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DOE OSTI2024

Newton-Raphson AC Power Flow Convergence Based on Deep Learning Initialization and Homotopy Continuation

Power flow forms the basis of many power system studies. With the increased penetration of renewable energy, grid planners tend to perform multiple power flow simulations under various operating conditions and not just selected snapshots at peak or light load conditions. Getting a converged AC power flow (ACPF) case remains a significant challenge for grid planners especially in large power grid networks. This paper proposes a two-stage approach to improve Newton-Raphson ACPF convergence and was applied to a 6102 bus Electric Reliability Council of Texas (ERCOT) system. The first stage utilizes a deep learning-based initializer with data re-training. Here a deep neural network (DNN) initializer is developed to provide better initial voltage magnitude and angle guesses to aid in power flow convergence. This is because Newton-Raphson ACPF is quite sensitive to the initial conditions and bad initialization could lead to divergence. The DNN initializer includes a data re-training framework that improves the initializer's performance when faced with limited training data. The DNN initializer successfully solved 3,285 cases out of 3,899 non-converging dispatch and performed better than random forest and DC power flow initialization methods. ACPF cases not solved in this first stage are then passed through a hot-starting algorithm based on homotopy continuation with switched shunt control. The hot-starting algorithm successfully converged 416 cases out of the remaining 614 non-converging ACPF dispatch. In conclusion, the combined two-stage approach achieved a 94.9% success rate, by converging a total of 3,701 cases out of the initial 3,899 unsolved cases.

Deep learning↗

NASA NTRS1993

Effects of internal yaw-vectoring devices on the static performance of a pitch-vectoring nonaxisymmetric convergent-divergent nozzle

An investigation was conducted in the static test facility of the Langley 16-Foot Transonic Tunnel to evaluate the internal performance of a nonaxisymmetric convergent divergent nozzle designed to have simultaneous pitch and yaw thrust vectoring capability. This concept utilized divergent flap deflection for thrust vectoring in the pitch plane and flow-turning deflectors installed within the divergent flaps for yaw thrust vectoring. Modifications consisting of reducing the sidewall length and deflecting the sidewall outboard were investigated as means to increase yaw-vectoring performance. This investigation studied the effects of multiaxis (pitch and yaw) thrust vectoring on nozzle internal performance characteristics. All tests were conducted with no external flow, and nozzle pressure ratio was varied from 2.0 to approximately 13.0. The results indicate that this nozzle concept can successfully generate multiaxis thrust vectoring. Deflection of the divergent flaps produced resultant pitch vector angles that, although dependent on nozzle pressure ratio, were nearly equal to the geometric pitch vector angle. Losses in resultant thrust due to pitch vectoring were small or negligible. The yaw deflectors produced resultant yaw vector angles up to 21 degrees that were controllable by varying yaw deflector rotation. However, yaw deflector rotation resulted in significant losses in thrust ratios and, in some cases, nozzle discharge coefficient. Either of the sidewall modifications generally reduced these losses and increased maximum resultant yaw vector angle. During multiaxis (simultaneous pitch and yaw) thrust vectoring, little or no cross coupling between the thrust vectoring processes was observed.

Asbury, Scott C.↗

DOE OSTI2022

MIDAS-DC-AC Tool: Fully Automating the Acquisition of AC Power Flow Solution (MIDAS-DC2AC)

MIDAS DC2AC is an automated tool for achieving a converged AC power flow solution from any dispatch, e.g., determined using DC power flow model based optimal power flow. The entire process is free of human interference. It is usually encountered in practice that, even with a DC power flow solution, acquiring the solved AC power flow solution, if exists, sometimes could be a challenging task, especially during the planning stage. It is also difficult to distinguish the unsolvable cases from diverging iterations. Manual adjustments to approach the desired power flow condition has been largely relied on in the past using lots of engineering heuristics. This tool provides a systematic way to first achieve a solvable AC power flow case by modifying the power flow condition, and then try to track the AC power flow solution while gradually removing the adopted changes. If all adopted changes can be completely removed, then the original AC power flow solution is obtained. Otherwise, insights for actionable controls are derived to help operation and planning. Currently, this tool has been implemented in Python using SIEMENS PTI PSS/E as power flow solver, where only adjusting generator terminal voltage set point is considered as an available means to try to turn an unsolved power flow to a solved one. In future, more means should be considered, including the operation of tap-changing transformers, switched shunts and redispatch of active power.

