficiency 2) Potential Overheating Smooth Operation 3) Limited Speed Range Simple Control Circuitry 4) Field Weakening Compatibility 5) Wasted Power

91. Speed control of a DC shunt motor through armature voltage is an effective and precise method for regulating motor speed in applications such as conveyor systems, industrial machines, and fans. It allows for smooth and continuous control over the motor's speed while maintaining constant field current for optimal motor performance.

92. Losses in DC Machine – In DC machine the energy loss takes place in the form of heat energy. The losses occurs in the armature and field of the DC machine. There are five types of losses  copper loss , brush loss , iron loss , stray loss and mechanical loss takes place in a DC machine.

93. Copper Loss in DC Machine winding The copper loss is  caused by the ohmic resistance offered by the winding of the DC machine. When the current flows through the winding the heat loss takes place in the winding. The heat loss is proportional to the square of the current and  the resistance of the winding. The copper loss in the winding is I 2 R. Where , I is the current flowing through the winding and R is the resistance of the winding.

94. The copper loss is also known as variable loss because the copper loss depends on the percentage loading of the machine. The loss increases with increase of loading on the machine . The DC machine has two types of winding- field and armature winding- and losses take place in both the winding. The supply is fed to armature through the carbon brushes and losses also takes place across the carbon brush due to ohmic voltage drop.

95.  Copper Loss in Armature Winding The armature of the DC machine has very low resistance. The resistance of the armature is denoted by Ra. Armature copper loss = Ia 2 Ra Where,  Ia  is the armature current and Ra is the armature winding resistance.  The maximum copper loss occurs in the armature winding, because the load current flows through the armature winding . The copper loss in the armature is about 25 to 30 % of the full load loss.

96. C opper loss in the field winding - DC supply is fed to the field winding for production of the flux in the DC machine. The resistance of the field winding is much more than the resistance of the armature winding. That is why the substantial copper loss takes place in the field winding even at the low field current . The copper loss in the field winding is expressed as;

97. Field winding copper loss = I f 2 R f Where, I f  is the field current and  Rf  is the field winding resistance.  The field winding copper loss is about 20-25 % of the full load loss of the DC machine. The copper loss in the field winding is a practically constant loss because the field current and the field resistance remains almost constant in the DC machine.

98. Brush Contact Resistance Loss The armature is a rotating part of the DC machine, and brushes are used to provide DC supply to the rotating part of the DC machine . Ideally , the contact resistance between the brush contacting area with commutator surface must be zero . However , in reality it is impossible to have zero contact resistance . The voltage drop takes place across the carbon brushes. The brush power drop depends upon the voltage drop across the brush and armature current.

99. Power Drop in Brush = PBD = V BD   I a Where, P BD  = Power drop in Brush V BD  = Voltage Drop in Brush   I a      =  Armature Current If the brush voltage drop is not given, it is generally assumed 2 volts drop across carbon brush and the power drop in brush is 2I a   .

100. Core Losses or Iron Losses in DC Machine The armature winding of the DC machine is wound around the magnetic core. The flux generated by the field coil gets linked to the armature conductors through magnetic core. Two types of losses namely hysteresis and eddy current loss occur in the magnetic core. The iron loss is almost constant therefore the iron loss or core loss is also called constant loss. The total core loss is about 20-25 % of the full load losses .

101. Mechanical Loss in DC Machine Losses occurring due to mechanical affects like friction etc. are called Mechanical Losses. In DC machine, the field is a stationary part and the armature is a rotating part. The armature rotates on the bearings. The energy loss in the form of heat occurs due to friction between the inner cage and outer cage of the bearing . The other mechanical loss is the  windage loss .

102. The air surrounding to the shaft offers resistance and, when DC machine rotates the loss caused by air resistance is called the windage loss. Mechanical losses are very small in magnitude as compared to copper loss & iron loss.

103. Stray Losses in DC Machine All the losses which are neighter copper, iorn , brush or mechanical type loss are classified under stray losses. Stray losses are also called as miscellaneous losses which are difficult to determine. The various reasons of the stray losses in DC machine are short circuit current undergoing commutation,distortion of flux etc. The stray losses in DC machine are about 1 % of the total losses.

104. Load testing of DC machines is a method used to assess the performance and operational characteristics of direct current (DC) motors or generators under specific load conditions. It involves applying various loads to the machine to evaluate its response, efficiency, and reliability. The load testing of DC machine is needed to determine the rating of a machine. When we run a machine, then some energy is lost in the machine, which converts into the heat and cause temperature rise . The load testing of DC machine

105. If a machine produces too much heat then it can affect the insulation of the machine and ultimately it can cause the breakdown of the machine. Therefore, the load must be set to a value that it can operate within the temperature limit. The maximum value of the load that can be delivered by the machine without any harm is called the continuous rating of that machine.

