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.

Same Procedure as Every Autumn: New Data for the Heat Pump System

October – time for updating documentation of the heat pump system again! Consolidated data are available in this PDF document.

In the last season there were no special experiments – like last year’s Ice Storage Challenge or using the wood stove. Winter was rather mild, so we needed only ~16.700kWh for space heating plus hot water heating. In the coldest season so far – 2012/13 – the equivalent energy value was ~19.700kWh. The house is located in Eastern Austria, has been built in the 1920s, and has 185m2 floor space since the last major renovation.

(More cross-cultural info:  I use thousands dots and decimal commas).

The seasonal performance factor was about 4,6 [kWh/kWh] – thus the electrical input energy was about 16.700kWh / 4,6 ~ 3.600kWh.

Note: Hot water heating is included and we use flat radiators requiring a higher water supply temperature than the floor heating loops in the new part of the house.

Heating season 2015/2016: Performance data for the 'ice-storage-/solar-powered' heat pump system

Red: Heating energy ‘produced’ by the heat pump – for space heating and hot water heating. Yellow: Electrical input energy. Green: Performance Factor = Ratio of these energies.

The difference of 16.700kWh – 3.600kWh = 13.100kWh was provided by ambient energy, extracted from our heat source – a combination of underground water/ice tank and an unglazed ribbed pipe solar/air collector.

The solar/air collector has delivered the greater part of the ambient energy, about 10.500kWh:

Heating season 2015/2016: Energy harvested from air by the collector versus heating-energy

Energy needed for heating per day (heat pump output) versus energy from the solar/air collector – the main part of the heat pump’s input energy. Negative collector energies indicate passive cooling periods in summer.

Peak Ice was 7 cubic meters, after one cold spell of weather in January:

Heating season 2015/2016: Temperature of ambient air, water tank (heat source) and volume of water frozen in the tank.

Ice is formed in the water tank when the energy from the collector is not sufficient to power the heat pump alone, when ambient air temperatures are close to 0°C.

Last autumn’s analysis on economics is still valid: Natural gas is three times as cheap as electricity but with a performance factor well above three heating costs with this system are lower than they would be with a gas boiler.

Is there anything that changed gradually during all these years and which does not primarily depend on climate? We reduced energy for hot tap water heating – having tweaked water heating schedule gradually: Water is heated up once per day and as late as possible, to avoid cooling off the hot storage tank during the night.

We have now started the fifth heating season. This marks also the fifth anniversary of the day we switched on the first ‘test’ version 1.0 of the system, one year before version 2.0.

It’s been about seven years since first numerical simulations, four years since I have been asked if I was serious in trading in IT security for heat pumps, and one year since I tweeted:

Heat Pump System Data: Three Seasons 2012 – 2015

We have updated the documentation of monthly and seasonal measurement data – now including also the full season September 2014 to August 2015.

The overall Seasonal Performance Factor was 4,4 – despite the slightly lower numbers in February and March, when was the solar collector was off during the Ice Storage Challenge.

Edit: I have learned from a question that the SPF is also calculated in BTU/Wh. ‘Our’ SPF uses the same units in nominator and denominator, so 4,4 is in Wh/Wh. The conversion factor is about 3,4 (note that I use a decimal comma BTW), so our SPF [kWh/kWh] is equivalent to an SPF [BTU/Wh] ~ 15.

Monthly Performance Factor, Heat Pump System

Monthly heating energy provided by the heat pump – total of both space heating and hot water water, related electrical input energy, and the ratio = monthly performance factor. The SPF is in kWh/kWh.

The SPF determines economics of heating with a heat pump.

It’s time to compare costs again, based on current minimum prices of electricity and natural gas in our region in Austria (published by regulator e-control):

  • We need about 20.000 kWh (*) of heating energy per year.
  • Assuming a nearly perfect gas boiler with an efficiency of 95%, we would need about 21.050 kWh of gas.
  • Cost of natural gas incl. taxes, grid fees: ~ 0,0600 € / kWh
  • Yearly energy costs for heating with gas would be: € 1.260
  • Given an SPF of 4,4 for the heat pump, 20.000 kWh heating energy demands translate to 4.545 kWh of electrical energy.
  • Costs of electricity incl. taxes, grid: ~ 0,167 € / kWh
  • Yearly energy costs for heating with the heat pump: € 760
  • Yearly savings with the heat pump: € 500 or 40% of the costs of gas.

