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.

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.


[*] 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!).

The Impact of Ambient Temperature on the Output Power of Solar Panels

I have noticed the impact of traversing clouds on solar power output: Immediately after a cloud has passed, power surges to a record value. This can be attributed to the focusing effect of the surrounding clouds and/or cooling of the panels. Comparing data for cloudless days in May and June, I noticed a degradation of power – most likely due to higher ambient temperatures in June.

We had a record-breaking summer here; so I wondered if I could prove this effect, using data taken at extremely hot days. There is no sensor on the roof to measure temperature and radiation directly at the panels, but we take data taken every 90 seconds for:

  • Ambient air temperature
  • Global radiation on a vertical plane, at the position of the solar thermal collector used with the heat pump system.

I was looking for the following:

  • Two (nearly) cloudless days, in order to rule out the impact of shadowing at different times of the days.
  • These days should not be separated by too many other days, to rule out the effect of the changing daily path of the sun.
  • Ideally, air temperature should be very different on these days but global radiation should be the the same.

I found such days: August 1 and August 12 2015:

Daily PV ouput energies and ambient temperatures in August 2015

Daily output of the photovoltaics generator (4,77 kW peak), compared to average and maximum air temperatures and to the global radiation on a vertical plane. Dotted vertical lines indicate three days nearly without clouds.

August 12 was  a record-breaking day with a maximum temperature of 39,5°C. August 1 was one of the ‘cool’ but still perfectly sunny days in August. The ‘cold day’ resulted in a much higher PV output, despite similar input in terms of radiation. For cross-checking I have also included August 30: Still fairly hot, but showing a rather high PV output, at a slightly higher input energy.

August 2015 in detail:

Daily PV ouput energies and ambient temperatures in August 2015 - details

Same data as previous plot, zoomed in on August. Dotted lines indicate the days compared in more detail.

Overlaying the detailed curves for temperature and power output over time for the three interesting days:

PV power and ambient temperature over time

Detailed logging of ambient air temperature and output power of the photovoltaic generator on three nearly cloudless days in August 2015.

The three curves are stacked ‘in reverse order’:

The higher the ambient air temperature, the lower the output power.

Note that the effect of temperature can more than compensate for the actually higher radiation for the middle curve (August 30).

I have used global radiation on a vertical plane as an indicator of radiation, not claiming that it is related to the radiation that would be measured on the roof – or on a horizontal plane, as it is usually done – in a simple way. We measure radiation at the position of our ribbed pipe collector that serves as a heat source for the heat pump; it is oriented vertically so that it resembles the orientation of that collector and allows us for using these data as input for our simulations of the performance of the heat pump system.

Our house casts a shadow on the solar collector and this sensor on the afternoon; therefore data show a cut-off in the afternoon:

Global radiation on solar collector, vertical plane, August 2015

Global radiation in W per square meter on a vertical plane, measured at the position of the solar collector. The collector is installed on the ground, fence-like, behind the house, about north-east of it.

Yet, if you compare two cloudless days where the sun traversed about the same path (thus days close in the calendar) you can conclude that solar radiation everywhere – including the position on the roof – was the same if these oddly shaped curves are alike.

This plot shows that the curves for these two days that differed a lot in output and temperature, August 1 and 12, were really similar. Actually, the cooler day with higher PV output, August 1, even showed the lower solar radiation due to some spikes. Since the PV inverter only logs every 5 minutes whereas our system’s monitoring logs every 1,5 minutes those spikes might have been averaged out in the PV power curves. August 30 clearly showed higher radiation which can account for the higher output energy. But – as shown above – the higher solar power could not compensate for the higher ambient temperature.


Logging setup:

Solar Power: Some Data for the First Month.

On May 4, 2015, we started up our photovoltaic generator. Here are some numbers and plots for the first month – and what I plan to do next.

Our generator has a rated power of 4,77 kWp (kilowatt peak), one module has 265 Wp. The generator would deliver 4,77 kW of electrical power under so-called standard testing conditions: An irradiance of 1000 W/m2 of light from the sun, a module temperature of 25%, and a standard spectrum of wavelengths determined by the thickness of the atmosphere light has to traverse (Air mass – AM 1,5, equivalent to sunlight hitting the earth at an angle of about 48° from the zenith).

Our 18 panels are mounted on two different roof areas, 10 of them (2,65 kWp) oriented south-east and 8 modules (2,12 kWp) south-west. The inclination relative to the surface of the earth is 30°, the optimum angle for PV at our latitude:

Plan of our house with PV modules.

