A power system staged state estimation method, system, device and medium

Abstract

This invention belongs to the field of power system analysis technology, and discloses a method, system, equipment, and medium for phased state estimation of power systems. The method includes: calculating the node admittance matrix based on the power system topology and branch parameters; configuring SCADA and PMU at the corresponding nodes of the power system to construct a measurement-state Jacobian matrix H; acquiring SCADA and PMU measurement data and performing time synchronization processing on the two types of measurement data; using a GM estimator to perform nonlinear robust state estimation on the SCADA measurement data to obtain a first estimation result; combining the first estimation result with the PMU measurement data, and performing linear robust state estimation on the combined data to obtain the power system state estimation result. By performing phased and differentiated processing on the two types of measurement data, the complementary advantages of SCADA's wide-area coverage and PMU's high-precision measurement are fully utilized, significantly improving the accuracy and reliability of state estimation in mixed measurement environments.

Description

Technical Field

[0001] This invention belongs to the field of power system analysis technology, specifically relating to a power system phased state estimation method, system, equipment, and medium. Background Technology

[0002] Power system state estimation is a core function of energy management systems (EMS). Its goal is to obtain the optimal estimate of the system's operating state (typically node voltage magnitudes and phase angles) given redundant measurements and network parameters, providing an accurate data foundation for subsequent advanced applications such as power flow analysis, security assessment, and optimized scheduling. Its basic mathematical model is as follows: ;in, z For measurement vectors, x For state vectors, It is a nonlinear measurement function. e This is the measurement error vector.

[0003] With technological advancements, two distinct types of measurement systems coexist in modern power systems: SCADA (Supervisory and Data Acquisition) systems and PMU (Phase Measurement Unit). SCADA systems have low sampling rates (seconds to minutes), primarily providing amplitude measurements such as node voltage amplitude, power flow, and power injection, but lack phase angle information. PMUs, on the other hand, are based on GPS synchronization and can achieve sampling rates of 30-60 times per second, directly providing high-precision voltage and current phasors (including amplitude and phase angle). Theoretically, the introduction of PMUs can significantly improve the accuracy and real-time performance of state estimation, but their deployment costs are high, preventing them from fully replacing SCADA in the short term. Therefore, how to efficiently and robustly integrate these two heterogeneous measurement data from SCADA and PMU to form a complementary hybrid state estimation system has become a key technological challenge in this field.

[0004] Traditional state estimation methods, such as weighted least squares, are typically based on the ideal assumption that measurement errors follow a Gaussian distribution. However, the actual operating environment of power systems is complex, and the distribution of measurement noise is often unknown and frequently deviates from the ideal Gaussian distribution assumption. For example: Heavy-tailed distribution: Actual measured noise may exhibit heavy-tailed characteristics such as Laplace distribution or Gaussian mixture distribution; Outlier contamination: Due to instrument malfunctions, communication errors, network attacks, etc., measurement data may contain impulse noise and outliers. Multiple types of bad data: including but not limited to measurement outliers, erroneous zero-injection assumptions, and bad data at key measurement points.

[0005] The state estimator designed under the Gaussian assumption will suffer a severe deterioration in estimation performance when faced with the above-mentioned non-ideal conditions. It is extremely sensitive to bad data, which will cause the estimation results to deviate significantly from the true value and even trigger iterative divergence.

[0006] To improve robustness, existing technologies have proposed several improved schemes. For example, CN114065118A discloses a robust state estimation method for power systems based on an exponential function. This scheme uses the maximum correlation entropy criterion to construct the objective function and employs an iterative reweighted least squares algorithm to solve it, exhibiting some adaptability to non-Gaussian noise. However, this scheme still has the following limitations: Single-stage unified processing framework: This scheme estimates SCADA and PMU measurements in the same stage, failing to fully consider the fundamental differences between the two in terms of sampling rate, accuracy, and characteristics. This unified processing approach actually dilutes the inherent high accuracy and synchronous phase angle advantages of PMU measurements, and does not fully utilize the complementary characteristics of SCADA and PMU measurements.

