# US 11,444,483 B2 · Adaptive state estimation for power systems

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- Number: US 11,444,483 B2
- Document ID: US11444483B2
- Status: Granted
- Kind: B2
- Application number: 16/741,882
- Filed: 2020-01-14
- Published: 2021-07-15
- Granted: 2022-09-13
- Earliest claimed: 2020-01-14
- Assignees: Hitachi Energy Switzerland AG
- Applicants: Hitachi Energy Switzerland AG
- Inventors: Xiaoming Feng
- Web page: https://patentgrep.com/patent/US11444483B2

## CPC

- H02J 13/12: Monitoring network conditions, e.g. electrical magnitudes or operational status
- H02J 13/13: characterised by the transmission of data to equipment in the power network
- G01R 19/2513: {Arrangements for monitoring electric power systems, e.g. power lines or loads; Logging}
- G06F 17/17: Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method ({G06F17/18 takes precedence } ; interpolation for numerical control G05B19/18)
- H02J 3/003: {Load forecast, e.g. methods or systems for forecasting future load demand}
- H02J 3/004: {Generation forecast, e.g. methods or systems for forecasting future energy generation}
- G06Q 10/04: Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" (market predictions or forecasting for commercial activities G06Q30/0202)
- H02J 13/333: the equipment forming part of substations
- 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
- H02J 2105/51: {according to a condition being electrical}
- H02J 2107/00: Circuit arrangements for communication specially adapted for monitoring, managing or controlling operation of power networks remotely
- Y04S 10/30: State monitoring, e.g. fault, temperature monitoring, insulator monitoring, corona discharge
- Y04S 40/12: characterised by data transport means between the monitoring, controlling or managing units and monitored, controlled or operated electrical equipment
- 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)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G06Q: INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- 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, methods, techniques and apparatuses of state estimation are disclosed. One exemplary embodiment is a method comprising determining, with a state estimator, a state estimate based on power grid data corresponding to characteristics of a power grid received from a plurality of local controllers; calculating, with the state estimator, a first gain matrix based on a Gauss-Newton method; updating, with the state estimator, the state estimate based on the first gain matrix; calculating, with the state estimator, a second gain matrix based on Newton's method; updating, with the state estimator, the state estimate based on the second gain matrix; and iteratively recalculating the second gain matrix and updating the state estimate based on the second gain matrix until the state estimate converges.

## Claims

### Claim 1

A method comprising: receiving, by a state estimator of a power grid, power grid data from a plurality of sensors in the power grid, from a plurality of local controllers in the power grid, or from both, wherein the power grid data correspond to characteristics of the power grid; determining, with the state estimator, a state estimate based on the power grid data; calculating, with the state estimator, a first gain matrix based on a Gauss-Newton method; updating, with the state estimator, the state estimate based on the first gain matrix; calculating, with the state estimator, a second gain matrix based on Newton's method; updating, with the state estimator, the state estimate based on the second gain matrix; iteratively recalculating, with the state estimator, the second gain matrix and updating the state estimate based on the second gain matrix until the state estimate converges; and sending, by the state estimator, the converged state estimate to a power grid controller of the power grid, wherein the power grid controller is configured to execute at least one power grid control application based on the converged state estimate.

### Claim 2 (depends on 1)

The method of claim 1 wherein updating the state estimate based on the first gain matrix and updating the state estimate based on the second gain matrix is also based on weighted least squares.

### Claim 3 (depends on 2)

The method of claim 2 wherein calculating the first gain matrix based on Gauss-Newton method includes based on the following equation, where GGN(Xk) is the Gauss-Newton gain matrix at iteration k, Xk is an estimated state vector at iteration k, H is a measurement function Jacobian matrix, and W is a weight matrix:
GGN(Xk)=H(Xk)TWH(Xk)

### Claim 4 (depends on 3)

The method of claim 3 wherein calculating the second gain matrix based on Newton's method includes based on the following set of equations: where GN(Xk) is the Newton's Method gain matrix at iteration k, Xk is the estimated state vector at iteration k, H is the Jacobian matrix of measurement functions, W is the weight matrix, i is the measurement index, wi is a weight for measurement index i, hi is the measurement function h at measurement index i, and zi is the power grid data at measurement index i, and Hess(hi(Xk)) is the Hessian matrix of measurement function of measurement i evaluated at the current state estimate:
GN(Xk)=H(Xk)TWH(Xk)−Σi=1mwiHess(hi(Xk))[zi−hi(X)]

### Claim 5 (depends on 1)

The method of claim 1 further comprising selecting, with the state estimator, the second gain matrix, wherein selecting the second gain matrix is in response to determining the second gain matrix is positive definite.

