energies Article
Wind Turbine Power Curve Design for Optimal Power Generation in Wind Farms Considering Wake Effect Jie Tian 1,2, *, Dao Zhou 1 , Chi Su 1 , Mohsen Soltani 1 , Zhe Chen 1 and Frede Blaabjerg 1 1 2
*
Department of Energy Technology, Aalborg University, 9220 Aalborg, Denmark;
[email protected] (D.Z.);
[email protected] (C.S.);
[email protected] (M.S.)
[email protected] (Z.C.);
[email protected] (F.B.) Sino-Danish Centre for Education and Research, 8000 Aarhus, Denmark Correspondence:
[email protected]; Tel.: +45-3066-6882
Academic Editor: David Wood Received: 2 December 2016; Accepted: 15 March 2017; Published: 20 March 2017
Abstract: In modern wind farms, maximum power point tracking (MPPT) is widely implemented. Using the MPPT method, each individual wind turbine is controlled by its pitch angle and tip speed ratio to generate the maximum active power. In a wind farm, the upstream wind turbine may cause power loss to its downstream wind turbines due to the wake effect. According to the wake model, downstream power loss is also determined by the pitch angle and tip speed ratio of the upstream wind turbine. By optimizing the pitch angle and tip speed ratio of each wind turbine, the total active power of the wind farm can be increased. In this paper, the optimal pitch angle and tip speed ratio are selected for each wind turbine by the exhausted search. Considering the estimation error of the wake model, a solution to implement the optimized pitch angle and tip speed ratio is proposed, which is to generate the optimal control curves for each individual wind turbine off-line. In typical wind farms with regular layout, based on the detailed analysis of the influence of pitch angle and tip speed ratio on the total active power of the wind farm by the exhausted search, the optimization is simplified with the reduced computation complexity. By using the optimized control curves, the annual energy production (AEP) is increased by 1.03% compared to using the MPPT method in a case-study of a typical eighty-turbine wind farm. Keywords: maximum power point tracking (MPPT); optimization; wake effect; wind power generation; wind farms
1. Introduction In recent years, wind power has increasingly been integrated into the power system worldwide. According to the International Energy Agency (IEA) wind report [1], wind energy production provided close to 4% of the world’s electricity demand in 2015. In many countries, the development of large-scale wind farms has already been started and tended to move from onshore to offshore. In 2015, the offshore wind sector had a strong year, with an estimated 3.4 GW connected to the power grid out of a world total amount of 12 GW. In wind farms, especially large-scale ones, the power loss due to the wake effect came to be of particular importance. According to a field investigation from onshore wind farms, the power loss due to the wake effect is about 5%–10% of overall power generation [2]. Because of the higher investment in offshore wind farms, the per-unit installation area is lower than for onshore wind farms. Thus, the power loss due to the wake effect in large-scale offshore wind farms may reach a higher value, up to approximately 15% [3,4]. In modern wind farms, a widely implemented active power control method is maximum power point tracking (MPPT) [5,6]. Each wind turbine is controlled by the MPPT method to generate the maximum active power at its current wind speed, without the consideration of the power loss due to the wake effect in the wind farm. Energies 2017, 10, 395; doi:10.3390/en10030395
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Many researchers have focused on the mitigation of power loss in the wind farm due to the wake effect. By the optimal control of each individual wind turbine, the total active power of the wind farm can be increased. By developing new active power controllers in [7], using the boundary layer tunnel experiments in [8], and analyzing the wind turbine load in [9], the authors concluded that the power loss in the wind farm due to the wake effect can be reduced by optimizing the pitch angle and tip speed ratio of each wind turbine. In [10,11], optimal pitch angle and tip speed ratio of all the wind turbines are selected at the same time by the optimization algorithms to maximize the total active power of the wind farm, where the wind speed of each wind turbine is estimated by the wake model with the ambient wind speed. The optimized pitch angle and tip speed ratio of each wind turbine are supposed to be implemented in the wind farm central controller. Thus, each wind turbine is controlled according to the estimated wind speed. Considering the estimation error of the wake models, there is a difference between the estimated wind speed and the real wind speed at the position of each wind turbine. In the case that the estimated wind speed is higher than the real wind speed, the optimized active power reference can be higher than the available active power. In this case, due to greater output power than input power, the rotor speed will be automatically decreased. Afterwards, according to aerodynamic model, due to the rotor speed decrease, the available active power will be further decreased. Then, the rotor speed will be further decreased. Gradually, the wind turbine will be halted [12]. In [13], the authors calculated the transient wind speed of each wind turbine by the computational fluid dynamics (CFD) method, where the computation complexity is the main drawback of this approach. In [14,15], online model free optimization methods are proposed to increase the total active power of the wind farm. This method generates the optimal pitch angle and tip speed ratio for each wind turbine by the comparison of the active power of the wind turbine and of its neighborhood wind turbines. The problem with this method is that the algorithm has to wait during the transition of wind conditions, as it takes time for the wind flow to transit from one steady-state condition to another. As acknowledged by the authors, this method is much more suitable for the steady-state wind conditions. In this paper, firstly, the optimal pitch angle and tip speed ratio of each wind turbine to maximize the total active power of the wind farm are selected by the exhausted search method. Compared with the particle swarm optimization (PSO)- and genetic algorithm (GA)-based optimization methods as adopted in [10,11], the advantage of by the exhausted search method is that the total active powers of the wind farm at all sets of the pitch angle and tip speed ratio of all the wind turbines are calculated. By the comparison of the total active power of the wind farm at all sets of the pitch angle and tip speed ratio of all the wind turbines, the implementation of the optimized pitch angle and tip speed ratio can be simplified. Secondly, considering the estimation error of the wake model, the optimal pitch angle curve and active power curve in terms of the wind speed are generated for each individual wind turbine with the optimized pitch angle and tip speed ratio. The optimized control curves are limited by the maximum rotor speed, the minimum rotor speed and the rated power. With the measurement of the real wind speed, the optimized pitch angle reference and the optimized active power reference can be obtained from the optimized control curves. As a consequence, each wind turbine is controlled according to the real wind speed at the position of the wind turbine. Compared with the method to implement the optimized pitch angle and tip speed ratio in the wind farm central controller, the active power reference will not be higher than the available active power. Thus, the wind turbine will not be halted. By the proposed method, the active power of the wind farm may not be maximized due to the wake model estimation error. However, the optimized control curves can be implemented at the wind directions where the wind farm has large power loss due to the wake effect. At these wind directions, a large amount of active power can be increased. Thus, the estimation error can be neglected. The remaining part of this paper is organized as follows. The doubly fed induction generator (DFIG) wind turbine and the MPPT method are addressed and described in Section 2. The wake effect and the proposed method to generate the optimized control curves are illustrated by case study in a two-turbine wind farm in Section 3. Afterwards, the case study is extended to a three-turbine wind
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and the proposed method to generate the optimized control curves are illustrated by case study in a Energies 2017, 10, 395 farm in Section 3. Afterwards, the case study is extended to a three-turbine wind 3 of 19 two-turbine wind farm with multi-wake in Section 4. The case study is analyzed in a typical Danish eighty-turbine wind farm real wind 5. study Finally, concluding drawn in Section 6.wind farm with with the multi-wake inprofile Sectionin4.Section The case is analyzed in remarks a typical are Danish eighty-turbine farm with the real wind profile in Section 5. Finally, concluding remarks are drawn in Section 6. 2. DFIG Wind Turbine and MPPT 2. DFIG Wind Turbine MPPT In this section, the and DFIG wind turbine and its active power control method is presented. As shown in Figure 1, the DFIG wind turbine generates active power fromisthe stator side of the In this section, the DFIG wind turbine and its activethe power control method presented. As shown generator. on theturbine slip, it also generates or absorbs active fromside the of rotor of the in Figure 1,Depending the DFIG wind generates the active power frompower the stator theside generator. generator. One of the active power control methods of the DFIG wind turbine is based on the active Depending on the slip, it also generates or absorbs active power from the rotor side of the generator. power in terms ofcontrol the wind speed.ofBy measurement of the windon speed, the active One of curve the active power methods thethe DFIG wind turbine is based the active powerpower curve reference and the pitch angle reference can be separately obtained from the active power curve in terms of the wind speed. By the measurement of the wind speed, the active power reference andand the the pitch angle curve.can be separately obtained from the active power curve and the pitch angle curve. pitch angle reference Blade and pitch drive DFIG
Pitch Controller
Gearbox
β* Wind speed sensor
Vw
Ps
Pr
RSC
Transformer GSC
Grid
PGSC
Vdc β*
P*
P* Vw
Vw
Power Controller
Ps+PGSC
Figure Figure 1. 1. DFIG DFIG wind wind turbine turbine and and its its active active power power control control method. method.
According to the aerodynamic model, the active power P generated by the turbine can be According to the aerodynamic model, the active power P generated by the turbine can be calculated by: calculated by: 2 11 2 p ( β, λ)v3 3 (1) PP = 2ρπR πR C C p ( , )v (1) 2 where ρ is the air density, R is the radius of the turbine blade, v is the wind speed, and Cp is the power where ρ is the air density, R to is the of theβturbine v is the wind speed, and Cpratio, is thedefined power coefficient, which is related the radius pitch angle and theblade, tip speed ratio λ. The tip speed coefficient, which is related to the pitch angle β and the tip speed ratio λ. The tip speed ratio, defined as the ratio of the blade tip speed over the speed of the incoming wind, is given by: as the ratio of the blade tip speed over the speed of the incoming wind, is given by: ωr R λ = r R (2) v (2)
v
where ω r is the rotor speed. where r is the rotor speed. Asωexpressed in Equation (1), at a specific wind speed, the active power generated by the wind As expressed in (1), atcoefficient. a specific wind active the power generated by the wind turbine is determinedEquation by the power By thespeed, MPPTthe method, wind turbine generates the turbine is determined by the power coefficient. By the MPPT method, the wind turbine generates the active power at the maximum power coefficient. The power coefficients of the National Renewable active at the (NREL) maximum power coefficient. power thethe National Renewable Energypower Laboratory 5 MW wind turbine inThe terms of thecoefficients pitch angleofand tip speed ratio are Energy Laboratory (NREL) 5 MW wind turbine in terms of the pitch angle and the tip speed ratio shown in Figure 2a [16]. It can be observed that the maximum power coefficient is obtained at are the shown in Figure 2a [16]. It can be observed that the maximum power coefficient is obtained at the pitch angle of 0◦ and the tip speed ratio of 7.55. pitchThe angle of 0° and of thethe tipNREL speed5ratio 7.55.wind turbine are shown in Table 1 [16]. With the MPPT parameters MW of DFIG The implemented, parameters of the MW DFIG wind angle, turbinethe aretip shown in ratio Tableand 1 [16]. MPPT method theNREL active5power, the pitch speed theWith rotorthe speed in method implemented, the active power, the pitch angle, the tip speed ratio and the rotor speed in terms of the wind speed of the NREL 5 MW DFIG wind turbine are shown in Figure 2b. It is noted terms of pitch the wind speed of the MWare DFIG wind turbine in Figure It isturbine noted that the angle and the tip NREL speed 5ratio respectively kept are at 0◦shown and 7.55 for the2b. wind that the pitch angle and thepower, tip speed ratiospeeds are respectively kept at m/s. 0° and forspeeds the wind turbine to generate the maximum at wind from 7 m/s to 10 At7.55 wind lower than to generate the maximum power, at wind speeds from 7 m/s to 10 m/s. At wind speeds lower than 7 7 m/s, the tip speed ratio is increased due to the minimum rotor speed limit of 6.9 rpm. Similarly, m/s, the speeds tip speed ratiothan is increased duetip to speed the minimum rotor speed of maximum 6.9 rpm. Similarly, at at wind higher 10 m/s, the ratio is decreased duelimit to the rotor speed wind speeds higher than 10 m/s, the tip speed ratio is decreased due to the maximum rotor speed limit of 12.1 rpm. When the wind speed is higher than the rated wind speed, the pitch angle controller limit of 12.1 rpm. When the wind speed higher than the rated wind speed, the pitch angle controller is activated to limit the active power noislarger than the rated power. is activated to limit the active power no larger than the rated power.
