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Chapter 2

Analysis of Wind Power Characteristics

Guojie Li, and Jing Zhi

Abstract

This chapter analyzes the characteristics of wind power production in Jiuquan wind power base, including probability distribution, fluctuation and randomness, correlation and complementarity, as well as upstream and downstream effect.

Keywords

Complementarity; Correlation; Extreme value; Fluctuation; Probability distribution; Ramp rate; Randomness; Upstream and downstream effect; Wind power characteristics

2.1. Basic Attributes of Wind Power

2.1.1. Basic Attributes of Wind Power Resources

Wind speed is generally distributed with a positive skew. Generally, the larger the wind force in a certain area is, the flatter the wind speed distribution curve of this area, and the peak value will reduce and shift to the right. In other words, the larger the wind force, the higher proportion of the high wind speed is.

There are a lot of curves used to model wind speed distribution, for example, Rayleigh distribution, logarithmic normal distribution, two-parameter Weibull distribution, three-parameter Weibull distribution, and Pearson curve.

Weibull distribution function

$F_{w} (x) = 1 - \exp [- {(\frac{x}{σ})}^{ξ}]$

(2.1)

Its probability density function is

$P (x) = \frac{ξ}{σ} {(\frac{x}{σ})}^{ξ - 1} \exp [- {(\frac{x}{σ})}^{ξ}]$

(2.2)

where ξ and σ are two parameters of Weibull distribution: ξ is the shape parameter and σ is the scale parameter. The case where σ = 1 is called the standard Weibull distribution.

The change of ξ makes a great impact on the distribution curve. If 0 < ξ < 1, the mode of distribution is zero and the distribution density is the decreasing function of x; if ξ = 1, the Weibull distribution is identical to the exponential distribution; if ξ = 2, the Weibull distribution is identical to the Rayleigh distribution; if ξ = 3.5, the Weibull distribution approximates the normal distribution. The larger ξ is, the smaller the variation range of the annual average wind speed is and vice versa.

The Weibull distribution is shown in Figure 2.1.

2.1.1.1. Wind speed probability distribution in Jiuquan wind power base

We selected seven wind measurement masts in Jiuquan, Gansu, specifically, Beidaqiao No. 5, Beidaqiao No. 13, Ganhekou No. 7, Ganhekou No. 10, Changma No. 13, Changma No. 17, and Qiaowan No. 5 wind measurement masts and measured the wind speed from May 2008 to April 2009 with the time interval of 10 min and at a height of 70 m. We used the dfittool toolbox of the MATLAB software to fit the wind speed data measured at the seven wind measurement masts with the Weibull distribution. Except for Beidaqiao No. 5 wind measurement mast, all the other wind measurement masts conform to Weibull distribution. Now we are going to explain this by taking Beidaqiao No. 13 as an example. See Figure 2.2, “Annual Wind Speed Probability Distribution of Beidaqiao No. 13 Wind Measurement Mast.”

In this figure, the bar chart represents the actual wind speed probability distribution and the curve is the fitting curve of Weibull distribution. The wind speed of Beidaqiao No. 13 wind measurement mast mainly ranges 3–9 m/s. The fitting result indicates Weibull distribution can well describe the statistical characteristics of wind speed. In the Weibull distribution the scale parameter σ is 8.57841 and the standard deviation is 0.0240686; the shape parameter ξ is 1.73886 and the standard deviation is 0.00646219.

Calculate the wind speed data measured at seven wind measurement masts with the dfittool toolbox of the MATLAB software and the calculation result is shown in Table 2.1. In this table the median wind speed refers to the median of all wind speed sequences arranged from strong to low, and the average wind speed refers to the annual average wind speed. The median wind speed and average wind speed reflect the richness of wind resources. Wind speed probability no more than 13 m/s or wind speed probability no more than 15 m/s refers to the probability of wind turbine operating below the rated power. When the average wind speed remains the same, the wind speed probability represents the wind power resource utilization rate of wind turbines. The larger the wind speed probability is, the higher the wind power resource utilization rate.

Judging from the median and average wind speed, Changma wind farm cluster has the richest wind power resources, followed by Beidaqiao and Ganhekou wind farm cluster, whereas Qiaowan wind farm cluster is relatively poor in wind power resources. However, in terms of the internal wind power resource distribution, wind power resource distribution is quite even in Ganhekou and Changma wind farm clusters; wind power resources vary greatly in Beidaqiao wind farm cluster; locations near Beidaqiao No. 13 wind measurement mast are rich in wind power resources, whereas locations near Beidaqiao No. 5 wind measurement mast are poor. On the premise that overall wind power resources are certain, the higher wind speed probability lower than the rated wind speed is, the lower the wind speed probability higher than the rated wind speed, and the higher the wind power resource utilization rate is. Data indicates Qiaowan wind farm cluster has the highest wind power resource utilization rate, followed by Changma wind farm cluster; Ganhekou and Beidaqiao wind farm clusters have the lowest wind power resource utilization rate. Both wind power resources and wind power resource utilization rate indicate Changma No. 13 and Changma No. 17 wind measurement masts are most suitable for wind farm construction while Beidaqiao No. 5 wind measurement mast is less suitable for wind farm construction or operation.

Figure 2.2 Annual wind speed probability distribution of Beidaqiao No. 13 wind measurement mast.

