# US 12,015,271 B2 · Power distribution network reliability index calculation method and apparatus based on mixed integer linear programming, and medium

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- Number: US 12,015,271 B2
- Document ID: US12015271B2
- Status: Granted
- Kind: B2
- Application number: 17/500,539
- Filed: 2021-10-13
- Published: 2022-02-03
- Granted: 2024-06-18
- Earliest claimed: 2019-05-24
- Assignees: Tsinghua University
- Applicants: Tsinghua University
- Inventors: Wenchuan Wu; Boming Zhang; Zihao Li; Hongbin Sun; Bin Wang; Qinglai Guo
- Web page: https://patentgrep.com/patent/US12015271B2

## CPC

- H02J 3/001: Arrangements for handling faults or abnormalities, e.g. emergencies or contingencies
- H02J 3/0012: characterised by the contingency detection means in AC networks, e.g. using phasor measurement units [PMU], synchrophasors or contingency analysis
- G05B 17/02: electric
- G06F 17/12: Simultaneous equations {, e.g. systems of linear equations}
- H02J 2103/30: Simulating, planning, modelling, reliability check or computer assisted design [CAD] of electric power networks
- H02J 2103/35: Grid-level management of power transmission or distribution systems, e.g. load flow analysis or active network management
- Y02E 60/00: Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y04S 40/20: Information technology specific aspects, e.g. CAD, simulation, modelling, system security
- H02J: ELECTRIC POWER NETWORKS; CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- 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

The disclosure provides power distribution network reliability index calculation method based on mixed integer linear programming. The method includes: establishing a model for optimizing reliability indexes of a power distribution network based on a mixed integer linear programming model, wherein the model comprises an objective function and constraint conditions, the objective function is for minimizing a system average interruption duration index (SAIDI); solving the model based on the objective function and the constraint conditions to obtain reliability indexes of the power distribution network; and controlling operation of the power distribution network based on the reliability indexes.

## Claims

### Claim 1

A power distribution network reliability index calculation method based on mixed integer linear programming, comprising:
determining installation status of components, fault isolation, load transformation supply and action rules of fault recovery when there is a branch fault of the power distribution network, wherein the components include circuit breakers and switches installed at the end of each branch, which are used to isolate the faulty branch circuits and reconfigure the network after a branch circuit failure, and to recover the original power supply network structure after the faulty branch is repaired;
establishing a model for optimizing reliability indexes of a power distribution network based on a mixed integer linear programming model, wherein the model comprises an objective function and constraint conditions, the objective function is for minimizing a system average interruption duration index (SAIDI);
solving the model based on the objective function and the constraint conditions to obtain reliability indexes of the power distribution network; and
determining the reliability of the power distribution network based on the reliability indexes, and controlling operation of the power distribution network based on the reliability indexes;
wherein establishing the model for optimizing reliability indexes of the power distribution network based on the mixed integer linear programming model comprises:
determining the objective function; and
determining the constraint conditions;
wherein the constraint conditions comprise a reliability index calculation constraint;
wherein the reliability index calculation constraint is determined by:
CID
i
=
∑
xy
∈
ϒ
λ
xy
⁢
τ
xy
SW
⁢
p
i
xy
+
∑
xy
∈
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λ
xy
(
τ
xy
RP
-
τ
xy
SW
)
⁢
(
1
-
q
i
xy
)
,
∀
i
∈
Ψ
LN
⁢
CIF
i
=
∑
xy
∈
ϒ
λ
xy
⁢
p
i
xy
,
∀
i
∈
Ψ
LN
⁢
SAIDI
=
∑
i
∈
Ψ
LN
NC
i
⁢
CID
i
∑
i
∈
Ψ
LN
NC
i
⁢
SAIFI
=
∑
i
∈
Ψ
LN
NC
i
⁢
CIF
i
∑
i
∈
Ψ
LN
NC
i
⁢
ASAI
=
1
-
SAIDI
8760
⁢
EENS
=
∑
h
∈
B
Δ
h
8760
⁢
∑
i
∈
Ψ
LN
CID
i
⁢
μ
h
⁢
L
i
where, CIDi represents a customer interruption duration of a node i, λxy represents an annual fault rate of a branch xy, τxySW represents an interruption period of fault isolation action of the branch xy, τxyRP represents an interruption period of fault restore of the branch xy, CIFi represents a customer interruption frequency of the node i, NCi represents a given number of customers of the node i, SAIDI represents a system average interruption duration index, SAIFI represents a system average interruption frequency index, ASAI represents a system average service availability index, EENS represents an expected energy not supplied, B represents a collection of all load levels, Δh represents a number of hours lasted per year for a load level h, μh≤1 represents a peak load ratio of the level h, and Li represents a peak load ratio of the node i.

