Newton-Raphson Approach Research Articles

Power-flow initialization of fixed-speed pump as turbines from their characteristic curves using unified Newton-Raphson approach

Power-flow initialization of fixed-speed pump as turbines from their characteristic curves using unified Newton-Raphson approach

Solving Stochastic Nonlinear Poisson-Boltzmann Equations Using a Collocation Method Based on RBFs

In this paper, we present a numerical scheme based on a collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is a generalized version of the non-linear Poisson–Boltzmann equations arising from a form of biomolecular modeling to the stochastic case. Applying the collocation method based on radial basis functions (RBFs) allows us to deal with the difficulties arising from the complexity of the domain. To indicate the accuracy of the RBF method, we present numerical results for two-dimensional models, we also study the stability of this method numerically. We examine our results with the RBF-reference value and the Chebyshev Spectral Collocation (CSC) method. Furthermore, we discuss finding the appropriate shape parameter to obtain an accurate numerical solution besides greatest stability. We have exerted the Newton–Raphson approach for solving the system of non-linear equations resulting from discretization by the RBF technique.

Soliton dynamics in optical fiber based on nonlinear Schrödinger equation

Optical fiber is a component of the green and sustainable internet. This paper analyzes the energy loss induced by the attenuation effect of electromagnetic waves during optical fiber propagation. The dynamics of the Hamiltonian, which was derived using the dynamics of the solution the Nonlinear Schrödinger equation (NLS) problem, were used to investigate the energy drop. In this study, the Newton-Raphson (NR) approach was used to establish the stationary solution of the NLS problem, and the fourth order Runge-Kutta method was used to evaluate the dynamics of the solution (RK4). In this study, numerous parameters are adjusted, including group wave dispersion, nonlinearity, attenuation parameter, and potential trap. The solution of the NR approach is fairly close to the analytical solution based on the analytical solutions. The dynamics of the NLS equation solution are greatly influenced by parameters. The obtained results reveal that for large attenuation parameter values, the strength of the propagating electromagnetic waves decreases quite quickly. The result also shows that the other parameters studied must be maintained at the best conditions to support the attenuation parameters and potential trap. This condition is an indicator in the choice of the fundamental material for producing optical fiber, which should have a low attenuation and dispersion effect.

Relation between the Branch-to-Node Incidence and Triangular Matrices in Radial Distribution Networks

The power flow solution is a classical problem in electrical engineering that has been studied for more than 60 years [1]. One of the most widely used methods corresponds to the Newton-Raphson approach, which is currently employed for analyzing power systems with meshed configurations and multiple generation sources, i.e., it is typically employed for power systems in high-voltage levels [2].

Highly nonlinear hyperelastic shells: Statics and dynamics

Investigated in this paper are comprehensive static, dynamic and internal-resonance analyses on a wide range of hyperelastic shell structures, including cylindrical, spherical, doubly-curved, and hyperbolic hyperelastic shallow shells. Donnell's nonlinear shell theory and the Mooney-Rivlin strain energy density model are used to formulate the hyperelastic shell structure. Coupled equations of motion are obtained using Hamilton's principle with highly nonlinear terms due to the curvature in the structure, together with the material nonlinearity and large deformations. The coupled equations of motion are converted to a large set of equations using a two-dimensional Galerkin technique and are solved by employing the Newton-Raphson approach and dynamic equilibrium technique. The strength of the current methodology and model is first verified by comparing the static response of the structure with those obtained by using a finite element software. After verifying the model, a detailed analysis of the bending behaviour of the structure under a time-independent pressure is presented. Moreover, the free and forced vibration responses of the shell structure are presented for different cases, showing that the curvature terms play a significant role in changing the mechanical response of the hyperelastic shell. Furthermore, it is shown that for specific sets of curvatures, internal resonances are present which leads to a complicated, rich nonlinear responses. The nonlinear forced vibration response of the hyperelastic shell is also presented for different shell types and resonances.

Comprehensive enhanced Newton Raphson approach for power flow analysis in droop-controlled islanded AC microgrids

One of the essential studies in the planning and operation of a microgrid is Power Flow (PF). Traditional PF methods are not applicable for droop-controlled islanded microgrids due to the absence of a slack bus in the system. The steady state characteristics of the system such as frequency, bus voltages, Distributed Generators’ (DG) output power, and actual loads’ demand are obtained based on the droop characteristics of the DGs, and also, the frequency and voltage dependency of the load. Therefore, in this paper, an Enhanced Newton Raphson (ENR) method is proposed for PF in the droop-controlled islanded microgrids. The proposed method is based on the well-known NR method but with a more comprehensive model that considers different droop schemes (resistive, inductive, and complex), load demand dependency on voltage and frequency, π line model, and shunt compensators. Moreover, a new index for selecting proper droop characteristics for any droop-controlled islanded microgrid is proposed. Five test systems with different scales, topologies, droop control strategies, and various load models are considered to evaluate the performance of the proposed method. The results are compared with the recently developed methods and steady-state results of Time-Domain simulations conducted in PLECS software. The results show that the proposed technique has excellent accuracy with low computational time and can be easily integrated into the currently available power system analysis tools.

