This continues until the difference between the upper and lower limits is equal to 1. Note that the column numbers refer tonode numbers, similar to the connectivity matrix. Abstract In this thesis, a strategy for phasor measurement unit PMU optimal placement and signal selection is proposed for monitoring critical oscillations in electric power systems. When the switch is closed, complete observabilityis achieved. Lastly, power flows from the distribution system to customer sites, which arehomes and businesses. Referring back to the example in Figure 3.

The outcome of this conference was the Paris Agreement. This, in addition to an increasingpower demand from utility users, is decreasing grid stability and increasing the chance of cascad-ing blackouts. Flow diagram of the hybrid greedy algorithm. Therefore, only one phase was considered. Therefore, node 2 is connected to node 1 and node 1 is an endnode. They tested their method on IEEE networks:

For a visual,we will reuse Figure 4.

In [29], they tried to reduce the computation time of the exhaustive search placemdnt. An even simpler DE scheme, denoted as DE2 here, can be derived from 4. However, there is still a chance that only twoor three nodes will be unobserved. The flow chart for a proposed strategy using DE algorithm based on Pareto method presented in this paper, is shown in Figure 2.

DE algorithm employs stochastic search technique and is one of later type amongst the evolutionary algorithms. Integer Programming [19] no yes optiaml noInteger Programming [27] no yes yes yesInteger Programming [28] no yes yes noExhaustive Search [29], [13] yes no yes noSimulated Annealing [29] yes no yes noGraph Theory [31] yes no no noGreedy Algorithm [32], [24] no no no yes30In conclusion, there has yet to be an algorithm that is simple to implement, have a computationtime low enough that is feasible to use in the real world, is highly redundant, considers networkreconfiguration and produces consistently minimal results.

# Incorporation of PMUs in power system state estimation – DRS

This preference can also be determined by comparing the SORI values. Therefore, a much more accurate PMU is required. The result is a vector of values as given by 3.

The lowersearch bound starts at 0. Some of the benefits are highlighted below [16]: The steps to this part of the algorithm are summarized below and an example followsto further explain the steps. The outcome of this conference was the Paris Agreement. Due to these challenges, there is currently a limit to the number of renewable energy sourcesthat can be connected to the grid.

How-ever, although this method should yield faster results than exhaustive, the results section in [29]show that this algorithm was much slower than their customized exhaustive method. Wil-son Eberle for their constant support throughout this endeavor. Heuristic algorithms can either produce a good approximation or anexact solution, depending on the algorithm itself [21].

A solution dominates a solution if and only if the two following conditions are true: Furthermore, plcaement of the papers described were ableto achieve consistently minimal results. To further explain this, a walkthrough will be done for the IEEE node network. TPES is calculated by the following: Additionally, specific placement goals may be different for transmission systems due totheir topology.

This algorithm is based on a greedy algorithm which has many benefits such as fast computation time and high reliability. For in-complete observability, state estimation would need to be implemented in order to estimate thevalues that are not being observed. However, the high cost of these devices, inaddition to the communication infrastructure that would be needed, makes it unfeasible to placethem at every node on a feeder.

This row number placemdnt correspond to the node that is connected to the end node. Solutions 1 and 3 are nondominated Pareto optimal solutions. Atfirst glance, placemfnt appears this method is extremely fast, provides minimal results, and provides a highredundancy.

## Mathematical Problems in Engineering

Deterministic algorithmsfollow a strict path. This combination of factors has not been considered together for the placement problem on thedistribution system.

This allows them tosynchronize measurements from distant locations, giving a real-time picture of the complete powersystem [9]. 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]. This algorithm is based on pju greedy algorithm which has many benefits such as fast computation time and high reliability. This corresponds to row 2. With the addition of renewable energy sources on the electrical grid, bidirectional power flow is now oc- curring and is causing previously unseen fluctuations in voltage.

Next, the nodes connected to end nodes can be identified.