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energies
Article

An Adaptive Frequency Strategy for Variable Speed
Wind Turbines: Application to High Wind Integration
Into Power Systems
Ana Fernández-Guillamón 1, * ID , Jorge Villena-Lapaz 2 , Antonio Vigueras-Rodríguez 3
Tania García-Sánchez 4 and Ángel Molina-García 1 ID
1
2
3
4

*

ID

,

Department of Electrical Engineering, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain;
angel.molina@upct.es
Alberta Electric System Operator, Calgary, AB T2P 0L4, Canada; jorge.villena@aeso.ca
Department of Civil Engineering, Universidad Politécnica de Cartagena, 30203 Cartagena, Spain;
avigueras.rodriguez@upct.es
Department of Electrical Engineering, Universidad Politécnica de Valencia, 46022 Valencia, Spain;
tagarsan@die.upv.es
Correspondence: ana.fernandez@upct.es; Tel.: +34-968-325357

Received: 10 May 2018; Accepted: 29 May 2018; Published: 4 June 2018




Abstract: This paper presents a new frequency controller for variable speed wind turbines connected
to the grid under power imbalance conditions. It is based on the fast power reserve emulation
technique, having two different operation modes: overproduction and recovery mode. In the first
mode, the active power provided by wind turbines is set over the mechanical power, reducing their
rotational speed. This overproduction power is estimated according to the frequency excursion.
In the second mode, the active power is established under the mechanical power to recover the initial
rotational speed through a smooth trajectory. The power system considered for simulation purposes
includes thermal, hydro-power and wind-power plants. The controller proposed has been evaluated
under different mix-generation scenarios implemented in Matlab/Simulink. Extensive results and
comparison to previous proposals are also included in the paper.
Keywords: frequency control; wind energy; renewable energy sources integration; power
system stability

1. Introduction
During the last decade, and due to aspects such as climate change, energy dependence, fossil
resource scarcity and the increasing costs of nuclear power [1], most developed countries have
promoted large-scale integration of Renewable Energy Sources (RES), mainly wind and PV power
plants [2]. This relevant integration of RES has raised important concerns in terms of grid stability
and reliability, mainly due to: (i) the nature of RES power variation [3] as well as the uncertainty in
the privately-owned renewable generators that puts the generation-load balance at risk [4]; (ii) the
reduction of the total system inertia by the decoupling between rotor mechanical speed and grid
frequency [5], or even the absence of rotating machines [6]. As the system inertia decreases, an increase
of primary frequency control (PFC) reserves is needed [7]. Traditionally, PFC reserves are provided by
synchronous generators [8], as depicted in Figure 1a. Under power imbalance conditions, PFC reserves
from conventional generation are traditionally released to compensate the disturbance and recover
the rate grid frequency. If these reserves cannot compensate for the mismatch, it could cause a
sharp decrease of the system frequency [9]. With the relevant penetration of wind power plants,
some proportional capacity of the system reserves must be provided by them [7,10] see Figure 1b.
Energies 2018, 11, 1436; doi:10.3390/en11061436

www.mdpi.com/journal/energies

Energies 2018, 11, 1436

2 of 21

Additional reserves can be then provided by renewables, reducing the primary reserves from
conventional generation units and providing enhanced solutions for weak and/or isolated power
systems [9,11]. Under this scenario of high RES penetration, transmission system operators have
required that not only conventional utilities contribute to ancillary services [12], but also renewables,
especially wind power plants [13]. Indeed, [14] affirms that the participation of the wind power plants
in the ancillary services such as grid frequency control becomes inevitable. For this reason, frequency
control strategies are being developed to effectively integrate Variable Speed Wind Turbines (VSWTs)
into the grid, in order to replace conventional power plants by maintaining a secure power system
operation [15]. Most of them are based on ‘hidden inertia emulation’, in order to enhance the inertia
response of VSWTs [16,17]. A classification for different control strategies based on principles for
inertia emulation concept can be found in [18]. One of the possible solutions to overcome this is called
fast power reserve emulation. It is based on supplying the kinetic energy stored in the rotating masses
to the grid as an additional active power, being afterwards recovered through an under-production
period (recovery). Overproduction is defined in the specific literature over the electrical pre-event
power reference [19–24] and the overproduction power is considered as constant and independent from
the frequency excursion severity [21–23]. Other proposals define the time that the wind power plant
must be overproducing independently from the event [19–22] or consider that it should last until the
wind turbine achieves its minimum speed limit [23]. Moreover, the transition from overproduction to
recovery is defined as an abrupt drop in the active generated power by VSWTs [21,23,24] or as a constant
slope [19,22]. A different strategy is described in [20], where the VSWTs of the wind power plant are
designed to recover at different times, avoiding ‘synchronization’. Most contributions consider a low
wind energy integration for simulations, between 10 and 20% [19,20,22], and only recent contributions
analyze penetration level scenarios up to 40% [10]. However, the renewable share is currently over
20% in different power systems. Actually, some countries have already experienced instantaneous
penetration higher than 50% (i.e., Spain, Portugal, Ireland, Germany and Denmark) [25]. Subsequently,
scenarios with a very relevant integration of wind energy should be considered and evaluated.
To overcome these drawbacks, and with the aim of improving the frequency response of power
systems with massive wind energy penetration, this paper describes and evaluates an alternative fast
power reserve emulation controller. The main contributions of this paper are summarized as follows:






The active power provided by VSWTs during the overproduction operation mode is defined
over the mechanical power instead of the pre-event electrical power. Such mechanical power
varies with the rotational speed instead of keeping constant as the former one. Moreover,
the overproduction power is estimated according to the frequency excursion, being thus an
‘adaptive’ overproduction strategy.
The active power provided by VSWTs during the recovery operation mode is defined below
the mechanical power to recover the rotational energy delivered in the overproduction mode.
It is defined as a parabolic trajectory until the rotational speed reaches the maximum power
tracking curve. Thereafter, that curve is followed. Because of that, it is considered as a ‘smooth’
recovery period.
The control strategy proposed has been tested under different scenarios, considering a maximum
wind energy integration of 45%. In all the scenarios, the proposed solution reduces significantly
the grid frequency deviations under power imbalance conditions.

The rest of the paper is organized as follows: in Section 2 the proposed frequency controller
for VSWTs is described and compared to previous approaches. The power system and the different
scenarios needed to assess the proposed control are discussed in Section 3. Simulation results are given
in Section 4. Finally, Section 5 gives the conclusions.

Energies 2018, 11, 1436
Energies2018,
2018,xxxx
Energies

3 of 21

44

Conventional  
Conventional  
power  
power  
plants
plants

PFC reserves of
PFC reserves of
conventional
conventional
power plants
power plants

PFC
PFC
reserves of
reserves of
RES
RES

RES
RES

Power imbalance
Power imbalance

Power imbalance
Power imbalance

Conventional  
Conventional  
power  
power  
plants
plants

Used
Used

Remaining
Remaining

RES
RES

RES
RES

(a)Current
Currentsituation
(a)
(a)situation

Conventional  
Conventional  
power  
power  
plants
plants

RES
RES

Used
Used

Used
Used

Remaining
Remaining

PFC reserves of
PFC reserves of
conventional
conventional
power plants
power plants

Remaining
Remaining

Conventional  
Conventional  
power  
power  
plants
plants

(b)Future
Futuresituation
(b)
(b)situation

Figure1.1.Change
ChangeininPFC
PFCreserves
reservesfrom
fromcurrent
currentto
tofuture
futurepower
powersystems
systems
Figure

Figure 1. Change in primary frequency control (PFC) reserves from current to future power systems:
experiencedinstantaneous
instantaneous penetrationhigher
higherthan
than50%
50%(i.e.
(i.e.Spain,
Spain,Portugal,
Portugal,Ireland,
Ireland,Germany
Germany
experienced
(a) Current
situation; (b) Futurepenetration
situation.

andDenmark)
Denmark)[27].
[27].Subsequently,
Subsequently,scenarios
scenarioswith
withaavery
veryrelevant
relevantintegration
integration of
of wind
wind energy
energy
and
shouldbe
beconsidered
consideredand
andevaluated.
evaluated.
should
2. Proposed Frequency
Strategy
for Wind
Turbines
Toovercome
overcomethese
thesedrawbacks,
drawbacks,and
andwith
withthe
theaim
aimof
ofimproving
improving the
the frequency
frequency response
response of
of
To
power
systemswith
with
massive
windenergy
energy
penetration,
thispaper
paperdescribes
describes
and
evaluates
an
power
systems
massive
wind
penetration,
evaluates
A new
frequency
control
strategy
for VSWTs
is this
presented
in thisand
work.
It an
is based on
alternativefast
fastpower
powerreserve
reserveemulation
controller. The
Themain
maincontributions
of this
paper are
controller.
paper
supplyingalternative
the
kinetic
energy
storedemulation
in the rotating
masses
ofcontributions
the VSWTof
inthis
order
toareenhance its
summarizedasasfollows:
follows:
summarized

inertial response. Three different operation modes are defined: normal operation, overproduction
Theactive
activepower
power
provided
byaVSWTs
VSWTs
during
the overproduction
overproduction
operation
mode
mode and recovery
mode.
Eachprovided
mode
sets
different
commanded
active power
Pcmdmode
to restore
the grid
• •The
by
during
the
operation
isis
defined
over
the
mechanical
power
instead
of
the
pre-event
electrical
power.
Such
over
the mechanical
power2,instead
of the
pre-event
electrical
power.VSWTs
Such frequency
frequency afterdefined
a power
imbalance.
In Figure
a general
scheme
of the
proposed
mechanicalpower
powervaries
varieswith
withthe
therotational
rotationalspeed
speed instead
instead of
of keeping
keeping constant
constant as
as the
the
mechanical
controller isEnergies
shown.
2018, xx
5
formerone.
one.Moreover,
Moreover,the
theoverproduction
overproductionpower
powerisisestimated
estimatedaccording
accordingto
tothe
thefrequency
frequency
former
excursion,
being
thus
an
’adaptive’
overproduction
strategy.
excursion, being thus an ’adaptive’ overproduction strategy.

