Cu en s’ Physical Componen s (CPC) concep in wind a m ha monic cu en
s udies
L. Sainz1 and J. Cunill-Solà2
1 Depa men o Elec ical Enginee ing
E.T.S.E.I.B, Technical Uni e si y o Ca alonia (UPC)
A . Diagonal 647, 08028 Ba celona (Spain)
Phone/Fax numbe :+0034 93 4011759/+0034 93 4017433, e-mail: [email p o ec ed]
2 Depa men o Elec ical Enginee ing
E.P.S.E.M, Technical Uni e si y o Ca alonia (UPC)
A . de les Bases 61-73, 08240 Man esa (Spain)
Phone/Fax numbe :+0034 93 8777263/+0034 93 8777202, e-mail: [email p o ec ed]
Abs ac . Ve y li le in o ma ion abou ac ual wind a m
ha monic measu emen s is a ailable in he li e a u e. This pape
analyzes he ha monic measu emen s o an 18 MW wind a m
wi h he CPC concep o de e mine i hey a e consumed o
injec ed by he wind a m and o s udy he di e en eac i e
powe de ini ions. The CPC concep is an app oach o powe
heo y ha p o ides a physical in e p e a ion o powe
phenomena in elec ical sys ems wi h linea , ime-in a ian
(LTI) loads and ha monic gene a ing loads (HGLs) such as
wind a ms.
Key wo ds
Wind powe gene a ion, ha monics, powe heo y.
1. In oduc ion
The inc easing numbe o wind a ms wo ldwide causes
powe quali y p oblems such as ha monic cu en
emissions [1]-[6]. These emissions p oduce ol age
dis o ion in ne wo ks, and hei measu emen and
inclusion in WT powe ce i ica es a e he e o e equi ed
by cu en s anda ds [7], [8]. Knowledge o hese
emissions is undamen al o s udy he in luence o wind
a ms on ne wo k ha monic dis o ion. Al hough hey a e
a well-known opic, e y ew s udies based on ac ual
measu emen s ha e been published [2]-[5]. Recen ly, he
ha monic cu en beha io o an 18 MW wind a m was
in es iga ed om a la ge numbe o measu emen s in [9].
The wind a m ha monic emissions we e s udied, and he
in luence o he wind a m wo king poin on hese
emissions was ex ensi ely analyzed. In addi ion, he
p obabili y densi y unc ions o he ha monic magni udes
and phase angles we e discussed and compa ed in de ail
wi h analy ical and empi ical dis ibu ions in he
li e a u e.
Wind a m ha monics and, in pa icula , powe
ansmission phenomena can be analyzed by he CPC
concep . The CPC concep is cu en ly he mos ad anced
o m o powe heo y o elec ic sys ems wi h pe iodic
and semi-pe iodic ol ages and cu en s. I explains
powe p ope ies o single- and h ee-phase sys ems wi h
LTI loads and HGLs [10]-13].
The pape analyzes he ha monic cu en measu emen s
in [9] and ela ed powe phenomena by he CPC concep .
2. Wind Fa m Measu emen s
A. Wind Fa m
The ha monic cu en s o he wind a m in he one-line
diag am o Fig. 1 we e ex ensi ely s udied in [9]. The
a m consis s o 30x600 kW WT squi el-cage induc ion
gene a o s (SCIGs) connec ed o he MV collec o wi h
20/0.69 kV ans o me s. The a ed powe o he wind
a m is PN = 18 MW and he a ed cu en a he MV
collec o is IN = 522 A. A 110/20 kV ans o me
subs a ion connec s he MV and HV busba s.
