Phase Angle Errors Research Articles

In- situ measurement of the current transformer burden in a current transformer testing system using a shunt resistor

Both the ratio error and phase angle error of a current transformer (CT) are significantly affected by the CT burden connected in series to the secondary terminal of the CT. Thus, the precise measurement of this CT burden is required for the evaluation of the CT errors. A method for measuring the CT burden in- situ in a CT testing system (CTTS) has been developed by employing the non-reactive type shunt resistor. For the measurement of the CT burden, the shunt resistor was connected in parallel to the secondary terminal of the CT under test in the CTTS. The burden values represented by the apparent power and the power factor can be calculated from the resistance (and reactance), which was obtained by measuring the ratio error (and phase angle error) as a function of the resistance of the shunt resistor. The uncertainties in the measurements of the apparent power and the power factor for the rated burdens studied were found to be less than 2.1%. The CT burden values obtained using our method were consistent with those measured using a digital multimeter within the corresponding uncertainties.

Precise vector control of CSI fed induction motor drive

A new, precise vector control algorithm for the current source inverter (CSI) fed induction motor drive is presented. The goal is to obtain the same performance that exists in PWM vector controlled drives. For that purpose, the problems of the existing vector controlled CSI fed induction motor drives are analyzed with the help of an adequate simulation model. For verification of the suggested algorithm, the prototype of the drive is developed. The frequency converter is a standard thyristor CSI and the complete control is implemented by software in the microcontroller. By eliminating the phase angle error and correcting the error of current magnitude the algorithm proposed in this paper can improve the dynamic performance of the CSI fed induction motor drive. The simulation and experimental results confirm the advantage of the proposed algorithm. Copyright © 2005 John Wiley & Sons, Ltd.

Simulation of Fractal Immittance by Self-Similar Ladder Circuits

Self-similar ladder circuits, with each set of R, C or L forming a geometric progression, have been examined as simulating fractal immittance, Y(ω)∝ωa or Z(ω)∝ω-a (0<|a|<1) with optional a-values. The correlation between the number of rungs n and the optimum bandwidth has been numerically calculated against a given criterion with respect to the phase angle. A five-decade bandwidth with a phase-angle error of ±1° was found to be attainable for |a|=0.25–0.75 by fourteen rungs or less, indicating the availability of self-similar ladders for hardware simulations of fractal immittance.

A Practical, Precise Method for Frequency Tracking and Phasor Estimation

Comprehensive analysis of discrete Fourier transform (DFT) error is given in this paper, including why it is accurate when used in the case of synchronous sampling and how error rises when sampling frequency does not synchronized to signal frequency. Simple but precise expressions of phase angle error and amplitude error are given. Practical formulas to calculate the true phase angle and amplitude are presented. The formulas are very simple and precise. Based on the formula to calculate true phase angle, a new frequency tracking method is developed. The proposed method can be calculated recursively. And, with notable accuracy improvement, the calculation burden is little more than the traditional DFT method. Also, an adaptive method to suppress the effect of harmonics is presented, which adds very little calculation burden with satisfying performance. The most distinguished feature of the proposed method is that it is not only precise, but also simple. Some examples are given to demonstrate the feasibility, precision, simpleness and robustness of the proposed method.

Frequency behavior of self-similar ladder circuits

The fractal immittance, Y ( ω )∝ ω a or Z ( ω )∝ω − a (0< a <1) with an optional a -value, has been found to be simulated using self-similar ladder circuits with each set of elements, R or C , forming a geometric progression. The optimum bandwidth B op is numerically calculated for a given criterion with respect to the phase angle as a function of the number of rungs n involved in the ladder. B op ≥5 with a phase-angle error of ±1/2° is found to be attainable for a =0.25–0.75 by 18 rungs or less, indicating the availability of the self-similar ladders for the hardware realization of fractal immittance.

On the characterization of voltage and current transducers in steady‐state distorted conditions

AbstractThe traceability of measurements performed to gauge information about the operation of electrical power systems under nonsinusoidal conditions is an important and live issue, usually neglected by the technical Standards. A generalized definition of the “composite error” is proposed in this paper as a meaningful index for the metrological characterization of voltage and current transducers in steady‐state nonsinusoidal conditions. In this connection, the relationship among the composite error, the classical ratio and phase‐angle errors and other parameters characterizing the waveforms of the transduced quantities are pointed out. Finally, problems involved in the measurement of the composite error in steady‐state distorted conditions are dealt with and the results of some experimental work are presented.

