Power systems with high renewable energy sources: A review of inertia and frequency control strategies over time

TLDR: This paper reviews the inertia concept in terms of values and their evolution in the last decades, as well as the damping factor values.

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.

Figures

Fig. 11. Inertia constant values (H) for different wind turbine technologies.

Fig. 13. Frequency response after an imbalance.

Fig. 1. Block diagram representation of the swing equation.

Table 4 Wind turbines frequency control proposals.

Fig. 17. Over-speed and under-speed control.

Fig. 2. Histogram of equivalent inertia in the German power system during 2012 [32].

Full text

UNCORRECTED PROOF
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Dept. of Electrical Engineering, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
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Renewable Energy Research Institute and DIEEAC-EDII-AB, Universidad de Castilla-La Mancha, 02071 Albacete, Spain
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Dept. of Electrical and Computer Engineering, Auburn University, 220 Broun Hall, Auburn, AL 36849, USA
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Keywords
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UNCORRECTED PROOF
A. Fernández-Guillamón et al. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx-xxx
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2. Inertia analysis in power systems
2.1. Modeling the inertial response of a rotational synchronous generator:
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L@= EGLAGF G> 9 KQF;@JGFGMK ?=F=J9LGJ AK G:L9AF=< $L AK ;GEEGFDQ J=
>=JJ=< LG 9K swing equation K== I  $L ;9F := =PHJ=KK=< AF L@= >GJE
G> 9 :DG;C <A9?J9E 9K K@GOF AF !A?  #=F;= L@= AFALA9D J=KHGFK= G> 9
KQF;@JGFGMK ?=F=J9LGJ LG 9 >J=IM=F;Q =N=FL AK ?GN=JF=< :Q ALK KLGJ=< CA
F=LA; =F=J?Q 9L L@= J9L=< >J=IM=F;Q 67

2.2. Aggregated swing equation: equivalent inertia constant and damping
factor analysis
$F GJ<=J LG 9HHDQ L@= KOAF? =IM9LAGF LG 9 HGO=J KQKL=E I  AK
J=OJALL=F DD KQF;@JGFGMK ?=F=J9LGJK 9J= J=<M;=< LG 9F =IMAN9D=FL JG
L9LAF? E9KK OAL@ 9F =IMAN9D=FL AF=JLA9 

:=AF? L@= FME:=J G> ?=F=J9LGJK ;GMHD=< LG L@= HGO=J KQKL=E
67 KM;@ 9K ;GFN=FLAGF9D HGO=J HD9FLK 9F< !.2/K $F L@= H9KL AL O9K
;GFKA<=J=< L@9L L@= =IMAN9D=FL AF=JLA9D ;GFKL9FL G> 9 HGO=J KQKL=E
O9K ;GFKL9FL 9F< LAE=AF<=H=F<=FL #GO=N=J <M= LG L@= - . AFL=?J9
LAGF 9F< L@= N9JA9LAGF AF L@=AJ ?=F=J9LAGF L@JGM?@GML L@= <9Q L@= K=9
KGF G> L@= Q=9J =L; AL AK MF<=JKLGG< L@9L ;@9F?=K OAL@ LAE= F
=P9EHD= G> L@AK N9JA9LAGF AK HJ=K=FL=< >GJ L@= "=JE9F HGO=J KQKL=E
<MJAF?  AF -=> 67 K== !A?  !JGE L@=K= <9L9 L@= ;MEMD9
Fig. 1. DG;C <A9?J9E J=HJ=K=FL9LAGF G> L@= KOAF? =IM9LAGF