Energies 2017, 10, 395 Energies 2017, 10, 395 1.2
0.4
0.5 0.4 0.5 0.3 0.4 0.2 0.3 0.1 0.2 0 0.1 80 20 P0 15 itch 60 40 10 80 an 20 5 o: λ 20 Pit 60gle: 0 0 d rati15 ch 40 β spee10 (° an 20 ) 0 0Tip 5 gle :λ o rati :β eed (° ip sp T(a) )
0.4 0.3 0.3 0.2 0.2 0.1 0.1 0
25
1.21
Active power Pitch angle Tip speed ratio Active power Rotorangle speed Pitch Tip speed ratio Rotor speed
1 0.8 0.8 0.6 0.6 0.4
25 20 20 15 15 10 10 5
0.4 0.2
5 0 3 5 7 9 11 13 15 17 19 21 23 25 Wind speed (m/s) 0 0 3 5 7 9 11 13 15 17 19 21 23 25 Wind speed (b) (m/s)
0.20
0
PitchPitch angleangle (°), (°), tip speed ratio ratio and rotor speed (rpm)(rpm) tip speed and rotor speed
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β: 0° λ: 7.55 β: Cp0° : 0.4852 λ: 7.55 Cp: 0.4852
Active power (pu) (pu) Active power
Power coefficient: Cp Cp Power coefficient:
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(a)
(b)
Figure 2. NREL 5 MW wind turbine with: (a) Power coefficient in respect to the pitch angle and the Figure 2. NREL 5 MW wind turbine with: (a) Power coefficient in respect to the pitch angle and the tip tip speed ratio; (b) active power curve with(a) thePower maximum powerinpoint tracking control. Figure 2. NREL 5 MW wind turbine with: coefficient respect to the (MPPT) pitch angle and the speed ratio; (b) active power curve with the maximum power point tracking (MPPT) control. tip speed ratio; (b) active power curve with the maximum power point tracking (MPPT) control. Table 1. Parameters of the NREL 5 MW wind turbine [16]. Table 1. Parameters of the NREL 5 MW wind turbine [16]. Table 1. Parameters of the NREL 5 MW wind turbine [16]. Parameter Value Rated power 5 MW Parameter Value Parameter Value Rotor diameter 126 m Rated power 5 MW Rated power 5 MW Cut-in, rated, wind speed 3 m/s,126 11.4 RotorCut-out diameter 126 m 25 m/s Rotor diameter mm/s, Min. and Cut-out Max. rotor speed 6.9 rpm, 12.1 rpm Cut-in, rated, Cut-out wind speed 3 m/s, 11.4 m/s, m/s Cut-in, rated, wind speed 3 m/s, 11.4 m/s, 2525 m/s Gearbox ratio 97:1 Min. 6.96.9 rpm, 12.1 rpm Min.and andMax. Max.rotor rotorspeed speed rpm, 12.1 rpm Number of pole-pairs 3 Gearbox ratio 97:1 Gearbox ratio 97:1 Number 3503Hz Synchronous frequency Numberof ofpole-pairs pole-pairs Synchronous frequency 50 50 HzHz Electrical generator efficiency 94.4% Synchronous frequency Electrical generator efficiency 94.4% Electrical generator efficiency 94.4%
3. Wake Effect and Active Power Maximization in a Two-Turbine Wind Farm 3. 3. Wake Effect in aa Two-Turbine Two-Turbine Wind WindFarm Farm Wake Effectand andActive ActivePower PowerMaximization Maximization in In the wind farm, the wind turbine causes the wind speed deficit to a column of its downstream the wind farm, turbine the wind windspeed speed deficitto toaair acolumn column of downstream airIn flow. This phenomenon is named ascauses the wake effect. The column of flow is the wake. In the wind farm,the thewind wind turbine the deficit ofcalled itsits downstream airair flow. This isis named as the wake effect. Thecolumn column is called wake. Many wake models have been developed to wake estimate the The wind speed deficit inflow theiswake [17,18]. The flow. Thisphenomenon phenomenon named effect. ofof airair flow called thethe wake. Katic wake model [19], which extends the previous work of Jensen [20], is one of the most widely Many wake models have been developed to estimate the wind speed deficit in the wake [17,18]. Many models been developed to estimate the wind speed deficit in the wake [17,18]. The used wake models. In[19], this paper, the Katic wake model is adopted to [20], estimate speed deficit Katic wake model [19], which extends thethe previous work of Jensen is one ofwind the most widely The Katic wake model which extends previous work of Jensen [20], isthe one of the most widely at the position of downstream wind turbines. used wake models. thispaper, paper, the Katic Katic wake model the wind speed deficit used wake models. InInthis the modelisisadopted adoptedtotoestimate estimate the wind speed deficit In this section, the wake effect is addressed and an active power control method to maximize at the position of downstream wind turbines. at the position of downstream wind turbines. theIntotal active power of theeffect wind is proposed. Case studies are carried out in to atotwo-turbine In this section, the wake effectisfarm is addressed andanan active power control method maximizethe this section, the wake addressed and active power control method maximize wind farm. The two-turbine wind farm is shown in Figure 3, where it is assumed that the two wind theactive total active the wind is proposed. studies are carried a two-turbine total powerpower of theofwind farm farm is proposed. CaseCase studies are carried out out in ain two-turbine wind turbines are the NREL 5 MW DFIG wind turbine and the distance between the two wind turbines is wind farm. The two-turbine wind farm is shown in Figure 3, where it is assumed that the two wind farm. The two-turbine wind farm is shown in Figure 3, where it is assumed that the two wind turbines 6.5 timesare thethe blade diameter. turbines NREL 5 MW DFIG wind turbine and the distance between the two wind turbines is are the NREL 5 MW DFIG wind turbine and the distance between the two wind turbines is 6.5 times 6.5 times the blade diameter. the blade diameter. α α
u u α=270° α=270°
North
Definition of the wind direction Definition of the
u
North
u v1,
1,
β1, P1
v2,
2,
v1,
1, β1, P1
v2,
2, β2, P2
wind direction
WT1 WT1
β2, P2
WT2 XD
WT2
XD
Figure 3. Layout of the wind farm with two NREL wind turbines in a line. XD: distance between the two wind turbines. Figure Layout thewind windfarm farm with with two two NREL distance between thethe Figure 3. 3.Layout ofofthe NREL wind windturbines turbinesinina aline. line.XD: XD: distance between two wind turbines. two wind turbines.
3.1. Wake Effect in Two-Turbine Wind Farm 3.1. Wake EffectininTwo-Turbine Two-Turbine WindFarm Farm 3.1. Wake TheEffect Katic wake model, Wind as shown in Figure 4a, estimates the downstream wind speed deficit 1−v2/u byKatic Equation [19]: as shown in Figure 4a, estimates the downstream wind speed deficit The wake(3) model, The Katic wake model, as shown in Figure 4a, estimates the downstream wind speed deficit 1−v2/u by Equation (3) [19]: 1−v2 /u by Equation (3) [19]:
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v2 = 1− u
1−
q
1 − Ct_1 ( β 1 , λ1 )
D 2 D + 2kXD cos ( ϕ) A
2
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Aol_12 AR
(3)
ol _12 v D 1 2 1 1 Ct _1 ( 1 , 1 ) u D 2kXD cos( ) AR wind speed, v2 is the wind speed of the downstream
(3)
where u is the ambient wind turbine, Ct is the u is2017, the10, ambient wind speed, v2 isturbine, the windwhich speed is of athe downstream wind turbine, tof is19the Energies 395 thrustwhere coefficient of the upstream wind function of the pitch angleC5and the tip thrust coefficient of the upstream wind turbine, which is a function of the pitch angle and the tip speed ratio [16], D is the blade diameter, XD is the distance between the two wind turbines, AR is the 2 Aol _12 the vdiameter, D ratio [16],AD is the blade XD is the distance between two wind turbines, AR(3) is the 2 bladespeed sweep area, is the overlap between the wake area of WT area of 1 1 1 C ( , ) 1 and the blade sweep t _1 1 1 ol_12 u D 2kXD cos( ) 1 Aand R blade sweep area, A ol_12 is the overlap between the wake area of WT the blade sweep area WT2 , and the decay constant k of 0.075 for the onshore wind farm and 0.04–0.05 for the offshoreofwind WT2, and uthe constant k ofspeed, 0.075vfor the wind and 0.04–0.05 for turbine, the offshore wind is decay the ambient the onshore windand speed of farm the downstream wind Ct isfacility the farms iswhere recommended in thewind Wind Atlas2 isAnalysis Application Program-WAsP help [21]. farms is recommended in the Wind Atlas Analysis and Application Program-WAsP help facility [21]. thrust coefficient of the upstream wind turbine, which is a function of the pitch angle and the tip The thrust coefficients of the NREL 5 MW wind turbine in terms of the pitch angle and the tip speed Thespeed thrust coefficients NREL 5 MWXD wind turbine in terms of the angle and theAtip ratio [16], D is of thethe blade diameter, is the distance between the pitch two wind turbines, R isspeed the ratio ratio areblade shown in Figure 4b [16]. are shown in Figure 4b [16]. sweep area, Aol_12 is the overlap between the wake area of WT1 and the blade sweep area of
WT1 α
u α=270° +φ
u
XD
D WT1
φ
v1
1
φ D (a)
North
k
WT2
XD XDcos (φ
u α=270° +φ
WT2
Definition of the wind direction v2
v1
Thrust coefficient Thrust coefficient
WT2, and the decay constant k of 0.075 for the onshore wind farm and 0.04–0.05 for the offshore wind farms is recommended in the Wind Atlas Analysis and Application Program-WAsP help facility1.5 [21]. North α The thrust coefficients of the NREL 5 MW wind turbine in2 terms of the pitch angle and the tip speed Definition of the u wind direction ratio are shown in Figure 4b [16]. 1.5
)
Aol
AR
v2
1
1
1.5
0.5 2
0 80 P1 itch 60 40 20 an 0.5 gle 0 (° ) 0
0.5
1.5
1
0
25 15 20 10 0 5 ratio peed 0.5 Tip s
80 25 (b) Pit 60 40 ch 15 20 10 0 20 an ratio gle 0 wind 0 5 turbines Figure 4. (a) Speed relationship between the upstream and downstream eed in Katic wake XDcos between the upstream and downstream sp (° ip Figure 4. (a) Speed relationship wind turbines in Katic wake T (φ) )
1
k
Aol
AR
model; (b) thrust coefficient of the NREL 5 MW wind turbine.
model; (b) thrust coefficient (a) of the NREL 5 MW wind turbine.
(b)
By Figure assuming offshore between decay constant is 0.04 MPPT method is implemented 4. (a) that Speedthe relationship the upstream andand downstream wind turbines in Katic wakein WT1 andassuming WTmodel; 2, the(b) downstream wind speed deficit calculated by Katic model appears in the four in By that the offshore decay constant is 0.04 and MPPT method is implemented thrust coefficient of the NREL 5 MW wind turbine. symmetrical wind direction ranges of 258°–270°, 270°–282°, 78°–90° and 90°–102°. The wind speed of WT1 and WT2 , the downstream wind speed deficit calculated by Katic model appears in the assuming that the offshore decay constant is 0.04 and MPPT method is implemented in 15a, ◦ ◦ ◦ ◦ ◦ ◦ ◦ WT 2 at By the wind directions α of from 270° to 282° with the resolution of 3° is shown in Figure four symmetrical wind direction ranges of 258 –270 , 270 –282 , 78 –90 and 90 –102◦ .WT The wind andthe WTambient 2, the downstream by Katic model the four where wind speed wind from 3speed m/s todeficit 25 m/scalculated with the resolution of 1 m/sappears is takenininto account. ◦ ◦ ◦ speed of WT2 at the wind directions α of from 270 to 282 with the resolution of 3 is shown in wind direction of 258°–270°, 78°–90° and 90°–102°. The speed. wind speed of be At symmetrical these wind directions, the ranges wind speed of WT1270°–282°, is the same as the ambient wind It can Figure 5a, the ambient wind speed from 3 m/s to 25 m/s with the resolution of 1 m/s is taken WTwhere 2 at the wind directions α of from 270° to 282° with the resolution of 3° is shown in Figure 5a, observed in Figure 5a that the wind speed of WT2 has the maximum deficit at the wind direction of into account. At wind directions, the wind ofthe WT asisthe ambient wind speed. where the these ambient speed from m/s to 25 speed m/s with resolution of 1 m/s taken into account. 1 is the same 270°, because WT2 is wind totally inside of3the wake of WT 1, where the overlap area equals to the blade these thethat windthe speed of WT 1 is the theoverlap ambient wind speed. It and can be It cansweep beAtobserved indirections, Figure 5a wind speed of same WT2asthe has the maximum deficit at the area wind of WT 2. With the increasing of the wind direction, area is reduced thuswind ◦in observed Figure 5aWT that the wind speed of WT 2 has the maximum deficit at the wind direction of direction of 270 , because is totally inside of the wake of WT , where the overlap area equals to 1 there is no wind speed deficit the wind speed deficit of WT2 2 is reduced. At the wind direction of 282°, 270°, because WT2 is totally inside of the wake of WT1, where the overlap area equals to the blade the blade sweep area of WT . With the increasing of the wind direction, the overlap area is reduced of WT2, and the wind speed 2 of WT2 is the same as the ambient wind speed. Meanwhile, the active sweep area of WT2. With the increasing of the wind direction, the overlap area is reduced and thus power of wind WT1 and WT2deficit at the wind direction of 270° is in Figure 5b. of 282◦ , there is no wind and thus the speed of WT Atshown the wind direction 2 is reduced. the wind speed deficit of WT2 is reduced. At the wind direction of 282°, there is no wind speed deficit
270° 273° 276° 270° 279° 273° 282° 276° 279° 282°
ActiveActive power power (MW) (MW)
21 18 24 15 21 12 18 9 15 6 12 3 9 36
Wind speed of WT2 (m/s)
Wind speed of WT2 (m/s)
speed deficit WTthe wind speed of WT aswind the ambient wind speed. Meanwhile, 2 , and 2 is of WTof 2, and windthe speed of WT 2 is the same as the the same ambient speed. Meanwhile, the active 6 ◦ the active power of1WT and at the wind of direction of 270in Figure is shown power and1WT 2 atWT the 2wind direction 270° is shown 5b. in Figure 5b. 24 of WT 5 46 5
3
4
WT1 WT2 WT1 WT2
2
3
1
2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Ambient wind speed(m/s) 0 3 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3 6 9 (a)12 15 18 21 24 (b) Ambient wind speed(m/s) Ambient wind speed (m/s) Figure 5. (a) Wind speed to 282 and at the ambient (a)deficit of WT2, at the wind directions of from 270(b) wind speeds of from 3 m/s to 25 m/s; (b) active power of WT1 and WT2 at the wind direction of 270°.
