wirenut1980
Senior Member
- Location
- Plainfield, IN
I am trying to model the voltage drop on the utility medium voltage system of a welder, connected phase to phase on a 480 volt system. The 480 Volt system is fed by a 1500 kva transformer, 12470 wye-480/277 V wye. For now I am only interested in the voltage drop looking from the primary terminals of the transformer.
I do not know the exact load details of the welder, but for now let's say the load is 250 + j500 kva.
The per unit source impedance looking from the primary terminals of the 1500 kva transformer is as follows (100 MVA base, V_base = 12.47 kv):
Z+ = 0.3293 + j1.6478 pu = 1.68 @ 78.7 deg
Z0 = 0.849 + j3.0054 pu = .0056 @ 63.5 deg
My model on paper consists of a series circuit with a 1 @ 0 deg, pu voltage source, the positive sequence impedance of one phase, the load calculated at 0.0025 + j0.005 VA (impedance unknown without calculation), and another positive sequence impedance to represent the return path of current to the source.
KVL around the series circuit gives me:
V_source = (Z+)*I + V_Load + (Z+)*I
V_source = (2*I*Z+) + (VA_pu/I^2)*I
V_source = (2)*(I)*(Z+) + (VA_pu)/I
Plugging in numbers:
1 @ 0 deg = (3.36 @ 78.7 deg)*I + (0.00056 @ 63.5 deg)/I
And this is where I am running into problems. Rearranging terms:
(3.36 @ 78.7 deg)*I^2 -(1 @ 0 deg)*I + (0.0056 @ 63.5 deg) = 0
A freakin polynomial with complex numbers, are you kidding me!:grin:
Is this even solveable, or did I go about this the wrong way? I am sure I have oversimplified this from the correct way to do it, but if this is oversimplified, then I don't think I'll be able to wrap my head around the correct way. There must be an easier way! Thanks to anyone who can help.:smile:
I do not know the exact load details of the welder, but for now let's say the load is 250 + j500 kva.
The per unit source impedance looking from the primary terminals of the 1500 kva transformer is as follows (100 MVA base, V_base = 12.47 kv):
Z+ = 0.3293 + j1.6478 pu = 1.68 @ 78.7 deg
Z0 = 0.849 + j3.0054 pu = .0056 @ 63.5 deg
My model on paper consists of a series circuit with a 1 @ 0 deg, pu voltage source, the positive sequence impedance of one phase, the load calculated at 0.0025 + j0.005 VA (impedance unknown without calculation), and another positive sequence impedance to represent the return path of current to the source.
KVL around the series circuit gives me:
V_source = (Z+)*I + V_Load + (Z+)*I
V_source = (2*I*Z+) + (VA_pu/I^2)*I
V_source = (2)*(I)*(Z+) + (VA_pu)/I
Plugging in numbers:
1 @ 0 deg = (3.36 @ 78.7 deg)*I + (0.00056 @ 63.5 deg)/I
And this is where I am running into problems. Rearranging terms:
(3.36 @ 78.7 deg)*I^2 -(1 @ 0 deg)*I + (0.0056 @ 63.5 deg) = 0
A freakin polynomial with complex numbers, are you kidding me!:grin:
Is this even solveable, or did I go about this the wrong way? I am sure I have oversimplified this from the correct way to do it, but if this is oversimplified, then I don't think I'll be able to wrap my head around the correct way. There must be an easier way! Thanks to anyone who can help.:smile:
