There are three main methods of generating power. Romulans, ever on the cutting edge, use a pocket black hole , while most comparable powers use antimatter engines to fuel warp powered vessels. Fusion is generally preferred for civilian or low-demand applications, ranging from deep space telescope arrays to colonists' houses to signal flares and androids; fusion reactors are also present as secondary or backup systems on board starships.
Rechargable batteries are also used; fairly compact batteries may provide many gigajoules of energy. Shuttles make use of krellide storage cells.
Ships are sometimes described as having extraordinarily low amounts of energy or power on hand; we must either assume that conservation of energy no longer applies, dismiss this evidence, dismiss many more episodes, or find a method by which the figures apply to some figure other than the actual energy reserves or total power generation of the vessels in question. There are some more compatible power and energy references, both explicit and implicit; these may be carefully used to produce a generally consistent picture of exawatt range power systems. On the other side, occasional feats performed require vastly greater amounts of energy or power. There are complications, but the only reasonable conclusion is that starships like the Enterprise commonly use exawatt range power, once all of these are considered.
Assorted references still place the warp core as relying on antimatter; however, in "The Battle," reference to "emergency storage cells" and "fusion generators" aboard the Stargazer reaffirm the presence of fusion generators and batteries. The Enterprise has many fusion reactors, and typically does not use all of them at once, as detailed in "Final Mission;" there are at least nine, and probably at least twelve such. Fusion reactors seem preferred groundside; they are in use in "Survivors" as well as "Legacy," and mentioned in "Galaxy's Child." They power the subspace telescope (Argus Array) seen in "The Nth Degree." Data has microfusion cells with which he is powered, and in "Liasons," we hear of microfusion flares. Diverting fusion reactors "four through nine" to the shield array doubles its power from standard. Warp power may then further be diverted. Normal shields are therefore powered with the equivalent power to six of these reactors; as shields do not normally consume warp power, the Enterprise has at least a dozen fusion plants on board, assuming a standardized size. Microfusion thrusters on shuttles burn deuterium, per "In Theory."
Aside from normal Hawking radiation, emitted in great quantities by small black holes, fine manipulation of the gravitational constant of a singularity produces controlled energy releases. A centimeter wide black hole with the normal gravitational constant G - roughly the size of that seen onscreen, if only the very brightest central core is the singularity - would have a mass roughly equal to Earth. If already under the influence of a warp field as intense as the one seen in "Deja Q," this could easily represent twice the mass of the moon.
In "The Dauphin," Riker states that a terawatt is "more power than our entire ship can generate" when faced with a terawatt comm signal. It is difficult to reconcile this with a massive starship that is capable of leaving a star system in a hurry, but remains one of very few explicit power rates given.
This is echoed in "The Masterpiece Society," in which Geordi describes the power output as being in the terawatt range. In the same episode, however, the Enterprise shifts a neutron star fragment larger than itself by routing warp power to the tractor beam. The explicitly stated density of 1014 T/m3 combines with a terawatt figure to produce an acceleration that might be generously described as nearly a nanometer per second squared that could be applied to the fragment - another evident contradiction. If a Galaxy class vessel's overall bulk density was half that of water, it would take nearly a month for a terawatt engine operating at perfect efficiency to move from Earth orbit to 2 AUs out from the Sun. This would render nearly every extrasystem transit seen in Star Trek impossible.
As an additional note, in "Disaster," at least "half a million" amps are
arcing across a conduit, filled with air. In order to arc through 2
meters of air, roughly 1.5 million volts of potential are required,
giving an intermittant power flow of three quarters of a terawatt; it
is not plausible that three quarters of the entire power grid of the
ship happens to be leaking through a stray conduit.
In "Peak Performance,"
Wesley's science project is used to provide 2 seconds of warp 1 power
to a Constellation class starship. If the globule of antimatter in
question (roughly a fist sized sphere contained in a larger ball) is
slush antideuterium, roughly half liquid and half solid by volume,
then it has a mass of ~83 grams. Warp 1 therefore requires an average
power of ~7.5 petawatts for a Constellation class starship. Wesley's
science project, if released into the environment, would have a yield
of ~3.6 megatons; a few fragments of dilithium crystal are sufficient
to channel this reaction. The greater size and high warp factors
available to a Galaxy class make the two figures roughly
By conservation of gravitational binding energy, this means that a couple yottajoules need to be supplied to put it in a stable high orbit. This could be done via seven hours at warp nine power fed through the tractor beam (700 exawatts) or the very quick application of a warp field (multiple zettawatts).
