Impedance test system and method and storage medium
By constructing a hardware-in-the-loop simulation system, the impedance characteristics of new energy power generation equipment are simulated, which solves the problem of inaccurate analysis results in existing technologies and achieves more accurate impedance characteristic analysis.
Patent Information
- Application Number
- CN202511140046.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-14
- Publication Date
- 2025-11-18
AI Technical Summary
Existing technologies for analyzing the impedance characteristics of new energy power generation equipment suffer from inaccurate results due to theoretical analysis methods, and analysis based on dynamic link libraries requires external verification and cannot guarantee accuracy.
A hardware-in-the-loop (HIL) simulation system is constructed, which simulates an ideal power grid through a new energy power generation unit, a power electronic converter model, a voltage disturbance source module, and a power grid model. It is connected to a real hardware controller, and the host computer sends control commands and disturbance source signals to collect the AC side current and voltage of the power electronic converter and calculate the impedance.
It directly reflects the influence of real-world environmental factors on impedance characteristics, yielding more accurate impedance analysis results without the need for external verification, thus improving the accuracy of the analysis.
Smart Images

Figure CN120971812A_ABST
Abstract
Description
Technical Field
[0001] The embodiments of the present invention relate to the field of real-time simulation of power systems, and particularly to an impedance testing system, method and storage medium. Background Technology
[0002] Currently, the proportion of new energy power generation equipment, mainly composed of power electronic converters, in the power system is gradually increasing, leading to a growing impact on the operational stability of the power system due to the nonlinear characteristics of these converters. Since impedance characteristics can significantly characterize the impact of new energy power generation equipment on the operational stability of the power system across different frequency bands, the analysis of the impedance characteristics of new energy equipment has become one of the grid connection indicators. Commonly used impedance characteristic analysis methods include theoretical impedance analysis and impedance characteristic analysis based on dynamic link libraries.
[0003] However, due to factors such as control delay and control strategy, the results obtained by theoretical impedance analysis may differ significantly from actual conditions, leading to inaccurate results. Furthermore, impedance characteristic analysis based on dynamic link libraries requires external verification, which cannot guarantee accuracy. Summary of the Invention
[0004] The purpose of this invention is to provide an impedance testing system, method, and storage medium that simulates actual power grid operation by connecting a simulated power grid to an actual controller. Connecting to an actual hardware controller directly reflects the influence of various factors in the real environment on impedance characteristics, making the impedance analysis results more consistent with reality. Furthermore, the obtained analysis results do not require external verification for accuracy and can effectively reflect the impedance characteristics of the power electronic converter in new energy power generation equipment.
[0005] To address this, embodiments of the present invention provide an impedance testing system, comprising: a host computer, a hardware controller, and a new energy grid-connected simulation model; the new energy grid-connected simulation model includes: a new energy power generation unit, a power electronic converter model, a voltage disturbance source module, and a power grid model; the host computer is used to send operating condition control commands to the hardware controller and to send disturbance source control commands to the new energy grid-connected simulation model; the hardware controller is used to control the new energy grid-connected simulation model to perform a frequency sweep operation according to the operating condition control commands, and during the frequency sweep operation, to collect the AC side current and the AC side voltage of the power electronic converter model; the host computer is used to calculate the impedance based on the AC side current and the AC side voltage.
[0006] An embodiment of the present invention also provides an impedance testing method applied to the impedance testing system described above. The method includes: setting the grid voltage amplitude, grid frequency, frequency sweep range, and disturbance signal of the power grid model; during the frequency sweep operation, acquiring the AC side current and AC side voltage corresponding to each sweep frequency within the frequency sweep range; and calculating the impedance based on the AC side current and AC side voltage.
[0007] Embodiments of the present invention also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the impedance testing method described above.
