Wind potential assessment for an efficient wind farm sizing

Abstract

The effectiveness of autonomous wind plants depends basically on the characterization, sizing, and environmental design and analysis of its renewable energy conversion system. This article presents an assessment on wind potential characterization to be used to compute the size of a wind farm turbine. Different methods are adopted to estimate parameters of the Weibull distribution. The modified maximum likelihood method is selected as the most accurate with reference to comparison between many approaches output results and measurements provided by the National Institute of Meteorology. Also, an artificial neural network–based algorithm is developed to optimize the MMLM parameters. The monthly wind potential distribution is consequently computed for Sfax, Tunisia. Obtained results are used to optimize the size calculation of wind turbine blades and battery capacity for a standalone wind farm. The proposed approach profitability is evaluated upon the lost produced energy.

Keywords

Estimation assessment sizing comparison wind potential artificial neural network

Introduction

In some remote areas, a major part of population does not have access to the electricity that inhibits their life. Installation of huge electricity production central is so costing. Hence, home autonomous plants such as wind turbines and photovoltaic panels are installed in isolated areas. Wind energy is considered the most attractive as it ensures high output power and it provides energy all the time contrary to photovoltaic energy which is available only during daylight (Brahmi and Chaabene, 2012). In order to be efficient, optimum sizing for wind energy installations should be carried out on the basis of the wind potential evaluation (Keyhani et al., 2010). The assessment is complicated because the wind speed and availability are stochastic. The wind speed probabilistic distribution is a recommended approach as it reproduces the wind signal (Akdag and Dinler, 2009; Celik, 2006). However, it requires the determination of the monthly distribution of wind energy. The wind speed variation should be estimated during a fixed time period (Islam et al., 2011). The forecasting methods of wind speed must be accurate to provide pragmatic wind speed. Many methods have been adopted in literature, such as artificial neural networks (ANNs) that use the propagation algorithm, fuzzy logic (Alexiadis et al., 1999; Damousis et al., 2004; Lawan et al., 2014; Ranganayaki and Deepa, 2016; Zhang et al., 2014), Kalman filter (Song et al., 2016), and also the kernel methods known by their generalization ability (Bouzgou, 2014). Commonly, wind speed is described by means of the Weibull function. Also, many researchers evaluated the use factor (UF) of wind energy (Ben Amar et al., 2008).

In addition, many attempts have been made to optimize the sizing of renewable energy plants. Among the used approaches, the space design generation which helps in selecting and optimizing the appropriate system configuration on the basis of desired objectives (Kulkarni et al., 2007, 2008, 2009). Sizing a wind/battery plant should take into account the wind potential and the load profile (Brahmi and Chaabene, 2012). As for the battery bank size, it is determined considering the number of days of autonomy (Puri, 2013; Yahyaoui et al., 2013). In case of hybrid systems sizing, the wind generator rating is usually treated to be of major weight compared to other the sources (Smaoui et al., 2015). Protogeropoulos et al. (1992) proposed a way to size the wind turbine on the basis of the month during which the wind availability is minimum and/or the peak load. Notton et al. (2011) coordinate different types of power curve images as well as the reliability of the system in terms of not met load time to compute wind turbine blades.

This work puts forward the sizing of wind energy–based plants. The sizing approach is structured around three steps: the modeling of wind conversion system, the load profile characterization, and the estimation of the wind potential. Well-known identification algorithms are illustrated and validated on the basis of measures on metrological data in order to select the most accurate approach that estimates the parameters of the Weibull model. The selected approach is improved by an ANN procedure based on wind potential measurements. Cost assessment is consequently established.

System modeling

The architecture of a standalone wind farm (wind/battery) is depicted in Figure 1. The considered system is mainly composed of an AC bus that gathers a wind generator connected to an AC/DC inverter. It is equipped by a maximum power point tracker (MPPT) to exploit the maximum of available wind energy. Battery is connected to a buck/boost DC/DC converter to ensure the continuous supplying of the load and to store the surplus of generated energy.