[0007] Fixed-form robust objective function: Although the exponential function it uses has a certain degree of robustness, the parameters are fixed and it lacks a special mechanism for targeted identification and suppression of special types of bad data such as bad leverage points (i.e. outliers with high influence in the measurement space).

[0008] Failed to completely break through the Gaussian assumption: The essence of this method is still similar to a robust correction of the Gaussian assumption. When the actual noise distribution differs greatly from Gaussian, it lacks adaptive adjustment capability, and its statistical efficiency and robustness are difficult to guarantee.

[0009] In summary, existing technologies still suffer from architectural flaws and theoretical limitations when dealing with the challenges of fusion of SCADA / PMU mixed measurements and robust estimation in non-Gaussian noise environments. Summary of the Invention

[0010] To address the shortcomings of existing technologies, this invention provides a phased state estimation method, system, device, and medium for power systems. By performing phased and differentiated processing on SCADA measurements and PMU measurements, it fully leverages the complementary advantages of SCADA's wide-area coverage and PMU's high-precision measurement, overcoming the problem that the high-precision advantage of PMU is "diluted" by SCADA measurements in traditional single-stage unified processing. This significantly improves the final accuracy and reliability of state estimation in mixed measurement environments.

[0011] This invention provides the following technical solution: The first objective of this invention is to provide a phased state estimation method for power systems, comprising: Calculate the node admittance matrix based on the power system topology and branch parameters; Configure SCADA and PMU at the corresponding nodes in the power system, and construct the measurement-state Jacobian matrix H; Acquire SCADA and PMU measurement data, and perform time synchronization processing on the two types of measurement data; The GM estimator is used to perform nonlinear robust state estimation on the SCADA measurement data to obtain the first estimation result; The first estimation result is combined with the PMU measurement data, and the combined data is subjected to linear robust state estimation using the GM estimator to obtain the power system state estimation result.

[0012] By employing phased and differentiated processing for SCADA and PMU measurements, the problem of the high-precision advantage of PMU being "diluted" by SCADA measurements in traditional single-stage unified processing is overcome. The first stage focuses on handling nonlinear SCADA measurements and achieving robust estimation, while the second stage linearly integrates the high-precision PMU measurements with the results from the first stage. This approach fully leverages the complementary advantages of SCADA's wide-area coverage and PMU's high-precision measurements, significantly improving the final accuracy and reliability of state estimation in mixed measurement environments.

[0013] As a further improvement of the present invention, the step of using the GM estimator to perform nonlinear robust state estimation on the SCADA measurement data to obtain a first estimation result includes: Input SCADA measurement data. Starting from a flat start, the GM estimator iteratively performs residual calculation, projection statistics calculation, robust scaling estimation, weight update and Givens rotation solution until convergence, and finally outputs the first estimation result.

[0014] When faced with nonlinearity and various types of bad data in SCADA measurements, it can systematically and progressively approximate the optimal robust estimation results.

[0015] As a further improvement of the present invention, the projection statistics calculation is used to identify and mark high-leverage measurement points. If the projection statistics value of a certain measurement point is greater than 2p / m, then the measurement point is marked as a potential lever. Here, p is the dimension of the state variable, and m is the sum of the total number of SCADA measurement points and the total number of PMU measurement points.

[0016] It provides objective criteria for quantifying the "influence" (leverage effect) of measurement points, automatically identifying potential bad leverage points with high influence in the measurement space. This solves the problem of traditional methods struggling to distinguish between "vertical outliers" and "bad leverage points," providing a crucial basis for targeted suppression of these special bad data points, thereby preventing high-leverage measurement points from affecting the estimation results.

[0017] As a further improvement of the present invention, the robust scaling estimate uses a low median estimator to estimate the robust standard deviation of the measurement noise.

[0018] As a further improvement of the present invention, the low median estimator adopts a two-layer low median structure.

[0019] An adaptive noise standard deviation estimation method independent of the Gaussian noise assumption is presented. Compared to traditional least squares variance estimation or median absolute deviation (MAD) estimation, the low-median estimator achieves higher statistical efficiency while maintaining a higher breakdown point (robust to outliers), thus providing more accurate and reliable scale (variance) information for the entire estimation process in unknown non-Gaussian noise environments. The robustness and stability of the scale estimation are enhanced through two low-median operations: an outer layer and an inner layer. This structure can more effectively resist the influence of multiple co-occurring outliers, ensuring that the estimated scale values ​​remain reliable even in heavily polluted noise environments.