The active
active power
power provided
provided by
by VSWTs
VSWTs during
during the
the recovery
recovery operation
operation mode
mode isis
• •The
defined
below
the
mechanical
power
to
recover
the
rotational
energy
delivered
in the
the
defined below the mechanical power to recover the rotational energy delivered in
overproduction
mode.
It
is
defined
as
a
parabolic
trajectory
until
the
rotational
speed
overproduction mode. It is defined as a parabolic trajectory until the rotational speed
reachesthe
themaximum
maximumpower
powertracking
trackingcurve.
curve.Thereafter,
Thereafter,that
thatcurve
curveisisfollowed.
followed. Because
Because
reaches
of that, it is considered as a ’smooth’ recovery period.
of that, it is considered as a ’smooth’ recovery period.
• The control strategy proposed has been tested under different scenarios, considering a
• The control strategy proposed has been tested under different scenarios, considering a
maximum wind energy integration of 45%. In all the scenarios, the proposed solution
maximum wind energy integration of 45%. In all the scenarios, the proposed solution
reduces significantly the grid frequency deviations under power imbalance conditions.
reduces significantly the grid frequency deviations under power imbalance conditions.
The rest of the paper is organized as follows: in Section 2 the proposed frequency controller
The rest of the paper is organized as follows: in Section 2 the proposed frequency controller
for VSWTs is described and compared to previous approaches. The power system and the
for VSWTs is described and compared to previous approaches. The power system and the

Figure 2. Scheme of the proposed VSWTs frequency controller

Figure 2. Scheme of the proposed Variable Speed Wind Turbines (VSWTs) frequency controller.
different scenarios needed to assess the proposed control are discussed in Section 3. Simulation
results are given in Section 4. Finally, Section 5 gives the conclusions.
2. Proposed frequency strategy for wind turbines
A new frequency control strategy for VSWTs is presented in this work.

It is based

Energies 2018, 11, 1436

4 of 21

2.1. Normal Operation Mode
The VSWTs operate at a certain point Pcmd according to their mechanical curve Pmt (ΩWT ).
The power controller compensates any change in the rotational speed ΩWT or in the wind speed VW ,
tracking the maximum available active power for a current wind speed PMPPT (VW ).
Under power imbalance conditions, and assuming a power supply-side decreasing, a frequency
(negative) deviation ∆ f is suffered by the power system. The proposed frequency controller is then
initialized through an adaptive overproduction strategy:
∆ f < −∆ f lim → Overproduction.
2.2. Overproduction Operation Mode
The active power provided by the VSWTs, Pcmd , involves the mechanical power Pmt (ΩWT )
obtained from the wind and an additional active power ∆POP taken from the rotational speed energy
stored in the rotor, Pcmd = Pmt (ΩWT ) + ∆POP . The proposed strategy results in a rotational speed
decreasing, and subsequently a reduction of the mechanical power provided by the blades. Regarding
to the additional power ∆POP , it is estimated proportionally to the frequency excursion evolution,
see Figure 3, which gives an adaptive response depending on the frequency excursion severity and thus
emulating PFC of conventional generation units [26,27]. This strategy gives a more realistic scenario,
a smoother response and, additionally, provides a frequency response in line with conventional
primary frequency performances. Previous approaches assume the overproduction as a constant value
and independent on the frequency excursion [21–23]. Moreover, the overproduction mode defined in
this work considers that mechanical power Pmt depends on the rotational speed Pmt (ΩWT ), whereas
most authors assumed that mechanical power was constant when rotational speed decreased [19–24].
This overproduction strategy remains active until the frequency excursion disappears, the rotational
speed reaches a minimum allowed value, or the commanded power is lower than the maximum
available active power.
∆ f > −∆ f lim or ΩWT < ΩWT,min or Pcmd < PMPPT (Ω MPPT ) → Recovery.
In previous contributions, the minimum rotational speed was considered as a constant value; i.e.,
ΩWT,min = 0.7 pu in [23]. Under this assumption, the rotational speed deviation interval, ∆Ω depends
on the initial rotational speed value Ω MPPT , giving different regulation ranges. To improve this
solution, the minimum rotational speed is proposed to be determined according to the initial value
Ω MPPT , being thus ΩWT,min = 0.7 · Ω MPPT . This way, ΩWT,min is a function of Ω MPPT and a 30% of
rotational speed deviation is allowed. Figure 4a shows the corresponding ∆ΩWT = Ω MPPT − ΩWT,min
differences depending on the wind speed values VW considering a fixed ΩWT,min . Figure 4b depicts the
proposed definition for ΩWT,min . In addition, Figure 5 compares the overproduction strategy discussed
xx
6
inEnergies
[23] and2018,
the alternative
approach proposed in this work.

Figure 3. Proposed relationship between ∆POP and ∆ f for VSWTs during
Figure 3. Proposed relationship between ∆POP and ∆ f for VSWTs during overproduction.
overproduction
The VSWTs operate at a certain point Pcmd according to their mechanical curve Pmt (ΩWT ).
The power controller compensates any change in the rotational speed ΩWT or in the wind
speed VW , tracking the maximum available active power for a current wind speed PMPPT (VW )

Energies
2018,xx
11, 1436
Energies
2018,
Energies
2018,
xx
Energies
2018,
xx
Energies 2018, xx

5 of 21

777
7

(a)wind
(b) for
(a)
Proposed
∆Ω
different
wind
(a)∆Ω
∆Ω
fordifferent
different
windspeeds
speedsVV
[24] (b)
(b) Proposed
Proposed ∆Ω
∆ΩWT
for different
different wind
(a)
∆Ω
for
different
wind
WT
WW, ,[24]
WT
WTfor
WT for
WT
(a) ∆ΩWT for different wind speeds VW , [24] speeds
(b)
Proposed
∆ΩWT for different wind
speeds
VV
speeds
V
W
W
W
Figure 4. Comparison between overproduction operation
modes.
speeds
VW (a) ∆ΩWT for different wind speeds
VW , [23];
(b) Proposed
∆ΩWT for different
wind speeds
VW .
Figure
Comparison
between
overproduction
operation modes
modes
Figure
4.4.Comparison
between
overproduction
operation

Figure 4. Comparison between overproduction operation modes
Figure 4. Comparison between overproduction operation modes

(a)
(a)Overproduction
Overproductionoperation
operationmode
modein
[24]
(a)
Overproduction
operation
mode
inin[24]
[24]
(a)
(a) Overproduction operation mode in [24]

(b) Overproduction
Overproduction(b) operation
operation mode
mode
(b)
(b)
Overproduction
operation
mode
(b)
Overproduction
operation
mode
proposed
proposed
proposed
Figure 5. Comparison between overproduction operation
modes; (a) Overproduction operation mode
proposed
in [23]; Figure
(b)
Overproduction
operationbetween
mode
proposed.
Figure
Comparison
between
overproductionoperation
operationmodes
modes
5.5.Comparison
overproduction

