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Power systems with high renewable energy sources: a review of inertia and
frequency control strategies over time
Ana Fern´andez-Guillam´ona,, Emilio G´omez-L´azarob, Eduard Muljadic,´
Angel Molina-Garc´ıaa
aDept. of Electrical Engineering, Universidad Polit´ecnica de Cartagena, 30202 Cartagena, Spain
bRenewable Energy Research Institute and DIEEAC-EDII-AB, Universidad de Castilla-La Mancha, 02071 Albacete, Spain
cDept. of Electrical and Computer Engineering, Auburn University, 220 Broun Hall, Auburn, AL 36849, USA
Abstract
Traditionally, inertia in power systems has been determined by considering all the rotating masses directly connected
to the grid. During the last decade, the integration of renewable energy sources, mainly photovoltaic installations and
wind power plants, has led to a significant dynamic characteristic change in power systems. This change is mainly
due to the fact that most renewables have power electronics at the grid interface. The overall impact on stability and
reliability analysis of power systems is very significant. The power systems become more dynamic and require a new set
of strategies modifying traditional generation control algorithms. Indeed, renewable generation units are decoupled from
the grid by electronic converters, decreasing the overall inertia of the grid. ‘Hidden inertia’, ‘synthetic inertia’ or ’virtual
inertia’ are terms currently used to represent artificial inertia created by converter control of the renewable sources.
Alternative spinning reserves are then needed in the new power system with high penetration renewables, where the lack
of rotating masses directly connected to the grid must be emulated to maintain an acceptable power system reliability.
This paper reviews the inertia concept in terms of values and their evolution in the last decades, as well as the damping
factor values. A comparison of the rotational grid inertia for traditional and current averaged generation mix scenarios
is also carried out. In addition, an extensive discussion on wind and photovoltaic power plants and their contributions
to inertia in terms of frequency control strategies is included in the paper.
Keywords: Inertia constant, Power system stability, Frequency regulation, Damping factor, Renewable energy sources,
Virtual inertia
Nomenclature
DFIG Double Fed Induction Generator
EU European Union
FSWT Fixed Speed Wind Turbine
HAWT Horizontal Axis Wind Turbine
PMSG Permanent Magnet Synchronous Generator
PV Photovoltaic
RES Renewable energy sources
ROCOF Rate Of Change Of Frequency
SCIG Squirrel Cage Induction Generator
VSWT Variable Speed Wind Turbine
WPP Wind Power Plant
1. Introduction
Presently, power system stability relies on synchronous
machines connected to the grid. They are synchronized
Email addresses: ana.fernandez@upct.es (Ana
Fern´andez-Guillam´on), emilio.gomez@uclm.es (Emilio
G´omez-L´azaro), mze0018@auburn.edu (Eduard Muljadi),
angel.molina@upct.es (´
Angel Molina-Garc´ıa)
to the grid and their stored kinetic energy is automati-
cally extracted in response to a sudden power imbalance.
For example, a sudden additional large load or a loss of
a large generation unit from the grid, will slow down the
machines on the grid and subsequently reduce grid fre-
quency [1]. However, the power systems generation fleet
is changing from conventional generation to renewable en-
ergy sources (RES) [2]. Limited fossil fuel reserves and
the importance of reducing greenhouse gases emissions are
the main reasons for this transition in the electrical genera-
tion [3]. For instance, wind, solar and biomass generations
overtook coal power in the EU for the first time during the
year 2017 [4]. However, some authors consider that only
half of the overall electricity demand can be provided by
RES [5, 6], despite the fact that it is expected that future
electrical grids will be based on RES, distributed genera-
tion and power electronics [7]. As an example, in Europe,
it is expected that 323 and 192 GW of wind and PV will
be installed in 2030, which will cover up to 30% and 18%
of the demand, respectively [8, 9].
