Adaptive state assessment for power systems

Abstract

Disclosed are systems, methods, techniques, and apparatus for state assessment. One exemplary embodiment is a method that includes determining a state assessment based on grid data corresponding to a characteristic of a grid, using a state assessor; calculating a gradient based on the state assessment, using the state assessor; calculating a first gain matrix based on a Gauss-Newton method and a second gain matrix based on a Newton method, using the state assessor; selecting the first gain matrix or the second gain matrix for calculating a correction to the state assessment, using the state assessor; calculating the correction to the state assessment, using the state assessor; updating the state assessment, using the state assessor; and determining, using the state assessor, whether the updated state assessment has converged.

Description

Technical Field

[0001] The present disclosure generally relates to state assessment in an electric power system under normal and very poor measurement quality conditions. Background Art

[0002] State assessment is an important and basic function for power system monitoring, risk analysis, control and optimization. In order to perform state assessment, data such as sensor measurements or equipment status are collected from components of the power system. Sometimes, the quality of the collected data is affected by severe erroneous data (for example, such as malicious data injection or sensor failure). Severe erroneous data may prevent the state assessment from converging. Existing state assessment systems are affected by many shortcomings and deficiencies. There are still unmet needs, including improving the convergence rate and the accuracy of erroneous data detection. For example, when the state assessment cannot converge, it is impossible to perform erroneous data detection and removal. Therefore, achieving a 100% or nearly 100% state assessment convergence rate under any data error condition is crucial to maintaining uninterrupted situational awareness in power system control. In view of these and other shortcomings in the art, the unique devices, methods, systems and techniques disclosed herein are highly desirable. Summary of the invention

[0003] In order to clearly, concisely and accurately describe the non-limiting exemplary embodiments of the present disclosure, the manner and process of making and using the non-limiting exemplary embodiments of the present disclosure, and to enable the practice, manufacture and use of the non-limiting exemplary embodiments of the present disclosure, reference will be made to certain exemplary embodiments (including the non-limiting exemplary embodiments shown in the accompanying drawings), and specific language will be used to describe the non-limiting exemplary embodiments. However, it should be understood that no limitation on the scope of the present disclosure is thereby formed, and the present disclosure includes and protects changes, modifications and additional applications of the exemplary embodiments that those skilled in the art will think of as a result of the present disclosure.

[0004] The present disclosure relates to a method, comprising: determining a state evaluation based on power grid data corresponding to characteristics of a power grid received from a plurality of local controllers using a state evaluator; calculating a first gain matrix based on a Gauss-Newton method using the state evaluator; updating the state evaluation based on the first gain matrix using the state evaluator; calculating a second gain matrix based on a Newton method using the state evaluator; updating the state evaluation based on the second gain matrix using the state evaluator; and iteratively recalculating the second gain matrix using the state evaluator and updating the state evaluation based on the second gain matrix until the state evaluation converges.

[0005] Various embodiments may preferably implement the following features:

[0006] Preferably, updating the state estimate based on the first gain matrix and updating the state estimate based on the second gain matrix are also based on a weighted least squares method.

[0007] Preferably, calculating the first gain matrix based on the Gauss-Newton method includes calculating the first gain matrix based on the following equation, wherein G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the measurement function Jacobian matrix, and W is the weight matrix:

[0008] G GN (x k )=H(x k ) T WH(x k )

[0009] Preferably, calculating the second gain matrix based on Newton's method includes calculating the second gain matrix based on the following set of equations: N (x k ) is the Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the Jacobian matrix of the measurement function, W is the weight matrix, i is the measurement coefficient, w i is the weight of the measurement coefficient i, h i is the measurement function h at measurement coefficient i, and z i is the grid data at the measurement coefficient i, and Hess(h i (x k )) is the Hessian matrix of the measurement function of measurement i evaluated at the current state evaluation:

[0010]

[0011] Preferably, the method further comprises selecting, with the state evaluator, a second gain matrix, wherein selecting the second gain matrix is ​​responsive to determining that the second gain matrix is ​​positive definite.

[0012] Preferably, updating the state estimate based on the second gain matrix comprises calculating a correction based on the second gain matrix and adding the correction to the state estimate.

[0013] Preferably, the state estimate converges when the modified norm is less than a first convergence threshold or wherein a gradient based on the state estimate is less than a second convergence threshold.

[0014] Preferably, the magnitude of the corrections calculated based on the second gain matrix is ​​limited to prevent overshoot.

[0015] Preferably, the method further includes removing erroneous data from the power grid based on the state assessment; calculating a second state assessment based on the power grid data without the erroneous data; iteratively recalculating a second gain matrix and updating the state assessment based on the second gain matrix until the state assessment converges; determining that the power grid data does not include erroneous data; and transmitting the state assessment to the power grid control system.

[0016] Preferably, the method further comprises receiving grid data comprising a plurality of circuit breaker states; determining that the plurality of circuit breaker states comprises erroneous data; and updating the plurality of circuit breaker states by removing the erroneous data from the plurality of circuit breaker states, wherein determining the state evaluation is based on the plurality of updated circuit breaker states.