Figure 5. Comparison between overproduction operation modes
Figure 5. Comparison between overproduction operation modes
2.3. Recovery Operation Mode
Inprevious
previouscontributions,
contributions, the
the minimum
minimum rotational
rotational speed
speed was
was considered
considered as
as aaa constant
constant
In
previous
contributions,
the
minimum
In
rotational
speed
was
considered
as
constant
In
previous
contributions,
the
minimum
rotational
speed
was
considered
as
a
constant
After
the
overproduction
period,
a
recovery
operation
mode
is
proposed
to
restore
the
rotational
value;i.e.
i.e.Ω
0.7pu
puin
in[24].
[24]. Under
Underthis
thisassumption,
assumption,the
therotational
rotationalspeed
speeddeviation
deviation
value;
i.e.
ΩΩWT,min
==0.7
0.7
pu
in
[24].
Under
WT,min=
value;
this
assumption,
the
rotational
speed
deviation
WT,min
speed
toΩ
the
initial=value

and provide
anthis
optimal
active power
from
the VSWTs.
With
the
value;
i.e.
0.7
pu
in
[24].
Under
assumption,
the
rotational
speed
deviation
MPPT
WT,min
interval,∆Ω
∆Ωdepends
dependson
onthe
theinitial
initialrotational
rotationalspeed
speedvalue
valueΩ
ΩMPPT
givingdifferent
differentregulation
regulation
interval,
∆Ω
depends
on
the
initial
rotational
MPPT,,,giving
interval,
speed
value

giving
different
regulation
aim of
minimizing
undesirable
frequency
oscillations
and
abrupt
changes
fromdifferent
the supply-side,
interval,
∆Ω
depends
onsolution,
the initial
rotational
speed
value
ΩMPPT
, proposed
giving
regulation
MPPT
ranges.
To
improve
this
the
minimum
rotational
speed
is
tobe
bedetermined
determined
ranges.
To
improve
this
solution,
the
minimum
rotational
speed
is
proposed
to
an
alternative
recovery
strategy
is
defined
and
evaluated.
This
proposal
is
based
on
a
parabolic
smooth
ranges.
To
improve
this
solution,
the
minimum
rotational
speed
is
proposed
to
be
determined
ranges.
To to
improve
this
solution,
the ,minimum
rotational
speed
isΩ
proposed
topower
be determined
recovery
strategy.
Three
points
are considered
to define
this trajectory:
(i)
mechanical
atWT,min
the isis
according
theinitial
initial
value
beingthus
thus
ΩWT,min
=
0.7···Ω
This
way,

according
to the
the
initial
value
ΩΩMPPT
, being
being

=
0.7
...This
way,

MPPT
MPPT
WT,min
WT,min
MPPT
according
to
value

,
thus

=
0.7

This
way,

is
WT,min is
according
to the
initialspeed
value
ΩMPPT
, being
thus
ΩWT,min
=
0.7 · Ω MPPT
. This way, Ω
MPPT
MPPT
WT,min
WT,min
minimum
rotational
achieved
during
the
frequency
excursion,
afunction
functionof
ofΩΩMPPT
andaa30%
30%of
ofrotational
rotationalspeed
speeddeviation
deviationisisallowed.
allowed.Figure
Figure4(a)
4(a)shows
showsthe
the
a
and
MPPT
a afunction
and
Figure 4(a)
4(a) shows
shows the
the
functionofofΩΩMPPT
andaa30%
30%of
ofrotational
rotational speed
speed deviation
deviation is
is allowed.
allowed. Figure
MPPT
corresponding∆Ω
∆ΩWT
=



differences
depending
on
the
wind
speed
values
corresponding
=



differences
depending
on
the
wind
speed
values
MPPT P1 :WT,min
WT= Ω MPPT
ΩWT,min
, Pmt (ΩWT,min
)) .
(WT,min
corresponding
differences
depending
on the
the wind
wind speed
speed values
values
MPPT − Ω
corresponding∆Ω
∆ΩWT
ΩWT,min
differences
depending on
WT =ΩΩ MPPT. −Figure
WT,min
V
considering
a
fixed
4(b)
depicts
the
proposeddefinition
definitionfor
forΩΩWT,min
In
V
W considering a fixed ΩWT,min
WT,min. Figure 4(b) depicts the proposed
WT,min. . In
W
VV
aafixed
. . Figure
4(b)
depicts
the
proposed
definition for
for Ω
ΩWT,min.. In
In
WWconsidering
considering
fixedΩ
ΩWT,min
Figure
4(b)
depicts
the
proposed
definition
(ii) mechanical
power
corresponding
to
the
middle
rotational
speed
deviation,
WT,min
WT,min
addition,Figure
Figure55compares
compares
theoverproduction
overproductionstrategy
strategydiscussed
discussedin
in[24]
[24]and
andthe
thealternative
alternative
addition,
the
addition,
in [24]
[24] and
and the
the alternative
alternative
addition,Figure
Figure55compares
comparesthe
theoverproduction
overproduction strategy
strategy discussed
discussed in
approachproposed
proposedin
inthis
thiswork.
work.
approach
P2 : (ΩV , PMPPT (ΩV )) ,
approach
approachproposed
proposedininthis
thiswork.
work.
where Ω is Ω

+ 0.5 · ∆Ω, and ∆Ω is Ω MPPT − ΩWT,min . (iii) maximum mechanical power

WT,min
2.3.Recovery
RecoveryVoperation
operation
mode
2.3.
mode
available
according
to
the wind speed,
2.3.
Recovery
operation
2.3. Recovery operationmode
mode

After the
the overproduction
overproduction period,
period,
a recovery
recovery operation
operation
mode isis proposed
proposed to
to restore
restore the
the
After
P3 : (aΩ
(Ω MPPT )) .mode
MPPT , PMPPT
After
proposed to
to restore
restore the
the
Afterthe
theoverproduction
overproduction period,
period, aa recovery
recovery operation
operation mode is proposed
rotational speed
speed to
to the
the initial
initial value
value ΩΩMPPT
and provide
provide an
an optimal
optimal active
active power
power from
from the
the
rotational
MPPT and
rotational
power from
from the
the
rotationalspeed
speedtotothe
theinitial
initial value
value Ω
ΩMPPT
and provide
provide an optimal active power
MPPT and
VSWTs. With
Withthe
theaim
aimof
ofminimizing
minimizingundesirable
undesirable
frequencyoscillations
oscillationsand
andabrupt
abruptchanges
changes
VSWTs.
frequency
VSWTs.
abrupt changes
changes
VSWTs. With
Withthe
theaim
aimofofminimizing
minimizing undesirable
undesirable frequency
frequency oscillations and abrupt
fromthe
thesupply-side,
supply-side,an
analternative
alternativerecovery
recoverystrategy
strategyisisdefined
definedand
andevaluated.
evaluated.This
Thisproposal
proposal
from
from
evaluated. This
This proposal
proposal
fromthe
thesupply-side,
supply-side,an
analternative
alternativerecovery
recovery strategy
strategy is
is defined and evaluated.

Energies 2018, 11, 1436

6 of 21

The commanded power before achieving P2 is determined according to
2
Pcmd = a · ΩWT
+ b · ΩWT + c, where a, b and c can be estimated by considering the three
mechanical power points aforementioned. Finally, the commanded power tracks the maximum
power curve available according to the power wind speed curve: Pcmd = PMPPT (ΩWT ). The normal
operation mode is then recovered when either Ω MPPT or PMPPT (Ω MPPT ) are respectively achieved,
ΩWT ' Ω MPPT or Pcmd ' PMPPT (Ω MPPT ) → Normal operation.
In [23] the recovery period is defined as Pcmd = Pmt − Pacc , being Pacc a constant underproduction
power value. Under this assumption, the higher Pacc , the faster the rotational speed recovers its
optimal initial value Ω MPPT . Despite the fact that a value of Pacc = 0.02 pu was fixed, the fast
and abrupt transition from overproduction to recovery operation mode may cause an additional
and severe frequency oscillation. The recovery operation mode defined in this work determines
the trajectory followed by the wind farm instead of fixing a certain underproduction power, Pacc .
In Figure 6, a comparison between the recovery mode proposed in [23] and the alternative strategy
described in this work is depicted. Furthermore, the recovery operation mode has been improved
by modifying P2 . The power in point P2 is then defined in accordance to the differences between
PMPPT (ΩV ) and Pmt (ΩV ), PMPPT (ΩV ) + x · ( Pmt (ΩV ) − PMPPT (ΩV )), where x has been considered
as 0.25, 0.50 and 0.75. When Pcmd achieves P2x , the active power is above the curve of PMPPT
proportionally
to the difference between Pmt (ΩWT ) and PMPPT (ΩWT ), providing an adaptive and
Energies
2018,
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2018,
9
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2018,
xx xx
smooth recovery response. In Figure 7, the different proposals for the recovery operation mode
are compared.

(a) Recovery operation mode in [24]

(b) Recovery operation mode proposed

(a)
(b) mode
(a) Recovery
Recovery operation
mode
(b)
operation
proposed
(a)
operation
modein
in[24]
[24]
(b)Recovery
Recovery
operation
mode
proposed
Figure
6. Comparison
between recovery
operation
modes
Figure 6. Comparison between recovery operation modes. (a) Recovery operation mode in [23];
Figure 6.
Comparison
between recovery operation modes
6.mode
Comparison
(b) RecoveryFigure
operation
proposed. between recovery operation modes

Figure
7. Different
proposals for
operation
mode.
Figure
7. Different
proposals
forrecovery
recovery
operation
mode

Figure 7. Different proposals for recovery operation mode
Figure 7. Different proposals for recovery operation mode

9 9

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7 of 21

In Figure 8a, the control strategy proposed in [23] is shown. Figure 8b summarizes the new
approach discussed
in this7.
work.
Moreover,
Figure 9for
compares
theoperation
VSWTs active
power variations
Figure
Different
proposals
recovery
mode
submitted to a frequency excursion, where ∆PWF = Pcmd − PMPPT (Ω MPPT ). As can be seen,
Energies
2018, xx
the proposed strategy offers a more adaptive and smoother power oscillation, which leads to reduce
possible frequency oscillations due to abrupt imbalances.

