US 12,007,422 B1 · Method and system for allocating optimal inertia in a power system

Abstract

Online estimation of area-level inertia can be used for frequency stability control in low-inertia power systems. This disclosure provides an area-level inertia online estimation method considering inter-area equivalent frequency dynamics. The disclosed method only needs one phasor measurement unit placed at any bus within each area. The inter-area equivalent frequency dynamics model for the multi-area power system is developed, which is employed to estimate area-level inertia under the small disturbance situation. Then, the area-level inertia estimation model boils down to a nonlinear parameter identification problem. The other boundary conditions of the disclosed method are derived by parameter identifiability.

A method for estimating area-level inertia in a power system, comprising:

partitioning the power system as a multi-area system, wherein:
a phasor measurement unit (“PMU”) is placed at a bus in at least one area of the multi-area system;
and
for an N-th area which contains only one generator and one bus, the PMU placement must be placed at the multi-area system;
measuring bus frequencies, power flow related data including amplitude and phase angle of bus voltage by the PMUs or SCADA/EMS as follows:
Measurable Variables
fB, i (∀iϵN)
from PMU
ECOI, i(ss), δCOI, i(ss), and
from power flow calculation
δCOI, i(0) (∀iϵN)
by SCADA/EMS
Ui(ss) and θi(ss) (∀iϵN)
from PMU or SCADA/EMS
fCOI, i(0) (∀iϵN)
from PMU or SCADA/EMS
specifying data window for inertia estimation during small disturbance situations;
preparing measured frequencies within the data window, wherein:
for the power flow data, variables at a linearization point correspond to a head of the data window, and variables at a system steady-state are utilized;
and
determining an internal reactance or an inertia of the N-th area according to an identifiability analysis;
estimating the area-level inertia by:
min
Ψ
^
*
(
∫
t
0
t
0
+
T
∑
i
∈
N
(
f
ˆ
B
,
i
(
Ψ
ˆ
)
-
f
B
,
i
)
2
⁢
dt
)
,
(
11
⁢
a
)
{circumflex over (Ψ)}={ĤA,i,{circumflex over (X)}A,i,{circumflex over (X)}L,ij}, (11b)
{circumflex over (f)}B,i=g({circumflex over (Ψ)},fCOI,i(0),δCOI,i(0),ECOI,i(ss),δCOI,i(ss),Ui(ss),θi(ss)), (11c)
wherein t0 is a moment corresponding to a linearization point;
T is a data window length;
a vector {circumflex over (Ψ)} consisting of parameters to be estimated in (11b);
based on {circumflex over (Ψ)} and power flow related variables, bus frequency dynamics are estimated in (11c);
wherein g(⋅) denotes:
2
⁢
H
A
,
i
⁢
d
⁢
Δ
⁢
f
COI
,
i
d
⁢
t
=
-
Δ
⁢
P
A
,
i
E
,
(
7
⁢
a
)
d
⁢
Δ
⁢
δ
COI
,
i
d
⁢
t
=
f
N
⁢
Δ
⁢
f
COI
,
i
,
(
7
⁢
b
)
ΔPA,iE=KA,i(ΔδCOI,i−Δθi), (7c)
K
A
,
i
=
E
COI
,
i
(
ss
)
⁢
U
i
(
ss
)
X
A
,
i
⁢
cos
⁡
(
δ
COI
,
i
(
s
⁢
s
)
-
θ
i
(
s
⁢
s
)
)
(
7
⁢
d
)
d
⁢
Δ
⁢
θ
i
d
⁢
t
=
f
N
⁢
Δ
⁢
f
B
,
i
.
(
8
)
Δ
⁢
P
A
,
i
E
=
∑
j
∈
N
,
j
≠
i
K
L
,
ij
(
Δ
⁢
θ
i
-
Δ
⁢
θ
j
)
,
(
9
⁢
a
)
K
L
,
ij
=
U
i
(
s
⁢
s
)
⁢
U
j
(
s
⁢
s
)
X
ij
⁢
cos
⁡
(
θ
i
(
s
⁢
s
)
-
θ
j
(
s
⁢
s
)
)
,
(
9
⁢
b
)
where KA,i is a linearization coefficient of a generator active power;
the superscript {⋅}(ss) denotes a steady-state value;
and where KA,i is a linearization coefficient of an inter-area active power;
obtaining an area equivalent internal reactance and an equivalent inter-area line reactance;
determining a real-time frequency stability level and a real-time degree of frequency spatial distribution based on the area equivalent internal reactance and the equivalent inter-area line reactance;
issuing an alarm in the event of a determined frequency instability;
and
when an online inertia level is low, allocating optimal inertia from battery storage and unit commitment optimization of synchronous generators;
wherein:
d
⁢
Δθ
i
d
⁢
t
=
f
N
⁢
Δ
⁢
f
B
,
i
.
(
8
)
transient processes of variables in (7)-(9) are determined by the initial conditions of state variables fCOI,i, δCOI,i, and θi;
in (7a) and (7b), the initial conditions of the state variables fCOI,i δCOI,i are their values at linearization points:
f
COI
,
i
i
⁢
n
⁢
i
⁢
t
=
f
COI
,
i
(
0
)
,
(
10
⁢
a
)
δ
COI
,
i
i
⁢
n
⁢
i
⁢
t
=
δ
COI
,
i
(
0
)
.
(
10
⁢
b
)
θi in (8) is a dependent variable of the state variables.

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Method and system for allocating optimal inertia in a power system

Life of this patent

Method and system for allocating optimal inertia in a power system

Life of this patent

Abstract

Claims1