Table 2.1

Wind Speed Data Distribution Statistics

Wind Farm Cluster	Wind Measurement Mast	Median Wind Speed (m/s)	Average Wind Speed (m/s)	Wind Speed Probability No More than 13 m/s (%)	Wind Speed Probability No More than 15 m/s (%)
Beidaqiao	Beidaqiao No. 5	6.1	7.29	83.2	90.16
	Beidaqiao No. 13	7	7.66	86.7	93.9
Ganhekou	Ganhekou No. 7	6.8	7.45	85.8	93.2
	Ganhekou No. 10	6.7	7.44	86.7	93.9
Changma	Changma No. 13	7.8	8.13	88.1	94.1
	Changma No. 17	7.8	8.07	89.5	95.1
Qiaowan	Qiaowan No. 5	6.9	7.18	92.1	96.8

2.1.1.2. Jiuquan wind power base extreme wind speed distribution

There are mainly two ways to calculate extreme climate probability statistics: one is to use the statistical distribution model to fit climatic elements and then analyze the extreme climate based on the probability of climatic elements; the other is to directly use the extreme value distribution theory to fit and analyze the extreme climate. Extreme distribution refers to the probability distribution of the maximum or minimum value in the climatic elements. Extreme value distribution functions such as Weibull, Gumbel, and Frechet are usually used for extreme climate fitting. In recent years, numerous experts have put forward the generalized extreme value distribution theory with stronger applicability and which has been widely used in fields such as climatic analysis and climatic change research.

1. Gumbel distribution (Extreme value I)

$G (z; μ, σ, ξ) = \exp {- \exp [- (\frac{z - μ}{σ})]}; - \infty < z < \infty$

(2.3)

2. Frechet distribution (Extreme value II)

$G (z; μ, σ, ξ) = {\begin{matrix} 0 & z \leq μ \\ \exp [- {(\frac{z - μ}{σ})}^{- 1 / ξ}] & z > μ \end{matrix}$

(2.4)

3. Weibull distribution (Extreme value III)

$G (z; μ, σ, ξ) = {\begin{matrix} \exp [- {(\frac{z - μ}{σ})}^{- 1 / ξ}] & z < μ \\ 0 & z \geq μ \end{matrix}$

(2.5)

In the formula, z is the extreme value, μ is the location parameter, σ is the scale parameter, and ξ is the shape parameter.

Each of these three extreme value distribution functions has its own characteristics. In the Weibull function, the distribution value has an upper limit, which means the maximum value should not exceed a certain value; the tail of the Frechet probability density distribution function is longer than that of the Gumbel probability density distribution function, which means higher probability of extreme values.

Given the location parameter and scale parameter, the above-mentioned three extreme value functions can be integrated and described with the generalized extreme value distribution theory of which the distribution function is

$G (z; μ, σ, ξ) = \exp {- {[1 + ξ (z - μ) / σ]}^{- 1 / ξ}}$

(2.6)

where if ξ < 0, the distribution function presents the Weibull distribution; if ξ approaches 0, the distribution function presents the Gumbel distribution; if ξ > 0, the distribution function presents the Frechet distribution. The integration of these three extreme value distribution functions breaks through the limitation of using only one extreme value distribution function.

See Table 2.2, “Extreme Wind Speed Statistics of Wind Measurement Masts.” Wind speed extreme values are mainly determined by 99% wind speed and 99.9% wind speed. Ninety-nine percent wind speed means that during a certain period of time the wind speed during 99% of the time is lower than this wind speed, or in other words, the wind speed in 1% of the time is higher than this wind speed. As a result, annually there are accumulatively 3.65 days when the wind speed is higher than this one. Similarly, 99.9% wind speed means that annually there are accumulatively 0.365 days, or 8.76 h, when the wind speed is higher than this one. These two indexes can reflect the extreme wind cases faced by wind farms.

It can be seen from Table 2.2 that for Qiaowan and Changma wind farm clusters there is still some margin between the 99.9% wind speed and the wind turbine's cutout wind speed of 25 m/s, which means it won't cause the frequent cutout of wind turbines or affect the security and stability of the power system; for Ganhekou wind farm cluster and Beidaqiao No. 13 wind measurement mast, the 99.9% wind speed is close to the cutout wind speed, which means the wind farms might start and stop frequently in a short cumulative time and shift between full-load power generation and cutout, forming a certain threat to the security and stability of the power system; for Beidaqiao No. 5 wind measurement mast, the 99.9% wind speed exceeds the cutout wind speed, which means the wind farms might start and stop frequently in a long cumulative time, forming a larger threat to the security and stability of the power system.

The impact of extreme wind cases on the power system is mainly manifested in its impact on the power system during the shift from the status of full-load power generation to cutout instead of during the cumulative downtime. As a result, the probability of extreme values seems even more critical. See Table 2.3, “Extreme Wind Speed Probability.”