### Claim 2 (depends on 1)

The method according to claim 1, wherein the constraint conditions further comprises at least one of a power balance constraint of the power distribution network, a branch power constraint, a transformer power constraint, a circuit breaker action constraint, and a switch action constraint.

### Claim 3 (depends on 2)

The method according to claim 2, wherein, the power balance constraint is determined by:
D
i
x
⁢
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y
=
∑
j
∈
Ψ
i
⁢
P
j
⁢
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i
x
⁢
⁢
y
,
∀
i
∈
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L
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,
∀
x
⁢
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y
∈
Υ
P
i
⁢
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j
x
⁢
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y
=
-
P
j
⁢
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i
x
⁢
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y
,
∀
i
⁢
⁢
j
∈
Υ
,
∀
x
⁢
⁢
y
∈
Υ
where, a superscript xy represents a scenario where a fault occurs in a branch xy, Dixy represents a load of a node i when the fault occurs in the branch xy, Pjixy represents a power of a branch ij flowing from a node j to the node i when the fault occurs in the branch xy, Pijxy represents a power of a branch ij flowing from the node i to the node j when the fault occurs in the branch xy, Ψi represents a collection of branches directly coupled to the node i, ΨLN represents a collection of nodes having loads, Υ represents a collection of all branches, and ∀xy∈Υ represents all branch fault scenarios.

### Claim 4 (depends on 2)

The method according to claim 2, wherein, the branch power constraint is determined by:
−Msiji,xy≤Pijxy≤Msiji,xy,∀ij∈Υ,∀xy∈Υ
−Msijj,xy≤Pijxy≤Msijj,xy,∀ij∈Υ,∀xy∈Υ
−PijC≤Pijxy≤PijC,∀ij∈Υ,∀xy∈Υ
where, M is a positive integer, siji,xy∈{0,1} represents a status of a switch close to a node i in a branch ij when a fault occurs in a branch xy, siji,xy=1 represents that the status of the switch is on, and siji,xy=0 represents that the status of the switch is off, sijj,xy∈{0,1} represents a status of a switch close to a node j in the branch ij when the fault occurs in the branch xy, sijj,xy=1 represents that the status of the switch is on, sijj,xy=0 represents that the status of the switch is off, PijC represents a rated transmission capacity of the branch ij.

### Claim 5 (depends on 2)

The method according to claim 2, wherein, the transformer power constraint is determined by:
Pfxy=Ptrfxy,∀f∈ΨF,trf∈Υ,∀xy∈Υ
Pfxy≤PfC,∀f∈ΨF,∀xy∈Υ
where, Pry represents a power of a transformer f when a fault occurs in a branch xy, Ptrfxy represents a power from a transformer node to a downstream node of a branch trf coupled to the transformer f when the fault occurs in the branch xy, ΨF represents a collection of all transformer nodes.

### Claim 6 (depends on 2)

The method according to claim 2, wherein, the circuit breaker action constraint is determined by:
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≤
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,
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∀
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≤
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x
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≤
1
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j
∈
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i
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=
1
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∀
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∈
Ψ
S
⁢
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S
⁢
p
i
x
⁢
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=
1
-
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i
x
⁢
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y
,
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,
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∀
i
∈
Ψ
L
⁢
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N
⁢
∀
x
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⁢
y
∈
Υ
where, a superscript B represents a circuit breaker action stage, a circuit breaker closest to a faulty branch at upstream of the faulty branch is activated to interrupt faulty current in the circuit breaker action stage, Fijxy,B represents a fault-affect mark of a branch ij in the circuit breaker action stage when the fault occurs in a branch xy, Fijxy,B=0 represents that the branch ij is affected by the fault and is in a power-off status in the circuit breaker action stage when the fault occurs in the branch xy, Fijxy,B=1 represents that the branch ij is in a normal operating status in the circuit breaker action stage when the fault occurs in the branch xy, Fixy,B represents a fault-affect mark of a node i in the circuit breaker action stage when a fault occurs in the branch xy, Fixy,B=0 represents that the node i is affected by the fault and is in a power-off status in the circuit breaker action stage when the fault occurs in the branch xy, Fixy,B=1 represents that the node i is in a normal operating status in the circuit breaker action stage when the fault occurs in the branch xy, Fjxy,B represents a fault-affect mark of a node j in the circuit breaker action stage when a fault occurs in the branch xy, Fjxy,B=0 represents that a node j is affected by the fault and is in a power-off status in the circuit breaker action stage when the fault occurs in the branch xy, Fjxy,B=1 represents that the node j is in a normal operating status in the circuit breaker action stage when the fault occurs in the branch xy; Ψss represents a collection of nodes with substations; ΥIS represents a collection of all branches with a switch close to the node I; ΥJS represents a collection of all branches with a switch close to the node J; ΥIB represents a collection of all branches with a circuit breaker close to the node I; ΥJB represents a collection of all branches with a circuit breaker close to the node J, Pixy represents a net injection power of the node i when the fault occurs in the branch xy;
a superscript NO represents the normal operating status, siji,NO represents a status of a switch close to the node i in the branch ij in a normal operating status, siji,NO=1 represents that the switch is on, siji,NO=0 represents that the switch is off, sijj,NO represents a status of a switch close to the node j in the branch ij in a normal operating status, sijj,NO=1 represents that the switch is on, and sijj,NO=0 represents that the switch is off;
biji,xy represents a status of a circuit breaker close to the node i in the branch ij when the fault occurs in the branch xy, biji,xy=1 represents that the circuit breaker is activated, biji,xy=0 represents that the circuit breaker is deactivated, bijj,xy represents a status of a circuit breaker close to the node j in the branch ij when the fault occurs in the branch xy, bijj,xy=1 represents that the circuit breaker is activated, bijj,xy=0 represents that the circuit breaker is deactivated, biji,NO represents a status of the circuit breaker close to the node i in the branch ij under a normal operating status, biji,NO=1 represents that the circuit breaker is activated, biji,NO=0 represents that the circuit breaker is deactivated, bijj,NO represents a status of the circuit breaker close to the node j in the branch ij under a normal operating status, bijj,NO=1 represents that the circuit breaker is activated, bijj,NO=0 represents that the circuit breaker is deactivated;
pixy represents a fault-influence marker of the node i when the fault occurs in the branch xy, pixy=1 represents that the node i is influenced by the fault when the fault occurs in the branch xy, pixy=0 represents that the node i is not influenced by the fault when the fault occurs in the branch xy.

### Claim 7 (depends on 2)

The method according to claim 2, wherein the switch action constraint is determined by:
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∈
Υ
where, a superscript PF represents a switch action stage, a faulty branch is isolated in the switch action stage, Fijxy,PF represents a maintenance-influence mark of a branch ij in the switch action stage when a fault occurs in a branch xy, Fijxy,PF=0 represents that the branch ij is influenced by maintenance of the faulty branch and is in a power-off status in the switch action stage when the fault occurs in the branch xy, Fijxy,PF=1 represents that the branch ij is not influenced by the maintenance of the faulty branch and is in a normal operating status in the switch action stage when the fault occurs in the branch xy, Fixy,PF represents a maintenance-influence mark of a node i in the switch action stage when a fault occurs in the branch xy, Fixy,PF=0 represents that the node i is influenced by maintenance of the faulty branch and is in a power-off status in the switch action stage when the fault occurs in the branch xy, Fixy,PF=1 represents that the node i is not influenced by the maintenance of the faulty branch and is in a normal operating status in the switch action stage when the fault occurs in the branch xy; Fjxy,PF represents a maintenance-influence mark of a node j in the switch action stage when a fault occurs in the branch xy, Fjxy,PF=0 represents that the node j is influenced by maintenance of the faulty branch and is in a power-off status in the switch action stage when the fault occurs in the branch xy, Fjxy,PF=1 represents that the node j is not influenced by the maintenance of the faulty branch and is in a normal operating status in the switch action stage when the fault occurs in the branch xy; siji,xy∈{0,1} represents a status of a switch close to a node i in a branch ij when a fault occurs in a branch xy, siji,xy=1 represents that the status of the switch is on, and siji,xy=0 represents that the status of the switch is off, sijj,xy∈{0,1} represents a status of a switch close to a node j in the branch ij when the fault occurs in the branch xy, sijj,xy=1 represents that the status of the switch is on, sijj,xy=0 represents that the status of the switch is off; Dixy represents a load of a node i when the fault occurs in the branch xy; Di represents a load of a node i under normal state;
qixy represents a status mark of the node i after the switch action stage and after that the fault occurs in the branch xy, qixy=1 represents that the node i is normally powered after the switch action stage and after that the fault occurs in the branch xy, qixy=0 represents that the node i is in a power-off status after the switch action stage and after that the fault occurs in the branch xy.

