Lumped Parameter Equivalent Circuit Research Articles

Lumped-parameter equivalent circuit modeling of solar cells with S-shaped I-V characteristics

In this paper, we propose a method to analytically solve some types of DC lumped-parameter equivalent circuit models for solar cells with S-shaped I-V characteristics measured under illumination. Based on the models proposed previously by other authors, we present the set of equations describing solar cell’s terminal current and voltage, derive the analytical solutions of I-V characteristics, and give discussions about the effects from the model parameters on solar cells’ I-V characteristics. The comparisons between the proposed solutions and the least square method results illustrate that the solution calculation scheme is not only both accurate and efficient, but also valid in the whole operation regime of solar cells especially for the S-shaped kink in the first quadrant. Finally, the solutions are validated by the reconstructed experimental data to demonstrate that they can be adopted in the practical applications of solar cells. As a result, the feature of the proposed solutions can decrease computation complexity, ease the extraction process of the solar cells’ model fitting parameters, and increase simulation accuracy.

A Lumped-Parameter Equivalent Circuit Modeling for S-Shaped I–V Kinks of Organic Solar Cells

We propose an improved lumped-parameter equivalent circuit model to describe S-shaped I–V kinks observed from organic solar cells. Firstly, to predict the S-shaped I–V kinks accurately in both the first and fourth quadrants, a shunt resistor in parallel with extraction diode is added to our previous model. Secondly, based on the Newton–Raphson method, we derive a solution to our improved circuit. Thirdly, our solution is verified by the method of least squares and experiments. Finally, compared with our previous work, the improved circuit has higher accuracy in demonstrating S-shaped I–V kinks in the first and fourth quadrants. Such an improved model is suitable for circuit simulations of organic solar cells.

Lumped-Parameter Equivalent Circuit Model for S-Shaped Current–Voltage Characteristics of Organic Solar Cells

A lumped-parameter equivalent circuit model is proposed to simulate the S-shaped current–voltage ( ${I}$ – ${V}$ ) characteristics exhibited in organic solar cells. First, we derive an explicit terminal current solution as a function of terminal voltage from the equation set of the three-diode lumped-parameter model proposed by Mazhari. Second, we improved Mazhari’s model to improve the accuracy and developed the explicit solution of our improved model to improve the efficiency. Third, we use the method of least squares, Newton–Raphson root-finding scheme, and experimental data to validate the solutions of Mazhari’s and our models. As a result, owing to high accuracy and efficiency of computation, our explicit calculation scheme, regarded as a useful tool, can help to implement Mazhari’s and our models into photovoltaic device and system simulators in compact format.

An analysis for S-shaped I-V characteristics of organic solar cells using lumped-parameter equivalent circuit model

A lumped-parameter equivalent circuit model of organic solar cells (OSCs) is proposed to analyze the S-shaped current-voltage (I-V) characteristics and the explicit solution to I-V equation is derived so that this model is suitable to be compactly implemented for the simulations of photovoltaic applications. Comparing our explicit solutions with the method of least squares and the Newton-Raphson root-finding scheme, the simulations quantificationally reproduce the S-shaped I-V characteristics of OSCs especially for both linear- and exponential-like S-shaped kink in the third and first quadrants, respectively. Simultaneously, the simulations facilitate us to qualitatively analyze the S-shaped I-V characteristics of OSCs influenced by the different model parameters. Furthermore, we verify the simulation results of our proposed model by using the reconstructed experimental data. Good agreements indicate that such a model can be used to accurately predict the S-shaped I-V characteristics of OSCs and regarded as a serviceable tool implemented compactly into simulations of the wide photovoltaic applications.

