Kirchhoff's Voltage Research Articles

Circuit synthesis based on a prescribed Lagrangian

On the basis of a prescribed quadratic Lagrangian, an algorithm of synthesis for an electric circuit is suggested here. That is, the circuit evolution equations are equivalent to the relevant Euler–Lagrange equations. The proposed synthesis is a systematic approach that allows one to realize any finite-dimensional physical system described by a quadratic Lagrangian in a lossless electric circuit so that their evolution equations are equivalent. The synthesized circuit is composed of (i) capacitors and inductors of positive or negative values for the respective capacitances and inductances, and (ii) gyrators. The circuit topological design is based on the set of L C LC fundamental loops (f-loops) that are coupled by G L C GLC -links each of which is a serially connected gyrator, capacitor, or inductor. The set of independent variables of the underlying Lagrangian is identified with f-loop charges defined as the time integrals of the corresponding currents. The EL equations for all f-loops account for the Kirchhoff voltage law whereas the Kirchhoff current law is fulfilled naturally as a consequence of the setup of the coupled f-loops and the corresponding charges and currents. In particular, the proposed synthesis provides for efficient implementation of the desired spectral properties in an electric circuit. The synthesis provides also a way to realize arbitrary mutual capacitances and inductances through elementary capacitors and inductors of positive or negative respective capacitances and inductances.

Fast Assessment Method for Transient Voltage Stability of Photovoltaic Receiving‐End Grid

The incorporation of renewable energy on a broad scale into power grids increases the complexity to the issue of transient voltage stability in power systems. This research presents a rapid evaluation technique for assessing the stability of voltage fluctuations in power grids that receive electricity from photovoltaic sources. At first, a receiving‐end system model was developed, which includes photovoltaics, and an alternative circuit of the virtual induction motor (IM) is obtained by utilizing the Thevenin equivalent. Second, the torque balance equation and the Kirchhoff voltage equation are interconnected to determine the unstable slip of the IM following a malfunction. Finally, by merging the unstable slip with the conventional transient stability discriminant index, the effects of different photovoltaic outputs, IM ratios, and system contact impedances on transient voltage stability are investigated. The proposed method avoids the computational burden of solving the differential‐algebraic equations describing the complex transient processes of the IM. It also obviates the necessity of iteratively modifying the receiving load or fault clearance time in the simulation platform to achieve the constrained stability condition of the system’s transient voltage. The transient stabilization of voltage results is efficiently obtained by directly solving algebraic equations.

On the zero state-response of the ℑ-order R-C circuit within the local fractional calculus

PurposeAs a powerful mathematical analysis tool, the local fractional calculus has attracted wide attention in the field of fractal circuits. The purpose of this paper is to derive a new -order non-differentiable (ND) R-C zero state-response circuit (ZSRC) by using the local fractional derivative on the Cantor set for the first time.Design/methodology/approachA new -order ND R-C ZSRC within the local fractional derivative on the Cantor set is derived for the first time in this work. By defining the ND lumped elements via the local fractional derivative, the -order Kirchhoff voltage laws equation is established, and the corresponding solutions in the form of the Mittag-Leffler decay defined on the Cantor sets are derived by applying the local fractional Laplace transform and inverse local fractional Laplace transform.FindingsThe characteristics of the -order R-C ZSRC on the Cantor sets are analyzed and presented through the 2-D curves. It is found that the -order R-C ZSRC becomes the classic one when = 1. The comparative results between the -order R-C ZSRC and the classic one show that the proposed method is correct and effective and is expected to shed light on the theory study of the fractal electrical systems.Originality/valueTo the best of the authors’ knowledge, this paper, for the first time ever, proposes the -order ND R-C ZSRC within the local fractional derivative on the Cantor sets. The results of this paper are expected to give some new enlightenment to the development of the fractal circuits.