UNCORRECTED PROOF
A. Fernández-Guillamón et al. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx-xxx
Fig. 2. #AKLG?J9E G> =IMAN9D=FL AF=JLA9 AF L@= "=JE9F HGO=J KQKL=E <MJAF? 
67
LAN= >J=IM=F;Q ;MJN= AK G:L9AF=< 9F< <=HA;L=< AF !A?  $L ;9F := K==F
L@9L <MJAF?  G> L@= Q=9J  L@= =IMAN9D=FL AF=JLA9 O9K MF<=J  K
 G> L@= Q=9J O9K MF<=J K 9F< GFDQ  G> L@= Q=9J ALK N9DM=
O9K MF<=J K
Fig. 3. MEMD9LAN= >J=IM=F;Q G> L@= =IMAN9D=FL AF=JLA9 AF L@= "=JE9F HGO=J KQKL=E
<MJAF? 
Table 2
9EHAF? >9;LGJ N9DM=K 'AL=J9LMJ= J=NA=O
-=>
19DM=
 F9DQKAK 4=9J
67 – +GO=JKQKL=EKL9:ADALQ 
67  /OG9J=9KOAL@FGFJ=@=9LL@=JE9DMFALK 
67  /OG9J=9KOAL@L@=JE9DMFALK 
67 – /@J==9J=9KOAL@FGFJ=@=9LL@=JE9DMFALK 
67  *F=9J=9OAL@FM;D=9JL@=JE9DOAF<9F<+1 
67 – /@J==9J=9KOAL@FGFDAF=9JL@=JE9DMFALK 
67  /OG9J=9KFGFJ=@=9LL@=JE9DMFALK 
67  /OG9J=9KOAL@L@=JE9DMFALK 
67  /OG9J=9KOAL@J=@=9LMFALK 
67  $ :MKKQKL=EOAL@@Q<JGHGO=J?9K9F<
OAF<LMJ:AF=K

67 – *F=9F<L@J==9J=9KOAL@FGFJ=@=9LL@=JE9D
MFALK

67 – /@J==9J=9KOAL@FGFJ=@=9LL@=JE9DMFALK 
67  /OG9J=9KOAL@FGFJ=@=9LL@=JE9DMFALK 
$F L@= K9E= O9Q 9K KQF;@JGFGMK ?=F=J9LGJK 9DD DG9<K 9J= ?JGMH=< AF
9F =IMAN9D=FL GF= OAL@ 9F =IMAN9D=FL <9EHAF? >9;LGJ  K KL9L=< AF
-=> 67 L@= AEH9;L G> 9F AF9;;MJ9L= N9DM= G> AK J=D9LAN=DQ KE9DD
A> L@= HGO=J KQKL=E AK KL9:D= :ML L@AK ;9F := 9 E9BGJ ;GFLJA:MLAGF MF
<=J <AKLMJ:9F;=K (GJ=GN=J AL AK =PH=;L=< LG <=;J=9K= 9;;GJ<AF?DQ LG L@=
MK= G> N9JA9:D= >J=IM=F;Q <JAN=K 67 /9:D=  KMEE9JAR=K L@= <A>>=J
=FL N9DM=K HJGHGK=< >GJ L@= <9EHAF? >9;LGJ AF L@= DAL=J9LMJ= GN=J J=;=FL
<=;9<=K
Q MKAF? I  9F =KLAE9LAGF G> L@= =IMAN9D=FL AF=JLA9 G> K=N
=J9D H9JLK G> L@= OGJD< @9K :==F ;9JJA=< GML :Q L@= 9ML@GJK /@= $FL=J
F9LAGF9D F=J?Q ?=F;Q $  HJGNA<=K ?DG:9D KL9LAKLA;K 9:GML =F=J?Q
67 Q ;GFKA<=JAF? L@= 9FFM9D 9N=J9?=< =D=;LJA;ALQ 9F 9N=J9?=< =IMAN
9D=FL AF=JLA9 ;GFKL9FL   HJGNA<=< :Q KM;@ ;GFN=FLAGF9D HGO=J HD9FLK
—/9:D=— ;9F := =KLAE9L=< )GL= L@9L >GJ L@AK =KLAE9LAGF S G> I 
AK J=HD9;=< :Q L@= 9FFM9D =D=;LJA;ALQ N9DM=   /@= =PHJ=KKAGF MK=< LG
=KLAE9L= L@= AF=JLA9 AK L@=F I  :=AF? L@= LGL9D =D=;LJA;ALQ KMH
HDA=< ;GFN=FLAGF9D  - . ?=F=J9LAGF OAL@AF 9 Q=9J

