Wind power potential for energy sustainability and climate change mitigation: A case study in Taiwan

Abstract

According to the latest Taiwan’s energy plan, nuclear power that provides approximately 16% of total electricity will be replaced by renewable energy sources by 2025. Wind power is of particular interest because Taiwan’s maritime climate and constant monsoons make it a feasible alternative that potentially generate a considerable amount of electricity. To better understand how wind power can provide stable electricity output and sequester CO₂ emissions, this study employs the Weibull distribution with a threshold regression model to estimate the electricity potential for 370 scheduled wind farm sites and refine electricity estimation according to observed data from all existing wind farms. The results show that, compared to the theoretical estimation models, our proposed refinement method can, in average, reduce estimating error by 87%. The results indicate that construction of all scheduled sites are not a cost-effective approach, and the government may focus on construction of stations that can generate electricity of more than 12 million kWh per year, if capital rationing do exist. Our insightful results thus convey constructive suggestions regarding sites selection, stability of wind speed, and electricity potential of each site, all of which can be helpful in decision making. It is also noteworthy to point out that unless future climate is far deviated from the observed data, wind power can be an effective substitute of nuclear power.

Keywords

Emission offset Weibull distribution threshold regression renewable energy sustainability

Introduction

Fossil fuels are considered to be a nonrenewable resource, which will eventually be depleted in the foreseeable future, and thus exploration of renewable energy sources is of particular interest for nations to enhance energy security and achieve sustainable development. Moreover, considerable amounts of anthropogenic emissions from the use of fossil fuel increase CO₂ concentration and speed up greenhouse effects, resulting in a severe environmental problem known as global climate shift.¹ Therefore, to avoid the adverse effects such as sea level rise and increased possibility of extreme events resulted by climate change, it is crucial to switch to low-carbon energy sources.^2,3

Taiwan, situated in the Pacific Ocean, imports most of its energy and suffers from the distortions of international energy market. Nowadays nuclear and thermal power plants have provided approximately 16% and 68% of electricity demand, respectively, leaving little space of costly renewable energy to penetrate the market. However, in the beginning of 2017 Taiwanese government announces that to combat climate change and to ensure sustainable social development, Taiwan is going to replace all nuclear power that may result in severe health and environmental problems to future generations by renewable energy before 2025. To achieve this goal, a comprehensive understanding about whether or not renewable energy can generate enough and stable electricity becomes important to Taiwan’s sustainable development. Among all renewable energy sources, wind power has been underscored because it is difficult to get a precise prediction due to uncertain wind resource, and thus, its information is less helpful in the nation-wide planning. Although Taiwan is a typical maritime climate island, wind power has not been well utilized and investigation of this natural resource is rarely conducted.^4,5 Based on latest assessment of General Circulation Models (GCMs) reported by Intergovernmental Panel on Climate Change (IPCC),⁶ wind farm might be attractive to Taiwanese government because the report indicates that with appropriate utilization of wind resource, a significant amount of electricity can be generated. Prior to this study, several works have examined the wind power potential in Taiwan, but their results are generally based on the “theoretical assumption” rather than “real data calculation,” implying the assumed electricity supply are highly unreliable and a large deviation of electricity estimation may actually cause problems. To provide a more robust and realistic measure, this study integrates both theoretical and empirical approaches to improve wind electricity estimation, which can be useful in future policy analysis.

There are 370 scheduled wind farm sites having been proposed for wind power generation in Taiwan, but limited information is available for policy makers to realize the energy potential from these sites. Under such circumstance, the proposed policies designed for wind farm construction may be neither effective nor efficient. Therefore, this study aims to explore the amount of electricity can be generated from these scheduled wind farm sites, and consequently estimates energy efficiency in all planned regions. Specifically, this study firstly collects hourly wind speed data of the meteorological station near to 16 existing wind farms, and then estimates the wind speed of existing wind farms according to the turbine height and altitude. To estimate the distribution of monthly wind speed, a precise wind speed estimation method called Weibull distribution is employed.^4,5,7 With this practice the theoretical wind power output can be calculated by fitting observed wind speed data to turbine’s power curve. Since the previous studies did not have a control group (i.e., they cannot compare their estimates before the site construction is eventually done), they are not able to predict the electricity potential precisely. However, by using empirical wind power data from existing sites, this study is able to further refines theoretical wind power estimation to estimate electricity generation from 370 scheduled wind farm by a threshold regression model. With such implementation, this study can provide more site-specific information to policy makers and the result is potentially useful for policy analysis.

