Comprehensive assessment of wind resources and the low-carbon economy: An empirical study in the Alxa and Xilin Gol Leagues of inner Mongolia, China

Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

Contents lists available at ScienceDirect

Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Comprehensive assessment of wind resources and the low-carbon economy: An empirical study in the Alxa and Xilin Gol Leagues of inner Mongolia, China He Jiang a, Jianzhou Wang b,n, Yao Dong c, Haiyan Lu d a

Department of Statistics, Florida State University, Tallahassee, FL 32306-4330, USA School of Statistics, Dongbei University of Finance and Economics, Dalian 116025, China c School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China d Faculty of Engineering and Information Technology, University of Technology, Sydney, Australia b

art ic l e i nf o

a b s t r a c t

Article history: Received 10 November 2013 Received in revised form 6 May 2015 Accepted 26 May 2015

Due to atmospheric pollution from fossil fuels, the reduction of wind turbine costs, and the rise of the lowcarbon economy, wind energy conversion systems have become one of the most significant forms of new energy in China. Therefore, to reduce investment risk and maximize profits, it is necessary to assess wind resources before building large wind farms. This paper develops a comprehensive system containing four steps to evaluate the potential of wind resources at two sites in Xilin Gol League and at additional two sites in Alxa League of Inner Mongolia, China: (1) By calculating the total scores of three indexes, including the effective wind power density (EWPD), wind available time (WAT) and population density (PD), an indexes method is applied to assess the theoretical wind energy potential from 2001 to 2010. (2) To judge the fluctuations in the wind speed, the Fisher optimal partition method and the Jonckheere–Terpstra test are used to analyze the changes in the average monthly and yearly wind speeds from 2001 to 2010. (3) Three probability density functions, i.e., Weibull, Gamma and Lognormal, are used to assess the wind speed frequency distribution in 2010. To enhance the evaluation accuracy, three intelligent optimization parameter estimation algorithms, i.e., the particle swarm optimization algorithm (PSO), differential evolution algorithm (DE) and ant colony algorithm (ACO), are used to estimate the parameters of these distributions. (4) It is helpful to analyze the wind characteristics when assessing wind resources and selecting wind turbines. Therefore, the optimal frequency distribution based on the best parameter estimation method can be chosen to calculate the wind power density, the most probable wind speed and the wind speed carrying the maximum energy. The experimental results show that Site 1 and Site 4 are more suitable for large wind farms than Site 2 or Site 3. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Low-carbon economic wind power development Theoretical wind energy potential Fluctuations in wind speed Wind speed frequency distribution Wind characteristics

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Our contribution and innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Assessment of the theoretical wind energy potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Description of the assessment method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Effective wind power density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Wind available time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. Population density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Analysis of the theoretical wind energy potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Abbreviations: EWPD, effective wind power density; WAT, wind available time; PD, population density; MM, method of moments; MLE, maximum likelihood estimation; PSO, particle swarm optimization algorithm; DE, differential evolution algorithm; ACO, ant colony algorithm n Corresponding author. Tel.: þ 8615339864602; fax: þ 8641184710484. E-mail address: [email protected] (J. Wang). http://dx.doi.org/10.1016/j.rser.2015.05.082 1364-0321/& 2015 Elsevier Ltd. All rights reserved.

1305 1309 1309 1310 1310 1310 1310 1311 1312

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

1305

Assessment of the fluctuations in the wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1313 4.1. Fisher optimal partition method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 4.1.1. Introduction of the assessment method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 4.1.2. Analysis of the stability of the average monthly wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 4.2. Jonckheere–Terpstra test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 4.2.1. Review of the statistical test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 4.2.2. Analysis of the stability of the average yearly wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 5. Assessment of the wind speed frequency distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 5.1. Three probability density functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 5.1.1. The Weibull distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 5.1.2. The Gamma distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315 5.1.3. The Lognormal distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315 5.2. Two traditional parameter estimation methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315 5.3. Three intelligent optimized parameter estimation algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315 5.3.1. Particle swarm optimization algorithm (PSO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315 5.3.2. Differential evolution algorithm (DE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316 5.3.3. Ant colony optimization algorithm (ACO). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317 5.4. Discussion and analysis of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317 5.4.1. Evaluation criteria of the estimated methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317 5.4.2. Comparison between the traditional and intelligent parameter estimation algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317 5.4.3. Comparison among three frequency distribution functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1318 6. Assessment of the wind power density, most probable wind speed and wind speed carrying the maximum energy . . . . . . . . . . . . . . . . . . . 1318 6.1. Definition of the wind characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1318 6.2. Calculation results using the wind characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1318 7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1318 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1319 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1319

4.

1. Introduction China is currently the world’s largest energy producer and consumer. It is also one of the few countries in the world with coal as its main energy source: Coal accounts for approximately 75% of the national energy production. Currently, coal resources are mainly used for thermal power, and thermal power provides the majority of the electric energy supply. In 2011, thermal power generation accounted for approximately 80.8% of all types of generation capacity. Therefore, it is generally considered that the proportion of coal in the energy and electricity supply is quite large. In addition, coal mining and burning have large negative environmental impacts [1,2]. To be specific, the national electricity coal consumption rate was approximately 333 g/ kW h in 2010, while the pollutant emissions produced per ton of coal burned are very large and the governance costs of the various pollutants are pretty high (see Table 1). In fact, China is already ranked the world’s second largest producer of carbon emission, behind only the United States. It is estimated that by 2020 the emissions of carbon dioxide and other greenhouse gases will surpass that of the United States’ [3]. Consequently, based on increasingly serious environmental damage, the development of the low-carbon economy and renewable energy is a critical and effective way to reduce environmental pollution, promote energy conservation and generate green electricity. Wind energy, which is a type of free, clean and environmentally friendly energy, is currently used by many leading developed and developing nations to fulfill their electricity demands. The wind energy situations all around the world can be seen in Fig. 1 [4,5]. Wind power has some advantages, including a short construction period, large reserves, renewable, nonpolluting, flexible

Table 1 Pollutant emission rates and control costs of the coal-fired power plants.

Pollutant emission rates (kg/t) Pollutant control costs (Yuan/kg)

XO2

NOX

CO

CO2

Dust

Dregs

18 6.53

8 6.29

17.31 1.00

0.26 0.02

110 0.12

30 0.10

investment and small operations and management staff compared with traditional power sources. The cost of producing wind energy has come down steadily over the last few years. The main cost is the installation of wind turbines, which is far below the cost of other renewable energy power generation techniques, such as biomass and solar. Moreover, wind turbines are an excellent method for the generation of energy in remote locations, such as mountain communities and remote countrysides. Considering these advantages of wind power, exploring new areas in which build wind farms is necessary. China’s wind power industry emerged over 20 years ago and entered a phase of particularly rapid growth in 2005 (see Fig. 2) [6]. To reduce investment risk and maximize profits, accurate wind energy resource assessment plays a vital role in wind farm planning. A large number of researchers have paid significant attention to wind energy assessment. Generally, a probability density function is a useful method to describe wind speed frequency distributions. For example, Ucar and Balo employed a Weibull distribution to perform wind energy potential assessments using the wind speed data collected by the six meteorological stations in Turkey and calculated the yearly energy output and capacity factor for four different turbines [7]. Pishgar-Komleh et al. used Weibull and Rayleigh distributions to evaluate wind speed and power density in Firouzkooh county of Iran [8]. Chang applied several types of mixed probability functions including the bimodal Weibull distribution and the mix Gamma–Weibull function to estimate wind energy potential in Taiwan [9]. The assessment of wind resources on a wind farm is the basis of wind power projects. Accurate and reasonable descriptions of wind energy resources will directly affect the wind turbine selection, generation capacity estimation and economic benefits. In many of China’s completed wind farms, there are significant differences between the actual generation capacity and the designed capacity [10]. One of the main reasons is the inaccuracy of traditional assessment method for the potential of wind resources. Therefore, this paper proposes a comprehensive method containing four steps to assess the potential of wind resources in Inner Mongolia of

1306

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

Fig. 1. Wind energy resource distribution in the world.