An Improved Organic Solar Cell Lumped-Parameter Equivalent Circuit Model

An improved lumped-parameter equivalent circuit model is proposed to describe S-shaped I–V characteristics of organic solar cells (OSCs). This model originates but differs from Mazhari’s model. As a minor but important modification, a shunt resistance is added to Mazhari’s model to increase the accuracy of simulating the S-shaped kink in the third quadrant. Subsequently, we present a terminal current-voltage equation set and derive an analytical solution to the improved model. Furthermore, we verify the analytical solution to our model by using the least square method and validate our model by using the experimental I–V curves examined from OSCs. Compared with Mazhari’s model, our model has greater accuracy in interpreting the S-shaped kink with linear-like rise in the third quadrant. As a result, our improved model is suitable to explain the S-shaped I–V characteristics of organic solar cells in the whole operational region, especially for the S-shaped kink in the third quadrant.

An Analytical Solution to Lumped Parameter Equivalent Circuit Model of Organic Solar Cells

In this paper, an analytical and closed-form solution to the lumped parameter equivalent circuit model of organic solar cells is proposed to complete the simulations of the S-shaped I-V characteristics. Based on the model previously proposed by Mazhari, the set of terminal current and voltage equations describing the three diodes is solved and the effects from the model parameters are illustrated. Our solutions are verified by being compared with the least square method results and experimental data, respectively. Good agreements show that our solution calculation scheme is not only both accurate and efficient, but also valid in the whole operation regime of solar cells, especially for the S-shaped kink on the condition where the terminal voltage is larger than the open circuit voltage. Such an analytical solution can play an important role in the simulations for I-V characteristics of solar cells, fast extractions of the model parameters, and implements into practical photovoltaic device simulators.

Core Losses Analysis of a Novel 16/10 Segmented Rotor Switched Reluctance BSG Motor for HEVs Using Nonlinear Lumped Parameter Equivalent Circuit Model

In this paper, a new nonlinear lumped parameter equivalent circuit model is proposed to calculate the core losses of a novel 16/10 segmented rotor switched reluctance motor (SSRM) for belt-driven starter generators. The model investigates the hysteresis, eddy current and anomalous losses by using the method of energy conservation. Four parameters are introduced in the proposed model to consider the effects of saturation and leakage flux in SSRM. They are the incremental leakage inductance, the incremental equivalent winding resistance, the incremental magnetizing inductance, and the incremental equivalent core-loss resistance. This model can overcome the hysteresis effects of winding resistance and leakage inductance on the current, and improve the accuracy of the parameters. To illustrate the advantages of the proposed model, an experiment platform is developed. Experimental results show that the proposed model can significantly improve the calculation accuracy of core losses of the SSRM. The accuracy is better than the conventional Epstein frame method. The proposed core-loss model and analysis method can be applied to other kinds of switched reluctance motors.

Numerical Study and Optimisation of a Novel Single-Element Dual-Frequency Ultrasound Transducer.

A dual-frequency ultrasound transducer (DFUT) is usually preferred for its numerous advantageous applications, especially in biomedical imaging and sensing. However, most of DFUTs are based on the combination of fundamental and harmonic operations, or integration of multiple different single-frequency ultrasound transducers, hindering perfect beam alignment and acoustic impedance matching. A novel single-element DFUT has been proposed in this paper. A small piezoelectric membrane is used as the high-frequency ultrasound transducer, which is stacked on a large non-piezoelectric elastic membrane with a groove used as the low-frequency capacitive ultrasound transducer. Such a capacitive-piezoelectric hybrid structure is theoretically analysed in details, based on the electrostatic attraction force and converse piezoelectric effect. Both the low and high resonance frequencies are independently derived, with a maximum deviation of less than 4% from the finite element simulations. Besides, a lumped-parameter equivalent circuit model of combining both the capacitive and piezoelectric ultrasound transducers was also described. Based on our dual-frequency structure design, a high-to-low frequency ratio of about 2 to more than 20 could be achieved, with easy and independent controllability of two frequencies, and the high-frequency operation shows at least an order-of-magnitude displacement sensitivity improvement compared with the conventional harmonic operations.