High-pass negative group delay analysis of single capacitor three-port circuit

PurposeThis paper aims to develop high-pass (HP) negative group delay (NGD) investigation based on three-port lumped circuit. The main particularity of the proposed three-port passive topology is the consideration of only a single circuit element represented by a capacitor.Design/methodology/approachThe methodology of the paper is to consider the S-matrix equivalent model derived from admittance matrix approach. So, an S-matrix equivalent model of a three-port circuit topology is established from admittance matrix approach. The frequency-dependent basic expressions are explored to perform the HP-NGD analysis. Then, the existence condition of HP-NGD function type is analytically demonstrated. The specific characteristics and synthesis equations of HP-NGD circuit with respect to the desired optimal NGD value are established.FindingsAfter computing the frequency expressions to perform the HP-NGD analysis, this study demonstrated the existence condition of HP-NGD function type analytically. The validity of the HP-NGD theory is verified by a prototype of three-port circuit. The proof-of-concept (POC) single capacitor three-port circuit presents an NGD response and characteristics from analytical calculation and simulation is in very good correlation.Originality/valueAn innovative theory of HP-NGD three-port circuit is studied. The proposed HP-NGD topology is constituted by only a single capacitor. After the topological description, the S-matrix model is established from the Y-matrix by means of Kirchhoff voltage law and Kirchhoff current law equations. A POC of single capacitor three-port circuit was designed and simulated with a commercial tool. Then, a prototype with a surface-mounted device component was fabricated and tested. As expected, simulation and measurement results in very good agreement with the calculated model show the feasibility of the HP-NGD behavior. This work is compared to other NGD-type function with diverse number of ports and components.

A generalized external circuit model for electrostatic particle-in-cell simulations

A fully self-consistent second order accuracy model for coupling a generalized external circuit and a one-dimensional bounded electrode-driven plasma was proposed in this paper. The plasma was embedded in the circuit as a non-linear element with a potential difference. Based on Kirchhoff's voltage law and the definition of current, the problem of solving the generalized external circuit was transformed into an initial value problem of a set of first-order ordinary differential equations which can be discretized numerically by the second-order backward differential formula. The charge conservation equation at the electrode plate was coupled to the above equation, and the voltage, current, and surface charge density at the next moment were solved by a differential equation solver. Dirichlet boundary conditions of Poisson's equation were obtained through the surface charge density σ0 of the generalized external circuit equation and the plasma density ρ of the Particle-in-Cell (PIC) model. The spatial distribution of plasma potential was solved by using the second-order central difference scheme. The obtained potential at the electrode plate can be used as the Robin boundary condition of the system of generalized external circuit equations. In this model, the loose coupling between the generalized external circuit and plasma was realized by the boundary condition, and the system was fully self-consistent based on the charge conservation law and energy conservation law. We simulated the capacitively coupled plasmas (CCP) under different external circuits as the example and verified the performance of the model. This model can be used to study the influence of different external circuit structures and parameters on plasma discharge, and can be used for any plasma sources driven by electrodes, like CCP, some vacuum electronic devices, and Z-Pinches.

Methods on the Determination of the Circuit Parameters in an Underwater Spark Discharge

We constructed an underwater discharge system to conduct a number of experiments. Considering the constant resistance of the plasma channel, we got an analytic expression for the current containing unknown parameters on the basis of the Kirchhoff voltage law. Therefore, we are required to determine the total circuit resistance R with the measured current data in hand. Three methods are employed to get this job done, namely, nonlinear least squares with three variables (NLS-TV), nonlinear least squares with a single variable (NLS-SV), and waveform calculation method (WCM). The Levenberg–Marquardt (L-M) algorithm and particle swarm optimization (PSO) algorithm are employed in NLS-TV and NLS-SV, and the root mean square error (RMSE), as well as an improved cosine similarity (ICS), was selected to evaluate the performance of algorithms. The results show that NLS-TV gives an optimal solution with the combination of the PSO algorithm and L-M algorithm. Then, by calculation, R = 1.3195 Ω , C = 0.56865 μF, and L = 17.172 μH. RMSE and ICS between fitted current data and measured one are 43.9689 and 0.9947, respectively. NLS-SV gives a satisfying solution either by PSO or by L-M, yet it needs information of angular frequency from the measured current waveform and the total inductance C . In this case, we get R = 1.3115 Ω , L = 16.969 μH, RMSE = 48.0883, and ICS = 0.9967. As for WCM, it is completely dependent on the measured current waveform and the total inductance C . The corresponding values of R and L are 1.2463 Ω and 16.993 μH. Also, we get RMSE = 52.1902 and ICS = 0.9728. For NLS-SV and WCM, the needed total capacitance during calculation is determined using the computed capacitance by NLS-TV. If the energy storage capacitance is used as the total capacitance, the obtained solution is frustrating. Therefore, independent use of NLS-SV or WCM demands a precise capacitance of the total circuit measured by an RLC meter. We also draw a conclusion that ignoring the capacitance of other parts of the circuit is incorrect and will lead to an enormous error during calculation.