Simulation of Fractal Immittance by Ladder Circuits

Fractal immittance FD, expressed by an admittance w α with an optional value of a within the range 0 <a<1, is simulated by ladder circuits with finite numbers of resistors and capacitors starting from the optimized circuit based on the distributed-relaxation-time (DRT) model. Thus designed DRT-equivalent ladder with a = 1/2, e.g., is found to be far more effective than the conventional ladder composed of identical rungs: for the bandwidth of 5 decades with a phase-angle error of ±2°, e.g., the conventional ladder involves 6.426 × 103 identical rungs, while 11 rungs are sufficient for the DRT-equivalent circuit.

Determination of phase angle and amplitude error of voltage and current transformers up to some 100 Hz for loss measurements on power transformers

For the load loss measurement of power transformers, current and voltage transformers with usually extremely low errors of phase angle and amplitude are used. However, even small errors of the measuring transformers may result in an error in the measured load loss. Therefore, national and international standards allow the correction of the measured value by the amount caused by phase angle and amplitude error of the measuring equipment [2–4]. The determination of the errors of phase angle and amplitude of measuring transformers is carried out on the basis of calibrated standard measuring transformers which are traceable to national standard equipment at rated frequency, e.g. at 50 and 60 Hz. For some applications – e.g. the load loss measurement of HVDC power transformers according to the draft of IEC standard 61378-2 [1] – a load loss measurement at frequencies other than rated frequency is required. For that, the errors of phase angle and amplitude of the measuring transformers must be known. This paper describes a method how to determine the phase angle and amplitude errors of the measuring transformers at arbitrary frequencies on the basis of the calibrated error values at rated frequency.

Optimization of Fractal Immittance Networks

Fractal immittance, Y(ω)∝ωa or Z(ω)∝ω−a (0<a<1), is simulated by the analogue circuits composed of resistors R and capacitors C based on the distributed-relaxation-time (DRT) models. The optimum interval of relaxation times to give the widest bandwidth is searched by the numerical calculation. It is found that the bandwidth of 5 decades with a phase-angle error, e.g., of ±0.5° for a =0.25, 0.5 and 0.75 can be realized using twenty or less R-C pairs.

An Exact Analysis of the Electrodynamometer Wattmeter Errors

When analysing electrodynamometer type wattmeters, the common assumption that potential coil current is linearly proportional to load voltage is only true for one of two alternative methods of connecting its current and potential coils. The present analysis avoids this. It also develops a single expression for the correction factor which includes connection and phase angle errors.

Self-field ac loss of Bi-2223 superconducting tapes

The self-field ac loss of a monofilamentary Bi-2223/Ag tape has been measured using an improved lock-in amplifier technique. To investigate the dependence of the ac power loss on the phase-angle error of the lock-in amplifier, theoretical calculations of the ac power loss of a flat superconducting strip in a perpendicular ac magnetic field were performed. The expressions derived also predict the dependence of the apparent loss on the size of the lead extension of the voltage contacts. For zero phase-angle error and an infinite lead extension the Norris formula is obtained. The voltage wave-form for ac current amplitudes greater than the tape's critical current has been measured and calculated. Theoretical predictions agree well with the experimental data.

Source Voltage Sensor-less Digital Control Using Observer for PWM Converter.

For promotion of low-priced and reliable PWM converters, it is important to decrease the number of parts which comprise a PWM converter. The proposed control method realizes an integrated control circuit using inexpensive DSP (Digital Signal Processor) to offer unity input power factor without a source voltage sensor. In the method, an observer estimates voltage instead of sensing it. Then, the phase-angle error between the estimated voltage wave and a sine wave generating input current command is made zero by a phase controller based on the Fourier series. The stability of the system is shown by the Popov's method. Experiments demonstrate the system achieves sinusoidal input current and unity power factor.

KrF excimer laser lithography with a phase‐shifting mask for gigabit‐scale ultra large scale integration

Resolution-enhancement technologies such as alternatingtype phase-shifting masks (PSMs), half-tone PSMs, and the off-axis illumination method in optical lithography are necessary for manufacturing gigabit-scale ultra large scale integration (ULSI) devices. Because an alternating-type PSM is the most effective way to enhance resolution, we examine the resolution capabilities of KrF excimer laser lithography combined with the use of an alternating-type PSM through simulations. Our goal is to apply this technique to attain pattern delineation smaller than 200 nm. We simulate light intensity profiles for various types of PSMs in terms of the 3-D mask structure, and find that a PSM structure with a spin-on glass (SOG) phase shifter on a Cr layer that is thinner than in a conventional mask is one of the best choices for KrF excimer laser lithography. We examine potential problems such as the durability of the SOG phase shifters to KrF excimer laser irradiation exposure, and phase angle error due to the surface topography of the Cr aperture patterns. From our experimental results, we confirm that the optical characteristics of the PSM are not degraded, and the phase angle can be controlled with an accuracy sufficient for gigabit-scale ULSI device fabrication. Improved PSMs with a thin Cr layer and SOG phase shifters were successfully used to fabricate several layers of experimental 1-Gbit dynamic random access memory (DRAM) devices with sufficient resolution capability.

