CN117913902A - Island micro-network state estimation method and system based on preset time observer - Google Patents
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Abstract
The invention provides an island micro-network state estimation method and system based on a preset time observer, which belong to the technical field of multi-agent distributed state estimation and comprise the following steps: establishing a state space equation based on a mathematical model of the island mode micro-grid system; constructing two local observers on each distributed power supply node based on a state space equation, and establishing a mathematical model of the local observers; according to the preset time and the local observer parameters, a conversion matrix of each local observer is designed; determining communication times, initial communication time and communication time interval, and realizing error gradual convergence by each observation node through communication cooperation before the initial communication time; after the initial communication moment is reached, based on the conversion matrix of each local observer and the execution of a distributed discrete communication algorithm, each node can obtain the state conversion information of all nodes within a preset time, and the real state of the system is calculated, so that the distributed state estimation of the preset time is realized.
Description
Technical Field
The invention belongs to the technical field of multi-agent distributed state estimation, and particularly relates to an island micro-network state estimation method and system based on a preset time observer.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The micro-grid system consists of a plurality of distributed power supplies and energy storage equipment, covers various energy forms such as solar photovoltaic, wind power generation, fuel gas and the like, and is provided with various energy conversion, control and management equipment. The devices cooperate with each other, coordinate and manage through an intelligent control system, and aim to utilize renewable energy resources to the greatest extent and improve the reliability and quality of a power supply system. When the main power grid fails or other abnormal conditions occur, the micro power grid can be switched into an island operation mode by cutting off the connection with the main power grid so as to prevent the fault from diffusing and ensure the stability and reliability of the internal operation of the micro power grid. In order to realize stable operation of the micro-grid in the island mode, a proper control algorithm is required to be adopted to maintain the stability of the internal voltage and frequency of the system, so that the normal operation of the internal load of the micro-grid is ensured.
State feedback is widely used in the design of microgrid control algorithms. Aiming at the actual engineering control problem, because it is difficult to directly measure and feed back all state information, an observer is generally adopted to estimate the state of the system through output information. Under the condition of facing complex environments, particularly large system dimension, the distributed sensor network is adopted to measure the complete output information of the system. At this point, a single centralized observer cannot meet an accurate estimate of the observed system state.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an island micro-network state estimation method based on a preset time observer, and a distributed observer based on multiple intelligent agents is introduced to realize the preset time distributed state estimation.
To achieve the above object, one or more embodiments of the present invention provide the following technical solutions:
in a first aspect, an island micro-mesh state estimation method based on a preset time observer is disclosed, including:
establishing a state space equation based on a mathematical model of the island mode micro-grid system;
constructing two local observers on each distributed power supply node based on a state space equation, and establishing a mathematical model of the local observers;
According to the preset time and the local observer parameters, a conversion matrix of each local observer is designed;
Determining communication times, initial communication time and communication time interval, and realizing error gradual convergence by each observation node through communication cooperation before the initial communication time;
after the initial communication moment is reached, based on the conversion matrix of each local observer and the execution of a distributed discrete communication algorithm, each node can obtain the state conversion information of all nodes within a preset time, and the real state of the system is calculated, so that the distributed state estimation of the preset time is realized.
As a further technical scheme, the mathematical model of the island mode micro-grid system is as follows:
wherein, Is/>Power angle of inverter of each distributed power supply,/>Is/>Relative frequency of individual distributed power supplies, where/>For frequency,/>For reference operating frequency,/>To measure the filter coefficient of the active power,/>For the frequency reduction gain,/>For the desired active power,/>For the actual active power,/>For the voltage of the inverter, the voltage level of the distributed power supply can be effectively maintained by adopting a limited time voltage method, thus/>Is constant,/>Is obtained by removing all physical busesDistributed power supply and/>Susceptance between distributed power supplies,/>Is a constant impedance load,/>Is a constant current load,/>Is a constant power load.
As a further technical scheme, when a state space equation is established, an inverter power angle and a relative frequency are selected as a system state of the distributed power supply, the inverter power angle is selected as a physical quantity measured by a sensor, and the inverter power angle measurement is performed based on phasor measurement unit detection equipment.
