An adaptive global efficiency optimization design method for bidirectional non-isolated converters

Abstract

The present invention discloses an adaptive global efficiency optimization design method for a bidirectional non-isolated converter, comprising: establishing a mapping relationship between losses associated with the switching frequency and the switching frequency based on the topology and operating conditions of the bidirectional non-isolated converter; determining the switching frequency corresponding to the optimal losses under different operating conditions based on the mapping relationship between the losses and the switching frequency, and optimizing the full-operating-condition efficiency of the bidirectional non-isolated converter through a multi-frequency control method; wherein all losses associated with the switching frequency include the switching losses, inductor losses, and drive losses of the bidirectional non-isolated converter. This method not only effectively improves full-operating-condition efficiency but also avoids frequency oscillation caused by sampling errors or sampling interference, ensuring stable operation of the converter. The method is particularly suitable for use in bidirectional energy flow applications such as energy storage systems.

Description

Technical Field

[0001] The present invention relates to a soft switching control strategy for a bidirectional non-isolated converter, and in particular to an adaptive global efficiency optimization design method for the bidirectional non-isolated converter. Background Art

[0002] In renewable energy power systems that include energy storage, bidirectional non-isolated converters are increasingly being used, particularly for bidirectional power conversion between different DC voltage buses. This conversion technology not only enables real-time energy management but also improves system reliability and availability. The bidirectional power flow capability also reduces the number of converter components, thereby enhancing system reliability.

[0003] At present, the control strategies for bidirectional non-isolated converters can be divided into two types: hard switching and soft switching. Soft switching control strategies are mainly divided into the following categories: (1) fixed-frequency minimum inductor current effective value control; (2) variable-frequency minimum inductor current effective value control; (3) multi-frequency minimum inductor current effective value control. Fixed-frequency minimum inductor current effective value control achieves zero voltage turn-on and optimizes the inductor current effective value, but only optimizes D1, D1, The three control variables restrict the four-switch buck-boost converter to a single switching frequency, making it impossible to optimize the inductor current RMS by changing the switching frequency. Variable-frequency minimum inductor current RMS control increases output power by reducing the switching frequency at high power levels, further optimizing efficiency compared to fixed-frequency control. However, the switching frequency only changes at high power levels, preventing overall efficiency from being optimized. Multi-frequency minimum inductor current RMS control fails to consider the impact of the inductor value selection on converter efficiency, and minimizing the inductor current RMS does not necessarily minimize total losses. Furthermore, multi-frequency minimum inductor current RMS control can cause frequency oscillations during the lookup table frequency conversion due to sampling errors or sampling interference, impacting converter stability. Summary of the Invention

[0004] Purpose of the invention: In response to the above problems, the present invention proposes an adaptive global efficiency optimization design method for a bidirectional non-isolated converter, which can optimize the overall global efficiency and prevent frequency oscillation caused by sampling errors or sampling interference, thereby improving the stability and efficiency of the four-switch buck-boost converter.

[0005] Technical solution: The technical solution adopted by the present invention is an adaptive global efficiency optimization design method for a bidirectional non-isolated converter, comprising the following steps:

[0006] (1) Optimizing the inductance parameters of the voltage step-up / down unit in the bidirectional non-isolated converter with the goal of minimizing the energy loss associated with the system in which the bidirectional non-isolated converter is located and the inductance of the voltage step-up / down unit in the bidirectional non-isolated converter;

[0007] (2) According to the topology and working conditions of the bidirectional non-isolated converter, the loss P related to the switching frequency is established. loss With the switching frequency f s The mapping relationship between all losses P related to the switching frequency loss Including switching loss, inductor loss and drive loss of bidirectional non-isolated converter;

[0008] (3) Based on loss P loss With the switching frequency f s The mapping relationship between them is used to solve the switching frequency corresponding to the optimal loss under different working conditions, and the full-operating efficiency optimization of the bidirectional non-isolated converter is achieved through the multi-frequency control method.

