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REVIEW 3 major objections 4 minor 30 references

Frequency Observations and Statistic Analysis of Worldwide Main Power Grids Using FNET/GridEye

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A bell curve describes frequency in seven of 13 power grids.

desk verdict A worthwhile 13-grid frequency survey whose 'almost normal' claim is a same-data overlay, not a tested result. read the letter →

arxiv 1908.03823 v1 pith:KRAOEHKQ submitted 2019-08-10 eess.SY cs.SY

Xianda Deng , Hongyu Li , Wenpeng Yu , Wang Weikang , Yilu Liu This is my paper · ORCID
classification eess.SYcs.SY
keywords worldwidepowergridsfrequencyobservationsstatisticalanalysisPMUapplicationbigdataFNET/GridEyenormaldistributiondisturbancerecorder
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using three months of distribution-level frequency data from the FNET/GridEye wide-area monitoring system, this paper describes the statistical behavior of 13 power grids across five continents. It divides them into two families: seven grids with single-peak frequency histograms and six with multi-peak histograms. For the single-peak family, the paper claims the measured frequency distribution is well approximated by a normal distribution built from the same data's mean and standard deviation. If this holds, frequency behavior in those grids can be summarized by two numbers, and the study offers a simple statistical typology for comparing grid operations worldwide.

What carries the argument

The key machinery is the frequency disturbance recorder (FDR), a low-cost distribution-level sensor that streams GPS-synchronized frequency measurements at ten samples per second to FNET/GridEye servers. Three months of data from one FDR per grid are cleaned, converted to per-unit frequency, and summarized as empirical probability density functions. The paper then fits a two-parameter normal distribution to the single-peak histograms using the sample mean and standard deviation, using the visual match between the fitted curve and the histogram as evidence. Daily means and standard deviations for EI, Egypt, and Japan are additionally used to reveal operating status such as Egypt's persistent under-frequency operation.

What would settle it

Take two or more FDRs located in different regions of the same interconnection (for example, the U.S. Eastern Interconnection) and compute their three-month frequency histograms separately; if the single- versus multi-peak classification or the fitted Gaussian mean and standard deviation differ markedly between the sensors, then the paper's per-grid statistics reflect local sensor behavior rather than grid-wide frequency status.

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Extended reading notes

Core claim

The central discovery is that for seven of the thirteen grids – the U.S. Eastern Interconnection, WECC, Hawaii, Germany, Japan, Australia, and Egypt – the empirical probability density function of frequency closely matches a Gaussian curve whose parameters are the empirically computed mean and standard deviation. The remaining six grids – ERCOT, Saudi Arabia, Northern Ireland, Ireland, England, and Bahamas – show multi-peak histograms that no single normal distribution can represent. The paper further shows that mainland grids generally have smaller frequency standard deviations than island grids, with Egypt as the largest-deviation outlier and Hawaii as a low-deviation island, and that most grids operate within NERC load-shedding thresholds.

Load-bearing premise

The entire cross-grid comparison rests on the assumption that a single frequency disturbance recorder per country captures the frequency behavior of the whole interconnection, with no validation against other sensors on the same grid.

Editorial extensions

If this is right

  • For single-peak grids, a normal distribution with the observed mean and standard deviation provides a workable empirical model, so frequency can be summarized by two numbers without a more complex model.
  • The single-peak/multi-peak taxonomy gives a simple way to compare frequency statistics across countries and could serve as a baseline for tracking how renewable penetration changes frequency behavior.
  • Mainland grids in this sample generally exhibit smaller frequency standard deviations than island grids, suggesting that interconnection size dampens frequency fluctuation; Egypt is an exception with the highest deviation, and Hawaii is an island with unusually low deviation.
  • Most studied grids keep their frequency deviations within NERC's under-frequency load-shedding thresholds, while Egypt's standard deviation approaches that limit, indicating a stressed system over the observation period.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the Gaussian behavior is persistent, mean and standard deviation could serve as simple health metrics: a shift in the mean or widening of the standard deviation after a policy change would be detectable with these two numbers alone.
  • The six multi-peak grids invite a mixture-of-Gaussians or heavy-tailed follow-up analysis, which the paper does not pursue.
  • The single-sensor assumption is directly testable: comparing two FDRs on the same interconnection would show whether the reported statistics are grid properties or sensor properties.
  • Because FNET/GridEye already deploys hundreds of FDRs in dozens of countries, the same histogram procedure could produce a global map of frequency statistics far beyond the 13 grids studied here.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript reports an observational statistical study of power frequency in 13 worldwide power grids using FNET/GridEye distribution-level frequency disturbance recorder measurements sampled at 10 Hz over roughly three months. For each grid it computes mean frequency and standard deviation, compares mainland versus island behavior, and classifies the empirical frequency distributions into single-peak and multi-peak families. It then selects EI, Egypt, and Japan for more detailed daily statistics, and claims that the single-peak distributions 'almost follow the normal distribution,' illustrating this by overlaying Gaussian curves on the histograms of seven grids. The paper concludes that the observed statistical characteristics can aid grid operators and future frequency regulation studies.