As a further technical solution, the mathematical model of the local observer is constructed by:
Setting up a system communication network topology Is strongly connected,/>For/>Laplace matrix,/>Is thatIs a finite non-empty set of nodes;
For distributed power supply observation nodes Establishing a local observer;
all local observers constitute two asymptotically converging observer systems, inside which communication and collaboration takes place.
As a further technical scheme, for the distributed power supply observation nodeEstablishing a local observer:
wherein, Is the observation node/>Estimated state of/>Representing a communication network topology adjacency matrix/>(1 /)Term, matrix/>Is an output feedback matrix, matrix/>Is an information interaction gain matrix,/>Representing the coupling gain.
As a further technical solution, when the distributed discrete communication algorithm is designed, the method specifically includes:
determining the number of times of observation node communication;
Determining communication initial time and communication interval;
and designing a distributed discrete communication algorithm information set.
As a further technical solution, the distributed discrete communication algorithm, when executed, specifically includes:
When the number of communication times is smaller than If node/>There is/>Node/>Acquiring neighboring nodes/>The information of the same node information in the known node information set is filtered and removed;
Screening and removing the same integral node information in the unknown node information set;
when reaching the preset convergence time And outputting the system state by each observation node.
In a second aspect, a microgrid state estimation system of a distributed preset time observer is disclosed, comprising:
A local observer building module configured to: establishing a state space equation based on a mathematical model of the island mode micro-grid system;
constructing two local observers on each distributed power supply node based on a state space equation, and establishing a mathematical model of the local observers;
According to the preset time and the local observer parameters, a conversion matrix of each local observer is designed;
A microgrid state estimation module configured to: determining communication times, initial communication time and communication time interval, and realizing error gradual convergence by each observation node through communication cooperation before the initial communication time;
after the initial communication moment is reached, based on the conversion matrix of each local observer and the execution of a distributed discrete communication algorithm, each node can obtain the state conversion information of all nodes within a preset time, and the real state of the system is calculated, so that the distributed state estimation of the preset time is realized.
The one or more of the above technical solutions have the following beneficial effects:
According to the method, two local observers are constructed at each distributed power supply observation node, a time lag is introduced to construct a balance relation between an estimated state and a system state, and the estimated state is converted into the system state through constructing a conversion matrix and a distributed discrete communication algorithm, so that state estimation is realized in preset time.
In the technical scheme of the embodiment, time delay is introduced to construct a balance relation between an estimated state and a system state, and the specific implementation mode is as follows: in the state estimation process, a system error, namely a homogeneous dynamic equation for estimating the difference between the state and the real state of the system, can be constructed by designing a local observer, and the current error can be represented by the product of the error of the past moment (namely the current moment minus the time lag) and the state transition matrix with the time lag (time lag) by the property of the state transition matrix.
The error can be represented by the product of the error at the past moment and a state transition matrix with time delay, and then the error is separated into an estimated state and a real state of the system, and the estimated state and the system state are respectively independent at the left side and the right side of the equation, so that the balance relation between the estimated state and the system state is constructed.
The error dynamic asymptote of the traditional asymptotically converged distributed state observer tends to 0, but can never reach 0, and the technical scheme of the embodiment can realize 0 error dynamic in any preset time, ensure the authenticity of state estimation, is suitable for a high-precision state estimation scene of a micro-grid system and is irrelevant to the initial state of the system, thereby not only having significant significance for improving the control performance of the micro-grid system, but also providing powerful support for coping with external interference and uncertainty.
The conventional observer with convergence of the preset time is only aimed at the centralized problem, but when the observer is used for the distributed observer, the problem that the state transition information cannot be known globally exists, and the state transition information is the key point of realizing the 0 error in the preset time.
Therefore, the technical scheme of the embodiment provides a discrete communication algorithm, and each node can obtain the state transition information of all nodes in a distributed manner in a preset time by selecting a proper initial communication time and a proper communication time interval, so that the real state of the system is calculated, and the distributed state estimation of the preset time is realized.
