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POLYPHASE CIRCUITS

POLYPHASE CIRCUITS. LEARNING GOALS. Three Phase Circuits Advantages of polyphase circuits. Three Phase Connections Basic configurations for three phase circuits. Source/Load Connections Delta-Wye connections. Theorem

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POLYPHASE CIRCUITS

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  1. POLYPHASE CIRCUITS LEARNING GOALS Three Phase Circuits Advantages of polyphase circuits Three Phase Connections Basic configurations for three phase circuits Source/Load Connections Delta-Wye connections

  2. Theorem For a balanced three phase circuit the instantaneous power is constant THREE PHASE CIRCUITS

  3. Proof of Theorem For a balanced three phase circuit the instantaneous power is constant

  4. Positive sequence a-b-c Y-connected loads Delta connected loads THREE-PHASE CONNECTIONS

  5. Line voltages Positive sequence phase voltages SOURCE/LOAD CONNECTIONS BALANCED Y-Y CONNECTION For this balanced circuit it is enough to analyze one phase

  6. Positive sequence a-b-c Positive sequence phase voltages Balanced Y - Y Relationship between phase and line voltages LEARNING EXAMPLE For an abc sequence, balanced Y - Y three phase circuit Determine the phase voltages The phasor diagram could be rotated by any angle

  7. Chosen as reference Abc sequence LEARNING EXAMPLE For an abc sequence, balanced Y - Y three phase circuit Because circuit is balanced data on any one phase is sufficient Determine line currents and load voltages

  8. Convert to an equivalent Y connection Example Relationship between phase and line voltages DELTA CONNECTED SOURCES

  9. Source is Delta connected. Convert to equivalent Y LEARNING EXAMPLE Determine line currents and line voltages at the loads Analyze one phase Determine the other phases using the balance

  10. Positive sequence phase voltages Line-phase current relationship DELTA-CONNECTED LOAD Method 1: Solve directly Method 2: We can also convert the delta connected load into a Y connected one. The same formulas derived for resistive circuits are applicable to impedances

  11. LEARNING EXTENSION Line-phase current relationship

  12. REPLACE IN THE THIRD AND SOLVE FOR R1 SUBTRACT THE FIRST TWO THEN ADD TO THE THIRD TO GET Ra

  13. Delta-connected load consists of 10-Ohm resistance in series with 20-mH inductance. Source is Y-connected, abc sequence, 120-V rms, 60Hz. Determine all line and phase currents Alternatively, determine first the line currents and then the delta currents Polyphase Line-phase current relationship LEARNING EXAMPLE

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