US 11,677,344 B2 · Stability evaluation method and system of direct-drive wind turbine generator

A stability evaluation method of direct-drive wind turbine generator, comprising:

measuring, with a Phasor Measurement Unit (PMU), variations of voltage, current, active power and PLL (Phase Locked Loop) angle at a terminal of direct-drive wind turbine generator in one oscillation period
2
⁢
π
ω
;
based on the measured variations, calculating terminal energy of direct-drive wind turbine generator with a terminal energy model of direct-drive wind turbine generator, wherein the terminal energy model of direct-drive wind turbine generator comprises:
Δ
⁢
W
P
⁢
M
⁢
S
⁢
G
⁡
(
t
)
=
∫
t
t
+
2
⁢
π
ω
⁢
Δ
⁢
⁢
P
e
⁢
d
⁢
⁢
Δ
⁢
⁢
θ
pll
+
∫
t
t
+
2
⁢
π
ω
⁢
(
Δ
⁢
i
d
⁢
d
⁢
Δ
⁢
u
q
-
Δ
⁢
i
q
⁢
d
⁢
Δ
⁢
u
d
)
where ΔPe is the variation of direct-drive wind turbine generator output active power compared with the steady-state value, Δθpll is the variation of PLL angle, Δid, Δiq, Δuq and Δud are respectively the variation of d-axis and q-axis components of current and voltage at the terminal of direct-drive wind turbine generator, ω is the oscillation frequency of dq axis;
obtaining energy negative gradient of direct-drive wind turbine generator according to discretized and average values of the terminal energy of direct-drive wind turbine generator, and assessing system stability level according to a value of the energy negative gradient, wherein the larger the value of the energy negative gradient is, the higher the system stability level is;
and
obtaining an adjustment law of critical parameters affecting the stability of the system based on the energy negative gradient with stability operation points and critical parameters PLL and transmission lines, which comprises the following steps S1-S2:
step S1:
applying the PLL dynamic function to the energy negative gradient expression, achieving the energy negative gradient with stability operation points and PLL critical parameters:
η
2
=
-
(
I
s
⁢
d
⁢
0
⁢
ω
⁢
cos
⁢
φ
c
2
+
I
s
⁢
q
⁢
0
⁢
ω
)
⁢
sin
⁢
φ
c
2
)
[
A_
⁢
(
t
)
⁢
Ω
u
-
⁢
α
u
⁢
e
α
u
⁢
t
+
dA_
⁢
(
t
)
d
⁢
t
⁢
Ω
u
-
⁢
e
α
u
⁢
t
]
❘
t
0
t
0
+
2
⁢
π
ω
-
U
s
⁢
d
⁢
0
⁢
ω
)
⁢
cos
⁡
(
φ
c
-
φ
R
⁢
L
)
2
[
A_
⁢
(
t
)
⁢
α
i
⁢
Ω
i
-
⁢
e
α
i
⁢
t
+
dA_
⁢
(
t
)
d
⁢
t
⁢
Ω
i
-
⁢
e
α
i
⁢
t
]
❘
"\[LeftBracketingBar]"
t
0
t
0
+
2
⁢
π
ω
+
(
I
s
⁢
d
⁢
0
⁢
ω
)
⁢
cos
⁢
φ
c
2
+
I
s
⁢
q
⁢
0
⁢
ω
⁢
sin
⁢
φ
c
2
)
[
A
+
(
t
)
⁢
Ω
u
+
⁢
α
u
⁢
e
α
u
⁢
t
+
dA
+
(
t
)
d
⁢
t
⁢
Ω
u
+
⁢
e
α
u
⁢
t
]
|
t
0
t
0
+
2
⁢
π
ω
+
U
s
⁢
d
⁢
0
⁢
ω
⁢
cos
⁡
(
φ
c
-
φ
R
⁢
L
)
2
[
A
+
(
t
)
⁢
α
i
⁢
Ω
i
+
⁢
e
α
i
⁢
t
+
dA
+
(
t
)
d
⁢
t
⁢
Ω
i
+