B. Ha monic cu en measu emen s
Measu emen s we e ca ied ou a he wind a m MV
collec o (Fig. 1) wi h he powe ne wo k analyze
AR5−L o CIRCUTOR (Fig. 2) acco ding o he
equi emen s o IEC 61400-21 [7] and IEC 61000-4-7 [8]
s anda ds. The analyze has a 0.5% ol age and cu en
HV Busba
MV Busba
(ac collec o )
110 kV
20 kV
To al wind a m
powe : 10 x 1.8 MW
Powe analyze
measu emen s
⋅⋅⋅ N = 30 WTs ⋅⋅⋅
50-Hz
S
y
s em
i
20 kV
0.69 kV
WT SCIG
PN = 600 kW
20 kV
0.69 kV
Fig. 1. One-line diag am o he wind a m.
accu acy class, a sampling equency su icien o
e alua e up o he 63 d ha monic o de and a 1Mb on-
boa d memo y o sa e all measu ed o calcula ed
pa ame e s o u u e e ie ing. The cu en clamps
employed in he measu emen s ha e a o al ull-scale
accu acy o 1% wi h a bandwid h o 10 Hz o 5 kHz. The
ac i e powe , P, and ol age and cu en wa e o ms,
and i, espec i ely, we e eco ded o e a 6-day pe iod
wi h a 10-minu e ime in e al be ween eadings, each
eco d being he 10-min a e age alue. The long s o age
pe iod made i possible o eco d da a o he whole
powe ange o he wind a m, and he 10-min a e age
alues p o ided su icien accu acy o he ol age and
cu en measu emen s. All he eco ded ol age and
cu en alues we e s o ed on a ha d disk and ea ed wi h
cus omized MATLAB so wa e o ha monic analysis.
Thus, assuming ha he magni ude o he cu en s is
s a iona y, he Fou ie ans o m was applied o a 20-ms
ec angula window p o iding a 50-Hz equency
esolu ion.
The cu en and ol age ha monics ( h and ih,
espec i ely) we e e alua ed up o he i ie h o de
(2.5 kHz o 50-Hz sys ems):
() 1, ,50 ( ,).
h
hx
h
x
xx h x i
φ
⇒=∠ = =…(1)
The wind a m ha monic cu en s and he in luence o he
wind a m wo king poin on hem we e analyzed. In
addi ion, sca e plo s o he ha monics (magni ude and
phase angle) e sus he wind a m ou pu powe we e
p o ided and he andom beha io o he ha monics was
examined om he expe imen al measu emen s. I could
be obse ed ha he dominan ha monics belonged o he
low-o de se (in pa icula , he highes we e 5 h and 7 h)
and ha a high-o de ha monic pa e n exis ed in he
cu en spec um be ween 1.0 and 2.0 kHz. A summa y
o he measu emen s in [9] is gi en in Fig. 3 o Fig. 5
conside ing he o al and indi idual ha monic cu en
dis o ions as ollows [7]:
P/PN (pu)
0.2 0.4 0.6 0.8 10
P/PN (pu)
0.2 0.4 0.6 0.8 10
−
180
0
180
φ
i5 (º)
φ
i7 (º)
Fig. 5. Phase angles o he wind a m 5 h and 7 h ha monic cu en s
e sus ou pu powe o he o al measu emen pe iod cou se.
P/PN (pu)
0.2 0.4 0.6 0.8 10
THDI (%)
0
1
3
2
P/PN (pu)
0.2 0.4 0.6 0.8 10
0
0.4
0.8
1.2
HDI1 (%)
0
1
3
2
HDI5 (%)
0
0.4
0.8
2
1.2
1.6
HDI7 (%)
Fig. 4. Wind a m ha monic dis o ion e sus ou pu powe o he
o al measu emen pe iod cou se.
P/PN (pu)
0
0.2
0.4
0.8
1
0.6
Da e and Time
11.30
7.4.08 23.00
10.30
22.00
9.30
21.00
8.30
20.00
7.30
19.00
6.30
18.00
5.30
8.4.08
9.4.08
10.4.08
11.4.08
12.4.08
13.4.08
0.6
0
1.2
1.8
2.4
3
THDI (%)
P/PN
THDI
Fig. 3. Time cou se o he o al ha monic dis o ion and ou pu
powe a io.
Fig. 2. Powe ne wo k analyze AR5-L o CIRCUTOR.
