Adjusting method and system suitable for traction power supply network
Patent Information
- Application Number
- ZA202408544
- Authority / Receiving Office
- ZA · ZA
- Patent Type
- Patents
- Current Assignee / Owner
- Priority Date
- 2022-06-09
- Filing Date
- 2024-11-11
- Publication Date
- 2026-09-30
- Estimated Expiration
- 2042-09-08
AI Technical Summary
In electrified railways, due to factors such as power supply capacity, line impedance, power supply arm length, and the influence of multiple vehicles, the traction converter causes the grid-side current characteristic spectrum to overlap with the resonant frequency of the traction network, causing high-frequency resonance and serious harm, such as causing high voltage on the locomotive. Accidents such as lightning arrester explosion, train high-voltage equipment protection switch operation, and traction substation tripping.
Provide an adjustment system and method adapted to the traction power supply network. The traction network pressure is obtained in real time through the network voltage monitoring module. The central control module determines the high-frequency resonance phenomenon and sends control signals to the rectifier module and transmission control module to adjust the switching frequency or power. , to eliminate high-frequency resonance. The system includes a network voltage monitoring module, a central control module, a transmission control module and a rectifier module. It uses rectification phase-off control and dynamic frequency shifting measures to increase the switching frequency and reduce motor power to avoid high-frequency resonance.
It effectively eliminates high-frequency resonance, prevents accidents, enhances the adaptability of trains in different power supply intervals, and improves the stability and safety of the traction converter system.
Abstract
Description
A regulation method and system adapted to traction power supply network
[0001] CROSS-REFERENCE TO RELATED APPLICATIONS
[0002] The present disclosure claims priority to Chinese patent application CN202210658929.8 filed on June 9, 2022, entitled “A method and system for regulating a traction power supply network,” the entire contents of which are incorporated by reference into the present disclosure. Technical Field
[0003] The present disclosure relates to the technical field of power electronic converter control, and in particular to a regulation method and system adapted to a traction power supply network. Background Art
[0004] High-power locomotives and EMUs are the core equipment of electrified railways, and high-power traction converters are the "heart" of locomotives and EMUs. Installed on the underside of the train, the traction converter's primary function is to convert electrical energy between DC and AC, controlling the starting, braking, and speed of the AC traction motors through voltage and frequency regulation.
[0005] The AC input side of the traction converter is a four-quadrant converter connected to the traction grid via a traction transformer. Under certain operating conditions, factors such as power supply capacity, line impedance, power arm length, the influence of multiple trains, and train-grid coupling can cause the grid-side current characteristic spectrum of the locomotive in certain power supply intervals to overlap with the traction grid resonant frequency, triggering high-frequency resonance. High-frequency resonance can be very harmful, such as damaging the locomotive's high-voltage lightning arrester, triggering protective switches on the train's high-voltage equipment, and in severe cases, causing accidents such as tripping the traction substation.
[0006] Summary of the Invention
[0007] The purpose of the present disclosure is to provide a regulation method and system adapted to a traction power supply network, which can improve the above-mentioned problems.
[0008] The present disclosure provides a regulation system adapted to a traction power supply network, the regulation system being applied to a train traction conversion system, the train traction conversion system comprising a traction transformer, a plurality of rectifier modules, a plurality of inverter modules and a plurality of motors, the regulation system comprising: a grid voltage monitoring module connected to the input end of the traction transformer, for obtaining the current grid voltage of the traction network in real time; a central control module, for determining whether a high-frequency resonance phenomenon currently occurs based on the current grid voltage of the traction network, and sending a control signal to each of the rectifier modules and / or transmission control modules to eliminate the high-frequency resonance phenomenon when a high-frequency resonance phenomenon currently occurs; a transmission control module, for sending a drive instruction to each of the motors according to the control signal, for controlling the current power of each of the motors; and the rectifier module adjusting the switching frequency or shutting down according to the control signal.
[0009] The present disclosure provides a regulation method adapted to a traction power supply network, which is executed by the central control module of the regulation system adapted to the traction power supply network as described in any one of the first aspects, and the regulation method includes: obtaining the current network voltage of the traction network, and calculating the harmonic content ratio and characteristic frequency therein; when the harmonic content ratio is greater than the ratio threshold, judging that a high-frequency resonance phenomenon currently exists; when a high-frequency resonance phenomenon currently occurs, sending a rectifier staggered phase control signal and a carrier initial value to each of the rectifier modules in the train traction converter system, so that all the rectifier modules whose characteristic frequency range of the network-measured current does not include the characteristic frequency operate in staggered phases.
