The Generalized Pythagorean Comma Harmonic Powers of a Fundamental Frequency Are Equivalent the Standing Wave Harmonic Fraction System

Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A Comma represents a physical harmonic system that is readily observable and can be mathematically simulated. The virtual harmonic is essential and indirectly measurable. The Pythagorean Comma relates to two discrete frequencies but can be generalized to any including infinite harmonics of a fundamental frequency, vF. These power laws encode the physical and mathematical properties of their coupling constant ratio, natural resonance, the maximal resonance of the powers of the frequencies, wave interference, and the beat. The hypothesis is that the Pythagorean power fractions of a fundamental frequency, vF are structured by the same harmonic fraction system seen with standing waves. Methods: The Pythagorean Comma refers to the ratio of (3/2)12 and 27 that is nearly equal to 1. A Comma is related to the physical setting of the maximum resonance of the powers of two frequencies. The powers and the virtual frequency are derived simulating the physical environment utilizing the Buckingham Π theorem, array analysis, and dimensional analysis. The powers and the virtual frequency can be generalized to any two frequencies. The maximum resonance occurs when their dimensionless ratio closest to 1 and the virtual harmonic closest to 1 Hz. The Pythagorean possible power arrays for a vF system or any two different frequencies are evaluated. Results: The generalized Pythagorean harmonic power law for any two different frequencies coupling constant are derived with a form of an infinite number of powers defining a constant power ratio and a single virtual harmonic frequency. This power system has periodic and fractal properties. The Pythagorean power law also encodes the ratio of logs of the frequencies. These must equal or nearly equal the power ratio. When all of the harmonics are powers of a vF the Pythagorean powers are defined by a consecutive integer series structured in the identical form as standard harmonic fractions. The ratio of the powers is rational, and all of the virtual harmonics are 1 Hz. Conclusion: The Pythagorean Comma power law method can be generalized. This is a new isomorphic wave perspective that encompasses all harmonic systems, but with an infinite number of possible powers. It is important since there is new information: powers, power ratio, and a virtual frequency. The Pythagorean relationships are different, yet an isomorphic perspective where the powers demonstrate harmonic patterns. The coupling constants of a vF Pythagorean power law system are related to the vFs raised to the harmonic fraction series which accounts for the parallel organization to the standing wave system. This new perspective accurately defines an alternate valid physical harmonic system.

Analysis and Design Aspects of a Series Power Semiconductor Array with Digital Waveform Control Capability for Single Phase AC Voltage Regulators and Other Applications

A series connected power semiconductor array, with digital control capability could be used for developing single phase AC regulators or other applications such as AC electronic loads. This technique together with an ordinary gapless transformer could be used to develop a low cost AC voltage regulator (AVR) to provide better or comparable specifications with bulky ferro-resonant AVR types. One primary advantage of the technique is that digital control can be used to minimize harmonics. Commencing with a review of AC voltage regulator techniques for single phase power conditioning systems, an analysis and design aspects of this technique is presented with experimental results for AVRs. Guidelines on how to utilize the technique in a generalized basis is also summarized together with a summary of a technique for achieving harmonic control.

Enhancement of Available Transfer Capability with Facts Device in the Competitive Power Market

In order to facilitate the electricity market operation and trade in the restructured environment, ample transmission capability should be provided to satisfy the demand of increasing power transactions. The conflict of this requirement and the restrictions on the transmission expansion in the restructured electrical market has motivated the development of methodologies to enhance the Available Transfer Capability (ATC) of the existing transmission grids. The insertion of FACTS devices in electrical systems seems to be a promising strategy to enhance ATC. In this paper, the viability and technical merits of boosting ATC using Thyristor Controlled Series Compensator (TCSC) is being analyzed. The work has been carried out on IEEE 30 bus and IEEE 118 bus systems. Bilateral and multilateral transactions are considered. Particle Swarm Optimization (PSO) algorithm and Genetic Algorithm (GA) are employed to obtain the optimal settings of TCSC.

Influence of the Phase of the Antenna Current Standing Wave on the Power Flux in Ion Cyclotron Heating

For ion cyclotron resonance heating, the current on the antenna surface exists in a form of standing wave, and the phase of the poloidal current standing wave affects significantly on the performance of the coupling. In this paper, a coupling calculation is carried out based on a practical model for the loop antenna. The ion cyclotron wave coupling performance depends greatly on the antenna current propagation constant and the phase of standing wave. For a small antenna-current-propagation constant, the antenna coupling performance is more sensitive to a π/2 change in the phase of standing wave.

