Kirchhoff's Voltage Law Research Articles

Memory Elements: A Paradigm Shift in Lagrangian Modeling of Electrical Circuits

AbstractMeminductors and memcapacitors do not allow a Lagrangian formulation in the classical sense since these elements are nonconservative in nature and the associated energies are not state functions. To circumvent this problem, a different configuration space is considered that, instead of the usual loop charges, consist of time-integrated loop charges. As a result, the corresponding Euler-Lagrange equations provide a set of integrated Kirchhoff voltage laws in terms of the element fluxes. Memristive losses can be included via a second scalar function that has the dimension of action. A dual variational principle follows by considering variations of the integrated node fluxes and yields a set of integrated Kirchhoff current laws in terms of the element charges. Although time-integrated charge is a somewhat unusual quantity in circuit theory, it may be considered as the electrical analogue of a mechanical quantity called absement. Based on this analogy, simple mechanical devices are presented that can serve as didactic examples to explain memristive, meminductive, and memcapacitive behavior.

A Novel Fault-Location Algorithm for Double-Circuit Transmission Lines Without Utilizing Line Parameters

This paper puts forward a novel algorithm for locating faults on double-circuit transmission lines using two-end unsynchronized current measurements. The algorithm does not require line parameters, which is a radical step forward compared to existing approaches, which require this information, so it can be considered as a settings-free algorithm. Only the positive-sequence current phasors during the fault are processed for determining the sought distance to fault and the synchronization angle, limiting thus the amount of data needed to be transferred from each line terminal. The proposed algorithm is derived by applying the Kirchhoff's voltage law around the parallel circuits loops during the fault. The algorithm is applicable for both transposed and untransposed double-circuit lines and is independent of the fault type. Evaluation studies using reliable Alternative Transients Program-Electromagnetic Transients Program simulation data verify that the accuracy of the proposed algorithm is very high under various fault resistances, fault locations, and source impedances.

Reconstruction of conductivity using the dual-loop method with one injection current in MREIT

Magnetic resonance electrical impedance tomography (MREIT) is to visualize the internal current density and conductivity of an electrically conductive object. Injecting current through surface electrodes, we measure one component of the induced internal magnetic flux density using an MRI scanner. In order to reconstruct the conductivity distribution inside the imaging object, most algorithms in MREIT have required multiple magnetic flux density data by injecting at least two independent currents. In this paper, we propose a direct method to reconstruct the internal isotropic conductivity with one component of magnetic flux density data by injecting one current into the imaging object through a single pair of surface electrodes. Firstly, the proposed method reconstructs a projected current density which is a uniquely determined current from the measured one-component magnetic flux density. Using a relation between voltage potential and current, based on Kirchhoff's voltage law, the proposed method is designed to use a combination of two loops around each pixel from which to derive an implicit matrix system for determination of the internal conductivity. Results from numerical simulations demonstrate that the proposed algorithm stably determines the conductivity distribution in an imaging slice. We compare the reconstructed internal conductivity distribution using the proposed method with that using a conventional method with agarose gel phantom experiments.

Incorporating Motion in Mesh-Based Magnetic Equivalent Circuits

Recent research has compared the numerical efficiency of magnetic equivalent circuit (MEC) models based upon Kirchhoff's voltage law (mesh equations) and Kirchhoff's current law (nodal equations). For stationary magnetic components, it was shown that mesh-based methods converge in significantly fewer iterations. Although the numerical advantages would seemingly apply to electric machines, two issues have limited the application of mesh-based MEC models to electric machines. With movement, the number of meshes (unlike the number of nodes) is position dependent. Additionally, the loss of an airgap element creates an infinite reluctance. In this paper, both issues are addressed. Specifically, it is first shown that a relatively straightforward algorithm can be used to dynamically update meshes with rotor position. In addition, it is shown that the mesh model remains stable for very large values of tube reluctance. Tube reluctance values that are large enough to cause numerical issues can be easily avoided by excluding a very narrow range of rotor positions. Based upon these results, a mesh-based MEC model of a wound-rotor synchronous machine is developed and is shown to provide a significant advantage over its nodal-based model equivalent.