[0020] As a further improvement of the present invention, the weight update includes: The weighting factor for each measurement point is calculated based on the projected statistics of each measurement point. Standardized residuals are constructed based on the weighting factor and robust scaling estimate. Huber ρ function is constructed based on the standardized residuals. The influence function and weight function are derived based on the Huber ρ function, and the weight values ​​of each measurement point are updated.

[0021] The Huber ρ function maintains a quadratic form (Gaussian optimal) when the residuals are small, and transforms into a linear form (Laplacian optimal) when the residuals are large. By adjusting the threshold c, it can adapt to noise with varying degrees of fat tails. The weighting function derived from the Huber ρ function can adaptively adjust the weight of each measurement point: assigning high weights to normal measurements with small residuals to maintain accuracy, and assigning low weights to outliers with large residuals to suppress their impact. This collaborative mechanism achieves unified and effective handling of vertical outliers and bad leverage points.

[0022] As a further improvement of the present invention, the step of combining the first estimation result with PMU measurement data and using a GM estimator to perform linear robust state estimation on the combined data to obtain the power system state estimation result includes: The first estimation result is combined with the PMU measurement data to form an augmented vector. The correlation between the two measurements is eliminated by pre-whitening. The GM estimator is then used for linear robust estimation to obtain the power system state estimation result.

[0023] By treating the first-stage estimation results as "pseudo-measurements" and combining them with the original PMU measurements to form an augmented vector, the nonlinear estimation problem is cleverly transformed into a linear one. Pre-whitening eliminates the correlation between measurement errors from different sources, enabling subsequent linear GM estimation to run more efficiently and stably. This approach fully utilizes the high-precision linear information of the PMU measurements to calibrate and enhance the first-stage results, while avoiding complex nonlinear iterations in the second stage, thus improving the final estimation accuracy while maintaining computational efficiency.

[0024] A second objective of this invention is to provide a phased state estimation system for power systems, used to implement the above-mentioned method, comprising: The measurement configuration module is configured to: calculate the node admittance matrix based on the power system topology and branch parameters; configure SCADA and PMU at the corresponding nodes of the power system; and construct the measurement-state Jacobian matrix H. The data acquisition and preprocessing module is configured to acquire SCADA and PMU measurement data and perform time synchronization processing on the two types of measurement data. The first estimation module is configured to: use the GM estimator to perform nonlinear robust state estimation on the SCADA measurement data to obtain the first estimation result; The second estimation module is configured to combine the first estimation result with the PMU measurement data, and then perform linear robust state estimation on the combined data to obtain the power system state estimation result.

[0025] A third objective of this invention is to provide a computer device comprising at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the program is executed by the processing unit, the processing unit performs the aforementioned method.

[0026] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program executable by an electronic device, which, when run on the electronic device, causes the electronic device to perform the above-described method.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows: By employing phased and differentiated processing for SCADA and PMU measurements, the problem of the high-precision advantage of PMU being "diluted" by SCADA measurements in traditional single-stage unified processing is overcome. The first stage focuses on handling nonlinear SCADA measurements and achieving robust estimation, while the second stage linearly integrates the high-precision PMU measurements with the results from the first stage. This approach fully leverages the complementary advantages of SCADA's wide-area coverage and PMU's high-precision measurements, significantly improving the final accuracy and reliability of state estimation in mixed measurement environments.

[0028] Projective statistics are used to identify and label high-leverage measurement points, providing a crucial basis for subsequent targeted suppression of these particularly bad data and preventing high-leverage measurement points from affecting the estimation results. A low median estimator is used to estimate the robust standard deviation of measurement noise, providing more accurate and reliable scale information for the entire estimation process in unknown non-Gaussian noise environments. Standardized residuals are constructed using projection statistics and robust scale estimates to build the Huber ρ function and derive the influence function and weight function, enabling adaptive updates of the weights of each measurement point.

