# 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.

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 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:

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.

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:

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:

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.

# 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.

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:

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:

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.

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:

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).

# 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).

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:

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):

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:

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.

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 …

… 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:

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.

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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

# Half a Year of Solar Power and Smart Metering

Our PV generator and new metering setup is now operational for half a year; this is my next wall of figures. For the first time I am combining data from all our loggers (PV inverter, smart meter for consumption, and heat pump system’s monitoring), and I give a summary on our scrutinizing the building’s electrical power base load.

For comparison: These are data for Eastern Austria (in sunny Burgenland). Our PV generator has 4.77kWp, 10 panels oriented south-east and 8 south-west. Typical yearly energy production in our place, about 48° latitude: ~ 5.300 kWh. In the first 6 months – May to November 2015 – we harvested about 4.000kWh.
Our house (private home and office) meets the statistical average of an Austrian private home, that is about 3.500 kWh/year for appliances (excl. heating, and cooling is negligible here). We heat with a heat pump and need about 7.200kWh electrical energy per year in total.

In the following plots daily and monthly energy balances are presented in three ways:

1. Total consumption of the building as the sum of the PV energy used immediately, and the energy from the utility.
2. The same total consumption as the sum of the heat pump compressor’s input energy and the remaining energy for appliances, computers, control etc.
3. Total energy generated by PV panels as the sum of energy used (same amount as contributing to 1) and the energy sold to the utility.

In summer there is more PV  energy available than needed and – even with a battery – the rest would needed to be fed into the grid. In October, heating season starts and more energy is needed by the heat pump that can be provided by solar energy.

This is maybe demonstrated best by comparing the self-sufficiency quota (ratio of PV energy and energy consumed) and the self-consumption quota (ratio of PV energy consumed and PV production). Number ‘flip’ in October:

In November we had some unusually hot record-breaking days while the weather became more typical at the end of the month:

This is reflected in energy consumption: November 10 was nearly like a summer day, when the heat pump only had to heat hot water, but on the colder day it needed about 20kWh (resulting in 80-100kWh heating energy).

In July, we had the chance to measure what the building without life-forms needs per day – the absolute minimum baseline. On July 10, 11, and 12 we were away and about 4kWh were consumed per day160W on average.

Note that the 4kWh baseline is 2-3 times the energy the heat pump’s compressor needs for hot water heating every day:

We catalogued all devices, googled for data sheets and measured power consumption, flipped a lot of switches, and watched the smart meter tracking the current consumption of each device.

Consumption minus production: Current values when I started to write this post, the sun was about to set. In order to measure the consumption of individual devices they have been switched an of off one after the other, after sunset.

We abandoned some gadgets and re-considered usage. But in this post I want to focus on the base load only – on all devices that contribute to the 160W baseline.

As we know from quantum physics, the observing changes the result of the measurement. It was not a surprise that the devices used for measuring, monitoring and metering plus required IT infrastructure make up the main part of the base load.

Control & IT base load – 79W

• Network infrastructure, telephone, and data loggers – 35W: Internet provider’s DSL modem / router, our router + WLAN access point, switch, ISDN phone network termination, data loggers / ethernet gateways for our control unit, Uninterruptible Power Supply (UPS).
• Control and monitoring unit for the heat pump system, controlling various valves and pumps: 12W.
• The heat pump’s internal control: 10W
• Three different power meters: 22W: 1) Siemens smart meter of the utility, 2) our own smart meter with data logger and WLAN, 3) dumb meter for overall electrical input energy of the heat pump (compressor plus auxiliary energy). The latter needs 8W despite its dumbness.

Other household base load – 39W

• Unobtrusive small gadgets – 12W: Electrical toothbrush, motion detectors, door bell, water softener, that obnoxious clock at the stove which is always wrong and can’t be turned off either, standby energy of microwave oven and of the PV generator’s inverter.
• Refrigerator – 27W: 0,65 kWh per day.

Non-essential IT networking infrastructure – 10W

• WLAN access point and router for the base floor – for connecting the PV inverter and the smart meter and providing WLAN to all rooms.

These are not required 24/7; you don’t lose data by turning them off. Remembering to turn off daily might be a challenge:

Non-24/7 office devices – 21W. Now turned off with a flip switch every evening, and only turned on when needed.

• Scanner/Printer/Fax: 8W. Surprisingly, there was no difference between ‘standby’ and ‘turned off’ using the soft button – it always needs 8W unless you really disconnect it.
• Server in hibernated state 4W. Note that it took a small hack of the operating system already to hibernate the server operating system at all. Years ago the server was on 24/7 and its energy consumption amounted to 500kWh a year.

Stuff retired after this ‘project’ – 16W.

• Radio alarm clock – 5W. Most useless consumption of energy ever. But this post is not meant as bragging about the smartest use of energy ever, but about providing a realistic account backed up by data.
• Test and backup devices – 7W. Backup notebooks, charging all the time, backup router for playground subnet not really required 24/7, timer switch most likely needing more energy than it saved by switching something else.
• Second old Uninterruptable Power Supply – 4W. used for one connected device only, in addition to the main one. It was purchased in the last century when peculiarities of the local power grid had rebooted  computers every day at 4:00 PM.

In total, we were able to reduce the base load by about 40W, 25% of the original value. This does not sound much – it is equivalent to a small light bulb. But on the other hand, it amounts to 350kWh / year, that is 10% of the yearly energy consumption!

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Logging setup:

• Temperature / compressor’s electrical power: Universal control UVR1611 and C.M.I. as data logger, logging interval 90 seconds. Temperature sensor: PT1000. Power meter:  CAN Energy Meter. Log files are exported daily to CSV files using Winsol. Logging interval: 90 seconds.
• PV output power: Datamanager 2.0 included with PV inverter Fronius Symo 4.5-3-M, logging interval 5 minutes.
• Consumed energy: Smart meter EM-210, logging interval 15 minutes.
• CSV log files are imported into Microsoft SQL Server 2014 for analysis and consolidation. Plots are created with Microsoft Excel as front end to SQL Server, from daily and monthly views on joined UVR1611 / Fronius Symo / EM-210 tables.

# 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 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:

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:

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 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.

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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:

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:

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:

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 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 (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.