Prediction Technique for Pressure Change in Rooms by Using an Equivalent Circuit Network

Room pressurization is an important ventilation design technique for preventing airborne contaminants in biological clean rooms. To design an air-conditioning system that controls room pressure, an analytic method is needed, that predicts and estimates the change in room pressure and duct pressure, since they influence each other. In this paper, we present a new technique for predicting room pressure and duct pressure. In our technique, this pressure propagation mechanism is replaced with an equivalent circuit network by considering the air volume as electrical current, the lifted pressure by the fan as a battery electromotive force, and the friction loss as an electrical resistance. The change in room pressure is represented as the equation of resistance to air leakage. By using this technique, Kirchhoff's Voltage Law is applied to the duct network and the pressure calculation can be solved without many variables at the junctions. In addition, combining the resistance coefficients for elements carrying the same degree of air volume simplifies the duct network. Therefore, convergence performance is improved and the computing time can be shortened. By comparing it with experimental results, we verify the validity of the method. Using this technique, the air-conditioning equipment can be evaluated under dynamic usage and the specification of the control devices can be optimized. The effectiveness of any new ideas for maintaining a stable system response can be examined.

A Fault Location Algorithm Based on Circuit Analysis for Untransposed Parallel Transmission Lines

This paper proposes a fault-location algorithm for ultra-high-voltage untransposed parallel transmission lines that only use the voltages and currents at the local end. The proposed algorithm uses the voltage equation for the faulted phase of the faulted line. The equation contains the fault distance, fault resistance, and fault current. To obtain the fault current, Kirchhoff's voltage law is applied on the loops of three phases consisting of the faulted line and the adjacent parallel line. The fault current can be represented in terms of the fault distance. Inserting the fault current into the voltage equation results in an equation that contains only two parameters (i.e., the fault distance and fault resistance). The fault distance is estimated by solving the equation. Test results indicated that the algorithm accurately estimates the fault distance regardless of the fault resistance and mutual coupling effects.

Generalized Partial-Element Equivalent-Circuit Analysis for Planar Circuits With Slotted Ground

A generalized partial-element equivalent-circuit (PEEC) method is proposed for modeling a planar circuit with a thin narrow slot on the ground. The approach is based on the coupled mixed potential integral equations for a problem with mixed electric and magnetic currents. The coupled integral equations are converted into a lumped-element circuit network using Kirchhoff's voltage law and Kirchhoff's current law of the circuit theory. The full-wave Green's functions for a grounded dielectric substrate problem are used. The interactions between electric current on a microstrip line and magnetic current on a slot are taken into account by introducing two kinds of controlled sources. This generalized PEEC model will be very useful in signal-integrity analysis for multilayered circuits. To validate the generalized model, three numerical examples consisting of microstrip lines and slots on the ground are presented. The results obtained by the proposed generalized PEEC model are compared with those obtained by commercial electromagnetic simulation software and published experimental results. Good agreement is obtained.

SPICE‐compatible stamps for semi‐discrete approximations of Maxwell's equations

AbstractThis article presents the formulation of equivalent circuit stamps derived from the semi‐discrete form of Maxwell's equations. In particular, when a rectangular Yee's lattice is used for the spatial discretization of Faraday's and Ampere's laws, the stamps assume simple forms in terms of lumped circuit elements and dependent sources. It is shown that there is a very close relationship between the semi‐discrete Maxwell's system and the mesh analysis formalism of Kirchhoff's voltage and current laws. Boundary conditions, including a first‐order absorbing boundary condition, are extended to equivalent circuit descriptions. The utilization of the SPICE‐compatible equivalent circuit stamp formalism for the numerical solution of Maxwell's equations using SPICE is illustrated for the case of the calculation of the resonant frequencies of a perfectly conducting, rectangular cavity resonator. Copyright © 2007 John Wiley & Sons, Ltd.

