They would solve the primary network first tobe completely observable while ignoring the secondary network. The steps of thiscalculation are summarized below: Typically, an algorithm will either providea good approximate solution reasonably fast or it produces a global optimum solution and is com-putationally expensive. Liwei Wang and Dr. Referring back to the example in Figure 3. PMUs were invented in the mid s [11] and havebeen used in transmission systems since the mid s [12].

The steps to this part of the algorithm are summarized below and an example followsto further explain the steps. The proposed algorithm is a hybrid greedy algorithm with one input: However, it can be seen that theproposed algorithm was much faster than the other works listed. The algorithm can be summarized in Figure 3. However, from Figure 3.

Therefore, it would be placed back and this part of the algorithm would end. However, due to its exhaustivenature, it is too computationally expensive for large networks [30]. To explain these steps further, an example is provided below.

Now, view Figure 2. Note that the column numbers refer tonode numbers, similar to the connectivity matrix. On the other hand, stochastic algorithms tend to have some randomness andmay take a slightly different path when the program is run.

Incorporation of PMUs in power system state estimation – DRS

It is faster than ppmu search pmmu all combinations are not tried[29]. Therefore, a much more accurate PMU is required. Additionally, I am grateful for the funding I received through Mitacs Accelerate, a collaborationwith Enbala Power Networks, for without which would have made it difficult for me pursue thisresearch. This combination of factors has not been considered together for the placement problem on thedistribution system. For each target vector, the mutation operation produces a new parameter vector called mutant vectorby adding the weighted difference between two randomly chosen vectors to a third also randomly chosen vector.


A goal forthis analysis would determine a target SORI value for any given distribution system. Alternatively, the best-case scenario would see two nodes unobserved.

Incorporation of PMUs in power system state estimation

This is an open access article distributed under the Creative Commons Optimwl Licensewhich permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The distribution system needs to be monitored in real time so that minor issues optial to grid stability can be noted and fixed before they cascade into system failure. It can be seen that the number of nodes in a system determines the size of the matrix.

optimal pmu placement thesis

For this equation, i corresponds to the node number and nis the total number of nodes for the given distribution network. The second issue is that power demand from utility users has been increasing plzcement to the in-creasing number of electronic devices being used and operated. The same process was usedfor each network and the three different cases. Percent CoverageFirst, the percent coverage was analyzed and compared between the proposed algorithm and theminimum case.

The only difference this algorithm has is insteps 1 and 3.

optimal pmu placement thesis

DE2 can be viewed as a greedier version of DE1, because it exploits the information of the best individual to guide the search. However, there is still a chance that only twoor three nodes will be unobserved.


The distribution system needs to be monitored in real time so that minor issues relating to grid stability can be noted and fixed before they cascade into system failure.

They tested their method onIEEE node and node test feeders. However, some customization was done in order to closer matchthe minimum case for all networks as well as make the algorithm more robust.

Then, the secondary network canbe solved. However, analysis is done by ignoring the effect of various noises that creep into the measurement system. Real world distribu-tion networks are comprised optimmal tens to hundreds of thousands of buses while transmission systemsrange between a few hundred to thousands of buses [19]. In solving the observability problem by SVD the matrix of 2. Include Metadata Specify width in pixels leave blank for auto-width: The test point will be the middle of the bound which is 8.

This meansthat they may be shifted during the configuration 1 and 2 portions of this tthesis. Recently, there has been increasedinterest in placing these devices at the distribution level. The proposed algorithm is a hybrid greedy algorithm with one input: