Output current is around 1A. Transformer rating is 220V/30V, 25W, but I am using it as a 220V/15V transformer with the middle terminal.
15V is too low, 30V is too high.
176V is 80% of 230V
The LM317 requires the input voltage to be 3V higher than the output for the output voltage to be regulated properly.
The rectifiers will loose 2V.
You'll also want to allow for at least a Volt of headroom for ripple on the filter capacitor.
12+3+2+1 = 18V.
The RMS voltage will be 18/√2 = 12.7V so the output voltage from the transformer must be over 12.7V when the primary is 176V.
The primary is rated to 220V, the secondary must be rated to:
12.7/ .8 = 15.9V
The nearest standard voltage is 18V.
Now when the primary voltage is 176V the secondary voltage will be 14.4V.
I took a glance at the datasheet but i am going to read it carefully. And I thought 10000uF would be enough, isn't it?
10,000µF should be enough.
So lets calculate the maximum allowable ripple:
The peak voltage is 14.4√2 = 20.36V
20.36 - 15 - 2 = 3.36V
Calculate the capacitor size:
[latex] C = \frac{10000 \times I}{V_{ripple}}=\frac{10000}{3.36} = 2972 \mu F[/latex]
The nearest E6 value is 3300µF but 10,000µF is much higher and higher is better.
What's the maximum voltage on the capacitor?
264 is 120% of 220V
The voltage at the secondary will be 18×1.2 = 21.6V
Peak voltage = 21.6V×√2 =30.5V
The transformer's output will increase by 10% when off load:
30.5×1.1 = 33.55V
So make sure the capacitor is rated to at least 35V.
With a 30V transformer the secondary voltage will be too high for the LM317 when it's set to low voltages and with a 15V transformer the voltage will be too low to avoid ripple.
P.S. Simulations were all fine but when I implemented the circuit it didn't go well.
Did you simulate it with a 1A load and vary the primary voltage of the transformer?