The study makes contributions in several aspects. First, the electricity potential does not solely rely on theoretical estimation. Instead, the site-specific characteristics such as height, altitude, landscape are integrated and consequently, our approach is likely to reduce estimation error reduced significantly. Second, the study examines the electricity potential from all potential sites, providing thorough information to policy makers in terms of sites selection and wind power associated with each site. With such information the government will be able to figure out that to what extent the wind power can substitute nuclear power. Third, the information of carbon emission reduction can be derived from the results. After knowledge regarding the quantity of emission that can be bought and sold has been revealed, influences of development of wind power on carbon trade market can be easily analyzed. Finally, our results can be used to assess policy analysis. For example, economic and environmental consequences related to specific policy can be examined. For example, how the economic benefits and energy transmission efficiency can be calculated in different sites can be investigated, given a budget constraint or a fixed amount of subsidy, may be derived from our proposed model.

Literature review

To ensure sustainable social development, switching to low-carbon fuels is a global trend in the recent decades.⁸ Because various benefits such as climate change mitigation, energy security, more employment opportunities, and improvement of economic growth may be accompanied with renewable energy development,⁹ the United States, Europe Union, and Brazil have formulated policies to promote the use and production of renewable energy. Meanwhile, the Japanese government has launched a scheme called “feed-in-tariff” to promote renewable energy industries in photovoltaic (PV), wind, small hydro, geothermal, and biomass.¹⁰ As a result, the production of renewable electricity expands considerably, providing approximately 3.2% of Japan’s total electricity demand.¹¹ These successful practices point out that as long as the promotion policies are well designed and launched, renewable energy could be an effective substitute of fossil fuels.

When Taiwan announces that he is going to replace all nuclear power with renewable energy by 2025, exploring renewable energy sources and estimating the net electricity output of these sources become an immediate task; otherwise the unstable electricity supply will be very likely to hamper Taiwan’s economic growth and industrial development. Among renewable energy technologies, bioenergy energy has been widely examined.^12–16 The results indicate that bioenergy can provide significant amount of ethanol and electricity, but total electricity generated is not sufficiently high to be the major energy source.^15,16 Kung and Chang¹⁵ point out that although the net energy conversion rate from biomass to bioenergy can be satisfactory, net electricity generation can only provide less than 3–4% of total energy demand, implying that to recover the electricity shrinkage due to the shutdown of nuclear power plant, multiple renewable energy technologies must be simultaneously applied.

Wind power, among other renewable energy alternatives, is currently attracting more attention of Taiwanese government who realizes its maritime climate could provide constant and sufficient wind resources, thereby offering considerable amount of electricity.¹⁷ In recent years, the wind farm construction has been widely studied, but most of these studies focus on the environmental impacts such as climate change mitigation.^18–21 Economic analysis has also been conducted, but most of them have been focused on the social benefits brought from renewable energy technologies.^22–27 In addition, due to the wind resource subject to change in different area, a single conversion rate of wind to electricity cannot be universally applied, many studies adopt life cycle analysis to examine economic effects such as social costs and payback time,^27–32 along with a series of public benefits evaluation.^33–37

Up to date, utilization of large turbine is considered to be a mature technology, but the technological maturity and effectiveness of medium wind turbines (MWT) must be further investigated.^37,38 For example, Katsigiannis and Stavrakakis³⁸ conduct an economic assessment of different wind turbines in Australia to investigate the optimal design of wind turbines, and Fadai³⁹ studies the feasibility of manufacturing wind turbines in Iran. Their results illustrate a useful framework by showing how wind turbines should be designed. Biswal and Shukla⁴⁰ further point out how costs may be estimated in different sites. Indeed, it is a difficult task to estimate the real wind speed for the whole year because the climate condition may vary year by year, in which deviation from historical patterns can be large. Therefore, the estimated electricity output may not be reliable if we simply apply a constant wind data. For example, economic measures must be estimated under the actual electricity generated by wind turbines rather than assumed data; otherwise such measures lose their insights. That is, the effectiveness of wind power plants in terms of electricity generation and per kWh cost/benefits should be measured based on the observed data so that policy makers can obtain more useful information.

To better estimate the electricity potential of Taiwan’s wind power development, this study gathers the 2012–2016 climate data of 370 scheduled farm sites, and then integrates the Weibull distribution with a threshold regression model to estimate the electricity generation from each site. Therefore, this study would be able to provide a more realistic result of wind power potential, which can be helpful for Taiwanese government to decide where to build the wind farm and to predict the net electricity output more accurately. Moreover, the results can be useful in the future economic and environmental analysis.

