Newton-Raphson Formulation Research Articles

Unified Power Flow Solver for Hybrid AC/DC Distribution Networks

Hybrid ac/dc distribution grids are gaining popularity due to their potential to conflate the benefits of both ac and dc grids. However, the complex structure of these grids imposes new challenges in power flow (PF) calculations due to multiple ac/dc interconnections, variety of converter operations, and constant dc power loads. This paper proposes a unified PF algorithm incorporating different types of ac/dc and dc/dc converters. The proposed approach is based on the Newton Raphson (NR) algorithm and uses the Modified-Augmented-Nodal-Analysis (MANA) formulation. The proposed formulation can handle arbitrary hybrid ac/dc configurations. The modular structure allows incorporating arbitrary devices and converter controllers. The formulation is built on the summation of line flows and their associated derivatives instead of bus power injections to handle connections with different types of buses equipped with various converters in a straightforward manner. The proposed algorithm is implemented in MATLAB and tested on the modified IEEE 33 bus test system for various configurations. Electromagnetic Transient (EMT) simulations confirmed the accuracy of the proposed method.Another original contribution of the paper is the demonstration of the improved convergence characteristics of MANA based formulation over classical NR formulation through comparisons of conditioning number.

MODFLOW as a Configurable Multi-Model Hydrologic Simulator.

MODFLOW 6 is the latest in a line of six "core" versions of MODFLOW released by the U.S. Geological Survey. The MODFLOW 6 architecture supports incorporation of additional hydrologic processes, in addition to groundwater flow, and allows interaction between processes. The architecture supports multiple model instances and multiple types of models within a single simulation, a flexible approach to formulating and solving the equations that represent hydrologic processes, and recent advances in interoperability, which allow MODFLOW to be accessed and controlled by external programs. The present version of MODFLOW 6 consolidates popular capabilities available in MODFLOW variants, such as the unstructured grid support in MODFLOW-USG, the Newton-Raphson formulation in MODFLOW-NWT, and the support for partitioned stress boundaries in MODFLOW-CDSS. The flexible multi-model capability allows users to configure MODFLOW 6 simulations to represent the local-grid refinement (LGR) capabilities available in MODFLOW-LGR, the multi-species transport capabilities in MT3DMS, and the coupled variable-density capabilities available in SEAWAT. This paper provides a new, holistic and integrated overview of simulation capabilities made possible by the MODFLOW 6 architecture, and describes how ongoing and future development can take advantage of the program architecture to integrate new capabilities in a way that is minimally invasive and automatically compatible with the existing MODFLOW 6 code.

A Stepwise Modelling Approach to Identifying Structural Features That Control Groundwater Flow in a Folded Carbonate Aquifer System

This paper concerns a stepwise modelling procedure for groundwater flow simulation in a folded and faulted, multilayer carbonate aquifer, which constitutes a source of good quality water for human consumption in the Apennine Range in Central Italy. A perennial river acts as the main natural drain for groundwater while sustaining valuable water-related ecosystems. The spatial distribution of recharge was estimated using the Thornthwaite–Mather method on 60 years of climate data. The system was conceptualized as three main aquifers separated by two locally discontinuous aquitards. Three numerical models were implemented by gradually adding complexity to the model grid: single layer (2D), three layers (quasi-3D) and five layers (fully 3D), using an equivalent porous medium approach, in order to find the best solution with a parsimonious model setting. To overcome dry-cell problems in the fully 3D model, the Newton–Raphson formulation for MODFLOW-2005 was invoked. The calibration results show that a fully 3D model was required to match the observed distribution of aquifer outflow to the river baseflow. The numerical model demonstrated the major impact of folded and faulted geological structures on controlling the flow dynamics in terms of flow direction, water heads and the spatial distribution of the outflows to the river and springs.

Assessment of Groundwater Recharge in Agro-Urban Watersheds Using Integrated SWAT-MODFLOW Model

