THREE PHASE vs SINGLE PHASE SUPPLY

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1 THREE PHASE vs SINGLE PHASE SUPPLY Presently 3-ø AC system is very popular and being used worldwide for power generation, power transmission, distribution and for electric motors. Three phase system has the following advantages as compare to single phase system: 1. Power to weight ratio of 3-ø alternator is high as compare to 1-ø alternator. Means for generation for same amount of Electric Power, the size of 3-ø alternator is small as compare to 1-ø Alternator. Hence, the overall cost of alternator is reduced for generation of same amount of power. Moreover, of due to reduction in weight, transportation and 1

2 installation alternator become convenient and less space is required to accommodate the alternator in power house. 2. For electric power transmission and distribution of same amount of power, the requirement of conductor material is less in 3-ø system as compare to 1-ø system. Hence, the 3-ø transmission and distribution system is economical as compare 1-ø system. 3. Let us consider the power produced by single phase supply and 3-phase supply at unity power factor. Wave form of power produce due 1-phase supply at unity power factor is shown in figure (C) and Wave form of power produced due to 3-phase supply is shown in figure (D) below. 2

3 From power wave forms shown in figure (C) and (D) above it is clear that in 3- phase system, the instantaneous power is always constant over the cycle results in smooth and vibration free operation of machine. Whereas in 1-ø system the instantaneous power is pulsating hence change over the cycle, which leads to vibrations in machines. Power to weight ratio of three phase induction motor is high as compare to single phase induction motor. Means for same amount of Mechanical Power, the size of three phase induction motor is small as compare to single phase induction motor. Hence, the overall cost of induction motor is reduced. Moreover, due to reduction in weight, transportation and installation of induction motor become convenient and less space is required to accommodate the Induction motor. 3-phase induction motor is self-started as the magnetic flux produced by 3- phase supply is rotating in nature with constant magnitude. Whereas 1-ø induction motor is not self-started as the magnetic flux produced by 1-ø supply is pulsating in nature. Hence, we have to make some arrangement to make the 1-ø induction motor self-started. Which further increase the cost of 1-ø induction motor. 3-phase motor is having better power factor and efficiency as compare to 1-ø motor. 3

4 Power to weight ratio of 3-phase transformer is high as compare to 1-ø transformer. Means for same amount of Electric Power, the size of 3-phase transformer is small as compare to 1-ø transformer. Hence, the overall cost of transformer is reduced. Moreover, due to reduction in weight, transportation and installation of transformer become convenient and less space is required to accommodate the transformer. If fault occurs in any winding of 3-phase transformer, the rest of two winding can be used in open delta to serve the 3-phase load which is not possible in 1-ø transformer. This ability of 3-phase transformer further increase the reliability of 3-phase transformer. A 3-phase system can be used to feed a 1-ø load, whereas vice-versa is not possible. DC rectified from 3-phase supply is having the ripple factor 4% and DC rectified from 1-ø supply is having the ripple factor 48.2 %. Mean DC rectified from 3-ø supply contains less ripples as compare to DC rectified from 1-ø supply. Hence the requirement of filter is reduced for DC rectified from 3-phase supply. Which reduce the overall cost of convector. From above it clear the 3-phase system is more economical, efficient, reliable and convenient as compare to 1-ø system. There are two types of system available in electric circuit, single phase and three phase system. In single phase circuit, there will be only one phase, i.e the current will flow through only one wire and there will be one return path called neutral line to complete the circuit. So in single phase minimum amount of power can be transported. Here the generating station and load station will also be single phase. This is an old system using from previous time. In 1882, new invention has been done on polyphase system, that more than one phase can be used for generating, transmitting and for load system. Three phase circuit is the polyphase system where three phases are send together from the generator to the load. Each phase are having a phase difference of 120, i.e 120 angle electrically. So from the total of 360, three phases are equally divided into 120 each. The power in three phase system is continuous as all the three phases are involved in generating the total power. The sinusoidal waves for 3 phase system is shown below- 4

