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
Multiobjective Optimization in Combinatorial Wind Farms System Integration and Resistive SFCL Using Analytical Hierarchy Process 1
Amirhasan Moghadasi, Arif Sarwat, Josep M. Guerrero
Abstract— This paper presents a positive approach for low voltage ride-through (LVRT) improvement of the permanent
magnet synchronous generator (PMSG) based on a large wind power plant (WPP) of 50MW. The proposed method utilizes the
conventional current control strategy to provide a reactive power requirement and retain the active power production during
and after the fault for the grid codes compliance. Besides that, a resistive superconducting fault current limiter (RSFCL) as an
additional self-healing support is applied outside the WPP to further increase the rated active power of the installation, thereby
enhance the dc-link voltage smoothness, as well as the LVRT capability of the 50MW WPP. This is achieved by limiting the
exceed fault current and diminishing the voltage dip level, leading to increase the voltage safety margin of the LVRT curve.
Furthermore, the effect of the installed RSFCL on the extreme load reduction is effectively demonstrated. A large WPP has a
complicated structure using several components, and the inclusion of RSFCL composes this layout more problematic for
optimal performance of the system. Hence, the most-widely decision-making technique based on the analytic hierarchy process
(AHP) is proposed for the optimal design of the combinatorial RSFCL and 50MW WPP to compute the three-dimensional
alignment in Pareto front at the end of the optimization run. The numerical simulations verify effectiveness of the proposed
approach, using the Pareto optimality concept.
Keywords—Low voltage ride-through, multi-objective optimization, superconducting fault current limiter, wind farm.
Wind turbines with the grid connected mode of the operation play the significant role toward in sustainable energy
development in the future. However, integration of large wind power plants (WPPs) can impose the adverse effects on the grid,
particularly under abnormal grid voltage conditions . Traditionally, wind turbine generators were tripped with circuit
breakers once the voltage at their terminals reduced below 80% because the penetration level of the wind power was extremely
small compared to the conventional generation systems and their impact on the grid was low. The trend towards integration of
more WPPs has raised serious concerns about the stability of existing power networks, increasing the fault current levels and
voltage reductions, thereby disconnecting a large wind farm. Recently, many power system operators in Europe and other parts
of the world are expanding and modifying their interconnection requirements for wind farms through technical standards
known as grid codes [2-4]. 2
Area A 50%
Area B 0
Fig 1. Danish grid codes. (a) LVRT requirement. (b) Reactive power support requirement
One of the critical demanding requirements, concerning the grid voltage support, is called low voltage ride-through (LVRT)
capability, which is regularly being included in the new grid codes. Fig. 1(a) a shows practical example of the LVRT curve
deﬁned by the Danish system operator for wind turbines (WTs) connected to the grid. Based on this regulation, if the voltage
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
only stipulated to disconnect from the grid when the voltage profile falls into the Area B. Besides the LVRT requirements,
some grid codes require large WTs to contribute to the voltage restoration of the power system by injecting the reactive power
during the fault and the recovery period , while maintaining the operating point above the area of Fig. 1(b).
Permanent magnet synchronous generators (PMSGs) with a full-rating converter offers a number of advantages for WTs,
including low maintenance requirements, more reactive power supply and better ride-through capability because power
electronic converters are decoupled completely from the grid [5-7]. However, there is a strong interaction between the turbine
control system and the mechanical loads the turbine experiences. The mechanical loads are divided into two distinct types:
extreme and fatigue loads. Extreme loads are loads that a given component needs to be able to withstand once; while fatigue
loads are accumulating over time and threaten to damage the turbine after several years of operation . An important source
of extreme loads may occur during fault events. At the beginning of the fault, the maximum power injected into the grid
reduces proportional the voltage sag amplitude, while power injected from the wind generator remains relatively constant. Due
to unbalance power between the mechanical-input power and the electrical-output power, the dc-link voltage as well as rotor
speed exceeds their safety limits which can potentially force the wind turbine to disconnect from the grid. The quickly growing
power ratings of the wind turbines simply exacerbate these problems. Thus, PMSG suffers from large variations of dc-link
voltage during and after the grid fault and extreme loads occurring either prior or during the shut-down process [3, 8, 9]. Any
control system that helps to avoid unnecessary faults or that improves the behavior during the shut-down process will reduce
turbine loads or contribute to turbine availability. 3
Several studies have been proposed in the literature to limit the dc-link voltage variations and improve the LVRT capability of
PMSG-based wind turbines [5-12]. Fast pitch control can help to reduce the input-mechanical power by rotating the blades
about their longitudinal axis, also called pitching, and consequently curbs dc-link voltage fluctuations. In , a logical fast
pitch controller along with fuzzy logic controller (FLC) for back to back converters has been proposed in order to enhance the
transient performance of WTs during severe network disturbances. Another solution is to permit the excess wind energy to be
temporarily stored in the turbine-generation shaft inertia during the grid faults [7, 11]. Although, techniques are the cheapest
solutions for enhancing the LVRT capability of PMSG-based wind turbines, but these have a very slow dynamic response due
to the mechanical constraints of the system, (the speed of the pitch actuator is slow to contribute alone to LVRT support). The
most well-known method that is being used for the PMSG-based WT systems is the braking chopper (BC) with the low cost
advantage and the simple control performance to consume this surplus power [14, 15]. However, in the large wind power plant,
including many single wind turbines, the overall cost of using the BCs will be dramatically increased. Moreover, it is difﬁcult
to improve the power quality at the output of the wind turbine systems since the BC can just dissipate the power .
