Aalborg Universitet Multiobjective Optimization in

37 electronic converters are decoupled completely from the grid [5-7]. However, there is a strong interaction between the turbine 38 control system an...

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Aalborg Universitet

Multiobjective Optimization in Combinatorial Wind Farms System Integration and Resistive SFCL Using Analytical Hierarchy Process Moghadasi, Amirhasan; Sarwat, Arif; Guerrero, Josep M. Published in: Renewable Energy DOI (link to publication from Publisher): 10.1016/j.renene.2016.03.073

Publication date: 2016 Document Version Early version, also known as pre-print Link to publication from Aalborg University

Citation for published version (APA): Moghadasi, A., Sarwat, A., & Guerrero, J. M. (2016). Multiobjective Optimization in Combinatorial Wind Farms System Integration and Resistive SFCL Using Analytical Hierarchy Process. Renewable Energy, 94, 366–382. https://doi.org/10.1016/j.renene.2016.03.073

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Multiobjective Optimization in Combinatorial Wind Farms System Integration and Resistive SFCL Using Analytical Hierarchy Process

Amirhasan Moghadasi, Arif Sarwat, Josep M. Guerreroc a,b

Energy Systems Research Laboratory, Florida International University, FL, USA c

Department of Energy Technology, Aalborg University, Aalborg, Denmark

Corresponding Authors’ Contact Information: Amirhasan Moghadasi

Office: EC3920 Lab: EC 3920 Phone (Lab): 305 348 2935 Email: [email protected] Mail: Florida International University (FIU) 10555 West Flagler St., EC3913 Miami, FL 33174

1

Multiobjective Optimization in Combinatorial Wind Farms System Integration and Resistive SFCL Using Analytical Hierarchy Process 1

Amirhasan Moghadasi, Arif Sarwat, Josep M. Guerrero

2 3

Abstract— This paper presents a positive approach for low voltage ride-through (LVRT) improvement of the permanent

4

magnet synchronous generator (PMSG) based on a large wind power plant (WPP) of 50MW. The proposed method utilizes the

5

conventional current control strategy to provide a reactive power requirement and retain the active power production during

6

and after the fault for the grid codes compliance. Besides that, a resistive superconducting fault current limiter (RSFCL) as an

7

additional self-healing support is applied outside the WPP to further increase the rated active power of the installation, thereby

8

enhance the dc-link voltage smoothness, as well as the LVRT capability of the 50MW WPP. This is achieved by limiting the

9

exceed fault current and diminishing the voltage dip level, leading to increase the voltage safety margin of the LVRT curve.

10

Furthermore, the effect of the installed RSFCL on the extreme load reduction is effectively demonstrated. A large WPP has a

11

complicated structure using several components, and the inclusion of RSFCL composes this layout more problematic for

12

optimal performance of the system. Hence, the most-widely decision-making technique based on the analytic hierarchy process

13

(AHP) is proposed for the optimal design of the combinatorial RSFCL and 50MW WPP to compute the three-dimensional

14

alignment in Pareto front at the end of the optimization run. The numerical simulations verify effectiveness of the proposed

15

approach, using the Pareto optimality concept.

16

Keywords—Low voltage ride-through, multi-objective optimization, superconducting fault current limiter, wind farm.

17

1.

Introduction

18

Wind turbines with the grid connected mode of the operation play the significant role toward in sustainable energy

19

development in the future. However, integration of large wind power plants (WPPs) can impose the adverse effects on the grid,

20

particularly under abnormal grid voltage conditions [1]. Traditionally, wind turbine generators were tripped with circuit

21

breakers once the voltage at their terminals reduced below 80% because the penetration level of the wind power was extremely

22

small compared to the conventional generation systems and their impact on the grid was low. The trend towards integration of

23

more WPPs has raised serious concerns about the stability of existing power networks, increasing the fault current levels and

24

voltage reductions, thereby disconnecting a large wind farm. Recently, many power system operators in Europe and other parts

25

of the world are expanding and modifying their interconnection requirements for wind farms through technical standards

26

known as grid codes [2-4]. 2

Vgrid

Vgrid U

U

90%

90%

Area A 50%

50%

Area A

Area B

20%

20%

Area B 0

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0%

20%

40%

60%

80%

100%

Time [s]

IR/In

(b)

(a)

27

Fig 1. Danish grid codes. (a) LVRT requirement. (b) Reactive power support requirement

28

One of the critical demanding requirements, concerning the grid voltage support, is called low voltage ride-through (LVRT)

29

capability, which is regularly being included in the new grid codes. Fig. 1(a) a shows practical example of the LVRT curve

30

defined by the Danish system operator for wind turbines (WTs) connected to the grid. Based on this regulation, if the voltage

31

remains at the level greater than 20% of nominal for a period less than 0.5 s, the WT should be connected to the grid. WTs are

32

only stipulated to disconnect from the grid when the voltage profile falls into the Area B. Besides the LVRT requirements,

33

some grid codes require large WTs to contribute to the voltage restoration of the power system by injecting the reactive power

34

during the fault and the recovery period [3], while maintaining the operating point above the area of Fig. 1(b).

35

Permanent magnet synchronous generators (PMSGs) with a full-rating converter offers a number of advantages for WTs,

36

including low maintenance requirements, more reactive power supply and better ride-through capability because power

37

electronic converters are decoupled completely from the grid [5-7]. However, there is a strong interaction between the turbine

38

control system and the mechanical loads the turbine experiences. The mechanical loads are divided into two distinct types:

39

extreme and fatigue loads. Extreme loads are loads that a given component needs to be able to withstand once; while fatigue

40

loads are accumulating over time and threaten to damage the turbine after several years of operation [8]. An important source

41

of extreme loads may occur during fault events. At the beginning of the fault, the maximum power injected into the grid

42

reduces proportional the voltage sag amplitude, while power injected from the wind generator remains relatively constant. Due

43

to unbalance power between the mechanical-input power and the electrical-output power, the dc-link voltage as well as rotor

44

speed exceeds their safety limits which can potentially force the wind turbine to disconnect from the grid. The quickly growing

45

power ratings of the wind turbines simply exacerbate these problems. Thus, PMSG suffers from large variations of dc-link

46

voltage during and after the grid fault and extreme loads occurring either prior or during the shut-down process [3, 8, 9]. Any

47

control system that helps to avoid unnecessary faults or that improves the behavior during the shut-down process will reduce

48

turbine loads or contribute to turbine availability. 3

49

Several studies have been proposed in the literature to limit the dc-link voltage variations and improve the LVRT capability of

50

PMSG-based wind turbines [5-12]. Fast pitch control can help to reduce the input-mechanical power by rotating the blades

51

about their longitudinal axis, also called pitching, and consequently curbs dc-link voltage fluctuations. In [13], a logical fast

52

pitch controller along with fuzzy logic controller (FLC) for back to back converters has been proposed in order to enhance the

53

transient performance of WTs during severe network disturbances. Another solution is to permit the excess wind energy to be

54

temporarily stored in the turbine-generation shaft inertia during the grid faults [7, 11]. Although, techniques are the cheapest

55

solutions for enhancing the LVRT capability of PMSG-based wind turbines, but these have a very slow dynamic response due

56

to the mechanical constraints of the system, (the speed of the pitch actuator is slow to contribute alone to LVRT support). The

57

most well-known method that is being used for the PMSG-based WT systems is the braking chopper (BC) with the low cost

58

advantage and the simple control performance to consume this surplus power [14, 15]. However, in the large wind power plant,

59

including many single wind turbines, the overall cost of using the BCs will be dramatically increased. Moreover, it is difficult

60

to improve the power quality at the output of the wind turbine systems since the BC can just dissipate the power [6].

61

Various control methods are also proposed to ensure proper converter operation during fault conditions. The formerly analyzed

62

converter control solutions [11, 17, 18], are based on the classical approach of using the linear proportional–integral (PI)

63

regulators and pulsewidth/space vector modulation (PWM/SVM). The particular problem is that a linear PI controller is

64

designed for normal network voltage levels, resulting in excessive currents at reduced voltage levels during the fault [10]. The

65

nonlinear control methods are introduced to improve the classical current control method [19, 20], but most of these methods

66

are complex and very sensitive to system parameters for practical applications, and need proper tuning of control [21].