5 The three phases can be used as single phase each. So if the load is single phase, then one phase can be taken from the three phase circuit and the neutral can be used as ground to complete the circuit. Why Three Phase is preferred Over Single Phase? There are various reasons for this question because there are numbers of advantages over single phase circuit. The three phase system can be used as three single phase line so it can act as three single phase system. The three phase generation and single phase generation is same in the generator except the arrangement of coil in the generator to get 120 phase difference. The conductor needed in three phase circuit is 75% that of conductor needed in single phase circuit. And also the instantaneous power in single phase system falls down to zero as in single phase we can see from the sinusoidal curve but in three phase system the net power from all the phases gives a continuous power to the load. Till now we can say that there are three voltage source connected together to form a three phase circuit. And actually it is inside the generator. The generator is having three voltage source s which are acting together in 120 phase difference. If we can arrange three single phase circuit with 120 phase difference, then it will become a three phase circuit. So 120 phase difference is must otherwise the circuit will not work, the three phase load will not be able to get active and it may also cause damage to the system. The size or metal quantity of three phase devices is not having much difference. Now if we consider the transformer, it will be almost same size for both single phase and three phase because transformer will make only the linkage of flux. So the three phase system will have higher efficiency compared to single phase because for the same or little difference in mass of transformer, three phase line will be out 5

6 whereas in single phase it will be only one. And losses will be minimum in three phase circuit. So overall in conclusion the three phase system will have better and higher efficiency compared to the single phase system. In three phase circuit, connections can be given in two types: 1. Star connection 2. Delta connection Star Connection In star connection, there is four wire, three wires are phase wire and fourth is neutral which is taken from the star point. Star connection is preferred for long distance power transmission because it is having the neutral point. In this we need to come to the concept of balanced and unbalanced current in power system. When equal current will flow through all the three phases, then it is called as balanced current. And when the current will not be equal in any of the phase, then it is unbalanced current. In this case, during balanced condition there will be no current flowing through the neutral line and hence there is no use of the neutral terminal. But when there will be unbalanced current flowing in the three phase circuit, neutral is having a vital role. It will take the unbalanced current through to the ground and protect the transformer. Unbalanced current affects transformer and it may also cause damage to the transformer and for this star connection is preferred for long distance transmission. The star connection is shown below- 6

7 In star connection, the line voltage is 3 times of phase voltage. Line voltage is the voltage between two phases in three phase circuit and phase voltage is the voltage between one phase to the neutral line. And the current is same for both line and phase. It is shown as expression below If a balance symmetrical load is connected across three phase voltage system in parallel, then the three currents will flow in neutral wire which quantities would be same, but they would be differ by 120 (out of phase), hence the vector sum of these three currents = 0. i.e. I R + I Y + I B = 0. Victorially The voltage between any two terminals or Voltage between Line and Neutral (Star Point) is called Phase voltage or Star voltage. And the voltage between two Lines is called Line to Line Voltage or Line Voltage 7

8 Voltage, Current and Power Values in Star Connection (Y) 1. Line Voltages and Phase Voltages in Star Connection We know that the Line Voltage between Line 1 and Line 2 (from fig 3a) is V RY = V R V Y. (Vector Difference) Thus, to find vector of V RY, increase the Vector of V Y in reverse direction as shown in the dotted form in the below fig 2. Similarly, on the both ends of vector V R and Vector V Y, make perpendicular dotted lines which look like a parallelogram as shown in fig (2). The Diagonal line which divides the parallelogram into two parts, showing the value of V RY. The angle between V Y and V R vectors is 60. Hence, if V R = V Y = V B = V PH, then V RY = 2 x V PH x Cos (60 /2) = 2 x V PH x Cos 30 = 2 x V PH x ( 3/2) Since Cos 30 = 3/2 = 3 V PH Similarly, V YB = V Y V B = 3 V PH And V BR = V B V R = 3 V PH Hence, it is proved that V RY = V YB = V BR is line voltages V L in Star Connection, Therefore, in Star Connection; V L = 3 V PH or V L = 3 E PH 8

9 It is seen from the fig 2 that; Line voltages are 120 apart from each other Line voltages are 30 leading from the corresponding phase voltages The angle Ф between line currents and respective line voltages are (30 +Ф), i.e. each line current is lagging (30 +Ф) from the corresponding line voltage. 2. Line Currents and Phase Currents in Star Connection It is seen from the fig (3a) that each line is in series with individual phase winding, therefore, the value of line current is same as in Phase windings to which the line is connected. i.e.; Current in Line 1 = I R Current in Line 2 = I Y Current in Line 3 = I B Since, the flowing currents in all three lines are same, and the individual current in each line is equal to the corresponding phase current, therefore; I R = I Y = I B = I PH. The phase current 9

