ELECTRICAL MACHINES Tyuteva Polina Vasilevna, PhD, Associate Professor Electrotechnical Complexes and Materials, Institute of Power Engineering, 8 building, 042 room, [email protected] DIRECT CURRENT MACHINES 1 DC machine construction Working principle of DC generator N Trev A S B - + V • Single Loop DC Generator Working principle of DC generator • When the loop rotates from its vertical position to its horizontal position, it cuts the flux lines of the field. As during this movement two sides of the loop cut the flux lines there will be an EMF induced in these both of the sides of the loop. • The value of induced EMF is: 푒푐표푛푡 = 퐵 ∙ 푙 ∙ 푣, • where 퐵 – magnetic flux density, 푙 - the active length of a conductor, 푣 – linear speed of conductor. • Total armature EMF is: 퐸푎 = 2 ∙ 푒푐표푛푡. • The value of EMF is variable as armature winding conductors run downwards N-pole and S-pole. As a result the direction of EMF in the conductors changes. Working principle of DC generator B, e 00 1800 3600 t • Magnetic flux density and EMF curve Working principle of DC generator e,i 00 1800 3600 t • Current curve through the load Working principle of DC generator e,i E t • Current through the load curve in case of more segments in commutator Working principle of DC generator • The value of armature EMF is defined by 푁 – number of turns in winding, 푎 – number of parallel paths in the armature winding, 2푝 – number of pairs of poles, Ф – magnetic flux of in air gap and 푛 – speed of rotation: 퐸푎 = 퐶 ∙ Ф ∙ 푛, • where 퐶 – constructional constant: 푝 ∙ 푁 푝 ∙ 푁 퐶 = , 퐶 = . 푒 60푎 푚 2휋 ∙ 푎 Working principle of DC generator • The output voltage of DC generator is smaller than induced EMF: 푈 = 퐸푎 − 퐼 ∙ 푅푎 − 2 ∙ ∆푈푏, • where ∆푈푎 – voltage drop across armature resistance: ∆푈푎= 퐼 ∙ 푅푎 + 2 ∙ ∆푈푏, • where 푅푎 – armature resistance, 퐼 – armature current, 2 ∙ ∆푈푏 – voltage drop across commutator-and-brush assembly. Typically the voltage drop across commutator- and-brush assembly is 2 ∙ ∆푈푏= 2 푉, so: 푈 = 퐸푎 − 퐼 ∙ 푅, • where 푅 – overall resistance of armature winding and commutator-and-brush assembly. Working principle of DC generator • As conductor moves in a magnetic field it cuts magnetic lines force: 퐹푐표푛푡 = 퐵 ∙ 푙 ∙ 푖푐표푛푡. • These electromagnetic forces create electromagnetic torque that in case of generator acts as decelerating torque, thus it acts against direction of armature rotation: 푀 = 퐶 ∙ Ф ∙ 퐼. • Output power of generator: 푃표푢푡 = 푈 ∙ 퐼. Working principle of DC motor • As conductor moves in a magnetic field it cuts magnetic lines force: 퐹푐표푛푡 = 퐵 ∙ 푙 ∙ 퐼푎. • And electromagnetic torque developed by the machine is given by: 푀 = 퐶 ∙ Ф ∙ 퐼푎. • The induced EMF: 퐸푎 = 퐶 ∙ Ф ∙ 푛 = 퐶 ∙ Ф ∙ 푤. • The voltage equation for the armature circuit of the motor is: 푈 = 퐸푎 + 퐼 ∙ 푅푎 + 2 ∙ ∆푈푏 표푟 푈 = 퐸푎 + 퐼 ∙ 푅. Working principle of DC motor • Output power of DC motor: 푃표푢푡 = 푤 ∙ 푀표푢푡, • where 푀표푢푡 – output torque of DC motor, 푤 – angular velocity. 2휋 ∙ 푛 푤 = . 60 So in DC generator 푼 < Е, and in DC motor 푼 > Е. Construction of DC Machine 3 7 4 2 5 9 8 6 1 Construction of DC Machine 1. Stator or inductor – stationary part of DC machine that houses the field windings and receives the supply. 2. Yoke. 3. Pole of DC machine. 4. Field winding. 5. Armature winding. 6. Rotor or Armature of DC machine – rotational part of DC machine. 7. Brushes. 8. Bearing. 9. Commutator. Pole cores and pole shoes of DC machine • Poles of DC machine: 1 – yoke, 2 – pole cores, 3 – pole coils of DC machine Armature Winding of DC machine Commutator of DC machine DIRECT CURRENT MACHINES 2 Armature reaction in DC machines • If the magnetic field windings of a dc machine are connected to a power supply and the rotor of the machine is turned by an external source of mechanical power, then a voltage will be induced in the conductors of the rotor. This voltage will be rectified into a DC output by the action of the machine's commutator. Now connect a load to the terminals of the machine, and a current will flow in its armature windings. This current flow will produce a magnetic field of its own, which will distort the original magnetic field from the machine's poles. This distortion of the flux in a machine as the load is increased is called armature reaction. Armature reaction in DC machines B τ τ N 1 1 GNA, MNA S Ia=0 • Flux distribution of a bipolar generator 퐼푎 = 0. Armature reaction in DC machines B τ τ 1 1 1 2 GNA, MNA If=0 • Flux distribution of a bipolar generator 퐼푓 = 0. Armature reaction in DC machines N B τ τ 2 2 1 3 1 1 4 2 S • Flux distribution of a bipolar generator, 1-1 – GNA, 2-2 – MNA, 훽 – neutral plane shift Armature reaction in DC machines • To reduce