Numerical models are employed widely to evaluate the hydrological components of a watershed but, traditionally, watershed models simplify either surface or subsurface flow module. In this setup, as a bridge between groundwater and surface water regimes, aquifer recharge is the most affected segment of the water balance. Since the watershed processes are increasingly changed, the need for a comprehensive model with detailed conceptualizing capacity of both groundwater and surface water flow systems is growing. This work focuses on the spatiotemporal groundwater recharge assessment in gauged and ungauged agro-urban watersheds in South Korea using the updated SWAT-MODFLOW model, which integrates the Soil and Water Assessment Tool (SWAT2012) and Newton–Raphson formulation for Modular Finite Difference Groundwater Flow (MODFLOW-NWT) in a single executable code. Before coupling, the setup, calibration, and verification of each model were performed separately. After integration, irrigation pumps and drain cells mapping to SWAT auto-irrigation and subbasins were initiated. Automatic calibration techniques were used for SWAT and MODFLOW-NWT models, but a manual calibration was used for the integrated model. A physical similarity approach was applied to transfer parameters to the ungauged watershed. Statistical model performance indicators revealed that the low streamflow estimation was improved in SWAT-MODFLOW. The spatiotemporal aquifer recharge distribution from both the stream seepage and precipitation showed a substantial change, and most of the aquifer recharge occurs in July–September. The areal annual average recharge reaches about 18% of the precipitation. Low-lying areas receive higher recharge consistently throughout a year. Overall, SWAT-MODFLOW exhibited reasonable versatility in evaluating watershed processes and produced valuable results with reasonable accuracy. The results can be an important input for policymakers in the development of sustainable groundwater protection and abstraction strategies for the region.

GEOCHEMICAL SPECIATION AND BATCH MODE SIMULATION IN THE CARBONATE DEPOSITIONAL ENVIRONMENTS

Geochemical modeling has been frequently used to understand and interpret water-rock interactions in sedimentary basins. Thermodynamic data, kinetic parameters, numerical methods, boundary history, and boundary conditions are factors affecting any geochemical modeling system. In the present study, we have attempted to establish a geochemical speciation model by comparing the interaction of formation water and carbonate rock in the carbonate depositional settings of Cambrian successions of Bachu and Tarim area. A comparative study of geochemical speciation has been performed using four different software: PHREEQCTM, GWBTM, TOUGHREACTTM, and GEODELING. GEODELING is a geochemical code simulator that we have developed, and the details are presented further in this work. All the software has been analyzed minutely, considering the distribution, mobility, and availability of chemical species in geological environments. Very similar results in speciation are observed while working with low-temperature systems. A discrepancy can be observed in the results while working with high temperatures. However, a thorough Newton-Raphson formulation, scaling of algebraic equations and master-species switching helps to reduce the possibility of failures of the numerical method used in PHREEQCTM.

On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

Developed generalised unified power flow controller model in the Newton–Raphson power‐flow analysis using combined mismatches method

This study proposes the generalised unified power flow controller (GUPFC) model in the hybrid current power mismatch Newton–Raphson formulation (HPCIM). In this model, active power, real and imaginary current components are injected at the terminals of series impedances of GUPFC. These injected values are calculated during the iterative process based on the desired controlled values and buses voltage at the terminals of GUPFC. The parameters of GUPFC can be calculated during the iterative process and the final values are updated after load flow convergence. Using the developed GUPFC model, the original structure and symmetry of the admittance and Jacobian matrices can still be kept, the changing of Jacobian matrix is eliminated. Consequently, the complexities of the computer load flow program codes with GUPFC are reduced. The HPCIM load flow code with the proposed model is written in C++ programming language. Where, the SuperLU library is utilised to handle the sparse Jacobian matrix. The proposed model has been validated using the standard IEEE test systems.

Analytical frequency modeling of a diode rectifier: formulation for SQP solving versus formulation for Newton-Raphson solving

Purpose Static converters generate current harmonics in grids. Numerous studies on analytical frequency models of converters are often required to carry out their harmonic modeling in the context of sizing by optimization. Some formulations are proposed to solve such models. Each formulation has its own advantages and drawbacks. The paper mainly focuses on two formulations: the first to be solved by Sequential Quadratic Programming (SQP) and the second to be solved by Newton-Raphson (NR). In this way, the paper presents the performances of each formulation and compares the results of both formulations for the modeling of a single-phase diode rectifier. Design/methodology/approach The paper aims to compare SQP formulation and NR formulation, and to propose the ways to improve their convergence. In the modeling, by using an explicit formulation of the state variables combined to a numerical method, equations are defined to reduce, as far as possible, the number of unknowns. Findings The difficulty is to find the good operating mode of the static converter. So, outside the equations and the constraints, the paper proposes to use the eigenvalues of the state space matrixes to initialize the duration of every configuration and to consider the operating symmetries of the static converter that allow to reduce the research area and also the variables calculated. Research limitations/implications The number of the conducting phase per half period is a priori, as the operating mode. Originality/value The modeling is based on the use of linear components, ideal switches and the static converter operates in steady-state. The main difficulties are to formulate the equations representing the non-controlled switching of semiconductors, and to solve them.