⁢
e
α
i
⁢
t
]
|
t
0
t
0
+
2
⁢
π
ω
-
2
⁢
ω
⁢
K
p
⁢
l
⁢
l
2
⁢
Ω
u
-
⁢
Ω
u
+
⁢
e
2
⁢
α
u
⁢
t
⁢
α
u
⁢
sin
⁢
φ
c
[
I
s
⁢
d
⁢
0
⁢
sin
⁡
(
φ
u
+
+
φ
u
)
-
I
s
⁢
q
⁢
0
⁢
cos
⁡
(
φ
u
+
+
φ
u
-
)
]
|
t
0
t
0
+
2
⁢
π
ω
Where A−, A+ respectively represent the amplitude of PLL angle variation Δθpll in sub-synchronous frequency and super-synchronous frequency;
Isd0, Isq0, Usd0, Usq0 are the original value of dq axes components of current and voltage of the terminal of direct-drive wind turbine generator;
αu and αi are the attenuation coefficients of oscillation components of voltage and current;
Ωu−, Ωu+, Ωi− and Ωi+ are respectively the amplitude coefficients of sub/super synchronous components of voltage and current;
φu− and φu+ are the initial phase angles of sub-synchronous and super-synchronous voltage;
φi− and φi+ are the initial phase angles of sub-synchronous and super-synchronous currents;
Ωu+=Ωi+X+, Ωu−=Ωi−X−, φu−=φi−+φRL and φu+=φi++φRL, where φRL is the phase angle of transmission lines;
kpθ and kiθ are the proportion gain and integration gain of PLL;
φ
c
=
arctan
⁢
ω
⁢
k
p
⁢
θ
k
i
⁢
θ
,
K
pll
=
❘
"\[LeftBracketingBar]"
k
p
⁢
θ
⁢
s
+
k
i
⁢
θ
s
2
-
U
s
⁢
q
⁢
0
(
k
p
⁢
θ
⁢
s
+
k
i
⁢
θ
)
❘
"\[RightBracketingBar]"
s
=
j
⁢
ω
;
applying the dynamic function of system transmission lines to the energy negative gradient expression, obtaining the energy negative gradient of critical parameters of transmission lines:
η
1
=
-
2
⁢
Ω
i
+
⁢
Ω
i
-
⁢
e
2
⁢
α
,
t
⁢
α
i
⁢
X
L
⁢
ωsin
⁡
(
φ
i
+
+
φ
i
-
)
❘
"\[RightBracketingBar]"
t
0
t
0
+
2
⁢
π
ω
+
2
[
Ω
i
-
2
⁢
e
2
⁢
α
,
t
⁢
α
i
⁢
ω
⁢
R
-
Ω
i
+
⁢
Ω
i
-
⁢
e
2
⁢
α
,
t
⁢
α
i
⁢
R
⁢
ωcos
⁡
(
φ
i
+
+
φ
i
-
)
]
❘
"\[LeftBracketingBar]"
t
0
t
0
+
2
⁢
π
ω
where Ωi− and Ωi+ are the amplitude coefficients of current sub-synchronous component and super-synchronous component respectively;
αi is the attenuation coefficients of oscillation components of current;
R and XL are line resistance and the equivalent reactance of the transmission lines;
φ1− and φi+ are the initial phase angles of sub-synchronous and super-synchronous currents;
and
step S2:
based on the constructed energy negative gradient with the critical parameters of stability operation points of direct-drive wind turbine generator, PLL and the transmission lines, obtaining influence pattern of these parameters on the energy negative gradient;
wherein the adjustment law comprises:
the stability level of system is improved by reducing Isd0 or increasing Isq0;
the more stable the system is the larger R is and the smaller XL is;
the system stability is enhanced by reducing PLL parameters Kp and Ki.

