Power network anomaly detection method and system

Abstract

The invention discloses a power network anomaly detection method and system, and relates to the technical field of intelligent power grid monitoring, and the method comprises the steps: constructing a neuron-like power network graph model, carrying out the node processing of equipment, introducing a multi-factor anomaly score function, and dynamically activating an abnormal node through combining with an improved Winner-Take-All mechanism; the connection weight is dynamically optimized through a topology-aware composite gradient descent method, and a multi-layer neural network structure is constructed to realize cross-layer forward propagation and feedback adjustment; and establishing an abnormal path model in combination with the propagation phase difference and the information entropy, identifying an abnormal path by using a propagation score function and a weighted shortest path algorithm, and carrying out fault tracing. According to the power network anomaly detection method provided by the invention, the neuron-like graph model is constructed, and a multi-factor anomaly activation mechanism is introduced, so that comprehensive perception of a power grid node state under a multi-dimensional time characteristic can be realized, and the anomaly recognition sensitivity and the multi-point simultaneous activation capability are effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of smart grid monitoring technology, and in particular to a power network anomaly detection method and system. Background Art

[0002] With the development of smart grids, the number of devices and data dimensions in power systems continues to grow, and network structures are becoming more complex and dynamic. To ensure stable system operation and rapid fault response, power network anomaly detection technology has gradually evolved from traditional rule-based and statistical methods to data-driven intelligent recognition models. In recent years, artificial intelligence methods such as neural networks and graph neural networks (GNNs) have been introduced into power system monitoring to mine potential anomaly patterns in high-dimensional time series signals. Algorithms with deep modeling capabilities are showing great potential, especially in complex topologies, localized fault location, and dynamic response. However, current methods often focus on individual node states or modeling based on global indicators, making it difficult to balance real-time performance, sensitivity, and traceability accuracy.

[0003] Existing power anomaly detection methods mainly include rule threshold method, statistical learning method and shallow neural network method. Although these methods are effective in specific scenarios, they generally have the following shortcomings: (1) They lack the ability to deeply model the topology of the power grid and cannot reflect the complex connection relationship and energy transmission path between devices; (2) Anomaly judgment often relies on single-point data deviation, ignoring the time change trend of state evolution and the collaborative relationship between adjacent nodes; (3) The ability to model the abnormal propagation path is weak, and the starting point and propagation path of the anomaly cannot be effectively identified, which limits the efficiency of fault location and response. Especially when multiple points of coordinated anomalies and local fluctuations exist at the same time, traditional methods often have a high false alarm rate and poor positioning ability. In contrast, the neuron-like network anomaly detection method proposed by us constructs a neuron-like graph model based on the physical topology of the power grid, adopts a multi-factor activation mechanism that integrates state offset, rate of change and phase disturbance, and introduces a dynamic and adaptive Winner-Take-All strategy, which fundamentally improves the sensitivity of anomaly recognition and multi-point recognition capability; at the same time, through topology-aware weight adjustment and multi-layer neural network structure, hierarchical detection from local to global is realized; further combining the phase difference, transfer entropy and connection strength in the propagation path, a composite propagation score function is designed, which effectively realizes abnormal path identification and fault source tracing, thereby solving the limitations of existing technologies in topology modeling, multi-source anomaly identification and path tracing. Summary of the Invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] Therefore, the technical problems solved by the present invention are: the existing power network anomaly detection methods have problems such as insufficient topology modeling capabilities, incomplete node collaborative identification, and missing anomaly tracing paths, as well as how to accurately identify multi-point anomalies based on the power network structure and achieve precise positioning of the fault path.

[0006] To solve the above technical problems, the present invention provides the following technical solutions: a method for detecting anomalies in a power network, comprising constructing a neuron-like graph model for a power network, abstracting various types of power equipment into neuron nodes, defining the connection relationship between devices as the directed edge of the graph, setting a competitive neuron anomaly detection mechanism, adopting a multi-factor anomaly scoring function, and combining an improved Winner-Take-All strategy to set a dynamic activation threshold to achieve parallel activation of multiple abnormal nodes; designing a topology-aware connection weight adaptive adjustment mechanism, adopting a composite gradient descent method to achieve dynamic optimization of connection strength, constructing a multi-level neural network structure, and performing anomaly detection in each layer of neurons through forward propagation, and achieving cross-layer optimization adjustment based on feedback signals; constructing an abnormal path propagation model based on propagation phase difference and information entropy, adopting a propagation scoring function that includes a combination of abnormal strength, connection weight, phase disturbance and transfer entropy, and combining a weighted shortest path algorithm to identify abnormal paths, and tracing faults by matching with historical abnormal patterns.