6 9 12 15 18 21 Ambient wind speed (m/s)
24
Figure 5. (a) Wind speed deficit of WT2, at the wind directions of from 270 to 282 and at the ambient
Figure 5.wind (a) Wind at the wind directions of WT from 270◦ to 282◦ and at the ambient 2 , (b) speeds speed of fromdeficit 3 m/s toof25WT m/s; active power of WT1 and 2 at the wind direction of 270°. wind speeds of from 3 m/s to 25 m/s; (b) active power of WT1 and WT2 at the wind direction of 270◦ .
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3.2. Active Power Maximization AtEnergies the wind direction of 270◦ , as expressed by Equation (1), the active power of WT1 is determined 2017, 10, 395 6 of 19 by the pitch angle and tip speed ratio of WT1 . Meanwhile, as expressed by Equation (3), the wind 3.2. Active Maximization by the pitch angle and tip speed ratio of WT1 . Compared with the speed of WT also determined 2 is Power MPPT method, bywind changing the pitch angle and tip speed ratio of(1), WTthe active power of1 WT 1 , the At the direction of 270°, as expressed by Equation active power of WT is 1 will be reduced. However, wind WT2ratio canofbeWT increased, which results in increase determined by thethe pitch anglespeed and tipofspeed 1. Meanwhile, as expressed bythe Equation (3), of the the wind 2 is also determined by the pitch angle and tip wind speed farm ratio of WTbe 1. Compared active power of speed WT2 .ofInWT consequence, the total active power of the can increased. ◦ with the MPPT method, by changing the pitch angle and tip speed ratio of WT 1, the active power of At the wind direction of 270 , the wind speed of WT1 is the same as the ambient wind speed. WT1 will be reduced. However, the wind speed of WT2 can be increased, which results in the increase The wind speed of WT2 can be calculated by Equation (3). The active power of WT1 and WT2 can of the active power of WT2. In consequence, the total active power of the wind farm can be increased. be calculated (1). ofBy assuming the of as WT the same the MPPT 1 is At by the Equation wind direction 270°, the windthat speed of pitch WT1 isangle the same the ambient windas speed. methodThe and WT is controlled by the MPPT method, the active power of WT , the wind speed of 2 wind speed of WT2 can be calculated by Equation (3). The active power of WT1 1and WT2 can be WT2 , the active power of WT and the total power inthe terms of method the tip speed calculated by Equation (1).2 ,By assuming thatactive the pitch angleof ofthe WT1wind is the farm same as MPPT 2 is be controlled by the MPPT method, power of WT 1, theof wind speed ofeffect WT2, the ratio ofand WTWT calculated. For instance, at the theactive ambient wind speed 9 m/s, the of the tip 1 can activeofpower 2, and the total active power of the wind farm in terms of the tip speed ratio of speed ratio WT1 of onWT the total active power generation is shown in Figure 6. In the case that WT1 is WT1 can be calculated. For instance, at the ambient wind speed of 9 m/s, the effect of the tip speed controlled by the MPPT method, where the tip speed ratio of WT1 is 7.55, WT1 generates the maximum ratio of WT1 on the total active power generation is shown in Figure 6. In the case that WT1 is active power, as shown in Figure 6a. The total active power of the wind farm is 0.37 pu, as shown in controlled by the MPPT method, where the tip speed ratio of WT1 is 7.55, WT1 generates the Figure 6d. If changing the tipasspeed of WT to 6.5, active power WT1farm is reduced, maximum active power, shownratio in Figure 6a.1 The totalthe active power of theofwind is 0.37 pu,as as shown in Figure 6a. The total6d. active powerthe oftip the wind farm is increased to thepower maximum of 0.38 pu, shown in Figure If changing speed ratio of WT 1 to 6.5, the active of WT1 value is reduced, as shown in Figure 6a. The totalwith activethe power of the wind farm is increased to increased. the maximum value of as shown in Figure 6d. Compared MPPT method, 0.01 pu can be 0.38 pu, as shown in Figure the MPPT method, 0.01 pusearch can be increased. The optimal tip speed ratio6d. of Compared 6.5 can bewith obtained by the exhausted method. Firstly, all the The optimal tip speed ratio of 6.5 can be obtained by the exhausted search method. Firstly, all possible total active power of the wind farm in terms of the tip speed ratios of WT1 with the resolution the possible total active power of the wind farm in terms of the tip speed ratios of WT1 with the of 0.1 isresolution calculated. Afterwards, the maximum total active power of the wind farm is selected. Then, of 0.1 is calculated. Afterwards, the maximum total active power of the wind farm is the corresponding optimal tip speed optimal ratio oftip WT be obtained, is 6.5. 1 can selected. Then, the corresponding speed ratio of WT1 can which be obtained, which is 6.5. 10
1=7.55 1=6.5
0.2
0.6
1=7.55
1=7.55 1=6.5
1=6.5
P2 (pu)
v2 (m/s)
P1 (pu)
0.4
0.6
1=7.55 1=6.5
9 8 7
P1+P2 (pu)
0.6
0.4 0.2
0.4 0.2 0.38 pu
6 0
5 0
4
8
12
0 0
4
1
(a)
8
12
0 0
4
1
(b)
0.37 pu
8
12
0
4
(c)
8
12
1
1
(d)
Figure 6. Comparison between WT1 operating at the tip speed ratio of 7.55 and 6.5, at the wind
Figure direction 6. Comparison between WT1 speed operating at(a) the tip speed ratio of 17.55 and the wind of 270° and ambient wind of 9 m/s: The active power of WT , where the6.5, baseat value ◦ and ambient wind speed of 9 m/s: (a) The active power of WT , where the base value direction of 270 1 is 5 MW; (b) the wind speed of WT2; (c) the active power of WT2, where the base value is 5 MW; (d) is 5 MW; theactive windpower speedofof thewhere activethe power of WT , where the(b) total theWT wind farm, base value is210 MW. the base value is 5 MW; (d) the 2 ; (c) total active power of the wind farm, where the base value is 10 MW. If the pitch angle of WT1 is considered as well, at the wind direction of 270° and ambient wind speed of 9 m/s, the total active power of the wind farm in terms of the pitch angle and◦ tip speed ratio If the pitch angle of WT1 is asoptimal well, at(OPT), the wind direction of 270 ambient of WT 1 is shown in Figure 7. considered As marked by the maximum total activeand power of the wind speed ofwind 9 m/s, the total active power of the wind farm in terms of the pitch angle and tip speed ratio farm of 0.39 pu is achieved at the pitch angle of 1.8° and the tip speed ratio of 6.9 of the WT 1. of WT1 Compared is shown with in Figure 7. As marked by optimal (OPT), the maximum total active power of the the WT1 controlled by the MPPT method where the total active power of the wind ◦ farm is 0.37 pu, the total active power of the wind farm can be increased by 0.02 pu. wind farm of 0.39 pu is achieved at the pitch angle of 1.8 and the tip speed ratio of 6.9 of the WT1 . pitch angle and tip speed ratio of WT1, which are 1.8° and 6.9 respectively, can also Compared The withoptimal the WT 1 controlled by the MPPT method where the total active power of the wind be obtained by the exhausted search method. Firstly, all the total active power of the wind farm in farm is 0.37 pu, the total active power of the wind farm can be increased by 0.02 pu. terms of the pitch angle and tip speed ratio of WT1 are calculated with the pitch angle resolution of The optimal pitch angle and tip speed ratio of WT1 , which are 1.8◦ and 6.9 respectively, can also 0.2° and tip speed ratio resolution of 0.1. Afterwards, the maximum total active power of the wind be obtained by be theselected. exhausted search method. Firstly, allpitch the total of the wind farm in farm can Finally, the corresponding optimal angle active and tippower speed ratio of WT 1 can terms ofbethe pitch which angle are and1.8° tipand speed ratio of WT1 are calculated with the pitch angle resolution of obtained, 6.9, respectively.
0.2◦ and tip speed ratio resolution of 0.1. Afterwards, the maximum total active power of the wind farm can be selected. Finally, the corresponding optimal pitch angle and tip speed ratio of WT1 can be obtained, which are 1.8◦ and 6.9, respectively.
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0.38
0.38
P1+P2 (pu)
P1+P2 (pu)
OPT: OPT:0.39 0.39pu pu
0.375 0.375
0.40.4
0.37 0.37
0.35 0.35
0.365 0.365
0.30.3 6 6
0.36 0.36 0.355 0.355
44
MPPT: 0.37 pu
β1
) (° ) β 1 (°
2 MPPT: 0.37 pu 7 2 7 6 0 5 1 6
8
9
8
0.35
9
0.35
0.345
0.345
0.34
0.34 0 5 1 Figure 7. Total active power of the wind farm in terms of the pitch angle and tip speed ratio of WT 1, Figure 7. Total active power of the wind farm in terms of the pitch angle and tip speed ratio of WT1 , Figure 7. Total power theambient wind farm terms of the pitch angle and tip speed ratio of WT 1, at◦ 270° windactive direction and of 9 m/s windinspeed.
