Lumped-parameter Equivalent Circuit Model Research Articles

Cut‐set matrix methods for frequency response analysis curves of lumped parameter equivalent circuit model of three‐winding power transformer

SummaryTo accurately and efficiently calculate the frequency response of the lumped parameter equivalent circuit model (LPECM) of a transformer winding is the basis for studying the simulation method of the frequency response analysis (FRA). In this paper, two different cut‐set matrix (CSM) methods, including fundamental cut‐set (FCS) and independent cut‐set (ICS) matrix methods, are proposed to calculate the FRA curves of the LPECM of a three‐winding power transformer. First, based on graph theory and electrical circuit laws, the basic CSM equation is deduced. Second, four different FCS matrix selection methods of the LPECM are introduced and the best FCS matrix is determined by deeply analyzing their characteristics. Then, an ICS matrix method is proposed to obtain the ICS of the LPECM. Furthermore, FCS and ICS are taken into the CSM equation to calculate the FRA results of the LPECM, respectively. Finally, the accuracy of the proposed methods is validated by Multisim software and the performance of these two methods is compared with node voltage matrix (NVM) method by analyzing the calculation time. The results show that FCS and ICS matrix methods both can be used to accurately obtain the FRA results of the LPECM of the three‐winding power transformer, but ICS is more simple than FCS matrix method due to avoiding the procedure for the selection of the tree. In addition, since ICS matrix method has the shortest running time among these methods, it can be used to improve the calculation efficiency of the FRA curves of the LPECM of a three‐winding power transformer.

Accurate Electromagnetic Force Analysis of Offshore Wind Power Transformer Windings Based on Fractional Order Lumped Parameter Model

Accurate calculation of the electromagnetic force distribution of transformer windings under different loads and fault conditions is of great significance for transformer maintenance, condition evaluation and life prediction. Due to the influence of offshore wind power systems, offshore wind power transformers have high harmonic content and large changes in load rates, which can easily cause the coil destabilization, winding deformation or even damage because of the uneven distribution of the electromagnetic force. To improve the accuracy of electromagnetic force calculation, this paper proposes a fractional order numerical method. First, a three-dimensional axisymmetric transformer model and a symmetrical lumped parameter equivalent circuit model are established, respectively, based on field-circuit coupling. Second, the fractional order approximation of circuit components is realized by using the improved Oustaloup filter. In the fractional order model, the transformer is replaced by the lumped parameter equivalent circuit model. Third, as in the calculation process for integer order electromagnetic force, the integer order current has a large error, and the current waveform does not match the actual power frequency. The fractional order current and electromagnetic force at the 0.9 order are closer to the rated value. Finally, the effects of different load rates, three-phase short circuits and harmonic conditions are studied with the fractional order model. Compared with the traditional integer order finite element electromagnetic model, the fractional order equivalent circuit model established in this paper is more accurate and suitable for electromagnetic force calculation. The proposed method is significant for the structural design and state detection of transformers and also could be applied in the analysis of other dry-type transformers.

Effect of the Electron Transport Layer Thickness on I–V Characteristics of the S-Shaped Kinks in Perovskite Solar Cells

In our experimental preparation of perovskite solar cells (PSCs), when the thickness of the electron transport layer (ETL) was changed from thin to thick, the current–voltage ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}$</tex-math> </inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{V}$</tex-math> </inline-formula> ) characteristics showed the changing laws of S-shaped kinks appearance, S-shaped kinks disappearance, and S-shaped kinks appearance. A lumped-parameter equivalent circuit model is proposed to reveal the intrinsic physical significances of the S-shaped kinks for this variation laws. The explicit solution of the model is derived using the deformed difference-microvariation (DM) principle combined with the region method, and the model parameters are extracted efficiently through the firefly optimization algorithm (FA). The proposed analytical solution enables the model to be compactly implemented in photovoltaic devices and circuit simulators, and the model is expected to point the direction for process optimization of devices.