Modelling of a 400-kV MSCDN Reactor for Computation of Voltage and Field Distributions During Switching Transients

In this paper, a model for the reactor of a 400-kV mechanically switched capacitor with damping network (MSCDN) based on an equivalent circuit representation is developed. The model is based on sub-dividing the physical reactor into sections which are sufficiently small to be represented by a lumped-parameter equivalent circuit. The circuit parameters are obtained for each section using analytical formulae based on the physical configuration of the reactor, the winding layout, and the insulation material. The model is then simulated in the ATP/EMTP program for the evaluation of transient voltage and field distributions along of the reactor. This helps in identifying possible failure scenarios which will allow designing measures to mitigate failures effectively during transients arising from switching operations. Further analysis of the results has revealed that there are substantial dielectric stresses imposed on the winding insulation that can be attributed to a combination of three factors. First, the surge arrester operation during the MSCDN energization, which causes steep voltage change at the reactor terminal. Second, the non-uniform voltage distribution, resulting in high stresses across the top inter-turn windings. Third, the rapid rate-of-change of voltage in the assumed worst-case reactor winding location. This is accompanied by a high dielectric (displacement) current through the inter-turn winding insulation. The results of this paper indicate that a synergistic effect of high electric field and high dielectric current occurring at worst energization, followed by the thermal effects of steady state operation may contribute to the failure of air-core reactors used on the 400-kV MSCDN.

S-Shaped ${I}$ – ${V}$ Characteristics of Organic Solar Cells: Solving Mazhari’s Lumped-Parameter Equivalent Circuit Model

We explain how to obtain closed-form analytic solutions from the set of equations that describe the three-diode lumped-parameter equivalent circuit model proposed by Mazhari [1] to portray the undesirable S-shape often observed in ${I}$ – ${V}$ characteristics of illuminated organic solar cells (OSCs), and occasionally seen in other types of solar cells. This allows quick extraction of the model’s parameter values by directly fitting the resulting closed-form solution to the cell’s measured ${I}$ – ${V}$ data. Such mathematical simplification of the extraction procedure facilitates individually studying the effect of each parameter on the illuminated OSC ${I}$ – ${V}$ characteristics, and thus on its power generation capacity. We illustrate application of the direct extraction procedure to measured ${I}$ – ${V}$ characteristics of an experimental OSC, which exhibits the illumination intensity-dependent S-shapes. The usefulness of the analytic solution to assess the effect of the model parameters is further corroborated by graphically illustrating the progression of a series of hypothetical synthetic ${I}$ – ${V}$ characteristics generated by this analytic solution using gradually changing the parameter values. Analysis of the results, in this case, indicates that activation of the diode that represents recombination is the key factor responsible for the emergence of the illuminated ${I}$ – ${V}$ curve’s S-shape.

Determination of Winding Lumped Parameter Equivalent Circuit by Means of Finite Element Method

In this paper, the finite element method is used in order to determine the electrical parameters of a machine winding lumped element model. Thanks to this model, it will be possible to determine the electrical behavior of electrical machine winding fed by a power converter and thus to study the distribution of the turn-to-turn maximum voltage stress as early as the design process. The suitability of the method is validated by comparison with measurements.

Dual EKF-Based State and Parameter Estimator for a LiFePO4 Battery Cell

This work presents the design of a dual extended Kalman filter (EKF) as a state/parameter estimator suitable for adaptive state-of-charge (SoC) estimation of an automotive lithium–iron–phosphate (LiFePO₄) cell. The design of both estimators is based on an experimentally identified, lumped-parameter equivalent battery electrical circuit model. In the proposed estimation scheme, the parameter estimator has been used to adapt the SoC EKF-based estimator, which may be sensitive to nonlinear map errors of battery parameters. A suitable weighting scheme has also been proposed to achieve a smooth transition between the parameter estimator-based adaptation and internal model within the SoC estimator. The effectiveness of the proposed SoC and parameter estimators, as well as the combined dual estimator, has been verified through computer simulations on the developed battery model subject to New European Driving Cycle (NEDC) related operating regimes.

