Typically, an algorithm will either providea good approximate solution reasonably fast or it produces a global optimum solution and is com-putationally expensive. Find and group the unobserved vertices into groups of no more than 3. The values on the table were taken from the results section in thesources listed. They tested their algorithm on three IEEE feeders: As the connectivity matrix is the sole input to the customized greedy algorithm, end nodesand nodes connected to end nodes must be identified from that matrix. The proposed algorithm is a hybrid greedy algorithm with one input: Now, view Figure 2.

University of British Columbia Library. One interpretation of the term optimum in multiobjective optimization is the Pareto optimum, see Figure 1. In step 3, after each iteration, the upper bound is decreased by one. The algorithm can be summarized in Figure 3. If complete observability is still achieved, save this configuration. For a visual,we will reuse Figure 4.

Casazza, Understanding electric power systems: University of British Columbia. Essentially, it would be a desired BOI vector as described earlier.

Optimal PMU Placement and Signal Selection for Monitoring Critical Power System Oscillations

Therefore, a much more accurate PMU is required. Again, it can be seen that the SORIvalues from the proposed algorithm either match or exceed the ones from other works, excludingthe ones for the node feeder. However, from Figure 3. Example of a two objective space for Pareto optimal solutions. Simple 7-node network with a switch. The aim was to have a simple, single input that would make it easy to implementin the real world.


optimal pmu placement thesis

This palcement comes out to be 7, In order to make these changes, traditional coal units willbe phased-out and an upgrade to the existing electricity grid will occur. The first section, Section 2. Essentially, it would be a desired BOI vector as described earlier. Flow diagram of the hybrid greedy algorithm.

Optimal Phasor Measurement Unit Placement for Monitoring of PEA Bowin Power

This placement can be seen below in Figure 3. H is the Jacobian matrix, and is the additive measurement error vector. Therefore, pacement would be able toachieve a higher SORI value.

optimal pmu placement thesis

Incomplete observability occurs when these conditions are not met. That is because the only information required is network connectivity,measurement type, and location. This matrix can be defined in 3.

If the trial vector obtains a better fitness value than the target vector, then the trial vector replaces the target vector in the following generation. It was assumed thatthe worst-case scenario was in effect: The steps to this part of the algorithm are summarized below and an example followsto further explain the steps.

Typically, it is assumed that the cost is the same at any location. The other noticeable difference is the number of nodes for each network.

To explain these steps further, an example is provided below. Transmission SystemsPlacement algorithms should be optimized for either the transmission system or the distributionsystem [18].


Incorporation of PMUs in power system state estimation

If the matrix is of full rank, that is,then the system is considered to be numerically observable [ 18 placemeny. This, in addition to an increasing power demand from utility users, is decreasing grid stability and increasing the chance of cascad- ing blackouts.

This value needs to be increased in order to reduce the amount ofgreenhouse gases being generated and, in turn, combat climate change. Comparatively, for the proposedalgorithm, it is fairly equally likely that either one, two, or three nodes will be unobserved. Lastly, distribution systems typically contain switches, whichneed to be accounted for in the placement algorithm.

optimal pmu placement thesis

This algorithm is based on a greedy algorithm which has manybenefits such as fast computation time and high reliability. These algorithms will beexplained and the papers will be analyzed to highlight the advantages, disadvantages, and limita-tions of the methods where present.

This row number will correspond to the node that is connected to the end node.