Assessing the Cost of Network Simplifications in Long-Term Hydrothermal Dispatch Planning Models

The sustainable utilization of hydro energy relies on accurate estimates of the opportunity cost of the water. This value is calculated through long-term hydrothermal dispatch problems (LTHDP), and the recent literature has raised awareness about the consequences of modeling simplifications in these problems. The inaccurate representation of Kirchhoff's voltage law under the premise of a DC power flow is an example. Under a non-linear AC model, however, the LTHDP becomes intractable, and the literature lacks an accurate evaluation method of different modeling alternatives. In this paper, we extend the state-of-the-art cost-assessment framework of network approximations for LTHDP and bring relevant and practical new insights. First, we increase the quality of the assessment by using an AC power flow to simulate and compare the performance of five policies based on different network approximations. Second, we find that the tightest network relaxation (based on semidefinite programming) is not the one exhibiting the best performance. Results show that the DC power flow with quadratic losses approximation exhibits the lowest expected cost and inconsistency gaps. Finally, its computational burden is lower than that exhibited by the semidefinite relaxation, whereas market distortions are significantly reduced in comparison to previously published benchmarks based on DC power flow.

High-speed auxiliary fault location element for distance relays in double-circuit lines

In multi-zone distance relays, zone-2 has an intentional time delay which is considered for the coordination among the other distance relays. This delay is unnecessary for faults that occur at the end of the protected line and causes the fault to be cleared after hundreds of milliseconds. On the other hand, high-speed fault clearance is an important issue of ensuring the stability of the power system. To address the above problem, an auxiliary fault location (AFL) element based on the proper Kirchhoff voltage law (KVL) loop in the negative- and zero-sequence circuits are designed for distance relays. The input signals to the AFL are the measured signals by local distance relay. The proposed AFL can reduce the zone-2 intentional time delay from 18-28 cycles to 3 cycles. In addition to this, AFL can improve limitations associated with similar methods such as the dependence of these methods to the fault resistance, remote source impedances, and line parameters variation. The AFL can accurately calculate the fault location, before issuing a trip command. Furthermore, to increase the accuracy, the shunt capacitances of the line are compensated by the algorithm. Numerous PSCAD simulation studies verify the effectiveness and applicability of the proposed scheme.

Loop Formulation in Hybrid Analytical Modeling for Solving 2-D Nonlinear Magnetostatic Problems

This article presents a novel formulation in hybrid analytic modeling (HAM) for solving 2-D nonlinear magnetic problems. This novel formulation, referred to as the loop formulation, solves the magnetic equivalent circuit (MEC) through Kirchhoff's voltage law, as opposed to the traditional node formulation, which uses Kirchhoff's current law. This allows one to solve the system iteratively using the Newton-Raphson method instead of the fixed-point method, providing a convergence rate up to four times faster. The novel HAM formulation also provides an excellent tradeoff between accuracy and computational time. It offers approximately one order of magnitude lower computation time for the same accuracy compared to finite-element analysis (FEA) on a slotless geometry.

Toward an Electrical Analog of the Cardiovascular System in Hemorrhage.

Current quantitative descriptions of the cardiovascular system in hemorrhagic shock focus on pressure based metrics. This approach is often incomplete; overlooking the important role of tissue perfusion. Electrical analogs to the cardiovascular system may offer a more complete description of hemorrhage. Application of fundamental concepts in electrical circuit theory (i.e.; Kirchhoff's Voltage Law and Ohm's Law) to analogs of the cardiovascular system offers a more refined description of this complex process. This manuscript hopes to serve as a starting point for a more mathematically robust, and clinically relevant description of hemorrhagic shock.

Interactive AR App for Real-Time Analysis of Resistive Circuits

An augmented reality app for real-time analysis of direct current in resistive circuits is presented. The app allows the manipulation of circuit elements and computes the values of voltage and current intensity using the loop method and applying the Kirchhoff's voltage law. The app can be used in theoretical classes and laboratories. The contributions of this paper are two-fold. First, the app has higher levels of interactivity than other apps in the same domain since it allows defining the configuration and the parameters of the circuit. Second, the app performs more complex computations than similar apps in real-time.

