Development type single-phase earth fault real-model test device and control method

Abstract

The invention relates to a development type single-phase earth fault real-model test device and a control method, the development type single-phase earth fault real-model test device is connected in a whole power grid and comprises a fault intelligent generation module, and the fault intelligent generation module comprises a dynamic resistance simulation unit and an intelligent switching control system. And the intelligent switching control system is used for controlling the access resistance value and the access time of the resistor in the dynamic resistance simulation unit. The dynamic resistance simulation unit structure is of a three-level resistance topology and is combined with a mixed switching matrix of a vacuum relay and a solid-state relay. The intelligent switching control system is used for realizing the switching of the resistor at a current zero crossing point, the intelligent switching control system comprises a low-power-consumption control circuit and a signal acquisition circuit, the structure is matched with the control method, the continuous or step dynamic change of the grounding resistor can be accurately simulated, the problem of transient impact in the resistor switching process is solved, and the stability of the grounding resistor is improved. And a standardized and quantifiable test platform is provided for performance assessment of power distribution network fault handling equipment.

Description

Technical Field

[0001] This invention relates to the field of power system testing and detection technology, and is an advanced single-phase grounding fault simulation test device and control method. Background Technology

[0002] Single-phase ground faults are the most common type of fault in distribution networks, accounting for 70%-80% of all distribution network faults. To verify the performance of new fault handling technologies and equipment, full-scale testing has become a core verification method because it can be conducted using real power equipment under conditions close to actual field conditions. However, existing full-scale testing devices and methods have the following key shortcomings: The scenario simulation lacks flexibility: Traditional fault simulation relies on manual line replacement, phase replacement and grounding medium replacement, which is not only inefficient and prone to human error, but also difficult to quickly switch between complex fault scenarios such as different grounding resistance, grounding medium (soil, sand, cement, etc.) and arc grounding.

[0003] Poor system scalability: The existing test system has a fixed structure and cannot be easily expanded or upgraded in terms of functionality according to new test requirements (such as new fault types or T-connection line topology).

[0004] The test lacks both safety and simulation accuracy: there are safety hazards in high-voltage and high-current test scenarios; conventional relay protection equipment cannot accurately distinguish between single-phase ground fault current and phase-to-phase short-circuit current, which can easily lead to protection maloperation or failure to operate; at the same time, traditional simulation and dynamic model test cannot reproduce the characteristics of real arc ground fault.

[0005] The existing devices lack the ability to simulate evolving faults. They can only simulate faults with fixed resistance values ​​and cannot reproduce the dynamic changes in grounding resistance caused by factors such as arc burning, insulation deterioration, and rainwater intrusion. They also cannot assess the response performance of protection devices to evolving faults. Furthermore, traditional resistor switching is prone to operation at arbitrary voltage / current phases, introducing transient impacts and high-frequency interference, which does not conform to the physical law of natural changes in resistance at the current zero-crossing point in real faults. The preset resistance-time (Rt) curve cannot be dynamically adjusted according to real-time grid parameters (ground capacitance current, system voltage fluctuations), resulting in a disconnect between simulated operating conditions and the actual field conditions. Summary of the Invention

[0006] In view of the shortcomings of the existing technology, the purpose of this invention is to provide an advanced single-phase grounding fault simulation test device and control method.

[0007] The present invention is achieved through the following technical solution: an advanced single-phase grounding fault simulation test device: connected in the overall power grid, including a fault intelligent generation module, wherein the fault intelligent generation module includes a dynamic resistance simulation unit and an intelligent switching control system, and the connection resistance value and connection time of the resistor in the dynamic resistance simulation unit are controlled by the intelligent switching control system. The dynamic resistance simulation unit is used to achieve switching from 100Ω to 5000Ω. The dynamic resistance simulation unit adopts a three-level resistance topology of main range module + fine adjustment module + error compensation module, combined with a hybrid switching matrix of vacuum relay + solid-state relay. The intelligent switching control system is used to switch the resistor at the zero-crossing point of the current. The intelligent switching control system includes a low-power control circuit and a signal acquisition circuit. The low-power control circuit is used to provide a stable and switchable power supply for the controller and actuator, and to implement low-power management and relay driving. The signal acquisition circuit is used to accurately sample, filter and digitize the electrical quantities of the power grid, and to provide real-time phase and amplitude information to the control unit to support zero-crossing judgment and timing calculation.

