Calculating wind turbine electricity production in residential developments
Calculating wind turbine electricity production for each month of the year helps to make the right choices when it comes to investing in residential wind energy.
At a time when energy bills are growing, an increasing number of private homeowners are becoming interested in the topic of renewable energy, and wind-energy in particular. “Green energy” draws people’s attention not only because of the prospect of lower energy bills, but also because of the opportunity to contribute to protecting the environment.
However, wind energy is not suitable for everyone, despite its appeal. There are several factors which a homeowner must consider when deciding whether to invest in a wind generator for their property. In this article, we describe the main parameters and make example calculations that help to make well informed choices.
Wind turbine key parameters
Cut-in speed, or starting wind speed, shows the point at which the wind turbine starts to produce electricity. If the wind speed is lower than the cut-in speed, no electricity is generated. Typically, the cut-in speed of wind turbines designed for domestic use varies from 2.2 to 4.5 m/s.
Rated speed defines at what speed a wind turbine will produce the amount of power it is quoting in its name. The Rated speed of a turbine depends on its size but is usually within the range of 6.7 to 22 m/s.
Type of wind turbine
There are different kinds of wind turbines. They can be divided according to the position of their axis and how they are mounted to be elevated above the ground. Whether a turbine will be connected to the electric grid needs to be decided before selecting the needed size.
Horizontal axis wind turbines produce more power but are more expensive and make more noise. In contrast, vertical axis turbines are less noisy, but they are less efficient and more difficult to maintain because turbine parts are not easily accessible.
Turbines that can be mounted on the roof are cheaper and easier to install, but they do not produce as much electricity as pole mounted turbines, which, however, are much more expensive. Also, local planning rules must be considered.
A wind turbine can operate in sync with the electricity grid. A grid-connected wind turbine can help reduce the consumption of electricity supplied by utilities, thereby reducing costs, or even producing profits. Grid connection ensures stable electricity supply. If grid connection is not practical or desired, the supply stability must be augmented through diversification of production, for example, by using a hybrid solar-wind production and/or considerable storage facility.
Calculating wind turbine monthly electricity production
Each turbine has a different power output for different wind speeds. These values are shown on the power curve that is included in the technical documentation for each turbine. Let’s take a generalized curve of a small wind turbine as an example. It is also worth paying attention to the fact that when talking about the power of the turbine, we mean the electrical power, not the mechanical, and such criteria as “turbine efficiency” refers to how much mechanical power has been converted into electrical power.
In order to calculate how much energy a wind turbine can produce in a month; we also need to understand what wind speeds prevail in our location. For the calculations we use location intelligence report obtained from https://atsea.fi. The handy paginated pdf contains all key environmental and climate data for our specific location as easily understandable statistical distributions. Such reports are available for every location in the world.
One of the graphs in the atSEA report shows wind speeds by month. It is clear from the graph that wind speeds vary considerably throughout the year, something that we must consider particularly for off-grid systems. To calculate the electricity production of a wind turbine, we use a table with probabilities of various wind speed brackets for each month which is also included in the atSEA report.
Let’s consider the power curve above and wind distribution to calculate how much energy our wind turbine can produce per month. For the calculation, let’s assume that our turbine has the following characteristics: 7 kW peak output, 3 m/s cut-in wind speed, 9 m/s rated speed. The amount of energy generated is equal to the power output multiplied by the time the turbine operates at that power output. The time the turbine operates at a particular power output is determined by the probability distribution of wind speeds.
For the calculation we will use the table on the right which shows the probability in percent of wind in various speed ranges for each month.
For example, in December, the probability of wind ranging from 9-11 meters per second is 18%, and all ranges with higher values account for 10%. Since the rated speed of the turbine is 9 m/s, we see that the turbine will operate at its rated power of 7 kW 28% of the total running time, which corresponds to about 208 hours (0.28 * 31 days * 24 hours) and 1456 kWh of energy generated in that month (208 hours * 7 kW).
We have calculated the amount of electricity that a wind turbine will generate when it reaches rated speed. Although wind speeds, which are less than the rated speed but above the cut-in speed, will generate less power, it still will be a significant amount of power.
Let’s calculate how much electricity is produced in the remaining sections of the curve where wind speeds are above the cut-in speed but do not reach the rated speed of the turbine. For example, at wind speeds of 3 to 5 meters per second, approximately 1 kW of energy is produced, and so on.
The amount of energy that will be generated in December in wind speed brackets from 3 m/s to 9 m/s is the sum of the three speed brackets (3-5, 5-7, 7-9):
[(0.17 * 1 kW) + (0.24 * 3.7 kW) + (0.24 * 6 kW)] * 31 days * 24 hours = 1859 kWh
Altogether, the example turbine is expected to generate an average of 3313 kWh each December. We can repeat the calculation for all other months (we use Excel for convenience). For example, July will generate less than half compared to December (1616 kWh).
The average annual electricity production of the example 7kW turbine mounted in our specific location would be 30 MWh, which with an average cost of electricity of 20 cent per kWh translates to 6000 dollars’ worth of electricity per year. If it is enough to justify the costs of purchasing, installation and annual maintenance depends on the costs and yields of available alternatives.
Impact of other limiting factors
In addition to the wind speed, one has to consider the typical direction of the winds. Let’s take a look at the wind rose provided in the atSEA report for our location. This graph shows that the predominant wind directions are south and southwest. This is important to consider when choosing the place where the wind turbine will be installed to ensure there are no large obstructions in the path of the wind.
Another important aspect is the terrain profile. Elevated locations are preferred, whereas land depressions might lead to significant performance losses. As visible from the elevation model in our atSEA report, our location is slightly elevated, but there are higher hills to South-West about 6km away which should be enough distance not to impact our turbine too much.
Thus, to assess the feasibility of installing a wind turbine, not only the parameters of the wind turbine itself must be taken into consideration, but also environmental parameters such as the probability distribution of wind speeds, wind direction and the local terrain. Thus, before making any investment decision, detailed local data should be consulted, and any technological choices based on evidence. There are plenty of choices when it comes to wind turbines and a tiny up-front investment in a location intelligence report can significantly increase the returns and reduce the risk of mis-investment.