[0010] The present disclosure provides a computer-readable storage medium storing a computer program. The computer program includes program instructions. When the program instructions are executed by a processor, the above-mentioned adjustment method for adapting to the traction power supply network is implemented.
[0011] In order to make the above-mentioned objects, features and advantages of the present disclosure more obvious and easy to understand, embodiments are listed below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0012] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the following briefly introduces the drawings required for use in the embodiments. The following drawings only show certain embodiments of the present disclosure and therefore should not be regarded as limiting the scope of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.
[0013] Figure 1 shows the topology of the common DC circuit traction converter for electric locomotives;
[0014] Figure 2 shows the topology of the independent DC circuit traction converter for electric locomotives;
[0015] FIG3 is a schematic diagram of the connection relationship of a regulation system adapted to a traction power supply network provided by the present disclosure;
[0016] FIG4 is a schematic structural diagram of the central control module of FIG3;
[0017] FIG5 is a flow chart of an adjustment method adapted to a traction power supply network provided by the present disclosure. DETAILED DESCRIPTION
[0018] The following will be combined with the accompanying drawings in the embodiments of the present disclosure to clearly and completely describe the technical solutions in the embodiments of the present disclosure. Obviously, the embodiments described are only part of the embodiments of the present disclosure, not all of the embodiments. Based on the embodiments of the present disclosure, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present disclosure.
[0019] Figures 1 and 2 show the topological structure of a traction converter. In rail transit, multiple operating modes are common. A traction converter is a key train component, installed on the underside of the train car. Its primary function is to convert electrical energy between DC and AC, controlling the starting, braking, and speed of the AC traction motors through voltage and frequency regulation. The traction grid is the power supply circuit specifically designed to provide power to electric locomotives or EMUs.
[0020] Figure 1 shows a topology with a common intermediate DC circuit, while Figure 2 shows a topology with fully independent shaft control. Regardless of the configuration, the four-quadrant converter controls the real-time phase of the traction transformer's secondary current, ensuring that the resulting current on the traction transformer's primary side has low harmonic content and a high power factor. If the four-quadrant converter's multiplex function is not properly implemented, current distortion or high-frequency harmonics may occur in the traction transformer's primary current, leading to severe high-frequency resonance.
[0021] This disclosure discloses a regulation method for a traction power supply network. Upon detecting high-frequency resonance in the traction network, the method first maximizes the number of rectifier modules and implements staggered operation to mitigate the high-frequency resonance. If the high-frequency resonance persists after maximizing the number of rectifier modules, dynamic frequency shifting is employed to simultaneously increase the switching frequency of the rectifier modules and reduce motor power, thereby mitigating the high-frequency resonance in the traction network.
[0022] As shown in Figure 3, the present disclosure provides a regulation system adapted to a traction power supply network, which is applied to a train traction conversion system. The train traction conversion system includes a traction transformer, multiple rectifier modules (n rectifier modules as shown in Figure 3), multiple inverter modules (n inverter modules as shown in Figure 3) and multiple motors (n motors as shown in Figure 3). The regulation system includes: a grid voltage monitoring module, connected to the input end of the traction transformer, for obtaining the current grid voltage of the traction network in real time; a central control module, for judging whether a high-frequency resonance phenomenon occurs according to the current grid voltage of the traction network, and sending a control signal to each rectifier module and / or transmission control module to eliminate the high-frequency resonance phenomenon when a high-frequency resonance phenomenon occurs; a transmission control module, for sending a drive instruction to each motor according to the control signal to control the current power of each motor; and the rectifier module adjusting the switching frequency or shutting down according to the control signal.
[0023] The present disclosure discloses a regulation system adapted for a traction power supply network, which is applied to a train traction converter system. The regulation system obtains the current grid voltage of the traction network in real time through a grid voltage monitoring module. A central control module determines whether high-frequency resonance is currently occurring based on the current grid voltage of the traction network. If high-frequency resonance is currently occurring, a control signal is sent to each rectifier module and / or transmission control module to eliminate the high-frequency resonance. The regulation system can prevent high-frequency resonance from occurring, or promptly control high-frequency resonance if it has already occurred, thereby preventing accidents from escalating and enhancing the train's adaptability to operating in different power supply ranges.
[0024] Among them, the rectifier module includes a four-quadrant converter, and the train traction converter system includes multiple four-quadrant converters.
[0025] As shown in Figure 4, the central control module includes a processor 801, an input device 802, an output device 803 and a memory 804. The processor 801, the input device 802, the output device 803 and the memory 804 are interconnected, for example, through a bus 805. The memory is used to store a computer program, and the computer program includes program instructions. The processor is configured to call the program instructions to execute the high-frequency resonance phenomenon judgment step and the high-frequency resonance phenomenon elimination step.
