Pi Sections Research Articles

Analyzing the Behavior of PI Section and T Section High Voltage Line Models in Harmonic Load Flow

Analyzing the Behavior of PI Section and T Section High Voltage Line Models in Harmonic Load Flow

On the Development of the Theory of Resonant Processes in Power Transformer Windings. Part 3. Transients in a Circuit with Two PI Sections

The development of electrical networks and widely used technical solutions lead to more frequent winding insulation failures in power transformers operating together with cable lines or long busbars, which are caused by resonant overvoltages. Recently, there have been cases of failures of 110–750 kV generator step-up transformers, 10–110 kV distribution transformers, and wind turbine transformers for voltage levels up to 35 kV. In the first and second parts of the article, an attempt is made to develop the theory of resonant processes in power transformer windings. The results of theoretical studies of the frequency responses in a homogeneous chain circuit containing two and four PI section were presented, and conclusions about the voltage resonance occurrence conditions were drawn. The third part of the article presents the results of theoretical studies of transients in a homogeneous chain circuit containing two PI sections. Analytical expressions are obtained for the transient voltage under the impact of a step voltage impulse and a voltage impulse with an exponentially rising front. The influence of the impulse front duration on the free transient voltage component amplitude is analyzed. Analytical expressions for the transient voltage in the considered equivalent circuit under the influence of undamped and damped sinusoidal voltage are given. Expressions for estimating the maximum resonant voltage amplification ratio under the influence of a damped sinusoidal voltage are obtained.

К развитию теории резонансных процессов в обмотках силовых трансформаторов.Ч. 2. Частотные характеристики схемы с четырьмя П-звеньями

In the first part of the article, the results from theoretical studies of frequency responses in a homogeneous chain circuit containing two PI sections were presented, and conclusions about the voltage resonance occurrence conditions were drawn. A circuit with two PI sections has a single independent node and one natural frequency, whereas transformer windings are more complex oscillatory circuits and have a much larger number of natural oscillation frequencies. The second part of the article presents the results from studies of frequency responses in a homogeneous chain circuit containing four PI sections, three independent nodes, and three natural oscillation frequencies. Analytical expressions for the admittances of the equivalent circuit individual parts and the voltages at the intermediate nodes, as well as expressions for the natural frequencies are obtained. Using an analysis of the frequency dependences of the admittances of the equivalent circuit parts, the conditions and frequency ranges under which voltage resonance may occur at the first, second, and third natural frequencies, are shown. It has been demonstrated that for the considered resonant circuits there is a critical frequency above which the conditions for voltage resonance are not satisfied. Formulas for impedances and voltages at intermediate nodes of a chain circuit with an arbitrary number of PI sections are given.

Mil-Std 1553 Cable Modeling for Fault Detection

Amongst major industries, the aircraft industry has gained momentum not only in public transportation, but also in defence, business and space sectors. The electrical, mechanical and electronic systems of an aircraft are all interconnected by different types of cables like hook up wires, cables for high speed data transmission, cables for power transmission, fire resistant cables, co-axial cables etc , with each type of cable having its own specifications. Military Standard 1553 (Mil-Std 1553) is one such cable primarily used for on-board aircraft sub-system communication and monitoring. Mil-Std 1553 protocol defines the physical and electrical properties of the cable. Mil-Std 1553 is a dual redundant bus, that is, there are two channels for a single bus communication. Mil-Std 1553 is prone to faults like opens or shorts because of its continuous wear and tear in aircraft environment. If a faulty cable is operated, then it possesses a high risk to the aircraft system .As of now ,there is no automatic fault detection system employed on Mil-Std 1553. Hence there is a need for automatic fault detection system on Mil-Std 1553 cables before the entire system collapses. In this regard, modeling of Mil-Std 1553 is very important since the developed model can be used for testing of the fault detection algorithm and further prototype development. Here, the Mil-Std 1553 cable has been modeled using SIMULINK/MATLAB. The cable is modeled under two different scenarios: considering only the Test Signal , considering both Test Signal and Data Signal. The cable is modeled considering all its electrical characteristics for three conditions, namely, No Fault condition, Open circuit condition and Short circuit condition. PI section is used as an elemental block for modeling of Mil-Std 1553.