### Claim 8 (depends on 1)

The method according to claim 1, wherein the power distribution network reliability indexes comprise the CIDi, CIFi, SAIDI, SAIFI, ASAI, and EENS.

### Claim 9

A power distribution network reliability index calculation apparatus based on mixed integer linear programming, comprising:
a processor; and
a memory for storing instructions executable by the processor;
wherein the processor is configured to perform:
determining installation status of components, fault isolation, load transformation supply and action rules of fault recovery when there is a branch fault of the power distribution network, wherein the components include circuit breakers and switches installed at the end of each branch, which are used to isolate the faulty branch circuits and reconfigure the network after a branch circuit failure, and to recover the original power supply network structure after the faulty branch is repaired;
establishing a model for optimizing reliability indexes of a power distribution network based on a mixed integer linear programming model, wherein the model comprises an objective function and constraint conditions, the objective function is for minimizing a system average interruption duration index (SAIDI);
solving the model based on the objective function and the constraint conditions to obtain reliability indexes of the power distribution network; and
determining the reliability of the power distribution network based on the reliability indexes, and controlling operation of the power distribution network based on the reliability indexes;
wherein the constraint conditions comprise a reliability index calculation constraint;
wherein the reliability index calculation constraint is determined by:
C
⁢
⁢
I
⁢
⁢
D
i
=
∑
x
⁢
⁢
y
∈
Υ
⁢
λ
x
⁢
⁢
y
⁢
τ
x
⁢
⁢
y
S
⁢
⁢
W
⁢
p
i
x
⁢
⁢
y
+
∑
x
⁢
⁢
y
∈
Υ
⁢
λ
x
⁢
⁢
y
⁡
(
τ
x
⁢
⁢
y
R
⁢
⁢
P
-
τ
x
⁢
⁢
y
S
⁢
⁢
W
)
⁢
(
1
-
q
i
x
⁢
⁢
y
)
,
∀
i
∈
Ψ
L
⁢
⁢
N
C
⁢
⁢
I
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⁢
F
i
=
∑
x
⁢
⁢
y
∈
Υ
⁢
λ
x
⁢
⁢
y
⁢
p
i
x
⁢
⁢
y
,
∀
i
∈
Ψ
L
⁢
⁢
N
S
⁢
⁢
A
⁢
⁢
I
⁢
⁢
D
⁢
⁢
I
=
∑
i
∈
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L
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N
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N
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C
i
⁢
C
⁢
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I
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D
I
∑
i
∈
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L
⁢
⁢
N
⁢
N
⁢
⁢
C
i
S
⁢
⁢
A
⁢
⁢
I
⁢
⁢
F
⁢
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I
=
∑
i
∈
Ψ
L
⁢
⁢
N
⁢
N
⁢
⁢
C
i
⁢
C
⁢
⁢
I
⁢
⁢
f
I
∑
i
∈
Ψ
L
⁢
⁢
N
⁢
N
⁢
⁢
C
i
A
⁢
⁢
S
⁢
⁢
A
⁢
⁢
I
=
1
-
S
⁢
⁢
A
⁢
⁢
I
⁢
⁢
D
⁢
⁢
I
8760
E
⁢
⁢
E
⁢
⁢
N
⁢
⁢
S
=
∑
h
∈
B
⁢
Δ
h
8
⁢
7
⁢
6
⁢
0
⁢
∑
i
∈
Ψ
L
⁢
N
⁢
C
⁢
⁢
I
⁢
⁢
D
i
⁢
μ
h
⁢
L
i
where, CIDi represents a customer interruption duration of a node i, λxy represents an annual fault rate of a branch xy, τxySW represents an interruption period of fault isolation action of the branch xy, τxyRP represents an interruption period of fault restore of the branch xy, CIFi represents a customer interruption frequency of the node i, NCi represents a given number of customers of the node i, SAIDI represents a system average interruption duration index, SAIFI represents a system average interruption frequency index, ASAI represents a system average service availability index, EENS represents an expected energy not supplied, B represents a collection of all load levels, Δh represents a number of hours lasted per year for a load level h, μh≤1 represents a peak load ratio of the level h, and Li represents a peak load ratio of the node i.