[0026] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor, or any conventional processor, etc.
[0027] The memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory. For example, the memory may also store information about the device type.
[0028] As shown in FIG5 , the present disclosure provides a regulation method adapted to a traction power supply network. The regulation method is executed by the central control module of the regulation system adapted to the traction power supply network. The regulation method may include steps 110 to 130 .
[0029] Step 110: Obtain the current voltage of the traction network and calculate the harmonic content ratio and characteristic frequency thereof.
[0030] After obtaining the current grid voltage of the traction network, the harmonic content ratio and characteristic frequency in the current grid voltage can be calculated through Fast Fourier Transform (FFT).
[0031] Step 120: When the harmonic content ratio is greater than the ratio threshold, it is determined that a high-frequency resonance phenomenon currently exists.
[0032] The percentage threshold can be set by those skilled in the art according to specific circumstances. The purpose is to screen out high-frequency resonance phenomena, and it can generally be set to 18%.
[0033] Step 130: When a high-frequency resonance phenomenon occurs, a rectifier staggered phase control signal and a carrier initial value are sent to each rectifier module in the train traction converter system, so that all rectifier modules whose characteristic frequencies are not included in the characteristic frequency range of the network-measured current operate in staggered phase.
[0034] In step 130 , the rectifier phase-shifting control signal includes an on control signal and an off control signal. Step 130 may include steps 131 to 132 .
[0035] Step 131: Send a shutdown control signal to the rectifier module whose characteristic frequency range of the network-measured current includes the characteristic frequency, and send an open control signal to other rectifier modules in the train traction converter system.
[0036] Step 132: Send the initial value of the carrier to each rectifier module whose characteristic frequency is not included in the characteristic frequency range of the network-measured current according to the following formula: k =(k-1)π / n, where A k represents the initial carrier value of the kth rectifier module, and n represents the number of rectifier modules in the train traction converter system.
[0037] Among them, the rectifier module whose characteristic frequency is not included in the characteristic frequency range of the network-measured current is the rectifier module that will not cause high-frequency resonance, that is, the rectifier module that can be put into use.
[0038] Generally, the number of four-quadrant modules in operation varies depending on whether the locomotive is lightly loaded or heavily loaded, and some fault conditions may cause some four-quadrant modules to be isolated. Therefore, after high-frequency resonance occurs, the available weights of the four-quadrant converter in the vehicle are immediately determined. Regardless of whether the vehicle is lightly loaded or heavily loaded, all available four-quadrant converter modules are put into operation, and staggered operation is performed according to the weights used. The staggered operation rules are set according to the modulation method and the position of each weight in the vehicle.
[0039] The present disclosure discloses a regulation method adapted to a traction power supply network. After high-frequency resonance is detected in the traction network, all rectifier modules that can be used in the train traction converter system are put into use, regardless of whether it is in a light-load state or a heavy-load state, and staggered phase operation is performed according to the number of times used, so as to improve the high-frequency resonance phenomenon of the traction network.
[0040] In an embodiment of the present disclosure, with continued reference to FIG. 5 , after sending the rectification staggered phase control signal and the carrier initial value to each rectifier module in the train traction converter system, the method may further include step 140 .
[0041] Step 140: When a high-frequency resonance phenomenon occurs, a frequency increase control signal is sent to each rectifier module in the train traction converter system to increase the switching frequency of each rectifier module; and a deceleration control signal is sent to each transmission control module to control each motor to reduce power.
[0042] In step 140 , the frequency-increasing control signal includes multiple levels of frequency-increasing control signals, each level of which corresponds to a switching frequency range. Sending the frequency-increasing control signal to each rectifier module in the train traction converter system to increase the switching frequency of each rectifier module may include steps 141 and 142 .
[0043] Step 141: Obtain the current switching frequency of the rectifier module.
[0044] Step 142: When the current switching frequency is within the i-th switching frequency range, send an (i+1)-th frequency increase control signal to the rectifier module, so that the current switching frequency rises to the (i+1)-th switching frequency range; wherein the minimum value of the (i+1)-th switching frequency range is greater than the maximum value of the i-th switching frequency range.
[0045] The deceleration control signal includes multiple levels of deceleration control signals, each level of deceleration control signal corresponding to a motor power range. Sending the deceleration control signal to each transmission control module so that the transmission control module controls each motor to reduce power may include steps 143 to 144.
[0046] Step 143: Obtain the current power of the motor.