New fish assemblages from the Middle Permian from the Guadalupe Mountains, West Texas, USA

Late Wordian/Capitanian (Guadalupian, Middle Permian) fish assemblages are described from the “McKittrick Canyon Limestone”, Lamar Limestone and Reef Trail Members of the Bell Canyon Formation in the Patterson Hills and the PI section (Hegler/Pinery Members) along Highway 62/180 in the Guadalupe Mountains, West Texas. The assemblages contain chondrichthyan teeth of Stethacanthulus meccaensis, Texasodus varidentatus, Cooleyella cf. amazonensis, C. cf. peculiaris, and the new genus and species Lamarodus triangulus; and buccopharyngeal denticles of undetermined symmoriiform; chondrichthyan scales of eight morphotypes; fragment of an actinopterygian jaw, isolated teeth; the scales of Alilepis sp., Varialepis sp. and undetermined elonichthyid and haplolepid fishes. Using microtomography, the vascularization system has been observed for the first time for the teeth of Texasodus varidentatus and a new taxon Lamarodus triangulus. The distribution of chondrichthyan taxa was analyzed for the known fish assemblages of the Early, Middle, and Late Permian of the world. The end-Guadalupian crisis in the evolution of chondrichthyan fishes involved substantially more taxonomic change than the Permian–Triassic mass extinction.

Advanced teaching method for balanced operations of overhead transmission lines based on simulations and experiment

An advanced teaching method for the analysis of balanced operations of overhead transmission lines has been described in this paper. The proposed educational method combines theoretical, simulation and experimental approaches with the purpose of a higher-level knowledge achievement. Several exercises have been defined and implemented in the teaching process. Some characteristic overhead transmission line steady state regimes, such as Ferranti effect, natural load flow and capacitive overhead transmission line behaviour, have been analysed. The special analysis has been carried out in order to determine the basic characteristics of the switching transients. Software package MATLAB/Simulink has been used for the estimation of system parameters and for the simulation analysis. Different overhead transmission line models have been compared and useful modelling guidelines have been recommended. Experimental calculations have been performed by using a physically scaled system consisting of multiple Pi sections representing 100 km length 400 kV overhead transmission line. The proposed method has been tested within High Voltage Engineering undergraduate course and useful application feedback from students has been obtained.

A Full Frequency-Dependent Cable Model for the Calculation of Fast Transients

The calculation of frequency-dependent cable parameters is essential for simulations of transient phenomena in electrical power systems. The simulation of transients is more complicated than the calculation of currents and voltages in the nominal frequency range. The model has to represent the frequency dependency and the wave propagation behavior of cable lines. The introduced model combines an improved subconductor method for the determination of the frequency-dependent parameters and a PI section wave propagation model. The subconductor method considers the skin and proximity effect in all conductors for frequency ranges up to few megahertz. The subconductor method method yields accurate results. The wave propagation part of the cable model is based on a cascaded PI section model. A modal transformation technique has been used for the calculation in the time domain. The frequency-dependent elements of the related modal transformation matrices have been fitted with rational functions. The frequency dependence of cable parameters has been reproduced using a vector fitting algorithm and has been implemented into an resistor-inductor-capacitor network (RLC network) for each PI section. The proposed full model has been validated with measured data.

A compact wideband harmonic suppressed 10 dB branch line coupler using cascaded symmetric PI sections

This article presents the size-miniaturized, wide-bandwidth, and harmonic-suppressed 10 dB branch line coupler (BLC) using cascaded symmetric PI sections. The complete design equations are derived to obtain the physical parameters of cascaded PI sections. To validate the proposed design, a 10 dB BLC operating at 0.9 GHz is designed, fabricated, and tested. The reported BLC is having dimensions of 0.175 λg × 0.25 λg and is 76.6% smaller than the conventional coupler. The measured results show that the designed coupler fractional bandwidth is >52% and up to 4th harmonic is suppressed with a level better than 20 dB. Good agreement is found between the theoretical predictions and experimental results. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:1610–1613, 2016

Design and Performance Analysis of a PWM dc–dc Buck Converter Using PI–Lead Compensator

This paper presents a proportional–integral–lead (PI–lead) compensator design based on frequency domain specifications to regulate the output voltage of pulse width modulated dc–dc buck converter. In this design, the parameters of PI–lead compensator are tuned in two parts such that the PI section improves the steady-state response, whereas lead section improves the transient response of the uncompensated system. Further, the detailed performance analysis is carried out in order to obtain optimal value of phase margin and gain crossover frequency for dc–dc buck converter. Finally, this control strategy is verified through MATLAB/Simulink simulation and is implemented on an experimental setup using dSPACE DS1104 digital signal processor. The experimental results validate the simulation results and indicate the robustness of the compensator under wide variations in input voltage, load current and desired output voltage.