[0009] Step (1) includes: establishing an energy loss relationship between the system in which the bidirectional non-isolated converter is located and the inductance of the voltage step-up and step-down unit, traversing the working range of the bidirectional non-isolated converter with the goal of minimizing energy loss, and obtaining the inductance of the voltage step-up and step-down unit corresponding to the minimum energy loss of the system during the entire working cycle as the inductance of the voltage step-up and step-down unit of the bidirectional non-isolated converter.

[0010] Generally, the system in which the bidirectional non-isolated converter is located includes an energy storage unit. Step (1) calculates energy loss based on the energy storage unit. The specific process is: establishing an energy loss relationship between the system in which the bidirectional non-isolated converter is located and the inductance of the voltage step-up / down unit, including: establishing a mapping relationship between the inductance of the voltage step-up / down unit in the bidirectional non-isolated converter and the energy loss of the energy storage unit in a discharge cycle according to a weighted operating time coefficient, wherein the weighted operating time refers to the charging and discharging time of the energy storage unit in different voltage ranges, and normalizing each weighted operating time to obtain the weighted operating time coefficient.

[0011] The optimal loss is the minimum loss; the calculation of the minimum loss includes: based on the loss P loss With the switching frequency f s The mapping relationship between the loss P under different working conditions loss Ergodic switching frequency f s , obtaining the switching frequency corresponding to the minimum loss under different working conditions, and obtaining the mapping relationship between the minimum loss and the switching frequency under different working conditions; the working conditions include the input voltage, output voltage and output current of the bidirectional non-isolated converter.

[0012] The calculation process of the optimal loss is as follows: First, based on the loss P loss With the switching frequency f s The mapping relationship between the loss P under different working conditions loss Ergodic switching frequency fs , obtaining the switching frequency corresponding to the minimum loss under different working conditions; then, the working conditions of the bidirectional non-isolated converter are segmented to obtain a mapping relationship between the suboptimal loss and the switching frequency with the minimum data volume; the working conditions include the input voltage, output voltage and output current of the bidirectional non-isolated converter.

[0013] The switching frequency f corresponding to the suboptimal loss currently calculated in the cycle calculation s n At the last switching frequency f s n-1 ±Δf s When the switching frequency is within the range, the last switching frequency f s n-1 Unchanged; the switching frequency f corresponding to the currently calculated suboptimal loss s n In ±Δf s When it is outside the range, the current calculated switching frequency f is used. s n .

[0014] The bidirectional non-isolated converter is a four-switch buck-boost converter topology.

[0015] The loss P loss The loss includes the conduction loss P on , turn-off loss P sw , drive and power supply loss P driver , iron loss P fe , copper loss P cu , loss P loss The expression is as follows:

[0016]

[0017] P driver =V driver Q g f s

[0018] P fe =V core P cv

[0019]

[0020] P loss =P on +P sw +P driver +P fe +P cu

[0021] Where, I Lrmsis the effective value of the inductor current, R ds(on) is the on-state resistance of MOSFET, t f is the MOSFET turn-off time, ΔI p is the MOSFET turn-off current, V dc is the MOSFET turn-off voltage, f s is the switching frequency, V driver is the driving voltage, Q g is the total gate drive charge, V core is the volume of the core, P cv is the core loss per unit volume, I dc is the DC component of the inductor current, I ac is the AC component of the inductor current, R dc is the winding DC resistance, R ac is the AC resistance of the winding.

[0022] The expression forms of the mapping relationship include: one-dimensional table form, two-dimensional table form, three-dimensional table form, piecewise function expression, curve form and surface form.

[0023] The present invention proposes a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the adaptive global efficiency optimization design method for a bidirectional non-isolated converter is implemented.