[0017] The present disclosure also relates to a state assessment system, comprising: a plurality of local controllers configured to transmit power grid data corresponding to characteristics of a power grid; and a state evaluator, comprising a processing device configured to execute a set of instructions effective for the following functions: determining a state assessment based on the power grid data corresponding to characteristics of the power grid received from the plurality of local controllers; calculating a first gain matrix based on a Gauss-Newton method; updating the state assessment based on the first gain matrix; calculating a second gain matrix based on Newton's method; updating the state assessment based on the second gain matrix; and iteratively recalculating the second gain matrix and updating the state assessment based on the second gain matrix until the state assessment converges.

[0018] Various embodiments may preferably implement the following features:

[0019] Preferably, updating the state estimate based on the first gain matrix and updating the state estimate based on the second gain matrix are also based on a weighted least squares method.

[0020] Preferably, calculating the first gain matrix based on the Gauss-Newton method includes calculating the first gain matrix based on the following equation, wherein G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the measurement function Jacobian matrix, and W is the weight matrix:

[0021] G GN (x k )=H(x k ) T WH(x k )

[0022] Preferably, calculating the second gain matrix based on Newton's method includes calculating the second gain matrix based on the following equation: N (x k ) is the Newton gain matrix at iteration k, x kis the evaluation state vector at iteration k, H is the Jacobian matrix of the measurement function, W is the weight matrix, i is the measurement coefficient, w i is the weight of the measurement coefficient i, h i is the measurement function h at measurement coefficient i, and z i is the grid data at the measurement coefficient i, and Hess(h i (x k )) is the Hessian matrix of the measurement function of measurement i evaluated at the current state evaluation:

[0023]

[0024] Preferably, the processing device is further configured to, in response to determining that the second gain matrix is ​​positive definite, execute a set of instructions effective to further select the second gain matrix.

[0025] Preferably, updating the state estimate based on the second gain matrix comprises calculating a correction based on the second gain matrix and adding the correction to the state estimate.

[0026] Preferably, the state estimate converges when the modified norm is less than a first convergence threshold or wherein a gradient based on the state estimate is less than a second convergence threshold.

[0027] Preferably, the magnitude of the corrections calculated based on the second gain matrix is ​​limited to prevent overshoot.

[0028] Preferably, the processing device is configured to execute a set of instructions further effective for: removing erroneous data from the power grid data; calculating a second state assessment based on the power grid data without the erroneous data; iteratively recalculating a second gain matrix and updating the second state assessment based on the second gain matrix until the second state assessment converges; determining that the power grid data does not include erroneous data; and transmitting the second state assessment to the power grid control system.

[0029] Preferably, the processing device is also configured to execute a set of instructions further effective for: receiving power grid data including a plurality of circuit breaker states; determining that the plurality of circuit breaker states include error data; and updating the plurality of circuit breaker states by removing the error data from the plurality of circuit breaker states, wherein determining the state evaluation is based on the plurality of updated circuit breaker states.

[0030] The present disclosure also relates to a method, comprising: determining a state evaluation based on power grid data corresponding to characteristics of a power grid using a state evaluator; calculating a gradient based on the state evaluation using the state evaluator; calculating a first gain matrix based on a Gauss-Newton method and a second gain matrix based on a Newton method using the state evaluator; selecting the first gain matrix or the second gain matrix for calculating a correction to the state evaluation using the state evaluator; calculating the correction to the state evaluation using the state evaluator; updating the state evaluation using the state evaluator; and determining whether the updated state evaluation has converged using the state evaluator.

[0031] Various embodiments may preferably implement the following features:

[0032] Preferably, when it is determined that the updated state estimate has not converged, the method comprises iteratively calculating the first matrix and the second gain matrix; selecting the first matrix or the second matrix; calculating a correction to the state estimate; and updating the state estimate until it is determined that the updated state estimate has converged.

[0033] Preferably, the method further comprises, after calculating the gradient, determining, using a state evaluator, whether the state estimate has converged.

[0034] Preferably, determining that the updated state estimate has converged comprises calculating a norm of the correction and determining whether the norm is below a given threshold.

[0035] Preferably, selecting the first gain matrix or the second gain matrix comprises determining that the second gain matrix is ​​positive definite.

[0036] Preferably, the method further comprises, after calculating the correction, limiting the magnitude of the correction using the state evaluator to prevent overshoot.

[0037] Preferably, the first gain matrix is ​​calculated based on the Gauss-Newton method based on the following equation, where G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the measurement function Jacobian matrix, and W is the weight matrix:

[0038] G GN (x k )=H(x k ) T WH(x k )

[0039] Preferably, the method further comprises, with the state evaluator, using the converged state evaluation to determine whether the power grid data includes erroneous data.

[0040] The present disclosure also relates to a state assessment system, comprising: a state assessor, comprising a processing device, the processing device being configured to execute a set of instructions effective for the following functions:

[0041] Determine a state assessment based on grid data corresponding to characteristics of the grid; calculate a gradient based on the state assessment; calculate a first gain matrix based on a Gauss-Newton method and a second gain matrix based on a Newton method; select the first gain matrix or the second gain matrix for calculating a correction to the state assessment; calculate the correction to the state assessment; update the state assessment; and determine whether the updated state assessment has converged.

[0042] Various embodiments may preferably implement the following features:

[0043] Preferably, the state assessment system further comprises a plurality of local controllers configured to transmit grid data corresponding to characteristics of the grid to the state assessor.

[0044] Preferably, the processing device determines that the updated state estimate has not converged, and the processing device is configured to iteratively calculate the first matrix and the second gain matrix, select the first matrix or the second matrix, calculate a correction to the state estimate, and update the state estimate until it is determined that the updated state estimate has converged.