Recurrence of the compound nucleus in neutron resonance reactions.

A semiclassical model of neutron resonance reactions has been developed, where time evolution and the recurrence of the compound nuclear system are explicitly considered. We have derived an average recurrence frequency of a multiple oscillator system as a function of the total excitation energy and oscillator number involved, where the tolerable phase angle error is assumed to be 1 rad. On the compound nuclei formed by neutron resonances, we have deduced effective oscillator numbers M and nuclear temperatures T. These values agree well with the traditional ones. As regards the time evolution of the compound nucleus, we have defined the ``coalescent phase'' where the neutron density is high on the target nuclear surface in a time duration \ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}21}$ s. It appears repeatedly like a pulse array with an interval of recurrence time, and continues during lifetime of resonance \ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}14}$ s. Fourier transforming the coalescent phases, we have found the S matrix, in which neutron reaction cross sections can be derived. They consist of equidistant fine structure resonances, with an envelope of a giant resonance. Triple uncertainty relations between energy and time were derived. Using this model, a smooth shift from the isolated resonance region to the continuum region could be predicted. \textcopyright{} 1996 The American Physical Society.

Single-Phase High Power Factor PWM Converter without Source Phase Angle and Voltage Detectors.

In this paper, the authors propose a current control system of a single-phase PWM AC/DC converter which eliminates detectors of the source phase angle and voltage. The sinusoidal input current and unity effective power factor are realized based on the estimated source voltage in the controller. The feature of the proposed estimation algorithm is that the estimations of the phase angle and crest value of the source voltage are independent each to each. The estimations are performed based on the current error between the actual and model currents. The orthogonal and in-phase components of the current error with respect to the estimated phase angle are proportional to the phase angle and crest value errors, respectively. Therefore, the estimations of them can be realized by feeding back the corresponding components of the current error.The effectiveness of the proposed current control system was confirmed by experiments. The stable estimation and control were achieved.

Compensation of errors in a voltage transformer by an electronic circuit

An automatic self-compensating technique for instrument (voltage) transformers has been presented. With the introduction of such an electronic compensator, even ordinary voltage transformers may behave with high accuracy and precision. Analytical and experimental results show that the compensator brings down the ratio and phase angle errors significantly. The arrangement presented is simple, but constitutes a definite modification of existing methods used for error compensation.

A precision transformer used for an audio-frequency power standard

A precision current transformer for the audio-frequency band in which an auxiliary current transformer equalizes the potential along the primary and secondary windings of the main current transformer is discussed. The arrangement results in a dramatic reduction of capacitive leakage current. In this way, a ratio error of less than 10 p.p.m. and phase angle error of less than 10 mu rad is achieved at frequencies up to 10000 Hz.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Velocity Errors of the Resolver Phase Shifter

An equivalent circuit is derived by applying the theory of two-phase symmetrical components to the rotating resolver phase shifter, in which a resistance and a capacitor are connected to the secondary windings of the resolver, and an output voltage equation for calculation of velocity errors is also derived on the basis of this equivalent circuit. Based on the analysis of the output voltage equation, effects of the rotor speed on the magnitude of the output voltage and the phase-angle error are investigated.

Balancing for a Flexible Rotor Considering the Vibration Mode : 2nd Report, Balancing in which Modal Influence Coefficients Contain Phase Angle Errors

The effectiveness of a modal-least squares balancing method is investigated with regard to a balancing of flexible rotors. The method combines features of both modal balancing and least squares balancing methods. Numerical simulations are carried out with influence coefficients which are assumed to have phase angle errors. The good balancing conditions that were obtained in the second balancing trial are also described.

Current Transformer Accuracy on Pulse-Burst-Modulated Circuits

The performance of metering-type current transformers connected in circuits with Pulse-Burst Modulation was studied. Measurements for Integral-Cycle and Half-Cycle Control are presented. Test results show that, when Integral-Cycle Control is used to regulate loads with power factors less than 0.95 lag, the recurrent transient component of the current could cause unacceptable increases in the current transformer phase-angle error. This paper considers four distinctive operation modes of Integral-Half- Cycle Control. It is shown that for only one of these modes the phase-angle error can be kept within acceptable limits. For this case the thyristor is turned on during an odd number of half- cycles and is off during an even number of half-cycles. A simple mathematical model explains the experimental results.