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In-Depth Information
NC
ac
min
FP
=
Δ
τβ
+
KK
(
Q
)
(13)
Σ
max
i
i
=
1
Based on the analysis of the section 3.2 and 3.3, then, the adjusting variables of the
formula (13) only are the compensation capacities of the reactive compensation nodes
(decision variable), after the formula derivation, the standard quadratic programming
form of objective function and constraints are shown as following:
1
Τ
Τ
obj
. min
F
=
Q HQ
+
f
Q
ci
ci
ci
2
NC
-
Ptg
⋅
φ
+ ≤
Q
α
Q
≤ ⋅
-
Ptg
φ
+
Q
(14)
l
l
min
l
l ci
,
ci
l
l
max
l
i
=
1
st
..
NL
VV
≤
-
β
Δ ≤
VV
k
min
s
k l
,
k
max
l
=1
where,
ci
Q
is a
NC
dimensions column vector which contains the reactive
compensation capacity of each reactive compensation node,
Q
T
ci
is the transposition
of
Q
;
H
is an
NC
×
NC
matrix, the specific equation is shown as following:
ci
2
H
=
V
τ βα
T
diag R
()
α
(15)
2
max
l
N
where,
diag R
(
)
is a
NL
×
NL
diagonal matrix, the diagonal elements are the
l
resistances of each branch.
f
is an
NC
dimensions column vector,
f
T
is the transposition of the vector
f
,
the specific equation is shown as following:
2
fKK
=-
V
α
T
diagRQ
(
)
(16)
ac
l
l
2
N
Through the above analysis, then it's ready for the next optimization calculation, the
specific calculation process is achieved by programming in MATLAB, next, can
verify the reasonable and the effective of the mathematical model and algorithm
which the paper proposed through a practical example.
4
Actual System Analysis
In a actual distribution network, the parameters are shown as following:
24
( low-voltage buses of 15 distribution
transformers as the reactive compensation nodes),
N
=
,
NL
=
23
,
KV
=
23
,
NF
=
15
,
NC
=
15
,15 load nodes,
the investment cost of the unit capacity of the compensation device is 7000
RMB/Mvar, the fixed cost is 10000 RMB, both are included in the comprehensive
cost of unit compensation capacity
β =
0.5 RMB/kwh
K
,
K
1%
,
V
=
110
V
,
τ
max
=3000h
.
a
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