Various control methods are also proposed to ensure proper converter operation during fault conditions. The formerly analyzed
converter control solutions [11, 17, 18], are based on the classical approach of using the linear proportional–integral (PI)
regulators and pulsewidth/space vector modulation (PWM/SVM). The particular problem is that a linear PI controller is
designed for normal network voltage levels, resulting in excessive currents at reduced voltage levels during the fault . The
nonlinear control methods are introduced to improve the classical current control method [19, 20], but most of these methods
are complex and very sensitive to system parameters for practical applications, and need proper tuning of control .
This paper proposes an effective approach using resistive superconducting fault current limiter (RSFCL) as the additional
support along with conventional converter control strategy based on PI regulators to further increase the rated active power of
the installation, thereby enhancing dc-link voltage smoothness as well as the LVRT capability of the 50MW WPP. By using
the RSFCL, the fault current is suppressed effectively and the voltage dip level of the WPP terminals is diminished, leading to
enlarge the voltage safety margin of LVRT curve. Up to the present time, as far as the authors are aware, there has been no
report on the RSFCL investigation in the large-scale of PMSG-based on WPP, which is the main motivation of this paper.
The first-cycle suppression of a fault current by a RSFCL can also reduce the activation of pitch angle control and can decrease
the effect of the extreme loads on the turbine components. A RSFCL is considered as self-healing technology since it
eliminates the need for any control action or human intervention due to its automatic excessive current detecting and automatic
recovering from non-superconducting to superconducting states [23, 24]. These significant features of RSFCL can demonstrate
that the proposed technique surpasses aforementioned methods using BCs and complicated nonlinear control system.
Wind Farm with 50 MW Capacity
Superconducting Fault Current Limiter Transformer 0.69/34.5 kV
Transformer 34.5/115 kV
RSFCL 115 kV, 60 HZ
Nacelle Pitch System
PMSG 2 MW, 0.69 kV
Back to Back Converter AC Filter Cdc
Fig. 2. Proposed combinatorial PMSG-based WPP and RSFCL.
However, a large WPP has a complicated structure using several components, and the inclusion of RSFCL composes this
scheme more problematic for optimal performance of the system. Hence, the further effort in this paper is centralized on the
most-widely decision-making technique based on the analytic hierarchy process (AHP) [25, 26], for the optimal performance
of the combinatorial RSFCL and 50 MW WPP. The technique creates the Pareto optimality for simultaneously optimizing 3-D
alignment that rarely reported the power system literatures. Effectiveness of the proposed approach, using the Pareto optimality
concept is veriﬁed by the numerical simulations. The optimization technique figures out all the nondominated solutions on the
Pareto front at the end of the optimization run.
Modeling of the PMSG-Based Wind Turbine
The structure of the proposed system including a 50-MW PMSG WPP and resistive SFCL is schematically shown in Fig. 2.
The constituents of the wind turbine are aerodynamic, mechanical, and electrical parts. The generator are completely decoupled
from the grid by power electronic converters (grid-side VSC and generator-side VSC which are connected back-to-back
through the common dc-link capacitance). PMSG-based WTs may be represented as a combination of subsystems. The
framework shown in Fig. 3 is typically used for modeling purposes, in which the relevant mathematical model has been cited in
the several literatures [6, 7, 10,], and it is summarily considered here.
λ =8.32 Tip Speed Ratio Calculation
Mechanical Block ωrotor
Cp=0.45 Rotor Power Coefficient Calculation
Aerodynamic Torque Calculation
Permanent Magnet Synchronous Generators
Pg, Qg Back to Back Converter
Control System Block (Pitch, Yaw and Power Control)
Fig. 3. Subsystems model used in PMSG-based wind turbine.
Two-mass Shaft Model including Gearbox
Fig. 4. Wind turbine characteristics.