Fig. 2. Wind power installed capacity in China from 2000 to 2011.

China, which can obtain more accurate and thorough evaluation results. It consists of four steps: (1) The first step is to evaluate the theoretical wind energy potential as discussed in Section 3. The theoretical wind energy potential can reflect the abundance of wind energy resources. This metric is usually considered one of the most significant factors in the evaluation of wind energy development potential, and it is also vital to microsite a wind farm. Based on the theoretical potential assignment, an indexes method can be

adopted to calculate the total score of three indexes: effective wind power density (EWPD, unit: W/m2), wind available time (WAT, unit: h) and population density (PD, unit: people/km2). The higher the score is, the higher the theoretical wind energy potential is. (2) The second step is to evaluate the fluctuations in the wind speed as discussed in Section 4. Due to the significant randomness and volatility of wind speed, wind power penetration presents drastic fluctuations when connected to the power grid. The

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

1307

Fig. 3. Flow chart of the comprehensive method.

fluctuations in the wind power penetration into the power system will threaten the security and stability of the power system and even lead to power grid collapse [11]. Consequently, it is very important to assess the fluctuations in the wind speed. Two statistical approaches, i.e., the Fisher optimal partition method and the Jonckheere–Terpstra test, can be used to determine if

average monthly and yearly wind speeds from 2001 to 2010 experience significant changes. The Fisher optimal partition method is a statistical clustering approach for many ordering sample. If the F-statistic is less than the critical value F α , each category has a significant difference. Otherwise, each category is similar. The Jonckheere–Terpstra test is a non-parametric method

1308

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

Fig. 4. Wind power density in Inner Mongolia.

Fig. 5. Four-time daily wind speed data from 2001 to 2010 at four sites.

for testing whether samples originate from the same distribution. If a probability p-value is greater than the given significant level α ðα ¼ 0:05Þ, the samples have the same distribution. Otherwise, there are significant differences between those samples. (3) The third step is to evaluate the wind speed frequency distribution using three probability density functions, i.e., the Weibull, Gamma and Lognormal distributions, as discussed in Section 5. Wind energy has high randomness, so the wind speed frequency distribution can be used to describe the statistical properties of wind energy [12]. It is helpful to select suitable wind turbines and estimate the generation capacity for the accurate description of wind speed frequency distributions. During the third step, to

obtain the best assessment results, three intelligent optimization algorithms, i.e., particle swarm optimization (PSO), differential evolution (DE) and ant colony optimization (ACO), are employed to estimate the parameters of the probability density functions. The main idea of intelligent optimization algorithms is to obtain the optimal parameters of different distributions in a given interval by minimizing the objective function. By comparing with the two traditional parameter estimation methods, i.e., the method of moments (MM) and maximum likelihood estimation (MLE), it is found that the evaluation performance of the distributions based on the three intelligent optimization parameter estimation algorithms are more accurate. The Weibull distribution based on the DE

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

parameter estimation algorithm presents the best results. (4) The last step in the evaluation of the wind characteristics is the calculation of the wind power density, the most probable wind speed and the wind speed carrying the maximum energy for the wind turbine selection using the optimal probability density function (Weibull distribution based on the DE parameter estimation algorithm) in Section 6. Section 7 concludes this study. The detailed assessment process can also be seen in Fig. 3. The Inner Mongolia Autonomous Region is the province with the largest wind energy resources; its available wind energy exploitation capacity is 101 MW, accounting for approximately 40% of the available wind energy exploitation capacity in the nation and ranking first in China [13]. Xilin Gol League is situated in the central part of Inner Mongolia. According to a preliminary estimate, Alxa League is approximately 210 MW, taking up 20% of the total wind energy reserves in the Inner Mongolia Autonomous Region [13]; the wind energy reserves in Xilin Gol League account for approximately 35% of the total reserves in Inner Mongolia [14]. Fig. 4 shows the wind power density in Inner Mongolia, including Xilin Gol League and Alxa League [15]; Four-time daily wind speeds from 2001 to 2010 are collected at four sites (see Fig. 5).

Table 2 Criterion and results of the wind energy theoretical potential. Criterion of the assessment method EWPD (W/m2) WAT (h) PD (People/km2) Score P i 100 4 200 45000 o 700 75 100–200 4000–5000 — 50 60–100 2000–4000 — 25 o 60 o 2000 Z 700 The total score P Total The grade of wind energy 95–100 I The highest potential area 75–94 II The second highest potential area 50–74 III Medium potential area 26–49 IV Low potential area 0–25 V No potential area Results of the assessment method Alxa League Xilin Gol League Parameters Site 1 Site 2 Site 3 Site 4 ρ (kg/m3) 1.225 1.225 1.225 1.225 EWPD (W/m2) 439.5877 228.5174 284.1413 565.198 N (Day) 3364 3269 3454 3553 WAT (h) 8073.6 7845.6 8289.6 8527.2 P (People) 180,000 180,000 1000,000 1000,000 A (km2) 270,000 270,000 202,580 202,580 0.67 0.67 4.94 4.94 PD (P/km2) ith index score

2. Our contribution and innovation Nomenclature The contribution and innovation of this study are as follows: ● There are significant differences between the actual generation capacity and the designed capacity in many of China’s completed wind farms, which are caused by the inaccuracies of the traditional assessment methods of potential wind resources. Thus, this paper develops a comprehensive method containing four steps to assess the potential of wind resources in Inner Mongolia of China. Through experimental simulation, it can obtain more accurate assessment results; ● By calculating the total score of three indexes, i.e., the effective wind power density (EWPD, unit: W/m2), wind available time (WAT, unit: h) and population density (PD, unit: people/km2), an indexes method is developed to assess the theoretical wind energy potential, which makes the assessment of wind resources more thorough; ● Two statistical approaches, i.e., the Fisher optimal partition method and Jonckheere–Terpstra test, are used for the first time to analyze the fluctuations in the average monthly and yearly wind speeds in Inner Mongolia of China, which directly effects the safe operation of wind power integrated into power gird; ● Three probability density functions, i.e., the Weibull, Gamma and Lognormal distributions, are applied to evaluate wind speed frequency distribution. To improve the evaluation of the accuracy, three intelligent optimization algorithms, i.e., particle swarm optimization (PSO), differential evolution (DE) and ant colony optimization (ACO), are used to estimate the parameters of these three distributions. In comparison with the traditional parameter estimation methods, these three intelligent parameter estimation algorithms produce more accurate wind speed frequency distributions; ● Based on the comparison analysis, the Weibull distribution using the DE parameter estimation algorithm shows the best evaluation performance of the wind speed frequency distribution, i.e., it is closest to the real wind speed frequency. Therefore, this method can be employed to calculate the wind characteristics (i.e., the wind power density, the most probable wind speed and the wind speed carrying the maximum energy), which is beneficial to realizing the wind energy features and the selection of the wind turbines.

