Following recent developments in the pricing of electricity for households with solar panels in the Netherlands, I got interested in the energy balance of our own household. A little over two years ago, we moved into a newly build house that qualifies as a “zero-on-the-meter house”. This qualification implies that — under certain assumptions — the house has a net energy balance of zero or below zero, i.e. the solar panels on the roof generate more energy than is consumed on an annual basis. Of course, this is based on assumptions on the efficiency of the solar array, our lifestyle and corresponding energy consumption patterns, but also on the weather. So far, however, it seems to be working out pretty well for us. In this article, I’d like to explore this energy balance and how recent changes in the pricing can lead to changes in our behavior.
Before we continue, it is important to know that our house is fully dependent on the power grid and is not connected to any other sources of energy such as natural gas. Our house is warmed using a low-temperature floor heating system that is connected to a water-water ground source heat pump. We cook on an induction stove, and our water is heated by an electric boiler. This makes things relatively simple, as we only have to consider our energy needs in terms of electricity.
Recent developments in the pricing of energy
The dutch government currently has a subsidy scheme in place to stimulate home owners to buy solar arrays. This “netting arrangement” (dutch: salderingsregeling) allows homeowners to a) deliver energy back to the power grid at the same rate as energy is bought by the homeowner (minus taxes etc). b) to cancel the energy delivered to the power grid against the energy bought from the energy supplier at the end of the year.
This subsidy scheme promotes energy production, because a net producer can have a near-zero energy bill and actually can make money on the excess energy. This scheme is criticized by the energy suppliers for several reasons. Foremost, power generation and power consumption are not well aligned in time on both the short and the long time scales. During the day, households generally consume most of their energy during the morning and evenings as they are away from home during the rest of the day. The solar arrays, however, produce most of their energy during the day, and none during the morning or night. When we consider the energy balance over the course of a year, the disparity is even greater as solar panels generate the vast bulk of the energy during the spring and summer, and fairly little during the autumn and winter. The energy consumption during winter is a lot greater than during summer, as people spend more time indoors then during the warmer months. Although the use of air conditioning is on the rise in the Netherlands, it is still not commonplace. In general the statement stands. The net overproduction causes very low — and sometimes negative — energy prices. In other words, energy suppliers have to pay their customers to “sell” them a unit of energy. The second argument is one of fairness: the energy suppliers have to pay for the netting and raise prices for each unit of energy for all customers to afford this. They consider this unfair, as customers without solar panels are now indirectly paying for the benefits of customers that own solar panels. The energy suppliers have now introduced all kinds of pricing structures to effectively negate most of cost benefits of the salderingsregeling.
I agree with the first argument and I think the salderingsregeling creates a perverse incentive to maximize production and keep consumption down. The saldersingsregeling has run its course and realized the goal of getting home owners to invest in solar energy. The pricing of energy should now be focused on keeping energy consumption down, while moving the bulk of the energy consumption to the daytime when there is a large amount of solar energy available.
I disagree, however, with the measures that are taken now to achieve this. These measures do reduce the cost (or maximize the profits) for the energy supplier, but do not stimulate a transition of energy consumption to different moments of the day. In previous times we had two tariffs: one for energy consumption during the day, and one for energy consumption during the night. This was aimed at stimulating energy consumption at night by making the night tariff lower. The same mechanism can be utilized now, but with a reversed tariff structure. Make the tariff for daytime consumption lower than that for the night time. This stimulates energy production during the day and benefits both people with and without solar panels.
Forecasting the production
To be able to say anything useful about the energy balance on an annual basis, we need to understand how much we consume and produce throughout the year. To forecast the energy production throughout the year, I need a model that calculates the position of the sun in the sky relative to our location and orientation of the solar panels; a model to then calculate the amount of radiation that hit the solar panels ; and a model to convert the incident power to electric power.
All three calculations can be done using the PV_Lib toolbox by Sandia National Laboratories (Matlab) or the community maintained pvlib for Python, but where would be the fun in that? I find it more satisfying to program this myself and decided to implement these three models:
- A basic ephemeris model that calculates the solar zenith and azimuth angles relative to our position for any given day of the year and time of day [1].
- The Erbs model to decompose the Global Horizontal Irradiance provided by weather models into diffuse and direct irradiation [2].