Among the different renewable sources available, PV
and wind (especially doubly fed induction generators,
DFIG [10]) are the two most promising resources for gen-
erating electrical energy [11]. Apart from their intermit-
Preprint submitted to Renewable & Sust. Energy Reviews https: // doi. org/ 10. 1016/ j. rser. 2019. 109369 April 8, 2020
arXiv:2004.02951v1 [eess.SY] 6 Apr 2020
tency, they are connected through power converters which
decouple them from the power system grid [12, 13]. There-
fore, the effective inertia of the electrical grid is reduced
when conventional generators are replaced by RES [14, 15],
affecting the system stability and reliability [16]. This fact
is considered as one of the main drawbacks of integrat-
ing a large amount of non-synchronous generators (i.e.
RES) into the grid [17], as the frequency stability and
its transient response is compromised [18]. Actually, low
system inertia is related with (i) a faster rate of change
of frequency (ROCOF) and (ii) larger frequency devia-
tions (lower frequency nadir during frequency dips) within
a short-time frame [19].
In this work, we conduct an extensive literature review
focusing on the inertia values for power systems and wind
power plants. The averaged inertia values are estimated
by different countries for the last two decades, by con-
sidering the ’effective’ rotating masses directly connected
to the grid. In addition, the damping factor evolution is
also included in the paper based on most of technical con-
tributions and analysis found in the literature. The rest
of the paper is organized as follows: inertia and damping
factor analysis for power systems is discussed in detail in
Section 2, determining the averaged inertia estimation for
different countries; control strategies and contributions to
integrate RES into grid frequency response is described in
Section 3; finally, the conclusion is given in Section 4.
2. Inertia analysis in power systems
2.1. Modeling the inertial response of a rotational syn-
chronous generator: inertia constant analysis
The group turbine-synchronous generator rotates due to
two opposite torques: (i) mechanical torque of the turbine,
Tmand (ii) electromagnetic torque of the generator, Te.
The motion equation is [20, 21]:
2Hdωr
dt =Tm−Te,(1)
where both the Tmand the Teare expressed in pu and H
the inertia constant in s. His given by:
H=1
2·J·ω2
base
Sbase
,(2)
being Jthe moment of inertia, ωbase the base frequency
and Sbase the base power. Hdetermines the time interval
during which the generator can supply its rated power only
using the kinetic energy stored in the rotational masses of
the generator. In Table 1, a review of Hvalues for different
types of generation units and rated power is shown.
Expressing Eq. (1) in terms of power, and considering
the initial status as 0, P=P0+ ∆P= (ωr0+ ∆ωr)·(T0+
∆T). For small deviations, the second order terms are
neglected due to their small values, thus ∆P'ωr0·∆T+
T0·∆ωr, being ∆P= ∆Pm−∆Peand ∆T= ∆Tm−∆Te.
Type of generating unit Rated power H(s) Reference Year
Thermal 500 −1500 MW 2.3−2 [22] 2008
Thermal 1000 MW 4 −5 [23] 2011
Thermal 10 MW 4 [24] 2007
Thermal Not indicated 4 −5 [25] 2012
Thermal (2 poles) Not indicated 2.5−6 [26] 1994
Thermal (4 poles) Not indicated 4 −10 [26] 1994
Thermal (steam) 130 MW 4 [12] 2012
Thermal (steam) 60 MW 3.3 [12] 2012
Thermal (combined cycle) 115 MW 4.3 [12] 2012
Thermal (gas) 90 −120 MW 5 [12] 2012
Thermal Not indicated 2 −8 [27] 2011
Hydroelectric 450 <n<514 rpm 10 −65 MW 2 −4.3 [22] 2008
Hydroelectric 200 <n<400 rpm 10 −75 MW 2 −4 [22] 2008
Hydroelectric 138 <n<180 rpm 10 −90 MW 2 −3.3 [22] 2008
Hydroelectric 80 <n<120 rpm 10 −85 MW 1.75 −3 [22] 2008
Hydroelectric Not indicated 4,75 [28] 2013
Hydroelectric n <200 rpm Not indicated 2 −3 [29] 1994
Hydroelectric n >200 rpm Not indicated 2 −4 [29] 1994
Hydroelectric Not indicated 2 −4 [26] 1994
Table 1: Summary of inertia values (H) for different generation
types.
Furthermore, in steady-state Tm0=Te0and ωr0= 1 pu.
Hence, ∆P= ∆Pm−∆Pe'∆Tm−∆Te.