Tan, Jin↗

DOE OSTI2022

DC-AC Tool: Fully Automating the Acquisition of AC Power Flow Solution

DC2AC is an automated tool for achieving a converged AC power flow solution from any dispatch, e.g., determined using DC power flow model based optimal power flow. The entire process is free of human interference. It is usually encountered in practice that, even with a DC power flow solution, acquiring the solved AC power flow solution, if exists, sometimes could be a challenging task, especially during the planning stage. It is also difficult to distinguish the unsolvable cases from diverging iterations. Manual adjustments to approach the desired power flow condition has been largely relied on in the past using lots of engineering heuristics. This tool provides a systematic way to first achieve a solvable AC power flow case by modifying the power flow condition, and then try to track the AC power flow solution while gradually removing the adopted changes. If all adopted changes can be completely removed, then the original AC power flow solution is obtained. Otherwise, insights for actionable controls are derived to help operation and planning. Currently, this tool has been implemented in Python using SIEMENS PTI PSS/E as power flow solver, where only adjusting generator terminal voltage set point is considered as an available means to try to turn an unsolved power flow to a solved one. In future, more means should be considered, including the operation of tap-changing transformers, switched shunts and redispatch of active power.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1988

Advanced electric propulsion research

Results are presented which show that hollow cathodes can be operated on ammonia but that sustained operation in the high pressures where arcjet thrusters operate (of the order of 1000 Torr) is difficult to achieve. The concept of using contoured, fine wire meshes attached across the screen grid apertures in an ion thruster to effect control of the ion beam divergence is introduced. The concept is compared to conventional (free sheath) ion extraction and is shown to be potentially attractive. The performance related effects of changing the anode and cathode locations and of interchanging hollow cathode and refractory filament electron sources within an 8-cm diameter, argon, ring cusp ion thruster discharge chamber are examined. The effects induced in discharge chamber performance by changes in magnetic field strength and configuration and in propellant flow distribution are also measured. Results are presented in terms of changes in the parameters that describe the effectiveness of primary electron utilization and ion extraction into the beam. The apparatus and instrumentation used to study hollow cathode operation at high electron emission levels (of the order of 100 A) is described.

Wilbur, Paul J.↗

NASA NTRS2000

Computational Investigation of the Aerodynamic Effects on Fluidic Thrust Vectoring

A computational investigation of the aerodynamic effects on fluidic thrust vectoring has been conducted. Three-dimensional simulations of a two-dimensional, convergent-divergent (2DCD) nozzle with fluidic injection for pitch vector control were run with the computational fluid dynamics code PAB using turbulence closure and linear Reynolds stress modeling. Simulations were computed with static freestream conditions (M=0.05) and at Mach numbers from M=0.3 to 1.2, with scheduled nozzle pressure ratios (from 3.6 to 7.2) and secondary to primary total pressure ratios of p(sub t,s)/p(sub t,p)=0.6 and 1.0. Results indicate that the freestream flow decreases vectoring performance and thrust efficiency compared with static (wind-off) conditions. The aerodynamic penalty to thrust vector angle ranged from 1.5 degrees at a nozzle pressure ratio of 6 with M=0.9 freestream conditions to 2.9 degrees at a nozzle pressure ratio of 5.2 with M=0.7 freestream conditions, compared to the same nozzle pressure ratios with static freestream conditions. The aerodynamic penalty to thrust ratio decreased from 4 percent to 0.8 percent as nozzle pressure ratio increased from 3.6 to 7.2. As expected, the freestream flow had little influence on discharge coefficient.

Deere, K. A.↗

NASA NTRS1989

Experimental results for labyrinth gas seals with honeycomb stators - Comparisons to smooth-stator seals and theoretical predictions

Experimental measurements are presented for the rotordynamic stiffness and damping coefficients of a teeth-on-rotor labyrinth seal with a honeycomb stator. Inlet circumferential velocity, inlet pressure, rotor speed, and seal clearance are primary variables. Results are compared to data for teeth-on-rotor labyrinth seals with smooth stators and to analytical predictions from a two-control-volume compressible flow model. The experimental results show that the honeycomb-stator configuration is more stable than the smooth-stator configuration at low rator speeds. At high rotor speeds, the stator surface does not affect stability. The theoretical model predicts the cross-coupled stiffness of the honeycomb-stator seal correctly within 25 percent of measured values. The model provides accurate predictions of direct damping for large clearance seals; however, the model predictions and test results diverge with increasing running speed. Overall, the model does not perform as well for low clearance seals as for high clearance seals.