[0007] As a preferred solution of the power network anomaly detection method described in the present invention, the neuron node state vector contains three types of real-time power parameters, among which voltage represents the amplitude of the node output voltage, current represents the actual power flow intensity of the node, and frequency represents the power frequency stability of the node power supply side. They are synchronously updated through a unified sampling period and remain fully involved in the anomaly score calculation process at each time step.

[0008] As a preferred solution of the power network anomaly detection method described in the present invention, the anomaly score function includes a state deviation normalization term, a hyperbolic tangent transformation term of the state change rate, and a cosine modulation term of the state phase disturbance. Each term has different time dimension characteristics, which are used to simulate the multimodal abnormal behavior of nodes under nonlinear dynamic disturbances, and are fused into a single anomaly score value in the form of weighted accumulation to guide the neuron activation state.

[0009] As a preferred solution of the power network anomaly detection method described in the present invention, the improved Winner-Take-All strategy includes a dynamic activation threshold determined by a linear combination of the median absolute deviation of the historical score sequence and the maximum anomaly score of the current time window. The threshold value is adaptively adjusted as the overall anomaly level of the node changes. During anomaly activation, multiple high-scoring nodes can be allowed to enter an abnormal state at the same time.

[0010] As a preferred solution of the power network anomaly detection method described in the present invention, the connection weight adaptive adjustment mechanism includes constructing a multi-source driven weight optimization expression by fusing the exponential decay function of the electrical distance between nodes, the gradient descent derivative of the error function, and the sensitivity modulation factor of the disturbance residual to the weight change. The weight update is recalculated at each time step to ensure that the connection strength is consistent with the actual topological state of the system in real time.

[0011] As a preferred solution of the power network anomaly detection method described in the present invention, the three-layer neural network structure includes a power supply layer composed of power plants and main substations, which monitors the fluctuation of power generation output and the overall voltage change trend of the system in real time; the transmission layer contains trunk transmission line nodes and intermediate substations, which are used to detect long-path abnormal propagation phenomena during energy transmission; and the distribution layer is composed of terminal load nodes, electricity meters and distribution switches to identify local abnormal changes on the user side.

[0012] As a preferred solution of the power network anomaly detection method described in the present invention, the abnormal path propagation model introduces the squared term of the abnormal intensity of each connection in the propagation path, the sinusoidal function modulation term of the phase angle difference between nodes, the logarithmic term of the connection transfer entropy and the topological connection reachability factor, and constructs a propagation score function in combination. As the path cost function, an improved weighted shortest path algorithm is used to identify the propagation path, model and visualize the abnormal diffusion path, and achieve high-precision fault source location in conjunction with historical abnormal data set matching.

[0013] Another object of the present invention is to provide a power network anomaly detection system that can solve the problems of insufficient topological relationship modeling, low anomaly recognition sensitivity, and poor multi-point fault recognition capability in current power network anomaly detection technology by constructing a neuron-like graph model and introducing a multi-factor dynamic activation mechanism.

[0014] As a preferred solution of the power network anomaly detection system described in the present invention, it includes:

[0015] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement a method for detecting abnormalities in a power network.

[0016] A computer-readable storage medium stores a computer program, which implements the steps of a power network anomaly detection method when executed by a processor.

[0017] Beneficial effects of the present invention: The power network anomaly detection method provided by the present invention constructs a neuron-like graph model and introduces a multi-factor anomaly activation mechanism, which can realize comprehensive perception of the power grid node status under multi-dimensional time characteristics, effectively improve the sensitivity of anomaly recognition and the ability of simultaneous activation of multiple points, and combine the electrical distance between nodes, error gradient information and disturbance residual change trend. Through the composite gradient descent model, the neuron connection strength is dynamically updated to achieve real-time response and adaptation to changes in the power grid topology structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0019] Figure 1 This is an overall flow chart of a power network anomaly detection method provided by the first embodiment of the present invention. DETAILED DESCRIPTION

[0020] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in this field without creative work should fall within the scope of protection of the present invention.