Modeling and Characteristic Analysis of Magnetic Coupling Mechanism in Seawater Environment

The electrical conductivity and dielectric constant of seawater are quite different from those of air, so it is necessary to explore the differences between wireless power transmission characteristics in the air and seawater. The equivalent circuit model of the magnetic coupling mechanism is of great significance to the analysis of the transmission characteristics. In this article, a more accurate model analyzing the wireless power transmission in seawater environment is proposed, in which all parameters of the model can be obtained by specific expressions. First, by establishing the electromagnetic field analysis model in the seawater environment, the distribution laws of underwater electric field intensity and magnetic induction intensity are obtained. Then, the equivalent self- and mutual resistances of eddy current loss are introduced based on electromagnetic field model, and the analytical solutions of them are given. The lumped parameter equivalent circuit model of the underwater magnetic coupling mechanism is further derived, and the influencing factors of eddy current loss equivalent resistances are explored, which can provide theoretical guidance for multi-objective system optimization. Finally, an underwater platform was built to verify the accuracy of the equivalent circuit model.

Loss Characterization of Giant Magnetostrictive Material Under Compressive Stress

The properties of giant magnetostrictive material (GMM) are very sensitive to external compressive stress. Knowledge of these key properties is of essential importance in practical applications such as high-power underwater transducers. Although the parameters of GMM have been extensively studied, characterization and analysis of magnetic, elastic, and piezoelectric losses under different compressive stresses are rarely reported due to the difficulty in experimentally realizing the ideal mechanical free or clamped boundary conditions. In this study, we designed a longitudinal transducer for complex parameters characterization of GMM. We successfully characterize the key three losses in GMM using a multi-degree-of-freedom (MDOF) lumped parameter equivalent circuit model (LECM), meticulously incorporating the surface contact damping, stiffness, and structural losses. MDOF LECM provides a novel idea for loss characterization of GMM under compressive stress. In contrast to prior-art parameters characterization based on the distributed parameter equivalent circuit model (DECM), the proposed characterization based on MDOF LECM shows apparent superiority in terms of global sensitivity. The intensive losses of GMM for ten-time characterizations show high stability and are all positive. Statistical analysis of intensive losses&#x2019; dependency on the compressive stress is performed. A longitudinal transducer is designed for experimental verification. Finally, 95% prediction and confidence intervals for the variation trend of the intensive losses in relationship with compressive stress are obtained.

State of Energy Estimation for Lithium-Ion Battery Pack via Prediction in Electric Vehicle Applications

Accurate state of energy (SOE) estimation of the battery pack is very important for the electric vehicle's driving range estimation, which is still a very challenging problem under actual vehicle application conditions at present. This paper proposes a method for estimating the SOE of the battery pack based on prediction, taking into account the future voltage and temperature changes of the battery pack. Firstly, a novel definition of the battery pack SOE is proposed, which considers the inconsistency of the battery pack. Secondly, the thermo-electric lumped parameter equivalent circuit model of a single cell in the battery pack is applied. The electrical parameters are identified using the forgetting factor recursive least-squares algorithm, and the extended Kalman filter is used to estimate the SOC of each cell. Finally, the future current, voltage and temperature response of the cell in the battery pack are accurately predicted and iterative calculations are performed to get SOE under the condition that the future output power of the battery pack is predicted by the Markov chain model method. The effectiveness of the proposed method is verified under dynamic conditions at different temperatures. The results show that the above method has high precision and good robustness, and can meet the needs of actual vehicle applications.

Lumped-Parameter Modeling and Performance Analysis of Fluid-Backed Piezoceramic Flexural Disc Acoustic Sensors

two-port lumped-parameter equivalent circuit model is presented to analyze the electroacoustic characteristics of piezoelectric flexural-mode acoustic sensors with fluid backing. The circuit parameters are determined from the measured electrical admittance spectra in water. Expressions for frequency-dependent receiving sensitivity are derived in terms of the equivalent circuit parameters under two extreme boundary conditions, namely, clamped and simply supported edges. The effect of geometric parameters of the composite flexural discs on the acoustic performance is analyzed. The model is validated by constructing flexural disc hydrophones of several dimensions and configurations, in which the overall thickness is much smaller than the radius. The model results agree well with the experimental data, validating the model. It is found that the receiving sensitivity of practical sensors lie in between clamped edge and simply-supported edge conditions which are the theoretical lower and upper bounds, respectively. Among all the sensors studied, the sensor with the lowest radius ratio (Rp/Rs) has the highest measured receiving sensitivity of -173 dB (ref. 1V/μPa) at low frequencies and -150 dB (ref. 1V/μPa) at resonance. The self-noise characteristics of these sensors are also analyzed with reference to underwater applications. The largest sensor has the highest Figure-of-Merit (FoM) with the measured M2C value of 743 × 10-28 V2F/μPa2, which is about three orders of magnitude higher than typical sensors. Piezoelectric sensors with high FoM is required to design acoustic systems with high Signal-to-Noise Ratio (SNR) with enhanced acoustic receiver characteristics.