67

This paper proposes an effective approach using resistive superconducting fault current limiter (RSFCL) as the additional

68

support along with conventional converter control strategy based on PI regulators to further increase the rated active power of

69

the installation, thereby enhancing dc-link voltage smoothness as well as the LVRT capability of the 50MW WPP. By using

70

the RSFCL, the fault current is suppressed effectively and the voltage dip level of the WPP terminals is diminished, leading to

71

enlarge the voltage safety margin of LVRT curve. Up to the present time, as far as the authors are aware, there has been no

72

report on the RSFCL investigation in the large-scale of PMSG-based on WPP, which is the main motivation of this paper.

73

The first-cycle suppression of a fault current by a RSFCL can also reduce the activation of pitch angle control and can decrease

74

the effect of the extreme loads on the turbine components. A RSFCL is considered as self-healing technology since it

75

eliminates the need for any control action or human intervention due to its automatic excessive current detecting and automatic

76

recovering from non-superconducting to superconducting states [23, 24]. These significant features of RSFCL can demonstrate

77

that the proposed technique surpasses aforementioned methods using BCs and complicated nonlinear control system.

78 4

Wind Farm with 50 MW Capacity

Superconducting Fault Current Limiter Transformer 0.69/34.5 kV

PCC CB1

1

2

Transformer 34.5/115 kV

Rshunt

CB3

CB2

25

Vgrid

Power Grid

CB4

RSFCL 115 kV, 60 HZ

Nacelle Pitch System

Hub Axis

Gearbox

PMSG 2 MW, 0.69 kV

Back to Back Converter AC Filter Cdc

Wind

Yaw System

79 80

Fig. 2. Proposed combinatorial PMSG-based WPP and RSFCL.

81

However, a large WPP has a complicated structure using several components, and the inclusion of RSFCL composes this

82

scheme more problematic for optimal performance of the system. Hence, the further effort in this paper is centralized on the

83

most-widely decision-making technique based on the analytic hierarchy process (AHP) [25, 26], for the optimal performance

84

of the combinatorial RSFCL and 50 MW WPP. The technique creates the Pareto optimality for simultaneously optimizing 3-D

85

alignment that rarely reported the power system literatures. Effectiveness of the proposed approach, using the Pareto optimality

86

concept is verified by the numerical simulations. The optimization technique figures out all the nondominated solutions on the

87

Pareto front at the end of the optimization run.

88

2.

Modeling of the PMSG-Based Wind Turbine

89

The structure of the proposed system including a 50-MW PMSG WPP and resistive SFCL is schematically shown in Fig. 2.

90

The constituents of the wind turbine are aerodynamic, mechanical, and electrical parts. The generator are completely decoupled

91

from the grid by power electronic converters (grid-side VSC and generator-side VSC which are connected back-to-back

92

through the common dc-link capacitance). PMSG-based WTs may be represented as a combination of subsystems. The

93

framework shown in Fig. 3 is typically used for modeling purposes, in which the relevant mathematical model has been cited in

94

the several literatures [6, 7, 10,], and it is summarily considered here.

95 5

Aerodynamic Block

λ =8.32 Tip Speed Ratio Calculation

Mechanical Block ωrotor

Cp=0.45 Rotor Power Coefficient Calculation

Aerodynamic Torque Calculation

Trotor

Permanent Magnet Synchronous Generators

ωe

Pg, Qg Back to Back Converter

Grid

Control System Block (Pitch, Yaw and Power Control)

96 97

Fig. 3. Subsystems model used in PMSG-based wind turbine.

98 99

101

Two-mass Shaft Model including Gearbox

Telectrical

vwind

100

Electrical Block

Fig. 4. Wind turbine characteristics.

2.1. Aerodynamic Model According to the Betz theory, the aerodynamic power generated by the rotor is given by [6] PA =

102

1 3 ρp R 2 vwind C p (λ , β ) 2

103

(1)

104

where ρ is the air density (kg/m3), R is the radius of the blade (m), vwind is the free-stream wind speed (m/s), and Cp (λ, β) is the

105

rotor power coefficient. In the PMSG-based WT, the obtained power depends on Cp, which is a function of both tip speed ratio

106

(TSR) λ and blade pitch angle β, in which the TSR is defined as

λ=

107

Rwrotor vwind

108 109

(2) where ωrotor is the rotational turbine speed. The numerical approximation of the power coefficient [27] is given by following

110

non-linear equations

111 112

 151  −0.58 β −0.002 β 2.14 −13.2  e C p λ , β= 0.73   λt 

(

)

λt =

λt

1 1

( λ − 0.02 β ) 113

18.4 −



0.003

( β 3 + 1)

In this paper, the optimal values of power coefficient (Cp-opt) and tip speed ratio (λopt) are 0.45 and 8.32, respectively. 6

(3) (4)

114 115

The mechanical torque on the rotor Trotor, which is produced by the blades of wind turbine can be calculated as PA/ωrotor. Also,

116

Fig. 4 illustrates the relation between the rotational turbine speed and aerodynamic power of the wind turbine, PA, for various

117

wind speeds vwind, with the blade pitch angle β=0o. βmax

ω*m

Pitch Servo

Controller

Rate Limiter

ωm

118 119

β

βmin

Fig. 5. Conventional pitch angle control used in FSIG-based wind turbine.

120

For each wind speed, the maximum power point can be acquired corresponding based on given Cp-opt =0.45 and λopt= 8.32

121

expressed as [27] 2  Rωrotor 

Pmax 0.5 rπ R  =

3

 × 0.45  8.32 

122

(5)

123

For an average wind speed of 12 m/s, which is used in this paper, the maximum turbine power output 2 MW and rotational

124

speed 1200 rpm are obtained.

125

The aerodynamic of wind turbines is controlled by pitch control approaches, which have been developed for large WTs. The

126

blades start to move around cut-in speed 4 m/s, and optimal aerodynamic efficiency is achieved at the wind speed rated about

127

12 m/s. The extra power obtained from wind speed between 4 and 12 m/s may be smoothly curtailed by spinning the blades

128

using a pitch control to avoid overloading the wind turbine system. Fig. 5 depicts the conventional pitch angle regulator in

129

which the input and output of the model are the rotational turbine speed ωrotor and blade angle β, respectively.

130

The yaw system of a typical turbine is significantly slower than the pitch system and the structural dynamics. Since the yaw

131

rates are so slow that there is very little interaction with the rest of the system behavior, it is often not considered at all. If

132

yawing is to be considered it can be modeled similar to the pitch system but with significantly lower bandwidth and rate limits.

133

The gearbox also plays an essential role in the WTs to adapt low-speed, high-torque rotation of the turbine rotor into the faster

134

rotation of the electrical generator. The critical issue in implementing the gearbox technology is the extreme loads, which may

135

lead to misalignment of the drive train and a gradual failure of the gear components, consequently increasing the capital and

136

operating cost of the WTs.

137 138 139

2.2. PMSG Model Based on the reference frame theory [6, 11], stator voltage equations in a d-q synchronous frame are modeled: vsd = Rs isd + Ls

7

d i sd −ωe Ld isq dt

(6)

vsq = Rs isq + Ls

140

d isq + ωω e Lq isd + eψ r dt

141

(7)

142

where vsd and vsq are the d- and q-axes stator voltages, isd and isq are the d- and q-axes stator currents, Rs and Ls are the stator

143

resistance and inductance, Ld and Lq are the d- and q-axes inductance, ψr is the rotor flux, and ωe is the electrical angular speed.

144

For the generator with surface-mounted permanent magnets, d- and q-axes inductances are the equal (Ld = Lq), resulting a

145

simple interpretation of the electromagnetic torque Telectrical and aerodynamic torque on the rotor Trotor expressed as

Telectrical =

146

3 pψ r isq 2

Trotor = J − Telectrical

147

d ωω rotor + b rotor dt

(8) (9)

148

where p is the number of machine pole pairs, J is moment of inertia for turbine-generator, ωm is shaft mechanical speed, and b

149

is friction coefficient.