An Improved Backward/Forward Sweep Load Flow Algorithm for Radial Distribution Systems

This letter presents an improved backward/ forward sweep algorithm for three-phase load-flow analysis of radial distribution systems. In the backward sweep, Kirchhoff's Current Law and Kirchhoff's Voltage Law are used to calculate the upstream bus voltage of each line or a transformer branch. Then, the linear proportional principle is adopted to find the ratios of the real and imaginary components of the specified voltage to those of the calculated voltage at the substation bus. In the forward sweep, the voltage at each downstream bus is then updated by the real and imaginary components of the calculated bus voltage multiplying with the corresponding ratio. The procedure stops after the mismatch of the calculated and the specified voltages at the substation is less than a convergence tolerance. The proposed algorithm is tested with three IEEE benchmark distribution systems. Results show that the algorithm is accurate and computationally efficient in comparing with two other commonly used methods

Biased graphs. VII. Contrabalance and antivoltages

We develop linear representation theory for bicircular matroids, a chief example being a matroid associated with forests of a graph, and bicircular lift matroids, a chief example being a matroid associated with spanning forests. (These are bias and lift matroids of contrabalanced biased graphs.) The theory is expressed largely in terms of antivoltages (edge labellings that defy Kirchhoff's voltage law) with values in the multiplicative or additive group of the scalar field. We emphasize antivoltages with values in cyclic groups and finite vector spaces since they are crucial for representing the matroids over finite fields; and integer-valued antivoltages with bounded breadth since they are crucial in constructions. We find bounds for the existence of antivoltages and we solve some examples. Other results: The number of antivoltages in an abelian group is a polynomial function of the group order, and the number of integral antivoltages with bounded breadth is a polynomial in the breadth bound. We conclude with an application to complex representation. There are many open questions.

Wiring Diagrams for Complex Reaction Networks

A graph-theoretic approach to developing reaction route (RR) networks is described that is a powerful new methodology for investigating the integrated architecture and dynamics of complex chemical and biological reaction systems. A distinct feature of our RR graphs is that while the edges represent reaction steps comprising the mechanism, the nodes simply represent their interconnectivity (not necessarily individual species, as has been the convention so far). As a result, all pathways can be traced simply as trails or walks on the RR graphs. Further, these networks are directly converted into wiring diagrams, allowing the use of electrical circuit theory, including Kirchhoff's current and voltage laws. Thus, they not only provide the reaction network topology but can be used to rigorously analyze network dynamics and the dominant pathways and bottleneck steps. We highlight the approach with three illustrations: (1) an enzymatic reaction system, (2) a heterogeneous catalytic process, and (3) an atmospher...

RLC effects in fine pitch anisotropic conductive film connections

PurposeThe resistance, capacitance and inductance of anisotropic conductive film (ACF) connections determine their high frequency electrical characteristics. The presence of capacitance and inductance in the ACF joint contributes to time delays and cross‐talk noise as well as simultaneous switching noise within the circuit. The purpose of this paper is to establish an experimental method for estimating the capacitance and inductance of a typical ACF connection. This can help to provide a more detailed understanding of the high frequency performance of ACF assemblies.Design/methodology/approachExperiments on the transient response of an ACF joint were performed using a digital oscilloscope capable of achieving the required ns resolution. An equivalent circuit model is proposed in order to quantify the capacitance (C) and inductance (L) of a typical ACF connection and this model is fitted to the experimental data. The full model consisted of two resistors, an inductor, and a capacitor.FindingsThe capacitance and inductance of a typical ACF connection were estimated from the measured transient response using Kirchhoff's voltage law. The method for estimation of R, L, and C from the transient response is discussed, as are the RLC effects on the high frequency electrical characteristics of the ACF connection.Research limitations/implicationsThere was decay time deviation between the calculation and the experiment. It may have resulted from the skin effect in the high frequency response and the adhesive surrounding joint as well. The main reason may be the capacitance zctric lost. Further research work will be done to determine more accurately the dielectric losses in anisotropic conductive adhesive (ACA) joint.Originality/valueThis paper presents a new method to characterise the high frequency properties of ACA interconnections and will be of use to engineers evaluating the performance of ACF materials in high frequency applications.