[0047] Step 144: When the current power is within the j-th motor power range, send a (j-1)-th level deceleration control signal to the motor to reduce the current power to the (j-1)-th level motor power range; wherein the maximum value of the (j-1)-th level motor power range is smaller than the minimum value of the i-th level motor power range.
[0048] In the disclosed method for regulating the traction power grid, if high-frequency resonance persists after maximizing the operation of the rectifier module, indicating that maximizing the operation of the four-quadrant converter module has not yet resolved the problem, further adjustments are made by adjusting the switching frequency of the four-quadrant converter. Dynamic frequency shifting simultaneously increases the switching frequency of the rectifier module and reduces motor power to improve the high-frequency resonance of the traction grid.
[0049] In an embodiment of the present disclosure, the method may further include: when the current switching frequency reaches the maximum frequency threshold, sending a frequency maintenance signal to the rectifier module so that the rectifier module maintains the current switching frequency; and continuing to send a deceleration control signal to the transmission control module until the current power of the motor is reduced to zero.
[0050] When the train power is operating at the maximum frequency threshold, the power is already low and the locomotive speed is low. If high-frequency resonance continues to occur in the traction network, the train power is further reduced while maintaining the maximum frequency threshold until it reaches zero. At this point, the locomotive power is cut off and no harmonics are injected into the grid.
[0051] In an embodiment of the present disclosure, after continuing to send a deceleration control signal to the transmission control module until the current power of the motor is reduced to zero, the method may also include: in the event that a high-frequency resonance phenomenon currently occurs, sending an alarm signal to the train control center to prompt that a current high-frequency resonance phenomenon that is not caused by the vehicle itself has occurred.
[0052] The train's motor power is zero, and the traction converter is in a pulse-blocked state. The traction network's background harmonics continue to be monitored. If high-frequency resonance persists, it's not caused by the train itself. The central control module reports this information to the driver, alerting them to the actual grid condition.
[0053] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the composition and steps of each example according to function. Whether these functions are performed in hardware or software may depend on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this disclosure.
[0054] In the several embodiments provided in the present disclosure, the disclosed terminal devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the above units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, or can be an electrical, mechanical or other form of connection.
[0055] The units described above as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units may be selected according to actual needs to achieve the objectives of the embodiments of the present disclosure.
[0056] In addition, the functional units in the various embodiments of the present disclosure may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.
[0057] If the above-mentioned integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. The technical solution of the present disclosure is essentially or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which 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 perform all or part of the steps of the method in each embodiment of the present disclosure. The aforementioned storage medium may include: 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.
[0058] The terms "first," "second," "the first," or "the second" used in various embodiments of the present disclosure may modify various components regardless of order and / or importance, but these terms do not limit the corresponding components. The above terms are configured solely for the purpose of distinguishing an element from other elements. For example, a first user device and a second user device represent different user devices, even though both are user devices. For example, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element without departing from the scope of the present disclosure.
[0059] When one element (e.g., a first element) is referred to as being “(operably or communicably) coupled” to another element (e.g., a second element) or “(operably or communicably) coupled to” another element (e.g., a third element) or “connected to” another element (e.g., a third element), it should be understood that the one element is directly connected to the other element or that the one element is indirectly connected to the other element via yet another element (e.g., the third element). When an element (e.g., a first element) is referred to as being “directly connected” or “directly coupled” to another element (the second element), there is no element (e.g., the third element) interposed therebetween.
[0060] The above description is merely an enumeration of embodiments of the present disclosure and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the present disclosure is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, but should also encompass other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the above-mentioned inventive concept. For example, a technical solution formed by replacing the above-mentioned features with (but not limited to) technical features with similar functions disclosed in this disclosure.
[0061] The foregoing is merely an enumeration of embodiments of the present disclosure and is not intended to limit the present disclosure. Those skilled in the art will readily appreciate that various modifications and variations of the present disclosure are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present disclosure shall be included within the scope of protection of the present disclosure.
Claims
1. A regulation system adapted to a traction power supply network, the regulation system being applied to a train traction converter system, the train traction converter system comprising a traction transformer, a plurality of rectifier modules, a plurality of inverter modules, and a plurality of motors, wherein: The regulating system comprises: A grid voltage monitoring module, connected to the input terminal of the traction transformer, for obtaining the current grid voltage of the traction grid in real time; a central control module, configured to determine whether a high-frequency resonance phenomenon currently occurs based on the current network voltage of the traction network, and, if a high-frequency resonance phenomenon currently occurs, to send a control signal to each of the rectifier modules and / or transmission control modules to eliminate the high-frequency resonance phenomenon; a transmission control module, configured to send a drive instruction to each of the motors according to the control signal, so as to control the current power of each of the motors; The rectifier module adjusts the switching frequency or turns off according to the control signal.