Modelling solar cell S-shaped I-V characteristics with DC lumped-parameter equivalent circuits a review

This article reviews and appraises the dc lumped-parameter equivalent circuit models that have been proposed so far for representing some types of solar cells that can exhibit under certain circumstances a detrimental S-shaped concave deformation within the energy-producing fourth quadrant of their illuminated I-V characteristics. We first present a very succinct recollection of lumped-parameter equivalent circuits that are commonly used to model conventional solar cells in general. We then chronologically present and discuss lumped-parameter equivalent sub-circuits that, combined with conventional solar cell equivalent circuits, are used to specifically represent the undesired S-shaped behaviour. The mathematically descriptive equations of each complete equivalent circuit are also examined, and closed form solutions for the terminal current and voltage as explicit functions of each other are presented and discussed whenever available. While comparing the most salient features and explaining the practical advantages and disadvantages of such equivalent circuit models, we offer some comments on possible directions for further improvement.

State-space Coil Modelling in Plasma Magnetic Confinement Devices

The need of robust and optimal control schemes is a key factor for the development of future fusion reactors. This paper has dealt with the state-space modelling of the Ultra-Low Iota Super Elongated Stellarator of the UPV/EHU, using a physical lumped parameter equivalent circuit approach. The model obtained has been validated by means of experimental output data showing an excellent matching with the real system. Besides, it has been designed a MPC scheme that has been successfully implemented both in simulation and experimentally using a real-time control platform.

Characteristic Tests and Electromagnetic Analysis of an HTS Partial Core Transformer

An experimental high temperature superconducting (HTS) transformer has been designed and built using GdBCO HTS tapes. The transformer is unique in that the magnetic circuit is comprised of air and an iron partial core. The HTS windings and iron core were immersed in a liquid nitrogen environment. Fundamental characteristics were obtained by no-load and load tests. The transformer had a smaller exciting current compared with the HTS air core transformer, and the voltage regulation was 1.67% at full load. A lumped parameter equivalent circuit that takes the ac loss was proposed and testified by tests. A 3-D “field-circuit” coupled model built in COMSOL was used to successfully analyze the electromagnetic characteristics of the transformer. The experimental results were consistent with the calculated and simulation values. The detail results will describe in this paper.

Tape-wound Rogowski coil for measuring large-magnitude pulsed currents

This paper presents design, calibration and testing of a new tape-wound Rogowski coil for measuring large-magnitude pulsed currents. The performance of the coil is tested by different impulse current waveforms up to 9 kA peak value. The coil is calibrated versus two commercial impulse-current transformers with different impulse current waveforms. The coil design is optimized to work in the differentiating mode and achieve useful bandwidth and sensitivity up to 1 MHz and 102 mV/kA, respectively. Waveform distortion of the coil output voltage is examined by using the lumped-element model to optimize the parameters of the external passive integrator. It is desired to optimize the integrator parameters and achieve the desired bandwidth without having droop and backswing. To do so, the coil frequency response is investigated by making fast Fourier transform (FFT) of the impulse current waveforms and PSPICE simulation of the lumped parameter equivalent circuit of Rogowski coil and the external integrator. Finally, it is found that the PSPICE calculated sensitivity for the optimized integrator parameters deviates from the corresponding measured one by a percentage relative error of–0.05%.

Equivalent circuit model of a coaxial excited microstrip‐fed quasi‐lumped element resonator antenna array

An approximate lumped-parameter equivalent circuit model of the quasi-lumped element resonator antenna array is presented. The array consists of six series resonant circuits of frequency-independent elements, each with an interdigital finger capacitor (IDC), and shorted across by a parallel narrow strip inductor. Each resonator exhibits an aperture size of 0.207λg × 0.2λg at a centre frequency of 5.8 GHz, with entire array size of 2.857λg × 1.07λg . The resulting design is fed by a microstrip line and excited by a coaxial feed probe. A simple equivalent circuit model representing the six resonant circuits as well as the coaxial feed probe circuit, using the magnetic-frill model approach but with the simplest uniform-current model is described to predict the characteristics of the proposed resonator (and by extension, the proposed array), the effects of the coaxial probe and the microstrip feed line. Simulated data obtained from a full wave analysis using finite integration technique commercial solver is compared with the Agilent advanced design system results of the equivalent circuit. The derived equivalent circuit model was validated both analytically and by numerical simulations.