### Claim 10 (depends on 9)

The apparatus according to claim 9, wherein the constraint conditions further comprises at least one of a power balance constraint of the power distribution network, a branch power constraint, a transformer power constraint, a circuit breaker action constraint, a switch action constraint.

### Claim 11 (depends on 10)

The apparatus according to claim 10, wherein, the power balance constraint is determined by:
D
i
xy
=
∑
j
∈
Ψ
i
⁢
P
ji
xy
,
∀
i
∈
Ψ
LN
,
∀
xy
∈
Υ
P
ij
xy
=
-
P
ji
xy
,
∀
ij
∈
Υ
,
∀
xy
∈
Υ
where, a superscript xy represents a scenario where a fault occurs in a branch xy, Dixy represents a load of a node i when the fault occurs in the branch xy, Pijxy represents a power of a branch ij flowing from a node j to the node i when the fault occurs in the branch xy, Pijxy represents a power of a branch ij flowing from the node i to the node j when the fault occurs in the branch xy, Ψi represents a collection of branches directly coupled to the node i, ΨLN represents a collection of nodes having loads, Υ represents a collection of all branches, and ∀xy∈Υ represents all branch fault scenarios.

### Claim 12 (depends on 10)

The apparatus according to claim 10, wherein, the branch power constraint is determined by:
−Msiji,xy≤Pijxy≤Msiji,xy,∀ij∈Υ,∀xy∈Υ
−Msijj,xy≤Pijxy≤Msijj,xy,∀ij∈Υ,∀xy∈Υ
−PijC≤Pijxy≤PijC,∀ij∈Υ,∀xy∈Υ
where, M is a positive integer, siji,xy∈{0,1} represents a status of a switch close to a node i in a branch ij when a fault occurs in a branch xy, siji,xy=1 represents that the status of the switch is on, and siji,xy=0 represents that the status of the switch is off, sijj,xy∈{0,1} represents a status of a switch close to a node j in the branch ij when the fault occurs in the branch xy, sijj,xy=1 represents that the status of the switch is on, sijj,xy=0 represents that the status of the switch is off, PijC represents a rated transmission capacity of the branch ij.

### Claim 13 (depends on 10)

The apparatus according to claim 10, wherein, the transformer power constraint is determined by:
Pfxy=Ptrfxy,∀f∈ΨF,trf∈Υ,∀xy∈Υ
Pfxy≤PfC,∀f∈ΨF,∀xy∈Υ
where, Pfxy represents a power of a transformer f when a fault occurs in a branch xy, Ptrfxy represents a power from a transformer node to a downstream node of a branch trf coupled to the transformer f when the fault occurs in the branch xy, ΨF represents a collection of all transformer nodes.