2.1. Aerodynamic Model According to the Betz theory, the aerodynamic power generated by the rotor is given by  PA =
1 3 ρp R 2 vwind C p (λ , β ) 2
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
rotor power coefficient. In the PMSG-based WT, the obtained power depends on Cp, which is a function of both tip speed ratio
(TSR) λ and blade pitch angle β, in which the TSR is defined as
(2) where ωrotor is the rotational turbine speed. The numerical approximation of the power coefficient  is given by following
151 −0.58 β −0.002 β 2.14 −13.2 e C p λ , β= 0.73 λt
( λ − 0.02 β ) 113
( 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
The mechanical torque on the rotor Trotor, which is produced by the blades of wind turbine can be calculated as PA/ωrotor. Also,
Fig. 4 illustrates the relation between the rotational turbine speed and aerodynamic power of the wind turbine, PA, for various
wind speeds vwind, with the blade pitch angle β=0o. βmax
Fig. 5. Conventional pitch angle control used in FSIG-based wind turbine.
For each wind speed, the maximum power point can be acquired corresponding based on given Cp-opt =0.45 and λopt= 8.32
expressed as  2 Rωrotor
Pmax 0.5 rπ R =
× 0.45 8.32
For an average wind speed of 12 m/s, which is used in this paper, the maximum turbine power output 2 MW and rotational
speed 1200 rpm are obtained.
The aerodynamic of wind turbines is controlled by pitch control approaches, which have been developed for large WTs. The
blades start to move around cut-in speed 4 m/s, and optimal aerodynamic efﬁciency is achieved at the wind speed rated about
12 m/s. The extra power obtained from wind speed between 4 and 12 m/s may be smoothly curtailed by spinning the blades
using a pitch control to avoid overloading the wind turbine system. Fig. 5 depicts the conventional pitch angle regulator in
which the input and output of the model are the rotational turbine speed ωrotor and blade angle β, respectively.
The yaw system of a typical turbine is significantly slower than the pitch system and the structural dynamics. Since the yaw
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
yawing is to be considered it can be modeled similar to the pitch system but with significantly lower bandwidth and rate limits.
The gearbox also plays an essential role in the WTs to adapt low-speed, high-torque rotation of the turbine rotor into the faster
rotation of the electrical generator. The critical issue in implementing the gearbox technology is the extreme loads, which may
lead to misalignment of the drive train and a gradual failure of the gear components, consequently increasing the capital and
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
d i sd −ωe Ld isq dt
vsq = Rs isq + Ls
d isq + ωω e Lq isd + eψ r dt
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
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.
For the generator with surface-mounted permanent magnets, d- and q-axes inductances are the equal (Ld = Lq), resulting a
simple interpretation of the electromagnetic torque Telectrical and aerodynamic torque on the rotor Trotor expressed as
3 pψ r isq 2
Trotor = J − Telectrical
d ωω rotor + b rotor dt
where p is the number of machine pole pairs, J is moment of inertia for turbine-generator, ωm is shaft mechanical speed, and b
is friction coefficient.
Power Control Strategy
Detail of the proposed power control scheme for the PMSG based on the full-power converter topology is illustrated in Fig. 6.
As it can be seen, it is schematically divided into two main blocks. On the one hand, controlling the active and reactive power
of the PMSG is obtained via a generator-side VSC. On the other hand, the management of the active and reactive power
released to the grid by the PMSG along with the dc-link regulation is accomplished via the grid-side VSC. The active and
reactive power references to be injected by the grid-side VSC are obtained, so that the whole wind farm can fulfill the grid
3.1. Generator-Side VSC Control
The control block diagram of generator-side VSC is shown in Fig. 6(a), which is based on stator voltage equations (6) and (7)
obtained in d-q synchronous frame. Several maximum power point tracking (MPPT) algorithms have been reported for the
PMSG-based WT [28-30]. The outcome of the MPPT unit provides the reference value of the rotational turbine speed (ω⃰rotor)
for the generator-side VSC controller. This paper mainly focuses on the converter control, and hence, the MPPT control
method was not discussed. The speed reference ω⃰m is acquired by a MPPT method mentioned in (5) in order to extract the
maximum amount of power with the actual wind force, while the rotational speed error is given as the input to a PI controller in
order to generate the q-axis stator current command (i*sq). Also, the reactive power produced by the wind turbine is regulated at
zero (i*sd=0) for unity power factor operation. The error between the reference dq-axis currents and the actual dq-axis currents,
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
angle θe calculated from the rotational speed of the PMSG is applied in a park transformation to engender gate signals using the
carrier wave of pulse width modulation (PWM) operation. 8
PI ω⃰ m MPPT
ωe·(Lq· isd + ψr)
6 pulses S1-S6
isq i*sd = 0
ωe· Ld· isq
(a) Grid-Side Converter
LC Filter Sg1
Vgrid Cf=1.3 mF
Cdc=16 mF Vdc=1.2 kV 6 pulses θs Sg1-Sg6 * i a,b,c abc
3-p voltage Transformer
I RVSC I cf
I A= (I
Grid Code Request
Current Calculation using (8) p
) – (I R)
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.
