Analysis of frequency measurements of the Nordic, Continental European, and Japanese-50-Hz power systems

When my former colleagues from the Center for Electric Power and Energy (CEE) at DTU published the data of their frequency measurements of the Nordic, Continental European, and Japanese-50-Hz power systems, I thought I need to analyze the data and publish some insights.

The frequency measurements are publicly available here (thanks for that):

• Nordic Power System Frequency of 2019: Thingvad, Andreas; Marinelli, Mattia (2020): Grid Frequency Measurements of the Nordic Power System during 2019. Technical University of Denmark. Dataset. https://doi.org/10.11583/DTU.12758573.v1 
• Continental European Power System Frequency of 2019: Thingvad, Andreas; Marinelli, Mattia (2020): Grid Frequency Measurements of the Continental European Power System during 2019. Technical University of Denmark. Dataset. https://doi.org/10.11583/DTU.12758429.v1
• Japanese 50 Hz Power System Frequency of 2020: Thingvad, Andreas; Calearo, Lisa; Marinelli, Mattia (2021): Grid Frequency Measurements of the 50 Hz Japanese Power System during 2020. Technical University of Denmark. Dataset. https://doi.org/10.11583/DTU.14038910.v1 

Overview of the frequency measurements

The following table shows a summary of the frequency measurements. All measurements come with a sample rate of 0.5 seconds and an accuracy of 10 mHz. All three datasets provide between approximately 54 and 59 million samples. The presented number of samples reflects only the days with measurements, i.e. all days without measurements are removed.

	Nordic 2019	Continental European 2019	Japanese 50 Hz 2020
Samle rate (s)	0.5	0.5	0.5
Accuracy (mHz)	10	10	10
Days measured (d)	340.8	342.5	317
Total samples	58,890,240	59,184,000	54,777,600

Frequency distribution

Let’s first look at the distributions of the frequencies over the whole measurement period. The plots below show the distributions for the three power systems with the same x-axes to make them easily comparable. The table below the figures summarizes the numerical results of the analysis.

In the plot, I also marked some interesting indicators, such as the mean, confidence interval ± 3σ (σ = standard deviation), and min/max of the distribution. The 3σ-confidence-interval contains 99.73 % of the measurements and gives a measure of how close the power system operates around its nominal frequency.

Clearly, the Continental European system shows the narrowest band followed by the Japanese and Nordic systems. Interestingly, the mean of all three systems is exactly 50 Hz up to the second decimal. We can also see that the Nordic system has the largest deviation from the nominal frequency in both positive and negative directions.

	Nordic 2019	Continental European 2019	Japanese 50 Hz 2020
mean frequency (Hz)	50.00	50.00	50.00
min. frequency (Hz)	49.60	49.80	49.81
max. frequency (Hz)	50.32	50.18	50.19
mean – 3σ (Hz)	49.87	49.94	49.90
mean + 3σ (Hz)	50.13	50.06	50.10

Frequency gradient – df/dt distribution

I tried to squeeze the data for more information. So, I calculated the derivative of the frequency (df/dt) to get a feeling of how much the frequency is changing each half a second.

The plots below show the distribution of the derivative df/dt, the corresponding mean, and the min/max of the distribution. This time the plot does not show the confidence interval because it is very narrow (please refer to the table below). Also, the y-axis is logarithmic because there are only a few occurrences of higher derivatives throughout the year.

Somewhat expected, the Continental European system shows the narrowest band also for the frequency derivative with a minimum of -0.07 Hz/s and a maximum of 0.06 Hz/s. The Nordic and Japanese systems have significantly higher derivatives in both directions. However, the confidence interval for all three systems is only 10 mHz which suggests that from a frequency gradient point of view they are very similar. None of the systems has significantly higher frequency gradients than the other. The min/max gradients might have been caused by an extreme (uncommon) event as they exactly appear once.

	Nordic 2019	Continental European 2019	Japanese 50 Hz 2020
mean df/dt (Hz/s)	0.00	0.00	0.00
min. df/dt (Hz/s)	-0.23	-0.07	-0.59
max. df/dt (Hz/s)	0.42	0.06	0.61
mean df/dt – 3σ (Hz/s)	-0.01	-0.01	-0.01
mean df/dt + 3σ (Hz/s)	0.01	0.01	0.01

Conclusions

Now, the question is, what can we learn from this analysis?

Definitely, comparing the frequency distributions we can relate whether we are talking about a large or small power system in terms of the total load. Larger power systems will usually have more (synchronous) generating units that on the one hand provide inertia and on the other hand participate in frequency regulation, thus contributing to frequency stabilization. Therefore, narrower frequency distributions would suggest a larger power system and vice versa.

Looking at the frequency gradient a more complete picture can be obtained by gaining additional information about the volatility of the power system.

However, geographical peculiarities and different grid codes also influence power system operations. This needs always be kept in mind when comparing two different power systems.

Further reading

For people interested in frequency analyses of the Australian grid I can recommend the following resources:

• The Australian Energy Market Operator (AEMO) produces a lot of frequency analysis reports in connection with their implementation of the mandatory primary frequency response program.
• Observations of differences in system frequency in the Mainland NEM (comparing 2019 to 2021) by Paul McArdle on WattClarity

If you are interested in more data, check out how to query data from the ENTSO-E transparency platform using the Python API.

I hope you find this article insightful.

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More insights within energy are to follow in the next article.