A three-phase power source with four conductors (L1, L2, L3, N) supplies three single-phase loads. The source voltage is 400 V. The phase sequence is 1, 2, 3.
The loads have the following characteristics and connections:
See added picture for cirucit drawing and currents.
Tried to solve this in octave, I think I mess up I4 and then In. I1 is correct.
I don´t think the KCL is wrong and I don see why Skc =P/pF is incorrect either.
One other error margin could be how I determine Ub but not certain. Help with this would be appreciated.
>> Uh = 400, al = exp(-1j*2*pi/3), u1 = Uh/sqrt(3), u2 = u1*al
Uh = 400, al = -0.5000 - 0.8660i, u1 = 230.94, u2 = -115.47 - 200.00i
>> P3=1500, pF=0.71, Ska=2500, Skb=3000, Skc=P3/pF
P3 = 1500 pF = 0.7100 Ska = 2500 Skb = 3000 Skc = 2112.7
>> Ua=u1-0, i3=conj(Ska/Ua)
Ua = 230.94 i3 = 10.825
>> Ub=u1-u2, i2=conj(Skb/Ub)
Ub = 346.41 + 200.00i i2 = 6.4952 + 3.7500i
>> Uc=u2-0, i5=conj(Skc/Uc)
Uc = -115.47 - 200.00i i5 = -4.5741 - 7.9225i
>> i1=i2+i3
i1 = 17.3205 + 3.7500i
>> i4=i5-i2
i4 = -11.069 - 11.673i
>> in=i3+i5
in = 6.2512 - 7.9225i
>> abs([i1,i4,in])
ans = (17.7218 16.087 10.092)A
The loads have the following characteristics and connections:
- Load A: 2.5 kW, 230 V, power factor = 1, connected between phase 1 and neutral ("L1-N").
- Load B: 3.0 kW, 400 V, power factor = 1, connected between phase 1 and phase 2 ("L1-L2").
- Load C: 1.5 kW, 230 V, power factor = 0.71 inductive, connected between phase 2 and neutral ("L2-N").
See added picture for cirucit drawing and currents.
Tried to solve this in octave, I think I mess up I4 and then In. I1 is correct.
I don´t think the KCL is wrong and I don see why Skc =P/pF is incorrect either.
One other error margin could be how I determine Ub but not certain. Help with this would be appreciated.
>> Uh = 400, al = exp(-1j*2*pi/3), u1 = Uh/sqrt(3), u2 = u1*al
Uh = 400, al = -0.5000 - 0.8660i, u1 = 230.94, u2 = -115.47 - 200.00i
>> P3=1500, pF=0.71, Ska=2500, Skb=3000, Skc=P3/pF
P3 = 1500 pF = 0.7100 Ska = 2500 Skb = 3000 Skc = 2112.7
>> Ua=u1-0, i3=conj(Ska/Ua)
Ua = 230.94 i3 = 10.825
>> Ub=u1-u2, i2=conj(Skb/Ub)
Ub = 346.41 + 200.00i i2 = 6.4952 + 3.7500i
>> Uc=u2-0, i5=conj(Skc/Uc)
Uc = -115.47 - 200.00i i5 = -4.5741 - 7.9225i
>> i1=i2+i3
i1 = 17.3205 + 3.7500i
>> i4=i5-i2
i4 = -11.069 - 11.673i
>> in=i3+i5
in = 6.2512 - 7.9225i
>> abs([i1,i4,in])
ans = (17.7218 16.087 10.092)A
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