US 11,777,313 B2 · Unit commitment method considering security region of wind turbine generator with frequency response control

Abstract

The present invention discloses a unit commitment method considering security region of wind turbine generators with frequency response control, and the main steps are: 1) determining security region of wind turbine generators when provides frequency response; 2) based on the security region of the wind turbine generators when provides frequency response, establishing a unit commitment model considering security region of wind turbine generators; and 3) calculating the unit commitment model considering the security region of the wind turbine generators by using mixed-integer linear programming method, and obtaining the operation result of the unit commitment considering the security region of the wind turbine generators with frequency response control. The present invention can be widely used in the setting of frequency response parameters of wind turbine generators dispatched in the prior art and the start-stop and output plans of synchronous generator.

A unit commitment method considering a security region of wind turbine generators with frequency response control, mainly comprises the following steps:

1) determining the security region of wind turbine generators when the wind turbine generators provide a frequency response;
2) based on the security region of the wind turbine generators when the wind turbine generators provide the frequency response, establishing a unit commitment model considering the security region of the wind turbine generators;
and
3) calculating the unit commitment model considering the security region of the wind turbine generators by using mixed-integer linear programming method, and obtaining the operation result of the unit commitment considering the security region of the wind turbine generators with frequency response control;
wherein the main steps of determining security region of wind turbine generators when the wind turbine generators provide the frequency response are as follows:
1) establishing an output model of wind turbine generators when the wind turbine generators provide the frequency response, namely:
Δ
⁢
P
w
PFR
=
K
w
⁢
Δ
⁢
f
⁢
and
(
1
)
Δ
⁢
P
w
IR
=
J
w
⁢
d
⁢
Δ
⁢
f
dt
(
2
)
in the above formulas, ΔPwPFR and ΔPwIR respectively represent a primary frequency response and a virtual inertia response provided by the wind turbine generators;
frequency response coefficient Kw=1/Kdroop-w;
Kdroop-w is droop control parameter of the wind turbine generators in primary frequency response control;
Jw is virtual inertia control parameter of the wind turbine generators;
Δf is system frequency deviation, and t refers to time;
2) establishing constraint condition of rotor rotational speed ωr, namely:
ωmin≤ωr≤ωmax (3)
in the above formulas, ωmin and ωmax respectively are the lowest speed and highest speed of the rotor rotational speed of the wind turbine generators;
3) establishing constraint conditions of wind power stability, and the main steps are as follows:
3.1) determining synchronization characteristics of the wind turbine generators, namely:
P
E
=
K
D
⁢
L
⁢
ω
r
3
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
⁢
and
(
4
)
P
E
=
P
M
=
0
.
5
⁢
ρ
⁢
π
⁢
R
2
⁢
C
P
(
β
,
λ
)
⁢
v
3
;
(
5
)
in the above formulas, PE is active output of the wind turbine generators;
KDL is de-load factor of the wind turbine generators;
when the wind turbine generators are working at maximum power tracking mode, coefficient KDL is the maximum power tracking coefficient, KDLωr3 is the output of the wind turbine generators when there is no virtual inertia response;
ρ is air density;
R is diameter of the rotor of the wind turbine generators;