674 more elements

A stability evaluation system of direct-drive wind turbine generator, comprising:

a Phasor Measurement Unit (PMU), a first processor, a second processor, a third processor and result output terminal, wherein
the PMU is used to collect variations of voltage, current, active power and PLL (Phase Locked Loop) angle at a terminal of direct-drive wind turbine generator in one oscillation period
2
⁢
π
ω
;
the first processor is used to calculate terminal energy of direct-drive wind turbine generator with a terminal energy model of direct-drive wind turbine generator based on the measured variations, wherein the terminal energy model of direct-drive wind turbine generator is:
Δ
⁢
W
PMSG
(
t
)
=
∫
t
t
+
2
⁢
π
ω
Δ
⁢
P
e
⁢
d
⁢
Δ
⁢
θ
pll
+
∫
t
t
+
2
⁢
π
ω
(
Δ
⁢
i
d
⁢
d
⁢
Δ
⁢
u
q
-
Δ
⁢
i
q
⁢
d
⁢
Δ
⁢
u
d
)
where ΔPe is the variation of direct-drive wind turbine generator output active power compared with a steady-state value, Δθpll is the variation of PLL angle, Δid, Δiq, Δuq and Δud are respectively the variation of d-axis and q-axis components of current and voltage at the terminal of direct-drive wind turbine generator, ω is the oscillation frequency of dq axis;
the second processor is used to assess stability level of direct-drive wind turbine generator according to a value of energy negative gradient which is obtained according to discretized and average values of the terminal energy of direct-drive wind turbine generator, wherein the larger the value of the energy negative gradient is, the higher the system stability level is;
the third processor is used to obtain an adjustment law of critical parameters affecting the stability of the system based on the energy negative gradient with stability operation points and critical parameters PLL and transmission lines;
and
the result output terminal is used to output the stability level of the system and the adjustment law of the critical parameters affecting system stability;
wherein the third processor is operable for
step S1:
applying the PLL dynamic function to the energy negative gradient expression, achieving the energy negative gradient with stability operation points and PLL critical parameters:
η
2
=
-
(
I
sd
⁢
⁢
0
⁢
ω
⁢
cos
⁢
⁢
φ
c
2
+
I
sq
⁢
⁢
0
⁢
ω
⁢
sin
⁢
⁢
φ
c
2
)
⁢
[
A
-
⁡
(
t
)
⁢
Ω
u
-
⁢
α
u
⁢
e
α
u
⁢
t
+
dA
-
⁡
(
t
)
d
⁢
t
⁢
Ω
u
-
⁢
e
α
u
⁢
t
]

t
0
t
0
+
2
⁢
π
ω
-
U
sd
⁢
⁢
0
⁢
ω
⁢
cos
⁢
⁢
(
φ
c
-
φ
R
⁢
L
)
2
⁡
[
A
-
⁡
(
t
)
⁢
α
i
⁢
Ω
i
-
⁢
⁢
e
α
i
⁢
t
+
dA
-
⁡
(
t
)
d
⁢
t
⁢
Ω
i
-
⁢
⁢
e
α
i
⁢
t
]