[0021] Example 1, with reference to Figure 1 , as an embodiment of the present invention, provides a power network anomaly detection method, comprising:

[0022] S1: Construct a neuron graph model for power networks, abstract various types of power equipment into neuron nodes, define the connection relationship between devices as directed edges of the graph, set up a competitive neuron anomaly detection mechanism, adopt a multi-factor anomaly scoring function, and combine the improved Winner-Take-All strategy to set a dynamic activation threshold to achieve parallel activation of multiple abnormal nodes.

[0023] Furthermore, structural topological data for each device in the power system (such as substations, power plants, load nodes, and transmission lines) is acquired to form a structural graph dataset. The neuron node state vector contains three real-time power parameters: voltage represents the magnitude of the node's output voltage, current represents the actual power flow intensity at the node, and frequency represents the power frequency stability of the node's power supply. These parameters are synchronously updated using a unified sampling cycle and fully participate in the anomaly score calculation process at each time step.

[0024] Abstract each electrical device in the power network as a neuron node V i , the connection relationship between devices is a directed edge E ij A weighted directed graph G(V,E,W) is constructed, where V is the set of all device nodes in the power grid; E is the connection relationship between nodes; and W is the connection strength between nodes, which represents the transmission capacity of information or energy.

[0025] Each node defines a state vector S i (t)=[v i (t),i i (t),f i (t)],v i (t),i i (t),f i (t) represent the voltage, current and frequency operating parameters of the device at time t respectively.

[0026] It should be noted that the anomaly score function consists of a state deviation normalization term, a hyperbolic tangent transformation term of the state change rate, and a cosine modulation term of the state phase disturbance. Each term has different time dimension characteristics, which are used to simulate the multimodal abnormal behavior of nodes under nonlinear dynamic disturbances, and are fused into a single anomaly score value in the form of weighted accumulation to guide the neuron activation state.

[0027] It should also be noted that the improved Winner-Take-All strategy includes a dynamic activation threshold determined by a linear combination of the median absolute deviation of the historical score sequence and the maximum anomaly score of the current time window. The threshold value is adaptively adjusted as the overall anomaly level of the node changes. During anomaly activation, multiple high-scoring nodes can be allowed to enter the abnormal state at the same time.

[0028] At each time t, calculate the anomaly score A for each node i (t), calculated based on the deviation between its state vector and the historical normal state:

[0029]

[0030] in is the historical average state of node i.

[0031] An improved WTA activation mechanism is introduced. By setting a dynamic activation threshold θ(t), nodes with scores higher than the threshold are regarded as abnormally activated nodes:

[0032] IfA i (t)≥θ(t), then V i is activated

[0033] The threshold θ(t) can be adaptively adjusted according to the variance of the current anomaly distribution, allowing multiple anomalies to be activated simultaneously and improving the detection capability of concurrent anomalies and local anomalies.

[0034] S2: Design a topology-aware adaptive adjustment mechanism for connection weights, use the composite gradient descent method to achieve dynamic optimization of connection strength, build a multi-level neural network structure, perform anomaly detection on neurons in each layer through forward propagation, and implement cross-layer optimization adjustment based on feedback signals.

[0035] Furthermore, the connection weight adaptive adjustment mechanism includes constructing a multi-source driven weight optimization expression by fusing the exponential decay function of the electrical distance between nodes, the gradient descent derivative of the error function, and the modulation factor of the sensitivity of the disturbance residual to the weight change. The weight update is recalculated at each time step to ensure that the connection strength is consistent with the actual topological state of the system in real time.

[0036] In the initial stage, the edge weights are set according to the electrical connection relationship and distance between nodes. Indicates the information transmission capability. The closer the voltage level, the higher the connection strength. The shorter the actual physical distance, the greater the initial weight.

[0037] According to the node status and historical data distribution, the gradient descent method is used to adjust the connection weights between neurons:

[0038]

[0039] in, is the connection strength from node p to node q at time t, α is the learning rate, γ is the topological attenuation coefficient, D pq is the electrical or geographical distance between nodes p and q, is the abnormality score of node p, is the error function of node q, which is usually defined as the square of the Euclidean distance between the predicted state and the actual state, Δ q (t) is the residual disturbance caused by abnormal propagation, is the sensitivity of the perturbation to the connection weights.

