Three Phase Motors Maths

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Three Phase Motors Maths
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Poles and Speed
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Power input to the Rotor

• S slip, either or pu
• n Synchronous speed (the speed the rotating mag
  flux rotates at and the speed the rotor is trying
  to get to. (rps or Hz)
• nR Rotor speed. (rps or Hz)
• nS Slip speed (rps or Hz)
• T torque (Nm)
• FR Frequency of the rotor currents. (Hz)
• F supply frequency (Hz)
• p No of pairs of poles
• P Power (W)
• ER Rotor emf at standstill (V)
• RR Rotor resistance (?)
• XR Rotor reactance (?)

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• Power developed by the rotor 2?nRT

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Power Factor

• It is common to define the Power Factor PF
• - as the cosine of the phase angle between
  voltage and current
• - or the "cosf".
• PF cos f where
• PF power factor
• f phase angle between voltage and current

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• The power factor defined by IEEE and IEC is the
  ratio between the applied active (true) power -
  and the apparent power, and can in general be
  expressed as
• PF P / S
• where PF power factor
• P active (true or real) power (Watts)
• S apparent power (VA, volts amps)

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Example - Power Factor

• A industrial plant draws 200 A at 400 V and the
  supply transformer and backup UPS is rated 200 A
  400 V 80 kVA.
• If the power factor - PF - of the loads is only
  0.7 - only 80 kVA 0.7 56 kW

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What is the PF issue?

• Any power factor less than 1 means that the
  circuit's wiring has to carry more current than
  what would be necessary with zero reactance in
  the circuit to deliver the same amount of (true)
  power to the resistive load

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• A low power factor is expensive and inefficient
  and some utility companies may charge additional
  fees when the power factor is less than 0.95.
• A low power factor will reduce the electrical
  system's distribution capacity by increasing the
  current flow and causing voltage drops.

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"Leading" or "Lagging" Power Factors

• Power factors are usually stated as "leading" or
  "lagging" to show the sign of the phase angle.
• With a purely resistive load current and voltage
  changes polarity in step and the power factor
  will be 1. Electrical energy flows in a single
  direction across the network in each cycle.
• Inductive loads - transformers, motors and wound
  coils - consumes reactive power with current
  waveform lagging the voltage.
• Capacitive loads - capacitor banks or buried
  cables - generates reactive power with current
  phase leading the voltage.

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