[0008] Compared to related technologies, this invention constructs a semi-physical hardware-in-the-loop simulation system. This system simulates an ideal power grid using a new energy power generation unit, a power electronic converter model, a voltage disturbance source module, and a power grid model. The simulated ideal power grid is connected to a real hardware controller. This connection directly reflects the impact of various factors in the real environment on impedance characteristics, making the impedance analysis results more realistic. The host computer sends operating condition control commands to the hardware controller and disturbance source control commands to the new energy grid-connected simulation model. The hardware controller controls the new energy grid-connected simulation model to perform a frequency sweep operation based on the operating condition control commands. During the frequency sweep operation, it collects the AC current and AC voltage of the power electronic converter model. The host computer calculates the impedance based on the AC current and AC voltage. The entire process requires no external means for accuracy verification, effectively reflecting the impedance characteristics of the power electronic converter in the new energy power generation equipment and obtaining relatively accurate impedance characteristic analysis results.
[0009] In addition, the power electronic converter model of the impedance testing system is a field-programmable gate array (FPGA) model; the power grid model is a central processing unit (CPU) model.
[0010] In addition, the host computer of the impedance testing system includes a waveform recording module and an impedance calculation module; the waveform recording module is used to record the AC side current and the AC side voltage during the frequency sweep operation; the impedance calculation module is used to calculate the impedance based on the data recorded by the waveform recording module.
[0011] In addition, the impedance testing method, after obtaining the AC side current and AC side voltage corresponding to each scanning frequency within the frequency sweep range, further includes: obtaining the positive sequence voltage, first positive sequence current, negative sequence voltage and first negative sequence current corresponding to each scanning frequency, the second negative sequence current corresponding to the first target frequency and the second positive sequence current corresponding to the second target frequency; the first target frequency is the absolute value of the difference between the scanning frequency and twice the grid frequency, and the second target frequency is the sum of the scanning frequency and twice the grid frequency; the step of calculating the impedance based on the AC side current and AC side voltage includes: calculating the impedance based on the positive sequence voltage, the first positive sequence current, the negative sequence voltage, the first negative sequence current, the second negative sequence current and the second positive sequence current.
[0012] In addition, the impedance calculation based on the positive-sequence voltage, the first positive-sequence current, the negative-sequence voltage, the first negative-sequence current, the second negative-sequence current, and the second positive-sequence current includes: calculating the positive-sequence self-impedance characteristic based on the positive-sequence voltage and the first positive-sequence current corresponding to the scanning frequency; calculating the positive-sequence coupling impedance characteristic based on the second negative-sequence current and the positive-sequence voltage; calculating the negative-sequence self-impedance characteristic based on the negative-sequence voltage and the first negative-sequence current corresponding to the scanning frequency; and calculating the negative-sequence coupling impedance characteristic based on the second positive-sequence current and the negative-sequence voltage.
[0013] In addition, after obtaining the AC side current and AC side voltage corresponding to each scanning frequency within the frequency sweep range, the method further includes: performing phase alignment processing on the AC side current and the AC side voltage.
[0014] In addition, after performing phase alignment processing on the AC side current and the AC side voltage, the method further includes: performing Fourier decomposition and positive and negative sequence decomposition on the AC side current and the AC side voltage to obtain the positive sequence voltage, the first positive sequence current, the negative sequence voltage, the first negative sequence current, the second negative sequence current, and the second positive sequence current.
[0015] In addition, after calculating the impedance based on the AC side current and AC side voltage, the method further includes: calculating the amplitude and phase of the impedance at each frequency point; and plotting the corresponding impedance characteristic Bode plot based on the amplitude and phase. Attached Figure Description
[0016] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.
[0017] Figure 1This is a schematic diagram of an impedance testing system according to an embodiment of the present invention;
[0018] Figure 2 This is a schematic diagram of the structure of the host computer in an impedance testing system according to an embodiment of the present invention;
[0019] Figure 3 This is a flowchart of an impedance testing method according to an embodiment of the present invention;
[0020] Figure 4 This is an overall flowchart of an impedance testing method according to an embodiment of the present invention;
[0021] Figure 5 This is a Bode plot of the positive-sequence self-admittance amplitude-frequency characteristic of an impedance testing method according to an embodiment of the present invention;
[0022] Figure 6 This is a Bode plot of the positive-sequence self-admittance phase-frequency characteristic of an impedance testing method according to an embodiment of the present invention. Detailed Implementation
[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been presented in the various embodiments of the present invention to enable the reader to better understand this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various changes and modifications based on the following embodiments.