### Claim 14 (depends on 10)

The apparatus according to claim 10, wherein, the circuit breaker action constraint is determined by:
F
xy
xy
,
B
=
0
⁢
-
(
1
-
s
ij
i
,
NO
)
⁢
M
+
F
i
xy
,
B
≤
F
ij
xy
,
B
≤
(
1
-
s
ij
i
,
NO
)
⁢
M
+
F
i
xy
,
B
,
∀
ij
∈
ϒ
I
S
,
ij
∉
ϒ
I
B
⁢
-
(
1
-
s
ij
j
,
NO
)
⁢
M
+
F
j
xy
,
B
≤
F
ij
xy
,
B
≤
(
1
-
s
ij
j
,
NO
)
⁢
M
+
F
j
xy
,
B
,
∀
ij
∈
ϒ
J
S
,
ij
∉
ϒ
J
B
⁢
-
(
1
-
b
ij
i
,
xy
)
⁢
M
+
F
i
xy
,
B
≤
F
ij
xy
,
B
≤
(
1
-
b
ij
i
,
xy
)
⁢
M
+
F
i
xy
,
B
,
∀
ij
∈
ϒ
I
B
⁢
-
(
1
-
b
ij
j
,
xy
)
⁢
M
+
F
j
xy
,
B
≤
F
ij
xy
,
B
≤
(
1
-
b
ij
j
,
xy
)
⁢
M
+
F
j
xy
,
B
,
∀
ij
∈
ϒ
J
B
⁢
F
ij
xy
,
B
=
F
i
xy
,
B
,
∀
ij
∉
ϒ
I
S
,
ij
∉
ϒ
I
B
⁢
F
ij
xy
,
B
=
F
j
xy
,
B
,
∀
ij
∉
ϒ
J
S
,
ij
∉
ϒ
J
B
⁢
∑
ij
∈
ϒ
i
B
b
ij
i
,
NO
+
∑
ij
∈
ϒ
j
B
b
ij
j
,
NO
-
1
=
∑
ij
∈
ϒ
i
B
b
ij
i
,
xy
+
∑
ij
∈
ϒ
j
B
b
ij
j
,
xy
⁢
0
≤
F
i
xy
,
B
≤
1
,
∀
i
∈
Ψ
LN
⁢
0
≤
F
ij
xy
,
B
≤
1
,
∀
ij
∈
ϒ
⁢
F
i
xy
,
B
=
1
,
∀
i
∈
Ψ
SS
⁢
p
i
xy
=
1
-
F
i
xy
,
B
,
∀
i
∈
Ψ
LN
⁢
∀
xy
∈
ϒ
where, a superscript B represents a circuit breaker action stage, a circuit breaker closest to a faulty branch at upstream of the faulty branch is activated to interrupt faulty current in the circuit breaker action stage, Fijxy,B represents a fault-affect mark of a branch ij in the circuit breaker action stage when the fault occurs in a branch xy, Fijxy,B=0 represents that the branch ij is affected by the fault and is in a power-off status in the circuit breaker action stage when the fault occurs in the branch xy, Fijxy,B=1 represents that the branch ij is in a normal operating status in the circuit breaker action stage when the fault occurs in the branch xy, Fixy,B represents a fault-affect mark of a node i in the circuit breaker action stage when a fault occurs in the branch xy, Fixy,B=0 represents that the node i is affected by the fault and is in a power-off status in the circuit breaker action stage when the fault occurs in the branch xy, Fixy,B=1 represents that the node i is in a normal operating status in the circuit breaker action stage when the fault occurs in the branch xy, Fjxy,B represents a fault-affect mark of a node j in the circuit breaker action stage when a fault occurs in the branch xy, Fjxy,B=0 represents that a node j is affected by the fault and is in a power-off status in the circuit breaker action stage when the fault occurs in the branch xy, Fjxy,B=1 represents that the node j is in a normal operating status in the circuit breaker action stage when the fault occurs in the branch xy; Ψss represents a collection of nodes with substations; ΥIS represents a collection of all branches with a switch close to the node I; σJS represents a collection of all branches with a switch close to the node J; ΥIB represents a collection of all branches with a circuit breaker close to the node I; ΥJB represents a collection of all branches with a circuit breaker close to the node J, pixy represents a net injection power of the node i when the fault occurs in the branch xy;
a superscript NO represents the normal operating status, siji,NO represents a status of a switch close to the node i in the branch ij in a normal operating status, siji,NO=1 represents that the switch is on, siji,NO=0 represents that the switch is off, sijj,NO represents a status of a switch close to the node j in the branch ij in a normal operating status, sijj,NO=1 represents that the switch is on, and sijj,NO=0 represents that the switch is off;
biji,xy represents a status of a circuit breaker close to the node i in the branch ij when the fault occurs in the branch xy, biji,xy=1 represents that the circuit breaker is activated, biji,xy=0 represents that the circuit breaker is deactivated, bijj,xy represents a status of a circuit breaker close to the node j in the branch ij when the fault occurs in the branch xy, biji,xy=1 represents that the circuit breaker is activated, bijj,xy=0 represents that the circuit breaker is deactivated, biji,NO represents a status of the circuit breaker close to the node i in the branch ij under a normal operating status, biji,NO=1 represents that the circuit breaker is activated, biji,NO=0 represents that the circuit breaker is deactivated, bijj,NO represents a status of the circuit breaker close to the node j in the branch ij under a normal operating status, bijj,NO=1 represents that the circuit breaker is activated, bijj,NO=0 represents that the circuit breaker is deactivated;
pixy represents a fault-influence marker of the node i when the fault occurs in the branch xy, pixy=1 represents that the node i is influenced by the fault when the fault occurs in the branch xy, pixy=0 represents that the node i is not influenced by the fault when the fault occurs in the branch xy.

