Coordinated Operation of Wind Turbines and Flywheel Storage for PrimaryFrequency Control Support

Francisco Dıaz-Gonzaleza, Melanie Haub, Andreas Sumpera,c, Oriol Gomis-Bellmunta,d

aIREC Catalonia Institute for Energy Research, C. Jardins de les Dones de Negre, 1, Pl. 2a, 08930 Sant Adria del Besos, SpainbFraunhofer Institute for Wind Energy and Energy System Technology (IWES), Konigstor 59, 34119 Kassel, Germany

cCentre d’Innovacio Tecnologica en Convertidors Estatics i Accionaments (CITCEA-UPC), Departament d’Enginyeria Electrica, UniversitatPolitecnica de Catalunya EU d’Enginyeria Tecnica Industrial de Barcelona, C. Comte d’Urgell, 187, Pl. 2, 08036 Barcelona, Spain

dCentre d’Innovacio Tecnologica en Convertidors Estatics i Accionaments (CITCEA-UPC), Departament d’Enginyeria Electrica, UniversitatPolitecnica de Catalunya ETS d’Enginyeria Industrial de Barcelona, Avinguda Diagonal, 647, Pl. 2, 08028 Barcelona, Spain

Abstract

This work assesses the participation of wind power plants in primary frequency control support. To participatein frequency control-related tasks, the wind power plants have to maintain a certain level of power reserves. In thisarticle, the wind power plant is equipped with a flywheel-based storage system to fulfil the power reserve requirementsset by the network operator. The article focuses on two main aspects: the definition of the control strategy to derate thewind turbines to provide a part of the required power reserves; and the coordinated regulation of the power reservesof the wind turbines and the flywheels while participating in primary frequency control. This coordinated regulationenables the wind power plant to maintain the net level of power reserves set by the network operator while alleviatingthe need of deloading the wind turbines. The performance of the proposed control schemes are shown by simulation.

Keywords: Primary Frequency Control, Wind Power Plants, Flywheel Storage, Grid Codes, deloading methods.

1. Introduction

The increasing importance of wind power plants(WPPs) in the electrical network affects system operationdue to the stochastic nature of wind power [1]. For thatreason, more stringent requirements are gradually devel-oped by system operators for the grid integration of WPPs[2, 3, 4]. These regulations require WPPs to behave inseveral aspects similar to conventional synchronized gen-erating units. Among other requirements, the participa-tion of WPPs in system frequency control-related tasks isset (as indicated, for instance, by the Irish operator [3]).

Wind turbines (WTs) are capable of providing systemfrequency control support [5, 6, 7, 8, 9]. In [5] an analy-

Email address: fdiazg@irec.cat. Tel. +34 933562615

Fax. +34 933563802 Corresponding Author

(Francisco Dıaz-Gonzalez)

sis on the effects of the displacement of the conventionalgenerating units in a power system with high penetrationof WPPs is proposed. Results highlight the necessity ofWPPs to participate in frequency control as the synchro-nized inertia of the system is lowered by the decouplingof the rotor inertia of the wind turbines by fast controlledpower electronics. Frequency stability may be compro-mised with reduced levels of synchronized inertia sincehigh rates of change of frequency can be registered.

For ensuring the constancy and stability of the fre-quency of the electrical network, a certain level of activepower reserves is required. These reserves are continu-ously regulated to match the power consumption and gen-eration in the network, but also in presence of power dis-turbances such as sudden trips of generating units in orderto participate in frequency control. Wind turbines have tobe operated not extracting the maximum available power

Preprint submitted to International Journal of Electrical Power and Energy Systems December 17, 2014

NomenclatureParametersA Area covered by WT blades, (m2) Poptdel Output of a WT while being deloaded, (MW)Cpopt Optimal Betz coefficient for WT, (-) P∗storage Power reserve that flywheels can handle, (MW)H Inertia constant for conventional generation, (s) Pwt Power generated by WTs measured at PCC, (MW)J f w Inertia of a flywheel unit, (kg·m2) Pwtmax Max. power WPP can extract from wind, (MW)KCp(·) Optimal torque coeficient for WT, (Ws2/rad2) T ∗e WT electrical torque reference, (Nm)n f w Number of flywheel units, (-) Toptdel WT torque while being deloaded, (Nm)R Primary control droop for synchronous gen., (-) vwmin Wind speed for which the WT achieves its ratedRwpp Primary frequency control droop for WPP, (-) speed while maintaining a power margin x, (m/s)Tloss Flywheel torque losses, (Nm) x Power margin, (-)vw Wind speed, (m/s) xcap+ Magnitude Pcap+ in per unit of the maximum ava-vwrated Rated wind speed for WTs, (m/s) ilable power that WTs can capture from wind, (-)x∗sd Steady state power margin ref. for the WPP, (-) xcap− Magnitude Pcap− in per unit of the maximum ava-δ Time constant, (s) ilable power that WTs can capture from wind, (-)ωmin Minimum operating speed for flywheels, (rad/s) x∗wt Total power margin reference for WTs, (-)ωmax Maximum operating speed for flywheels, (rad/s) x∗wtsd

Power margin reference in steady state, (-)ωtrated Rated speed for WTs, (rad/s) β Pitch angle, (degrees)

βmax Pitch angle for power margin x at rated windVariables speed, (degrees)Cpdel Betz coefficient for a WT while being deloaded, (-) ∆ f Frequency deviation, (-)fe Electrical frequency of the network, (Hz) ∆t( fe) Time length that flywheels would be required toPcap+ Power that flywheels can inject for 30 min, (MW) inject or absorb power continuously, (s)Pcap− Power that flywheels can absorb for 30 min, (MW) ∆x Power margin interval, (-)Pload Network load demand, (MW) ∆xwt Power margin variation required to WTs, (-)Plosswt Power losses in the WPP collection grid, (MW) ω f w Flywheel speed, (rad/s)Popt Max. power WTs can extract from wind, (MW) ωt Turbine speed, (rad/s)

from the wind but maintaining a certain power margin inorder to participate in primary frequency control.

But maintaining a power margin is a major drawbackfrom the point of view of the operators of WPPs, as theyare losing revenues from not selling up to 10% of theavailable power that can be captured from wind in normaland continuous operation. In addition, the primary fre-quency support WPPs can provide, depends on the windspeed and the control techniques applied for regulatingthe power margin.

From the above mentioned considerations, it could beinteresting to the owner of a WPP to connect an energystorage system in the point of common coupling of thegenerating facility with the external grid. In this casethe wind turbines could be operated extracting the max-imum available power from the wind. The energy stor-age system would provide the required power reserves forthe participation of the WPP in primary frequency control

therefore. The economic viability of the project would bedetermined by a cost-benefit analysis considering the costof the storage system against the alternative of operatingthe wind turbines in a deloaded mode in a continuous ba-sis.

Of course, from the point of view of the network op-eration, the inclusion of an energy storage system in thepoint of connection of a generation facility could not bethe better allocation. The installation of the storage facil-ity near the network loads in order to reduce transmissionlosses could be preferable. However, it is also interest-ing to study the allocation of the storage system in thepoint of connection of a WPP for several reasons: i) Theexploitation of the high-ramp power rates and short timeresponses of an adequate storage technology could lead toa great system primary frequency support from the pointof common coupling of the wind facility to the grid; ii)To install a storage facility could help the WPP to fulfil

2

the gradually increasing requirements of the grid codesregarding the grid integration of renewable-based powerplants [1].

Several energy storage devices suitable for frequencycontrol - related tasks can be found. Among them,the literature considers the application of large scalestorage systems like pumped-hydro, compressed-air andhydrogen-based systems. Also, it is worth noting that bat-teries, flow batteries and those storage devices with veryhigh ramp power rates and short time responses like Su-perconducting Magnetic Energy Storage (SMES) and fly-wheels are specially well-suited for this application [1].Remarkable characteristics of flywheels are their veryhigh ramp power rates, high cyclability and energy effi-ciency (around 90% [10, 11]). On the other hand, stand-ing losses are non-negligible. In fact, self-discharge ratesare about 20% of the stored capacity per hour [12].

