Analyzing Electric Circuits with Computer Algebra

This report shows how starting from classic electric circuits embodying commonly electric components we have reached semi-complicated circuits embodying the same components that analyzing the signal characteristics requires a Computer Algebra System. Our approach distinguishes itself from the electrical engineers’ (EE) approach that relies on utilizing commercially available software. Our approach step-by-step shows how Kirchhoff’s rules are applied conducive to the needed circuit information. It is shown for the case at hand the characteristic information is a set of coupled differential equations and that with the help of Mathematica numeric solutions are sought. Our report paves the research road for unlimited creative similar circuits with any degree of complications. Occasionally, by tweaking the circuits we have addressed the “what if” scenarios widening the scope of the investigation. Justification of the accuracy of our analysis for the generalized circuits is cross-checked by arranging the components symmetrizing the circuit leading to an intuitively predictable reasonable result. Mathematica codes are embedded assisting the interested reader in producing and extending our results.

Three Dimensional Electric Circuits with Multiple Capacitors and Resistors

Two cubical 3D electric circuits with single and double capacitors and twelve ohmic resistors are considered. The resistors are the sides of the cube. The circuit is fed with a single internal emf. The charge on the capacitor(s) and the current distributions of all twelve sides of the circuit(s) vs. time are evaluated. The analysis requires solving twelve differential-algebraic intertwined symbolic equations. This is accomplished by applying a Computer Algebra System (CAS), specifically Mathematica. The needed codes are included. For a set of values assigned to the elements, the numeric results are depicted.

Integrated Experimental and Simulation Investigation of Breakdown Voltage Characteristics Across Electrode Configurations in SF_(6) Circuit Breakers

This study investigates the breakdown voltage characteristics in sulfur hexafluoride(SF6)circuit breakers,employing a novel approach that integrates both experimental investigations and finite element simulations.Utilizing a sphere-sphere electrode configuration,we meticulously measured the relationship between breakdown voltage and electrode gap distances ranging from 1 cm to 4.5 cm.Subsequent simulations,conducted using COMSOL Multiphysics,mirrored the experimental setup to validate the model’s accuracy through a comparison of the breakdown voltage-electrode gap distance curves.The simulation results not only aligned closely with the experimental data but also allowed the extraction of detailed electric field strength,electric potential contours,and electric current flow curves at the breakdown voltage for gap distances extending from 1 to 4.5 cm.Extending the analysis,the study explored the electric field and potential distribution at a constant voltage of 72.5 kV for gap distances between 1 to 10 cm,identifying the maximum electric field strength.A comprehensive comparison of five different electrode configurations(sphere-sphere,sphere-rod,sphere-plane,rod-plane,rod-rod)at 72.5 kV and a gap distance of 1.84 cm underscored the significant influence of electrode geometry on the breakdown process.Moreover,the research contrasts the breakdown voltage in SF6 with that in air,emphasizing SF6’s superior insulating properties.This investigation not only elucidates the intricate dynamics of electrical breakdown in SF6 circuit breakers but also contributes valuable insights into the optimal electrode configurations and the potential for alternative insulating gases,steering future advancements in high-voltage circuit breaker technology.

3D_Multi Resistor Electric Circuit

This report addresses the issues concerning the analysis of an electric circuit composed of multiple resistors configured in a 3-Dimension structure. Noting, all the standard textbooks of physics and engineering irrespective of the used components are circuits assembled in two dimensions. Here, by deviating from the “norm” we consider a case where the resistors are arranged in a 3D structure;e.g., a cube. Although, independent of the dimension of the design the same physics principles apply, transitioning from a 2D to a 3D makes the corresponding analysis considerably challenging. In general, with no exception, depending on the used components the analysis faces with solving a set of either algebraic or differential-algebraic equations. Practically, this interfaces with a Computer Algebra System (CAS). The main objective is symbolically to identify the current distributions and the equivalent resistor (s) of cubically assembled resistors.

Analysis of Non-Sinusoidal Steady Electric Field of ±500 kV Converter Transformer

The line side winding is under the fundamental frequency AC voltage, while the valve side winding contains not only fundamental AC voltage component, but also the DC voltage component, fundamental AC voltage component, and higher harmonic voltage components when the converter transformer is at its normal operating condition, and the electric field of converter transformer is a non-sinusoidal steady one. To analyze the non-sinusoidal steady electric field containing the DC component, fundamental AC and higher harmonic components, the voltage spectrum of the valve winding in a ±500 kV converter transformer is firstly analyzed, and the non-sinusoidal periodic steady electric field is obtained by the fast discrete Fourier transform. Different resistivity of the oil and oil-immersed paper is adopted to simulate the aging of oil paper insulation at operation, and get the non-sinusoidal steady electric field.