Mesh analysis for extracting the S-parameters of lumped element RF and microwave circuits

This paper demonstrates the applicability of basic mesh current circuit analysis techniques, usually learned in the first year of engineering studies, to lumped element RF circuits, which are usually taught with more sophisticated analysis techniques. As an example, the S-parameters of the 90° lumped element hybrid coupler is derived using the traditional mesh current analysis, and compared to that of the distributed micro-strip response. The distributed transmission line coupler is transformed into equivalent lumped element PI sections, and then combined for the resulting lumped element coupler. Mesh current analysis is then utilized to demonstrate the equivalence between the lumped element coupler and the micro-strip coupler as well as the ability to easily simulate the effects of finite inductor Q on the circuit's performance.

Improved calculations for no-load transformer switching surges

This paper deals with a modeling of components and calculation of transient overvoltages that build up on the transformer primary terminals after the transformer has been switched off by a vacuum circuit breaker (VCB). The transformer is connected to the circuit breaker by a cable. The transient overvoltages are calculated for different cable lengths, and the cumulative probability of different arc angles is investigated. In this study two cases are considered: transient overvoltages due to steady-state magnetizing current switching, and transient overvoltages due to inrush current switching. It is shown that the case of inrush current switching is worse, as virtual current chopping is possible. The cable is modeled by pi sections, whereas the transformer model is based on a terminal impedance. The VCB re-ignitions are modeled by means of withstand voltage characteristics and high-frequency quenching capability. Due to shortage of field tests, this work uses only literature references to compare the results with actual measurements.

Improved Calculations for No Load Transformer Switching Surges

This paper deals with a modeling of components and calculation of transient overvoltages that build up on the transformer primary terminals after the transformer has been switched off by a vacuum circuit breaker (VCB). The transformer is connected to the circuit breaker by a cable. The transient overvoltages are calculated for different cable lengths, and the cumulative probability of different arc angles is investigated. In this study two cases are considered: transient overvoltages due to steady-state magnetizing current switching, and transient overvoltages due to inrush current switching. It is shown that the case of inrush current switching is worse, as virtual current chopping is possible. The cable is modeled by pi sections, whereas the transformer model is based on a terminal impedance. The VCB re-ignitions are modeled by means of withstand voltage characteristics and high-frequency quenching capability. Due to shortage of field tests, this work uses only literature references to compare the results with actual measurements.

Microgimbal torsion beam design using open, thin-walled cross sections

A thin-film micromolding process enabled the construction of microtorsional springs with unique cross-sectional designs by combining high-aspect-ratio beams with horizontal surface features. Cross sections such as T-bars, pi sections, and channels were utilized in creating torsional springs with low torsional stiffnesses and high in- and out-of-plane bending stiffnesses. Experimental modal analysis was used to determine torsional stiffnesses as low as 0.13 /spl mu/N/spl middot/m/deg with T-bar springs 45 /spl mu/m tall, 50 /spl mu/m wide, and 100 /spl mu/m long. Springs of the same outer dimensions but with solid rectangular cross sections were calculated to have torsional stiffnesses of at least two orders of magnitude greater. Several microgimbals were constructed using the thin-film micromolding process with various torsional spring designs. Modal analysis was used to experimentally determine pitch and roll natural frequencies. Torsional stiffness models for open, thin-walled sections that included warping effects were developed and used to analytically predict the torsional natural frequencies of tested spring designs to within 20%.

Comparison of Waveshape Quality of Artificial Lines Used for Short-Line Fault Breaking Tests on HV Circuit Breakers

The authors present a comparison of the waveshape quality of six different artificial-line circuits used to produce the high rate-of-rise of recovery voltage specified by ANSI and IEC standards. For a purely capacitive and inductive pi-section circuit, it is shown that even eight pi sections do not meet the requirements. With the addition of a resistance in the first branch, this circuit design produces adequate solutions but requires a large number of components. The analysis reveals that the KEMA circuit easily meets the requirements for the rated peak factor of 1.6 but for the 1.8 peak factor a compensation would be required for the initial part of the wave. The simplest circuit comprising only three (RLC) components meets the specifications with a high voltage-peak overstress factor of 1.3. >

An algorithm for digital impedance calculation using a single pi section transmission line model [Discussion with author reply

The full paper by W.J. Smolinski appears in IEEE Transactions on Power Apparatus and Systems, Vol. 98, No.5, Sept./Oct. 1979, pp. 1546-1551. The discussion and closure were inadvertently omitted and are given herein.

