Chromatic Analysis of Wind Power Generation

A. T. Sufian, J. Lawton and G. R. Jones

Introduction

The generation of electric power from wind-driven generators (Figure ll.l) relies upon sufficient wind being available. In situations where there is an absence of sufficient wind, there is an intention to transfer power from another area where there is sufficient wind to produce power. For example, power interconnections between the United Kingdom and Germany allow power to be supplemented from one to another when one is short of wind but the other has sufficient wind. However, in practice, it needs to be ascertained how frequently both areas may have wind deficiencies which coincide with each other. Data about the power generation from wind at different times in the United Kingdom and Germany is available (Renewal Energy Foundation; Fraunhofer Institute) and has been analysed to provide a quantitative evaluation of such behaviour. The adaptation of chromatic analysis of such a situation is described.

Wind Speed Data

Wind speed data for the United Kingdom and Germany for an 8-month period (January and December 2015-2018) has been considered as a percentage of the maximum wind speed for each month and normalised to be in the range 0 (minimum) to 1 (maximum). Typical wind speed data from the United Kingdom (Renewable Energy Foundation) and Germany (Fraunhofer Institute) normalised in this way is shown in Figure 11.2 as a function of days over a period of 1 month (January 2015).

Data Analysis

Chromatic Analysis

Wind speed data of the form shown in Figure И.2 has been analysed by chromatically processing the data for each country using three non-orthogonal detectors in the time domain (R, G, B) with triangular responses to provide uniform sensitivity over the whole range being addressed (Chapter 1). The detector outputs are processed to yield values of chromatic parameters H. L, S, with H being the dominant time along the signal time period, L the effective strength of the signal over that period and

View of wind farm for electric power production

FIGURE 11.1 View of wind farm for electric power production.

S the spread (Chapter l). The values of each of these parameters (H, L. S) for the UK and Germany wind power signals are compared on graphs of the UK versus Germany values (Figure 11.3) over a number of selected time periods.

The dominant time H —> 0 corresponds to the early part of the signal, whereas H —> 1 corresponds to the final part of the chosen time period. The effective strength L —> 0 indicates no signal, whilst L —> 1 is a maximum signal. The spread S —> 0 indicates a wide spread, whilst S —» 1 indicates no spread.

Statistical Analysis with Chromatic Parameters

The chromatic parameters H, L, S have been further processed to highlight various statistical features using a Bland and Altman plot (Bland and Altman, 1986). This is based upon the difference between the values of a chromatic parameter (H, L or S) between the United Kingdom and Germany [e.g., (UK)L - (Germany)L] versus the mean of the UK plus Germany values (e.g., [(UK)L + (Germany) L]/2]; Figure 11.4).

A mean difference (MD = (sum of [UK - Germany])/[number of data sets]) = 0 indicates no difference between the United Kingdom and Germany. The spread of the data from the mean difference yields a limit of agreement (LoA) indicating the standard deviation(s), which is a limit

Result showing typical time variation of normalised wind speeds in the United Kingdom and Germany (January 2015) (Sudan et al„ 2019)

FIGURE 11.2 Result showing typical time variation of normalised wind speeds in the United Kingdom and Germany (January 2015) (Sudan et al„ 2019).

Graph comparing values of a chromatic parameter (H, L or S) of the United Kingdom and Germany (Sufian et al., 2019)

FIGURE 11.3 Graph comparing values of a chromatic parameter (H, L or S) of the United Kingdom and Germany (Sufian et al., 2019).

General form of a Bland and Altman plot (Sufian et al., 2019) plus physical implications

FIGURE 11.4 General form of a Bland and Altman plot (Sufian et al., 2019) plus physical implications.

of spread of data from MD (i.e., LoA is given by LoA = MD +/- 1.96 s [s = standard deviation]; Bland and Altman, 1986). An MD = 0 and a small spread of LoA implies that the United Kingdom and Germany wind speed values are not significantly different.

Figure 11.4 shows two areas within which no power exchange between the United Kingdom and Germany would occur due to either the wind speed difference (DL) or the wind speed magnitude (ML) being too low (Figure 11.4).

Results of Test Data Analysis

The previous methods of data analysis have been applied to the chromatic parameters H, L, S for three different-duration time periods of an 8-month test period of wind power production in both the United Kingdom and Germany. The durations of the three time periods analysed were a month from each of the 8 months monitored, weekly for the 8 months and every 3 days for the 8 months.

Examples of the deployment of the chromatic signal processors (R, G, B) over a month of data for the three different time durations (month, week, 3 days) are shown in Figure ll.5a-c, respectively.