This work considers the inclusion of a flywheel-basedstorage plant in the point of common coupling (PCC) of aWPP with the external grid. The flywheels are consideredto be part of the WPP and provide part of the power re-serves indicated by the system operator to the WPP. Thisway, the WPP participates in primary frequency control.Wind turbines are required to operate to some extent in adeloaded mode depending on the level of power reservesof the flywheels, i.e. depending on their State of Charge(SoC). Thus, the required power reserves by the systemoperator to the wind facility can be computed by the sumof the power reserves of the flywheels and the power re-serves provided by the wind turbines. The latter can bededuced from the capability of the wind turbines to in-crease their generation level up to the maximum availablepower that can be extracted from the wind. Conceptually,the scope of the work responds to Figure 1.

Two contributions from the present work can bepointed out:

• The design of the central control system of the WPPand the local controllers of the wind turbines andthe flywheels. These control systems are in chargeof regulating the power reserves maintained by thewind turbines and the flywheels under network dis-turbances and also in normal operating conditions.In case of a network disturbance, i.e. of a systemfrequency deviation from its set-point, the power re-serves of the wind turbines and the flywheels are im-

Flywheel control

Variable speed windturbine modeling

Section II-B

Flywheel energy storagedevice modeling

Section II-CStartStop

Wind modelingSection II-A

Low-level control algorithmSection II-C

Tfw*

Torque reference computation algorithm

Section III-D

Inst. currents of PMSM

vw

P(W

)

P(W

)

Inst. voltages of PMSM

P(W

)

To external grid

Pwt

Pfw

Measurements

Control signals

Power flow

Wind emulation

ωfw

Flywheel storage

Power system

Control signals

Power flow

Central control system of the WPP

Fast local controller of the wind turbines

Distribution of the power reserve requirements between wind turbines and storage

Fast local controller of the storage

Total power reserves of WPP in steady state conditions required by the system operator

ΔPΔf

ΔPΔf

Hz

s

frequency disturbance

The fast local controllers ramp up and down the power output of the WPP for primary

frequency control support

Variable speed wind turbines

Wind Power Plant

Figure 1: Conceptual diagram of the scope of the work

mediately activated by their local controllers. Thisactivation though, is supervised by the central con-trol system of the WPP, and this is the main contri-bution of the article.

• The determination of the control method to allowthe wind turbines to maintain a certain power mar-gin from the maximum available power that can beextracted from the wind. This control method is in-cluded in the local controller of the wind turbines. Itis adopted and adapted from that presented in [13].This is intended as a minor contribution of the paper.

2. Proposed control schemes for the wind power plant

In regard of the main contributions of the article, thissection deals with the presentation of control techniquesfor enabling a wind turbine to operate maintaining apower margin from the maximum available power thatcan be extracted from the wind. Also, the proposed cen-tral control system of the WPP to manage the power re-serves of the wind turbines and the flywheels is detailed.

2.1. Deloaded operation of wind turbines

2.1.1. State of the artConventionally, wind turbines are operated at maxi-

mum aerodynamic efficiency to maximize power genera-tion. At partial-load region, the turbine speed is controlled

3

by the regulation of the aerodynamic torque, leading theso-called optimal torque (or power) - omega curve [14].Applying this approach, the optimal aerodynamic poweris computed as

P∗opt = KCp(β) · ω2t , (1)

where ωt is the turbine speed and KCp is the so-calledoptimal aerodynamic torque coefficient, which dependson the aerodynamics of the turbine and the pitch angleβ. This pitch angle is kept constant at partial load region,but at full-load region, it is continously regulated so as therated speed of the turbine is not overcome.

This control strategy cannot be applied for deratingwind turbines. Basically, there are two options for en-abling a wind turbine to maintain a certain level of powerreserves and thus to participate in frequency control-related tasks. These options are overspeeding and pitch-ing techniques of wind turbines for deloaded operation.Both are based on operating the wind turbines not extract-ing the maximum available power from wind. Overspeed-ing techniques are carried out applying the so-called de-loaded optimum torque (or power) - omega curves T − ω[15, 16, 17, 18, 19]. These curves impose operating pointsout of the optimum T −ω curve that allows extracting themaximum available power from the wind. The deloadedoptimum T − ω curves are defined up to the rated speedof the turbine as presented in Figure 2. As can be noted,following these operating curves, the rated speed of theturbine is reached for wind speeds much lower than nom-inal.

As an example, following the deloaded optimum T −ωcurve for the power margin x = 0.20 pu, the wind turbineachieves its rated rotational speed for wind speeds around7.5 m/s. Note that, at maximum efficiency, the rated windspeed for the turbine is around 10.1 m/s. Once the windturbine reaches its rated speed, combined regulations be-tween the electrical torque and the pitch angle are neededin order to maintain the desired power margin level. Oth-erwise the wind turbine would overcome its speed ratings.

In the literature different approaches to the configura-tion of the deloaded operating curves can be found. In[18], the implementation of a droop characteristic in thedeloaded T−ω, between 99% and 100% of the rated speedof the turbine is proposed. The end point of this line cor-responds to 100% of the rated speed of the turbine. At

0.5 1 1.5 20

2

4

6

8

10

12x 10

5

Rotor speed [rad/s]T

urbi

ne to

rque

[Nm

]

vw=10 m/s

vw=9.5 m/s

vw=9 m/s

vw=8.5 m/s

vw=8 m/s

vw=7.5 m/s

vw=7 m/s

x=0.01

x=0.20

minimum operatingrotor speed

rated rotor speed

optimum torque curve vw=10.5 m/s

Figure 2: Deloaded optimum T − ω curves for a DFIG-based wind tur-bine of 1.5MW of rated power for power margins up to 20%. Ratedwind speed 10.1 m/s

this point, the electrical torque reference is set as that ofmaintaining the desired power margin with respect to therated power of the turbine. This approach cannot ensurethe required power margin while operating at wind speedsbelow but near rated, i.e. while operating following thisdroop characteristic between 99% and 100% of the ratedspeed.

In the literature different approaches to the definitionof the deloaded operating curves can be found. In [13] astrategy to ensure the required power margin at all operat-ing ranges of a wind turbine is proposed. For wind speedsnear and above nominal, when the rated rotor speed isreached, a three dimensional look-up-table which inputsthe pitch angle and the required power margin is applied.The look-up-table provides the electrical power setpointof the wind turbine. For the computation of this three di-mensional look-up-table, and to the best of the knowledgeof the authors of the present work, the power margin is de-fined in this article from the ratio between the developedelectrical power and the rated power of the turbine.

In the present chapter, the power margin x (in pu) isdefined from the ratio between the generated electricalpower Poptdel and the maximum power that can be ex-tracted from the wind. Mathematically, this can be for-

4

mulated as

(1 − x) =

PoptdelPopt

if vw ≤ vwrated

PoptdelPrated

if vw > vwrated

(2)

2.1.2. Proposed control methodThe present article proposes an strategy for ensuring

the required power margin for the full operating range of awind turbine. Overspeeding techniques are implementedfor rotor speeds below the rated speed. In this operat-ing range, the wind turbine is governed by the deloadedT − ω curves of Figure 2. Pitch angle is zero in this oper-ating range. Once the rated speed of the turbine has beenreached, the electrical torque reference is determined by asecond look-up-table. As in [13], this look-up-table inputsthe pitch angle, which is regulated so that the rated ro-tor speed of the turbine is not overcome, and the requiredpower margin. As a difference with [13], the output of thelook up table is not the electrical power setpoint, but theelectrical torque reference to the generator. Moreover, thismagnitude is determined from the definition of the powermargin presented in (2).