Table 2.2

Extreme Wind Speed Statistics of Wind Measurement Masts (m/s)

Wind Farm Cluster	Wind Measurement Mast	99% Wind Speed	99.9% Wind Speed
Beidaqiao	Beidaqiao No. 5	19.6	27.8
	Beidaqiao No. 13	18.8	24.4
Ganhekou	Ganhekou No. 7	19.1	24.7
	Ganhekou No. 10	19.2	24.7
Changma	Changma No. 13	19	21.8
	Changma No. 17	18.6	21.8
Qiaowan	Qiaowan No. 5	17.1	20.2

Table 2.3

Extreme Wind Speed Probability

Wind Farm Cluster	Wind Measurement Mast	Probability of Wind Speed Higher than 25 m/s (%)
Beidaqiao	Beidaqiao No. 5	3
	Beidaqiao No. 13	2
Ganhekou	Ganhekou No. 7	3
	Ganhekou No. 10	4
Changma	Changma No. 13	3
	Changma No. 17	1
Qiaowan	Qiaowan No. 5	0

It can be learned from Table 2.3 that except for Qiaowan wind farm cluster, the wind speed in all other wind farm clusters has exceeded 25 m/s, of which the frequency of this wind speed in Ganhekou, 4%, is the highest.

2.1.2. Characteristics of Annual Distribution of Wind Power Generation

Wind power generation in Jiuquan Wind Power Base has the following characteristics:

1. This area has rich wind resources year-round. According to the data collected in Qiaowan, Ganhekou, Changma, and Beidaqiao wind measurement masts in Jiuquan, the daily average wind speed year-round is above 3 m/s. The number of days with the daily average wind speed at 3 m/s and above accounts for 51% of the whole year; the number of days with the daily average wind speed at 13 m/s and above accounts for 5% of the whole year.

2. Wind speed is highly seasonal. The average wind speed between March and May in Jiuquan is quite high, whereas the average wind speed between October and the following February is quite low.

3. Wind speed fluctuates sharply. In Qiaowan, Ganhekou, Changma, and Beidaqiao every month, and most days in a year the wind speed will fluctuate between approaching zero and rated wind speed.

Figure 2.3 and Figure 2.4 are the “Curve of Annual Distribution of Monthly Average Wind Speed” and “Curve of Annual Cumulative Probability of Daily Average Wind Speed” in Jiuquan, respectively; the data were collected between June 2008 and May 2009. Figure 2.5 is “Typical Daily Average Wind Speed Curve in a Month.”

2.1.3. Characteristics of Daily Distribution of Wind Power Generation

Strong wind power generation in Jiuquan Wind Power Base mainly appears in the lowest power consumption period at night; meanwhile, during the daytime wind power generation fluctuates sharply. See Figure 2.6, “Curve of Typical Daily Distribution of Wind Power Generation in Jiuquan.”

Figure 2.3 Curve of annual distribution of monthly average wind speed.

Figure 2.4 Curve of annual cumulative probability of daily average wind speed.

Figure 2.5 Typical daily average wind speed curve in a month.

Figure 2.6 Curve of typical daily distribution of wind power generation in Jiuquan.

2.2. Fluctuation and Randomness of Wind Power Generation

2.2.1. Fluctuation of Wind Power Generation

According to wind measurement data, most days in Jiuquan Wind Power Base the wind speed ranges between approaching zero and rated wind speed. Correspondingly, most days wind power generation fluctuates between approaching zero and rated output. See Figure 2.7, “Annual Distribution of Converted Daily Average Wind Power Generation.” It can be seen from Figure 2.7 that the daily average wind power generation in Jiuquan fluctuates quite sharply with the minimum value approaching zero and the maximum value approaching 24 h full load.

Figure 2.7 Annual distribution of converted daily average wind power generation.

2.2.2. Wind Power Generation Ramp Rate

Wind power generation ramp rate is:

$ramp rate = \frac{current wind power output - wind power output a moment earlier}{wind power output a moment earlier} \times 100 %$

(2.7)

According to statistics of the dispatch department, the maximum 1, 5, and 15 min wind power generation in Jiuquan Wind Power Base in March and April 2011 were 113, 206, 415, 229, 423, and 555 MW, respectively, accounting for 2.97, 5.41, and 10.89% and 5.56, 10.26, and 13.46% of the total installed wind power capacity, respectively.

According to 15 min wind power generation data of Jiuquan Wind Power Base, between January and June 2011, the maximum wind power generation ramp rate was 22.18% and the minimum ramp rate was 0%. The maximum 15 min wind power generation ramp rate of lower than 1% accounts for 13.97%; lower than 2%, 25.17%; lower than 3%, 34.30%; lower than 5%, 48.54%; lower than 10%, 69.22%; lower than 20%; 86.61%; lower than 100%, 99.35%.

2.2.3. Randomness of Wind Power Generation

2.2.3.1. Uneven wind power generation year-round

Take the wind measurement data collected in 2008 in Jiuquan Wind Power Base as an example. The daily average wind power generation in 6 consecutive days from August 9 to 14 reached or approached the rated output, while the daily average wind power generation in 6 consecutive days from August 21 to 26 was lower than the 20% rated output, and the daily average wind power generation in one or two days even approached 0. The daily average wind power generation in 4 days out of the 6 consecutive days from September 20 to 25 reached or approached the rated output, while the daily average wind power generation in 10 consecutive days from September 8 to 17 was lower than the 20% rated output.

The actual operation data of existing wind farms in Jiuquan Wind Power Base also prove that there might emerge the situation in which for several consecutive days the wind power generation output is high or low. See Figure 2.8 for EMS record. For 15 days from November 1 to 15 the wind power generation output is high, while from January 30 to February 14 the wind power generation output is low.

2.2.3.2. Wind power generation output on adjacent days varies greatly

August 25, 2009, and August 26, 2009, are typical adjacent days. The daily power generation capacity on these two days is almost identical, but the curves of wind power generation on these two days vary greatly from each other. See Figure 2.9 for details.