In addition, because the system dynamic equation in the technical scheme of the embodiment is more common, the design method of the invention has stronger applicability.
Additional aspects of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a schematic diagram of the power angle measurement of the present invention;
FIG. 2 is a block diagram of a simulated micro-grid system of the present invention;
FIG. 3 is a simulated communication network topology of the present invention;
FIG. 4 is a diagram of the state of estimation and system state of the 1 st local observer during simulation according to the present invention;
FIG. 5 is a diagram of the state of estimation and system state of the 2 nd local observer during simulation according to the present invention;
FIG. 6 is a diagram of the state of estimation and system state of the 3 rd local observer during simulation according to the present invention;
FIG. 7 is a diagram of the state of estimation and system state of the 4 th local observer in simulation according to the present invention;
FIG. 8 is a step diagram of an implementation of the present invention;
Fig. 9 is a flow chart of a distributed discrete communication algorithm of the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention.
Embodiments of the invention and features of the embodiments may be combined with each other without conflict.
A multi-agent based distributed observer in which each local observer receives a portion of the system output information and cooperatively communicates throughout the observer network to effect an estimate of the system state. In evaluating the performance of a control system, particularly in the case of high control accuracy requirements or interference attacks on the system, reducing the dependence of state estimation on output information becomes a key goal. In order to rapidly reduce the error dynamics of the distributed observer and thus achieve faster convergence, it is necessary to study the convergence of the distributed observer. The introduction of the finite time state estimation ensures that the real state of the system is acquired in finite time, and the distributed preset time observer can acquire the real state of the system in the preset time of a user on the basis of convergence in finite time and is irrelevant to the initial state of the system, so that the method has remarkable significance for improving the control performance of the micro-grid system and provides powerful support for coping with external interference and uncertainty.
Aiming at the limitation of the existing distributed preset time observer in the field of island mode micro-grid system state reconstruction, less research is carried out, and in terms of system form, the invention provides a design method of the distributed preset time observer. Firstly, parameters of a local observer are designed by solving a linear matrix inequality, the local observer forms two asymptotically convergent observer systems, and communication and cooperation are carried out inside the observer systems. And then determining a conversion matrix of each local observer according to the observer convergence time preset by a user and the designed local observer. Finally, a distributed discrete communication algorithm is designed, and through selecting proper initial communication time and communication time interval, each node can obtain state transition information of all nodes in preset time, and the real state of the system is calculated, so that distributed state estimation of the preset time is realized. In addition, the distributed preset time observer design method can be used for realizing the preset time distributed state estimation by a general continuous linear time invariant system similar to the dynamic model of the island mode micro-grid system.
Example 1
Referring to fig. 8, the embodiment discloses an island micro-mesh state estimation method based on a preset time observer, which includes:
Step one: and establishing a state space equation of the island mode micro-grid system. Referring to fig. 2, the mathematical model of the island mode micro-grid system is:
(1)
wherein, Is/>Power angle of inverter of each distributed power supply,/>Is/>Relative frequency of individual distributed power supplies, where/>For frequency,/>For reference operating frequency,/>To measure the filter coefficient of the active power,/>For the frequency reduction gain,/>For the desired active power,/>For the actual active power,/>For the voltage of the inverter, the voltage level of the distributed power supply can be effectively maintained by adopting a limited time voltage method, thus/>Is constant,/>Is obtained by removing all physical busesDistributed power supply and/>Susceptance between distributed power supplies,/>Is a constant impedance load,/>Is a constant current load,/>Is a constant power load.
The model is built based on the primary control principle of a distributed power supply of a voltage-controlled voltage source inverter, a ZIP load model is applied, and meanwhile, a system model is simplified according to system properties.
The advantages are as follows:
The ZIP model considers the constant resistance, the linear resistance and the nonlinear characteristics of the load, describes the load behavior more accurately, and is beneficial to improving the stability and the robustness of the control system.
The simplified model can reduce the system calculation complexity and improve the calculation efficiency, especially in the real-time control and optimization process.
An effective and feasible solution is provided for primary control of a distributed power system, and the system has practicability and operability.
