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This study presents a generalised representation of voltage source converter (VSC) based high voltage direct current (HVDC) systems appropriate for power flow studies using the Newton–Raphson method. To reach this aim, the active loads and ideal synchronous machines are employed in order to incorporate both converter losses and power balance, respectively. Also, considering different aspects of computer implementation, the proposed solution method uses the conventional Newton–Raphson method. The proposed representation considers practical restrictions, switching and conduction losses of semiconductors, and different control strategies for VSC-HVDC stations. Moreover, the proposed generalised representation of VSC-HVDC systems can be easily extended to incorporate the multi-terminal VSC-HVDC grids in an efficient manner. To investigate the application of the proposed representation for VSC-HVDC systems and load flow solution, three test systems including the standard IEEE 30 bus and IEEE two area RTS-96 networks are used and discussion on results is provided. Results show that the proposed algorithm is able to solve AC–DC power flow problems very efficiently with considerably less time in comparison to other existing algorithms.

Two mismatch functions (power or current) and three coordinates (polar, Cartesian and complex form) result in six versions of the Newton–Raphson method for the solution of power flow problems. In this paper, five new versions of the Newton power flow method developed for single-phase problems in our previous paper are extended to three-phase power flow problems. Mathematical models of the load, load connection, transformer, and distributed generation (DG) are presented. A three-phase power flow formulation is described for both power and current mismatch functions. Extended versions of the Newton power flow method are compared with the backward-forward sweep-based algorithm. Furthermore, the convergence behavior for different loading conditions, R / X ratios, and load models, is investigated by numerical experiments on balanced and unbalanced distribution networks. On the basis of these experiments, we conclude that two versions using the current mismatch function in polar and Cartesian coordinates perform the best for both balanced and unbalanced distribution networks.

Identifying and estimating uncertain and dynamic photovoltaic characteristics with high accuracy is important when modeling solar photovoltaic (PV) systems. It is critical to have effective and accurate parameters when transforming the complete PV system from solar energy to electrical energy. Therefore, we propose and apply for the first time a unique physics-based metaheuristic algorithm known as the Resistance–Capacitance Optimization Algorithm (RCOA), which is based on the concept of resistance–capacitance circuit response, and it was obviously inspired by the output response of a Resistor–Capacitor (RC) circuit when the input is connected or disconnected suddenly. The RC circuit's total time response can be divided into steady-state and transient-state. Both of these stages of the RC circuit are essential to model the algorithm properly. It is proposed that the RCOA be used as a single-objective algorithm that is simple, reliable, and has zero sensitive parameters, thereby being a parameter-free algorithm. The validity of the proposed RCOA is tested on the solar PV cell/module equivalent circuit parameter estimation of the three-diode PV model. The proposed algorithm combines an improved version of the Newton–Raphson method to find the optimal PV parameters in fewer iterations. The performance of the RCOA is compared with state-of-the-art algorithms, and the obtained results prove the superiority of the RCOA. The proposed methodology was found to be a trustworthy tool and it is proved through a statistical analysis and non-parametric test. Also, the results have revealed that the RCOA has superior reliability and accuracy when estimating the three-diode PV model parameters. It could be used as a viable approach for parameter identification problems in PV systems. With the average Friedman’s ranking test value of 1.6666 and the average runtime of 17.08, the RCOA stands first among all selected algorithms.

Finding the equivalent circuit parameters for photovoltaic (PV) cells is crucial as they are used in the modeling and analysis of PV arrays. PV cells are made of silicon. These materials have a nonlinear characteristic. This distorts the sinusoidal waveform of the current and voltage. As a result, harmonic components are formed in the system. The PV cell is the smallest building block of the PV system and produces voltages between 0.5 V and 0.7 V. It serves as a source of current. The amount of radiation hitting the cell determines how much current it produces. In an ideal case, a diode and a parallel current source make up the equivalent circuit of the PV cell. In practice, the addition of a series and parallel resistor is made to the ideal equivalent circuit. There are many equivalent circuits in the literature on modeling the equivalent circuit of a PV cell. The PV cell single–diode model is the most used model due to its ease of analysis. In this study, the iterative method by Newton–Raphson was used to find the equivalent circuit parameters of a PV cell. This method is one of the most widely used methods for determining the roots of nonlinear equations in numerical analysis. In this study, five unknown parameters (Iph, Io, Rs, Rsh and m) of the PV cell equivalent circuit were quickly discovered with the software program prepared based on the Newton–Raphson method in MATLAB.