[0008] The main range module includes resistors of 3200Ω, 1600Ω, 800Ω, and 400Ω, connected in series. The 400Ω resistor is connected in parallel with the circuit formed by the series connection of the 3200Ω, 1600Ω, and 800Ω resistors. The fine adjustment module includes resistors of 200Ω, 100Ω, 80Ω, 40Ω, 20Ω, and 10Ω, all connected in parallel with the main range module. The error compensation module includes resistors of 5Ω, 2Ω, and 1Ω, connected in parallel to the main circuit as needed.

[0009] The hybrid switching matrix includes a high-voltage vacuum relay for controlling the switching state of the main range module and a high-speed solid-state relay for controlling the switching state of the fine adjustment module and the error compensation module. The high-voltage vacuum relay has a rated withstand voltage ≥15kV, a rated current ≥10A, and a mechanical life ≥100,000 cycles. The high-speed solid-state relay has a response time ≤0.1ms and is arc-free during switching. Each of the main range module, fine adjustment module, and error compensation module has an independent switching device. The drive circuit has a built-in opto-isolation unit, which is used to prevent signal crosstalk between modules and absorb transient energy during switching to eliminate sudden changes in loop current.

[0010] The low-power control circuit includes a step-down filter power supply based on capacitor step-down and silicon controlled rectifier, a voltage regulation and overvoltage protection circuit, a reverse-current protection diode and a current limiting element, and a low-power electronic switching unit with a field-effect transistor as the switch, so that the system maintains the lowest power consumption when switching between standby and operation phases; the low-power control circuit provides a 16 V / 48 V drive voltage for the magnetic latching relay and, together with the current limiting element and drive timing output control signal, accepts microcontroller instructions to realize precise timing control of the relay, so as to ensure that the resistor is engaged or disengaged within the target voltage cycle.

[0011] The low-power control circuit uses two-phase AC power (A and B), combined with capacitor C1 and a thyristor rectifier to form a capacitor-based step-down rectified and filtered power supply. A field-effect transistor (FET) is selected as the low-power electronic switch. The FET's power consumption is adjusted via the MCU_IO1 pin of the microcontroller control signal: when high, the FET is turned on, and the forward current flows to GND through the thyristor rectifier bridge; when low, the FET is turned off. The circuit has a built-in overvoltage protection unit, which includes Zener diodes D1 and D2 and resistor R3. Zener diode D1 breaks down in reverse after the voltage exceeds the limit, cutting off the current flowing to the microcontroller; diode D2 prevents reverse current flow, and resistor R3 limits the current. The low-power control circuit can output 16V and 48V, maintaining a stable output voltage through charging / discharging mode switching.

[0012] The signal acquisition circuit includes a voltage input based on voltage divider and anti-interference filtering, an analog front-end and ADC interface, and peripheral circuitry for a dedicated metering chip RN7302. The RN7302 performs voltage / current acquisition, phase detection, normalization, and calibration, and reports zero-point / edge information and power grid parameters to the MCU via a digital interface. The MCU then uses this measurement data and the relay operating time T stored in Flash memory to... r Perform timing calculations and generate precise input / output control commands.

[0013] The control method for resistor switching in the aforementioned advanced single-phase ground fault simulation test device: The switching control program first reads the relay action duration data from the Flash memory and completes the calibration before entering the normal working process: Resistor connection: Start phase current zero-point detection. When zero point is detected, start timer. The timing duration is half a grid cycle minus the relay action time. After the timing threshold is reached, send closing command. The relay completes connection at the next zero point of the grid after the action time. Resistor disconnection: Start phase current zero-point detection. When zero point is detected, start a timer. The timing duration is 5 / 4 power grid cycles minus the relay action time. After reaching the threshold, send a disconnection command. The relay completes the disconnection at the next peak of the power grid after the action time.