[0024] Beneficial effects: Compared with the existing technology, the present invention has the following advantages: the present invention reduces the loss of the bidirectional non-isolated converter circuit from a global perspective by optimizing the selection of the inductance of the voltage step-up and step-down unit and combining it with multi-frequency control calculated based on the optimal operating frequency; by increasing the frequency hysteresis loop, the frequency oscillation phenomenon caused by sampling error or sampling interference in the bidirectional non-isolated converter can be prevented, thereby improving the stability and efficiency of the four-switch step-up and step-down converter. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a four-switch buck-boost converter topology;

[0026] Figure 2 This is the overall control block diagram of the four-switch buck-boost converter;

[0027] Figure 3 It is the overall control flow chart of the four-switch buck-boost converter;

[0028] Figure 4 is the loss of the four-switch buck-boost converter under different inductance values ​​in the embodiment of the present invention;

[0029] Figure 5 This is a table of optimal switching frequencies for a four-switch buck-boost converter under different operating conditions in an embodiment of the present invention;

[0030] Figure 6 Schematic diagram of a process in which the switching frequency of a four-switch buck-boost converter is unstable due to sampling error or sampling interference in an embodiment of the present invention;

[0031] Figure 7 It is a schematic diagram of the frequency hysteresis scheme described in the present invention. DETAILED DESCRIPTION

[0032] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] The adaptive global efficiency optimization design method of the bidirectional non-isolated converter according to the present invention comprises the following steps:

[0034] (1) Optimizing the inductance parameters of the voltage step-up / down unit in the bidirectional non-isolated converter with the goal of minimizing the energy loss associated with the system in which the bidirectional non-isolated converter is located and the inductance of the voltage step-up / down unit in the bidirectional non-isolated converter;

[0035] (2) According to the topology and working conditions of the bidirectional non-isolated converter, the loss P related to the switching frequency is established. loss With the switching frequency f s The mapping relationship between all losses P related to the switching frequency loss Including switching loss, inductor loss and drive loss of bidirectional non-isolated converter;

[0036] (3) Based on loss P loss With the switching frequency f s The mapping relationship between them is used to solve the switching frequency corresponding to the optimal loss under different working conditions, and the full-operating efficiency optimization of the bidirectional non-isolated converter is achieved through the multi-frequency control method.

[0037] Step (1) includes: establishing an energy loss relationship between the system in which the bidirectional non-isolated converter is located and the inductance of the voltage step-up and step-down unit, traversing the working range of the bidirectional non-isolated converter with the goal of minimizing energy loss, and obtaining the inductance of the voltage step-up and step-down unit corresponding to the minimum energy loss of the system during the entire working cycle as the inductance of the voltage step-up and step-down unit of the bidirectional non-isolated converter.

[0038] A system in which a bidirectional non-isolated converter is located includes an energy storage unit. Establishing an energy loss relationship between the system in which the bidirectional non-isolated converter is located and the inductance of a voltage step-up / down unit includes establishing a mapping relationship between the inductance of the voltage step-up / down unit in the bidirectional non-isolated converter and the energy loss of the energy storage unit during a discharge cycle based on a weighted operating time coefficient. The weighted operating time refers to the charge and discharge time of the energy storage unit in different voltage ranges. The weighted operating time coefficient is obtained by normalizing each weighted operating time.

[0039] The optimal loss in the above step (3) can be the minimum loss. The calculation of the minimum loss includes: based on the loss P loss With the switching frequency f s The mapping relationship between the loss P under different working conditions loss Ergodic switching frequency f s , obtaining the switching frequency corresponding to the minimum loss under different working conditions, and obtaining the mapping relationship between the minimum loss and the switching frequency under different working conditions; the working conditions include the input voltage, output voltage and output current of the bidirectional non-isolated converter.

[0040] Preferably, the optimal loss in the above step (3) adopts the suboptimal loss, and the calculation process is: first, based on the loss P loss With the switching frequency f s The mapping relationship between the loss P under different working conditions loss Ergodic switching frequency f s , obtaining the switching frequency corresponding to the minimum loss under different working conditions; then, the working conditions of the bidirectional non-isolated converter are segmented to obtain a mapping relationship between the suboptimal loss and the switching frequency with the minimum data volume; the working conditions include the input voltage, output voltage and output current of the bidirectional non-isolated converter.