[0040] It should be noted that the three-layer neural network structure includes a power supply layer composed of power plants and main substations, which monitors the fluctuation of power generation output and the overall voltage change trend of the system in real time; a transmission layer containing trunk transmission line nodes and intermediate substations, which is used to detect long-path abnormal propagation phenomena during energy transmission; and a distribution layer composed of terminal load nodes, electricity meters and distribution switches, which identifies local abnormal changes on the user side.

[0041] Specifically, the hierarchical division divides the entire neural network into three layers based on the functional structure of the power system: the power supply layer, which includes power stations and main substations, monitors system-level power generation and voltage fluctuations; the transmission layer, which covers trunk transmission lines and intermediate stations, monitors anomalies during energy transmission; and the distribution layer, which covers end users, meters, and load nodes, is primarily responsible for local anomaly detection and load fluctuation identification. Each layer of neurons calculates anomaly outputs based on its input and state; anomaly signals are reported layer by layer, gradually converging to the power supply layer. The upper layer can reversely adjust the WTA thresholds and connection weights of each layer based on the anomaly activation signals collected from the lower layers to enhance the model's global consistency and detection sensitivity.

[0042] S3: Construct an abnormal path propagation model based on propagation phase difference and information entropy. Use a propagation scoring function that combines abnormal strength, connection weight, phase disturbance, and transfer entropy. Combined with a weighted shortest path algorithm, identify abnormal paths and trace faults by matching them with historical abnormal patterns.

[0043] Furthermore, the abnormal path propagation model introduces the squared term of the abnormal intensity of each connection in the propagation path, the sinusoidal function modulation term of the phase angle difference between nodes, the logarithmic term of the connection transfer entropy and the topological connection reachability factor, and constructs a propagation score function in combination. It uses this function as the path cost function and uses an improved weighted shortest path algorithm to identify the propagation path, model and visualize the abnormal diffusion path, and achieve high-precision fault source location by matching historical abnormal data sets.

[0044] The abnormally activated nodes are constructed as a subgraph G′(V′,E′), where the nodes are activated neurons and the edges are abnormal propagation paths. Define the abnormal propagation weight ω ij :

[0045]

[0046]

[0047] Among them, ξ xy (t) is the propagation intensity of the anomaly from node x to y at time t, is the abnormal transfer entropy value of the connection history, representing the degree of information flow asymmetry, Ω xy (t) is the current connection weight, Γ xy is the current phase difference, is the node phase angle, χ xy is the topological accessibility factor (1 or 0), indicating whether there is a structural connection, Ψ * (t) is the minimum abnormal path sequence at time t.

[0048] Example 2 is the second embodiment of the present invention, which is different from the previous embodiment in that:

[0049] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0050] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0051] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.

[0052] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0053] Embodiment 3 is the third embodiment of the present invention, which provides a system for detecting anomalies in a power network, including a power network neural graph modeling module, a topology-aware connection optimization module, and an abnormal path identification module;

[0054] Among them, the power network neural graph modeling module is used to construct a power network neuron graph model, abstract various types of power equipment into neuron nodes, define the connection relationship between devices as the directed edge of the graph, set a competitive neuron anomaly detection mechanism, adopt a multi-factor anomaly scoring function, and combine the improved Winner-Take-All strategy to set a dynamic activation threshold to achieve parallel activation of multiple abnormal nodes; the topology-aware connection optimization module is used to design a topology-aware connection weight adaptive adjustment mechanism, adopt a composite gradient descent method to achieve dynamic optimization of connection strength, and construct a multi-level neural network structure. Each layer of neurons performs anomaly detection through forward propagation, and realizes cross-layer optimization adjustment based on feedback signals; the abnormal path identification module is used to construct an abnormal path propagation model based on propagation phase difference and information entropy, adopts a propagation scoring function that includes the combined calculation of abnormal strength, connection weight, phase disturbance and transfer entropy, and combines the weighted shortest path algorithm to identify abnormal paths, and perform fault tracing by matching with historical abnormal patterns.

[0055] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for detecting anomalies in a power network, characterized in that: include: A neuron-like graph model for power networks is constructed, abstracting various types of power equipment into neuron nodes. The connections between devices are defined as directed edges in the graph. A competitive neuron anomaly detection mechanism is established, using a multi-factor anomaly scoring function combined with an improved Winner-Take-All strategy to set dynamic activation thresholds and enable parallel activation of multiple abnormal nodes. Design a topology-aware connection weight adaptive adjustment mechanism, use a composite gradient descent method to achieve dynamic optimization of connection strength, build a multi-layer neural network structure, use forward propagation to detect anomalies in each layer of neurons, and achieve cross-layer optimization and adjustment based on feedback signals; An abnormal path propagation model based on propagation phase difference and information entropy is constructed. A propagation scoring function that combines abnormal strength, connection weight, phase disturbance and transfer entropy is adopted, and a weighted shortest path algorithm is combined to identify abnormal paths. Fault tracing is performed by matching with historical abnormal patterns.