!A?  K@GOK 9 KA?FA>A;9FL ;@9F?= AF L@= 9N=J9?=< ?=F=J9LAGF EAP
:=LO==F  9F<  /@= LGL9D =D=;LJA;ALQ ;GFKMEHLAGF @9K :==F AF
;J=9K=< :Q EGJ= L@9F  OAL@AF L@=K= LOG <=;9<=K #GO=N=J - .
?=F=J9LAGF @9K GFDQ AF;J=9K=< :Q  AF L@= K9E= LOG <=;9<=K (GJ=
GN=J L@= K@9J= G> L@= <A>>=J=FL J=F=O9:D= KGMJ;=K @9K ;@9F?=< KA?
FA>A;9FLDQ $F<==< L@= ;GFLJA:MLAGF K@9J= >JGE @Q<JGHGO=J @9K :==F
KMJH9KK=< :Q :AGE9KK :AG>M=DK OAF< 9F< +1 9K=< GF L@= 9HHJG9;@
HJ=NAGMKDQ <=K;JA:=< !A?  <=HA;LK L@= <A>>=J=F;=K :=LO==F L@= AF=J
LA9 ;GFKL9FL >GJ <A>>=J=FL ;GFLAF=FLK AF  9F< AF  0 @9K J=
Fig. 4. "=F=J9LAGF EAP AF L@= OGJD< ;@9F?= :=LO==F  9F< 


UNCORRECTED PROOF
A. Fernández-Guillamón et al. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx-xxx
Fig. 5. IMAN9D=FL AF=JLA9 ;GFKL9FLK =KLAE9L=< AF L@= OGJD< :Q ;GFLAF=FL @9F?= :=LO==F  9F< 
<M;=< L@= =IMAN9D=FL AF=JLA9 ;GFKL9FL :Q F=9JDQ  $F ;GFLJ9KL L@= J=
<M;LAGF G> AF=JLA9 AF KA9 0. 9F< .GML@ E=JA;9 DA=K :=LO==F  9F<

 EGJ= =PL=FKAN= 9F9DQKAK AK ;GF<M;L=< >GJ L@= 0 O@=J= 9F 9N=J
9?= AF=JLA9 J=<M;LAGF G>  K ;9F := =KLAE9L=< $F !A?  9F GN=JNA=O
G> L@= =NGDMLAGF G> L@= =IMAN9D=FL AF=JLA9 AF KGE= 0 ;GMFLJA=K AK KME
E9JAR=< .AEAD9J AF>GJE9LAGF AK ?AN=F AF !A?  O@=J= L@= J=<M;LAGF
Fig. 6. IMAN9D=FL AF=JLA9 ;GFKL9FLK =KLAE9L=< AF 0 @9F?= :=LO==F  9F< 
Fig. 7. IMAN9D=FL AF=JLA9 J=<M;LAGF AF 0 :=LO==F  9F< 
G> L@= =IMAN9D=FL AF=JLA9 AK ADDMKLJ9L=< >GJ L@GK= 0 ;GMFLJA=K O@A;@ @9N=
KM>>=J=< 9 J=<M;LAGF D9J?=J L@9F    !A?  J=HJ=
K=FLK L@= =IMAN9D=FL AF=JLA9 =NGDMLAGF G> 0 9K O=DD 9K AF L@J== <A>>=J=FL
;GMFLJA=K $J=D9F< .H9AF 9F< =FE9JC !GJ L@= 0 - . KMHHDQ @9K AF
;J=9K=< F=9JDQ :Q  AF DAF= OAL@ L@= J=<M;LAGF G> ALK AF=JLA9 ;GFKL9FL
J=>=J LG !A?  .AEAD9J LG L@= ?=F=J9LAGF EAP AF L@= OGJD< OAF< :AG
E9KK :AG>M=DK 9F< +1 @9N= KMJH9KK=< L@= <=N=DGHE=FL G> @Q<JGHGO=J
O@A;@ @9K <J9KLA;9DDQ KDGO=< <GOF AF J=;=FL Q=9JK
2.3. Modi@ed equivalent inertia analysis: emulating hidden and virtual
inertia from RES
/G G:L9AF L@= E9PAEME HGO=J >JGE L@= F9LMJ9D J=KGMJ;= :GL@ OAF<
9F< +1 HGO=J HD9FLK 9J= ;GFLJGDD=< :Q HGO=J ;GFN=JL=JK MKAF? L@= E9P
AEME HGO=J HGAFL LJ9;CAF? (++/ L=;@FAIM= 67 /@AK HGO=J ;GF
N=JL=J HJ=N=FLK OAF< 9F< +1 HGO=J HD9FLK LG <AJ=;LDQ ;GFLJA:ML= LG
L@= AF=JLA9 G> L@= KQKL=E :=AF? L@MK J=>=JJ=< LG 9K ‘<=;GMHD=<’ >JGE
L@= ?JA< 67 K 9 ;GFK=IM=F;= LG =>>=;LAN=DQ AFL=?J9L= - . AFLG L@=
?JA< >J=IM=F;Q ;GFLJGD KLJ9L=?A=K @9N= :==F <=N=DGH=< 6–7 .M;@
E=L@G<K 9J= ;GEEGFDQ F9E=< 9K KQFL@=LA; =EMD9L=< GJ NAJLM9D AF=J
LA9 67 $> L@AK =EMD9LAGF G> AF=JLA9 ;GEAF? >JGE - . O9K AF;DM<=< AF
HGO=J KQKL=EK AL OGMD< @9N= LG := ;GFKA<=J=< LG =KLAE9L= L@= =IMAN9
D=FL AF=JLA9 /@=F L@AK EG<Aa=< =IMAN9D=FL AF=JLA9 OGMD< @9N= LOG <A>
>=J=FL ;GEHGF=FLK KQF;@JGFGMK AF=JLA9 ;GEAF? >JGE ;GFN=FLAGF9D
?=F=J9LGJK 9F< =EMD9L=<NAJLM9D AF=JLA9 ;GEAF? >JGE - .
6–7 EG<A>QAF? I  LG I  AK L@= FME:=J G>
Fig. 8. NGDMLAGF G> =IMAN9D=FL AF=JLA9 AF 0 9F< KGE= ;GMFLJA=K :=LO==F  9F<