[0041] Among various bidirectional non-isolated converter topologies, the Four Switches Buck-Boost (FSBB) is widely used in systems containing energy storage media such as batteries and supercapacitors due to its advantages such as the same polarity of input and output voltages, wide input voltage range, and few passive components. Figure 1 The present invention takes a four-switch buck-boost converter, a topology widely used in bidirectional non-isolated converters, as an example to introduce in detail a method for designing an adaptive global efficiency optimization of a bidirectional non-isolated converter.

[0042] In the four-switch buck-boost converter topology, there are Q1, Q2 bridge arms, Q3, Q4 bridge arms, and an inductor L. The converter has the following four control variables: Q1 duty cycle D1, Q3 duty cycle D2, Q1 and Q3 phase difference The switching frequency f of Q1, Q2, Q3, and Q4 s The overall control program block diagram and closed-loop flow chart of the four-switch buck-boost converter are as follows: Figure 2 、 3 As shown, the voltage loop output adjustment value T u , used to stabilize the output voltage, and optimize the efficiency by outputting the operating frequency through a two-dimensional table lookup and a frequency hysteresis loop. sThe new solution proposed in the optimization section.

[0043] According to the inductor volt-second balance principle within a switching cycle, the input and output voltage relationship of the four-switch buck-boost converter can be obtained as follows:

[0044]

[0045] By designing the inductance to change the circuit loss, under the premise of meeting the maximum output power limit, the loss throughout the working cycle will first decrease and then increase as the inductance increases. Therefore, there is a point where the loss is minimum. When the corresponding inductance is selected at this time, the four-switch buck-boost converter has the lowest loss.

[0046] According to the calculation of the loss under different switching frequencies, the frequency corresponding to the minimum loss is selected as the switching frequency. The loss is divided into conduction loss (P on ), turn-off loss (P sw ), drive and power supply loss (P driver ), iron loss (P fe ), copper loss (P cu ), its total loss P loss The expression is as follows:

[0047]

[0048] P driver =V driver Q g f s (4)

[0049] P fe =V core P cv (5)

[0050]

[0051] P loss =P on +P sw +P driver +P fe +P cu (7)

[0052] Where, I Lrms is the effective value of the inductor current, R ds(on) is the on-state resistance of MOSFET, t f is the MOSFET turn-off time, ΔI p is the MOSFET turn-off current, V dc is the MOSFET turn-off voltage, f s is the switching frequency, V driver is the driving voltage, Qg is the total gate drive charge, V core is the volume of the core, P cv is the core loss per unit volume, I dc is the DC component of the inductor current, I ac is the AC component of the inductor current, R dc is the winding DC resistance, R ac is the winding AC resistance. Furthermore, the losses at different frequencies are calculated and the frequency corresponding to the minimum loss is found as the switching frequency for this operating condition, thereby reducing the losses.

[0053] If a sampling error or sampling interference occurs in the four-switch buck-boost converter, the operating conditions recognized by the system will keep changing, which will cause the output switching frequency f s The switching frequency of the converter is always in dynamic adjustment. For this reason, a frequency hysteresis loop is designed. s Greater than the previous switching frequency f s '+Δf s Or less than the previous switching frequency f s '-Δf s Only then can the switching frequency f be output s , ensuring the reliable operation of the four-switch buck-boost converter.

[0054] Calculate the total loss in the four-switch buck-boost converter for different inductor values, such as Figure 4 As shown, select the inductance L with the smallest loss a As the inductance in the four-switch buck-boost converter, the input voltage, output voltage, and output current are sampled during the operation of the four-switch buck-boost converter and the data is transmitted to a digital processor, such as an MCU. In the digital processor, the sampling data and the output current are sampled. Figure 5 The mapping relationship shown in the figure outputs the initial switching frequency. Figure 6 The problem of unstable switching frequency caused by sampling error or interference is shown in the figure. The initial switching frequency is adjusted as follows: Figure 7 The switching frequency f of this cycle is output after the frequency hysteresis loop shown s , which enables the four-switch buck-boost converter to minimize the total loss while avoiding the phenomenon of frequent dynamic adjustment of the switching frequency.