We analyzed the wind power generation of Jiuquan Wind Power Base first phase project based on wind measurement data collected from June 2008 to May 2009. See Figure 2.10, “Cumulative Probability Curve of Daily Average Output Change Rate on Adjacent Days.” It can be seen from Figure 2.10 that days when the daily average generation output change rate on adjacent days reach 50% and above account for about 15% of the total days. The maximum daily average generation output change rate on adjacent days is 91%.

Figure 2.8 High/Low wind power generation output for 15 consecutive days.

Figure 2.9 Wind power generation output on two typical adjacent days.

2.2.4. Wind Power Generation Probability Distribution

Select active power data on transformer primary side of all wind farms in 2009 and the sampling time of the analysis data is 10 min. We used the dfittool toolbox of the MATLAB software to fit the power data of six selected wind farms (see Table 2.4) with the Weibull distribution and the generalized extreme value distribution and found among wind power the 0 element accounts for too large a proportion. This is because the effective wind speed of wind turbines usually ranges between 3 and 25 m/s. If the wind speed is not within this range, then the output power of wind turbines will be 0. Therefore, the resulting wind power probability distribution is not consistent with the Weibull distribution and the generalized extreme value distribution. See Figure 2.11, “Power Probability Distribution in Changma Wind Farm.”

Figure 2.10 Cumulative probability curve of daily average output change rate on adjacent days.

Table 2.4

Wind Power Main Point Statistics (MW)

Wind Farm Cluster	Wind Farm Name	Median Power	Average Power	90% Power	99% Power	99.9% Power
Beidaqiao	Anxi	11.4	6.61	28.4	40	48.9
Ganhekou	Xiangyang	14.4	10.63	32.7	44.2	48.6
Ganhekou	Daliang	10.6	10.68	32.2	40.6	43.6
Wind farm cluster	Wind farm name	Median power	Average power	90% power	99% power	99.9% power
Changma	Changma (1)	8	9.96	28.8	43	43.6
	Sanshilijingzi	10.6	10.46	33.8	45.4	48
	Changma (2)	16.7	16.51	40.5	51.7	66

It can be seen from Figure 2.11 that since 0 power accounts for too large a proportion, it is impossible to fit the power data with the curve. After the 0 element is deleted, the fitting result is shown in Figure 2.12. Judging from the curve, the shape parameter of the Weibull distribution fitting ξ is 1.06334 and the standard deviation is 0.00307248; the scale parameter σ is 12.436 and the standard deviation is 0.0447734. The standard deviation of the scale parameter is too large, so it is inconsistent with the Weibull distribution. The shape parameter of the generalized extreme value distribution fitting ξ is 0.475705 and the standard deviation is 0.005168; the scale parameter σ is 5.675 and the standard deviation is 0.0245282; the location parameter μ is 5.71562 and the standard deviation is 0.0262282. The parameter error of the generalized extreme value distribution fitting is larger than that of the Weibull distribution fitting.

Figure 2.11 Power probability distribution in Changma wind farm.

Figure 2.12 Wind power fitting diagram with the 0 element deleted.

We used the dfittool toolbox of the MATLAB software to conduct statistical calculations on the power data of the six selected wind farms (with the 0 element deleted). See Table 2.4 for the calculation results.

The median wind power and average wind power reflect the power generating capability of wind farms. It can be seen from the statistical data in Table 2.4 that in terms of wind power generating capacity, Changma (2) is the largest, followed by Xiangyang and Anxi and Changma (1) is the smallest; in terms of wind resource distribution, wind resources are evenly distributed in Ganhekou and Beidaqiao while wind power varies severely in Changma wind farm cluster.

2.3. Correlation and Complementarity of Wind Power Generation

2.3.1. Correlation of Long timeScale Wind Power Generation

Geographically, wind farms in Jiuquan Wind Power Base are relatively concentrated. As a result, regarding long-time large-area wind, the power generation change trend in all wind farms is very close to each other. Although the geographical dispersion effect can reduce the correlation of wind power generation and improve complementarity, its effect is mainly concentrated within the range below the timescale of hour. Within the range of long timescale, wind power generation in different wind farms shows a high correlation between each other. As a result, the total wind power generation output in Jiuquan Wind Power Base fluctuates greatly.

We analyzed the wind power generation in Beidaqiao and Ganhekou wind farm clusters. See Figure 2.13 for the correlation of wind power generation in timescale of hour and above measured in Beidaqiao and Ganhekou Wind Farm Cluster between May 4 and May 10, 2009. In the long timescale, the wind power generation in these two wind farm clusters is highly correlated with each other.

Figure 2.13 Wind power generation correlation in timescale of hour and above.

In this section, we will discuss the wind power correlation between wind farms and wind farm clusters and between wind farms and the Jiuquan Wind Power Base. Specifically we study the correlation characteristics of short-term and long-term wind power in wind farms with different geographical locations in four categories, namely, 1, 2, 5 and 10 h.

