2 - Circuit Analysis: A Graph-Theoretic Foundation

Introduction to Circuit Analysis and Design

Introduction to Linear Circuit Analysis and Modelling

Optimal design and dynamic performance analysis of a fractional-order electrical network-based vehicle mechatronic ISD suspension

Modern societies would not survive without electricity and at the same time electrical faults could cause and have caused many catastrophes—mainly deadly fires—to our societies. There are two types of electricity sources: the voltage source such as generators, charged batteries and capacitors, and the current source such as charged inductors, current-regulated rectifiers, and superconducting magnetic energy storage. An “ideal” voltage source—that is often-sought-or-intentionally engineered—generates a constant voltage irrespective of its load current, and an “ideal” current source injects a constant current irrespective of its load voltage. However, two problems exist: (1) voltage or current sources do not represent many emerging natural/renewable energy sources such as wind turbine generators, photovoltaic cells, and fuel cells, whose output voltage and current are strongly dependent on each other, and (2) a short-circuit fault to an artificially-made and controlled “ideal” voltage source or an open-circuit fault to an “ideal” current source can cause catastrophic failures of the source itself and its surrounding circuits due to large (theoretically infinite) short-circuit current or open-circuit voltage. Here we introduce an impedance source concept to represent, characterize, and model those electricity sources whose output voltage and current are strongly dependent on each other. First, we found that many electric sources with no feedback (or active) control of their output voltage and/or current are a natural impedance source with inherent fault protection at short-circuit or open-circuit faults. Second, any electrical source can be artificially controlled to mimic a natural impedance source. Finally, we show how to apply natural impedance sources and nature-mimicking artificially-controlled sources to the electricity grid—the most complex machine ever made by human beings—to realize electricity grids that are naturally stable, self-protected against electrical faults, and resilient to natural and human-made events.

This paper implements low‐cost GaN‐based three‐phase voltage and current sources to validate power protecting relays. This proposal develops a voltage generator that uses three single‐phase full‐bridge converters equipped with an LC filter and an isolating transformer. It also includes a current generator using three single‐phase half‐bridge converters furnished with an LCL filter. Both voltage and current testing sources are assembled employing GaN transistor technology, which enables operation at high switching frequencies and passive filters with low‐value components. Experimental tests are conducted to confirm and validate the operation and dynamic performance of voltage and current testing sources. Finally, the performance of the voltage and current signal generator is assessed by testing a commercial protection system (SEL‐451) through directional current function. This is achieved by emulating a fault condition, where three voltage and current signals are generated to trigger the trip signal after surpassing the relay threshold.

This paper describes a method to avoid the singular problem at the “S‐control” algorithm. The “S‐control” is proposed to determine the correct operating state in any bipolar transistor network (BTN). Each diode of the Ebers‐Moll model is replaced with a directional switch called an S‐branch which has “on” and “off” states. The switch status is changed by the S‐control algorithm. However, the matrix singular problem occurs in the process of the S‐control. The singular matrix is formed by a cutset of only current sources or a loop of only voltage sources. The singular problem is solved by the signdiscrimination method by which the sign of each node voltage is judged by the introduction of small immittances in cutset (loop) of only current (voltage) sources formed in process of the S‐control. The S‐control algorithm will be continued to obtain the next switch state unless the limit cycle is not generated.

Many combinatorial optimization problems such as the min cost flow problem are equivalent to the solution of appropriate DC circuits made up of positive resistors, voltage sources, current sources and ideal diodes. Simulating the DC circuit is an alternative approach to the approximate solution of such problems. However, conventional simulators such as SPICE are too slow for this purpose. This paper describes the structure and performance of a fast DC analyzer built at EE department, IIT Bombay specifically for solving large circuits consisting of positive resistors, voltage sources, current sources and diodes. Using the simulator, we have analyzed circuits composed of diodes, positive resistors, current and voltage sources of size up to 700,000 nodes and 1.2 million edges on a 3.0 GHz, 1GB RAM, PIV processor in at most 1.2 hrs. We also report a comparative study of the performance of our DC analyzer with that of fastest commercial simulator.