The computation of this second look-up-table is pre-sented as follows. Given a power margin x, the wind tur-bine achieves its rated speed at a wind speed below ratedvwmin . From this wind speed on (up to the rated wind speedfor the wind turbine vwrated ), the required power marginis achieved with a proper combination of the pitch angleβ and the electrical torque. Mathematically, the comple-mentary of the power margin (1 − x) can be expressed as

Poptdel

Popt=

0.5ρAv3wCpdel (vw, ωtrated , β)

0.5ρAv3wCpopt (vw, ωtopt , 0)

=Cpdel (vw, ωtrated , β)Cpopt (vw, ωtopt , 0)

= (1 − x),(3)

where vwε[vwlim , vwrated ] and there is one minimum windspeed vwlim for each power margin x. Therefore, solvingthis equation for each wind speed vw and power margin x,the required pitch angle for each case can be calculated.Then, for each combination (vw, β), it is possible to findthe required deloaded optimum torque as

Toptdel =Poptdel

ωtrated

. (4)

0 0.5 1 1.5 2 2.5 33

4

5

6

7

8

9x 10

5

Pitch angle, [degrees]T

urbi

ne to

rque

[Nm

]

(max

,Topt

del

) for power margin x

x=0.01

x=0.20

x=0.03

x=0.02

Figure 3: Proposed torque curves depending on the pitch angle and thepower margin x

Applying this procedure, the torque curves of Figure 3 canbe drawn.

Note that for each power margin x, there is a pitch anglethat corresponds to the deloaded operating point at ratedwind speed, denoted as βmax. From this pitch angle on,the electrical torque for the required deloaded operationbecomes constant, as it is simply calculated as

Toptdel|β≥βmax=

Prated(1 − x)ωtrated

. (5)

The proposed strategy for the determination of thetorque reference at all operating ranges leads to the con-trol scheme for deloaded operation of the wind turbine ofFigure 4.

As presented, the control system inputs five signals:the frequency deviation ∆ f from its nominal value, thepower margin reference in steady state conditions x∗wt sd,the rated rotational speed of the turbine ωt rated, and themeasurement of the rotational speed of the turbine ωt andthe pitch angle β.

Given a frequency deviation ∆ f , the power / frequencydroop characteristic for the primary frequency controloutputs an increment or decrement in the desired powermargin of the wind turbine in per unit values ∆x. Then,this variation is added to the required steady state power

5

Pitch controller & actuator

ωt_rated

β

ΔfΔx

Steady state power margin

x*wt

ωt

T

ωPrimary control

droop

T*e

N

N

x*wt_sd

T

β

β

β>0 & ωt≥ωt_rated

-1/N

Steady state margin x*sd

1δs+1

0

f(x*wt,Pwt,ωfw)

Wind power plant Pwt

x*wt

x*wt_sd

Pcap+

Pcap-

xcap+

xcap-

Wind power plant control level

Local control system of wind turbines

Local control system of flywheels

ΔxΔf

ΔfΔxwt

Primary control droop

x*wt_sd-xcap-

-xcap+

Δx

0.2

0

Δf

Primary control droop

Δx

Δf X

Pcap+

xcap+

xcap+≠0

x*wt

Pcap+

xcap+

ΔxPcap+

Pcap-

Pcap+

Pcap-

(Figure 4)

T

ω

T

β P*fw

ωfw

P*fw

1/nfw

ωfw

T*fw

To low level control

algorithm of flywheel (ref

[21])

ωfw

Annotations

Measurement / input control signal

Output signal

* The measurement signal Pwt is obtained from the PCC of the wind power plant

dynamic dead zone

capacity of the flywheel plant to absorb and inject power

C’

C’

Machine side

converter

Grid side converter

EPMSM

Ext

ern

al G

rid

Grid Side Converter Controller

Machine Side Converter Controller

T*fw i*sdE* ild*

E

ilabcu*clαβ u*csαβ

isabc

Eθr

ulabc

Power computation

Eq (81)nfw

Equation of motionEq (80)

Power conv. model1

λ s + 1 External grid

x_

T*fw

Tloss

Tfw

ωfw

Pfw iqdfw

vqd

1δs+1

P*storageΔx

Δf

Pwt_max

Figure 4: Control scheme for deloaded operation of a variable speedwind turbine for its participation in primary frequency control

margin x∗wt sd, given the total power margin reference x∗wt.The steady state power margin reference refers to thepower margin to be maintained in normal operating condi-tions of the grid, i.e. in case of having a steady frequencylevel of 50 or 60 Hz, depending on the network. This con-trol signal can be provided by the network operator.

Considering that the rotational speed of the wind tur-bine is lower than the rated, the electrical torque refer-ence T ∗e is obtained accessing to the T − ω curve (Figure2). This torque reference is sent to the low level controlalgorithm of the rotor-side power converter of the windturbine, i.e. the inner current control loop for the con-verter.

Once the rated speed of the wind turbine is reached, theregulation of the pitch angle comes into play. A conven-tional speed controller drives the pitch actuator. This waythe speed of the turbine is not exceeded. In this operatingrange, the torque reference for the generator is obtainedaccessing to the T − β curves of Figure 3. It is worth not-ing that the electrical torque reference varies according tothe slow dynamics of the pitch controller in this operatingrange.

The pitch control system includes a PI controller. Thetuning of this lineal controller has been carried out so thatno greater gradients than ±10 degrees per second in thepitch angle are reached. Also, the controller leads a sec-ond order type temporal response on a step-profiled ref-erence, with a damping around 0.6-0.7. The maximumpitch angle is limited to 30 degrees.

2.2. Management of the power reserves of the wind tur-bines and the flywheels for frequency control support

The central control system of the WPP determines thepower reserves that the wind turbines have to provide insteady state conditions, i.e. while experiencing an steadynetwork frequency of 50 or 60 Hz, depending on the net-work, and taking into account the power reserves that theflywheels are capable of providing. Since a part of the to-tal power reserves required to the overall power plant isprovided by the flywheels, the need of deloading the windturbines so that they can maintain a certain power marginfrom the maximum available power they can extract fromthe wind is alleviating. In fact, the regulation of the powermargin of the wind turbines is carried out just to handlethe power margin that the storage facility cannot satisfy.The central control system does not govern the rampingup and down of the power of the wind turbines and theflywheels in the event of a frequency deviation. The fastlocal controllers of these elements are responsible of do-ing that instead.

The central control scheme of the overall power plantis presented in Figure 5, where it is also depicted the localcontrol system of the flywheels and the wind turbines.

As can be noted, the central control system of the WPPreceives four input signals: the steady state power mar-gin reference for the WPP (considering the wind turbinesand the flywheels) x∗sd, which is provided by the networkoperator; the total power margin reference for the windturbines x∗wt; the power output of the wind turbines at thepoint of common coupling of the WPP with the networkPwt; the rotational speed of the flywheels ω f w; and theelectrical frequency of the network fe. It is consideredthat all flywheel units rotate at the same speed as they re-ceive the same control references.

From these inputs, the central controller provides fiveoutput signals: the steady state power margin referencefor the wind turbines x∗wt sd, as well as the signals Pcap+,Pcap−, xcap+ and xcap−. These four output signals areneeded to inform the local controllers of the wind turbinesabout the power margin that the flywheels can handle andthus, to limit their fast power output ramping up and downin the event of a frequency deviation.