3.2. Grid-Side VSC Control
The proposed grid-side converter controller is provided in Fig. 6(b) to calculate the current references to be inserted by the
grid-side VSC in order to fulﬁll the grid code requirements. Further, this controller preserves the dc-link capacitor voltage at
the set value 1.2 kV, which assures the active power swapping from the PMSG to the grid. In the steady state condition, the
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
PI controller from the dc-link voltage regulator, and q* transformed into the instantaneous power α-β method based on α-β-0
reference frame . It has been mathematically formulated as
I* 1 α = 2 I * vα +vβ 2 β
− vβ p* + p
The angle θs for the Park transformation is detected from the three-phase voltages at the low-voltage side of the grid
transformer by using a phase-locked loop (PLL). Finally, gate signals are generated for grid side VSC switches using the
Hysteresis module , shown in Fig. 6(b). Under a grid voltage dip, the reactive current, IRVSC in proportion to the voltage
reduction should be provided during the fault in order to meet the LVRT requirement according to the characteristic shown in
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
active power production related to the voltage sag magnitude, while the generator continues to provide active power at nominal
value. In this case, the dc-link voltage exceeds its safety limits, leading a system malfunction or even a component failure.
However, the rapidly rising the dc-link voltage, under a system fault, is difﬁcult to be avoided by only using the PI controller.
For this reason, this paper proposes a RSFCL used in outside of the wind farm, as shown in Fig. 2. The RSFCL makes it
possible to suppress the dc-link voltage ﬂuctuations by limiting the magnitude of the fault current, thereby increasing the
output active power capacity and improving the LVRT capability of the wind farm. A further analysis is accomplished in
Electro-Thermal Modeling of a RSFCL
The resistive superconducting fault current limiters (RSFCLs) have been launched and introduced into the network as a self-
healing technology to curb prospective fault currents immediately to a manageable level by suddenly raising the resistance
value [22, 23]. Furthermore, after the fault current is profitably repressed, the RSFCL can be restored to the primary state
without additional aid. RSFCL has a simple structure with a lengthy superconductor wire inserted in series with the
transmission lines. With the recent breakthrough of second-generation high-temperature superconductor (HTS) wires, the
SFCL has become more viable . Considering the superconducting material, BSCC-2223 is the conductor, which has
commonly been utilized for most of the tentative RSFCLs [32, 33].
To preserve the superconductor from detrimental hot spots during the operation, the shunt resistance, Rshunt is essential. This
parallel resistance must be contacted all over the length of the superconductor, and it regulates the controlled current to elude
over-voltages likely occurring when the resistance of the superconductor increases much quicker. The current limiting behavior
of the RSFCL can be modeled by the resistance transition of HTS tapes in terms of the temperature and the current density, as
defined by the following equation 
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
Equivalent Voltage source PCC
RSFCL 50 MW WPP
Fig. 7. Equivalent circuit of proposed system in fault condition.
where Tc, Tb, Jc0, Vsc, and Asc are critical temperature, liquid nitrogen temperature, critical current density, superconductor
volume, and cross section, respectively. Also, isc, Ic, ρf, and ρn are short-circuit current, critical current, ﬂux ﬂow resistivity, and
normal resistivity, respectively. In this description (9), three possible states for superconductor are; 1) the ﬂux-creep state at a
temperature and a current under the critical rate; 2) the ﬂux ﬂow state at a current over the critical value, but a temperature
under the critical rate; and 3) the normal conductive state at a temperature higher the critical amount.
According to the equivalent circuit of the proposed combination, shown in Fig. 7, if the asymmetrical component of the fault
current is ignored, the short-circuit current through the RSFCL branch can be stated by the following equations
iRSFCL (t ) =
Vm Rshunt sin (ωt ) × RSFCL + Rshunt 2 R + ( LT ω ) 2
where R=Rtrans+Rshunt║RSFCL, LT is the inductance of the transformer, and Vm is the magnitude low voltage side of interfacing
transformer. The total fault energy dissipated in the HTS tapes, Qsc is calculated using (13), where ∆tsc is the duration of the
fault . Qsc − 3ph = 3
RSFCL iRSFCL (t ) dt
Substituting (12) into (13) gives the following
∆tsc sin (2ω∆t sc ) − 2 2 4ω R + ( LT ω ) 2 2
= Qsc −3ph
The RSFCL model should be a reasonable approximation of transient SFCL behavior during faults and, therefore, should
consider thermal properties. The thermal model of RSFCL has been generically estimated as follows  T (t ) = T0 +
∫ Qsc (t ) − Pcool (t ) dt
where T0 is ambient temperature, Csc is the heat capacity of the superconductor, and Pcool is the power cooling.