2.3.1.1. Correlation between wind farms in one wind farm cluster and between wind farm clusters

We will take the wind power correlation between Changma (1) Wind Farm and Sanshilijingzi Wind Farm in Changma wind farm cluster as an example to analyze the wind power correlation. Figure 2.14 and Figure 2.17 are the correlation coefficient probability density distribution curve and probability cumulative distribution curve of wind power measured in Changma (1) Wind Farm and Sanshilijingzi Wind Farm in timescale of 1, 2, 5 and 10 h in 2009, respectively. The horizontal axis is the correlation coefficient, and the vertical axis is the probability density/probability. In this part we will use the 10-min-interval data to calculate the correlation coefficient in timescale of 1, 2, 5 and 10 h (Figures 2.15–2.17).

The longer the timescale is, the more the numerical distribution of correlation coefficient tends toward positive correlation and zero, which means that within the long-time timescale the wind power of different wind farms in the same wind farm cluster is highly positively correlated or unrelated with each other with the negative correlation weakening gradually; the shorter the timescale is, the more evenly the numerical distribution of correlation coefficient is distributed, which means that within the short-time timescale the wind power of different wind farm clusters reflects more randomness and mutual independence. However, since the two selected wind farms are in the same wind farm cluster and highly correlated with each other, with the increase of timescale the correlation coefficient approaches 1 more and more. What's more, in the distribution of correlation coefficient in various timescales 1 always dominates.

Figure 2.14 Correlation coefficient of Changma (1) wind farm and Sanshilijingzi wind farm in Changma wind farm cluster with an interval of 1 h. (a) Correlation coefficient probability density distribution; (b) Correlation coefficient probability cumulative distribution.

Figure 2.15 Correlation coefficient of Changma (1) wind farm and Sanshilijingzi wind farm in Changma wind farm cluster with an interval of 2 h. (a) Correlation coefficient probability density distribution; (b) Correlation coefficient probability cumulative distribution.

Figure 2.16 Correlation coefficient of Changma (1) wind farm and Sanshilijingzi wind farm in Changma wind farm cluster with an interval of 5 h. (a) Correlation coefficient probability density distribution; (b) Correlation coefficient probability cumulative distribution.

Figure 2.17 Correlation coefficient of Changma (1) wind farm and Sanshilijingzi wind farm in Changma wind farm cluster with an interval of 10 h. (a) Correlation coefficient probability density distribution; (b) Correlation coefficient probability cumulative distribution.

See Table 2.5 for the correlation of wind power between different wind farms in the same wind farm cluster and between different wind farm clusters in the timescale of 1, 2, 5 and 10 h.

In Table 2.5 the average value of correlation coefficient represents the high or low correlation of the wind power between different wind farm clusters. Within the range of all timescales, the overall correlation of wind power between different wind farm clusters is positive correlation with the difference lying in the strength of positive correlation. With the increase of timescale, the overall correlation between all wind farm clusters gradually becomes stronger. If different wind farms in the same wind farm cluster are located close to each other, the wind conditions in these wind farms are similar; due to the impact of location, temperature, and terrain; the wind speed and wind direction in different wind farm clusters vary greatly from one to another and therefore the wind power correlation is relatively weak. Particularly the wind power correlation coefficient in Ganhekou and Changma wind farm clusters is relatively small and concentrated between 0.11 and 0.14. In Table 2.5 the average value of the correlation coefficient in the timescale of 2 h is smaller than that in the timescale of 1 h because the wind farm wind power generation restricted by the power grid has a great impact on the correlation coefficient.

Table 2.5

Analysis of Average Value of Wind Power Correlation Coefficient of Different Wind Farms in the Same Wind Farm Cluster

Wind Farm	Timescale
Wind Farm	1 h	2 h	5 h	10 h
Xiangyang-Daliang	0.4969	0.6010	0.6232	0.6419
Changma-Sanshilijingzi	0.4877	0.5533	0.5580	0.5612
Beidaqiao-Ganhekou	0.1738	0.2653	0.2608	0.2632
Ganhekou-Changma	0.1173	0.1114	0.1212	0.1340

2.3.1.2. Correlation between wind farm cluster and Jiuquan wind power base

The power collection of all wind farm clusters is the total power of wind farm base. Now we are going to take the correlation between Changma wind farm cluster and Jiuquan Wind Farm Base as an example to analyze the correlation between wind farm cluster and wind power base. Figures 2.18–2.21 reflect the correlation in different timescales.

The analysis of correlation coefficient between wind farm cluster and wind power base is similar to the analysis of correlation coefficient between wind farms that are similar to each other, only that the correlation coefficient between wind farm cluster and wind power base is mainly concentrated between 0.6 and 1. Therefore, the wind power correlation between wind farm cluster and wind power base is relatively strong. What's more, the larger the correlation coefficient is, the greater the impact of the wind power of wind farm cluster on the total power of the wind power base is. See Table 2.6, “Average Value of Power Correlation Coefficient between Wind Farm Cluster and Wind Power Base.”

It can be seen from Table 2.6 that all the correlation coefficients are positive values. The correlation coefficient of wind power between Beidaqiao wind farm cluster and Jiuquan Wind Power Base is the smallest and has the smallest impact on Jiuquan Wind Power Base; both the correlation coefficient of wind power between Ganhekou wind farm cluster and Jiuquan Wind Power Base and that between Changma wind farm cluster and Jiuquan Wind Power Base are relatively large, which means they have a larger impact on Jiuquan Wind Power Base; with the increase of the timescale of correlation, the correlation coefficient also constantly increases, but with decreasing degree; when the timescale increases to a certain value, the correlation coefficient will remain unchanged.