2. The power network anomaly detection method according to claim 1, wherein: The neuron node state vector contains three types of real-time power parameters, among which voltage represents the amplitude of the node output voltage, current represents the actual power flow intensity of the node, and frequency represents the power frequency stability of the node power supply side. It is synchronously updated through a unified sampling period and remains fully involved in the anomaly score calculation process at each time step.

3. The power network anomaly detection method according to claim 2, wherein: The anomaly score function consists of a state deviation normalization term, a hyperbolic tangent transformation term of the state change rate, and a cosine modulation term of the state phase disturbance. Each term has different time dimension characteristics and is used to simulate the multimodal abnormal behavior of nodes under nonlinear dynamic disturbances. The functions are fused into a single anomaly score value in the form of weighted accumulation to guide the neuron activation state.

4. The power network anomaly detection method according to claim 3, wherein: The improved Winner-Take-All strategy includes a dynamic activation threshold determined by a linear combination of the median absolute deviation of the historical score sequence and the maximum anomaly score of the current time window. The threshold value is adaptively adjusted as the overall anomaly level of the node changes. During anomaly activation, multiple high-scoring nodes can be allowed to enter an abnormal state at the same time.

5. The power network anomaly detection method according to claim 4, wherein: The connection weight adaptive adjustment mechanism includes forming a multi-source driven weight optimization expression by fusing the exponential decay function of the electrical distance between nodes, the gradient descent derivative of the error function, and the modulation factor of the sensitivity of the disturbance residual to the weight change. The weight update is recalculated at each time step to ensure that the connection strength is consistent with the actual topological state of the system in real time.

6. The power network anomaly detection method according to claim 5, wherein: The three-layer neural network structure includes a power supply layer consisting of power plants and main substations, which monitors the fluctuation of power generation output and the overall voltage change trend of the system in real time; a transmission layer containing trunk transmission line nodes and intermediate substations, which is used to detect long-path abnormal propagation phenomena during energy transmission; and a distribution layer consisting of terminal load nodes, electricity meters and distribution switches, which identifies local abnormal changes on the user side.

7. The power network anomaly detection method according to claim 6, wherein: The abnormal path propagation model introduces the squared term of the abnormal intensity of each connection in the propagation path, the sinusoidal function modulation term of the phase angle difference between nodes, the logarithmic term of the connection transfer entropy, and the topological connection reachability factor to construct a propagation score function. This function is used as the path cost function. An improved weighted shortest path algorithm is used to identify the propagation path, model the abnormal diffusion path, and visually trace the source. In combination with the matching of historical abnormal data sets, high-precision fault source location is achieved.

8. A system using the power network anomaly detection method according to any one of claims 1 to 7, characterized in that: It includes a power network neural graph modeling module, a topology-aware connection optimization module, and an abnormal path identification module; The power network neural graph modeling module is used to construct a power network neuron graph model, abstracting various types of power equipment into neuron nodes. The connection relationship between devices is defined as the directed edge of the graph. A competitive neuron anomaly detection mechanism is set up, using a multi-factor anomaly scoring function and an improved Winner-Take-All strategy to set a dynamic activation threshold and realize the parallel activation of multiple abnormal nodes. The topology-aware connection optimization module is used to design a topology-aware connection weight adaptive adjustment mechanism, adopt a composite gradient descent method to achieve dynamic optimization of connection strength, construct a multi-level neural network structure, perform anomaly detection on neurons in each layer through forward propagation, and achieve cross-layer optimization adjustment based on feedback signals; The abnormal path identification module is used to build an abnormal path propagation model based on propagation phase difference and information entropy. It adopts a propagation scoring function that combines abnormal strength, connection weight, phase disturbance and transfer entropy, and combines it with a weighted shortest path algorithm to identify abnormal paths. Fault tracing is performed by matching with historical abnormal patterns.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the power network anomaly detection method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the power network anomaly detection method according to any one of claims 1 to 7 are implemented.

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