Hawkins, Larry↗

NASA NTRS1994

Mixing and Noise Benefit Versus Thrust Penalty in Supersonic Jets Using Impingement Tones

This paper reports the results of an experimental investigation on the effect of impingement tones generated by obstacles of various geometries on the spreading of a supersonic jet flow. A rectangular supersonic jet was produced using a convergent-divergent nozzle that was operated near its design point (with shocks minimized). The immersion of obstacles in the flow produced an intense impingement tone which then propagated upstream (as feedback) to the jet lip and excited the antisymmetric hydrodynamic mode in the jet, thus setting up a resonant self-sustaining loop. The violent flapping motion of the jet due to excitation of the antisymmetric mode, combined with the unsteady wakes of the obstacles, produced large changes in jet mixing. It was possible to control the frequency and amplitude of the impingement tone excitation by varying the nozzle-to-obstacle distance and the obstacle immersion. By proper shaping of the obstacles it was possible to reduce the thrust penalty significantly.

Raman, Ganesh↗

NASA NTRS1994

Computational Fluid Dynamic Modeling of Rocket Based Combined Cycle Engine Flowfields

Computational Fluid Dynamic techniques are used to study the flowfield of a fixed geometry Rocket Based Combined Cycle engine operating in rocket ejector mode. Heat addition resulting from the combustion of injected fuel causes the subsonic engine flow to choke and go supersonic in the slightly divergent combustor-mixer section. Reacting flow computations are undertaken to predict the characteristics of solutions where the heat addition is determined by the flowfield. Here, adaptive gridding is used to improve resolution in the shear layers. Results show that the sonic speed is reached in the unheated portions of the flow first, while the heated portions become supersonic later. Comparison with results from another code show reasonable agreement. The coupled solutions show that the character of the combustion-based thermal choking phenomenon can be controlled reasonably well such that there is opportunity to optimize the length and expansion ratio of the combustor-mixer.

Daines, Russell L.↗

DOE OSTI2022

Conservative Numerical Schemes with Optimal Dispersive Wave Relations: Part II. Numerical Evaluations

A new energy and enstrophy conserving scheme (EEC) for the shallow water equations is proposed and evaluated using a suite of test cases over the global spherical or bounded domain. The evaluation is organized around a set of pre-defined properties: accuracy of individual operators, accuracy of the whole scheme, conservation of key quantities, control of the divergence variable, representation of the energy and enstrophy spectra, and simulation of nonlinear dynamics. The results confirm that the scheme is between the first and second order accurate, and conserves the total energy and potential enstrophy up to the time truncation errors. Here, the scheme is capable of producing more physically realistic energy and enstrophy spectra, indicating that it can help prevent the unphysical energy cascade towards the finest resolvable scales. With an optimal representation of the dispersive wave relations, the scheme is able to keep the flow close to being non-divergent, and maintain the geostrophically balanced structures with large-scale geophysical flows over long-term simulations.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1996

An Algebraic Multigrid Solver for Navier-Stokes Problems in the Discrete Second-Order Approximation

An algebraic multigrid scheme is presented for solving the discrete Navier-Stokes equations to second-order accuracy using the defect-correction method. Solutions have been obtained for problems involving both structured and unstructured meshes, with the resolution and resolution grading controlled by global and local mesh refinements. The solver is efficient and robust to the extent that no underrelaxation of variables has been required to ensure convergence, but rates of convergence can be improved with small amounts of underrelaxation of the velocity-pressure coupling. Provided that the computational mesh can resolve the flow field, convergence characteristics are almost mesh independent. Rates of convergence actually improve with refinement, asymptotically approaching mesh independent values. For extremely coarse meshes where dispersive truncation errors would be expected to prevent convergence (or even induce divergence), solutions can still be obtained by using explicit underrelaxation in the iterative cycle.

Webster, R.↗

NASA NTRS2015

Computational Fluid Dynamics Modeling of a Supersonic Nozzle and Integration into a Variable Cycle Engine Model

This paper covers the development of an integrated nonlinear dynamic simulation for a variable cycle turbofan engine and nozzle that can be integrated with an overall vehicle Aero-Propulso-Servo-Elastic (APSE) model. A previously developed variable cycle turbofan engine model is used for this study and is enhanced here to include variable guide vanes allowing for operation across the supersonic flight regime. The primary focus of this study is to improve the fidelity of the model's thrust response by replacing the simple choked flow equation convergent-divergent nozzle model with a MacCormack method based quasi-1D model. The dynamic response of the nozzle model using the MacCormack method is verified by comparing it against a model of the nozzle using the conservation element/solution element method. A methodology is also presented for the integration of the MacCormack nozzle model with the variable cycle engine.

