PV Solar versus Heat Pump - they are not mutually exclusive alternatives. There's no reason you can't do both, if each one is itself justified on a life cycle basis.
The relevant life-cycle cost comparison for the heat pump would be between it and the propane furnace. To model the heat pump's performance reasonably accurately requires you to input the typical hourly outdoor temperature (or at least the average daily temperature) for your location during the heating season, because the heat pump's efficiency (Coefficient of Performance, "COP") and heat output both vary significantly with outdoor temperature. But a quick comparison alternative is the
operating cost comparison method I discuss below.
Heat pumps (I assume we're talking about conventional outside air-sourced heat pumps, not "ground-source" - i.e., "geothermal") are ideal in climates where both wintertime heating and summertime (forced air) air conditioning are needed. And the incremental cost of the heat pump above and beyond the cost of an air conditioning system is quite small.
Today's R134 heat pumps are able to collect some heat from air even below zero, Fahrenheit. Today's typical units provide a COP of about 2.0 at zero degrees outside. In other words, they yield twice as much heat as would the same amount of electricity used to make heat via resistance coils (electric baseboard heat, "heater strips", etc.)
However, the amount of heat a heat pump can deliver
declines pretty much linearly with ambient (outside) temperature. And the building's space heating needs
increase pretty much linearly as the outside temperature drops. For a heat pump/air conditioning system appropriately sized for your summertime a/c load, the point at which the heat pump is just barely able to keep up with the wintertime heat demand depends on several factors - how "tight" the building is, how well insulated, how much air exchange there is with traffic into and exiting the building, interior heat sources (lighting, number of occupants, etc.). But as a ballpark answer, a heat pump appropriately sized for summertime a/c cooling in SE Pennsylvania is probably capable of providing enough heat in wintertime down to somewhere around 25 degrees or so outdoors. Below this outdoor temperature, it is necessary either to keep the heat pump running and meet the deficit with supplemental electrical resistance heater strips, or switch to an alternate fuel source, in your case, propane, in a "dual fuel" setup.
In this way, you minimize your use of expensive propane or electrical resistance heating to only the coldest days, while the incremental initial cost of the (propane-avoiding) heat pump is quite small, assuming you were going to put in summertime forced air a/c in any case.
Why not just put in a larger heat pump to cover the wintertime demand? Because the biggest mistake in sizing air conditioners is to put in too large a unit. Air "conditioning" requires both cooling the inside air and removing its excess humidity. And a heat pump big enough to keep the building warm on the coldest winter nights in SE Pennsylvania would be much too big for satisfactory summertime cooling. ASHRAE has a comfort chart that shows a range of temperatures judged as comfortable. At lower humidity, higher temperature is comfortable (and vice versa). An oversized a/c (or heat pump unit in a/c mode) will cool the air too quickly, and do a poor job of removing excess moisture, leaving your building prone to cool but swamp-like summertime humidity, mold growth, etc. The Image Permanence Institute (www.dpcalc.org) has a calculator which shows mold risk at a range of temperatures and relative humidity. It says there is low risk of mold at RH under 65%, and low risk of metal corrosion for RH under 55% for temperatures under 80 degrees. However, for human comfort, an even lower RH goal, in the 45 to 50% range, is probably optimal. This requires the a/c system not be oversized - if anything, slightly undersized. At this RH level, most people can be comfortable at around 76-78 degrees. This puts less of a load on the a/c system than needing to cool the building to 72 degrees in summertime, to maintain comfort at a higher RH.
Multi-stage or variable speed heat pumps, if constrained to use only part of their capacity in normal summertime conditions and full capacity only in winter, can partly compensate for this problem. It is indeed what I chose for my own system. But that adds a level of complexity to the analysis I don't want to get into here.
Suppose you choose to go "dual fuel" instead of supplementary electrical resistance heater strips for really cold weather? What is
the operating cost "balance point" that tells you when to switch from heat pump to propane? You can easily calculate it from your heat pump specs, cost of electricity, furnace efficiency and cost of propane (or natural gas, if available).
Natural gas prices are usually expressed per therm; electricity prices per KWh, and propane per gallon. To compare, there are two steps for each - The trick is to convert one to the other set of units, and to consider the efficiency factor (for furnace) or COP (for heat pump), to calculate for either source the cost of the heat (measured in the same units, either KWh or Therms) of heat
delivered to the building. You need to remember that KWh is a measure of energy, and can be used to measure either an amount of electrical energy or an amount of heat energy.
Example: My current cost per KWh of electricity (residential rate in central NC) is $0.09 per KWh. My cost for natural gas (January 2022) is $1.465 per therm. My furnace efficiency is 95%, so my cost per therm of heat delivered into the house is $1.542. This can be converted into its equivalent cost per KWh, using the KWh/therm conversion factor, 29.3. Doing the conversion, the cost of natural gas heat delivered into my house ($1.542/therm) equals $0.0526 per KWh of heat. So natural gas is cheaper, right? - NO! Not exactly. Remember, the heat pump requires less electricity to run than the amount of heat it moves. The heat pump's "COP" is the ratio of the amount of heat moved (measured in KWh of heat), to the amount of electricity used (measured in KWh of electricity).
Let's review - My natural gas heat costs me costs $0.0526 per KWh of heat. My heat pump's electricity costs me $0.09. And my heat pump's COP varies according to outdoor temperature. For example, at 20 degrees, its COP is about 2.5. So at 20 degrees my cost of heat into the house, delivered by the heat pump is $0.09 divided by 2.5, or $0.036 per KWH of heat delivered. (At zero degrees outside (COP 2.0), my heat pump costs $0.045 to run, per KWH of heat delivered into the house).
To summarize, even at zero degrees, the heat pump ($0.045/KWh of heat) is a cheaper source of heat than the natural gas furnace ($0.0526/KWh of heat). And since propane is much more expensive than natural gas, the difference is even greater.
The problem is, if the heat pump' is appropriately sized for its summertime load, its output at zero degrees - or even at 20 degrees outside - will be inadequate to maintain reasonable indoor temperature. For example, my nominal "3 Ton" heat pump can deliver 36,000 BTU/hr at 50 degrees outdoor ambient, but only 18,000 BTU/hr at 10 degrees. (And varies pretty linearly between these limits). So, although the heat provided by my heat pump is cheaper per therm of heat delivered than my high-efficiency condensing gas furnace even down to zero, it is intentionally sized such that it can only provide enough heat to maintain my house's temperature down to around 18 degrees outside. Below that, I must
supplement with electric resistance heating when it is so cold outside the heat pump can't keep up, or
switch over to natural gas heat.
Based on the large difference in operating cost, it is obvious to me the minimum life-cycle cost is obtained by using the heat pump as much as possible. The only question is, do you want to
supplement or do you want to
switch on those coldest days and nights?
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Hugh Willis
Old Engrs Never Really Retire
GREENSBORO, NC
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Original Message:
Sent: 01-11-2022 11:00 AM
From: Roya Taheri
Subject: Life Cycle Cost Analysis of PV Solar versus Heat Pump
My client is asking for a comparison of between Life Cycle Cost Analysis of PV Solar versus Heat Pump, for an office building, in SE. Pennsylvania.
Can anyone help me find the answer?