10 Line Current = Phase Current I L = I PH In simple words, the value of Line Current and Phase Current is same in Star Connection. 3. Power in Star Connection In a three phase AC circuit, the total True or Active power is the sum of the three phase power. Or the sum of the all three phase powers is the Total Active or True Power. Hence, total active or true power in a three phase AC system; Total True or Active Power = 3 Phase Power Or P = 3 x V PH x I PH x CosФ.. Eq (1) Good to Know: Where Cos Φ = Power factor = the phase angle between Phase Voltage and Phase Current and not between Line current and line voltage. We know that the values of Phase Current and Phase Voltage in Star Connection; I L = I PH V PH = V L / 3.. (From V L = 3 V PH ) Putting these values in power eq. (1) P = 3 x (V L / 3) x I L x CosФ.. (V PH = V L / 3) 10

11 P = 3 x 3 x (V L / 3) x I L x CosФ. {3 = 3x 3} P = 3 x V L x I L x CosФ Hence proved; Power in Star Connection, P = 3 x V PH x I PH x CosФ or P = 3 x V L x I L x CosФ Similarly, Total Reactive Power = Q = 3 x V L x I L x SinФ Good to know: Reactive Power of Inductive coil is taken as Positive (+) and that of a Capacitor as Negative (-). Also, the total apparent power of the three phases Total Apparent Power = S = 3 x V L x I L Or, S = (P 2 + Q 2 ) Delta Connection In delta connection, there is three wires alone and no neutral terminal is taken. Normally delta connection is preferred for short distance due to the problem of unbalanced current in the circuit. The figure is shown below for delta connection. In the load station, ground can be used as neutral path if required. In this system of interconnection, the starting ends of the three phases or coils are connected to the finishing ends of the coil. Or the starting end of the first coil is connected to the finishing end of the second coil and so on (for all three coils) and it looks like a closed mesh or circuit as shown in fig In more clear words, all three coils are connected in series to form a close mesh or circuit. Three wires are taken out from three junctions and the all outgoing currents from junction assumed to be positive. 11

12 In Delta connection, the three windings interconnection looks like a short circuit, but this is not true, if the system is balanced, then the value of the algebraic sum of all voltages around the mesh is zero. When a terminal is open, then there is no chance of flowing currents with basic frequency around the closed mesh. Good to Remember: at any instant, the EMF value of one phase is equal to the resultant of the other two phases EMF values but in the opposite direction. Delta or Mesh Connection System is also called Three Phase Three Wire System (3-Phase 3 Wire) and it is the best and suitable system for AC Power Transmission. In delta connection, the line voltage is same with that of phase voltage. And the line current is 3 times of phase current. It is shown as expression below, 12

13 Voltage, Current and Power Values in Delta Connection (Δ) 1. Line Voltages and Phase Voltages in Delta Connection It is seen from fig 2 that there is only one phase winding between two terminals (i.e. there is one phase winding between two wires). Therefore, in Delta Connection, the voltage between (any pair of) two lines is equal to the phase voltage of the phase winding which is connected between two lines. Since the phase sequence is R Y B, therefore, the direction of voltage from R phase towards Y phase is positive (+), and the voltage of R phase is leading by 120 from Y phase voltage. Likewise, the voltage of Y phase is leading by 120 from the phase voltage of B and its direction is positive from Y towards B. If the line voltage between; Line 1 and Line 2 = V RY Line 2 and Line 3 = V YB Line 3 and Line 1 = V BR Then, we see that V RY leads V YB by 120 and V YB leads V BR by 120. Let s suppose, V RY = V YB = V BR = V L (Line Voltage) Then V L = V PH I.e. in Delta connection, the Line Voltage is equal to the Phase Voltage. 2. Line Currents and Phase Currents in Delta Connection 13

14 It will be noted from the below (fig-2) that the total current of each Line is equal to the vector difference between two phase currents flowing through that line. i.e.; Current in Line 1= I 1 = I R I B Current in Line 2 =I 2 = I Y I R Current in Line 3 =I 3 = I B I Y {Vector Difference} The current of Line 1 can be found by determining the vector difference between I R and I B and we can do that by increasing the I B Vector in reverse, so that, I R and I B makes a parallelogram. The diagonal of that parallelogram shows the vector difference of I R and I B which is equal to Current in Line 1= I 1. Moreover, by reversing the vector of I B, it may indicate as (-I B ), therefore, the angle between I R and -I B (I B, when reversed = -I B ) is 60. If, I R = I Y = I B = I PH. The phase currents Then; The current flowing in Line 1 would be; I L or I 1 = 2 x I PH x Cos (60 /2) 14

