Initial Steady-state Conditions Research Articles

A frequency-domain finite element model for simulating high temperature superconductors using the J-A and T-A formulations

Abstract The AC losses, the current density and the magnetic field are important variables to design devices made of High Temperature Superconductors (HTS). These variables are often numerically computed using a transient finite element analysis even though the interest may lay in the steady-state regime of the device. The need for solving time-dependent variables has led to improve the computation time with efficient finite element models (FEM) relying on different formulations. These transient FEM are computationally slow and demanding in terms of resources. In the present work, an alternative path is taken with the development of a frequency-domain FEM using a phasor representation to alleviate the computation burden. This model does not have the versatility of the transient models. However, it can generate the initial steady-state conditions for a subsequent transient analysis. It is perfectly adapted to study the steady-state regime of HTS devices operated in AC conditions. In this phasor modelling approach, the Root Mean Square (RMS) resistivity of the superconductor is introduced. It is subsequently approximated by an exponential function introducing a factor to ease its implementation in the commercial software COMSOL Multiphysics with the most recent and fastest formulations T-A and J-A. The case studies encompass single BSCCO and REBCO tapes as well as a CORC cable or specifically, in the present work, a CORT (Conductor on Round Tube). The results of the time- and frequency-domain FEM simulations are compared against experimental data. The comparison of the models' results is carried out comparing the current density distributions as well as the AC losses. The comparison against experimental data is only conducted on the AC losses. In the present case, it is used to quantify thoroughly the accuracy of the numerical results compared to the measurements. A reasonable agreement between those results and the experimental data was found. 

Fault tolerant control system for an ROV based on a novel integral sliding mode control and a state and fault observer in the presence of thruster limitations

This paper presents a novel fault tolerant control system for remotely operated vehicles in the presence of unknown system dynamics and unknown thruster faults and failures while accounting for magnitude and rate limits of the thrusters. The proposed control system consists of a novel integral sliding mode control (ISMC) and a new state and fault observer. The proposed ISMC utilizes a novel asymptotic sliding surface to enhance the performance of the control system during both initial transients and steady-state conditions. The observer takes thrusters system dynamics into account and provides estimation of faults and failures. Control allocation is utilized for fault accommodation and to separate the high-level control system and the low-level thruster controllers. Stability analyses are carried out and it is shown that the state observer is guaranteed to be fixed-time convergent while the fault observation error is input-to-state stable. It is also shown that the ISMC-based closed-loop control system is uniformly-ultimately bounded with practically fixed-time reaching phase. Simulations are carried out and comparisons are made with several fixed-time and finite-time control systems. The results outline the superior performance of the proposed control system in terms of positioning accuracy and fault tolerance during initial transients and steady-state conditions.

Acceleration-feedback-based finite-time platoon control for interconnected vehicular system

The platoon control problem of interconnected vehicular systems is investigated in this paper studies. A finite-time adaptive sliding mode control (SMC) method based on acceleration feedback is developed to achieve platooning of interconnected vehicular systems subject to external disturbances and string stability of the closed-loop platoon system is analyzed. The string stability of the closed-loop system is achieved by applying the constant spacing (CS) strategy in the proposed adaptive sliding mode controller under zero initial steady-state error conditions. A novel error definition method is proposed to transform the non-zero initial steady-state error into the zero initial steady-state error so that the proposed algorithm can be independent of the initial steady-state errors and reduce the large transient response caused by non-zero initial steady-state errors. The salient feature of the proposed SMC law is that it does not need to know the disturbance boundary in advance. Finally, simulations and experiments are conducted to demonstrate the advantages and effectiveness of the proposed algorithm.

Harmonic state estimation based on discrete exponential expansion, singular value decomposition and a variable measurement model

In this contribution, a method for harmonic state estimation (HSE) of electrical systems using the discrete exponential expansion (DEE), singular value decomposition (SVD) and a variable measurement model is presented. Variable harmonics, interharmonics, and subharmonics can be estimated using this DEE-SVD time-domain methodology, depending on the number of state variables in the system model and the measurements related through a variable measurement equation, which is proposed as a function of a variable number of measurements and their derivatives to define over, normal and under-determined conditions, respectively. The observability analysis can be verified using the SVD and the resulting null-space vectors, if the electrical system is not completely observable; this analysis can define observable system areas. The HSE regularly receives a limited number of measurements from the system, performs the state estimation and evaluates the global state of the actual harmonic condition. The discrete exponential expansion Newton method determines the periodic steady-state under a particular harmonic condition, obtains a convenient initial steady-state condition to apply the SVD and performs the HSE with a small state estimation error. Noisy measurements adversely affect the state estimation and may increase the state estimation error. The time-domain DEE-HSE can be used to enhance the operation and control of electrical systems under harmonic distortion conditions, e.g., to control active and passive harmonic filters. The state estimation results have been validated through direct comparison against the response obtained with the PSCAD/EMTDC® simulator.

