Grid Verification Research Articles

Towards formal verification of smart grids: An effective modelling approach and some first experimentation

Nowadays, smart grids are used widely around the world when they enable detecting, reacting and pro-acting to changes in usage and many concerns with the power system, as well as having self-healing capabilities. Some smart grids have recently been created and operational in Vietnam. To ensure the effectiveness of the smart grids, the correctness of the system designs must be studied carefully before the explosion of the use of smart grids, particularly in developing countries such as Vietnam. As formal methods, including formal verification and model checking, recently play more important role in verifying smart grid properties such as load balancing and fault resilience, the effectiveness of formal verification depends mostly on system modeling and verification techniques. Recent researches have shown the feasibility of applying model-checking tools in smart grid verification, and also the inability to test complex properties and systems. In our opinion, the inability could be come from the complicating of the models of the system-under-test. In this study, we suggested a new method for representing smart grids using Colored Petri Net (CPN), a formal representa- tion language. In comparing to the current modeling approach, the new model allows engineers transforms complex grids into simple models. Moreover, based on the advantages of the “color” aspect of the CPN, the result model can be easily upgraded to adapt to the changes of the original smart grids without re- modeling. Also in this study, a basic case study for representing a smart grid, which consists of multiple power sources and multiple consumers, will be shown. The model will be configured to capture some problems that may happen in the grid such as the changing of the capacity of the power sources. The verification experimentation conducted on the case study shows the usefulness of the proposed method.

Heat transfer intensification of NEPCM-water suspension filled heat sink cavity with notches cooling tubes by applying the electric field

The effects of an electric field on heat transfer, free convection, and entropy generation of nano-encapsulated phase change material (NEPCM) dissolved in water in a complex inclined chamber are studied. The enclosure consists of a rectangular cavity heated from below and the remaining walls are considered adiabatic. The fluid is cooled by eight cooling tubes, each with four notches. The effects of the electric field, inclination angle (ζ = 45° and ζ = 90°), and Rayleigh number (Ra = 103, 104, and 105) in equal concentration of NEPCM (ϕ = 2 %) are studied using ANSYS Fluent CFD code. The dimensionless form of fluid governing equations, electric potential equation, electric charge density equation, and entropy generation equation are used to set the primitive parameters. Grid verification and validation tests are performed to ensure the reliability of the solution. Calculations show that with increasing Ra, the average Nusselt number (Nuave) decreases from ζ = 45° to 90°, but when an electric field is applied, the results are reversed. As the Rayleigh number increases in conjunction with the electric field, the buoyancy effect becomes more pronounced. Furthermore, owing to its high heat transfer potential and lowest irreversibility, the straight cavity (ζ = 90°) is desirable at Ra = 105.

INVESTIGATION ABOUT THE HYDRODYNAMIC COUPLING CHARACTERISTICS OF CONTRA-ROTATING AZIMUTH PROPULSOR

A numerical study is conducted to determine the hydrodynamic coupling characteristics of a contra-rotating azimuth propulsor (CRAP) in open-water conditions. The detached-eddy simulation (DES) method is utilized to run simulations. A grid verification is conducted and the numerical results are validated based on a puller-type podded propeller. The hydrodynamic forces (i.e., thrusts and torques) are in accordance with the experimental data. The validated numerical method is utilized for subsequent CRAP simulations. The hydrodynamic performance and hydrodynamic coupling characteristics of CRAP are quantitatively analyzed according to forward propeller (FP), rear propeller (RP), and pod unit (PU) indicators with special focus on the hydrodynamic forces and the corresponding unsteadiness. PU appears to have essentially the same effect on the hydrodynamic performance of FP and RP. RP has a weak effect on the hydrodynamic performance of FP, while FP intensely affects that of RP. In general, the CRAP unsteadiness is dominated by RP, especially under heavy loading conditions.

