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The harmonic propagation within the multi-bus network will unavoidably generate the voltage harmonics as expressed below: dot{V}_{Line} = Z_{Line_h} cdot dot{I}_{h} (1 where (dot{V}_{Line}) is the harmonic voltage matrix; (dot{I}_{h}) is the harmonic current matrix and Z Line_h is the corresponding order harmonic impedance matrix, respectively.
So, next we will discuss how to get the mismatch value of two graphs' nodal voltage matrix.
The mismatch value of two graphs' nodal voltage matrix can be calculated by the distance of node voltages sequence between any two nodes in the distance matrix.
In other words, we need to find the best node mapping relation of two probability graphs so that the mismatch value of two graphs' nodal voltage matrix is minimum and less than the threshold.
Therefore, in order to determine probability isomorphic of two probability graphs, we need to evaluate whether the mismatch value of two graphs' nodal voltage matrix is less than the threshold.
Suppose S and S′ are the node voltage matrix of probability graph g and g′, k is graph node size of g and g′, so there is k kind of possible node mapping relations of S i (i = 1,..., k) and S j (j = 1,..., k), S i and S j is the node voltage sequence in corresponding g and g′.
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Given the mismatch threshold ε of node voltage sequence matrix and the probability mismatch threshold θ of the adjoint matrix, two probability graph distance matrix Dist (N, N′) are obtained using the circuit simulation method.
A radial test distribution grid, which consist of five PV systems, is used to calculate power flow and, in turn, the voltage sensitivity matrix.
This study utilizes the voltage sensitivity matrix and quasi-static analysis in order to develop a coordinated Q V) characteristic for each PV system along a radial feeder using only the local measurement and drooping technique concepts.
Then the Hungarian Algorithm is used to get the node optimal matching sequence and the mismatch value of node voltage sequence matrix.
The best time complexity of the algorithm is O(1), i.e. the minimum mismatch sequence of node voltage sequence matrix is the mapping sequence of probability isomorphism, the worst time complexity of which is O k!), when we need to enumerate all possible nodes mapping relationship.
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