Consideration of the influence of supports in modeling the electromagnetic fields of 25 kV traction networks under emergency conditions

Single-phase 25 kV traction networks of electrified alternating current(AC)railways create electromagnetic fields(EMFs)with significant levels of intensity.The most intense magnetic fields occur when short circuits exist between the contact wire and rails or ground.Despite the short duration of exposure,they can adversely affect electronic devices and induce significant voltages in adjacent power lines,which is dangerous for operating personnel.Although numerous investigations have focused on modeling the EMF of traction networks and power lines,the challenge of determining the three-dimensional electromagnetic fields near metal supports during the flow of a short-circuit current through them is yet to be resolved.In this case,the field has a complex spatial structure that significantly complicates the calculations of intensities.This study proposes a methodology,algorithms,software,and digital models for determining the EMF in the described emergency scenarios.During the modeling process,the objects being studied were represented by segments of thin wires to analyze the distribution of the electric charge and calculate the intensities of the electric and magnetic fields.This approach was implemented in the Fazonord software,and the modeling results show a substantial increase in EMF levels close to the support,with a noticeable decrease in the levels as the distance from it increases.The procedure implemented in the commercial software Fazonord is universal and can be used to determine electromagnetic fields at any electrical power facility that includes live parts of limited length.Based on the proposed procedure,the EMF near the supports of overhead power lines and traction networks of various designs could be determined,the EMF levels at substations can be calculated,and the influence of metal structures located near traction networks,such as pedestrian crossings at railway stations,can be considered.

Industrial frequency single-phase AC traction power supply system for urban rail transit and its key technologies

To avoid stray current and maintain the benefit of no phase-split in the DC traction power supply system, an AC traction power supply system was proposed for the urban public transport such as metro and light rail transit. The proposed system consists of a main substation （MSS） and cable traction network （CTN）. The MSS includes a single-phase main traction transformer and a negative-se- quence compensation device, while the CTN includes double-core cables, traction transformers, overhead catenary system, rails, etc. Several key techniques for the proposed system were put forward and discussed, which can be summarized as （1） the power supply principle, equivalent circuit and transmission ability of the CTN, the cable-catenary matching technique, and the selection of catenary voltage level; （2） the segmentation technology and status identification method for traction power supply network, distributed and centralized protection schemes, etc.; （3） a power supply scheme for single-line MSS and a power supply scheme of MSS shared by two or more lines. The proposed industrial frequency single-phase AC traction power supply system shows an excellent technical performance, good economy, and high reliability, hence provides a new alternative for metro and urban rail transit power supply systems.

Hybrid compensation method for traction power quality compensators in electrified railway power supply system

In order to improve the Power Quality(PQ)of traction power supply system and reduce the power rating and operation cost of compensator,a Static VAR Compensator(SVC)integrated Railway Power Conditioner(RPC)is presented in this paper.RPC is a widely used device in the AC electrified railway systems to enhance the PQ indices of the main network.The next generation of this equipment is Active Power Quality Compensator(APQC).The major concern of these compensators is their high kVA rating.In this paper,a hybrid technique is proposed to solve aforementioned problems.A combination of SVC as an auxiliary device is employed together with the main compensators,i.e.,RPC and APQC that leads on to the reduction of power rating of the main compensators.The use of proposed scheme will cause to reduce significantly the initial investment cost of compensation system.The main compensators are only utilized to balance active powers of two adjacent feeder sections and suppress harmonic currents.The SVCs are used to compensate reactive power and suppress the third and fifth harmonic currents.In this paper firstly,the PQ compensation procedure in AC electrified railway is analyzed step by step.Then,the control strategies for SVC and the main compensators are presented.Finally,a simulation is fulfilled using Matlab/Simulink software to verify the effectiveness and validity of the proposed scheme and compensation strategy and also demonstrate that this technique could compensate all PQ problems.

Electrical characteristics of new three-phase traction power supply system for rail transit

A novel three-phase traction power supply system is proposed to eliminate the adverse effects caused by electric phase separation in catenary and accomplish a unifying manner of traction power supply for rail transit.With the application of two-stage three-phase continuous power supply structure,the electrical characteristics exhibit new features differing from the existing traction system.In this work,the principle for voltage levels determining two-stage network is dissected in accordance with the requirements of traction network and electric locomotive.The equivalent model of three-phase traction system is built for deducing the formula of current distribution and voltage losses.Based on the chain network model of the traction network,a simulation model is established to analyze the electrical characteristics such as traction current distribution,voltage losses,system equivalent impedance,voltage distribution,voltage unbalance and regenerative energy utilization.In a few words,quite a lot traction current of about 99%is undertaken by long-section cable network.The proportion of system voltage losses is small attributed to the two-stage three-phase power supply structure,and the voltage unbal-ance caused by impedance asymmetry of traction network is less than 1‰.In addition,the utilization rate of regenerative energy for locomotive achieves a significant promotion of over 97%.

