The Heat Source Paradox

It is not a paradox – it is a straight-forward relation between a heat pump system’s key data:

The lower a heat pump’s performance factor is, the smaller the source can be built.

I would not write this post, hadn’t I found a version of this statement with a positive twist  used in an advert!

In this post I consider a heat pump a blackbox that converts input energy into output heat energy – it ‘multiplies’ energy by a performance factor. A traditional mechanical heat pump uses electrical input energy to drive a mechanical compressor. The uncommon Rotation Heat Pump utilizes the pressure gradient created by centrifugal forces and thus again by electrical power.

But a pressure difference can also be maintained by adsorption/desorption processes or by changing the amount of one fluid dissolved in another; Einstein’s famous refrigerator uses a more complex combination of such dissolution/evaporation processes. Evaporation or desorption can be directly driven by heat: A gas heat pump thus ‘multiplies’ the energy from burning natural gas (and in addition, a heat pump and a gas boiler can be combined in one unit).

The overall performance factor of a gas heat pump – kWh heating energy out over kWh gas in – is about 1,5 – 2. This is lower than 4 – 5 available with mechanical compressors. But the assessment depends on the costs of kWh gas versus kWh electrical energy: If gas is four times cheaper (which nearly is the case in Germany) than burning natural gas in a traditional boiler without any ‘heat pump multiplication’, then the classical boiler can be more economical than using a heat pump with an electrical compressor. If gas is ‘only’ two times as cheap, then a gas heat pump with an overall performance number of ‘only’ 2 will still beat an electrical heat pump with a performance factor of 4.

While the gas heat pump may have its merits under certain market conditions, its performance number is low: For one kWh of gas you only get two kWh of heating energy. This  means you only need to provide one kWh of ‘ambient’ energy from your source – geothermal, water, or air. If the performance factor of an electrical heat pump is 4, you multiply each kWh of input energy by 4. But the heat source has to be able to supply the required 3 kWh. This is the whole ‘paradox’: The better the heat pump’s performance is in terms of heating energy over input energy, the more energy has to be released by a properly designed heat source, like ground loops sufficiently large, a ground-water well providing sufficient flow-rate, an air heat pump’s ventilator powerful enough, or our combination of a big enough solar/air collector plus water tank.

Illustration of the ‘heat source paradox’: The lower the performance number (ratio of output and input energy), the lower is the required ambient energy that has to be provided by ‘the environment’. The output heating energy in red is the target number that has to be met – it is tied to the building’s design heat load.

If you wish to state it that way, a heat pump with inferior performance characteristics has the ‘advantage’ that the source can be smaller – less pipes to be buried in the ground or a smaller water tank. And in an advert for a gas heat pump I found it spelled out exactly in this way, as a pro argument compared to other heat pumps:

The heat source can be built much smaller – investment costs are lower!

It is not wrong, but it is highly misleading. It is like saying that heating electrically with a resistive heating element – and thus a performance number of 1 – is superior because you do not need to invest in building any source of ambient energy at all.

Photovoltaic Generator and Heat Pump: Daily Power Generation and Consumption

You can generate electrical power at home but you cannot manufacture your own natural gas, oil, or wood. (I exempt the minority of people owning forestry). This is often an argument for the combination of heat pump and photovoltaic generator.

Last year I blogged in detail about economics of solar power and batteries and on typical power consumption and usage patterns – and my obsession with tracking down every sucker for electrical energy. Bottom line: Despite related tinkering with control and my own ‘user behaviour’ it is hard to raise self-consumption and self-sufficiency above statistical averages for homes without heat pumps.

In this post I will focus on load profiles and power generation during several selected days to illustrate these points, comparing…

  • electrical power provided by the PV generator (logged at Fronius Symo inverter).
  • input power needed by the heat pump (logged with energy meter connected to our control unit).
  • … power balanced provided by the smart meter: Power is considered positive when fed into the grid is counted  (This meter is installed directly behind the utility’s meter)

A non-modulating, typical brine-water heat pump is always operating at full rated power: We have a 7kW heat pump – 7kW is about the design heat load of the building, as worst case estimate for the coldest day in years. On the coldest day in the last winter the heat pump was on 75% of the time.

Given a typical performance factor of 4 kWh/kWh), the heat pump needs 1/4 of its rated power as input. Thus the PV generator needs to provide about 1-2 kW when the heat pump is on. The rated power of our 18 panels is about 5kW – this is the output under optimum conditions.

Best result near winter solstice

If it is perfectly sunny in winter, the generator can produce enough energy to power the heat pump between 10:00 and 14:00 in the best case.

