# US 11,909,218 B1 · Energy management of distribution-level integrated electric-gas systems with fast frequency reserve

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- Number: US 11,909,218 B1
- Document ID: US11909218B1
- Status: Granted
- Kind: B1
- Application number: 18/222,707
- Filed: 2023-07-17
- Granted: 2024-02-20
- Earliest claimed: 2023-07-17
- Applicants: North China Electric Power University
- Inventors: Cheng Wang; Tianshu Bi; Guoyi Xu; Rui Zhang
- Web page: https://patentgrep.com/patent/US11909218B1

## CPC

- H02J 3/46: Controlling the sharing of generated power between the generators, sources or networks
- H02J 2103/30: Simulating, planning, modelling, reliability check or computer assisted design [CAD] of electric power networks
- H02J: ELECTRIC POWER NETWORKS; CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY

## Abstract

In this disclosure, the energy management problem of the D-IEGS with FFR is analyzed, so as to enhance the frequency stability of the main grid. The post-disturbance frequency response behaviors of both the main grid and the D-IEGS are precisely depicted, where the dead zones, limiting ranges and time constant of the governors are considered. The frequency regulation units of the D-IEGS include GTs and P2G units, whose impacts of providing frequency regulation service on the gas networks are quantified. Considering the time-scale similarity of the frequency dynamics and the dynamics of the GDN, the gas flow dynamics model is adopted. The frequency response dynamics of the GTs and P2G units, and the gas flow dynamics of the GDN, a variable-step difference scheme and a binary variable reduction method are devised.

## Claims

### Claim 1

A method for managing a fast frequency response (FFR) of a distribution-level integrated electric-gas system (D-IEGS), the method comprising:
operating a D-IEGS wherein:
an active power disturbance uncertainty is modeled as:
ΔPdis,te=zteuΔPdis,te−−ztedΔPdis,te+, ∀te
{zteu, zted∈{0,1}, zteu+zted≤1}, (11)
wherein te represents a scheduling period of a power system; ΔPdis,te is an aggregated active power disturbance; ΔPdis,te− is a negative active power disturbance; ΔPdist,te+ is a positive active power disturbance; and zteu and zted are binary variables, and represent a disturbance type,
FFR incremental outputs can be described by:
{tilde over (P)}gte,k=Pgte+(zgteu−zgted)ΔPte,kg, 1≤k≤N
{zgteu, zgted∈{0,1}, zgteu+zgted≤1} (12)
{tilde over (P)}pte,k=Ppte−(zpteu−zpted)ΔPte,kp, 1≤k≤N
{zpteu, zpted∈{0,1}, zpteu+zpted≤1} (13)
wherein ΔPte,kg and ΔPte,kp denote the incremental active power outputs/consumption of gas-fired turbines (GTs) and power-to-gas (P2G) units during an FFR regulation process; k is an index for frequency dynamics difference time step and N is a total number of time steps; zgteu and zgted are binary variables, representing an uncertainty of GT active power outputs; zpteu and zpted are binary variables, representing an uncertainty of P2G active power consumption; Pgte is a steady-state active power outputs of GT; Ppte is a steady-state active power consumption of P2G; and {tilde over (P)}gte,k and {tilde over (P)}pte,k are an uncertain active power outputs of GT and an uncertain active power consumption of P2G, respectively, and
a gas load uncertainty can be quantified by:
M
~
g
⁢
τ
g
=
{
P
~
gt
e
,
k
/
η
g
,
τ
∈
[
1
,
N
]
P
gt
e
/
η
g
,
τ
∈
(
N
,
N
g
]
,
M
~
p
⁢
τ
g
=
{
P
~
pt
e
,
k
⁢
η
p
,
τ
∈
[
1
,
N
]
P
pt
e
⁢
η
p
,
τ
∈
(
N
,
N
g
]
(
14
)
wherein {tilde over (M)}gτg and {tilde over (M)}pτg represent a gas consumption uncertainty of the GTs and a gas generation uncertainty of the P2G units; {tilde over (P)}gte,k, {tilde over (P)}pte,k, Pgte, Ppte, and N are as defined in the formulas (12) and (13); ηg is an energy conversion efficiency of GT; ηp is an energy conversion efficiency of P2G; τ is a time resolution of a gas flow model; and Ng is a number of gas flow time difference steps in one power system scheduling period;
initializing an energy management main problem of the D-IEGS as follows:
min
x
c
T
⁢
x
+
b
T
⁢
y
˜
(
15
)
s
.
t
.
Ax
+
B
⁢
y
˜
≤
d
||
F
i
⁢
x
+
g
i
||
2
≤
K
i
T
⁢
x
+
f
i
,
i
∈
ℒ
wherein {tilde over (y)} denotes an FFR reserve vector; x is a vector of all the remaining decision variables; A, B, Fi, Ki, d, gi, fi, c and b are constant coefficient matrices or vectors; i and are an index and a set of second-order cone (SOC) constraints;
solving a feasibility-check sub-problem to test the operation constraint violation against a worst-case uncertainty, wherein the feasibility-check sub-problem is as follows:
s
.
t
.
max
z
min
s
≥
0
,
x
1
T
⁢
s
Ex
+
G
⁢
s
+
H
⁢
z
≤
h
-
C
⁢
y
˜
*
||
F
i
⁢
x
+
g
i
||
2
≤
K
i
T
⁢
x
+
f
i
,
i
∈
ℒ
(
16
)
where z denotes boolean uncertainty variables; s denotes relax variables; {tilde over (y)}* is a solution of a master problem; x, Fi, Ki, gi, fi are as defined in the formula (15); and E, G, H, h, C are constant coefficient matrices or vectors, and if an objective value of (16) is positive, it indicates the energy management strategy of the D-IEGS is not robust to all the possible frequency disturbances and the following constraints is added to the main problem:
E
⁢
x
j
+
C
⁢
y
˜
+
H
⁢
z
j
*
≤
h
(
17
)
||
F
i
⁢
x
j
+
g
i
||
2
≤
K
i
T
⁢
x
j
+
f
i
,
i
∈
ℒ
wherein j is an iteration index; zj* represents an identified worst-case uncertainty in jth iteration; xj is a new variable vector added to the main problem; and remaining variables are as defined in the formulas (15) and (16), and solve the main problem and the feasibility-check sub-problem again; and
adjusting power generation of GTs and P2G units based on the new variables to change node gas injection and gas distribution network (GDN).