A lot of people have trouble figuring out how the power system works and end up building ships that run out of power too quickly or don't work at all. Once it is explained, though, it's not very hard.
First of all, you must understand cycles. All things that make or take energy have the amount listed in units per cycle. Basically, cycles are a way to split up a second of play, like frames in a video. There are twenty cycles per second. Weapons take the listed amount of energy for each cycle that they fire, and generators produce the listed amount each cycle.
Generators CREATE energy for your ship to use. RTGs produce 55 energy per cycle, quad-RTGs produce 220 per cycle, and fusion generators can produce up to 1000 energy per cycle.
For example, if you have two xeon engines on your ship, they require 90 energy (45 each) per cycle. If you put two RTGs on your ship, they produces 110 per cycle, which means that you are making enough energy to use both xeons. If you take damage and lose one of your RTGs, you are only producing 55 energy per cycle... enough to run one engine(45), but not both(90).
Batteries STORE energy for use when you need it. If you are using more energy than your generators are making, your ship takes the rest of the energy it needs from your batteries. Once the batteries are empty whatever it was that was taking energy turns off. When you're using less than you're generating, the extra energy goes back into your batteries.
In order to make e-beams last for a long time, you have to put lots of reactors on your ship. If you put 5 plasma batteries and 1 RTG on your ship, you make 55 energy per cycle and batteries store 25,000. An e-beam takes 550 enegy per cycle, but your RTG produces 55, so the e-beam takes 495 energy from your batteries each cycle. If you do the math (495 energy x 20 cycles), you find out that the e-beam will be taking 9900 energy out of your batteries each second. Basically, your batteries will be empty in about 2.5 seconds. Then it will take another 20 seconds for all your batteries to refill... not good.
If you make a ship with 10 reactors and 1 battery, it makes 550 energy per cycle. That's how much the e-beam needs, so it doesn't have to take any energy out of your batteries and your e-beam will last forever(unless you use your engines).