Conventional Perturbation Method Research Articles

Analytical solutions of cylindrical and spherical dust ion-acoustic solitary waves

Abstract In the present work, employing the conventional reductive perturbation method to the field equations of an unmagnetized dusty plasma consisting of inertial ions, Boltzmann electrons and stationary dust particles in the nonplanar geometry we derived cylindrical(spherical) KdV and mKdV equations. Being aware of the fact that there exists no exact analytical solution for the progressive waves for such evolution equations we presented the exact analytical solution of a generalized form of such evolution equations in the planar geometry and used this solution to obtain an analytical approximate progressive wave solution to the generalized evolution equation. Then the progressive wave solutions for the cylindrical(spherical) KdV and m-KdV equations is obtained as some special cases. The analytical approximate solutions so obtained are compared with the numerical solutions of these equations. The results reveal that both solutions are in a good agreement. One advantage of present analytical approximate solution is that it allows readers to gain information, share understandings, or carry out a physical parametric study on the evolution solution behavior as well as the solution calculation has no CPU time-consuming or round off error.

Solar Array Fed Synchronous Reluctance Motor Driven Water Pump: An Improved Performance Under Partial Shading Conditions

An improved performance of a photovoltaic (PV) pumping system employing a synchronous reluctance motor (SynRM) under partial shading conditions is proposed. The system does not include the dc-dc converter that is predominantly being utilized for maximizing the output power of the PV array. In addition, storage batteries are also not contained. A conventional inverter connected directly to the PV array is used to drive the SynRM. Further, a control strategy is proposed to drive the inverter so that the maximum output power of the PV array is achieved while the SynRM is working at the maximum torque per Ampere condition. Consequently, this results in an improved system efficiency and cost. Moreover, two maximum power point tracking (MPPT) techniques are compared under uniform and partial shadow irradiation conditions. The first MPPT algorithm is based on the conventional perturbation and observation (P&O) method and the second one uses a differential evolution (DE) optimization technique. It is found that the DE optimization method leads to a higher PV output power than using the P&O method under the partial shadow condition. Hence, the pump flow rate is much higher. However, under a uniform irradiation level, the PV system provides the available maximum power using both MPPT techniques. The experimental measurements are obtained to validate the theoretical work.

A MPPT strategy with variable weather parameters through analyzing the effect of the DC/DC converter to the MPP of PV system

In order to achieve the maximum power point (MPP) of photovoltaic (PV) system as quickly as possible and improve the MPPT adaptability to the varying weather conditions, in this paper, a maximum power point tracking (MPPT) control strategy with variable weather parameters (VWP) is proposed. In this strategy, the MPP difference between PV system with and without DC/DC converter is analyzed and used as the theoretical basis of acquiring the MPP control signal. Meanwhile, the direct relationship between control signal and VWP is found out by the curve-fitting technique, which is the key work to implement this proposed strategy. Finally, some simulation experiments show that the proposed control strategy is feasible and available to track the MPP successfully, and has better MPPT performance than conventional perturbation and observation (P&O) method under different weather conditions and than fuzzy control method under fast changing weather conditions.

Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations

Homotopy perturbation method is combined with Laplace transformation to obtain approximate analytical solutions of non-linear differential equations. An example is given to elucidate the solution process and confirm reliability of the method. The result indicates superiority of the method over the conventional homotopy perturbation method due its flexibility in choosing its initial approximation.

Modulation of electron-acoustic waves in a plasma with kappa distribution

In the present work, employing a one dimensional model of an unmagnetized collisionless plasma consisting of a cold electron fluid, hot electrons obeying κ velocity distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations of such a plasma, we obtained the nonlinear Schrödinger equation as the evolution equation. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation, as opposed to the plasma with vortex distribution, the amplitude wave assumes a shock wave type of solution. Finally, the modulational stability of the wave is studied and it is observed that the wave is modulationally stable for all admissible wave numbers.

Experimental characterization of a nonlinear vibration absorber using free vibration

Knowledge of the nonlinear characteristics of a vibration absorber is important if its performance is to be predicted accurately when connected to a host structure. This can be achieved theoretically, but experimental validation is necessary to verify the modelling procedure and assumptions. This paper describes the characterization of such an absorber using a novel experimental procedure. The estimation method is based on a free vibration test, which is appropriate for a lightly damped device. The nonlinear absorber is attached to a shaker which is operated such that the shaker works in its mass-controlled regime, which means that the shaker dynamics, which are also included in the measurement, are considerably simplified, which facilitates a simple estimation of the absorber properties. From the free vibration time history, the instantaneous amplitude and instantaneous damped natural frequency are estimated using the Hilbert transform. The stiffness and damping of the nonlinear vibration absorber are then estimated from these quantities. The results are compared with an analytical solution for the free vibration of the nonlinear system with cubic stiffness and viscous damping, which is also derived in the paper using an alternative approach to the conventional perturbation methods. To further verify the approach, the results are compared with a method in which the internal forces are balanced at each measured instant in time.