A coreless hybrid coil design for the wireless power charging system

In the dynamic magnetic coupling wireless charging system, the optimal design of the resonant coil structure is one of the key technologies to ensure the power transmission with the high efficiency. In this paper, based on the good static characteristics of system, a hybrid structure coil is proposed to improve the efficiency and the dynamic anti-offset ability of system. Based on the simplified circuit model of the PP compensation network, the efficiency and the output power of system under the optimal load impedance are derived based on Kirchhoff voltage law. According to the efficiency expression, the number of the turns of the hybrid coil and the radius of the coil are optimized, and the parameter design method of the hybrid coil under the specific environment is given. In order to evaluate the dynamic performance of the system, a quantitative evaluation index is given, which synthesizes three kinds of the dynamic characteristics of the axial, the radial and the angular. Finally, the feasibility of the designed coil is verified by the finite element simulation.

Method for extracting motor impedance characteristics online

Due to increases in switching frequency, the electromagnetic interference of motor drive systems has been receiving more attention. In a motor drive system, the devices in the inverter produce serious electromagnetic interference during high-frequency switching. It is necessary to model the motor drive system to predict the electromagnetic interference level. Extraction of the motor impedance characteristic is necessary for the modeling of a motor drive system. At present, most research only studies the measurement method of a motor in the static state. However, motor impedance characteristics in the static state cannot represent motor impedance characteristics in operation. In this paper, an online measurement method of motor impedance characteristics is proposed. For the three-phase asymmetric circuit caused by modulation, the motor impedance characteristics in operation are calculated by establishing Kirchhoff voltage equations. A precision power scope PX8000 is used to measure the harmonic components of single-phase voltage, single-phase current, and common-mode current. The time-delay difference of the precision power scope PX8000 between different probes is also considered. Experiments prove that the time-delay difference does not affect the measurement results. Through comparing the motor impedance characteristics measured by different filters, the method of extracting the motor impedance characteristics online is validated. Finally, the motor impedance characteristics in the static state and the motor impedance characteristics of online extraction are experimentally compared. The motor impedance characteristics of the online extraction method proposed in this paper have more advantages than traditional methods.

A Regularized Tensor Completion Approach for PMU Data Recovery

This article presents a novel data recovery framework for missing synchrophasor measurements. The imputation accuracy for the existing data recovery methods is significantly reduced when there are consecutive data losses across multiple data streams. Besides, the recovered data do not necessarily meet the physical constraints of the power grid. To tackle these issues, a regularized low rank tensor completion (LRTC) method is proposed to incorporate the domain knowledge (e.g., Kirchhoff's voltage and current laws, and three phase circuit relationships) as the regularization terms in order to efficiently exploit the data inter-dependencies for a better recovery. We leverage the tensor decomposition and completion as powerful tools to extract the latent structures of phasor measurement unit (PMU) data for the recovery process. Specifically, we first construct the tensor model of the PMU data and then formulate the LRTC problem as a rank minimization by leveraging the low rank property of the PMU measurements and adding the regularization terms into the LRTC problem in order to improve the imputation accuracy. An efficient algorithm based on alternating direction method of multipliers (ADMM) is developed to solve the regularized LRTC problem. The experiments using the real PMU dataset show that the proposed approach exhibits better imputation accuracy, compared with the conventional matrix completion methods.

Accurate fault location element for series compensated double-circuit transmission lines utilizing negative-sequence phasors

Obtaining the accurate fault location in the series compensated double-circuit transmission lines (SCDCTL) is a challenge due to the presence of series compensator, fault resistance, and mutual the coupling between parallel lines. Although by using the pilot fault location methods, the effect of all the aforementioned factors can be eliminated and the location of the fault can be calculated. However, the number of communication channels available for pilot schemes is limited. In addition, the reliability of the communication links for long transmission lines may be particularly reduced. On the other hand, most of the non-pilot methods need to calculate the series compensator data and the accuracy of the fault location in them depends on the accuracy of the series compensator parameters. To improve the limitation of conventional impedance-based methods, this paper presents a non-pilot accurate fault location element (FLE) for conventional distance relays in SCDCTL. The main concept of the proposed method is considering the proper Kirchhoff voltage law (KVL) loop in the negative-sequence circuit of SCDCTL. Consideration of the shunt capacitances of lines ensures accuracy of the achieved fault location formula. It is shown that the designed FLE can improve limitations associated with similar methods such as the dependence of these methods to the fault resistance, mutual coupling between the parallel lines, and the series compensator (SC) parameters. To investigate the performance of the proposed FLE, several factors are considered in the simulation analysis including different fault resistances, fault locations, and fault types. Besides, the influence of current transformer (CT) saturation, measurement errors, external faults, bypassing of the Metal Oxide Varistor (MOV), and effect of noise on the proposed scheme is studied. Evaluation study using PSCAD verify the effectiveness and applicability of the proposed scheme.