1309

NP population size of DE D length of the chromosome F mutation facto CR crossover rate X r2 ; X r3 random chosen vectors of DE yi mutant vector of DE uji parent of DE xji offspring of DE NCHO the number of permissible iteration ant the number of ants d dimension of the independent variables X j ðj A ½1; mÞ location of elite ants X i ði ¼ 1; 2; …; mÞ location of the common ants every group X 0i location of the ants after update H height R reference height VH wind speed at height H VR wind speed at height R α Power law exponent P wind power density V MP most probable wind speed V OP wind speed carrying maximum energy ρH low atmospheric density ρ air density vi average daily wind speed Pi ith index score P Total the total score of the development potential PE regional population A regional area βðkÞ non-negative slope Bðn; mÞ objective function of classification J T statistic Z the standardized test statistic v 4-time daily wind speed c Weibull scale parameter k Weibull, Gamma shape parameter θ Gamma scale parameter μ variance of v β mean value of v

1310

N xxi vvi c1 ; c2 w pbest gbest

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

density (EWPD, unit: W/m2), wind available time (WAT, unit: h) and population density (PD, unit: people/km2) are applied.

search space of PSO the position of the particle the velocity of the particle positive acceleration constants inertia weight current best position global best position

3. Assessment of the theoretical wind energy potential Wind is the flow of gases on a large scale. Wind speed, or wind flow velocity, is a fundamental atmospheric rate, which is caused by air moving from a high pressure to a low pressure. Wind energy is produced by wind turbines. Wind power is extracted from airflows using wind turbines or sails to produce mechanical or electrical power. In fact, the development of wind energy in an area depends on the abundance of the wind energy resources, which is the premise for the large-scale use of wind power. The theoretical wind energy potential can reflect the abundance of the wind energy resources, so it can be considered one of the most significant factors in the evaluation of the wind energy development potential.

3.1.1. Effective wind power density Wind energy, which is affected by weather, climate, topography, etc., is not a stable energy source and has seasonal changes. Due to the technological limitations of wind turbines, wind power is not available when the wind speed is too high or too low. Specifically, when the wind speed is less than 3 m/s, wind turbines cannot start; when the wind speed exceeds 20 m/s, the security of the wind turbine will be threatened; therefore, wind turbines are available only when the wind speed is within the range 3–20 m/s. When the average daily wind speed is 3 to 20 m/s, the kinetic power can be called the effective wind power density (EWPD, unit: W/m2). According to the “Wind resource assessment handbook” written by the United States Renewable Energy Laboratory [17] and the “Assessment methods of wind energy resources in wind farms of China” [18], EWPD can be calculated as follows: EWPD ¼

n 1 X ρ U v3i 2n i ¼ 1

ð2Þ

ð1Þ

where ρ is air density, vi is the average daily wind speed between 3 and 20 m/s, and n is the total number of days of the 10-year average daily wind speed between 3 and 20 m/s. Four-times daily wind speed data within 3–20 m/s are used to calculate the average daily wind speed. If the wind speed data exceed this interval, we would delete it. Therefore, when we calculate EWPD, the wind speed data over 10 years should be used. After calculating EWPD, the corresponding score P 1 can be reached based on Table 2.

where P i is ith index score (unitless), P Total is the total score of the wind energy development potential (unitless), and m is the number of indexes. After calculating P Total value, the theoretical wind energy potential can be confirmed based on the criterion of Table 2. In this section, three indexes, i.e., the effective wind power

3.1.2. Wind available time When the wind speed is between 3 and 20 m/s, the sustainable utilization for hours is called the wind available time (WAT, unit: h). According to the “Wind resource assessment handbook” written by the United States Renewable Energy Laboratory [17]

3.1. Description of the assessment method The evaluation method follows [16]: P Total ¼

m 1X P mi¼1 i

Table 3 Statistical results of the Fisher optimal partition method and the Jonckheere–Terpstra test. Alxa League Daily

Site 1

Fisher optimal partition method (n¼ 10, m is the number of optimal Classification 2001–2002, 2003, partitions, B(n, m) is the objective function of classification) 2004, 2005, 2006, 2007, 2008–2010 m 7 B(n, m) 15.7346 F statistic 2.723 F(m  1, n– 8.94 m) Test Fo F(6, 3) Result Stable Alxa League Site 1 Yearly Jonckheere–Terpstra Test (significant level α ¼ 0:05) Yearly Yearly variance mean value 2001 7.5357 8.5574 2002 7.793 9.95 2003 7.2144 12.0591 2004 7.978 10.3939 2005 7.7569 10.8999 2006 7.9129 10.3937 2007 8.2211 11.2205 2008 7.6988 10.3526 2009 6.9853 10.3974 2010 7.5188 9.693 p-Value 0.655 0.929 Test 40.05 40.05 Result Stable Stable

Xilin Gol League Site 2

Site 1

Site 2

2001–2005, 2006– 2008, 2009–2010

2001, 2002, 2003, 2004, 2005–2007, 2008, 2009–2010 7 10.5726 0.2736 8.94

2001, 2002, 2003– 2004, 2005–2010

3 35.4345 3.5923 4.74 Fo F(2, 7) Stable Site 2 Yearly mean value 6.311 6.3841 6.0273 6.6139 6.0747 6.4962 6.322 6.0545 5.4769 5.8213 0.128 4 0.05 Stable

Fo F(6, 3) Stable Xilin Gol League Site 3 Yearly Yearly Yearly variance variance mean value 6.7546 6.333 8.6031 7.6599 6.9354 9.0247 7.5482 6.8235 9.0691 6.5226 7.268 8.9942 7.0819 6.8211 8.5638 5.3913 6.8488 10.0125 6.728 6.8301 8.8668 5.9453 6.8862 9.3936 6.2206 6.3981 8.8527 6.0979 6.5418 8.471 0.04 0.655 0.531 o 0.05 4 0.05 40.05 Unstable Stable Stable

4 40.0572 1.472 4.76 Fo F(3, 6) Stable Site 4 Yearly mean value 8.2691 8.898 8.9304 9.068 8.5208 8.8471 8.4615 8.4524 8.1968 8.2609 0.06 40.05 Stable

Yearly variance 11.7552 11.5669 12.1864 12.4983 11.6342 13.2534 12.8384 11.693 11.8642 12.0577 0.421 40.05 Stable

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

and the “Assessment methods of wind energy resources in wind farms of China” [18], WAT is defined as: WAT ¼

n  24 10

ð3Þ

3.1.3. Population density Population density (PD) is the population living in a unit area of land. Usually, the unit is per square kilometer for the resident population. The formula is as follows: PD ¼ PE=A

where n is the total number of days where the 10-year average daily wind speed was between 3 and 20 m/s. After calculating the WAT, the corresponding score P 2 can be found according to Table 2.

1311

ð4Þ

where PE is the regional population (unit: people), and A is regional area (unit: km2). After calculating the PD (unit: p/km2), the corresponding score P 3 can be obtained based on Table 2.

