In previous decades when Anthemia lacked the source of fuel that they use now, it was largely a steam based society. Which means that you might see some relics of that society in the older parts of the city. Later though, as steam power proved itself to be inefficient, an industrial revolution of sorts came along. A new source was needed. Some genius-- that students learn of in their middle school years --came along and crafted a very simple form of energy.
The energy is something reminiscent to magick in that it flows and is renewable in nearly any format. The name for this particular energy is still largely undecided, but the people call it's application and study, Thaumaturgy. This energy does not only flow easily but it's properties allow it to be easily distributed through a system, unlike magick. So if there was a collection of machinery assigned to do one job, this energy could provide for it, and it only needed to be provided by a human, just a small wick of their energy could equate to several weeks of work by machinery. Which means there are specific humans, paid by the government mainly, who use part of their energy to power and maintain the entirety of the city's energy. Also, it's easy for anyone to replicate as well, so it's commonly used by Scholar's to power their inventions should they need it.
There are other sources of energy availale around the world as well.In Ura, the desert wastes, there are crystals that contained pure, and un-tampered magical essences that can be used as fuel in place of humans. In various areas of the country, people are paid to mine for the gems. Leviathan, Anima, and Anthemia have a part in the development of this energy the crystals harness, but something is keeps them from being able to patent and use it. In Leviathan, the aquatic stronghold, there are hydrothermal vents that can be used to power their city, found within the deepest parts of their land. Though, it isn't as potent as Thaumaturgy energy and is very dangerous for humans to be near considering it's incredible temperature. Anima relies on the same energies as Anthemia.