The same paper that used the exhaustive search method also explored simulated annealing [29]. The percent coverage can be calculated using 4. The result is a vector of values as given by 3. The test point will be the middle of the bound which is 8. DE2 can be viewed as a greedier version of DE1, because it exploits the information of the best individual to guide the search. Previous works have only focused on one or two of these items.

This preference can also be determined by comparing the SORI values. This hybrid greedy algorithm is comprised of five parts: Computation speed is extremely important as real-world distribution net-works can be comprised of hundreds of thousands of buses. In this case, when removed, complete observabilitywould not occur. However, from Figure 3. Therefore, only one phase was considered.

And last, but not least, I would like to thank my dad, John Kerns, for his unending support. For this, lmu process is started with 10 PMUs those are allocated in normal condition. Next, the nodes connected to end nodes can be identified.

Typically, an algorithm will either providea good approximate solution reasonably fast or it produces a global optimum solution and plafement com-putationally expensive. Therefore, a much more accurate PMU is required.

## Mathematical Problems in Engineering

Thiscan be seen in Table 4. Real world distribu-tion networks are comprised of tens to hundreds of thousands of buses while transmission systemsrange between a few hundred to thousands of buses [19]. Therefore, opitmal million different placement configurations would be tried and plxcement to see if complete observ-ability occurs.

The first type of nodes removed were end nodes. Recently, there has been increasedinterest in placing these devices at the distribution level. If one of the combinations can make the system completely observed, the test placment becomesthe upper limit. Is complete observability achieved? Usually denoted as matrix A, its formal definition9is defined in 2.

This, in addition to an increasing power demand from utility users, is decreasing grid stability and increasing the chance of cascad- ing blackouts.

Lastly, power flows from the distribution system to customer sites, which arehomes and businesses. Usually denoted as matrix A, its formal definition9is defined in 2. The key goal of this research was to enable a way tomonitor the distribution system placemennt existing technology and be as economical as possible.

Line impedances are known. Referring to Figure 3.

## Optimal Phasor Measurement Unit Placement for Monitoring of PEA Bowin Power

Now, in order to achieve the minimal case seen in Figure 4. This continues until thedifference between the upper and lower limit is one. Again, the column numbers refer to the node numbers.

Again, minimal results were achieved using this customized simulated annealing algorithm. They explained that a change innetwork configuration can have a large impact on optimal PMU placement.

How-ever, due to the fact that distribution networks can have hundreds thesiz thousands of buses, it isimportant to decrease the computation time as much as possible in order to find a solution in areasonable amount of time for real-world networks.

If there is a largerand more complex network, such as the node, depending on how the unobserved nodes aregrouped, different non-optimal results may occur. They are listed as follows: Referring thesjs Figure 3. The optimization algorithms used in these papers were: Application of PMUs results in making the state estimation equations linear, leading to easier and more accurate solution [ 1 — 3 ].

# Optimal Phasor Measurement Unit Placement for Monitoring of PEA Bowin Power

Another issue with this method is the way they described how to choosea primary network. In [13], which is written by the same authors as [29], they supply another exhaustive searchalgorithm that has the same preprogramming steps. If a system had two switches for example, it would have four configurations: This value is very56important as a higher SORI value thesia to a more reliable system.

Only two papers includedthe SORI calculation in their results, [29] and [13]. Therefore, node 2 is connected to node 1 and node 1 is an endnode. Casazza, Understanding electric power systems: