On Photovoltaic Generators and Scattering Cross Sections

Subtitle: Dimensional Analysis again.

Our photovoltaic generator has about 5 kW rated ‘peak’ power – 18 panels with 265W each.

PV Generator: 10 modules oriented south-east

South-east oriented part of our generator – 10 panels. The remaining 8 are oriented south-west.

Peak output power is obtained under so-called standard testing condition – 1 kWp (kilo Watt peak) is equivalent to:

  • a panel temperature of 25°C (as efficiency depends on temperature)
  • an incident angle of sunlight relative to zenith of about 48°C – equivalent to an air mass of 1,5. This determines the spectrum of the electromagnetic radiation.
  • an irradiance of solar energy of 1kW per square meter.
Simulated direct irradiance spectra for air mass=0 to 10 with SMARTS 2.9.5

Simulated spectra for different air masses (Wikimedia, User Solar Gate). For AM 1 the path of sunlight is shortest and thus absorption is lowest.

The last condition can be rephrased as: We get 1 kW output per kW/minput. 1 kWp is thus defined as:

1 kWp = 1 kW / (1 kW/m2)

Canceling kW, you end up with 1 kWp being equivalent to an area of 1 m2.

Why is this a useful unit?

Solar radiation generates electron-hole pairs in solar cells, operated as photodiodes in reverse bias. Only if the incoming photon has exactly the right energy, solar energy is used efficiently. If the photon is not energetic enough – too ‘red’ – it is lost and converted to heat. If the photon is too blue  – too ‘ultraviolet’ – it generates electrical charges, but the greater part of its energy is wasted as the probability of two photons hitting at the same time is rare. Thus commercial solar panels have an efficiency of less than 20% today. (This does not yet say anything about economics as the total incoming energy is ‘free’.)

The less efficient solar panels are, the more of them you need to obtain a certain target output power. A perfect generator would deliver 1 kW output with a size of 1 m2 at standard test conditions. The kWp rating is equivalent to the area of an ideal generator that would generate the same output power, and it helps with evaluating if your rooftop area is large enough.

Our 4,77 kW generator uses 18 panels, about 1,61 m2 each – so 29 m2 in total. Panels’ efficiency  is then about 4,77 / 29 = 16,4% – a number you can also find in the datasheet.

There is no rated power comparable to that for solar thermal collectors, so I wonder why the unit has been defined in this way. Speculating wildly: Physicists working on solar cells usually have a background in solid state physics, and the design of the kWp rating is equivalent to a familiar concept: Scattering cross section.

An atom can be modeled as a little oscillator, driven by the incident electromagnetic energy. It re-radiates absorbed energy in all directions. Although this can be fully understood only in quantum mechanical terms, simple classical models are successful in explaining some macroscopic parameters, like the index of refraction. The scattering strength of an atom is expressed as:

[ Power scattered ] / [ Incident power of the beam / m2 ]

… the same sort of ratio as discussed above! Power cancels out and the result is an area, imagined as a ‘cross-section’. The atom acts as if it were an opaque disk of a certain area that ‘cuts out’ a respective part of the incident beam and re-radiates it.

The same concept is used for describing interactions between all kinds of particles (not only photons) – the scattering cross section determines the probability that an interaction will occur:

WirkungsquerschnittSkizze

Particles’ scattering strengths are represented by red disks (area = cross section). The probability of a scattering event going to happen is equal to the ratio of the sum of all red disk areas and the total (blue+red) area. (Wikimedia, User FerdiBf)

First Year of Rooftop Solar Power and Heat Pump: Re-Visiting Economics

After I presented details for selected days, I am going to review overall performance in the first year. From June 2015 to May 2016 …

  • … we needed 6.600 kWh of electrical energy in total.
  • The heat pump consumed about 3.600 kWh of that …
  • … in order to ‘pump it up to’ 16.800 kWh of heating energy (incl. hot tap water heating). This was a mild season! .
  • The remaining 3.000kWh were used by household and office appliances, control, and circulation pumps.

(Disclaimer: I am from Austria –> decimal commas and dot thousands separator 🙂

The photovoltaic generator …

  • … harvested about 5.600kWh / year – not too bad for our 4,8kW system with panels oriented partly south-east and partly south-west.
  • 2.000 kWh of that were used directly and the rest was fed into the grid.
  • So 30% of our consumption was provided directly by the PV generator (self-sufficiency quota) and
  • 35% of PV energy produced was utilized immediately (self-consumption quota).

Monthly energy balances show the striking difference between summer and winter: In summer the small energy needed to heat hot water can easily be provided by solar power. But in winter only a fraction of the energy needed can be harvested, even on perfectly sunny days.

Figures below show…

  • … the total energy consumed in the house as the sum of the energy for the heat pump and the rest used by appliances …
  • … and as the sum of energy consumed immediately and the rest provided by the utility.
  • The total energy ‘generated’ by the solar panels, as a sum of the energy consumed directly (same aqua bar as in the sum of consumption) and the rest fed into the grid.

Monthly energy balances for photovoltaic generator: Energy used directly versus fed into grid

Monthly energy balances: Electrical energy used in total and energy used by the heat pump.

In June we needed only 300kWh (10kWh per day). The PV total output was more then 700kWh, and 200kW of that was directly delivered by the PV system – so the PV generator covered 65%. It would be rather easy to become autonomous by using a small, <10kWh battery and ‘shifting’ the missing 3,3kWh per day from sunny to dark hours.

But in January we needed 1100kWh and PV provided less than 200kWh in total. So a battery would not help as there is no energy left to be ‘shifted’.

Daily PV energy balances show that this is true for every single day in January:

Monthly energy balances for photovoltaic generator in January 2016: Energy used directly versus fed into grid.

We harvest typically less than 10 kWh per day, but we need  more than 30kWh. On the coldest days in January, the heat pump needed about 33kWh – thus heating energy was about 130kWh:

Monthly energy balances in January 2016: Electrical energy used in total and energy used by the heat pump.

Our house’s heat consumption is typical for a well-renovated old building. If we would re-build our house from scratch, according to low energy standards, we might need only 50-60% energy at best. Then heat pump’s input energy could be cut in half (violet bar). But even then, daily total energy consumption would exceed PV production.

Economics

I have covered economics of the system without battery here and our system has lived up to the expectations: Profits were € 575, the sum of energy sales at market price  (€ 0,06 / kWh) and by not having to pay € 0,18 for power consumed directly.

In Austria turn-key PV systems (without batteries) cost about € 2.000 / kW rated power – so we earned about 6% of the costs. Not bad – given political discussions about negative interest rates. (All numbers are market prices, no subsidies included.)

But it is also interesting to compare profits to heating costs: In this season electrical energy needed for the heat pump translates to € 650. So our profits from the PV generator nearly amounts to the total heating costs.

Economics of batteries

Last year’s assessment of the economics of a system with battery is still valid: We could increase self-sufficiency from 30% to 55% using a battery and ‘shift’ additional 2.000 kWh to the dark hours. This would result in additional € 240 profits of per year.

If a battery has a life time of 20 years (optimistic estimate!) it must not cost more than € 5.000 to ever pay itself off. This is less than prices I have seen in quotes so far.

Off-grid living and autonomy

Energy autonomy might be valued more than economical profits. Some things to consider:

Planning a true off-grid system is planning for a few days in a row without sunshine. Increasing the size of the battery would not help: The larger the battery the larger the losses, and in winter the battery would never be full. It is hard to store thermal energy for another season, but it is even harder to store electrical energy. Theoretically, the area of panels could be massively oversized (by a factor – not a small investment), but then even more surplus has to be ‘wasted’ in summer.

The system has to provide enough energy per day and required peak load in every moment (see spikes in the previous post), but power needs also to be distributed to the 3 phases of electrical power in the right proportion: In Austria energy meters calculate a sum over 3 phases: A system might seem ‘autonomous’ when connected to the grid, but it would not be able to operate off-grid. Example: The PV generator produces 1kW per phase = 3kW in total, while 2kW are used by a water cooker on phase 1. The meter says you feed in 1kW to the grid, but technically you need 1kW extra from the grid for the water cooker and feed in 1kW on phase 2 and 3 each; so there is a surplus of 1kW in total. Disconnected from the grid, the water cooker would not work as 1kW is missing.