[0024] The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.
[0025] Embodiments of the present invention relate to an impedance testing system, such as... Figure 1 As shown, it includes: a host computer, a hardware controller, and a new energy grid-connected simulation model; the new energy grid-connected simulation model includes: a new energy power generation unit, a power electronic converter model, a voltage disturbance source module, and a power grid model; the host computer is used to send operating condition control commands to the hardware controller and disturbance source control commands to the new energy grid-connected simulation model; the hardware controller is used to control the new energy grid-connected simulation model to perform frequency sweeping actions according to the operating condition control commands, and during the frequency sweeping action, it collects the AC side current and AC side voltage of the power electronic converter model; the host computer is used to calculate the impedance based on the AC side current and AC side voltage.
[0026] The power electronic converter model is a Field Programmable Gate Array (FPGA) model; the power grid model is a Central Processing Unit (CPU) model. Combining a CPU+FPGA structure to form the circuit model of new energy equipment enables more accurate scanning results.
[0027] Specifically, a power electronic converter model, a voltage disturbance source module, and a power grid model can be built on a host computer. The host computer downloads these models to the real-time simulator via TCP / IP for execution. Furthermore, the host computer sets the disturbance source signals for the real-time simulator via TCP / IP and monitors the status and operating conditions of the hardware controller via the TCP / IP communication protocol to ensure complete control over the frequency sweep process. During the frequency sweep, the simulation results of the simulation model communicate with the hardware controller via I / O. After the frequency sweep is completed, the host computer inputs the acquired data into the impedance calculation module to obtain the equipment impedance results.
[0028] like Figure 2 As shown, the host computer includes a waveform recording module and an impedance calculation module. The waveform recording module records the AC side current and AC side voltage during the frequency sweep process. The impedance calculation module calculates the impedance based on the data recorded by the waveform recording module. The impedance calculation is explained in detail in the following embodiments. Additionally, the host computer includes an impedance scanning module and an ideal voltage source to power the impedance scanning module. The impedance scanning module can output positive or negative sequence disturbance signals of arbitrary frequency and amplitude, and the scanning frequency band can be customized according to the frequency sweep requirements. Simultaneously, based on the customized frequency band, after completing the scan of one frequency point, it can detect whether all frequency points in the band have been traversed. If not, it automatically proceeds to the scan of the next frequency point until all frequency points in the customized frequency band have been scanned, thus achieving automated impedance scanning. After the scanning data is continuously recorded for each frequency point by the waveform recording module, the impedance of each frequency point is generated by the impedance calculation module. The module can also output impedance amplitude-frequency Bode plots and phase angle-frequency Bode plots, providing a reference for power grid stability and controller strategy modification.
[0029] Compared to related technologies, this invention constructs a semi-physical hardware-in-the-loop simulation system. This system simulates an ideal power grid using a new energy power generation unit, a power electronic converter model, a voltage disturbance source module, and a power grid model. The simulated ideal power grid is connected to a real hardware controller. This connection directly reflects the impact of various factors in the real environment on impedance characteristics, making the impedance analysis results more realistic. The host computer sends operating condition control commands to the hardware controller and disturbance source control commands to the new energy grid-connected simulation model. The hardware controller controls the new energy grid-connected simulation model to perform a frequency sweep operation based on the operating condition control commands. During the frequency sweep operation, it collects the AC current and AC voltage of the power electronic converter model. The host computer calculates the impedance based on the AC current and AC voltage. The entire process requires no external means for accuracy verification, effectively reflecting the impedance characteristics of the power electronic converter in the new energy power generation equipment and obtaining relatively accurate impedance characteristic analysis results.
