Before deregulation, Centerpoint, then known as Houston Power & Light, was a generator, transmission/distribution and retail electric provider. It was a public utility. Oncor, formerly Dallas Power & Light was the same.
As public utilities, they were granted a statutory monopoly on their services in their service area. Both CP and Oncor have been publicly traded and privately owned at various points prior to deregulation. That is somewhat anathema to the concept of a public utility.
At deregulation, generation, transmission/distribution, and retail electric providers were separated. Oncor and Centerpoint maintained their monopolies, however. I'm not sure if it's still a statutory monopoly or just a practical one, as they own all the power lines and ain't no one gonna challenge them in that.
So, they are privately owned** public utilities with a de jure or de facto monopoly and they therefore pretty much suck for everyone except their owners.
**NB when I say "privately owned," I mean including publicly traded, which is just a form of private ownership. Which is to be distinguished by owned by a public entity, as in Austin Energy. Private or public, they all have problems, but at least the real public utilities are ultimately answerable to the public.