It is important that you have enough powerplants to keep your kingdom powered. If you run out of power, your offensive and defensive armies will both be 20% weaker than usual, your residences can hold less civilians, and the population increases far slower than usual. With about 12-15% of your land as powerplants (a bit more for Mountainous), you can usually do fine.

The best way to never go powerless is to always try to have an excess of power. If you only gain a little bit, make a lot of new powerplants the next time you attack and gain new land. The powerplants will not only keep your kingdom powered, but you can also use the power to shield your kingdom against misisles or attacks, or shield the probes (requires 2 power/sent probe) so that you lose far less probes when sending them out and also are more likely to succeed with your probings.

The numbers below are what power different things require, for an ordinary kingdom (Mountainous need 20% more, and Volcanic Inferno only 30% of this). However, it is impossible to calculate exactly how much power you will need, since there is a +-10% random factor to power production as well, according to BCartfall. For military units, you only count military which you already have (not what you have in training), and which is not sent out. Units which are out with a war leader after an attack do not need power until they return:

Dragoons, Laser Dragoons, Troopers, Laser Troopers, Soldiers and Scientists – 0.7 power each
Tanks and Tactical Fighters (also Tactical Fighters which are not supported) – 1.4 power each
Buildings (including in construction) – 1.75 power each
Population – 0.25 power each

Shields
If you want to, you can use shields for your kingdom, but they require a bit of power. But they can be useful, especially if you are Volcanic Inferno, and since you only require a few extra powerplants in order to get enough extra energy, it is a low cost for the extra defense bonus which they give you by decreasing the offensive power of attackers or stopping shields. Military shields decrease the offensive power of someone attacking you with as most 10%. Military shields protect your kingdom against as most 100% of incoming missiles, and probe shields increase the probability that people who probe your kingdom will fail.
Shields, the amount of power needed/hour:
Full Military shields = 2,25X land
Full Missile shields = 1,67X land
Full Probe shields = 5X land

You can see in the shield room how much power is required for the different shields.
If you can afford shields and feel that you are a good target: use them. Especially the military ones (if you only use those on 10% (maximum), 2,25x your land power/hour is needed).

You can also use military shields for your units when attacking, to decrease the unit losses by 25-50%. The cost of that is 5 power for every biological unit (Soldier/Trooper/Dragoon) and 15 power for every mechanical unit (Tank/Fighter/Tactical Fighter) used in the battle.

Missiles
Missiles can be used to make a kingdom lose land and population. You can only make one missile strike every 24 hours, and there is also a NW cap on who you can nuke. Kingdoms which your alliance is at war with have to be between 0.25x and 4x your own Net worth, while kingdoms which you are not at war with can be between 0.5x and 2x your Net worth. Remember that it will annoy a lot of people if you use missiles on someone just for fun. You also don't gain anything at all from nuking people. Missiles also give a little bit of Net Worth.
In order to build fusion missiles, you will need to have finished Fusion Technology research, while Energy Missiles require Energy Core research in order to be built.

Nuclear Missile (25 NW, costs 5000 money) - Damage: 2 land, 150 population, max 0.5% of land, 5% of pop.
Fusion Missile (75 NW, costs 16000 money) - Damage: 4 land, 400 population, max: 1% of land, 2,5% of pop.
Energy Missile (150 NW , costs 15000 money and 10000 power) - Damage: 8 land, 1k population, max: 1% of land, 5% of population.

An important change in round 6 of SKv2 was that you now lose one honor for every unit of land damaged from a missile launched from your kingdom... but that´s only as long as you are not at war with the target kingdom.

You can use the calculator below to calculate how many missiles to send to do maximum possible damage to a target.