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The coherence phenomenon of the power system in the dynamic process, that is, the consistency or similarity of the dynamic characteristics of different units, correctly identifying the homology group is of great significance for studying the stability of the power system. There are many methods for identifying coherent clusters, such as numerical integration method, state space method, eigenvector method, modal equivalence method, weak coupling method, etc., which have various defects, such as complex formula derivation, large amount of calculation, or cannot be used in large systems. In fact, there is no strict homology in the system. The so-called coherence is just that the dynamic characteristics of different units are similar, but there is a strict boundary. According to this characteristic of power system, the fuzzy clustering method is applied to the identification of power system coherence group. Firstly, the fuzzy state method is used to process the system state matrix, and the fuzzy equivalence matrix reflecting the degree of coherence between units is obtained. The cutoff coefficient can easily identify the homology group of the system. The physical meaning of this method is clear, the calculation is simple, there is no dimensionality disaster problem, and it can be used for the identification of large-scale system coherent clusters. This paper uses 10 machines and 24 machines. As an example, two test systems are given to identify the results of coherent clusters under different conditions, and the results of homomorphic recognition of feature roots are used to prove that the fuzzy clustering method is simple, flexible and reliable. When the equivalence relation matrix is ​​used for generator coherent identification, it is generally assumed that the generator correlation group is independent of the disturbance, so the linearized system model can be used; the generator correlation group is independent of the details of the generator model, so a simple generator model can be used. Neglect the excitation system and the prime mover speed control system when the generator adopts the Eq constant model
The self-multiplication of R is the same as the multiplication of the matrix, but the rule of taking the big and small is used in the value of the element. That is, if the ith row and the column of R are multiplied, the R2n is satisfied by the squaring method. After transitivity, and 21 becomes a fuzzy equivalence relation matrix, which can be used to perform fuzzy cluster analysis to identify the system's coherence group 3 coherent group identification. If R is a fuzzy equivalence relation matrix, then for any given 汜, can get a; V-cut classification matrix," embodies the coherence relationship between the units at the V level. The value of the following formula is for the matrix, and its element value is only 0 1 two possibilities, if a 2-line element is If 1 appears in the same position, the unit corresponding to the two elements is the coherent unit; if there are multiple lines of elements appearing at the same position, the unit corresponding to these line elements is a coherent group. The fuzzy clustering method is used to identify any speculations of people who do not need to be in the same group, and has sufficient flexibility. The level of coherence is high, and a large V value can be taken. If the level of homology is low, a smaller V value is taken. In addition, this method of coherent group identification is basically a logical calculation, there is no rounding error, so there is no dimensionality disaster problem, and it can be used for the identification of large-scale power system coherence groups. 1J. 4 Feature root reduction based on homology identification In general, there are two types of electromechanical oscillation modes in the power system, that is, the regional oscillation mode and the regional oscillation mode. The regional oscillation mode exists inside the coherent group and is dominated by the units inside the coherence group, but is basically irrelevant to the units outside the coherence group. The regional oscillation mode exists between the homology group and is dominated by the homology group. According to this feature, the eigenvalues ​​of the regional oscillation mode and the eigenvalues ​​of the regional oscillation mode can be calculated by using different state equations respectively, thereby realizing the reduction of the system model.
For the regional oscillation mode, they are dominated by the units within the coherent group, but are basically independent of the units outside the coherence group. If the system state matrix is ​​rearranged according to the distribution of the coherence group, the regional oscillation mode eigenvalues ​​can utilize the corresponding coherence group. Corresponding sub-blocks of the corresponding state matrix are obtained. Since the internal generators of the homology group are relatively few, the dimension of the corresponding sub-block of the state matrix is ​​very low. By applying the QR method to the sub-state matrix, the characteristic root of the regional oscillation mode can be obtained. In addition, all the eigenvalues ​​obtained are obtained. Among them, the smallest one is caused by ignoring the influence of the external unit of the coherence group. It is often small, corresponding to the 0 eigenvalue of the system, and should be rounded off for the regional oscillation mode, which is dominated by the coherent group. In the case of a cluster, the dynamic process of the internal unit is similar. The generator can be equivalent to a generator by accumulating the equation of the rotor motion of the unit, thus reducing the system state equation.
By using the QR method for this reduced-order state equation, the characteristics of the regional oscillation mode can be obtained. Similarly, among all the eigenvalues ​​obtained, the smallest one eigenvalue corresponds to the 0 eigenvalue of the system, and should be discarded. n sets of m coherent system, if each coherent group has /1/2..., /, generator, then /1+/2+...+1m=n, then the regional oscillation obtained by the above method Mode nm, the number of characteristic roots of the regional oscillation mode is m-1, and the sum of the two is n-m+m-1=n-1, which is exactly equal to the total number of characteristic roots of the electromechanical mode of the system. The system model of the reduced order system, but still obtains the complete electromechanical mode de-gathering machine of the system, and the results obtained by using the Gnham state space in 24 machines are completely consistent. The identification results of the homophone group of the 24-machine system are different as shown in Table 4. 2 Fuzzy equivalence relation matrix collinear number table 3 X When different values ​​are taken, the recognition result of the 10-machine system coherent group is the same as that of Table 3 and Table 4. X takes different values, and different CMC identification results are obtained. The value of X depends on the problem being studied. Generally speaking, the stricter the homology requirement (X takes a larger value), the more coherent groups are obtained, and the number of units in each coherent group The less the homology requirement (X takes a smaller value), the fewer the number of coherent groups obtained, and the more units in each coherent group. In addition, the value of X is also related to the specific system. For example, the X value of the 10-machine system can be taken to be 0.9 or more, and after 24 systems, when the X value is greater than 0.6, there is no homophone group.
Table 4 Identification results of the homophone group of the 24-machine system when X takes different values. identification group identification result 5.2 Characteristic root calculation results Table 5 and Table 6 respectively show the reduced-order model of 10 and 24 machine systems when X takes different values. The obtained eigenvalue calculation results are compared. The table also gives the eigenvalue exact values ​​obtained by the full-order model and the reduced-order method calculation error.
Table 5 order full-order reduced-order method error reduction method error reduction method error number model table 6 24 machine system characteristic root calculation result order full-order reduced order method error reduction method error reduction order method error number model from Table 5 and Table 6 It can be seen that the maximum error obtained by the homomorphic recognition and the reduced order model is 3.42%, while the maximum error is only 0.92% when the =Q9 is recognized. This shows that it is feasible to use the fuzzy clustering method to identify the coherent group of the power system. In addition, this method can be convenient and flexible to choose between the degree of reduction of the model and the accuracy of calculation: X takes a larger value, the requirements for homology are stricter, the calculation accuracy is higher, but the model is less stepped; For smaller values, the homology requirements are more relaxed, and the calculation accuracy is worse, but the model is more downgraded.
6 Conclusions Fuzzy clustering method is a very effective method for identifying coherent clusters of power system. It is simple in principle, small in computation and reliable in method. It is suitable for large-scale power systems. In addition, this method can be simplified in system and equivalent. Flexible and convenient selection between sexes to meet the needs of research questions. This research topic was supported by the Ph.D.
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