Positions of our PV panels on the roof.

We aimed at using our 30° upper roof spaces most efficiently while staying below the ‘legal threshold’ of 5 kW, avoiding a more complicated procedure for obtaining a permit to install them.

The standard conditions are typically met in spring here – not in summer – as the efficiency of solar panels gets worse with increasing temperature: for our panels -0,44% of rated power per °C in temperature difference. If the temperature is 60°C, peak power (for otherwise same irradiance and spectrum) would drop by 15% . We can already see this effect, when comparing two nearly cloudless days in May and in June. The peak power is lower in the first days of June when maximum daily air temperatures were already about 30°C:

PV power over time, for a day in May versus a day in June

Total output power (AC) of the PV generator and input power (DC) for each string as a function of time for two days. 1) May 11 – maximum ambient air temperature 23°C. 2) June 5 – maximum ambient air temperature 30,5°C.

The temperature-dependence of performance might in part explain impressive spikes in power you see after clouds have passed: The modules have a chance to cool off, and immediately after the cloud has gone away the output power is then much higher than in case of constant irradiance. Here is a typical example of very volatile output:

PV power over time, data points taken every few seconds.

Output power of our PV generator when clouds are passing. The spikes (clear sky) show a peak power much higher than the constant value on a cloudless day in May; the troughs correspond to clouds shadowing the panels. The data logger included with the inverters only logs a data point every 5 minutes, so I parsed the inverter’s website instead to grab the current power displayed there every second (Using the inverter’s Modbus TCP interface would be the more professional solution, but parsing HTTP after reverse engineering the HTML structure is usually a quick and dirty ‘universal logging interface’.)

The maximum intermittent power here was about 4,4 kW!

Another explanation for the difference is local ‘focussing’ of radiation by specific configuration of clouds reflecting more radiation into one direction: Consider a cloudless region surrounded by clouds – a hole in the clouds so to speak. Then radiation from above might be reflected at the edges of that hole at a very shallow angle, so that at some place in the sunny spot below the power might be higher than if there were no clouds at all. Here is another article about this phenomenon.

A PV expert told me that awareness of this effect made recommendations for sizing the inverter change: From using one with a maximum power about 20% lower than the generator’s power a few years ago (as you hardly ever reach the rated power level with constant radiation) to one with matches the PV peak output better.

The figures from May 11 and June 5  also show that the total power is distributed more evenly throughout the day as if we would have had a ‘perfect’ roof oriented to the south. In the latter case the total energy output in a year would be higher, but we would not be able to consume as much power directly. But every kWh we can use immediately is worth 3 times a kWh we have to sell to the utility.

The next step is to monitor the power we consume in the house with the same time resolution, in order to shift more loads to the sunny hours or to identify some suckers for energy. We use more than 7000 kWh per year; more than half of that is the heat pump’s input energy. Our remaining usage is below the statistical average in Austria (3700 kWh per 2-person household) as we already did detective work with simpler devices.

Smart meters are to be rolled out in Austria in the next years, by 2020 95% of utilities’ clients should be equipped with them. These devices measure energy consumption in 15-minute intervals; they send the data to the utility daily (which runs a web portal where clients can access their data) but must also have a local interface for real-time logging given to clients on request. As a freshly minted owner of a PV generator I got a new ‘smart’ meter by the utility; but this device is just a temporary solution, not connected to the utility’s central system. It will be replaced by a meter from another vendor in a few years. Actually, in the past years we could read off the old analogue Ferraris meter and submit the number at the utility’s website. This new dumb smart meter, in contrast, requires somebody to visit us and read off the stored data once a year again, using its infrared interface.

I did some research on all possible options we have to measure the power we consume, the winner was another smart meter plus integrated data logger and WLAN and LAN interfaces. It has been installed yesterday ‘behind’ the official meter:

Our power meters in the distribution cabinet

Our power distribution cabinet. The official (Siemens) smart meter is the rather large box to the left; our own smart meter with integrated data logger is is the small black one above it – the one with the wireless LAN antenna.

