Optimal scheduling method for peak regulation of cascade hydro-photovoltaic complementary power generation system
Disclosed is an optimal scheduling method for peak regulation of a cascade hydro-photovoltaic complementary power generation system. The method includes: establishing an objective function of optimal scheduling for peak regulation of the cascade hydro-photovoltaic complementary power generation system; establishing a photovoltaic power station output constraint condition considering uncertainty; optimizing a mixed integer linear model by performing linear processing on the constraint condition; and obtaining a scheduling solution by solving the mixed integer linear model. According to the present disclosure, a unit commitment of a hydro-power station and an operational solution of a reservoir are considered, so that photovoltaic output can be consumed by fully using a characteristic that the hydro-power unit is easy to regulate, and a demand for peak regulation of a power grid can be satisfied.
1 . An optimization scheduling method for a peak regulation of a cascade hydro-PV complementary power generation system, comprising:
establishing an objective function of optimization scheduling for the peak regulation of the cascade hydro-PV complementary power generation system; and establishing a cascade hydro-power constraint condition considering a unit commitment and the PV power station output constraint condition considering uncertainty;
performing linear processing on the constraint condition, and constructing a mixed integer linear model of optimization scheduling for the peak regulation of the cascade hydro-PV complementary power generation system based on the objective function and a linearized constraint condition; and
solving the mixed integer linear model of optimization scheduling for the peak regulation of the cascade hydro-PV complementary power generation system so as to obtain a scheduling scheme for the cascade hydro-PV complementary power generation system;
controlling operation of the cascade hydro-PV complementary power generation system based on the scheduling scheme;
wherein the establishing an objective function of optimal scheduling for peak regulation of the cascade hydro-photovoltaic complementary power generation system comprises:
taking a minimized maximum residual load of a receiving-end grid during a scheduling period as the objective function:
min
f
=
max
(
P
load
(
t
)
-
∑
i
=
1
N
h
∑
g
=
1
G
i
P
i
,
g
(
t
)
-
P
s
e
(
t
)
,
)
,
∀
t
∈
T
wherein f is a maximum residual load of the receiving-end grid; P load (t) is a load at moment t; P i,g (t) is active output of a g th generating unit in an i th cascade hydro-power station at the moment
t
;
P
s
e
(
t
)
is generating power of the photovoltaic power station at the moment t; T is a total time period of the scheduling period; N h is the total number of cascade hydro-power stations; and G i is the number of generating units involved in the i th cascade hydro-power station;
the establishing a cascade hydro-power constraint condition considering a unit commitment and a photovoltaic power station output constraint condition considering uncertainty comprises:
establishing a photovoltaic power station output constraint as:
P
s
e
(
t
)
=
P
_
s
(
t
)
+
P
s
ˆ
(
t
)
P
^
s
L
(
t
)
≤
P
s
ˆ
(
t
)
≤
P
s
U
(
t
)
wherein P s (t) is an expected value of the generating power of the photovoltaic power station at the moment t; {circumflex over (P)} s (t) is a power deviation of the photovoltaic power station at the moment t; and
P
ˆ
s
L
(
t
)
,
P
^
s
U
(
t
)
are a lower limit and an upper limit of the power deviation at the moment t, respectively; and
establishing a cascade hydro-power constraint considering the unit commitment, which comprises:
a hydro-power unit output constraint:
P
i
,
g
(
t
)
=
η
i
,
g
H
i
(
t
)
q
i
,
g
(
t
)
u
i
,
g
(
t
)
P
i
,
g
min
≤
P
i
,
g
(
t
)
≤
u
i
,
g
(
t
)
P
i
,
g
max
wherein η i,g is a hydro-power conversion coefficient of the g th generating unit in the i th cascade hydro-power station; H i (t) is a power generation water head of a unit in the i th cascade hydro-power station at the moment t; q i,g (t) is a power generation flow of the g th generating unit in the i th cascade hydro-power station at the moment
