Optimal Placement of Phasor Measurement Units with Linear and Non-linear Models

Abstract—This article presents a non-linear programming-based model for the optimal placement of phasor measurement units. The optimal phasor measurement units placement is formulated to minimize the number of phasor measurement units required for full system observability and to maximize the measurement redundancy at all buses in a power system. A sequential quadratic programming algorithm is used for the solution of the proposed model. The existence of power flow and injection measurements, the limited phasor measurement units channel capacity, the lack of communication facilities in substations, and the single phasor measurement units loss are also incorporated into the initial proposed formulation. The non-linear programming model is applied to IEEE 14- and 118-bus test systems in MATLAB. The accuracy and the effectiveness of the proposed method is verified by comparing the simulation results to those obtained by a binary integer programming model also implemented in MATLAB. The comparative study shows that the proposed non-linear programming model yields the same number of phasor measurement units as the binary integer programming model. A remarkable advantage of the non-linear programming against binary integer linear programming is its capability to give more than one optimal solution, each one having the same minimum number of phasor measurement units (same minimum objective value), but at different locations.     

A tool for the evaluation and selection of state estimatormeasurement schemes

This paper describes an approach for evaluating and selecting the measurement scheme for power system state estimation. The approach utilizes a computer package which has been developed for analyzing all the power system state estimation related functions. In the proposed approach the measurement configuration is selected so that the following criteria are met: measurement system observability and reliability, bad data detectability and identifiability, state estimation accuracy. The necessary algorithms to analyze the above criteria are described     

Transformer tap setting observability in state estimation

In conventional state estimation, transformer tap settings are treated as fixed network parameters. This may reduce the accuracy of state estimation algorithm, when a tap measurement is in error or an unmeasured tap is unknown. This paper presents a numerical observability analysis algorithm for a state estimation model which treats transformer tap settings as state variables and provides for turns ratio and phase-shift angle measurements. The proposed model is transformed to a conventional node frame of reference, by introducing one fictitious bus and one fictitious branch for each transformer with tap estimation enabled. For an unobservable system, observable islands are determined and additional measurements are directly provided for placement. Test results are presented.     

Swelling,compression and tribological behaviors of bentonite‐modified polyacrylate‐type hydrogels

Hydrogel was synthesized from acrylamide and 2‐acryloylamido‐2‐methylpropanesulfonic acid monomers (ratio: 50/50 wt %) and crosslinked with 0.25 wt % of methylene‐bisacrylamide. This hydrogel was also modified by adding 4 wt % of sodium bentonite (NB). Selected properties of the hydrogels with and without NB were investigated and compared. Their water uptake was measured gravimetrically; the compression and compression creep were assessed by dynamic‐mechanical and thermo‐mechanical analysis (DMA and TMA, respectively) techniques. The friction and wear of the hydrogels were determined in a shaft(metal)‐on‐plate(hydrogel) type testing configuration under water lubrication. The hydrogel was transparent and exhibited very high equilibrium water content (>99 wt %). The latter was less affected; however, the hydrogel became slightly more hazy after NB incorporation. The crosslink density of the hydrogels was deduced from swelling and compression tests and compared with the theoretical values. Modification by NB enhanced the ultimate compression strength and reduced the related compression strain. The compression creep response under both loading and deloading strongly depended on the level of the initial load. A very low friction coefficient (～ 0.003) and a relatively high specific wear rate (～ 0.05 mm³/N m) were registered under water lubricated sliding wear using a metallic counterpart with high surface roughness. Scanning electron microscopy combined with energy dispersive spectroscopy delivered additional information on the NB dispersion and surface structure of the hydrogels. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

A robust method for equality constrained state estimation

This paper presents a robust method for the solution of the equality constrained state estimation problem. The problem is formulated as a weighted least squares (WLS) problem with equality constraints. Traditionally the problem is solved iteratively by the normal equations with equality constraints (NE/C). One problem of NE/C is that the gain matrices are not positive definite and extra logic is required to process the zero pivots during Gaussian elimination. In this. paper, positive definite gain matrices are formulated and triangularization is performed symbolically using sparsity techniques. The method is illustrated with a six-bus system and the IEEE 14-bus system     

A reduced model for power system observability: analysis andrestoration

An algorithm for observability analysis and restoration in power system state estimation is presented. The problem of P-δ, Q-V and complete observability is addressed. In the proposed algorithm, groups of buses are represented by supernodes and the problem of observability analysis and restoration is examined with a reduced network. The proposed algorithm is easily implemented and it is independent of the state estimation solution algorithm. In case of unobservability, the proposed methodology identifies directly the maximal islands and determines the number and the placement of the required pseudomeasurements for observability restoration. Results from several test cases are presented     

Anteriorly displaced transverse fractures of the sacrum in adolescents: report of two cases

A fracture of the sacrum at the level of the first and second segments, with forward displacement of the first segment, is a very rare injury in adolescents. The cases of two patients, who both suffered a displaced transverse fracture of the sacrum with resulting neural disturbance, are reported here. We consider that these unstable fractures may be treated surgically, by extensive laminectomies of the lumbosacral area and posterolateral fusion. Stabilization of the displaced fracture is possibly preferable, because it provides the prerequisites for early mobilization and reduces pain.     