(*) As indicated in the PDF, In the past year only the ground floor was heated by the heat pump. So we needed only 13.300 kWh. In the first floor we got rid of the remainders of the old roof truss. The season 2012/2013 was more typical, requiring about 19.700 kWh.

The last winter was not too extreme – we needed 100 kWh maximum heating energy per day. The collector was capable of harvesting about 50 kWh / day:

Daily energy balances, heat pump system, season 2014-2015

Daily energies: 1) Heating energy delivered by the heat pump. Heating energy = electrical energy + ambient energy from the tank. 2) Energy supplied by the collector to the water tank, turned off during the Ice Storage Challenge. Negative collector energies indicate cooling of the water tank by the collector during summer nights. 200 kWh peak in January: due to the warm winter storm ‘Felix’.

Ice formation in this season was mainly triggered by turning off the solar collector deliberately. As soon as we turn the collector on again in March the ice was melted quickly, and the temperature increased to the set value of 8°C – a value picked deliberately to prepare for cooling in summer:

Temperatures and ice formation, heat pump system, season 2014-2015

Daily averages of the air temperature and the temperature in the water tank plus volume of ice created by extracting heat from the heat source (water tank).


Solar Energy, Batteries, and Autonomy

This is the third post in my series on our photovoltaic generator. It had been a part of previous post with the data for the first month, but I cut and saved it as the other post was so long already.

I am now also able to present data for two months of operations: Below is an updated plot of daily energy balances in the second month. Again, I am combining data from our photovoltaic inverter’s logging and from our meters that track the difference of consumption and fed-in energy.

There are two ways to judge the system’s performance in relation to your ‘autonomy’ and economics:

  • Self-sufficiency quota: Which part of energy consumption in the house is harvested from the solar panels?
  • Self-consumption quota: Which percentage of the PV power created can be  consumed immediately.

Energy from PV = data from our inverter’s data logger. Energy from / fed-into grid: Calculated from data logged by our smart meter(s). Arrows indicate which axis to use. By mid of June, our own smart meter had been installed so we did not have to read off the dumb smart meter’s display manually any more.

June was sunny and hot: We harvested more energy due to the higher number of sunny days, but we did not reach May’s daily high score of 32,88 kWh again: Longer days cannot compensate for the reduction of the efficiency of the panels due to higher ambient air temperatures (as discussed in the previous post).

Comparing May and June I noticed:

  • We need less energy per day on average: 10 kWh instead of 11 kWh. Either we spend more time outside than sitting in front of a computer, need less light, or (most likely) we are too obsessed with playing with our new metering gadgets and optimizing our energy consumption.
  • As a consequence – especially in combination with a higher average PV energy output of 25,5 kWh versus 22,1 kWh – our self-consumption quota slightly decreased: We could use only 25,8% of PV power directly, versus 27,5% in the month before.
  • For the same reason, we are more ‘autonomous’, self-sufficiency quota increased: On average 66% of the energy needed in the house was directly delivered by the solar panels (Before: 55%).

Now the tantalizing questions are:

Which quotas will be reach for a full year? How would those numbers change if you had a battery? Would this justify the investment?

The following is my personal assessment, based on our (Austrian) market of electricity and our way of using electrical energy as home owners.

My assessment is based on the following:

  • I pay three times more for electrical power than I will earn when feeding in to the grid (about € 0,18 versus € 0,06).
  • Thus the goal is to maximize the amount of energy used in house and only sell to the utility if you cannot use your power.
  • A battery can store the surplus of energy harvested during the day, so that you can consume it in the night or when clouds pass.
  • The ‘profit’ from having it battery is thus the difference in costs of power and feed-in tariffs (€ 0,12), multiplied by the energy you are able to ‘shift’ to the darker hours.