150

3.

Power Control Strategy

151

Detail of the proposed power control scheme for the PMSG based on the full-power converter topology is illustrated in Fig. 6.

152

As it can be seen, it is schematically divided into two main blocks. On the one hand, controlling the active and reactive power

153

of the PMSG is obtained via a generator-side VSC. On the other hand, the management of the active and reactive power

154

released to the grid by the PMSG along with the dc-link regulation is accomplished via the grid-side VSC. The active and

155

reactive power references to be injected by the grid-side VSC are obtained, so that the whole wind farm can fulfill the grid

156

code requirements.

157

3.1. Generator-Side VSC Control

158

The control block diagram of generator-side VSC is shown in Fig. 6(a), which is based on stator voltage equations (6) and (7)

159

obtained in d-q synchronous frame. Several maximum power point tracking (MPPT) algorithms have been reported for the

160

PMSG-based WT [28-30]. The outcome of the MPPT unit provides the reference value of the rotational turbine speed (ω⃰rotor)

161

for the generator-side VSC controller. This paper mainly focuses on the converter control, and hence, the MPPT control

162

method was not discussed. The speed reference ω⃰m is acquired by a MPPT method mentioned in (5) in order to extract the

163

maximum amount of power with the actual wind force, while the rotational speed error is given as the input to a PI controller in

164

order to generate the q-axis stator current command (i*sq). Also, the reactive power produced by the wind turbine is regulated at

165

zero (i*sd=0) for unity power factor operation. The error between the reference dq-axis currents and the actual dq-axis currents,

166

isd, isq are used as inputs to the linear PI controllers to produce dq-axis voltage commands, v*sd, v*sq after the decoupling. The

167

angle θe calculated from the rotational speed of the PMSG is applied in a park transformation to engender gate signals using the

168

carrier wave of pulse width modulation (PWM) operation. 8

169

PMSG

3-p current

S3

S1

Vdc/2

Generator-Side Converter

S5

2Cdc

Aerodynamic Part

ωe ωm

S4

d-q

ids i*sq

PI ω⃰ m MPPT

abc

θe

1 p

Aerodynamic Control

2Cdc

Vdc/2

d dt

S2

ωe·(Lq· isd + ψr)

iqs

6 pulses S1-S6

v*sq

PI

*

d-q

v

a,b,c

PWM

isq i*sd = 0

v*sd

PI isd

170 171

S6

ωe· Ld· isq

abc

θe

(a) Grid-Side Converter

Grid

Vdc/2

LC Filter Sg1

Sg2

Lf=0.25 mH

Sg3

Vdc/2

Icf

Vgrid Cf=1.3 mF

Sg4

Sg5

Hystersis d-q

Vdc V

* dc

abc

Sg6

Cdc=16 mF Vdc=1.2 kV 6 pulses θs Sg1-Sg6 * i a,b,c abc

172 173

3-p voltage Transformer



q*=I*RVgrid

i*α i*β

q

Imax

vα vβ

0.5

I R*

Imin

I RVSC I cf

p*=I AVgrid+ploss

*

I A= (I

Grid Code Request

0.9

*

*

PLL Vgrid

Vgrid

Current Calculation using (8) p



*

ploss PI

θs

α-β

max 2

*

area A

0.2 0

0.5

1

IR

2

) – (I R)

(b)

174

Fig. 6. Proposed power control strategy for WPP. (a) Control block diagram of the generator-side VSC. (b) Control block diagram of the grid-side VSC.

175

3.2. Grid-Side VSC Control

176

The proposed grid-side converter controller is provided in Fig. 6(b) to calculate the current references to be inserted by the

177

grid-side VSC in order to fulfill the grid code requirements. Further, this controller preserves the dc-link capacitor voltage at

178

the set value 1.2 kV, which assures the active power swapping from the PMSG to the grid. In the steady state condition, the

179

maximum capacity of current, Imax is used to produce 2 MW active power (IRVSC=0). In the next stage, p*, which is added to the

180

PI controller from the dc-link voltage regulator, and q* transformed into the instantaneous power α-β method based on α-β-0

181

reference frame [23]. It has been mathematically formulated as

9

I*  1  α = 2 I *  vα +vβ 2  β

182

 vα  vβ 

− vβ   p* + p

 vα  



loss 

q*

 

(10)

183 184

The angle θs for the Park transformation is detected from the three-phase voltages at the low-voltage side of the grid

185

transformer by using a phase-locked loop (PLL). Finally, gate signals are generated for grid side VSC switches using the

186

Hysteresis module [31], shown in Fig. 6(b). Under a grid voltage dip, the reactive current, IRVSC in proportion to the voltage

187

reduction should be provided during the fault in order to meet the LVRT requirement according to the characteristic shown in

188

Fig. 1(b).

189

Injection of reactive power has the highest priority in area A, but free capacity of current, I*A must also be utilized to retain the

190

active power production related to the voltage sag magnitude, while the generator continues to provide active power at nominal

191

value. In this case, the dc-link voltage exceeds its safety limits, leading a system malfunction or even a component failure.

192

However, the rapidly rising the dc-link voltage, under a system fault, is difficult to be avoided by only using the PI controller.

193

For this reason, this paper proposes a RSFCL used in outside of the wind farm, as shown in Fig. 2. The RSFCL makes it

194

possible to suppress the dc-link voltage fluctuations by limiting the magnitude of the fault current, thereby increasing the

195

output active power capacity and improving the LVRT capability of the wind farm. A further analysis is accomplished in

196

Section 5.

197

4.

Electro-Thermal Modeling of a RSFCL

198

The resistive superconducting fault current limiters (RSFCLs) have been launched and introduced into the network as a self-

199

healing technology to curb prospective fault currents immediately to a manageable level by suddenly raising the resistance

200

value [22, 23]. Furthermore, after the fault current is profitably repressed, the RSFCL can be restored to the primary state

201

without additional aid. RSFCL has a simple structure with a lengthy superconductor wire inserted in series with the

202

transmission lines. With the recent breakthrough of second-generation high-temperature superconductor (HTS) wires, the

203

SFCL has become more viable [26]. Considering the superconducting material, BSCC-2223 is the conductor, which has

204

commonly been utilized for most of the tentative RSFCLs [32, 33].

205

To preserve the superconductor from detrimental hot spots during the operation, the shunt resistance, Rshunt is essential. This

206

parallel resistance must be contacted all over the length of the superconductor, and it regulates the controlled current to elude

207

over-voltages likely occurring when the resistance of the superconductor increases much quicker. The current limiting behavior

208

of the RSFCL can be modeled by the resistance transition of HTS tapes in terms of the temperature and the current density, as

209

defined by the following equation [23]

10

210

211

RSFCL

 0, if isc < I c and T < Tc     if isc > I c , T < Tc     Vsc  J  T −Tc      =  ρ f 2  Jc 0  T −T  +1    c b   A   sc    V T    ρ n sc   , if T > Tc  2   Asc  Tc   

(11)

212

Equivalent Voltage source PCC

Rshunt isc

iRSFCL

jXt

Rt

Grid bus

RSFCL 50 MW WPP

3-pahse Fault

213 214

Fig. 7. Equivalent circuit of proposed system in fault condition.

215

where Tc, Tb, Jc0, Vsc, and Asc are critical temperature, liquid nitrogen temperature, critical current density, superconductor

216

volume, and cross section, respectively. Also, isc, Ic, ρf, and ρn are short-circuit current, critical current, flux flow resistivity, and

217

normal resistivity, respectively. In this description (9), three possible states for superconductor are; 1) the flux-creep state at a

218

temperature and a current under the critical rate; 2) the flux flow state at a current over the critical value, but a temperature

219

under the critical rate; and 3) the normal conductive state at a temperature higher the critical amount.