The action of the central control system of the WPPshould be so that it does not counteract with the fast con-trol actions of the local controllers. Fast control actions of

6

Pitch controller & actuator

ωt_rated

β

∆f∆x

Steady state power margin

x*wt

ωt

T

ωPrimary control

droop

T*e

N

N

x*wt_sd

T

β

β

β>0 & ωt≥ωt_rated

-1/N

Steady state margin x*sd

1δs+1

0

f(x*wt,Pwt,ωfw)

Wind power plant

Pwt

x*wt

x*wt_sd

Pcap-

Pcap+

xcap-

xcap+

Wind power plant control level

Local control system of wind turbines

Local control system of flywheels

∆x∆f

∆f∆xwt

Primary control droop

x*wt_sd-xcap-

-xcap+

∆x

0.2

0

∆f

Primary control droop

∆x

∆f X

Pcap+

xcap+

xcap+≠0

x*wt

Pcap+

xcap+

∆xPcap+

Pcap-

Pcap+

Pcap-

(Figure 4)

T

ω

T

β P*fw

ωfw

P*fw

1/nfw

ωfw

T*fw

To low level control

algorithm of flywheel (ref

[21])

ωfw

Annotations

Measurement / input control signal

Output signal

* The measurement signal Pwt is obtained from the PCC of the wind power plant

dynamic dead zone

capacity of the flywheel plant to absorb and inject power

C’

C’

Machine side

converter

Grid side converter

EPMSM

Ext

ern

al G

rid

Grid Side Converter Controller

Machine Side Converter Controller

T*fw i*sdE* ild*

E

ilabcu*clαβ u*csαβ

isabc

Eθr

ulabc

Power computation

Eq (81)nfw

Equation of motionEq (80)

Power conv. model1

λ s + 1 External grid

x_

T*fw

Tloss

Tfw

ωfw

Pfw iqdfw

vqd

1δs+1

P*storage∆x

∆f

Pwt_max

fe

Figure 5: Central control system and local controllers of the wind turbines and the flywheels

the central control system may affect the stability of theWPP as they would compete with the fast actuation of thelocal controllers of the flywheels and wind turbines. Forthat reason, the outputs of the central control system areaffected by a first order type filter with a time constant ofδ =5 seconds. This time constant is chosen taking into ac-count that the time constant of the pitch actuator is in theorder of 2 seconds, and the time constant of the responseof the storage units are in the order of milliseconds.

Following contents detail the processes carried out bythe central control system to provide the previously men-tioned output signals.

As it can be noted in Figure 5, the input signalsPwt, x∗wt, ω f w and fe serve to compute the functionf (Pwt, x∗wt, ω f w, fe). This function determines the capacityof the flywheels to continuously inject or absorb powerfor up to 30 minutes. This is the period of time indicatedin the ENTSO-E’s recommendations [4] for the definitionof the processes involving primary frequency control inthe event of a frequency deviation.

The power (in MW) that the flywheels can continuouslyabsorb for up to 30 minutes is denoted as Pcap−. The ex-pression of this value in per unit of the maximum avail-able power that the wind turbines can capture from windis denoted as xcap−. Similarly, the power (in MW) that the

flywheels can inject continuously for up to 30 minutes isnamed Pcap+, and in per unit xcap+. The signals Pcap+ andPcap− are computed as

Pcap+ =n f w

2

J f w(ω2f w − ω

2min) − Tloss(ω f w − ωmin)∆t( fe)

∆t( fe)

,(6)

Pcap− =n f w

2

J f w(ω2f w − ω

2max) − Tloss(ω f w − ωmax)∆t( fe)

∆t( fe)

,(7)

where J f w is the inertia of a flywheel unit in kgm2, ω f w

is the speed in rad/s, ωmin and ωmax are the operating lim-its, Tloss is the torque losses (which is almost constant forhigh-tech flywheels), n f w is the number of flywheel unitsof the storage plant and ∆t( fe) is the time in seconds thatthe flywheels would be required to inject or absorb powercontinuously. This value is 30 minutes in normal operat-ing conditions, but it also represents the remaining timethat the flywheels must exchange power from the event ofa system frequency deviation, so that is why this is ex-pressed as a function of the input signal fe, the electricalfrequency of the network.

To compute xcap+ and xcap−, it is necessary to esti-mate the maximum power that wind turbines, as a global,could capture from wind at maximum efficiency, Pwt max

7

(in MW). This is carried out from the measurement of thepower generated by the wind turbines at the point of com-mon coupling of the WPP with the external grid and theirtotal power margin reference x∗wt,

Pwt max =Pwt + Plosswt

1 − x∗wt. (8)

To compute Pwt max, it is necessary to estimate the elec-trical power losses in the internal grid of the WPP (i.e,cables, power transformers, etc.) that transfers the powerof the wind turbines to the point of common coupling withthe external network. The power losses are represented bythe magnitude Plosswt . It is assumed, as an approximation,that its value is a percentage of the power measured in thepoint of common coupling with the external grid, e.g. ofabout 3%.

The ratio between Pcap+ and Pwt max leads xcap+,

xcap+ =Pcap+

Pwt max. (9)

Analogously,

xcap− =Pcap−

Pwt max. (10)

The subtraction between the steady state power marginreference of the WPP x∗sd and the power margin that theflywheels can handle xcap+ is the power margin that thewind turbines have to provide in steady state,

x∗wt sd = x∗sd − xcap+. (11)

It is important to note that x∗wt sd is bounded to 0% for con-sistency. Negative values of x∗wt sd would not have sense.

As previously noted, the outputs of the central controlsystem Pcap+, xcap+, Pcap− and xcap− are used by the localcontrollers of the wind turbines and the flywheels to limitthe ramping up and down of the power injected into thegrid by these elements in the event of a frequency devi-ation (Figure 5). The local controllers are equipped witha primary control droop which translates the detected fre-quency deviation to a certain decrement (or increment) inthe total power margin reference.

Considering a frequency deviation, the WPP is requiredto ramp up or down its power injection into the grid in-crementing or decrementing the total power margin ∆x.From the point of view of the flywheels, this means to ab-sorb or inject power respectively. In any case, the fraction

of the total power margin increment or decrement (ex-pressed in MW) set by the primary control droop that theflywheels can handle is

P∗storage = ∆xPcap+

xcap+

= ∆xPcap−

xcap−= ∆x · Pwt max. (12)

As shown in Figure 5, P∗storage is bounded by the power ca-pacity of the flywheels Pcap+ and Pcap−. Then, the torquereference of each flywheel unit is computed by divid-ing the above-computed power reference by the rotatingspeed ω f w and the number of flywheel units n f w.

In the event of a frequency deviation, the primary con-trol droop of the local control system of the wind turbinesoutput the power margin increment ∆x, as the local con-trol system of the storage facility does. However, the lo-cal control systems of the wind turbines apply a dynamicdead zone to the signal ∆x, in which the limits of the deadzone are xcap+ and xcap−. This block outputs zero for in-puts within the dead zone. Also, it offsets inputs signalsby either the negative or positive limits of the dead zonewhen outside of it. The output of this dynamic dead zoneis the actual power margin increment required to the windturbines ∆xwt. For instance, for an input ∆x = 0.07, and−xcap− = 0.05, ∆xwt results ∆xwt = 0.07 − 0.05 = 0.02.By applying this strategy, the regulation of the power mar-gin of the wind turbines comes into play just to handle thepower margin increment that the storage facility cannotsatisfy.

Once the power margin increment of the wind turbinesis obtained, it is added to the steady state power marginset by the central control system of the WPP. The obtainedpower margin set point x∗wt is then transmitted to the de-loaded optimum torque omega curves of the wind turbines(see Figure 5) in order to develop the adequate electricaltorque to fulfill the power margin requirements.

3. Simulation results

This section evaluates the performance of the previ-ously proposed control systems for wind turbines and fora WPP equipped with energy storage devices for enablingtheir participation in primary frequency control. Firstly,the network topology is presented. Secondly, simulationresults regarding the regulation of the deloading level of

8

wind turbines are presented. Finally, the proposed strat-egy for the coordinated regulation of the power reservesof the wind turbines and the flywheels is evaluated.

3.1. Network topology and configurationIn order to analyse the effect of the active power reg-

ulation of wind facilities for primary frequency control,a simple power system is proposed. Figure 6 shows thenetwork topology. The network comprises a non-reheatsteam turbine-based conventional power plant, a WPP anda load. The WPP is equipped with a flywheel-based stor-age facility.

The model of the conventional generating unit includesa third order type model of a synchronous generator, cou-pled to a non-reheat steam turbine. The electrical modelof the generator is detailed extensively in [20], while themodel of the steam turbine is explained in [21]. Thepower generation of the steam turbine is governed by aprimary controller as detailed also in [21].