Figure 2.18 Correlation coefficient in timescale of 1 h. (a) Correlation coefficient probability density distribution; (b) Correlation coefficient probability cumulative distribution.

Figure 2.19 Correlation coefficient in timescale of 2 h. (a) Correlation coefficient probability density distribution; (b) Correlation coefficient probability cumulative distribution.

Figure 2.20 Correlation coefficient in timescale of 5 h. (a) Correlation coefficient probability density distribution; (b) Correlation coefficient probability cumulative distribution.

Figure 2.21 Correlation coefficient in timescale of 10 h. (a) Correlation coefficient probability density distribution; (b) Correlation coefficient probability cumulative distribution.

Table 2.6

Average Value of Power Correlation Coefficient between Wind Farm Cluster and Wind Power Base

Wind Farm Cluster	Time Interval
Wind Farm Cluster	1 h	2 h	5 h	10 h
Beidaqiao	0.2805	0.3558	0.3546	0.3636
Ganhekou	0.7163	0.7661	0.7723	0.7753
Changma	0.7162	0.7660	0.7723	0.7773

2.3.2. Complementarity of Wind Power Generation in Short Timescale

2.3.2.1. Analysis of complementarity of wind farm wind power generation

In Jiuquan Wind Power Base first phase project, 5.8 GW wind power is mainly comprised of 200 MW wind farms. Now we are going to take the 200 MW wind farms as an example to analyze the wind power generation characteristics of wind farms. Each wind farm in Jiuquan Wind Power Base has approximately 134 wind turbines with rated capacity of 1.5 MW. The typical layout of the wind farms is the square of 11 rows × 12 wind turbines with a row space of 900 m and a separation distance of 300 m. It takes 12.5 min for a gust in the positive direction with the ideal wind speed of 12 m/s (the median of rated wind speed range between 10.5 and 13 m/s) to pass through a wind farm. The wind peak and wind valley reach wind turbines at different times. Wind turbines in different locations of the wind direction are complementary to each other, reducing the wind farm wind power generation change rate in the timescale below a few minutes. At this time the wind farm wind power generation change rate is 8%/min (16 MW). See Figure 2.22 for details. In addition, the randomness of wind speed strengthens the complementarity of wind turbines within the wind farm, which is conducive to reducing wind farm wind power generation change rate.

Figure 2.22 Wind farm generation change on the condition of ideal wind speed.

2.3.2.2. Analysis of complementarity of wind power generation of wind farm clusters and Jiuquan wind power base

The wind power generation characteristics of wind farm clusters and Jiuquan Wind Power Base are mainly influenced by geographical dispersion effect among wind farms. Wind farms of Jiuquan Wind Power Base first phase project are divided into four wind farm clusters with an east-west span of about 105 km and a south-north span of 40 km. Given the wind speed is 12 m/s, it takes 14–49 min for the wind to blow through the single wind farm cluster from different directions. Given the annual average wind speed in Jiuquan is 5–6.5 m/s, it takes 34 min to 2 h for the wind to blow through the single wind farm cluster from different directions. In other words, the timescale of single wind farm cluster wind power generation change reaches dozens of minutes to several hours. Due to the geographical dispersion effect among wind farms in wind farm clusters, the wind speed in different wind farms reaches the peak and valley at different times; the largest generation change rate in different wind farms appears at different times; the wind farm cluster generation change rate in the timescale below several hours is reduced. Even if bad conditions are considered, for example, the wind speed in wind farm clusters increases from 0 to 12 m/s, then the generation change rate per minute in a single wind farm cluster is 2.04%∼7.143%; for the whole Jiuquan Wind Power Base, the generation change rate per minute is reduced to 0.69%∼1.8%.

In the timescale below hour, wind turbine generation and wind farm generation are complementary to each other to a certain degree, which reduces the total generation change rate in Jiuquan Wind Power Base. Due to the limited distance between wind farms, this kind of complementarity is mainly reflected within the range of short timescale.

In case of strong winds or low winds in Jiuquan Wind Power Base, the wind peak passes wind farms in different locations successively. As a result, the generation change rate of various wind farms differs and the dispersion effect among wind farms reduces the total generation change rate of Jiuquan Wind Power Base. Now we are going to select some typical cases when the wind speed increases and decreases to analyze the generation of Jiuquan Wind Power Base.

2.3.2.3. Simulating wind power generation complementarity based on wind measurement data

Shown in Figure 2.23 are the curves of generation of Jiuquan Wind Power Base and various wind farm clusters.

Generation change rate is defined as:

$Generation change rate = \frac{| current output - output at a previous time point |}{rated installed capacity} \times 100 %$

(2.8)

See Figure 2.24 for the generation change rate and total generation change rate of Jiuquan Wind Power Base and all wind farm clusters at this time. The time with the total generation change rate exceeding 10%/10 min accounts for only 14% of the ramp time; by comparison, in some wind farm clusters the time with the generation change rate exceeding 10%/10 min accounts for 64% of the ramp time. The proportion of the time with the generation change rate exceeding 10%/10 min to the total time of all wind farm clusters is as follows: 18% for Beidaqiao wind farm cluster, 0 for Changma wind farm cluster, 13% for Ganhekou wind farm cluster, and 45% for Qiaowan wind farm cluster.

Shown in Figure 2.25 are the curves of generation of Jiuquan Wind Power Base and all wind farm clusters when the wind speed in Changma wind farm cluster and Ganhekou wind farm cluster reduces.