In the design of robotic manipulators, achieving dexterity within a large workspace along with structural lightness remains a significant challenge. Conventional industrial robots, including serial and parallel robots, suffer from a trade-off between weight and workspace dexterity. In contrast, cable-driven parallel robots (CDPRs) offer excellent lightweight performance and a large workspace. However, their applicability is limited because their workspaces are constrained by surrounding frames. This paper is related to a 6-DOF manipulator that integrates an articulated manipulator with a CDPR. The end effector is a platform whose orientation is directly controlled by four cables, enabling 6-DOF motion with a lightweight structure. The manufactured prototype and architecture, as well as mechanisms involved in the efficient transmission of cable tensile forces, are detailed. The forward kinematics is analyzed, and the numerical solution using the Newton–Raphson method is reviewed. Simulations are conducted to validate the solution and confirm its feasibility. Furthermore, a position control method that incorporates platform statics is introduced. Experimental results confirm the trajectory tracking performance in both translational and orientational motions.

In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order α of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.

Adaptation of renewable energy is inevitable. The idea of microgrid offers integration of renewable energy sources with conventional power generation sources. In this research, an operative approach was proposed for microgrids comprising of four different power generation sources. The microgrid is a way that mixes energy locally and empowers the end-users to add useful power to the network. IEEE-14 bus system-based microgrid was developed in MATLAB/Simulink to demonstrate the optimal power flow. Two cases of battery charging and discharging were also simulated to evaluate its realization. The solution of power flow analysis was obtained from the Newton–Raphson method and particle swarm optimization method. A comparison was drawn between these methods for the proposed model of the microgrid on the basis of transmission line losses and voltage profile. Transmission line losses are reduced to about 17% in the case of battery charging and 19 to 20% in the case of battery discharging when system was analyzed with the particle swarm optimization. Particle swarm optimization was found more promising for the deliverance of optimal power flow in the renewable energy sources-based microgrid.

This paper describes a new strategy for optimizing the switching angles of a three-phase inverter in a photovoltaic system. It presents non-traditional solutions to the problem of selective harmonic elimination (SHE) in three-phase inverter (VSI)-fed induction motor drives. The aforementioned problem was solved independently by using hybrid genetic algorithms (HGAs) and a modified Newton–Raphson method. GAs can obtain the correct solution even if the first generation is arbitrary. The solution then converges rapidly. The modified Newton–Raphson method is used to solve transcendental equations of the SHE pulses width modulation (SHEPWM) technique, which is a unique method that produces all possible solutions without assuming the initial angles. This modified technique is not complex and ensures rapid convergence to the solution. A real-time experimental verification of the SHEPWM technique was performed in the OP5600 RT-Lab simulator. The results obtained show that the proposed SHEPWM algorithm controls the fundamental voltage and effectively eliminates the desired harmonics, and that the evolution of the signal quality increases according to the modulation index. For M=1.1 the SHE-PWM gives the best result: a current THD of 5% for a switching frequency of 1150 Hz.

PurposeThe purpose of this paper is to suggest an implicit integration method for updating the constitutive relationships in the newly proposed anisotropic egg-shaped elastoplastic (AESE) model and to apply it in ABAQUS.Design/methodology/approachThe implicit integration algorithm based on the Newton–Raphson method and the closest point projection scheme containing an elastic predictor and plastic corrector are implemented in the AESE model. Then, the integration code for this model is incorporated into the commercial finite element software ABAQUS through the user material subroutine (UMAT) interface to simulate undrained monotonic triaxial tests for various saturated soft clays under different consolidation conditions.FindingsThe comparison between the simulated results from ABAQUS and the experimental results demonstrates the satisfactory performance of this implicit integration algorithm in terms of effectiveness and robustness and the ability of the proposed model to predict the characteristics of soft clay.Research limitations/implicationsThe rotational hardening rule in the AESE model together with the implicit integration algorithm cannot be considered.Originality/valueThe singularity problem existing in most elastoplastic models is eliminated by the closed, smooth and flexible anisotropic egg-shaped yield surface form in the AESE model. In addition, this notion leads to an efficient implicit integration algorithm for updating the highly nonlinear constitutive equations for unsaturated soft clay.

We consider a system in which the charged particle orbits under the influence of the electromagnetic field of three dipoles located on a system of three celestial bodies. Using well-known bivariate iterative scheme, known as Newton–Raphson (NR) iterative scheme, we numerically evaluated the positions of the stationary points (SPs) or equilibrium points (EPs) or libration points (LPs) and the linked basins of convergence (BoCs), and we also evaluated their linear stability. Moreover, we unveiled how the parameters, entering the effective potential function, affect the convergence dynamics of the system. Moreover, we also unveiled how the involved parameters affect the geometry of the zero velocity curves (ZVCs). Further, the correlation with the required number of iterations and the regions of convergence as well as the probability distributions associated to the BoCs is illustrated. In order to quantify the degree of final-state uncertainty of the BoCs, the basin entropy (BE) and for the fractality of boundaries of BoCs, the boundary basin entropy (BBE) are computed.