[0014] The normal working process is as follows: After the system starts up, it first reads the Flash memory to check if it contains calibration data for the relay action duration. If no valid calibration information is detected, the system will generate an error message and enter the calibration process on the calibration bench. If the calibration data exists, it will be read and stored in an internal variable, and the system will then switch to normal operation. During normal operation, the device executes corresponding connection or disconnection operations based on externally input commands. When the system receives a connection command, it first performs zero-point or edge detection. If no zero-point is detected, the device remains in a waiting state. After a zero-point is detected, the system starts a timer and compensates for a time delay of (10-Tr) ms, where Tr is the inherent operating time of the relay. After the timer expires, the control unit issues a connection control command to activate the relay. The relay completes its operation after its own operating time Tr ms, thus achieving the connection of the resistor within the current voltage cycle. When the system receives a cut-off command, the process is similar to the input operation. Zero point or edge detection is also required. After zero point is detected, the system sets a timer delay of (25-Tr) ms and issues a cut-off control command after the timer is completed, causing the relay to disconnect. The relay finally cuts off the resistor after completing the action time Tr ms. This action will take effect in the following voltage cycle.

[0015] The beneficial effects of this invention are as follows: 1. Realistic reproduction of evolving faults: It can accurately simulate the dynamic changes in grounding resistance under scenarios such as electric arc burning, insulation degradation, and rainwater intrusion, filling the technical gap that fixed resistance devices cannot simulate the fault development process. 2. Ensuring test accuracy and safety: The zero-crossing current switching design eliminates transient impacts and high-frequency interference, matching the physical laws of real faults; the three-level resistor topology and error compensation module achieve resistance accuracy of ≤±0.5%, and millisecond-level time control ensures test repeatability; 3. Enhance test flexibility and adaptability: Supports the customization, storage and retrieval of multiple types of Rt change curves, and can adjust the simulation logic according to real-time power grid parameters to adapt to the test requirements of different distribution network topologies and fault scenarios; 4. Enhance the depth of equipment performance assessment: Provide a standardized platform for assessing the dynamic response capabilities of fault selection, location, and protection devices. It can fully capture the transient electrical characteristics of nodes with changing resistance, thereby improving the reliability and reference value of test results. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is an overall connection diagram of the device of the present invention with the power grid.

[0018] Figure 2 This is a schematic diagram of a dynamic resistance simulation unit; Figure 3 This is a schematic diagram of a low-power control circuit. Figure 4 This is a schematic diagram of the signal acquisition circuit. Figure 5 This is a flowchart of the switching control process; Figure 6 A schematic diagram of the precise resistor insertion process; Figure 7 This is a schematic diagram of the precise removal process of a resistor. Figure 8 This is a waveform diagram of the voltage applied at the non-zero point of the resistor in Example 1; Figure 9 This is a waveform diagram of the resistor being switched on at zero point in Example 1; Figure 10 This is a waveform diagram of the resistor peak cutoff voltage in Example 1; Figure 11 This is the current waveform when the resistor is disconnected from the power grid in Example 1; Figure 12 This is a graph showing the resistance change in Example 2. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0020] A simulated single-phase ground fault test device is proposed, employing a modular architecture. Through the collaborative design of a central control unit and a fault intelligent generation module, it achieves accurate simulation of evolving single-phase ground faults. The overall connection relationship is as follows: Figure 1As shown. The fault intelligent occurrence module is the core execution unit and must meet the following design specifications: ① Resistance value coverage of the entire range of 100Ω~5000Ω, supporting any target resistance value combination; ② Compatible with various types of Rt change curves such as linear, exponential decay, logarithmic decay, piecewise step, and smooth transition; ③ Resistance value combination error ≤ ±1%, time axis control accuracy ≤ 1ms, and no transient impact during switching; ④ Support for custom curve parameters, preview, storage, and retrieval, adapting to the needs of multiple testing scenarios.

[0021] 1. Dynamic Resistance Simulation Unit Architecture

[0022] The dynamic resistance simulation unit adopts a three-level resistance topology of "main range module + fine adjustment module + error compensation module" and a hybrid switching matrix of "vacuum relay + solid-state relay" to achieve accurate switching across the full range of 100Ω to 5000Ω. Its structure is shown in Figure 2.