Methodology

The average wind power output estimation is essential in selecting potential wind farm site.¹⁷ It requires long-period wind speed data to achieve better wind power output estimation. However, it is costly to collect measured data at potential sites, especially in nationwide investigation. In this study, we use measured wind speed data from all meteorological stations in Taiwan to explore potential wind farm sites. Wind farms are usually built in open filed, but not meteorological stations. Different terrain characteristic and altitude lead to distinct wind speed. Therefore, we first adjust the wind speed of wind farm by neighbor meteorological station’s according to the turbine height and altitude, and the wind speed distribution can be achieved by fitting Weibull distribution. With such practice the theoretical wind power output can be estimated by fitting observed wind speed data to turbine’s power curve. We further utilize actual power output to refine theoretical wind power estimation for better performance by threshold regression. The resulted model can be applied to estimate other meteorological stations’ average wind power output. The methodology is briefly introduced as follows.

Wind speed distribution

For the estimation of the electricity generation of wind turbine, hourly data from meteorological station is used. In near ground, wind speed is affected significantly by atmospheric stability, surface roughness, and height interval. It is also necessary to adjust the observed wind speed data to the hub height. Power law equation has been set as the reference model addressed by the present study because of its good performance of capturing the vertical wind profiles.⁴¹ The power law equation is as follows^41,42

v_{w} = v_{m} {(\frac{h_{w}}{h_{m}})}^{α}

(1)

where

v_{w}

is wind speed at wind farm altitude plus hub height

h_{w}

v_{m}

is wind speed at meteorological station altitude

h_{m}

and

α

is wind speed shear exponent, depending on wind speed, atmospheric stability, and the height interval.

Wind speed varies dramatically in different time period. It is essential to retrieve wind characteristics for better wind power estimations. Because Weibull distribution has various shapes of distribution and previous studies^4,7 show that it is expected to give the best representation of wind characteristics in Taiwan, it is used to model wind speed. The two-parameter Weibull distribution consists of scale and shape parameters, and the distribution of wind speed can be estimated by Weibull distribution. The probability density function (p.d.f.) of Weibull distribution is as follows

f (v; λ, k) = \frac{k}{λ} {(\frac{v}{λ})}^{k - 1} e^{- {(\frac{v}{λ})}^{k}}; v \geq 0

(2)

where

k > 0

is the shape parameter and

λ > 0

is the scale parameter of the distribution.

Among methods to estimate Weibull distribution parameters, maximum likelihood estimator (MLE) outperforms than others.^43,44 Hence, we apply the MLE method to estimate the Weibull distribution parameters $k$ and $λ$ iteratively using the following equations

k = {(\frac{\sum_{i = 1}^{n} v_{i}^{k} ln (v_{i})}{\sum_{i = 1}^{n} v_{i}^{k}} - \frac{\sum_{i = 1}^{n} ln (v_{i})}{n})}^{- 1}

(3)

λ = {(\frac{1}{n} \sum_{i = 1}^{n} v_{i}^{k})}^{1 / k}

(4)

where

v_{i}

is the average wind speed at ith hour (m/s) and

n

is the number of nonzero wind speeds.

Electricity generation evaluation

Because of limitation of wind turbines, the wind energy cannot be extracted completely. Between cut-in and rated wind speeds, the power generated is expected to increase with wind speed and wind turbines can produce constant power ( $P_{R}$ ) between rated and cut-out wind speed. The actual wind power output is determined by the turbine’s power curve, which can be well described by the following quadratic equation^5,17

P (V) = {\begin{matrix} 0 & V < V_{I} \\ (b_{0} + b_{1} V + b_{2} V^{2} + b_{3} V^{3} + b_{4} V^{4}) P_{R} & V_{I} \leq V < V_{R} \\ P_{R} & V_{R} \leq V < V_{O} \\ 0 & V \geq V_{O} \end{matrix}

(5)

where

V_{I}

is cut-in wind speed,

V_{R}

is rated wind speed,

V_{O}

is cut-off wind speed, and

P_{R}

is rated power.

For convenience of calculation, we further estimate the normalized power curve of wind turbine by the following quadratic equation

NP (V) = {\begin{matrix} 0 & V < V_{I} \\ b_{0} + b_{1} V + b_{2} V^{2} + b_{3} V^{3} + b_{4} V^{4} & V_{I} \leq V < V_{R} \\ 1 & V_{R} \leq V < V_{O} \\ 0 & V \geq V_{O} \end{matrix}

(6)

After achieving the parameters $λ, k, b_{0}, b_{1}, b_{2}, b_{3}, b_{4}$ of Weibull distribution and the power curve of wind turbine, we calculate the expected electricity generation as follows

\begin{array}{l} E_{P} = \int_{V_{I}}^{V_{O}} P (V) f (V; λ, k) d V \\ = P_{R} \int_{V_{I}}^{V_{R}} (b_{0} + b_{1} V + b_{2} V^{2} + b_{3} V^{3} + b_{4} V^{4}) f (V; λ, k) d V + P_{R} \int_{V_{R}}^{V_{O}} f (V; λ, k) d V \end{array}

