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УДК 621.382
R. Bazylevych, V. Andrienko
"Lviv Polytechnic" National University,
Software Department
HIERARCHICAL ISLANDING OF POWER SYSTEM
© Bazylevych R. , Andrienko V., 2016
The features of using the method of optimal scheme reduction for islanding of power systems
is reviewed. A modified algorithm for series-parallel folding with the formation of hierarchically
nested clusters is offered. The advantages of the algorithm is grounded and its implementation in the
application for islanding of power system is described.
Keywords – power system islanding, data reduction, clustering.
Introduction
Partitioning of schemes for selected criteria is an important task, which is used in many applied
applications. One of this approaches for its solution is the optimal method of scheme reduction [1-3],
which confirmed its effectiveness and high performance, what is especially important for the problems of
high and very high dimensionality [3], making it more appropriate for power system islanding. Quick
power system islanding creates conditions to avoid the spread of the wave energy blackout in large areas,
which occurred in many cases and performed much damage, therefore this issue is devoted to a number of
publications [5-9]. Appropriate use may be developing an algorithm and software for hierarchical
islanding, that in such cases there is more than a single-selection as an important focus of the accident. In
redistributions waves crash, hierarchical islanding allows predicting and disconnect if necessary following
grid nodes that can enter the emergency area that will minimize damage. In the article considering the
modified algorithm and proposed method of optimal folding scheme, which reduces the time to determine
the transmission lines to disable them.
Method of optimal reduction of scheme
An important factor in the method of optimal folding scheme, which determines the quality of the
result, is selection criterion for combining a strongly bound elements into groups - clusters. A common
criterion is a difference between internal and external connections in the group of elements, which is
considered as a candidate for selection to the next level of grouping. There are clusters of greater value for
this criterion. In the process of combining of elements and created in the previous steps clusters, based
clotting tree that reflects the structure of hierarchically nested groups of strongly connected components.
The intersection of this tree corresponds to some partition scheme on the part number and size of which
depend on the level of decomposition, can be arbitrary.
To determine the value of the criterion of association must calculate the difference between the
number of internal and external connections of items (clusters). Connections between the elements of the
prior level of convolution in new treated as internal node, and all the ties what bind new established node
with other elements, are considered external. Since, the procedure for determining this value is repeated
many times at each level of convolution, it must have high performance.
In the process of identifying candidates for the association of the selected criteria ambiguity may
arise, that is to form groups that have the same value and it is competing, then you need to opt for one of
the possible association of two or more of their number. In such cases, to select candidates for the
association introduced additional criteria, such as weight (number of combined elements) clusters, the
number of external connections and some others.
Criterion for determining candidates for the association can be written as follows:
ij   E inij  E exij  max ,
where,
(1)
i, j  1, N , N – number of power system elements;
Δij – difference between external and internal connections of nodes;
∑Einij - number of internal connections of elements that form the new node;
∑Eexij - number of it external connections.
At each step of the algorithm must calculate temporary value of differences, between the amounts
of internal and external connections of candidates for union. You need to calculate the values for all
potential nodes. To creating a new node, doing by selecting the highest value of all the candidates.
Significant computational cost requires finding candidates for association. A modification of the
algorithm reduces the cost of computation by increasing the need of memory of such calculation [2].
Modified algorithm for constructing optimal tree of reduction
Modified algorithm for constructing optimal tree of reduction have the following features:
1. The value of the number of internal connections of potential new node is decomposed into two
components: internal number of connections of i - th and j – th node.
E
in
ij
  E in i  E in j  E comij ,
(2)
where,
Ecom – number of connections between this two nodes.
2. External connections - are connections between elements and new created node elements that do
not belong. Number of connection can also be divided into two components for each of the nodes:
E
ex
ij
  E ex i  E ex j ,
(3)
3. If initially, to determine the number of all connections for each element, we get its value nCon.
The value of the number of external connections can be obtained if from the value of nCon subtract the
number of internal connections. Given this formula to determine the number of external connections for
two potential nodes would be:
E
E
 nConi   E inij
ex
i
ex
j
,
 nCon j   E in ij
(4)
(5)
4. Using formulas (2), (3), (4) and (5) write based formula (1) in factored form:
ij   E inij  E exij 
  E ini  E in j  E comij  [( nConi   E in ij )  (nCon j   E in ij )] 
  E in i  E in j  E
com
ij
[( nConi  ( E in i  E in j  E comij )) 
 (nCon j  ( E in i  E in j  E comij ))];
5. Opening the brackets, we get the final formula:
ij  3 * ( E in i  E in j  E comij )  (nConi  nCon j );
(6)
Modified reduction method eliminates the need for constant terms identical values. It retains the
necessary intermediate data and the corresponding values increasing number of internal and external
connections.
In the implementation of the method for each step, necessary to calculate only one value ∑Ecomij,
nConi and nConj and can be calculated in the initialization stage, as the sum of all values in the list of all
elements in adjacency matrix, and then for each new node - this value is the sum of the relative values of
the two nodes that forming current node. Similarly ∑Einij defined as the sum ∑Eini + ∑Einj + Ecomij not
require additional computation at each step, but only change gradually during convolution of scheme.
Features of program implementation of method
Presentation of structure of lists processing through which embodied software implementation of
the modified method is shown in Figs 1, 2 and 3. These three stages sequentially display of the lists, as
well as changes in convolution parameters of the scheme.
Fig.1. Data Load Stage
Fig.2. Data Initialization Stage
Fig.3. Data Convolution Stage
Conclusion
To improve the performance of the algorithm of hierarchial islanding can be rational data using
from the previous steps by increasing memory usage. To implement this method may use to apply
additional lists storing data on the number of all connections of node, its internal communications, as well
as all intermediate values at each step of the algorithm. In consideration of real-time computing is worth
considering adding operations that take place at each step of the algorithm. The number of empty runs
cycle due to the increased number of entries of the nodes (and thus records the current values of internal
amounts of total connections, sub-elements, clasters, etc.) and a decrease free nodes will dramatically
affect the growing number of empty runs cycle in program implementation.
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