Phasor formulas

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sdg.matiaan
2021-03-29 09:43

So to give a phasor for 3 wires, the minimum is to give:
1) the voltages on the 3 phases (also referred to as V, voltage to neutral, not between phases)
2) the currents on the 3 phases (also referred to as I)
3) the angles between each of the voltages and the corresponding current (I'll refer to it as VIa for the lack of a clear standard)
(so this accounts for 12 values)

Other things that can not be calculated and is often omitted:
4) each of the voltage angles
5) current on the 4th wire
6) phase rotation

the main formulas I work with is:
kVA = V x I / 1000
kVA =  sqrt( kW ? + kvar ? )
kVA total = kVA red + kVA white + kVA blue
kW = V x I x cos(VIa) / 1000
kvar = V x I x sin(VIa) / 1000
pf = kW / kVA
V to neutral = √3 * V to V (if you are given the voltages in V to V rather than V to neutral, in a 3 phase system)

things that can be calculated if you have the values above:
(sometimes these things are given and you have to calculate the values above)
7) kVA (demand) of each phase and combined (also referred to as S or Apparent Power or Demand or kVA or MD or Maximum Demand or NMD or Notified Maximum Demand or Access or Network Access - people often use these terms interchangeably although they don't always mean exactly the same thing)
kVA red = V red * I red / 1000
kVA white = V red * I white / 1000
kVA blue = V red * I blue / 1000
kVA = kVA red + kVA white + kVA blue
8) kW of each phase and combined (also referred to as P or Active Power)
kW red = kVA red * cos(VIa red)
kW white = kVA white * cos(VIa white)
kW blue = kVA blue * cos(VIa blue)
kW total = kW red + kW white + kW blue
9) kvar of each phase and combined (also referred to as Q or Reactive Power)
kvar red = kVA red * sin(VIa red)
kvar white = kVA white * sin(VIa white)
kvar blue = kVA blue * sin(VIa blue)
kvar total = kvar red + kvar white + kvar blue
10) power factor of each phase (also referred to as pf)
pf red = kW red / kVA red
pf white = kW red / kVA white
pf blue = kW red / kVA blue
pf total = kW total / kVA total
11) leading or lagging power factor (which is usually evident from [9])
kvar total > 0 : lagging
kvar total < 0 : leading

This comes to 44 values:
1 x 4 (I - of each of the 4 lines)
5 x 4 (V, kVA, kW, kvar, pf - of each phase + total)
6 x 3 (V angles, I angles - for each of the 3 phases)
2 x 1 (leading/lagging, phase rotation)


Tags: 3 phasephasor
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