at 270 wind direction and 9 m/s ambient wind speed. at 270° wind direction and 9 m/s ambient wind speed. At the wind direction of 270°, the WT2 will not cause the power loss to the wind farm, as there ◦ , the WT will not cause the power loss to the wind farm, as there is At the wind direction of 270 is wind turbine behind 2 along direction. Therefore, WT2loss should be controlled by the Atno the wind direction ofWT 270°, the the WT2wind 2 will not cause the power to the wind farm, as there MPPT method to generate maximum active power of WT2 at itsWT current wind be speed. The total no wind turbine behind WT along the direction. Therefore, controlled by is no wind turbine behind WT 2 along thewind wind direction. Therefore, WT2 2should should be controlled by the the 2 the active power of the wind farm can be maximized by optimizing the pitch angle and tip speed ratio MPPT method to generate the maximum active power of WT at its current wind speed. The total method to generate the maximum active power of WT22 its current wind speed. The total WT1. Itof is the evident the pitch angle maximized and tip speed ratio of WT1 isthe optimized at theand ambient wind activeofpower wind pitch angle tip wind farm farm can can be be maximized by optimizing optimizing tip speed speed ratio ratio speeds of 7 m/s to 11 m/s. When the ambient wind speed is lower than 7 m/s and higher than 11 m/s, of WT It is is evident the pitch angle and tip speed ratio of WT WT11. It WT11 is optimized at the the ambient ambient wind wind the rotor speed is limited by 6.9 rpm and 12.1 rpm. To simplify the problem, the pitch angle and tip speeds of m/s to 11 m/s. When the the ambient ambient wind speed is lower speeds of 77ratio m/s of When lower than than77m/s m/s and higher higher than than 11 11m/s, m/s, speed WTm/s. 1 is just optimized at the ambient wind speeds from 7 m/s to 11 m/s, as shown in the rotor speed is limited by 6.9 rpm and 12.1 rpm. To simplify the problem, the pitch angle and tip speed limited 12.1 rpm. To simplify the problem, Figure 8a. speed ratio of WT is just optimized at the ambient wind speeds from 7 m/s to 11 m/s, as shown 1 is just optimized at the ambient wind speeds from 7 m/s to 11 m/s, as shown in 1 the MPPT method and the optimized method, the active power of WT1, the active Comparing in Figure 8a. Figure 8a. of WT2 and the total active power of the wind farm at the ambient wind speeds from 7 m/s to power Comparing the MPPT method and optimized method, active power WT 11 m/s are shown in Figure 8b. It can bethe seen that the active powerthe of WT 1 is reduced. However, theactive method the optimized method, the active power of of WT11, the the active active power of WT 2 is increased. Overall, the active power of the wind farm is increased. power of WT and the total active power of the wind farm at the ambient wind speeds from 7 m/s power to 2 and the total active power of the wind farm at the ambient wind speeds from 7 m/s
1.2 0.8
Active power (pu)
1 0.6 0.8 0.4 0.2
20 P1-MPPT β1-MPPT 1-MPPT ωr1-MPPT P 1-OPT P1-MPPT β1-OPT β1-MPPT 1-OPT 1-MPPT ωr1-OPT
25 15
20
10
15 5
10
Active power (MW) Active power (MW)
Active power (pu)
1
Pitch angle (° ), tipangle speed Pitch (°),ratio tip speed ratio and rotor and rotor speed (rpm)speed (rpm)
to m/s shown in Figure It can be seen active power of WT is reduced. However, 11 11 m/s areare shown in Figure 8b. 8b. It can be seen thatthat the the active power of WT 1 is 1 reduced. However, the 1.2 25 12 the active power of WT is increased. Overall, the active power of the wind farm is increased. -MPPT-270° active power of WT 2 is 2 increased. Overall, the active power ofWT the wind farm is increased. 1 8 12 6 10 4
8
2
WT1-OPT-270° WT2-MPPT-270° WT2-OPT-270° WF-MPPT-270° WT1-MPPT-270° WF-OPT-270°
WT1-OPT-270° WT2-MPPT-270° WT2-OPT-270° WF-MPPT-270° WF-OPT-270°
6 0 ω -MPPT r1 10 0 0 45 6 7 8 9 10 11 12 13 0.4 3 5 7 9 11 13 15 P 171-OPT 19 21 23 25 Ambient wind speed(m/s) Wind speedβ1(m/s) -OPT 2 5 0.2 (a) 1-OPT (b) ωr1-OPT 0 0 Figure08. (a) Optimized pitch angle, tip speed ratio, blade speed 1, at 12 the wind 5 6and 7active 8 power 9 of 10WT11 13 3 5 7 9 11 13 15 17 19 21 23 25 direction of 270°;Wind (b) comparison power wind of WTspeed(m/s) 2, and the total active Ambient speed (m/s)of the active power of WT1, active 0.6
power of the wind farm between the WT1 controlled by MPPT method and the optimized method, at (a) (b) the wind direction of 270°.
Figure 8. (a) Optimized pitch angle, tip speed ratio, blade speed and active power of WT1, at the wind Figure 8. (a) Optimized pitch angle, tip speed ratio, blade speed and active power of WT1 , at the wind Due of to 270°; the wind farm layout, Figure the power loss of the wind farm caused by direction (b) comparison ofas theshown activein power of 6, WT 1, active power of WT2, and the total active direction ofeffect 270◦ ;appears (b) comparison of the active power of wind WT1 , active power of WT active 2 , and the total the wake within the four symmetrical direction of 258°–270°, 270°–282°, power of the wind farm between the WT1 controlled by MPPT methodareas and the optimized method, at power of the wind farm between the WT controlled by MPPT method and the optimized method, 1 the maximum power loss appears at the wind directions 78°–90° and 90°–102°. It can be expected that the wind direction of 270°. ◦ at wind of 270 loss . reduces with the wind direction change from 270° to 282°, from 270° of the 270° and direction 90°. The power
to 258°, from 90° to 102° and from 90° to 78°. At the wind directions that the wind farm has no power Due to the wind farm layout, as shown in Figure 6, the power loss of the wind farm caused by loss due to the wake effect, WT1 as andshown WT2 should be controlled by the MPPT method tofarm maximize the Due to the wind farm layout, in Figure 6,wind the power loss of the wind caused by the the wake effect appears within the four symmetrical direction areas of 258°–270°, 270°–282°, ◦ ◦ ◦ ◦ ◦ –90◦ total active power of the wind farm. wake effect appears within the four symmetrical wind direction areas of 258 –270 , 270 –282 , 78 78°–90° and 90°–102°. Itpitch can be expected thatratio, the maximum power loss appears atWT the1 at wind directions The optimized angle, tip speed rotor speed and active power of the wind ◦ . It can be expected that the maximum power loss appears at the wind directions of 270◦ and 90◦ –102 of 270° and 90°. loss reduces with the wind direction change from 270° to 282°, from 270° directions of The 270°,power 276° and 282° are shown in Figure 9a. Comparing WT1 controlled by ◦ ◦ ◦ MPPT method ◦ ◦
and 90 .from The power loss reduces wind from 270thetowind 282 ,farm fromhas 270notopower 258 , to 258°, 90° to 102° and fromwith 90°the to 78°. Atdirection the windchange directions that ◦ to 102◦ and from 90◦ to 78◦ . At the wind directions that the wind farm has no power loss from 90 loss due to the wake effect, WT1 and WT2 should be controlled by the MPPT method to maximize the due the wake effect, WT WT2 should be controlled by the MPPT method to maximize the total 1 andfarm. totaltoactive power of the wind activeThe power of the wind farm. optimized pitch angle, tip speed ratio, rotor speed and active power of WT1 at the wind
directions of 270°, 276° and 282° are shown in Figure 9a. Comparing WT1 controlled by MPPT method
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The optimized pitch angle, tip speed ratio, rotor speed and active power of WT1 at the wind Energies 2017, 10, 395 8 of 19 directions of 270◦ , 276◦ and 282◦ are shown in Figure 9a. Comparing WT1 controlled by MPPT method and and the optimized method, the optimized total active power of the wind farm at the wind directions of Energies 10, 395 method, the optimized total active power of the wind farm at the wind directions 8 of 19 the2017, optimized ◦ and 282◦ are shown in Figure 9b. It is clear that the total active power of the wind farm can 270◦of , 276 270°, 276° and 282° are shown in Figure 9b. It is clear that the total active power of the wind farm andbe theincreased optimized method, thedirection optimized active of wind farm at amount the wind be increased mostly at the wind oftotal 270◦of . Moreover, thethe increased amount of the active power can mostly at the wind direction 270°.power Moreover, the increased ofdirections the active ◦ ◦ of 270°, 276° and 282° are shown in Figure 9b. It is clear that the total active power of the wind farm in the windinfarm reduces the with increase of windofdirection from 270 282to.282°. power the wind farmwith reduces the increase wind direction fromto 270°
20 25 P1-OPT-270° β1_OPT-270° 1_OPT-270° 15 20 ω _OPT-270° P1r1-OPT-270° P1_OPT-276° ββ1_OPT-270° 1_OPT-276° 1_OPT-270° 15 10 ω1r1_OPT-276° _OPT-270° ωr1_OPT-276° _OPT-276° P 1 _OPT-282° βP11_OPT-276° β11_OPT-276° _OPT-282° 10 5 ω1r1_OPT-282° _OPT-276° ω _OPT-282° r1 P1_OPT-282° β1_OPT-282° 50 17ω1_OPT-282° 19 21 23 25 r1_OPT-282°
0.81 0.6 0.8 0.4 0.6 0.2 0.4 0 0.2
3 5 7 9 11 13 15 Wind speed (m/s) 0 0 3 5 7 9 11 13 15 17 19 21 23 25 (a) Wind speed (m/s)
WF-MPPT-270° WF-OPT-270° WF-MPPT-276° WF-MPPT-270° WF-OPT-276° WF-OPT-270° WF-MPPT-282° WF-MPPT-276° WF-OPT-282° WF-OPT-276°
10 12 8 10
ActiveActive powerpower (MW) (MW)
1 1.2
Pitch angle (°), tip(° speed Pitch angle ), tip speed ratio and (rpm) (rpm) ratiorotor andspeed rotor speed
ActiveActive powerpower (pu) (pu)
can be increased mostly at the wind direction of 270°. Moreover, the increased amount of the active 25 power in1.2 the wind farm reduces with the increase of wind 12 direction from 270° to 282°.
6 8 4 6
WF-MPPT-282° WF-OPT-282°
42 20
5
6
0 5
6
7 8 9 10 11 12 13 Ambient wind speed(m/s) 7 8 9 10 11 12 13 (b) Ambient wind speed(m/s)
Figure 9. (a) Optimized pitch power of WT1, at the wind (a) angle, tip speed ratio, blade speed and active(b) Figure 9. (a) Optimized pitch angle, tip speed ratio, blade speed and active power of WT1 , at the wind directions of 270°, 276° and 282°; (b) comparison of the total active power of the wind farm between ◦ ◦ ◦ Figureof 9. 270 (a) Optimized pitch speed ratio,ofblade speedactive and active power of WT 1, atfarm the wind directions , 276 and 282angle, ; (b) tip comparison the total power of the wind between the MPPT method and the optimization method, to maximize the total active power of the wind farm directions of 270°, 276° and 282°; (b) comparison of maximize the total active power of thepower wind farm between the MPPT method and the optimization method, to the total active of the wind farm by selecting the optimal pitch angle and tip speed ratio for WT1, at the wind directions of 270°, 276° the MPPT method and the optimization method, to maximize the total active power of the wind farm ◦ ◦ by selecting and 282°.the optimal pitch angle and tip speed ratio for WT1 , at the wind directions of 270 , 276 by selecting the optimal pitch angle and tip speed ratio for WT1, at the wind directions of 270°, 276° ◦ and 282 . and 282°.
4. Wake Effect and Active Power Maximization in a Three-Turbine Wind Farm
4. Wake Effect andand Active Power Maximization Three-Turbine Wind Farm 4. Wake Effect Active Power Maximization inand aa Three-Turbine Wind Farm In this section, case studies of the wake effectin the proposed optimization method are carried out inInathis three-turbine wind farm. The three-turbine wind farm isoptimization shown in Figure 10,are where is In this section, case studies ofofthe wake effect andthe theproposed proposed optimization method are itcarried section, case studies the wake effect and method carried assumed that the two wind turbines are the NREL 5 MW DFIG wind turbine and the distance outa in a three-turbine wind farm.The The three-turbine three-turbine wind is is shown in Figure 10, where it is it is out in three-turbine wind farm. windfarm farm shown in Figure 10, where between two wind turbines is the 6.5 times bladeDFIG diameter. assumedthe that theadjacent two wind turbines are NRELthe 5 MW wind turbine and the distance
assumed that the two wind turbines are the NREL 5 MW DFIG wind turbine and the distance between between the two adjacent wind is the 6.5 times blade diameter. the two adjacent wind turbines is turbines 6.5 times bladethe diameter. α α
u u
u
v1,
1,
β1, P1
v1,
1,
β1, P1
Definition of the wind direction Definition of the
North North
wind direction v2,
v2,
2,
2,
β2, P2
v3,
β2, P2
v3,
3, 3,
β3, P3
β3, P3
u α=270° α=270°
WT1 WT1
WT3
WT2 XD XD
WT2
XD
WT3
XD
Figure 10. Layout of the wind farm with 3 NREL 5 MW DFIG wind turbines.