220

According to the equivalent circuit of the proposed combination, shown in Fig. 7, if the asymmetrical component of the fault

221

current is ignored, the short-circuit current through the RSFCL branch can be stated by the following equations

iRSFCL (t ) =

222

Vm Rshunt sin (ωt ) × RSFCL + Rshunt 2 R + ( LT ω ) 2

(12)

223

where R=Rtrans+Rshunt║RSFCL, LT is the inductance of the transformer, and Vm is the magnitude low voltage side of interfacing

224

transformer. The total fault energy dissipated in the HTS tapes, Qsc is calculated using (13), where ∆tsc is the duration of the

225

fault [34]. Qsc − 3ph = 3

226

∫ ∆t

2

RSFCL iRSFCL (t ) dt

(13)

sc

227

Substituting (12) into (13) gives the following

 ∆tsc sin (2ω∆t sc )  −  2 2  4ω R + ( LT ω )  2  2

228

= Qsc −3ph

3Vm RSFCL

11

(14)

229

The RSFCL model should be a reasonable approximation of transient SFCL behavior during faults and, therefore, should

230

consider thermal properties. The thermal model of RSFCL has been generically estimated as follows [24] T (t ) = T0 +

231 232

1 Csc

t

∫ Qsc (t ) − Pcool (t ) dt

(15)

0

where T0 is ambient temperature, Csc is the heat capacity of the superconductor, and Pcool is the power cooling.

233

(b) (a)

234

Fig 8. HTS wire cost [35]. (a) Dollar per Kiloamp per Meter. (b) Dollar per Meter.

235

4.1 Economic Feasibility of the RSFCL

236

Several main factors affect for determining the actual size and the cost of a resistive SFCL, such as the length of applied

237

superconducting wire, the cooling machinery, the geometry of RSFCL module, and the rated power and voltage system, where

238

RSFCL must be installed. Practically, the whole superconducting length is used in form of helix to shape the superconducting

239

tube. In reality, several tubes may be connected in parallel to achieve a particular resistance in form of cylindrical geometry.

240

The rough estimation for the RSFCL size can be achieved based on design details of the RSFCL projects in the worldwide

241

[35]. Accordingly in this paper, the RSFCL module installed in the transmission system with voltage rate of 34.5 kV and power

242

rate of 50 MVA would be much less than 4 m in both diameter and height.

243

After recent progress of the economical second-generation HTS wires, SFCLs are becoming more practicable, due to low

244

manufacturing costs, low ac losses, higher current densities, and better operational performances, and is eventually expected to

245

be at least a factor of ten lower in the cost than the presently available HTS conductor [36]. The cost of HTS wire is generally

246

described by two parameters: the maximum amount of current that the HTS wire can conduct; and the manufacturing cost per

247

meter of wire. Fig. 8 illustrates how the HTS wire cost of RSFCL is expected to decrease over the next two decades as

248

production increases. The impact of cooling system on the future competitiveness of the RSFCL devices is critical. The 1999

249

benchmark cost of a medium-sized cryogenic refrigeration unit was about $60,000/kWcold at 77K. Economies of scale typical

250

of the cooling refrigeration industry were applied to represent the expected decline in refrigeration costs. This declining cost 12

251

model indicates that as large numbers of cryogenic refrigeration units are manufactured, the cost will drop to less than

252

$20,000/kWcold [37].

253

5.

Numerical Simulation Analysis

254

The wind farm shown in Fig. 2 consists of the 25 wind turbines rated at 2 MW, which totally supply the maximum 50 MW to

255

the grid, where the base wind speed is designed as 12 m/s based on (p-ωrotor) characteristic curve (Fig. 5). To perform a realistic

256

design, all aspects of a WT need to be considered.

257

258 259

Fig 9. Combinatorial PMSG-based WT and RSFCL model using FAST aeroelastic simulator and the SimPowerSystems.

260

Thus, a holistic wind turbine model was utilized including aerodynamic and mechanical simulations through the FAST

261

software, as well as concurrent electrical simulations through the SimPowerSystems toolbox for MATLAB/Simulink. The

262

FAST aeroelastic wind turbine simulator developed by the National Renewable Energy Laboratory (NREL) to perform detailed

263

simulations of direct-drive and geared wind turbines [38]. The modeling of the RSFCL was also accomplished using MATLAB

264

programming to combine its electrical and thermal properties as discussed in Section 4. A top-level view of the model is shown

265

in Fig. 9. The characteristics of the preferred wind farm and selected resistive RSFCL parameters are given in Appendix A,

266

Table 1 and Table 2. The simulation results are carried out for the 50 MW system to verify the effective performance of the

267

RSFCL on the dc-link voltage smoothness and the extreme load reduction. All simulations were executed using a fixed-step 13

268

solver with a 5 μs step size. A three-phase symmetrical grid fault is considered, since the fault ride-through capability of the

269

regional grid codes mostly refer to this type of fault. Thus, a three-phase fault is applied in the middle of the transmission line

270

at t= 4 s and is cleared after 200 ms, resulting in a 70% depth of the voltage dip at the PCC. To assess the damping behavior of

271

the RSFCL, simulations are carried out for without and with the presence of the RSFCL. The expediency of the RSFCL

272

component for managing the fault current, as well as resistance and temperature variations of the RSFCL is demonstrated in

273

Fig. 10. The peak current for phase a in the pre-fault value is 850 A and then exceeds 14.2 kA without connecting RSFCL,

274

whereas with the RSFCL incorporated on the main road of the wind farm, the fault current is limited effectively to reach about

275

5.1 kA (see Fig. 10(a)).

276 277

(a)

278 279

(b)

280 281

(c)

282

Fig. 10. RSFCL model response. (a) Fault current waveform without and with RSFCL in a single-phase system. (b) Resistance variation in flux flow and

283

normal state. (c) Temperature rise.

284

Fig. 10(b) illustrates the limiting resistance of the RSFCL, which went up to 7.1 Ω in the flux flow state and rise to reach a

285

normal stat value of 15 Ω after ten cycles of the fault. A retrieval of the Fig 10(b) and (c) will determine, when a fault takes

286

place at t = 4s, the quench time (a transition from a superconducting mode to a resistive mode) is initiated by going through the 14

287

flux-flow state during of 0.1s and then to the normal state at a temperature rise of 90° K (critical temperature for HTS tap). Fig.

288

11(a) shows the voltage profile at the PCC in the proposed integration system during a three-phase short circuit. In the absence

289

of the reactive injection and RSFCL, the voltage reduction of 70% occurs. In this case, the voltage at the PCC cannot be

290

restored to the nominal value because of an instability issue on the proposed system and the WPP must be disconnected from

291

the grid. With the adoption of the reactive injection control, the voltage dip is decreased, reaching 50% before recovering

292

immediately to the nominal value upon clearing the fault. Based on the reactive power support requirement (Fig. 1(b)), for a

293

50% voltage reduction, all the capacity of the wind farm is occupied by reactive power.

294

295 296

(a)

297 298

(b)

299 300

Fig. 11. Operation of the proposed combinatorial WPP and RSFCL during and after fault (a) Voltage profile at wind farm terminal (b) dc-link voltage with and

301

As can be observed in Fig. 12(b), the reactive power injected during the fault (without RSFCL) allows the wind farm to satisfy

302

the specifications of grid code requirements such as increasing the LVRT capacity. However, due to the lack of output active

303

power in the grid-side VSC and consequently the earlier-mentioned unbalanced power during the fault, the dc-link voltage is

304

significantly increased to about 1.14 pu, where a regular reactive power control with no RSFCL is used i.e., 14.58 % over

305

voltage (Fig. 11(b)). This effort proposes the RSFCL as an additional supporting method besides the reactive power control to

306

improve the LVRT capability and smoothen the dc-link voltage of the wind farm. This method increases the voltage stability

without RSFCL.

15

307

margin with respect to the LVRT curve as shown in Fig. 11(a), in which using the RSFCL significantly reduces the magnitude

308

of the voltage sag to around 20%. In addition, the peak value of the dc-link voltage transient is reduced when using the RSFCL,

309

evident by its decline it to 1.05 p.u (less than 5% over voltage), as shown in Fig. 11(b). Fig. 12(a) illustrates the active power

310

output of the wind farm with and without the RSFCL, in which it is considerably kept at rated value of 50 MW before

311

occurring the fault. After installing RSFCL, the drop in the active power decreased from 0 MW to 35 MW and back to the

312

normal operation gradually as the fault is cleared. That is, the presence of the RSFCL increases the retaining of the active

313

power production for the PMSG-WPP by approximately 60%, during the fault condition.