Figure 1.

Block diagram of wind farm.

Wind energy conversion system

The mechanical power $P_{a e r}$ is expressed by (equation (1))

P_{a e r} = \frac{1}{2} ρ \cdot S \cdot C_{p} \cdot v^{3}

(1)

$C_{p}$ is the power rate coefficient.

The mechanical torque is given by

C_{a e r} = \frac{P_{a e r}}{Ω_{t}} \Leftrightarrow C_{a e r} = \frac{1}{2} ρ \cdot S \cdot C_{p} \cdot v^{3} \frac{1}{Ω_{t}}

(3)

$Ω_{t}$ represents the tip-speed ratio. The turbine torque $C_{a e r}$ is adapted to the machine torque $C_{g}$ by a gearbox with gain G

C_{g} = \frac{C_{a e r}}{G}

(4)

The vector control strategy applied to the permanent magnet synchronous machine (PMSG) imposes the following reference stator currents

{\begin{cases} i_{s q_r e f} = \frac{C_{e m_r e f}}{p ϕ_{m d}} \\ i_{s d_r e f} = 0 \end{cases}

(5)

where $C_{e m_r e f}$ is the electromagnetic reference torque. To ensure the maximum power point from the PMSG, this electromagnetic torque is given by the following expression (Chinchilla et al., 2006)

C_{e m_r e f} = \frac{ρ π R^{5} C_{p m a x}}{2 λ_{o p t}^{5}} Ω^{2}

(6)

The pump motor model

The motor power is expressed as

P_{m o t} = η_{m o t} P_{e}

(7)

$η_{m o t}$ is motor efficiency.

The centrifugal pump power is expressed as (Kasbadji Merzouk and Merzouk, 2006; Mathew et al., 2002a, 2002b; Pallabazzer, 1995)

P_{u} = η_{p u m p} P_{e} = ρ_{w a t e r} \cdot g \cdot H \cdot Q

(8)

where $H$ is height of rise $(m)$ , $Q$ represents the water flow $(m^{3} / s)$ , $g$ is the gravity acceleration $({m / s}^{2})$ , and $ρ$ is the water density $({kg / m}^{3})$ . For a time step $Δ T$ , the volume of pumped water ${(m}^{3})$ is given by

V_{w a t e r} = Q \cdot Δ T

(9)

Storage system

A nonlinear dynamic model of a lead–acid battery is used to determine the instantaneous depth of discharge $(d o d)$ . Figure 2 represents the equivalent circuit (De Soto et al., 2006).

Figure 2.

Equivalent circuit of a lead–acid battery cell.

The depth of discharge $(d o d)$ is given by

d o d = \frac{C_{R}}{C_{p}}

(10)

C_{p} = I_{B}^{K} \times T

(11)

$k$ is the Peukert’s coefficient, and $C_{R}$ is the stored charge in the battery. The instantaneous capacity of the battery is given by

\frac{δ C_{R}}{δ t} = \frac{I_{B}^{K}}{3600}

(12)

The algebraic value of the battery current is given by

I_{B} = \frac{E - \sqrt{E^{2} - 4 R P_{B}}}{2 R}

(13)

where $E = n (2.15 - d o d \times (2.15 - 2))$ . The battery voltage is expressed by

V_{B} = E - R \times I_{B}

(14)

The output power is

P_{B} = V_{B} \times I_{B} = (E - R \times I_{B}) \times I_{B}

(15)

Sizing approach description

First, Weibull distribution parameters are estimated by applying many classical methods. Then, the more accurate method is selected since it provides minim error between estimated and measured wind speed. A synthesis of the different approaches is shown. An ANN is applied to the output of the most accurate approach in order to evaluate the wind potential in Sfax. Considering a typical agricultural farm load profile, sizes of different components of the plant are calculated. The sizing algorithm depends on

The needed load profile;

The wind potential;

The models of the plant components.

The computed sizes should ensure the load supply throughout the year, while protecting the battery against excessive discharge (Figure 3).