On the hydrothermal behavior and entropy analysis of buoyancy driven magnetohydrodynamic hybrid nanofluid flow within an octagonal enclosure fitted with fins: Application to thermal energy storage

Minimum entropy generation is usually considered a foremost criterion for an effective operation of the thermal storage system. Minimization of entropy is very significant because entropy minimization improves the proficiency of any device or system. The hydrothermal consequences of buoyancy-driven flow through the octagonal enclosure reveal major importance and those geometrical shapes are introduced in several technological and engineering applications like solar collectors, microfluidic heat sinks, nuclear power plants, heat exchangers, etc. Various types of fins are frequently operated in many devices or engineering fields related to electric transformers, heat exchangers, automobile radiators, gas turbines, air-cooled engines, semiconductor devices, hydrogen fuel cells, etc. Nanofluids disclose promising heat transport compared to traditional coolants. Furthermore, hybrid nanofluids are efficient and promising in heat transmission compared to usual nanofluids because of double metallic tiny particles' presence within the host medium. With this objective, the current study enlightens the hydrothermal conduct and entropy analysis of magnetized Ag-MgO-water hybrid nanofluid stream passing through the octagonal cavity and circular cylinder. Several rectangular heated fins are attached to the inner hot cylinder. The bottom and upper surfaces are heated, and vertically parallel walls are cold, whereas the inclined faces are made insulated. Similarity alternations are conducted to leading equations to have dimensionless profiles. The Galerkin-finite-element tactic has been merged to reconnoiter the solutions. Grid verification, assessment with the remaining works, and experimental verifications are completed to reveal the model's precision. Several velocities, streamlines, Bejan number, isotherms, entropy generation, and Nusselt number plots are addressed to expose the outcome of different fin lengths on the flow. Requisite diagrams are represented to unveil the parametric influences like nanoparticle concentrations (0.00 ≤ ϕ2 ≤ 0.015), Rayleigh number(103 ≤ Ra ≤ 105), and Hartmann number (0 ≤ Ha ≤ 100). The analysis concludes that entropy increases for nanoparticle concentrations, and Rayleigh numbers, while the decrease is reported for the magnetic number. A similar impact is perceived for heat transport. Higher fins' length reduces the entropy.

Magneto-turbulent natural convection and entropy generation analyses in liquid sodium-filled cavity partially heated and cooled from sidewalls with circular blocks

Liquid sodium is a promising candidate working fluid in the new solar system and high-density heat sources in industrial applications. In this study free convective flow, heat transfer, and entropy generation of liquid sodium in a hot square enclosure with 16 and 64 cylindrical solid blocks are studied. The cavity is partially heated and cooled from sidewalls with three different locations of heater and cooler named CONF1–3. The effects of the magnetic field in the form of Hartmann number (Ha = 0 and 100), and flow condition in the form of the Rayleigh number (Ra = 106, and 107) are investigated. For tuning the CFD code primitive parameter, the dimensionless forms of the governing equations are used. The ANSYS Fluent equations solver conjugated with a nondimesionlization scheme are used in the turbulent region due to the behavior of liquid metal. The grid verification and validation tests are carried out to ensure the accuracy of the data. Two correlations for average Nusselt number and entropy generation are proposed to simplify calculations. The results discovered that the average Nusselt number and entropy generation increase with increasing the Rayleigh number for each value of the Hartmann number.

Magneto-fluid dynamic and second law analysis in a hot porous cavity filled by nanofluid and nano-encapsulated phase change material suspension with different layout of cooling channels