- A very simple photovoltaics model (AC power to the grid is approximately DC power to from the panels, which in turn is just equal to the total incident irradiation multiplied by an average efficiency value).
The ephemeris model that I implemented does not compensate for the fact that the Earth is an oblate spheroid (it is not actually a sphere, but lets assume that it is for simplicity sake), and ignores that the Earth’s orbit around the sun is actually elliptical. If you are looking for a model that calculates the solar angles very accurately, you can look into the Solar Position Algorithm by Reda and Andreas from the National Renewable Energy Laboratory [6]. The Erbs model that is used to decompose the Global Horizaontal Irradiance (GHI) into the direct and diffuse irradiation components needed for photovoltaics calculations is a simple model that has reasonable accuracy and requires only a single model parameter, which makes it easy to implement. Even with the limitated accuracies of the implemented models, you will see that the model is effective for our purposes and still provides reasonably accurate results (within 15% or so). It is good enough to talk about trends, but not good enough for commercial purposes.
Using the ephemeris model [1], the relative position of the sun with respect to our position can be calculated for any day and time of the year. With that information available, the next step requires data for the Global Horizontal Irradiance (GHI). For this I used two sources: 1) the photovoltaic geographical information system of the European Commission [3] for historical data and data for the Typical Meteorological Year (sort of an average, representative set based on the historical data), and 2) the weather models of the Royal Netherlands Meteorological Institute KNMI [4], which are made available as preprocessed datasets of the KNMI Weer API of Weerlive/Meteoserver [5] for the hourly weather forecast.
The Global Horizontal Irradiance (GHI) is the amount of terrestrial irradiance that is incident on a surface that is tangent and horizontal to the surface of the Earth. This parameter is cheap to measure, but not in itself useful for calculations on solar power generation. GHI is the sum of the Diffuse Horizontal Irradiance (DHI) and Direct Normal Irradiance (DNI). Both DNI and DHI are necessary to calculate how much light hits the solar panels directly and indirectly. The decomposition of GHI into DNI and DHI can be performed using decomposition models, of which the Erbs model is just one of many [2]. I chose it over the other models because it has reasonable accuracy, but is still fairly simple to implement. It only requires the zenith angle of the sun (which follows from the ephemeris model) and the GHI.
Using the GHI, DNI and DHI estimated, and the solar zenith and azimuth angles calculated we can estimate the total amount of power generated by the solar panels. For this we need to take into account the direct normal irradiance is incident on the solar panel under an angle, that the diffuse component is incident from all directions and not all directions contribute in equal proportions, and that some light is incident via reflections in the environment first.
Forecast for a full year of production
Using the Typical Meteorological Year data for our location, I calculated the expected total irradiance per unit of area of solar panel (solar panel tilt angle of 50 degrees) and normalized the data by dividing all values by the maximum. This gives us relative values for each panel azimuth angle. The results are shown in Figure 1 below.
It is interesting to see that the maximum is not achieved with the solar panels turned towards the south (panel azimuth of 180 deg), but about 15 degrees towards the south-south-east. This is due to our time zone of GMT+1, which causes a 15 degree offset between the local time and the solar time. Also interesting is that having the same solar panels facing north still results in about 40% of the maximum achievable power. This can be attributed to the fact that the sun passes overhead and the panels are also tilted towards the sky and diffuse light is also incident on the panels.
When we express the results in total energy produced, we find that the maximum lies at 2944 kWh/year. Our panels are actually oriented at a zenith angle of 196 degree (south-south-west) and should produce 2830 kWh/year. This agrees fairly well with the generation we’ve seen over the past 2+ years that we lived in this house. This is a good sanity check for my models and shows that the model works at least well enough to talk about trends and orders of magnitude.
Seasonal variation
The model used above calculates the production on an hourly basis and then integrates over the full year to get the total energy production for the year. Ofcourse, we can also consider the same data on a more granular level. Because the underlying data uses the Typical Meteorological Year (this just uses representative data sets for each month, e.g. Jan 2009 for January, Feb 2014 for February, Mar 2010 for March, etc), the day-to-day variation is quite large. One degree up in terms of time scale, however, these day-to-day variations more or less cancel out and we can look at the general trends. If we look at the month to month energy production over the year (see Figure 3 below), we can clearly see that the bulk of the solar energy is collected during the summer months (in the Northern hemi-sphere, that is).