2015-12-31: Photovoltaics and Power Consumption, Heat Pump's Compressor

But such cloudless days are rare, and in the cold and long nights considerable electrical energy is needed, too.

Too much energy in summer

On a perfect summer day hot water could even be heated twice a day by solar power:

2015-07-01: Photovoltaics and Power Consumption, Heat Pump's Compressor

These peaks look more impressive than they are compared to the base load: The heat pump needs only 1-2kWh per day compared to 10-11kWh total consumption.

Harvesting energy in spring

On a sunny day in spring the PV output is higher than in summer due to lower ambient temperatures. As we still need space heating energy this energy can also be utilized better:

2016-04-29: Photovoltaics and Power Consumption, Heat Pump's Compressor

The heat pump’s input power is similar to the power of a water heater or an electrical stoves. At noon on a perfect day both the heat pump and one appliance could be run on solar power only.

The typical day: Bad timing

On typical days clouds pass and power output changes quickly. This is an example of a day when sunshine and hot water cycle did not overlap much:

2016-03-29: Photovoltaics and Power Consumption, Heat Pump's Compressor

At noon the negative peak (power consumption, blue) was about 3,5kW. Obviously craving coffee or tea was string than the obsession with energy efficiency. Even the smartest control system would not be able to predict such peaks in both solar radiation and in erratic user behavior. Therefore I am also a bit sceptical when it comes to triggering the heat pump’s heating cycle by a signal from the PV generator, based on current and ‘expected’ sunshine and weather data from internet services (unless you track individual clouds).

No, You Cannot ‘Power Your Home’ by One Hour of Cycling Daily

In the past days different versions of an article had popped up in my social media streams again and again – claiming that you could power your home for 24 hours by cycling for one hour.

Regular readers know that I craft my statements carefully in articles about energy, nearly as in the old times when submitting a scientific paper to a journal, with lots of phrases like Tentatively, we assume…

But in this case, I cannot say it more politely or less distinctly:

No, you cannot power your home by one hour of cycling unless the only electrical appliance in your home is the equivalent of one energy-efficient small computer. I am excluding heating and cooling anyway.

Yes, I know the original article targeted people without access to the power grid. But this information seems to have been lost in uncritical reshares with catchy headlines. Having seen lots of people – whose ‘Western’ homes will never be powered by a treadmill – discussing and cheering this idea, I want to contribute some numbers [*].

This is all the not-exactly-rocket-science math you need, so authors not adding conclusive numbers to their claims have no excuses:

Energy in kWh = Power in Watts times hours divided by 1000

Then you need to be capable to read off your yearly kWh from your utility bill, divide by 365, and/or spot the power in Watts indicated on appliances or to be googled easily.

A professional athlete can cycle at several 100 Watts for some minutes (only) and he just beats a toaster (which needs a power of 500-1000W):

So an average person cannot cycle at more than 100-200W for one hour, delivering 0,2kWh during that hour at best.

With that energy you can power a 20W notebook or light bulb for 10 hours, and nothing more.

Anything with rotating parts like water well pumps, washing machines, or appliances for cutting or mixing need much more power than that, usually a few 100W. Cycling for one hour can drive one device like that for less than half an hour.

An electric stove or a water heater needs about 2kW peak power, at half of the maximum such appliances would consume 1kWh in one hour. An energy-efficient small fridge needs 0,5kWh per day, a large one up to 4kWh.

A TV set could need 150W[**], so you might just be able to power it while watching. I don’t say that this is a bad idea – but it is just very different from ‘powering your home’.

I’ll not link those click-bait articles but an excellent website instead (for the US): Here you can estimate your daily consumption, by picking all your appliances from a list, and learn about the power each one needs. At least it should give you some feeling for the numbers, to be compared with the utility bill, and to identify the most important suckers for energy.

http://energy.gov/energysaver/estimating-appliance-and-home-electronic-energy-use

I have scrutinized our base load consumption in this article: In summer (without space heating) our house needs about 10kWh of electrical energy per day, including 1-2 kWh for heating of hot water by the heat pump. The base load – what the house needs when we are away – is about 4kWh per day.

There are numerous articles with energy statistics for different countries, I pick one at random, stating – in line with many others – that a German household needs about 10kWh per day and one in the US about 30kWh. But even for Nigeria the average value per home is about 1,5kWh, several times the output of one hour of cycling.

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[*] I’ve added this paragraph on Feb. 8 for clarification as the point came up in some discussions on my post.

[**] Depends on size, see for example this list for TVs common in Germany. I was rather thinking of a bigger one, in line with the typical values given also by the US Department of Energy (300W for a plasma TV!).