50 2
2
NN
,(1,3),
h
hh
h
ii
THDI HDI h
II
=
===
∑
…(2)
whe e IN is he wind a m a ed cu en and ih he
undamen al and ha monic magni udes o he cu en a
he MV collec o . Fig. 3 shows he ime cou se o he
THDI and he wind a m ou pu powe . Fig. 4 shows he
sca e plo o he THDI and HDIh (h = 1, 5 and 7) e sus
he wind a m ou pu powe . Fig. 5 con ains he phase
angle sca e plo s o he mos signi ican ha monic
cu en s (i.e., 5 h and 7 h ha monics) e sus he ou pu
powe . The ollowing ema ks on he measu emen s can
be made:
- The undamen al cu en inc eases p opo ionally
wi h he wind a m ou pu powe while he ha monic
cu en s a y s ochas ically.
- In spi e o he andom beha io o wind a m
ha monic cu en s, hese a e usually modeled as ixed
cu en injec ions due o hei small a ia ion wi h
espec o he wind a m ope a ing poin . In
acco dance wi h IEC 61000 s anda ds, he magni udes
adop ed o ha monic cu en injec ions a e gene ally
he 95% non-exceeding p obabili y alues o hese
cu en s.
- De e minis ic models a e usually based on he
a i hme ic sum o he a e age o he 95% pe cen ile
alues o measu ed wind a m ha monic cu en s.
These models a e he simples ones and compensa e
o he lack o in o ma ion abou ha monic cu en
phase angles. Ne e heless, hey lead o
o e es ima ion o sys em ha monic dis o ion because
he andom a ia ion o ha monics (in pa icula hei
phase angles) is dis ega ded.
In [9], a comple e s udy o he wind a m ha monic
cu en s ochas ic beha io was pe o med om he ield
measu emen s.
The analysis o he wind a m ha monic measu emen s in
[9] can be heo e ically suppo ed wi h he CPC concep .
In pa icula , he o igin o he ha monic cu en s
measu ed in he abo e s udy can be analyzed (i.e. we he
hese cu en s a e consumed o injec ed by he wind
a m). The CPC concep is an ad anced o m o powe
heo y sys ems wi h non-sinusoidal ol age and cu en s
[10]-[13]. Thus, he nex Sec ion summa izes some o he
powe heo y concep s in oduced by he CPC app oach
in he p esence o HGL [12].
3. CPC in Single-Phase Ci cui s wi h HGLs
Le us conside he single-phase ne wo k in Fig. 6,
o med by wo subne wo ks, he dis ibu ion sys em and
he cus ome load, and he ol age and cu en , ( ) and
i( ), measu ed a he c oss-sec ion be ween he
dis ibu ion sys em and he cus ome load. I ( ) and i( )
belong o he linea space LT
2, i.e.
2
0
1
() ( ), () ( ,),
T
x
x kT x d x i
T
=± <∞ =
∫(3)
whe e k is any in ege numbe and T, called he pe iod o
x( ), is a nonze o eal numbe , hey can be exp essed wi h
he Fou ie se ies:
0
1
() 2Re () ( ,),
h
j
h
h
hh
x
X Xe x x i
ω
∞
=∈Η
=+ = =
∑∑ (4)
whe e xh( ) is he ha monic o o de h o he quan i y x( ),
Η ep esen s he se o ha monic o de s h, including
h = 0, o ha monics wi h nonze o complex ms alues
.
Xh
j
h
h
XXe
α
=(5)
The ins an aneous powe a he c oss-sec ion in Fig. 6 is
he a e o elec ic ene gy W( ) low om he dis ibu ion
sys em o he cus ome load and can be exp essed as a
sum o ha monics as ollows:
()
() ()() () ().
hh
hh
dW
p i i
d ∈Η ∈Η
===
∑∑ (6)
The ac i e powe is he a e age alue o he
ins an aneous powe o e a single pe iod o he ol age
and cu en :
*
0
1
() ()() Re
cos ( ),
hh
T
h
h
h
hh h h h V I
hh
Pp i VI
T
VI P
ϕϕαα
∈Η
∈Η ∈Η
== = =
===−
∑
∫
∑∑ (7)
whe e
cos
hhh h
PVI
ϕ
=
(8)
is he ac i e powe o he h h ha monic o de .