A maximum power point tracking method with variable weather parameters based on input resistance for photovoltaic system

In order to greatly improve the maximum power point tracking (MPPT) speed and adaptability to the varying weather conditions for photovoltaic (PV) system, in this paper, a MPPT method with variable weather parameters (VWP) considered specially from input resistance standpoint is proposed. As well as other VWP methods, it can also track the maximum power point (MPP) as quickly as possible. In this method, the approximate relationship between control signal and PV cell parameters (Vm and Im) is firstly built by studying the input resistance of PV system deeply, then the relationship between VWP and Vm,Im is found by the curve fitting technique. Through these relationships, the bridge between control signal and VWP is built successfully, which is the key work to implement the direct MPPT control. Finally, some simulation experiments show that the proposed method is feasible and available to track the MPP successfully and has better MPPT rapidity, accuracy, stability and adaptability than conventional perturbation and observation (P&O) method and fuzzy control method.

The analysis and model formulation of a coupled micro-probe and elastic thin plate subjected to electrostatic force

The mathematical model of coupled probe-plate system subjected to the ac and dc voltages is constructed. Among that, the coupled interacting force between probe and plate is the electrostatic force due to the ac and dc voltages, and the coupled displacements of beam and plate occur simultaneously. It is different to the conventional micro-/nano-actuator which is constructed by two independent fixed/mobile conducting electrodes. It is worth noting that the pull-in phenomenon of the coupled system subjected to the dc voltage only is discovered as a significant difference with respect to the conventional one. In this study, the analytical method for the coupled vibration is presented; the suitability of the conventional perturbation method is investigated; the relationship between the coupled frequencies of the system and the frequencies of the probe and plate is also found. This relationship is defined as the coupled characteristic phenomenon here.

Novel current sensing photovoltaic maximum power point tracking based on sliding mode control strategy

A novel maximum power point tracking method based on a sliding mode control strategy is proposed to harvest the maximum power from solar panels more effectively by controlling the duty cycle of DC–DC buck converter to which they connect. This method utilises a sliding mode strategy to achieve fast tracking speed and reduced oscillation at steady state. Furthermore, unlike most of other methods which require feedback signals from both voltage and current sensors, this method only requires current feedback information to generate control actions; so reducing the capital cost and the complexity of the system. The system modelling, development of the sliding mode control method, definition of the sliding surface and an analysis of stability are presented in this paper. Numerical results demonstrated that compared with conventional perturbation and observation method, a much faster tracking speed and efficiency improvement up to 5% can be achieved.

Modulation of Electron-Acoustic Waves in a Plasma with Vortex Electron Distribution

Abstract In the present work, employing a one-dimensional model of a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we study the amplitude modulation of electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the nonlinear Schrödinger equation as the evolution equation of the same order of nonlinearity. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation it is found that the NLS equation with fractional power assumes envelope type of solitary waves.

A direct adaptive neural control for maximum power point tracking of photovoltaic system

This paper represents a novel direct adaptive neural control (DANC) method for maximum power point tracking (MPPT) of photovoltaic (PV) systems. A DC/DC buck converter to regulate the output power of the photovoltaic system is considered. The direct adaptive neural control scheme operates on MPP and improves the performance of solar energy conversion efficiency. The online adaptation procedure is based on learning law of the δ rule and only the system output error is required. The prime contributions of this study are a simple and effective solution for MPPT, the fast learning and the straightforward digital implementation. The performance of direct adaptive neural controller on photovoltaic sources with different characteristics is assessed. The simulation results confirm the feasibility and effectiveness of the DANC. The proposed MPPT control system is compared to the conventional perturbation and observation (P&O) method.

An Intelligent MPPT controller based on direct neural control for partially shaded PV system

The development of an effective maximum power point tracking (MPPT) algorithm is important in order to achieve maximum power operation in a photovoltaic system (PV). In this study, a direct neural control (DNC) scheme is developed. The intelligent MPPT controller consists of a hybrid learning mechanism; an on-line learning rule based on gradient decent method and an off-line learning rule based on Big Bang–Big Crunch (BB–BC) algorithm. The effectiveness of the proposed system is tested under partial shading conditions by applying the cascaded converter topology. The feasibility of the DNC is evaluated by the simulation results and compared to the conventional perturbation and observation (P&O) method.

Study on Automatic Control Method of Photovoltaic Power Systems

Maximum power point tracking (MPPT) algorithm directly affect the conversion efficiency of photovoltaic power generation system independent of energy, the thesis of common strengths and weaknesses of the MPPT algorithm to summarize, the traditional method of perturbation and observation maximum power point tracking algorithm is improved and build a simulation model, the simulation model are direct and network controllers and input grid and grid-independent photovoltaic power generation system model of network simulation, and network time from both the grid conditions, and the impact of current network waveforms and grid voltage waveform analyzed. Simulation results observed with the conventional perturbation method were compared and analyzed to verify the effectiveness of the improved method.

