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Transactions on Power Systems
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Abstract — Forming multiple micorgrids with distributed
generators (DGs) offers a resilient solution to restore critical loads
from natural disasters in distribution systems. However, more
dummy binary and continuous variables are needed with the
increase of the number of microgrids, which will therefore in-
crease the complexity of this model. To address this issue, this
letter presents a new model to reformulate the micorgrid formu-
lation problem in resilient distribution networks. Compared with
the traditional model, the number of both binary and continuous
variables is greatly reduced, such that the computational per-
formance is significantly improved. Numerical results on IEEE
test systems verify the effectiveness of the proposed model.
Index Terms — Resilient distribution system, microgrid, radi-
ality constraint, distributed generator (DG)
I. INTRODUCTION
Fast and efficient restoration is a key step to increase the re-
silience of distribution systems [1]. With an increasing pene-
tration of distributed generators (DGs), intentional islanding
from DGs is regarded as an efficient measure to increase power
system resilience by supplying critical load after component
outages. Specifically, [2]-[3] proposed heuristic and exhaustive
search algorithms to find the optimal islands. Since the heuris-
tic or exhaustive search approaches may not guarantee the
global optimal solution, the mixed integer linear programming
was thus employed in [4], where a microgrid formation scheme
was proposed to pick up the critical load after major faults,
assuming that every controllable DG formed an island mi-
crogrid. This work is insightful for distribution system restora-
tion with DG, but its implementation requires an increasing
number of decision variables with the number of microgrids,
and the computation burden hinders its practicality. Therefore,
this letter will propose a new mathematical formulation for the
model in [4] to reduce the number of decision variables and
improve the computational performance.
II. A NEW MODEL FOR MICROGRIDS FORMATION
Microgrids formation for the resilient distribution system
forms different network cells by sectionalizing switches, where
there is only one DG in each microgrid to guarantee a
self-adequate system. The objective is to maximize the total
weighted sum of loads picked up after natural disasters, while
satisfying the operation constraints and topology constraints.
This work was supported in part by National Key Research and Development
Program of China (2016YFB0901903), in part by National Natural Science
Foundation of China (51577147, 51607137, 51637008), in part by China
Postdoctoral Science Foundation (2015M580847) and in part by Natural Sci-
ence Basis Research Plan in Shaanxi Province of China (2016JQ5015).
The authors are with the State Key Laboratory of Electrical Insulation and
Power Equipment, Shaanxi Province Key Laboratory of Smart Grid, Xi’an
Jiaotong University, Xi’an, Shaanxi, 710049, China.
A. Operation Constraints:
For microgrids, we use the same linearized DistFlow model
as [4] to formulate microgrid operation constraints, which gives
constraints (1)-(6). Specifically, (1) implies power balance; (2)
is the DistFlow equation. Specifically, if the branch is closed,
the voltage difference of this branch is constrained by power
flow and the branch flow should be limited; otherwise, the
voltage difference is arbitrary and the branch flow must be zero;
(3) gives voltage limit at each bus; (4) and (5) refer to the DG
output limits; (6) denotes the load demand limit.
,,
,,
DG j L j js ij
s j i j
DG j L j js ij
s j i j
P P H H
Q Q G G
, j
(1)
0
0
max max max max
1
1
,
ij ij ij ij ij j i
ij ij ij ij ij
ij ij ij ij ij ij ij ij ij ij
M c r H x G U U U
M c r H x G U
S c H S c S c G S c
,,ij
(2)
min max
j j j
U U U
,
\j DG
(3)
0
jj
UU
,
j DG
(4)
min max
,,,DG j DG j DG j
PPP
,
min max
,,,DG j DG j DG j
QQQ
,
j DG
(5)
0
,,
0
L j L j
PP
,
j
(6)
where U
j
is the voltage magnitude of bus j; P
DG,i
and Q
DG,i
are
the active and reactive power output of DG at bus j; P
L,i
and Q
L,i
are the restored active and reactive load demand at bus j; H
js
and G
js
is the active and reactive power from bus j to bus s; c
ij
denotes the status of branch ij, if c
ij
=1, the branch is closed
otherwise, the branch is opened. r
ij
and x
ij
are the resistance and
reactance of branch ij; U
0
j
is the specified voltage value at the
DG bus j; and are the set of buses and branches; {DG} is the
set of DGs; P
DG,i
min
and P
DG,i
max
are the minimum and maxi-
mum active power limits of DG at bus i; Q
DG,i
min
and Q
DG,i
max
are the minimum and maximum reactive power limits of DG at
bus i; U
i
min
and U
i
max
are the minimum and maximum voltage
limits at bus i; P
0
L,i
is the load demand at normal condition;
(j)
and
(j) are the set of all parents and children of bus j; S
ij
max
is
the capacity of the branch ij; M is a large number.
B. Topology Constraints
According to [4], node clustering constraints, microgrid
connectivity constraints and branch-node constraints are con-
sidered to realize the partition of the distribution network into
several microgrids. However, distribution systems, different
from the transmission systems, have the property that the to-
pology is radial. Therefore, if the radiality can be achieved, all
the constraints related to topology in [4] will be satisfied. In this
term, the aforementioned constraints in [4] are redundant and
Tao Ding, Member, IEEE, Yanling Lin, Student Member, IEEE, Gengfeng Li, Member, IEEE,
Zhaohong Bie, Senior Member, IEEE
A New Model for Resilient Distribution Systems
by Microgrids Formation