Expansion and reorganization of water distribution networks by connecting sub‐networks via single or multiple pipes are common practices in developing cities to serve newly developed areas. In that context, the existing large network is often replaced with its equivalent simplified network for the optimal design of the upcoming sub‐networks to avoid the computational burden. The reservoir‐pump model is frequently used by practicing hydraulic engineers to replace an existing one; however, such a model should be applied only when the networks are connected through a single pipe. In this study, a new network reduction methodology is developed for multi‐port connections utilizing the analogy between electrical circuits and hydraulic networks. The equivalent simple network is obtained by suitably applying the generalized Thevenin theorem for electrical circuits. The number of network elements in the equivalent network is significantly reduced compared to the ones obtained by the existing water distribution network (WDN) reduction methods. Therefore, it is possible to reorganize and expand a large existing network system from a prior knowledge of its most sensitive parts. The accuracy and robustness of the proposed methodology are investigated on realistic WDNs by comparing the results with EPANET, for both Demand Driven Analysis and Pressure Driven Analysis. However, as of now, an electrical simulator is required to implement the proposed methodology due to the absence of current dependent voltage source model in hydraulic simulators. The proposed network reduction method can be of enormous utility for hydraulic engineers and opens up an opportunity to implement new elements in hydraulic simulators.

a.c. circuit analysis

The calculation of electrical transients in power systems is important for insulation coordination. Most of the compiiter programs in current use are based on the nodal admittance method. This paper describes a computer program for the calculation of electrical transients based on a new approach which enables the use of more sophisticated numerical integration routines. The program can cope with linear network elements like resistors, capacitors, reactors, voltage and current sources and also with non‐linear network elements like surge arresters and arc models. The description of the models and their parameters is stored in libraries separate from the main program. The user can define his own models.

– We propose a fast simulation model of wind generator with a frequency converter, such as a doubly-fed type. The aim of the model is to provide a model that can evaluate an impact of wind generator system (WG) on utility side in both transient and relatively long term normal operation. Through, some simulation software based on root mean square value, for example EUROSTAG, provides a unified method that can handle both short-term and long-term analysis. But it is difficult for RMS based model to handle with a behavior of WG with a frequency converter under system fault condition. So we have developed an instantaneous value based fast simulation model that can handle with both short-term and relatively longer-term analysis.. Keywords : Wind power generation, Fast simulation model, Simplification for converter 1. Introduction The integration of wind generator system (WG) has large influences over a variety of operational conditions. These operational conditions vary from short-term, such as a transient behaviour during a fault, to longer-term, such as power fluctuation under a normal operation. In order to harness WG successfully, the impact of WG must be analyzed in both short and long term. As a result, both short-term and long-term simulation models for WG are required, and it is high burden in view of cost and maintenance. For longer-term analysis, the focus point is mainly active and reactive power swing due to wind fluctuation, and a simulation model based on root mean square value (RMS) is suitable. There are already some RMS based simulation tools that can handle with both long and short term analysis, such as MATLAB. But, in short-term analysis, a simulation model for WG should be represented in detail manner, and a model based on an instantaneous value is appropriate. Because, under a fault condition, WG with FRT(fault ride through) function acts in complex manner, and the behavior during a fault condition could have a large impact over a subsequent longer-term situation. It means that a simulation model for WG based on an instantaneous value is suitable. But it is very time consuming to conduct a long-term analysis with a model based on an instantaneous value. To solve this problem, we have developed and evaluate a fast simulation model for WG based on an instantaneous value that can handle with relatively longer-term analysis. In this study, we first developed a simulation model for WG to conduct both short-term and long-term analysis. Our aim of the model is to evaluate an impact of WG on utility side. The developed model is doubly-fed type. It includes pitch control, frequency conversion, start-up and shut-down function, and FRT(Fault Ride Through) so that we can evaluate WG under a various operational conditions. Then we applied a simplification method to the simulation model so that the model can handle with relatively longer-term analysis. The method of simplifica-tion is to model self-commutated converters in frequency converter as a pair of voltage and current source. The AC side of converter is represented as a voltage source, whereas the DC side of converter is represented as a current source. Through this kind of simplification may be popular in simplifying a self-commutated converters, we do not see any report that evaluates this simplification method under various operational conditions of WG. So, we evaluate this simplification method in this study.

