On the topic of heat pumps, you could also use a TPV for geothermal power. Since there are no moving parts and presumably no huge steam engine installation, it would be more feasible to have one of these in your back yard. The grid powers a heat pump, you compress the fluid till it hits 2000°C, and your TPV extracts power. The heat pump itself is >100% efficient, so overall you can steal a fair bit of electricity from the ground. Right?
The facts have already been stated that refute your what if. Whether you missed it or not, you're arguing for a perpetual motion machine.
The Layman's version of the 3 Laws of Thermodynamics are:
1) You can't win
2) You can't cheat
3) You can't even choose not to playFor instance, take a Brayton thermodynamic cycle. It's motor cycle, but you can literally just reverse the arrows on this cycle, it becomes a reversed Brayton cycle, which corresponds to a heat pump (or a refrigeration machine, depending on which inlet of the machine you're interested in). In practice, the reversing of the arrow means the reversing of the fluid flow, which means compression processes are now expansion processes and vice versa.
Carnot theory does still apply. The COP (Coefficient Of Performance) of a Carnot heat pump is 1/n, where n is the usual Carnot efficiency of a heat engine.
With n=1/3, you get a COP of 1/1/3 = 3 = 300%
Carnot efficiencies consider ideal machines. So ideal Carnot batteries have a n * 1/n = 100% efficiencies. It means you can't increase the efficiency of a heat engine by putting a heat pump in front of it. In an ideal case (ignoring all losses and inefficiencies), you would get the same efficiency. In practice, you can only be worse.
Are you sure you aren't confusing the coefficient of performance with the efficiency? If a heat pump was >100% efficient, I could cool my house by leaving my refrigerator door open.
Steam turbines alone can be operated at higher temperatures by using mercury instead of water. Some plants using this approach were built in the 1920/30s.
The waste heat from the gas turbine would power the steam turbine. Something like a combined cycle gas turbine, but with a closed loop for the gas turbine (say, helium) rather than combustion.
"Evaluated herein is one E-TES concept, called Firebrick Resistance-Heated Energy Storage (FIRES), that stores electricity as sensible high-temperature heat (1000–1700 °C) in ceramic firebrick, and discharges it as a hot airstream to either (1) heat industrial plants in place of fossil fuels, or (2) regenerate electricity in a power plant. … We report that systems of 100–1000 s MWh may be cycled daily, and discharged at a constant heat rate typically for 70–90% of the storage capacity. Traditional insulation can reasonably limit heat leakage to less than 3% per day. Preliminary cost estimates indicate a system cost near $10/kWh, substantially less expensive than batteries."
Think of the steam turbine as a baseline. Like rating a vehicle in horse power.