Significance. The dataset assembled here is valuable: simultaneous multi-grid frequency observations across 13 systems are rare, and the reported means and standard deviations provide a useful descriptive baseline for cross-grid frequency behavior. If the single-peak/multi-peak classification and the Gaussian approximation for single-peak grids were rigorously established, the paper would provide a simple empirical model of interest to frequency-control and reserve-sizing studies. However, the central normality claim is currently supported only by an in-sample visual overlay, and the classification is made by eye; as presented, the scientific contribution is descriptive rather than confirmatory. The paper would be strengthened materially by adding quantitative distributional tests, unimodality criteria, and sensitivity analysis.

major comments (3)
  1. [Section III, Figs. 7 and 8] The headline claim that single-peak frequency distributions 'almost follow the normal distribution' is not supported by the evidence reported. The red normal curves in Fig. 8 are constructed from the sample mean and standard deviation of the very same histogram data, so the agreement is an in-sample property, not an independent test. No goodness-of-fit statistic (e.g., Kolmogorov-Smirnov, Anderson-Darling), tail-quantile comparison, or alternative distribution benchmark (e.g., Laplace, Student-t) is provided, and the qualifier 'almost' is never defined. Since each grid contributes millions of samples (10 samples/s for three months), exact Gaussianity would be rejected by any classical test; the practically relevant question is whether the Gaussian approximation holds within some stated tolerance, and the manuscript does not quantify that tolerance.
  2. [Section III, Fig. 7 and Table I] The single-peak versus multi-peak classification of the 13 grids is based on visual inspection of one histogram per grid, with no unimodality test, no bin-width sensitivity analysis, and no quantitative criterion for what constitutes a peak. For borderline cases such as Egypt (Fig. 7(g)), whose histogram appears skewed and heavy-tailed, the inclusion in the 'single-peak normal' family is not self-evident; for ERCOT and the multi-peak group, the visible secondary modes could be artifacts of binning or of a sensor-specific event. Without a reproducible classification rule, the claim that the 13 grids divide into these two families is not robust.
  3. [Section II, last paragraph] The cross-grid comparison assumes that one FDR per country represents the frequency behavior of the entire interconnection, justified only by Refs. [29]-[30]. For large systems such as EI and WECC, a single distribution-level sensor can be influenced by local load or generation events, and the manuscript provides no validation against other sensors on the same grid or against control-area frequency statistics. Consequently, the reported mean, standard deviation, and the single/multi-peak classification could reflect local sensor behavior rather than grid-wide frequency status, which limits the generality of the cross-grid conclusions.
minor comments (4)
  1. [Section III, Fig. 6] The manuscript states that three months of data are retrieved for the 13 grids, but the daily analysis in Fig. 6 is described as using a one-month period; the discrepancy should be clarified.
  2. [Introduction, paragraph 1] The phrase 'due to its clean, low-cost and inexhaustible features' refers to renewable energy sources but uses a singular pronoun; please revise for grammatical consistency.
  3. [References] Reference [2] appears to be a URL fragment appended to the National Conference of State Legislatures reference without proper formatting, and several references (e.g., [13]) are not cited in the text; the reference list should be checked for completeness and consistency.
  4. [Section II, paragraph 2] The sentence 'The frequencies in all mainland power grids have smaller standard deviations, comparing to the frequencies in island power grids' is contradicted by the paper's own observation that Egypt, a mainland grid, has the highest standard deviation; rephrase to acknowledge the exceptions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper reports descriptive statistics and an in-sample normal fit, and it does not present any fitted parameter as a prediction or derive its claims from self-citation.

full rationale

The paper's central claims are empirical observations: the mean and standard deviation of frequency measurements in 13 grids, a visual single-peak/multi-peak classification, and a statement that single-peak distributions 'almost follow the normal distribution.' The normal curves in Fig. 8 are generated from the sample means and standard deviations of the same data, but this is an in-sample descriptive fit, not a prediction from first principles. The paper never claims to predict the distribution from independent inputs, nor does it rename a fitted parameter as a derived result. The one-FDR-per-grid representativeness assumption is supported by prior FNET literature (refs [29]-[30]), including some overlapping authors, but that citation is an external empirical claim about intra-system frequency differences, not a load-bearing self-referential theorem, and it does not make the statistical classification circular. No equation is shown to reduce to its own inputs, and no fitted quantity is called a prediction. The lack of goodness-of-fit tests or unimodality criteria is a methodological weakness, but it is not circularity under the stated rules. Therefore, the appropriate finding is no significant circularity.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new theoretical entities or physical parameters. The only 'fitted' objects are the normal reference curves in Fig. 8, whose mean and standard deviation are taken from the same data being described, so they are descriptive summaries rather than independently fitted model parameters. The main load-bearing assumptions are the representativeness of a single FDR per grid, the representativeness of the observation windows, and the unspecified bad-data filter.

