Three-Phase Systems Professor Mohamed A. El-Sharkawi El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Single Phase El-Sharkawi@University of Washington
El-Sharkawi@University of Washington AC Waveform One Cycle Voltage or Current Peak Maximum Time El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington ac Waveform El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington AC Representation w t v El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington How AC is Generated Stator N S Rotor Windings El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington X N S ϕ 900 2700 Angle 1800 3600 El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Alternating Current v N S N S N S N S . N S N S N S N S N S El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Reference V2 w t v 1 2 q El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Reference V2 w t v 1 2 q El-Sharkawi@University of Washington El-Sharkawi@University of Washington
v i Voltage and Current can be Out of Phase load V I + _ i v q w t V I is the phase shift of current also known as the power factor angle It is due to the presence of inductive and capacitive elements. El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Example If V=120 V and Z=4 + j3 , calculate the current and power factor. V Z I + _ Lagging V I Notice that the pf angle is the angle of the impedance El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Polarities Z I + _ Load V I + _ Source El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Three-Phase El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Three-Phase va N S N S N S N S N S N S N S N S I b vb I a vc I c El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Three-Phase Generator El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Three-phase system v aa' bb' cc' Reference 120o vaa’ vbb’ vcc’ 120o 120o Time El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Why do we use 3-phase systems? Three-phase system produces rotating magnetic field. Three-phase motors can start without the need for extra equipment. For the same physical size, a three-phase generator produces more power than a single phase generator. Three-phase lines transmit more power. Three-phase lines are more reliable. In distribution circuit, you can operate the system with one missing phase. El-Sharkawi@University of Washington El-Sharkawi@University of Washington
c b a ¢ ¢ c b ¢ a How is Three-Phase System Connected? X X X El-Sharkawi@University of Washington El-Sharkawi@University of Washington
How is Three-Phase System Connected? Any three-phase generator has 6 terminal wires Transmitting 6 wire over a long distance is expensive Instead, three-wire system is used by connecting the six wires as Y or Delta El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Y-Connected Source a n c ¢ b ¢ X X c b X a ¢ El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Y-Connected Source El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Y-Connected Source c c v cn v an Reference n a v bn El-Sharkawi@University of Washington b
Delta-Connected Source ¢ b ¢ X X c b X a ¢ El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Delta () Connection: Source El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
El-Sharkawi@University of Washington
Phase and LineVoltages El-Sharkawi@University of Washington
El-Sharkawi@University of Washington c Phase voltage v cn v an Reference a n a b v bn c b v an v bn v cn n El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington cn c Line-to-line voltage v bc v ca n v an a n c b a Reference v ca v ab v bn b v ab v bc El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington ca n v bn cn an v ab -v bn Reference v bc Reference v ab ca bc bn b n an a cn c El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Keep in mind Unless stated in the problems, the following assumptions are to be used: All voltages are line-to-line quantities All powers are for the three phases El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Example Let v ab Calculate the line-to-line voltage Vab v an Reference El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Main Conclusions Line-to-line voltage is greater than phase voltage by Line-to-line voltage leads phase voltage by El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Y-Load connection Load Most loads are connected in Y To have access to the ground potential To balance the voltage across the load Each load impedance (Z) is called load impedance Voltage across the load impedance is called load voltage Load current a + Three-phase feeder I Z a I b n Z Z + + b I c El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Main Conclusions for Y-Connected Load Load voltage is equal to the Phase voltage Line current is equal to load current by El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Delta-Load connection Mostly in industrial loads No Access to ground Used to increase voltage across the load Each load impedance (Z) is called load impedance Voltage across the load impedance is called load voltage Load current a - + Three-phase feeder Ica Z Iab Z - + c Z b - + Ibc El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Y-Connection