Aplicación AR Interactiva para el Análisis en Tiempo Real de Circuitos Resistivos

An augmented reality app for real-time analysis of direct current in resistive circuits is presented. The app allows the manipulation of circuit elements and computes the values of voltage and current intensity using the loop method and applying the Kirchhoff's voltage law. The app can be used in theoretical classes and laboratories. The contributions of this paper are two-fold. First, the app has higher levels of interactivity than other apps in the same domain since it allows defining the configuration and the parameters of the circuit. Second, the app performs more complex computations than similar apps in real-time.

U=RIsolve: A Web-Based Application for Learning Electrical Circuit Analysis [Education

Learning circuit analysis is often a challenging issue for Electrical Engineering undergraduate students. During the course's early stages, procedures such as the correct identification of Branches, Nodes and Loops, the expression of Kirchhoff Current and Voltage Laws, as well as the application of analysis/simplification Theorems and Algorithms, usually embed tricky and error-prone steps for beginners. While circuit simulators offer a validation for theoretical and experimental analysis, they do not explain how to obtain the results nor the fundamental laws supporting them. In this regard, a new web-based framework, - dubbed U=RIsolve (read as you resolve) - for teaching and self-learning the Node Voltage Method (NVM) is presented in this paper. The U=RIsolve application goes far beyond the capabilities of traditional circuit simulators, as it outputs the fundamental circuit information, the methodology, the equations and the results related to the NVM. An outlook of the application main features, user interface and usage in electrical circuit analysis is provided, along with the future implementations.

The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative

Local fractional calculus has gained wide attention in the field of circuit design. In this paper, we propose the zero-input response(ZIR) of fractal RC circuit modeled by local fractional derivative(LFD) for the first time. With help of the law of switch and the Kirchhoff Voltage Laws, the transient local fractional ordinary differential equation is established, and the corresponding exact solution behavior defined on Cantor sets is presented. What we found especially interesting was that the fractal RC becomes the ordinary one in the particular case κ = 1. The results obtained in this paper reveal that the local fractional calculus is a powerful tool to analyze the fractal circuit systems.

Optimal current flow technique for distribution systems with renewable energy generation

This article presents an optimal current flow (OCF) technique for analyzing distribution systems with renewable energy generation. The overall aim of this study is to reduce the complexity of the traditional nonlinear models by representing the problem as a quadratic optimization network flow model with linear constraints. The objective of the OCF method is minimization of renewable generation costs with or without consideration of transmission losses. Taking advantage of the topological characteristic of the distribution system, the network constraints are represented by Kirchhoff current and voltage laws. In addition, the model considers the capacity limits of the distribution components (renewable generators, transformers and lines current flow). The robustness and fastness of the OCF method is tested on 34-bus, 69-bus, and 400-bus systems under balanced and unbalanced, conditions and in radial or meshed distribution systems under different load scenarios. The results demonstrate the accuracy, and efficiency of the proposed approach in determining the optimal operation of a distribution system with renewable energy generation.

Media Analisis Rangkaian Listrik Menggunakan Pendekatan Numerik Gauss-Jordan, Gauss-Seidel, dan Cramer

The aim of this study is create an analysis media for calculating the electric current in a closed circuit with one or more loops. Gauss-Jordan, Gauss-Seidel, and Cramer methods were used in this study. This media is packaged into Graphic User Interface (GUI) with matlab language program assisting. In this study, Linear Equation System (SPL) was obtained from kirchhoff current law and kirchhoff voltage law concepts. Gauss-Seidel method is not always convergent for each formed SPL, because it can only be applied when coefficient matrix A was diagonally dominant. The application of this analysis media made the calculation of closed circuit electric current with one or more loops became accurate and time saving.