A three diode model for industrial solar cells and estimation of solar cell parameters using PSO algorithm

A new lumped-parameter equivalent circuit model using three-diodes is presented in this work for large area (∼154.8 cm2) industrial silicon solar cells. The estimation of values of ideality factors n1 (>1) and n2 (>2) using a Particle Swarm Optimization (PSO) algorithm for the two-diode model of the industrial samples has been found not to be in conformity with the theoretical values (n1 = 1 and n2 = 2 in the literature). The two diodes of the two-diode model are not able to define the different current components of the solar cells clearly. A model with three-diodes has been proposed to better explain the experimental data. In the proposed model, we considered the series resistance, Rs, of the solar cell to vary with the current flowing through the solar cell device. All the parameters of the proposed model have been estimated using a PSO algorithm and they were compared with the parameters of the two-diode model. The new model has been found to be a better model to define clearly the different current components of the large size industrial silicon solar cells.

Radio‐frequency transport Electromagnetic Properties of chemical vapour deposition graphene from direct current to 110 MHz

We report measurement of the radio-frequency (RF) transport electromagnetic properties of chemical vapour deposition (CVD) graphene over the DC to 110 MHz frequency range at room temperature. Graphene on Si/SiO2 substrate was mounted in a shielded four terminal-pair (4TP) adaptor which enabled direct connection to a calibrated precision impedance analyser for measurements. Good agreement is observed for the DC four-probe resistance and the 4TP resistance at 40 Hz, both yielding R ~ 104 {\Omega}. In general the apparent graphene channel electromagnetic properties are found to be strongly influenced by the substrate parasitic capacitance and resistance, particularly for high-frequencies f > 1 MHz. A phenomenological lumped-parameter equivalent circuit model is presented which matches the frequency response of the graphene 4TP impedance device over approximately seven decades of the frequency range of the applied transport alternating current. Based on this model, it is shown for the first time, that the intrinsic graphene channel resistance of the 4TP device is frequency-independent (i.e. dissipationless) with RG ~ 105 {\Omega} or sheet resistance of approximately 182 {\Omega} / sq. The parasitic substrate impedance of the device is found shunt RG with RP ~ 2.2 {\Omega} in series with CP ~ 600 pF. These results suggest that our new RF 4TP method is in good agreement with the conventional DC four-probe method for measuring the intrinsic sheet resistance of single-atom thick materials and could potentially open up new applications in RF electronics, AC quantum Hall effect metrology and sensors based on graphene 4TP devices operating over broad range of frequencies.

Theoretical systems of triboelectric nanogenerators

Triboelectric nanogenerator (TENG) technology based on contact electrification and electrostatic induction is an emerging new mechanical energy harvesting technology with numerous advantages. The current area power density of TENGs has reached 313W/m2 and their volume energy density has reached 490kW/m3. In this review, we systematically analyzed the theoretical system of triboelectric nanogenerators. Starting from the physics of TENGs, we thoroughly discussed their fundamental working principle and simulation method. Then the intrinsic output characteristics, load characteristics, and optimization strategy is in-depth discussed. TENGs have inherent capacitive behavior and their governing equation is their V–Q–x relationship. There are two capacitance formed between the tribo-charged dielectric surface and the two metal electrodes, respectively. The ratio of these two capacitances changes with the position of this dielectric surface, inducing electrons to transfer between the metal electrodes under short circuit conditions. This is the core working mechanism of triboelectric generators and different TENG fundamental modes can be classified based on the changing behavior of these two capacitances. Their first-order lumped-parameter equivalent circuit model is a voltage source in series with a capacitor. Their resistive load characteristics have a “three-working-region” behavior because of the impedance match mechanism. Besides, when TENGs are utilized to charge a capacitor with a bridge rectifier in multiple motion cycles, it is equivalent to utilizing a constant DC voltage source with an internal resistance to charge. The optimization techniques for all TENG fundamental modes are also discussed in detail. The theoretical system reviewed in this work provides a theoretical basis of TENGs and can be utilized as a guideline for TENG designers to continue improving TENG output performance.