Therefore, if small variations around the steady-state
conditions are considered, Eq. (1) can be written as Eq. (3)
in the time domain, or as Eq. (4) if the Laplace transform
is applied.
d∆ωr
dt =1
2H(∆Pm−∆Pe) (3)
∆ωr=∆Pm−∆Pe
2H·s(4)
Some loads (especially inverter-based loads) can also be
modified to work as a load resource (demand response ca-
pability) under frequency deviations (e.g., motors driving
compressors, pumps, industry loads, HVAC-heating ven-
tilation air conditioning...). This fact can be modeled by
including the damping factor D. As an example, for a
synchronous machine, the electrical power Pecan be then
expressed as follows,
∆Pe= ∆PL+D·∆ωr,(5)
where PLrepresents the load independent from frequency
excursions.
Substituting Eq. (5) into Eq. (4), the mathematical rep-
resentation of the motion of a synchronous generator is
obtained. It is commonly referred to as swing equation,
see Eq. (6). It can be expressed in the form of a block di-
agram as shown in Figure 1. Hence, the initial response of
a synchronous generator to a frequency event is governed
by its stored kinetic energy at the rated frequency [30],
∆ωr=∆Pm−∆PL
2H·s+D(6)
2.2. Aggregated swing equation: equivalent inertia con-
stant and damping factor analysis
2
Figure 1: Block diagram representation of the swing equation
Ref. Value (puMW /puHz ) Analysis Year
[26] 1–2 Power system stability 1994
[35] 0.83 Two areas with non-reheat thermal units 2011
[36] 1.66 Two areas with thermal units 2011
[37] 1–1.8 Three areas with non-reheat thermal units 2012
[38] 2 One area with nuclear, thermal, wind and PV 2012
[39] 0.5 – 0.9 Three areas with non-linear thermal units 2013
[40] 0.83 Two areas non-reheat thermal units 2013
[41] 0.83 Two areas with thermal units 2013
[42] 0.83 Two areas with reheat units 2015
[43] 0.8 IEEE 9 bus system with hydro-power, gas and wind turbines 2016
[44] 1–1.8 One and three areas with non-reheat thermal units 2017
[45] 1–1.8 Three areas with non-reheat thermal units 2018
[46] 1 Two areas with non-reheat thermal units 2018
Table 2: Damping factor values. Literature review
In order to apply the swing equation to a power system,
Eq. (6) is rewritten. All synchronous generators are re-
duced to an equivalent rotating mass with an equivalent
inertia Heq,
Heq =
GCP S
X
i=1
Hi·Sbase,i
Sbase
,(7)
being GC P S the number of generators coupled to the
power system [31], such as conventional power plants and
FSWTs. In the past, it was considered that the equiva-
lent inertial constant Heq of a power system was constant
and time-independent. However, due to the RES integra-
tion and the variation in their generation throughout the
day, the season of the year, etc., it is understood that Heq
changes with time. An example of this variation is pre-
sented for the German power system during 2012 in [32],
see Figure 2. From these data, the cumulative frequency
curve is obtained and depicted in Figure 3. It can be seen
that during 50% of the year 2012, the equivalent inertia
was under 5.7 s; 10% of the year, Heq was under 5 s; and
only 1% of the year, its value was under 4 s.
In the same way as synchronous generators, all loads are
grouped in an equivalent one with an equivalent damping
factor Deq. As stated in [33], the impact of an inaccurate
value of Deq is relatively small if the power system is stable,
but this can be a major contribution under disturbances.
Moreover, it is expected to decrease accordingly to the
use of variable frequency drives [34]. Table 2 summarizes
the different values proposed for the damping factor in the
literature over recent decades.