t
0
t
0
+
2
⁢
⁢
π
ω
+
⁢
(
I
sd
⁢
⁢
0
⁢
ω
⁢
cos
⁢
⁢
φ
c
2
+
I
sq
⁢
⁢
0
⁢
ω
⁢
sin
⁢
⁢
φ
c
2
)
⁡
[
A
+
⁡
(
t
)
⁢
Ω
u
+
⁢
α
u
⁢
e
α
u
⁢
t
+
d
⁢
A
+
⁡
(
t
)
d
⁢
t
⁢
Ω
u
+
⁢
e
α
u
⁢
t
]
⁢
|
t
0
t
0
+
2
⁢
π
ω
⁢
+
⁢
U
sd
⁢
⁢
0
⁢
ω
⁢
cos
⁡
(
φ
c
-
φϕ
R
⁢
L
)
2
⁡
[
A
+
⁡
(
t
)
⁢
α
i
⁢
Ω
i
+
⁢
e
α
i
⁢
t
+
d
⁢
A
+
⁡
(
t
)
d
⁢
t
⁢
Ω
i
+
⁢
e
α
i
⁢
t
]
⁢
|
t
0
t
0
+
2
⁢
π
ω
⁢
-
⁢
2
⁢
⁢
ω
⁢
⁢
K
pll
2
⁢
Ω
u
-
⁢
Ω
u
+
⁢
e
2
⁢
α
u
⁢
t
⁢
α
u
⁢
sin
⁢
⁢
φ
c
⁡
[
I
s
⁢
d
⁢
0
⁢
sin
⁡
(
φ
u
+
+
φ
u
-
)
-
I
s
⁢
q
⁢
0
⁢
cos
⁡
(
φ
u
+
+
φ
u
-
)
]
⁢
|
t
0
t
0
+
2
⁢
π
ω
Where A−, A+ respectively represent the amplitude of PLL angle variation Δθpll in sub-synchronous frequency and super-synchronous frequency;
Isd0, Isq0, Usd0, Usq0 are the original value of dq axes components of current and voltage of the terminal of direct-drive wind turbine generator;
αu and αi are the attenuation coefficients of oscillation components of voltage and current;
Ωu−, Ωu+, Ωi− and Ωi+ are respectively the amplitude coefficients of sub/super synchronous components of voltage and current;
φu− and φu+ are the initial phase angles of sub-synchronous and super-synchronous voltage;
φi− and φi+ are the initial phase angles of sub-synchronous and super-synchronous currents;
Ωu+=Ωi+X+, Ωu−=Ωi−X−, φu−=φi−+φRL and φu+=φi++φRL, where φRL is the phase angle of transmission lines;
kpθ and kiθ are the proportion gain and integration gain of PLL;
φ
c
=
arctan
⁢
ω
⁢
k
p
⁢
θ
k
i
⁢
⁢
θ
,
K
pll
=

k
p
⁢
θ
⁢
s
+
k
i
⁢
⁢
θ
s
2
-
U
s
⁢
q
⁢
0
⁡
(
k
p
⁢
θ
⁢
s
+
k
i
⁢
⁢
θ
)

s
-
j
⁢
⁢
ω
;
applying the dynamic function of system transmission lines to the energy negative gradient expression, obtaining the energy negative gradient of critical parameters of transmission lines:
η
1
=
-
2
⁢
Ω
i
+
⁢
Ω
i
-
⁢
e
2
⁢
α
i
⁢
t
⁢
α
i
⁢
X
L
⁢
ω
⁢
⁢
sin
⁡
(
φ
i
+
+
φ
i
-
)

t
0
t
0
+
2
⁢
π
ω
+
2
⁡
[
Ω
i
-
2
⁢
e
2
⁢
α
i
⁢
t
⁢
α
i
⁢
ω
⁢
⁢
R
-
Ω
i
+
⁢
Ω
i
-
⁢
⁢
e
2
⁢
α
i
⁢
t
⁢
α
i
⁢
R
⁢
⁢
ω
⁢
⁢
cos
⁡
(
φ
i
+
+
φ
i
-
)
]

t
0
t
0
+
2
⁢
π
ω
where Ωi− and Ωi+ are the amplitude coefficients of current sub-synchronous component and super-synchronous component respectively;
αi is the attenuation coefficients of oscillation components of current;
R and XL are line resistance and the equivalent reactance of the transmission lines;
φ1− and φi+ are the initial phase angles of sub-synchronous and super-synchronous currents;
and
step S2:
based on the constructed energy negative gradient with the critical parameters of stability operation points of direct-drive wind turbine generator, PLL and the transmission lines, obtaining influence pattern of these parameters on the energy negative gradient, wherein the adjustment law comprises:
the stability level of system is improved by reducing Isd0 or increasing Isq0;
the more stable the system is the larger R is and the smaller XL is;
the system stability is enhanced by reducing PLL parameters Kp and Ki.