Figure 3.

Proposed sizing approach.

Sizing of the wind conversion system

Initially, the surface swept by the blades of the wind turbine is fixed to

{\hat{S}}_{w i n d} = \frac{m e a n (E_{n e e d})}{m e a n (E_{m o n t h l y} / m 2)}

(16)

Then, this surface is adjusted thanks to an iterative calculation that converges while a minimum of lost energy is obtained.

Battery sizing

The stored energy in a battery is given by the following equation

E_{t o t} = C \times V_{b a t}

(17)

The technology of the selected battery allows $80 %$ as maximum depth of discharge $(D O D_{m a x} = 80 %)$ . The usable energy $E_{u s a b l e}$ in the battery is expressed by equation (18)

E_{u s a b l e} = E_{t o t} \times D O D_{\max} = E_{j} \times J_{a u t}

(18)

where $E_{j}$ is the daily needy energy and $J_{a u t}$ is the number of autonomy days. Hence

C = \frac{E_{j} \times J_{a u t}}{V_{b a t} D O D_{m a x}}

(19)

Wind potential assessment

Weibull description

The general form of the Weibull distribution, which is a two parameter function, for wind speed is among the widely used models. The essential factor in wind potential assessment is the distribution of wind speed. It characterizes the velocity function of two parameters (k, c) (Lim and Jeong, 2010). The general Weibull distribution function is given by equation (20)

F (\bar{v}) = 1 - e^{{(\frac{v}{c})}^{k}}

(20)

where k is the shape parameter and c is the scale parameter $(in m / s)$ . The probability of observing a classified speed $\bar{v}$ is defined by equation (21)

\begin{matrix} f (\bar{v}) = \frac{d F (\bar{v})}{d \bar{v}} = \frac{k}{c} {(\frac{v}{c})}^{k - 1} e^{{(- \frac{v}{c})}^{k}} & v > 0 \end{matrix}

(21)

Comparative study of numerical methods for identifying and estimating of Weibull parameters

Many methods are used in the estimation of k and c. The commonly used approaches are as follows:

Least squares method (LSQ);

Maximum likelihood method (MLM);

Modified maximum likelihood method (MMLM);

Rayleigh distribution.

LSQ

Named also “Weibull plot,” an efficient fit of the Weibull cumulative frequency distribution is applied (equation (20)) (Mohammadi and Mostafaeipour, 2013). It can be given by a straight line

\ln (- \ln (1 - (F (v)))) = k \ln (v) - k \ln (c)

(22)

The plotting of $\ln (v)$ against $\ln {- (1 - \ln (F (v)))}$ is affine with an intercept $k \ln (c)$ with the y-axis and a slope $k$ . Let $y = \ln (- \ln (1 - (F (v)))) = a \ln (v) - b$

\begin{array}{l} a = k \\ b = k \ln (c) \\ x = \ln (v) \end{array}

Using the LSQ method applied on measures database vectors (Y, X), the Weibull parameters are accordingly estimated. Consider

X = (\begin{matrix} x_{1} \\ x_{2} \\ ⋮ \\ ⋮ \\ x_{n} \end{matrix}), Y = (\begin{matrix} y_{1} \\ y_{2} \\ ⋮ \\ ⋮ \\ y_{n} \end{matrix}), H = (\begin{matrix} x_{1} & 1 \\ x_{2} & 1 \\ ⋮ & ⋮ \\ ⋮ & ⋮ \\ x_{n} & 1 \end{matrix}), ε = (\begin{matrix} ε_{1} \\ ε_{2} \\ ⋮ \\ ⋮ \\ ε_{n} \end{matrix}), θ = [\begin{matrix} a \\ b \end{matrix}]

where ε is the white noise vector. The estimated vector $\hat{θ}$ is given by

\hat{θ} = {(H^{T} H)}^{- 1} H^{T} Y

(23)

MLM

Maximum likelihood is a statistical method proposed by Stevens and Smulders (Chang, 2011; Costa et al., 2012; Li, 2011). Through numerical iterations, MLM is solved to identify the parameters of Weibull distribution. Shape and scale parameters are estimated by equations (24) and (25), respectively

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

(24)

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

(25)

where n is the number of data values.