Distributed utility planning using probabilistic production costing and generalized benders decomposition

Summary form only given, as follows. Regulatory changes and advances in distributed resources (DR) technology have lead utilities to consider DRs as alternatives to central station generation and T&D investments. This paper presents a comprehensive planning and production simulation model that simultaneously evaluates central and local investments to determine the optimal mix for long-term expansion. The model can also be viewed as optimizing DRs while simulating a perfectly competitive wholesale power market. The model is a mixed integer linear stochastic program that enforces Kirchhoff's current and voltage laws, and is solved using generalized Benders decomposition (GBD). The formulation includes multiarea probabilistic production costing as a subproblem. DRs and local distribution reinforcements are modeled as integer variables, while transmission and central generation options are represented as continuous variables. The model is applied to a ten-year multi-area example that suggests that DRs are able to modify capacity additions and production costs by changing demand and power flows.

A non-a priori approach to analyze electrical machines modeled by FEM connected to static converters

This paper presents a method for direct coupling electrical machines, represented by two-dimensional (2-D) finite elements with the external circuit. The movement is taken into account by means of the moving band technique. The field and circuit equations are calculated automatically and then solved simultaneously using a time step procedure. The major contribution of this work is the fact that the whole system is calculated automatically, i.e., the electromagnetic field (Maxwell equations) and the converter circuit (Kirchhoff voltage and current laws and the elements characteristics equations) are strongly coupled in a unique set taking into account the movement. In order to validate the implemented procedure, a permanent magnet generator feeding a flyback converter is simulated and tested.

Distributed Utility Planning Using Probabilistic Production Costing and Generalized Benders Decomposition

Regulatory changes and advances in distributed resources (DR) technology have lead utilities to consider DRs as altematives to central station generation and T&D investments. This paper presents a comprehensive planning and production simulation model that simultaneously evaluates central and local investments to determine the optimal mix for long-term expansion. The model can also be viewed as optimizing DRs while simulating a perfectly competitive wholesale power market. The model is a mixed integer linear stochastic program that enforces Kirchhoff's current and voltage laws, and is solved using generalized Benders decomposition (GBD). The formulation includes multiarea probabilistic production costing as a subproblem. DRs and local distribution reinforcements are modeled as integer variables, while transmission and central generation options are represented as continuous variables. The model is applied to a ten-year multi-area example that suggests that DRs are able to modify capacity additions and production costs by changing demand and power flows.

IDENTIFICATION OF VOLTAGE-CURRENT OPERATORS SATISFYING TELLEGEN'S THEOREM

Let [Formula: see text] be a directed nonseparable network composed of a finite set ℬ of branches and F(u,i), an operator defined on the set of all ordered pairs of voltages and currents. It is proved that, if [Formula: see text] is neither a cutset nor a loop, and contains both a loop and a cutset with unequal numbers of opposite directed branches, and [Formula: see text] for all branch voltages [Formula: see text] and currents [Formula: see text] satisfying Kirchhoff's voltage and current laws respectively in every loop and cutset of [Formula: see text], then F is biadditive. This substantially strengthens an old theorem of Kishi and Kida in which, [Formula: see text] was allowed to vary over the set of all networks and physically reveals that the power is essentially the only continuous voltage-current operator which, when associated with a branch, yields Tellegen's famous theorem. It is also proved that, conversely, if F is biadditive, then the above sum is zero for an arbitrary network [Formula: see text]. The topological assumptions imposed on [Formula: see text] are thoroughly examined and shown to be necessary. Finally, similar analytic characterizations of eulerian and bipartite networks, respectively in terms of voltage and current operators with zero sums of values over all network branches are given.