(7)

However, the amount of expected electricity generation is usually different from actual output. It may result from mechanical limitation, the variation of wind speed and other unobserved factors. Due to the complexity of mapping the expected electricity generation to actual output, the expected electricity may not be described by a single function. Therefore, we further apply a threshold regression model proposed by Bai and Perron⁴⁵ to model the difference between expected and actual electricity generation. With such applications, we can automatically detect structural change to decide the forms of functions to be used, and consequently achieve better performance. The equation of threshold regression is depicted as follows

\begin{matrix} P_{P} = C_{l} + β_{1 l} E_{P} + β_{2 l} E_{P}^{2} + β_{3 l} E_{P}^{3} + β_{4 l} E_{P}^{4} + ε; E_{P} \in I_{l}, \\ l = 1, \dots, L \end{matrix}

(8)

where

P_{P}

is actual electricity generation,

E_{P}

is expected electricity generation,

I_{l}

is the lth threshold interval, and

L

is the number of threshold intervals.

Results and discussion

Data set

In this study, wind power data set is collected from Taipower Corporation, the official electricity authority of Taiwan. Currently there are 16 operating wind farms, and their information is shown in Table 1. There are eight turbine models used in Taipower, and each model has its own hub height. Latitude, longitude, and altitude of wind farm are the coordinate data of one wind turbine inside it. The nearest meteorological station (Neighbor Station) is selected to estimate the wind speed of wind farm. Figure 1 shows the locations of 16 wind farm sites and their corresponding neighbor meteorological stations.

Table 1.

Wind farm information.

Wind farm	Latitude (meter)	Longitude (meter)	Altitude (meter)	Turbine model	Hub height (meter)	Neighbor station	Altitude (meter)
Shimen	25.2928	121.5796	62	Vestas V47/660	68.5	Fugueijiao	196
Linkou	25.1243	121.3070	6	Vestas V80/2000	67	Luzhu	19
Luzhu	25.1180	121.2762	11	Enercon E44/900	55	Luzhu	19
Guanyuan	25.0695	121.1208	7	GE Energy 1.5se/1500	65	Guanyin	29
Datan	25.0297	121.0511	8	GE Energy 1.5se/1500	65	Guanyin	29
	25.0297	121.0511	8	Vestas V80/2000	67	Guanyin	29
	25.0297	121.0511	8	Enercon E70/2300	64	Guanyin	29
Xiangshan	24.7373	120.8836	4	Gamesa G80/2000	76	Xiangshan	15
Zhonggang	24.3044	120.5440	3	Zephyros 2000	67	Wuqi	31.73
Zhonghuo	24.2132	120.4869	11	Zephyros 2000	67	Longjing	20
Zhanggong	24.1582	120.4412	4	Vestas V80/2000	67	Shengang	24
Wanggong	23.9989	120.3654	0	Enercon E70/2300	64	Puyan	15
Mailiao	23.8181	120.2575	8	Vestas V80/2000	67	Fangyuan	12
Sihu	23.6323	120.1424	2	Vestas V80/2000	67	Sihu	23
Hengchun	21.9549	120.7437	52	GE Energy 1.5se/1500	65	Maobitou	35
Zhongtun	23.6200	119.6102	12	Enercon E40/600	46	Penghu	10.7
Huxi	23.5886	119.6740	15	Enercon E44/900	55	Penghu	10.7
Jinsha	24.4890	118.4509	15	Vestas V80/2000	67	Kinmen	47.88

Figure 1.

The location for 16 wind farms and neighbor meteorological stations.

Electricity of these farms is measured monthly and the average hourly electricity generation of each farm is displayed in Table 2. It is obvious that the electricity outputs exhibit seasonal patterns, implying that the electricity generation cannot be calculated simply by multiply month output by number of operating months. Because of the occasional monsoons, it is generally to have the highest electricity output during October to March. To test the stability of wind speed, 2012–2016 hourly wind speed data of the 16 existing and 370 scheduled farms is collected from Central Weather Bureau, Taiwan.

Table 2.

Hourly electricity generation of wind farms (in kWh).