New Way to Quantize Time-Dependent RLC Electric Circuit and Quantum Fluctuations

According to the physical mechanism of the generation of the resistance or the electron phonon interaction, a new method is proposed to quantize the RLC electric circuit. Calculations show that the quantum fluctuations under this new quantization are smaller than those by the traditional effective Hamiltonian method. And squeezed states can be generated if the inductance and capacity are time dependent. Meanwhile, the shortcoming of the traditional method that the electric charge and current will vanish in the long time limit is overcome.

Extreme Learning Machine-Based Thermal Model for Lithium-Ion Batteries of Electric Vehicles under External Short Circuit

External short circuit(ESC)of lithium-ion batteries is one of the common and severe electrical failures in electric vehicles.In this study,a novel thermal modelis developed to capture the temperature behavior of batteries under ESC conditions.Experiments were systematically performed under different battery initial state of charge and ambient temperatures.Based on the experimental results,we employed an extreme learming machine(ELM)-based thermal(ELMT)model to depict battery temperature behavior under ESC,where a lumped-state thermal model was used to replace the activation function of conventional ELMs.To demonstrate the effectiveness of the proposed model,wecompared the ELMT model with a multi-lumped-state thermal(MLT)model parameterized by thegenetic algorithm using the experimental data from various sets of battery cells.It is shown that the ELMT model can achieve higher computa-tional efficiency than the MLT model and better fitting and prediction accuracy,where the average root mean squared error(RMSE)of the fitting is 0.65℃ for the ELMT model and 3.95℃ for the MLT model,and the RMES of the prediction under new data set is 3.97℃ for the ELMT model and 6.11℃ for the MLT model.

Nonzero Temperature Squeezing of the Time—Dependent Harmonic Oscillator and the Applications to the Capacitive Coupled Electric Circuit

A new way to calculate the nonzero temperature quantum fluctuations of the time-dependent harmonicoscillator is proposed and the properties of squeezing are exactly given. The method is applied to the capacitive coupledelectric circuit. It is explicitly shown that squeezing can appear and the squeezing parameters are related to the physicalquantities of the coupled circuit.

Development of hydraulic power unit and accumulator charging circuit for electricity generation,storage and distribution

It is the purpose of the present paper to convert hydraulic energy to electric energy and saves both the pressure and electrical energy for re - use during the next system upstroke using two secondary units coupled to induction motor to drive cylinder loads. During upstroke operation, the variable pump/motor （P/M） driven by both electric motor and the second （P/M） works as hydraulic pump and output flow to the cylinders which drive the load. During load deceleration, the cylinders work as pump while the operation of the two secondary units are reversed, the variable （P/M） works as a motor generating a torque with the electric motor to drive the other （P/M） which transforms mechanical energy to hydraulic energy that is saved in the accumulator. When the energy storage capacity of the accumulator is attained as the operation continues, energy storage to the accumulator is thermostatically stopped while the induction motor begins to work as a generator and generates electricity that is stored in the power distribution unit. Simulations were performed using a limited PT2 Block, i.e. 2nd-order transfer function with limitation of slope and signal output to determine suitable velocity of the cylinder which will match high performance and system stability. A mathematical model suited to the simulation of the hydraulic accumulator both in an open-or close-loop system is presented. The quest for improvement of lower energy capacity storage, saving and re-utilization of the conventional accumulator resulting in the short cycle time usage of hydraulic accumulators both in domestic and industrial purposes necessitates this research. The outcome of the research appears to be very efficient for generating fluctuation free electricity, power quality and reliability, energy saving/reutilization and system noise reduction.

Modeling of the Earth’s Planetary Heat Balance with Electrical Circuit Analogy

The integral heat model for the system of the Earth’s surface—the atmosphere—the open space based on the electrical circuit analogy is presented. Mathematical models of the heat balance for this system are proposed. Heat circuit which is analog of the electrical circuit for investigating the temperature dependencies on the key parameters in the clear form is presented.

New Breakdown Electric Field Calculation for SF6 High Voltage Circuit Breaker Applications

The critical electric fields of hot SF6 are calculated including both electron and ion kinetics in wide ranges of temperature and pressure, namely from 300 K up to 4000 K and 2 atmospheres up to 32 atmospheres respectively. Based on solving a multi-term electron Boltz- mann equation the calculations use improved electron-gas collision cross sections for twelve SF6 dissociation products with a particular emphasis on the electron-vibrating molecule interactions. The ion kinetics is also considered and its role on the critical field becomes non negligible as the temperature is above 2000 K. These critical fields are then used in hydrodynamics simulations which correctly predict the circuit breaker behaviours observed in the case of breaking tests.