Analysis of the Kalinin-3 coolant transient benchmark by SKETCH-N/SKAZKA code system

The switching off of the one of four main circulation pumps results in the Kalinin-3 Coolant Transient Benchmark. The benchmark contains four exercises, but this article shows the results of the exercise two of the VVER-1000 reactor core calculation. Reactor core analysis code SKETCH-N/SKAZKA is used to simulate the steady-state and transient conditions of the VVER reactor. The reactor core boundary conditions for the problem are provided by ATHLET/BIPR-VVER code.In the initial steady-state condition and at the end of the transient the power distribution is compared with the nuclear power plant (NPP) data. The average error in 3-D power distribution is 3.6%. The average difference in fuel assembly (FA) power is less than 2%. In the transient calculation, we compared with the experimental data the reactor power and axial offset. There is close agreement between the numerical results and NPP data.

Experimental investigation on the extreme cold start-up of an air compressor for electric heavy vehicles

Engine-driven reciprocating air compressors are employed on fuel-powered heavy vehicles to actuate a number of auxiliary systems, like brakes and suspensions. Electrically-driven sliding-vane air compressors turn particularly suited for electric heavy vehicles. Unlike in fuel-powered vehicles, the compressor is not heated up in the case of electric mobility, a situation that may lead to potential issues in extreme cold weathers. This paper investigates experimentally the start-up of a sliding-vane air compressor designed specifically for electric heavy vehicles. The compressors, equipped with instruments, is positioned in a climatic chamber. During the tests, the chamber is set to a desired ambient temperature, 0, -10, -20, - 30 °C or 20 °C taken as reference following ISO 1217, and the compressor is started-up when a steady-state initial condition is achieved. The delivery pressure is controlled at 10 bar(g) and all measurements are recorded until a temperature of 80 °C is reached in the air-lube oil separator. No issues are encountered during the tests, such as sudden damage due to improper lubrication. Moreover, the curves of the measured temperature within the air-lube oil separator show similar trends but higher initial plateaus and lower slopes at lower ambient temperatures resulting into lower oil flow rates, higher energy spent for heating up the system as well as higher warm-up times, from 15 minutes at 20 °C up to 69 minutes at -30 °C.

Critical Loading Characterization for MTDC Converters Using Trajectory Sensitivity Analysis

This paper introduces a new technique to characterize the ac grids stability connected to multiterminal high-voltage direct current networks. The proposed method identifies the maximum active powers that converters can exchange with an ac network without losing the transient stability using trajectory sensitivity analysis. Therefore, the generators' rotor angles variations due to various converters active powers exchange are measured and normalized. Consequently, the norm of each trajectory vector is used as an indicator of the system proximity to instability. To enhance the accuracy of the method for online stability assessment applications, the steady-state initial conditions of the sensitivity network variables are precisely obtained using the Newton shooting method. For this purpose, the detailed differential and algebraic models representing the dynamics of the ac and dc networks have been formulated and analytically solved simultaneously with the sensitivity network. Comprehensive simulation studies on the IEEE 68-bus benchmark system are carried out using PSCAD/EMTDC for validation purposes. Results show that the modified approach provides more accurate results compared to the normal trajectory sensitivity analysis with less time compared to multiple time-domain simulations.

Dynamic analysis of millimetre-scale fixed bed reactors for Fischer-Tropsch synthesis

Dynamic performance of a milli-scale fixed bed reactor for Fischer-Tropsch synthesis (FTS) was studied using a dynamic pseudo-homogeneous 1D reactor model. The model uses detailed kinetics to describe the rates of FTS product formation. Dynamic responses of the process variables and main performance indicators, including productivity of C5+ hydrocarbons and CH4 selectivity, to input step changes, were analyzed. Total of 7 inlet variables were used in step-change-response analysis, with different magnitudes of change and for two initial steady-state conditions. Reactor simulations show highly nonlinear behavior due to phenomena coupling and fast dynamics due to system small scale and intensified rates within. In addition, reactor model shows instability related to thermal runaway with certain magnitudes of step change of coolant temperature and feed flow rate. The analysis outlines the effects of potential process disturbances on operation of milli-scale fixed bed reactor for FTS and provides general guidelines for control systems.