[0045] Preferably, the processing device is configured to determine, after calculating the gradient, whether the state estimate has converged.

[0046] Preferably, in order to determine that the updated state estimate has converged, the processing device is configured to calculate a norm of the correction and determine whether the norm is below a given threshold.

[0047] Preferably, for selecting the first gain matrix or the second gain matrix, the processing device is configured to determine that the second gain matrix is ​​positive definite.

[0048] Preferably, the processing device is arranged to, after calculating the correction, limit the magnitude of the correction to prevent overshoot.

[0049] Preferably, the first gain matrix is ​​calculated based on the Gauss-Newton method based on the following equation, where G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the measurement function Jacobian matrix, and W is the weight matrix:

[0050] G GN (x k )=H(x k ) T WH(x k )

[0051] Preferably, the processing device is configured to use the converged state assessment to determine whether the power grid data includes erroneous data.

[0052] Exemplary embodiments of the present disclosure include unique systems, methods, techniques and apparatus for erroneous data detection reduction systems. Additional embodiments, forms, objects, features, advantages, aspects and benefits of the present disclosure will become apparent from the following description and accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 An exemplary electrical grid is shown.

[0054] Figure 2 is a flow chart illustrating an exemplary erroneous data reduction process.

[0055] Figure 3 is a flow chart illustrating an exemplary state evaluation process of an exemplary erroneous data reduction process.

[0056] Figure 4 It shows Figure 3 Graphs of results of various instances of an exemplary state assessment process are shown in FIG.

[0057] Figure 5 It is a comparison Figure 3 A table of results of an exemplary condition assessment process and a conventional condition assessment process shown in FIG. DETAILED DESCRIPTION

[0058] refer to Figure 1 , an exemplary power grid 100 is shown. It should be understood that the power grid 100 includes a state evaluator 150 and a power grid control system 160. The state evaluator 150 can be implemented in various applications, including power transmission systems, power distribution systems, industrial automation systems, or other types of systems configured to generate state assessments based on multiple collected data. The state evaluator 150 can be incorporated into a power grid control system 160, such as an energy management system, a distribution management system, an advanced distribution management system, or a microgrid control system, by way of example only. It should be understood that the topology of the power grid 100 is shown for the purpose of explanation and is not intended to be a limitation of the present disclosure. Although the power grid 100 is shown using a single-line diagram, the power grid 100 can be configured to transmit single-phase power, multi-phase power, or DC power.

[0059] The power grid 100 is configured to generate power and provide the generated power to coupled loads. The power grid 100 includes a power generation system 110 , a transmission network 120 , a substation 130 , a distribution network 140 , and a state evaluator 150 .

[0060] The power generation system 110 includes an AC power source 111, a step-up transformer 113, a plurality of controllable devices including a circuit breaker 117, a plurality of sensors 119, and a remote terminal unit (RTU) 115. The AC power source 111 is configured to generate AC power and output the generated power. The transformer 113 is configured to receive the generated power from the AC power source 111, increase the voltage of the power, and output the power to the transmission network 120. The circuit breaker 117 is configured to selectively isolate the AC power source 111 from the transmission network 120.

[0061] The plurality of sensors 119 are configured to measure electrical characteristics of the power generation system 110, and may include, by way of example only, voltage sensors, voltage transformers, current sensors, and current transformers. The RTU 115 is configured to communicate with the plurality of sensors 119, the plurality of controllable devices, and the state evaluator 150. The RTU 115 may receive measurements from the plurality of sensors 119, receive device states from the controllable devices, and transmit the received data to the state evaluator 150. By way of example only, the measurements received by the RTU 115 may include voltage phase angles, voltage amplitudes, injected power, and power flows. By way of example only, the device states may include the open / closed state of each circuit breaker of the power generation system 110. In certain embodiments, any RTU may be replaced with another type of local controller that is configured to receive data and communicate with the state evaluator 150.

[0062] The transmission network 120 is configured to transmit AC power from the transformer 113 to a plurality of substations including the substation 130. The network 120 includes a plurality of transmission lines (such as the transmission line 121), a plurality of controllable devices (such as the circuit breaker 123), and a transmission bus 125. In certain embodiments, the transmission network 120 includes a plurality of sensors configured to measure electrical characteristics of the network 120, such as bus voltage magnitude, bus voltage phase angle, and power flow, by way of example only. The transmission network 120 may also include a controller (such as an RTU) configured to receive measurements from the plurality of sensors, receive device states from the plurality of controllable devices, and transmit the received data to the state evaluator 150.

[0063] The substation 130 is configured to receive AC power from the transmission network 120, reduce the voltage of the received power, and output the modified AC power to the distribution network 140. The substation 130 includes a step-down transformer 131, a distribution bus 133, a plurality of controllable devices (such as a circuit breaker 135), a plurality of sensors 138, and an RTU 139. The step-down transformer 131 is configured to receive AC power from the transmission network 120, reduce the voltage of the received power, and output the modified power to the distribution bus 133. The circuit breaker 135 is configured to selectively isolate the distribution network 140 from the distribution bus 133.