[0030] It is worth mentioning that all modules involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this invention, this embodiment does not introduce units that are not closely related to solving the technical problem proposed by this invention; however, this does not mean that other units are absent from this embodiment.
[0031] This invention relates to an impedance testing method, applied to the impedance testing system described in the above embodiments. The impedance testing method is as follows: Figure 3 As shown, it includes:
[0032] Step 301: Set the grid voltage amplitude, grid frequency, sweep frequency range, and disturbance signal for the grid model.
[0033] Specifically, after building and running a semi-physical simulation model of an ideal power grid, a specific operating condition of the equipment is selected, and its normal operation is ensured. This guarantees the smooth progress of subsequent simulation tests. The grid voltage amplitude of the ideal power grid is U. base The power grid frequency is f base The frequency sweep range is {f1, f2, f3, ..., f}. n The disturbance signal is a voltage disturbance with an amplitude of 5% of the grid voltage amplitude, and its frequency is the positive and negative sequence three-phase voltage of all scanning frequencies within the frequency sweep range. Specifically, the positive and negative sequence three-phase voltages of each scanning frequency can be set separately through the impedance scanning module. After completing the simulation test at one scanning frequency, the system switches to the next scanning frequency to achieve the frequency sweep action. After starting the hardware-in-the-loop simulation test platform, the platform needs to be run stably at 90% of its rated power to ensure the accuracy of the simulation results.
[0034] Step 302: During the frequency sweep operation, acquire the AC side current and AC side voltage corresponding to each scanning frequency band within the frequency sweep range.
[0035] Fourier decomposition and positive / negative sequence decomposition are performed on the AC side current and AC side voltage to obtain the positive-sequence voltage, first positive-sequence current, negative-sequence voltage, and first negative-sequence current corresponding to each scanning frequency, the second negative-sequence current corresponding to the first target frequency, and the second positive-sequence current corresponding to the second target frequency. The first positive-sequence current and the first negative-sequence current are response currents under disturbances of the same frequency, while the second positive-sequence current and the second negative-sequence current are current responses at coupling frequencies with a frequency doubled. The coupling frequencies with a frequency doubled include the first target frequency and the second target frequency, where the first target frequency is the absolute value of the difference between the scanning frequency and twice the grid frequency, |f|. p -2f base The second target frequency is the sum of the scanning frequency and twice the grid frequency, f. p +2f base f p It is the scanning frequency corresponding to the current frequency sweep action, f1≤f p ≤f n , p∈[1,n]. Calculate the impedance based on the positive-sequence voltage, the first positive-sequence current, the negative-sequence voltage, the first negative-sequence current, the second negative-sequence current, and the second positive-sequence current.
[0036] Step 303: Calculate the impedance based on the AC side current and AC side voltage.
[0037] Specifically, the positive-sequence self-impedance characteristic can be calculated based on the positive-sequence voltage and the first positive-sequence current corresponding to the scanning frequency; the positive-sequence coupling impedance characteristic can be calculated based on the second negative-sequence current and the positive-sequence voltage; the negative-sequence self-impedance characteristic can be calculated based on the negative-sequence voltage and the first negative-sequence current corresponding to the scanning frequency; and the negative-sequence coupling impedance characteristic can be calculated based on the second positive-sequence current and the negative-sequence voltage.
[0038] The frequency sweep process of the hardware-in-the-loop simulation system in this solution is explained in detail below, such as... Figure 4 As shown, after building and running the hardware-in-the-loop simulation system for an ideal power grid, the frequency sweep range is determined to be f1≤f p ≤f n , p∈[1,n]. With the scanning frequency set to f1, positive-sequence and negative-sequence voltage disturbance signals with a disturbance amplitude of 5% of the grid voltage amplitude and a frequency of f1 are injected respectively, and the voltage and current on the AC side of the grid connection point are recorded respectively. The AC side current and AC side voltage are phase-aligned, and then the voltage and current signal with an initial phase of 0 for phase A is extracted. Through positive-negative sequence decomposition and Fourier decomposition, a frequency of f1 is obtained. p ,|fp -2f base |,f p +2f base Calculate the positive and negative sequence voltages and currents, and determine the impedance characteristics.