The model of the DFIG-based wind turbines includingthe electrical and mechanical models, as well as the lowlevel control algorithms of the power converters are fullyexplained in [22].

Regarding the storage plant, it is worth noting that fly-wheels are commonly made up of a permanent magnetsynchronous machine, mechanically coupled to a rotat-ing disk. The power exchange with the external gridis through a set of back-to-back power converters. Themodel of the flywheel unit as well as the low level controlalgorithm of its power converters can be found in [23].

The present work considers a storage plant comprisedby several flywheel units in parallel so that it can achievethe required power and energy capacity for participatingin primary frequency control. High-speed flywheels com-monly regulate hundreds of kilowatts for a few minutes.Therefore, it is needed to dispose several flywheels to reg-ulate tens of megawatts for up to 30 minutes.

According to the Irish network operators EirGrid andSoni, on their publication “All Island TSO Facilitation ofRenewables Studies” [24], the Irish network has set thehighest binding electricity target in the EU from renew-able sources by 2020. In particular, 40% of electricity tocome from renewables has been accorded. Some of theassumptions made in this study from the Irish networkoperators will be used in the current work for defining arealistic network with high penetration of wind power.

In the above mentioned work [24], the so-called “op-erational metric 1” has been defined. This magnitude de-fines the ratio of wind generation plus import and systemload plus export. It is intended as the “inertialess penetra-tion”. Upper levels of this ratio than 60-80% are intendedto be only technically viable with major adaptations of thepower system. These adaptations refer, among others, tothe threshold levels of the rate of change of frequency forthe relays at distribution level of more than the actual levelof ±0.6Hz/s.

Considering an “inertialess penetration” of 50%, theexpected ratio between the synchronized kinetic energyof the system Ek (in MWs) and the load level Pload (inMW) is around 6 seconds, and this is, therefore, the iner-tia constant of the conventional synchronized generation.For a Pload = 1000 MW, the installed capacity of windfacilities becomes Pwpp=50%·Pload=500 MW.

Finally, the largest severity of the power imbalance inthe network model has to be determined for the analysisperformed in the present study. For doing that, and ac-cording to [24], the so-called “operational metric 2” is de-fined. This magnitude is the ratio of kinetic energy storedin conventional generators plus load and the largest sever-ity of the power imbalance. This ratio can be intendedas an indicator of frequency stability. Stable operation ofthe 2020 scenario in the Irish network is considered withan “operational metric 2” greater than 20-30 MWs/MW.Considering that the kinetic energy stored in conventionalgenerators is Ek = 1000MW·6s = 6000MWs, the largestseverity of power imbalance is Pimb = 6000MWs

30MWs/MW =

200MW.The flywheel-based storage system is sized so that it

has twice the power and energy capacity of a storage plantthe manufacturer of flywheels Beacon Power has commis-sioned for frequency regulation [25]. This system is ableto continuously regulate 20 MW for 15 minutes at fullload, extending its operation for lesser loads. The storageplant proposed in the present work is composed by 400flywheel small units. Each unit can continuously regulate100 kW for 15 minutes. Operated at partial load, one cancome up with a storage plant that can continuously reg-ulate 20 MW for 30 minutes. All units are connected inparallel, as in the above mentioned commercial solution.A summary of the parameters for the network configura-tion is presented in Table 1.

The characteristic parameters of the particular model

9

Win

d p

ow

er

pla n

t

Rotor side converter controller

High level control

Pitch controller Pitch actuator

Doubly-fed generator’s model

vqds

ψqds

v'qdr

ωe

Aerodynamics + Drive train

Cp(λ,β)Eq’s. (49)-(51)

T’t (Cp,vw)Eq. (48)

ωm

vw

T’t

Tg

P/2

ωr

ωt

Flux linkagesEq’s. (56)-(62)

Electrical currents

Eq’s. (63)-(66)

ψ'qdr

ψqdm i'qdr

iqds

Electrical torque Eq. (45)

-1

DFIG

Grid side conv.

Rotor side conv.

Grid side converter controller

Q*l E*

Rotor side converter controller

ωm

Q*s

GB

High level controlβ*

ωr

iabcr

iabcs

vabcs

v*qdr

Grid

measurements

control signals

T*g

ωmPI

controllerωm_rated

βmax

βmin

1

Tpitch·s +1β

E

vabcl

iabcl

E

ωr

iqdr

Stator flux linkages

Eq’s (41)-(42)

iqds ψqds Stator flux linkages’ angleEq’s (71)-(72)

Orientation of qd magnitudes Eq’s (73)-(76)

θψs Current references

Eq’s (67)-(68)

PI

1

i*qdrc

iqdrc

Decoupling terms

Eq’s (69)-(70)

1

v*qdrc

MPT algorithmEq. (79) (for

partial load op.)

T*g

Q*s

Pitch actuator & control

ωm

ωm

β

vqdrc

Orientation of qd magnitudes Eq’s (77)-(78)

v*qdr

current saturation

voltage

saturation

Rotor side conv.

iqdsc

Drive trainEq’s.(46)-(47)

rs jx’d

I1

E1

r13 jx13

V3

Load

Synchr. Gen of thermal unit

1

3

r23 jx23

I2V2

2 rt13+jxt13rt23b+jxt23brt23a+jxt23a

Aggregated model of a DFIG-based wind

turbines

line 2-3 line 1-3

Flywheel storage

Ifw

Iwt

Figure 6: Network topology. The wind power plant is equipped with a flywheel-based storage system

Table 1: Parameters for the study caseParameter Value UnitsRated power of conventional generation 1000 MVAPrimary control droop of conv. genera-tion R

0.05 pu

Inertia constant of conventional genera-tion H

6.0 s

Largest power imbalance in the network 200.0 MVARated power of WPP 500.0 MVAPrimary control droop of WPP Rwpp 0.1 puLimits of ∆x of primary control of WPP 0.1 puSteady state power margin of WPP x∗sd 0.1 puRatings of flywheel-based storage plant 20-30 MW-

min

Number of flywheel units n f w 400 puMaximum power consumption of theload

1200 MVA

of each component of the system are presented in the Ap-pendix.

3.2. Regulation of the deloading level of wind turbinesThe following paragraphs evaluate the performance of

the proposed control scheme for governing the deloadedlevel of the wind turbines (Section 2.1). Three differentscenarios have been proposed: i) the wind speed is low,much lower than the rated level for the wind turbine, andtherefore the pitch angle is zero at all times; ii) the windspeed is higher than in the previous case, but still lowerthan the rated wind speed level for the wind turbine. Thepitch angle could be different from zero depending on therequired power margin; iii) the wind speed is very high,higher than the rated wind speed of the wind turbine, and anon-minimum pitch angle is therefore required regardlessthe required power margin.

In the first scenario, the desired power margin of thewind turbine x∗wt can be achieved just overspeeding thewind turbine. Figure 7 plots the response of the turbine ona power margin increment from x∗wt = 0.10 to x∗wt = 0.15in just 0.4 seconds. This increment could be representa-tive of the power margin variation required in responseof the largest severity of power imbalance in the network(200 MW) as defined in Section 3.1. The wind speed ismaintained constant at 7.5 m/s.

As shown, since the wind speed is low, the rated ro-tor speed is not achieved even while derating the tur-bine. Therefore, the pitch angle is zero at all times and

10

35 40 45 50 55 608

10

12

14

16

Mar

gin

[%]

35 40 45 50 55 604.5

5

5.5

6

6.5x 10

5

Pow

er [W

]

35 40 45 50 55 603000

3200

3400

3600

Tor

que

[Nm

]

Elect. torqueMech. torque

35 40 45 50 55 60500

1000

1500

2000R

otor

cur

rent

mod

ule

[A]

35 40 45 50 55 601.5

1.6

1.7

1.8

Time [s]

Tur

bine

spe

ed [r

ad/s

]

35 40 45 50 55 60-1

-0.5

0

0.5

1

Time [s]

Pitc

h an

gle

[deg

]

10%15%

with margin 0%

rotor current maximum module

rated turbine speed

Figure 7: Performance evaluation of the proposed control system for de-loaded operation. The power margin reference x∗wt is incremented from0.10 to 0.15 pu. The wind turbine is subjected to a low wind speed of7.5 m/s

the torque reference is obtained from the deloaded T − ωcurves of Figure 2.