[0064] The plurality of sensors 138 are configured to measure electrical characteristics of the substation 130, and may include, by way of example only, a voltage sensor, a voltage transformer, a current sensor, and a current transformer. The RTU 139 is configured to communicate with the plurality of sensors 138, the plurality of controllable devices, and the state evaluator 150. The RTU 139 may receive measurement values ​​from the plurality of sensors 138, receive device states from the plurality of controllable devices, and transmit the received data to the state evaluator 150. By way of example only, the measurement values ​​received from the RTU 139 may include a voltage phase angle, a voltage amplitude, an injected power, and a power flow. By way of example only, the device state may include an open / closed state of each circuit breaker of the substation 130.

[0065] The power distribution network 140 is configured to transmit AC power received from the substation 130 to a plurality of coupled loads. The network 140 includes a plurality of distribution lines (such as distribution lines 147 and 143), a plurality of controllable devices (such as circuit breakers 141), and a distribution bus 145. In certain embodiments, the power distribution network 140 includes sensors configured to measure electrical characteristics of the network 140, such as bus voltage amplitude, bus voltage phase angle, and power flow, by way of example only. The power distribution network 140 may also include a controller (such as an RTU) configured to receive measurements from a plurality of sensors, receive device states from a plurality of controllable devices, and transmit the received data to a state evaluator 150.

[0066] State evaluator 150 is configured to receive measurements and device status data from RTU 115 and RTU 139. In certain embodiments, state evaluator 150 is configured to receive data from other devices of grid 100, such as, by way of example only, intelligent electronic devices, programmable logic controllers, protection relays, phasor measurement units, or microgrid controllers.

[0067] State evaluator 150 is configured to determine portions of grid 100 that are not isolated by controllable devices of grid 100, also referred to as grid topology, using data received from RTUs 115 and 139. Using the received data and the grid topology, state evaluator 150 is configured to evaluate a plurality of states of grid 100, such as, for example only, a plurality of node voltage magnitudes and phase angles.

[0068] In order to evaluate the state of the power grid 100, the state evaluator 150 uses a set of equations and matrices described in detail below to determine a series of state evaluations. After determining the initial state evaluation, the state evaluator iteratively updates the state evaluation until the updated state evaluation converges. In order to update the value of the state evaluation, the state evaluator 150 calculates a correction, which is added to the previous value of the state evaluation. The correction can be calculated using a gain matrix that is calculated using a Gauss-Newton method or a Newton method. The state evaluator 150 determines which method to use based on the numerical characteristics of the relevant gain matrix. As described in more detail below, the state evaluator 150 can calculate the first set of corrections using the Gauss-Newton method and then calculate the remaining corrections using the Newton method until the state evaluation converges. As shown in more detail below, using the Gauss-Newton method to calculate an initial set of corrections and then using the Newton method to calculate the remaining corrections has a higher probability of convergence than using either method alone.

[0069] Once state evaluator 150 has evaluated the plurality of states, state evaluator 150 is configured to use the plurality of evaluated states to identify erroneous data received from a data source such as RTU 115 or RTU 139, remove the erroneous data from a set of data used to evaluate the plurality of states, evaluate the plurality of evaluated states again without using the erroneous data, and output a transformed state evaluation for use in grid control system 160. By way of example only, the erroneous data may include data received from a faulty sensor or data received from a network intruder. The erroneous data may include a single erroneous data point or a plurality of erroneous data points.

[0070] State evaluator 150 includes input / output device 151, processing device 153, and memory device 155. State evaluator 150 may be a standalone device, an embedded system, or a plurality of devices configured to perform the functions described with respect to state evaluator 150. For example, state evaluator 150 may be a remote server.

[0071] The input / output device 151 enables the state evaluator 150 to communicate with a plurality of external devices including the RTUs 115 and 139. For example, by way of example only, the input / output device 151 in various embodiments may include a network adapter, network credentials, interface, or port (e.g., a USB port, a serial port, a parallel port, an analog port, a digital port, VGA, DVI, HDMI, FireWire, CAT 5, Ethernet, fiber optic, or any other type of port or interface). The input / output device 151 includes hardware, software, and / or firmware. It is contemplated that the input / output device 151 includes more than one of these adapters, credentials, or ports, such as a first port for receiving data and a second port for transmitting data.

[0072] Processing device 153 can be a programmable type, a dedicated hard-wired state machine or a combination thereof. For example only, device 153 may include multiple processors, arithmetic logic units (ALUs), central processing units (CPUs), digital signal processors (DSPs) or field programmable gate arrays (FPGAs). For the form of processing device 153 with multiple processing units, distributed, pipelined or parallel processing can be appropriately used. Processing device 153 can be dedicated to only perform the operations described herein, or can be used in one or more additional applications. In the form shown, processing device 153 is a programmable type that executes processes and processes data according to programming instructions (such as software or firmware) stored in memory device 155. Alternatively or additionally, programming instructions are at least partially defined by hard-wired logic or other hardware. Processing device 153 may include one or more components of any type suitable for processing signals received from input / output device 151 or elsewhere and providing desired output signals. These components may include digital circuits, analog circuits or a combination of both.

[0073] Memory devices 155 may be of one or more types, such as, by way of example only, solid-state, electromagnetic, optical, or a combination of these forms. Additionally, memory devices 155 may be volatile, non-volatile, temporary, non-temporary, or a combination of these types, and some or all of memory devices 155 may be of a portable type, such as, by way of example only, a disk, a tape, a memory stick, or a cassette. Furthermore, in addition to or in lieu of storing programming instructions, memory devices 155 may store data that is operated on by processing device 153, such as, by way of example only, data representing signals received from or sent to input / output device 151.