[0029] It can completely break free from the constraints of the Gaussian noise assumption in a mixed measurement environment of SCADA and PMU, maintain strong robustness to various actual noise distributions (including heavy-tailed distribution, mixed distribution, and pollution distribution) and bad data, and maintain near-optimal statistical efficiency, so as to provide accurate and reliable state estimation for power systems. Attached Figure Description

[0030] Figure 1 A flowchart of a phased state estimation method for power systems; Figure 2 The flowchart for the first-stage nonlinear robust state estimation; Figure 3 This is a flowchart for the second-stage linear robust state estimation. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] The present invention will now be described in further detail with reference to the accompanying drawings: like Figure 1 As shown, this embodiment provides a phased state estimation method for a power system, including: Calculate the node admittance matrix based on the power system topology and branch parameters; specifically: Obtain the single-line diagram and branch parameters (resistance, reactance, and susceptance) of the power system, construct the node-branch correlation matrix, and calculate the node admittance matrix Y. The calculation formula is as follows:

[0033] in, Y for Complex matrices, nFor the number of nodes, G Here is the conductance matrix. B This is the susceptance matrix.

[0034] Configure SCADA and PMU at the corresponding nodes in the power system, and construct the measurement-state Jacobian matrix H; specifically: SCADA measurement configuration At each measurement point, the power injection was measured. Power flow and voltage amplitude In this embodiment, SCADA is configured on each node; PMU measurement configuration. At each measurement point, the voltage phasor is measured. Current phasor The role of the PMU is to enhance the accuracy of state estimation. In this embodiment, the PMU is only configured on a few nodes. The location and number of nodes configured with the PMU can be adjusted according to the actual situation.

[0035] Acquire SCADA and PMU measurement data, and perform time synchronization processing on the two types of measurement data; specifically: SCADA sampling period is 2-4 seconds, data format is [node number, measurement type, measurement value, timestamp], and measurement vector is... The PMU sampling rate is 30~60Hz, and the data format is [PMU number, phasor value, GPS timestamp]. The measurement vector is... The PMU data is downsampled to the SCADA time scale, and the timestamps are aligned using interpolation or nearest neighbor methods.

[0036] The GM estimator is used to perform nonlinear robust state estimation on the SCADA measurement data, and the first estimation result is obtained; for example... Figure 2 As shown, the first-stage nonlinear robust state estimation includes: Input SCADA measurement data. Starting from a flat start, the GM estimator iteratively performs residual calculation, projection statistics calculation, robust scaling estimation, weight update and Givens rotation solution until convergence, and finally outputs the first estimation result.

[0037] Projective statistical calculations are used to identify and mark high-lever measurement points. The calculation formula is as follows:

[0038] in, For the first i Projected statistical values ​​of each measurement point; For the Jacobian matrix, the first... i Row data, i.e., the first row i Measurement data for each measurement point, each measurement A row that makes up the Jacobian matrix.

[0039] Leverage point determination criteria: like Then the measurement point is marked as a potential lever point, where p Let the dimension of the state variables be . m This is the sum of the total number of SCADA measurement points and the total number of PMU measurement points; The weighting factor for each measurement point is calculated using projection statistics. :

[0040] Projective statistical calculations can simultaneously handle two fundamentally different types of bad data: vertical outliers and bad leverage points.

[0041] Robust scaling estimation uses a low-median estimator with a two-layer low-median structure to estimate the robust standard deviation of measurement noise. The calculation formula is:

[0042] The outer lomed sequence uses the order statistic [(m+1) / 2], and the inner lomed sequence uses the order statistic [m / 2]+1. For bias correction factors for a limited sample, , Let be the residuals of the i-th measurement and the j-th measurement, respectively. The formula for calculating the residuals is:

[0043] in For the first i One actual measured value, For the first k Next iteration state estimation The calculation of the first i A theoretical measurement value, For the first i The nonlinear measurement function corresponding to each measurement.