To determined estimated profits I need to compare our self-sufficiency or self-consumption quotas with and without a battery. In June 2016 I will have data for the latter – energy generation and consumption for every 15-minute time slot. A battery can then be added in a simulation using this logic:

  • Energy not consumed in the house is used for charging the battery unless it if fully charged already.
  • If the solar power is not sufficient to cover current demands, energy is delivered by the battery – unless it has reached its minimum allowed capacity (80% of nominal capacity for Li-in batteries, 50% for lead-acid ones).
  • The conversion of energy is not perfect and battery losses need to be accounted for.

Before I will be able to do this, I play with ballpark numbers, see e.g. inverter vendor SMA’s planning guide (diagrams and examples p.32), or somebody else’s load profile. This tool by a German developer allows for playing with the size of the battery and PV generator interactively (the legend of the plot is in German, but the monthly balances and input fields are titled in English).

Those tools and diagrams need the following input data:

  • Yearly energy consumption: About 7500 kWh in our case, more than 4000 kWh is for the heat pump.
  • Yearly energy harvest from solar panel: Using one of the free PV simulation tools that take into account weather data (e.g. PVGIS provided by the European union) we should end up with 5300 kWh.
  • Size of the battery and percentage of usable capacity. I play with a hypothetical Li-ion battery with 10 kWh, thus 8 kWh maximum energy.

At the German website you can pick different load profiles, I compare different ones that might be similar to our usage pattern.

The results indicate that …

  • the estimated self-sufficiency quota for a full year would be about 30% for our system; and it would increase from about 30% to 55% on adding a battery.
  • we might be able to shift less than 2000 kWh per year by the battery. Note that calculations based on self-consumption quota also include the battery losses – about 500 kWh per year – so data based on the self-sufficiency quota should be used to see the real usable energy.

Multiplying this with the difference in costs and profits (€ 0,12 per kWh) would result in a profit added by the battery of about € 240 per year. BTW this is less than 50% of the profit gained by using the PV generator without the battery.

I researched prices of Li-ion batteries before we purchased our generator and the cheapest one I found was a 8 kWh battery (nominal capacity) for € 6500. Tesla has recently announced its Li-ion Powerwall home battery with 10 kWh, to be sold to $ 3500 to contractors. Prices for installations and price difference between a ‘classical’ inverter and one that can manage a battery not included (less than € 500 here). If you have the battery installed together with the panels, there should not be much additional installation efforts though, compared to the time needed for working on the roof. But I think a 10 kWh battery will not be cheaper than something like € 4000 unless one more ‘disruption’ hits the industry.

So the estimated profits of € 240 are considerably less than 10% of the costs of the battery. Since the estimated life-time of the battery is 10-20 years it is likely not to pay itself off until it has to be replaced again. (No interest rates and realistic net present value considered.) The solar panels will last for decades and still deliver power – though at a slowly deteriorating efficiency – when the payback period has passed.

Those 2000 kWh might even have been too optimistic: The more energy you can use immediately, the less economic is the battery – as there is less energy left to be shifted at all:

  • We use the office during the day: I had always noticed that electricity bills from the past clearly show if we were commuting to a workplace far away or using our own office.
  • We use a heat pump, and we schedule the hot water cycle to match the sunny hours.

I think that you should try to use energy more efficiently first – before adding a battery to shift unnecessary loads. The decision for a battery should be based on an optimized load profile.

For example, Tesla presents some data for a typical energy consumption of devices on their Powerwall website – see bottom of this page. A refrigerator should use 4,8 kWh a day? If I’d have such a refrigerator I would rather replace this than investing into a battery. A modern fridge should not use more more than a kWh per day.

Using a heat pump in middle Europe I might have an unusual view of autonomy. But I believe heating energy in northern latitudes is often neglected in discussions about becoming more self-sufficient by using solar and wind power. If you don’t want to depend on a utility, why would you want to depend on the vendors of fossil fuel or wood – and related financial markets and volatile prices? Here, we have a very reliable power infrastructure, access to 100% green power harvested locally (wind or hydro). But oil and gas have to be imported, and the energy for heating in winter is several times the electrical energy consumed by appliances.