314 315

(a)

316 317

(b)

318 319

320 321

Fig. 12. Operation of the proposed combinatorial WPP and RSFCL during and after fault (a) Active and reactive power at the PCC without the RSFCL. (b) Active and reactive power at the PCC with the RSFCL.

(a)

16

322 323

(b)

324

Fig. 13. Dynamic performance of the turbine side with and without applying the RSFCL. (a) Rotational turbine speed. (b) Aerodynamic rotor torque.

325 326

(a)

327 328

(b)

329

Fig. 14. Dynamic performance of the generator side with and without applying the RSFCL. (a) Rotational generator speed. (b) Generator torque.

330

5.1 Effect of RSFCL on Extreme Load Reduction on WT Structure

331

In order to analyze the impact of the RSFCL on WT extreme loads, a combination of the FAST model and SimPowerSystems

332

can accurately simulate detailed aerodynamics and mechanical aspects of the wind turbine. In this study, it is assumed that

333

wind speed at the hub remains constant at 12 m/s. Rotational speed and mechanical torque responses of the rotor turbine and

334

generator are shown in Fig. 13 and Fig. 14, respectively. As it can be seen, the rotational speeds and mechanical torque

335

increase during the fault period, which may lead to power system instability and is detrimental for the turbine generator system

336

if the fault duration is long and proper auxiliary devices are not used (no controller). However, RSFCL can limit the rate of 17

337

rising of machine speed and the aerodynamic torque imposed on rotor/shaft in order to make better stability.

338

In this work, a number of the degrees of freedom available in the simulation model are used for analysis of the extreme loads,

339

including tower fore-aft and sideways modes, tower yaw mode, and blade flap wise and edgewise modes. All these modes are

340

depicted in Fig. 15, which contains illustrations of a wind turbine seen from the front and side views. The failure at the system

341

causes extreme loads on structural parts of the WTs. Figs. 16-18 show the simulation results of several key loadings, such as

342

hub loadings, blade root loadings, and tower base loadings, of the proposed WPP, which are compared without and with the

343

presence of the RSFCL.

Edgewise Blade Mode

Flapwise Blade Mode Yaw

Tower Sideways Mode

Tower Sideways Mode

Tower Fore-aft Mode Yaw

Edgewise Blade Mode

344

Tower Fore-aft Mode

Edgewise Blade Mode

Flapwise Blade Mode

(a)

(b)

345 346

Fig. 15. Wind turbine structure. (a) Wind turbine from the front, illustrating sideways and blade edgewise modes. (b) Wind turbine from the side, illustrating fore-aft, blade flapwise, and yaw modes.

347 348

(a)

349 18

350

(b)

351

Fig. 16. Dynamic performance of the WT under the extreme load with and without the RSFCL. (a) Yaw moments. (b) Pith Actuator Force.

352

Fig. 16 depicts hub loadings, including the pitch actuator force and yaw moments, during the three-phase fault. The impact of

353

the installed RSFCL on yaw moments is effectively demonstrated by 20% reduction in the magnitude of the value during the

354

fault in proportion to the case with no using RSFCL, as shown in Fig. 16(a). With the onset of the fault, the pitch actuator force

355

first shows a dip then a rise, and then it reduces to a negative value and finally increases to zero and becomes constant. Rise in

356

the pitch actuator force after it reached negative value is due to large inertia of the rotor. However, application of RSFCL

357

shows a promising solution for reducing the fluctuation of the pitch actuator force, as illustrated in Fig. 16(b).

358 359

(a)

360 361

(b)

362

Fig. 17. Dynamic performance of the WT under the extreme load with and without the RSFCL. (a) Blade flapwise moment. (b) Blade edgewise moment.

363

During the fault, blade experiences moments in flapwise bending and edgewise bending in the blade root. Fig. 17(a) shows the

364

average flapwise bending moment in the blade root. The axial wind force, gravity force and centrifugal force contributes the

365

most to the flapwise bending moment in the blade root. However, the average value of the flapwise moment is almost zero in

366

normal operating state of the WT. At the beginning of the fault, the rotor speed increases, therefore the contribution of

367

centrifugal force in flapwise bending moment in the blade root also increases. As the failure clear quickly after 200 ms, the

368

flapwise moment fluctuations in the blade root gradually smooth, because the contribution because the axial aerodynamic force

369

on rotor becomes negligible. Fig. 17(b) shows the average edgewise bending moment in the blade root. The rotor torque also 19

370

causes edgewise moment in the blade root and its contribution is estimated by the average value of the edgewise moment. As

371

can be seen, there are several fluctuation trends in the value of the edgewise moment. After clearing the fault, fluctuations trend

372

to fade off fast in edgewise bending moment in the blade root due to the large stiffness in edgewise direction of the blade. In

373

both figures, RSFCL can significantly dampen the oscillations of the flapwise moment and edgewise moment.

374

The WT tower experiences fore-aft and side-to-side bending moment at the tower base, as shown in Fig. 18. Fore-aft bending

375

moment is mainly due to rotor thrust loading. Tower motions happen due to the tower’s dynamic interaction with rotor blades.

376

Due to large fluctuations in axial aerodynamic force on rotor, the tower fore-aft moment also fluctuates.

377

378 379

(a)

380 381

(b)

382

Fig. 18. Dynamic performance of the WT under the extreme load with and without the RSFCL. (a) Tower fore-aft moment. (b) Tower side-to-side moment.

383

Once a fault happens in the system, the value of the tower fore-aft moment first increases and then decreases due to the inertia

384

of the tower, as shown in Fig. 18(a).

385

The tower fore-aft moment first decreases and then increases because of the inertia of tower. The tower fore-aft motion is

386

unable to quickly dampen because the complete weight of the WT operates on the tower base. Fig. 18(b) shows the side-to-side

387

bending moment in the tower base. The rotor torque that operates on the tower top through gearbox/generator support can lead

388

to the side-to-side tower moment at the tower base. Because of the large inertia of tower, the tower shows fluctuations on the 20

389

value of the side-to-side moment after clearing the fault, as can be seen in Fig. 18(b).

390

The results indicate that the proposed RSFCL has significant effect for reducing the fluctuations on the, blade flapwise add

391

edgewise moments, pitch actuator force and yaw moments, and tower fore-aft and side-to-side moments. Therefore, RSFCL

392

can be a promising solution for wind turbine controller performance with respect to extreme loads happening to mechanical

393

and aerodynamic parts during the severe disturbances.

394

6.

Optimal Scheme Performance

395

The obtained results in Section 5 for the proposed combinatorial 50-MW wind farm and RSFCL confirmed that further

396

improvements in dc-link smoothness, extreme load, and LVRT capability of a wind farm can be achieved by increasing the

397

SFCL resistance as much as possible. However, as stated in (14), the high-resistance SFCL means a substantial amount of

398

energy is dissipated in the form of heat, resulting damage on SFCL construction and cooling system. This large energy

399

dissipation would lengthen the recovery time of the RSFCL (transition from resistive state to superconducting state) after

400

clearing the fault. Also, as stated in Section 3.2, for overcoming the unbalance power between the generator and converter, the

401

active power output of the wind farm, PWPP should be appropriately increased during the fault to diminish the fluctuations of

402

dc-link capacitor voltage. However, depending on the grid code, reactive power production has highest priority during the

403

fault, occupying some portion of the maximum capacity of apparent power, and leading reduction in PWPP. Hence, there is a

404

tradeoff between three above mutually contradicting criteria, SFCL resistance, energy dissipation, and active power output of

405

the WPP in order to achieve an optimal design of combinatorial 50-MW wind farm and resistive SFCL.