The appa en powe is de ined as he p oduc o he
ol age and cu en ms alues:
2
() ( ,),
h
h
x
Xx i
∈Η
==
∑(9)
( )
i( )
Dis ibu ion
sys em
Cus ome
load
Fig. 6. C oss-sec ion be ween dis ibu ion sys em and
cus ome load.
and i can be exp essed as ollows:
22
2
222
22
222
() ()
1
2
,
sh
s
h
s h
s
s
S i
PQ
P
PVV
V
VV
PDQ
∈Η ∈Η ∈Η
==
 
=+ − + =
 
 

=++
∑∑ ∑ (10)
whe e Ds and Q a e he sca e ed and eac i e powe
in oduced by L. S. Cza necki [13] and
sin
hhh h
QVI
ϕ
=(11)
is he eac i e powe o he h h ha monic o de .
The powe de ini ions in oduced in (10) by he CPC
concep p o ide be e unde s anding o ene gy low and
powe phenomena in elec ic sys ems and s udy
p ocedu es o he enhancemen o powe ansmission
e iciency and quali y. The e o s in he de ini ions
in oduced in powe heo y by di e en au ho s ha e also
been cla i ied om he CPC concep , o example he
de ini ion o eac i e and dis o ion powe in oduced in
1927 by Budeanu and suppo ed by he IEEE S anda d
Dic iona y [14]:
222
sin , .
BhhhB B
h
QVI DSPQ
ϕ
∈Η
==−−
∑(12)
The physical phenomena ha cha ac e ize he ha monic
ene gy lows in non-sinusoidal condi ions a he c oss-
sec ion in Fig. 6 can be analyzed om he phase angle
ϕ
h
be ween he ol age and he cu en ha monics, h and ih,
a he c oss-sec ion, o om he ha monic ac i e powe
Ph (8). Thus, i |
ϕ
h | ≤ π/2, he e is an a e age componen
o ene gy low a he h h ha monic o de om he
dis ibu ion sys em owa ds he cus ome load, i.e. Ph ≥ 0.
I |
ϕ
h | > π/2, he e is an a e age componen o ene gy
low a he h h ha monic o de om he cus ome load
back he dis ibu ion sys em, i.e. Ph < 0. Conside ing he
p e ious analysis, he se Η o all he ha monic o de s
can be decomposed in o sub-se s ΗA and ΗB
(ΗA ∪ ΗB = Η) as ollows
A
B
i o 0,
2
i o 0,
2
hh
hh
hP
hP
π
ϕ
π
ϕ
∈
Η≤≥
∈
Η><
(13)
and he ol age and cu en s can be exp essed as
AB
() () () () ( ,).
hhh
hh h
x
x x x x i
∈Η ∈Η ∈Η
== + =
∑
∑∑ (14)
Tha is, he consume load can be conside ed as a
ecei e o a ha monic sou ce o he ha monics
belonging o he sub-se ΗA o ΗB, espec i ely. This
(b)
(a)
h
ih
Zh
jCh
Ph
h
ih
eh
Zh
ZCh
Ph
Fig. 7. Equi alen ci cui s: a) Fo ha monics h ∈ ΗA. b) Fo
ha monics h ∈ ΗB.
Da e and Time
11.30
7.4.08 23.00
10.30
22.00
9.30
21.00
8.30
20.00
7.30
19.00
6.30
18.00
5.30
8.4.08
9.4.08
10.4.08
11.4.08
12.4.08
13.4.08
P5 (kW)
−
2.5
−
2
−
1.5
−
0.5
0
−
1
P7 (kW)
−
1
−
0.75
−
0.5
0.5
0
−
0.25
0.25
P1 (MW)
−
25
−
20
−
15
−
5
0
−
10
Fig. 8. Time cou se o he undamen al, i h and se en h
ha monic ac i e powe s.
decomposi ion allows he ne wo k in Fig. 6 o be
desc ibed as a supe posi ion o he wo ne wo ks in Fig. 7
since sub-se s ΗA and ΗB do no con ain common
ha monic o de s h (ΗA ∩ ΗB = 0) and he ol age and
cu en s belonging o hem a e mu ually o hogonal. In
Fig. 7(a) and Fig. 7(b), he cus ome load is modeled as
an LTI load and a ha monic cu en sou ce, espec i ely,
and he dis ibu ion sys em is modeled as a ha monic
ol age sou ce and a passi e ene gy ecei e ,
espec i ely.