[0039] The specific parameters involved in the above impedance characteristic calculation process can be:
[0040] The injected positive-sequence voltage disturbance signal is:
[0041]
[0042] The injected negative sequence voltage disturbance signal is:
[0043]
[0044] When a positive-sequence voltage disturbance signal is injected, the AC side voltage of the power electronic converter is measured. With AC side current Phase alignment is performed, with the initial phase of the ideal grid A-phase voltage at 0 as the data start time, and voltage and current results of at least 1 second are extracted. With current During the simulation, since the ideal grid voltage is obtained using a fixed trigonometric function, the simulation time is checked to ensure it is within acceptable limits. The initial phase of the ideal grid A-phase voltage at the beginning can be determined by using an integer multiple of the voltage value. With current The positive-sequence voltage U with a scanning frequency of f1 is obtained through Fourier decomposition and positive-negative-sequence decomposition. pos (f1), the first positive sequence current I with scanning frequency f1 pos (f1) and frequency |f1-2f base |The second negative sequence current I neg (|f1-2f base |). The positive-sequence self-impedance characteristic Y is calculated based on the positive-sequence voltage and the first positive-sequence current. 11 (f1),
[0045]
[0046] Based on the second negative-sequence current and the positive-sequence voltage, the positive-sequence coupling impedance characteristic Y is calculated. 21 (f1-2f base ),
[0047]
[0048] I pos (2f base -f1) represents 2f base -f pThe positive sequence current corresponding to the frequency.
[0049] When a negative sequence voltage disturbance signal is injected, the AC side voltage of the power electronic converter is also measured. With AC side current After phase alignment, Fourier decomposition, and positive / negative sequence decomposition, the negative sequence voltage U with frequency f1 is obtained. neg (f1), the first negative sequence current I with frequency f1 neg (f1), frequency is f1+2f base The second positive sequence current I pos (f1+2f base Negative sequence self-impedance characteristic Y 22 (f1) is,
[0050]
[0051] Positive sequence coupling impedance characteristic Y 12 (f1+2f base )for,
[0052]
[0053] The impedance characteristics at a scanning frequency f1 can be obtained using the above method. When the scanning frequency is adjusted to f... p In this case, simply adjust the above steps and the scanning frequency of the impedance characteristic from f1 to f p Impedance calculations for different scanning frequencies can then be performed.
[0054] After each impedance characteristic calculation, it is determined whether p equals n, i.e., whether the simulation test of all frequencies within the frequency sweep range has been completed. If p = n is not satisfied, the positive and negative sequence voltage disturbance signals are injected and the impedance characteristic calculation is repeated at p+1 until p = n is satisfied, completing the simulation of all sweep frequencies within the frequency sweep range. The frequency sweep operation is then exited, and the frequency band from f1 to f2 under 90% rated power is obtained. n The voltage and current waveform data obtained during the frequency sweep process are input into the impedance calculation module. The impedance calculation module calculates the amplitude and phase of the impedance at each frequency point based on the positive and negative sequence self-impedance characteristic formula and the positive and negative sequence coupled impedance characteristic formula, and plots the impedance characteristic Bode plot, as shown below. Figure 5 The image shows the positive-sequence self-admittance magnitude-frequency Bode plot. Figure 6 The figure shows the phase-frequency Bode plot of the positive-sequence self-admittance.
[0055] The impedance characteristic simulation test described above can also be used to perform frequency sweeps for other power conditions. This method is applicable to the impedance characteristic calculation of many new energy devices such as wind turbines, photovoltaics, energy storage, and SVG, providing a reference for grid stability and controller strategy modification. The entire frequency sweep process is more in line with real-world conditions, and this method does not require external verification, thus enabling faster detection of the impedance characteristics of new energy devices.
[0056] This invention relates to a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the method embodiments described above.
[0057] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.
[0058] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.