Heat transfer, free convective flow and entropy generation of water, Al2O3-water, and nano encapsulated phase change material (NEPCM) diluted in water as NEPCM-water suspension in a hot enclosure is studied. The enclosure is a square porous cavity which heated from below, and the remained walls are thermally insulated. The cavity is cooled by four cooling channels with three different configurations (CONF 1–3). By considering internally heat generation, the impacts of the magnetic field (Ha = 0 and 100), Darcy number (Da=0.001 and 100) and laminar Rayleigh number (Ra=104, 105, and 106) at an equal concentration of nanoparticle and NEPCM (ϕ=2%) are evaluated by finite volume method (FVM) using ANSYS Fluent. The dimensionless form of the governing equations and entropy generation are used to tune the primitive parameters of the CFD code. The validation test and grid verification check are performed to guarantee the accuracy of the results. The results show that the average Nusselt number decreases from CONF1 to CONF3. The buoyancy effect amplified in higher Rayleigh number and porous medium while the magnetic field controls the buoyancy-driven flow. In addition, at low Rayleigh number, the cavity that contains the NEPCM-water suspension is desirable due to its heat transfer capability and low irreversibility.

Analysis of propeller wake field and vortical structures using [formula omitted] SST Method

CFD simulations are conducted to study the wake field behind a marine propeller in open water conditions at various advance coefficients. The local variables (velocity, pressure) and the wake structure characteristics are analyzed extensively using mean, Root Mean Square (RMS) and Fourier analysis of data. The integral variables (forces/moments) and their correlations with local variables are also investigated. Additionally, the iterative and grid verification studies are conducted to evaluate numerical uncertainty of the simulations. The results showed good agreement between the integral variables obtained by the simulations and those of experiments available in the literature, which confirmed the validity of the computational method employed in this work. Fourier analysis studies on integral variables showed that the rotation of the whole propeller determines the fluctuation of side forces at high J, while at low J, mostly rotation of individual blades affects the side forces. The local flow studies suggested strong correlation between the advance coefficient and the characteristics of vortical structures including their formations, trajectories, and stabilities.

Heat transfer performance investigation on a finned tube adsorbent bed with a compound parabolic concentrator (CPC) for solar adsorption refrigeration

In this work, activated carbon-methanol was used as the working pair in a solar adsorption refrigeration system (SAR). The thermal conductivity of the activated carbon was very poor, resulting in performance delays of the system. To improve the performance of the heat transfer for the adsorbent bed, a new adsorbent bed with finned tubes was designed and studied using commercial computational fluid dynamics (CFD) software. Two-dimensional (2D) numerical models of two kinds of adsorbent tubes (finned and smooth tubes) were constructed and simulated. The two different 2D numerical models had similar cell numbers and the same boundaries and initial conditions. An experiment for a grid verification model of the designed finned tube was conducted, and the model of the finned tube was validated via comparison between the numerical and experimental results. In addition, the heat performances of the newly designed finned tube and the smooth tube were compared in this paper. The temperature gradients of the activated carbon in the smooth and finned tubes were approximately 28.1 °C and 4 °C during isosteric heating, respectively. The conclusions are that the fins had a large effect on the thermal performance of SAR, and the possibility that the methanol was adsorbed again by the activated carbon of the lower temperature part in the finned tubes during isobaric heating was decreased greatly. Moreover, the radial heat loss of the finned tube wall was also less than the smooth tube, which may be an important factor for improving the performance of the system effectively.

A Distributed Barrier Coverage Mechanism for Supporting Full View in Wireless Visual Sensor Networks

Barrier coverage is one of the most important issues in intruder detection applications. Visual sensors can give more accurate information of intruder but also raise the problem of large data volume for information exchange and processing. Constructing a disjoint full-view barrier using minimal number of visual sensors has been the main goal for handling the barrier coverage problem. This paper presents a decentralized FBCA mechanism which consists of Region Partitioning Phase, Grid Excluding Phase, Grid Verification Phase and Full-View Barrier Construction Phase. In Region Partitioning Phase, the given $R $ is partitioned into a set of equal-sized grids, aiming to simplify the construction problem of the full-view barrier. In Grid Excluding Phase, a certain amount of grids is removed, aiming to reduce the computational complexity. In Grid Verification Phase, each visual sensor aims to check if its neighboring grids satisfy the full-view coverage criteria. Finally, the Full-View Barrier Construction Phase aims to construct as many as possible full-view barriers. Experimental study shows that the proposed FBCA outperforms existing work SP, and likely approaches to the optimal solution (MCSPS) in terms of the average success ratio for constructing a full-view barrier.