the adverse effects of armature reaction and to improve the machine’s performance, following methods are used: • Brush Shift. • Inter Pole. • Compensating Winding. Commutation in DC Machine • The currents induced in armature conductors of a DC generator are alternating. These currents flow in one direction when armature conductors are under N-pole and in the opposite direction when they are under S-pole. As conductors pass out of the influence of a N-pole and enter that of S-pole, the current in them is reversed. This reversal of current takes place along magnetic neutral axis or brush axis i.e. when the brush spans and hence short circuits that particular coil undergoing reversal of current through it. This process by which current in the short-circuited coil is reversed while it crosses the MNA is called commutation. Physical Concept of Commutation in DC Machine • At the first position, the brush is connected the commutator bar 2 (as IC IC shown in fig.). Then the total current conducted by 2IC the commutator bar 2 into 1 2 3 the brush is 2퐼퐶. 2IC Physical Concept of Commutation in DC Machine • When the armature starts to move right, then the brush comes to contact of I I C x x C bar a. Then the armature current flows through two I +x IC-x C paths and through the bars 1 2 3 1 and 2 (as shown in fig.). The total current ( 2퐼퐶) 2IC collected by the brush remain same. Physical Concept of Commutation in DC Machine • As the contact area of the bar a with the brush increases and the contact IC IC area of the bar 2 decreases, the current flow through the bars increases 1 2 3 and decreases simultaneously. When the contact area become same 2IC for both the commutator bar then same current flows through both the bars. Physical Concept of Commutation in DC Machine • When the brush contact area with the bar 2 decreases further, then the y current flowing through the IC I y C coil changes its direction and starts to flow counter- IC+y I -y C clockwise. 1 2 3 2IC Physical Concept of Commutation in DC Machine • When the brush totally comes under the bar 1 and disconnected with the bar 2 IC IC then current 퐼퐶 flows through the coil in the 2IC counter-clockwise direction 1 2 3 and the short circuit is removed. In this process 2I the reversal of current or C the process of commutation is done. The current reversal in the coil undergoing commutation i Tc Ideal commutation Actual commutation with inductance taken into account t Spark at trailing edge of brush Brushes reaches Brushes reaches clears beginning of segment b end of segment a Methods of improving commutation There are two main methods of improving commutation. These are •Resistance commutation •EMF commutation Resistance commutation A B C I I C x x C IC-x IC+x 1 2 3 R1 R2 2IC EMF commutation The voltage rise in the short circuit coil due to inductive property of the coil, which opposes the current reversal in it during the commutation period, is called the reactance voltage. We can produce reversing EMF in two ways • 1. By brush shifting. • 2. By using inter-poles or commutating poles. DIRECT CURRENT MACHINES 3 No-load characteristic or magnetization curve of DC generator 퐸 = 푓 푖푓 , when 퐼푎 = 0 and 푛 = 푐표푛푠푡 Е 1,15Urated Er +if -if Ifмах -Е The terminal or external characteristics of DC generators 푈 = 푓 퐼 , 푖푓 = 푐표푛푠푡(푟푓 = 푐표푛푠푡),푛 = 푐표푛푠푡. U, V • Voltage regulation is U0 ΔU defined by: 푈 − 푈 ∆푈 = 0 푟 ∙ 100% = 푈0 = 5 … 10%. 0 Ir Ia,A The terminal or external characteristics of DC generators 푈 = 푓 퐼 , 푖푓 = 푐표푛푠푡(푟푓 = 푐표푛푠푡),푛 = 푐표푛푠푡. • 1 - separately excited DC generator, U, V • 2 - shunt wound DC • 3 - cumulatively 3 compound wound DC 1 generator 2 • 4 - differentially 4 compounded self- excited DC Ia,A Control characteristic of DC generators 푖푓 = 푓 퐼푎 when 푈 = 푐표푛푠푡,푛 = 푐표푛푠푡. i , A • 1 - separately excited f 4 DC generator, 1,2 • 2 - shunt wound DC • 3 - cumulatively i 3 f0 compound wound DC generator • 4 - differentially Ia, A compounded self- excited DC Load characteristics of DC generators 푈 = 푓 푖푓 when 퐼푎 = 푐표푛푠푡, 푛 = 푐표푛푠푡. No-load U Load c b Ur a c' b' ab-a'b'=Iara a' bc>b'c' if Load characteristics of DC generators 푈 = 푓 푖푓 when 퐼푎 = 푐표푛푠푡, 푛 = 푐표푛푠푡. U, V • 1 - separately excited No-load DC generator, 3 • 2 - shunt wound DC 1,2 • 3 - cumulatively 4 compound wound DC generator • 4 - differentially compounded self- if,A excited DC Short circuit characteristics of DC generators 퐼푎 = 푓 푖푓 when 푈 = 0, 푛 = 푐표푛푠푡 • Terminal voltage is defined by: Ia, A 푈 = 퐸푎 − 퐼푎 ∙ 푅푎, • So in case short circuit mode 푈 = 0 and 퐸푎 퐼푎 = , 푅푎 • as 푅푎 is negligible small if, A value we have to decrease EMF 퐸푎 or 퐼푎 armature current will be extremely high.