Characterization of a New DC-Glow Discharge Plasma Set-Up to Enhance the Electronic Circuits Performance

The (DC-GDPAU) is a DC glow discharge plasma experiment that was designed, established, and operated in the Physics Department at Ain Shams University (Egypt). The aim of this experiment is to study and improve some properties of a printed circuit board (PCB) by exposing it to the plasma. The device consists of cylindrical discharge chamber with movable parallel circular copper electrodes (cathode and anode) fixed inside it. The distance between them is 12 cm. This plasma experiment works in a low-pressure range (0.15 - 0.70 Torr) for Ar gas with a maximum DC power supply of 200 W. The Paschen curves and electrical plasma parameters (current, volt, power, resistance) characterized to the plasma have been measured and calculated at each cm between the two electrodes. Besides, the electron temperature and ion density are obtained at different radial distances using a double Langmuir probe. The electron temperature (KTe) was kept stable in range 6.58 to 10.44 eV;whereas the ion density (ni) was in range from 0.91 × 1010 cm−3 to 1.79 × 1010 cm−3. A digital optical microscope (800×) was employed to draw a comparison between the pre-and after effect of exposure to plasma on the shaping of the circuit layout. The experimental results show that the electrical conductivity increased after plasma exposure, also an improvement in the adhesion force in the Cu foil surface. A significant increase in the conductivity can be directly related to the position of the sample surfaces as well as to the time of exposure. This shows the importance of the obtained results in developing the PCBs manufacturing that uses in different microelectronics devices like those onboard of space vehicles.

Equilibrium Composition of a Plasma in the Low Voltage Air Circuit Breaker Contaminated by the Vapor of AgSnO2 Alloy Electrical Contacts

When the circuit breaker cuts the electric current, an electric arc is created between its electrodes. The success or failure of breaking the electric current by the circuit breaker depends strongly on the physico-chemical properties of the electric arc created, such as the composition of which depends on the material of the electrical contacts. In this work, we determine the equilibrium composition of the electric arc in the low voltage air circuit breaker with silver tin dioxide alloy contacts, in a temperature range from 500 K to 15,000 K and at atmospheric pressure. We use the Gibbs free energy minimization method and develop a computer code to determine the equilibrium composition of the created plasma. The analysis of the results obtained shows that O2 particles with a dissociation energy of 5.114 eV, NO with a dissociation energy of 6.503 eV, and N2 dissociation 9.756 eV dissociate around 3500 K, 5000 K, and 7500 K, respectively. We note that the electro-neutrality is established between the electrons and the cations: Ag+ and NO+, for temperatures lower than 6500 K. For temperatures higher than 6500 K, the electro-neutrality is established between the electrons and the cations: N+, O+, and Ag+. The numerical density of the electrons increases when the proportion of the vapor of the electrical contacts increases in the mixture, in particular for temperatures lower than 11,000 K.

Modeling of the Coupling of the Lightning Shock Wave Flow Circuit in the High Voltage Electrical Network

This article focuses on the aggression of lightning overload on the equipment of the electrical network of sites where storm activity is very dense;and the electrocution of people located in the direct environment of the high-voltage substation during the flow of lightning current to the ground through the ground socket. The modeling of the flow circuit of the shock wave consisting of guard wire, lightning arrester and ground socket couple to the transformer of the high voltage substations, thanks to the approach of a servo block, led to the synthesis of a PID regulator (corrector) whose action is to reject the effects of the overvoltage on the network equipment and to significantly reduce or even cancel the effects of the step or touch voltage due to the distribution of the potential around the ground socket;and thus improve the quality of service of the high-voltage transmission and distribution electricity network, especially in stormy times.

Three-dimensional Model Analysis of Electric Field Excited by Multi-circuit Intersecting Overhead Transmission Lines

This work is carried out to predict the special distribution of electric field induced by multi-circuit intersecting overhead high-voltage (HV) transmission lines (TLs) within a large range without any expensive and time-consuming computation. The two main parts of the presented methodology are 1) setting up a three-dimensional (3D) model to calculate the electric field based on combining ca- tenary equations with charge simulation method and 2) calculating the hybrid electric field excited by multi-circuit intersecting TLs using coordinate transformation and superposition technique. Examples of different TLs configurations, including a 220 kV single-circuit hori- zontally configured TLs, a 500 kV single-circuit triangularly configured TLs and a combination of the 220 kV TLs and the 550 kV TLs, are illustrated to verify the validity of this methodology. A more complicatal configurations, including a 500 kV double-circuit TLs and two 220 kV single-circuit horizontally configured TLs, are also calculated. Conclusions were drawn from the simulation: 1) The presented 3D model outperforms 2D models in describing the electric field distribution generated by practical HV TLs with sag and span. 2) Coordinate trans- formation and superposition technique considerably simplify the electric field computation for multi-circuit TLs configurations, which makes it possible to deal with complex engineering problems. 3) The electric field in the area covered by multiple intersecting overhead TLs is distorted and the hybrid electric field strength in some partial region increases so sharply that it might exceed the admissible value. 4) The configuration parameters of the TLs and the spatial configuration of multi-circuit TLs, for instance, the height of TLs, the length of span and the intersection angle of multiple circuits, influence the strength and the distribution of hybrid electric field. The influence regularities sum- marized in this paper can be referred by future TL designs to meet the electromagnetic environmental protection regulations.