### Claim 15 (depends on 10)

The apparatus according to claim 10, wherein the switch action constraint is determined by:
F
xy
xy
,
PF
=
0
⁢
-
(
1
-
s
ij
i
,
xy
)
⁢
M
+
F
i
xy
,
PF
≤
F
ij
xy
,
PF
≤
(
1
-
s
ij
i
,
xy
)
⁢
M
+
F
i
xy
,
PF
,
∀
ij
∈
ϒ
I
S
⁢
-
(
1
-
s
ij
j
,
xy
)
⁢
M
+
F
j
xy
,
PF
≤
F
i
xy
,
PF
≤
(
1
-
s
ij
j
,
xy
)
⁢
M
+
F
j
xy
,
PF
,
∀
ij
∈
ϒ
J
S
⁢
F
ij
xy
,
PF
=
F
i
xy
,
PF
,
∀
ij
∉
ϒ
I
S
⁢
F
ij
xy
,
PF
=
F
j
xy
,
PF
,
∀
ij
∉
ϒ
J
S
⁢
0
≤
F
i
xy
,
PF
≤
1
,
∀
i
∈
Ψ
LN
⁢
0
≤
F
ij
xy
,
PF
≤
1
,
∀
ij
∈
ϒ
⁢
F
i
xy
,
PF
=
1
,
∀
i
∈
Ψ
SS
⁢
D
i
xy
=
D
i
⁢
q
i
xy
,
∀
i
∈
Ψ
LN
⁢
q
i
xy
=
F
i
xy
,
P
,
∀
i
∈
Ψ
LN
⁢
1
-
p
i
xy
≤
q
i
xy
,
∀
i
∈
Ψ
LN
⁢
∀
xy
∈
ϒ
where, a superscript PF represents a switch action stage, a faulty branch is isolated in the switch action stage, Fijxy,PF represents a maintenance-influence mark of a branch ij in the switch action stage when a fault occurs in a branch xy, Fijxy,PF=0 represents that the branch ij is influenced by maintenance of the faulty branch and is in a power-off status in the switch action stage when the fault occurs in the branch xy, Fijxy,PF=1 represents that the branch ij is not influenced by the maintenance of the faulty branch and is in a normal operating status in the switch action stage when the fault occurs in the branch xy, Fixy,PF represents a maintenance-influence mark of a node i in the switch action stage when a fault occurs in the branch xy, Fixy,PF=0 represents that the node i is influenced by maintenance of the faulty branch and is in a power-off status in the switch action stage when the fault occurs in the branch xy, Fixy,PF=1 represents that the node i is not influenced by the maintenance of the faulty branch and is in a normal operating status in the switch action stage when the fault occurs in the branch xy, Fjxy,PF represents a maintenance-influence mark of a node j in the switch action stage when a fault occurs in the branch xy, Fjxy,PF=0 represents that the node j is influenced by maintenance of the faulty branch and is in a power-off status in the switch action stage when the fault occurs in the branch xy, Fjxy,PF=1 represents that the node j is not influenced by the maintenance of the faulty branch and is in a normal operating status in the switch action stage when the fault occurs in the branch xy; siji,xy∈{0,1} represents a status of a switch close to a node i in a branch ij when a fault occurs in a branch xy, siji,xy=1 represents that the status of the switch is on, and siji,xy=0 represents that the status of the switch is off, sijj,xy∈{0,1} represents a status of a switch close to a node j in the branch ij when the fault occurs in the branch xy, sijj,xy=1 represents that the status of the switch is on, sijj,xy=0 represents that the status of the switch is off; Dixy represents a load of a node i when the fault occurs in the branch xy; Di represents a load of a node i under normal state;
qixy represents a power status of the node i after the switch action stage and after that the fault occurs in the branch xy, qixy=1 represents that the node i is normally powered after the switch action stage and after that the fault occurs in the branch xy, qixy=0 represents that the node i is in a power-off status after the switch action stage and after that the fault occurs in the branch xy.

### Claim 16 (depends on 9)

The apparatus according to claim 9, wherein the power distribution network reliability indexes comprise the CIDi, CIFi, SAIDI, SAIFI, ASAI, and EENS.