A predictive governing control method of the pumped-storage unit based on lumped-parameter model equivalence

The speed governor is known as one of the most important control parts in the pumped-storage unit (PSU). When operating in transient processes, the stability of the PSU’s hydraulic and mechanical states maintains by the precise regulation of the speed governor. For the sake of improving the governing control performances, the lumped-parameter equivalent circuit model is first introduced for precise modelling of hydraulic-mechanical characteristics of PSU. Subsequently, a multi-variable generalized predictive control system based on receding horizon technique is applied at every sampling instant to optimize the control trajectory within certain finite time horizon. To validate the effectiveness of the proposed predictive control method, the simulation experiment of governing movements during turbine start-up process is conducted under a nonlinear lumped-parameter numerical simulation platform of PSU by comparative case studies, the overall control performance of the proposed control scheme is evaluated and compared with that of the traditional PID algorithm. Simulation results indicate that the proposed governing control method can achieve stronger frequency fluctuation alleviation and hydraulic oscillation damping performances than traditional PID.

An Analytical Effective-Diode-Based Analysis of Industrial Solar Cells From Three-Diode Lumped-Parameter Model

Three-diode lumped-parameter equivalent circuit model conforms to photovoltaic device physics and processes an exact analysis for I- V characteristics of industrial solar cells, because it explains the different leakage current components especially for recombination current resulting from defects or grain boundaries. However, three-diode model's complete circuit topology leads to complicated transcendental I- V equation without analytical solution so that low computation efficiency limits three-diode model's applications in photoelectric simulations. In this article, an effective-diode method is proposed to simplify three-diode model, derive accurate and efficient terminal current-voltage solution to three-diode model, and acquire electrostatic characteristics of the solar cells. The calculated values have good agreements with numerical iteration results and experimental data measured from solar cells, respectively. Finally, the effective-diode method performs an important role of solving three-diode model analytically, predicting I- V characteristics of industrial solar cells accurately, and providing three-diode model's practicability and development in solar cells' simulations.

Capacitively coupled discharge as a tunable impedance element for RF systems

A concept of plasma-based reconfigurable radio-frequency (RF) components is studied experimentally. The concept's main idea is to control the real and imaginary parts of impedance experienced through a weak high-frequency signal applied to the RF discharge electrodes by varying the plasma excitation frequency and/or power. To prove the concept, an experimental setup was built that enabled the application of both strong plasma excitation RF and weak RF/microwave signals to the same set of electrodes. Three different plasma cells were examined. The largest system had 5 cm diameter electrodes with 2 cm gap, and the experiments were conducted in argon at 1 Torr. The impedance characteristics of the plasmas as experienced by the probing signal in the range of 270–3000 MHz demonstrated wide variability and a complex non-monotonic behavior at high frequencies. Experiments with a smaller cell that had 1 cm diameter electrodes and 2 mm gap also showed the controllability of the real and imaginary parts of the impedance, including transition from capacitive to inductive behavior. Because of the smaller size comparable with the probing signal wavelength, the high-frequency behavior of this system can be described with a simple lumped-parameter equivalent circuit model. The smallest system studied in this work utilized a commercial sealed gas discharge tube as an RF plasma cell and also demonstrated wide impedance tunability and transition from capacitive to inductive behavior. These results could potentially be useful for plasma-based electronically reconfigurable RF electronics, particularly in applications involving high power where alternative solutions experience problems.

An Improved Surface-Potential-Based Model for MOSFETs Considering the Carrier Gaussian Distribution

In this article, an improved surface-potential-based current model for MOSFETs is proposed to characterize the Gaussian distribution phenomenon of carrier concentration. First, the lumped parameter equivalent circuit model is established. Then, in order to improve the current model accuracy for the large width-length ratio (WLR) transistors, the channel carrier distribution is studied. Based on this, the conventional drain-source current model is modified. Besides, the parameters related to the carrier distribution along the channel are extracted. In order to validate the improved model, different WLR transistors were fabricated and measured. Furthermore, the model calculation results are compared with the measurement data. The root-mean-square error (RMSE) of drain-source current is reduced from 3.537 to 0.354 μA in the subthreshold region and decreased by 76% in the linear region. As a result, the proposed model is reliable and predictable, which is helpful for the RF circuits design.