Claims
1. An impedance testing system, characterized in that, include: Host computer, hardware controller, and new energy grid connection simulation model; The new energy grid connection simulation model includes: a new energy power generation unit, a power electronic converter model, a voltage disturbance source module, and a power grid model; The host computer is used to send operating condition control commands to the hardware controller and to send disturbance source control commands to the new energy grid connection simulation model; The hardware controller is used to control the new energy grid-connected simulation model to perform frequency sweeping action according to the operating condition control command, and to collect the AC side current and AC side voltage of the power electronic converter model during the frequency sweeping action. The host computer is used to calculate the impedance based on the AC side current and AC side voltage.
2. The impedance testing system according to claim 1, characterized in that, The power electronic converter model is a field-programmable gate array (FPGA) model. The power grid model is a central processing unit (CPU) model.
3. The impedance testing system according to claim 1, characterized in that, The host computer includes: a waveform recording module and an impedance calculation module; The waveform recording module is used to record the AC side current and the AC side voltage during the frequency sweep operation. The impedance calculation module is used to calculate the impedance based on the data recorded by the waveform recording module.
4. An impedance testing method, characterized in that, The method, applied to the impedance testing system as described in any one of claims 1 to 3, comprises: Set the grid voltage amplitude, grid frequency, frequency sweep range, and disturbance signal for the grid model; During the frequency sweep operation, the AC side current and AC side voltage corresponding to each scanning frequency band within the frequency sweep range are acquired; The impedance is calculated based on the AC side current and AC side voltage.
5. The impedance testing method according to claim 4, characterized in that, After obtaining the AC side current and AC side voltage corresponding to each scanning frequency within the frequency sweep range, the method further includes: Obtain the positive-sequence voltage, first positive-sequence current, negative-sequence voltage, and first negative-sequence current corresponding to each scanning frequency, the second negative-sequence current corresponding to the first target frequency, and the second positive-sequence current corresponding to the second target frequency; the first target frequency is the absolute value of the difference between the scanning frequency and twice the grid frequency, and the second target frequency is the sum of the scanning frequency and twice the grid frequency; The calculation of impedance based on the AC side current and AC side voltage includes: The impedance is calculated based on the positive sequence voltage, the first positive sequence current, the negative sequence voltage, the first negative sequence current, the second negative sequence current, and the second positive sequence current.
6. The impedance testing method according to claim 5, characterized in that, The step of calculating impedance based on the positive-sequence voltage, the first positive-sequence current, the negative-sequence voltage, the first negative-sequence current, the second negative-sequence current, and the second positive-sequence current includes: The positive-sequence self-impedance characteristic is calculated based on the positive-sequence voltage and the first positive-sequence current corresponding to the scanning frequency. The positive sequence coupling impedance characteristics are calculated based on the second negative sequence current and the positive sequence voltage. The negative sequence self-impedance characteristics are calculated based on the negative sequence voltage and the first negative sequence current corresponding to the scanning frequency. The negative sequence coupling impedance characteristics are calculated based on the second positive sequence current and the negative sequence voltage.
7. The impedance testing method according to claim 5, characterized in that, After obtaining the AC side current and AC side voltage corresponding to each scanning frequency within the frequency sweep range, the method further includes: The AC side current and the AC side voltage are phase aligned.
8. The impedance testing method according to claim 7, characterized in that, After performing phase alignment processing on the AC side current and the AC side voltage, the method further includes: Fourier decomposition and positive / negative sequence decomposition are performed on the AC side current and the AC side voltage to obtain the positive sequence voltage, the first positive sequence current, the negative sequence voltage, the first negative sequence current, the second negative sequence current, and the second positive sequence current.
9. The impedance testing method according to claim 4, characterized in that, After calculating the impedance based on the AC side current and AC side voltage, the method further includes: Calculate the amplitude and phase of the impedance at each frequency point; Draw the corresponding impedance characteristic Bode plots based on the amplitude and phase.
10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the impedance testing method according to any one of claims 4 to 9.