A.c. circuit analysis

D.G. circuit analysis

In this chapter, the problems of the first chapter are fully solved, in detail, step-by-step, and with multiple methods, by using mesh analysis, nodal analysis, and heuristic techniques. In all the problems’ solutions, Kirchhoff current law (KCL) and Kirchhoff voltage law (KVL) as well as the concepts of mesh current, node voltage, supermesh, and supernode are clearly described. Moreover, in the application of circuit theorems, the concepts of open circuit voltage, short-circuit current, Thevenin voltage, Thevenin resistance, Norton current, and Norton resistance are explained. In addition, this chapter shows how to deal with circuit components like resistors, dependent current and voltage sources, and independent current and voltage sources.

The three-stage generator (TSG), as one of the most used more-electric aircraft generators, is crucial for the stable operation of aircraft power supply systems. The presence of numerous converters in cascade with the generator leads to complex physical and control dynamic interactions, which affect the stability of the ac bus voltage. To address the stability issue, two major contributions are made in this article. First, a dual-port modular impedance/admittance modeling method suitable for cascaded system with TSG and pulse width modulation (PWM) rectifier (TSG-PWM) is presented. In this method, a dual-port network is formed by Thevenin's theorem and Norton's theorem to analyze the modules’ stability directly. Due to the advantages of modular modeling, this method also offers generality and scalability. Subsequently, a self-defined stability margin criterion based on the Gershgorin circle theorem is proposed. This criterion can determine the ac bus voltage stability state of the actual system accurately. Compared to the generalized Nyquist stability criterion, it permits the definition of stability margins based on system requirements prior to the system design. In addition, the proposed criterion enables the determination of parameter thresholds at the stability boundary with minimal computational effort. Finally, the proposed stability criterion is validated through a hardware-in-the-loop platform using the derived dual-port network model of the cascaded system. Theoretical and experimental results agree well.

This work presents the equivalent electrical circuit (EEC) analysis of the 2-way Doherty Power Amplifier (DPA). For this purpose, the sub-amplifiers used in the 2-way DPA are modeled using real voltage sources instead of ideal sources. For the first time, the general voltage and current equations for each node of the EEC are determined using circuit theory with transmission line concepts. The analysis results explain some of the empirical practices carried out in other works to tune the 2-way DPA response, such as offset lines or asymmetrical bias voltages, etc. This analysis allows us to examine the impact that the auxiliary sub-amplifier bias voltage has on the efficiency of the 2-way DPA, suggesting the use of the phase-to-amplitude distortion (AM-PM) of the auxiliary sub-amplifier to eliminate the compensation lines that are commonly implemented arbitrarily in the 2-way DPA, whose objective is to synchronize the output signals of the subamplifiers. The experimental data of a 20 W (43 dBm) 2-way DPA designed and fabricated for a central frequency of 1.875 GHz with GaN transistors validate the proposed idea, resulting in a compact design and a significantly reduced design time.

Introduction to Circuit Analysis and Design

In this paper, Lorentzian norm based adaptive filter (LAF) is implemented to control voltage source converter (VSC) for improvement in power quality of three phase four wire wind based distributed generation system. This control algorithm operates VSC to control the terminal voltage and frequency in allowable range. In addition to above, neutral current compensation, load balancing, reactive power, and harmonic compensation are also carried out. Therefore, in the system, the generator always supplies the active fundamental component of load current. The LAF is derived from a sliding window type objective function with Lorentzian norm of past errors to overcome bad effect of impulsive environment on system. Hence, it is most suitable filter in wind-based distributed generation system application in order to neutralize the effect of wind impulses on the voltage and frequency of the generator. The entire system comprises induction generator, VSC, and star-delta transformer and nonlinear load is developed in MATLAB Simulink followed by a prototype in the laboratory. The control performance of the said filter is evaluated and validated by simulation and experimental analysis. After performance observation, results are found satisfactory.

With the advantages of simple topology, voltage matching, electrical isolation, and bi-directional energy control, Triple Active Bridge (TAB) has become an active exploration and attempt for the flexible interconnection of DC ports. The high-frequency chain current (HFCC) calculation is the crucial step of zero voltage switching (ZVS) regions and current stresses, providing the basis for the subsequent performance optimization of TAB. Due to the number of switches increasing, TAB´s degrees of freedom (the phase shift angles and duty cycles) have multiplied compared with its two-port topology. The existing current calculation methods of TAB are challenging to balance accuracy and simplicity. Currently, the simple and accurate HFCC model considering all the TAB variables can hardly be found in the literature. This paper proposes a unified and novel solution for TAB HFCC calculation based on the superposition theorem, Thevenin theorem, and time domain method. It can get the uniform formula of the HFCC when all the control variables change. Based on the formula derived, this paper further presents the corresponding ZVS and current stress analysis of TAB. A multi-objective optimal control method is proposed, demonstrating efficiency improvement. Moreover, the trade-offs between the control simplicity and optimization effect are analyzed based on the proposed HFCC model. The modulation pattern with the least algorithmic complexity for efficiency maximization is found. The validity and accuracy of the proposed method have been verified experimentally.