In this embodiment, the power angle of the inverter is selectedAnd relative frequency/>As a system state of the distributed power supply, an inverter power angle is selected as a physical quantity measured by a sensor, and the inverter power angle measurement is performed based on a phasor measurement unit (Phasor Measurement Unit, PMU) detection device. Wherein, the power angle testing principle is shown in figure 1, and is selectedAs a system state, a system state equation is:
(2)
wherein, Is the state of the system,/>Is a system matrix which can be obtained by (1) formula calculation,/>Is the output matrix. /(I)Is the measurement output of the system,/>,/>And/>Satisfy/>,/>,/>Is the observation node/>Received output measurement value, and/>. Island microgrid system/>Is observable, distributed power system/>It need not be observable.
The state equation shows the differential relation of the system state in a concise way, has strong generalization, and most systems have the expression form of the system state, so that the adaptability of the design is strong from the side.
Step two: and establishing a mathematical model of the local observer. Setting up a system communication network topologyIs strongly connected,/>For/>Laplace matrix,/>Is/>Is a finite non-empty set of nodes. For distributed power observation node/>Establishing a local observer:
(3)
wherein, Is the observation node/>Estimated state of/>Representing a communication network topology adjacency matrix/>(1 /)Term, matrix/>Is an output feedback matrix, matrix/>Is an information interaction gain matrix,/>Representing the coupling gain.
All local observers constitute two asymptotically converging observer systems, inside which communication and collaboration takes place.
The local observer parameter design steps are as follows:
1. Pair system Performing observability decomposition:
(4)
wherein, ,/>Representing the dimension of the observable subspace, and/>Is observable.
2. Calculating the forward vectorSatisfy/>And/>。
3. Order theAnd/>Satisfy/>Wherein/>,。
4. Order the,/>The following formula is satisfied:
(5)
5. Selection of Satisfy/>。
6、Is a positive definite matrix and satisfies:
(6)
7. The gain matrix is:
(7)
The design steps described above are applicable to meeting the system properties, i.e., the system Is an observable system and has strong adaptability. In addition, the design step is based on solving the inequality of the linear matrix and the equation of the linear matrix, so that the solution is simple and easy to realize, and the operability is strong.
Asymptotic convergence demonstration is performed as follows, and an error system is constructed:
(8)
(9)
wherein, ,/>。
Selecting Lyapunov functionWherein/>Is positive matrix, pair/>And (3) derivative:
(10)
Order the Then/>. Thus is provided with
(11)
From step 3And step 4, can obtain
(12)
Wherein,,/>。
(13)
Wherein,。
Thus (2)The two observer systems are designed to converge asymptotically.
Step three: and designing a conversion matrix of each local observer according to the preset time and the local observer parameters. The product of the conversion matrix of the local observer and the estimated state at the past moment is the communication content in the subsequent distributed discrete communication algorithm, and the real state of the system is formed after the distributed communication algorithm is finished.
Order the,/>The dynamic equation of (2) is:
(14)
wherein, ,/>。
Order the,/>The dynamic equation of (2) is:
(15)
wherein, ,/>,/>Wherein/>。
The dynamic equation of the systematic error is:
(16)
the solution of the dynamic equation is:
(17)
wherein, And presetting convergence time for a user. Thus (2)
(18)
Defining a transformation matrix,/>Wherein/>,. Thus is provided with
(19)
The transformation matrix of the local observer is thus:
(20)
wherein, ,/>The expression form of the state estimation is:
(21)
Referring to fig. 9, step three: design of distributed discrete communication algorithm.
(1) Determining the number of times of observation node communication:
using strong connectivity graphs Observer networks communicating by/>The sub-discrete-time communication is such that for the/>The distributed power supply observation nodes obtain information of all nodes of the communication network, wherein/>,/>For/>Personal node to the/>Shortest distance of directed path of individual node,/>。
(2) Determining communication initial time and communication interval:
Assume that the convergence time preset by the user is Initial communication time is/>Each communication has a time interval ofSelect proper/>Make/>And (3) obtaining the product.