Optimization of Voltage Security with Placement of FACTS Device Using Modified Newton–Raphson Approach: A Case Study of Nigerian Transmission Network

Power flow reliability, voltage security and transmission congestion management are paramount operational issues in a power system. Flexible AC transmission system (FACTS) controllers are suitable technologies that can provide compensation and dynamic control of power system transmission parameters to enhance effective performance and reliability. The interline power flow controller (IPFC), if optimally placed, can regulate the impedance of multiple lines to improve active power transfer capacity and voltage profile. This study examines the performance of IPFCs for voltage enhancement by suppressing fluctuation. A modified Newton–Raphson load flow problem with an incorporated IPFC variable has been formulated with the objective to improve voltage stability and maintain active power flow. The effectiveness of the proposed method was tested on the Nigerian 41 bus transmission network. The obtained result of the system with an IPFC placed at the weakest bus of the network was compared with Newton–Raphson load flow analysis of the same network without an IPFC. The results of load flow analysis for Case 1 (the system without an IPFC) showed that the transmission network without an IPFC had a real power loss of 4.699488 p.u., and reactive power loss of 4.467413 p.u., whereas the integration of an IPFC to the power flow formation in Case 2 resulted in the reduction in the transmission network’s overall losses to 0.55297 p.u. and −38.3329 p.u. The modified method proves effective as the power system network with an IPFC returns a more stable voltage profile and improves active power flow. In addition, this method, similar to all other mathematical optimization approaches, returns a strong accurate result but may be a drawback in terms of longer computational time compared with metaheuristic methods which are preferred for a larger network system.

Mathematical modelling, performance evaluation and exergy analysis of a hybrid photovoltaic/thermal-solar thermoelectric system integrated with compound parabolic concentrator and parabolic trough concentrator

This article discusses the electrical and thermal performance of a hybrid concentrator photovoltaic thermal and solar thermoelectric generator (CPV/T-STEG) system using a compound parabolic concentrator (CPC) and a parabolic trough concentrator (PTC). For the first time, the idea of merging imaging and non-imaging concentrators for a CPV and TEG hybrid system is examined, providing an option to retrofit or remodel existing PTC-based CSP systems. The thermal resistance concept is applied to establish a steady-state mathematical model of the proposed hybrid CPV/T-STEG system. A Newton-Raphson iterative approach is employed to solve the mathematical model and compute the temperature in every layer of the hybrid system. After validation, the mathematical model is employed to evaluate the overall performance of the hybrid system. The modelling results revealed that the electrical and thermal output of the developed hybrid system were higher by 2 and 1.6 times, respectively, when compared with the prior parabolic trough-based hybrid CPV/T-STEG system described in the literature. The effects of ambient temperature, wind speed, flow rate, number of TEGs, and solar concentration ratio on the electrical and thermal performance were investigated. The optimal number of TEGs required for maximum electrical performance under different solar concentration ratios is also obtained. Finally, the hybrid system’s exergy efficiency is investigated for various solar concentration ratios. The simulation results revealed that the increase in the Reynolds number from 100 to 2000 improves the net electrical and thermal efficiency by 10.21% and 5.7%, respectively. At a fixed solar concentration ratio (CCPC=4suns and WPTC=2WCPC), the electrical efficiency of TEG drops by 81.4%, but the thermal efficiency increases by 16.81%, provided that the number of TEGs is increased from 1 to 17. The highest exergy of the hybrid system is 8.36% when CCPC=2suns and WPTC=2WCPC. Due to the poor efficiency of commercial TEGs, the overall exergy efficiency of the hybrid system decreases with an increasing solar concentration ratio. In the proposed hybrid system, a fluid channel separates both the PV and TEG modules; hence the electrical conversion efficiencies of both modules are not closely related.