A battery does not provide off-grid capabilities automatically, nor do PV panels provide backup power when the sun is shining but the grid is down: During a power outage the PV system’s inverter has to turn off the whole system – otherwise people working on the power lines outside could be hurt by the power fed into the grid. True backup systems need to disconnect from the power grid safely first. Backup capabilities need to be compliant with local safety regulations and come with additional (potentially clunky / expensive) gadgets.

 

Alien Energy

I am sure it protects us not only from lightning but also from alien attacks and EMP guns …

So I wrote about our lightning protection, installed together with our photovoltaic generator. Now our PV generator is operational for 11 months and we have encountered one alien attack, albeit by beneficial aliens.

The Sunny Baseline

This is the electrical output power of our generator – oriented partly south-east, partly south-west – for some selected nearly perfectly cloudless days last year. Even in darkest winter you could fit the 2kW peak that a water cooker or heat pump needs under the curve at noon. We can heat hot water once a day on a really sunny day but not provide enough energy for room heating (monthly statistics here).

PV power over time: Sunny days 2015

Alien Spikes and an Extended Alien Attack

I was intrigued by very high and narrow spikes of output power immediately after clouds had passed by:

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

There are two possible explanations: 1) Increase in solar cell efficiency as the panels cool off while shadowed or 2) ‘focusing’ (refraction) of radiation by the edges of nearby clouds.

Such 4kW peaks lasting only a few seconds wide are not uncommon, but typically they do not show up in our standard logging, comprising 5-minute averages.

There was one notable exception this February: Power surged to more than 4kW which is significantly higher than the output on other sunny days in February. Actually, it was higher than the output on the best ever sunny day last May 11 and as high as the peaks on summer solstice (Aliens are green, of course):

PV power over time: Alien Energy on Feb 11, 2016

Temperature effect and/or ‘focusing’?

On the alien attack day it was cloudy and warmer in the night than on the sunny reference day, February 6. At about 11:30 the sun was breaking through the clouds, hitting rather cool panels:

PV power over time: February 2016 - Output Power and Ambient Temperature

At that day, the sun was lingering right at the edge of clouds for some time, and global radiation was likely to be higher than expected due to the focusing effect.

Global Radiation over time: February 2016

The jump in global radiation at 11:30 is clearly visible in our measurements of radiation. But in addition panels had been heated up before by the peak in solar radiation and air temperature had risen, too. So the different effects cannot be disentangled easily .

Power drops by 0,44% of the rated power per decrease in °C of panel temperature. Our generator has 4,77kW, so power decreases by 21W/°C panel temperature.

At 11:30 power was by 1,3kW higher than power on the normal reference day – the theoretical equivalent of a panel temperature decrease by 62°C. I think I can safely attribute the initial surge in output power to the unusual peak in global radiation only.

At 12:30 output power is lower by 300W on the normal sunny day compared to the alien day. This can partly be attributed to the lower input radiation, and partly to a higher ambient temperature.

But only if input radiation is changing slowly, panel temperature has a simple, linear relationship with input temperature. The sun might be blocked for a very short period – shorter than our standard logging interval of 90s for radiation – and the surface of panels cools off intermittently. It is an interesting optimization problem: By just the right combination of blocking period and sunny period overall output could be maximized.

Re-visiting data from last hot August to add more dubious numbers

Panels’ performance was lower for higher ambient air temperatures …

PV power over time: August 2015 - Output Power and Ambient Temperature

… while global radiation over time was about the same. Actually the enveloping curve was the same, and there were even negative spikes at noon despite the better PV performance:

Global Radiation over time: August 2015

The difference in peak power was about 750W. The panel temperature difference to account for that would have to be about 36°. This is three times the measured difference in ambient temperature of 39°C – 27°C = 12°C. Is this plausible?

PV planners use a worst-case panel temperature of 75°C – for worst-case hot days like August 12, 2015.

Normal Operating Cell Temperature of panels is about 46°C. Normal conditions are: 20°C of ambient air, 800W/m2 solar radiation, and free-standing panels. One panel has an area of about 1,61m2; our generator with 18 panels has 29m2, so 800W/m2 translates to 23kW. Since the efficiency of solar panels is about 16%, 23kW of input generates about 3,7kW output power – about the average of the peak values of the two days in August. Our panels are attached to the roof and not free-standing – which is expected to result in a temperature increase of 10°C.