By using Eq. (7), an estimation of the equivalent inertia
Heq of several parts of the world has been carried out by
the authors. The International Energy Agency (IEA) pro-
vides global statistics about energy [47]. By considering
Figure 2: Histogram of equivalent inertia Heq in the German power
system during 2012, [32]
1 10 50 100
2.5
3
3.5
4
4.5
5
5.5
6
Cumulative frequency (%)
Heq (s)
Figure 3: Cumulative frequency of the equivalent inertia Heq in the
German power system during 2012
3
Conventional sources: coal,
fuel, gas and nuclear
80%
Others
3%
Renewable
sources
20%
Hydro-power
92%
Biomass + Biofuel
5%
(a) Generation mix in 1996
Conventional sources: coal,
fuel, gas and nuclear
76%
Others
2%
Renewable
sources
24%
Hydro-power
68%
Biomass + Biofuel
9%
Wind
power
16%
PV
5%
(b) Generation mix in 2016
Figure 4: Generation mix in the world: change between 1996 and
2016
the annual averaged electricity, an averaged equivalent in-
ertia constant (Heq) provided by such conventional power
plants —Table 1— can be estimated. Note that for this
estimation, Sof Eq. (7) is replaced by the annual electric-
ity value (Eg). The expression used to estimate the inertia
is then Eq. (8), being Eg,total the total electricity supplied
(conventional+RES generation) within a year.
Heq =
GCP S
X
i=1
Hi·Eg,i
Eg,total
.(8)
Figure 4 shows a significant change in the averaged gen-
eration mix between 1996 and 2016. The total electric-
ity consumption has been increased by more than 80%
within these two decades. However, RES generation has
only increased by 4% in the same two decades. Moreover,
the share of the different renewable sources has changed
significantly. Indeed, the contribution share from hydro-
power has been surpassed by biomass, biofuels, wind, and
PV. Based on the approach previously described, Figure 5
depicts the differences between the inertia constant for dif-
ferent continents in 1996 and in 2016. EU has reduced the
equivalent inertia constant by nearly 20%. In contrast, the
reduction of inertia in Asia, USA, and South America lies
between 2.5 and 3%.
A more extensive analysis is conducted for the EU,
where an average inertia reduction of 0.6 s can be esti-
mated. In Figure 6, an overview of the evolution of the
equivalent inertia in some EU countries is summarized.
Similar information is given in Figure 7, where the reduc-
tion of the equivalent inertia is illustrated for those EU
Figure 5: Equivalent inertia constants estimated in the world by
continent. Change between 1996 and 2016
Figure 6: Equivalent inertia constants estimated in EU-28. Change
between 1996 and 2016
4
Denmark
Lithuania
Germany
Spain
Portugal
Sweeden
Luxembourg
UK
Finland
Romania
Austria
Ireland
Malta
Italy
0
10
20
30
40
50
60
Reduction of Heq (%)
Figure 7: Equivalent inertia reduction in EU-28 between 1996 and
2016.
1996
1998
2000
2002
2004
2006
2008
2010
2012
2014
2016
1.5
2
2.5
3
3.5
4
4.5
Year
Heq (s)
Europe
Ireland
Spain
Denmark
Figure 8: Evolution of equivalent inertia in EU-28 and some countries
between 1996 and 2016.
countries which have suffered a reduction larger than 15%
(Heq reduction >15%). Figure 8 represents the equivalent
inertia evolution of EU, as well as in three different coun-
tries (Ireland, Spain, and Denmark). For the EU, RES
supply has increased nearly by 20%, in line with the re-
duction of its inertia constant (refer to Figure 9). Similar
to the generation mix in the world, wind, biomass, biofuels,
and PV have surpassed the development of hydro-power,
which has drastically slowed down in recent years.
2.3. Modified equivalent inertia analysis: emulating hid-
den and virtual inertia from RES
To obtain the maximum power from the natural re-
source, both wind and PV power plants are controlled by
power converters using the maximum power point track-
ing (MPPT) technique [48]. This power converter pre-
vents wind and PV power plants to directly contribute
to the inertia of the system, being thus referred to as
Conventional sources: coal,
fuel, gas and nuclear
86%
Wind power
1%
Others
1%
Renewable
sources
14%
Hydro-power
90%
Biomass + Biofuel
8%
(a) Generation mix in 1996
Conventional sources: coal,
fuel, gas and nuclear
69%
Biomass
+ Biofuel
21%
Others
2%
Renewable
sources
31%
Wind
power
30%
Hydro-power
37%
PV
10%
(b) Generation mix in 2016
Figure 9: Generation mix in Europe: change between 1996 and 2016.