Initially, the shape factor is fixed to 2 because experiences proved that k varies between 1.7 and 2.3 in major of cases.

MMLM

In order to make this method more precise (Chang, 2011; Costa et al., 2012; Li, 2011) and the available data restraint, a modification in the estimation of the shape parameter k is involved. The novel expression of k is given by

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

(26)

Rayleigh distribution

Rayleigh distribution is a particular case of Weibull distribution, considering k = 2, (Bivona et al., 2003; Rosen et al., 1999). The cumulative distribution function is given using following expression (equation (27))

F (v) = 1 - \exp (- \frac{π}{4} {(\frac{v}{v_{m e a n}})}^{2})

(27)

The density function is expressed by equation (28)

f (v) = \frac{π}{2} \frac{v}{v_{m e a n}} \exp (- \frac{π}{4} {(\frac{v}{v_{m e a n}})}^{2})

(28)

The Rayleigh distribution depends only of the mean speed which is calculated by

v_{m e a n} = \frac{1}{n} \sum_{i = 1}^{n} v_{i}

(29)

The ANN-based estimation approach

In the previous approaches while applied to the Weibull method, a classified speed must be used. Accordingly, the size of the database is restricted. The problem becomes accentuated in case of non-windy weather. To overcome this limitation, an ANN is added. Thus, ANN generates a huge data from meteorological measurements. As a result, the frequency for any speed is obtained (Figure 1).

The ANN controller is used to estimate the optimum photovoltaic implication coefficient for given solar and wind potentials. The architecture of the adopted neural network is composed of three layers (Figure 4). The input layer contains one neuron as it disposes of one input (wind speed $v$ ). The hidden layer includes five neurons; this number is fixed following the execution of empirical rules which start with a high number of neurons and eliminate the unnecessary ones on condition to reach network stability and output accuracy. The output layer contains one neuron that provides the frequency $F_{v}$ .

Figure 4.

The architecture of the ANN-based approach.

The activation function of neurons is given by the hyperbolic tangent function (Haykin, 1998)

Y = f (U) = W_{0} \times \tanh (W_{1} \times U + b_{1}) + b_{0}

(30)

Wind speed extrapolation

The wind speed increases with altitude. Commonly, the wind speed is estimated at 20 and 30 m of altitude. Consequently, the study of the feasibility of any wind farm needs to estimate the wind speeds at the various altitudes. Based on the mean speed $(V_{a})$ at height $Z_{a}$ , the mean speed $V_{m} (z)$ at the height $z$ is given as

V_{m} (z) = V_{a} {(\frac{z}{z_{a}})}^{α}

(31)

where $α = x - 0.088 \log (V_{a}) / 1 - 0.0881 \log (Z_{a} / 10)$ and the coefficient x at Sfax, Tunisia, is fixed to $0.31$ .

Results and discussion

In order to evaluate their performances, developed approaches are tested using database offered by the National Institute of Meteorology (NIM). Monthly measured and estimated data were compared by calculating the normalized mean bias error (NMBE) expressed by

N M B E (%) = 100 \frac{\sum_{i = 1}^{N} | E s t i m a t i o n (i) - m e a s u r e (i) |}{\sum_{i = 1}^{N} m e a s u r e (i)}

(32)

where N is the number of measures of 1-year meteorological data at Sfax airport station at height of 12 m (Figure 5).

Figure 5.

Measured wind speed in Sfax.

Figure 6 provides estimated and measured wind speed frequencies for all months. The MMLM is the most accurate one as it returns a monthly error between 2.3419% and 11.6330%. The LSQ method provides an error interval of [0.1007, 18.9902]. This is due to its graphic based calculation. The Rayleigh method returns high error as it considers a constant k. The MMLM approach is recognized efficient because it engenders an acceptable error interval [0.2266, 17.5336] (Table 1).