Step 1: Define the class diameter Class diameter can represent the degree of difference among each class. The smaller the diameter is, the smaller the difference is. Assuming that a class is Gi;j ¼ fyi ; yi þ 1 ; …; yj g; j 4 i, and its diameter Dði; jÞ is the sample of the Total Sum of Squares (TSS), Dði; jÞ ¼

j X

ðyr  yij Þ2

ð5Þ

r¼i

yij ¼

j 1 X y j  iþ 1 r ¼ i r

ð6Þ

where yr is the sample characteristic value; yij is the mean value. Step 2: Calculate the objective function Suppose that n sample can be classified into m classes: fyj1 ; yj1 þ 1 ; …; yj2  1 g; fyj2 ; yj2 þ 1 ; …; yj3  1 g; ⋯fyj1m ; yjm þ 1 ; …; yjm þ 1  1 g, where j1 ; j2 ; …; jm are m points of division, its subscripts satisfy 1 ¼ j1 4 j2 4 ⋯ 4 jm Z jm þ 1  1 ¼ n. The aim is to find a series of dividing point and minimize the total classification diameter. Its objective function of classification is defined as Bðn; mÞ ¼ min

m X

Dðjr ; jr þ 1  1Þ

ð7Þ

r¼1

provided n ¼ jm þ 1  1. Following the theorem m 1 class dividing points before optimal m class partition are optimal dividing points formed by m  1 partition segments before optimal m class partition, it is not difficult to verify the following recurrence formula: Bðn; mÞ ¼ min ½Bðj  1; m  1Þ þ Dðj; nÞ mrjrn

ð8Þ

Suppose that the sample can be classified into m class, and jm can minimize Eq. (8), that is Bðn; mÞ ¼ Bðjm  1; m  1Þ þ Dðjm ; nÞ

ð9Þ

It is easy to find the mth class Gnm ¼ fyjm ; yjm þ 1 ; …; yn g. Then, the m  1th dividing point jm  1 can satisfy Bðjm  1; m  1Þ ¼ Bðjm  1  1; m  2Þ þ Dðjm  1 ; jm  1Þ

ð10Þ

and the m  1th class Gnm  1 ¼ fyjm  1 ; yjm  1 þ 1 ; …; yjm  1 g can be found. In a similar way, all of the classes can be found. The optimal partition occurs when the number of classes is m. Step 3: Solve the optimal partition There are two ways to determine the optimal partition: (1) plotting the curve variation based on the number of the optimal partition m and the minimum objective function Bðn; mÞ and taking the m value at the bend of the curve as the number of the best classification   Bðn;m  1Þ and (2) calculating a non-negative slope β ðmÞ ¼ Bðn;mÞ . If β ðmÞ is very large, it indicates that m classes is better than m  1 m  ðm  1Þ classes. If βðmÞ is close to zero, it is not necessary to continue to classify. Generally, m is the number of the optimal partitions when β ðmÞ is maximized. Step 4: Test the partition result To test the partition result, the F-test can be applied. The F statistic is defined as follows: 2P n 1 6 6i ¼ 1 F¼ m  14

ðxi  xÞ2  Bðn; mÞ 1 n  mBðn; mÞ

ð11Þ

Let the significant level be α ¼ 0:05. If F 4 F α , each class has a significant difference in all of the partitions. That is, the wind speed is unstable; otherwise, this partition is optimal for the same m, but each class does not have a significant difference. That is, the wind speed does not change much.

1312

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

3.2. Analysis of the theoretical wind energy potential First, the wind power density usually expresses the kinetic energy of the wind, but not all of the kinetic energy of the wind can be used. The wind power density is valid only when the wind speed is in the valid range, which is called the effective wind power density. The effective wind power density not only reflects the frequency of the wind speed, but also the real-time status of the air density. Therefore, the effective wind power density can be used to reveal the abundance and quality of wind energy resources. Second, from the technical perspective of wind turbines, it is difficult to use wind turbines when the wind speed is too high or too low. Therefore, wind available time can be chosen as the criteria determining if the wind is useful. Third, wind power can utilize large-scale wind energy. A large wind power plant covers a large area, generally requiring tens or even hundreds of square kilometers of open area. Furthermore,

running wind turbines create significant amounts of noise and large disturbances, which have negative impacts on human environments. Therefore, developing wind power near cities that have dense populations is forbidden. In fact, population density directly reflects the size and grade of settlements. Therefore, population density, as an indicator of human environment suitability, can better reflect urban distribution restrictions for wind energy resource potential. Based on the preceding analysis, including abundance, effective wind and human environment factors of wind energy resources, this section calculates the total score of three indexes: effective wind power density, wind available time and urban population density to evaluate the theoretical wind energy potential at four sites. Due to the definition of EWPD (see Eq. (2)), the wind speed data from 2001 to 2010 can be collected from four sites. Three index values can be calculated according to Eqs. (2)–(4). As shown in Table 2, the values of the EWPD at the four sites are greater than 200 W/m2. The values of

Fig. 6. The relative curve between Bðn; mÞ and m at four sites.

Table 4 Traditional parameter estimation methods.

Weibull

Method

Formula

MM

k¼

   1:086 σ v

MLE c¼ Gamma

MM

1 θ ¼ kn

μ ¼ 1n 1 n

n P i¼1

! vi

σ¼

n

i¼1

2

MLE

v¼

n P

vki lnðvi Þ

vk i ¼ 1 i

1

Pn 

i ¼ 1

lnðvi Þ

n

2

n P i¼1

P k

vi

lnðkÞ ψ ðkÞ ¼ ln P

ln vk

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n R1 P t 1 ðvi  vÞ2 ΓðxÞ ¼ 0 t x  1 e dt n1 i¼1

i ¼ 1 P n

k¼

vi θ ¼ σv

k ¼ σv2

MLE

Relative formulas

1 n

c ¼ Γð1 þv 1=kÞ !1=k P

β¼

k

1 n

ðln vk  μÞ2 n

n P i¼1

1=2

! vi  1n

n P i¼1

lnðvi Þ

ψðkÞ ¼ dΓðkÞ ΓðkÞ

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

1313

Fig. 7. The detailed process of the three intelligent optimization algorithms.

the WAT at the four sites are greater than 5000 h, and values of the PD at the four sites are less than 700 people/km2. Based on the criteria in Table 2, the corresponding index scores can be found:P 1 ; P 2 ; P 3 at the four sites are equal to 100. According to Eq. (1), the total score P Total is also equal to 100 at the four sites. P Total ¼ 100 directly corresponds to ‘the highest potential area’. Therefore, the four sites belong to the highest grade of wind energy potential areas, which means that these four sites have abundant wind energy resources.

4. Assessment of the fluctuations in the wind speed Wind is not a stable resource. It is affected by weather, climate, topography and other factors, so it has significant daily and seasonal variations. The instability of wind has a significant negative impact on the energy output of wind turbines, the utilization efficiency and development costs of wind energy, and other aspects. Consequently,

the assessment of the fluctuations in the wind speed is also a key factor when building wind farm. To improve the accuracy of the assessment of wind energy resources, the average yearly and monthly wind speed data from recent years are often used to perform wind resource analyses. The assessment of the fluctuations in the average monthly wind speed is conductive to scheduling power grid maintenance plans. The assessment of the fluctuations in the average yearly wind speed is beneficial to the macroscopic location and wind energy assessment of large wind farms. Moreover, the variation in the wind direction variation has a certain effect on the wind energy and wind turbines, but Inner Mongolia has prevailing south-west winds year round, so the wind direction is stable and has a weak influence. The Fisher optimal partition method [19] and the Jonckheere–Terpstra test [20] can be applied to analyze the fluctuations in the average monthly and yearly wind speeds from 2001 to 2010. Four-time daily wind speed data in the range of 3–20 m/s are used to calculate the average monthly and yearly wind speeds.