Optimal Integration of Dispersed Generation in Medium-Voltage Distribution Networks for Voltage Stability Enhancement

This study addresses the problem of the maximization of the voltage stability index (λ-coefficient) in medium-voltage distribution networks considering the optimal placement and sizing of dispersed generators. The problem is formulated through a mixed-integer nonlinear programming model (MINLP), which is solved using General Algebraic Modeling System (GAMS) software. A numerical example with a 7-bus radial distribution network is employed to introduce the usage of GAMS software to solve the proposed MINLP model. A new validation methodology to verify the numerical results provided for the λ-coefficient is proposed by using recursive power flow evaluations in MATLAB and DigSILENT software. The recursive evaluations allow the determination of the λ-coefficient through the implementation of the successive approximation power flow method and the Newton–Raphson approach, respectively. It is effected by fixing the sizes and locations of the dispersed sources using the optimal solution obtained with GAMS software. Numerical simulations in the IEEE 33- and 69-bus systems with different generation penetration levels and the possibility of installing one to three dispersed generators demonstrate that the GAMS and the recursive approaches determine the same loadability index. Moreover, the numerical results indicate that, depending on the number of dispersed generators allocated, it is possible to improve the λ-coefficient between 20.96% and 37.43% for the IEEE 33-bus system, and between 18.41% and 41.98% for the IEEE 69-bus system.

Polar Coordinates based N-R Method for Load Modelling in Electrical Power Distribution Systems

In this paper, load modelling has been done in electrical distribution system using local real time test data. This distribution system supplies base loads, residential, industrial, commercial and composite loads. Using power and current-mismatch functions in polar form, a comprehensive framework for applying the Newton–Raphson method to solve power flow problems is presented. The Newton–Raphson approach for solving power flow problems can be applied in six different ways using these two mismatch functions. For load (PQ)buses and generator (PV) buses, we propose a theoretical framework for analyzing these versions. In addition, we compare newly created versions of the Newton power flow method to current variants in this study. Numerical studies on distribution networks are used to study the convergence behavior of all approaches. The measurements are formed for short term load forecasting with different types of realistic loads such as base loads, residential, industrial, commercial and composite loads. The long-term load forecasting and their losses also has been performed along with short term load forecasting. The results are obtained and validated through MATLAB.

Modelling and analysis of nonlinear vibrations for a coupling hard-coated ring disc-cylindric shell structure under piecewise-continuous coupling conditions

Considering the strain-dependant characteristic of coatings, a unified nonlinear modelling approach is presented for investigating the nonlinear vibration characteristics of a coupling hard-coated ring disc-cylindric shell structure. The piecewise-continuous coupling conditions are proposed and simulated by distributing piecewise-continuous artificial springs in the circumferential direction of the junction between the shell and disc. According to Sanders’ shell theory and the Kirchhoff plate theory, the equations of motion of the coupling hard-coated ring disc-cylindric shell structure are created by the Rayleigh-Ritz method. By employing the multi-segment partitioning strategy, a general approach is proposed for introducing the strain-dependant characteristic into the equations of motion. According to the Newton-Raphson approach, an innovative efficient algorithm is developed for solving the nonlinear equations of motion. The astringency on the number of hard-coated segments is discussed. Comparison investigations are performed to verify the presented method. Further numerical simulations show that the strain-dependant characteristic of coatings induces the soft nonlinear vibration characteristics and contributes to the vibration reduction of structures. Moreover, the damping mechanism of the strain-dependant characteristic is revealed, and the influence of piecewise-continuous coupling conditions on nonlinear vibrations is investigated.

Local approximate Gaussian process regression for data-driven constitutive models: development and comparison with neural networks

Hierarchical computational methods for multiscale mechanics such as the FE2 and FE-FFT methods are generally accompanied by high computational costs. Data-driven approaches are able to speed the process up significantly by enabling to incorporate the effective micromechanical response in macroscale simulations without the need of performing additional computations at each Gauss point explicitly. Traditionally artificial neural networks (ANNs) have been the surrogate modeling technique of choice in the solid mechanics community. However they suffer from severe drawbacks due to their parametric nature and suboptimal training and inference properties for the investigated datasets in a three dimensional setting. These problems can be avoided using local approximate Gaussian process regression (laGPR). This method can allow the prediction of stress outputs at particular strain space locations by training local regression models based on Gaussian processes, using only a subset of the data for each local model, offering better and more reliable accuracy than ANNs. A modified Newton–Raphson approach specific to laGPR is proposed to accommodate for the local nature of the laGPR approximation when solving the global structural problem in a FE setting. Hence, the presented work offers a complete and general framework enabling multiscale calculations combining a data-driven constitutive prediction using laGPR, and macroscopic calculations using an FE scheme that we test for finite-strain three-dimensional hyperelastic problems.