Wind farm	Jan.	Feb.	March	April	May	June	July	Aug.	Sep.	Oct.	Nov.	Dec.	Avg.
Shimen	295	246	193	123	102	98	93	95	172	280	280	367	194
Linkou	1,031	879	733	482	369	397	362	300	550	987	859	1,133	673
Luzhu	415	340	279	160	140	150	138	101	206	395	354	512	279
Guanyuan	886	785	624	401	340	402	323	262	446	855	719	967	584
Datan1	754	673	521	347	338	448	327	268	399	650	600	830	513
Datan2	1,110	969	777	576	545	686	539	442	593	1077	918	1,250	790
Datan3	964	866	686	452	462	591	418	389	578	910	788	1,182	691
Xiangshan	727	620	449	308	326	491	288	270	346	738	584	859	502
Zhonggang	803	713	431	290	221	241	196	147	255	573	580	840	441
Zhonghuo	645	583	410	260	164	159	163	122	254	553	509	738	380
Zhanggong	1,189	1044	785	489	322	357	289	272	471	944	848	1,169	681
Wanggong	1,373	1199	829	500	337	393	344	296	546	1039	894	1,300	754
Mailiao	1,066	940	638	379	243	319	253	207	338	741	619	1,035	565
Sihu	1,034	904	609	344	217	324	291	246	298	679	627	959	544
Hengchun	703	608	580	447	311	339	328	301	293	624	672	851	505
Zhongtun	417	354	270	170	103	114	90	86	175	324	327	451	240
Huxi	627	533	392	230	130	130	118	123	260	499	493	674	351
Jinsha	789	703	626	364	379	425	390	276	506	918	748	959	590
Avg.	838	733	555	358	285	343	280	238	380	726	641	902	524

Estimating distribution of wind speed

To estimate the distribution of wind speed in each farm site, we take hub height and altitude into account and make adjustment in accordance with site-specific characteristics. The formulation of this step is expressed in equation (1). This adjustment is not to eliminate the seasonality of wind speed; instead, we aim to estimate the distribution of wind speed more accurately. Therefore, as shown in Table 3, the adjusted data set still retains seasonality when the wind speed shear exponent is set as 0.143.

Table 3.

The adjusted wind speed data (m/s).

Wind Farm	Jan.	Feb.	March	April	May	June	July	Aug.	Sep.	Oct.	Nov.	Dec.	Avg.
Shimen	1.62	1.71	1.75	1.86	1.97	1.95	1.94	1.89	1.90	1.89	1.97	1.97	1.87
Linkou	3.44	3.34	3.08	2.61	2.39	2.62	2.77	2.52	3.07	3.59	3.24	3.75	3.04
Luzhu	3.39	3.29	3.04	2.57	2.36	2.58	2.73	2.49	3.03	3.54	3.20	3.69	2.99
Guanyuan	3.36	3.19	2.90	2.32	2.32	2.61	2.50	2.31	2.58	3.23	2.88	3.39	2.80
Datan1	3.37	3.19	2.91	2.32	2.33	2.62	2.51	2.31	2.58	3.24	2.89	3.39	2.81
Datan2	3.38	3.20	2.92	2.33	2.34	2.63	2.52	2.32	2.59	3.25	2.90	3.41	2.82
Datan3	3.36	3.19	2.90	2.32	2.32	2.61	2.50	2.31	2.58	3.23	2.88	3.39	2.80
Xiangshan	1.39	1.50	1.33	1.27	1.40	1.70	1.66	1.43	1.27	1.18	1.10	1.20	1.37
Zhonggang	6.42	6.07	4.94	4.17	3.81	4.20	4.20	3.87	4.47	5.70	4.98	6.19	4.92
Zhonghuo	3.97	3.74	3.21	2.62	2.43	2.71	2.87	2.55	2.81	3.56	3.22	4.06	3.14
Zhanggong	5.00	4.76	3.78	3.11	2.77	2.97	3.10	2.91	3.66	4.73	4.27	5.22	3.86
Wanggong	5.42	5.21	3.89	2.96	2.77	3.11	3.08	2.84	3.29	4.39	4.01	5.52	3.87
Mailiao	4.23	4.10	3.40	2.87	2.64	2.93	2.96	2.84	3.13	3.75	3.42	4.16	3.37
Sihu	4.55	4.40	3.64	2.94	2.69	3.10	2.94	2.37	2.75	3.76	3.40	4.43	3.41
Hengchun	4.45	4.24	4.28	3.30	2.76	2.63	2.84	2.67	3.13	3.78	4.74	5.09	3.66
Zhongtun	6.58	6.16	5.15	3.98	3.40	3.50	3.20	3.57	4.61	6.26	5.82	7.06	4.94
Huxi	6.76	6.33	5.28	4.09	3.49	3.60	3.28	3.67	4.74	6.43	5.98	7.25	5.08
Jinsha	3.46	3.26	3.12	2.68	2.54	2.58	2.48	2.35	3.15	3.74	3.42	3.71	3.04
Avg.	4.12	3.94	3.42	2.79	2.60	2.81	2.78	2.62	3.07	3.85	3.57	4.27	3.32

Based on the adjusted dataset, the parameters of Weibull distribution can be estimated by equations (2) to (4). With estimated Weibull distribution parameters the p.d.f. of estimated wind speed can be calculated, and consequently the wind speed of each scheduled site can be calculated. The error criterion is determined by the root mean squared error (RMSE) shown in equation (9)

R M S E = \sqrt{\frac{1}{N} \sum_{i} {({\hat{V}}_{l} - V_{i})}^{2}}

(9)

where

\hat{V_{i}}

is the estimated monthly average wind speed from Weibull distribution and

V_{i}

is the adjusted monthly average wind speed.

