Distribution Transformer Winding Losses Due to Nonsinusoidal Currents

Increased transformer winding losses are an important consideration in determining the overall impact of harmonic currents in a power system. Frequently, losses due to harmonic currents are assumed to vary with the square of frequency. The purpose of this paper is to compare winding loss calculations from a finite element method with measured losses in single phase distribution transformers and to test the principle of superposition of harmonic losses due to nonsinusoidal currents. The results confirm both the finite element method and the principle of superposition. Furthermore, it is shown that, due primarily to inaccuracy in measuring 60 Hz eddy current losses, application of the commonly accepted frequency squared rule can yield overly pessimistic loss predictions for typical power system harmonic frequencies.     

Influence of harmonics on power distribution system protection

The effects of nonsinusoidal voltages and currents on the performance of static underfrequency and overcurrent relays are experimentally studied. The tests were conducted in such a way that the frequency, amplitude and phase shift of individual harmonics could be adjusted in a controlled manner by using a waveform generator with a phase-locking circuit. The relationship between the harmonic currents and voltages was modeled in terms of the power system impedance within residential distribution systems. It was found that for harmonic voltage and current amplitudes (as they occur in distribution systems), underfrequency relays and the time delay operation of overcurrent relays show a marked deterioration in performance. The instantaneous operating characteristics of overcurrent relays, however, are hardly affected by the presence of harmonic currents     

Evaluation of reactive power meters in the presence of highharmonic distortion

Four reactive power meters, operating on different principles, were tested under nonsinusoidal conditions. Different definitions of the reactive power are discussed. Because the definition and meaning of the nonsinusoidal reactive power are still being actively debated, the readings of the tested meters were compared with four nonsinusoidal reactive powers and the first harmonic reactive power, to verify whether these readings can be interpreted as approximate measures of the different definitions. A digital instrument, programmed to measure each of these powers, was used as a reference     

A novel, DSP based algorithm for optimizing the harmonics and reactive power under non-sinusoidal supply voltage conditions

This paper presents a simple control algorithm for a shunt active filter for compensation of harmonics and reactive power under nonsinusoidal supply voltage conditions. Under nonsinusoidal supply conditions, any attempt to achieve unity power factor results in a nonsinusoidal current, which increases the total harmonic distortion (THD). On the other hand, attempt at getting harmonic free current may not yield unity power factor because of the harmonics present in the voltage waveform. The proposed algorithm optimizes this trade-off using the Lagrange multiplier technique and achieves the best compromise. It does not employ the normally used p-q theory and is applicable to both single phase and three phase systems. With the proposed technique, it is possible to obtain an optimized power factor satisfying the specified THD limit. The algorithm has been tested under various supply and load conditions using MATLAB simulations and validated with an experimental prototype based on DSP TMS320LF2407A.     

用户层多谐波源的责任区分方法

为了区分公共耦合点处的用户谐波责任,论文提出了一种基于非正弦功率分解的谐波辨识方法。在分析用户谐波传播机理的基础上,以系统畸变电压为基,对馈线电流进行正交分解。引入非谐波电压、非谐波电流及谐波电流的概念,以此为基础计算负载线性度,实现用户层的谐波定位。采用多端口网络理论建立多谐波源的网络方程,以独立分量分析法对馈线谐波电流进行解耦。在不求解网络谐波参数和谐波源特性未知的情况下,以负熵为目标函数,通过分离观测量还原出用户发射的原始谐波电流,实现谐波责任量化。仿真算例验证了该方法的有效性,可实现谐波源定位、谐波全电流计算,是对用户层谐波责任估计的有益探索。     

Effect of harmonic distortion in reactive power measurement

The authors present the effect of harmonics on reactive power measurements and offer a new method for calculating active, reactive apparent, and residual power in nonsinusoidal conditions. The method considers common and uncommon harmonic components of voltage and current waveforms. It properly defines all power components at different harmonic frequencies, such as rotating real power, quadrature power, and the residual power (distortion). Each component is calculated correctly at different frequencies to define its physical meaning. A computer algorithm is developed to calculate all the power components for any distorted voltage and current waveforms     

Rectifier Harmonics in Power Systems

The effect of rectifier harmonic currents on power systems is described. Rectifiers and inverters require nonsinusoidal waves of current. These current waves are made up of a number of sine waves which are harmonics of the fundamental wave. These harmonic currents can excite resonant circuits causing them to ``ring' and produce large oscillating currents. Criteria as to possible problem areas are discussed and illustrated with case studies. Examples of application of filters to ``trap' these harmonic currents are included.     

The Systematic Errors of a Time-Division Power Converter under Sinusoidal and Nonsinusoidal Conditions

Systematic errors of an astable multivibrator based time-division active power converter are analyzed. Results of a computer simulation for sinusoidal and nonsinusoidal input signals are compared with test measurements of a standard converter. The paper shows that a conversion error of the power converter can be estimated from the harmonic content of the input waveforms.     