Pipe roughness identification of water distribution networks: A Tensor method

The identification of pipe roughnesses in a water distribution network is formulated as a nonlinear system of algebraic equations which turns out to be demanding to solve under real-world circumstances. This paper proposes an enhanced technique to numerically solve this identification problem, extending the conventional Newton–Raphson approach with second-order derivatives in the determination of the search direction. Despite the requirement to solve a nonlinear equation to obtain a search direction, the application of the Hadamard/Schur product operator enables the resulting formulation to be represented compactly and thus facilitates the development of an efficient and more robust solving-technique. Algorithms on the basis of this more enhanced solving method are then compared to a customized Newton–Raphson approach in simulation examples.

DRL-Based Sum-Rate Maximization in D2D Communication Underlaid Uplink Cellular Networks

Device-to-device (D2D) communication affords the benefits of improved network spectral efficiency, throughput, energy efficiency, and delay performance. However, D2D communication underlaid cellular uplinks are degraded by interference between D2D user equipment (DUE) and cellular user equipment (CUE) that use the same frequency band. In this context, researchers have proposed the optimization of the transmit power of the devices to mitigate interference. This power allocation problem is generally modeled as a NP-hard combinatorial optimization problem with linear constraints; therefore, traditional optimization methods are ineffective in addressing the problem. In this paper, we apply a deep reinforcement learning (DRL) algorithm to optimize the transmit power for both DUEs and CUEs in the context of D2D communication underlaid uplink cellular networks, which can solve the optimization problem via optimal decision-making together with efficient deep network training. Our simulation results show that the proposed algorithm affords a near-global-optimum solution with lower computation complexity than exhaustive search, and outperforms the fixed-power, weighted minimum mean square error (WMMSE), gradient descent method, and Newton-Raphson approaches.

Optimal power flow solution of an integrated power system using elephant herd optimization algorithm incorporating stochastic wind and solar power

ABSTRACT In this paper an improved optimization strategy is proposed to address issues related to uncertainty of the optimum power flow (OPF) considering the cost analysis. Elephant Herd Optimization (EHO) method roused by the crowding conduct of elephant gathering has been modified to achieve the minimization of the objective functions. Initially, the OPF is analyzed with the Newton-Raphson (N-R) approach by considering only conventional resources, later on the wind and PV-based power scheduling is performed. The output power of the wind and PV systems is computed from the Weibull probability distribution function (PDF) and Lognormal PDF. Initially, the objective function is defined to analyze the power loss, voltage deviation, carbon emissions and generation cost. The defined multi-objective function is solved for PV and Wind power generation costs, emission, voltage stability, and losses. The considered constraints are the cost of generation and the risks associated with the renewable energy sources apart from voltage and reactive power limits. Moreover, the penalty deviation charges have also been considered during extreme conditions for sustainable power sources. The proposed approach has been applied to IEEE 57 bus system and the resulting emissions, generation cost, losses and voltage deviation are evaluated and the direct, reserve, and penalty costs of wind and PV are analyzed It is contrasted to standard approaches such as Differential Evolutionary (DE) and Firefly Algorithm (FA) to substantiate the efficiency of the EHO method. The proposed approach is deployed in the MATLAB for various cases.

A New Double Truncated Generalized Gamma Model with Some Applications

The generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis. Indeed, we know that, from the above, it is unbounded. Data have a bounded service area in a variety of applications. A new five-parameter bounded generalized Gamma model, the bounded Weibull model with four parameters, the bounded Gamma model with four parameters, the bounded generalized Gaussian model with three parameters, the bounded exponential model with three parameters, and the bounded Rayleigh model with two parameters, is presented in this paper as a special case. This approach to the problem, which utilizes a bounded support area, allows for a great deal of versatility in fitting various shapes of observed data. Numerous properties of the proposed distribution have been deduced, including explicit expressions for the moments, quantiles, mode, moment generating function, mean variance, mean residual lifespan, and entropies, skewness, kurtosis, hazard function, survival function, r th order statistic, and median distributions. The delivery has hazard frequencies that are monotonically increasing or declining, bathtub-shaped, or upside-down bathtub-shaped. We use the Newton Raphson approach to approximate model parameters that increase the log-likelihood function and some of the parameters have a closed iterative structure. Six actual data sets and six simulated data sets were tested to demonstrate how the proposed model works in reality. We illustrate why the Model is more stable and less affected by sample size. Additionally, the suggested model for wavelet histogram fitting of images and sounds is very accurate.