We will combine its data with the logging of ‘PV energy harvested’ provided by the inverter of the PV panels – an inverter we picked also because of the wealth of options and protocols for accessing it [*]

For the first month we can just have a look at daily energy balances from two perspectives (reading off the display of the dumb smart meter manually every day):

  1. The energy needed by appliances in the house and for hot water heating by the heat pump – 11 kWh per day: On average 56,5% in the first month come from the solar panels (self-sufficiency quota), and the rest was provided by the grid.
  2. The daily energy output of the solar generator was 23 kWh per day on average – either consumed in the house – this is the same cyan bar as in (1) – or fed into the grid. In this month we consumed 27% of the PV power directly (self-consumption quota).
Daily energy balance: 1) The energy we consume in the house - partly from PV, partly from the grid and 2) The energy harvested by the PV generator - party used directly, partly fed into the grid.

Daily energy balance: 1) The energy we consume in the house – partly from PV, partly from the grid (left axis) and 2) The energy harvested by the PV generator – party used directly, partly fed into the grid (right axis).


[*] For German-speaking readers: I wrote a summary about different solutions for metering and logging in this case in this German article called ‘The Art of Metering’ – options are to use the official meter’s IR interface with yet another monitoring ‘server’, your own unrelated meter (as we did), a smart meter integrated with the inverter and using the inverter’s own data logging capabilities), or building and programming your own smart meter from scratch.

“An Unprecedented Test for Europe’s Electricity System”

And we will not be able to contribute – by a hair. We have just ordered our photovoltaic generator, and installation is planned for April.

It is the (partial) Solar Eclipse on March 20 that made Europe’s Transmission System Operators (TSOs) release an announcement:

Under a clear morning sky on 20 March 2015, some 35000 MW of solar energy, which is the equivalent of nearly 80 medium size conventional generation units, will gradually fade from Europe’s electrical system before being gradually re-injected: all in the space of two hours.

Managing this event on the world’s largest interconnected grid is an unprecedented challenge for European TSOs. Solar eclipses have happened before but with the increase of installed photovoltaic energy generation, the risk of an incident could be serious without appropriate countermeasures

This paper shows the grid operators’ model and calculations.  20 GW would already correspond to a shift in frequency of 1 Hz – which is huge (from this German article on control mechanisms in the EU power grid). The TSOs’ benchmark is the speed of the  sunrise / sunset, and the solar eclipse’s shadow is faster.

I mentioned before on this blog that I think the power grid is a remarkable and most underestimated achievement in engineering as well as in the design of associated financial markets. In every single instant supply and demand of power have to be balanced exactly – so turning on and off an appliance immediately has to trigger a change in power provided by generators.

Grid operators today emerged from the split of monolithic power companies that integrated both power generation and distribution. Monopolies run by government, allegedly privileged and maybe as ‘popular’ as the stereotype ancient evil telephone company, emerged into a set of distinct players – operators of power plants and operators of the grid. They are now part of a complex market comprising also consumers, different kinds of traders, and agencies. Regulators needs to make sure that there is both fair competition and safe supply of electrical power to anyone in the long run.

For decades the grid had to deal with centralized, large generators only, and both the physical infrastructure  and the smartness of control systems needs to be continuously adapted to deal with a huge number of small, dispersed generators whose output is volatile. Commentators stated that unbundling of grid operations and power generation  caused players in the market to focus on their individual goals whereas ‘thinking holistic systems’ in not fostered anymore.

So TSOs might be concerned about the rapid increase of the number of generators of renewable energies as they are not the ones profiting most from energy sold anymore (their fees are regulated), but they need to care for safe and reliable distribution nonetheless. The development of the smart grid had been called the largest global IT infrastructure project ever – and this is perhaps not even doing the electrical engineering part justice. In Europe nearly all homes need to be equipped with smart meters until 2020 – which is a challenge given restrictive data protection laws and logistics.

It is  impressive that German TSOs can handle this today in such a reliable fashion:

Electrical power from different sources in Germany.At noon more than one third of power generated – about 20 GW  –  can come from photovoltaic generators, and some of that has to be exported to other countries. But this has to be compared to energy generated, that is power integrated over time: About 6% of all energy generated in a year is from solar generators – 32,8 TWh (Solar power in Germany, data for 2014).

Since a year has 8.760 hours, the average power is thus

32.800 GWh / 8.760 hours = 3,74 GW.

So the average solar power is only a fraction of peak solar power. And this is, unfortunately, why we should not over-hype record powers in solar energy generation. The challenge of the near future is storing, intelligent re-distribution, and management of consumption of electrical energy.

All Kinds of Turbines

Dave asked an interesting question, commenting on the heat-from-the-tunnel project:

Has anyone considered the fact that the water can be used to first drive turbines and then distributed to supply the input source for the heat pumps?

I am a water turbine fan, and every time I spot a small hydro power plant on a hiking map, I have to find it.