Figure 10.10. Layout ofofthe with33NREL NREL5 5MW MW DFIG wind turbines. Figure Layout thewind wind farm farm with DFIG wind turbines. 4.1. Multi-Wake Effect 4.1. Multi-Wake Effect 4.1. Multi-Wake Effect The Katic wake model estimates the wind speed deficit in multiple wakes by summing all the The Katic wakecaused model by estimates the wind speed deficit At in multiple by summing all wind the wind speed deficits the upstream wind turbines. windwakes direction of 270°, the The Katic wake model estimates the wind speed deficit inthe multiple wakes by summing all the wind speed deficits caused by the upstream wind turbines. At the wind direction of 270°, the wind speed deficit at the position of WT3 1 − v3/u can be calculated by: ◦ , the wind windspeed speed deficits caused by the upstream wind turbines. At the wind direction of 270 deficit at the position of WT3 12− v3/u can be calculated by: 2 2 speed deficit at the position of WT − v3 /uvcan be calculated 2 , 2 ) 3v1 v23 (by: 3 2 13 ( 1 , 1 ) 2 2 2 1 1 1 (4) 1 )) 2 v23 ( 2u,v2 )(β v3 21 vu3 1v13v13 ( β( 1u1,,λ 23 2 , λ2 ) 1 1 (4) = 1− (4) 1− + 1 −u u u u uu where v3 is the wind speed at the position of WT3, β1 and λ1 are the pitch angle and tip speed ratio of where v3 is speed at theangle position of WT 3, β1 and λ1 are the pitch angle and tip speed ratio of WT β2the andwind λ2speed are theatpitch andof tip speed ratio WT2.the Referring to Equation (3),speed the wind where v131,, and is the wind the position WT and of λWT pitch angle and tip ratio of 3 , β1ratio 1 are WT and β 2 and λ2 are the pitch angle and tip speed 2. Referring to Equation (3), the wind speed deficit at the position of WT3 caused by WT1 1 − vof 13(β1,λ1)/u and the wind speed deficit at the WT1 ,speed and βdeficit and λ are the pitch angle and tip speed ratio of WT . Referring to Equation (3), the 2 at32caused the position of2WT by WT1 1 − v13(β1,λ1)/u2 and the wind speed deficit at the wind position of WT by WT 1 − 3vcaused 23(β2,λ2)/u can be expressed as: position of WT3 caused by WT2 1 − v23(β2,λ2)/u can be expressed as:
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speed deficit at the position of WT3 caused by WT1 1 − v13 (β1 ,λ1 )/u and the wind speed deficit at the position of WT3 caused by WT2 1 − v23 (β2 ,λ2 )/u can be expressed as: Energies 2017, 10, 395
v13 ( β 1 , λ1 ) Energies 2017, 10, 395 1−
u
1−
=
q
1 − Ct_1 ( β 1 , λ1 )
v ( , ) 1 13 1 1 1 1 Ct _1 ( 1 , 1 ) v13 ( 1u , 1 ) 1 q 1 1 Ct _1 ( 1 , 1 )
D D + 4kXD2 cos( ϕ)
Aol _13 D 2 4kXD Dcos( ) AARol _13 D
v23 ( β 2 , λ2 ) u D R 1− − 1 − Ct_2 ( β 2 , λ2)D 4kXDD cos( )2 Aol A v23= ( 2 , 1 _ 23 2) u 1 D + 2kXD ( ϕ) 1 1 Ct _ 2 ( 2 , 2 ) cos 2
2
Aol_13 AR
9 of 19
9 of 19
(5)
(5)
2
Aol_23 AR
D 2kXD v ( u, ) Dcos( ) AARol _ 23 1 23 2 2 1 1 Ct _ 2 ( 2 , 2 ) the overlap between the wake area WT u 2kX D cos( ) theARblade D of 1 and
(5) (6)
(6)
where Aol_13 , which is sweep area(6) of WT3, where Aol_13, which is the overlap between the wake area of WT1 and the blade sweep area of WT3, and Aol_23 , which is the overlap between the wake area of WT and the blade sweep area of WT3 , and A between thethe wake areaarea of WT and12the sweepsweep area ofarea WT3of , are where Aol_23 ol_13, ,which whichisisthe theoverlap overlap between wake of 2WT andblade the blade WT3, are shown in Figure shown Figure11. and Aol_23 ,inwhich is11. the overlap between the wake area of WT2 and the blade sweep area of WT3, are shown in Figure 11. α
α
WT1
v1
α=270° +φ
α=270° +φ
φ
v1
DX
φ
Dcos(φ
1
1
k
k
WT3
XD
v2
φ
v2
)
WT3
XD
WT2
XD D
u
WT2
XD
WT1
North
Definition of the wind direction
u
u
North
Definition of the wind direction
u
φ
XDcos (φ
k
1
1
v3
k
v3
Aol_13
Aol_13
Aol_23 AR
Aol_23 AR
)
XDcos (φ) XDcos Figure 11. Katic wake model. WT3is is in in the of WT and WT 2. (φ) wakes Figure 11. Katic wake model. WT themultiple multiple wakes of 1WT 3 1 and WT2 .
In Figure Figure 11, it is11. noted Aol_13 is smaller ol_23, which indicates that the wind direction Katicthat wake model. WT3 is than in theAmultiple wakes of WT1 and WT2.
21
273° 276° 279° 270° 282° 273°
18
24
15 2112
18 9
276° 279° 282°
15 6 12 3 9 6 3
3
6 9 12 15 18 21 Ambient wind speed (m/s)
(a)
24
Active power (MW) Active power (MW)
Wind speed of WT3 (m/s)
Wind speed of WT3 (m/s)
In range Figure 11, itthe is WT noted smaller than whichthan indicates that the wind direction where 3 hasthat windAspeed deficit caused by A WT 1 is,smaller the wind direction range ol_13 is ol_23 where the WT 3 has wind speed deficit caused by WT 2 . Consequently, the wind direction ranges in range where the WT has wind that speed deficit caused byAWT is smaller thanthat thethe wind direction In Figure 11,3 it is noted Aol_13 is smaller than ol_23,1which indicates wind directionrange which thehas three-turbine winddeficit farm has power lossWT are the same as wind direction ranges in which whererange the WT wind speed caused by . Consequently, the wind direction ranges in where the WT 3 has wind speed deficit caused by WT 1 is smaller than the wind direction range 3 2 the two-turbine wind farm has the power loss, which are four symmetrical wind direction ranges of where the WT 3 has wind speed deficit caused by WT 2 . Consequently, the wind direction ranges which the three-turbine wind farm has power loss are the same as wind direction ranges in in which 258°–270°, 270°–282°, 78°–90° and 90°–102°. which the three-turbine wind farm has power loss areare thefour same as wind direction ranges in which the two-turbine wind farm has the power loss, which symmetrical wind direction ranges of With the MPPT method implemented in WT1, WT2 and WT3, the wind speed of WT3 is shown in the two-turbine the power which are four symmetrical wind direction ranges of ◦ , 270◦ –282wind ◦ , 78◦farm ◦ has ◦ –102◦loss, 258◦ –270 –90 and 90 . Figure 12a, at the wind directions from 270° to 282° with the resolution of 3°. It can be observed in 258°–270°, 270°–282°, 78°–90° and 90°–102°. With the 12a MPPT inthe WTmaximum WTat3 ,the thewind wind speed of of270°. WT3There is shown in Figure that method the wind implemented speed of WT3 has deficit direction 1 , WT2 and With the MPPT method implemented ◦in WT1, WT 2 and WT3, the wind speed of WT3 is shown in ◦ with is no at wind at the wind 282°. Moreover, the active power 1, WT and Figure 12a, thespeed winddeficit directions fromdirection 270 toof282 the resolution of 3◦ .ofItWT can be 2observed in Figure 12a, atwind the wind directions from 270° to 282°12b. with the resolution of 3°. It can be observed in WT3that at the direction ofof270° is shown inmaximum Figure ◦ . There is FigureFigure 12a the wind speed WT has the deficit at the wind direction of 270 3 3 has the maximum deficit at the wind direction of 270°. There 12a that the wind speed of WT no wind speed deficit at the wind direction of 282◦ . Moreover, the active power of WT1 , WT2 and WT3 is no wind 6 Moreover, the active power of WT1, WT2 and 24 speed deficit ◦at the wind direction of 282°. at theWT wind direction of 270 is shown in Figure 12b. 270° 3 at the wind direction of 270° is shown in Figure 12b. 5 4
6
3
5
2
4
1
WT1 WT2 WT3
WT1 WT2 WT3
3
0
22 3 4 5 6 7 8 9 10 11 12 13 14 15 1 Ambient wind speed(m/s) 0 (b) 2 3 4 5 6 7 8 9 10 11 12 13 14 15
3 12. 6 (a) Wind 9 12 Figure speed15 of WT18 3; (b) 21 active24 power of WT1, WT2 and WT3, at the wind direction of 270°. Ambient wind speed (m/s) 4.2. Active Power Maximization (a)
Ambient wind speed(m/s) (b)
Figure 12. (a) Wind speed of WT3; (b) active power of WT1, WT2 and WT3, at the wind direction of 270°.
Figure 12. (a) Wind speed of WT3 ; (b) active power of WT1 , WT2 and WT3 , at the wind direction ◦. of 270 4.2. Active Power Maximization
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270◦ ,
At the wind direction of as no power loss is caused by WT3 to the wind farm due to its At the wind direction of 270°, as no power loss is caused by WT3 to the wind farm due to its position, WT3 should be controlled by the MPPT method. The control curves of WT1 and WT2 can position, WT3 should be controlled by the MPPT method. The control curves of WT1 and WT2 can be be optimized to maximize the total active power of the wind farm. At the wind direction of 270◦ optimized to maximize the total active power of the wind farm. At the wind direction of 270° and at and at a fixed ambient wind speed u, in the case of m sets of pitch angle and tip speed ratio of WT1 a fixed ambient wind speed u, in the case of m sets of pitch angle and tip speed ratio of WT1 and that and that m sets of pitch angle and tip speed ratio of WT2 are assumed, m × m possible total active m sets of pitch angle and tip speed ratio of WT2 are assumed, m × m possible total active power of the power the wind farm areasexpected, shown Figure 13.toAccording Equations (1),the (3)active and (5), windoffarm are expected, shown inasFigure 13.inAccording Equationsto (1), (3) and (5), thepower activeof power of WT , the wind speed of WT and the wind speed deficit caused by WT WT 1 2 wind speed deficit caused by WT1 to WT 1 to WT1, the wind speed of WT2 and the 3 are 3 aredetermined determinedby bythe thepitch pitchangle angleand andtip tipspeed speedratio ratioofofWT WT . At a fixed wind speed of WT , according 2 1. 1At a fixed wind speed of WT2, according to Equations (1)(1) and the wind wind speed speeddeficit deficitcaused causedbybythe the WT 2 to to Equations and(6), (6),the theactive activepower powerof ofWT WT22 and and the WT 2 to WTWT are determined by the pitch angle and tip speed ratio of WT . Then, the wind speed of WT 3 3 are determined by the pitch angle and tip speed ratio of WT22. Then, the wind speed of WT3 is3 is determined both byby thethe pitch angle and tiptip speed ratio ofof WT WT determined both pitch angle and speed ratio WT 1 and WT , asexpressed expressedby byEquation Equation(4). 1 and 2 , 2as Controlled by theby MPPT method, the active power of WT can be calculated byby Equation (1). (4). Controlled the MPPT method, the active power of 3WT 3 can be calculated Equation (1). three-turbinewind wind farm, the angle and tip tip speed ratioratio of WT and1WT 2 can In In thethe three-turbine theoptimal optimalpitch pitch angle and speed of1 WT and WT2 be be selected by the searchsearch method. Firstly, allFirstly, the total power of thepower wind farm canalso also selected by exhausted the exhausted method. allactive the total active of the in terms pitch and angle tip speed of WTratio 1 andof WT 2 are calculated with a resolution. wind farm of in the terms of angle the pitch and ratio tip speed WT and WT are calculated with a 1 2 Afterwards, the maximum total active of the ofwind farm farm can can be selected. Finally, thethe resolution. Afterwards, the maximum total power active power the wind be selected. Finally, corresponding optimalpitch pitchangle angleand andtip tipspeed speed ratio ratio of of WT WT1 and WT2 can be obtained. corresponding optimal 1 and WT2 can be obtained.