[0023] (1) Selection and topology of three-level resistor modules

[0024] All resistor modules are made of non-inductive nickel-chromium alloy (temperature coefficient ≤ ±50ppm / ℃) and are sealed and insulated (withstand voltage ≥12kV, protection rating IP54). Specific configurations are shown in the table below. Table 1: Resistor Module Configuration Parameter Table

[0025] (2) Hybrid switching matrix design

[0026] To address the issues of slow response and transient impact during switching in traditional switches, switching devices are configured differently at the module level: a. Main range module switching: High-voltage vacuum relays (rated withstand voltage ≥15kV, rated current ≥10A, mechanical life ≥100,000 times) are selected to adapt to the high voltage and high current conditions of the main circuit and ensure the safety of switching with large resistance values. b. Fine adjustment / compensation module switching: High-speed solid-state relays (response time ≤ 0.1ms, no arcing during switching) are selected to achieve precise switching at the millisecond level with small resistance values, avoiding transient impacts; c. Matrix topology: It adopts a "hierarchical independent drive" architecture, with each module corresponding to an independent switching device. The drive circuit has a built-in opto-isolation unit (isolation voltage ≥2500V) to eliminate signal crosstalk between modules and absorb transient energy at the moment of switching to eliminate sudden changes in loop current.

[0027] 2. Design of Intelligent Switching Control System

[0028] The core objective of the intelligent switching control system is to achieve precise switching of resistors at the current zero-crossing point and avoid system overvoltage. Specifically, it includes three parts: low-power control circuit, signal acquisition circuit, and switching control process.

[0029] (1) Low power control circuit

[0030] The circuit uses two-phase AC power (A and B), combined with capacitor C1 and a thyristor rectifier to form a capacitor-based step-down rectified and filtered power supply. A field-effect transistor (FET) is selected as a low-power electronic switch, and its power consumption can be adjusted via a microcontroller control signal (MCU_IO1 pin): when high, the FET is turned on, and the forward current flows to GND through the thyristor rectifier bridge; when low, the FET is turned off. The circuit has a built-in overvoltage protection unit: Zener diode D1 (with a withstand voltage threshold of 48V) can reverse break down after the voltage exceeds the limit, cutting off the current flowing to the microcontroller; diode D2 provides anti-current reverse flow function, and resistor R3 is responsible for current limiting. The power output adapts to the needs of different devices: when powering a magnetically latched relay, VCC is 16V, which rises to 48V after receiving an action command to drive the relay; VDD provides a 3.3V operating voltage for the microcontroller. Oscilloscope testing shows that the circuit can maintain a stable output voltage through charging and discharging mode switching, and its control waveform is shown in Figure 3.

[0031] (2) Signal acquisition circuit

[0032] Voltage acquisition is based on the voltage divider principle. The analog signal is converted by AD and then input to the dedicated metering chip RN7302. This chip is compatible with three-phase three-wire / four-wire systems and can complete the acquisition, correction and processing of parameters such as grid voltage and current. Its main circuit and peripheral circuit are shown in Figure 4 (a is the main circuit for signal acquisition, and b is the peripheral circuit for the acquisition chip).

[0033] (3) Resistor switching control process

[0034] The switching control program must first read the relay action duration data from the Flash memory and complete the calibration before entering the normal working process. The specific logic is shown in Figure 5. Resistor connection: Start phase current zero-point detection. When zero point is detected, start timer. The timing duration is half a grid cycle minus the relay action time. After the timing threshold is reached, send closing command. The relay completes connection at the next zero point of the grid after the action time. The process is shown in Figure 6. Resistor disconnection: Start phase current zero-point detection. When zero point is detected, start a timer. The timing duration is 5 / 4 power grid cycles minus the relay action time. After reaching the threshold, send a disconnection command. The relay completes disconnection at the next peak of the power grid after the action time. The process is shown in Figure 7.