Figure 8 plots the response of the turbine on the samepower margin increment. The wind speed is maintainedconstant at 8.5 m/s.

The wind speed is lower than the rated wind speed forthe turbine (10.1 m/s). However, the rated rotor speedof the turbine is achieved for a power margin x∗wt of 0.15pu. From this point on the pitch angle is not zero andthe torque reference is obtained from the second look-up-table (see Figure 3), which inputs the pitch angle and therequired power margin. It is worth noting that the tur-bine speed is maintained within its operating limits dueto the combined regulations of the electrical torque andthe pitch angle. The temporal response of the speed ofthe turbine presents just a little overshot between 40 and41 seconds. The peak value of the rotor speed during thisovershot overpasses in just 0.4% the rated rotor speed.

The primary frequency control support that the windturbines can provide is evaluated in Figure 9. Neither theflywheels, nor other control schemes apart from the con-trol scheme for deloading the wind turbines (Figure 4) isapplied.

A step increase in the load of 200 MW is applied to

35 40 45 50 55 608

10

12

14

16

Mar

gin

[%]

35 40 45 50 55 607

8

9

10x 10

5

Pow

er [W

]

35 40 45 50 55 60

4000

4200

4400

4600

Tor

que

[Nm

]

Elect. torqueMech. torque

35 40 45 50 55 60500

1000

1500

2000

Rot

or c

urre

nt m

odul

e [A

]

35 40 45 50 55 601.73

1.735

1.74

1.745

1.75

Time [s]

Tur

bine

spe

ed [r

ad/s

]

35 40 45 50 55 60-0.2

0

0.2

0.4

0.6

Time [s]

Pitc

h an

gle

[deg

]

10%

with margin 0%

rotor current maximum module

rated turbine speed

15%

Figure 8: Performance evaluation of the proposed control system for de-loaded operation. The power margin reference x∗wt is incremented from0.10 to 0.15 pu. The wind turbine is subjected to a low wind speed of8.5 m/s

45 47 49 51 53 55 57 59 61 63 65

49.5

49.6

49.7

49.8

49.9

50

50.1

Time [s]

Fre

quen

cy [H

z]

v

w=7.5 m/s

vw

=8.5 m/s

vw

= 11 m/s

no frequency control support by WPP

Figure 9: Network frequency excursion due to a sudden change in theload level of 200 MW. Wind turbines participate in primary frequencycontrol under different load conditions. The flywheels are not involved

11

the system, which provokes a network frequency distur-bance. As can be noted, the maximum rate of change offrequency (registered at the beginning of the disturbance)is the same in all cases as the synchronized inertia of thesystem does not vary. Considering wind speeds below therated (7.5 m/s and 8.5 m/s), both the frequency nadir andthe steady state level of the frequency after the disturbanceare improved with the participation of wind turbines inprimary frequency support. In this region, the regulationof the power margin maintained by the wind turbines ismainly carried out by overspeeding the turbines. As pre-viously noted in Figure 7 and Figure 8 this regulation isvery fast and also implies the exchange of kinetic energyof the rotor of the turbines with the network. These as-pects favours the provided primary frequency support tothe network.

Considering wind speeds above rated (blue line in Fig-ure 9), the power regulation of the wind turbines is influ-enced by the dynamics of the pitch control. These dynam-ics are much slower than those involved in overspeedingtechniques. Also, since the rotational speed of the tur-bines is kept constant, there is no kinetic energy of therotor of the turbines exchanged with the network. Theseaspects lead a lower frequency nadir than applying over-speeding techniques. On the other hand, since a varia-tion in the power margin reference of the turbines ∆x im-plies the regulation of high power, the new steady statefrequency level achieved after the network disturbance ismuch higher than in the case of considering low windspeed levels.

3.3. Coordinated activation of the power reserves of thewind turbines and the flywheels under a network dis-turbance

The following set of simulations concerns the coordi-nated regulation of the power margin developed by thecomponents within the WPP, i.e. the wind turbines and theflywheels, so that it can fulfil the power margin require-ments set by the network operator in steady state condi-tions and also during a network disturbance.

This coordinated regulation of the power margin de-veloped by the components of the WPP is carried out bythe central control system of the WPP and the local con-trollers of the wind turbines and the flywheels (Figure 5).

In order to evaluate the performance of the proposedcontrol systems under different load conditions of the

wind turbines, two wind speed levels have been consid-ered. Firstly, a wind speed level low enough to permit thewind turbines to fulfil their power margin reference x∗wtby just applying overspeeding techniques is considered.Secondly, a wind speed level above the rated so the re-quired power margin of the wind turbines is governed bytheir pitch control is applied. Additionally, a third analy-sis concerning variable wind speed is included, in order toevaluate the performance of the controllers under realisticoperating conditions.

3.3.1. Low wind speed levelAs in the previous simulations, a sudden power imbal-

ance in the network which the generating units of the sys-tem (both the conventional generating unit and the WPP)have to compensate through their primary frequency con-trollers is considered.

Figure 10 plots the total power margin developed bythe WPP. As a reminder, the total power margin for theWPP is determined from the sum of the steady state powermargin reference for the WPP x∗sd and the power marginincrement or decrement set by the primary control droop∆x. As can be noted in Figure 10, at time 60 secondsa sudden system load increase is considered. This pro-vokes the system frequency to drop to a level below 50Hz, and therefore the WPP is required to reduce the de-veloped power margin, i.e. to increase its power injectionto the grid. The steady state power margin reference forthe WPP is set to x∗sd = 0.10 with respect to the maximumavailable power that could be extracted from wind.

The required power margin is provided by the powerreserves of the wind turbines and the energy stored inthe flywheels. The variation of the power margin of thewind turbines is carried out as soon as the primary controldroop of the local controllers of the wind turbines out-put an increment or decrement power margin variation ∆xgreater than the power margin the storage facility can han-dle. This can be appreciated in Figure 11.

As can be observed, the developed power margin by thewind turbines previous to the network disturbance is aboutxwt = 0.034 pu. The total power margin required by thesystem operator is x∗sd = 0.10 pu. Thus, the storage facil-ity, which State of Charge (SoC) is 100%, is in charge ofhandling a power margin x f w = 0.10 − 0.034 = 0.066 pu.The network disturbance provokes that the primary con-trol droops of the local controllers of the flywheels and the

12

55 57.5 60 62.5 65 67.5 70 72.5 75-6

-4

-2

0

2

4

6

8

10

12

Time [s]

Pow

er m

argi

n [%

]

Reference xsd* + x

Actual power margin

Figure 10: Power margin developed by the wind power plant. At timet=60 seconds there is a sudden increase of the system load level. Thewind turbines are exposed to a wind speed of 8.5 m/s

55 57.5 60 62.5 65 67.5 70 72.5 75-8

-6

-4

-2

0

2

4

6

8

10

12

Time [s]

Pow

er m

argi

n [%

]

WPP power margin reference x*sd

+x

Power margin ref. for WTs (steady state) x*wt_sd

Actual power margin of WTs

Power marginmaintained by the

wind turbines

Power marginmaintained by the

flywheels

The power margin of the wind turbines arevaried as soon as overtaking the x theflywheels can handle

Figure 11: Power margin developed by the wind power plant. Detail ofthe power margin developed by the wind turbines and the flywheels. At60 seconds simulation time there is a network disturbance. The windturbines are exposed to a wind speed of 8.5 m/s

wind turbines output a decrement in the developed powermargin ∆x. Then, the total power margin reference forthe WPP becomes x∗sd + ∆x. The regulation of the powerreserves of the wind turbines is carried out as soon as thefrequency deviation requires a decrement in the developedpower margin greater than the maximum power marginthe storage facility can handle xcap+.