Nonlinear loads are always needed to operate electrical equipment. Example, motor drives, inverters, rectifiers, etc. However nonlinear loads can create electrical power quality problems such as harmonic. Harmonics has two sources, voltage source and current source. To reduce voltage harmonic distortion, a shunt passive filter can be used. Meanwhile, to reduce harmonic current distortion can use a series passive filter. What if there is harmonic case that has voltage and current source, a combination of series and shunt passive filters is needed. There are two types of passive filters, namely single tuned shunts and C-type passive filters. The first model uses combination of series and shunt single tuned passive filter. Next this combination is called HPF1. The second model uses combination of series and C-type passive filters. Next this combination is called HPF2. The third model uses Harmonic Power Sharing (HPS). Then all of these combinations are tried in case studies. The results of the experiment are that HPF2 has the best results of all models in reducing THD and IHD-V, but HPF1 has the best results than all models in reducing TDD and IHD-I. Although the TDD values are not too much different.

Standard converter topologies are usually presented with a voltage source as the input supply to the converters. However, a photovoltaic (PV) array has the I-V characteristics of a current source not a voltage source. This thesis details the design process of modifying the standard Buck and synchronous Buck converter topologies to function with either a voltage or current source input, making them universal DC-DC step down converters. This is accomplished by placing a capacitor at the converter's input to supply the pulsating current required for the Buck topologies to function properly. The equations for determining the capacitor's size and RMS current rating are derived, and a prototype of each topology was constructed and analyzed. Also, the issues that arose during the integration of the converter's into the SuPER system are discussed. The Cal Poly Sustainable Power for Electrical Resources (SuPER) project seeks to build a stand alone photovoltaic (PV) unit that can supply the energy needs of a single family home. Before the start of this thesis the SuPER project was using an off-the-shelf DC-DC converter to step down the PV array's voltage, perform maximum power point tracking, and act as a charge controller for the battery. One goal of the project is to have a Cal Poly built DC-DC converter that can perform all the functions of the off-the-shelf DC-DC converter currently being used.

The work presented in this article investigates the behaviour of the current in the load impedances of a lossless coaxial cable, with homogeneous metalic shielding, presenting an electrically small aperture defect in the shield. The cable, located above a ground plane, is illuminated by a plane wave. The initial problem was broken up into two separated problems treated by Transmission Lines theory [1]. The aperture penetrating field, is initially modelled by a couple of electric and magnetic dipoles [2]. According to the formalism of C. D. Taylor and C. W. H. Harrisson the aperture can be represented by a voltage and current sources [3]. The external line is described using standard Transmission Line Theory. The internal line takes into account the diffusion and diffraction effect with localised elements to simulate the associated parasitic sources. Circuit analysis has been made using the software EMCAP 2000. Influences of electric and geometric parameters have been investigated in the frequency domain: 10 KHz-1GHz.

The first Electric Circuits course is a core component of all engineering undergraduate curricula that include not only Electrical but other engineering disciplines such as Computer, Mechanical and Civil Engineering programs worldwide. The Electric Circuits Concept Inventory (ECCI) is a set of multiple choice questions that measures students' understanding of DC Circuit analysis. The topics include (i) fundamental conceptual circuit topics (ii) Circuit laws and (iii) Circuit analysis techniques. In a companion paper [1], we presented a rationale for ECCI. In this paper, we present a set of multiple-choice questions suggested for inclusion in the ECCI focusing on (ii) DC Circuit laws and (iii) DC Circuit analysis techniques. We examine the various concepts tested in each question and relate its importance to a quality overall course in Electric Circuits. We welcome more additions to this growing repertoire of questions that we plan to build and use in finalizing the ECCI test especially in AC Circuit analysis topics.