106. Load testing can be considered both direct and indirect, depending on the specific objectives and methods used : Direct Load Testing: Direct load testing involves directly applying a known load to the DC machine and measuring its response to that load. This type of testing is typically more straightforward and provides immediate and precise information about the machine's performance .

107. In direct load testing, you apply mechanical or electrical loads to the machine and observe parameters such as speed, current, torque, and temperature. This data is collected and analyzed to assess how well the machine handles different loads, its efficiency, and whether it operates within its specified performance range.

108. Indirect Load Testing: Indirect load testing refers to assessing the DC machine's performance without applying a physical load directly to it . Instead, it involves various analytical and diagnostic techniques to evaluate the machine's condition and performance indirectly. Indirect load testing may include analyzing historical data, conducting diagnostic tests (e.g., insulation resistance tests, vibration analysis), and performing calculations based on the machine's specifications and operational data.

109. It can also involve simulation and modeling to predict the machine's behavior under different load scenarios . Direct load testing involves physically applying loads to the machine and directly measuring its performance parameters. This method provides real-world performance data. Indirect load testing involves various diagnostic and analytical methods that assess the machine's performance without the need for applying physical loads directly. This method is often used for predictive maintenance and condition monitoring.

110. Back-to Back testing of DC machines.. Back-to-back testing of DC machines, also known as regenerative testing or Hopkinson's test  . Hopkinson's test is a method of testing the efficiency of DC machines. This test requires two identical shunt machines which are mechanically coupled and also connected electrically in parallel.

111. It requires two identical machines that are coupled to each other . One of these two machines is operated as a generator to supply the mechanical power to the motor and the other is operated as a motor to drive the generator . The motor takes its input from the supply and the mechanical output of the motor drives the generator. The electrical output of the generator is used in supplying the input to the motor. Therefore, the output of each machine is fed as input to the other .

112. When both the machines are run at rated load, the input from the supply is equal to the total losses of both the machines. Thus, the power input form the supply is very small . Connection Diagram- The connection diagram of Hopkinson’s test is shown in the figure.

113. In the connection diagram, the machine M acts as a motor and is started from the supply with the help of starter. The switch S is kept open. The field current of the machine M is adjusted with the help of field rheostat R m  to make the motor to run at its rated speed. The machine G acts as a generator .

114. As the G is driven by the machine M, hence it runs at rated speed of M. The field current of the machine G is so adjusted with the help of its field rheostat R g   that the armature voltage of the generator G is somewhat higher than the supply voltage. When the voltage of the generator is equal to and of the same polarity of the busbar voltage, the switch S is closed and the generator is connected to the busbar .

115. Now, both the machines are connected in parallel across the supply voltage. Under this condition, the generator neither taking any current from nor giving any current to the supply, thus it is said to be float. Now , by adjusting the excitation of the machines with the help of the field rheostats, any load can be thrown on the machines.

116. Advantages: Efficiency Assessment: Back-to-back testing allows for a precise assessment of the efficiency of DC machines. By comparing the electrical power input to the motor and the electrical power output from the generator, you can calculate efficiency accurately. Dynamic Response Testing: This method is well-suited for evaluating the dynamic response of DC machines. It enables the testing of rapid acceleration, deceleration, and load changes, which is crucial for applications requiring precise control, such as electric locomotives and industrial drives .

117. High-Power Testing: Back-to-back testing is particularly useful for testing large and high-power DC machines, including electric locomotives, industrial motors, and large generators. Closed-Loop Operation: The closed-loop configuration allows the electrical energy generated by the generator machine to be fed back into the power supply system or absorbed by load banks, reducing energy wastage and making the testing process more environmentally friendly .

118. Fault Detection: Anomalies in the behavior of the machines, such as abnormal vibrations or electrical imbalances, can be detected during back-to-back testing, allowing for early fault detection and preventive maintenance. Controlled Testing Environment: Back-to-back testing provides a controlled environment for evaluating the machines, allowing for consistent and repeatable testing conditions.

119. Disadvantages: Complex Setup: The setup for back-to-back testing can be complex and requires two compatible DC machines, which may not be readily available or cost-effective for smaller machines. Space and Infrastructure: Conducting back-to-back testing requires a dedicated testing facility with sufficient space to accommodate the machines and associated equipment.

120. High Initial Cost: The equipment and infrastructure required for back-to-back testing can be expensive to acquire and set up, making it less practical for some organizations . Energy Dissipation: The electrical energy generated by the generator machine needs to be either returned to the power supply grid or dissipated as heat using load banks. This energy dissipation can be inefficient and costly.

121. Complex Data Analysis: Analyzing the data collected during back-to-back testing can be complex and may require specialized expertise to interpret the results accurately. Limited Application: Back-to-back testing is most beneficial for high-power DC machines and may not be practical or cost-effective for smaller machines or applications.