Fig 8. HTS wire cost . (a) Dollar per Kiloamp per Meter. (b) Dollar per Meter.
4.1 Economic Feasibility of the RSFCL
Several main factors affect for determining the actual size and the cost of a resistive SFCL, such as the length of applied
superconducting wire, the cooling machinery, the geometry of RSFCL module, and the rated power and voltage system, where
RSFCL must be installed. Practically, the whole superconducting length is used in form of helix to shape the superconducting
tube. In reality, several tubes may be connected in parallel to achieve a particular resistance in form of cylindrical geometry.
The rough estimation for the RSFCL size can be achieved based on design details of the RSFCL projects in the worldwide
. Accordingly in this paper, the RSFCL module installed in the transmission system with voltage rate of 34.5 kV and power
rate of 50 MVA would be much less than 4 m in both diameter and height.
After recent progress of the economical second-generation HTS wires, SFCLs are becoming more practicable, due to low
manufacturing costs, low ac losses, higher current densities, and better operational performances, and is eventually expected to
be at least a factor of ten lower in the cost than the presently available HTS conductor . The cost of HTS wire is generally
described by two parameters: the maximum amount of current that the HTS wire can conduct; and the manufacturing cost per
meter of wire. Fig. 8 illustrates how the HTS wire cost of RSFCL is expected to decrease over the next two decades as
production increases. The impact of cooling system on the future competitiveness of the RSFCL devices is critical. The 1999
benchmark cost of a medium-sized cryogenic refrigeration unit was about $60,000/kWcold at 77K. Economies of scale typical
of the cooling refrigeration industry were applied to represent the expected decline in refrigeration costs. This declining cost 12
model indicates that as large numbers of cryogenic refrigeration units are manufactured, the cost will drop to less than
Numerical Simulation Analysis
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
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
design, all aspects of a WT need to be considered.
Fig 9. Combinatorial PMSG-based WT and RSFCL model using FAST aeroelastic simulator and the SimPowerSystems.
Thus, a holistic wind turbine model was utilized including aerodynamic and mechanical simulations through the FAST
software, as well as concurrent electrical simulations through the SimPowerSystems toolbox for MATLAB/Simulink. The
FAST aeroelastic wind turbine simulator developed by the National Renewable Energy Laboratory (NREL) to perform detailed
simulations of direct-drive and geared wind turbines . The modeling of the RSFCL was also accomplished using MATLAB
programming to combine its electrical and thermal properties as discussed in Section 4. A top-level view of the model is shown
in Fig. 9. The characteristics of the preferred wind farm and selected resistive RSFCL parameters are given in Appendix A,
Table 1 and Table 2. The simulation results are carried out for the 50 MW system to verify the effective performance of the
RSFCL on the dc-link voltage smoothness and the extreme load reduction. All simulations were executed using a fixed-step 13
solver with a 5 μs step size. A three-phase symmetrical grid fault is considered, since the fault ride-through capability of the
regional grid codes mostly refer to this type of fault. Thus, a three-phase fault is applied in the middle of the transmission line
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
the RSFCL, simulations are carried out for without and with the presence of the RSFCL. The expediency of the RSFCL
component for managing the fault current, as well as resistance and temperature variations of the RSFCL is demonstrated in
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,
whereas with the RSFCL incorporated on the main road of the wind farm, the fault current is limited effectively to reach about
5.1 kA (see Fig. 10(a)).
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
normal state. (c) Temperature rise.
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
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
place at t = 4s, the quench time (a transition from a superconducting mode to a resistive mode) is initiated by going through the 14
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.
11(a) shows the voltage profile at the PCC in the proposed integration system during a three-phase short circuit. In the absence
of the reactive injection and RSFCL, the voltage reduction of 70% occurs. In this case, the voltage at the PCC cannot be
restored to the nominal value because of an instability issue on the proposed system and the WPP must be disconnected from
the grid. With the adoption of the reactive injection control, the voltage dip is decreased, reaching 50% before recovering
immediately to the nominal value upon clearing the fault. Based on the reactive power support requirement (Fig. 1(b)), for a
50% voltage reduction, all the capacity of the wind farm is occupied by reactive power.