Research on the variable speed system of large power alternating current motor

The development status of the variable speed system of large power AC(alternating current)motor drive in China is introduced.The large power AC drive fed by AC-AC converters(cycloconverters)has developed greatly,and some innovations on the theory and engineering technique have been realized.They have been applied to rolling mills,mine hoists,and so on,and remarkable economic and social benefit has been achieved.The development of AC drive fed by large power IGCT(integrated gate commutated thyristors)AC-DC-AC converter is also introduced.It has excellent performance and reliable operation,and has been used in traction.

Single-Phase to Three-Phase Inverter with Small DC-Link Capacitor for Motor Drive System

The electrolytic-capacitor-less(EL-cap-less)technique has been attracting more and more interests in these years.The EL-cap-less single-phase to three-phase inverter(STI)with front-end diode rectifier is applied to home electrical appliances.In EL-cap-less systems,film-type capacitor is used to suppress the high-frequency ripple components instead of smoothing the DC-link voltage.By using the EL-cap-less solution,reliability can be improved,lifetime can be increased and high power factor(PF)also can be realized.The EL-cap-less STI brings the opportunity to simplify system structure and lower cost.Because a certain DC-link capacitance is still required,the real PF is limited.To further improve the PF,the ripple components of current references are made in synchronous with the DClink voltage.And the capacitance chosen guideline of the film-type capacitor also be presented.A prototype is built to verify its real performance.

Design and Analysis of the Main AC/DC Converter System for ITER

A design of the main AC/DC converter system for ITER is described and the configuration of the main AC/DC converters is presented. To reduce the reactive power absorbed from the converter units, the main AC/DC converters are designed to be series-connected and work in a sequential mode. The structure of the regulator of the converter system is described. A simulation model was built up for the PSCAD/EMTDC code, and the design was validated accordingly. Harmonic analysis and reactive power calculation of the converters units are presented. The results reveal the advantage of sequential control in reducing reactive power and harmonics.

Influences of ±800 kV Yunnan-Guangdong HVDC System on Security and Stability of China Southern Power Grid

The interaction mechanism between AC and DC systems in a hybrid AC-DC transmission grid is discussed with PSS/E software. Analysis shows that receiving-end AC faults may cause much more damage on the HVDC system operation than the sending-end AC faults in a multi-infeed HVDC system, and the damage severity depends on the power recovering rate of the HVDC systems. For HVDC systems with slow power recovering rate, the receiving-end AC faults may probably be a critical factor to constrain power transfer limits. Larger capacity of HVDC system means not only higher power transfer-limit of the parallel connected AC-DC transmission grid, but also more expensive stabilizing cost.

Practice and Prospect of AC/DC Hybrid Power Grid in Southern China

China Southern Power Grid is a unique EHV AC/DC hybrid transmission network that operates in China. In its service area, the distribution of energy resources and the development of economy are extremely unbalanced, so long-distance and bulk power transmission are needed; besides, the geography and climate conditions are serious, rains, fogs, lightning and typhoon as well as high temperature are common all the year round. Facing these challenges, the power grid enhanced stability control, improved the equipment and strengthen the network structure. In the future, the power grid plans to optimize the disposition of power sources and build digitalized power system.

Systematic Evaluation of Deep Neural Network based Dynamic Modeling Method for AC Power Electronic System

Since the high penetration of renewable energy complicates the dynamic characteristics of the AC power electronic system(ACPES),it is essential to establish an accurate dynamic model to obtain its dynamic behavior for ensure the safe and stable operation of the system.However,due to the no or limited internal control details,the state-space modeling method cannot be realized.It leads to the ACPES system becoming a black-box dynamic system.The dynamic modeling method based on deep neural network can simulate the dynamic behavior using port data without obtaining internal control details.However,deep neural network modeling methods are rarely systematically evaluated.In practice,the construction of neural network faces the selection of massive data and various network structure parameters.However,different sample distributions make the trained network performance quite different.Different network structure hyperparameters also mean different convergence time.Due to the lack of systematic evaluation and targeted suggestions,neural network modeling with high precision and high training speed cannot be realized quickly and conveniently in practical engineering applications.To fill this gap,this paper systematically evaluates the deep neural network from sample distribution and structural hyperparameter selection.The influence on modeling accuracy is analyzed in detail,then some modeling suggestions are presented.Simulation results under multiple operating points verify the effectiveness of the proposed method.