406

For optimization purposes, this section implements multi-criteria decision making (MCDM) methodology based on analytical

407

hierarchy process (AHP) detailed in the authors’ prior work [23]. One of the outstanding characteristics of the MCDM

408

technique is the creation of the Pareto optimality for simultaneous multiobjective optimization in which algorithm figures out

409

all the nondominated solutions on the Pareto front (optimality) at the end of the optimization run. AHP is established as

410

beneficial technique providing the promising solutions to the complicated decision-making problems with different criteria.

411

The proposed optimization model contains three predefined criteria and two constraints that are expressed as  1  1   Min  , , Q SC   RSFCL PWPP   

412 413

Subject to

max  TSFCL − 423 < 0    point (Vgrid , ∆tsc ) within Area A

414

(16)

415

Where, maximum SFCL appeared resistance, RSFCL maximum active power output of the WPP, PWPP and minimum energy

416

dissipation, Qsc are desirable. The proposed system (combination of 50 MW WPP and RSFCL) should be designed in such a 21

417

way that the following criteria are satisfied: 1) TSFCLmax < 432° for safe solder melting; and 2) fulfill Danish grid code

418

requirement including LVRT and reactive power support requirement.

419

Based on (11), any change in the dimensions of the superconducting wires as well as fault durations may affect fault current

420

limiting performance of RSFCL, and consequently the optimum design of the proposed system. Therefore, in this optimization,

421

variable parameters are superconducting wire volume (Vsc), superconducting wire cross section (Asc) and duration of the fault

422

(∆tsc). The constraints of the selected variables for the optimization problem are shown in Appendix (Table 3).

423

Considerately, if each variable is changed in 10 steps, three variables would create 103 = 1000 alternatives when utilized in the

424

electrical simulation model. These cases (378) that exceed the predefined optimization constraints must be omitted from

425

feasible options. optimal

RSFCL

Alt.1

C3

C2

C1 Criteria

PWPP

Qsc

. . .

Alt.2

426

Alt.784

427

Fig. 16. Hierarchy process for optimal combinatory PMSG-based WT and RSFCL.

428

The goal of AHP method is to find a best case (desired solution) among the remnant number of 784 alternatives that can

429

maximize each criterion satisfaction. Basically, for 784 alternatives (Ai, i=1, 2,…, 784) and 3 criteria (Cj, j=1, 2, 3), there are

430

four steps considering decision problems by AHP as follows:

431

Step 1) Scrutinize the relation between objectives, criteria and alternatives to build the multi-layers hierarchical structure.

432

Fig. 16 shows the multi-layers hierarchical structure for optimal combinatorial PMSG-based WT and RSFCL including optimal

433

layer, criterion layer, and alternative layer.

434

Step 2) Compose a pairwise comparison matrix by assigning each alternative/criterion an optional number from 1/9 to 9. In

435

this article, the three-point performance rating scale is defined for the importance of criteria, 9 (high), 5 (medium), and 1 (low).

436

Based on the explanation in [23], if the importance of criteria C1, C2, C3 are ranked as high (C1=9), medium (C2=5), and low

437

(C3=1), respectively, the criteria pairwise comparison matrix C=[c]3×3 can be expressed by C1

438

[C ]3×3

C1 (R SFCL )  c11

C2

C3

c12 c13   C c22 c23  = 2 (PWPP )  c21 C3 (Qsc ) c32 c33   c31

 C1 / C1 C1 / C2 C1 / C3  C / C C / C C / C  2 1 2 1 2 3 =  C3 / C1 C3 / C2 C3 / C3 

 1 5 / 9  1 / 9

9/5 1 1/ 5

9 5  1 

439

(17)

440

A similar method is applied to estimate the value of alternative pairwise comparison matrix Ai=[aij]784×784 (i=1, 2, 3) with 22

441

respect to each criterion.

442

Step 3) Compute the relative weight (priority) of the compared factor for the criterion according to the judgment matrix C

443

and A. The criteria and alternatives weight vectors can be obtained by adding the array elements of each row of C and A matrix

444

and then dividing by the sum of the element of columns. Here, the weight vector matrix of criteria wcj (j=1, 2, 3) can be

445

estimated by  wc1  w   c2   wc 3 

446

 1 + (9 / 5) + 9  1  (5 / 9) + 1 + 5  =  (1 + 9 / 5 + 9) + (5 / 9 + 1 + 5) + (1 / 9 + 1 / 5 + 1)  (1 / 9) + (1 / 5) + 1

 0.60   0.334    0.066 

447

(18)

448

The analysis of the simulation results represents the degree of importance of alternative i in criterion j, i.e., dij, which is divided

449

by its maximum value. This is followed by splitting the alternation range to 9 parts, allocating a proportional number from 1 to

450

9 into each alternative aij as

 dij aij =Integer   0.11 Max i dij 

451

( )

   

(19)

452

Since, a pairwise comparison matrix of the alternative Ai is compatible; it forms the calculation of the alternative weight vector

453

simple via normalizing the elements of each column, reaching to waij. These calculations can be formulated as

454

waij =

aij 784

(20)

∑ aij i =1

455

The sum of the entire alternative weight vector with respect to the each criteria waij and the criteria weight vector wcj for j=1, 2,

456

3 & i= 1, 2,…, 784, forms a decision matrix (784×3) as

Criteria C1 ( wc1

C2 wc2

C3 wc3 )

A1

wa11

wa12

wa13

A2

Alts.

457 458

wa21

wa22

wa23

. . .

. . .

. . .

. . .

A784

wa(784)1

wa(784)2

wa(784)3

Step 4) Calculate the best alternative, i.e., the highest priority value.

459

Usually, the criteria can be classified into the two opposite groups called the benefit and cost criteria [37]. A benefit criterion

460

means that the better alternative has the higher grade. The inverse scenario is expressed true for the cost criteria. In this

461

optimization study, the total energy dissipated is cost and the other criteria, i.e., the resistance of SFCL and power output of the

462

PMSG, are benefit. Thus, the optimization problem can be summarized as a standard format for aggregating alternatives to 23

463

rank them based on the ratio performance approach detailed in [37], as given by

 ( wai1 × wc1 ) + ( wai2 × wc2 )  * max PAHP = = 464  for i 1, 2, ... , 784 i wai3 × wc3   465

(21)

466

For three levels criteria comparison, this weight vector must be calculated 25 times (33 − 2) by changing the importance of the

467

criteria with respect to each other. The run results of the algorithm are shown in Table 4. As earlier mentioned, the Pareto

468

optimality plays the significant role in choosing the best solution for optimization of all three criteria: resistance of SFCL,

469

energy dissipation in SFCL, and active power output of the WT. However, for an approximate set of three-dimensional Pareto-

470

optimal solutions, a search is performed for the tradeoff values between the optimums of the objective functions, using AHP, at

471

the end of each optimization run, as shown in Fig. 17.

472

Total Energy Dissipated (kJ)

473

500 400 300 200 100 50

Case No.1

40 30 20 PMSM Active Power (MW)

10 0

10

20

30

40

50

SFCL Resistance (Ohm)

474 475 476

Fig. 17. Multi-objective optimization using AHP, Pareto front for three criteria.

477

The corresponding AHP optimization results are illustrated in Table 4. It is the tradeoff values between the 25 given set of

478

mutually contradicting criteria. Referring to Table 4, if higher priority is given to the RSFCL, so case 9 (H-L-L) in which 26.15

479

Ω must be chosen. Similarly, for the power output of the PMSG-WPP or total energy dissipated priority selection, cases 20 and

480

24 (L-H-L and L-L-H) in which PPMSG= 28.59 MW and Qsc= 128.92 kJ must be selected, respectively. Moreover, the higher

481

and lower active power delivered during the fault are obtained in case 1 (82.7 % of total capacity) and case 9 (32.7 %),

482

respectively.

483

7.