An Efficient State Variable Transmission Line Model

Lumped models of distributed systems (power transmission lines) are considered. It is shown that models derived by a finite Fourier cosine transform are quite efficient, when compared to conventional pi and tee section models, in that the number of state variables is minimized. This paper is an introduction to the use of distributed system "modes of response" in developing these lumped models for single and multiconductor transmission lines including ground conduction and skin effect.

Preliminary Attempts at Restoration of the Sung Dynasty Seagoing Vessel in Ch'uan-Chou Bay

When the Sung dynasty seagoing vessel was unearthed in Ch'üan-chou Bay, the structure above the pi section (area between the two sides at the bottom of the vessel which was commonly called the "fan-shen", likewise below) was completely destroyed. Basically all that was left was the bottom section of a vessel. The keel was perfectly preserved; it had a joint [joining two sections] and an overall length of 17.65 m. The front section was joined by a tenon to a bow-post (i.e., the upright wood that ran at an angle from the bow of the vessel [down] to the main keel). The bow post was 4.50 m. long and was slanted at an angle of 65°. From the keel to the broken perimeters [of the hulk] on both sides were preserved fourteen planks; these fourteen hull planks were arranged into a five-step-shaped structure. The first through the fourth steps formed an oblique line, and each step protruded 5 cm., and each had three to four planks, all of which were overlapped in two layers. The fourth step planks had four rows which protruded 10 mm. and were structured in three layers. The fourth step was built along the straight line stretching from the first to the fourth step as it rose toward the vessel's surface. It was slightly arched. At the shou section (the bow, likewise below), in addition to the bow post, there was also preserved partial hull planks. At the wei section (the stern, likewise below) there was preserved the bottom half of the rudder mount as well as several stern hull planks. The diameter of the rudder cavity was 38 cm.; the mouth of the rudder cavity was 30 cm. across; the rudder post was angled at 22°. At the aft section were still preserved the remains of a piece of a capstan shaft. Although some hold bulkheads of the vessel were destroyed, the position of the thirteen holds was clearly visible. The walls of the eighth hold, which was relatively well preserved, were formed of lap tenons from the sixth cross plank, a total height of 1.98 m.; the tenon grove on the uppermost cross plank was still preserved, which makes clear that this point was not the uppermost. The watertight holes were all preserved, positioned in every hold wall contiguous with the location of the keel, and all used high-quality timber - they were made from camphorwood and cedar. Especially well preserved were the front and middle mast mounts in the first and the sixth holds.

An Extension of the Concept of Stop and Pass Bands of a Zobel Type Filter to a General Reciprocal Two Port Network Which has a Non-loxodromic Transformation (Correspondence)

The conventional treatment of the Zobel filter starts with symmetrical T or pi sections of pure reactance and then develops the iterative measures of the network; the fixed points and the propagation constant. It is shown that the propagation constant is either pure real (stop band) or pure imaginary (pass band). These iterative measures can be worked out for the general T section. Fig. 1 shows the nomenclature used for the symmetrical T section and the general two port.

A Simple Circuit for Frequency Standards Employing Overtone Crystals

A simple oscillator suitable for use as a primary standard of frequency has been developed. Employing a new quartz crystal unit operating in the fifth overtone mode at 5 megacycles, this oscillator has exhibited a frequency stability better than 1 part per billion over periods of several hours; over extended periods the frequency drifts less than 10 parts per billion per month. The oscillator comprises a single stage Class A amplifier with a pi section feedback network; this circuit minimizes the influence of variations in electron tubes and circuit components. Class A operation is accomplished by amplified automatic amplitude control that also holds the crystal dissipation to less than a microwatt. A novel feature is use of a resistor in parallel with the crystal to suppress oscillation at the fundamental and unwanted overtone frequencies, without significantly affecting the frequency stability.

A Microwave Impedance Bridge

A six-arm waveguide structure is described which is a true microwave equivalent of a Wheatstone bridge. A theoretical analysis of the equivalent circuit of the device has been made, using the symmetry properties of the structure. The resulting relation among the admittances of the various arms is exactly that of a Wheat-stone bridge with shunting susceptances across each pair of terminals. A device of this sort for use at 10 cm has been built and tested, and was found to behave as predicted. With this bridge it is possible to measure any impedance to about the same accuracy as with a standing-wave detector. A valuable feature of this instrument is that the standard impedances required are three variable reactances (movable shorting plungers) and a Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> termination. The data are obtained in the form of three lengths, the positions of the movable shorts. Since the device is the complete equivalent of a Wheatstone bridge, it can also be used as a four-terminal lattice section in filter design or in any other related application requiring the microwave equivalent of a lattice section. This allows all the greater flexibility which lattice sections have, as compared to tee or pi sections commonly used in microwave work.