(3) Designing a distributed discrete communication algorithm information set:
Assume a system strong connectivity map Each node in the network can acquire information of adjacent nodes and store and calculate the information. Each node is provided with a known node information set, an unknown node information set and a node sum information set, wherein each set is described as follows:
3-1), known node information set is defined as Wherein/>,A kind of electronic device
(22)
Wherein,,/>Is the initial communication time,/>Is the delay time and/>。
3-2), Unknown node information set is defined asWherein/>,,/>A kind of electronic device
(23)
3-3), Node sum information set is defined asWherein/>,
(24)
(4) The distributed discrete communication algorithm performs the following steps:
4-1) when the number of communication times is smaller than If node/>There is/>Node/>Acquiring neighboring nodes/>And filtering and removing the same node information in the known node information set: /(I),Wherein/>. And then screening and removing the same integral node information in the unknown node information set: if for/>,/>And/>Then/>,。
4-2), IfThen/>,/>,/>,/>。
4-3), IfThen/>,/>,/>,/>。
4-4), Repeating the above steps until the number of communications is equal toThe time taken to execute the algorithm is;
4-5) When a preset convergence time is reachedWhen each observation node outputs the system state/>。
The execution flow is simple and easy to implement; the node information is prevented from being repeated by the distributed information interaction and the information screening, the parallelization processing improves the execution efficiency and the calculation speed of the algorithm, and the robustness and the expandability of the system are improved. The iteration termination condition can be directly determined according to the system, and is clear and convenient.
An island micro-grid simulation block diagram is shown in fig. 2, and a local observer communication network topology diagram is shown in fig. 3. The island micro-grid system comprises 4 distributed power sources, 4 local loads and 3 groups of transmission buses, and the island micro-grid model parameters are shown in the following table 1:
TABLE 1
The initial state of the system is taken as x (0) = [0.8 0 0.9 0 0.9 0 0.8 0], the expected estimated time d=0.07 s is selected, the discrete communication time interval is 0.01s, and the initial communication time is 0.05s. The local observer outputs are set to 0 before the end of communication, and the local observers output estimated states after the end of communication. The simulation results are shown in fig. 4-7, and the local observer can achieve the state estimation of the preset time after the distributed discrete communication is finished, namely, the estimated state at the moment of 0.07s is consistent with the state of the system.
Example two
It is an object of the present embodiment to provide a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, which processor implements the steps of the above method when executing the program.
Example III
An object of the present embodiment is to provide a computer-readable storage medium.
A computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the above method.
Example IV
An object of the present embodiment is to provide a microgrid state estimation system of a distributed preset time observer, including:
A local observer building module configured to: establishing a state space equation based on a mathematical model of the island mode micro-grid system;
establishing a mathematical model of the local observer based on the state space equation;
According to the preset time and the local observer parameters, a conversion matrix of each local observer is designed;
A microgrid state estimation module configured to: determining communication times, initial communication time and communication time interval, and realizing error gradual convergence by each observation node through communication cooperation before the initial communication time;
after the initial communication time is reached, a distributed discrete communication algorithm is executed, and after the preset time is reached, each observation node outputs system state information.
The steps involved in the devices of the second, third and fourth embodiments correspond to those of the first embodiment of the method, and the detailed description of the embodiments can be found in the related description section of the first embodiment. The term "computer-readable storage medium" should be taken to include a single medium or multiple media including one or more sets of instructions; it should also be understood to include any medium capable of storing, encoding or carrying a set of instructions for execution by a processor and that cause the processor to perform any one of the methods of the present invention.
It will be appreciated by those skilled in the art that the modules or steps of the invention described above may be implemented by general-purpose computer means, alternatively they may be implemented by program code executable by computing means, whereby they may be stored in storage means for execution by computing means, or they may be made into individual integrated circuit modules separately, or a plurality of modules or steps in them may be made into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the invention, but rather, it is intended to cover all modifications or variations within the scope of the invention as defined by the claims of the present invention.
