ELL100: INTRODUCTION TO ELECTRICAL ENGG. Course Instructors: J.-B. Seo, S. Srirangarajan, S.-D. Roy, and S. Janardhanan Department of Electrical Engineering, IITD

AC power generation Magnetic flux Magnetic flux density Flux depends on orientation of surface with respect to B field.

AC power generation Induced emf (electro-magnetic force) in a closed loop equals negative of time rate of change of magnetic flux through the loop (Faraday’s Law)

AC power generation Induced emf (electro-magnetic force) in a closed loop equals negative of time rate of change of magnetic flux through the loop (Faraday’s Law) Assume that N S Water turning a turbine (hydroelectric) Gasoline Motor turning a shaft (AC generator) Note that for

AC power generation Induced emf (electro-magnetic force) in a closed loop equals negative of time rate of change of magnetic flux through the loop (Faraday’s Law) Assume that N S Water turning a turbine (hydroelectric) Gasoline Motor turning a shaft (AC generator) Note that for

AC power generation Induced emf (electro-magnetic force) in a closed loop equals negative of time rate of change of magnetic flux through the loop (Faraday’s Law) Assume that N S Water turning a turbine (hydroelectric) Gasoline Motor turning a shaft (AC generator) Note that for

AC power generation N S

Generating three-phase voltage

Generating three-phase voltage Single-phase voltage  Three-phase voltage can be also generated with three single-phase voltage Load Load Load

Generating three-phase voltage Single-phase voltage  Three-phase voltage can be also generated with three single-phase voltage Load – This can be combined as a single neutral line Load Load

Two methods of source connections  voltages between the lines a,b,c and the neutral line n: phase voltages.  voltages between the lines Vab, Vbc, Vca: phase voltages.

Two methods of source connections

Phase sequence Balanced phase voltages are equal in magnitude and are out of phase with each other by 120. There are two possible ways in which a source can be balanced Positive or abc sequence Negative or acb sequence

Phase sequence Balanced phase voltages are equal in magnitude and are out of phase with each other by 120. There are two possible ways in which a source can be balanced Positive or abc sequence Negative or acb sequence

Recalling the Y-Delta conversions (in Two port networks)

Balanced three phase load Similar to the source, the load can also be Delta or Wye connected. A balanced load: the phase impedances are equal in magnitude and in phase.

Connections with loads

Balanced Wye-Wye Connection – 1 Balanced load: Line voltage (or line-to-line voltage)

Balanced Wye-Wye Connection – 1 Balanced load: Line voltage (or line-to-line voltage)

Balanced Wye-Wye Connection – 1 Balanced load: Line voltage (or line-to-line voltage)

Balanced Wye-Wye Connection – 2 By KVL, the current along the line (line current): Voltage across neutral line is zero: it can be removed Phase current is the current in each phase of the source of load. In Y-Y system, the line current is the same as the phase current.

Balanced Wye-Wye Connection – 2 By KVL, the current along the line (line current): Voltage across neutral line is zero: it can be removed Phase current is the current in each phase of the source of load. In Y-Y system, the line current is the same as the phase current.

Example of Y-Y system Neutral line

Balanced Wye-Delta Connection – 1 Phase voltage Line voltage is Phase current can be Alternatively,

Balanced Wye-Delta Connection – 1 Phase voltage Line voltage is Phase current can be Alternatively,

Balanced Wye-Delta Connection – 2 Line currents are obtained by KCL Magnitude of line currents:

Example A balanced abc-sequence Y-connected source with is connected to a Delta-connected balanced load per phase. Calculate the phase and line currents. Using and we have The phase current is The line current

Balanced Delta-Delta Connection Assuming a positive sequence, the phase voltages for a delta-connected source are  The line voltages are the same as the phase voltage The phase currents The line currents are obtained from the phase currents by applying KCL at nodes A, B, and C

Balanced Delta-Delta Connection Assuming a positive sequence, the phase voltages for a delta-connected source are  The line voltages are the same as the phase voltage The phase currents The line currents are obtained from the phase currents by applying KCL at nodes A, B, and C

Example A balanced -connected load having an impedance is connected to a -connected, positive-sequence generator having . Calculate the phase currents of the load and the line currents.

Balanced Delta-Wye Connection Assuming the abc sequence, the phase voltages of a delta-connected source are These are also the line voltages as well as the phase voltages. In order to get the line current, apply KVL to loop aANBba,

Balanced Delta-Wye Connection In order to get the line current, apply KVL to loop aANBba, Since we assume the abc sequence, The phase currents are equal to the line currents.

Delta-Wye Transformation Another possible way to analyze the Delta-Star connection. Transform Delta connected source to Star connected source Analyze the Y-Y connection. Observing the phase voltage to line voltage relation in the Y-Y connection

Example A balanced Y-connected load with a phase impedance of is supplied by a balanced, positive sequence -connected source with a line voltage of 210 V. Calculate the phase currents. Use as a reference .

Power in a Balanced system For a Y-connected load, the phase voltages are the phase currents lag behind their corresponding phase voltages by The total instantaneous power in the load is the sum of the instantaneous powers in the three phases

Power in a Balanced system Applying the trigonometric identity, Thus the total instantaneous power in a balanced three-phase system is constant—it does not change with time as the instantaneous power of each phase does.

Power in a Balanced system The average power per phase for either the -connected load or the Y-connected load is p/3, or The reactive power per phase The apparent power per phase The complex power per phase

Power in a Balanced system The total average power is the sum of the average powers in the phases The total reactive power The total complex power

Advantage of three-phase circuit Consider an amount of power PL being transmitted at the same line voltage VL using Single phase supply 3-phase balanced supply Power dissipation in transmission

Advantage of three-phase circuit Power dissipation in transmission If same amount of power loss is to be allowed Ratio of material required for transmission wires In other words, a 3-phase supply can deliver power, and follow power loss constraints using only 75% of the material as an equivalent single phase supply.