Conduction mechanisms in Ta2O5/SiO2 and Ta2O5/Si3N4 stacked structures on Si

In this paper, the conduction mechanisms in Ta2O5/SiO2 and Ta2O5/Si3N4 stacked structures on Si are investigated both experimentally and theoretically. Amorphous Ta2O5 films (20–60 nm thick) were deposited by low pressure chemical vapor deposition or electron cyclotron resonance plasma enhanced chemical vapor deposition and some layers were annealed for crystallization at 800 °C in O2. The Si3N4 layers were formed by plasma nitruration or low pressure chemical vapor deposition. The SiO2 films studied were intentionally obtained by dry oxidation of the Si substrates, or as a result of the Ta2O5 deposition process (due to the oxidizing atmosphere), or of the Ta2O5 postdeposition annealing treatment under O2. The conduction mechanisms were identified by comparing the experimental current–voltage traces to the theoretical curves calculated in steady-state regime by using the Kirchhoff voltage law and the current continuity equation. In amorphous Ta2O5, the conduction mechanisms identified are the electronic hopping process and the Poole–Frenkel effect. For the corresponding interfacial SiO2 or Si3N4 films, the current transport is governed by tunneling processes or trap-modulated mechanisms, depending on the nature and deposition method of these interfacial layers. In crystalline Ta2O5 on SiO2 capacitors, no combination of basic conduction mechanisms can correctly fit the experimental curves, certainly due to the complex structure of crystalline Ta2O5 (high inhomogeneity and cracks).

Theoretical and experimental study of the conduction mechanism in Al/Ta 2O 5/SiO 2/Si and Al/Ta 2O 5/Si 3N 4/Si structures

The conduction mechanisms in Al/Ta 2O 5/SiO 2/n-Si and Al/Ta 2O 5/Si 3N 4/n-Si capacitors were studied from both the experimental and theoretical points of view. Amorphous Ta 2O 5 thin films were deposited by plasma enhanced chemical vapour deposition from TaF 5 on thermally grown SiO 2 and low pressure chemical vapour deposited Si 3N 4. To identify the conduction processes, the experimental current–voltage traces were compared to theoretical curves calculated in steady-state regime by using the current continuity equation and the Kirchhoff voltage law. In Ta 2O 5/SiO 2 capacitors, an electronic hopping conduction process and a field emission were identified in SiO 2, associated with a Poole–Frenkel effect in Ta 2O 5. In Ta 2O 5/Si 3N 4 structures, an electronic hopping conduction process and a Fowler–Nordheim tunneling were observed in Si 3N 4 with an electronic conduction and a Poole–Frenkel effect in Ta 2O 5. The electric field is localised in the nitride layer, and the leakage current densities of the Ta 2O 5/Si 3N 4 capacitors are reduced by the increase of the Si 3N 4 thickness.

Tellegen's theorem for 2-isomorphic networks

Let 𝒩 and 𝒩˜ be directed networks having the same number of branches labelled correspondingly. It is proved that one of them can be reorientated so that uTĩ=iTũ for all vectors of corresponding branch voltages u, ũ and currents i, ĩ satisfying Kirchhoff's voltage and current law in every loop and cutset of 𝒩 and 𝒩˜ if and only if under imposed correspondence of branches the networks are 2-isomoprhic. This is an ‘if and only if’ version of the converse of Tellegen's famous theorem established recently by the author and shows that Tellegen's theorem can in general be formulated for 2-isomorphic networks. Copyright © 1999 John Wiley & Sons, Ltd.

A new approach to modeling three-phase transformer connections

The modeling of three-phase transformer connections for power-flow and short-circuit studies can take on many forms, depending upon the assumptions made. Too many times, simplifying assumptions lead to answers that are totally wrong. Exact models of the various connections must be used if correct results are to be achieved. The exact models must satisfy Kirchhoff's voltage and current laws, and the ideal relationship between the voltages and currents on the two sides of the transformer windings and the models must represent any phase shift that is a result of the particular connection. New models for all common three-phase transformer connections have been developed that satisfy all of the requirements stated above. This paper limits the discussion to the ungrounded wye-delta connection and the model developed for use in power-flow and short-circuit studies.