### Claim 17

A non-transitory computer-readable storage medium having stored therein instructions that, when executed by a processor of a terminal, causes the terminal to perform a power distribution network reliability index calculation method based on mixed integer linear programming, the method comprising:
determining installation status of components, fault isolation, load transformation supply and action rules of fault recovery when there is a branch fault of the power distribution network, wherein the components include circuit breakers and switches installed at the end of each branch, which are used to isolate the faulty branch circuits and reconfigure the network after a branch circuit failure, and to recover the original power supply network structure after the faulty branch is repaired;
establishing a model for optimizing reliability indexes of a power distribution network based on a mixed integer linear programming model, wherein the model comprises an objective function and constraint conditions, the objective function is for minimizing a system average interruption duration index (SAIDI);
solving the model based on the objective function and the constraint conditions to obtain reliability indexes of the power distribution network; and
determining the reliability of the power distribution network based on the reliability indexes, and controlling operation of the power distribution network based on the reliability indexes;
wherein establishing the model for optimizing reliability indexes of the power distribution network based on the mixed integer linear programming model comprises:
determining the objective function; and
determining the constraint conditions;
wherein the constraint conditions comprise a reliability index calculation constraint;
wherein the reliability index calculation constraint is determined by:
C
⁢
⁢
I
⁢
⁢
D
i
=
∑
x
⁢
⁢
y
∈
Υ
⁢
λ
x
⁢
⁢
y
⁢
τ
x
⁢
⁢
y
⁢
S
⁢
⁢
W
⁢
p
i
x
⁢
⁢
y
+
∑
x
⁢
⁢
y
∈
Υ
⁢
λ
x
⁢
⁢
y
⁡
(
τ
x
⁢
⁢
y
R
⁢
⁢
P
-
τ
x
⁢
⁢
y
S
⁢
⁢
W
)
⁢
(
1
-
q
i
x
⁢
⁢
y
)
,
∀
i
∈
Ψ
L
⁢
⁢
N
C
⁢
⁢
I
⁢
⁢
F
i
=
∑
x
⁢
⁢
y
∈
Υ
⁢
λ
x
⁢
⁢
y
⁢
p
i
x
⁢
⁢
y
,
⁢
∀
i
∈
Ψ
L
⁢
⁢
N
⁢
S
⁢
⁢
A
⁢
⁢
I
⁢
⁢
D
⁢
⁢
I
=
∑
i
∈
Ψ
L
⁢
⁢
N
⁢
N
⁢
⁢
C
⁢
i
⁢
C
⁢
⁢
I
⁢
⁢
D
i
∑
i
∈
Ψ
L
⁢
⁢
N
⁢
N
⁢
⁢
C
⁢
i
S
⁢
⁢
A
⁢
⁢
I
⁢
⁢
F
⁢
⁢
I
=
∑
i
∈
Ψ
L
⁢
⁢
N
⁢
N
⁢
⁢
C
⁢
i
⁢
C
⁢
⁢
I
⁢
⁢
F
i
∑
i
∈
Ψ
L
⁢
⁢
N
⁢
N
⁢
⁢
C
⁢
i
A
⁢
⁢
S
⁢
⁢
A
⁢
⁢
I
=
1
-
S
⁢
⁢
A
⁢
⁢
I
⁢
⁢
D
⁢
⁢
I
8
⁢
7
⁢
6
⁢
0
E
⁢
⁢
E
⁢
⁢
N
⁢
⁢
S
=
∑
h
∈
B
⁢
Δ
h
8
⁢
7
⁢
6
⁢
0
⁢
∑
i
∈
Ψ
L
⁢
⁢
N
⁢
C
⁢
⁢
I
⁢
⁢
D
i
⁢
μ
h
⁢
L
i
where, CIDi represents a customer interruption duration of a node i, λxy represents an annual fault rate of a branch xy, τxySW represents an interruption period of fault isolation action of the branch xy, τxyRP represents an interruption period of fault restore of the branch xy, CIFi represents a customer interruption frequency of the node i, NCi represents a given number of customers of the node i, SAIDI represents a system average interruption duration index, SAIFI represents a system average interruption frequency index, ASAI represents a system average service availability index, EENS represents an expected energy not supplied, B represents a collection of all load levels, Δn represents a number of hours lasted per year for a load level h, μh≤1 represents a peak load ratio of the level h, and Li represents a peak load ratio of the node i.