I think the way it works here, and in the UK, is all based around the difference between the wholesale and retail prices of energy. Where the generator is also the retailer, like ΔΕΗ, the generator part of the business sells electricity to the retail part of the business at the wholesale price. The retail part then adds on its overheads and profit margin and comes up with a price to the consumer. A new, smaller business can also buy electricity at the same wholesale price from the generator. If it can find ways of operating at lower overheads, perhaps with better technology and/or lower paid staf, and possibly accepting a smaller profit margin it can sell the electricity to the consumer at a lower price. In some cases the newcomer may also be a generator in their own right, perhaps using alternative energy sources, which, possibly in part due to subsidies, they can also provide energy more cheaply.
That's the theory but it is not the whole story. People have ideas. Ideas are wonderful things. They are free to be discussed, challenged, supported disproved, developed or forgotten. Governments everywhere take ideas and turn them into ideologies. Ideologies are hideous beasts. They develop a life of their own, it is virtually impossible to challenge them or change them in any way. Even Hercules would not be able to slay one. Everything has to be manipulated to fit the ideology. When Adam Smith wrote "On the wealth of nations" it was a wonderful idea. It became known as free market capitalism and it was a theory to try to explain what happens when people trade freely with each other. It was not a perfect theory but it was a brilliant first insight into how people behave economically. As an explanation it works quite well where there is a market based on capital and it is free, as you might expect. As an ideology it is used by governments to control the way markets work to fit their own idea of what the theory means. An artificial market, like that for energy, is the result. In physical reality the market for energy is somewhere between a natural monopoly, i.e. a single cable entering your house connected to a single national grid, and an oligopoly, i.e. a very limited number of generators feeding energy into that grid. It is not a free market and you can't make it into one, only pretend.