Modelling of Single Stage Inverter for PV System Using Optimization Algorithm

MPPT control algorithm and lossless inverter can be improving the efficiency of photovoltaic system. Amount of solar radiation exposed on the panel is affected by buildings and tree shadows. Such partially shaded cells lead to the existence of multiple mpps and the problem can be regarded as an optimization problem. The control algorithm named seeker optimization algorithm (soa) is implemented in this paper to find the global mpp instead local maxima obtained in case of conventional perturbation and observation (p&o) method, incremental conductance and other solution methodologies. Switching losses are minimized by single stage inverter configuration. The proposed system output voltage is a rectified sine wave. Simulation model is developed in psim that couples soa algorithm coded in matlab. Finally it will improve the overall efficiency and reduce the switching losses of the solar photovoltaic system.

A modified calibration method for complex permittivity measurement

This work proposes a calibration method to determine the complex permittivity of materials based on the cavity-perturbation method. The method can characterize a sample with relative large in volume or high in dielectric constant, which significantly broadens the scope of the conventional perturbation method. The theory is validated with a full wave solver and an experiment was conducted. A sample of silicon carbide was heated using high-power microwave and characterized with low-power signal, all operating in the same cavity but staggered in time sequence. The complex permittivity of the silicon carbide varying with temperature was measured and discussed. The proposed approach heats and measures the sample strictly by microwave techniques, which fosters the study of microwave∕material interaction.

Maximum power point tracking control strategies with variable weather parameters for photovoltaic generation systems

In this paper, on the basis of studying the mathematical models of PV generation systems, two maximum power point tracking (MPPT) control strategies with variable weather parameters are proposed. In these proposed strategies, the direct relationships between the weather parameters and the MPPT control signals have been found. Therefore, the MPPT control of PV generation systems can be implemented by measuring the external environmental parameters directly. As such, the transient-state performance of output power can greatly improved under varying weather conditions. Finally, simulated experiments show that the maximum power points of PV systems can be accurately tracked by using these control strategies, and that the output power of PV system using the first proposed MPPT control strategy has better transient-state performance than that using the conventional perturbation and observation (P&O) method.

An observation on the periodic solutions to nonlinear physical models by means of the auxiliary equation with a sixth-degree nonlinear term

It is a fact that in auxiliary equation methods, the exact solutions of different types of auxiliary equations may produce new types of exact travelling wave solutions to nonlinear equations. In this manner, various auxiliary equations of first-order nonlinear ordinary differential equation with distinct-degree nonlinear terms are examined and, by means of symbolic computation, the new solutions of original auxiliary equation of first-order nonlinear ordinary differential equation with sixth-degree nonlinear term are presented. Consequently, the novel exact solutions of the generalized Klein–Gordon equation and the active-dissipative dispersive media equation are found out for illustration purposes. They are also applicable, where conventional perturbation method fails to provide any solution of the nonlinear problems under study.

A computationally efficient steady-state electrode-level and 1D + 1D cell-level fuel cell model

Computational efficiency is highly important for upscaling detailed electrode-level and cell-level models to the system level required for the design and control of fuel cells. We present a computationally efficient 1D+1D fuel cell model based on a combination of analytical and numerical approaches. On the electrode level, we develop approximate analytical solutions for the 1D current/potential distribution via a hybrid algorithm of power-law approach and perturbation method. Compared to the conventional perturbation method, this work keeps the intrinsic nonlinearity of electrochemical kinetics, while providing clearer physical meaning than some purely mathematical methods like the Adomian decomposition method. By integrating the resulting overpotential profile into mass transfer models, concentration overpotentials are obtained and the thermodynamic framework is then used for analyzing the H2/CO electrochemical co-oxidation kinetics. A novel expression is also presented to interconvert volume- and area-specific exchange current densities. On the cell level, a linear relationship between local current density and solid temperature is further developed for efficient 1D+1D thermal along-the-channel numerical simulations without requiring computational iterations. Both the electrode-level and cell-level macroscopic fuel cell models are validated against full numerical solutions available in the open literatures over a wide range of operating conditions. With the hybrid analytical/numerical approximation in two dimensions, the computational framework is predicted to be sufficiently efficient for real-time simulations.

A New Improved Perturbation and Observation MPPT Control Algorithm in Photovoltaic System

The conventional perturbation and observation (P&O) method is combined by the target tracking technique of data fusion, the adaptive multi-mode MPPT control algorithm is put forward for the first time. The reasonable and long step is selected to insure tracking velocity, the target tracking algorithm is adoptted for weaken and restrain vibration, the target maneuvering detection technique is put to use to judge whether the system is “lose control ” in fast variation environments, the repeat starting up perturbation and observation (P&O) method in order to strengthen system stability .The experimental result shows the correctness and validity of the method.

A New Improved Perturbation and Observation MPPT Control Algorithm in Photovoltaic System

The conventional perturbation and observation (P&O) method is combined by the target tracking technique of data fusion, the adaptive multi-mode MPPT control algorithm is put forward for the first time. The reasonable and long step is selected to insure tracking velocity, the target tracking algorithm is adoptted for weaken and restrain vibration, the target maneuvering detection technique is put to use to judge whether the system is “lose control ” in fast variation environments, the repeat starting up perturbation and observation (P&O) method in order to strengthen system stability .The experimental result shows the correctness and validity of the method.