UNCORRECTED PROOF
A. Fernández-Guillamón et al. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx-xxx
Fig. 9. "=F=J9LAGF EAP AF MJGH= ;@9F?= :=LO==F  9F< 
- . ;GFF=;L=< LG L@= ?JA< L@JGM?@ =EMD9LAGFNAJLM9D ;GFLJGD E=L@G<K
9F< AK L@= AF=JLA9 ;GFKL9FL G> L@= =EMD9L=<NAJLM9D ?=F=J9LAGF MFAL

/@AK EG<Aa=< =IMAN9D=FL AF=JLA9 =PHJ=KK=< AF I  AK ?J9H@A;9DDQ
ADDMKLJ9L=< AF !A?  :9K=< GF 67 )GL= L@= <A>>=J=FL J=HJ=K=FL9
LAGF :=LO==F L@= ;GMHDAF? G> 1.2/ 9F< +1 LG L@= ?JA< /@= J=9KGF
LG L@AK AK L@9L 2++ @9K ‘@A<<=F’ <=HDGQ9:D= AF=JLA9 :9K=< GF L@= CA
F=LA; =F=J?Q KLGJ=< AF L@=AJ :D9<=K <JAN= LJ9AF 9F< =D=;LJA;9D ?=F=J9LGJK
O@=J=9K +1 @9K FG KLGJ=< CAF=LA; =F=J?Q <M= LG L@= 9:K=F;= G> JGL9L
AF? E9KK=K ;LM9DDQ EG<=JF 1.2/ @9N= JGL9LAGF9D AF=JLA9 ;GFKL9FLK
;GEH9J9:D= LG L@GK= G> ;GFN=FLAGF9D ?=F=J9LGJK 67 #GO=N=J
L@AK AF=JLA9 AK ‘@A<<=F’ >JGE L@= HGO=J KQKL=E HGAFL G> NA=O <M= LG L@=
;GFN=JL=J 67 !GJ AFKL9F;= AF /9:D=  9F< !A?  L@= AF=JLA9 ;GF
KL9FL G> K=N=J9D LQH=K G> OAF< LMJ:AF=K 9J= KMEE9JAR=< 9F< EGKL G>
L@=E 9J= OAL@AF L@= J9F?= K AF DAF= OAL@ N9DM=K HJ=K=FL=< >GJ ;GF
N=FLAGF9D MFALK AF /9:D=  K 9 ;GFK=IM=F;= AL AK ;GEEGFDQ ;GFKA<
=J=< L@9L 1.2/ HJGNA<= ‘=EMD9L=< @A<<=F AF=JLA9’ 9K JGL9LAGF9D AF=JLA9
;GMD< := HJGNA<=< :Q L@=E 6–7 *F L@= GL@=J @9F< +1 AFKL9DD9
LAGFK <GFL @9N= 9FQ JGL9LAF? E9KK=K 67 @9NAF? 9F AF=JLA9 ;GFKL9FL
67 /@=J=>GJ= <M= LG L@AK 9:K=F;= G> JGL9LAGF9D E9KK=K 9F< KM:
K=IM=FLDQ 9:K=F;= G> AF=JLA9 L@= KH=;Aa; DAL=J9LMJ= J=>=JK LG L@= ‘=EM
Fig. 10. +GO=J KQKL=E OAL@ KQF;@JGFGMK @A<<=F 9F< NAJLM9D AF=JLA9
Table 3
2AF< LMJ:AF=K AF=JLA9 ;GFKL9FLK H 9;;GJ<AF? LG J9L=< HGO=J 9F< J=>=J=F;=
/QH=G>OAF<LMJ:AF= -9L=<HGO=J H K -=>=J=F;= 4=9J
)GLAF<A;9L=< )GLAF<A;9L=< 67 
)GLAF<A;9L=< (2  67 
)GLAF<A;9L=< (2  67 
)GLAF<A;9L=< C2  67 
#2/OAL@.$"  C2  67 
!.2/ C2  67 
!.2/ )GLAF<A;9L=<  67 
1.2/ (2  67 
1.2/ (2  67 
/QH=K – (2 67 
!$" (2  67 
!$" C2  67 
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Frequently asked questions