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
As can be observed in Fig. 12(b), the reactive power injected during the fault (without RSFCL) allows the wind farm to satisfy
the speciﬁcations of grid code requirements such as increasing the LVRT capacity. However, due to the lack of output active
power in the grid-side VSC and consequently the earlier-mentioned unbalanced power during the fault, the dc-link voltage is
significantly increased to about 1.14 pu, where a regular reactive power control with no RSFCL is used i.e., 14.58 % over
voltage (Fig. 11(b)). This effort proposes the RSFCL as an additional supporting method besides the reactive power control to
improve the LVRT capability and smoothen the dc-link voltage of the wind farm. This method increases the voltage stability
margin with respect to the LVRT curve as shown in Fig. 11(a), in which using the RSFCL significantly reduces the magnitude
of the voltage sag to around 20%. In addition, the peak value of the dc-link voltage transient is reduced when using the RSFCL,
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
output of the wind farm with and without the RSFCL, in which it is considerably kept at rated value of 50 MW before
occurring the fault. After installing RSFCL, the drop in the active power decreased from 0 MW to 35 MW and back to the
normal operation gradually as the fault is cleared. That is, the presence of the RSFCL increases the retaining of the active
power production for the PMSG-WPP by approximately 60%, during the fault condition.
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.
Fig. 13. Dynamic performance of the turbine side with and without applying the RSFCL. (a) Rotational turbine speed. (b) Aerodynamic rotor torque.
Fig. 14. Dynamic performance of the generator side with and without applying the RSFCL. (a) Rotational generator speed. (b) Generator torque.
5.1 Effect of RSFCL on Extreme Load Reduction on WT Structure
In order to analyze the impact of the RSFCL on WT extreme loads, a combination of the FAST model and SimPowerSystems
can accurately simulate detailed aerodynamics and mechanical aspects of the wind turbine. In this study, it is assumed that
wind speed at the hub remains constant at 12 m/s. Rotational speed and mechanical torque responses of the rotor turbine and
generator are shown in Fig. 13 and Fig. 14, respectively. As it can be seen, the rotational speeds and mechanical torque
increase during the fault period, which may lead to power system instability and is detrimental for the turbine generator system
if the fault duration is long and proper auxiliary devices are not used (no controller). However, RSFCL can limit the rate of 17
rising of machine speed and the aerodynamic torque imposed on rotor/shaft in order to make better stability.
In this work, a number of the degrees of freedom available in the simulation model are used for analysis of the extreme loads,
including tower fore-aft and sideways modes, tower yaw mode, and blade flap wise and edgewise modes. All these modes are
depicted in Fig. 15, which contains illustrations of a wind turbine seen from the front and side views. The failure at the system
causes extreme loads on structural parts of the WTs. Figs. 16-18 show the simulation results of several key loadings, such as
hub loadings, blade root loadings, and tower base loadings, of the proposed WPP, which are compared without and with the
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
Tower Fore-aft Mode
Edgewise Blade Mode
Flapwise Blade Mode
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.
Fig. 16. Dynamic performance of the WT under the extreme load with and without the RSFCL. (a) Yaw moments. (b) Pith Actuator Force.
Fig. 16 depicts hub loadings, including the pitch actuator force and yaw moments, during the three-phase fault. The impact of
the installed RSFCL on yaw moments is effectively demonstrated by 20% reduction in the magnitude of the value during the
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
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
the pitch actuator force after it reached negative value is due to large inertia of the rotor. However, application of RSFCL
shows a promising solution for reducing the fluctuation of the pitch actuator force, as illustrated in Fig. 16(b).
Fig. 17. Dynamic performance of the WT under the extreme load with and without the RSFCL. (a) Blade flapwise moment. (b) Blade edgewise moment.
During the fault, blade experiences moments in flapwise bending and edgewise bending in the blade root. Fig. 17(a) shows the
average flapwise bending moment in the blade root. The axial wind force, gravity force and centrifugal force contributes the
most to the flapwise bending moment in the blade root. However, the average value of the flapwise moment is almost zero in
normal operating state of the WT. At the beginning of the fault, the rotor speed increases, therefore the contribution of
centrifugal force in flapwise bending moment in the blade root also increases. As the failure clear quickly after 200 ms, the
flapwise moment fluctuations in the blade root gradually smooth, because the contribution because the axial aerodynamic force
on rotor becomes negligible. Fig. 17(b) shows the average edgewise bending moment in the blade root. The rotor torque also 19
causes edgewise moment in the blade root and its contribution is estimated by the average value of the edgewise moment. As
can be seen, there are several fluctuation trends in the value of the edgewise moment. After clearing the fault, fluctuations trend
to fade off fast in edgewise bending moment in the blade root due to the large stiffness in edgewise direction of the blade. In
both figures, RSFCL can significantly dampen the oscillations of the flapwise moment and edgewise moment.
The WT tower experiences fore-aft and side-to-side bending moment at the tower base, as shown in Fig. 18. Fore-aft bending
moment is mainly due to rotor thrust loading. Tower motions happen due to the tower’s dynamic interaction with rotor blades.
Due to large fluctuations in axial aerodynamic force on rotor, the tower fore-aft moment also fluctuates.
