I would imagine this would have minimal effect and runs the risk of short cycling the compressor if you stack them to close by the over shoot in the time frame. The systems just chase a DT, they look like they blast the system because they are chasing that DT, if the heat exchange is high they will drive harder, if its low they will drive lower. 

I also would like to think, if this had real benefits it would have been programmed in to one of the manufacturer software designs by now and they would be bragging about it.

It was just a thought, because I'm looking to get a Grant r290 6.5Kw and the tech data sheet shows 

A7 W35 7.62Kw COP 4.95

A7 W55 7.23Kw COP 3.00

That's a big difference in efficiency if its starting off heating a fully cold cylinder and just blasting it. It could also output more energy (on paper at least) at the lower flow temperature; so the initial stage should be quicker and more efficient.

I’m not a huge fan of AI, but comparing one scenario to another and working out the maths definitely has its uses.

I asked:

“Heating a 200L DHW cylinder from 15°C to 55°C — compare immersion vs single-stage 55°C vs two-stage 35°C and 55°C.”

The energy saving is notable.

Heat Required

For 200L:

Heat energy needed = ~9.3 kWh thermal

1. 3kW Immersion Heater

An immersion is essentially 100% efficient electrically:

Electrical input = 9.3 kWh
Heater power = 3 kW

Time:

9.3 ÷ 3

≈ 3.1 hours

Result

Energy used: 9.3 kWh electricity
Time: ~3 h 6 min

2. Heat Pump — 7.23kW, COP 3.0

A COP of 3 means:

For every 1 kWh electricity, you get 3 kWh of heat.

Electrical energy needed:

9.3 ÷ 3.0

≈ 3.1 kWh electricity

Time:

9.3 ÷ 7.23

≈ 1.29 hours
≈ 1 h 17 min

Result

Energy used: ~3.1 kWh electricity
Time: ~1 h 17 min

3. Two-Stage Heat Pump Strategy

Stage 1: 15°C → 35°C

Temperature rise = 20°C (half the total)

Thermal energy needed:

~4.65 kWh thermal

Using:

7.62 kW output
COP 4.95

Electricity:

4.65 ÷ 4.95

~0.94 kWh

Time:

4.65 ÷ 7.62

~0.61 h
≈ 37 min

Stage 2: 35°C → 55°C

Again ~4.65 kWh thermal

Using:

7.23 kW
COP 3.0

Electricity:

4.65 ÷ 3.0

~1.55 kWh

Time:

4.65 ÷ 7.23

~0.64 h
≈ 39 min

Combined Two-Stage Result

Total electricity

0.94 + 1.55

≈ 2.49 kWh

Total time

37 + 39 min

≈ 1 h 16 min

Overall Comparison (200L Example)

3kW immersion
Electrical use: ~9.3 kWh
Time: ~3 h 6 min

Heat pump COP 3.0
Electrical use: ~3.1 kWh
Time: ~1 h 17 min

Two-stage heat pump
Electrical use: ~2.5 kWh
Time: ~1 h 16 min

Key Takeaways

The heat pump is roughly 3× cheaper to run than immersion.

The staged heat-pump approach saves a further ~20% electricity versus running COP 3.0 throughout.

Time difference between the two HP approaches is minimal because the output powers are similar.

The staged approach gives an effective overall COP of:

9.3 ÷ 2.49 ≈ 3.73

So effectively:

Immersion COP = 1
Single-stage HP COP = 3
Two-stage strategy COP = 3.7+

If useful, I can also:

calculate this for your actual cylinder size
estimate running cost at your tariff
include standing losses
compare legionella cycles
model realistic COP degradation vs tank temperature

@singlespeed, I’d be a little careful relying too heavily on out-of-the-box AI for this sort of thing. General AI is very good at explaining thermodynamic principles and doing broad maths comparisons, but once you get into the messy real-world behaviour of actual heat pump systems (compressor modulation, cylinder stratification, defrosts, controller logic and ramping behaviour) it starts becoming a lot less reliable. 

That said, I do think your thinking is directionally correct.

Heat pump efficiency absolutely drops as cylinder temperature rises because the compressor has to work progressively harder to achieve higher condensing temperatures. So in theory, spending more of the DHW cycle at lower temperatures should improve overall COP.

The interesting bit is that many modern inverter heat pumps already sort of do this internally. They don’t necessarily just whack the flow temperature straight to maximum and sit there for the entire cycle. Better units will modulate output, compressor speed and flow temperatures dynamically as the cylinder warms up.

My own view is that manually staging multiple schedules probably won’t deliver a huge real-world gain on most systems because the heat pump controller is already trying to optimise itself within its own operating envelope. You may also introduce additional stop/start inefficiencies and confuse the control logic slightly.

Where I do think there’s merit is avoiding unnecessarily high DHW temperatures in the first place. That’s where the biggest gains usually are. Heating a cylinder to 45C instead of 50+ daily will materially improve efficiency over a season.

Personally, I’d probably let the machine do its thing rather than trying to outsmart it with multiple back-to-back schedules. 

@editor "The interesting bit is that many modern inverter heat pumps already sort of do this internally. They don’t necessarily just whack the flow temperature straight to maximum and sit there for the entire cycle. Better units will modulate output, compressor speed and flow temperatures dynamically as the cylinder warms up".

Thanks Marz. I haven't seen any data or explanation of the strategy of dufferebt units getting from cold to the required set point. 

It's good to hear that some are actually work that way already.