# Solving for phase currents given line currents and line voltages in 3 phase unbalanced delta load

I am given the line currents and the line voltages for an unbalanced 3-phase delta connected load but need to solve for the phase currents on the legs of the delta load.

I know that:

$$I_{L1} = I_{a} - I_{b}$$ $$I_{L2} = I_{b} - I_{c}$$ $$I_{L1} = I_{c} - I_{a}$$ $$I_{L1} + I_{L2} + I_{L3} = 0$$

where $$\I_{a}, I_{b},\$$ and $$\I_{c}\$$ are the phase currents, hence:

$$\pmatrix{I_{a}&I_{b}&I_{c}} \pmatrix{1&0&-1\\-1&1&0\\0&-1&1} = \pmatrix{I_{L1}&I_{L2}&I_{L3}}$$

So far, I have used a method where I right-multiplied both sides by the pseudoinverse of $$\pmatrix{1&0&-1\\-1&1&0\\0&-1&1}$$

Under the assumption that

$$ABB^{-1}=A=CB^{-1}$$

Solving for the pseudoinverse of the matrix gives: $$B^{-1} = \frac{1}{3}\pmatrix{1&-1&0\\0&1&-1\\-1&0&1}$$

But something about this seems really sketchy. Most of the examples and lectures I have found deal with solving for line currents given the phase currents or phase impedances, not the other way around.

How do I solve for the phase currents knowing only the line currents and the line to line voltages?

• A diagram with the currents would be nice Jul 2, 2021 at 2:25