(a)
(a) Control
strategy
in [24]
(a) Recovery
operation
mode
in [24]
Figure 8.

(b) mode
(b) (b)
Adaptive
smooth
proposed
Recoveryand
operation
proposedcontrol
strategy

Comparison
of frequency control
strategies
for VSWT.
(a) Control
strategy
Figure
6. Comparison
between
recovery
operation
modes

in [23];

Energies
2018,
xx
Energies
2018,
xxsmooth
(b)
Adaptive
and
proposed control
Figure
8. Comparison
ofstrategy.
frequency control strategies for VSWT

1010

ΔP
ΔP
WW
F F

Normal 
Normal 
Normal 
Normal 
operation
operationOverproduction
operation
OverproductionRecovery
Recovery operation

k ⋅kΔf
⋅ Δf

00

(a) ∆P
∆P(a)
[24]
WF in
(a)
WF in [24]

(b)
(b)
proposed
WF
(b)∆P
∆P
WF proposed

Figure
9. Additional
Additional
active
of
power
plants:
ofofstrategies
9.
activeofpower
power
ofwind
wind
power
plants:comparison
comparison
strategies
active power
wind power
plants:
comparison
of strategies.
(a)
∆PWF in [23];
FigureFigure
9. Additional
(b) ∆PWF proposed.

Cases of Study
3.3.Cases
of Study

3. Cases of Study
3.1. PowerFigure
system modeling
7. Different
3.1. Power
system
modeling
3.1. Power
System
Modeling

proposals for recovery operation mode

From
the
supply-side,
the power
considered
for simulation
purposes
involve
From
the the
supply-side,
the power
systemsystem
considered
for simulation
purposes
involve conventional
From
supply-side,
the power
system
considered
for simulation
purposes
involve
conventional
generating
units
such
as
thermal
and
hydro-power
plants,
and
wind
power have
generating
units
such
as
thermal
and
hydro-power
plants,
and
wind
power
plants,
Simulations
conventional generating units such as thermal and hydro-power plants, and wind power
plants,
Simulations
have been carried
in Matlab/Simulink.
The total capacity
of theUSA).
beenplants,
carriedSimulations
out in Matlab/Simulink
(2016out
Student
Suite Version, MathWorks,
have been carried
out
in Matlab/Simulink.
The total Natick,
capacityMA,
of the
power
systemofisthe
1350
MW. system
Simplified
governor-based
models
have been used
to simulate
both used
The total
capacity
power
is
1350
MW.
Simplified
governor-based
models
have
been
power system is 1350 MW. Simplified governor-based models have been used to simulate both
thermal
andthermal
hydro-power
plants according
to [28],
see Figures
10(a)
10(b).10a,b.
In Appendix
A, A,
to simulate
both
and hydro-power
plants
according
to [26],
seeand
Figure
In Appendix
thermal and hydro-power plants according to [28], see Figures 10(a) and 10(b). In Appendix A,
the different
the parameters
the diagrams
block diagrams
are presented.
To simulate
thepower
the different
valuesvalues
of theof
parameters
of the of
block
are presented.
To simulate
the wind
the different values of the parameters of the block diagrams are presented. To simulate the
wind
power
plant,
an
equivalent
generator
with
n-times
the
nominal
power
of
one
wind
plant, an equivalent generator with n-times the nominal power of one wind turbine is assumed [28],
wind power
plant, an equivalent
generator
with
n-times the
nominal
power ofcontroller
one wind
is assumed
being n [29,30].
the totalThe
number
of turbines
[31,32].
The frequency
beingturbine
n the total
number[30],
of turbines
frequency
controller
introduced
in Section 2 is added
turbine is assumed
[30],
n to
thethe
total
number
turbines
[31,32].
The
controller
in Section
2 isbeing
added
wind
powerof
plant
model
in order
to frequency
provide
frequency
to theintroduced
wind power
plant model
in order
to
provide
frequency
response
under
power
imbalances.
introduced
in
Section
2
is
added
to
the
wind
power
plant
model
in
order
to
provide
frequency
under power imbalances.
With those
considerations,
theseen
blockindiagram
theAppendix
VSWT
With response
those considerations,
the block diagram
of the
VSWT can be
Figure of
10c.
B
response
under
power
imbalances.
With
those
considerations,
the
block
diagram
of
the
can the
be seen
in Figure
10(c).
Appendix
explains the different blocks of the VSWT model. VSWT
explains
different
blocks
of the
VSWT B
model.
canAbesimplified
seen in Figure
10(c).
B explains
blockscan
of the
VSWT
diagram
in Appendix
terms of variations
of the
the different
power system
be seen
in model.
Figure 11,
A
simplified
diagram
in
terms
of
variations
of
the
power
system
can
be
seen
in
being the generated extra power ∆Pg = ∆PWF + ∆PT + ∆PH (the sum of the activeFigure
power11,
being
the of
generated
∆Pand
∆PWF + ∆Pplants),
(the
of the active power
g =hydro-power
T + ∆PHand
variation
the wind extra
power,power
thermal
∆Psum
L the demand variation.
variation
of
the
wind
power,
thermal
and
hydro-power
plants),
and
∆P
the
demand variation.
L
The frequency excursion can be thus estimated from the following expression,
(a)
Control
strategy
in
[24]
(b)
Adaptive
and
smooth
The frequency excursion can be thus estimated
from the following expression,proposed control
1
strategy
∆f =
· (∆Pg − ∆PL ),
(1)
2 Heq s1+ Deq
∆f =
· (∆P − ∆P ),
(1)

9

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11

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8 of 21

Energies 2018, xx

11
11

11

(a)Block
Blockdiagram
diagramofof
thermalplant
plantmodel
model
(a)
(a)
Block
diagram
thermal
(a)
a athermal
plant
model

(b)
Block
diagram
ahydro-power
hydro-power
plant
model
(b)
(b)
Block
diagram
ofofof
a ahydro-power
plant
model
(b)
Block
diagram
plant
model

(c) Block
model
and
thethe
proposed
frequency
controller
(c)and
Blockdiagrams
diagramsofofa aVSWT
VSWT
model
proposed
frequency
controller
(c)(c)Block
of a VSWT
the proposed
controller
(a) Block diagram
of adiagrams
thermal plant
modelmodel and
(b) Block
diagramfrequency
of a hydro-power
plant model

Figure
10.
Power
plants
models
Figure
10.
Power
plants
models
Figure 10. Power plants models.
(a) Block
diagram
of
a thermal
plant model; (b) Block diagram of a
Figure
10.
Power
plants
models
hydro-power plant model; (c) Block diagrams of a VSWT model and the proposed frequency controller.
A simplified diagram in terms of variations of the power system can be seen in Figure 11, being the
generated extra power ∆Pg = ∆PWF + ∆PT + ∆PH (the sum of the active power variation of the wind
power, thermal and hydro-power plants), and ∆PL the demand variation. The frequency excursion can
be thus estimated from the following expression,
∆f =

2 Heq

1
· (∆Pg − ∆PL ),
s + Deq

(1)

(c) Block diagrams of a VSWT model and the proposed frequency controller

where Deq is the equivalent damping factor of the loads and Heq is the equivalent inertia constant of
Figure
the system, determined as Equation
(2) 10. Power plants models
N

∑ Hi · SB,i

i =1

Heq =
,
(2)
SB
Figure 11. Simplified diagram of the
modeled power system
Figure 11. Simplified diagram of the modeled power system
Figure
Simplified
diagram
modeled
Hi refers to the
inertia11.
constant
of power
plant of
i, Sthe
the ratedpower
powersystem
of power plant i, SB is the
B,i is
rated power of the power system and N is the total number of conventional generators.

Figure
11.11.
Simplified
ofthe
themodeled
modeled
power
system
Figure
Simplifieddiagram
diagram of
power
system.

