I have preached the merits of inverter-driven HVAC units for years. I'm more of a fan of the Daikin and Mitsubishi systems, tho.
I've seen the results of investing in the Daikin systems with power bills. First was my mother's house about 2 years ago (since sold).
The second is a current co-worker who finished a 3300 sf home in central GA. I designed two systems for his home, both single port condensing units, one a 4-ton system and the other a 1.5 ton system for upstairs. 5.5 tons on 3300 square feet is unreal in Georgia, they keep their house at 68-69 in the summer during the day (wife is at home) and 64-65 at night he tells me.
The house is spray-foamed, as I recommended.
He said he power bill for the month of June was $132. This is an all-electric home with a heat pump water heater, 4 occupants and they stay more than comfortable. Conversely, my 2500 sf home is poorly insulated, 6 tons of AC, gas water heater, gas cooking but two pool pumps and we keep it at 68-69 at night and setpoint when we are away is 80 (never gets to 76). Our power bill in June, July and August averages $320/mo for the last 6 years.
I need to bite the bullet and take my own medicine and install a 5-ton multi-port condensing unit and new air handlers. I suspect I would reduce our annual energy costs by $2400+ per year. That savings would pay for the new system in 3 years.