If the mass of the Enterprise is between 5 and 25 million tons,
the trip taken under its own power via an advanced modification of
warp drive in "Where None Have
Gone Before" would require a similar consumption of energy on
this reasoning (3-15 zettajoules). An engine that can output 12.75
exawatts is up to this task; it would also be able to escape from a
skimming orbit of a Sunlike star within a matter of minutes, as seen
in "Half a Life" as well
as "Relics." We may
therefore wisely consider GCS output to be at least 12.75 exawatts,
with a peak consumption of roughly 100-1,000 exawatts being quite
reasonable during the application of a warp field.
"New Ground" - an out-of-control soliton wave, intended to efficiently transport a small vessel at what is cited as 98% overall efficiency. When amplified by a factor of twelve and having a predicted final energy of two hundred times its original energy, the wave poses a threat of destroying not only a colony three light years away, but "taking most of the planet with it." That this is considered a more efficient method of travel than normal warp drive suggests that the requirement of largely reducing a planet to rubble with 200 times the energy to transport a small vessel. Depending on the degree and mechanism of destroying the planet (as well as the precise nature of the planet, which could readily be somewhat smaller or larger than Earth), we may suggest that the original wave had an energy of between 50-1,000,000 yottajoules (5x1025-1x1028J). The nature of the system being more efficient than normal warp drive and the Enterprise being every bit as large as other ships intended for such use (if not larger) suggests that the Enterprise can probably generate similar quantities of energy within the span of a three light year trip. If we call this one day's travel, and go with the lower estimate, this gives a somewhat reasonable 580 exawatts. However, at the highest speeds exhibited by the Enterprise, and the higher end of the range of wave energies, this would suggest a power generation into a range not reasonable for a vessel powered by slush antideuterium. The lower figures are therefore preferred.
The only other plausible method of fitting "New Ground" with the most consistent scales of power generation and warp travel is to substantially shrink the planet Lemma 2 down to a small planetoid rather than assuming it to be a nearly Earth-sized planet.
In "Allegiance," Geordi states that operating engine efficiency is 93%. This is improved during the episode to 96%. In a notably similar example in "New Ground," Data notes that the low energy loss of the soliton wave (<2%) makes it 450% more efficient than the warp drive of the Enterprise. This could refer to the efficiency of the warp engines at either a bit over 91%, which would lie closely in line with the above figures, although it could also be interpreted as placing warp drive efficiency at ~21.8%. In "Chains of Command," Jellico demands a 15% increase in warp coil efficiency, suggesting engine efficiency below 85%. The highest efficiency figure mentioned in the series is 99%.
These efficiencies are too high to allow a single order of magnitude's gap between base system output and use... and too low to be the entire story.
Assuming efficiency between 80-99% and a normal generation level of 12.75 exawatts, this means the Enterprise must annihilate 143-177 kg of matter per second normally, and produce 0.13-3.2 exawatts of waste heat normally. This also means the Enterprise must somehow sink or radiate waste heat/energy at a rate comparable to a world-wide nuclear war while the warp core is in operation - dozens to hundreds of megatons every second.
We may suggest that this waste energy is somehow recycled into another form, e.g., trilithium, which is known to be highly volatile and a waste product of the Enterprise's warp drive, as noted in "Starship Mine;" it is also possible that some portion of this represents energy loss through the generation of neutrinos while converting matter into energy or back into matter. The ability of cloaked ships to remain undetected at warp while ships have sensitive neutrino detectors suggests this is not a significant source of energy loss.
The problem of fuel capacity is easier to solve. The Enterprise has, after all, Bussard ramscoops that can be used to suck interstellar hydrogen; if these may be operated at warp speed, the 10-21 kg/m3 of interstellar hydrogen typically present can be taken partial advantage of. By reconverting energy gained from matter/antimatter reactions back into antimatter, the Enterprise can breed its own antimatter stores from collected matter.
A ramscoop with a cross section roughly equal to the Enterprise's front end would need to travel roughly 10 billion times the speed of light. In order to avoid consuming fuel too quickly, the ramscoop would need to be extended tens or hundreds of kilometers outward. As this does not exceed the limits to which the deflectors can be extended, it is quite possible that the Enterprise is largely self-sustaining so long as it can keep cruising peacefully.
These "terawatt" references are a definitive limit on usable starship power, although average expenditure is 900 TW and peaks at tens to hundreds of EW. (Efficiency is ~0.0001% or so.)
12.75 million exawatts is the only explicit warp core generation figure, seems high due to fuel requirements.