In this paper, we show that spatial correlation of renewable energy outputs greatly influences the robustness of the power grids against large fluctuations of the effective power. First, we evaluate the spatial correlation among renewable energy outputs. We find that the spatial correlation of renewable energy outputs depends on the locations, while the influence of the spatial correlation of renewable energy outputs on power grids is not well known. Thus, second, by employing the topology of the power grid in eastern Japan, we analyze the robustness of the power grid with spatial correlation of renewable energy outputs. The analysis is performed by using a realistic differential-algebraic equations model. The results show that the spatial correlation of the energy resources strongly degrades the robustness of the power grid. Our results suggest that we should consider the spatial correlation of the renewable energy outputs when estimating the stability of power grids.

1.
H.
Sakaguchi
and
T.
Matsuo
,
J. Phys. Soc. Jpn.
81
,
074005
(
2012
).
2.
M.
Nagata
,
N.
Fujiwara
,
G.
Tanaka
,
H.
Suzuki
,
E.
Kohda
, and
K.
Aihara
,
Eur. Phys. J. Spec. Top.
223
,
2549
(
2014
).
3.
See http://www.jema-net.or.jp/Japanese/res/solar/mokuhyo.html for the bar graph of introduction amount.
4.
P. J.
Menck
,
J.
Heitzig
,
N.
Marwan
, and
J.
Kurths
,
Nat. Phys.
9
,
89
(
2013
).
5.
P. J.
Menck
,
J.
Heitzig
,
N.
Marwan
,
J.
Kurths
, and
H. J.
Schellnhuber
,
Nat. Commun.
5
,
3969
(
2014
).
6.
G.
Filatrella
,
A. H.
Nielsen
, and
N. F.
Pedersen
,
Eur. Phys. J. B
61
,
485
(
2008
).
7.
L.
Buzna
,
S.
Lozano
, and
A.
Díaz-Guilera
,
Phys. Rev. E
80
,
066120
(
2009
).
8.
S.
Lozano
,
L.
Buzna
, and
A.
Díaz-Guilera
,
Eur. Phys. J. B
85
,
231
(
2012
).
9.
M.
Rohden
,
A.
Sorge
,
M.
Timme
, and
D.
Witthaut
,
Phys. Rev. Lett.
109
,
064101
(
2012
).
10.
D.
Witthaut
and
M.
Timme
,
New J. Phys.
14
,
083036
(
2012
).
11.
F.
Dörfler
and
F.
Bullo
,
SIAM J. Control Optim.
50
,
1616
(
2012
).
12.
M.
Nagata
,
I.
Nishikawa
,
N.
Fujiwara
,
G.
Tanaka
,
H.
Suzuki
, and
K.
Aihara
, in
Proceedings of 2013 International Symposium on Nonlinear Theory and its Application
(
2013
), pp.
69
72
.
13.
J.
Machowski
,
J.
Bialek
, and
D. J.
Bumby
,
Power System Dynamics: Stability and Control
, 2nd ed. (
Wiley
,
2008
).
14.
K.
Schmietendorf
,
J.
Peinke
,
R.
Friedrich
, and
O.
Kamps
,
Eur. Phys. J. Spec. Top.
223
,
2577
(
2014
).
15.
A.
Gajduk
,
M.
Todorovski
,
J.
Kurths
, and
L.
Kocarev
,
New J. Phys.
16
,
115011
(
2014
).
16.
M.
Lei
,
L.
Shiyan
,
J.
Chuanwen
,
L.
Hongling
, and
Z.
Yan
,
Renewable Sustainable Energy Rev.
13
,
915
(
2009
).
17.
H.
Nagoya
,
S.
Komami
, and
K.
Ogimoto
,
IEEJ Trans. Electron., Inf. Syst.
131
,
1688
(
2011
).
18.
H.
Nagoya
,
M.
Hosokawa
,
M.
Ishimaru
,
S.
Komami
, and
K.
Ogimoto
,
IEEJ Trans. Electr. Electron. Eng. B
133
,
255
(
2013
).
19.
P.
Milan
,
M.
Wächter
, and
J.
Peinke
,
Phys. Rev. Lett.
110
,
138701
(
2013
).
20.
P. G.
Lind
,
I.
Herráez
,
M.
Wächter
, and
J.
Peinke
,
Energies
7
,
8279
(
2014
).
21.
L.
Chen
,
R.
Liu
,
Z.-P.
Liu
,
M.
Li
, and
K.
Aihara
,
Sci. Rep.
2
,
342
(
2012
).
22.
J. D.
Hamilton
,
Time Series Analysis
(
Princeton University Press
,
1994
).
23.
F.
Hellmann
,
P.
Schultz
,
C.
Grabow
,
J.
Heitzig
, and
J.
Kurths
,
Sci. Rep.
6
,
29654
(
2016
).
24.
H.-D.
Chiang
,
F.
Wu
, and
P.
Varaiya
,
IEEE Trans. Circuits Syst.
34
,
160
(
1987
).
25.
D.
Witthaut
,
M.
Rohden
,
X.
Zhang
,
S.
Hallerberg
, and
M.
Timme
,
Phys. Rev. Lett.
116
,
138701
(
2016
).
26.
P.
Kundur
,
Power System Stability and Control
(
McGraw-Hill, Inc.
,
New York
,
1994
).
27.
J.
Machowski
,
J.
Bialek
, and
D.
Bumby
,
Power System Dynamics: Stability and Control
(
John Wiley and Sons, Inc.
,
Chichester, UK
,
2008
).
28.
B.
Schäfer
,
M.
Matthiae
,
M.
Timme
, and
D.
Witthaut
,
New J. Phys.
17
,
015002
(
2015
).
29.
T.
Hiratsuka
,
K.
Nozaki
,
M.
Kato
, and
Y.
Hirata
,
Renewable Energy Power Qual. J.
1
,
105
(
2013
).
30.
See http://www.tepco.co.jp/ir/tool/annual/index-j.html for the annual report of Tokyo Electric Power Company Inc.
31.
See http://www.tohoku-epco.co.jp/ir/report/annual\_report/index.html for the annual report of Tohoku Electric Power Company Inc.
32.
See https://gephi.org/ for the introduction of Gephi.
33.
See http://wiki.openmod-initiative.org/wiki/Transmission_network_datasets for the real-world parameters of the power grids.
34.
Y.
Hirata
,
D. P.
Mandic
,
H.
Suzuki
, and
K.
Aihara
,
Philos. Trans. R. Soc. London A
366
,
591
(
2008
).
35.
Y.
Hirata
,
K.
Aihara
, and
H.
Suzuki
,
Eur. Phys. J. Spec. Top.
223
,
2451
(
2014
).
You do not currently have access to this content.