Figure 6.

Measured and estimated wind speed frequency.

Table 1.

Monthly errors obtained from the four approaches.

	NMBE (%)
	LSQ	MLM	MMLM	Rayleigh
January	7.1256	4.6279	2.3419	3.8278
February	0.2724	0.6066	0.0025	0.5623
March	0.5061	0.4598	−0.2930	0.4446
April	0.3186	0.8640	0.2804	0.7861
Mai	2.8032	2.8975	1.8590	2.7575
June	0.2748	0.2568	0.1371	0.2364
July	0.3521	0.4158	0.2582	0.3945
August	18.990	17.534	11.633	16.3416
September	0.3507	0.5927	0.3027	0.5352
October	0.8026	1.4581	0.8603	1.3580
November	0.2584	0.3778	0.2445	0.3480
December	0.1007	0.2266	0.1136	0.2085
Mean	2.5353	2.2385	1.0669	2.0526

NMBE: normalized mean bias error; LSQ: least squares method; MLM: maximum likelihood method; MMLM: modified maximum likelihood method.

Figure 7 shows the density function of the wind speed according to different methods for four seasons.

Figure 7.

Season validation of density function of different methods.

The ANN-based MMLM has been improved as given in previous section. Table 2 shows the obtained monthly values of k and c.

Table 2.

Monthly shape parameter k and scale parameter c in Sfax, Tunisia.

	$k$ k	$c$ c
January	1.2554	3.2379
February	1.2115	4.2832
March	1.2730	3.1508
April	1.3978	4.7438
May	1.3002	4.3565
June	1.4283	5.2307
July	1.2931	4.3608
August	1.5771	5.2983
September	1.8210	6.6653
October	1.3978	4.7438
November	1.5559	4.4244
December	1.6560	6.6908

Based on the shape and scale parameters, the wind potential is evaluated. Wind power density per m² of a site can be expressed by

P_{m} = \frac{1}{2} ρ_{a i r} C_{p} (1 + 3 I^{2}) c^{3} Γ (1 + \frac{3}{k}) {(\frac{z}{z_{a}})}^{3 α}

(33)

where Γ is the defined Gamma function, which is given by

Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t

where $ρ$ is the air density $(ρ = 1.225 {kg / m}^{3})$ , I is the turbulence, and $C_{p}$ is the power coefficient. The corresponding monthly energy is expressed as follows (equation (34))

E_{m} (kWh / month) = \frac{24 \times 365}{1000} P_{m}

(34)

The characteristic speeds (the mean speed $V_{M}$ , the energetic speed $V_{E}$ , and the frequent speed $V_{F}$ ) can be computed as

V_{M} = c Γ (1 + \frac{1}{k})

(35)

V_{E} = c Γ {(1 + \frac{2}{k})}^{\frac{1}{k}}

(36)

V_{F} = c Γ {(1 - \frac{1}{k})}^{\frac{1}{k}}

(37)

Using Table 2, the density $f (v)$ distribution is depicted by Figure 8. For 2 months (January and February), estimations follow measures.

Figure 8.

ANN-based approach estimation of f(v).

Wind potential shown in Figure 9 presents a non stationary variation while its maximum is in April and its minimum is in December.

Figure 9.

Monthly wind energy distribution.

An agricultural farm is chosen as a case study to compute the sizes of its generators that fulfill the farm required energy. Load profiles (in per unit of $KWh$ ) are defined for quarter-hour time step for each day over 1 year. Official and floating holidays, all seasonal, weekly, and daily influences (Friedl et al., 2007) are considered. Daily farm energetic consumption profiles are shown in Figure 10. The curves present two peaks: at the morning (6 a.m.) and at the evening (7 p.m.).

Figure 10.

Daily farm energetic consumption.

Following the execution of the sizing algorithm (section “Wind potential assessment”), the obtained wind generator blades and battery capacity are $S_{w i n d} = 67.7733 m 2$ and $C_{b a t} = 1200 Ah$ , respectively.