[0044] The low median estimator does not require a pre-set noise model and can automatically adapt to unknown distributions. The low median estimator has a Gaussian efficiency of 82% and a breakdown point of 25%, which is significantly better than the MAD (Median Absolute Deviation) estimator's 37% Gaussian efficiency and 50% breakdown point.

[0045] Standardized residuals are constructed using weighting factors and robust scaling estimates. Based on standardized residuals Construct the Huber ρ function and derive the influence function and weight function. Update the weight values ​​of each measurement point using the weight function, and then use Givens rotation numerical solution. Iterate until convergence to obtain the first estimation result. This enables nonlinear robust state estimation for SCADA.

[0046] The Huber ρ function is expressed as:

[0047] in, To standardize the residuals, For robust standard deviation c=1.5 is the threshold.

[0048] By using the Huber function with a defined threshold, rather than a continuous exponential function, near-optimal performance can be maintained under different noise distributions.

[0049] Influence function Represented as:

[0050] Weighting function Represented as:

[0051] The iterative equation is expressed as:

[0052] in, , For SCADA measurement vectors, It is a nonlinear measurement function. This represents the number of iterations.

[0053] To avoid the numerical problems associated with matrix inversion, Givens rotation is used to transform the iterative equation into:

[0054] QR decomposition is used to solve the problem to ensure numerical stability.

[0055] During the iteration process, the zero-injection measurement is dynamically weighted, specifically including: In the first iteration, the initial weights of all zero-injection measurements are set to be the same as the initial weights of ordinary non-zero-injection measurements in the current iteration; Starting from the second iteration, the weights of each zero-injection measurement are dynamically adjusted based on the standardized residuals calculated in the previous iteration; the dynamic adjustment includes: If the absolute value of the standardized residual of a zero-injection measurement is less than a set threshold, it is determined to be a "good zero injection" and its weight is restored to a higher value; if the absolute value of the standardized residual of a zero-injection measurement is greater than or equal to the set threshold, it is determined to be a "bad zero injection" and its weight is reduced to a lower value. The adjusted weights will be used for the state update calculation in this iteration, and the above judgment and adjustment process will be repeated in subsequent iterations until convergence.

[0056] The first estimation result is combined with the PMU measurement data, and the GM estimator is used to perform linear robust state estimation on the combined data to obtain the power system state estimation result; specifically: The first estimation result PMU measurement data The two measurements are combined into an augmented vector, and the correlation between the two measurements is eliminated through pre-whitening. The GM estimator is then used for linear robust estimation to obtain the power system state estimation result.

[0057] The augmented vector (measurement model) is represented as:

[0058] in, ; , I It is the identity matrix. M PMU measurement matrix; For the error vector, , These are the error vectors of the first estimation result and the PMU measurement error vector, respectively. Pre-whitening treatment includes: Constructing the covariance matrix P :

[0059]

[0060] in, For PMU measurement error covariance, The error covariance of the first estimation result. .

[0061] For covariance matrix P Cholesky decomposition yields the matrix S ,calculate S inverse of a matrix S -1 ,use S -1 Left multiply the original measurement vector Z Whitening measurements were obtained. y :

[0062] Using the same transformation matrix S -1 For the original coefficient matrix APerform the corresponding transformation to obtain A The corresponding transformation matrix of the matrix G :

[0063] Linear robust iteration is performed using the same Huber function and iteration strategy as in the first phase:

[0064] in j For the number of substitutions, This is the weight matrix. It is the first j The state correction amount for the next iteration.

[0065] when The iteration stops at a certain point, and the final output is the state estimation result of the power system.

[0066] In summary, the method provided in this embodiment processes SCADA measurements and PMU measurements in stages and with differentiation, overcoming the problem that the high-precision advantage of PMU is "diluted" by SCADA measurements in traditional single-stage unified processing. The first stage focuses on processing nonlinear SCADA measurements and achieving robust estimation, while the second stage linearly fuses the high-precision PMU measurements with the results of the first stage. This fully leverages the complementary advantages of SCADA's wide-area coverage and PMU's high-precision measurements, significantly improving the final accuracy and reliability of state estimation in mixed measurement environments.