[0074] Grid control system 160 is configured to receive the converged state assessment and execute a grid control application using the converged state assessment valid for grid 100. Grid control applications may include real-time control applications such as, by way of example only, contingency analysis, optimal power flow, economic dispatch, voltage / var control, or network switching. It should be understood that any or all of the aforementioned features of components of grid 100 may also be present in other components disclosed herein.

[0075] refer to Figure 2 , which is a flow chart illustrating an exemplary erroneous data reduction process 200 for an electrical grid. The process 200 may be implemented in whole or in part in one of the exemplary state evaluators disclosed herein. It should be understood that a variety of variations and modifications to the process 200 are contemplated, including, for example, omitting one or more aspects of the process 200, adding additional conditions and operations, and reorganizing or separating operations and conditions into independent processes.

[0076] Process 200 begins at operation 201, in which a state evaluator receives grid data corresponding to electrical or physical characteristics of a grid. By way of example only, the grid data may include on / off circuit breaker states and measurements including voltage phase angle, voltage magnitude, injected power, and power flow. The source of the grid data may include a plurality of sensors and a plurality of circuit breakers.

[0077] Process 200 proceeds to operation 203, in which topological processing of the power grid using the received power grid data is performed. For example, the on / off circuit breaker state can be used to generate the power grid topology. In some embodiments, the state evaluator can receive the power grid topology from another controller or multiple controllers of the power grid.

[0078] Process 200 proceeds to operation 205 where preliminary erroneous data detection and removal is performed. By way of example only, erroneous data may be detected by performing a range or consistency check, for example.

[0079] Process 200 proceeds to operation 207 where a state evaluator attempts to evaluate multiple states of the electrical grid by determining a first state evaluation and then iteratively updating the state evaluation using a series of corrections calculated based on the Gauss-Newton method until the state evaluation converges.

[0080] If the state evaluation converges during operation 207, process 200 proceeds to operation 211. If the state evaluation fails to converge, process 200 proceeds to operation 209, where a state evaluation is performed using a combination of the Gauss-Newton method and the Newton method. Once the state evaluation converges, process 200 proceeds to operation 209.

[0081] During operation 211, the converged state evaluation is used to determine whether the grid data includes erroneous data. If it is determined that the grid data includes erroneous data, the erroneous data is removed from the grid data, and process 200 returns to operation 207, in which the state evaluation is performed again using the grid data minus the erroneous data. Operations 207, 209, and 211 are repeated until it is determined that the grid data does not include erroneous data. Operation 211 can be performed by a state evaluator or another controller of the grid.

[0082] Once it is determined that the grid data does not include erroneous data, process 200 proceeds to operation 213 where the status assessment is transmitted to one or more grid control applications. The grid control applications may include real-time control applications such as, for example only, emergency analysis, optimal power flow, economic dispatch, voltage / var control, or network switching.

[0083] refer to Figure 3 , which illustrates an exemplary state assessment process 300 (such as Figure 2 209 in the process 300). Process 300 may be implemented in whole or in part in one of the exemplary state evaluators disclosed herein. It should be understood that a variety of variations and modifications to process 300 are contemplated, including, for example, omitting one or more aspects of process 300, adding additional conditions and operations, and reorganizing or separating operations and conditions into independent processes.

[0084] Process 300 begins at operation 301, in which a state evaluator determines an initial state evaluation using power grid data. By way of example only, the state evaluation may be determined by calculating the state evaluation using a set of equations, or the state evaluation may be determined based on the power grid data without using a set of equations. By way of example only, the state evaluation may include node voltage magnitudes, node voltage phase angles, currents, power flows, and transformer taps.

[0085] Process 300 proceeds to operation 303, where the state evaluator calculates a gradient based on the state estimate. For example, the state evaluator may calculate the gradient based on the following equation, where H(x k ) is the Jacobian matrix of the measurement function at iteration k, h is the measurement function vector, k is the iteration counter, W is the weight matrix containing the weights for each step,

[0086] Δz(x k ) is the residual at iteration k, and is the gradient of equation (1) at iteration k.

[0087]

[0088]

[0089] in:

[0090]

[0091] Δx k =x k+1 -x k (4)

[0092] Δz(x k )=zh(x k ) (5)

[0093] Process 300 proceeds to condition 305, in which the state evaluator determines whether the state estimate has converged. The state evaluator can determine whether the state estimate has converged by determining whether the following equation is satisfied, where is the norm of the Jacobian matrix of the state evaluation vector x at iteration k, and ε J is the convergence threshold of the norm.

[0094]

[0095] Just for example, the convergence threshold ε J Can be 10 -3 , 10 -5 or 10 -7 If the state estimate has converged, process 300 proceeds to end operation 319 where the state evaluator determines that the solution is the most recently computed state estimate. If the state estimate has not converged, process 300 proceeds to operation 307.