### Claim 6 (depends on 1)

The method of claim 1 wherein updating the state estimate based on the second gain matrix includes calculating a correction based on the second gain matrix and adding the correction to the state estimate.

### Claim 7 (depends on 6)

The method of claim 6 wherein the state estimate converges when a norm of the correction is less than a first convergence threshold or when a gradient based on the state estimate is less than a second convergence threshold.

### Claim 8 (depends on 6)

The method of claim 6 wherein the size of the correction calculated based on the second gain matrix is limited so as to prevent overshoot.

### Claim 9 (depends on 1)

The method of claim 1 further comprising:
removing false data from the power grid data based on the state estimate;
calculating a second state estimate based on the power grid data without the false data;
iteratively recalculating the second gain matrix and updating the second state estimate based on the second gain matrix until the second state estimate converges;
determining the power grid data does not include false data; and
transmitting the second state estimate to the power grid controller.

### Claim 10 (depends on 1)

The method of claim 1 further comprising:
receiving the power grid data including a plurality of circuit breaker statuses;
determining the plurality of circuit breaker statuses includes false data; and
updating the plurality of circuit breaker statuses by removing the false data from the plurality of circuit breaker statuses,
wherein determining the state estimate is based on the plurality of updated circuit breaker statuses.

### Claim 11

A power grid comprising:
a plurality of local controllers structured to transmit power grid data corresponding to characteristics of the power grid;
a state estimator including a processing device configured to execute a set of instructions effective to:
determine a state estimate based on the power grid data received from the plurality of local controllers,
calculate a first gain matrix based on Gauss-Newton method,
update the state estimate based on the first gain matrix,
calculate a second gain matrix based on Newton's method,
update the state estimate based on the second gain matrix,
iteratively recalculate the second gain matrix and update the state estimate based on the second gain matrix until the state estimate converges, and
after the state estimate converges, send the state estimate to a power grid controller of the power grid; and
the power grid controller configured to:
receive the state estimate sent by the state estimator; and
control operation of the power grid using the received state estimate.

### Claim 12 (depends on 11)

The power grid of claim 11 wherein updating the state estimate based on the first gain matrix and updating the state estimate based on the second gain matrix is also based on weighted least squares.

### Claim 13 (depends on 12)

The power grid of claim 12 wherein calculating the first gain matrix based on Gauss-Newton method includes based on the following equation, where GGN(Xk) is the Gauss-Newton gain matrix at iteration k, Xk is an estimated state vector at iteration k, H is a measurement function Jacobian matrix, and W is a weight matrix:
GGN(Xk)=H(Xk)TWH(Xk)

### Claim 14 (depends on 13)

The power grid of claim 13 wherein calculating the second gain matrix based on Newton's method includes based on the following equation where GN(Xk) is the Newton's Method gain matrix at iteration k, Xk is the estimated state vector at iteration k, H is the Jacobian matrix of measurement functions, W is the weight matrix, i is the measurement index, wi is a weight for measurement index i, hi is the measurement function h at measurement index i, and zi is the power grid data at measurement index i, and Hess(hi(Xk)) is the Hessian matrix of measurement function of measurement i evaluated at the current state estimate:
GN(Xk)=H(Xk)TWH(Xk)−Σi=1mwiHess(hi(Xk))[zi−hi(X)]

### Claim 15 (depends on 11)

The power grid of claim 11 wherein the processing device is further configured to execute the set of instructions further effective to select the second gain matrix in response to determining the second gain matrix is positive definite.

### Claim 16 (depends on 11)

The power grid of claim 11 wherein updating the state estimate based on the second gain matrix includes calculating a correction based on the second gain matrix and adding the correction to the state estimate.

### Claim 17 (depends on 16)

The power grid of claim 16 wherein the state estimate converges when a norm of the correction is less than a first convergence threshold or when a gradient based on the state estimate is less than a second convergence threshold.

### Claim 18 (depends on 16)

The power grid of claim 16 wherein the size of the correction calculated based on the second gain matrix is limited so as to prevent overshoot.

### Claim 19 (depends on 11)

The power grid of claim 11 wherein the processing device is configured to execute the set of instructions further effective to:
remove false data from the power grid data;
calculate a second state estimate based on the power grid data without the false data;
iteratively recalculate the second gain matrix and update the second state estimate based on the second gain matrix until the second state estimate converges;
determine the power grid data does not include false data; and
transmit the second state estimate to the power grid controller.

### Claim 20 (depends on 1)

The method of claim 1 wherein the power grid data is not received from the plurality of sensors.