Three-dimensional tuning of idiophone bar modes via finite element analysis.

The timbre of marimba and other idiophone bars can sometimes be polluted by untuned torsional modes, leading to substandard instruments or rejected materials. Makers have complained of problems with these untuned modes over a specific range of notes. Marimba, vibraphone, and similar idiophone bars are tuned by carving one side of the bar to bring up to three flexural modes into harmonic relationships. Torsional and other mode types are commonly left untuned. The relative frequency of these untuned modes with respect to the fundamental mode will vary along the keyboard. This paper investigates tuning both torsional and flexural modes simultaneously. This tuning is achieved using sophisticated carved geometries, and without employing concentrated masses or additional materials. Bars are modeled using three-dimensional finite elements. Geometry is defined by a large number of input parameters. Algorithms are implemented to identify bar modes automatically, eliminating the need for human intervention. Tuning is performed via a Newton-Raphson approach using the Moore-Penrose generalized matrix inverse to solve systems of tuning equations. This method is found to be effective at finding satisfactory bar geometries in proximity to initial conditions. Numerous example marimba and vibraphone bar models are provided, representing both typical and atypical modal tuning ratios.

Improved quasi-steady-state power flow calculation for district heating systems: A coupled Newton-Raphson approach

District heating systems have a considerable storage capability due to their dynamic thermal behavior (i.e. the thermal inertia of the water flow). Using this storage can support a secure, reliable, and efficient integrated energy system operation with a high share of volatile renewable energy sources. To use this flexibility, a joint analysis is necessary that includes the dynamic thermal behavior. Existing methods determine the dynamic thermal behavior by separated hydraulic and thermal equation systems, which are solved consecutively. This complicates the analysis because dependencies between temperatures and mass flow rates are not depicted directly. Also, this decoupled representation does not allow an easy analysis of the interactions in an integrated energy system as is already possible in steady-state analysis. Thus, this paper extends the steady-state methods by including the dynamic thermal behavior. The equations describing the hydraulic and dynamic thermal behavior are joined in a single equation system and solved simultaneously in a coupled Newton-Raphson power flow calculation. For this, the dynamic thermal behavior is described by the node method. At the same time, the accuracy of the node method is improved by enhancing the temperature-gradient method. The validation shows a high accuracy independently of the simulation time increment. Because the method is based on the steady-state analysis it enhances the wide area of application by introducing the dynamic thermal behavior. With its high accuracy and its coupled approach, the method is suitable for future investigations of the interdependencies of integrated energy systems.

Accurate initialization of islanded microgrid including induction motor load using unified power-flow approach

An increased integration of distributed generators into microgrids presents a technical challenge to maintain voltage and frequency stability, especially in islanded or autonomous operation. For stability assessment of the microgrid, a proper initialization is particularly needed to get the right steady-state operating point when the widely used induction motor (IM) loads are mainly considered. Since a conventional power-flow approach is not straightforward and suitable for initializing the IM loads in the isolated microgrid network due to an unavoidable discrepancy between initial-bus scheduled and actual values of IM’s reactive powers. To eliminate this mismatch, this paper presents a precise power-flow initialization using a unified Newton–Raphson approach. The correct steady-state initializations are demonstrated using 6bus and 13bus microgrid systems. IEEE standard 33, 38, and 69bus distribution networks are employed to explore computational performances of the proposed algorithm for the case where a large number of IM loads are incorporated via distribution feeder loads.

Switching Bayesian dynamic linear model for condition assessment of bridge expansion joints using structural health monitoring data

Age-related deterioration and premature failure have been primary concerns for bridge expansion joints. It is essential to improve the understanding of their operational performance. The existing approaches mainly formulate the deterministic/probabilistic temperature-displacement relationship (TDR) model to assess the structural condition of bridge expansion joints. Nevertheless, it is not easy to guarantee a strong correlation between representative temperature and displacement. Rather than establishing the TDR model, this work uses the displacement response to evaluate the expansion joint condition by combining the Bayesian dynamic linear model (BDLM) with Markov-switching theory. The external temperature effect on the displacement is modeled by the superposition of harmonic components in BDLM. The expectation–maximization (EM) algorithm initialized by the subspace method is employed to optimize the initial parameters. The presented approach is validated through the simulated data, and then it is applied to the expansion joint of a long-span bridge. Results show that EM with the subspace method involves high computational accuracy and efficiency in estimating unknown parameters compared to the Newton-Raphson approach. The switching BDLM successfully identifies the degradation process of expansion joints and offers the transition probability from the normal to other states.