Design and kinematic analysis of 3PSS-1S wrist for needle insertion guidance

In this work it is presented a complete kinematic analysis of the 3PSS-1S parallel mechanism for its implementation as a spherical wrist for a needle insertion guidance robot. The spherical 3PSS-1S mechanism is a low weight and reduced dimension parallel mechanism that allows spherical movements providing the requirements needed for the serial–parallel robotic arm for needle insertion guidance. The solution of its direct kinematic is computed with a numerical method based on the Newton–Raphson formulation and a constraint function of the mechanism. The input–output velocity equation is obtained with the use of screw theory. Three types of singular postures are identified during simulations and verified in the real prototype. The 3PSS-1S can perform pure rotations of ±45°, ±40°, ±60° along the x, y, z axes respectively.

A Unified Gas and Power Flow Analysis in Natural Gas and Electricity Coupled Networks

The restructuring of energy markets has increased the concern about the existing interdependency between the primary energy supply and electricity networks, which are analyzed traditionally as independent systems. The aim of this paper is focused on an integrated formulation for the steady-state analysis of electricity and natural gas coupled systems considering the effect of temperature in the natural gas system operation and a distributed slack node technique in the electricity network. A general approach is described to execute a single gas and power flow analysis in a unified framework based on the Newton-Raphson formulation. The applicability of the proposed approach is demonstrated by analyzing the Belgian gas network combined with the IEEE-14 test system and a 15-node natural gas network integrated with the IEEE-118 test system.

The free (open) boundary condition (FBC) in viscoelastic flow simulations

The Free (or Open) Boundary Condition (FBC, OBC) was proposed by Papanastasiou et al. (A New Outflow Boundary Condition, Int. J. Numer. Meth. Fluids, 1992; 14:587–608) to handle truncated domains with synthetic boundaries where the outflow conditions are unknown. In the present work, implementation of the FBC has been extended to viscoelastic fluids governed by explicit differential constitutive equations. As such we consider here the Criminale-Ericksen-Filbey (CEF) model, which also reduces to the Second-Order Fluid (SOF) for constant material parameters. The Finite Element Method (FEM) is used to provide numerical results in simple Poiseuille flow where analytical solutions exist for checking purposes. Then previous numerical results are checked against Newtonian highly non-isothermal flows in a 4:1 contraction. Finally, the FBC is used with the CEF fluid with data corresponding to a Boger fluid of constant material properties. Particular emphasis is based on a non-zero second normal-stress difference, which seems responsible for earlier loss of convergence. The results with the FBC are in excellent agreement with those obtained from long domains, due to the highly convective nature of viscoelastic flows, for which the FBC seems most appropriate. The FBC formulation for fixed-point (Picard-type) iterations is given in some detail, and the differences with the Newton–Raphson formulation are highlighted regarding some computational aspects.

Free (open) boundary condition: some experiences with viscous flow simulations

SUMMARYThe free (or open) boundary condition (FBC, OBC) was proposed by Papanastasiou et al. (A new outflow boundary condition, International Journal for Numerical Methods in Fluids, 1992; 14:587–608) to handle truncated domains with synthetic boundaries where the outflow conditions are unknown. In the present work, implementation of the FBC has been tested in several benchmark problems of viscous flow in fluid mechanics. The FEM is used to provide numerical results for both cases of planar and axisymmetric domains under laminar, isothermal or non‐isothermal, steady‐state conditions, for Newtonian fluids. The effects of inertia, gravity, compressibility, pressure dependence of the viscosity, slip at the wall, and surface tension are all considered individually in the extrudate‐swell benchmark problem for a wide range of the relevant parameters. The present results extend previous ones regarding the applicability of the FBC and show cases where the FBC is inappropriate, namely in the extrudate‐swell problem with gravity or surface‐tension effects. Particular emphasis has been given to the pressure at the outflow, which is the most sensitive quantity of the computations. In all cases where FBC is appropriate, excellent agreement has been found in comparisons with results from very long domains. The formulation for Picard‐type iterations is given in some detail, and the differences with the Newton–Raphson formulation are highlighted regarding some computational aspects. Copyright © 2011 John Wiley & Sons, Ltd.

The AC-AC Γ-controller Modeling for Power Flow and Transient Stability Studies

The steady-state and transient stability simulation of a pulse-width modulated AC-link Γ-controller is presented. Such a device is composed of a shunt-phase shifter transformer, filter capacitors, a vector switching converter, and a series injection transformer. Its operating principle is based on generating an AC voltage with controllable magnitude and phase angle injected in series with the line for regulating the complex power flow. This article describes the modifications in the Newton-Raphson formulation for including such a controller. Results of transient stability simulations are exposed, showing the applicability of the device for such purposes.