A heat pump the best way to utilize solar and wind power for heating, but you have to face solar energy’s obvious disadvantage: You cannot store summer’s surplus of PV energy for winter (not until a commercially feasible combined fuel cell plus electrolyzer will be available). PV energy from generators that fit onto typical roofs are too small to cover heating energies in winter. Our expected PV output in the coldest months will be less than 10 kWh per day, whereas the heat pump might need up to 35 kWh (one quarter of heating energy). And lest we not forget power versus energy: The heat pump always operates at full power, with its rated power being determined by a worst case minimum ambient temperature. You will need to input something like 2-3 kW for a rather short period. The more average power you need, the more often the heat pump is turned on. So you also need 2-3 kW of solar power or battery output power – a challenge given irradiance in winter and typical battery inverter’s output powers.

In summer a 10 kWh battery the capacity of Tesla’s will be fully charged quickly: You can expect half a year of autonomy, but have to feed in your surplus to the grid. In winter, the battery will hardly be charged as all power is consumed immediately. So the estimated self-sufficiency quota will be well below the absolute theoretical maximum of yearly PV energy harvest over yearly energy consumption (about 70% in our case).

Perhaps you wonder why I am only pontificating on the economics of batteries. I haven’t mentioned the battery’s function as a backup system yet for these reasons:

  • Expected downtime per utility client here is less than an hour per year.
  • In winter a backup system would certainly be more interesting if you depend on a heat pump – but, as mentioned above, the battery will hardly every be charged. The storage  and latency built in in heat pump systems will cover the typical downtimes easily. You use a storage of heat rather than one of electrical energy.
  • You might need to plan carefully which devices are allowed to run during a blackout, as the output power of inverters is limited, and typically of the same order as an electric stove or a water cooker (2 – 3 kW – as high as the heat pump’s input power!). If I only want to be sure that my computer does not crash or want to have a chance to look up the utility’s website, then I’d rather go for a UPS (Uninterruptable Power Supply). A UPS is a battery you connect your important devices to directly, whereas a battery-powered backup system plus inverter needs to maintain a small AC network, controlling frequency and voltage like The Big Grid.
  • A full-featured backup system compliant with our local safety regulations will need some components not included in vendors’ turn-key system. At least a few months ago it was hard to obtain a definitive and unambiguous statement about what exactly the full backup solution would entail.

Another thing I am still waiting for is the option to use a car battery (easily) also as a home storage battery. AFAIK car batteries as the Tesla’s do not allow for bidirectional charging and consumption. (Edit Dec. 2015: Nissan’s LEAF can do that but this solution had not been available in Europe yet).

But fossil fuel burnt by cars are much tougher to get rid of in Austria than fossil fuel burnt in homes. Statistics show it is seems very hard to reduce the former, whereas the latter is gradually decreasing as people prefer heat pumps or pellet stoves today.

I have reduced my carbon footprint drastically in recent years: by driving much less and turning to ‘remote work’. Now we would be ready to replace one of our two cars by an electrical one, as we can plan better when and how it will be used. But why buy the battery twice – one for the car that seldom uses it and one for the home?

That said, one should always keep in mind seemingly unrelated investments and not apply double standards. For example, a lightning protection system for a house like ours costs about € 4000. So if I pay that for mitigating an event due every 1000 years (estimated by a tool provided by our national weather agencies – probability of a lightning strike) – I sort of nearly feel obliged or entitled to buy a battery.

I am also aware of the fragility, if not absurdity, of financial forecasts in times like this – I don’t even need to factor in the collapse of the eurozone or something. I have just heard rumours about drastic changes to be made to utilities’ pricing models. Utilities here start to lose money when serving PV system owners: In those € 0,18 per kWh fees for transmission via the grid are included. But if you deliver energy to the grid you are not charged for kWh transmitted. Transmission system operators have to swallow your energy and are burdened with managing the volatility of renewable energy. Currently running costs of electricity are high whereas the fixed costs like metering (which I factored in in that € 0,18) are negligible. An envisaged model might comprise a rather high base fee instead – no matter if you are a consumer and/or run a power plant – plus low running costs of about € 0,10 / kWh. If those rumours come true, it would become more interesting to go off-grid completely which is not an option given the constraints I outlined above (summer/winter, heat pump, high peak power of appliances).