[0067] This embodiment provides a phased state estimation system for a power system to implement the above method, including: The measurement configuration module is configured to: calculate the node admittance matrix based on the power system topology and branch parameters; configure SCADA and PMU at the corresponding nodes of the power system; and construct the measurement-state Jacobian matrix H. The data acquisition and preprocessing module is configured to acquire SCADA and PMU measurement data and perform time synchronization processing on the two types of measurement data. The first estimation module is configured to: use the GM estimator to perform nonlinear robust state estimation on the SCADA measurement data to obtain the first estimation result; The second estimation module is configured to combine the first estimation result with the PMU measurement data, and then perform linear robust state estimation on the combined data to obtain the power system state estimation result.

[0068] This embodiment provides a computer device, including at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the program is executed by the processing unit, the processing unit performs the above-described method.

[0069] This embodiment provides a computer-readable storage medium storing a computer program executable by an electronic device, which, when run on the electronic device, causes the electronic device to perform the above-described method.

[0070] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A phased state estimation method for a power system, characterized in that, include: Calculate the node admittance matrix based on the power system topology and branch parameters; Configure SCADA and PMU at the corresponding nodes in the power system, and construct the measurement-state Jacobian matrix H; Acquire SCADA and PMU measurement data, and perform time synchronization processing on the two types of measurement data; The GM estimator is used to perform nonlinear robust state estimation on the SCADA measurement data to obtain the first estimation result; The first estimation result is combined with the PMU measurement data, and the combined data is subjected to linear robust state estimation using the GM estimator to obtain the power system state estimation result.

2. The method according to claim 1, characterized in that, The first estimation result obtained by using the GM estimator to perform nonlinear robust state estimation on the SCADA measurement data includes: Input SCADA measurement data. Starting from a flat start, the GM estimator iteratively performs residual calculation, projection statistics calculation, robust scaling estimation, weight update and Givens rotation solution until convergence, and finally outputs the first estimation result.

3. The method according to claim 2, characterized in that, The projection statistics calculation is used to identify and mark high-leverage measurement points. If the projection statistics value of a measurement point is greater than 2p / m, the measurement point is marked as a potential lever. Here, p is the dimension of the state variable, and m is the sum of the total number of SCADA measurement points and the total number of PMU measurement points.

4. The method according to claim 2, characterized in that, The robust scaling estimate uses a low median estimator to estimate the robust standard deviation of the measurement noise.

5. The method according to claim 4, characterized in that, The low median estimator employs a two-layer low median structure.

6. The method according to claim 2, characterized in that, The weight update includes: The weighting factor for each measurement point is calculated based on the projected statistics of each measurement point. Standardized residuals are constructed based on the weighting factor and robust scaling estimate. Huber ρ function is constructed based on the standardized residuals. The influence function and weight function are derived based on the Huber ρ function, and the weight values ​​of each measurement point are updated.

7. The method according to claim 1, characterized in that, The step of combining the first estimation result with PMU measurement data and using a GM estimator to perform linear robust state estimation on the combined data to obtain the power system state estimation result includes: The first estimation result is combined with the PMU measurement data to form an augmented vector. The correlation between the two measurements is eliminated by pre-whitening. The GM estimator is then used for linear robust estimation to obtain the power system state estimation result.

8. A phased state estimation system for a power system, used to implement the method as described in any one of claims 1 to 7, characterized in that, include: The measurement configuration module is configured to calculate the node admittance matrix based on the power system topology and branch parameters. Configure SCADA and PMU at the corresponding nodes in the power system, and construct the measurement-state Jacobian matrix H; The data acquisition and preprocessing module is configured to acquire SCADA and PMU measurement data and perform time synchronization processing on the two types of measurement data. The first estimation module is configured to: use the GM estimator to perform nonlinear robust state estimation on the SCADA measurement data to obtain the first estimation result; The second estimation module is configured to combine the first estimation result with the PMU measurement data, and then perform linear robust state estimation on the combined data to obtain the power system state estimation result.

9. A computer device, characterized in that, It includes at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program that, when executed by the processing unit, causes the processing unit to perform the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores a computer program executable by an electronic device, which, when run on the electronic device, causes the electronic device to perform the method as described in any one of claims 1 to 7.

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