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Here is the constraint:

$$\text{Pa} + \text{Pb}=a + b \sqrt{\text{Ir}^2 +\text{Ii}^2} + c (\text{Ir}^2 +\text{Ii}^2)$$

Here $\text{Pa}, \text{Pb}, \text{Ir},$ and $\text{Ii}$ are variables. $a, b, c$ are given parameters.

$\text{Pa} >0$, $\text{Pb}>0$, $-\text{Imax} \leq \text{Ir} \leq \text{Imax}$, and $-\text{Imax} \leq \text{Ii} \leq \text{Imax}$

ə̷̶̸͇̘̜́̍͗̂̄︣͟
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Ghulam Mohy-ud-din
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    Are $Ir$ and $Ii$ real variables? If real, then where is the square root of a complex number? If complex, what do you mean by the bound constraints on $Ir$ and $Ii$? – Brian Borchers Dec 05 '22 at 01:56
  • Thanks for bringing that up, $Ir$ and $Ii$ are real variables with bounds, I have corrected my questions. – Ghulam Mohy-ud-din Dec 05 '22 at 03:07
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    Do the answers esp. the one dealing with squares using McCormick envelope help?https://or.stackexchange.com/questions/1052/linearize-or-approximate-a-square-root-constraint – Sutanu Majumdar Dec 05 '22 at 03:41

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