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9 of 21

3.2. Description of the Scenarios
Taking into account the contribution of the different sources from the supply-side in the
EU-28 during 2016, see Table 1, four different scenarios have been studied. The first scenario
corresponds to the current European supply-side situation, where 75% comes from thermal power
plants (conventional and nuclear plants), 12% from hydro-power plants and 13% from non-manageable
sources, mainly wind, and other renewables that do not provide frequency control. According to
the relevant presence of wind energy, in the rest of scenarios the non-manageable sources have been
considered to be just wind power plants. Moreover, the frequency controllers indicated in Section 2
(approach of [23] and the new scheme proposed in this work) have been included in the wind power
plant model, keeping constant the capacity of the hydro-power plant (12%). Both thermal and wind
capacities have changed depending on the scenarios in order to simulate a power system with high
integration of RES. As a consequence, the total inertia of the power system is reduced, due to the
fact that VSWTs and thus wind power plants are decoupled from the grid. The considered scenarios
for simulation purposes are summarized in Table 2, where Heq has been determined according to
Equation (2). To evaluate the VSWTs frequency controller, three power imbalances (∆PL,1 = 0.025,
∆PL,2 = 0.050, ∆PL,3 = 0.100) have been considered, resulting in 12 different scenarios.
Table 1. Contribution of sources in EU-28 in 2016 [31].
Source

Contribution (%)

Conventional thermal

48.6

Nuclear

25.8

Hydro

12.0

Wind

9.7

Geothermal

0.2

Other

3.7

Table 2. Capacity of each generating unit and total RES integration.
Source

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Thermal plant

75%

73%

58%

43%

Hydro-power plant

12%

12%

12%

12%

Wind power plant

Others

15%

30%

45%

Heq

4.15 s

4.05 s

3.29 s

2.54 s

4. Results
With the aim of evaluating the suitability of the proposed VSWTs frequency controller, three
different strategies have been analyzed:
1.
2.
3.

Thermal and hydro-power plants with frequency control (without frequency response from wind
power plants).
Thermal and hydro-power plants with frequency control and wind power plants with the
frequency controller of [23].
Thermal and hydro-power plants with frequency control and wind power plants with the
proposed frequency controller.

When wind power plants are excluded from frequency control, frequency excursions by
considering the different scenarios are shown in Figure 12. As wind power integration increases,
without providing frequency response, the lowest point or Nadir becomes more and more significant,

Energies 2018, 11, 1436

achieving −302 mHz in scenario 4 considering the same value of ∆PL , being over 1.5 times in
comparison to the first one. With regard to the stabilization time (defined as the time interval taken by
the frequency deviation to be within the range |∆ f | < 10 mHz [32]), it enhances slightly. In scenario 4,
it is 1.3 times over the first one, increasing from 28 to 34 s. The rate of change of frequency (ROCOF)
also increases with the integration of wind energy without frequency response, from 83 mHz/s
in scenario 1 to 132 mHz/s in scenario 4. Therefore, the more wind power integration into grids,
the more sensitive is the power system under imbalance conditions. Subsequently, a more unstable
grid results from the integration of renewables without implementing any frequency response. Similar
2018,
xx
relationships
are found when ∆PL = 0.050 and ∆PL = 0.100 (Figure 12b,c, respectively). In Figure 13,
a comparison among Nadir, stabilization time and ROCOF for the different scenarios and ∆PL = 0.050
is depicted. Results are shown in pu, considering as base the results of scenario 1, where there are no
wind power plants.

0

0

−50 −50

−100

−100−100

−200

∆ f (mHz)

∆ f (mHz)

0

∆ f (mHz)

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−150−150
−200−200

−400

−250
−250

Scenario 1
Scenario 1
Scenario 2
Scenario 2
Scenario 3
Scenario 3
Scenario 4
Scenario 4

−300
−300
0

−300

0

10

10
20

20

30

30

40

−500

Scenario 1
Scenario 2
Scenario 3
Scenario 4

−600

50
60
70
80
90
40
100
50
60
70
80
90
100
Time (s)
Time (s)

0

(a)

20

10

30

40

50
60
Time (s)

70

80

90

100

(b)

(a) Considering ∆PL = 0.025

(b) Considering ∆PL = 0.050

0

∆ f (mHz)

−200
−400
−600
−800
−1,000

Scenario 1
Scenario 2
Scenario 3
Scenario 4

−1,200
0

10

20

30

40

50

(c)
Time (s)

60

70

80

90

100

Figure 12. Frequency excursions(c)
forConsidering
scenarios 1–4 without
power plant control. (a) Considering
∆PL =wind
0.100
∆PL = 0.025; (b) Considering ∆PL = 0.050; (c) Considering ∆PL = 0.100.

Figure 12. Frequency excursions for scenarios 1–4 without wind power plant control
To overcome previous frequency excursion drawbacks, and to determine the most suitable
recovery strategy of the smooth controller proposed in this work, the four different recovery strategies
are analyzed hereinafter. They are represented for the scenario 2, considering ∆PL = 0.050 in Figure 14a
and ∆PL = 0.100 in Figure 14b. Due to the low value of the power of point P2 (see Figure 7),
the frequency deviation presents undesirable oscillations when the wind power plant is within the

1.5

NADIR
tstab
ROCOF

14

−800
−1,000

Scenario 1
Scenario 2
Scenario 3
Scenario 4

−1,200
0

10

20

30

40

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50
60
Time (s)

70

80

90

100

11 of 21

(c) Considering ∆PL = 0.100

recovery operation mode. This effect is especially significant in the original proposal, and it is
Figure 12. Frequency excursions for scenarios 1–4 without wind power plant control
reduced as the power considers the difference between the actual mechanical power Pmt (ΩWT ) and the
maximum mechanical power available according to the wind speed PMPPT (ΩWT ). Actually, the best
response is obtained when P2 is defined as PMPPT (ΩV ) + 0.75 · ( Pmt (ΩWT ) − PMPPT (ΩWT )). Because
of that, the rest of the results only consider that case (x = 0.75).

(pu)

1.5

NADIR
tstab
ROCOF

1
0.5
0

Scenario 1 Scenario 2 Scenario 3 Scenario 4

Figure
13.
NADIR,
stabilization
time
ROCOF:
comparison
for
the different
Figure 13.
Nadir,
stabilization
time and the
rate and
of change
of frequency
(ROCOF):
comparison
for the
scenarios
without
windwind
power
plant
control
∆PLL==0.050.
0.050
different scenarios
without
power
plant
controlfor
for ∆P
50

100

0

0

−100
−200

−100

∆ f (mHz)

∆ f (mHz)

−50

−150
−200

−300
−400
−500

−250

x=0
x = 0.25
x = 0.50
x = 0.75

−300
0

20

40

60
80
Time (s)

(a)

100

120

x=0
x = 0.25
x = 0.50
x = 0.75

−600
−700
140

0

20

40

60
80
Time (s)

100

120

140

(b)

Figure 14. Frequency excursion for scenario 2. Comparison among values of x. (a) Considering
∆PL = 0.050; (b) Considering ∆PL = 0.100.

Figures 15–17 summarize the different scenarios including frequency response from VSWTs when
∆PL = 0.025, ∆PL = 0.050 and ∆PL = 0.100, respectively. Figures 15a, 16a and 17a refer to the controller
indicated in [23]. Figures 15b, 16b and 17b use the new proposal of this work, assuming x = 0.75
in line with the previous discussion. According to the results, scenarios 2–4 present two different
well-identified frequency shifts: (i) due to the power imbalance and (ii) due to the supply-side decrease
as a consequence of the step from overproduction to recovery operation mode of the VSWTs frequency
controller, see Figure 8.

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12 of 21

(a)

(b)

Figure 15. Comparison between frequency excursion for scenarios 1–4 including wind power plant
controls and considering ∆PL = 0.025. (a) Controller from [23]; (b) Proposed control with x = 0.75.

∆ f (mHz)

0

−100

−200

−300

Scenario 1
Scenario 2
Scenario 3
Scenario 4

−400
0

20

60

40

(a)

80

100 120
Time (s)

140

160

180

200

(b)

Figure 16. Comparison between frequency excursion for scenarios 1–4 including wind power plant
controls and considering ∆PL = 0.050. (a) Controller from [23]; (b) Proposed control with x = 0.75.

0

∆ f (mHz)

−200

−400

−600

Scenario 1 and ∆PL
Scenario 2 and ∆PL
Scenario 3 and ∆PL
Scenario 4 and ∆PL

−800
0

(a)

20

40

60

80

100
Time (s)

120

140

= 0.100
= 0.100
= 0.100
= 0.100

160

180

(b)

Figure 17. Comparison between frequency excursion for scenarios 1–4 including wind power plant
controls and considering ∆PL = 0.100. (a) Controller from [23]; (b) Proposed control with x = 0.75.

