US 12,007,422 B1
Method and system for allocating optimal inertia in a power system
Tianshu Bi, Beijing (CN); Cheng Wang, Beijing (CN); Jiahao Liu, Beijing (CN); and Guoyi Xu, Beijing (CN)
Assigned to NORTH CHINA ELECTRIC POWER UNIVERSITY, Beijing (CN)
Filed by NORTH CHINA ELECTRIC POWER UNIVERSITY, Beijing (CN)
Filed on Jan. 11, 2024, as Appl. No. 18/410,614.
Application 18/410,614 is a continuation of application No. 18/207,508, filed on Jun. 8, 2023.
Int. Cl. G01R 21/133 (2006.01); G01R 19/25 (2006.01); G01R 31/08 (2020.01)
CPC G01R 21/1331 (2013.01) [G01R 19/2513 (2013.01); G01R 31/088 (2013.01)] 1 Claim
OG exemplary drawing
 
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 (∀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:

OG Complex Work Unit Math
Ψ={ĤA,i,XA,i,XL,ij},  (11b)
fB,i=g(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 Ψ consisting of parameters to be estimated in (11b); based on Ψ and power flow related variables, bus frequency dynamics are estimated in (11c);
wherein g(⋅) denotes:

OG Complex Work Unit Math
ΔPA,iE=KA,i(ΔδCOI,i−Δθi),  (7c)

OG Complex Work Unit Math
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:

OG Complex Work Unit Math
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:

OG Complex Work Unit Math
θi in (8) is a dependent variable of the state variables.