An approach to expediting phase equilibrium calculations for polydisperse polymers

It is shown that the equilibrium ratio between mole fractions of a polymer pseudo-component in any two phases is related to the molar mass of the pseudo-component in a simple way. The relationship permits evaluating all the equilibrium ratios for the polymer components in terms of any two. This property holds true for all the equations of state commonly used for polymer–solvent phase equilibria. The consequence is that only two equilibrium equations have to be solved for any polydisperse polymer, regardless of the number of pseudo-components. Equilibrium for the other pseudo-components is guaranteed when the dependence between the equilibrium ratios is accounted for. The paper presents a Newton–Raphson formulation of cloud-point calculations equivalent to that proposed by Koak and Heidemann but with a reduced number of equations to be solved regardless of the number of components used to characterize the polymer. It is shown that computations of many different kinds can be performed within the same general problem formulation.

A modified Newton–Raphson method

AbstractIn this paper, we propose the following modified Newton–Raphson iteration formulation: In case r=1, the obtained formulation reduces to the Newton–Raphson formulation. The present technique circumvent pitfalls of the Newton–Raphson iteration method. Some examples are illustrated. Copyright © 2004 John Wiley & Sons, Ltd.

Analysis of a Ball Bearing With Waviness Considering the Centrifugal Force and Gyroscopic Moment of the Ball

This research presents an analytical method to calculate the characteristics of the ball bearing under the effect of the waviness in its rolling elements and the centrifugal force and gyroscopic moment of ball. The waviness of rolling elements is modeled by using sinusoidal function, and the centrifugal force and gyroscopic. moment of ball are included in the kinematic constraints and force equilibrium equations to produce the nonlinear governing equations. To improve the convergence of the numerical solution of the nonlinear governing equations, it includes the derivatives of the gyroscopic moment and load-deflection constant of each race in the Newton-Raphson formulation. The accuracy of this research is validated by comparing with the prior research, i.e., (i) the contact force, contact angle in case of considering only the centrifugal force and gyroscopic moment of ball, and (ii) the contact force and vibration frequencies in case of considering only the waviness, respectively. It investigates the stiffness, contact force, displacement and vibration frequencies of the ball bearing, considering not only the centrifugal force and gyroscopic moment of ball but also the waviness of the rolling elements.

Novos desenvolvimentos numa formulação de injeção de corrente para solução do fluxo de potência

Este artigo apresenta uma metodologia genérica de representação de dispositivos de controle no problema de fluxo de potência, utilizando-se uma formulação Newton Raphson esparsa expressa em termos de equações de injeção de corrente em coordenadas retangulares. Tal formulação possui a mesma trajetória de convergência da formulação convencional em coordenadas polares. Os resultados obtidos validam a metodologia proposta.

Developments in the Newton Raphson power flow formulation based on current injections

This paper describes a sparse Newton Raphson formulation for the solution of the power flow problem, comprising 2n current injection equations written in rectangular coordinates. The Jacobian matrix has the same structure as the (2n/spl times/2n) nodal admittance matrix, in which each network branch is represented by a (2/spl times/2) block. Except for PV buses, the off-diagonal (2/spl times/2) blocks of the proposed Jacobian equations are equal to those of the nodal admittance matrix. The results presented show that the proposed method leads to a substantially faster power flow solution, when compared to the conventional Newton Raphson formulation, expressed in terms of power mismatches and written in polar coordinates.

An Efficient Computation Model for Calculating Surface Contact Pressures Using Measured Surface Roughness

The efficient Newton-Raphson iterative solver is implemented for calculating the surface contact pressure under rough contact conditions. The improvement in computation efficiency is achieved by coupling the surface elastic deformation equation and the force equilibrium equation using the Newton-Raphson formulation and solving the two equations simultaneously. The developed model is first demonstrated in solving the classic Hertzian contact problem to verify the model accuracy. Results show the developed model converges extremely fast (in less than three iterations) and computation error in the contact width is within the discretization limit. For rough contact cases, the presented procedures also achieve the converged solutions rapidly; however, a relaxation factor is needed. Presented at the 51st Annual Meeting in Cincinnati, Ohio May 19–23, 1996

Fast-decoupled transient stability

Presents an improved method for computing transient stability using a fast-decoupled formulation of the transient energy function. The new formulation offers significant savings in computer time as compared to the existing Newton-Raphson formulation. It therefore represents a suitable technique for online transient stability computations in utility control centres.