So we had been close to normal conditions at noon radiation-wise, and if we had been able to crank ambient temperature down to 20°C in August, panel temperature had been about 46°C + 10°C = 56°C.

I am boldly interpolating now, in order to estimate panel temperature on the ‘colder’ day in August:

Air Temperature Panel Temperature Comment
20°C 56°C Normal operating conditions, plus typical temperature increase for well-vented rooftop panels.
27°C 63°C August 1. Measured ambient temperature, solar cell temperature interpolated.
39°C 75°C August 12. Measured ambient temperature.
Panel temperature is an estimate for the worst case.

Under perfectly stable conditions panel temperature would have differed by 12°C, resulting in a difference of only ~ 250W (12°C * 21W/°C).

Even considering higher panel temperatures at the hotter day or a non-linear relationship between air temperature and panel temperature will not easily give you the 35° of temperature difference required to explain the observed difference of 750W.

I think we see aliens at work again:

At about 10:45 global radiation for the cooler day, August 1, starts to fluctuate – most likely even more wildly than we see with the 90s interval. Before 10:45, the difference in output power for the two days is actually more like 200-300W – so in line with my haphazard estimate for steady-state conditions.

Then at noon the ‘focusing’ effect could have kicked in, and panel surface temperature might haved fluctuated between 27°C air temperature minimum and the estimated 63°C. Both of these effects could result in the required additional increase of a few 100W.

Since ‘focusing’ is actually refraction by particles in the thinned out edges of clouds, I wonder if the effect could also be caused by barely visible variations of the density of mist in the sky as I remember the hot period in August 2015 as sweltry and a bit hazy, rather than partly cloudy.

I think it is likely that both beneficial effects – temperature and ‘focusing’ – will always be observed in unison. On February 11 I had the chance to see the effect of focusing only (or traces of an alien spaceship that just exited a worm-hole) for about half an hour.

Wormhole travel as envisioned by Les Bossinas for NASA________________________________

Further reading:

On temperature dependence of PV output power – from an awesome resource on photovoltaics:

On the ‘focusing’ effect:

  • Can You Get More than 100% Solar Energy?
    Note especially this comment – describing refraction, and pointing out that refraction of light can ‘focus’ light that would otherwise have been scattered back into space. This commentator also proposes different mechanism for short spikes in power and increase of power during extended periods (such as I observed on February 11).
  • Edge-of-Cloud Effect

Source for the 10°C higher temperature of rooftop panels versus free-standing ones: German link, p.3: Ambient air + 20°C versus air + 30°C

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:

Having Survived the Hottest July Ever (Thanks, Natural Cooling!)

July 2015 was the hottest July ever since meteorological data had been recorded in Austria (since 248 years). We had more than 38°C ambient air temperature at some days; so finally a chance to stress-test our heat pump system’s cooling option.

Heating versus cooling mode

In space heating ‘winter’ mode, the heat pump extracts heat from the heat source – a combination of underground water / ice tank and unglazed solar collector – and heats the bulk volume of the buffer storage tank. We have two heating circuits exchanging heat with this tank – one for the classical old radiators in ground floor, and one for the floor heating loops in the first floor – our repurposed attic.

Space heating with solar collector on, heat pump system punktwissen,

Space heating mode: The heat pump (1) heats the buffer tank (7), which in turn heats the heating circuits (only one circuit shown, each has its circuit pump and mixer control). Heat source: Solar collector (4) and water / ice storage (3) connected in a single brine circuit. The heat exchanger in the tank is built from the same ribbed pipes as the solar collector. If the ambient temperature is too low too allow for harvesting of energy the 3-way valve (5) makes the brine flow bypass the collector.

The heat pump either heats the buffer tank for space heating, or the hygienic tank for hot tap water. (This posting has a plot with heating power versus time for both modes).

We heat hot tap water indirectly, using a hygienic storage tank with a large internal heat exchanger. Therefore we don’t need to fight legionella by heating to high temperatures, and we only need to heat the bulk volume of the tank to 50°C – which keeps the Coefficient of Performance high.