Small Pelton turbine

Pelton turbine. The small regional utility has several of them, the flow rate is typically a few 100 liters per second. The NSA should find an image of myself in the reflections.

This does not mean I have developed intuition for the numbers, so I have to do some cross-checks.

You can harvest either kinetic or potential energy from a flowing river in a hydro power plant. Harvesting kinetic energy could be done by something like the ‘under-water version’ of a wind turbine:

Seaflow raised 16 jun 03

Tidal stream generator, rotor raised (Wikimedia user Fundy)

The tunnel produces a flow of 300 liters per second but this information is not yet sufficient for estimating mechanical power.

The kinetic energy of a mass m moving at velocity v is:  \frac{mv^{2}}{2}. From the mean velocity in a flow of water we could calculate the energy carried by flow by replacing m in this expression by mass flow.

If 300 liters per second flow through a pipe with an area of 1 m2, the flow velocity is equal to  0,3 m3/s divided by this area, thus 0,3 m/s. This translates to a kinetic energy of:

\frac{300 ^{.} 0,3^{2}}{2} W = 13,5 W

… only, just enough for a small light bulb.

If the cross-section of the pipe would be ten times smaller, the power would be 100 times larger – 1,35 kW.

(Edit: This is just speculating about typical sizes of the natural pipe determined by rocks or whatever. You cannot create energy out of nothing as increasing velocity by a sort of funnel would decrease pressure. I was rather thinking of a river bed open to ambient air – and ambient pressure – than a closed pipe.)

On the other hand, if that water would be allowed to ‘fall’, we could harvest potential energy:

Mill Wheel

Also this mill wheel is utilizing potential energy from the height difference of a few meters. (Critically inspected by The Chief Engineer, photo by elkement)

This is how commercial hydro power plants work, including those located at rivers in seemingly flat lowlands.

The potential energy of a point mass at height h is mgh, g being the acceleration due to gravity (~ 10m/s2). Assuming a usable height of 10m, 300kg/s would result in about

300 . 10 . 10 W = 30kW – quite a difference!

Of course there are huge error bars here but the modest output of kinetic energy is typical for the topography of planet earth.

Mass flow has to be conserved, and it enters both expressions as a factor. If I am interested in comparing potential and kinetic energies relative to each other, it is sufficient to compare \frac{v^{2}}{2} to gh.

Cross-checking this for a flow of water we know more about:

The Danube flows at about 3-10 m/s, so

\frac{v_{Danube}^{2}}{2} = 4,5 – 50m2/s2

But we cannot extract all that energy: The flow of water would come to a halt at the turbine – where should the water go then? For the same reasons there is a theoretical maximum percentage of wind power that turbines can harvest, even if perfectly frictionless.

In addition, such a turbine would need to be much smaller than the cross-section of the river. Mass flow needs to be conserved: when part of the water slows down, it gets spread over a larger cross-section.

So the realistic \frac{v_{Danube}^{2}}{2} will be smaller.

I have stumbled upon an Austrian startup offering floating turbines, designed for operations in larger rivers and delivering about 70kW at 3,3m/s flow velocity (Images on the German site). This is small compared to the overall kinetic energy of the Danube of about several MW, calculated from 2.000m3/s (mass flow near Vienna) and about 3m/s.

Verbund kraftwerk ybbs-persenbeug 1956

The first hydro power plant at the Danube in Austria, built in 1959 – an icon of post World War II reconstruction (Wikimedia). The plant is currently modernised, the rated power will be increased by 5% to 250MW. Utilized difference in height: 10m.

So the whole kinetic energy – that cannot be extracted anyway – is still small compared to the rated power of typical power plants which are several 100MW!

If the water of the Danube ‘falls’ about 10m then

gh_{Danube} ~ 100

… which is much larger than realistic values of \frac{v_{Danube}^{2}}{2}! Typical usable kinetic energies are lower than typical potential energies.

So if tunnel drain water should drive a turbine, the usable height is crucial. But expected powers are rather low compared to the heat power to be gained (several MW) so this is probably not economically feasible.

I was curious about the largest power plants on earth: Currently the Chinese Three Gorges Dam delivers 22GW. I have heard about plans in Sweden to build a plant that could deliver 50GW – a pumped hydro storage plant utilizing a 50km tunnel between two large lakes, with a difference in altitude of 44m (See the mentions here or here.)

Dreischluchtendamm hauptwall 2006

Three Gorges Dam in China (Wikimedia user Filnko)