’decoupled’ from the grid [49]. As a consequence, to ef-
fectively integrate RES into the grid, frequency control
strategies have been developed [50, 51, 52]. Such methods
are commonly named as synthetic, emulated or virtual in-
ertia [53]. If this emulation of inertia coming from RES was
included in power systems, it would have to be considered
to estimate the equivalent inertia. Then, this modified
equivalent inertia would have two different components:
(i) synchronous inertia coming from conventional gener-
ators, HSand (ii) emulated/virtual inertia coming from
RES, HEV [54, 55, 34, 56, 57], modifying Eq. (7) to Eq. (9).
EV G is the number of RES connected to the grid through
emulation/virtual control methods, and HEV is the inertia
constant of the emulated/virtual generation unit.
Heq =
HS
z }| {
GCP S
X
i=1
Hi·Sbase,i +
HEV
z }| {
EV G
X
j=1
HEV ,j ·Sbase,j
Sbase
.(9)
This modified equivalent inertia expressed in Eq. (9)
is graphically illustrated in Figure 10, based on [58].
Note the different representation between the coupling of
VSWT and PV to the grid. The reason to this is that WPP
has ’hidden’ deployable inertia based on the kinetic energy
stored in their blades, drive train and electrical generators,
whereas PV has no stored kinetic energy due to the ab-
sence of rotating masses. Actually, modern VSWT have
rotational inertia constants comparable to those of conven-
tional generators [30, 59, 60]. However, this inertia is ’hid-
den’ from the power system point of view due to the con-
5
DC/AC
Figure 10: Power system with synchronous, hidden and virtual iner-
tia.
verter [61]. For instance, in Table 3 and Figure 11, the in-
ertia constant of several types of wind turbines are summa-
rized, and most of them are within the range 2−6 s, in line
with values presented for conventional units in Table 1. As
a consequence, it is commonly considered that VSWT pro-
vide ’emulated hidden inertia’, as rotational inertia could
be provided by them [62, 63, 64, 65]. On the other hand,
PV installations don’t have any rotating masses [11, 66],
having an inertia constant H≈0 [67]. Therefore, due to
this absence of rotational masses and, subsequently, ab-
sence of inertia, the specific literature refers to the ’emu-
lated synthetic/virtual inertia’ provided by such PV power
plants [68, 69, 70, 71].
With regard to the equivalent inertia estimation for the
EU, and considering the averaged hidden inertia of WPP
depicted in Table 3, the inertia change is reduced around
0.3 s, corresponding to 50% of the value determined in
Section 2.2. Figure 12 presents the evolution of the equiv-
alent inertia in the same EU countries of Figure 6, being
the dark blue values those due to the hidden inertia pro-
vided by VSWTs. As can be seen, by considering the
hidden inertia of VSWT leads to a smaller reduction of
the equivalent inertia.
3. RES frequency control strategies
3.1. Preliminaries
Generation and load in the power systems must be
continuously balanced to maintain a steady frequency.
Under any generation-load mismatch, grid frequency
changes [94]. Moreover, significant deviations from the
nominal value may cause under/over frequency relay op-
erations, and even lead to the disconnection of some loads
Type of wind turbine Rated power H(s) Reference Year
Not indicated Not indicated 2 −5 [12] 2012
Not indicated 2 MW 4.45 [72] 2007
Not indicated 2 MW 2.5 [73] 2003
Not indicated 16 ·600 kW 3.7 [74] 2003
HAWT with SCIG 200 kW 1.2 [75] 2010
FSWT 10 ·500 kW 3.2 [76] 2005
FSWT Not indicated 3.5 [77] 2005
VSWT 2 MW 6 [78] 2006
VSWT 3.6 MW 5.19 [79] 2008
Types 1, 2, 3 1–5 MW 2.4−6.8 [80] 2005
DFIG 2 MW 3.5 [81] 2003
DFIG 660 kW 4 [82] 2006
DFIG 1.5 MW 6.35 [83] 2009
DFIG 1.5 MW 4.41 [83] 2009
DFIG 3.6 MW 4.29 [84] 2011
DFIG 2 MW 3.5 [85] 2003
DFIG 2 MW 2.5 [86] 2004
DFIG 660 kW 4 [24] 2007
DFIG (WPP) 300 MW 1 [87] 2007
DFIG 750 MW 5.4 [88] 2005
DFIG 2 MW 3 [89] 2013
DFIG 1.5 MW 3 [90] 2012
DFIG 2 MW 0.5 [91] 2006
DFIG 2 MW 3.5 [92] 2003
PMSG 455 kW 2.833 [93] 1996
Table 3: Wind turbines inertia constants Haccording to rated power
and reference
012345
0
2
4
6
P (MW)
H (s)
DFIG
FSWT
VSWT
SCIG
PMSG
Figure 11: Inertia constant values (H) for different wind turbine
technologies
6
Figure 12: Equivalent averaged inertia constants estimated in EU-28
considering emulated inertia provided by WPPs (1996–2016).