701 more elements

A non-transitory machine-readable storage medium comprising instructions that when executed cause a processor of a computing device to:

measuring, by a Phasor Measurement Unit (PMU), variations of voltage, current, active power and PLL (Phase Locked Loop) angle at a terminal of direct-drive wind turbine generator in one oscillation period
2
⁢
π
ω
;
based on the measured variations, calculating terminal energy of direct-drive wind turbine generator with a terminal energy model of direct-drive wind turbine generator, wherein the terminal energy model of direct-drive wind turbine generator is:
Δ
⁢
W
P
⁢
M
⁢
S
⁢
G
⁡
(
t
)
=
∫
t
t
+
2
⁢
π
ω
⁢
Δ
⁢
P
e
⁢
d
⁢
Δ
⁢
θ
pll
+
∫
t
t
+
2
⁢
π
ω
⁢
(
Δ
⁢
i
d
⁢
d
⁢
Δ
⁢
u
q
-
Δ
⁢
i
q
⁢
d
⁢
Δ
⁢
u
d
)
where ΔPe is the variation of direct-drive wind turbine generator output active power compared with the steady-state value, Δθpll is the variation of PLL angle, Δid, Δiq, Δuq and Δud are respectively the variation of d-axis and q-axis components of current and voltage at the terminal of direct-drive wind turbine generator, ω is the oscillation frequency of dq axis;
obtaining energy negative gradient of direct-drive wind turbine generator according to discretized and average values of the terminal energy of direct-drive wind turbine generator, and assessing system stability level according to a value of the energy negative gradient, wherein the larger the value of the energy negative gradient is, the higher the system stability level is;
and
obtaining an adjustment law of critical parameters affecting the stability of the system based on the energy negative gradient with stability operation points and critical parameters PLL and transmission lines, which comprises the following steps S1-S2:
step S1:
applying the PLL dynamic function to the energy negative gradient expression, achieving the energy negative gradient with stability operation points and PLL critical parameters:
η
2
=
-
(
I
s
⁢
d
⁢
0
⁢
ω
⁢
cos
⁢
φ
c
2
+
I
s
⁢
q
⁢
0
⁢
ω
)
⁢
sin
⁢
φ
c
2
)
[
A_
⁢
(
t
)
⁢
Ω
u
-
⁢
α
u
⁢
e
α
u
⁢
t
+
dA_
⁢
(
t
)
d
⁢
t
⁢
Ω
u
-
⁢
e
α
u
⁢
t
]
❘
"\[LeftBracketingBar]"
t
0
t
0
+
2
⁢
π
ω
-
U
s
⁢
d
⁢
0
⁢
ω
)
⁢
cos
⁡
(
φ
c
-
φ
R
⁢
L
)
2
[
A_
⁢
(
t
)
⁢
α
i
⁢
Ω
i
-
⁢
e
α
i
⁢
t
+
dA_
⁢
(
t
)
d
⁢
t
⁢
Ω
i
-
⁢
e
α
i
⁢
t
]
❘
"\[LeftBracketingBar]"
t
0
t
0
+
2
⁢
π
ω
+
(
I
s
⁢
d
⁢
0
⁢
ω
)
⁢
cos
⁢
φ
c
2
+
I
s
⁢
q
⁢
0
⁢
ω
⁢
sin
⁢
φ
c
2
)
[
A
+
(
t
)
⁢
Ω
u
+
⁢
α
u
⁢
e
α
u
⁢
t
+
dA
+
(
t
)
d
⁢
t
⁢
Ω
u
+
⁢
e
α
u
⁢
t
]
|
t
0
t
0
+
2
⁢
π
ω
+
U
s
⁢
d
⁢
0
⁢
ω
⁢
cos
⁡
(
φ
c
-
φ
R
⁢
L
)
2
[
A
+
(
t
)
⁢
α
i
⁢
Ω
i
+
⁢
e
α
i
⁢
t
+
dA
+
(
t
)
d
⁢
t
⁢
Ω
i
+
⁢
e
α
i
⁢
t
]
|
t
0
t
0
+
2
⁢
π
ω
-
2
⁢
ω
⁢
K
p
⁢
l
⁢
l
2
⁢
Ω
u
-
⁢
Ω
u
+
⁢
e
2
⁢
α
u
⁢
t
⁢
α
u
⁢
sin
⁢
φ
c
[
I
s
⁢
d
⁢
0
⁢
