Update: as a follow-up to this project, I have upgraded my power supply to a new digital design.
digital_bench_power_supply_09 digital_bench_power_supply_08
Read more here. You can still find the previous, analogue design below, which is simpler and easier to build:

Variable regulated power supply

Having a variable regulated power supply that can output precise voltages in the 0 .. 30Volts interval is a great add-on for any electronics lab. Especially when it's a high power supply that can handle as much as 20Amps of current.
high_power_variable_power_supply_2 high_power_variable_power_supply_3 high_power_variable_power_supply_4
For this article, I'm going to show you my variable regulated power supply, built from scratch, the circuit diagram I've used and a few safety tips. It's based on the LM317 that controls a few high power bipolar transistors connected in parallel, to achieve a 0..30V voltage interval and a maximum current of 20Amps.

Step by step guide

First thing we need is a high power transformer. I've ordered a custom toroidal unit, with a primary for 220V mains, and two secondaries one of 24Volts, 10Amps max and another one of 12V, 0.5Amps max. It's very heavy and it was quite expensive. I also needed a rectifier bridge, and got one capable of handling 400V at 35A max:
high power supply-1 high power supply-2

For the project enclosure, I opted for a computer power source metal casing, scrapped from a defective unit: little space but eventually there was enough to fit everything inside and still keep it well organised.
An aluminum heat-sink was added to the case, fixed tightly with several screws so the case itself would also absorb some of the extra heat, for better efficiency. Part of the case was cut so that I could fit a voltmeter and some power transistors directly on the aluminum heatsink:
high power supply-3 high power supply-4 high power supply-5

To regulate the output, I've decided to use the LM317 to control 6 power transistors (TIP3055 NPN) connected in parallel. The design is illustrated below:
LM317 30V variable high power supply-6 20A max

The low power secondary would be used to obtain 12V and 5V with the L7812/L7805, to power the digital voltmeter applied on the high power secondary and also various microcontroller projects that don't require too much current.

I've soldered everything on a test board, using tick copper wire were needed (eg. for the connections to the transistors). A few holes in the front panel and I was able to place the 5k pot for coarse voltage adjustments (and a second 1K pot for fine adjustments, connected in series with the first), the LEDs, the fuse, and the black array of wire connectors for the output (The variable regulated output, the max regulated output, the non rectified alternative current output, the low power 5V and 12V output, etc).
P1020061 P1020069

My transformer gives 10A max at 24V, but the regulator block can handle up to 20A max, because of the 6 transistors. I preferred adding a few extra transistors, to distribute the load and help dissipate heat better. If you need more current or less, simply change the number of transistors to suit your needs.

This supply is extremely reliable. I've used it for more then a year now, the initial design had 4x 2N3055, but they failed quite frequently because of my high voltage experiments that produced spikes transmitted back to the supply circuit. The TIP3055 seems to be almost indestructible, so I highly recommend it.
The neon bulb works as a snubber, to protect the supply against high voltage kick backs. I'm not sure you need that if you're only doing low voltage stuff.

Here are some variants created by my readers

Borys supply:

Abhishek's Supply:

John's Supply:
As a common effort of several people, this circuit diagram comes with several improvements. You can read the comments below for more details. Instead of the 2n3055 I recommend the TIP3055.

John also provided a regulated power supply that has a nice current control feature, but it uses the LM723 instead:

Here is the ready-built supply, using LM723:

Phil's Supply:
Phil provided several helpful advises (see comments section) for others willing to build a power supply. He also experimented with multiple circuits, seeking for the better alternative.

Vanja's Supply:
Vanja create a supply with the LM723 , similar to John's. See it here, including the circuit diagram:
LM723_vanja vanja_1 vanja_2 vanja_3

poparamiro's Supply:
poparamiro built this supply to power a set of fans, to use them in overclocking:
lm317_supply_1 lm317_supply_2 lm317_supply_3 lm317_supply_4

nachtfalke's Supply:
nachtfalke's variant also uses a toroidal transformer and 6xTIP3055 power transistors. Again with applications in overclocking, here is yet another nice, clean build:
lm317_supply_c_01 lm317_supply_c_02 lm317_supply_c_03 lm317_supply_c_04

lm317_supply_c_05 lm317_supply_c_06 lm317_supply_c_07 lm317_supply_c_08

Stefan's Supply:
Stefan did an excellent work with his nice construction. Here are a few pics showing his version:
stefan_variable_regulated_power_supply_01 stefan_variable_regulated_power_supply_02 stefan_variable_regulated_power_supply_03 stefan_variable_regulated_power_supply_04

stefan_variable_regulated_power_supply_05 stefan_variable_regulated_power_supply_06 stefan_variable_regulated_power_supply_07 stefan_variable_regulated_power_supply_08

stefan_variable_regulated_power_supply_09 stefan_variable_regulated_power_supply_10 stefan_variable_regulated_power_supply_11 stefan_variable_regulated_power_supply_12

stefan_variable_regulated_power_supply_13 stefan_variable_regulated_power_supply_14 stefan_variable_regulated_power_supply_15

Digital Supply:
As a follow-up to this project, I have upgraded my power supply to a new digital design. Read more here.
digital_bench_power_supply_09 digital_bench_power_supply_08 digital_bench_power_supply_01

For switched power supplies, see this article.

Related Post