Table 4 shows the estimation error of wind speed by RMSE which are between 0.0036 and 0.0244. The largest error is detected at Huxi station, which may be resulted from the largest average wind speed. In general, the estimation error is within a relatively small range and the overall estimated results are acceptable.

Table 4.

Estimating error of wind speed (m/s).

Wind farm	Actual	Estimated	RMSE	NRMSE
Shimen	1.8684	1.8638	0.0081	0.0043
Linkou	3.0358	3.0281	0.0153	0.0051
Luzhu	2.9923	2.9847	0.0151	0.0051
Guanyuan	2.8000	2.7929	0.0149	0.0053
Datan1	2.8053	2.7983	0.0149	0.0053
Datan2	2.8163	2.8093	0.0150	0.0053
Datan3	2.8000	2.7929	0.0149	0.0053
Xiangshan	1.3679	1.3691	0.0036	0.0026
Zhonggang	4.9171	4.9098	0.0157	0.0032
Zhonghuo	3.1446	3.1424	0.0095	0.0030
Zhanggong	3.8555	3.8547	0.0130	0.0034
Wanggong	3.8734	3.8688	0.0133	0.0034
Mailiao	3.3676	3.3670	0.0107	0.0032
Sihu	3.4136	3.3996	0.0220	0.0064
Hengchun	3.6570	3.6473	0.0184	0.0050
Zhongtun	4.9419	4.9301	0.0237	0.0048
Huxi	5.0758	5.0636	0.0244	0.0048
Jinsha	3.0403	3.0364	0.0089	0.0029
Total	3.3207	3.3144	0.0154	0.0046

NRMSE: normalized root mean squared error; RMSE: root mean squared error.

Estimating electricity output

Power curve is the measurement of electricity output under various wind speeds, given a normal climate condition. Therefore, each wind turbine must have its own power curve. Currently there are eight turbine models deployed by Taipower including Enercon E40/600, Vestas V47/660, Enercon E44/900, GE Energy 1.5se/1500, Vestas V80/2000, Gamesa G80/2000, Zephyros 2000, and Enercon E70/2300, and their power curves can be estimated, which are shown in Figure 2. Since the manufactory of model Zephyros 2000 has been taken over, we will use the power curve of Vestas V80/2000 in station Zhonggang and Zhonghuo. We estimate the power curve using equation (6). Table 5 shows the wind turbine characteristics and normalized power curve estimation, where E40, V47, E44, GE1.5, V80, G80, E70 stand for the turbine models Enercon E40/600, Vestas V47/660, Enercon E44/900, GE Energy 1.5se/1500, Vestas V80/2000, Gamesa G80/2000, Enercon E70/2300, respectively. The power curves are fitting well because of small RMSE values.

Figure 2.

Power curves of turbines deployed by Taipower.

Table 5.

Wind turbine characteristics and normalized power curve fitting.

Wind turbine	E40	V47	E44	GE1.5	V80	G80	E70
Cut-in wind speed (V_I)	2.5	4.5	3	3	3.5	3.5	2.5
Rated wind speed (V_R)	13	14	17	13	14.5	15	15.5
Cut-off wind speed (V_O)	25	25	25	24	25	25	25
Rated power (P_R)	600	660	910	1500	2000	2000	2310
b0	−0.2623	2.1005	0.3193	−0.8200	0.0754	0.6611	0.0233
b1	0.2096	−1.2047	−0.1741	0.5957	−0.0227	−0.3436	0.0060
b2	−0.0611	0.2306	0.0274	−0.1535	−0.0046	0.0535	−0.0099
b3	0.0080	−0.0162	−0.0007	0.0169	0.0024	−0.0019	0.0025
b4	−0.0003	0.0004	0.0000	−0.0006	−0.0001	0.0000	−0.0001
RMSE	0.0067	0.0069	0.0153	0.0092	0.0076	0.0136	0.0112