Circuit representation, experiment and analysis of parallel-cell triboelectric nanogenerator

An optimal linear system approximation of nonlinear fractional-order memristor–capacitor charging circuit

Traditional equivalent circuit models (ECMs) have difficulties in estimating battery internal states due to the lack of relevant physics, such as the lithium diffusion in active particles. Here we configure a circuit network to describe the lithium diffusion and define it as a new high-level circuit element called diffusion-aware voltage source. The circuit representation is proven equivalent to the discretized diffusion equation. The new voltage source gives the electrode potential as a function of the surface concentration and thus automatically incorporates the diffusion overpotential. We show that an ECM with the proposed diffusion-aware voltage sources (called “shell ECM”) can reproduce the single particle model simulation results, making it a trustworthy easy-to-implement substitute. Furthermore, the simplest shell ECM consisting of a single diffusion-aware voltage source and a resistor is validated against experimental constant-current discharges at various rates. The diffusion-aware voltage source can be used to measure diffusivity by fitting the diffusion resistance against experimental data. The viability of the shell ECM for onboard usage is confirmed by implementation into a battery management system of WAE Technologies. By tracking the internal concentration states, the shell ECM demonstrates robustness to dynamic applied-current profiles.

This paper presents a unified approach for the modeling and analysis of electro-mechanical systems. First, the need for a unified approach is justified in view of the presence of electro-mechanical dynamic coupling. Next, linear graphs are promoted as a useful tool for unified modeling of multi-domain systems, where the existing analogies across domains can be exploited. Finally, Thevenin's theorem is extended to mechanical systems. Specifically, equivalent circuits of Thevenin and Norton are integrated with linear graphs, in the frequency domain, to facilitate analytical modeling. The choice of a particular equivalent circuit is shown to depend on the problem objective. Worked examples are provided throughout to illustrate the approaches presented in the paper.

CHAPTER 25 - THE ARGAND DIAGRAM

A multiconductor interconnect is modeled using resistors and linear-dependent current and voltage sources. The analysis of a high-speed circuit including lossy interconnection buses is then reduced to simulation of the circuit together with the equivalent circuits of the interconnects. The authors present a new method for the crosstalk and transient analysis of lossy interconnects with arbitrary termination circuits. In order to analyze an interconnect containing N signal conductors, they derive closed-form formulas to determine its transfer functions, and they apply the inverse Fourier transform to obtain its time-domain pulse response functions. Two types of equivalent circuit models can be formulated once the pulse response functions of the interconnect are found. The circuit schematics of the models depend on the number of the signal conductors, irrespective of the physical parameters of the interconnect. These models are compatible with standard circuit simulation tools since they consist of linear resistive networks and linear-dependent sources only. Two example circuits are studied to examine the accuracy and efficiency of the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

It has long been known that electrical circuits have equivalent mechanical circuits, and that the correspondence between the two can be established in two ways, namely, either voltage \rightleftarrows force, current \rightleftarrows velocity, capacitance \rightleftarrows compliance, etc., or voltage \rightleftarrows velocity, current \rightleftarrows force, capacitance \rightleftarrows mass, etc. If, however, one searches for a mechanical model which preserves the elegance and strength of Argand's vectorial diagram, in which voltages at or near the center frequency of a band-pass circuit can be represented by stationary or slowly rotating phasors, the classical equivalent mechanical circuits are inadequate, and a new form of equivalence must be adopted. This article describes this new equivalence which is obtained, for a large class of important circuits, by dropping Kirchhoff's laws and utilizing Thevenin's theorem, so that the mechanical models so established give a correct and easily visualized representation of input and output voltages; albeit intermediate points in the electrical circuits do not correspond generally to intermediate points in the mechanical model.

The electricity grid is unidirectional operating in a passive way and consequently it is not yet ready to accept high penetration of renewable energy sources (RES). Further research is required to assess the impact of distributed Photovoltaic (PV) generation on power quality and establish the necessary measures for the restructuring of the electricity grid to ensure its optimum operation. In this paper, appropriate models are developed in order to assess the effects of PV generation. Thevenin's theorem is used to develop the equivalent circuit representing the exact distribution grid behaviour. The Thevenin equivalent circuit in combination with a verified PV system model are employed to study the power quality response of the distribution grid in the presence of PV via simulation and the results are compared to actual measurements yielding good agreement.