[0035] Example 1: Low-voltage switch prototype testing A low-voltage synchronous switch prototype was built and connected to the switching test bench. The test steps are as follows: (1) Insulation protection treatment was applied to the switching switch; (2) The on / off interval of the 12V switching signal was adjusted by the time relay on the cabinet door panel (the interval time matched the capacitor discharge time); (3) After completing the line connection and self-test, the power supply of the test bench was turned on and the main switch was closed; (4) The “start” button was pressed to output 380V AC power, and the “stop” button was pressed to cut off the power. The switching switch can be switched cyclically according to the set frequency; (5) The electrical parameters at both ends of the capacitor were monitored by an oscilloscope: the grid voltage fluctuated significantly during random switching, while the zero-point input and peak cut-off mode of the present invention can achieve stable switching without overvoltage and without inrush current.

[0036] like Figures 8-11 As shown in the waveform diagram, we can see that the grid voltage fluctuated significantly during the random switching experiment. The synchronous switch designed in this paper can achieve zero-point switching and peak-point switching, and no overvoltage or inrush current phenomenon occurred in the grid during the switching process.

[0037] Example 2: Typical Case of Developmental Fault Simulation Test objective: To simulate a phase A ground fault on a 10kV line (initial resistance 4000Ω, metallic ground fault that drops to 300Ω within 20s) and evaluate the response performance of the protection device under test. The resistance change curve is shown in Figure 12.

[0038] Implementation steps: 1. Equipment preparation: Set up the test system and complete the placement and wiring connection of the mobile resistance box; 2. Parameter settings: Set the parameters in the human-machine interface of the central measurement and control unit: the faulty line is Line 1, the faulty phase is phase A; the total resistance is 4000Ω at t=0ms, drops to 2000Ω at t=1s and changes stepwise according to the preset logic, and the total fault duration is 20s; 3. Test execution: After the control unit completes the safety self-test, it triggers a fault at the zero-crossing angle of the voltage; it drives the high-speed switching matrix to adjust the resistor combination according to the preset time nodes, the high-precision waveform recorder records the electrical waveform throughout the process, and the dedicated protection unit monitors the test safety in real time; 4. Data Analysis: An analysis report is automatically generated after the test, focusing on comparing the zero-sequence current / voltage change characteristics at the resistance change nodes with the action records of the tested equipment to complete the performance evaluation.

Claims

1. A simulated single-phase ground fault test device, characterized in that: Connected to the overall power grid, it includes a fault intelligent generation module, which includes a dynamic resistance simulation unit and an intelligent switching control system. The intelligent switching control system controls the connection resistance value and connection time of the resistor in the dynamic resistance simulation unit. The dynamic resistance simulation unit is used to achieve switching from 100Ω to 5000Ω. The dynamic resistance simulation unit adopts a three-level resistance topology of main range module + fine adjustment module + error compensation module, combined with a hybrid switching matrix of vacuum relay + solid-state relay. The intelligent switching control system is used to switch the resistor at the zero-crossing point of the current. The intelligent switching control system includes a low-power control circuit and a signal acquisition circuit. The low-power control circuit is used to provide a stable and switchable power supply for the controller and actuator, and to implement low-power management and relay driving. The signal acquisition circuit is used to accurately sample, filter and digitize the electrical quantities of the power grid, and to provide real-time phase and amplitude information to the control unit to support zero-crossing judgment and timing calculation.

2. A simulated single-phase ground fault test device, characterized in that: The main range module includes resistors of 3200Ω, 1600Ω, 800Ω, and 400Ω, connected in series. The 400Ω resistor is connected in parallel with the circuit formed by the series connection of the 3200Ω, 1600Ω, and 800Ω resistors. The fine adjustment module includes resistors of 200Ω, 100Ω, 80Ω, 40Ω, 20Ω, and 10Ω, all connected in parallel with the main range module. The error compensation module includes resistors of 5Ω, 2Ω, and 1Ω, connected in parallel to the main circuit as needed.

3. The advanced single-phase ground fault simulation test device according to claim 1, characterized in that: The hybrid switching matrix includes a high-voltage vacuum relay for controlling the switching state of the main range module and a high-speed solid-state relay for controlling the switching state of the fine adjustment module and the error compensation module. The high-voltage vacuum relay has a rated withstand voltage ≥15kV, a rated current ≥10A, and a mechanical life ≥100,000 cycles. The high-speed solid-state relay has a response time ≤0.1ms and is arc-free during switching. Each of the main range module, fine adjustment module, and error compensation module has an independent switching device. The drive circuit has a built-in opto-isolation unit, which is used to prevent signal crosstalk between modules and absorb transient energy during switching to eliminate sudden changes in loop current.