[0055] They are introduced below.

[0056] like Figure 4As shown in the figure, the charging and discharging time of energy storage media such as batteries in different voltage ranges is defined as weighted working time. The relationship between the inductance and the total loss in the four-switch buck-boost converter is established by loss calculation formulas (2) to (6) within the weighted working time. As shown in formula (7), the total loss P corresponding to different inductances can be obtained by substituting different inductances. loss As the inductance increases, the total loss P loss It first decreases and then increases, and there is a lowest point. When the corresponding inductance L is selected a When , the total energy of the four-switch buck-boost converter is minimized in the entire operating range.

[0057] For different input voltages and output powers, after calculating the losses corresponding to different switching frequencies, the switching frequency corresponding to the minimum loss is selected to form the following: Figure 5 The mapping relationship shown in Figure 5 The specific data in the example is given for a 3kW prototype with 210V~330V input and 270V output. From this, a frequency table corresponding to the global optimal efficiency can be formed. The obtained data is segmented to obtain the mapping relationship between the suboptimal loss and switching frequency with the smallest amount of data. In actual operation, the input voltage V is collected. in , output voltage V o And the output current I o And transmit the sampled data to the digital processor, which can be used to calculate the suboptimal P loss With f s The mapping relationship outputs the optimal switching frequency and optimizes the global efficiency of the four-switch buck-boost converter.

[0058] However, when the four-switch buck-boost converter has sampling error or sampling interference, the output frequency is as shown in the following figure. Figure 6 As shown in the table, a slight error will cause the frequency to change back and forth between the two tables, resulting in unnecessary dynamic adjustment of the switching frequency. Therefore, a frequency hysteresis loop is designed as shown in the attached figure. Figure 7 As shown, only when the switching frequency output by the table is greater than the frequency f at the previous moment s '+Δf s Or less than the frequency f at the previous moment s '-Δf s To ensure the reliable operation of the four-switch buck-boost converter, Δf s Generally less than 0.5 times the current switching frequency.

[0059] In one embodiment, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned adaptive global efficiency optimization design method for a bidirectional non-isolated converter when executing the computer program.

[0060] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0061] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0062] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0063] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

Claims

1. An adaptive global efficiency optimization design method for a bidirectional non-isolated converter, characterized in that: The following steps are involved: (1) Optimizing the inductance parameters of the voltage step-up / down unit in the bidirectional non-isolated converter with the goal of minimizing the energy loss associated with the system in which the bidirectional non-isolated converter is located and the inductance of the voltage step-up / down unit in the bidirectional non-isolated converter; (2) According to the topology and working conditions of the bidirectional non-isolated converter, the loss P related to the switching frequency is established. loss With the switching frequency f s The mapping relationship between all losses P related to the switching frequency loss Including switching loss, inductor loss and drive loss of bidirectional non-isolated converter; (3) Based on loss P loss With the switching frequency f s The mapping relationship between them is used to solve the switching frequency corresponding to the optimal loss under different working conditions, and the full-operating efficiency optimization of the bidirectional non-isolated converter is achieved through the multi-frequency control method.

2. The adaptive global efficiency optimization design method for a bidirectional non-isolated converter according to claim 1, characterized in that: Step (1) includes: establishing an energy loss relationship between the system in which the bidirectional non-isolated converter is located and the inductance of the voltage step-up and step-down unit, traversing the working range of the bidirectional non-isolated converter with the goal of minimizing energy loss, and obtaining the inductance of the voltage step-up and step-down unit corresponding to the minimum energy loss of the system during the entire working cycle as the inductance of the voltage step-up and step-down unit of the bidirectional non-isolated converter.