As presented in Figure 11, the actual power margindeveloped by wind turbines does not follow the powermargin reference x∗sd + ∆x during the transient state pro-voked by the network disturbance, until achieving the newsteady state. This is due to the fact that since the op-erating points of the wind turbines require applying justoverspeeding techniques, there is kinetic energy releasedto the network from the speed regulation of the wind tur-bines. This surplus of energy released during the tran-sient state complements the primary frequency supportprovided by the WPP.

To evaluate the provided frequency control support,Figure 12 plots the frequency excursion of the network.The red line plots the case of no frequency control sup-port by the WPP. Only conventional synchronized gener-ating units are in charge of developing this task therefore.With the participation of the WPP (the flywheels are fullycharged), the obtained frequency profile is depicted by theblue line. As can be noted, higher frequency nadir andalso higher frequency level at the new steady state afterthe disturbance can be obtained in this case.

As can be observed in Figure 12, the contribution of theWPP in primary frequency control depends on the SoC ofthe flywheels. Considering the flywheels discharged, i.e.leaving the wind turbines alone for carrying out the task,it can be obtained a higher frequency nadir than in thecase the flywheels are also participating. This is due tothe fact that in this case, the power margin of the windturbines is regulated by just applying overspeeding tech-niques. Thus, some kinetic energy of the rotor of the tur-bines is exchanged with the network from the variation oftheir rotational speeds. As previously noted in the article,this surplus of energy injected to the grid improves theperformance of the provided primary frequency support.Therefore, if the flywheels are discharged, the wind tur-bines have to satisfy the net variation of the power marginrequirements, and then they are speeded down in a higherextent than in the case the required power margin decre-ment is satisfied also by the flywheels, leading a higher

13

55 57.5 60 62.5 65 67.5 70 72.5 75

49.5

49.6

49.7

49.8

49.9

50

50.1

Time [s]

Fre

quen

cy [H

z]

freq. support by wind turbines + storagefreq. support by wind turbinesno freq. support by wind power plant

Figure 12: Frequency deviation caused by a sudden load increase. Redline plots the case of no frequency support by the wind power plant.Blue line shows the obtained performance from the support of the windpower plant (wind turbines and flywheels). Green line presents the ob-tained result considering the flywheels discharged. The wind turbinesare exposed to a wind speed of 8.5 m/s

kinetic energy exchanged with the network.

3.3.2. Wind speed above ratedThis section deals with the evaluation of the perfor-

mance of the proposed controllers for the WPP whilehaving wind speeds above the rated wind speed of thewind turbines. The wind speed level is set to 11 m/s (therated wind speed is 10.1 m/s) and the flywheels are fullycharged. Figure 13 plots the power margin developed bythe WPP while having a network disturbance.

As can be noted in Figure 13, the developed power mar-gin by the WPP follows the reference x∗sd + ∆x to a largedegree. From a certain point the developed power mar-gin is transiently different from the reference level. At thebeginning of the frequency deviation, the flywheel stor-age activates very fast its power reserves, so the developedpower margin matches with the reference. This occurs un-til the regulation of the power margin of the wind turbinescomes into play. Since the regulation of the power marginof the wind turbines depends, in this case, on the slow dy-namics of their pitch actuator, the regulation of the powermargin is not fast enough to follow the reference duringthe transient state.

55 57.5 60 62.5 65 67.5 70 72.5 750

2

4

6

8

10

12

Time [s]

Pow

er m

argi

n [%

]

Reference xsd* + x

Actual power margin

Figure 13: Actual power margin developed by the wind power plant andits reference value x∗sd + ∆x. The wind speed is 11 m/s

The dynamics of the pitch actuator of a wind turbineare shown in Figure 14 (bottom left corner). Figure 14also plots the speed and torque of the turbine. As shownthe turbine speed is varied in a very little extent. More-over, the speed of a flywheel is presented in the top leftcorner. As shown, the flywheel starts injecting power intothe grid as soon as detecting the frequency variation dueto the network disturbance. As a result, its SoC, i.e. its ro-tational speed becomes continuously reduced. However,it is important to note that there are no fast changes in thespeed of the flywheel, which favours the slow dynamics ofthe control signals xcap+, xcap−, Pcap+ and Pcap−. Finally,it is worth noting the continuous (but slowly) dischargingof the flywheel prior to the network disturbance. This isdue to the standing losses of the storage device. An strat-egy for maintaining a particular SoC of the flywheels insteady state conditions is required for ensuring the opti-mal operation of the storage devices. The determinationof this optimal SoC depends on the cost associated to thelosses of the flywheels among other aspects. This definesan optimization problem which is out of the scope of thearticle.

Figure 15 plots the frequency excursion due to the net-work disturbance at 60 seconds simulation time. The redline plots the case of no frequency control support by theWPP. Only conventional generating units are in charge of

14

55 60 65 70 751669

1670

1671

1672

1673

1674

1675

Fly

whe

el s

peed

[rad

/s]

55 60 65 70 751.74

1.741

1.742

1.743

1.744

1.745

1.746

1.747

Tur

bine

spe

ed [r

ad/s

]

55 60 65 70 753.6

3.8

4

4.2

4.4

4.6

Time [s]

Pitc

h an

gle

[deg

]

55 60 65 70 757700

7800

7900

8000

8100

8200

8300

Time [s]

Tor

que

[Nm

]

Mech. torqueElect. torque

Figure 14: Flywheel speed before and after detecting the network dis-turbance at time 60 seconds. Also, it is shown the speed, the pitch angleand the mechanical and electrical torque developed by wind turbines.The wind turbines are exposed to a wind speed of 11 m/s

this task in this case. With the participation in primaryfrequency control of the WPP (the flywheels are charged)the obtained frequency excursion is depicted by the blueline. As can be noted, the contribution of the wind tur-bines and the flywheels improve the obtained frequencynadir and also the new steady state after the disturbance.

Figure 15 also plots the case of considering the fly-wheels discharged. The primary frequency control sup-port the wind turbines can provide in this case (theirpower margin is affected by the dynamics of the pitch ac-tuator) is as good as the support provided by the WPPwhen considering the fast actuation of the flywheels. Thisis due to the fact that despite the flywheels responds inthe range of milliseconds to a power request, its powerinjection is governed by the slow dynamics imposed bythe output of the primary control droop of its local controlsystem, i.e. the slow dynamics of the frequency excur-sion.

From the analysis performed in this Section 3.3, it isworth to remark that the main advantage of including theflywheels in the WPP is the reduction of the power mar-gin that the wind turbines have to maintain during net-work disturbances and also in steady state conditions. Inthis regard, Table 2 depicts the assignment of the requiredpower reserve to the WPP between the flywheels and the

55 57.5 60 62.5 65 67.5 70 72.5 75

49.5

49.6

49.7

49.8

49.9

50

50.1

Time [s]

Fre

quen

cy [H

z]

freq. support by wind turbinesno freq. support by wind power plantfreq. support by wind turbines + storage

Figure 15: Frequency deviation caused network disturbance. Red lineplots the case of no frequency support by the wind power plant. Blueline shows the obtained performance from the contribution of the windpower plant (wind turbines and flywheels). Green line presents the resultconsidering the flywheels discharged. The wind turbines are exposed toa wind speed of 11 m/s

wind turbines. As it can be noted, the flywheels, whilebeing fully charged, are capable of providing up to thenet level of power reserves of the WPP depending on thewind speed, enabling the wind turbines to operate at max-imum efficiency in a continuous basis (as for 7.0 m/s windspeed).

3.3.3. Variable wind speedPrevious sections, by considering constant wind speed

for the WPP, permitted to clearly evaluate how the de-signed control system works, while also serving as illus-trative examples for the understanding of magnitudes suchas the previously presented power margin. This sectiongoes a step forward and shows the performance of thedesigned control system under realistic wind speed con-ditions. For the sake of completeness, the electrical loadinstalled at bus 3 (see Figure 6) also presents a time vary-ing demand profile, noticeably disrupting the constancyof the electrical frequency of the network.