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.
Once a fault happens in the system, the value of the tower fore-aft moment first increases and then decreases due to the inertia
of the tower, as shown in Fig. 18(a).
The tower fore-aft moment first decreases and then increases because of the inertia of tower. The tower fore-aft motion is
unable to quickly dampen because the complete weight of the WT operates on the tower base. Fig. 18(b) shows the side-to-side
bending moment in the tower base. The rotor torque that operates on the tower top through gearbox/generator support can lead
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
value of the side-to-side moment after clearing the fault, as can be seen in Fig. 18(b).
The results indicate that the proposed RSFCL has significant effect for reducing the fluctuations on the, blade flapwise add
edgewise moments, pitch actuator force and yaw moments, and tower fore-aft and side-to-side moments. Therefore, RSFCL
can be a promising solution for wind turbine controller performance with respect to extreme loads happening to mechanical
and aerodynamic parts during the severe disturbances.
Optimal Scheme Performance
The obtained results in Section 5 for the proposed combinatorial 50-MW wind farm and RSFCL conﬁrmed that further
improvements in dc-link smoothness, extreme load, and LVRT capability of a wind farm can be achieved by increasing the
SFCL resistance as much as possible. However, as stated in (14), the high-resistance SFCL means a substantial amount of
energy is dissipated in the form of heat, resulting damage on SFCL construction and cooling system. This large energy
dissipation would lengthen the recovery time of the RSFCL (transition from resistive state to superconducting state) after
clearing the fault. Also, as stated in Section 3.2, for overcoming the unbalance power between the generator and converter, the
active power output of the wind farm, PWPP should be appropriately increased during the fault to diminish the fluctuations of
dc-link capacitor voltage. However, depending on the grid code, reactive power production has highest priority during the
fault, occupying some portion of the maximum capacity of apparent power, and leading reduction in PWPP. Hence, there is a
tradeoff between three above mutually contradicting criteria, SFCL resistance, energy dissipation, and active power output of
the WPP in order to achieve an optimal design of combinatorial 50-MW wind farm and resistive SFCL.
For optimization purposes, this section implements multi-criteria decision making (MCDM) methodology based on analytical
hierarchy process (AHP) detailed in the authors’ prior work . One of the outstanding characteristics of the MCDM
technique is the creation of the Pareto optimality for simultaneous multiobjective optimization in which algorithm figures out
all the nondominated solutions on the Pareto front (optimality) at the end of the optimization run. AHP is established as
beneficial technique providing the promising solutions to the complicated decision-making problems with different criteria.
The proposed optimization model contains three predefined criteria and two constraints that are expressed as 1 1 Min , , Q SC RSFCL PWPP
max TSFCL − 423 < 0 point (Vgrid , ∆tsc ) within Area A
Where, maximum SFCL appeared resistance, RSFCL maximum active power output of the WPP, PWPP and minimum energy
dissipation, Qsc are desirable. The proposed system (combination of 50 MW WPP and RSFCL) should be designed in such a 21
way that the following criteria are satisﬁed: 1) TSFCLmax < 432° for safe solder melting; and 2) fulfill Danish grid code
requirement including LVRT and reactive power support requirement.
Based on (11), any change in the dimensions of the superconducting wires as well as fault durations may affect fault current
limiting performance of RSFCL, and consequently the optimum design of the proposed system. Therefore, in this optimization,
variable parameters are superconducting wire volume (Vsc), superconducting wire cross section (Asc) and duration of the fault
(∆tsc). The constraints of the selected variables for the optimization problem are shown in Appendix (Table 3).
Considerately, if each variable is changed in 10 steps, three variables would create 103 = 1000 alternatives when utilized in the
electrical simulation model. These cases (378) that exceed the predeﬁned optimization constraints must be omitted from
feasible options. optimal
. . .
Fig. 16. Hierarchy process for optimal combinatory PMSG-based WT and RSFCL.
The goal of AHP method is to ﬁnd a best case (desired solution) among the remnant number of 784 alternatives that can
maximize each criterion satisfaction. Basically, for 784 alternatives (Ai, i=1, 2,…, 784) and 3 criteria (Cj, j=1, 2, 3), there are
four steps considering decision problems by AHP as follows:
Step 1) Scrutinize the relation between objectives, criteria and alternatives to build the multi-layers hierarchical structure.
Fig. 16 shows the multi-layers hierarchical structure for optimal combinatorial PMSG-based WT and RSFCL including optimal
layer, criterion layer, and alternative layer.
Step 2) Compose a pairwise comparison matrix by assigning each alternative/criterion an optional number from 1/9 to 9. In
this article, the three-point performance rating scale is deﬁned for the importance of criteria, 9 (high), 5 (medium), and 1 (low).