Transient analysis and validation with experimental data of supercritical CO2 integral experiment loop by using MARS

To develop a cycle operation strategy for a supercritical carbon dioxide (S-CO2) Brayton cycle, a series of MARS code simulation results were compared to experimental data from an SCIEL compressor test, which was collected at both component and whole-loop level. The simulation results show reasonable agreement with the experimental results. The MARS code was used to simulate behavioral responses at varying scenarios, the valve control for cycle operation, a power swing to simulate load following behavior, and an effect of the heat sink reduction to simulate failure. The electric power output of the turbine decreased to 50% of that during normal operation through valve control. After power swing, the system reverted to the initial steady-state conditions. The fluid behavior in precooler and the eventual change in the system were identified through the scenario of the heat sink reduction. The simulations provide a notable insight into the responsiveness of an SCIEL to these variable scenarios. Even though the MARS code was specifically developed for analysis of water reactor transients, its field of application may be extended to analyze the S-CO2 Brayton cycle, and may thus assist with the development of control strategies for SCIEL and the S-CO2 Brayton cycle.

Consistent initial conditions for the Saint-Venant equations in river network modeling

Abstract. Initial conditions for flows and depths (cross-sectional areas) throughout a river network are required for any time-marching (unsteady) solution of the one-dimensional (1-D) hydrodynamic Saint-Venant equations. For a river network modeled with several Strahler orders of tributaries, comprehensive and consistent synoptic data are typically lacking and synthetic starting conditions are needed. Because of underlying nonlinearity, poorly defined or inconsistent initial conditions can lead to convergence problems and long spin-up times in an unsteady solver. Two new approaches are defined and demonstrated herein for computing flows and cross-sectional areas (or depths). These methods can produce an initial condition data set that is consistent with modeled landscape runoff and river geometry boundary conditions at the initial time. These new methods are (1) the pseudo time-marching method (PTM) that iterates toward a steady-state initial condition using an unsteady Saint-Venant solver and (2) the steady-solution method (SSM) that makes use of graph theory for initial flow rates and solution of a steady-state 1-D momentum equation for the channel cross-sectional areas. The PTM is shown to be adequate for short river reaches but is significantly slower and has occasional non-convergent behavior for large river networks. The SSM approach is shown to provide a rapid solution of consistent initial conditions for both small and large networks, albeit with the requirement that additional code must be written rather than applying an existing unsteady Saint-Venant solver.

Dynamic Monte Carlo transient analysis for the Organization for Economic Co-operation and Development Nuclear Energy Agency (OECD/NEA) C5G7-TD benchmark

Abstract With ever-advancing computer technology, the Monte Carlo (MC) neutron transport calculation is expanding its application area to nuclear reactor transient analysis. Dynamic MC (DMC) neutron tracking for transient analysis requires efficient algorithms for delayed neutron generation, neutron population control, and initial condition modeling. In this paper, a new MC steady-state simulation method based on time-dependent MC neutron tracking is proposed for steady-state initial condition modeling; during this process, prompt neutron sources and delayed neutron precursors for the DMC transient simulation can easily be sampled. The DMC method, including the proposed time-dependent DMC steady-state simulation method, has been implemented in McCARD and applied for two-dimensional core kinetics problems in the time-dependent neutron transport benchmark C5G7-TD. The McCARD DMC calculation results show good agreement with results of a deterministic transport analysis code, nTRACER.

Solution of PDEs for First-Order Photobleaching Kinetics using Krylov Subspace Spectral Methods

We solve the first order reaction-diffusion equations which describes binding-diffusion kinetics using photobleaching scanning profile of confocal laser scanning Microscopes approximated by a Gaussian laser profile. We show how to solve the first order photobleaching kinetics partial differential equations with prebleach steady state initial conditions using a time-domain method known as a Krylov Subspace Spectral method (KSS method). KSS are explicit methods for solving time-dependent variable-coefficient partial differential equations (PDEs). KSS methods are advantageous compared to other methods because of its high resolution and its superior scalability. We will apply Gaussian Quadrature rules in the spectral domain developed by Golub and Meurant to solve PDEs. We present a simple rough analytical solution, as well as a computational solution that is first-order accurate. We then use this solution to examine short and long time behaviors.