Development of value-added polyethylene grades with extended service lifetime: Weathering resistant flame retarded materials for outdoor applications

The current article deals with the development of different novel, tailor-made polyolefin formulations exhibiting both low flammability and high weathering resistance, so as to provide value-added polyethylene grades with extended service lifetime. Two low-density (LDPE) and one linear low-density (LLDPE) polyethylene grades were modified via melt compounding with an additive system comprising: (a) a nitrogen-phosphorous intumescent system for flame retardance and (b) a hindered amine light stabilizer and a benzophenone-type UV absorber for UV/heat stabilization, at a total loading of 30–35 wt%. The target was to reach V0 classification in UL94V flammability tests, while to a large extent maintaining the mechanical properties, such as, tensile and impact strength of the investigated polymers, thus ensuring that the additives do not interfere significantly with the material quality. Subsequently, the compounds were subjected to separate artificial UV and heat aging at 100°C for 1500 h; the formulations showed good flame retardance, even after prolonged artificial weathering, but there was an observable, although acceptable, decrease in the mechanical properties. Nevertheless, all the results show that the developed polyethylene compounds are very promising for outdoor applications, such as, irrigation piping and profiles, where long-term weathering stability is important, and where flame retardance is important for safety during storage.     

Study of thermomechanical,structural and antibacterial properties of poly(lactic acid) reinforced with graphene oxide nanoparticles via melt mixing

Addition of graphene oxide (GO) to poly(l ‐lactic acid) (PLLA) offers an alternative approach for tuning its crystallinity, improving its mechanical properties and transfusing an antibacterial behavior. GO/PLLA nanocomposites were prepared by melt extrusion, thus avoiding the potentially toxic, for biomedical applications, residue of organic solvents. Fourier transform infrared spectroscopy verified the formation of intermolecular hydrogen bonds. Using differential scanning calorimetry experiments concerning the isothermal crystallization of PLLA and PLLA containing 0.4 wt% GO, a two‐dimensional disc‐like geometry of crystal growth was determined, whereas at 125 and 130 °C the nanocomposite developed three‐dimensional spherulitic growth. Higher crystallization rate constant values suggest that the incorporation of 0.4 wt% GO accelerated the crystallization of PLLA. The lowest crystallization half‐time for PLLA was observed at 115 °C, while at 110 °C GO caused its highest decrease, accompanied by the highest increase in melting enthalpy (ΔH_m), as compared to that of PLLA, after completion of isothermal crystallization. Their ΔH_m values increased with T_ic, whereas multiple melting peaks transited to a single one with increasing T_ic. GO improved the PLLA thermal stability, tensile strength and Young's modulus. Incorporation of 0.8 wt% GO endowed PLLA with another potential application as a biomaterial since the derived composite presented good thermomechanical properties and effective prohibition of Escherichia coli bacteria attachment and proliferation. This effect was more prominent under simulated sunlight exposure than in the dark. The preparation method did not compromise the intrinsic properties of GO. © 2020 Society of Chemical Industry     

The effect of poly(ethylene glycol) mixed with poly(l‐lactic acid) on the crystallization characteristics and properties of their blends

The non‐isothermal and isothermal crystallizations of extruded poly(l ‐lactic acid) (PLLA) blends with 10, 20 and 30 wt% poly(ethylene glycol) (PEG) were investigated with differential scanning calorimetry. The formation of α‐form crystals in the blend films was verified using X‐ray diffraction and an increase in crystallinity indexes using Fourier transformation infrared spectroscopy. Crystallization and melting temperatures and crystallinity of PLLA increased with decreasing cooling rate (CR) and showed higher values for the blends. Although PLLA crystallized during both cooling and heating, after incorporation of PEG and with CR = 2 °C min^?1 its crystallization was completed during cooling. Increasingly distinct with CR, a small peak appeared on the lower temperature flank of the PLLA melting curve in the blends. A three‐dimensional nucleation process with increasing contribution from nuclei growth at higher CR was verified from Avrami analysis, whereas Kissinger's method showed that the diluent effect of 10 and 20 wt% PEG in PLLA decreased the effective energy barrier. During isothermal crystallization, crystallization half‐time increased with temperature (T_ic) for the blends, decreased with PEG content and was lower than that of pure PLLA. In addition, the Avrami rate constants were significantly higher than those of pure PLLA, at the lower T_ic. Different crystal morphologies in the PLLA phase were formed, melting in a broader and slightly higher T_m range than pure PLLA. The crystallization activation energy of PLLA decreased by 56% after the addition of 10 wt% PEG, increasing though with PEG content. Finally, PEG/PLLA blends presented improved flexibility and hydrophilicity. © 2019 Society of Chemical Industry