Power systems are needed for the obvious reasons. They provide energy needed operate anything and everything. Any device, ship, or armor that does something requires a power source.
In ships, and most armors, power sources are almost always built with the ability to be ejected so that a loss of containment does not cause unnecessary destruction.
Combat damage suffered to the power source will usually not result in an explosion. Power sources are designed to shut down safely if their controlling units are damaged. Only catastrophic damage that occurs instantly to both the control units and to the reaction chambers will allow the chance of an explosion.
Most modern science fiction seem to assume that electricity is the only method to power things. Doctor Who and and a few other examples do seem to use something other than Electricity but it is never stated. 20,000 Leagues Under the Sea by Verne used the then experimental Electricity to power the Nautilus, but it does raise the question: What else is there that could replace Electricity as the method to transfer power from station to station? Microwaves are a possibility, maybe some as yet unconcieved way to transfer power via wires, that may be even safer than electricity, is possible.
Batteries store power for future use. They can not recharge themselves, but must be recharged by one of the other power supplies.
On ships batteries are a secondary power supply only which are able to sustain a ship's emergency functions (lights, life support, and maneuvering thrusters) at times when the ship's main power supply is off-line or when all power is being directed to perform a special task such as reinforcing shields or boosting the power of a weapon. The batteries, when not in use, receive a steady charge from the main power source. While powering all ship functions they tend to last only a few hours, if only used to power limited functions they can last several years.
Armors are able to utilize batteries as their main power supply, as long as they are recharged regularly. Batteries are also used to augment or supplement a second onboard power source, such as Solar Power or External Power sources.
Other devices commonly use batteries, either as disposable cartridges or as a rechargeable power supply.
Chemical reactors generate power from reactors that occur between two normally stable chemicals that react with each other to produce energy. These reactors require a mixing chamber to generate the actual reaction, and two separate fuel tanks for each of the two chemicals used by the reactor. The two things that users of a chemical reactor need to keep in mind are to be sure they can refuel both kinds of chemicals when they get low, and they need to be sure they do not mix up which chemical goes into which tank. The resulting reaction would be bad.
Ships, armors and other devices can all use chemical reactors to mixed success, all depending on the amount available for their twin fuel tanks.
Contained anomaly power sources are used almost exclusively by space ship sized constructs or larger.
Zero gravity chambers and inertial dampers make it possible to contain and harness seemingly large and impossible natural phenomena which can be tapped for power. The Natural Power source could be anything from entire planets, stars, or Black Holes. Black Holes are preferred for ships due to their small size. The life span and power output of such devices is nearly limitless. Due to the nature of the power sources being contained, if containment is lost the the vessel which had been containing it will suddenly be contained by it, as it is crushed or burned. Surprisingly planets produce relatively little amounts of energy, and need to be replaced often when they are used as a source of power.
External power is, obviously, power provided from outside the thing using it. The power could be relayed via cable, or via some sort of energy beam such as a microwave beam.
The drawbacks to this power source are its range and line of sight. A fighter craft relying on a microwave beam for power cannot fly behind a ship or it will loose power, nor can it fly too far away because the energy in the beam dissipates with distance. If the fighter craft were being powered by a cable, then its range would be limited, literally by the leash it was on. Also if the power source is damaged then all devices using it are suddenly helpless without power.
Ships, armor, and other devices all utilize external power sources the same way.
Fission reactors work by splitting atoms and utilizing the energy released by the reaction. The fission reactors also have a tendency to generate large amounts of Heat which must be regulated. Fusion reactors fuse atoms together to create energy but most do not need the same kind of cooling concerns as the Fission Reactor. Both types of reactors utilize radio active gasses... usually in their cooling or post use matter conduction tubes. If the gas is released it will radiate the any equipment or personnel that is exposed. Exposure to the gas almost always is fatal, although death is usually not immediate.
Although it requires more fuel for its reactions than fission, fusion is often preferred because it creates less waste. Fission is feared by the public as a whole because of all the bad press it received during the time it was first used, when many accidents occurred because it was not yet understood.
Ships frequently use both fission and fusion reactors... they are safe to shut down, and will usually not explode in combat situations. Waste from fission reactors can easily be dropped into stars or black holes, and additional fuel for Fusion reactors can be gathered out of the vastness of space itself, although it is in greater quantities in nebula's and near planets. Some fusion reactors are built to require special fuel sources which cannot be found naturally, which will require the ship to come back for refueling from time to time. The life time of a fission reactor is in the range of decades without resupply. Fusion reactors will last for as long as they have fuel.
