Umm... What's the math behind that? Because I think you'll likely find an error in it.
Well since you're challenging me you should really present the math showing I'm wrong but I'll bite.
Base assumption here is that were doing sunny day heating only. That of course gives the direct DC system an advantage but it's also the premise of this thread. I'm also assuming I'm doing it here in my climate using my cost data.
I just put in a 32Kw PV system and 54k btu/hr of hyper heat heat pumps this year. All in materials cost for the heat pumps was $8500. So that's $8500/(54000/3.412)= $0.54 per thermal output watt.
PV modules are at around $0.25 per STC watt so around $0.29 per NOCT watt. My hybrid inverters and ac switchgear came in around $0.50 per watt but I'll be generous and cut that in half assuming straight grid tie inverters. My array structure and DC BOS came in at $0.28/watt so combined cost (PV + inverter+BOS) /inverter efficiency is around $0.82/.95= $0.86 per ac electrical watt. COP runs about 2.5 in my climate so that reduces thePV+inverter+BOS cost to $0.86/2.5= $0.34 per thermal output watt. Adding the heat pump the combined cost is about $0.88 per delivered thermal watt. Plus I still have to use the grid for load matching.
If I used direct DC resistance heating instead I could connect to simple baseboard heaters, which dont care if they get DC or AC, so no inverter or inverter efficiency loss. But I will have impedance mismatch loss between the resistive load and the PV array IV curve. I've run those kind of numbers before and they typically work out to around 30% mismatch loss. The baseboard heaters cost about $0.07 per thermal watt and of course have a COP of 1.0. So no COP based cost reduction for the PV or DC BOS. So combined I get $0.07+ ($.29+$.28)/.7 = $0.88 per DC electrical wall or thermal watt.
Such a coincidence. I promise I wasn't trying to make them come out the same.
I can't use the EG4 hybrid heat pumps in my coldish climate but if I did the heat pump cost per thermal watt number would be better and you wouldn't need the inverter so the numbers would swing the other way. Thats why I said we're getting close to the breakeven point, not quite there yet.
I didn't include any PV or heat pump installation costs. Having recently installed both Id call that a wash. Personally Id rather connect MCs than flare linesets. Also I didn't include the tax credits, which are more favorable for PV than for heat pumps.
And what could be simpler than a pv array connected to a baseboard heater with a mechanical thermostat? Nothing to break or maintain.
Anyhow, let me know if you find a math error, I certainly could have made one.