# US 11,029,344 B2 · Sensitivity based Thevenin index for voltage stability assessment considering N-1 contingency

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- Number: US 11,029,344 B2
- Document ID: US11029344B2
- Status: Granted
- Kind: B2
- Application number: 16/108,188
- Filed: 2018-08-22
- Published: 2019-05-09
- Granted: 2021-06-08
- Earliest claimed: 2017-11-07
- Assignees: Geiri Co Ltd, State Grid Jiangxi Electric Power Co, State Grid Corp Of China, Geirina Inc.
- Applicants: Xiaohu Zhang; Di Shi; Xiao Lu; Zhehan Yi; Qibing Zhang; Zhiwei Wang
- Inventors: Xiaohu Zhang; Di Shi; Xiao Lu; Zhehan Yi; Qibing Zhang; Zhiwei Wang
- Web page: https://patentgrep.com/patent/US11029344B2

## CPC

- H02J 13/12: Monitoring network conditions, e.g. electrical magnitudes or operational status
- G01R 19/2513: {Arrangements for monitoring electric power systems, e.g. power lines or loads; Logging}
- G05B 13/048: {using a predictor}
- H02J 3/00: Circuit arrangements for AC mains or AC distribution networks
- H02J 3/0012: characterised by the contingency detection means in AC networks, e.g. using phasor measurement units [PMU], synchrophasors or contingency analysis
- H02J 13/00: Circuit arrangements for providing remote monitoring or remote control of equipment in a power distribution network
- H02J 2103/30: Simulating, planning, modelling, reliability check or computer assisted design [CAD] of electric power networks
- Y02B 90/20: Smart grids as enabling technology in buildings sector (smart grids supporting the management or operation of end-user stationary applications in general, or like technologies with no associated climate change mitigation effect Y04S20/00)
- Y02E 60/00: Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y04S 10/30: State monitoring, e.g. fault, temperature monitoring, insulator monitoring, corona discharge
- Y04S 20/00: Management or operation of end-user stationary applications or the last stages of power distribution; Controlling, monitoring or operating thereof
- 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
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- 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)
- Y02B: CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
- 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

Systems and method are disclosed for monitor long-term voltage stability in a power system by estimating post-contingency operating point(s) considering PV-PQ transitions based on the current operating point; predicting a sensitivity based Thevenin index (STI) for each contingency using the estimated operating condition; and determining a voltage stability assessment (VSA) considering N−1 contingency.

## Claims

### Claim 1

A method for determining long-term voltage stability in a power system, comprising:
estimating post-contingency operating point(s) of the power system considering PV-PQ transitions based on the current operating point;
predicting a sensitivity based Thevenin index (STI) for each contingency using the estimated operating condition; and
determining a voltage stability assessment (VSA) considering N−1 contingency, wherein the current operating states {tilde over (θ)},{tilde over (V)}, further comprising determining post-contingency operating states as:
[
θ
c
V
c
]
=
[
θ
~
V
~
]
⁡
[
f
θ
f
V
g
θ
g
V
]
-
1
⁢
Δ
⁢
⁢
F
inj
where ({tilde over (θ)}, {tilde over (V)}) is an operating point under base case; (θc,Vc) is an operating point following a contingency; Δ Finj is a vector containing the active and reactive bus injection changes which are numerically equal to the active and reactive line flow on an outage branch; fθ and fV represents the partial derivative of active power injection expression with respect to voltage angle θ and voltage magnitude V; gθ and gV denotes the partial derivative of reactive power injection expression with respect to voltage angle θ and voltage magnitude V; and
operating a power generator adapted to be connected to a power grid and controlled by a processor.

### Claim 2 (depends on 1)

The method of claim 1, further comprising:
obtaining current operating states;
estimating a post-contingency operating point θc,Vc for every considered contingency, where θc and Vc represent the predicted bus voltage angle and bus voltage magnitude after a contingency;
determining corresponding sensitivities based on the presence of PV-PQ transition following the contingency; and
determining the STI for each considered contingency.

### Claim 3 (depends on 1)

The method of claim 1, comprising estimating an operating point after a foreseen transmission contingency.

### Claim 4 (depends on 1)

The method of claim 1, comprising construction of a Jacobian matrix based on a system topology with a contingency line ij in an outage.