Figure 13.13. Relationship of the variables in the farm farm with three wind turbines, at the wind Figure Relationship of the variables in wind the wind with three wind turbines, at thedirection wind ◦. of 270 direction of 270°. ◦ and wind direction and ambient wind speed m/s,the theactive activepower powerofofWT WTand 1 and AtAt thethe wind direction of of 270270° ambient wind speed of of 1111 m/s, the 1 the wind speed of WT 2 in terms of the pitch angle and tip speed ratio of WT1 are shown in Figure wind speed of WT2 in terms of the pitch angle and tip speed ratio of WT1 are shown in Figure 14a,b. 14a,b. In the case that WT1 is controlled by the MPPT method, the pitch angle and the tip speed ratio of WT1 are 0° and 7.55 respectively. Due to the rotor speed limit of 12.1 rpm, the tip speed ratio of
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OPT P1 (pu)
1
V2 (m/s)
In the case that WT1 is controlled by the MPPT method, the pitch angle and the tip speed ratio of WT1 areEnergies 0◦ and 7.55 Due to the rotor speed limit of 12.1 rpm, the tip speed ratio of11WT 2017, 10,respectively. 395 of 19 1 is ◦ limited at 7.26. When WT1 is operating at the pitch angle of 0 and tip speed ratio of 7.26, the active WT1 is at 7.26. WTof1 is operating at the pitch angle of 0° and tip speed ratio of 7.26, the powers oflimited WT2 , the windWhen speeds WT 3 , the active powers of WT3 and the total active powers of the active powers of WT 2, the wind speeds of WT3, the active powers of WT3 and the total active powers wind farm in terms of the pitch angle and tip speed ratio of WT2 are respectively shown in Figure 14c–f. of the wind farm in terms of the pitchpower angle of and speed ratio WT 2 are respectively shown in As shown in Figure 14f, the total active thetipwind farm is of 0.58 pu. Figure 14c–f. As shown in Figure 14f, the total active power of the wind farm ◦ At the wind direction of 270 and ambient wind speed of 11 m/s, selectedisby0.58 thepu. exhausted search At the wind direction of 270° and ambient wind speed of 11 m/s, selected by the exhausted search ◦ method, the optimal pitch angle and tip speed ratio of WT1 are 2.2 and 6.7 respectively. The optimal method, the optimal pitch angle and tip speed ratio of WT1 are 2.2° and 6.7 respectively. The optimal pitch angle and tip speed ratio of WT2 are 2.8◦ and 6.5 respectively. When the WT1 is operating at the pitch angle and tip speed ratio of WT2 are 2.8° and 6.5 respectively. When the WT1 is operating at the optimal pitch angle and tip speed ratio of WT1 as shown in Figure 14a,b marked with OPT, the active optimal pitch angle and tip speed ratio of WT1 as shown in Figure 14a,b marked with OPT, the active powers of WT2 , the wind speeds of WT3 , the active powers of WT3 and the total active powers of the powers of WT2, the wind speeds of WT3, the active powers of WT3 and the total active powers of the wind farm in terms of the pitch angle and tip speed ratio of WT are respectively shown in Figure 14g–j. wind farm in terms of the pitch angle and tip speed ratio of 2WT2 are respectively shown in Figure As 14g–j. shownAs inshown Figure in 14j,Figure the total power of power the wind farm is increased to 0.615 pu. Compared 14j, active the total active of the wind farm is increased to 0.615 pu. with the MPPT method, the total active is increased 0.035 pu.by 0.035 pu. Compared with the MPPT method, thepower total active power isby increased
MPPT
0.8
10 9.5 9 8.5
OPT
6
0.6
(°
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4 (° )
7 λ1
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0.61 0.59 0.57 0.55 6
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Figure 14. (a) Active power of WT1 where the base value is 5 MW; (b) wind speed of WT2, in terms of Figure 14. (a) Active power of WT1 where the base value is 5 MW; (b) wind speed of WT2 , in terms the pitch angle and tip speed ratio of WT1; (c) active power of WT2 where the base value is 5 MW; (d) of the pitch angle and tip speed ratio of WT1 ; (c) active power of WT2 where the base value is 5 MW; wind speed of WT3; (e) active power of WT3 where the base value is 5 MW; (f) total active power of (d) the wind speed of where WT3 ; (e) powerisof15WT the base 5 MW; (f)tip total active power 3 where wind farm theactive base value MW, in terms of thevalue pitchisangle and speed ratio of of the wind farm where the base value is 15 MW, in terms of the pitch angle and tip speed ratio WT2,when WT1 is operating at the pitch angle and tip speed ratio of 0° and 7.23, respectively; (g) activeof WTpower operating at the pitch speed ratio 0◦3; and 7.23, power respectively; active 2 ,whenofWT 1 2iswhere WT the base value is angle 5 MW;and (h) tip wind speed of of WT (i) active of WT3(g) where power of WT where the base value is 5 MW; (h) wind speed of WT ; (i) active power of WT where 2 3 3 the base value is 5 MW; (j) total active power of the wind farm where the base value is 15 MW, in theterms base value 5 MW; (j) and totaltip active power farm the base is 15angle MW,and in terms of theispitch angle speed ratio of of the WTwind 2,when WTwhere 1 is operating at value the pitch tip of the pitch angle and tip6.7. speed ratio of WT2 ,when WT1 is operating at the pitch angle and tip speed speed ratio of 2.2° and ratio of 2.2◦ and 6.7.
With the optimized pitch angle and tip speed ratio of WT1 and WT2, the optimized pitch angle and active curvepitch of WTangle 1 and WT2, at the wind directions from 270° to 282°, with the resolution With thepower optimized and tip speed ratio of WT1 and WT2 , the optimized pitch angle of 6°, are shown in Figure 15a,b. It can, be observed that the pitch angle ◦and tip◦speed ratio of WT1 and active power curve of WT1 and WT 2 at the wind directions from 270 to 282 , with the resolution and WT2 are optimized at the wind speeds from 7 m/s to 11 m/s. Comparing the MPPT method and ◦ of 6 , are shown in Figure 15a,b. It can be observed that the pitch angle and tip speed ratio of WT1 and the proposed active power control method, the active power of WT1, WT2, WT3 and the total active WT2 are optimized at the wind speeds from 7 m/s to 11 m/s. Comparing the MPPT method and the power of the wind farm at the wind direction of 270° are shown in Figure 15c, with the ambient wind proposed active power control method, the active power of WT1 , WT2 , WT3 and the total active power speeds in the range of from 3 m/s to 11 m/s with a resolution of 1 m/s. It can be seen that, at the of the wind farm at the wind direction of 270◦ are shown in Figure 15c, with the ambient wind speeds ambient wind speed of from 7 m/s to 13 m/s, the active power of WT1 is reduced. However, the active in the range of from 3 m/s to 11 m/s with a resolution of 1 m/s. It can be seen that, at the ambient powers of WT2 and WT3 are increased. Overall, the active power of the wind farm is increased. wind speed of from m/s to 13 m/s, the active power WTtip reduced. active powers 1 isspeed As shown in 7Figure 15a,b, the optimal pitch angleofand ratioHowever, of WT1 arethe 2.0° and 6.8, at of WT and WT are increased. Overall, the active power of the wind farm is increased. 3 of 9 m/s at the position of WT2. The optimal pitch angle and tip speed ratio of WT2 the 2wind speed As1.8° shown in at Figure 15a,b, the of optimal pitch angle and tip 2speed ratio of WT 2.0◦ofand 1 are are and 6.9 the wind speed 9 m/s at the position of WT . The optimized pitch angle WT6.8, 1 at the wind speed of 9 m/s at the position of WT . The optimal pitch angle and tip speed ratio of WT 2 is larger than the optimized pitch angle of WT2, because of greater power loss caused by WT1 2 arecompared 1.8◦ and 6.9 the speed of 9 Itm/s at the position of WT2 . The optimized angle of wind WT1 is to at WT 2 towind the wind farm. is evident that the optimized pitch angle of pitch the upstream larger thanisthe optimized pitch angle of WTangle greater power loss causedand by the WToptimized turbine larger than the optimized pitch of theofdownstream wind turbine 2 , because 1 compared to WT to theratio wind It is evident that the optimized of the upstream wind tip 2speed offarm. the upstream wind turbine is smallerpitch than angle the optimized tip speed ratioturbine of the is downstream wind turbine. Moreover, as shown in Figure 14j, the total active power of the wind larger than the optimized pitch angle of the downstream wind turbine and the optimized tipfarm speed hasofathe slight difference, lessturbine than 0.003 pu, when WT 2 is operating in the ratio pitchof angle range from ratio upstream wind is smaller thanthe the optimized tip speed the downstream 1.5° to 4° and in the tipasspeed ratio range from 6 tototal 7. Consequently, problem, the wind turbine. Moreover, shown in Figure 14j, the active power to of simplify the windthe farm has a slight ◦ ◦ optimized control curves of WT 1 and WT 2 can be assumed to be the same. difference, less than 0.003 pu, when the WT2 is operating in the pitch angle range from 1.5 to 4 and
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in the tip speed Energies 2017, 10, 395ratio
range from 6 to 7. Consequently, to simplify the problem, the optimized control 13 of 19 curves of WT1 and WT2 can be assumed to be the same. Furthermore, at WT 1 and WT 2 in at the the wind wind direction directionof of270°, 270◦ ,asasthe theoptimized optimizedcontrol controlcurves curvesofof WT WT 1 and 2 the three-turbine wind farm is almost the the same as the control curves of WT in the twoin the three-turbine wind farm is almost same as optimized the optimized control curves of1 WT in the 1 turbine windwind farm,farm, the optimized control curves of WT 1 in 1the wind farm cancan simply be two-turbine the optimized control curves of WT in two-turbine the two-turbine wind farm simply implemented in WT 1 and WTWT 2 in 2the wind farm. Thus, the computation complexity can be implemented in WT in three-turbine the three-turbine wind farm. Thus, the computation complexity 1 and be fromfrom m × m to where m is the of possible sets of pitch angleangle and tip speed ratio canreduced be reduced × m, m to m, where m isnumber the number of possible sets of pitch and tip speed of each windwind turbine. ThisThis simplification cancan be be extended into the ratio of each turbine. simplification extended into thewind windfarms farmswith with more more wind turbines in a line, e.g., in the wind farm with ten turbines in a line, the optimized control curves of WT11 in the two-turbine wind farm at the wind direction of 270° 270◦ can simply be implemented in all the 10 to m. upstream wind turbines. The computation complexity will be reduced from from m m10
20 P1-OPT-270° β1_OPT-270° 1_OPT-270° ωr1_OPT-270° P1_OPT-276° β1_OPT-276° 1_OPT-276° ωr1_OPT-276° P1_OPT-282° β1_OPT-282° 1_OPT-282° ωr1_OPT-282°
0.8 0.6 0.4 0.2
15 10 5
1 Active power (pu)
1
20 P2-OPT-270° β2_OPT-270° 2_OPT-270° ωr2_OPT-270° P2_OPT-276° β2_OPT-276° 2_OPT-276° ωr2_OPT-276° P2_OPT-282° β2_OPT-282° 2_OPT-282° ωr2_OPT-282°
0.8 0.6 0.4 0.2
0 0 3 5 7 9 11 13 15 17 19 21 23 25 Wind speed of WT1 (m/s)
0
(a)
15 10 5
0 3 5 7 9 11 13 15 17 19 21 23 25 Wind speed of WT2 (m/s)
(b) WT1-MPPT-270° WT1-OPT-270° WT2-MPPT-270° WT2-OPT-270° WT3-MPPT-270° WT3-OPT-270° WF-MPPT-270° WF-OPT-270°
15
Active power (MW)
25 Pitch angle (°), tip speed ratio and rotor speed (rpm)
1.2
25 Pitch angle (°), tip speed ratio and rotor speed (rpm)
Active power (pu)
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0 5
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7 8 9 10 11 12 13 14 15 Ambient wind speed(m/s)
(c) Figure 15. (a) Optimized pitch angle, tip speed ratio, active power and rotor speed of WT1 in the threeFigure 15. (a) Optimized pitch angle, tip speed ratio, active power and rotor speed of WT1 in the turbine wind farm; (b) optimized pitch angle, tip speed ratio, active power and rotor speed of WT2 in three-turbine wind farm; (b) optimized pitch angle, tip speed ratio, active power and rotor speed of the three-turbine wind farm; (c) comparison of the active power of WT1, WT2, WT3 and the total active WT2 in the three-turbine wind farm; (c) comparison of the active power of WT1 , WT2 , WT3 and the power of the wind farm between the MPPT method and the proposed active power control method, total active power of the wind farm between the MPPT method and the proposed active power control at 270° wind direction. method, at 270◦ wind direction.
5. Wake Effect and Active Power Maximization in a Large-Scale Wind Farm 5. Wake Effect and Active Power Maximization in a Large-Scale Wind Farm In this section, the proposed method to maximize the total active power of the wind farm is In this section, the proposed method to maximize the total active power of the wind farm is demonstrated in an eighty-turbine wind farm. The layout of the wind farm is shown in Figure 16, which demonstrated in an eighty-turbine wind farm. The layout of the wind farm is shown in Figure 16, is the same as the Horns Rev offshore wind farm in Denmark [22]. A total of 80 NREL 5 MW DFIG wind which is the same as the Horns Rev offshore wind farm in Denmark [22]. A total of 80 NREL 5 MW turbines in the wind farm with 6.5 diameters of distance between the two adjacent wind turbines in the DFIG wind turbines in the wind farm with 6.5 diameters of distance between the two adjacent same row or in the same column are assumed. Finally, the annual energy production (AEP) of the wind wind turbines in the same row or in the same column are assumed. Finally, the annual energy farm is calculated and compared between the MPPT method and the proposed method.