[0096] During operation 307, the state estimator calculates two gain matrices, one of which will be used to update the state estimator. The first gain matrix is ​​calculated using the Gauss-Newton method. For example, the first gain matrix can be calculated using the following set of equations, where G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluated state vector at iteration k, H is the Jacobian matrix of the measurement function, and W is the weight matrix:

[0097] G GN (x k )=H(x k ) T WH(x k ) (7)

[0098] The second gain matrix is ​​calculated using Newton's method. For example, the second gain matrix can be calculated using the following set of equations: N (x k) is the Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the Jacobian matrix of the measurement function, W is the weight matrix, i is the measurement coefficient, w i is the weight of the measurement coefficient i, h i is the measurement function h at measurement coefficient i, and z i is the grid data at the measurement coefficient i, and Hess(h i (x k )) is the Hessian matrix of the measurement function of measurement i evaluated at the current state evaluation, where

[0099] The process 300 then proceeds to operation 309, in which the state evaluator selects either the Gauss-Newton method or the Newton method for calculating the correction. If the state evaluator determines that the use of the Gauss-Newton method is causing or will cause the state estimation to fail to converge, the state evaluator may select the Newton method. For example, in response to determining that the gain matrix of the Newton method is positive definite, the state evaluator may select the Newton method.

[0100] Process 300 proceeds to operation 311, in which the state evaluator calculates the correction using the selected method, also known as calculating the state update. To calculate the correction using the Gauss-Newton method, the following equation can be used:

[0101] Δx k =G GN (x k ) -1 H(x k ) T WΔz(x k ) (9)

[0102] To calculate the correction using Newton's method, the following equation can be used:

[0103] Δx k =G N (x k ) -1 H(x k ) T WΔz(x k ) (10)

[0104] Process 300 proceeds to operation 313, where the state estimator limits the size of the correction calculated in operation 311 to prevent the state estimator from overshooting the solution. For example, the state estimator may limit the size of the correction calculated in operation 311 using the following set of equations, where ||Δx k||∞ is the norm of the correction at iteration k, and α is the maximum correction constant.

[0105]

[0106] The constant α is determined to effectively constrain the state vector x in one step k For example, the constant α may be 0.05 pu for voltage amplitude, or 25 degrees for voltage phase angle.

[0107] Process 300 proceeds to operation 315 where the state evaluator updates the state estimate by adding the state correction calculated in operations 311 and 313 to the previous state estimate value, as shown in the following equation:

[0108] x k+1 =x k +Δx k (12)

[0109] The process 300 then proceeds to condition 317 where the state evaluator determines whether the state estimate has converged. The state evaluator may determine whether the state estimate has converged by determining whether the following equation is satisfied, where ||Δx k || ∞ is the modified norm at iteration k, and ε x is the convergence threshold of the modified norm:

[0110] ||Δx k || ∞ <ε x (13)

[0111] Just for example, the convergence threshold ε J Can be 10 -3 , 10 -5 or 10 -7 If the state estimate has converged, process 300 proceeds to end operation 319, where the state evaluator determines that the solution is the most recently computed state estimate. If the state estimate has not converged, process 300 increments the iteration count and returns to operation 303. Process 300 continues to perform operations 303 through 315 until the state estimate converges, as determined by condition 305 or 317.

[0112] refer to Figure 4, which is a chart 400 showing one hundred instances of an exemplary state assessment process 300. The chart 400 shows how many iterations are required to converge to a solution for each of the instances, and what method is used for each iteration. The chart 400 includes a plurality of columns, each of which includes a plurality of blocks. Each column represents a complete state assessment, and each block represents a state assessment of the state assessment. Each state assessment of the state assessment can be updated using either the Gauss-Newton method or the Newton method. Each block identified as iteration one is an initial state assessment. For example, instance 1 uses the Gauss-Newton method to update the first iteration, and then uses the Newton method to update the remaining ten state assessments, at which point the final state assessment converges.

[0113] refer to Figure 5 Table 500 shows the simulated measurement conditions with severe data errors when using conventional methods and Figure 3 Table 500 shows state evaluation in test systems of different complexity of the exemplary state evaluation process 300. Table 500 includes multiple rows, each row corresponding to a test system of a certain complexity. Column 503 indicates the number of instances executed for each test system. Columns 505 and 507 show the results of simulated state evaluation using only the Gauss-Newton method calculation steps. Columns 509 and 511 show the results of simulated state evaluation using only the Newton method to calculate the correction. Columns 513 and 515 show the results of simulated state evaluation using the exemplary process 300.

[0114] The results shown include the percentage of instances where the state assessment for each method converged, and the percentage of instances where the converged state assessment represents a stable solution. If the phase angle difference between any two adjacent nodes is less than 90 degrees, the converged state assessment is stable. As shown in table 500, the exemplary state assessment process 300 converges in a significantly higher percentage of instances than any of the conventional methods. In addition, the exemplary state assessment process 300 reaches a stable solution in a significantly higher percentage of instances than any of the conventional methods.

[0115] A further written description of several exemplary embodiments will now be provided. One embodiment is a method comprising: determining, with a state evaluator, a state evaluation based on grid data corresponding to characteristics of a grid received from a plurality of local controllers; calculating, with the state evaluator, a first gain matrix based on a Gauss-Newton method; updating, with the state evaluator, the state evaluation based on the first gain matrix; calculating, with the state evaluator, a second gain matrix based on Newton's method; updating, with the state evaluator, the state evaluation based on the second gain matrix; and iteratively recalculating, with the state evaluator, the second gain matrix and updating the state evaluation based on the second gain matrix until the state evaluation converges.