Control Theory↗

DOE OSTI2026

Influence of conical wire array geometry on plasma flow and temperature profiles of radiatively cooled jets

The influence of conical wire array geometry on the formation and dynamics of pulsed-power driven plasma jets is investigated. In the experiments, the jet becomes isolated from the inflows as it passes through an aperture, allowing the study of its intrinsic evolution for different conical angles. Here, our results show that, regardless of the array opening angle, the jets are supersonic, highly collisional, and exhibit an exponential axial density decay with a characteristic scale length of 𝐿 𝑛 ≈ 3 mm, significantly shorter than the overall length of the jet. In contrast, axial velocity systematically increases with larger array opening angles. The near invariance of the density profile is attributed to a compensating mechanism between geometric divergence and axial acceleration, consistent with an asymptotically steady flow regime. Additionally, temperature measurements reveal ion-electron thermal decoupling near the base of the jet, with equilibration downstream. Analysis of radiative cooling and collisional energy exchange timescales indicates that the plasma evolves in a radiatively stable regime and that the two-temperature profile is fully described by the competition between both methods. These findings provide valuable information into the internal structure and evolution of pulsed-power plasma jets in regimes dominated by geometric shaping and radiative cooling, demonstrating experimental control over flow acceleration and collimation relevant to both laboratory and astrophysical contexts.

Physics - Plasma physics↗

NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗

NASA NTRS2014

Computational Fluid Dynamics Modeling of a Supersonic Nozzle and Integration into a Variable Cycle Engine Model

Thrust↗

NASA NTRS1961

Annular Internal-External-Expansion Rocket Nozzles for Large Booster Applications

For large-thrust booster applications, annular rocket nozzles employing both internal and external expansion are investigated. In these nozzles, free-stream air flows through the center as well as around the outside of the exiting jet. Flaps for deflecting the rocket exhaust are incorporated on the external-expansion surface for thrust-vector control. In order to define nozzle off-design performance, thrust vectoring effectiveness, and external stream effects, an experimental investigation was conducted on two annular nozzles with area ratios of 15 and 25 at Mach 0, 2, and 3 in the Lewis 10- by 10-foot wind tunnel. Air, pressurized to 600 pounds per square inch absolute, was used to simulate the exhaust flow. For a nozzle-pressure-ratio range of 40 to 1000, the ratio of actual to ideal thrust was essentially constant at 0.98 for both nozzles. Compared with conventional convergent-divergent configurations on hypothetical boost missions, the performance gains of the annular nozzle could yield significant orbital payload increases (possibly 8 to 17 percent). A single flap on the external-expansion surface of the area-ratio-25 annular nozzle produced a side force equal to 4 percent of the axial force with no measurable loss in axial thrust.

Connors, James F.↗

NASA NTRS1973

The choking pressure ratio of a critical flow venturi

The critical flow venturi has many important applications in the measurement and control of gas flow. In many of these applications, it is desirable to minimize the pressure loss required to maintain critical flow conditions. The performance of the venturi may be characterized by the ratio of outlet static pressure to inlet total pressure just sufficiently small to produce critical flow. This ratio is called choking pressure ratio. The optimization of diffusers for critical flow venturis is discussed and suggestions for designs practice are presented. Test results are given for six different diffuser configurations, and a comparison is made with data on 11 configurations from other investigators. It is shown that, for the small divergence angles considered, a simply defined diffuser effectiveness parameter is approximately independent of flow conditions and may be used to predict choking pressure ratio.

Hillbrath, H. S.↗

NASA NTRS2011

Generalized Jeans' Escape of Pick-Up Ions in Quasi-Linear Relaxation

Jeans escape is a well-validated formulation of upper atmospheric escape that we have generalized to estimate plasma escape from ionospheres. It involves the computation of the parts of particle velocity space that are unbound by the gravitational potential at the exobase, followed by a calculation of the flux carried by such unbound particles as they escape from the potential well. To generalize this approach for ions, we superposed an electrostatic ambipolar potential and a centrifugal potential, for motions across and along a divergent magnetic field. We then considered how the presence of superthermal electrons, produced by precipitating auroral primary electrons, controls the ambipolar potential. We also showed that the centrifugal potential plays a small role in controlling the mass escape flux from the terrestrial ionosphere. We then applied the transverse ion velocity distribution produced when ions, picked up by supersonic (i.e., auroral) ionospheric convection, relax via quasi-linear diffusion, as estimated for cometary comas [1]. The results provide a theoretical basis for observed ion escape response to electromagnetic and kinetic energy sources. They also suggest that super-sonic but sub-Alfvenic flow, with ion pick-up, is a unique and important regime of ion-neutral coupling, in which plasma wave-particle interactions are driven by ion-neutral collisions at densities for which the collision frequency falls near or below the gyro-frequency. As another possible illustration of this process, the heliopause ribbon discovered by the IBEX mission involves interactions between the solar wind ions and the interstellar neutral gas, in a regime that may be analogous [2].

Moore, T. E.↗