Armors have to be more careful while using Fission and Fusion reactors. Power output is greatly diminished because they must be much smaller. For armors the greatest operational problem becomes regulating the heat of the reaction. If the reactors get too hot it could destabilize the reaction, causing it to shutdown at an inconvenient moment, or they could damage or melt the armor that contains them. There is another large problem with armors that use fission and fusion reactors. If the armor is destroyed or damaged and abandoned, then a containment team must go back and retrieve the reactor... otherwise the reactor could develop leaks and radiate the entire area.
Matter/anti-matter reactors are used almost exclusively by ships only. They work by mixing matter with anti-matter in a controlled reaction. The matter and anti-matter annihilate each other as soon as they are bought into contact with each other, resulting in a tremendous release of energy which is much greater than a Fission or Fusion reaction. A bi-polar crystal is is most commonly used to control the rate that the matter and anti-matter enter the reaction chamber to ensure that the reaction does not get out of control. If the crystal develops a flaw, however, the results could be catastrophic.
The problem with this form of reactor is in the containment of the antimatter. It must be contained in a field so that it does not come into contact with anything except itself. The most common type of containment is a magnetic field, although other forms of force fields or containment could be used. If antimatter containment is lost, or if the matter/anti-matter reaction looses control, the result is explosive... often resulting in the destruction of the ship, as well as whatever matter happens to be near by. Whatever happens to be near by could be your enemy's ship, in which case you could take it with you, but it could also be your home planet, which would sustain considerable damage.
Life itself creates power. Organic substances can be genetically grown with the thought of energy production as its primary purpose. Although it seems natural for this type of power source to be used in things which have been organically constructed, it can also be utilized in any anything, including things mechanical. It is also important to note that organically constructed ships/armor/devices do not necessarily use an organic power source.
Organic energy sources require food to feed from. This could be air, light, or waste from other ship systems. Organic energy sources that feed off of light do not count as solar... they may feed off of solar energy, but they are vastly superior to solar panels both in their output and in that they do not need constant exposure to light to operate at full strength.
It is also possible for the organic power source to obtain its own form of sentience... in which case it will act in unpredictable ways. While it will usually produce energy so as not to raise any questions, it may give some areas more powers than requested. It can also interfere with warp systems, by causing power surges to alter destinations. It is rare for the Organic power source to ever be more ambitious than that.
Organic power sources can be used by ships, armors, and any other device the same way... only the amount used, and how it is stored is changed. Smaller devices can use organic power sources that are contained in small pellets
Magic can provide power in one of two ways. First the object being powered can be magically operated from an outside source... if the being providing the magic is destroyed then the thing being magically powered is rendered inert. The Magical power could come either from a being, or maybe from a magical object.
Second, the thing can be enchanted, providing its own magic from within... But the object is only going to have a limited reserve to draw from before it must rest to replenish it magical reserves (manna). If it over exerts itself, and totally runs out of manna, then it is dead.
With both forms of magical power supply, the thing powered feeds off of the magic, slowly draining the source of its power the same way a Chemical Power supply does, except that a Magical Power source will replenish with rest.
Similar to Magical power sources is Mystical... With mystical power supply the powered objects draw power from one (or more) of the five basic elements... But they do not deplete that element. The more of the element they are around, the more power and strength they have, the less of the element is around the weaker they become, but they do not deplete the element just by drawing power from it.
The elements are: Fire, Water, Air, Land, and Life.
Although not a traditional element, Willpower can also be used as a power source in a similar fasion.
Solar power is power taken from the sun, usually by solar panels, although chemical coverings may also be used. The key to solar power is that the more power you need the larger the panels/treated surfaces must be. Also on cloudy days (or under artificial light sources) the performance of this power source is greatly hindered, and if the panels are completely away from the sun and light then the power output is zero.
Ships can use solar panels can be used to help recharge their batteries but little else. In order to create the amount of energy that a ship requires, the solar panels must be so large as to be unwieldy in combat situations and near atmospheres. Also, if the ship is in deep space, away from a star, then the power output is next to nothing.
Armors can use solar power to greater success, but tend to suffer when not in direct sunlight during combat situations. Also, without frequent in-depth maintenance, an armor's solar power system will slowly become less effective.
Other devices can use solar power to much greater success, especially large stationary or orbiting devices. Smaller devices (handguns, calculators, comm units) may use solar power to recharge the the batteries that act as their primary power source.