Table 6 shows the estimates of electricity output where “Actual” stands for the average hourly actual wind power output, “Expected” represents the hourly expected wind power output, and “Estimated” is the hourly wind power output refined by threshold regression, all of which can be calculated by equation (7). The normalized root mean squared error (NRMSE) can be calculated by RMSE/actual. Traditionally the expected electricity output is based on wind speed estimation and power curve of turbine used. The estimated “Expected” electricity output is then refined to “Actual” electricity output with a threshold regression model. The results show that our approach can, in average, reduce estimating error by approximately 87%. “Estimated” values of NRMSE are around 0.1339 with the largest value occurring in Shimen station. This may be explained by that because Shimen station is built in coastal area, but its neighbor meteorological station (Fugueijiao) is located in mountain, showing that differences of site-specific characteristics would result in distinct wind speeds, thereby producing noisy results. The results show that, in terms of fitness of data and power curves, estimates obtained from our approach outperform estimates from previous studies, implying that an additional step of accommodating a threshold regression model can eliminate estimation errors considerably and could be a feasible and attractive approach.

Table 6.

Wind power output estimation (kWh).

Wind farm	Actual	Expected	Estimated	RMSE (expected)	RMSE (estimated)	NRMSE (expected)	NRMSE (estimated)
Shimen	194.27	2.91	196.80	215.03	38.46	1.1069	0.1980
Linkou	673.47	71.70	661.04	667.36	75.04	0.9909	0.1114
Luzhu	278.62	21.15	283.94	289.85	33.61	1.0403	0.1206
Guanyuan	584.06	30.77	579.28	607.72	55.00	1.0405	0.0942
Datan1	513.01	31.00	536.36	522.44	60.60	1.0184	0.1181
Datan2	790.17	51.33	768.89	788.56	113.11	0.9980	0.1431
Datan3	690.54	45.91	661.48	694.48	79.71	1.0057	0.1154
Xiangshan	501.70	2.55	494.27	554.10	56.08	1.1044	0.1118
Zhonggang	440.81	306.92	456.99	197.85	53.21	0.4488	0.1207
Zhonghuo	380.02	89.17	382.23	353.39	49.92	0.9299	0.1314
Zhanggong	681.50	163.85	682.85	588.66	83.41	0.8638	0.1224
Wanggong	754.17	178.48	726.71	654.81	121.64	0.8683	0.1613
Mailiao	564.84	95.95	560.34	551.31	67.71	0.9760	0.1199
Sihu	544.32	119.04	567.31	494.52	72.26	0.9085	0.1328
Hengchun	504.75	80.01	509.47	456.63	60.40	0.9047	0.1197
Zhongtun	240.17	92.81	255.56	171.17	43.08	0.7127	0.1794
Huxi	350.63	117.69	355.46	272.98	45.47	0.7785	0.1297
Jinsha	590.25	56.36	600.91	577.72	66.58	0.9788	0.1128
Total	523.82	89.15	523.82	520.36	70.12	0.9934	0.1339

So far we have determined that the threshold regression model can better estimate the power curves and electricity potential of existing sites. The next step is to estimate the wind power output for all meteorological stations to investigate the which scheduled sites are prominent, if not dominant. The markers plotted In Figure 3 represent meteorological stations in Taiwan while the darker ones tell which sites have higher predicted electricity output. The results show that most meteorological stations located in small islands usually perform well, as well as some coastal stations located in northeast area. Among all scheduled sites, the Dongjidao station is found to have the largest predicted wind power output of about 1606 kW per hour. Table 7 presents the predicted electricity output from the top 20 stations.

Figure 3.

Potential farm sites distributions in Taiwan.

Table 7.

Meteorological stations of top 20 wind power output (kW/hr).

Station	Estimated power	Station	Estimated power
Dongjidao	1606	Yushan	770
Pengjiayu	1562	Sandiaojiao	734
Xiyu	1455	Datunshan	713
Dongju	1368	Wuqi	708
Lanyu	1194	Huayu	700
Bitoujiao	1135	Qigu	690
Yushanfengkou	1132	Gueishandao	687
Xinwu	832	Beimen	649
Ludao	827	Wufengshan	628
Wuzhihshan	782	Penghu	615

If Dongjidao station is picked with turbine model of Enercon E70/2300, it could produce 14.07 million kWh per year, and be capable of replacing 3.52 million liters of gasoline or 5204 tons of coal. The carbon emission reduction could be 7441 tons, equivalent to the afforestation benefits of approximately 752 ha. Table 8 displays the benefits from Dongjidao station. Because the average electricity consumption per family is 3600 kWh annually, the annual estimated electricity supply from Dongjidao station would be able to satisfy the needs of approximately 3869 families.

Table 8.

The effectiveness of potential Dongjidao farm.

