So here is how I picture wisdom essence and intelligence working together.

Intelligence= A measure of how difficult a spell the caster is able to use.  For example a level 1 spell might require 5 intel while a level 5 spell might need 20 or something similar.

Wisdom= The amount of magic the caster can use before becoming exhausted and no longer able to focus on casting spells.  (ie mana)

Essence= The total power or force that a caster is able to put into every spell he/she casts.  For example a Fireball's damage, the number of units summoned or their level, the +bonus of an enchantment or the -stat of a curse type spell would depend on the casters essence.  The other uses for essence could still remain such as healing part of the world or imbuing heroes.

How it would work in theory.

Say I have 3 Casters with my army.

Sovereign- Int=10 Essence=15 Wisdom=10

Hero1- Int-7 Ess=4 Wis=15

Hero2- Int=15 Ess=4 Wis=7

Not to insult anyone's intelligence:

So in following that line of reasoning all casters casting the same spell the sovereign would do the most damage.

Hero 1 and 2 would do the same, but hero 2 would run out of mana the fastest. 

Now looking at the spell they can cast, Hero 2 could cast the highest level spells but has such low wisdom that he could maybe only cast one.  The sovereign would be able to cast mid level spells with a lot of power but not as many as hero one.  This makes it a balancing act on where you want to put your stat points just for casting.

Now for a few other ideas on how to use essence and also how to get some=

Essence for powerful magic items- Have some that can just be created using mana but more powerful relic type items should require essence as well as mana and resources.

Essence for More Power-  Give the option to Over Power spells (requires researching) allowing the caster to put his essence into the spell for a large increase in casting power.  Basically it would be like burning yourself out to put more power into your spell but when it comes to that or total defeat it may be worth it.

Essence to all other combat stats- Have essence provide a small boost to all combat stats. 

Essence for Bribes- Maybe in order for a weaker empire to ally with a stronger one an offer of some essence could tip the scales in favor of more so than gold or materials. Also maybe for recruiting some more powerful creatures to your side (dragons).

Essence for Game Changing spells- For example summoning a volcano under a city should require more than just mana.

Extra ways to gain Essence-

Crystals- +1 essence for each crystal under your control for each caster. (But if caster goes below 1 natural essence he is no longer a caster so has no effect)

Essence from the slain- Killing an enemy sovereign or caster should yield some essence to the victor maybe based on the total essence of the caster killed.

Essence at birth- There should be some % chance of every sovereign's child to be born with the ability to cast.  (Sacrifice your children evil one?) Perhaps harvest it from your children if you are that evil.

Locations of great power-  Some Quest locations or map locations that may or may not be heavily guarded but are heavily seeped in magic may be drawn from by the first person to discover and safely reach it.

Magic items- Have some items that can be found that grant essence when worn or perhaps even drank.

Feel free to add your ideas.