Cost assessment

An investigation on the plant cost is carried out in order to determine the plant profitability (Eftichios et al., 2006)

\begin{matrix} C_{t o t a l} = N_{w} \times (C_{w} + n_{y} M_{w}) + N_{b a t} \times (C_{b a t} + y_{b} C_{b a t} + (n_{y} - y_{b} - 1) M_{b}) \\ + (n_{c h o p} C_{c h o p} (y_{c h o p} + 1) + n_{c h o p} M_{c h o p} (n_{y} - y_{c h o p} - 1) \\ + (n_{i n v} C_{i n v} (y_{i n v} + 1) + n_{i n v} M_{c h o p} (n_{y} - y_{i n v} - 1) \end{matrix}

(38)

where $C_{b}$ (€/battery) is the battery cost, $M_{b a t}$ (€/battery per year) is the maintenance cost for one battery, $C_{c h o p}$ (€/chopper) is the chopper cost, $M_{c h o p}$ (€/chopper per year) is the maintenance cost for one chopper, $C_{i n v}$ (€/inverter) is the cost of the inverter, $M_{i n v}$ (€/inverter per year) is the maintenance cost for one inverter, $N_{w}$ is the number of wind generators, $N_{b a t}$ is the number of batteries, $n_{y}$ is the installation lifetime (estimated to 20 years), $C_{w}$ (€/wind turbine) is the wind conversion system cost, $M_{w}$ is the wind conversion system maintenance cost, $y_{b a t}$ is the number of times the batteries are replaced during $n_{y}$ years, $n_{c h o p}$ is the number of choppers, $y_{c h o p}$ is the number of times the chopper is replaced during $n_{y}$ years, and $y_{i n v}$ is the number of the inverter replaced during $n_{y}$ years. All costs are described in Table 3.

Table 3.

Cost parameters for the installation components (Eftichios et al., 2006).

Parameters	Name	Values
C_bat (€/battery)	The battery cost	264
M_bat (€/battery per year)	The maintenance cost for one battery	2.64
C_chop (€/chopper)	The chopper cost	200
M_chop (€/chopper per year)	The maintenance cost for one chopper	2
C_inv (€/inverter)	The cost of the inverter	1942
M_inv (€/inverter per year)	The maintenance cost for one inverter	19.42
C_w (€/1 W)	The cost production of 1 W by the wind generator	2.6
M_w (€/1 W per year)	The maintenance cost for one 1 W by the wind generator	0.026

The effectiveness of the system sizing and the economic study request a computing of the system profitability. Referring to Tunisian prices of electricity provided by the electric power provider company (Tunisian Company of Electricity and Gas: STEG), the cost of 1 kWh is 0.061 €, the license fees are 1 (€/kW/month), and taxes are 30% of the whole charges. As the installation need is 30,834 kWh/year, the total cost of the yearly consumption is 3.230 K€. Hence, the profitability is calculated as follows

Profitability = \frac{Cost of the renewable plant}{Price of the yearly consumption}

(39)

Total cost = 17.5 K€, cost STEG = 3.230 K€, and profitability = 5.4 years.

Conclusion

An optimum sizing algorithm is developed to provide the optimal size of wind generator supplying an autonomous agriculture farm. The sizing approach is based on the wind potential estimation, the plant components models, and the load profile characterization. The MMLM is selected as the most accurate method to estimate wind potential. Based on ANN, the Weibull parameters estimation is adjusted to deliver accurate values of k and c. The monthly wind energy distribution is computed for Sfax, Tunisia, then validated by measures. Referring to the yearly energy balance, the algorithm offers generator sizes that are able to cover the farm energy need. Finally, an investigation on the plant cost is carried out in order to show the sizing profitability. In future work, the introduction of a third Weibull parameter should improve the wind potential estimation.

Footnotes

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) received no financial support for the research, authorship, and/or publication of this article.

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