Source and Load Line current Transmission Line Source Load I Load current a a a + + I Z V I a an a I n b n V V Z Z cn bn + I c + + b c + b I I I b c c b I c El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington For balanced system El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington cn I c q n V an Reference I b q V bn I a q El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Neutral Current of Balanced Load I c For balanced system I a I b El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Single-Phase Representation Ia Va Va Z Ia + _ El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Delta () Connection Source and Load Line current Transmission Line Source Load Phase current I Load current a a a - + - + Ica Ica Z Iab Iab Z V ca V - ab + - + I c Z b c b b - + V bc Ibc - + Ibc I c El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Delta () Connection: Source Ia a _ Ica + Ia is line current Iab is generator current Vca Vab Iab _ Ib + b Vbc c _ + Ibc Ic El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Kirchhoff’s Current law at node a Transmission Line Load I Load current c c - + Ibc Ica Reference v bc ab ca a b c Z Z - q + I b Z a a - + Iab I q b q Voltage Diagram Vab is chosen reference El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Line Currents Reference v bc ab ca a b c V ab Refere q I ab q I ca I bc q q El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Line Currents V ab Refere q I ab 300 I ca -Ica I a El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Example Iab V ab q 300 Let Reference 100 I Calculate the phase current Iab of a delta circuit a El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Main Conclusions for Delta-Connected Load Load voltage is equal to the line-to-line voltage Line current is greater than load current by Line current lags the load current by El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Mixed Connection Line current Transmission Line Source Load Phase current I Load current a a a + I Z Ica a Iab V ca V I ab b n Z Z - I c b c b I b c V bc Ibc I c El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Y- Transformation a b c Ia Ib Ic Z a b c Ia Ib Ic ZY El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Y- Transformation El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Y- Transformation a b c Ia Ib Ic Z a b c Ia Ib Ic ZY THEN El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Example 1. Calculate the current of the load 2. Calculate the equivalent Y load 3. Calculate the load current of the equivalent Y load b c Ia Ic Van = 120 v a Ib Z = 4 + j 3 El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington b c Ia Ic Van Ib Z Part 1: Part 2: Part 3: The load current in load is equal to El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Example Calculate the line current Z2 = 12 - j 9 Z1 = 4 + j 3 Ia a b c Van = 120 v c b b c Ic El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Change delta to Y Z2y = 4 - j 3 Z1 = 4 + j 3 Ia a b c Van = 120 v b b c c Ic El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Zeq = 25/8 Ia a b c Van = 120 v b c Ic El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Instantaneous Electric Power [p(t)] V I Fixed average Zero average El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Instantaneous Electric Power [p(t)] El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Real Power (Average P) El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Real Power (Average P) p wt El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Reactive Power [Q] Important points! Frequency of h(t) is double the frequency of supply voltage Average value of h(t) is zero w t h(t) q p El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Real power Reactive power El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Complex Power (S) IMPORTANT is the power factor angle V I Real Power Reactive Power El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Power of 3-phase circuits Iphase Vphase For Single phase IMPORTANT is the angle between phase voltage and phase current. Use voltage as a reference For 3-phase El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Real Power in Delta Circuit b c Ia Ib Ic Iab Ica Ibc + _ El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Reactive Power in Delta Circuit b c Ia Ib Ic Iab Ica Ibc + _ El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Real Power in Y Circuit a b c Ia Ib Ic Va Vc Vb El-Sharkawi@University of Washington El-Sharkawi@University of Washington
Reactive Power in Y Circuit b c Ia Ib Ic Va Vc Vb El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Example Calculate the load power b c Ia Ic Van = 120 v a Ib Z = 4 - j 3 El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington b c Ia Ic Van Ib Z V ab I ca V an 300 q n I ab I bc 300 I a El-Sharkawi@University of Washington El-Sharkawi@University of Washington
El-Sharkawi@University of Washington Method #1 Method #2 Keep in mind The pf angle is the angle of the load impedance. It is the same as the angle between the phase voltage and the phase current El-Sharkawi@University of Washington El-Sharkawi@University of Washington