v is wind speed;
Cp is power coefficient of the wind turbine generators;
PM is mechanical power of the wind turbine generators;
and β is pitch angle of the wind turbine generators;
wherein, the tip speed ratio λ is shown as follows:
λ
=
R
⁢
ω
r
v
(
6
)
3.2) determining limit operating rotational speed ωrc of the wind turbine generators, and the limit operating rotational speed ωrc of the wind turbine generators meets the following formula:
∂
(
K
D
⁢
L
⁢
ω
r
3
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
)
∂
ω
r
=
∂
(
0.5
ρπ
⁢
R
2
⁢
C
P
(
β
,
R
⁢
ω
r
v
)
⁢
v
3
)
∂
ω
r
(
7
)
3.3) substituting the limit operating rotational speed ωrc of the wind turbine generators into formula (5), and calculating to obtain limit operating point of the wind turbine generators
(
ω
r
⁢
c
,
0.5
ρ
⁢
π
⁢
R
2
⁢
C
P
(
β
,
R
⁢
ω
r
⁢
c
v
)
⁢
v
3
)
;
3.4) connecting extreme operating points at each wind speed to form stability boundary of the wind turbine generators, and substituting formula (6) into formula (7), and calculating limit tip speed ratio λc;
and the limit tip speed ratio λc meets the following formula:
3
⁢
K
D
⁢
L
(
λ
⁢
v
R
)
2
=
0
.
5
⁢
ρ
⁢
π
⁢
R
2
⁢
∂
(
C
P
(
β
,
λ
)
)
∂
λ
⁢
v
R
⁢
v
3
=
0
.
5
⁢
ρ
⁢
π
⁢
R
3
⁢
∂
(
C
P
(
β
,
λ
)
)
∂
λ
⁢
v
2
(
8
)
3.5) establishing expression formula of the relationship between wind speed and rotor rotational speed on the stability boundary of the wind turbine generators, namely:
v
=
R
⁢
ω
r
λ
c
;
(
9
)
3.6) substituting formula (9) into formula (5), and calculating to obtain expression formula of the stability boundary of the wind turbine generators, namely:
P
c
=
0.5
ρπ
⁢
R
5
⁢
C
P
(
β
,
λ
c
)
λ
c
3
⁢
ω
r
3
=
K
c
⁢
ω
r
3
(
10
)
3.7) based on formula (10), updating the limit operating point of the wind turbine generators to (ωrc, Kcωr3);
3.8) establishing stability constraints of the wind turbine generators when the wind turbine generators provide the frequency response, and it is divided into the following three situations:
I) when the wind turbine generators are operating at the lowest speed, the wind turbine generators do not provide the frequency response, and the frequency response of the wind turbine generators is as follows:
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
=
0
⁢
ω
r
⁢
0
<
ω
min
(
11
)
in the above formulas, ωr0 is the rotor rotational speed in initial operating state of the wind turbine generators;
II) when the limit operating rotational speed ωrc is less than the lowest speed ωmin, the stability constraints of the wind turbine generators when the wind turbine generators provide the frequency response are as follows:
K
D
⁢
L
⁢
ω
min
3
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
≤
f
M
(
ω
min
)
⁢
ω
r
⁢
c
<
ω
min
(
12
)
in the above formulas, fM(ωmin) is the mechanical power of the wind turbine generators at the lowest rotational speed ωmin;
III) when ωrc≥ωmin, the stability constraints of the wind turbine generators when the wind turbine generators provide the frequency response are as follows:
K
D
⁢
L
⁢
ω
r
⁢
c
3
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
≤
K
c
⁢
ω
r
⁢
c
3
(
13
)
4) establishing output constraints of the wind turbine generators when the wind turbine generators provide the frequency response, and the main steps are as follows:
4.1) updating the active output PE* of the wind turbine generators, namely:
P
E
*
=
(
1
-
d
w
)
⁢
P
w
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
;
(
14
)
in the above formulas, Pw is available power of the wind turbine generators;
dw is reserve coefficient of the wind turbine generators, and (1−dw)Pw is actual output of the wind turbine generators when does not provide the frequency response output;