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production (AEP) of the wind farm is calculated and compared between the MPPT method and the proposed method. Energies 2017, 10, 395 14 of 19
North
α
Definition of the wind Energies 2017, 10, direction 395
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u
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6 1 2 3 4 5 6 7 8 9 10 5 1 α=270°2 5 6
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13 2 3 4 5 6 2α=352° X (km)
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7 3 8 4
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Y (km)
Y (km)
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5
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8 9 5 α=311°6
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400000 420000 440000 460000 480000 6120000
Figure 16.α=352° Location and layout of the wind farm, where each wind 480000 turbine WTm_n is labeled with its X (km) 400000 where 420000 440000 Figure 16. Location and layout α=311° of the wind farm, each 460000 wind turbine WTm_n is labeled with its row No. m and its column No. n. row No. m and its column No. n. Figure 16. Location and layout of the wind farm, where each wind turbine WTm_n is labeled with its
Total active power of the wind farm (pu)
Total active power of the wind farm (pu)
5.1. Wake Effect row No. m and its column No. n. 5.1. Wake Effect In the eighty-turbine wind farm, controlled by the MPPT method, the total active powers of the 5.1. Wake In the eighty-turbine MPPT method, the range total active powers of the wind farm areEffect shown in wind Figurefarm, 17. Incontrolled Figure 17, by thethe wind directions in the of from 0° to 360° ◦ to 360◦ wind farm are shown in Figure 17. In Figure 17, the wind directions in the range of from 0 In the eighty-turbine wind farm, controlled by the total powers of the with a resolution of 1° and the ambient wind speeds of MPPT 4 m/s,method, 6 m/s, 8the m/s, 10active m/s, 12 m/s and 14 m/s with resolution of shown 1◦ andThe ambient wind speeds of 4directions m/s, 8 m/s, m/s, m/sare and wind farm inthe Figure 17.speed In Figure the wind in the range of 10 from 0°turbines to12 360° areataken into are account. wind at 17, the position of the6 m/s, downstream wind aby resolution of 1° and the ambient wind speeds of 4 m/s, 6 m/s, 8 m/s, 10 m/s, 12 m/s and 14 m/s 14 calculated m/s with are taken into account. The wind speed at the position of the downstream wind turbines (3)–(6), where the decay constant k = 0.04 is assumed. In Figure 17, it can be observedare are by taken into where account.the The windconstant speed atk the position of the downstream wind turbines are calculated (3)–(6), decay = wake 0.04 iseffect assumed. Figure 17, it can beat observed that that the large amount of power loss due to the in theInwind farm appears the wind calculated by (3)–(6), where the decay constant k = 0.04 is assumed. In Figure 17, it can be observed thedirections large amount of power loss62°, due90°, to the wake the200°, wind221°, farm242°, appears the 311°, wind327° directions of around 20°, 41°, 115°, 131°,effect 147°, in 172°, 270°,at 295°, and that the amount power loss◦ due to the wake effect in◦ the wind farm appears at◦ the wind ◦ , large ◦ , 62 ◦ , 90◦of ◦ , 131 ◦ ,potential ◦ , 200to ◦ ,increase ◦ , total ◦ ,active ◦ , power ◦ and ◦ of 352°. around 20 41 , 115 , 147 172 221 , 242 270 295 311 , 327 At these wind directions, there is huge the of the wind directions of around 20°, 41°, 62°, 90°, 115°, 131°, 147°, 172°, 200°, 221°, 242°, 270°, 295°, 311°, 327° and 352 . with thedirections, proposed active power Atfarm these352°. wind there is huge to increase thethe total active ofthe thewind wind farm At these wind directions, therecontrol ispotential huge method. potential to increase total activepower power of with theactive proposed activecontrol power control method. with thefarm proposed power method. 1
0.8
1 0.8
u = 4 m/s
u = 4 m/s u = 6 m/s u = 6 m/s = 8 m/s u = 8u m/s u =m/s 10 m/s u = 10 u =m/s 12 m/s u = 12 u =m/s 14 m/s u = 14
0.6 0.6 0.4 0.4 0.2 0.2 0
0
0 0
30
30
60
60
90
90
120 150 180 210 240 270 300 330 360
120 150 180 210 240 270 300 330 360 Wind direction(° ) Wind direction(° )
Figure 17. Total active power of the wind farm by using the MPPT method. Figure 17. Total active power of the wind farm by using the MPPT method. Figure 17. Total active power of the wind farm by using the MPPT method.
5.2. Active Power Maximization
5.2.5.2. Active Power Maximization Active Maximizationwind farm, at the wind direction of 270°, the wind turbine in one row will InPower the eighty-turbine
notthe cause the power loss to the wind in other rows of because the smallturbine decay constant. Inrow In In the eighty-turbine wind farm, at the direction of270°, 270◦ ,of the wind turbine one will eighty-turbine wind farm, atturbines the wind wind direction the wind inin one row will thisthe case,power the wind farm can bewind seen as eight isolated ten-turbine wind farms asthe shown in Figure 18. notnot cause loss to the turbines in other rows because of small decay constant. cause the power loss to the wind turbines in other rows because of the small decay constant. In As discussed and concluded in Section 4.2, at the wind direction of 270°, the optimized control curves In this this case, case, thewind windfarm farmcan canbe beseen seenasaseight eightisolated isolatedten-turbine ten-turbine wind farms shown in Figure the wind farms as as shown in Figure 18. 18. of WT1 in the two-turbine wind farm can simply be implemented in WT1–WT9 in the ten-turbine wind As discussed and concluded in Section 4.2, at the wind direction of 270°, the optimized control curves of WT1 in the two-turbine wind farm can simply be implemented in WT1–WT9 in the ten-turbine wind
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As discussed and concluded in Section 4.2, at the wind direction of 270◦ , the optimized control curves of WT1 in the two-turbine wind farm can simply be implemented in WT1 –WT9 in the ten-turbine wind farm. Thus, the optimization computation complexity in the ten-turbine wind farm will be reduced Energies 2017, 10, 395 15 of 19 from m10 to m. With the optimized control curves of WT1 in the two-turbine wind farm as shown in Figure 15aThus, implemented in WTcomputation the MPPT implemented in WT 1 –WT9 and with 10 , the total farm. the optimization complexity in the method ten-turbine wind farm will be reduced activefrom power of m. theWith ten-turbine windcontrol farm iscurves shown Figure where thewind totalfarm active powerinof the m10 to the optimized of in WT 1 in the19, two-turbine as shown ten-turbine wind farm can be increased at the wind speeds from 7 m/s to 14 m/s. In the Figure 15a implemented in WT 1–WT9 and withambient the MPPT method implemented in WT 10, the total ◦ active power of the ten-turbine wind farm is shown in Figure 19, where the total active power of the eighty-turbine wind farm, at the wind direction of 270 , the optimized control curves of the wind ten-turbine windcolumn farm canare bethe increased at thethe ambient wind control speeds from 7 m/s to 1_1 14 ,m/s. In the turbines in the same same, e.g., optimized curves of WT WT2_1 , WT3_1 , eighty-turbine wind farm, at the wind direction of 270°, the optimized control curves of the wind WT4_1 , WT5_1 , WT6_1 , WT7_1 and WT8_1 in the eighty-turbine wind farm are the same as the optimized turbines in the same column are the same, e.g., the optimized control curves of WT1_1, WT2_1, WT3_1, control curves of WT1 in the ten-turbine wind farm. WT4_1, WT5_1, WT6_1, WT7_1 and WT8_1 in the eighty-turbine wind farm are the same as the optimized As shown in Figure 17, the large amount of power loss due to the wake effect in the eighty-turbine control curves of WT1 in the ten-turbine wind farm. ◦ 115◦ , 131◦ , 147◦ , 172◦ , 200◦ , wind farm atFigure the wind directions of around 20◦ ,loss 41◦due , 62◦to, 90 Asappears shown in 17, the large amount of power the ,wake effect in the eighty◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ , the eighty-turbine wind 221 ,turbine 242 , 270 311 , 327 352 . At theofwind direction of 90 wind, 295 farm ,appears at theand wind directions around 20°, 41°, 62°, 90°, 115°, 131°, 147°, 172°, farm 200°, can also seen as eight isolated farms. The optimized control curves of WT1 221°,be 242°, 270°, 295°, 311°, 327°ten-turbine and 352°. At wind the wind direction of 90°, the eighty-turbine wind ◦ at thefarm wind of as 270 inisolated the two-turbine shown in Figure canofsimply candirection also be seen eight ten-turbinewind wind farm farms.as The optimized control15a curves WT1 be at the wind of 270° windwind farm farm. as shown in Figure can simply be◦ and implemented in direction WTm_1 -WT the two-turbine eighty-turbine At the wind 15a direction of 172 m_9 in the ◦ in WTm_1 -WTm_9 in the farm.eight-turbine At the wind direction of 172° andoptimized 352°, 352 , implemented the eighty-turbine wind farm caneighty-turbine be seen as 10wind isolated wind farms. The the eighty-turbine wind farm can be seen as 10 isolated eight-turbine wind farms. The optimized ◦ control curves of WT1 at the wind direction of 270 in the two-turbine wind farm as shown in Figure 15a control curves of WT1 at the wind direction of 270° in the two-turbine wind farm as shown in Figure can simply be implemented in WT8_n –WT2_n and WT1_n –WT7_n respectively in the eighty-turbine 15a can simply be implemented in WT8_n–WT2_n and WT1_n–WT7_n respectively in the eighty-turbine wind farm. At the wind directions of 41◦ , 131◦ , 221◦ and 311◦ , the wind farm can be seen as the isolated wind farm. At the wind directions of 41°, 131°, 221° and 311°, the wind farm can be seen as the isolated windwind farms. However, thethe isolated differentnumber number wind turbines. In each farms. However, isolatedwind windfarms farms have have different of of wind turbines. In each of of ◦ in the the isolated wind farms, the optimized control curves of WT at the wind direction of 270 1 wind direction of 270° in the twothe isolated wind farms, the optimized control curves of WT1 at the two-turbine farmcan canalso alsobe beimplemented implemented upstream wind turbines in each isolated turbine wind wind farm in in thethe upstream wind turbines in each isolated windwind farms. Besides, as the distance between windturbines turbines larger than in the ten-turbine farms. Besides, as the distance betweentwo twoadjacent adjacent wind is is larger than in the ten-turbine the optimized pitch angleisissmaller smaller than than in thethe tip tip speed ratioratio is larger windwind farm,farm, the optimized pitch angle inFigure Figure15a 15aand and speed is larger than in Figure 15a. than in Figure 15a. the rectangular layout wind farms at the wind directions where the windfarm farmshould shouldnot notseem In theInrectangular layout wind farms at the wind directions where the wind seem isolated or in the nonrectangular layout wind farms, the optimal pitch angle and tip speed ratio isolated or in the nonrectangular layout wind farms, the optimal pitch angle and tip speed ratio of all of all the wind turbines can be selected by the exhausted search or by the PSO- or GA-based the wind turbines can be selected by the exhausted search or by the PSO- or GA-based optimization optimization algorithms. Then, optimal control curves of each individual wind turbine need to be algorithms. Then, optimal control curves eachand individual wind turbine need to be with the generated with the optimized pitch of angle tip speed ratio. In this case, thegenerated computation optimized pitch angle speed However, ratio. In this case, the computation complexity cannot be reduced. complexity cannotand be tip reduced. other solutions may be implemented to reduce the However, other solutions may be implemented reduce computation complexity to separate computation complexity (e.g., to separate theto wind farmthe into number of zones or use (e.g., the method proposed [23]). In this of paper, theortypical regular layout wind farms are studied. In the eightythe wind farmininto number zones use the method proposed in [23]). In this paper, the typical turbine wind farm with the rectangular layout, at the wind directions of 20°, 62°, 115°, 147°, 200°, regular layout wind farms are studied. In the eighty-turbine wind farm with the rectangular layout, ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ 242°, 295° and 327°, the wind farms cannot be considered as isolated wind farms. Considering the be at the wind directions of 20 , 62 , 115 , 147 , 200 , 242 , 295 and 327 , the wind farms cannot smalleras power loss wind in thefarms. wind farm due to wake thepower large computation complexity and to thewake considered isolated Considering theeffect, smaller loss in the wind farm due estimation error of the wake model, the wind farm operator can make a trade-off whether to do the effect, the large computation complexity and the estimation error of the wake model, the wind farm optimization at these wind directions. operator can make a trade-off whether to do the optimization at these wind directions. α u
v1 ,
1,
β1, P1
Definition of the wind direction v5,
5,
North
β5, P5
v10,
10,
β10, P10
u α=270° WT1 XD
WT2 XD
WT3 XD
WT4 XD
WT5 XD
WT6 XD
WT7 XD
WT8 XD
WT9 XD
Figure Layout thewind windfarm farm with with 10 DFIG wind turbines. Figure 18. 18. Layout ofof the 10 NREL NREL55MW MW DFIG wind turbines.