We Have Come a Long Way: Rooftop Solar Power Now!

We had considered it already a few years ago – when we decided to live and work in the middle of a dusty and noisy construction site for a few months:

Day -1

The day before the carpenters’ invasion. Classical Pannonian home, former small farmhouse, built in the 1920s, and renovated in stages.

House at the point of maximum destruction (Attic rebuilding project)

Less than 24 hours later – March 3, 2008: Near the point of maximum destruction. Tons of firewood!

Attic rebuild completed.

In summer 2009 we declared the project done, including all fine-tuning such as turning two trees into more firewood or artwork.

The upper part of the roof is inclined by 30° – which is the optimum angle for photovoltaic panels – whereas the windows in the steeper roof surface works as ‘solarthermal collectors’ in winter.

But we had no photovoltaic modules installed as the scope of our project had already been extended from The roof should be repaired! to Replace the roof truss, replace the gas boiler, add insulation … add a second ‘open space office’ storey to the house!

The price an end-user paid for a turnkey PV system was about 3 times higher than today (German source). Prices of PV systems became lower everywhere but systems are still more expensive in the US.

But today an Austrian home owner only pays about € 2.000 per kWpeak (rated power) for a turn-key system, including photovoltaic modules, supporting construction, inverter, installation, and paperwork with utilities.

A ‘small’ 5 kW PV generator yields about 5.000 kWh per year. The system is more economical if you consume as much energy as possible in your home as you pay much more per kWh (~ € 0.19) than the utility pays you for energy fed into the grid (~ € 0,06 / kWh). A typical Austrian home needs about 3.500 kWh electrical energy per year – heating not included. We use about 7.300 kWh because of the heat pump; we believe that we will be able to use more than 50% of the power generated.

The payback period of the investment will be longer than 10 years, but I’d rather compare yearly profits with other ‘save’ investments: If we use 3.500 kWh of our solar energy, we would save € 665. Adding € 90 for sales of the remaining 1.500 kWh results in + € 755 / year – equivalent to 7,6% of the investment costs. Running costs are typically estimated to be 1-2% of the investment costs; so yearly profits are still more than 5%.

It is considered unlikely that prices of modules will plummet even more, so we decided we finally do it this spring!

We chose these black modules, also for aesthetic reasons:

Black PV modules

Modules BenQ, 265 Wpeak, mono-crystalline. 18 modules = 4,77 kWpeak rated power

Installation started exactly at the day of the grid-threatening solar eclipse. Our unusual – and high! – mansard roof was the first challenge, to be met with an ad-hoc innovation:

PV Installation Range Extender

Patents pending: The ecological, biomass-based, scalable, PV installation range extender!

On the upper roof surface there was not too much space to walk besides the modules. We started crafting theories about those guys being super-human life-forms, equipped with spider-man-style bionic gloves and shoes, genetically engineered for that type of work – like the special agents in the Bourne movies.

Then the sun was about to set, and they were still working …

Before Dusk

Working on the roof oriented south-west. Half an hour before sunset (my excuse for the even worse photo quality than usual).

… and they still kept working until all modules had been installed – long after sunset! They worked with lamps on the roof! Or their eyes had been enhanced with super-sensitive camera implants.

The image also shows that the modules are not visible from the ground. But the Chief Engineer can enjoy watching the modules from his office desk:

PV modules on south-east roof

The roof oriented south-east – as seen from the window. The thermal collector for the heat pump (the ‘fence’) is visible in the background.

So we will use the sun’s energy in two different ways now:

  • Generating electricity with our new panels, to power the heat pump – among other appliances. 25% of heating energy is electrical energy.
  • Harvesting energy from the ambient air via convection with the unglazed solar thermal collector. 75% of heating energy stems from this ‘ambient’ energy from the heat source, the combination of solar collector and water tank.