Assessment of URANS surface effect ship models for calm water and head waves

Surface effect ship (SES) air cushion and seal models are implemented in an URANS hydrodynamics solver. The air cushion is modeled either as a prescribed pressure patch, or as a compressible isothermal/adiabatic ideal stagnant air with fan and leakage flows. The seals are either discretized as hinged bodies or modeled as 2D planing surfaces with hydrodynamic interaction. Verification and validation studies are performed using T-Craft experimental data for calm water resistance, sinkage and trim at Froude number (Fr)=0.1–0.6; impulsive heave and pitch decay at Fr=0; and wave-induced resistance and motion predictions in head waves at Fr=0 and 0.6. The compressible air cushion model with fan and leakage flows perform better than those without the fan and leakage flows and the prescribed pressure patch model. The hinged seal model performs better than the 2D planing surface model, but is computationally expensive for time accurate simulations. Therefore, the 2D planing surface model is used for the validation studies. SES simulations on grids with 5.3M cells show grid verification intervals of 6%, which are comparable to those reported for displacement and semi-planing hull studies on similar grid sizes. On an average calm water and impulsive motion predictions compare within 8.5% of the experimental data, and wave-induced motion predictions show somewhat larger error of 13.5%. The errors levels are mostly comparable to those for displacement and semi-planing and planing hulls. The study identifies that most critical advancement needed for SES simulations is the seal modeling including fluid structure interaction.

Verification of the Power and Ground Grids Under General and Hierarchical Constraints

As part of power distribution network verification, one should check if the voltage fluctuations exceed some critical threshold. The traditional simulation-based solution to this problem is intractable due to the large number of possible circuit behaviors. This approach also requires full knowledge of the details of the underlying circuitry, not allowing one to verify the power distribution network early in the design flow. Contrary to previous work on power distribution network verification, we consider the power and ground (P/G) grids together and describe an early verification approach under the framework of current constraints. Then, we present a solution technique in which tight lower and upper bounds on worst case voltage fluctuations are computed via linear programs. Experimental results indicate that the proposed technique results in errors in the range of a few millivolts. In addition to P/G grid verification techniques, we also provide very efficient solution technique to power (single) grid verification under hierarchical current constraints.

A Selected Inversion Approach for Locality Driven Vectorless Power Grid Verification

Vectorless power grid verification is a practical approach for early stage safety check without input current patterns. The power grid is usually formulated as a linear system and requires intensive matrix inversion and numerous linear programming (LP), which is extremely time-consuming for large-scale power grid verification. In this paper, the power grid is represented in the manner of domain-decomposition approach, and we propose a selected inversion technique to reduce the computation cost of matrix inversion for vectorless verification. The locality existence among power grids is exploited to decide which blocks of matrix inversion should be computed while remaining blocks are not necessary. The vectorless verification could be purposefully performed by this manner of selected inversion, while previous direct approaches are required to perform full matrix inversion and then discard small entries to reduce the complexity of LP. Meanwhile, constraint locality is proposed to improve the verification accuracy. In addition, a concept of quasi-Poisson block is introduced to exploit grid locality among realistic power grids and a scheme of pad-aware partitioning is proposed to enable the selected inversion approach available for practical use. Experimental results show that the proposed approach could achieve significant speedups compared with previous approaches while still guaranteeing the quality of solution accuracy.