Conclusion 24

484

The paper proposes an effective approach using RSFCL as the additional support along with conventional converter control

485

strategy based on the PI controller to further increase the rated active power of the installation, thereby enhancing dc-link

486

voltage smoothness as well as the LVRT capability of the 50 MW WPP. Moreover, that was demonstrated that RSFCL can be

487

a promising solution for improving wind turbine controller performance with respect to extreme loads on the wind turbine

488

structure. With this approach, it is expected that the activation of the dc braking chopper and fast pitch angle control could be

489

reduced in order to meet the international grid code requirements. An important feature of the proposed method is that a

490

conventional PI control can be used, performing the reactive and reactive current injection, while the dc-link voltage never

491

exceeds its safety limits. A further study is carried out to determine optimal performance of the combinatorial 50 MW PMSG-

492

WPP and RSFCL. Therefore, the simultaneous and transformative approach based on the AHP method for the multiobjective

493

optimization of embedded system has been introduced. A reconciliation between the three objecting functions, namely,

494

resistive of SFCL, output power of PMSG, and energy dissipated in RSFCL has elicited by a 3-D alignment in the Pareto front

495

having nondominated 25 solutions. However, a designer would be capable of selecting any of the solutions setting on the

496

Pareto front without erratic problems on optimality.

497 498 499

Table 4. Achieved Optimal Alternatives Using AHP Method Case No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Priority

wc1

wc2

wc3

VSC (m3)

ASC (m2)

∆tsc (s)

RSFCL (Ω)

PPMSG (MW)

QSC (kJ)

H-H-H H-H-M H-H-L H-M-H H-M-M H-M-L H-L-H H-L-M H-L-L M-H-H M-H-M M-H-L M-M-H M-M-L M-L-H M-L-M M-L-L L-H-H L-H-M L-H-L L-M-H L-M-M L-M-L L-L-H L-L-M

0.33 0.39 0.47 0.39 0.47 0.60 0.47 0.60 0.82 0.22 0.26 0.33 0.26 0.45 0.33 0.45 0.71 0.05 0.07 0.09 0.07 0.09 0.14 0.09 0.14

0.33 0.39 0.47 0.22 0.26 0.33 0.05 0.07 0.09 0.39 0.47 0.60 0.26 0.45 0.07 0.09 0.14 0.47 0.60 0.82 0.33 0.45 0.71 0.09 0.14

0.33 0.22 0.05 0.39 0.26 0.07 0.47 0.33 0.09 0.39 0.26 0.07 0.47 0.09 0.60 0.45 0.14 0.47 0.33 0.09 0.60 0.45 0.14 0.82 0.71

5.00E-04 4.30E-04 1.85E-04 4.65E-04 1.85E-04 1.85E-04 3.60E-04 3.25E-04 2.90E-04 3.95E-04 3.60E-04 5.00E-04 2.55E-04 3.25E-04 2.90E-04 3.60E-04 5.00E-04 4.30E-04 2.20E-04 1.50E-04 4.30E-04 2.90E-04 2.90E-04 5.00E-04 3.95E-04

9.20E-07 1.04E-06 1.04E-06 1.04E-06 9.20E-07 1.04E-06 9.20E-07 9.20E-07 1.28E-06 9.20E-07 1.04E-06 1.40E-06 1.04E-06 1.52E-06 1.16E-06 1.52E-06 1.88E-06 1.76E-06 1.64E-06 1.16E-06 1.88E-06 1.64E-06 1.76E-06 1.88E-06 1.76E-06

0.26 0.32 0.38 0.38 0.44 0.44 0.8 0.74 0.68 0.26 0.26 0.32 0.38 0.5 0.62 0.68 0.62 0.2 0.2 0.26 0.32 0.38 0.38 0.74 0.62

44.59 29.54 12.72 31.94 26.23 19.72 31.63 27.53 26.15 34.67 24.73 18.95 17.51 10.45 16.01 11.57 10.51 10.31 7.07 8.28 9.04 8.01 6.95 10.51 9.47

41.35 44.75 25.53 40.94 32.19 20.82 41.71 31.31 16.35 43.42 38.92 23.22 40.74 29.36 29.72 25.89 18.26 39.31 22.31 28.59 34.76 25.25 20.37 30.22 25.96

143.43 200.95 252.17 234.51 252.17 291.99 492.73 466.48 448.68 155.92 168.14 211.95 252.17 331.38 409.45 448.68 409.45 131.39 131.39 231.62 211.97 252.17 252.17 128.92 207.13

25

500

501

Acknowledgement

502

The authors would like to thank Ms. Bonnie Jonkman, the Senior Scientist of National Wind Technology Center (NWTC),

503

National Renewable Energy Laboratory (NREL), for her critical and extensive support for using the FAST version 8.

504

Appendix A

505

See Table 1, Table 2 and Table 3.

506 507

508

Table. 1. Limits of Variables for Optimization Problem Symbol

Quantity

Value

Prated T0 Ic0 Cp Pcool VSC ASC Rsh ρn ρf

Critical Temperature for HTS tape liquid nitrogen temperature Critical current Specific heat of HTS Cooling power HTS Volume HTS Cross section Shunt resistance of HTS Normal resistivity Flux flow resistivity

15 77 °K 5 kA 3 MJm-3K-1 700 kW 3e-4m3 1e-6m2 120 Ω 4e-8 Ωm 1e-9 Ωm

Table. 2. Parameters of the Proposed PMSG-WPP for Simulation Symbol Pt vwind R ρ Cp-opt λopt Prated Vrms f ψr ωm Rs Ls Rr Ld, Lq P H

Quantity Wind Turbine Parameters Rated turbine power Rated wind speed Blade radius Air density Optimal power coefficient Optimal tip speed ratio PMSG Parameters Rated generator power Rated rms line-line voltage Rated frequency Rated rotor flux Rated speed Stator winding resistance Stator winding inductance Rotor resistance d, q-axis synchronous inductance Number of Poles Mechanical time constant

Value 2 MW 12 m/s 46 m 1.225 0.45 8.32 2 MW 0.69 kV 60 Hz 17 Wb 1200 0.015 pu 0.057 pu 0.105 pu 8.75 mH 6 2.5 sec

509 Table. 3. Limits of Variables for Optimization Problem

510 Symbol

Quantity

Min Value

Step

Max Value

VSC ASC

Volume of HTS Cross section of HTS

5e-4m3 1e-6m2

5e-4m3 5e-6m2

1e-3m3 1e-5m2

26

∆tsc

511 512

1

2

3

4

5

6

7

529 530 531 532 533

A. Moghadasi and A. Islam, “Enhancing LVRT capability of FSIG wind turbine using current source UPQC based on

Z. Zhang; Y. Zhao; W. Qiao; L. Qu, "A discrete-time direct torque control for direct-drive PMSG-based wind energy

Ki-Hong K., Yoon J., Dong L., Heung, K.: ‘LVRT scheme of PMSG wind power systems based on feedback linearization’, IEEE Trans, Power Electron., 2012, 27, (5), pp. 2376-2384.

8

527 528

A. Moghadasi, A. Islam, "Enhancing LVRT capability of FSIG wind turbine using current source UPQC based on

conversion systems," in Industry Applications, IEEE Transactions on, July-Aug. 2015, 51, (4), pp.3504-3514.

525 526

Mohseni M, Islam SM., “Review of international grid codes for wind power integration: Diversity, technology and a

resistive SFCL,” IET Gener. Transm. Distrib., 2014, 8, (3), pp. 563 – 572.

523 524

A. Moghadasi, A. Sarwat, J. M. Guerreo, “A comprehensive review of low-voltage-ride-through methods for fixed-

resistive SFCL," T&D Conference and Exposition, 2014 IEEE PES, 2014, pp. 14-17.

521 522

Muyeen, S. M., Takahashi, R, Murata, T, Tamura, J.: ‘A variable speed wind turbine control strategy to meet wind

case for global standard. Renew. Sustain. Energy Rev., 2012; 16, (6), pp. 3876–3890.

519 520

0.8 s

speed wind power generators”, Renewable and Sustainable Energy Reviews, 2016, 55, pp.823-839.

517 518

0.2 s

farm grid code requirements’, IEEE Trans. Power Syst., 2010, 25, (1), pp. 331-340.

515 516

0s

REFERENCES

513 514

Duration of the fault

Yaramasu, V., Bin Wu, Alepuz, S., et al.: ‘Predictive control for low-voltage ride-through enhancement of three-levelboost and NPC-converter-based PMSG wind turbine’, IEEE Trans, Indust. Electron., 2014, 61, (12), pp. 6832-6843.