3. The adaptive global efficiency optimization design method for a bidirectional non-isolated converter according to claim 2, characterized in that: The system where the bidirectional non-isolated converter is located includes an energy storage unit, and an energy loss relationship related to the inductance of the system where the bidirectional non-isolated converter is located and the voltage step-up and step-down unit is established, including: according to the weighted working time coefficient, a mapping relationship between the inductance of the voltage step-up and step-down unit in the bidirectional non-isolated converter and the energy loss of the energy storage unit during a discharge cycle is established, where the weighted working time refers to the charging and discharging time of the energy storage unit in different voltage ranges, and each weighted working time is normalized to obtain the weighted working time coefficient.

4. The adaptive global efficiency optimization design method for a bidirectional non-isolated converter according to claim 1, wherein: The optimal loss in step (3) is the minimum loss; The calculation of minimum loss includes: based on the loss P loss With the switching frequency f s The mapping relationship between the loss P under different working conditions loss Ergodic switching frequency f s , obtaining the switching frequency corresponding to the minimum loss under different working conditions, and obtaining the mapping relationship between the minimum loss and the switching frequency under different working conditions; the working conditions include the input voltage, output voltage and output current of the bidirectional non-isolated converter.

5. The adaptive global efficiency optimization design method for a bidirectional non-isolated converter according to claim 1, characterized in that: The calculation process of the optimal loss in step (3) is as follows: First, based on the loss P loss With the switching frequency f s The mapping relationship between the loss P under different working conditions loss Ergodic switching frequency f s , obtaining the switching frequency corresponding to the minimum loss under different working conditions; then, the working conditions of the bidirectional non-isolated converter are segmented to obtain a mapping relationship between the suboptimal loss and the switching frequency with the minimum data volume; the working conditions include the input voltage, output voltage and output current of the bidirectional non-isolated converter.

6. The adaptive global efficiency optimization design method for a bidirectional non-isolated converter according to claim 1, characterized in that: The switching frequency f corresponding to the suboptimal loss currently calculated in the cycle calculation s n At the last switching frequency f s n-1 ±Δf s When the switching frequency is within the range, the last switching frequency f s n-1 Unchanged; the switching frequency f corresponding to the currently calculated suboptimal loss s n In ±Δf s When it is outside the range, the current calculated switching frequency f is used. s n .

7. The adaptive global efficiency optimization design method for a bidirectional non-isolated converter according to claim 1, characterized in that: The bidirectional non-isolated converter is a four-switch buck-boost converter topology.

8. The adaptive global efficiency optimization design method for a bidirectional non-isolated converter according to claim 7, characterized in that: The loss P of the four-switch buck-boost converter loss Including: conduction loss P on , turn-off loss P sw , drive and power supply loss P driver , iron loss P fe , copper loss P cu , the loss expressions are as follows: P driver =V driver Q g f s P fe =V core P cv P loss =P on +P sw +P driver +P fe +P cu Where, I Lrms is the effective value of the inductor current, R ds(on) is the on-state resistance of MOSFET, t f is the MOSFET turn-off time, ΔI p is the MOSFET turn-off current, V dc is the MOSFET turn-off voltage, f s is the switching frequency, V driver is the driving voltage, Q g is the total gate drive charge, V core is the volume of the core, P cv is the core loss per unit volume, I dc is the DC component of the inductor current, I ac is the AC component of the inductor current, R dc is the winding DC resistance, R ac is the AC resistance of the winding.

9. The adaptive global efficiency optimization design method for a bidirectional non-isolated converter according to claim 1, characterized in that: The expression forms of the mapping relationship include: one-dimensional table form, two-dimensional table form, three-dimensional table form, piecewise function expression, curve form and surface form.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the adaptive global efficiency optimization design method for the bidirectional non-isolated converter according to any one of claims 1 to 8 is implemented.

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