Heating hot water, solar collector off, heat pump system punktwissen

Hot tap water heating mode: The flow of water heated by the heat pump is diverted to the hygienic storage tank (6). Otherwise, the heat source is used in the same way as for space heating. In this picture, the collector is ‘turned off’ – corresponding to heating water on e.g. a very cold winter evening.

In summer, the still rather cold underground water tank can be used for cooling. Our floor heating loops become cooling loops and we simply use the cool water or ice in the underground tank for natural (‘passive’) cooling. So the heat pump can keep heating water – this is different from systems that turn an air-air heat pump into an air conditioner by reverting the cycle of the refrigerant.

Heating hot water in parallel to cooling is beneficial as the heat pump extracts heat from the underground tank and cools it further!

Space cooling while heating hot water, heat pump system punktwissen

Cooling mode: Via automated 3-way valve (9) brine is diverted to flow through the heat exchanger in the buffer tank (7). Water in the buffer tank is cooled down so water in the floor ‘heating’ / cooling loops. If the heat pump operates in parallel to heat hot tap water, it cools the brine.

How we optimize cooling power this summer

Water tank temperature. You could tweak the control to keep the large ice cube as long as possible, but there is a the trade-off: The cooler the tank,  the lower the heat pump’s performance factor in heating mode. This year we kept the tank at 8°C after ‘ice season’ as long as possible. To achieve this, the solar collector is bypassed if ambient temperature is ‘too high’. The temperature in the tank rose quickly in April – so our ice is long melted:

Temperatures and performance factors, July 2015

The red arrow indicates the end of the ice period; then the set temperature of the tank was 8°C (‘Ice storage tank’ is rather a common term denoting this type of heat source than indicating that it really contains ice all the time.) Green arrows indicate three spells of hot weather. The tank’s temperature increased gradually, being heating by the surrounding ground and by space cooling. At the beginning of August its temperature is close to 20°C, so cooling energy has nearly be used up completely.

At the beginning of July the minimum inlet temperature in the floor loops was 17°C, determined by the dew point (monitored by our control system that controls the mixer accordingly); at the end of the month maximum daily ambient air temperatures were greater than 35°C, and the cooling water had about 21°C.

Room temperature. Cooling was activated only if the room temperature in the 1st floor was higher than 24°C – this allows for keeping as much cooling energy as possible for the really hot periods. We feel that 25°C in the office is absolutely OK as temperatures outside are more then 10°C higher.

Scheduling hot water heating. After the installation of our PV panels we set the hot water heating time slots to periods with high solar radiation – when you have more than 2 kW output power on cloudless days. So we utilized the solar energy generator in the most economic way and the heat pump supports cooling exactly when cooling is needed.

Using the collector for cooling in the night. If the ambient temperature drops to a value lower than the tank temperature, the solar collector can actually cool the tank!

Ventilation. I have been asked if we have forced ventilation, ductwork, and automated awnings etc. No, we haven’t – we just open all the windows during the night and ‘manually operated’ shades attached to the outside of the windows. We call them the Deflector Shields:

Ventilation: Night

Manually operated ventilation – to be shut off at sunrise. We had already 30°C air temperature at 08:00 AM on some days.

Deflector shields: Day

South-east deflector shields down. We feel there is still enough light in the (single large) room as we only activate the subset of shields facing the sun directly.

These are details for two typical hot days in July:

Temperature and cooling power for two days in July

The blue line exhibits the cooling power measured for the brine ‘cooling’ circuit. If the heat pump is off, cooling power is about 1 kW; during heat pump operations (blue arrows) 4 kW can be obtained. Night-time ventilation is crucial to keep room temperatures at reasonable levels.

The cooling power is lower than so-called standard cooling load as defined in AC standards – the power required to keep the temperature at about 24°C in steady-state conditions, when ambient temperature would be 30°C and no shades are used. For our attic-office this standard cooling power would amount to more than 10 kW which is higher than the standard (worst case) heating load in winter.

Overall electrical energy balance

I have been asked for a comparison of the energy needed in the house, the heat pump in particular, and the energy delivered by the PV panels and fed in to the grid.