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With regard to the power imbalance condition, the frequency shift decreases as the wind
energy integration increases. This reduction is due to the fast support provided by VSWTs under
a generation-load mismatch. It is more noticeable when the proposal of [23] is considered, as the
overproduction power is constant and independent from the frequency deviation. Actually, if the
demand variation is small (i.e., ∆PL = 0.025), the overproduction mode of the approach indicated
in [23] may cause an overfrequency instead of an underfrequency, since the additional active power
definition ∆POP (see Figure 15a, scenarios 3 and 4). This drawback does not occur if the adaptive
frequency controller proposed in this work is used, as seen in Figure 15b. Considering the case in
which ∆PL = 0.050, a reduction of 70% is obtained with the approach of [23], from 391 mHz in the first
scenario to 117 in the last one. This reduction accounts for the 44%, reaching 215 mHz in scenario 4
with the new controller proposal. Finally, when ∆PL = 0.100, both frequency controllers have similar
responses during the firsts seconds, reaching a Nadir ' 750 mHz.
With respect to the second frequency shift, it increases with high wind power plant integration,
as it increase leads to a greater wind power generation reduction when switching from overproduction
to recovery. The underfrequency value can decrease to 2 Hz in scenario 4 with the approach indicated
in [23], due to the sudden drop of generation from VSWTs, see Figure 9. Nevertheless, this second
excursion is reduced using the smooth recovery proposal of this work, decreasing up to 163, 266,
450 mHz for scenario 4 when ∆PL = 0.025, ∆PL = 0.050, ∆PL = 0.100, respectively. This fact
brings out that the new proposed adaptive and smoother controller gives an improvement of the
frequency response, being suitable for power systems with high wind power penetration. In Figure 18,
a comparison between both frequency deviations corresponding to both frequency control strategies
considering ∆PL = 0.050 are depicted.

Figure 18. Comparison between ∆ f 1 and ∆ f 2 for the different scenarios depending on the wind power
plant control and considering ∆PL = 0.050.

Regarding to ROCOF, its behavior depends on the scenario and ∆PL . In general, it can be said that
ROCOF decreases in scenarios 2 and 3, but increases in scenario 4. Actually, it is higher than the ROCOF
of scenario 1 when the wind power plant frequency controller of [23] is analyzed. The stabilization time
increases with the wind power plant integration, as a result of the second frequency dip. In the last
scenario, the stabilization time is around 280 s for the control strategy indicated in [23] (independently
from the value of ∆PL ), varying between 80 and 140 s for the proposed approach. Figures 19 and 20
compare Nadir, stabilization time and Nadir for ∆PL = 0.050. The increasing of the stabilization
time in [23] is due to the fact that when the wind power plant changes from recovery to normal
operation mode, a third frequency shift occurs. Despite it is not so noticeable compared to the second
frequency excursion, see Figures 15a, 16a and 17a, it can achieve up to 70 mHz for scenario 4.

500
0

Scenario 2

Scenario 3

Scenario 4

Comparisons between ∆ f 1 and ∆ f 2 for the different scenarios depending
on the wind power plant control and considering ∆PL = 0.050

Figure
18.
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11, 1436

10

(pu)

8

14 of 21

NADIR
tstab
ROCOF

6
4
2
0

Scenario 1 Scenario 2 Scenario 3 Scenario 4

Figure
Energies
2018,19.
xx NADIR, stabilization time and ROCOF: comparison for the different
18
Figure 19. Nadir, stabilization time and ROCOF: comparison for the different scenarios considering
scenarios considering ∆PL = 0.050 and including wind power plant control
∆PL = 0.050 and including wind power plant control from [23].
from [24]
5

∆ f (mHz)

ΩWT (pu)

(pu)

the control strategy indicated NADIR
in [24] (independently from the value of ∆PL ), varying between
tstab
4
80 and 140 s for the proposed
approach. Figures 19 and 20 compare NADIR, stabilization
ROCOF
time and NADIR for ∆PL = 0.050. The increasing of the stabilization time in [24] is due to
3
the fact that when the wind power plant changes from recovery to normal operation mode, a
2
third frequency shift occurs.
Despite it is not so noticeable compared to the second frequency
excursion, see Figures 15(a)-17(a),
it can achieve up to 70 mHz for scenario 4.
1
In Figure 21 the wind power plant response of scenario 2 and ∆PL = 0.050 with the
0 is depicted. Between points [1] − [2], the VSWT is working in
frequency controller of [24]
Scenario 1 Scenario 2 Scenario 3 Scenario 4
the normal operation mode, providing its maximum power PMPPT = 0.745 pu. Because of
Figure 20. NADIR, stabilization time and ROCOF: comparison for the different
Figure
20.variation
Nadir, stabilization
time and
ROCOF:iscomparison
for the different
considering
that,
the
of active power
provided
0 (see definition
of ∆PWFscenarios
in Section
2). The
scenarios
considering
∆P
andpower
including
the proposed wind power plant
L = 0.050
∆P
=
0.050
and
including
the
proposed
wind
plant
control.
rotational
speed of the machine is Ω MPPT = 1.197 pu. At time t = 20 s, the power imbalance
L
control
occurs, activating the overproduction mode (points [2] − [3]). Hence, the variation of active
In Figure
21 the
power
plant
response
of scenario
and
∆PL ==0.10.050
with the
power
provided
by wind
the wind
power
plant
is constant
and equal2 to
∆PWF
pu. This
frequency
controller ofto
[23]
depicted. active
Between
points
[1]–[2],by
thethe
VSWT
is working
in the normal
value corresponds
theisadditional
power
provided
VSWTs
in this operation
operation
its maximum
powerkinetic
PMPPTenergy
= 0.745
pu. machine.
Because of
the variation of
mode,mode,
∆POP , providing
which is taken
from the stored
of the
Asthat,
a consequence,
active
provided
0 (see
of ∆PWFfrom
in 1.2
Section
2).=The
rotational
of the
machine
[1] ≡
[2]
[1]
thepower
rotational
speedis of
the definition
VSWT decreases

1.197
to the speed
minimum
value
MPPT
[5]
0
is Ω Ω
=
1.197
pu.
At
time
t
=
20
s,
the
power
imbalance
occurs,
activating
the
overproduction
MPPT
WT,min = 0.700 pu, corresponding to a 42% of decrease in 30 s. When ΩWT reaches
1.1
mode (points [2]–[3]).
Hence, the variation of active
power provided by the wind power plant
−100
is constant and equal to ∆PWF = 0.1 pu. This value1 corresponds to the additional active power
provided by the−200VSWTs in this operation mode, ∆POP , which is taken from the stored kinetic energy
0.9
of the machine.−300
As a consequence, the rotational speed of the VSWT decreases from Ω MPPT = 1.197
0.8
to the minimum value ΩWT,min = 0.700 pu, corresponding
to a 42% of decrease in 30 s. When ΩWT
−400
reaches its minimum value, the frequency controller0.7 changes to recovery operation mode (points
[3] ≡ [4]
[4]–[5])). The sudden
drop
of150the200variation
of active
power
(points
[3]–[4])
causes a second
0
50generated
200
250
300
350
100
150
400
0
50
250
300
350
100
400
Time (s)
(s)
frequency departure, being thisTime
deeper
than that due to the power imbalance. This power variation is
∆PWF = P[4] − P[3] = (a)
−0.27
− 0.1deviation
= −0.37 pu. Apart from that,
it is important
Frequency
(b) Rotational
speed to notice that it takes
around 250 s to restore the rotational speed to the initial value Ω MPPT .
[2] [3]
Regarding to0.1 Figure
22, the wind power plant response of scenario 2 and ∆PL = 0.050
5 · 10
with the proposed
controller considering x =P (pu)
0.75 is shown. In this case, the rotational
[1]
0
speed decreases from
1.197 to 1.117[5] pu in 20 s (points [2]–[3]). Despite it takes less time
[1]
· 10
than in Figure−5 21,
the reduction of rotational speed is also lower, only 0.07%. Furthermore,
−0.1
the second frequency
departure caused by the drop from overproduction to recovery (points [3]–[4]:
−0.15
∆PWF = P[4] − P[3−]0.2 = −0.015 − 0.075 = −0.090 pu) is negligible in comparison to the one indicated
in Figure 21. The−0.25
wind power plant needs only 80 s to restore the rotational speed to the initial value
[4]
2
−0.3 equation of the parabola in this case is:P
(points [4]–[5]). The
cmd = 19.06 · ΩWT − 43.93 · ΩWT + 26.02.
0
50
200
250
300
350
100
150
400
∆PWF (pu)

−2

−2

Time (s)

(c) Variation of wind power

(pu)

(d) Frequency control strategy

Figure 21. Wind power plant response for scenario 2 and frequency controller of
[24]

scenarios considering ∆PL = 0.050 and including the proposed wind power plant
control
Energies 2018, 11, 1436

15 of 21

[1] ≡ [2]
1.2 [1] ≡ [2]
1.2

0

0

1.1
1.1

∆ f (mHz)
∆ f (mHz)

ΩWT (pu)
ΩWT (pu)

−100
−100
−200
−200

1

1

0.9
0.9

−300
−300

0.8
0.8

−400
−400

0.7
0.7
0

50

0

100
100

50

150
150

200
250
200 (s) 250
Time
Time (s)

300
300

350
350

0

400
400

0

[3] ≡ [4]
[3] ≡ [4]
50
50

(a) Frequency
(a) deviation
0.10.1
5 ·−10
2
5 · 10

100
100

150
150

200
250
200 (s) 250
Time
Time (s)

300
300

350
350

400
400

(b) Rotational
(b) speed

[2] [2] [3] [3]

−2

0 0

P (pu)

[1[]1]
[1] [1]

[5[]5]

−2
5 ·−10
2
−5−
· 10

∆PWF (pu)
∆PWF (pu)

[1]
[1]
[5]
[5]

−0.1
−0.1
−0.15
−0.15
−0.2
−0.2
−0.25
−0.25
−0.3
−0.3
0
0

[4]
50

[4]

50

100
100

150
150

200
250
200
250
Time (s)
Time (s)

300
300

350
350

400
400

(pu)

(c) Variation(c)of wind power

(d) Frequency(d)
control strategy

Figure
Wind power
plantplant
response
for scenario
2 and
frequency2controller
of [23]. (a) Frequency
Figure
21.21. Wind
power
response
for
scenario
and frequency
controller of
deviation; (b) Rotational speed; (c) Variation of wind power; (d) Frequency control strategy.
[24]
1.2

[1] ≡ [2]

[1]

1.19

−50

1.18

−100

1.17
ΩWT (pu)

∆ f (mHz)

0

−150
−200

1.16
1.15

[5]

1.14

−250

1.13

−300

1.12
0

20

40

60
80
Time (s)

100

120

140

1.11

[3] ≡ [4]
0

(a)

20

40

60
80
Time (s)

(b)
Figure 22. Cont.