t
;
P
i
,
g
min
and
P
i
,
g
max
are a lower limit and an upper limit of active power output of the g th generating unit in the i th cascade hydro-power station, respectively; and u i,g is an operating state variable of the g th generating unit in the i th cascade hydro-power station, wherein if the generating unit is activated, u i,g (t) is 1, and otherwise, u i,g (t) is 0;
a hydro-power unit vibration zone limit constraint:
(
P
i
,
g
(
t
)
-
P
_
i
,
g
k
)
(
P
i
,
g
(
t
)
-
P
_
i
,
g
t
)
≥
0
wherein
P
_
i
,
g
k
and
P
_
i
,
g
k
are upper and lower output limits of a k th vibration zone of the g th generating unit in the i th cascade hydro-power station, respectively;
a hydro-power unit climbing ability limit constraint:
-
Δ
P
¯
i
,
g
≤
P
i
,
g
(
t
+
1
)
-
P
i
,
g
(
t
)
≤
Δ
P
_
i
,
g
wherein Δ P i,g is a climbing ability of the g th generating unit in the i th cascade hydro-power station;
a hydro-power unit on/off and minimum on/off duration constraint:
y
i
,
g
(
t
)
-
y
~
i
,
g
(
t
)
=
u
i
,
g
(
t
)
-
u
i
,
g
(
t
-
1
)
y
i
,
g
(
t
)
+
y
~
i
,
g
(
t
)
≤
1
y
i
,
g
(
t
)
+
∑
i
=
t
+
1
max
{
t
+
α
i
,
g
-
1
,
T
]
y
~
i
,
g
(
l
)
≤
1
y
~
i
,
g
(
t
)
+
∑
i
=
t
+
1
max
{
t
+
β
i
,
g
-
1
,
T
]
y
i
,
g
(
l
)
≤
1
y
i
,
g
(
t
)
,
y
~
i
,
g
(
t
)
∈
{
0
,
1
}
wherein y i,g (t) and {tilde over (y)} i,g (t) are on and off operational variables of the g th generating unit in the i th cascade hydro-power station at the moment t, respectively, wherein if the generating unit is activated, y i,g (t) is 1, and otherwise, y i,g (t) is 0; if the generating unit is deactivated, {tilde over (y)} i,g (t) is 1, and otherwise, {tilde over (y)} i,g (t) is 0; and α i,g and β i,g are minimum on duration and minimum off duration of the g th generating unit in the i th cascade hydro-power station, respectively;
a hydro-power unit power generation flow limit constraint:
u
i
,
g
(
t
)
q
i
,
g
min
≤
q
i
,
g
(
t
)
≤
u
i
,
g
(
t
)
q
i
,
g
max
wherein
q
i
,
g
min
and
q
i
,
g
max
are upper and lower limits of the power generation flow of the g th generating unit in the i th cascade hydro-power station, respectively;
an abandoned water flow limit constraint:
0
≤
s
i
(
t
)
≤
s
i
max
wherein s i (t) is a total abandoned water flow (m3/s) of the i th cascade hydro-power station at the moment t, and
s
i
max
is the upper limit of an abandoned water flow of the i th cascade hydro-power station;
a reservoir water level limit constraint:
Z
i
min
≤
Z
i
(
t
)
≤
Z
i
max
wherein Z i (t) is a water level of a reservoir corresponding to the i th cascade hydro-power station at the moment
t
;
Z
i
min
and
Z
i
max
are a lower limit and an upper limit of the water level of the reservoir corresponding to the i th cascade hydro-power station, respectively, and a dead water level and a normal water level of the reservoir are taken separately;
a cascade water flow balance constraint:
V
i
(
t
)
=
V
i
(
t
-
1
)
+
[
I
i
(
t
)
+
∑
g
q
i
-
1
,
g
(
t
-
τ
i
-
1
)
+
s
i
-
1
(
t
-
τ
i
-
1
)
-
∑
g
q
i
,
g
(
t
)
-
s
i
(
t
)
]
Δ
t
wherein V t (t) is a water storage capacity of the reservoir corresponding to the i th cascade hydro-power station at the moment t; I i (t) is a natural incoming water flow of the i th cascade hydro-power station at the moment t; τ i-1 is a time lag of water flow between an i−1st cascade hydro-power station and the i th cascade hydro-power station; and Δt is a length of a time period in the scheduling period;
a water level-reservoir capacity relationship constraint:
Z
i
(
t
)
=
f
(
V
i
(
t
)
)
a tail water level-discharge flow relationship constraint:
Z
i
d
(
t
)
=
f
(
∑
g
q
i
,
g
(
t
)
+
s
i
(
t
)
)
wherein
Z
i
d
(
t
)
is a tail water level of the reservoir corresponding to the i th cascade hydro-power station at the moment t; and
a water head constraint:
H
i
(
t
)
=
1
2
[
Z
i
(
t
)
+
Z
i
(
t
-
1
)
]
-
Z
i
d
(
t
)
H
i
min
≤
H
i
(
t
)
≤
H
i
max
wherein
H
i
min
and
H
i
max
are a lower limit and an upper limit of the power generation water head of the generating unit in the i th cascade hydro-power station, respectively.