free parameters (1)
  • Sample mean and standard deviation for each of the seven single-peak grids (EI, WECC, Hawaii, Germany, Japan… = Computed from the same data under study; values shown in Figs. 4-5 but not tabulated in the text
    The normal curves in Fig. 8 are parameterized by the sample mean and sample standard deviation of the exact same frequency data they are compared against, so the comparison is a descriptive in-sample fit rather than an independent validation.
assumptions (4)
  • domain assumption A single distribution-level FDR measurement is representative of the frequency of the entire interconnection
    The analysis uses one FDR per grid; the paper cites refs [29]-[30] for small intra-system frequency differences, but gives no validation that the selected sensor's statistics match the whole grid or other sensors.
  • domain assumption The three-month (and one-month for the detailed study) observation window is representative of normal and transient operation
    The paper claims the data reflects both normal operation and transient status, but gives no check for seasonal or event-driven bias in the window.
  • domain assumption The bad-data filter removes only measurement errors and does not selectively remove valid frequency excursions
    Section II states 'Pre-process the measurements and filter bad data' without specifying the criteria, so the filter could bias the distribution tails.
  • ad hoc to paper The normal distribution is the appropriate baseline for 'single-peak' frequency distributions
    The paper selects the normal model without comparing to other single-peak distributions (e.g., Laplace, Student-t) or justifying it from system dynamics; this is the model used to produce the red curves in Fig. 8.

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Cite this review

Pith. "Pith review of Frequency Observations and Statistic Analysis of Worldwide Main Power Grids Using FNET/GridEye." pith.science (2026). https://pith.science/paper/KRAOEHKQ

@misc{pith2026190803823,
  author       = {Pith},
  title        = {Pith review of: Frequency Observations and Statistic Analysis of Worldwide Main Power Grids Using FNET/GridEye},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KRAOEHKQ}},
  note         = {Machine review of arXiv:1908.03823}
}
read the original abstract

With the increasing renewable energy sources, concerns about how renewable energy sources impact frequency have risen. There are few reports regarding power frequency status in worldwide main power grids and what are differences of frequency status between power grids in mainland and island. FNET/GridEye, a wide-area measurement system collecting frequency and phase angle data at the distribution level, provides an opportunity to observe and study the power frequency in different power grids over the world. In this paper, 13 different power grids, spreading at different mainland and islands over the world, are observed and compared. A more detail statistical analysis was conducted for typical power grids in three different places, e.g., U.S Eastern Interconnection (EI), Egypt, and Japan. The probability functions of frequency based on the measured data are calculated. The distributions of frequency in different power grids fall into two categories, e.g., single-peak distribution and multi-peak distribution. Furthermore, a meaningful insight that the single-peak distributions of the frequency almost follow the normal distribution is found. The frequency observations and statistic analysis of worldwide main power grids using FNET/GridEye could help the power system operators understand the frequency statistical characteristic more deeply.

Figures

Figures reproduced from arXiv: 1908.03823 by the authors.

Figure 1
Figure 1. FDR Worldwide deployment map. Though research has been conducted on studying the power frequency in the actual power grids, a few papers reported the power frequency in the worldwide main power grids, and thus the insights for the worldwide power system frequency are seldom offered. Using the data from FDRs, this paper offers the statistical analysis of the frequency in the different regions, which is helpful for th… view at source ↗
Figure 2
Figure 2. The prototype of UGA. At the FNET/GridEye data center, a data concentrator is employed to receive and process FDR steaming data. After filtering out bad data, all the data are achieved into a database for data analysis [23]. The streaming data is visualized and published at http://fnetpublic.utk.edu/, while historical data is accessible with further privilege authorization. With a vast volume of frequency measuremen… view at source ↗
Figure 4
Figure 4. Mean of frequency in power grids in different regions [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: The standard deviation of frequency in power grids in different regions According to [31], the highest relay setting of load shedding frequency f required by North American Electric Reliability Corporation (NERC) is 59.3 Hz (0.9883333 p.u.) <f<59.5 Hz (0.9916667 p.u.).…
Figure 6
Figure 6. Figure 6: Standard deviation and mean of frequency in each day in three power grids. (a) Standard deviation (b) Mean. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]
Figure 7
Figure 7. Figure 7: Probability density function of frequency in different power grids. (a) EI, U.S. (b) WECC, U.S. (c) Hawaii, U.S. (d) Germany. (e) Japan. (f) Australia. (g) Egypt. (h) ERCOT, U.S. (i) Saudi Arabia. (j) Northern Ireland. (k) Ireland. (l) England. (m) Bahamas. (a) (b) (c)…
Figure 8
Figure 8. Figure 8: Comparison of probability density function obtained by statistics and the corresponding normal distribution. (a) EI, U.S. (b) WECC, U.S. (c) Hawaii, U.S. (d) Germany. (e) Japan. (f) Australia. (g) Egypt [PITH_FULL_IMAGE:figures/full_fig_p004_8.png]

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Reference graph

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