Internal Reactance Research Articles

Designing Air-Cored Axial Flux Permanent Magnet Generator with Double Rotor

The development of renewable energy is carried out to reduce the use of fossil energy, which is decreasing in existence, increasing in price, and having a very long recovery cycle. One of the uses of technology to support renewable energy development is a synchronous machine that can be used to utilize wind and water energy. One type of synchronous machine that is widely used today is the radial flux machine. However, there is a saturation point in their development. Axial flux machines also called disc type machines, are an alternative to radial flux machines due to their compact shape and high-power density. Axial flux machines can be operated as small to medium-scale power plants. Besides that, they are ideal for low-speed applications. An axial flux permanent magnet (AFPM) generator is designed and built in this study. This generator design consists of a dual rotor with twelve permanent magnets and a single stator with nine coils. The primary material used for the stator and rotor is acrylic, while the permanent magnet uses neodymium N52. It is necessary to know the stator and rotor parameters such as distribution factor (kd), pitch factor (kp), and winding factor (kw) for designing the AFMP generator. The AFPM generator is designed to produce a phase voltage of 4.03 V at a nominal speed of 500 r/min. Based on the measurement results, it was found that the phase voltages at a rotating speed of 500 r/min for each phase are VR = 2.94 V, VS = 2.97 V, and VT = 2.95 V. There are differences in the test results and the design. It can be caused by design simplicity that does not consider magnetic saturation and internal reactance, which cannot be ignored but is not included in the calculation.

Analysis of the Interactive Influence of the Active Power Recovery Rates of DFIG and UHVDC on the Rotor Angle Stability of the Sending-End System

At present, systems for wind power transmission by ultra-high voltage direct current (UHVDC) and ultra-high voltage alternating current (UHVAC) have been constructed and are operating in China. The installed capacity of the doubly fed induction generator (DFIG) and the rated power of the UHVDC in a system involving wind power transmission by the UHVDC/UHVAC (WIND-UHVDC/AC) are very large, and the active power recovery rates of the DFIG and UHVDC after a short-circuit fault is cleared will seriously affect the rotor angle stability of the sending-end system. Therefore, it is significant to analyze the active power recovery rates of the DFIG and UHVDC for the safe operation of the WIND-UHVDC/AC system. First, the influence of the active power of the DFIG and UHVDC on the electrical power of the synchronous generator (SG) in the sending-end system is deduced mathematically. Second, the impact of the active power recovery rates of the DFIG and UHVDC on the deceleration areas of the SG are analyzed, respectively, and the effects of the variation in the equivalent internal reactance of the SG on the leftward shift and downward shift of the electrical power curve are studied. Then, the mechanism of the interactive influence of the active power recovery rates of the DFIG and UHVDC on the rotor angle stability is further analyzed. Finally, the theoretical analysis is validated using a typical WIND-UHVDC/AC system and an actual WIND-UHVDC/AC system in China's Northwest Power Grid. The analysis in this paper provides a theoretical foundation and a reference for the stability control strategy for the WIND-UHVDC/AC systems.

Rotor Speed-Free Estimation of the Frequency of the Center of Inertia

This letter proposes a formula to estimate the frequency of the center of inertia based exclusively on measures of bus frequencies, obtained, for example, from phasor measurement units, the network admittance matrix, and two parameters of synchronous generators, namely, the inertia constant and the internal reactance. The proposed formula can be utilized online and requires a highly reduced set of measures of bus frequencies. The letter discusses the theoretical background of the proposed expression and tests it with a 1479-bus model of the all-island Irish transmission system.

Study on dispersion phenomena of electromechanical disturbance propagation in power systems

Summary The physical phenomenon of electromechanical disturbance propagation has been modeled in the form of a wave. Usually wave has dispersion features while propagating with a nonlinear medium. In this paper, the dispersion relation of discrete- and continuum-model for the power system is derived. And then, the influences on dispersion characteristics of different factors (such as generator internal reactance and transmission line resistance) are studied. The relationships of the propagation velocity and attenuation characteristics of disturbance with the power grid's parameters are revealed. Finally, this paper shows simulations based on a chain system and a New England benchmark system to help to validate the rationality and accuracy of the theoretical analysis. This work is helpful to analyze the electromechanical oscillations of power systems and control the propagation of disturbance. Copyright © 2016 John Wiley & Sons, Ltd.