100

120

140

−250

1.13

−300

1.12
0

20

40

Energies 2018, 11, 1436

60
80
Time (s)

100

120

140

1.11

[3] ≡ [4]
0

20

(a) Frequency deviation
·10−2
·10−2
[2]
8
8

6

100

120

140

16 of 21

[2]

P (pu)

4

∆PWF (pu)

∆PWF (pu)

60
80
Time (s)

(b) Rotational speed

6

4

40

2

0

0

2

[3] [3]

[4] [4]

−2 −2
−4 −4
0

[1[]1]

[1] [1]

[5][5]
0

20 20

40 40

60 60
8080
Time
Time
(s)(s)

100
100

120
120

140
140

(c)of wind power
(c) Variation

(pu)

(d) Frequency(d)
control strategy

Figure 22. Wind power plant response for scenario 2 and adaptive and smoother frequency controller
Figure
22. Wind power plant response for scenario 2 and adaptive and smoother
with x = 0.75. (a) Frequency deviation; (b) Rotational speed; (c) Variation of wind power; (d) Frequency
frequency
controller with x = 0.75
control strategy.

5. Conclusions
A new control for VSWTs has been proposed in order to allow them to participate in
frequency control. It is based on two operation modes: overproduction and recovery, varying the active
power provided by the VSWTs through the ’hidden’ kinetic inertia stored in their rotating masses.
It is tested within four different supply-side scenarios consisting of thermal, hydro-power and wind
power plants. In each scenario, wind power plants have increased their capacity from 15 to 45%, at the
time that thermal plants have decreased from 73 to 43% in order to estimate the frequency response of
a future power system with high integration of renewable energy sources.
Results show that the Nadir can be reduced a 45% if the wind power plant control proposed
participates in frequency control, compared to current situations in which only conventional plants
provide frequency control. A secondary frequency dip is identified due to the change from
overproduction to recovery periods, consequently increasing the stabilization time. Results are also
compared to a previous proposal, improving Nadir, stabilization time and especially the secondary
frequency excursion. Actually, it is due to the lack of coordination between power plants, as well as the
different time response of the supply-side operation units. New aggregated and coordinated strategies
are being analyzed by the authors to minimize the impact of these secondary deviations.
Author Contributions: All authors contributed equally to this work.
Acknowledgments: This work was supported by “Fundación Séneca—Agencia de Ciencia y Tecnología
de la Región de Murcia” (ref. 19379/PI/14) and “Ministerio de Educación, Cultura y Deporte” of Spain
(ref. FPU16/04282).
Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript:
a
b
c
n
CP
Deq

First parameter of the parabola
Second parameter of the parabola
Third parameter of the parabola
Number of VSWT in the wind power plant
Power coefficient
Equivalent damping factor of the power system

Energies 2018, 11, 1436

Heq
Hi
Pacc
Pcmd
Pe
Pe f
PMPPT
Pmt
P1
P2
P3
SB
SB,i
VW
β
∆f
∆ f lim
∆Pg
∆PH
∆PL
∆POP
∆PT
∆PWF
∆Ω
λ
Ωerr
ΩWT
ΩWT,min
Ω MPPT
Ωre f
ΩV

17 of 21

Equivalent inertia constant of the power system
Inertia constant of each generator unit
Acceleration power
Commanded power of the VSWT
Active power provided by the wind power plant
Active measured power provided by the wind power plant
Maximum power point tracking of the VSWT
Mechanical power of the VSWT

First point to calculate the parabola: P1 : ΩWT,min , Pmt (ΩWT,min )
Second point to calculate the parabola: P2 : (ΩV , PMPPT (ΩV ))
Third point point to calculate the parabola: P3 : (Ω MPPT , PMPPT (Ω MPPT ))
Rated power of the power system
Rated power of each power generation unit
Wind speed
Pitch angle
Frequency excursion
Value at which frequency controller of the VSWT activates
Variation of active power of the power system: ∆Pg = ∆PWF + ∆PT + ∆PH
Variation of active power of the hydro-power plant
Variation of power demand
Additional active power in overproduction operation mode
Variation of active power of the thermal plant
Variation of active power of the wind power plant
Rotational speed deviation: ∆Ω = Ω MPPT − ΩWT,min
Tip speed ratio
Rotational speed error: Ωerr = ΩWT − Ωre f
Rotational speed of the VSWT
Minimum rotational speed of the VSWT
Rotational speed at maximum power point tracking
Rotational reference speed
Middle value between ΩWT,min and Ω MPPT : ΩV = ΩWT,min + 0.5 · ∆Ω

Appendix A. Parameters for Simulations
Tables A1 and A2 summarize the thermal and hydro-power plant parameters.
Table A1. Thermal power plant parameters [26].
Parameter

Name

Value (puthermal )

TG

Speed relay pilot valve

0.20

FHP

Fraction of power generated by high pressure section

0.30

TRH

Time constant of reheater

7.00

TCH

Time constant of main inlet volumes and steam chest

0.30

RT

Speed droop

0.05

I (s)

Integral controller

1.00

Hthermal

Inertia constant

5.00 s

Energies 2018, 11, 1436

18 of 21

Table A2. Hydro-power plant parameters [26].
Parameter

Name

Value (puhydro )

TG

Speed relay pilot valve

0.20

TR

Reset time

5.00

RT

Temporary droop

0.38

RP

Permanent droop

0.05

TW

Water starting time

1.00

RH

Speed droop

0.05

I (s)

Integral controller

1.00

Hhydro

Inertia constant

3.00 s

Appendix B. Wind Turbine Model
The wind turbine model is based on [29,30]. Parameters of the wind turbine model are
summarized in Table A4 The mechanical power Pmt is obtained (in pu) from
Pmt =

0.5
3
· CP · ρ · Ar · VW
,
Sn

(A1)

being Sn the rated power, ρ the air density, Ar the swept area by the blades, CP the power coefficient
and VW the wind speed. The power coefficient CP is estimated by
CP (λ, β) =

4

4

∑ ∑ αi,j βi λ j .

(A2)

i =0 j =0

This expression gives the mathematical representation of the CP curves, depending on the pitch
angle β and the tip speed ratio λ,
Ω0 · R · ΩWT
λ=
,
(A3)
VW
where Ω0 is the rotor base speed (rad/s), ΩWT refers to the rotor speed (pu), R is the rotor radius (m)
and VW is the wind speed (m/s). Coefficients of αi,j are taken from Table A3.
Table A3. Coefficients αi,j to calculate CP (λ, β)
ij

0

1

2

3

4

0

−4.19 · 10−1

2.18 · 10−1

−1.24 · 10−2

−1.34 · 10−4

1.15 · 10−5

1.57 · 10−2

−1.01 · 10−2

2.15 · 10−3

−1.49 · 10−4

1.48 · 10−5

−9.48 · 10−6

1.62 · 10−6

−7.15 · 10−8

1
2
3
4

−6.76 · 10−2
−8.60 · 10−4

6.04 · 10−2
5.71 · 10−4

−1.39 · 10−2
−1.05 · 10−4

1.07 · 10−3

−2.39 · 10−5

5.99 · 10−6

−8.91 · 10−8

2.79 · 10−6

4.97 · 10−10

The reference rotational speed Ωre f is estimated from the maximum power tracking based on the
measured active power Pe f
Ωre f = −0.67 · Pe2f + 1.42 · Pe f + 0.51,
(A4)
being Pe f the active power generated Pe after a delay T f .

Energies 2018, 11, 1436

19 of 21

The rotational speed of the wind turbine ΩWT is determined from
ΩWT (s) =

Pe (s) − Pmt (s)
,
2HWT · s

(A5)

being HWT the inertia constant of the wind turbine. The speed controller is modeled as a PI controller,
based on the rotational speed error Ωerr
TcmdΩerr =



K pt +

Kit
s



Ωerr .

(A6)

Table A4. Wind power plant parameters [29].
Parameter

Name

Value (puWF )

Vw

Wind speed

10.000 m/s

HWT

Inertia constant

5.190 s

Ω0

Base rotational speed

1.335 rad/s

Tf

Time delay to measure Pe

5.000 s

Tcon

Time delay to generate the current Iinj

0.020 s

VWT

Wind turbine voltage

1.00

K pt

Proportional constant of speed controller

3.000

Kit

Integral constant of speed controller

0.600

References
1.
2.
3.
4.
5.
6.
7.
8.

9.

10.

Huber, M.; Dimkova, D.; Hamacher, T. Integration of wind and solar power in Europe: Assessment of
flexibility requirements. Energy 2014, 69, 236–246. [CrossRef]
Tselepis, S.; Nikoletatos, J. Renewable Energy Integration in Power Grids; The International Renewable Energy
Agency: Masdar City, United Arab Emirates, 2015.
Bevrani, A.G.H.; Ledwich, G. Renewable energy sources and frequency regulation: Survey and new
perspectives. IET Renew. Power Gener. 2010, 4, 438–457. [CrossRef]
Bahrami, S.; Amini, M.H. A decentralized trading algorithm for an electricity market with generation
uncertainty. Appl. Energy 2018, 218, 520–532. [CrossRef]
Zhang, W.; Fang, K. Controlling active power of wind farms to participate in load frequency control of
power systems. IET Gener. Transm. Distrib. 2017, 11, 2194–2203. [CrossRef]
Shah, R.; Mithulananthan, N.; Bansal, R.; Ramachandaramurthy, V. A review of key power system stability
challenges for large-scale PV integration. Renew. Sustain. Energy Rev. 2015, 41, 1423–1436. [CrossRef]
Du, P.; Matevosyan, J. Forecast system inertia condition and its impact to integrate more renewables.
IEEE Trans. Smart Grid 2018, 9, 1531–1533. [CrossRef]
Li, D.Y.; Li, P.; Cai, W.C.; Song, Y.D.; Chen, H.J. Adaptive Fault Tolerant Control of Wind Turbines
with Guaranteed Transient Performance Considering Active Power Control of Wind Farms. IEEE Trans.
Ind. Electron. 2017, 65, 3275–3285. [CrossRef]
Bao, Y.; Xu, J.; Liao, S.; Sun, Y.; Li, X.; Jiang, Y.; Ke, D.; Yang, J.; Peng, X. Field Verification of Frequency
Control by Energy-Intensive Loads for Isolated Power Systems with High Penetration of Wind Power.
IEEE Trans. Power Syst. 2018, 1. [CrossRef]
Toulabi, M.; Bahrami, S.; Ranjbar, A.M. An Input-to-State Stability Approach to Inertial Frequency Response
Analysis of Doubly-Fed Induction Generator-Based Wind Turbines. IEEE Trans. Energy Convers. 2017,
32, 1418–1431. [CrossRef]

Energies 2018, 11, 1436

11.

12.

13.
14.

15.
16.
17.

18.
19.

20.
21.
22.
23.

24.
25.
26.
27.

28.

29.
30.

20 of 21

Ochoa, D.; Martinez, S. Proposals for Enhancing Frequency Control in Weak and Isolated Power Systems:
Application to the Wind-Diesel Power System of San Cristobal Island-Ecuador. Energies 2018, 11, 910.
[CrossRef]
Aho, J.; Buckspan, A.; Laks, J.; Fleming, P.; Jeong, Y.; Dunne, F.; Churchfield, M.; Pao, L.; Johnson, K. A tutorial
of wind turbine control for supporting grid frequency through active power control. In Proceedings of
the 2012 American Control Conference (ACC), Montreal, QC, Canada, 27–29 June 2012; pp. 3120–3131.
[CrossRef]
Kayikçi, M.; Milanovic, J.V. Dynamic contribution of DFIG-based wind plants to system frequency
disturbances. IEEE Trans. Power Syst. 2009, 24, 859–867. [CrossRef]
Toulabi, M.; Bahrami, S.; Ranjbar, A.M. Application of Edge theorem for robust stability analysis of a power
system with participating wind power plants in automatic generation control task. IET Renew. Power Gener.
2017, 11, 1049–1057. [CrossRef]
Yingcheng, X.; Nengling, T. Review of contribution to frequency control through variable speed wind
turbine. Renew. Energy 2011, 36, 1671–1677. [CrossRef]
Sun, D.; Sun, L.; Wu, F.; Zu, G. Frequency Inertia Response Control of SCESS-DFIG under Fluctuating Wind
Speeds Based on Extended State Observers. Energies 2018, 11, 830. [CrossRef]
Tavakoli, M.; Pouresmaeil, E.; Adabi, J.; Godina, R.; Catalao, J.P. Load-frequency control in a multi-source
power system connected to wind farms through multi terminal HVDC systems. Comput. Oper. Res. 2018,
96, 305–315. [CrossRef]
Alsharafi, A.S.; Besheer, A.H.; Emara, H.M. Primary Frequency Response Enhancement for Future Low
Inertia Power Systems Using Hybrid Control Technique. Energies 2018, 11, 699. [CrossRef]
El Itani, S.; Annakkage, U.D.; Joos, G. Short-term frequency support utilizing inertial response of DFIG wind
turbines. In Proceedings of the 2011 IEEE Power and Energy Society General Meeting, San Diego, CA, USA,
24–29 July 2011; pp. 1–8.
Keung, P.K.; Li, P.; Banakar, H.; Ooi, B.T. Kinetic energy of wind-turbine generators for system frequency
support. IEEE Trans. Power Syst. 2009, 24, 279–287. [CrossRef]
Hansen, A.D.; Altin, M.; Margaris, I.D.; Iov, F.; Tarnowski, G.C. Analysis of the short-term overproduction
capability of variable speed wind turbines. Renew. Energy 2014, 68, 326–336. [CrossRef]
Hafiz, F.; Abdennour, A. Optimal use of kinetic energy for the inertial support from variable speed wind
turbines. Renew. Energy 2015, 80, 629–643. [CrossRef]
Tarnowski, G.C.; Kjar, P.C.; Sorensen, P.E.; Ostergaard, J. Variable speed wind turbines capability for
temporary over-production. In Proceedings of the 2009 IEEE Power & Energy Society General Meeting,
Calgary, AB, Canada, 26–30 July 2009; pp. 1–7.
Kang, M.; Kim, K.; Muljadi, E.; Park, J.W.; Kang, Y.C. Frequency control support of a doubly-fed induction
generator based on the torque limit. IEEE Trans. Power Syst. 2016, 31, 4575–4583. [CrossRef]
Tielens, P.; Hertem, D.V. Receding Horizon Control of Wind Power to Provide Frequency Regulation.
IEEE Trans. Power Syst. 2017, 32, 2663–2672. [CrossRef]
Kundur, P.; Balu, N.J.; Lauby, M.G. Power System Stability and Control; McGraw-hill: New York, NY, USA,
1994; Volume 7.
Margaris, I.D.; Papathanassiou, S.A.; Hatziargyriou, N.D.; Hansen, A.D.; Sorensen, P. Frequency control in
autonomous power systems with high wind power penetration. IEEE Trans. Sustain. Energy 2012, 3, 189–199.
[CrossRef]
Pyller, M.; Achilles, S. Aggregated Wind Park Models for Analyzing Power System Dynamics. In Proceedings
of the 4th International Workshop on Large-Scale Integration of Wind Power and Transmission Networks
for Offshore Wind Farms, Billund, Denmark, 20–21 October 2003.
Ullah, N.R.; Thiringer, T.; Karlsson, D. Temporary primary frequency control support by variable speed
wind turbines–Potential and applications. IEEE Trans. Power Syst. 2008, 23, 601–612. [CrossRef]
Miller, N.W.; Sanchez-Gasca, J.J.; Price, W.W.; Delmerico, R.W. Dynamic modeling of GE 1.5 and 3.6 MW
wind turbine-generators for stability simulations. In Proceedings of the 2003 IEEE Power Engineering
Society General Meeting (IEEE Cat. No.03CH37491), Toronto, ON, Canada, 13–17 July 2003; Volume 3,
pp. 1977–1983.

Energies 2018, 11, 1436

31.
32.

21 of 21

Electricity Statistics 2016 (in GWh). 2017. Available online: http://ec.europa.eu/eurostat/statisticsexplained/index.php/File:Electricity_Statistics_2016_(in_GWh)-T1.png (accessed on 1 June 2018).
ENTSOE.
Network Code on Load-Frequency Control and Reserves. 2013. Available online:
https://www.entsoe.eu/ (accessed on 1 June 2018).
c 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access

article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).


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