Validation of OpenFOAM numerical methods and turbulence models for incompressible bluff body flows

A verification and validation study was performed using the open source computational fluid dynamics solver OpenFOAM version 2.0.0 for incompressible bluff body fluid flows. This includes flow over a backward facing step, a sphere in the subcritical regime, and delta wing with sharp leading edge. The study investigates solver scalability, and accuracy of numerical methods and turbulence models available in the solver. Grid verification study shows mostly monotonic convergence with averaged grid uncertainty <5% for integral quantities and up to 10% for local variables. The solver shows good strong scalability up to 192 processors on a mesh with 11M cells. The study identifies that the 2nd order linear upwind scheme is most efficient and accurate for Reynolds Averaged Navier Stokes (RANS) simulations, while the 1st/2nd order blended limited linear scheme is best for simulations employing hybrid RANS/Large Eddy Simulation (HRL). PIMPLE and SIMPLE pressure–velocity coupling methods are identified to be best for HRL and RANS simulations, respectively. The validation study showed that drag and mean velocity predictions compared within 5% of the experimental data, whereas larger errors were predicted for turbulent kinetic energy and instability frequency predictions. OpenFOAM predictions compared within 6% of FLUENT results for backward facing step and sphere cases, and performed better than the latter for the delta wing vortex breakdown predictions. Overall, OpenFOAM is found to be a reliable research solver; however, it is more sensitivity to grid quality than FLUENT, which needs to be further investigated.

Verification of Computing Grids with Special Edge Conditions by Infinite Petri Nets

A technique of the computing grid verification using invariants of infinite Petri nets was presented. Models of square grid structures in the form of parametric Petri nets for such edge conditions as connection of edges and truncated devices were constructed. Infinite systems of linear algebraic equations were composed on parametric Petri nets for calculating p-invariants; their parametric solutions were obtained. P-invariant Petri nets are structuraly conservative and bounded that together with liveness are the properties of ideal systems. Liveness investigation based on siphons and traps can be implemented by using p-invariants of modified nets.

Forced convective heat transfer and thermal efficiency assessment in square channel equipped with 10° wavy thin rib

Forced convective heat transfer and thermo-hydraulic efficiency in the heat exchanger square channel (HESC) inserted with 10° wavy thin rib (WTR) are reported numerically. The effects of rib height, pitch distance and flow velocity on flow and heat transfer profiles are considered. The rib height to the channel height; e/H or HR, is varied in the range 0.05–0.30, while the rib pitch to the channel height; P/H or PR, is varied in the range 0.50–1.25. The air velocity in the HESC inserted with the WTR is considered in terms of Reynolds number. The Reynolds numbers (Re = 100–2000) for the present investigation is analyzed at the inlet condition. The finite volume method (commercial code) with SIMPLE algorithm is picked to solve the present problem. The numerical model of the HESC inserted with the WTR is validated for both grid independence and verification of the smooth HESC. The numerical results of the HESC inserted with the WTR are printed in terms of flow and heat transfer profiles. The values of Nusselt number, friction factor and thermal efficiency factor in the HESC inserted with the WTR are also plotted. As the numerical result, it is found that the WTR in the HESC can produce the vortex flow that the reason for the enhancements of heat transfer and efficiency. The increment of the heat transfer ability in the HESC is detected when increasing rib height and Reynolds number. In addition, the greatest thermal efficiency factor in the HESC inserted with the WTR is around 3.43 at HR = 0.20, PR = 1, and Re = 2000.

선체 저항에 대한 수치 해석의 통계적 신뢰도 분석

A wide scope of numerical simulations was performed to predict model-ship resistances by using STAR-CCM+ and OpenFOAM. The numerical results were compared with experimental measurements in towing tank to analyze statistical reliability of the present simulations. Based on the normal distribution of resistance errors in 113 cases of container carriers, tankers and very large crude-oil carriers, the confidence intervals of numerical error were estimated as [-2.64%,+2.32%] and [-1.82%, +1.87%] with 95% confidence in STAR-CCM+ and OpenFOAM, respectively. The resistance errors of liquefied natural gas carriers with single- and twin-skeg were confident in the ranges of [-2.51%,+2.64%] and [-2.29%, +1.46%], respectively. The grid uncertainty of resistance coefficients for KCS was also quantitatively analyzed by using a grid verification procedure. The grid uncertainty of OpenFOAM (5.1%) was larger than 4.4% uncertainty of STAR-CCM+ although OpenFOAM provided statistically more confident results than those of STAR-CCM+. It means that a grid system verified under a specific condition does not automatically lead to statistical reliability in general cases.