Power output	Energy saving			Carbon reduction
(kwh)	Fuel (1000 L)	Coal (ton)	Gas (ton)	Emission reduction (ton)	Afforestation benefit (hectare)
14065894	3,516	5,204	2,321	7441	752

Practical implications of this study

We have shown that our approach can better fit the power curve, estimate electricity output according to site-specific characteristics, and predict the electricity supply of all scheduled sites. However, some aspects such as the usefulness of the results, the robustness of the analysis, and possible economic and environmental consequences merit more discussion.

The usefulness of the results. We point out that sites with highest electricity output are usually located in nearby islands, implying that more efforts in terms of materials, transportation costs, and electricity transmission are required. Therefore, although the results have indicated some potential sites, it is too early to conclude that those sites must be selected. It is also noteworthy to understand that even certain sites have highest electricity potential; they may not do better than low electricity potential sites because global climate change has been considered to be an important factor altering the temperature and precipitation, all of which could have influences on wind stability and continuity.

The robustness of this analysis. Prior to this study, seldom studies focus on the accuracy of estimates of electricity outputs because they do not have sufficient information to do so. With data collected from existing stations, this study is able to conduct a comparative analysis by fitting the power curves with actual data set. However, this does not guarantee that this work finishes all tasks. For example, how the economic effects from those scheduled sites can be measured and realized, or how much the society should afford in terms of tax deduction or subsidy must be investigate to provide a more general picture about wind power development. Knowing the electricity output of each site is useful, but linking this information to a boarder category is even more important.

The economic and environmental consequences must be investigated. As has been seen that the economic and environmental associated with wind power development should be analyzed before the policy makers can make final decision. The question is “how do we measure these benefits and via what techniques?” The answer to this question may be complex because many factors such as emission price, per kWh benefit and cost, site construction and maintenance costs play a role and all of them need to be evaluated. One suggestion is to use lifecycle analysis, which can decompose the total costs into separate components. After that sensitivity analysis may also help because it can analyze the influence of individual factor under various conditions. Same approach can be applied to examine environmental benefits. However, it is noteworthy that carbon sequestration is calculated by comparing with the use of fossil fuels. If the wind power development is used to substitute nuclear power, such measures may not be adequate since nuclear power does not emit CO₂ as gasoline, coal, or diesel, and the gains from emission trade may be removed or modified. In addition to carbon sequestration, environmental benefits may include the reduced exposure to radiative matters or increased quality of nearby watershed, but different analytical frameworks may be required to accomplish these tasks.

It is noteworthy to point out that the results are estimated based on the past climate data and reliability of the estimates may be reduced if some uncontrollable factors have changed. For example, if future climate deviates from current patterns significantly, the usefulness of results provided in this study may be limited, and the actual electricity output from wind power development must be adjusted and recalculated.

Conclusion

Previous studies show that wind power can be an attractive renewable energy source to Taiwan, but poorly fitted power curves cannot provide accurate measures about how much electricity can be actually produced, thereby offering little information to decision makers. This study points out that by utilizing a threshold regression model, along with the adjustment of wind speed data of existing farm sites, the power curves can be better fitted and the estimation errors of electricity output can be largely reduced. With such application the electricity potential of 370 scheduled farm sites can be estimated, providing a basis for future site selection.

In general, our approach may be universally applied because we have demonstrated that the power curves can be well fitted, the approach used in this study may be universally applied. However, since the site-specific characteristics and climate conditions could exhibit larger difference in different countries, parameters provided in this study may not be suitable for other countries and regions. Keeping the global circulation data updated and employing the IPCC climate change projections may help, but uncertainty will not be eliminated.

Footnotes

Acknowledgements

We thank for the assistance of Dr. Bruce McCarl at Texas A&M University and Dr. Chi-Chung Chen at National Chung-Hsing University for their modeling opinion.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: We appreciate the financial support from the Distinguished Young Scholar Program of Jiangxi Province (20171BCB23047), University Social Science Foundation of Jiangxi (JC17205), and Scientific Program of Jiangxi’s Department of Education (GJJ160437).

Chih-Chun Kung obtained his PhD from Texas A&M University in 2010. Chih-Chun is currently working as a professor at Hubei University of Economics, China

Li-Jiun Chen received her PhD from National Taiwan University in 2012. Li-Jiun is currently a assistant professor at Feng Chia University, Taiwan.

Tsung-Ju Lee received his PhD from National Jiaotung University. Tsung-Ju is currently a assistant professor at National Penghu University of Science and Technology, Taiwan.

Xianling Jiang is a professor in School of International Trade and Economic at University of International Business and Economics, China.

Ruiqi Lin is a graduate student at Jiangxi University of Finance and Economics, China.

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