4.2) establishing output constraints of the wind turbine generators when the wind turbine generators provide the frequency response, namely:
(
1
-
d
w
)
⁢
P
w
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
≤
P
w
max
(
15
)
in the above formulas, Pwmax is the maximum output of wind turbine generators;
5) combining formula (10), formula (12), formula (13) and formula (15), the security region of the wind turbine generators meets formula (16) to formula (19), namely:
K
w
=
0
;
J
w
=
0
ω
r
⁢
0
<
ω
min
;
(
16
)
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
≤
f
M
⁢
(
ω
min
)
-
K
DL
⁢
ω
min
3
ω
rc
<
ω
min
;
(
17
)
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
≤
K
c
⁢
ω
rc
3
-
K
DL
⁢
ω
rc
3
ω
rc
≥
ω
min
;
and
(
18
)
-
K
w
⁢
Δ
⁢
f
-
J
w
⁢
d
⁢
Δ
⁢
f
dt
≤
P
w
max
-
(
1
-
d
w
)
⁢
P
w
.
(
19
)
wherein the main steps of establishing a unit commitment model considering the security region of the wind turbine generators are as follows:
1) With the goal of minimizing the operating cost of the traditional synchronous generator, establishing the objective function, namely:
min
∑
i
=
1
T
∑
g
∈
ζ
[
(
c
g
⁢
P
g
,
i
+
c
g
nl
⁢
N
g
,
i
on
)
⁢
Δ
⁢
t
+
c
g
su
⁢
N
g
,
i
su
]
;
(
20
)
in the above formulas, ζ is a set of traditional synchronous generators;
cg is marginal cost;
cgnl is no-load cost;
cgsu is start-up cost;
Pg,i is active power of the traditional synchronous generator;
Ng,ion is online synchronous generator;
Ng,isu is synchronous generator turned on at step i;
T is total optimization time scale;
Δt is unit time interval;
variables with the subscript i represent variables of the i-th step;
variables with subscript g represent variables related to traditional synchronous generator g;
variables with subscripts g,i represent related variables of the traditional synchronous generator g at the i-th step;
2) establishing constraints of traditional unit commitment, which include power flow constraints, synchronous generator constraints, system frequency stability constraints, frequency change rate constraints, frequency lowest point constraints, and wind turbine generators security region constraints;
2.1) power flow constraints are as follows:
∑
g
∈
ζ
P
g
,
i
+
∑
w
∈
W
(
1
-
d
w
,
i
)
⁢
P
w
,
i
=
L
i
i
∈
T
(
21
)
in the above formulas, W is a set of wind turbine generators;
Li is total load of the system;
the wind turbine generators parameters are all aggregate parameters;
variables with subscript w represent variables related to wind turbine generators w;
variables with subscripts w,i represent related variables of wind turbine generators w at step i;
2.2) synchronous generator constraints are shown in formula (22) to formula (28);
N
g
,
i
on
⁢
P
g
min
≤
P
g
,
i
≤
N
g
,
i
on
⁢
P
g
max
(
22
)
N
g
,
i
on
=
N
g
,
i
-
1
on
+
N
g
,
i
su
-
N
g
,
i
sd
(
23
)
N
g
,
i
off
=
N
g
,
i
-
1
off
+
N
g
,
i
sd
-
N
g
,
i
su
(
24
)
P
g
,
i
-
P
g
,
i
-
1
≤
Δ
⁢
P
g
max
⁢
N
g
,
i
-
1
on
+
Δ
⁢
P
g
su
⁢
max
(
N
g
,
i
on
-
N
g
,
i
-
1
on
)
(
25
)
P
g
,
i
-
P
g
,
i
-
1
≥
-
Δ
⁢
P
g
max
⁢
N
g
,
i
on
+
Δ
⁢
P
g
sd
⁢
max
(
N
g
,
i
-
1
on
-
N
g
,
i
on
)
(
26
)
∑
i
k
=
i
+
1
-
Δ
⁢
t
g
up
N
g
,
k
su
≤
N
g
,
i
on
(
27
)
∑
k
=
i
+
1
-
Δ
⁢
t
g
dw
i
N
g
,
k
sd
≤
N
g
,
i
off
(
28
)
in the above formulas, Pgmin and Pgmax are the minimum value and maximum value of the synchronous generator output, respectively;
ΔPgmax is the maximum value of output change of the synchronous generator;
ΔPgsu max and ΔPgsd max are the maximum upward and downward climbing power of the synchronous generator, respectively;
Ng,isd is the number of synchronous generators shut down in step i;
Ng,ioff is the number of synchronous generators offline at step i;
Δtgup and Δtgup are the minimum start and stop time of the unit;
i∈T;
g∈ζ;