Scalable Multilevel Vectorless Power Grid Voltage Integrity Verification

With the current aggressive integrated circuit technology scaling, vectorless power grid voltage integrity verification becomes key to designing reliable power delivery networks. To address the challenges of existing vectorless power grid verification methods that suffer from excessively long optimization time and poor scalability to large power grid designs, in this paper, we present a scalable multilevel vectorless power grid verification method which can efficiently tackle very large scale power grid verifications. By taking advantage of a series of coarsest to coarser grid verifications, the finest power grid verification can be accomplished in a more efficient way. To gain good efficiency, global and local “critical regions” for power grid verification are introduced, while power grid structure and electrical properties are exploited to facilitate identifying the worst case voltage drops across the entire chip. The proposed multilevel power grid verification algorithm allows more flexible tradeoffs between verification cost and solution quality, while providing the desired conservative upper/lower bounds for worst case voltage drops. Extensive experimental results show that our approach can efficiently handle very large power grid designs without sacrificing the final power grid verification accuracy. For example, finding the worst voltage drop for a flip-chip power grid design with one million nodes takes less than two hours.

Verifying RLC Power Grids With Transient Current Constraints

Vectorless power grid verification is a powerful method that evaluates worst-case voltage noises without detailed current waveforms using optimization techniques. It is extremely challenging when considering RLC power grids because inductors are difficult to tackle and multiple time steps should be evaluated after the discretization of the system equation. In this paper, we study integrated RLC power grids with both VDD and GND networks, and introduce transient constraints to restrict the waveform of each current source for sign-off verification. We rigorously prove that the vectorless verification can be decomposed into two subproblems-the well-studied power grid transient analysis problem and a linear programming (LP) problem that optimizes an affine function of currents under current constraints-and propose to verify the power grid by transient simulation and noise optimization. A variable reduction algorithm is further proposed to generate reduced-size LP problems with a user-specified error tolerance, so that the conservative bounds of voltage noises can be computed efficiently. Experimental results show that the proposed algorithm achieves significant speedup (e.g., up to more than 100× with 5 mV error) over the standard LP solver in solving the LP problems, and the proposed transient constraints make the noise estimations more realistic.

Corrigendum to “A Realistic Early-Stage Power Grid Verification Algorithm Based on Hierarchical Constraints” [Jan 12 109-120

The authors for the above titled paper were incorrectly listed. The correct list of authors is presented here.

Maximum Circuit Activity Estimation Using Pseudo-Boolean Satisfiability

With lower supply voltages, increased integration densities and higher operating frequencies, power grid verification has become a crucial step in the very large-scale integration design cycle. The accurate estimation of maximum instantaneous power dissipation aims at finding the worst-case scenario where excessive simultaneous switching could impose extreme current demands on the power grid. This problem is highly input-pattern dependent and is proven to be NP-hard. In this paper, we capitalize on the compelling advancements in satisfiability (SAT) solvers to propose a pseudo-Boolean SAT-based framework that reports the input patterns maximizing circuit activity, and consequently peak dynamic power, in combinational and sequential circuits. The proposed framework is enhanced to handle unit gate delays and output glitches. In order to disallow unrealistic input transitions, we show how to integrate input constraints in the formulation. Finally, a number of optimization techniques, such as the use of gate switching equivalence classes, are described to improve the scalability of the proposed method. An extensive suite of experiments on ISCAS85 and ISCAS89 circuits confirms the robustness of the approach compared to simulation-based techniques and encourages further research for low-power solutions using Boolean SAT.