1314

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

α ðα ¼ 0:05Þ, we should reject the null hypothesis, which means

4.1. Fisher optimal partition method 4.1.1. Introduction of the assessment method The Fisher optimal partition method is a statistical clustering approach for many ordering time series. The aim is to determine whether each class has a significant difference in the optimal partition or not, thus it can be used to judge the fluctuations in the data. The detailed steps of the Fisher optimal partition method can be described as follows [19]: 4.1.2. Analysis of the stability of the average monthly wind speed The Fisher optimal partition method can be applied to judge the fluctuations in the average monthly wind speed from 2001 to 2010 at four sites. Based on the 4-time daily wind speed from 2001 to 2010 at four sites (wind speeds within the range 3–20 m/s are used), the average monthly data during these ten years can be calculated. After finishing the three steps, including solving the class diameter, objective function, and the optimal partition by the Fisher method, the corresponding parameters values can be obtained in Table 3. The curve variation based on the number of the optimal partitions m and the minimum objection function Bðn; mÞ at the four sites can also be observed in Fig. 6. At Site 1, the number of optimal partitions is 7 because β ð7Þ 4 β ð6Þ ðβð7Þ ¼ 10:815; β ð6Þ ¼ 6:7084Þ, the minimum objective function Bð10; 7Þ is approximately 16 and statistic F o Fð6; 3Þ. At Site 2, the number of the optimal classification is 3 because β ð3Þ 4 β ð2Þðβð3Þ ¼ 9:7339; β ð2Þ ¼ 7:1267Þ, Bð10; 3Þ is approximately 35 and statistic F o Fð2; 7Þ. At Site 3, the number of the optimal partition is 7 because βð7Þ 4 βð6Þðβ ð7Þ ¼ 7:2086; β ð6Þ ¼ 4:5261Þ, Bð10; 7Þ is approximately 11 and statistic F o Fð6; 3Þ. At Site 4, the number of the optimal classification is 4 because βð4Þ 4 β ð3Þðβ ð4Þ ¼ 9:9428 ; βð3Þ ¼ 7:181Þ, the minimum objective function Bð10; 4Þ is approximately 40 and statistic F o Fð3; 6Þ. To sum up, it is found that statistic F is less than Fðm  1; n  mÞ at the four sites. Based on the definition of the hypothesis test, the average monthly wind speed during these ten years can be classified into the optimal m class, but there are not significant differences between each class. In other words, the changes in the monthly wind speed from 2001 to 2010 are not obvious, so the average monthly wind speed does not undergo large changes at the four sites. 4.2. Jonckheere–Terpstra test 4.2.1. Review of the statistical test The Jonckheere–Terpstra test [20] is a nonparametric test for ordering the differences among samples. The null hypothesis is that several independent samples are from the same population. Its statistic J  T is computed by U ij ¼ fnumber of times X i o X j g: X U ij ð12Þ J T ¼ ioj

where X ¼ ½X 1 ; X 2 ; ⋯; X N  represents several independent samples, and N is the number of independent samples. Asymptotic p-values for the Jonckheere–Terpstra test are obtained using the normal approximation for the distribution of the standardized test statistic. The standardized test statistic Z is computed as

that these samples are not from the same population, i.e., the change in the average yearly wind speed is unstable; otherwise, these samples are from the same population, i.e., average yearly wind speed does not undergo a large change. 4.2.2. Analysis of the stability of the average yearly wind speed Based on the 4-time daily wind speed data collected from 2001 to 2010 at the four sites (wind speeds within the range 3–20 m/s are used), the average yearly wind speed can be obtained (see Table 3). The Jonckheere–Terpstra test can judge whether several independent samples are from the same distribution, i.e., whether the average yearly wind speeds during the ten years have the same distribution or not. Using Eqs. (12) and (13), the p-values of average yearly value and yearly variance at the four sites can be found (see Table 3). For the average yearly value, the p-values at Site 1 and Site 3 are the same, and they are greater than the pvalues at Site 2 and Site 4. If the significance level is 0.05, it is easy to find that all p-values are greater than 0.05. This result illustrates that the average yearly value at each site is from the same distribution, i.e., the average yearly value of the wind speed from 2001 to 2010 does not change significantly at the four sites. For the yearly variance, the p-values at Site 1, Site 3 and Site 4 are far greater than 0.05, but the p-value of Site 2 is a slightly less than 0.05, which indicates that the distributions of the yearly variance at Site 1, Site 3 and Site 4 are the same, but at Site 2, the distribution is different. Above all, with regard to Site 1, Site 3 and Site 4, the average yearly wind speeds do not indicate large changes. Although the average yearly value is stable at Site 2, the instability of the variance indicates that the fluctuations in the yearly wind speed are large. Therefore, compared with Site 2, the wind energies at Site 1, Site 3 and Site 4 are more stable.

5. Assessment of the wind speed frequency distribution The variation in the wind speed with height is given by the power-law equation:  α VH H ¼ ð14Þ R VR where α is the power law exponent, which varies with ground level height, time of day, season, and nature of the terrain. In this work, we assume its value is 0.185 [21]. V H is the wind speed at height H, and V R is the reference wind speed at reference height R. 5.1. Three probability density functions This work adopts three probability density functions, including the Weibull, Gamma and Lognormal, to estimate the wind speed frequency distribution. Reviews of the three distributions are given in the following sections.

ð13Þ

5.1.1. The Weibull distribution The Weibull probability distribution function for wind speed is given as follows:    k  1 vk dFðvÞ k v ¼ f ðv; k; cÞ ¼ exp½   ð15Þ dv c c c

where J is the statistic J  T, and Ni is the number of the ith samples. If the p-value is less than the significance level

where v is wind speed, c is the Weibull scale parameter with units equal to wind speed units, and k is the dimensionless Weibull shape parameter. c and k need to be determined. If the shape parameter is equal to 2, then the distribution is called the cumulative Rayleigh distribution [22].

N P J  ðN 2  N2i Þ=4 i¼1 Z ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N P N 2i ð2Ni þ 3ÞÞ=72 ðN 2 ð2N þ 3Þ  i¼1

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

1315

Fig. 8. Frequency distributions of three probability density functions via the optimal parameter estimation methods.

5.1.2. The Gamma distribution The probability density function of the Gamma distribution can be expressed as [23,24]   1 1 k1 v f ðv; k; θÞ ¼ k v exp  ð16Þ θ θ Γ ðkÞ where v is wind speed, both k and θ need to be determined.

5.1.3. The Lognormal distribution The probability density function of a Lognormal distribution is [25] " # 1 ðln v  μÞ2 ð17Þ f ðv; μ; β Þ ¼ pffiffiffiffiffiffiexp  2 vβ 2π 2β where v is the wind speed and, both μ and β need to be determined.

5.3.1. Particle swarm optimization algorithm (PSO) The PSO algorithm is composed of 5 main steps [26]: Step 1: Initialize the position vector xx and associated velocity vv of all particles (the number of particles is N) in the population randomly. Then, set a maximum velocity and a maximum particle movement amplitude to decrease the cost of evaluation and to obtain a good convergence rate. Step 2: Evaluate the fitness of each particle via the fitness function. There are many options when choosing a fitness function. Trial and error is often required to find a good one. Step 3: Compare the particle’s fitness evaluation with the particles’ best solution. If the current value is better than the previous best solution, replace it and set the current solution as the local best. Compare the individual particle’s fitness with the population’s global best. If the fitness of the current solution is better than the global best, set the current solution as the new global best. Step 4: Change velocities and position using Eqs. (18)–(20). vvdi ¼ w  vvdi þ c1  randðÞ  ðpbest di  xxdi Þ þ c2  randðÞ

5.2. Two traditional parameter estimation methods There are two simple traditional methods to estimate the parameters for three distributions, including the method of moments (MM) and the maximum likelihood estimation (MLE). The formulas are shown in Table 4.