Based on the explanation in , if the importance of criteria C1, C2, C3 are ranked as high (C1=9), medium (C2=5), and low
(C3=1), respectively, the criteria pairwise comparison matrix C=[c]3×3 can be expressed by C1
C1 (R SFCL ) c11
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
A similar method is applied to estimate the value of alternative pairwise comparison matrix Ai=[aij]784×784 (i=1, 2, 3) with 22
respect to each criterion.
Step 3) Compute the relative weight (priority) of the compared factor for the criterion according to the judgment matrix C
and A. The criteria and alternatives weight vectors can be obtained by adding the array elements of each row of C and A matrix
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
estimated by wc1 w c2 wc 3
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
The analysis of the simulation results represents the degree of importance of alternative i in criterion j, i.e., dij, which is divided
by its maximum value. This is followed by splitting the alternation range to 9 parts, allocating a proportional number from 1 to
9 into each alternative aij as
dij aij =Integer 0.11 Max i dij
Since, a pairwise comparison matrix of the alternative Ai is compatible; it forms the calculation of the alternative weight vector
simple via normalizing the elements of each column, reaching to waij. These calculations can be formulated as
∑ aij i =1
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,
3 & i= 1, 2,…, 784, forms a decision matrix (784×3) as
Criteria C1 ( wc1
C3 wc3 )
. . .
. . .
. . .
. . .
Step 4) Calculate the best alternative, i.e., the highest priority value.
Usually, the criteria can be classified into the two opposite groups called the benefit and cost criteria . A beneﬁt criterion
means that the better alternative has the higher grade. The inverse scenario is expressed true for the cost criteria. In this
optimization study, the total energy dissipated is cost and the other criteria, i.e., the resistance of SFCL and power output of the
PMSG, are benefit. Thus, the optimization problem can be summarized as a standard format for aggregating alternatives to 23
rank them based on the ratio performance approach detailed in , as given by
( wai1 × wc1 ) + ( wai2 × wc2 ) * max PAHP = = 464 for i 1, 2, ... , 784 i wai3 × wc3 465
For three levels criteria comparison, this weight vector must be calculated 25 times (33 − 2) by changing the importance of the
criteria with respect to each other. The run results of the algorithm are shown in Table 4. As earlier mentioned, the Pareto
optimality plays the significant role in choosing the best solution for optimization of all three criteria: resistance of SFCL,
energy dissipation in SFCL, and active power output of the WT. However, for an approximate set of three-dimensional Pareto-
optimal solutions, a search is performed for the tradeoff values between the optimums of the objective functions, using AHP, at
the end of each optimization run, as shown in Fig. 17.
Total Energy Dissipated (kJ)
500 400 300 200 100 50
40 30 20 PMSM Active Power (MW)
SFCL Resistance (Ohm)
474 475 476
Fig. 17. Multi-objective optimization using AHP, Pareto front for three criteria.
The corresponding AHP optimization results are illustrated in Table 4. It is the tradeoff values between the 25 given set of
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
Ω must be chosen. Similarly, for the power output of the PMSG-WPP or total energy dissipated priority selection, cases 20 and
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
and lower active power delivered during the fault are obtained in case 1 (82.7 % of total capacity) and case 9 (32.7 %),
The paper proposes an effective approach using RSFCL as the additional support along with conventional converter control
strategy based on the PI controller to further increase the rated active power of the installation, thereby enhancing dc-link
voltage smoothness as well as the LVRT capability of the 50 MW WPP. Moreover, that was demonstrated that RSFCL can be
a promising solution for improving wind turbine controller performance with respect to extreme loads on the wind turbine
structure. With this approach, it is expected that the activation of the dc braking chopper and fast pitch angle control could be
reduced in order to meet the international grid code requirements. An important feature of the proposed method is that a
conventional PI control can be used, performing the reactive and reactive current injection, while the dc-link voltage never
exceeds its safety limits. A further study is carried out to determine optimal performance of the combinatorial 50 MW PMSG-
WPP and RSFCL. Therefore, the simultaneous and transformative approach based on the AHP method for the multiobjective
optimization of embedded system has been introduced. A reconciliation between the three objecting functions, namely,
resistive of SFCL, output power of PMSG, and energy dissipated in RSFCL has elicited by a 3-D alignment in the Pareto front
having nondominated 25 solutions. However, a designer would be capable of selecting any of the solutions setting on the
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
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
The authors would like to thank Ms. Bonnie Jonkman, the Senior Scientist of National Wind Technology Center (NWTC),
National Renewable Energy Laboratory (NREL), for her critical and extensive support for using the FAST version 8.
See Table 1, Table 2 and Table 3.
Table. 1. Limits of Variables for Optimization Problem Symbol
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
Volume of HTS Cross section of HTS
529 530 531 532 533
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