Literature Review

Sarmas, Elissaios; Xidonas, Panos; Doukas, Haris

doi:10.1007/978-3-030-53743-2_4

Cited by 2 publications

(43 citation statements)

References 113 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This study takes into account the realistic scenario where the channel capacity is varied to measure phasors' voltage and current running in the connectivity lines and produces global solutions with strict optimality conditions [13][14][15][16][17][18][19][20][21].…”

Section: Contribution Of This Studymentioning

confidence: 99%

“…The initial step is to identify if the solution achieved by the optimization algorithm is feasible or not. In the case of producing the sequence of points, we first derive a feasible estimate point in which the objective value is less than the older one on the previous trial point [13][14][15][16][17][18][19][20][21].…”

Section: Optimization Models Studied For the Opp Modelmentioning

confidence: 99%

“…Heuristic algorithms work together with BBA to find a solution of the same quantity and quality in a minimal running time [25,26]. Furthermore, transforming the binaryinteger programming into a nonlinear polynomial model shows the robustness required to find a proper number of PMUs and their placement sites for a fixed number of channels [13][14][15][16][17][18][19][20][21][22][23][24]. The numerical optimization challenge is to run mathematical as well as heuristic algorithms, including BBA, SQP, IPMs, GPSA, GA, and BPSO, to discover the best combination between the proper PMU number and the upper bound of channel capacity without increasing the cost of installation [56][57][58][59][60].…”

Section: Optimization Models Studied For the Opp Modelmentioning

confidence: 99%

“…The integer programming models declare the integer variables representing "yes" or "no" decisions, meaning that they are taking two values, i.e., zero or one [13][14][15][16]. Such integer problems are declared as follows [13][14][15][16][17][18]:…”

Section: Binary-integer Programming Model Considering An Unlimited Nu...mentioning

confidence: 99%

“…where Φ(x) is defined as a Boolean constraint, and n the number of the decision variables. The problem's solution is the set of assignment values that produces the best objective value while the logical constraints are satisfied [13][14][15][16].…”

Section: Binary-integer Programming Model Considering An Unlimited Nu...mentioning

confidence: 99%

See 4 more Smart Citations

Mathematical Models for the Single-Channel and Multi-Channel PMU Allocation Problem and Their Solution Algorithms

Theodorakatos,

Babu,

Theodoridis

et al. 2024

Algorithms

View full text Add to dashboard Cite

Phasor measurement units (PMUs) are deployed at power grid nodes around the transmission grid, determining precise power system monitoring conditions. In real life, it is not realistic to place a PMU at every power grid node; thus, the lowest PMU number is optimally selected for the full observation of the entire network. In this study, the PMU placement model is reconsidered, taking into account single- and multi-capacity placement models rather than the well-studied PMU placement model with an unrestricted number of channels. A restricted number of channels per monitoring device is used, instead of supposing that a PMU is able to observe all incident buses through the transmission connectivity lines. The optimization models are declared closely to the power dominating set and minimum edge cover problem in graph theory. These discrete optimization problems are directly related with the minimum set covering problem. Initially, the allocation model is declared as a constrained mixed-integer linear program implemented by mathematical and stochastic algorithms. Then, the integer linear problem is reformulated into a non-convex constraint program to find optimality. The mathematical models are solved either in binary form or in the continuous domain using specialized optimization libraries, and are all implemented in YALMIP software in conjunction with MATLAB. Mixed-integer linear solvers, nonlinear programming solvers, and heuristic algorithms are utilized in the aforementioned software packages to locate the global solution for each instance solved in this application, which considers the transformation of the existing power grids to smart grids.

show abstract