5.3. Three intelligent optimized parameter estimation algorithms Three intelligent optimized methods are employed to estimate the parameters of the three probability density functions. They are described as follows:

 ðgbest di xxdi Þ xxdi ¼ xxdi þ vvdi w ¼ wmax 

wmax  wmin iteration iter_ max

ð18Þ ð19Þ ð20Þ

where pbest is the best fitness value at certain time and gbest is the global best value. The positive constants c1 and c2 are the cognitive and social components that the acceleration constants are responsible for varying the particle velocity towards pbest and gbest, respectively. iter_max is the maximum number of iterations, and iteration is the current number of iteration [27].

1316

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

Fig. 9. Assessment results of the comprehensive method.

Step 5: Repeat Step 2 to Step 4 until a predefined number of iterations is completed.

5.3.2. Differential evolution algorithm (DE) In DE, an optimized task consisting of D parameters can be described by a D-dimensional vector. A population of NP solution vectors is randomly created at the beginning. The main steps are given below [28]: Step 1: Mutation For each target vector xi;G ; i ¼ 1; 2; 3…; NP, a mutant vector is produced by yi;G þ 1 ¼ xr1;G þ F  ðxr2;G xr3;G Þ, where random indexes r 1 ; r 2 ; r 3 A f1; 2; …; NPg are mutually different integers and F 4 0. The randomly chosen integers r 1 ; r 2 and r 3 are also chosen to differ from the running index i so that NP must be greater than or equal to 4 to allow for this condition. F A ½0; 2 is a real and

constant factor that controls the amplification of the differential variation ðxr2;G  xr3;G Þ. Step 2: Crossover To increase the diversity of the perturbed parameter vectors, the crossover is represented. The trial vector is ui;G þ 1 ¼ ðu1i;G þ 1 ; u2i;G þ 1 ; …; uDi;G þ 1 Þwhere ( uji;G þ 1 if randbðjÞ r CR or j ¼ rnbrðiÞ uji;G þ 1 ¼ ð21Þ if randbðjÞ 4 CR or j a rnbrðiÞ xji;G In Eq. (21), randbðjÞð A ½0; 1Þ is the jth evaluation of a uniform random number. CRð A ½0; 1Þ is the crossover constant. rnbrðiÞð A f1; 2; …; DgÞ is a randomly chosen index, which requires that ui;G þ 1 obtain at least one parameter from yi;G þ 1 . Step 3: Selection All solutions in the population have the same probability of being selected as parents independent of their appropriateness value. The child produced after the mutation and crossover

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

operation is evaluated. Then, the performance of the child vector and its parent is compared and the better one is selected. If the parent is still better, it is retained in the population.

1317

Step 7: If f opt ðX ij Þ ði A ½1; part; j A ½1; mÞ is less than the given solution error condition 10  2, then go to Step 8, otherwise go to Step 3. Step 8: Output ncho and f opt ðX ij Þ ðiA ½1; part; j A ½1; mÞ. 5.4. Discussion and analysis of the results

5.3.3. Ant colony optimization algorithm (ACO) The ant colony optimization algorithm (ACO) uses artificial ants to construct solutions by incrementally adding components that are chosen to consider heuristic information of the problem and pheromone trails that reflect the acquired search experience [29]. Step 1: Initialize the number of permissible iterations NCHO, the number of real iterations ncho and the number of ants ANT. Step 2: The definitional domain is divided into part sub-regions according to Eq. (22), and every sub-region can be defined as Eq. (23). 8 i ði ¼ 1; 2; …; partÞ; m ants are assigned randomly in every sub-region, and every ant is defined as ant ij ði ¼ 1; 2; …; part; j ¼ 1; 2; …; mÞ. The ACO sets the initial pheromone concentration according to Eq. (24). li ¼

maxi  mini part

grpi ¼ ½mini þ li U ðj  1Þ; mini þli U j

ð22Þ ð23Þ

where i A ½1; d; jA ½1; part and d is the dimension of the independent variables. f ðX ij Þ is the objective function.  τðijÞ ¼ exp  f ðX ij Þ i ¼ 1; 2; …; part; j ¼ 1; 2; …; m ð24Þ Step 3: Assume that the pheromone of the current ant’s location is τij ði ¼ 1; 2; …; part; j ¼ 1; 2…; mÞ. Calculate the pheromone of the elite ant and determine τmaxi of every group according to Eq. (25).

τ max i ¼ maxðτi1 ; τi2 ; …; τij Þ ði ¼ 1; 2; …; part;

j ¼ 1; 2; …; mÞ ð25Þ

The global optimal solution corresponds to ant pheromone τkl ¼ maxðτmax1 ; τmax2 ; …; τmaxi Þ, i ¼ 1; 2; …; part; k A ½1; part; l A ½1; m, so we can obtain the location Xkl of the ants.  elite X X Step 4: If X i  X j  Z j max10 min j, then 8 < τi X i þ α1 1  τi ðX j  X i Þ; if α1 o0:5 τj X 0i ¼ ð26Þ : τi X i þ α1 ð1  τi ÞX j ; otherwise     X X If X i  X j  o j max10 min j, then let w ¼ X i  X j  ( X i þ wd δd ρ; ρ o ρ0 X 0i ¼ X i  wd δd ρ; ρ 4 ρ0

ð27Þ

where X j ðj A ½1; mÞ is the location of the elite ants in this generation, X i ði ¼ 1; 2; …; mÞ is the location of the common ants in every group, X 0i is the location of the ants after the update, α1 A ð 1; 1Þ, ρ A ð0; 1Þ, ρ0 A ð0; 1Þ, δ A 0:1  randð1Þ. Step 5: Get the current optimal solution f opt ðX ij Þ ði ¼ ½1; part; j A ½1; mÞ according to the new location of the ants, and update the pheromones of each ant in each sub-region based on Eq. (28).

τðijÞ ¼ ρτðijÞ þ e  f ðX ij Þ

ð28Þ

Step 6: ncho ¼ ncho þ 1, if ncho 4 NCHO, go to Step 8, otherwise go to Step 7.

5.4.1. Evaluation criteria of the estimated methods To estimate the accuracy of each estimated method, the first criterion is the correlation coefficient R2 , which can be calculated by [30,31] PN ðy  xi Þ2 ð29Þ R2 ¼ 1  PiN¼ 1 i 2 i ¼ 1 ðyi  yÞ The second is the root mean square error, RMSE, which is given as follows [30,31]: " #0:5 N 1X 2 RMSE ¼ ðy  xi Þ ð30Þ Ni¼1 i where N is the total number of intervals, yi is the frequencies of observed wind speed data, xi is the estimated frequency value, and y is the average of yi values. If the R2 magnitude is larger or the RMSE value is smaller, the method is better. 5.4.2. Comparison between the traditional and intelligent parameter estimation algorithms In this section, Weibull, Gamma and Lognormal distributions can be applied to evaluate the frequency distribution of the 4-time daily wind speed data in 2010 at 10 m, 30 m, 40 m, 60 m, 80 m and 100 m at the four sites. Based on the equations of Table 4, the parameters can be easily calculated using the traditional estimated methods. For intelligent optimized parameter estimation algorithms, let all of the objective functions f ¼ RMSE. Their aims are to minimize f , thus finding the optimal parameters of the different probability density function, such as the scale parameter c and shape parameter k in the Weibull distribution, k and θ in the Gamma distribution, and μ and β in the Lognormal distribution. At first, in the PSO technique, we assume that the length of the particles N is 2 because two parameters need to be determined, the number of the particles is N ¼30, the two positive acceleration constants are c1 ¼ c2 ¼ 2, and the maximum speed of the particles does not exceed 0.1. We evaluate the fitness of each particle via the objective function f ¼ RMSE. According to Eqs. (18)–(20), if the current location is better than the previous one, we replace it and set the current solution as the optimal location (pbest). If the current optimal solution is better than the global best, we set the current optimal solution as the new optimal position and value (gbest). The algorithm would stop when the number of iterations is 100. Second, parameters can be initialized in DE algorithm: population size NP ¼20, length of the chromosome D ¼2 because two parameters need to be estimated, and the maximum generations number g ¼100. Moreover, let the mutation factor F¼0.9 and the crossover rate CR ¼0.5. The fitness values of all of the first generation are calculated and recorded according to the objective function f ¼ RMSE. If the offspring’s fitness value is better than the parent’s fitness, the offspring will replace the parent. Otherwise, the parent will be kept. The algorithm will stop when the generation number is 100. Third, for the ACO algorithm, Section 5.3.3 describes the algorithm in detail. Some parameters can be initialized as follows: d¼ 2, ant ¼36, part ¼9, NCHO¼100 and ρ0 ¼0.5. The objective function is f ¼ RMSE. Indeed, we are not only interested in the simulation of ant colonies but also in the use of artificial ant colonies as a two-dimension optimization tool. Using the ant

1318

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

pheromones, the location of the elite ants can be found, and the current optimal solution f opt can also be calculated. The algorithm stops when the number of iterations is 100. These three intelligent optimization algorithms are also shown in Fig. 7 To present how a theoretical probability function matches with the observation data, two types of statistical errors are considered the judgement criteria. The larger the R2 , the better the fit, and the smaller the RMSE, the better the fit. Based on the results from Tables 5–10, three intelligent optimization algorithms have higher R2 and lower RMSE than the traditional estimated approaches. Specifically, for the Weibull distribution, the DE, ACO and PSO algorithm gives the minimum, moderate, and maximum RMSE and the maximum, moderate, and minimum R2 , respectively, at the four sites except for Site 3. At Site 3, the estimation using PSO yields better results than ACO, whereas DE still shows the highest accuracy. In the Gamma distribution, DE continues to maintain the best precision, followed by ACO, and PSO ranks third at the four sites. Fig. 8 presents frequency distributions of the three probability density functions using the best parameter estimation algorithm. However, the performance of the Lognormal distribution is different from the other two. ACO has the highest precision, and the next best is DE followed by the PSO algorithm at Site 1, Site 2 and Site 3. At Site 4, DE still has the best performance. To sum up, different intelligent parameter estimation algorithms present different performances for various types of data, but the performances of the three intelligent parameter estimation algorithms are better than conventional methods. 5.4.3. Comparison among three frequency distribution functions Some comparisons have been made based on measured wind speed data. Tables 5 and 6 show the parameters and forecasting accuracies of the Weibull distribution; all R2 are more than 0.85 and RMSE are between 0.005 and 0.01 at the four sites. The best parameter estimation method is DE. Tables 7 and 8 present the performances of the Gamma distribution, all R2 are greater than 0.7 and RMSE are between 0.01 and 0.02 at the four sites. The best parameter estimation method is DE. Tables 9 and 10 give the results of Lognormal distribution, all R2 exceed 0.4 and RMSE are between 0.01 and 0.03 at the four sites. The best parameter estimation method is ACO. In addition, as shown in Fig. 7 the frequency distributions of the Gamma and Lognormal functions skew slightly to the left, and the frequency distribution of the Weibull function matches very well with the observations for assessing the wind speed frequency distributions. Through comparison, it can be perceived that the Weibull distribution has the highest R2 and the lowest RMSE, i.e., the actual wind speed frequency obeys the Weibull distribution. In particular, the Weibull distribution based on the DE parameter estimation algorithm has the best performance, which will be applied to evaluate the wind power density, the most probable wind speed and the wind speed carrying the maximum energy.

some references, this term is called the optimum wind speed [31]. The wind turbines can be chosen with a rated wind speed, which matches the maximum wind speed energy to maximize the energy output. If V OP is determined for one site, the optimal rated wind speed of the wind turbine will be obtained. The rated velocity of a wind turbine is the lowest wind velocity corresponding to its rated power, which is the constant power produced by the wind turbine due to technical and economic reasons [32]. Therefore, it is beneficial to calculate these three wind characteristics for wind resources assessment and wind turbines selection. Based on the above analysis, the Weibull distribution based on the DE parameter estimation algorithm shows the optimal wind speed frequency distribution, so the definition can be presented [33]:   Z 1 1 kþ3 P¼ P d ðVÞf ðVÞdV ¼ ρc3 Γ 2 k 0   1 kþ3 3 ¼ ð1:225expð  H=10:7ÞÞc Γ ð31Þ 2 k  V MP ¼ c  V OP ¼ c

1=k k1 k

kþ2 k

ð32Þ

1=k ð33Þ

where ρ is the air density, H is the height, the c and k are calculated using the best parameter estimation method. 6.2. Calculation results using the wind characteristics After choosing the optimal frequency assessment and parameter estimation method, the Weibull distribution based on the DE intelligent parameter estimation algorithm can be applied to calculate the wind power density, most probable wind speed and wind speed carrying the maximum energy in 2010 at six hub heights for wind resources assessment and wind turbines selection. The results are summarized in Table 11. For the 10-m level, the most probable wind speeds at Site 1 and Site 4 are greater than 7 m/s, and the wind speed carrying the maximum energy is greater than 11 m/s. At Site 2 and Site 3, the most probable wind speed is approximately 5 m/s, and the wind speed carrying the maximum energy is approximately 9 m/s. In fact, these three wind characteristics increase with height throughout the entire year. It is found that the wind power density, the most probable wind speed and the wind speed carrying the maximum energy at Site 1 and Site 4 are larger than those at Site 2 and Site 3. Therefore, compared with Site 2 and Site3, Site 1 and Site 4 have higher wind power densities, most probable wind speeds and wind speeds carrying the maximum energy in 2010.