Analysis of delta-omega and fuzzy logic power system stabilizers under several operating conditions

Power system stabilizers (PSSs) have become very common in the operation of large electric power systems. The stability of electric power systems is increased by the use of power system stabilizers. It is a challenging task to design a stabilizer that delivers good performance in a wider range of operating conditions and under disturbances. This paper presents a fuzzy logic power system stabilizer (FLPSS) and demonstrates the good performance of this stabilizer under a wide range of operating conditions and disturbances. The performance of FLPSS is compared with that of a speed deviation (delta-omega) PSS in the variation of four different operating conditions, i.e., inertia constant (H), automatic voltage regulator (AVR) gain (Ka), internal reactance (Xe), and reactive power (Q).

Negative Permeability of Single-ring Split Ring Resonator in the Visible Light Frequency Region

AbstractNegative permeability of single-ring split ring resonator (s-SRR) is theoretically investigated in the visible light frequency region [1, 2]. To estimate magnetic responses of conductive elements precisely, we determined internal impedance by considering the delay of the current inside the metal structure. The increase of the surface resistivity, which is the real part of the internal impedance, results in the decrease of the resonator's Q-value. This means the degradation of the tunable range of the permeability. The increase of the internal reactance results in the reduction of the resonant frequency. In our calculation, the surface resistivity saturates at the inherent frequency of each metal as the frequency increases. On the silver case, the saturation value is 0.4 Ω and this value is remarkably smaller than that of gold and copper. On the other hand, the internal reactance is increasing as the frequency increases independently of metal. We concluded that the internal reactance is dominant factor to realize the negative magnetic permeability in the optical frequency region. We also show the frequency dependence of the magnetic permeability of s-SRRs. In the case of s-SRRs made of copper, the minimum value of the magnetic permeability becomes positive value at 550 THz even in the high filling factor condition (11%). In the case of s-SRRs made of gold, only on the filling factor was 11%, the minimum value of the magnetic permeability takes negative value in the entire visible range. On the other hand, the silver SRR exhibits negative magnetic permeability in the visible range even under the low filling factor condition of 3%. Moreover, we concluded that reducing the geometrical capacitance and using silver for SRR are necessary to realize the negative magnetic permeability in the visible light range.

Power system short circuit planning for superconducting power transmission

Short circuit capacity of large power generation facilities is limited by the internal reactance of the generator and the impedance of connecting bus work and transformers. In the event of a fault on a generator get away circuit, d-c offset could double the short circuit current on the cable for a period of from 3 to 5 cycles after the fault initiation. High performance circuit breakers (PCBs) can shorten this fault duty time to 1 cycle (17 msec). If a superconducting cable is arbitrarily designed for 10X rated current fault withstand, its capital and operating cost may be dramatically increased. What can be done? First, a careful look at generator step up transformers and circuit breaker capability shows a marked tendency for this equipment to have very high costs if the generator bus connection scheme is planned to allow very large fault currents. However, the power system designer can set up the circuit arrangement so that massive fault currents are avoided. Second, the development of fault current limiting devices promises the possibility of holding fault current levels below 2X or 3X rated current. DC superconducting cables do not require this extra fault duty consideration, because the rectifier inverter system protects them. Usual fault conditions on d-c cable are such that less than 2X rated current will occur on the cable during a fault. Because a-c superconducting cables include very high fault current capability in their design, a careful trade-off study with current limiters, generator bus layout alternatives and possible d-c cable application should be done to assure that the final design may more readily achieve reasonable economics.

Effective resistance and reactance of a conductor of trapezoidal cross-section placed in semiclosed slot

The paper is an extension of a previous one and discusses the distribution of current in a conductor which has a cross-section in the form of a symmetrical trapezium and is placed in a slot with a narrow opening. An approximate solution is obtained by assuming that the upper and lower surfaces of the conductor are defined by concentric cylinders. It is found that the current density at any point may be expressed as an infinite series of Bessel functions, each term involving an arbitrary constant which is determinable by reference to the assumed boundary conditions. From this result, the complex impedance per unit length of the conductor is determined and hence also the effective resistance and the internal reactance.

Conditions for optimum noise performance of transistor amplifiers with a reactive source

When driven from a purely reactive source, conventional noise figure is undefined for a two-port network such as an audio amplifier. In order to assess the noise performance of small-signal amplifiers driven from reactive sources such as capacitor microphones, a signal-to-wideband-average-noise ratio is defined. It is shown that for transducers where output is related to internal reactance by a simple transformer relationship and where the Thevenin equivalent internal impedance is a pure series R and L or C , there exists an optimum value of internal reactance for maximum signal-to-noise ratio when used with a given noisy amplifier. The equations for optimum reactance and signal-to-average-noise ratio are general and include low-frequency dependence of the transistor noise generators, equalization or frequency dependence of amplifier gain, and source resistance as well as reactance. Solutions are given for the practical audio case with typical low-noise audio transistors for both inductive and capacitive transducers.