### Claim 5 (depends on 1)

The method of claim 1, comprising determining corresponding sensitivities as one predictor step of continuation of power flow (CPF) when dλ is a continuation parameter with:
[
f
θ
f
V
f
λ
P
g
θ
g
V
g
λ
Q
0
0
1
]
⁡
[
d
⁢
⁢
θ
dV
d
⁢
⁢
λ
]
=
[
0
0
1
]
where dλ represents the load increment; dθ and dV denote the change of voltage angle and voltage magnitude respectively; fpλ,gpλ indicate the amount of active and reactive power injection change as a function of dλ.

### Claim 6 (depends on 5)

The method of claim 5, comprising obtaining sensitivities when there are generators reaching their reactive power limit after the contingency as:
[
f
θ
f
V
f
V
i
f
λ
P
g
θ
g
V
g
V
i
g
λ
Q
g
θ
i
g
V
i
g
V
i
i
g
λ
Q
,
i
0
0
0
1
]
⁡
[
d
⁢
⁢
θ
dV
dV
i
d
⁢
⁢
λ
]
=
[
0
0
0
1
]
where bus i is the bus which transforms from PV bus to PQ bus; fVi is the partial derivative of active power injection expression at other PV and PQ buses with respect to bus voltage magnitude at bus i, i.e., Vi; gVi is the partial derivative of reactive power injection expression at other PQ buses with respect to bus Vi; gθi, gVi, gVii, represent the partial derivative of reactive power injection expressions at bus i with respect to θ,V and Vi; gλQ,i is the partial derivative of reactive power injection expression at bus i with respect to the load scaling factor A.

### Claim 7 (depends on 1)

The method of claim 1, comprising determining STI for each contingency and load bus in parallel.

### Claim 8 (depends on 1)

The method of claim 1, comprising determining a plurality of contingencies in parallel.

### Claim 9

A system to control a power system, comprising:
a power generator;
a power grid coupled to the power generator; and
a processor to control the power grid with code for:
estimating post-contingency operating point(s) of the power system considering PV-PQ transitions based on the current operating point;
predicting a sensitivity based Thevenin index (STI) for each contingency using the estimated operating condition;
determining a voltage stability assessment (VSA) considering N−1 contingency; and
determining corresponding sensitivities as one predictor when dλ is a continuation parameter with:
[
f
θ
f
V
f
λ
P
g
θ
g
V
g
λ
Q
0
0
1
]
⁡
[
d
⁢
⁢
θ
dV
d
⁢
⁢
λ
]
=
[
0
0
1
]
where dλ represents the load increment, dθ and dV denote the change of voltage angle and voltage magnitude respectively, fpλ,gpλ indicate the amount of active and reactive power injection changes as a function of dλ; and where fθ and fV represents the partial derivative of active power injection expression with respect to voltage angle θ and voltage magnitude V−gθ and gV denotes the partial derivative of reactive power injection expression with respect to voltage angle θ and voltage magnitude V.

### Claim 10 (depends on 4)

The system of claim 4, further comprising code for:
obtaining current operating states;
estimating a post-contingency operating point θc,Vc considering the presence of PV-PQ transition for every considered contingency;
determining corresponding sensitivities following the contingency; and
determining the STI for each considered contingency.

### Claim 11 (depends on 9)

The system of claim 9, comprising code for obtaining sensitivities when there are PV-PQ transitions as:
[
f
θ
f
V
f
V
i
f
λ
P
g
θ
g
V
g
V
i
g
λ
Q
g
θ
i
g
V
i
g
V
i
i
g
λ
Q
,
i
0
0
0
1
]
⁡
[
d
⁢
⁢
θ
dV
dV
i
d
⁢
⁢
λ
]
=
[
0
0
0
1
]
where bus i is the bus which transforms from PV bus to PQ bus; fVi is the partial derivative of active power injection expression at other PV and PQ buses with respect to bus voltage magnitude at bus i, i.e., Vi; gVi is the partial derivative of reactive power injection expression at other PQ buses with respect to bus Vi; gθi,gVi,gVii represent the partial derivative of reactive power injection expressions at bus i with respect to θ,V and Vi; gλQ,i is the partial derivative of reactive power injection expression at bus i with respect to the load scaling factor λ.

### Claim 12 (depends on 9)

The system of claim 9, comprising code for determining STI for each contingency and load bus in parallel.

### Claim 13 (depends on 9)

The system of claim 9, comprising code for determining a plurality of contingencies in parallel.