sin
⁡
(
φ
u
+
+
φ
u
)
-
I
s
⁢
q
⁢
0
⁢
cos
⁡
(
φ
u
+
+
φ
u
-
)
]
|
t
0
t
0
+
2
⁢
π
ω
Where A−, A+ respectively represent the amplitude of PLL angle variation Δθpll in sub-synchronous frequency and super-synchronous frequency;
Isd0, Isq0, Usd0, Usq0 are the original value of dq axes components of current and voltage of the terminal of direct-drive wind turbine generator;
αu and αi are the attenuation coefficients of oscillation components of voltage and current;
Ωu−, Ωu+, Ωi− and Ωi+ are respectively the amplitude coefficients of sub/super synchronous components of voltage and current;
φu− and φu+ are the initial phase angles of sub-synchronous and super-synchronous voltage;
φi− and φi+ are the initial phase angles of sub-synchronous and super-synchronous currents;
Ωu+=Ωi+X+, Ωu−=Ωi−X−, φu−=φi−+φRL and φu+=φi++φRL, where φRL is the phase angle of transmission lines;
kpθ and kiθ are the proportion gain and integration gain of PLL;
φ
c
=
arctan
⁢
ω
⁢
k
p
⁢
θ
k
i
⁢
θ
,
K
pll
=
❘
"\[LeftBracketingBar]"
k
p
⁢
θ
⁢
s
+
k
i
⁢
θ
s
2
-
U
s
⁢
q
⁢
0
(
k
p
⁢
θ
⁢
s
+
k
i
⁢
θ
)
❘
"\[RightBracketingBar]"
s
=
j
⁢
ω
;
applying the dynamic function of system transmission lines to the energy negative gradient expression, obtaining the energy negative gradient of critical parameters of transmission lines:
η
1
=
-
2
⁢
Ω
i
+
⁢
Ω
i
-
⁢
e
2
⁢
α
,
t
⁢
α
i
⁢
X
L
⁢
ωsin
⁡
(
φ
i
+
+
φ
i
-
)
❘
"\[LeftBracketingBar]"
t
0
t
0
+
2
⁢
π
ω
+
2
[
Ω
i
-
2
⁢
e
2
⁢
α
,
t
⁢
α
i
⁢
ω
⁢
R
-
Ω
i
+
⁢
Ω
i
-
⁢
e
2
⁢
α
,
t
⁢
α
i
⁢
R
⁢
ωcos
⁡
(
φ
i
+
+
φ
i
-
)
]
❘
"\[LeftBracketingBar]"
t
0
t
0
+
2
⁢
π
ω
where Ωi− and Ωi+ are the amplitude coefficients of current sub-synchronous component and super-synchronous component respectively;
αi is the attenuation coefficients of oscillation components of current;
R and XL are line resistance and the equivalent reactance of the transmission lines;
φ1− and φi+ are the initial phase angles of sub-synchronous and super-synchronous currents;
and
step S2:
based on the constructed energy negative gradient with the critical parameters of stability operation points of direct-drive wind turbine generator, PLL and the transmission lines, obtaining influence pattern of these parameters on the energy negative gradient;
wherein the adjustment law comprises:
the stability level of system is improved by reducing Isd0 or increasing Isq0;
the more stable the system is the larger R is and the smaller XL is;
the system stability is enhanced by reducing PLL parameters Kp and Ki.

672 more elements

Stability evaluation method and system of direct-drive wind turbine generator

Life of this patent

Stability evaluation method and system of direct-drive wind turbine generator

Life of this patent

Abstract

Claims8