See Figure 2.26 for the generation change rate and total generation change rate of Jiuquan Wind Power Base and all wind farm clusters at this time.

Figure 2.23 Curves of Jiuquan wind power base and wind farm clusters when the wind speed increases.

Figure 2.24 Generation change rate and total generation change rate of Jiuquan wind power base and all wind farm clusters when the wind speed increases.

Figure 2.25 Curves of generation of Jiuquan wind power base and all wind farm clusters when the wind speed in Changma wind farm cluster and Ganhekou wind farm cluster reduces.

Figure 2.26 Generation change rate and total generation change rate of Jiuquan wind power base and all wind farm clusters when the wind speed in Changma wind farm cluster and Ganhekou wind farm cluster reduces.

In Jiuquan Wind Power Base the time with the total generation change rate exceeding 3%/10 min accounts for only 19% of the total time. The proportion of the time with the generation change rate exceeding 3%/10 min to the total time in all wind farm clusters is as follows: 46% for Beidaqiao wind farm cluster, 15% for Changma wind farm cluster, 38% for Ganhekou wind farm cluster, and 11% for Qiaowan wind farm cluster.

2.4. Upstream and Downstream Effect of Wind Power Generation

2.4.1. Upstream and Downstream Relationship of Wind Power Resources

We selected Ganhekou No. 7 wind measurement mast and Qiaowan No. 5 wind measurement mast to conduct the wind power upstream and downstream analysis from August 27 to 29, 2008. See Figure 2.27 for wind speed data.

A common method used to calculate the upstream and downstream effect is to stagger the time of collecting wind measurement data at these two wind measurement masts with a certain time interval and then calculate the correlation coefficient between these two groups of wind measurement data. The largest correlation coefficient between two groups of data collected with a certain time interval indicates that for similar wind conditions it takes this time interval for the wind to pass from one wind farm to another. See Figure 2.28 for the correlation coefficient between the two groups of wind measurement data collected at Ganhekou No. 7 wind measurement mast and Qiaowan No. 5 wind measurement mast with a certain time interval. The horizontal ordinate represents the interval between the time of collecting wind measurement data at Ganhekou No. 7 wind measurement mast and the time of collecting wind measurement data at Qiaowan No. 5 wind measurement mast. Positive values represent the former precedes the latter while negative values represent the opposite.

Figure 2.27 Wind data collected at Ganhekou No. 7 wind measurement mast and Qiaowan No. 5 wind measurement mast.

Figure 2.28 Correlation coefficient between two groups of wind measurement data collected at Ganhekou No. 7 wind measurement mast and Qiaowan No. 5 wind measurement mast with a certain time interval.

It can be seen from Figure 2.28 that the time of collecting wind measurement data at Ganhekou No. 7 wind measurement mast is 110 min before the time of collecting wind measurement data at Qiaowan No. 5 wind measurement mast and that the correlation coefficient between these two groups of data collected with a time interval of 110 min is the largest, which can indicate that it takes 110 min for the west wind to pass from Ganhekou No. 7 wind measurement mast to Qiaowan No. 5 wind measurement mast.

See Figure 2.29, “Wind Direction Progress at Ganhekou No. 7 Wind Measurement Mast and Qiaowan No. 5 Wind Measurement Mast.” By comparing Figure 2.27 and Figure 2.29 we can find that in Figure 2.27 on the horizontal ordinate after 150 min the curve of wind measurement data collected at Ganhekou No. 7 wind measurement mast is ahead of those collected at the Qiaowan No. 5 wind measurement mast. By observing Figure 2.29 we will find on the horizontal ordinate after 150 min that the wind is indeed the west wind, which is consistent with intuition. It indicates clear upstream and downstream relationship of the wind power resources.

Figure 2.29 Wind direction progress of Ganhekou No. 7 wind measurement mast and Qiaowan No. 5 wind measurement mast.

See Figure 2.30, “Wind Rose Plot of Ganhekou No. 7 Wind Measurement Mast and Qiaowan No. 5 Wind Measurement Mast.”

Then we selected Ganhekou No. 7 wind measurement mast and Qiaowan No. 5 wind measurement mast on which to conduct the wind power upstream and downstream analysis from September 7 to 8, 2008. See Figure 2.31 for wind speed data.

See Figure 2.32, “Correlation Coefficient between Two Groups of Wind Measurement Data Collected at Qiaowan No. 5 Wind Measurement Mast and Changma No. 13 Wind Measurement Mast with a Certain Time Interval.” The time interval ranges between −300 and 300 min.

It can be seen from Figure 2.32 that the time of collecting wind measurement data at Ganhekou No. 7 wind measurement mast is −120 min before (or 120 min after) the time of collecting wind measurement data at Qiaowan No. 5 wind measurement mast and that the correlation coefficient between these two groups of data collected with a time interval of 110 min is the largest, which can indicate it takes 120 min for the south wind to pass from Changma No. 13 wind measurement mast to Qiaowan No. 5 wind measurement mast.

See Figure 2.33, “Wind Direction Progress of Qiaowan No. 5 Wind Measurement Mast and Changma No. 13 Wind Measurement Mast” and Figure 2.34, “Wind Rose Plot of Qiaowan No. 5 Wind Measurement Mast and Changma No. 13 Wind Measurement Mast.” By observing Figure 2.33 and Figure 2.34 we find that the dominating wind is generally the south wind, which reflects the south wind suddenly appearing at Changma No. 13 wind measurement mast and then passing to Qiaowan No. 5 wind measurement mast. This indicates the clear upstream and downstream relationship of the wind power resources.