[0116] In some forms of the foregoing method, updating the state estimate based on the first gain matrix and updating the state estimate based on the second gain matrix are also based on a weighted least squares method. In some forms, calculating the first gain matrix based on the Gauss-Newton method includes based on the following equation, where G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the measurement function Jacobian matrix, and W is the weight matrix: G GN (x k )=H(x k ) T WH(x k ). In some forms, calculating the second gain matrix based on Newton's method includes calculating the second gain matrix based on the following set of equations: N (x k ) is the Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the Jacobian matrix of the measurement function, W is the weight matrix, i is the measurement coefficient, w i is the weight of the measurement coefficient i, h i is the measurement function h at measurement coefficient i, and z i is the grid data at the measurement coefficient i, and Hess(h i (x k )) is the Hessian matrix of the measurement function of measurement i evaluated at the current state evaluation: In some forms, the method includes selecting a second gain matrix using a state evaluator, wherein selecting the second gain matrix is ​​responsive to determining that the second gain matrix is ​​positive definite. In some embodiments, 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. In some forms, 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. In some forms, the magnitude of the correction calculated based on the second gain matrix is ​​limited to prevent overshoot. In some forms, the method also includes removing erroneous data from the power grid based on the state estimate; calculating a second state estimate based on power grid data without erroneous data; iteratively recalculating the second gain matrix and updating the state estimate based on the second gain matrix until the state estimate converges; determining that the power grid data does not include erroneous data; and transmitting the state estimate to a power grid control system. In some forms, the method includes receiving power grid data including a plurality of circuit breaker states; determining that the plurality of circuit breaker states include erroneous data; and updating the plurality of circuit breaker states by removing the erroneous data from the plurality of circuit breaker states, wherein determining that the state estimate is based on a plurality of updated circuit breaker states.

[0117] Another exemplary embodiment is a state assessment system comprising: a plurality of local controllers configured to transmit grid data corresponding to characteristics of a grid; and a state evaluator comprising a processing device configured to execute a set of instructions effective for: determining a state assessment based on the grid data corresponding to characteristics of the grid received from the plurality of local controllers; calculating a first gain matrix based on a Gauss-Newton method; updating the state assessment based on the first gain matrix; calculating a second gain matrix based on Newton's method; updating the state assessment based on the second gain matrix; and iteratively recalculating the second gain matrix and updating the state assessment based on the second gain matrix until the state assessment converges.

[0118] In some forms of the foregoing state estimation system, updating the state estimation based on the first gain matrix and updating the state estimation based on the second gain matrix are also based on a weighted least squares method. In some forms, calculating the first gain matrix based on the Gauss-Newton method includes based on the following equation, where G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the measurement function Jacobian matrix, and W is the weight matrix: G GN (x k )=H(x k ) T WH(x k ). In some forms, wherein calculating the second gain matrix based on Newton's method comprises calculating the second gain matrix based on the following equation: N (x k ) is the Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the Jacobian matrix of the measurement function, W is the weight matrix, i is the measurement coefficient, w i is the weight of the measurement coefficient i, h i is the measurement function h at measurement coefficient i, and z i is the grid data at the measurement coefficient i, and Hess(h i (x k )) is the Hessian matrix of the measurement function of measurement i evaluated at the current state evaluation: In some forms, the processing device is further configured to execute a set of instructions further effective to select the second gain matrix in response to determining that the second gain matrix is ​​positive definite. In some forms, 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. In some forms, the state estimate converges when the norm of the correction is less than a first convergence threshold or where the gradient based on the state estimate is less than a second convergence threshold. In some forms, the size of the correction calculated based on the second gain matrix is ​​limited to prevent overshoot. In some forms, the processing device is configured to execute a set of instructions further effective to the following functions: remove erroneous data from the power grid data; calculate a second state estimate based on the power grid data without erroneous 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 that the power grid data does not include erroneous data; and transmit the second state estimate to the power grid control system. In some forms, the processing device is further configured to execute a set of instructions further effective to: receive power grid data including a plurality of circuit breaker states; determine that the plurality of circuit breaker states include erroneous data; and update the plurality of circuit breaker states by removing the erroneous data from the plurality of circuit breaker states, wherein the determined state evaluation is based on the plurality of updated circuit breaker states.

[0119] It is contemplated that various aspects, features, processes, and operations from various embodiments may be used in any of the other embodiments unless explicitly stated to the contrary. Certain operations illustrated may be computer implemented by a processing device including a computer program product executing on a non-transitory computer-readable storage medium, wherein the computer program product includes instructions that cause the processing device to perform one or more of the operations, or issue commands to other devices to perform one or more operations.

[0120] Although the present disclosure has been shown and described in detail in the drawings and the foregoing description, the present disclosure should be considered to be illustrative rather than restrictive in nature, and it should be understood that only certain exemplary embodiments are shown and described, and it is desired to protect all changes and modifications that fall within the spirit of the present disclosure. It should be understood that although the use of words such as "better", "preferably", "preferred" or "more preferred" used in the above description indicates that the described feature may be more ideal, it may not be necessary, and embodiments lacking the feature may be considered to be within the scope of the present disclosure, and the scope of the present disclosure is defined by the appended claims. When reading the claims, it is intended that when words such as "one", "one", "at least one" or "at least a portion" are used, unless otherwise explicitly stated in the claims, it is not intended to limit the claims to only one item. The term "of" may mean an association or connection with another item, as well as belonging to or being in contact with another item, which is determined by the context in which it is used. Unless explicitly indicated to the contrary, the terms "coupled to", "coupled with...", etc. include indirect connections and couplings, and also include but are not limited to direct couplings or connections. Unless expressly stated to the contrary, when the language "at least a portion" and / or "a portion" is used, the item may include a portion and / or the entire item. The term "based on" includes using the identified value to perform a function.