Analyzing S-Shaped I–V characteristics of solar cells by solving three-diode lumped-parameter equivalent circuit model explicitly

In order to analyze and optimize new generation solar cells’ electrostatic performances, lumped-parameter equivalent circuit model is a common method to simulate S-shaped I–V characteristics including linear, exponential, or exponential-like current kinks. Unfortunately, three-diode lumped-parameter model is still inevitable to be solved generally in numerical iteration method. The absence of explicit solution to three-diode lumped-parameter model is actually the main bottleneck of implementing the model into photovoltaic device and circuit simulators in compact. In this paper, to overcome the problem of three-diode model’s implementation into simulators, we proposed an explicit solution to the model based on the regional approach, where high accuracy and low computation time cost are the main features of such a solution. Analytical derivation and correction for the solution to transcendent I–V equation in three-diode model leads to high computation accuracy, and avoidance of numerical iteration methods introduces low computation time cost. Finally, numerical iteration results and reconstructed experimental data of solar cells are used to validate the accuracy and applicability of our proposed explicit solution. As a result, high accuracy and efficiency of the explicit solution make it possible to implement three-diode lumped-parameter equivalent circuit model into photovoltaic device and circuit simulators and explain I–V characteristics of new generation solar cells.

Modelling solar cells’ S-shaped I-V characteristics with an analytical solution to lumped-parameter equivalent circuit model

In this paper, an analytical solution to three-diode lumped-parameter equivalent circuit model is proposed to simulate and present S-shaped I-V characteristics of next generation solar cells, which are observed frequently in perovskite and organic solar cells, and occasionally in other kinds of solar cells. In general, because complicated transcendental equation includes three exponent items resulting from three diodes, the absence of an analytical solution has become a bottleneck that limits the adoptions of solar cells’ three-diode lumped-parameter model into practical applications and device simulations. To break through the above bottleneck, the analytical solution is derived in the regional approach, completed in Matlab platform, and verified by reconstructed experimental data measured from real solar cells. Such an analytical solution processes the key feature with high precise and efficiency. High precise results from the mathematical operations of the analytical solution to lumped-parameter model and high efficiency results from the avoidance of numerical iteration methods. In addition, this analytical solution facilitates researchers to accurately determine short circuit current and open circuit voltage, quickly extract model parameters in lumped-parameter circuit, and in detail assess effects from model parameters on DC characteristics of solar cells. Finally, the proposed analytical solution is able to be used to reproduce S-shaped I-V characteristics of solar cells, assist in extracting fitting parameters in three-diode lumped-parameter equivalent circuit model, and complete implementation of model into semiconductor device and circuit simulators.

An explicit method to extract fitting parameters in lumped-parameter equivalent circuit model of industrial solar cells

An explicit parameter-extraction method is proposed to estimate the values of fitting parameters in lumped-parameter equivalent circuit model of industrial solar cells. The explicit method is based on polynomial fitting curves on Matlab platform, TCAD device simulation results of Silvaco Atlas, and experimental data of silicon-based solar cells’ current-voltage characteristics. Such an explicit parameter-extraction method can be directly applied into the analytical solutions to one-diode lumped-parameter equivalent circuit model to complete the simulations for electrostatic properties of solar cells. First, the current-voltage characteristics of industrial silicon-based solar cells are also derived analytically as the previous works completed by other researchers and the four key factors especially for the maximum power formula are solved through the effective diode approach. Second, polynomial curve is used to fit current-voltage characteristics from simulation and experiment results of solar cells under illumination. Third, the polynomial fitting result, the short circuit current, and the open circuit voltage are used to extract explicitly all of five parameters included in the one-diode lumped-parameter equivalent circuit model for industrial solar cells. Finally, the extracted fitting parameters are substituted into the analytical solution to current-voltage characteristics and the obtained current-voltage characteristics are compared with device simulation results from Silvaco Atlas and experimental data from silicon-based solar cells. As a result, such an explicit extraction procedure could be regarded as a fast and accurate method to estimate model parameters in industrial solar cells, which is important for not only photoelectric device simulations but also process analysis.

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.