Performance of PSS to Damp Power Oscillations Caused by an HVDC Link in AC-DC Power System

HVDC (High Voltage Direct Current) systems are increasingly being applied to improve power system operation and controllability. However, inappropriate setting of HVDC controller may have a detriment effect on the system performance. Generally, PSS (Power System Stabilizer) is known as a simple concept, easy to perform, and computationally effective to enhance damping of power system oscillations through excitation control of synchronous generator. This paper examines the effectiveness of the PSS to enhance the dynamic performance of AC-DC power systems and to compensate the negative damping of HVDC system. The dynamic performance is evaluated by examining the system response to various disturbances. In order to ensure the reliability of the simulation test results as well as the performance of the PSS, detailed HVDC modeling is adopted using SimPowerSystems toolbox in the MATLAB, and some important conclusions are drawn.

Investigation of Shunt Active Power Filters in Railway Systems, Substation Installation

This paper investigates the performance of SAPFs （shunt active power filters） which are introduced in order to address the quality issues in electrified railway supply systems. These filters can be installed at either the S/S （substation） end or at the SP （sectioning post） of the railway feeding power system. In this investigation novel control algorithms, based on the synchronously rotating frame of reference, are proposed for the case when the SAPF is installed at the substation end and its performance is assessed. The effectiveness of the proposed control algorithms are illustrated via Matlab/SimPower computer simulations and validated via comparisons with other publications. This investigation demonstrated that when the SAPF is installed at the substation side, it can effectively compensate for the higher harmonic supply current. In addition, the reactive power demand is fully compensated for, leading to close to unity power factor. However, the voltage drop/sag at the locomotive power supply feed point is only partially compensated for.

不平衡电网下AC-DC矩阵变换器的新型模型预测控制

为降低AC-DC矩阵变换器在输入不平衡条件下网侧有功功率波动,以及离散型模型预测控制中开关频率不固定的问题,提出一种新型模型预测控制方法。通过根据电网电流相位角选择有效矢量,避免了传统模型预测控制评估价值函数计算的负担。提出了一种二阶扩展复数卡尔曼滤波器,计算精度可以达到泰勒级数展开的二阶项,新型模型预测控制能够在不平衡电网系统中应用。仿真结果表明:所提控制策略在输入电压不平衡工况下,能够有效抑制网侧电流谐波,稳定系统输出的有功功率,并且表现出良好的性能。

Study on Transformer Magnetic Biasing Control Method for AC Power Supplies

This paper presents a novel transformer magnetic biasing control method for high-power high-performance AC power supplies. Serious consequences due to magnetic biasing and several methods to overcome magnetic biasing are first discussed. The causes of the transformer magnetic biasing are then analyzed in detail. The proposed method is based on a high-pass filter inserted in the forward path and the feedforward control. Without testing magnetic biasing of transformer, this method can eliminate magnetic biasing of transformer completely in real-time waveform feedback control systems though the zero error of the Hall effect sensors varies with time and temperature. The method has already been employed in a 90KVA AC power supply. It is shown that it offers improved performance over existing ones. In this method, no sensors are used such that the zero error of the Hall effect sensors has not any influence on the system. It is simple to design and implement. Furthermore, the method is suitable for various power applications.

基于ACE与YOLOv5的电力遥感图像检测算法

针对电力遥感图像采集时存在大量浓烟以及数据样本少等问题,提出一种基于对数变换的改进型自动色彩均衡与改进后YOLOv5s模型的遥感图像去雾检测算法,旨在通过提高数据集的图像质量进而提高检测网络的检测精度。构建的改进型自动色彩均衡对电力遥感图像去雾增强,并通过图像质量和特征提取两方面进行了实验数据对比,实验结果表明改进的自动色彩均衡算法优于其它算法。其次,通过YOLOv5s检测算法对增强后的数据集进行训练,引入mosaic数据增强算法,并通过构建ghost卷积模块和NAM注意力模块降低了网络参数、提升了网络检测精度。

Research on power electronic transformer applied in AC/DC hybrid distribution networks

The AC/DC hybrid distribution network is one of the trends in distribution network development, which poses great challenges to the traditional distribution transformer. In this paper, a new topology suitable for AC/DC hybrid distribution network is put forward according to the demands of power grid, with advantages of accepting DG and DC loads, while clearing DC fault by blocking the clamping double sub-module(CDSM) of input stage. Then, this paper shows the typical structure of AC/DC distribution network that is hand in hand. Based on the new topology, this paper designs the control and modulation strategies of each stage, where the outer loop controller of input stage is emphasized for its twocontrol mode. At last, the rationality of new topology and the validity of control strategies are verified by the steady and dynamic state simulation. At the same time, the simulation results highlight the role of PET in energy regulation.