Claims

1. A state assessment method, comprising: determining, using a state evaluator, a state assessment based on grid data corresponding to a characteristic of the grid (301); The state evaluator is used to evaluate the state, including calculating a gradient based on the following equation (303): Among them, H(x k ) is the Jacobian matrix of the measurement function at iteration k, k is the iteration counter, W is the weight matrix containing the weights for each step, Δz(x k ) is the residual at iteration k, x k is the evaluation state vector at iteration k, and is the gradient of equation (1) at iteration k; Utilizing the state evaluator to calculate a first gain matrix based on a Gauss-Newton method and a second gain matrix based on a Newton method (307); selecting, using the state estimator, the first gain matrix or the second gain matrix for calculating a correction to the state estimate (309); calculating, using the state evaluator, a correction to the state estimate (311); updating the state estimate using the state evaluator (313); and A determination is made, using the state evaluator, based on the gradient or the revision whether the updated state estimate has converged.

2. The method according to claim 1, wherein: When it is determined that the updated state assessment has not converged, the method includes iteratively calculating the first gain matrix and the second gain matrix (307); selecting the first gain matrix or the second gain matrix (309); calculating a correction of the state assessment (311); and updating the state assessment until it is determined that the updated state assessment has converged (313).

3. The method according to claim 1 or 2, wherein: The method also includes determining, using the state evaluator, whether the state estimate has converged after calculating the gradient.

4. The method according to claim 1 or 2, wherein: Determining that the updated state estimate has converged includes calculating a norm of the revision and determining whether the norm is below a given threshold.

5. The method according to claim 1 or 2, wherein: Selecting the first gain matrix or the second gain matrix includes selecting the second gain matrix in response to determining that the second gain matrix is ​​positive definite.

6. The method according to claim 1 or 2, wherein: The method also includes limiting the magnitude of the correction using the state evaluator after calculating the correction to prevent overshoot.

7. The method according to claim 1 or 2, wherein: Calculating the first gain matrix based on the Gauss-Newton method is based on the following equation: G GN (x k )=H(x k ) T WH(x k ), Among them, G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the measurement function Jacobian matrix, and W is the weight matrix.

8. The method according to claim 1 or 2, wherein: The method also includes determining, with the state evaluator, whether the grid data includes erroneous data using the converged state evaluation.

9. A status assessment system comprising: A state evaluator comprising a processing device configured to execute a set of instructions effective to: determining a condition assessment based on the grid data corresponding to a characteristic of the grid; Based on the state evaluation, a gradient is calculated based on the following equation: Among them, H(x k ) is the Jacobian matrix of the measurement function at iteration k, k is the iteration counter, W is the weight matrix containing the weights for each step, Δz(x k ) is the residual at iteration k, x k is the evaluation state vector at iteration k, and is the gradient of equation (1) at iteration k; Calculate a first gain matrix based on a Gauss-Newton method and calculate a second gain matrix based on a Newton method; selecting the first gain matrix or the second gain matrix for calculating a correction to the state estimate; calculating a correction to the state assessment; updating the status assessment; and A determination is made based on the gradient or the correction whether the updated state estimate has converged. 10 . The state assessment system of claim 9 , further comprising a plurality of local controllers configured to transmit the grid data corresponding to characteristics of the grid to the state assessor.

11. The state assessment system according to claim 9 or 10, wherein: When the processing device determines that the updated state assessment has not converged, the processing device is configured to iteratively calculate the first gain matrix and the second gain matrix, select the first gain matrix or the second gain matrix, calculate a correction to the state assessment, and update the state assessment until it is determined that the updated state assessment has converged.

12. The state assessment system according to claim 9 or 10, wherein: The processing device is configured to determine whether the state estimate has converged after calculating the gradient.

13. The state assessment system according to claim 9 or 10, wherein: To determine that the updated state estimate has converged, the processing device is configured to calculate a norm of the revision and determine whether the norm is below a given threshold.

14. The state assessment system according to claim 9 or 10, wherein: To select the first gain matrix or the second gain matrix, the processing device is configured to select the second gain matrix in response to determining that the second gain matrix is ​​positive definite.

15. The state assessment system according to claim 9 or 10, wherein: The processing device is configured to, after calculating the correction, limit the magnitude of the correction to prevent overshoot.

16. The state assessment system according to claim 9 or 10, wherein: The first gain matrix is ​​calculated based on the Gauss-Newton method based on the following equation: GN (x k )=H(x k ) T WH(x k ), Among them, G GN (x k ) is the Gauss-Newton gain matrix at iteration k, x k is the evaluation state vector at iteration k, H is the measurement function Jacobian matrix, and W is the weight matrix.

17. The state assessment system according to claim 9 or 10, wherein: The processing device is configured to use the converged state assessment to determine whether the power grid data includes erroneous data.

18. A computer program product on a non-transitory computer readable storage medium, wherein: The computer program product comprises instructions for causing a processing device to perform the method of any one of claims 1 to 8.

Images