4. CPC in Wind Fa m S udy
A. Ac i e powe s udy
As men ioned in he p e ious Sec ion, he sign o he
ha monic ac i e powe s Ph (8) allows de e mining
whe he he wind a m ha monic cu en s occu because
o he supply ha monic ol ages o hey a e gene a ed in
he wind a m. Thus, Fig. 8 shows he ime cou se o he
undamen al and he mos signi ican ha monic ac i e
powe s measu ed a he MV collec o o he wind a m.
F om his igu e, i can be no ed ha
- The ac i e undamen al powe P1 lows om he
wind a m back he dis ibu ion sys em because i s
sign is nega i e. This powe nea ly coincides wi h he
ou pu powe in Fig. 3 because he ha monic powe
con ibu ion is small.
- The ac i e i h and se en h ha monic powe s P5 and
P7 low om he wind a m back he dis ibu ion
sys em because hei sign is nega i e, oo. This means
ha he measu ed ha monic cu en s a e gene a ed by
he wind a m.
B. Reac i e powe s udy
Fig. 9 shows he ime cou se o he eac i e powe s
calcula ed om he de ini ions p esen ed in he p e ious
Sec ion [Cza necki, ha monic and Budeanu eac i e
powe s, i.e. (10), (11) and (12)]. F om his igu e, i can
be no ed ha
- The Cza necki eac i e powe Q is always posi i e
and i s cancella ion is achie ed only when all
ha monic eac i e powe s a e cancelled.
- The Budeanu eac i e powe QB is simply he sum o
he ha monic eac i e powe s o all ha monics and i s
cancella ion does no necessa ily mean he
cancella ion o such ha monic powe s. In ac , he
physical meaning o he ha monic eac i e powe s
[i.e., he ampli ude o he al e na ing componen o
he ins an aneous powe (6)] is los in he Budeanu
de ini ion.
- This undamen al eac i e powe Q1 nea ly coincides
wi h he Budeanu eac i e powe because he
ha monic powe con ibu ion is small. This
undamen al powe co esponds o an induc i e
consume and does no change signi ican ly o e he
ime cou se, i.e. wi h he di e en wind a m ou pu
powe s.
5. Conclusion
The pape p esen s he measu emen s o SCIGs wind
a m ha monic beha io and analyzes he powe
ha monic phenomena om hese measu emen s and he
CPC concep . The ha monic cu en injec ed om he
wind a m back he dis ibu ion sys em is demons a ed
wi h he obse a ion o he ac i e ha monic powe sign.
Da e and Time
11.30
7.4.08 23.00
10.30
22.00
9.30
21.00
8.30
20.00
7.30
19.00
6.30
18.00
5.30
8.4.08
9.4.08
10.4.08
11.4.08
12.4.08
13.4.08
Q (M a )
0
2
8
4
6
QB (M a )
−8
−6
0
4
8
2
−4
−2
6
Q1 (M a )
−8
−6
0
4
8
2
−4
−2
6
Q5 (k a )
−16
−14
−8
−4
0
−6
−12
−10
−2
Q7 (k a )
−3
−2.5
−2
−1
0
−1.5
−0.5
Fig. 9. Time cou se o he eac i e powe s.

The eac i e powe is calcula ed om i s di e en
de ini ions and he esul s a e discussed and compa ed.
Acknowledgemen
This esea ch is ca ied ou wi h he inancial suppo o
g an DPI2010-15448, which he au ho s g a e ully
acknowledge.
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