9

Farhadi M. and O. Mohammed O.: ‘Event based protection scheme for a multi-terminal hybrid dc power system,’ IEEE Trans. Smart Grid, 2015, 6, (4), pp.1658–1669.

10 Yonghao G., Chunghun K., Chung C., "Nonlinear control for PMSG wind turbine via port-controlled Hamiltonian system," in PowerTech, 2015 IEEE Eindhoven, July 2015, pp.1-6. 11 Mullane, A., Lightbody, G., Yacamini, R.: ‘Wind-turbine fault ride-through enhancement’, IEEE Trans, Power Syst., 2005, 20, (4), pp.1929-1937.

534

12 Alepuz, S., Calle, A., Busquets, S., Kouro, S., Bin Wu.: ‘Use of stored energy in PMSG rotor inertia for low-voltage

535

ride-through in back-to-back NPC converter-based wind power systems’, IEEE Trans, Indust. Electron., 2013, 60, (5),

536

pp. 1787-1796.

537

13 Ibrahim, R.A., Hamad, M.S., Dessouky, Y.G., Williams, B.W.: ‘A novel topology for enhancing the Low Voltage Ride

538

through capability for grid connected wind turbine generators’, Energy Conversion Congress and Exposition (ECCE),

539

Raleigh, NC, Sept. 2012, pp.2389-2395.

540 541

14 Muyeen SM., Ali, MH., Murata, T., Tamura, J.: ‘Transient stability enhancement of wind generator by a new logical pitch controller’, IEEJ Trans. Power and Energy., 2006, 126, (8), pp. 742–752.

542

15 Amei, K., Takayasu, Y., Ohji, T., Sakui, M.: ‘A maximum power control of wind generator system using a permanent

543

magnet synchronous generator and a boost chopper circuit’, in Proc. Power Convers. Conf., Osaka, Japan, 2002,

544

pp.1447-1452.

545 546

16 Luo, F., Ma, D.S.: "Design of digital tri-mode adaptive output buck-boost power convertor for high efficient integrated systems," IEEE Trans. Indust. Electron., 2010, 57, (6), pp.2151-2160. 27

547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568

17 Farhadi M. and O. Mohammed O.: ‘Adaptive Energy Management in Redundant Hybrid DC Microgrid for Pulse Load Mitigation’, IEEE Trans. Smart Grid, 2015, 6, (1), pp.54-62. 18 Farhadi M. and O. Mohammed O.: ‘Performance enhancement of actively controlled hybrid DC microgrid and pulsed power load,’ IEEE Trans. Ind. Appl., 2105, 51, (5), pp.3570–3578. 19 Deng, F., Chen , Z.: ‘Low-voltage ride-through of variable speed wind turbines with permanent magnet synchronous generator’, in Proc. IEEE IECON, Porto, Portugal, Nov. 2009, pp. 621–626. 20 Mullane, A., Lightbody, G., Yacamini, R.: ‘Wind-turbine fault ride-through enhancement’, IEEE Trans. Power Syst., 2005, 20, (4), pp. 1929–1937. 21 Matas, J., Castilla, M., et al.: ‘Feedback linearization of direct-drive synchronous wind-turbines via a sliding mode approach’, IEEE Trans. Power Electron., 2008, 23, (3), pp. 1093–1103. 22 Elshiekh. M.E., Mansour. D.A., Azmy A.M.: ‘Improving Fault Ride-Through Capability of DFIG-Based Wind Turbine Using Superconducting Fault Current Limiter’, IEEE Trans. Appl. Superconduct., 2013, 23, (3), pp. 1204-1208. 23 Ye, L., Lin, L.: ‘Study of Superconducting Fault Current Limiters for System Integration of Wind Farms’, IEEE Trans. Appl. Superconduct, 2010, 20, (3), pp.1233-1237. 24 Heydari, H., Moghadasi, A.H.: ‘Optimization scheme in combinatorial UPQC and SFCL using normalized simulated annealing’, IEEE Trans. Power Deliv., 2011, 26, (3), pp.1489-1498. 25 Kim, S.-Y., Kim, W.-W., Kim, J.-O.: ‘Determining the location of superconducting fault current limiter considering distribution reliability’, IET Gener. Transm. Distrib., 2012, 6, (3), p. 240-246. 26 Vahid Vahidinasab., ‘Optimal distributed energy resources planning in a competitive electricity market: Multiobjective optimization and probabilistic design’, Renewable Energy, 2015, 66, pp.345-363. 27 Moghadasi, A.H., Heydari, H., Farhadi, M.: ‘Pareto optimality for the design of SMES solenoid coils verified by magnetic field analysis’, IEEE Trans. Appl. Superconduct, 2011, 21, (1), pp.13-20.

569

28 Rosyadi, M., Muyeen, S.M., Takahashi, R., Tamura, J.: ‘Low voltage ride-through capability improvement of wind

570

farms using variable speed permanent magnet wind generator’, Electrical Machines and Systems (ICEMS), Beijing,

571

china, Aug. 2011, pp.1,6, 20-23.

572

29 Jaramillo, F., Kenne, G., Lamnabhi, F.: ‘A novel online training neural network-based algorithm for wind speed

573

estimation and adaptive control of PMSG WT system for maximum power extraction’, Renewable Energy, 2015, 86,

574

pp.38-48.

575

30 Hosseini, S.H.; Farakhor, A.; Haghighian, S.K., "Novel algorithm of maximum power point tracking (MPPT) for

576

variable speed PMSG wind generation systems through model predictive control," in Electrical and Electronics

577

Engineering (ELECO), 8th International Conference on, 2013 , pp.243-247.

578

31 Adhikari, J.; Prasanna, I.V.; Panda, S.K., "Maximum power-point tracking of high altitude wind power generating

579

system using optimal vector control technique," in Power Electronics and Drive Systems (PEDS), IEEE 11th

580

International Conference on , 2015, pp.773-778.

581 582 583 584

32 Hunping, S., Nilles, J.L.: ‘High-accuracy hysteretic current-mode regulator for powering microprocessors’, Applied Power Electronics Conf. APE, Twenty-First Annual IEEE, March 2006, pp., 19-23. 33 Janowski, T., Kozak, S., et al.: ‘Analysis of transformer type superconducting fault current limiters’, IEEE Trans. Appl. Superconduct., 2007, 17, (2), pp. 1788–1790.

28

585 586

34 Gyore, A., Semperger, S., et al.: “Experimental analysis of different type HTS rings in fault current limiter,” IEEE Trans. Appl. Superconduct., 2007, 17, (2), pp. 1899–1902.

587

35 Blair, S.M., Booth, C.D., Singh, N.K., Burt, G.M.: ‘Analysis of energy dissipation in resistive superconducting fault-

588

current limiters for optimal power system performance’, IEEE Trans. Appl. Superconduct, 2011, 21, (4), pp.3452,

589

3457.

590 591 592 593

36 S. Eckroad, ‘Superconducting Fault Current Limiters,’ Electrical Power Research Institute (EPRI), Technology Watch 2009. 37 Mulholland, J., Sheahen, T., Mcconnel, B., ‘Method for estimating future markets for high-temperature superconducting power devices,’ IEEE Trans. Appl. Superconduct, 2002, 12, (2), pp.1784, 1789.

594

38 NREL, NWTC Information Portal, https://nwtc.nrel.gov/FAST.

595

39 Odgaard, P., Larsen, L., Wisniewski, R., Hovgaard, T.: ‘On using Pareto optimality to tune a linear model predictive

596 597 598 599 600

controller for wind turbines’, Renewable Energy, 2016, 87, pp.884-891. 40 Li, H., Yang, C., Hu, Y., Liao, X., Zeng, Z., Zhe, C,: ‘An improved reduced-order model of an electric pitch drive system for wind turbine control system design and simulation’, Renewable Energy, 2016, 93, pp.188-200. 41 Heydari, H., Sharifi, R.: ‘Three-dimensional pareto-optimal design of inductive superconducting fault current limiters’, IEEE Trans. Appl. Superconduct, 2010, 20, (5), pp.2301-2311.

29