Figure 2.30 Wind rose plot of Ganhekou No. 7 wind measurement mast and Qiaowan No. 5 wind measurement mast. (a) Ganhekou No. 7 wind measurement mast; (b) Qiaowan No. 5 wind measurement mast.

Figure 2.31 Wind data collected at Qiaowan No. 5 wind measurement mast and Changma No. 13 wind measurement mast.

Figure 2.32 Correlation coefficient between two groups of wind measurement data collected at Qiaowan No. 5 wind measurement mast and Changma No. 13 wind measurement mast and with a certain time interval.

Figure 2.33 Wind direction progress of Qiaowan No. 5 wind measurement mast and Changma No. 13 wind measurement mast.

Figure 2.34 Wind rose plot of Qiaowan No. 5 wind measurement mast and Changma No. 13 wind measurement mast. (a) Qiaowan No. 5 wind measurement mast; (b) Changma No. 13 wind measurement mast.

2.4.2. Upstream and Downstream Relationship of Wind Power Generation

2.4.2.1. Upstream and downstream relationship of wind power generation of different wind farms in the same wind farm cluster

We studied the upstream and downstream relationship between Xiangyang wind farm and Daliang wind farm in the Ganhekou wind farm cluster and then analyzed the upstream and downstream relationship of generation between wind farms in the same wind farm cluster based on the upstream and downstream relationship of wind speed. Since in wind farms there might emerge cases such as overhaul and generating unit tripping due to too small wind speed, we selected data collected at two wind farms with nonzero output power from November 17 to 18, 2009. Shown in Figure 2.35 is the generation of the two wind farms during this period.

See Figure 2.36, “Correlation Coefficient between Two Groups of Wind Measurement Data Collected at Xiangyang Wind Farm and Daliang Wind Farm with a Certain Time Interval.” When the generation of Xiangyang wind farm is put off for 60 min, the correlation between it and the generation of Daliang wind farm is the largest, being 0.718. However, it cannot indicate the relationship between the generation of these two wind farms is the upstream and downstream relationship with a time interval of 60 min because suppose the average wind speed is 7–8 m/s, the distance with a time interval of 60 min exceeds the distance between two wind farms (the farthest distance between two wind farms in the same wind farm cluster is 10 km and generally the distance is 5–6 km). It should be the result of the interaction of factors such as terrain and restriction on wind power integration by the power grid.

Now we are going to take the upstream and downstream relationship between Changma wind farm and Sanshilijingzi wind farm in the Changma wind farm cluster as another example. See Figure 2.37 for the generation of these two wind farms from November 17 to 18, 2009.

Figure 2.35 Generation of Xiangyang wind farm and Daliang wind farm.

Figure 2.36 Correlation coefficient between two groups of wind measurement data collected at Xiangyang wind farm and Daliang wind farm with a certain time interval.

Figure 2.37 Generation of Changma wind farm and Sanshilijingzi wind farm.

Figure 2.38 Correlation coefficient between two groups of wind measurement data collected at Changma wind farm and Sanshilijingzi wind farm with a certain time interval.

See Figure 2.38, “Correlation Coefficient between Two Groups of Wind Measurement Data Collected at Changma Wind Farm and Sanshilijingzi Wind Farm with a Certain Time Interval.” When the generation of Changma wind farm is put off for 10 min, the correlation between it and the generation of Sanshilijingzi wind farm is the largest, being 0.8443. It indicates the relationship between the generation of these two wind farms is the upstream and downstream relationship with a time interval of 10 min because suppose the average wind speed is 7–8 m/s, the distance with a time interval of 10 min is identical to the distance between two wind farms (the distance between two wind farms is 5–6 km). The correlation coefficient between these two groups of wind measurement data collected at these two wind farms with a time interval of 10 min is larger than that between Xiangyang wind farm and Daliang wind farm in the Ganhekou wind farm cluster. So the correlation between these two wind farms is stronger.

2.4.2.2. Upstream and downstream relationship of generation between wind farm clusters

Now we are going to take Ganhekou and Changma wind farm clusters as an example to study the upstream and downstream relationship of generation between them. Shown in Figure 2.39 is the generation of these two wind farm clusters from November 8 to 10, 2009.

See Figure 2.40, “Correlation Coefficient between Two Groups of Wind Measurement Data Collected at Ganhekou Wind Farm and Changma Wind Farm with a Certain Time Interval.” When the time of collecting wind measurement data at Ganhekou wind farm cluster is 40 min before the time of collecting wind measurement data at Changma wind farm cluster, the correlation coefficient between these two groups of data collected at these two wind farm clusters is the largest. Given the distance and average wind speed, the upstream and downstream relationship between these two wind farm clusters conforms to reality. Compared with the upstream and downstream relationship between wind farms in the same wind farm cluster, the correlation coefficient between upstream and downstream wind farm clusters is smaller, being 0.597.

Figure 2.39 Generation of Ganhekou wind farm cluster and Changma wind farm cluster.

Figure 2.40 Correlation coefficient between two groups of wind measurement data collected at Ganhekou wind farm and Changma wind farm with a certain time interval.

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Table of Contents for Chapter 2. Analysis of Wind Power Characteristics

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