2.3) the system frequency stability constraints are as follows:
2
⁢
H
i
⁢
d
⁢
Δ
⁢
f
dt
+
(
D
i
⁢
L
i
+
K
i
)
⁢
Δ
⁢
f
=
-
Δ
⁢
L
i
(
29
)
wherein, Di is the load damping coefficient;
Hi is the system inertia time constant;
Ki is the frequency response coefficient;
wherein, the system inertia time constant Hi is shown as follows:
H
i
=
∑
g
∈
ζ
H
g
⁢
P
g
max
⁢
N
g
,
i
on
f
0
+
π
⁢
∑
w
∈
W
J
w
,
i
(
30
)
in the above formulas, Hg is the inertia time coefficient of synchronous generator;
The optimized variables in formula (30) are the virtual inertia control parameters Jw,i of the online synchronous generator Ng,ion and the wind turbine generators at i-th step;
f0 is the reference frequency of the power system;
frequency response coefficient Ki is shown as follows:
K
i
=
∑
g
∈
ζ
K
g
⁢
P
g
max
⁢
N
g
,
i
on
f
0
+
2
⁢
π
⁢
∑
w
∈
W
K
w
,
i
(
31
)
in the above formulas, Kg=1/Kdroop-g;
Kdroop-g is the droop control parameter of the synchronous generator;
the optimized variables in formula (31) are the frequency response parameter Kw,i of the online synchronous generator Ng,ion and the wind turbine generators at the i-th step;
system frequency deviation Δf is shown as follows:
Δ
⁢
f
⁡
(
t
)
=
(
e
-
(
D
i
⁢
L
i
+
K
i
)
2
⁢
H
i
⁢
t
-
1
)
⁢
Δ
⁢
L
i
(
D
i
⁢
L
i
+
K
i
)
(
32
)
frequency change rate dΔf/dt is shown as follows:
d
⁢
Δ
⁢
f
⁡
(
t
)
dt
=
-
Δ
⁢
L
i
2
⁢
H
i
⁢
e
-
(
D
i
⁢
L
i
+
K
i
)
2
⁢
H
i
⁢
t
(
33
)
2.4) frequency change rate constraints are shown as follows:
❘
"\[LeftBracketingBar]"
(
d
⁢
Δ
⁢
f
⁡
(
t
)
dt
)
❘
"\[RightBracketingBar]"
≤
Δ
⁢
L
i
2
⁢
H
i
≤
(
d
⁢
Δ
⁢
f
dt
)
max
(
34
)
2.5) frequency lowest point constraints are shown as follows:
❘
"\[LeftBracketingBar]"
Δ
⁢
f
⁡
(
t
)
❘
"\[RightBracketingBar]"
≤
❘
"\[LeftBracketingBar]"
Δ
⁢
f
nadir
,
i
❘
"\[RightBracketingBar]"
=
Δ
⁢
L
i
(
D
i
⁢
L
i
+
K
i
)
≤
Δ
⁢
f
max
(
35
)
2.6) Based on formula (1), formula (2), formula (32) to formula (35), establishing the equation of the frequency response provided by the wind turbine generators, namely:
-
K
w
,
i
⁢
Δ
⁢
f
⁡
(
t
)
-
J
w
,
i
⁢
d
⁢
Δ
⁢
f
⁡
(
t
)
dt
(
36
)
=
-
K
w
,
i
⁢
(
e
-
(
D
i
⁢
L
i
+
K
i
)
2
⁢
H
i
⁢
t
-
1
)
⁢
Δ
⁢
L
i
(
D
i
⁢
L
i
+
K
i
)
+
J
w
,
i
⁢
Δ
⁢
L
i
2
⁢
H
i
⁢
e
-
(
D
i
⁢
L
i
+
K
i
)
2
⁢
H
i
⁢
t
=
(
-
K
w
,
i
⁢
Δ
⁢
L
i
(
D
i
⁢
L
i
+
K
i
)
+
J
w
,
i
⁢
Δ
⁢
L
i
2
⁢
H
i
)
⁢
e
-
(
D
i
⁢
L
i
+
K
i
)
2
⁢
H
i
⁢
t
+
K
w
,
i
⁢
Δ
⁢
L
i
(
D
i
⁢
L
i
+
K
i
)
≤
max
⁢
{
K
w
,
i
⁢
Δ
⁢
L
i
(
D
i
⁢
L
i
+
K
i
)
,
J
w
,
i
⁢
Δ
⁢
L
i
2
⁢
H
i
}
≤
max
⁢
{
K
w
,
i
⁢
Δ
⁢
f
max
,
J
w
,
i
(
d
⁢
Δ
⁢
f
dt
)
max
}
;
2.7) substituting formula (36) into formula (17) to formula (19) to establish the security region constraints of the wind turbine generators, which are shown as formula (37) to formula (43) respectively:
K
w
=
0
;
J
w
=
0
ω
r
⁢
0
<
ω
min
(
37
)
K
w
,
i
⁢
Δ
⁢
f
max
≤
f
M
(
ω
min
)
-
K
DL
⁢
ω
min
3
ω
rc
<
ω
min
(
38
)
J
w
,
i
(
d
⁢
Δ
⁢
f
dt
)
max
≤
f
M
(
ω
min
)
-
K
DL
⁢
ω
min
3
ω
rc
<
ω
min
(
39
)
K
w
,
i
⁢
Δ
⁢
f
max
≤
K
c
⁢
ω
rc
3
-
K
DL
⁢
ω
r
⁢
c
3
ω
rc
≥
ω
min
(
40
)
J
w
,
i
(
d
⁢
Δ
⁢
f
dt
)
max
≤
K
c
⁢
ω
r
⁢
c
3
-
K
DL
⁢
ω
r
⁢
c
3
ω
rc
≥
ω
min
(
41
)
K
w
,
i
⁢
Δ
⁢
f
max
≤
P
w
max
-
(
1
-
d
w
,
i
)
⁢
P
w
,
i
(
42
)
J
w
,
i
(
d
⁢
Δ
⁢
f
dt
)
max
≤
P
w
max
-
(
1
-
d
w
,
i
)
⁢
P
w
,
i
;
(
43
)
wherein frequency response control parameters of the wind turbine generators are set based on the security region of the wind turbine generators when the wind turbine generators provide the frequency response.

1,805 more elements

Unit commitment method considering security region of wind turbine generator with frequency response control

Life of this patent

Unit commitment method considering security region of wind turbine generator with frequency response control

Life of this patent

Abstract

Claims1