from the grid [95]. Consequently, frequency stability is
related to the ability of a power system to maintain the
operating frequency close to its nominal value (i.e., 50 or
60 Hz, depending on the region) when an imbalance situ-
ation occurs [96]. Hence, frequency control is an essential
component of a secure and robust electrical power sys-
tem [97].
Frequency control is traditionally implemented by ad-
justing real power generation to balance the load. This
traditional scheme has a hierarchical structure, and in Eu-
rope it is usually composed of three layers: primary, sec-
ondary and tertiary, from fast to slow timescales [98]. The
primary and secondary controls are automatic, while ter-
tiary control is manually executed by the transmission sys-
tem operator [99].
The primary frequency control (PFC) operates at a
timescale up to low tens of seconds and uses a governor
to adjust the mechanical power input around a set-point
based on the local frequency deviation [100]. It is the auto-
matic response of the turbine governors in response to the
deviations of the system frequency and depends on the
setting of the speed-droop characteristics of each power
plant [101]. Therefore, each generating unit can be mod-
eled with its speed governing system [102]. However, it
does not restore grid frequency to its nominal value [103].
In Europe, primary control is triggered before the fre-
quency deviation exceeds ±20 mHz [104].
Secondary frequency control or automatic generation
control (AGC) removes the steady-state frequency devi-
ation generated by the PFC [105]. An integral controller
modifies the turbine governor set-point to bring the fre-
Figure 13: Frequency response after an imbalance
Inertia and
frequency
control
techniques
PV power
plant
De-loading
technique
Using ESS
Wind
power plant
Using ESS
De-loading
technique
Pitch angle
control
Over speed
control
Inertial
response
Droop
control
Hidden
inertia
emulation
Fast power
reserve
Figure 14: Inertia and frequency control techniques for RES
quency back to its nominal value [106]. It also keeps the
scheduled exchanges between the different areas of an in-
terconnected power system to their expected values [107].
In Europe, the time-frame is from seconds up to typically
15 min after an incident [104]. Figure 13 gives an example
of a typical frequency excursion, where primary frequency
control and AGC time intervals are shown.
Finally, the main objective of the tertiary frequency
control is to perform an economically efficient generation-
dispatch (economic dispatch) [108]. Moreover, it is also
intended to relieve transmission congestions and restoring
the secondary control reserves [109]. This is also called
security-constrained-economic dispatch (SCED).
An increase in the penetration level of RES addresses a
decreasing of the number of synchronous generators, lead-
ing to an initial decline in system inertia and power re-
serves for primary and secondary control [110]. Subse-
quently, low inertia is related to larger frequency devia-
tions after a generation-load mismatch event [111], having
implications on frequency related power systems dynam-
ics [112]. It is important to note that the rate of change
of frequency (ROCOF) is strongly affected by the inertia
available in the system [113]. By this means, it is nec-
essary that RES become an active role in grid frequency
regulation, providing active power support under distur-
bances [114]. The different technologies proposed to give
additional inertia and frequency control from RES are usu-
ally classified as summarized in Figure 14.
7
3.2. PV power plant frequency control strategies
PV power plants can use ESS such as batteries [115,
116, 117], super-capacitors [118, 119] and flywheels [117] in
order to provide additional active power in an imbalanced
situation.