The adopted wind model is explained and utilised inprevious work of the authors of the present article [28].This model is adopted here to represent the wind speedthe WPP is exposed to. It comprises a quasi-constant av-

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Table 2: Power reserve allocation between wind turbines and flywheels(fully charged)

Wind speed (m/s)7.0 8.0 9.0 10.0 11.0Required reserve to the WPP in (MW)16.7 25.3 35.9 49.2 50.7

Power reserve allocationW. turbines (MW) 0.0 5.3 15.9 29.3 30.7Flywheels (MW) 20.0 20.0 20.0 20.0 20.0Flywheels share(%)

120.0 79.3 55.7 40.7 39.5

erage component (in the range of minutes) and a vary-ing wind speed component, which depends on determin-istic (wind shear, tower shadow, the presence of obsta-cles) and stochastic factors (wind turbulence). This modelcorresponds to the so-called ”Effective wind model” anddetailed explanations can be found in [29]. The quasi-constant average component of the wind corresponds to avarying average trend (in the range of minutes) that hasbeen extracted from the NREL’s online database for windspeeds [30]. In regard of the load demand, it is variedperiodically in incremental and decremental steps of 200MW so as to provoke, as a consequence of the inducedtransient power unbalance in the network, the electricalfrequency to go under and above its nominal value.

Figure 16 graphically describes the above presentedsimulation scenario. The variable wind power profile cor-responding to the above introduced time varying windspeed trend can be found in the upper subplot. The sub-plot in the middle depicts the time varying load demand.Altogether affect the electrical frequency of the networkas represented in the subplot below, grey line. The vari-ability of this frequency profile is diminished by the sup-port provided by the WPP while compared to the case theWPP is not providing this, as depicted by the blue line.

The WPP is required to regulate its power reserves ac-cording to the above presented frequency variation. Fig-ure 17 depicts the performance of the WPP controllers tocontinuously adjust the output of the installation so as totrack the total power margin reference x∗sd + ∆x (as a re-minder, this reference is given by the sum of the steadystate power margin reference for the WPP and the power

10 20 30 40 50 60 70 80 90 100 110 120100

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200

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wer

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eed

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0.8

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dem

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10 20 30 40 50 60 70 80 90 100 110 12049

49.5

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cy [H

z]

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Figure 16: Time varying profiles for wind power and load demand, af-fecting the electrical frequency

margin increment or decrement set by the primary controldroop). As can be noted, the actual power margin of theWPP successfully tracks the reference but presents cyclicspikes at the abrupt changes in frequency profile. As com-mented in previous sections of this article, these spikes aredue to the surplus of energy injected or absorbed from thenetwork while varying the kinetic energy of the wind tur-bines for power margin regulation through overspeedingtechniques.

The total power margin developed by the WPP insteady state conditions xsd is the sum of the power marginprovided by the flywheels (signal xcap+, proportional tothe energy stored in the flywheels) and the power marginprovided by the wind turbines xwt sd (see Section 2.2). Inorder to satisfy the reference x∗sd, the power margin of thewind turbines are varied depending on the state of chargeof the flywheels and this distribution can be graphicallyevaluated in Figure 18. As can be noted, the power mar-gin developed by the wind turbines (blue line) increasesto compensate the decrement in the power margin that theflywheels can handle (green line) due to their progressivedischarge associated to the standing losses. The resultantsatisfies the power margin reference set by the networkoperator x∗sd = 10 (red line).

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Pow

er m

argi

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41 42 43 44-20

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x*sd

+x

Figure 17: Power margin developed by the wind power plant under vari-able wind and load demand conditions.

10 20 30 40 50 60 70 80 90 100 110 1200

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er m

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Sta

te o

f Cha

rge

[pu]

xwt_sd

xcap+

xsd

Figure 18: Time varying profiles for wind power and load demand, af-fecting the electrical frequency

4. Conclusions

The main conclusions of the presented work are out-lined as follows:

• A control method for derating variable-speed windturbines has been developed. This control methodcombines overspeeding techniques and pitchingtechniques. From the application of the designedmethod, the wind turbines can be operated so thatthey maintain a power margin from the maximumavailable power that can be extracted from wind. Themethod is applicable to all wind speed ranges of vari-able speed wind turbines; both above and below therated wind speed level.

• The frequency control support that the wind turbinescan provide permits to improve the frequency nadirand the steady state level of the frequency in caseof a power unbalance in the network. The contri-bution of the wind turbines though, is subjected tothe applied control techniques. For instance, in caseof governing the power margin through overspeed-ing techniques, the frequency control support theycan provide is augmented by the kinetic energy ofthe rotor of the turbine exchanged with the networkdue to the variation of their rotating speed.

• Looking at the contribution of the WPP to primaryfrequency control, it is worth noting that the appli-cation of the designed central control system of theWPP and the local controllers of the wind turbinesand the flywheels, allow the management of the levelof reserves maintained by the wind turbines in func-tion of the SoC of the flywheels. The inclusion of theflywheels in the WPP reduces the need of operatingthe wind turbines in a deloaded mode, enabling themto operate extracting the maximum available powerfrom the wind and thus maximizing the revenues ofthe WPP operator while still providing the primaryfrequency control support to the network.

5. Acknowledgments

This work was supported by KIC InnoEnergy SE un-der the project Smart Power and by the German Ministryfor Environment, Nature Conservation and Nuclear Safety

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within the project “Wind park control for grid integra-tion”.

Appendix

The characteristic parameters of the synchronous gen-erator of the conventional power plant are extracted from[21] (in p.u. stator base): rated power 1000 MVA, ratedstator line-to-line voltage 18 kV, rs = 0.0033, xd = 1.65,xq = 1.57, xls = 0.15, x′d = x′q = 0.275, T ′d0 = 6.5 s,T ′q0 = 1.25 s. The parameters of its speed governor are[21] (in p.u. stator base): R = 0.05, TG = 0.2 s. Theparameter of the non-reheat turbine is [21]: TCH = 0.3 s.

The characteristic parameters of the DFIG are [26]:rated mechanical power 1.5 MW, rated stator line-to-linevoltage 690 V, rated rotor speed 1750 rpm, rs = 2.65 mΩ,r′r = 2.63 mΩ, xls = 0.053Ω, x′lr = 0.042Ω, xm = 1.72,poles P = 4, inertia Jg = 100 kg·m2. The characteris-tic parameters of the turbine are: R = 41.7 m, inertiaJt = 3 · 106 kg·m2, damping coefficient D = 7.5 · 105

Nms/rad, stiffness k = 12 · 107 Nm/rad, gear-box ra-tio N = 105, rated wind speed vw = 10.1 m/s. Theaerodynamic parameters are [27]: c1 = 0.73, c2 = 151,c3 = 0.58, c4 = 0.0002, c5 = 2.14, c6 = 13.2, c7 = 18.4,c8 = −0.02, c9 = −0.003.

The characteristic parameters of a flywheel unit are[25]: rated power 100 kW, operating speed limits 16 − 8krpm, torque losses Tloss = 1.19 Nm, inertia J f w = 86.4kg· m2.

The characteristic parameters (in per unit) of the powertransformers of the system are [21]: copper losses 0.1% ofrated power, short-circuit voltage ε = 0.15 pu, leakage re-actance 0.1 pu. The particular ratings of each transformerare: ratings of the step-up power transformer for the volt-age of the conventional generating unit 1000 MVA - 220kV / 18 kV; ratings of the step-up transformers for thevoltage of the WPP 500 MVA - 220 kV / 30 kV and 500MVA - 30 kV / 690 V.

The characteristic parameters of the lines are: r13 =

r23 = 0.0212Ω/km, x13 = x23 = 0.116Ω/km, length=50km.

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