Exact correlations in a single-file system with a driven tracer

We study the effect of a single driven tracer particle in a bath of other particles performing the random average process on an infinite line using a stochastic hydrodynamics approach. We consider arbitrary fixed as well as random initial conditions and compute the two-point correlations. For quenched uniform and annealed steady-state initial conditions we show that in the large time T limit the fluctuations and the correlations of the positions of the particles grow subdiffusively as and have well-defined scaling forms under proper rescaling of the labels. We compute the corresponding scaling functions exactly for these specific initial configurations and verify them numerically. We also consider a non-translationally invariant initial condition with linearly increasing gaps where we show that the fluctuations and correlations grow superdiffusively as at large times.

Spatial analysis of aquifer response times for radial flow processes: Nondimensional analysis and laboratory-scale tests

• Nondimensional model of groundwater pumping, injection and recovery is analyzed. • Time scales for pumping, injection and recovery processes to reach steady state is considered. • Closed form expressions for the time scale, including spatial dependence, are given. • Time scales are equivalent for pumping, injection and recovery. • Theoretical predictions are validated with new laboratory measurements. A fundamental concept in groundwater hydrology is the notion of steady state, or equilibrium conditions. When a system at some initial steady state condition is perturbed by pumping, a transient cone of depression will develop and the system will approach a new steady state condition. Understanding the time scale required for the transient process to occur is of practical interest since it would help practitioners decide whether to use a steady state model or a more complicated transient model. Standard approaches to estimate the response time use simple scaling relationships which neglect spatial variations. Alternatively, others define the response time to be the amount of time taken for the difference between the transient and steady state solutions to fall below some arbitrary tolerance level. Here, we present a novel approach and use the concept of mean action time to predict aquifer response time scales in a two-dimensional radial geometry for pumping, injection and recovery processes. Our approach leads to relatively simple closed form expressions that explicitly show how the time scale depends on the hydraulic parameters and position. Furthermore, our dimensionless framework allows us to predict the response time scales for a range of applications including small scale laboratory problems and large scale field problems. Our analysis shows that the response time scales vary spatially, but are equivalent for pumping, injection and associated recovery processes. Furthermore, the time scale is independent of the pumping or injection flow rate. We test these predictions in a laboratory scale aquifer and find that our physical measurements corroborate the theoretical predictions.

Effect of Spray Cone Angle on Flame Stability in an Annular Gas Turbine Combustor

AbstractEffect of fuel spray cone angle in an aerogas turbine combustor has been studied using computational fluid dynamics (CFD) and full-scale combustor testing. For CFD analysis, a 22.5° sector of an annular combustor is modeled and the governing equations are solved using the eddy dissipation combustion model in ANSYS CFX computational package. The analysis has been carried out at 125 kPa and 303 K inlet conditions for spray cone angles from 60° to 140°. The lean blowout limits are established by studying the behavior of combustion zone during transient engine operation from an initial steady-state condition. The computational study has been followed by testing the practical full-scale annular combustor in an aerothermal test facility. The experimental result is in a good agreement with the computational predictions. The lean blowout fuel–air ratio increases as the spray cone angle is decreased at constant operating pressure and temperature. At higher spray cone angle, the flame and high-temperature zone moves upstream close to atomizer face and a uniform flame is sustained over a wide region causing better flame stability.

ICONE23-2041 FIRST ANALYSIS OF AGS0, LT2 AND E9 CABRI TESTS WITH THE NEW SFR SAFETY CODE ASTEC-NA

Within the framework of the European JASMIN project, the ASTEC-Na code is being developed for safety analysis of severe accidents in SFR. In the first phase of validation of the ASTEC-Na fuel thermo-mechanical models three in-pile tests conducted in the CABRI experimental reactor have been selected to be analysed. We present here the preliminary results of the simulation of two Transient Over Power tests and one power ramp test (AGS0, LT2 and E9, respectively) where no pin failure occurred during the transient. We present the comparison of ASTEC-Na results against experimental data and other safety code results for the initial steady state conditions prior to the transient onset as well as for the fuel pin behaviour during the transients.

