## 6 Observability of the graph
### Constrained Nonlinear Programming Model
[CrossRef]
* (34) [PERSON]; [PERSON]; [PERSON]; [PERSON] A Community-based Partitioning Approach for phasor Measurement Unit Placement in Large systems. _Electr. Power Compon. Syst._**2016**, _44_, 1317-1329. [CrossRef]
* (35) [PERSON]; [PERSON]; [PERSON] A PMU Placement Scheme Considering Realistic Costs and Modern Trends in Relaying. _IEEE Trans. Power Syst._**2017**, _32_, 552-561. [CrossRef]
* (36) [PERSON]; [PERSON]; [PERSON] Optimal substation-based joint allocation of PMUs and measuring channels considering network expansion planning. _Int. J. Electr. Power Energy Syst._**2019**, _106_, 274-287. [CrossRef]
* (37) [PERSON]; [PERSON]; [PERSON] The branch-and-bound algorithm in optimizing mathematical programming models to achieve power grid observability. _Axioms_**2023**, _12_, 1040. [CrossRef]
* (38) [PERSON]; [PERSON]; [PERSON] Calculating Global Minimum Points to Binary Polynomial Optimization Problem: Optimizing the Optimal PMU Localization Problem as a Case-Study. _J. Phys. Conf. Ser._**2024**, _2701_, 012001. [CrossRef]
* (39) [PERSON]; [PERSON]; [PERSON]; [PERSON] Binary particle swarm optimisation-based optimal substation coverage algorithm for phasor measurement unit installations in practical systems. _IET Gener. Transm. Distrib._**2016**, _10_, 555-562. * (40) [PERSON]; [PERSON]; [PERSON]; [PERSON] Optimal phasor measurement unit placement for numerical observability in the presence of conventional measurement using semi-definite programming. _IET Gener. Transm. Distrib._**2015**, \(9\), 2427-2436. [CrossRef]
* (41) [PERSON]; [PERSON]; [PERSON] A Generalized Pattern Search Algorithm Methodology for solving an Under-Determined System of Equality Constraints to achieve Power System Observability using Synchrophasors. _J. Phys. Conf. Ser._**2021**, _2090_, 012125. [CrossRef]
* (42) [PERSON]; [PERSON]; [PERSON]; [PERSON] Implementation of optimization-based algorithms for maximum power system observability using synchronized measurements. _AIP Conf. Proc._**2023**, _2872_, 120006. * _[PERSON] et al. (2015)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] Redundancy based PMU placement in state estimation. _Sustain. Energy Grids Netw._**2015**, \(2\), 23-31. [CrossRef]
* _[PERSON] et al. (2021)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] Realistic method for placement of phasor measurement units through optimization problem formulation with conflicting objectives. _Electr. Power Compon. Syst._**2021**, _49_, 474-487. [CrossRef]
* [PERSON] and [PERSON] (2017) [PERSON]; [PERSON] A Multi-objective PMU Placement Method in Power System via Binary Gravitational Search Algorithm. _Electr. Power Comp. Syst._**2017**, _45_, 1832-1845. [CrossRef]
* _[PERSON] et al. (2013)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] Numerical observability method for optimal phasor measurement units placement using recursive Tabu search method. _IET Gener. Transm. Distrib._**2013**, \(7\), 347-356. [CrossRef]
* _[PERSON] et al. (2017)_ [PERSON]; [PERSON]; [PERSON] Binary PSO Algorithm for Optimal PMUs Placement. _IEEE Trans. Ind. Inform._**2017**, _13_, 3124-3133. * _[PERSON] and [PERSON] (2017)_ [PERSON]; [PERSON] Multiple Solutions of Optimal PMU Placement Using Exponential Binary PSO Algorithm for Smart Grid Applications. _IEEE Trans. Ind. Appl._**2017**, _53_, 2550-2559. [CrossRef]
* _[PERSON] and [PERSON] (2016)_ [PERSON]; [PERSON] [PERSON] Optimal PMU placement for full observability of the power network with maximum redundancy using modified binary cuckoo optimization algorithm. _IET Gener. Transm. Distrib._**2016**, _10_, 2817-2824. [CrossRef]
* _[PERSON] and [PERSON] (2016)_ [PERSON]; [PERSON] Genetic algorithm-based phasor measurement unit placement method considering observability and security criteria. IET Gener. _Transm. Distrib._**2016**, _10_, 270-280. [CrossRef]
* _[PERSON] et al. (2023)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] Research on optimization procedure of PMU positioning problem achieving maximum observability based on heuristic algorithms. _AIP Conf. Proc._**2023**, _2872_, 120032. * _[PERSON] et al.