A different strategy to be considered is the ‘de-loading
technique’ of the PV plant. It is based on operating these
generating units below their optimal generation point, in
order to have a certain amount (headroom) of active power
to supply real power to the grid in case of a frequency-dip
contingency [120]. In general, PV power plants operate
at the maximum power point tracking mode according to
certain meteorological conditions (i.e., temperature Tand
irradiation G), maximizing the revenues from selling en-
ergy [121]. Contributions focused on this technique can be
found in [122, 123, 124, 125, 126, 127]. By curtailment, we
are operating the PV plant at a de-loaded point Pdel, below
PMP P , so that the PV plants are able to support system
frequency, as some power reserves ∆P=PMP P −Pdel are
available. As depicted in Figure 15, Pdel involves two dif-
ferent voltages: (i) over the maximum power point voltage,
Vdel,1> VM P P and (ii) under the maximum power point
voltage, Vdel,2< VMP P . Due to stability concerns, the de-
loaded voltage corresponds to the higher value Vdel,1[128].
3.3. Wind power plant frequency control strategies
As in the PV power plants, wind power plants can also
use ESS to provide additional power boost during an im-
balanced situation (i.e., frequency dips). Batteries [116],
super-capacitors[118, 129] and flywheels [130] are proposed
in the literature review.
Wind turbines have two possibilities to operate with the
de-loading technique: (i) pitch angle control and (ii) over-
speed control [61]. The pitch angle control consists of in-
creasing the pitch angle from β0to β1for a constant wind
speed VW, keeping the rotor speed at the maximum power
point ΩMP P (Figure 16). This way, the power supplied
Pdel is below the maximum available aerodynamic power
PMP P . Therefore, a certain amount of active power re-
serve is available to supply additional generation in case of
a frequency deviation occurs [131, 132, 133, 134]. The over-
speed control shifts the de-loaded power Pdel towards the
right of the maximum power PMP P , maintaining the pitch
angle β0for a constant wind speed VW, see Figure 17(a).
When frequency response is provided, rotor speed has to
be reduced from Ωdel,1to ΩM P P , releasing kinetic energy
to the system [135, 136, 137, 138]. As depicted in Fig-
ure 17(b), a third possibility could be to set the turbine to
operate the rotor speed below the rotor speed for MPPT
operation. In that case, the rotor speed must increase
from Ωdel,2to ΩM P P utilizing some power extracted from
the turbine. As a consequence, the frequency response is
reduced, and could even be opposite to the desired behav-
ior during the first seconds. Because of this, it is usually
considered as a ‘detrimental strategy’ [139, 140].
(a) Vdel,1> VMP P
(b) Vdel,2< VMP P
Figure 15: Deloading techniques for PV
Figure 16: Pitch control
8
(a) Over-speed control
(b) Under-speed control
Figure 17: Over-speed and under-speed control
With regard to providing an inertial response from wind
power plants, the main idea is to increase the output power
of the VSWT for a few seconds. One or more supplemen-
tary loops are introduced into the active power control,
which are only activated under frequency deviations. Both
blades and rotor inertia are then used to provide primary
frequency response under power imbalance situations. The
kinetic energy stored in the rotating masses is supplied to
the grid as an additional active power [141].
The droop control emulates the behavior of a gover-
nor in a conventional synchronous generator, respond-
ing to the changes in the system frequency. The active
power supplied by the VSWTs changes proportionally to
the frequency deviation ∆fas illustrated in Figure 18(a),
where RW T is the droop control setting (speed adjustment
rate). Subsequently, the variation of power is defined as
Eq. (10), where ∆Pis the signal given to the power con-
verter to release the stored kinetic energy. The increase of
the active power output results in a decrease in the rotor
speed [142, 143, 144, 145].
