how to calculate inrush transformer
You can consider a transformer as an inductance (the magnetizing inductance of teh transforemer, equal to the primary inductance), in parallel with a resistor (the reflected load).
Now you are applying an aC voltage to this circuit. You know how to calculate the current and you know it will be sinusoidal, which means it will have an average value of zero.
But what happens if you apply a DC voltage (actually, a step voltage) to this circuit? The current will ramp up exponentially to a value determined mostly by the resistance in series with the circuit. When you remove the DC, which is like applying a negative step, the current will ramp down exponentially to zero, with a time constant given by the resistor in parallel with the inductor.
So, you have a fast exponential when appling the voltage and a slow exponential when removing it.
Well, when you apply an AC voltage, in the beginning it looks much like applying a DC voltage, because only one part of the sinewave is "visible" to the circuit when you apply it. As time goes by, the actual voltage does look like an AC voltage, after at least one cycle, because now the average is truly zero.
So, when you connect an AC voltage you will see much the same phenomenon, which means the current will go up rapidly (although it maintains the sinusoidal shape) and then come down as a sinusoid riding on an exponential.
That makes the first peak larger than the steady-state current peaks.
To minimize the inrush current, you should switch the voltage on at 90°.
Take a look at the pictures.