4. The advanced single-phase ground fault simulation test device according to claim 1, characterized in that: The low-power control circuit includes a step-down filter power supply based on capacitor step-down and silicon controlled rectifier, a voltage regulation and overvoltage protection circuit, a reverse-current protection diode and a current limiting element, and a low-power electronic switching unit with a field-effect transistor as the switch, so that the system maintains the lowest power consumption when switching between standby and operation phases; the low-power control circuit provides a 16 V / 48 V drive voltage for the magnetic latching relay and, together with the current limiting element and drive timing output control signal, accepts microcontroller instructions to realize precise timing control of the relay, so as to ensure that the resistor is engaged or disengaged within the target voltage cycle.

5. The advanced single-phase ground fault simulation test device according to claim 4, characterized in that: The low-power control circuit uses two-phase AC power (A and B), combined with capacitor C1 and a thyristor rectifier to form a capacitor-based step-down rectifier and filter power supply. A field-effect transistor (FET) is selected as the low-power electronic switch. The FET power consumption is adjusted by the MCU_IO1 pin of the microcontroller control signal: when the level is high, the FET is turned on, and the forward current flows to GND through the thyristor rectifier bridge; when the level is low, the FET is turned off. The circuit has a built-in overvoltage protection unit, which includes a Zener diode D1, a diode D2, and resistor R3. The Zener diode D1 breaks down in reverse after the voltage exceeds the limit, cutting off the current flowing to the microcontroller. The diode D2 prevents reverse current flow, and the resistor R3 limits the current. The low-power control circuit can output 16V and 48V, and maintains a stable output voltage by switching between charging and discharging modes.

6. The advanced single-phase ground fault simulation test device according to claim 1, characterized in that: The signal acquisition circuit includes voltage input based on voltage divider and anti-interference filtering, analog front-end and ADC interface, and peripheral circuitry for the dedicated metering chip RN7302. The RN7302 performs voltage / current acquisition, phase detection, normalization, and calibration, and reports zero-point / edge information and grid parameters to the MCU via a digital interface. The MCU then uses this measurement data and the relay operating time T stored in Flash memory to perform the calculations. r Perform timing calculations and generate precise input / output control commands.

7. The resistor switching control method in a simulated single-phase ground fault test device according to any one of claims 1-6, characterized in that: The switching control program first reads the relay action duration data from the Flash memory and completes the calibration before entering the normal working process: Resistor connection: Start phase current zero-point detection. When zero point is detected, start timer. The timing duration is half a grid cycle minus the relay action time. After the timing threshold is reached, send closing command. The relay completes connection at the next zero point of the grid after the action time. Resistor disconnection: Start phase current zero-point detection. When zero point is detected, start a timer. The timing duration is 5 / 4 power grid cycles minus the relay action time. After reaching the threshold, send a disconnection command. The relay completes the disconnection at the next peak of the power grid after the action time.

8. The resistor switching control method according to claim 7, characterized in that: The normal working process is as follows: After the system starts up, it first reads the Flash memory to check if it contains calibration data for the relay action duration. If no valid calibration information is detected, the system will generate an error message and enter the calibration process on the calibration bench. If calibration data exists, it is read and stored in an internal variable, and the system then switches to normal operation. During normal operation, the device executes corresponding connection or disconnection operations based on externally input commands. When the system receives a connection command, it first performs zero-point or edge detection. If no zero-point is detected, the device remains in a waiting state. After a zero-point is detected, the system starts a timer and compensates for a time delay of (10-Tr) ms, where Tr is the inherent operating time of the relay. After the timer expires, the control unit issues a connection control command to activate the relay. The relay completes its operation after its own operating time Tr ms, thus achieving the connection of the resistor within the current voltage cycle. When the system receives a cut-off command, the process is similar to the input operation. Zero point or edge detection is also required. After zero point is detected, the system sets a timer delay of (25-Tr) ms and issues a cut-off control command after the timer is completed, causing the relay to disconnect. The relay finally cuts off the resistor after completing the action time Tr ms. This action will take effect in the following voltage cycle.

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