7. Conclusion 6. Assessment of the wind power density, most probable wind speed and wind speed carrying the maximum energy 6.1. Definition of the wind characteristics The wind power density P takes into account the wind speed frequency distribution, the dependence of the wind power on the air density and the cube of the wind speed. Thus, the wind power density can be considered a better indicator of the wind resources than the wind speed. The most probable wind speed V MP is the most frequent wind speed for a given wind probability distribution. The wind speed carrying the maximum energy V OP is the speed that generates the most energy from the wind energy [8]. In

In the process of wind power generation, it is critical to seek the region with rich wind energy and good stability for enhancing the collection efficiency of the power plant. Therefore, this work develops a new comprehensive approach with four steps to assess the theoretical wind energy potential, the fluctuations in wind speed, wind speed frequency distribution and wind power density, most probable wind speed and wind speed carrying the maximum energy at four sites in Xilin Gol League and Alxa League of Inner Mongolia. The innovation is that three indexes, EWPD, WAT and PD, are first employed to estimate the theoretical wind energy potential. The experiment shows that the four sites have the highest theoretical wind energy potential. Then, the Fisher optimal

H. Jiang et al. / Renewable and Sustainable Energy Reviews 50 (2015) 1304–1319

partition method and the Jonckheere–Terpstra test are introduced to judge the fluctuation in the average monthly and yearly wind speeds over ten years. As shown in the analysis, with the exception of Site 2, the average monthly and yearly wind speeds at the other sites do not experience large changes. Moreover, three probability density functions (two parameters of the Weibull, Gamma and Lognormal distributions) are employed to assess the wind speed frequency distribution. Two traditional parameter estimation methods and three intelligent optimization algorithms are used to determine the parameters of these distributions. The results show that Weibull based on the DE parameter estimation algorithm has the best performance. Based on the optimal parameter values, the wind power density, most probably wind speed and wind speed carrying the maximum energy can also be calculated for wind resources assessment and wind turbines selection. It is found that these wind characteristics are larger at Site 1 and Site 4 than at Site 2 and Site 3. To sum up, this comprehensive method illustrates that Site 1 and Site 4 have richer and more stable wind speeds and are more suitable for large wind farms than Site 2 and Site 3. The detailed results can be observed in Fig. 9. Although government policy has driven the development of wind power in China and simultaneously promoted the deployment of domestic wind power technology and the advancement of wind farms, several challenges to its continued growth have emerged. Transmission and integration with the power grid has become the largest barrier to the development of China’s wind power industry. These challenges potentially threaten the sustainable and stable growth of the wind power industry but can be addressed by policy reform and additional research efforts. In addition, the proportion of China’s total electricity generation that comes from wind power is still low. Therefore, China needs to strive to exploit more wind energy resources, particularly in the resource-rich areas. Acknowledgments This research was supported by the National Natural Science Foundation of China (71171102/G0107). References [1] Wang SH, Jin Y. Wind power generation of Chinese road. Sci Technol Inf 2012;8:129. [2] China’s Energy Policy, Information Office of the State Council, Beijing; October, 2012. [3] Saidur R, Islam MR, Rahim NA, Solangi KH. A review on global wind energy policy. Renewable Sustainable Energy Rev 2010;14:1744–62. [4] The Global Call for Climate Action. Wind power. Available from 〈http:// tcktcktck.org/climate-solutions/wind-power〉. [5] Pishgar-Komleh SH, Keyhani A, Seffedpari P. Wind speed and power density analysis based on Weibull and Rayleigh distributions (a case study: Firouzkooh county of Iran). Renewable Sustainable Energy Rev 2015;42:313–22.

1319

[6] Zhang H.T. China’s energy structure adjustment. Available from 〈http://www. doc88.com/p-276338558655.html〉; 2012. [7] Ucar A, Balo F. Evaluation of wind energy potential and electricity generation at six locations in Turkey. Appl Energy 2009;86:1864–72. [8] Keyhani A, Ghasemi-Varnamkhasti M, Khanali M, Abbaszadeh R. An assessment of wind energy potential as a power generation source in the capital of Iran. Tehran Energy 2010;35:188–201. [9] Chang TP. Estimation of wind energy potential using different probability density functions. Appl Energy 2011;88:1848–56. [10] Wang M, Zeng LH. Study of wind speed frequency distribution model. J Hydroelectr Eng 2011;30(6):204–9 In Chinese. [11] Zhang LF, Wang ZP. Influences of wind power integration on power system. Jiangsu Electr Eng 2011;30(2):81–4 In Chinese. [12] Gong WJ, Li WX, Zhang GM. The estimation algorithm on the probabilistic distribution parameters of wind speed based on Weibull distribution. Renewable Energy Resour 2011;29(6):20–3 In Chinese. [13] Alxa League wind power planning. Available from 〈http://wenku.baidu.com/ view/3c9344d1c1c708a1284a44fe.html〉; 2012. [14] Zhao YS, Li RT. Wind resource conditions and wind farms construction in Xilin Gol League. Inn Mongolia Sci Technol Econ 2012;10:57–8. [15] NCC. National Climate Center. Available from 〈http://ncc.cma.gov.cn/wind/? area=neimeng〉. [16] Li K, He FN, Xi JC. The development potential regional analysis of China’s land wind energy resources. Resour Sci 2010;32(9):1672–8. [17] Bailey BH, McDonald SL. Wind resource assessment handbook. New York: AWS Scientific. Inc; 1997. [18] People’s Republic of China Standard: assessment methods of wind energy resources in wind farms, GB/T18710-2002. [19] Liu KL, Wang YT, Hu SY, Gao B. Application of Fisher optimal dissection method to flood season division. Adv Sci Technol Water Resour 2007;3:27 June. [20] Xue W. SPSS statistical analysis methods and applications. Beijing: Publishing House of Electronics Industry; 2009. p. 1. [21] Dong Y, Wang JZ, Jiang H, Shi XM. Intelligent optimized wind resource assessment and wind turbines selection in Huitengxile of Inner Mongolia, China. Appl Energy 2013;109:239–53. [22] Saleh H, Abou El-Azm Aly A, Abdel-Hady S. Assessment of different methods used to estimate Weibull distribution parameters for wind speed in Zafarana wind farm, Suez Gulf, Egypt. Energy 2012;44:710–9. [23] Carta JA, Ramı0 rez P, Vela0 zquez S. A review of wind speed probability distributions used in wind energy analysis Case studies in the Canary Islands. Renewable Sustainable Energy Rev 2009;13:933–55. [24] Gamma distribution, Wikipedia. Available from 〈http://en.wikipedia.org/wiki/ Gamma_distribution〉; 2012. [25] Lognormal distribution, Wikipedia. Available from 〈http://en.wikipedia.org/ wiki/Log-normal_distribution〉; 2012. [26] Behrang MA, Assareh E, Noghrehabadi AR, Ghanbarzadeh A. New sunshinebased models for predicting global solar radiation using PSO (particle swarm optimization) technique. Energy 2011;36:3036–49. [27] Shayeghi H, Safari A, Shayanfar HA. PSS and TCSC damping controller coordinated design using PSO in multi-machine power system. Energy Convers Manage 2010;51:2930–7. [28] Aboosadi ZA, Jahanmiri AH, Rahimpour MR. Opimization of tri-reformer reactor to produce synthesis gas for methanol production using differential evolution (DE) method. Appl Energy 2011;88:2691–701. [29] Pedemonte M, Nesmachnow S, Cancela H. A survey on parallel ant colony optimization. Appl Soft Comput 2011;11:5181–97. [30] Dahmouni AW, Ben SM, Askri F, Karkeni C, Ben SN. Wind energy in the Gulf of Tunis, Tunisia. Renewable Sustainable Energy Rev 2010;14:1303–11. [31] Johnson GL. Wind energy systems. USA: Prentice-Hall; 1985. [32] Lu L, Yang H, Burnett J. Investigation on wind power potential on Hong Kong islands-an analysis of wind power and wind turbine characteristics. Renewable Energy 2002;27:1–12. [33] Alimi SE, Maatallaha T, Dahmouni AW, Nasrallaha SB. Modeling and investigation of the wind resource in the gulf of Tunis, Tunisia. Renewable Sustainable Energy Rev 2012;16:5466–78.