The Realization of High-Frequency Impedance Standards Using Air-Spaced Coaxial Lines

Impedances of devices with coaxial inlets, having small reflection coefficients relative to a given characteristic resistance, can be determined accurately (± 0.1 per cent) by comparison with the nominally calculable characteristic impedance of a quarter-wavelength, air-spaced coaxial line in which the inner conductor is supported by the inner conductors of the apparatus connected at each end. In carrying out such comparisons, errors may be introduced by the presence of small series impedances at the connections between the rigid coaxial lines. Such connections cannot be eliminated because they must be made and broken during the process of making comparisons. Errors may also arise from the distributed resistance and the internal reactance of the line conductors, as well as from departure of the lines from uniformity in diameter. This paper describes experimental techniques for measuring these residuals and discusses their effects. The design requirements of suitable air-spaced coaxial lines as standards are stated, together with a brief mention of techniques for making comparisons with the standards.

Effective resistance and reactance of a solid cylindrical conductor placed in a semi-closed slot

The paper is concerned with the investigation of the current distribution over the cross-section of a solid cylindrical conductor lying in a slot with a narrow opening. It is found that the current density at any point is expressible as the sum of an infinite series of Bessel functions, each including an arbitrary constant which is determinable by making a reasonable assumption regarding the boundary conditions. By means of this result it is possible to determine the complex impedance of the conductor, and hence its equivalent resistance and internal reactance per unit length.

Electrical precipitation of solids from smelter gases

The fundamental principles of the process in its simplest form are set forth. It is shown why the Cottrell process during recent years has in a large measure supplanted the bag-house and dust chamber in treating smelter gases. The commonly accepted theory concerning the manner in which the dust particles is charged and precipitated is given. It is pointed out that the thing most important to the operating man is how the particles may be enabled to give up their charge to the electrodes under all conditions, rather than the manner in which they receive it. The various types of treaters in common use are described and discussed. The advantages of straight line treaters over those in which the gases are by-passed are emphasized. It is shown that the gas is ionized much more efficiently for a given power consumption and the construction simplified and reduced by arranging the electrodes in the flue so that their electric fields are in series with each other. It is shown that this is accomplished by causing the gas to flow parallel to the electrostatic lines instead of at right angles to them, as in all other types. The factors of lead and copper metallurgy are given which control the amount of sulphuric acid and water vapor in the gases. It is also pointed out that these things are a measure of the successful operation when treating smelter gases. The physical rather than the chemical structure of the dust in suspension is shown to be the all-important matter. Several theories are given as to why flue dust is so much easier precipitated than fume. A number of photo-micrographs are given to illustrate the difference in physical structure between fume and dust. Two methods are featured of obtaining sufficient conductivity in a dry precipitated coating to permit the electric charge to leak through it to the electrode. The theory of selective absorption is advanced as an explanation of how aqueous vapor added to the gas stream functions in this respect. The method of adding very finely atomized sulphuric acid is shown to be the most practical, it not having certain disadvantages of the water and its higher boiling point permitting a wider field of application. Its action is shown to be due to the fine acid particles being precipitated with the dust particles thereby imparting conductive film to the particles by diffusion. The amount of free sulphuric acid in grams per 1000 cu. ft. of gas which permits a good precipitation on gas without conditioning is given from tests made on a large installation. The theory of back ionization and phenomena of discontinuous dielectric are discussed. Electrical matters are shown to be secondary to treater design and to the conditioning gas. All that can be expected of electrical equipment is to stress the space between electrodes to the economical limit. Local conditions must govern choice of electrical equipment. The tendency to regard electrical phenomena, such as surging which as a rule accompanies poor precipitation as causes rather than effects, is cited. Effects of conditioning gas in reducing surges is shown. Internal reactance in transformer best suited to precipitation work is discussed, also possibility of exceeding the practical limit and wasting power on treatable gas by carrying voltage up to the point of disruption; necessity of knowing electrical values in the treater, and these are best obtained with milliammeter and electrostatic voltmeter; finally, the subject of proportioning the plant investment between electrical equipment and treater is covered.