WT10
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Active Activepower power(MW) (MW)
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50 50 40 40
MPPT-270° MPPT-270° OPT-270° OPT-270°
30 30 20 20 10 10 00
10 11 11 12 12 13 13 14 14 15 15 16 16 55 66 77 88 99 10 Ambient wind wind speed(m/s) speed(m/s) Ambient
Figure 19. 19. Comparison Comparison of of the the total total active active power power of of the the wind wind farm farm as as shown shown in in Figure Figure 15 15 between between the the Figure MPPT method method and and the the proposed proposed active active power power control controlmethod methodat atthe thewind winddirection directionof of270 270°. ◦. MPPT proposed active power control method at the wind direction of 270°.
10.0% 10.0% (a) (a)
Frequency Frequencyof ofoccurrence occurrence (%/(m/s)) (%/(m/s))
5.3. Annual Annual Energy Energy Production Production 5.3. 5.3. Annual Energy Production In this this subsection, subsection, the the annual annual energy energy production production (AEP) (AEP) of of the the eighty-turbine eighty-turbine wind wind farm farm is is In In this subsection, the annual energy production (AEP) of the eighty-turbine wind farm is compared between the MPPT method and the proposed active power control method. The AEP is compared between AEP is compared between the the MPPT MPPT method method and andthe theproposed proposedactive activepower powercontrol controlmethod. method.The The AEP calculated by by WAsP, WAsP, which which is is the the industry industry standard standard software software for for wind wind resource resource assessment assessment and and siting calculated is calculated by WAsP, which is the industry standard software for wind resource assessmentsiting and of wind turbines and wind farms [21]. The annual wind direction and wind speed distribution at the the of wind turbines and wind farms [21]. The annual wind direction and wind speed distribution at siting of wind turbines and wind farms [21]. The annual wind direction and wind speed distribution location of of the the wind wind farm, farm, as as shown shown in in Figure Figure 20, 20, is is taken taken into into account. account. In In Figure Figure 20a, 20a, the wind wind rose rose location at the location of the wind farm, as shown in Figure 20, is taken into account. In Figure the 20a, the wind is separated into 36 sectors with 10° for each. ◦ is separated into 36 withwith 10° for rose is separated intosectors 36 sectors 10 each. for each.
15 15
Mean wind wind speed speed in in all all Mean sectors: 8.21 8.21 m/s m/s sectors:
10 10 55 00 0 0
10 15 15 20 20 55 10 Wind speed speed (m/s) (m/s) Wind (b) (b)
Figure 20. 20. (a) (a) Wind Wind direction direction distribution distribution in in each each rose rose sector; sector; (b) (b) wind wind speed speed distribution distribution in in all all sectors. sectors. Figure Figure 20. (a) Wind direction distribution in each rose sector; (b) wind speed distribution in all sectors.
As shown shown in in Figure Figure 17, 17, the the active active power power of of the the wind wind farm farm is is the the same same at at the the wind wind directions directions As As shown in Figure 17, the active power of the wind farm is the same at the wind directions from from 269° to 273°. This is because, at these wind directions, each wind turbine has the same power from 269° to 273°. This is because, at these wind directions, each wind turbine has the same power ◦ to 273◦ . This is because, at these wind directions, each wind turbine has the same power loss due 269 loss due to the wake effect. Thus, the optimized control curves of each wind turbine are the same at loss due to the wake effect. Thus, the optimized control curves of each wind turbine are the same at to the wind wake directions. effect. Thus, the optimized control curves of each arewith the same at these wind these wind directions. However, the active active power of the the windwind farmturbine decreases with the wind wind direction these However, the power of wind farm decreases the direction directions. However, the active power of the wind farm decreases with the wind direction changing changing from 269° to 265° and from 273° to 275°, because of the reduced power loss. To simplify the changing from 269° to 265° and from 273° to 275°, because of the reduced power loss. To simplify the ◦ to 265◦ and from 273◦ to 275◦ , because of the reduced power loss. To simplify the problem, from 269 problem, the the optimized optimized control control curves curves of of each each wind wind turbine turbine at at the the wind wind direction direction of of 270° 270° are are problem, ◦ are implemented at all the optimized control curves of each wind turbine at the wind direction of 270 implemented at all the wind directions in the wind rose sector from 265° to 275°. It is the same case implemented at all the wind directions in the wind rose sector from 265° to 275°. It is the same case ◦ to 275◦ . It is the same case in the wind directions the wind directions in the wind 90°, rose sectorand from 265Consequently, in the the wind directions around 90°, 172° 172° and 352°. Consequently, to to calculate calculate the the AEP AEP of of each each wind wind in wind directions around 352°. ◦ , 172◦ and 352◦ . Consequently, to calculate the AEP of each wind turbine in the rose sectors around 90 turbine in in the the rose rose sectors sectors of of 85°–95°, 85°–95°, 165°–175°, 165°–175°, 265°–275° 265°–275° and and 345°–355°, 345°–355°, the the optimized optimized control control turbine ◦ –95◦ , 165◦ –175◦ , 265◦ –275◦ and 345◦ –355◦ , the optimized control curves generated at the wind of 85 curves generated at the wind direction of 90°, 172°, 270° and 352° are respectively implemented at curves generated at the wind direction of 90°, 172°, 270° and 352° are respectively implemented at ◦ , 172◦ , 270◦ and 352◦ are respectively implemented at the wind directions in the wind direction of 90 the wind directions in the wind rose sector of 85°–95°, 165°–175°, 265°–275° and 345°–355°. the wind directions in the wind rose sector of 85°–95°, 165°–175°, 265°–275° and 345°–355°. ◦ , 265◦ –275◦ and 345◦ –355◦ . rose sector of 85◦ –95 , 165◦ –175 Comparing the ◦MPPT MPPT method and the the proposed proposed active active power power control control method, method, the the AEP AEP of of each each Comparing the method and Comparing the MPPT method and the proposed active power control method, the AEP of each wind turbine at the wind directions in the rose sectors of 85°–95°, 165°–175°, 265°–275° and 345°–355°, wind turbine at the wind directions in the rose sectors of 85°–95°, 165°–175°, 265°–275° and 345°–355°, ◦ , 265◦ –275◦ and 345◦ –355◦ , wind turbine atand the shown wind directions 85◦ –95◦ ,that 165◦the –175AEP are calculated calculated and shown in Tables Tablesin22 the androse 3. It Itsectors can be beof observed that the AEP of the the wind wind turbines turbines in in are in and 3. can observed of are and shown in Tables 2 and It can be observed that the AEP of the wind turbines the the calculated first two two rows rows or columns columns along the 3. wind direction are reduced, reduced, but the the AEP of the the other in wind the first or along the wind direction are but AEP of other wind first two rows or columns along direction but the AEP of by the other wind turbines turbines are increased. increased. The AEPthe ofwind the wind wind farmare arereduced, respectively increased by 19.2%, 19.2%, 12.7%, 11.0% turbines are The AEP of the farm are respectively increased 12.7%, 11.0% 3 are increased. The AEP of the wind farm are respectively increased by 19.2%, 12.7%, 11.0% and 15.2% and 15.2% 15.2% in in the the four four wind wind rose rose sectors. sectors. Overall, Overall, 1.36 1.36 ×× 10 103 GWh GWh more more energy energy is is produced produced in in the the four four and 3 GWh more energy is produced in the four wind 6 GWh in the four wind rose sectors. Overall, 1.36 × 10 rose 6 wind rose sectors with the proposed active power implemented. Compared with the 1.31 × 10 wind rose sectors with the proposed active power implemented. Compared with the 1.31 × 10 GWh AEP of of the the wind wind farm farm with with the the MPPT MPPT method method implemented implemented in in all all the the wind wind directions directions from from 0° 0°to to 360°, 360°, AEP
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sectors with the proposed active power implemented. Compared with the 1.31 × 106 GWh AEP of the wind farm with the MPPT method implemented in all the wind directions from 0◦ to 360◦ , an increase of 1.03% can be noticed. If the proposed active power control method is also implemented at other wind directions, this percentage can be larger. Table 2. Comparison of annual energy production (AEP; GWh) between the MPPT method and the proposed active power control method in the wind rose sectors of 265◦ –275◦ and 85◦ –95◦ .
AEP
265◦ –275◦ Sector
85◦ –95◦ Sector
MPPT
OPT
MPPT
OPT
WT1_1 WT1_2 WT1_3 WT1_4 WT1_5 WT1_6 WT1_7 WT1_8 WT1_9 WT1_10
1356.6 977.8 835.4 760.8 713.9 689.1 669.2 658.7 642.7 631.2
1280.9 949.7 880.7 840.4 815.6 798.6 786.8 780.4 814.0 859.3
85.5 86.8 88.7 90.5 94.5 99.1 108.9 127.1 167.4 288.4
142.3 130.7 122.5 123.4 125.6 128.8 134.2 143.3 161.0 262.8
Total
63,482.2
70,450.4
9895.4
11,795.4
Increased
11.0%
19.2%
Table 3. Comparison of AEP (GWh) between the MPPT method and the proposed active power control method in the wind rose sectors of 345◦ –355◦ and 165◦ –175◦ . 345◦ –355◦ Sector
165◦ –175◦ Sector
MPPT
OPT
MPPT
OPT
WT1_1 WT2_1 WT3_1 WT4_1 WT5_1 WT6_1 WT7_1 WT8_1
382.9 234.1 185.3 162.5 148.4 142.3 136.1 134.0
348.4 232.1 208.8 195.5 188.1 183.4 194.1 207.0
169.9 173.0 180.1 187.7 203.9 230.1 283.7 435.2
248.7 233.8 222.7 228.1 237.0 252.0 278.4 400.0
Total
15,255.2
17,573.2
18,635.2
21,006.9
AEP
Increased
15.2%
12.7%
As the proposed active power control method maximizes the active power of the wind farm by reducing the power loss due to the wake effect, the increased active power of the wind farm depends on the amount of power loss at each wind direction. At the wind directions where the power loss is small, the active power of the wind farm can be increased slightly. Due to the estimation error of the wake model, the proposed active power may not be able to maximize the active power generation in the wind farm, at the wind direction where the power loss is small. However, at the wind directions where the power loss is large, compared with the significantly increased active power of the wind farm, the power loss due to the estimation error of the wake model can be neglected. Moreover, the proposed active power control method generates the optimal control curves at separate wind directions. Consequently, the optimal control curves can be generated and implemented at the wind directions where the wind farm has the largest power loss.
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6. Conclusions Due to the wake effect, there is a significant amount of power loss in large scale wind farms. By the optimization of the pitch angle and tip speed ratio for the wind turbines in the wind farm, the total active power of the wind farm can be increased. In this paper, the optimized pitch angle and tip speed ratio are firstly selected for each wind turbine by exhausted search method. Then, the optimized pitch angle curve and active power curve in terms of the wind speed are generated for each wind turbine with the optimized pitch angle and tip speed ratio. With the optimized control curves, the wind turbine can be controlled according to the real wind profile at the position of the wind turbine, where both the wind speed and wind direction are taken into account. In typical regular layout wind farms, due to the slight difference of the optimized pitch angle and tip speed ratio between the upstream and the downstream wind turbines, and due to the small variation of the total active power of the wind farm in a large range of pitch angle and tip speed ratio of the wind turbines analyzed by the exhausted search method, the optimized control curves of the upstream wind turbines can be simplified to be the same. As a consequence, the optimization computation complexity is greatly reduced. A case study in an eighty-turbine wind farm shows that the AEP of the wind farm is able to be increased by 1.03%, by using the proposed control method compared to the MPPT method. Moreover, the proposed method can be implemented to any wind farm layout with random wind profile at different locations. Acknowledgments: The authors would like to thank the Aalborg University and the Sino-Danish Centre for Education and Research for the funding support. Author Contributions: Jie Tian and Dao Zhou conceived and designed the simulations; Jie Tian performed the simulations; Jie Tian, Dao Zhou, Chi Su, Zhe Chen and Frede Blaabjerg analyzed the data; Mohsen Soltani contributed materials tools; Jie Tian wrote the paper. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
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