2 . The optimization scheduling method for a peak regulation of a cascade hydro-PV complementary power generation system according to claim 1 , wherein the performing linear processing on the constraint condition, comprising:
converting the hydro-power unit output constraint, by using a McCormick convex envelope relaxation method, into the following linear constraint:
P
i
,
g
(
t
)
≥
η
i
,
g
(
q
i
,
g
min
H
i
(
t
)
+
H
i
min
q
i
,
g
(
t
)
-
q
i
,
g
min
H
i
min
)
P
i
,
g
(
t
)
≥
η
i
,
g
(
q
i
,
g
max
H
i
(
t
)
+
H
i
max
q
i
,
g
(
t
)
-
q
i
,
g
max
H
i
max
)
P
i
,
g
(
t
)
≤
η
i
,
g
(
q
i
,
g
min
H
i
(
t
)
+
H
i
max
q
i
,
g
(
t
)
-
q
i
,
g
min
H
i
max
)
P
i
,
g
(
t
)
≤
η
i
,
g
(
q
i
,
g
max
H
i
(
t
)
+
H
i
min
q
i
,
g
(
t
)
-
q
i
,
g
max
H
i
min
)
performing linear processing on the unit vibration zone limit constraint:
∑
k
=
1
K
+
1
z
i
,
g
k
(
t
)
=
u
i
,
g
(
t
)
∑
k
=
1
K
+
1
z
i
,
g
k
(
t
)
P
_
safe
,
i
,
g
k
≤
P
i
,
g
(
t
)
≤
∑
k
=
1
K
+
1
z
i
,
g
k
(
t
)
P
_
safe
,
i
,
g
k
wherein, K is the number of vibration zones of the g th generating unit in the i th cascade hydro-power station; K+1 is the number of safe operating zones of the g th generating unit in the i th cascade hydro-power station;
z
i
,
g
k
(
t
)
is an indicator variable, and
z
i
,
g
k
(
t
)
is 1 if the output, is within a k th safe operating zone at moment t, of the g th generating unit in the i th cascade hydro-power station, and 0 otherwise;
P
_
safe
,
i
,
g
k
,
P
_
safe
,
i
,
g
k
are upper and lower limits of the k th safe operating zone of the g th generating unit in the i th cascade hydro-power station, respectively, and meet
P
_
safe
,
i
,
g
1
=
P
i
,
g
min
,
P
_
safe
,
i
,
g
k
=
P
_
i
,
g
k
+
1
,
P
_
safe
,
i
,
g
k
=
P
_
i
,
g
k
,
P
_
safe
,
i
,
g
K
+
1
=
P
i
,
g
max
;
and
performing piecewise linear processing on the water level-reservoir capacity relationship constraint and tail water level-discharge flow relationship constraints respectively.
3 . The optimization scheduling method for a peak regulation of a cascade hydro-PV complementary power generation system according to claim 2 , wherein the solving the mixed integer linear model of optimization scheduling for the peak regulation of the cascade hydro-PV complementary power generation system so as to obtain a scheduling scheme for the cascade hydro-PV complementary power generation system, comprising:
solving the mixed integer linear model of optimization scheduling for the peak regulation of the cascade hydro-PV complementary power generation system by using a CPLEX12.9 solver, so as to obtain the active power output of each generating unit in the cascade hydro-power station at each moment.