Performance of beam-type piezoelectric vibration energy harvester based on ZnO film fabrication and improved energy harvesting circuit

We demonstrate a piezoelectric vibration energy harvester with the ZnO piezoelectric film and an improved synchronous electric charge extraction energy harvesting circuit on the basis of the beam-type mechanical structure,especially investigate its output performance in vibration harvesting and ability to generate charges.By establishing the theoretical model for each of vibration and circuit,the numerical results of voltage and power output are obtained.By fabricating the prototype of this harvester,the quality of the sputtered film is explored.Theoretical and experimental analyses are conducted in open-circuit and closed-circuit conditions,where the open-circuit mode refers to the voltage output in relation to the ZnO film and external excitation,and the power output of the closed-circuit mode is relevant to resistance.Experimental findings show good agreement with the theoretical ones,in the output tendency.It is observed that the properties of ZnO film achieve regularly direct proportion to output performance under different excitations.Furthermore,a maximum experimental power output of 4.5 mW in a resistance range of 3 kΩ-8 kΩis achieved by using an improved synchronous electric charge extraction circuit.The result is not only more than three times the power output of classic circuit,but also can broaden the resistance to a large range of 5 kΩunder an identical maximum value of power output.In this study we demonstrate the fundamental mechanism of piezoelectric materials under multiple conditions and take an example to show the methods of fabricating and testing the ZnO film.Furthermore,it may contribute to a novel energy harvesting circuit with high output performance.

Study of the selective effect on cells induced by nanosecond pulsed electric field with the resistor-capacitor circuit model

A resistor-capacitor(RC)circuit model is proposed to study the effect of nanosecond pulsed electricfield on cells according to the structure and electrical parameters of cells.After a nanosecond step fieldhas been applied,the variation of voltages across cytomembrane and mitochondria membrane both in nor-mal and in malignant cells are studied with this model.The time for selectively targeting the mitochondriamembrane and malignant cell can be evaluated much easily with curves that show the variation of voltageacross each membrane with time.Ramp field is the typical field applied in electrobiology.The voltagesacross each membrane induced by ramp field are analyzed with this model.To selectively target the mito-chondria membrane,proper range of ramp slope is needed.It is relatively difficult to decide the range ofa slope to selectively affect the malignant cell.Under some conditions,such a range even does not exist.

A study on equivalent circuit model of lead-acid battery for electric vehicles

A 100Ah@42V lead-acid battery package for electric vehicles are used for study. 1he hybrid pulse test is applied to the battery package to acquire enough data, by which the partnership for a new generation of vehicles （PNGV） equivalent circuit model parameters are identified by the least square method. Then, the PNGV model is verified under two conditions, i.e., the composite pulse excitation and the constant-current respectively. The corresponding maximum relative errors of output voltage are less than 3 % and 3.5 %. Results show that the present PNGV equivalent circuit model and verification method is effective, which can satisfy requirement of simulation of power system of electric vehicles.

Research on Total Electric Field for DC Lines Converted from Double-Circuit AC Lines

With rapid growth of power demand, transmission capacity is also in urgent need of upgrading. In some cases, converting existing AC transmission lines to DC lines can Improve the transmission capacity and reduce the construction investment. In this paper, the upstream finite element method was expanded to calculate the total electric field of same tower multi-circuit DC lines converted from double-circuit AC lines, and the validity of the algorithm was confirmed by experiments. Taking a DC line converted from a typical same tower 500 kV double-circuit AC transmission line as an example, the surface electric field and the ground total electric field in different pole conductor arrangement schemes were calculated and analyzed, and the critical height of pole conductors for DC lines in residential and non-residential area were determined. Then, the corridor width of DC and AC lines at critical height in residential and non-residential areas before and after AC-DC line transformation were compared. The results indicate that for DC lines converted from common 500 kV double-circuit AC lines, the ground total electric field can meet the requirements of corresponding standard with appropriate pole conductor arrangement schemes.