PV numbers in July were not much different from June’s – here is the overview on June and July, maximum PV power on cloudless days has decreased further due to the higher temperatures:

Daily energy balance, PV generation and self-consumption-2015-06-and-2015-07In July, our daily consumption slightly decreased to 9-10 kWh per day, the heat pump needs 1-2 kWh of that. The generator provides for 23 kWh per day,

Currently the weather forecast says, we will have more than 35°C each noon and 20-25° minimum in the night until end of this week. We might experience the utter depletion of our cooling energy storage before it will be replenished again on a rainy next weekend.

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).

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[*] 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.

Two Weeks After Lift-Off

After a little delay our photovoltaic generator went online – we had been waiting for the delivery of this sophisticated addition to our office decoration:

Office Decoration

People on G+ had very cool suggestions, such as a rotating alien-fighting device throwing darts. Closest to the truth were: fuse box and fire alarm.

The box containing two knobs (actually the large box does not contain a lot):

Box with switches for PV DC cable

Two switches that are connected to that big red button downstairs, positioned next to the inverter for our PV panels:

big-red-button

We have two strings of modules, oriented perpendicular to each other; so irradiation on these is different. I add an overlay to a screenshot from Google Maps:

Plan of our house with PV modules.

Solar panels subject to different irradiance are connected in different strings – serial connections of modules; otherwise output power would suffer. The inverter has two inputs for two such strings and two MPP trackers that try to find the Maximum Power Point for each generator, by constantly probing each string’s current versus voltage curve.

Each strings is connected to one of the little red knobs, which are part of yet another safety mechanism. The inverter converts DC current from the panels to standard 3-phase AC output voltage (230 V each phase). It has surge protection (another grey boy, but downstairs) and can shut off power at its DC and AC connectors – but then there is still a voltage drop across the DC cable from the roof to the inverter.

DC voltages supplied by our PV generators are about 400V, but generally they can be close to 1000V. This is a risk for firefighters connecting themselves to the circuit via a jet of water. You ‘cannot turn the panels off’ as long as there is sunlight! In order to make sure that the voltage drops to zero as close as possible to the panels, those switches are installed.

That ‘firefighters’ switch is semi-mandatory here. Lightning protection is not mandatory too, but we decided we should finally have one. Since safety standards and costs of such protection have grown exponentially in recent years, we can brag with a Faraday cage with tighter meshes and taller antenna-style tips than all our neighbours.

Alien EMP Protection

I am sure it protects us not only from lightning but also from alien attacks (see image below) and EMP guns – and the wiring goes well with the surface-mounted aluminium tube for the DC and AC cables for the PV generator.

Alien EMP Protection

The big red button is in the tech gadget closet on the left side of the driveway.

Firefighters will pull or push the red button in case of a fire. We decided for the pull option as you are less likely to pull than push something accidentally.

What we did not know before installation: The switch will also be activated automatically in case of a power outage – this means: about every 2 years for a few minutes. but when the big red button has been activated you need to switch power on again upstairs in the roof, too!

Normally, the switch box would be tucked away in an attic, above a dropped ceiling. We have no attic anymore – this is all office space, 3,5 high in the center. We could have squeezed the box into the insulation. But then after every power outage we would have needed to climb up there, remove roof tiles and switch on power again. So we spontaneously decided to have it installed on the ceiling, above the Chief Engineer’s desktop:

Office Decoration

Last Monday The Metering Guy from the utility finally installed a smart meter, capable of metering both consumption and feed-in to the grid. He had to disconnect from the grid to do so. We switched on the inverter in bright daylight – and there was no power! Panic – what happened? I fetched the laptop and the inverter’s manual, ready for troubleshooting – until The Chief Engineer walked by, carrying a ladder, and grinning mischievously:

Have you perhaps triggered the firefighters’ switch when disconnecting from the grid?

I had forgotten about the switch only about 15 minutes after I putting big signs for firemen! But at least we knew it worked!

After one more controlled test of a power outage we were finally online. This is what power generation looks like on a nearly perfect sunny day now (2015-05-11).

PV Power over Time, 2015-05-11

Since May 5 we have consumed 11kWh / day on average; about 55% of this have been provided directly by the solar panels. Daily energy generation was about 23kWh; we used 27% of the power generated.