This effect is most prominent for north-facing solar arrays. For solar arrays that are turned towards the sun at least part of the day (east/west and especially south-facing arrays) have a similar, but considerably broader peak. Production is low from October through February, when the average temperatures are low and the energy consumption is highest.
Daily energy consumption and production
Retrieving incoming and outgoing power at fuse box level
Measurements of the incoming and outgoing power is necessary to get a better insight in the energy production and consumption over the day. Fortunately, most of the heavy lifting is already done by the manufacturer of the energy meter. Both the incoming and outgoing powers are measured by the smart energy meter that is part of our mains electrical installation. According to the DSMR standard [7], the smart meters used in the Netherlands have a P1 port available that can be used to access this information and is particularly intended for the end-user. For our generation meter that runs on the DSMRv5 standard, a telegram is published to that P1 port every second and that contains information on the actual instantaneous power on all phases, the voltages, the currents, and so forth. This information is very useful for this exercise.
There are plenty of commercial of the shelf solutions that you can connect to the P1 port of the smart meter. These devices read the telegram that is published by the meter, parse it into human readable information and publish it to an app or web environment. These devices can be bought for approximately 20-30 EUR [8]. Because I don’t like the idea of our energy consumption data being published to an off-site server and because I figured that these telegrams are not particularly difficult to parse, I used a Raspberry Pi with some Python code instead. Details on how to do this are available in separate article on this blog (see here).
Getting data from the solar panel inverter
On the production side of things, the inverter of the solar array provides statistics as well. I wrote a separate article here (click) to explain how I got access to those statistics without going through the cloud service of the manufacturer.
Produced, Delivered and Consumed
The smart meter registers the power delivered to the end-user and the power to the energy-supplier separately. When the power delivered to the end-user is positive, the power delivered to the energy-supplier is zero and vice versa. To calculate the actual power consumed at any moment, we simply use: consumed = produced + to_user – to_supplier.
Shifting energy consumption
This begs the question: how much energy can we (my family) shift in our energy consumption? With the simulations and the data acquisition setup, we’ll have to wait for data.
To be continued.
Bibliography
[1] S.G. Bowden and C. Honsberg, Solar Power Labs at Arizona State University, “Chapter 2.4: Terrestrial Solar Radiation”, URL: https://www.pveducation.org/pvcdrom/terrestrial-solar-radiation Accessed: 28 June 2024
[2] C. Bertrand, G. Vanderveken, M. Journée, “Evaluation of decomposition models of various complexity to estimate the direct solar irradiance over Belgium”, Renewable Energy, 74 (2015). p618-626, DOI: 10.1016/j.renere.2014.08.042, Mirror: https://sci-hub.se/10.1016/j.renene.2014.08.042
[3] European Commission, Photovoltaic Geographical Information System, https://re.jrc.ec.europa.eu/pvg_tools/en/#HR, Accessed: 28 june 2024
[4] Royal Netherlands Meteorological Institute KNMI, KNMI Data Platform – Weather Forecasts, URL: https://dataplatform.knmi.nl/group/weather-forecast. Accessed: 28 june 2024
[5] Weerlive / Meteoserver, KNMI Weer API, URL: https://weerlive.nl/delen.php, Accessed: 28 june 2024
[6] I. Reda and A. Andreas, “Solar Position Algorithm for Solar Radiation Applications”, Technical Report NREL/TP-560-34302, (2008). URL: https://www.nrel.gov/docs/fy08osti/34302.pdf Accessed: 29 june 2024
[7] Netbeheer NL, “DSMR 5.0.2 P1 Companion Standard – Dutch Smart Meter Requirements”, (2016), URL: netbeheernederland.nl/publicatie/dsmr-502-p1-companion-standard, Accessed: 29 june 2024
[8] P1Meter.nl, “De beste P1 Meter voor het meten van energieverbruik”, URL: https://www.p1meter.nl/beste-p1-meter/, Accessed: 29 june 2024
[9] Sandia, “Hay and Davies Sky Diffuse Model”, URL: https://pvpmc.sandia.gov/modeling-guide/1-weather-design-inputs/plane-of-array-poa-irradiance/calculating-poa-irradiance/poa-sky-diffuse/hay-and-davies-sky-diffuse-model/, Accessed: 30 june 2024
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