Q1. What are the contributions mentioned in the paper "Power systems with high renewable energy sources: a review of inertia and frequency control strategies over time" ?

This paper reviews the inertia concept in terms of values and their evolution in the last decades, as well as the damping factor values. 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. 

Q2. What are the different types of ESS used in PV power plants?

PV power plants can use ESS such as batteries [115–117], super-capacitors [118,119] and flywheels [117] in order to provide additional active power in an imbalanced situation. 

Q3. What is the drawback of the fast power reserve technique?

The fast power reserve technique is based on supplying the kinetic energy stored in the rotating masses of the wind turbine to the grid as additional active power. 

Q4. What is the promising resource for generating electricity?

Among the different renewable sources available, PV and wind (especially doubly fed induction generators, DFIG [10]) are the two most promising resources for generating electrical energy [11]. 

Q5. What is the reason for the decrease in inertia?

Their findings indicate that, nowadays, Europe presents a significant averaged inertia decreasing –around 20% in the last two decades–, mainly due to the renewable integration decoupled from the grid –from 14% in 1996 to 31% in 2016–. 

Q6. What is the effect of a significant deviation from the nominal value on the grid?

significant deviations from the nominal value may cause under/over frequency relay operations, and even lead to the disconnection of some loads from the grid [95]. 

Q7. How many GW of wind and PV will be installed in 2030?

As an example, in Europe, it is expected that 323 and 192GW of wind and PV will be installed in 2030, which will cover up to 30% and 18% of the demand, respectively [8,9]. 

Q8. What is the pitch angle control technique?

The pitch angle control consists of increasing the pitch angle from tofor a constant wind speed , keeping the rotor speed at the maximum power point (Fig. 16). 

Q9. What is the equivalent inertia of a generation mix in the EU?

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. 

Q10. What is the purpose of this paper?

The paper provides significant information for wind turbines frequency control strategies and studies of current power systems with high renewable energy source integration. 

Q11. What is the relationship between low system inertia and frequency?

low system inertia is related with a faster rate of change of frequency (ROCOF) and larger frequency deviations (lower frequency nadir during frequency dips) within a short-time frame [19]. 

Q12. Why is the term ‘emuFig. 10’ used?

due to this absence of rotational masses and, subsequently, absence of inertia, the specific literature refers to the ‘emuFig. 

Q13. What is the equivalent inertia of a generation unit?

9. Generation mix in Europe: change between 1996 and 2016.RES connected to the grid through emulation/virtual control methods, and is the inertia constant of the emulated/virtual generation unit. 

Q14. What is the main drawback of integrating a large amount of non-synchronous generators?

This fact is considered as one of the main drawbacks of integrating 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]. 

Q15. What is the equivalent inertia of a power converter?

This power converter prevents wind and PV power plants to directly contribute to the inertia of the system, being thus referred to as ‘decoupled’ from the grid [49].