15 = 2 x I PH x Cos 30 = 2 x I PH x ( 3/2) Since Cos 30 = 3/2 = 3 I PH i.e. In Delta Connection, The Line current is 3 times of Phase Current Similarly, we can find the reaming two Line currents as same as above. i.e., I 2 = I Y I R Vector Difference = 3 I PH I 3 = I B I Y Vector difference = 3 I PH As, all the Line current are equal in magnitude i.e. I 1 = I 2 = I 3 = I L Hence IL = 3 I PH It is seen from the fig above that; The Line Currents are 120 apart from each other Line currents are lagging by 30 from their corresponding Phase Currents The angle Ф between line currents and respective line voltages is (30 +Ф), i.e. each line current is lagging by (30 +Ф) from the corresponding line voltage. 3. Power in Delta Connection & GAIN We know that the power of each phase Power / Phase = V PH x I PH x CosФ And the total power of three phases; Total Power = P = 3 x V PH x I PH x CosФ.. (1) We know that the values of Phase Current and Phase Voltage in Delta Connection; BEAM 15

16 I PH = I L / / 3.. (From IL = 3 I PH ) V PH = V L Putting these values in power eq. (1) P = 3 x V L x ( I L / 3) x CosФ (I PH = I L / / 3) P = 3 x 3 x V L x ( I L / 3) x CosФ { 3 = 3x 3 } P = 3 x V L x I L x CosФ Hence proved; Power in Delta Connection, P = 3 x V PH x I PH x CosФ. or P = 3 x V L x I L x CosФ Good to Know: Where Cos Φ = Power factor = the phase angle between Phase Voltage and Phase Current and not between Line current and line voltage. Good to Remember: In both Star and Delta Connections, The total power on balanced load is same. I.e. total power in a Three Phase System = P = 3 x V L x I L x CosФ Good to know: Balanced System is a system where: All three phase voltages are equal in magnitude All phase voltages are in phase by each other i.e. 360 /3 = 120 All three phase Currents are equal in magnitude All phase Currents are in phase by each other i.e. 360 /3 = 120 A three phase balanced load is a system in which the load connected across three phases are identical. 16

17 In three phase circuit, star and delta connection can be arranged in four different ways- 1. Star-Star connection 2. Star-Delta connection 3. Delta-Star connection 4. Delta-Delta connection But the power is independent of the circuit arrangement of the three phase system. The net power in the circuit will be same in both star and delta connection. The power in three phase circuit can be calculated from the equation below, Since, there is three phases, so the multiple of 3 is made in the normal power equation and the PF is power factor. Power factor is a very important factor in three phase system and some times due to certain error, it is corrected by using capacitors. Comparison between Star and Delta Connections Star (Y) Connection In STAR connection, the starting or finishing ends (Similar ends) of three coils are connected together to form the neutral point. A common wire is taken out from the neutral point which is called Neutral. Delta (Δ) Connection In DELTA connection, the opposite ends of three coils are connected together. In other words, the end of each coil is connected with the start of another coil, and three wires are taken out from the coil joints There is a Neutral or Star Point Three phase four wire system is derived from Star Connections (3-Phase, 4 Wires System) We may Also derived 3 Phase 3 Wire System from Star No Neutral Point in Delta Connection Three phase three wire system is derived from Delta Connections (3-Phase, 3 Wires System) 17

18 Connection Line Current is Equal to Phase Current. i.e. Line Current = Phase Current I L = I PH Line Voltage is Equal to Phase Voltage. i.e. Line Voltage = Phase Voltage V L = V PH Line Voltage is 3 times of Phase Voltage. i.e. V L = 3 V PH The Total Power of three phases could be found by P = 3 x V L x I L x CosФ. Or P = 3 x V PH x I PH x CosФ The speeds of Star connected motors are slow as they receive 1/ 3 voltage. In Star Connection, the phase voltage is low as 1/ 3 of the line voltage, so, it needs low number of turns, hence, saving in copper. Low insulation required as phase voltage is low In Power Transmission, Star Connection system is general and typical to be used. Line Current is 3 times of Phase Current. i.e. I L = 3 I PH The Total Power of three phases could be found by P = 3 x V L x I L x CosФ or P = 3 x V PH x I PH x CosФ The speeds of Delta connected motors are high because each phase gets the total of line voltage In Delta connection, The phase voltage is equal to the line voltage, hence, it needs more number of turns. Heavy insulation required as Phase voltage = Line Voltage. In Power Distribution and industries, Delta Connection is general and typical to be used. 18

19 STAR DELTA TRANSFORMATIONS 19

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70 PHASE CONTROLLED RECTIFIERS OR CONVERTERS 70

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