Claims (10)
1. The island micro-mesh state estimation method based on the preset time observer is characterized by comprising the following steps of:
establishing a state space equation based on a mathematical model of the island mode micro-grid system;
constructing two local observers on each distributed power supply node based on a state space equation, and establishing a mathematical model of the local observers;
According to the preset time and the local observer parameters, a conversion matrix of each local observer is designed;
Determining communication times, initial communication time and communication time interval, and realizing error gradual convergence by each observation node through communication cooperation before the initial communication time;
after the initial communication moment is reached, based on the conversion matrix of each local observer and the execution of a distributed discrete communication algorithm, each node can obtain the state conversion information of all nodes within a preset time, and the real state of the system is calculated, so that the distributed state estimation of the preset time is realized.
2. The island micro-grid state estimation method based on the preset time observer according to claim 1, wherein the mathematical model of the island mode micro-grid system is:
;
wherein, Is/>Power angle of inverter of each distributed power supply,/>Is/>Relative frequency of individual distributed power supplies, where/>For frequency,/>For reference operating frequency,/>To measure the filter coefficient of the active power,/>For the frequency reduction gain,/>For the desired active power,/>For the actual active power,/>For the voltage of the inverter, the voltage level of the distributed power supply can be effectively maintained by adopting a limited time voltage method, thus/>Is constant,/>Is obtained by removing all physical busesDistributed power supply and/>Susceptance between distributed power supplies,/>Is a constant impedance load,/>Is a constant current load,/>Is a constant power load.
3. The island micro-net state estimation method based on a preset time observer according to claim 1, wherein when a state space equation is established, an inverter power angle and a relative frequency are selected as a system state of a distributed power supply, the inverter power angle is selected as a physical quantity measured by a sensor, and the inverter power angle measurement is performed based on a phasor measurement unit detection device.
4. The island micro-mesh state estimation method based on the preset time observer as set forth in claim 1, wherein the mathematical model of the local observer is constructed by:
Setting up a system communication network topology Is strongly connected,/>For/>Laplace matrix,/>Is/>Is a finite non-empty set of nodes;
For distributed power supply observation nodes Establishing a local observer;
all local observers constitute two asymptotically converging observer systems, inside which communication and collaboration takes place.
5. The island micro-mesh state estimation method based on a preset time observer according to claim 1, wherein for a distributed power observation nodeEstablishing a local observer:
;
wherein, Is the observation node/>Estimated state of/>Representing a communication network topology adjacency matrix/>(1 /)Term, matrix/>Is an output feedback matrix, matrix/>Is an information interaction gain matrix,/>Representing the coupling gain.
6. The island micro-mesh state estimation method based on a preset time observer according to claim 1, wherein the distributed discrete communication algorithm is designed by:
determining the number of times of observation node communication;
Determining communication initial time and communication interval;
and designing a distributed discrete communication algorithm information set.
7. The island micro-mesh state estimation method based on a preset time observer according to claim 1, wherein the distributed discrete communication algorithm, when executed, specifically comprises:
When the number of communication times is smaller than If node/>There is/>Node/>Acquiring neighboring nodes/>The information of the same node information in the known node information set is filtered and removed;
Screening and removing the same integral node information in the unknown node information set;
when reaching the preset convergence time And outputting the system state by each observation node.
8. The utility model provides a little electric wire netting state estimation system of distributed preset time observer which characterized in that includes:
A local observer building module configured to: establishing a state space equation based on a mathematical model of the island mode micro-grid system;
constructing two local observers on each distributed power supply node based on a state space equation, and establishing a mathematical model of the local observers;
According to the preset time and the local observer parameters, a conversion matrix of each local observer is designed;
A microgrid state estimation module configured to: determining communication times, initial communication time and communication time interval, and realizing error gradual convergence by each observation node through communication cooperation before the initial communication time;
after the initial communication moment is reached, based on the conversion matrix of each local observer and the execution of a distributed discrete communication algorithm, each node can obtain the state conversion information of all nodes within a preset time, and the real state of the system is calculated, so that the distributed state estimation of the preset time is realized.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method of any of the preceding claims 1-7 when the program is executed.
10. A computer readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, performs the steps of the method of any of the preceding claims 1-7.
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