∆P=−∆f
RW T
(10)
Hidden inertia emulation for wind turbines is character-
ized by an emulation of the inertial response of a tradi-
tional synchronous generator. There are two types of hid-
den inertia emulation controls: (i) one loop and (ii) two
loops. In the first case, an additional power ∆Pbased on
the ROCOF is added to PMP P after a generation deficit,
(a) Droop characteristic
(b) Block diagram of droop control [146]
Figure 18: Droop control for VSWTs
thus, reducing the generator speed and releasing the stored
kinetic energy of the rotating blades [147, 148, 149]. The
drawback of this control strategy is that frequency is not
restored to its nominal value [150]. An additional loop
proportional to the frequency deviation ∆fis then added,
as indicated in Figure 19(b). This second loop lasts until
the frequency is restored to f0[78, 151]. Figure 20 com-
pares the frequency responses by considering one or two
loops controllers.
The fast power reserve technique is based on supply-
ing the kinetic energy stored in the rotating masses of
the wind turbine to the grid as additional active power.
Afterward, the energy extracted is recovered through an
under-production period. When the frequency deviation
surpasses the predefined threshold value, the additional
active power is provided, decreasing the rotational speed
of the rotor. Overproduction power was initially defined
as a constant value [79, 152, 153, 154, 155, 156]. However,
new approaches consider it as variable [157, 158, 159] by
considering other limits (e.g. toque limit, the current limit
of the power electronic switches, etc). The recovery period
is used to restore both power and rotational speed to their
pre-event values. Different techniques have also been pro-
posed in the references listed. Figure 21 shows the fast
power reserve emulation control indicated in [152].
Table 4 presents an overview of the application of some
of the techniques. It includes the integration of wind power
plants (WPP) and the power imbalance ∆P; both in the
percentage of the total capacity of the system. As can be
seen, some strategies are combined, in order to improve the
frequency deviation after the generation-load mismatch.
9
(a) One loop
(b) Two loops
Figure 19: Hidden inertia emulation controllers
Figure 20: Frequency response of the one loop and two loops con-
trollers
Ref. Type of control WPP (%) ∆P(%) Year
[160] Droop 46 14 2012
[160] Hidden inertia (i) 46 14 2012
[160] Dro op + Hidden inertia (i) 46 14 2012
[161] Variable droop 30 – 2011
[162] De-loading by pitch 24 3 2016
[162] De-loading by pitch 50 4 2016
[163] Fast power reserve 57 8.5 2017
[164] Hidden inertia (ii) 25 1.7 2012
[165] Dynamic droop + Hidden inertia (i) 10 8.5, 10, 11 2016
[166] Dro op + Hidden inertia (i) 15 2 2016
[166] Dro op + Hidden inertia (i) 50 2 2016
[167] Fast power reserve 12.5 6.25 2015
[168] Hidden inertia (i) 20 8.33 2015
[168] Droop 20 8.33 2015
[168] Droop 20 8.33 2015
[169] Hidden inertia (ii) 30 2.5 2013
[170] Hidden inertia (i) 38 2.3 2012
[170] De-loading by pitch + Over-speed 38 2.3 2012
[170] Hidden inertia (i) + Pitch + Over-speed 38 2.3 2012
Table 4: Wind turbines frequency control proposals
(a) P−Ω curve
(b) Power variation
Figure 21: Fast power reserve emulation technique [152]
10
4. Conclusion
An extensive literature review focused on inertia esti-
mation for power systems and wind power plants is con-
ducted by the authors. The contribution of PV power
plants as a ’virtual inertia’ is also discussed in the pa-
per, as well as a detailed analysis of the damping fac-
tor evolution. Averaged inertia values are estimated for
different regions and countries for the last two decades.
Conventional generation units are considered accordingly,
summarizing their inertia constant values in accordance
with each type of technology and rated power. Our find-
ings indicate that, nowadays, Europe presents a significant
averaged inertia decreasing –around 20% in the last two
decades–, mainly due to the renewable integration decou-
pled from the grid –from 14% in 1996 to 31% in 2016–.
With regard to wind turbines, they present inertia values
similar to conventional generation units –between 2 and
6 s depending on technologies–, which is commonly con-
sidered as ’emulated hidden inertia’. The paper provides
significant information for wind turbines frequency control
strategies and studies of current power systems with high
renewable energy source integration.
Funding
This work was supported by the Spanish Education,
Culture and Sports Ministry [FPU16/04282].
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