A simple optimization study
Designing an energy system for a modern building in a cost-effective manner is not an easy task. Besides environmental and legislative constraints, architects and engineers face the primary objective of minimizing the total cost of ownership of the system which, ultimately, means striking a balance between the investment cost and the long-term energy savings that it will bring. Consequently, it becomes evident that the cost of energy directly influences the design choices.
Moreover, given that buildings are expected to operate for several decades, it is crucial to consider potential changes and developments in the energy market and any decision must carefully take into account future trends and dynamics of energy prices.
The purpose of this blog is to delve into the impact of energy prices on the optimal design of modern buildings equipped with solar panels, batteries, and heat pumps. By examining the interplay between energy prices and these technologies, we aim to uncover valuable insights that can inform the decision-making processes of building designers, architects, and energy policy makers.
Assumptions
We assume a single home with an electricity consumption of 6300 kWh/year and a heating demand of around 18000 kWh/year. The building is located in Eastern Switzerland at an elevation of 750 m above sea level. Average ambient temperatures range from -1°C in January to 16°C in July. The building has a flat roof and shall be equipped with a photovoltaic system, mounted with an angle of ten degrees facing east and west direction. The heating system of the building incorporates an air heat pump, a water tank for the storage of warm water, and one for the heating system. The building has a strong exposure to the south with significant window areas, resulting in a rapid heat-up when the sun is shining. It is a well-insulated brick and concrete building. Hence, the structure incorporates a considerable heat storage capacity.
As a baseline case study, we consider a simple energy price model as follows: buying price is 0.35 CHF/kWh, selling price is 0.13 CHF/kWh. It’s worth noticing that, for our study, the energy price remains constant throughout the year and is not influenced by specific hours or days. Some countries or regions may have different energy pricing models, such as discounted rates during night time or weekends, or a fully variable price, driven by energy supply and demand. To ensure a generic approach, we are currently considering the flat energy price structure as described above.
Results and discussion
First of all, we find the optimal sizing of our energy system with a baseline price model, which will give us a reference design. Assuming a maximum available area for solar panels of 80 m2 and with components prices based on the Swiss market, the optimization exploits the maximum available area and chooses an average sized battery of 5.9 kWh.
We also obtain an optimal size for the heat pump and the water storage tanks which we are going to keep fixed to these reference values for the rest of the analysis, as we want to focus on the solar panels and battery design problem. We will address the topic of heating systems in a later post.
We will use two different ways to change the price of energy, while always keeping the flat rate model:
- We assume a fixed ratio between buying and selling prices. This is the most intuitive way to run a sensitivity study, where both prices vary linearly together, for example using 50% of the baseline values, then moving to 75% and so on.
- We assume a fixed offset between buying and selling prices. This is actually a more realistic scenario because, that difference between the two values, represents fees and taxes paid for the grid usage, which we can consider to be constant.
Interestingly, despite the two options looking quite similar in terms of absolute numbers, they produce very different results. This proves how important it is to know the energy market and to include it in the design process.
Let’s start with the simple case, which is the first option: we clearly see how, when the energy prices increase, having a photovoltaic system combined with a battery becomes more and more valuable. This can be easily explained: the higher the price of energy, the better it is to invest in self-sufficiency and rely less on the grid.
Let’s look now at the second option: once again, the higher the energy price, the more valuable solar panels are. The battery, on the other hand, shows a quite interesting behaviour. To understand this, let’s compare the system operation with and without a battery: a system with a battery is able to store any over production from the solar panels and use it again when there is an energy demand not covered by the production (e.g. during evenings or nights), on the contrary, in a system without a battery, any energy surplus will be sold to the grid and any demand higher than the production has to be bought back. What is driving the choice then, is the trade-off between the battery price and efficiency against the money lost when selling and buying back energy. The interaction of these quantities can lead to completely different results, not only in absolute numbers, but even in terms of sensitivity and correlation, which makes it very difficult to judge a design choice based on intuition and experience.
Thanks to modelling and optimization tools such as atbMod and atbOpt developed by AIMotroniX, engineers and architects can simulate and explore any possible scenario within a few minutes and gain a better knowledge and understanding of the complex implications of their design choices.
Finally, it is worth noticing that we have assumed the possibility to buy and sell energy at any time and at any power level. We already discussed in a previous post the problem of power limitations in the grid. Power limitations may introduce a completely different drive for the design and control choices of energy systems. Such constraints can be seamlessly integrated in the atbMod and atbOpt environment. This will be thoroughly discussed in a future article.
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This text has been co-authored by real people from AIMotroniX in collaboration with Bing AI Chat