Applying a wide-area measurement system to validate the dynamic model of a part of European power system

In this paper a validation of dynamic model of a Slovenian power system using WAMS is presented. For this purpose a dynamic model of a part of the ENTSO-E system was constructed by applying two professional dynamic-simulation software tools that use different approaches to obtain mathematical solutions for the model to solve the problem. The simulation results were compared with each other as well as with the measurements gathered by the WAMS. Namely, Slovenia has almost full coverage of PMU measurements at the high-voltage level (220- and 400-kV) buses. This fact has been used to adapt the model, especially for the representation of the rest of the ENTSO-E network, as well as for the validation of the results and explaining the physical background for the existing differences. WAMS measurements for several different events occurring during 2010 and 2011 were used to adapt the model, which then exhibits a good match in all situations recorded by the WAMS. The physical background for the resulting deviations is presented. However, it should be pointed out that, after the model was finalized, for all the validated cases the system element parameters remained unchanged. Of course, depending on the simulated case, the initial steady-state conditions were set according to the measurements.

A Hybrid Dynamic Optimization Approach for Stability Constrained Optimal Power Flow

Stability-constrained optimal power flow (SOPF) is an effective and economic tool to enhance stability performance by adjusting initial steady-state operating conditions, with the consideration of rotor angle and short-term voltage performance criteria. SOPF belongs to the category of dynamic optimization problems which are computationally expensive. In order to reduce its computational complexity, a hybrid dynamic optimization approach is proposed for efficient and robust solving SOPF problems. Based on the direct multiple shooting method, this approach combines the algorithmic advantages from existing direct sequential and simultaneous approaches. Coarse-grained parallelism among multiple shooting intervals is explored. A modular-based implementation architecture is designed to take advantage of the loose coupling between time-domain simulation and optimization. Case studies on various test systems indicate that the proposed approach is able to reduce computation time compared with other direct approaches for dynamic optimization. Also, the investigated parallelizations are effective to achieve acceleration on a symmetric multiprocessing platform.

Soil compressibility in transient unsaturated seepage analyses

Most levee underseepage and uplift analyses are based on steady-state seepage and can yield conservative results. Although computations are simpler and steady-state seepage parameters are easier to determine and readily available, transient unsaturated seepage analyses are more representative of levee seepage conditions because boundary conditions acting on the levee or floodwall and saturation change with time, which induce pore-water pressure and seepage changes with time in the embankment and foundation strata. In addition, these boundary conditions, e.g., flood surge or storm event, are rapid such that steady-state conditions may not have time to develop in the embankment and some foundation materials. Transient seepage analyses using a floodwall case study indicate that as soil compressibility of the underseepage layer decreases, rapid landside pore-water pressures increase and can approach steady-state values. The transient results also indicate that uplift factors of safety during the flood event are about 22% higher than those at steady state. The effect of soil compressibility can delay or accelerate the onset of uplift water pressure increase from the initial steady-state conditions.

Using Compressed Air Injection to Control Seawater Intrusion in a Confined Coastal Aquifer

Seawater intrusion into groundwater is an important problem in many coastal regions. Freshwater injection has been widely used to avoid seawater contaminating freshwater systems, but is not an attractive solution where freshwater is limited. We investigated the effects of injecting compressed air on seawater movement in a confined coastal aquifer using a numerical simulation. We used TOUGH2/EOS7 software to analyze the effects of injecting compressed air in preventing seawater intruding into a hypothetical confined coastal aquifer (Henry’s problem), simulating steady-state initial conditions and comparing the results with the literature sources. We then performed a transient-state numerical simulation to quantify the seawater intrusion control efficiency achieved by injecting air. The results showed that injecting compressed air can mitigate seawater intrusion: Saltwater was ejected from the aquifer and the seawater circulation disappeared. The injected air flowed upward and spread laterally near the top of the aquifer because of the groundwater and air densities. Injecting air significantly increased the groundwater and gas pressures near the air injection zone and at the top of the aquifer. The air injection rate increased rapidly, then increased gradually. Freshwater injection was also simulated using settings similar to those used for air injection, and this showed that seawater intrusion is prevented more efficiently by freshwater injection than air injection. However, freshwater resources are valuable, whereas air is readily available, so injecting air to mitigate seawater intrusion has great potential. The modeling approach that we used will be used as a foundation for future work.