# US 11,906,556 B1 · Online estimation of area-level inertia considering inter-area equivalent frequency dynamics

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- Number: US 11,906,556 B1
- Document ID: US11906556B1
- Status: Granted
- Kind: B1
- Application number: 18/207,508
- Filed: 2023-06-08
- Granted: 2024-02-20
- Earliest claimed: 2023-06-08
- Assignees: North China Electric Power University
- Applicants: North China Electric Power University
- Inventors: Tianshu Bi; Cheng Wang; Jiahao Liu; Guoyi Xu
- Web page: https://patentgrep.com/patent/US11906556B1

## CPC

- G01R 21/1331: {Measuring real or reactive component, measuring apparent energy}
- G01R 19/2513: {Arrangements for monitoring electric power systems, e.g. power lines or loads; Logging}
- G01R 31/088: {Aspects of digital computing}
- Y02E 60/00: Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y04S 10/22: Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- Y02E: REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y04S: SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS

## 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.

## Claims

### Claim 1

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 ( ∀i ∈ N )
from PMU
ECOI,i(ss), δCOI,i(ss), and
from power flow calculation
δCOI,i(0) ( ∀i ∈ N )
by SCADA/EMS
Ui(ss) and θi(ss)
from PMU or SCADA/EMS
( ∀i ∈ N )
fCOI,i(0) ( ∀i ∈ N )
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
^
B
,
i
(
Ψ
^
)
-
f
B
,
i
)
2
⁢
dt
)
,
(
11
⁢
a
)
Ψ
^
=
{
H
^
A
,
i
,
X
^
A
,
i
,
X
^
L
,
ij
}
,
(
11
⁢
b
)
f
^
B
,
i
=
g
⁡
(
Ψ
^
,
COI
,
i
(
0
)
,
δ
COI
,
i
(
0
)
,
E
COI
,
i
(
ss
)
,
δ
COI
,
i
(
ss
)
,
U
i
(
ss
)
,
θ
i
(
ss
)
)
,
(
11
⁢
c
)
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
C
⁢
O
⁢
I
i
,
(
7
⁢
b
)
Δ
⁢
P
A
,
i
E
=
K
A
,
i
(
Δδ
COI
,
i
-
Δθ
i
)
,
(
7
⁢
c
)
K
A
,
i
=
E
COI
,
i
(
ss
)
⁢
U
i
(
s
⁢
s
)
⁢
S
⁢
S
X
A
,
i
⁢
cos
⁡
(
5
COI
,
i
(
ss
)
-
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
(
Δθ
i
-
Δθ
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;
when an online inertia level is low, allocating optimal inertia from battery storage and unit commitment optimization of synchronous generators.