The Bland and Altman plots for the effective magnitude (L) corresponding to the three time durations (month, week, 3 days) extending over the 8-month test period are shown in Figure 11.6a-c, respectively.

Similar Bland and Altman plots have been obtained for the H and S chromatic parameters.

The monthly processed L data (Figure 11.6a) showed a small amount of power magnitude shifts over the 8-month test period. Flowever, the differences between the United Kingdom and Germany were small. The LoA was less than 0.15, far less than the acceptable power exchange limit (DL = 0.5), although UK wind was slightly stronger than that in Germany, as indicated by MD > 0. The dominant time H data showed a similar trend, with the UK and Germany values being close, as were the trends with the spread of power S.

For the weekly processed L data (Figure 11.6b), there was a higher scatter of data, but the difference between the UK and Germany wind power remained low, with LoA less than 0.3 less than the acceptable power exchange limit DL. There were similar trends in the dominant time (H) and spread (S).

Chromatic processors

FIGURE 11.5 Chromatic processors (R, G, B) superimposed upon normalised time-varying wind power graphs for United Kingdom and Germany 1-month window (Sufian et al., 2019). (a) One-month duration; (b) 1-week duration; (c) 3-day duration.

Bland and Altman plots for eight 1-month based chromatic processing

FIGURE 11.6 Bland and Altman plots for eight 1-month based chromatic processing: (a) effective magnitude (chromatic L) based: (b) dominant time (chromatic H) based; (c) spread (chromatic S) based.

The 3-day processed L data (Figure 11.6c) showed a variation in the effective magnitude and wind speed difference between the United Kingdom and Germany. However, the acceptable power exchange from the United Kingdom to Germany was only 5% of the data. The remaining L data were below the acceptable power exchange limit DL, with LoA below 0.4, indicating that no substantial power exchange between the United Kingdom and Germany was practicable. Similar trends were observed for the dominant time (H) and spread (S).

Summary and Overview

Chromatic analysis of the variation in power produced in the United Kingdom and Germany in combination with Bland and Altman graphs provided quantitative insight about addressing power shortages by transferring power between the two countries.

Chromatic processing combined with Bland and Altman plots provided a means for quantifying the likelihood of wind-generated electric power being transferred between the United Kingdom and Germany in the event of low wind occurrence in one country. A primary indication of whether there is an imbalance in the wind power between the United Kingdom and Germany is given by the chromatic effective magnitude parameter (L). The dominant time parameter (H) provides an additional indication of whether the wind power levels coincide in the two countries. The chromatic spread parameter enables the distribution of wind power levels in the countries to be compared.

The L-based Bland and Altman plot showed that the wind speed was slightly stronger in the United Kingdom. On a monthly basis (over an 8-month observation period), results were all close to zero, indicating that no power transfer was warranted. The L-based Bland and Altman plots for weekly and 3-day analysis showed increased data scatter but fell within the no power exchange boundary (DL) and had a relatively low limit of agreement, supporting the conclusion that power transfer to correct for wind deficiency was not feasible.

The dominant time (H) results showed more than 80% correlation between the UK and Germany wind profiles, with few affected by time shifts between both countries (Sufian et al., 2019), supporting the effective magnitude (L) results (monthly, weekly, 3 days) that power transfer to correct for wind deficiency was not feasible.

The spread results (S) for the United Kingdom and Germany showed that the wind speed was slightly more spread in Germany, but they were correlated to be within the no power exchange boundary (DL) and had a low limit of agreement (Sufian et al. 2019), providing further evidence for the non-feasibility conclusions.

Since the United Kingdom and Germany lie, respectively, at the west and east of a span of 1,500 km across northern Europe, it is reasonable to conclude that the results obtained are relevant to the entire region. The chromatic analysis and Bland and Altman processing indicated a high correlation between wind power-based production in midwinter across northern Europe. Therefore, at that time, when wind is the dominant source of electricity, interconnections will add little to system security.

References

Bland. J. M. and Altman, D. (1986). Statistical methods for assessing agreement between two methods of clinical measurements. Lancet. 327(8476), 307-310. February 08, 1986.

Fraunhofer Institute. Available at https://www.energy charts. De/power.htm Renewal Energy Foundation. Available at https://www.ref.org.uk/energy-data

Sufian. A. T. Jones, G.R. and Lawton, J. (2019). Chromatic Analysis of Wind Generated Power Technical Report. Center for Intelligent Monitoring Systems. Department of Electrical Engineering an Electronics. The University of Liverpool.

12 Chromatic Comparison of

 
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