2. The regulation system adapted to the traction power supply network according to claim 1, wherein: The rectifier module includes a four-quadrant converter, and the train traction converter system includes multiple four-quadrant converters.
3. The regulation system adapted to the traction power supply network according to claim 1, wherein: The central control module includes a processor, an input device, an output device and a memory, which are interconnected. The memory is used to store a computer program, and the computer program includes program instructions. The processor is configured to call the program instructions to execute the high-frequency resonance phenomenon judgment step and the high-frequency resonance phenomenon elimination step.
4. A method for regulating a traction power supply network, the method being executed by the central control module of the regulation system for regulating a traction power supply network according to any one of claims 1 to 3, wherein: The method comprises: Obtaining the current grid voltage of the traction network and calculating the harmonic content ratio and characteristic frequency thereof; When the proportion of the harmonic content is greater than the proportion threshold, it is determined that a high-frequency resonance phenomenon currently exists; In the event of a high-frequency resonance phenomenon, a rectifier staggered phase control signal and a carrier initial value are sent to each rectifier module in the train traction converter system, so that all the rectifier modules whose characteristic frequency range of the network-measured current does not include the characteristic frequency operate in staggered phase.
5. The adjustment method adapted to the traction power supply network according to claim 4, wherein: The rectification mis-phase control signal includes an on control signal and an off control signal; Sending a rectifier staggered phase control signal and a carrier initial value to each rectifier module in the train traction converter system so that all rectifier modules whose characteristic frequency range of the network-measured current does not include the characteristic frequency operate in staggered phases, including: Sending a shutdown control signal to the rectifier module whose characteristic frequency range of the network-measured current includes the characteristic frequency, and sending an opening control signal to the other rectifier modules in the train traction converter system; The carrier initial value is sent to each rectifier module whose characteristic frequency range of the network-measured current does not include the characteristic frequency according to the following formula: k =(k-1)π / n, where A k represents the initial value of the carrier of the kth rectifier module, and n represents the number of the rectifier modules in the train traction converter system.
6. The method for adjusting the traction power supply network according to claim 4, wherein: After sending the rectification phase-shift control signal and the carrier initial value to each of the rectification modules in the train traction converter system, the method further includes: In the current situation of high-frequency resonance phenomenon, Sending a frequency-increasing control signal to each of the rectifier modules in the train traction converter system, so that the switching frequency of each of the rectifier modules increases; And a deceleration control signal is sent to each of the transmission control modules, so that the transmission control module controls each of the motors to reduce power.
7. The method for adjusting the traction power supply network according to claim 6, wherein: The frequency-up control signal includes a multi-level frequency-up control signal, and each level of the frequency-up control signal corresponds to a switching frequency range; Sending a frequency increase control signal to each of the rectifier modules in the train traction converter system so that the switching frequency of each of the rectifier modules increases includes: Obtaining the current switching frequency of the rectifier module; When the current switching frequency is within the i-th switching frequency range, sending an (i+1)-th frequency increase control signal to the rectifier module so that the current switching frequency increases to the (i+1)-th switching frequency range; wherein the minimum value of the (i+1)-th switching frequency range is greater than the maximum value of the i-th switching frequency range; The deceleration control signal includes multiple levels of deceleration control signals, each level of the deceleration control signal corresponds to a motor power range; Sending a deceleration control signal to each of the transmission control modules so that the transmission control module controls each of the motors to reduce power, including: Obtaining the current power of the motor; When the current power is within the j-th level motor power range, a (j-1)-th level deceleration control signal is sent to the motor so that the current power is reduced to the (j-1)-th level motor power range; wherein the maximum value of the (j-1)-th level motor power range is smaller than the minimum value of the i-th level motor power range.
8. The method for adjusting the traction power supply network according to claim 7, wherein: The method further comprises: When the current switching frequency reaches the maximum frequency threshold, a frequency holding signal is sent to the rectifier module so that the rectifier module maintains the current switching frequency; and a deceleration control signal is continued to be sent to the transmission control module until the current power of the motor is reduced to zero.
9. The adjustment method adapted to the traction power supply network according to claim 8, wherein: After continuing to send the deceleration control signal to the transmission control module until the current power of the motor decreases to zero, the method further includes: In the current situation of high-frequency resonance phenomenon, Send an alarm signal to the train control center to indicate that a current high-frequency resonance phenomenon not caused by the train has occurred.
10. A computer-readable storage medium, wherein: The computer-readable storage medium stores a computer program, wherein the computer program includes program instructions. When the program instructions are executed by a processor, the method according to any one of claims 4 to 9 is implemented.