Powers in nonsinusoidal situations-a review of definitions andphysical meaning

The author expands on the physical meaning of the reactive power in nonsinusoidal situations. The sinusoidal waveform case is surveyed, viewing the active current as a component of identical waveform with the voltage. This approach, when extended to nonsinusoidal waveforms, supports Fryze's model for apparent power, S²=p ²+Q²_F. It is proved that the total reactive power Q_F is composed from four distinctive types of elementary reactive powers. Each of the basic reactive powers is identified as the amplitude of an oscillation of instantaneous power. The separation of Q_F in Q ₁, the reactive power at the system frequency, and in Q_H, the reactive power at harmonic frequencies, is recommended as an effective mean for monitoring filter efficacy and power-factor compensation. Two major recommendations are supported by the results of this study: abolish the power model using distortion power, and measure the active power of the system frequency separately from the active power of the harmonics     

Parameter determination of a nonsinusoidal periodic signal harmonic based on the modified sine transform

An algorithm is presented for determining the amplitude and the initial phase of the oscillations of the kth harmonic included in the structure of the nonsinusoidal periodic signal. The algorithm differs from the well-known Euler–Fourier method based on sine and cosine transforms. The qualitative difference of the proposed method consists in the use of the cosine function, which is an analytic solution of a modified sine transform, the structure of which includes a sinusoidal factor with a complex argument that contains a variable phase angle. The coordinates of the maximum of this functional dependence, which is raised to a positive integer power to improve the accuracy of determining the parameters, are uniquely associated with the amplitude and the initial phase of oscillations of the kth harmonic of the nonsinusoidal signal. The considered method minimizes the use of nonlinear operations and at its core has the element inherent in the selective filter. The possibility of obtaining information on the parameters of the first voltage and current harmonics with the required accuracy enhances the reliability of the evaluation of processes occurring in the power system in the conditions of interference in the form of higher harmonics. An example problem is solved in the MS Excel environment.     

Q'HARM-a harmonic power-flow program for small power systems

The salient features of a harmonic power-flow program called Q'HARM, are described. Two kinds of harmonic-producing components, the line-commutated six-pulse bridge rectifier and the gaseous discharge lighting load supplied from nonsinusoidal sources, are accurately modelled in this program. Case studies involving the use of Q'HARM for a small power system including converters and gaseous discharge lamps are described. The results include the effect of filters and the computed values of telephone influence indices. It is also shown that the maximum values of telephone influence indices for the different harmonics occur at different points on any transmission line in the system     

Harmonic response tests on distribution circuit potentialtransformers

Experimental data are presented that show the performances of distribution circuit potential transformers operating with nonsinusoidal waveforms. Four standard magnetic voltage transformers designed for 60 Hz power applications and rated from 7.2 kV to 20 kV were tested. Ratio correction factor and phase angle measurements were conducted at rated 60 Hz voltage with harmonic distortion levels at and below 8%. Test results indicate that potential transformers rated up to 20 kV experience errors of less than 5% at harmonic frequencies up to 3500 Hz when operating into typical induction watthour meter burdens. The phase angle response is essentially linear over the frequency range used to test the transformers, with a typical phase angle of about -10° at frequencies of approximately 3 to 3.5 kHz     

单相非正弦电路电流分解与功率定义的研究

为进一步认识单相非正弦电路中的功率现象,获得电路补偿的信息和条件,对任意波形下的非正弦单相电路的功率进行了重新的定义。在傅氏分解的基础上,构造了欧氏赋范空间,通过坐标的正交变换得到电流向量在电压向量上的投影。投影的范数反映了有功电流和无功电流在电路中的分配比例。采用电压范数和电流范数乘积定义的功率具有明确的物理意义和数学表达,并可得到无功补偿在几何上的解释。给出了计算实例和仿真波形图。该方法是传统正弦功率理论的推广,对谐波抑制和无功补偿具有指导意义。     

一种基于瞬时无功功率的电能计量方法

针对目前非正弦不平衡条件下电能计量时不同谐波功率会正负抵消的现象,提出一种基于瞬时无功功率来计量相功率的电能计量方法。该方法通过改变广义瞬时无功功率计量中p-q坐标系的旋转方向和速度,得到三相三线制系统中电压、电流的任一谐波的正负序分量,进而求得正负序功率。最后将正负序功率转换成相功率,从而得到非正弦不平衡条件下的系统功率。文中方法不仅可以获得不同次谐波的功率,实现功率的正反向计量,避免不同次谐波功率抵消的现象,而且计算量小,计算精度高。最后通过Matlab仿真验证了文中方法的准确性。     

Transformer design and application considerations for nonsinusoidalload currents

The use of adjustable-speed drives requires transformers capable of withstanding high levels of harmonic currents under normal operating conditions. Experience has been that overheating problems are much more common with dry-type transformers than with liquid-filled transformers. Transformer insulation life is determined by the hot spot temperature but confirmation of hot spot temperature rise is one performance characteristic which is ignored in industry standards. This is especially important for transformers rated for nonsinusoidal load currents. The design of transformers for nonsinusoidal load currents should include an analysis of the eddy loss distribution in the windings and calculation of the hot spot temperature rise. Calculations and thermal tests giving only average winding temperature rises are not sufficient. Thermal tests with nonsinusoidal currents and measurements of hot spot temperature rises are extremely difficult on large transformers. The combination of testing and analysis may be the only economically practical approach. Analysis indicates that the dry type transformer hot spot temperature is very sensitive to the eddy loss magnitude and distribution. The Underwriters Laboratories Inc. (UL) K-factor rated dry type transformer and the recommended practices given in ANSI/IEEE C57.110 are reviewed. When purchasing transformers subject to nonsinusoidal load currents, considerations should be given to the manufacturer's development program and capability to calculate the eddy loss distribution and hot spot temperatures     

Shunt capacitor sizing for radial distribution feeders withdistorted substation voltages

An algorithm for optimizing shunt capacitor sizes on radial distribution lines with nonsinusoidal substation voltages such that the RMS voltages and their corresponding total harmonic distortion lie within prescribed values is presented. The problem is formulated as a combinatorial optimization problem with inequality constraints. A simple heuristic numerical algorithm that is based on the method of local variations is proposed to determine an optimal solution. An example shows that optimal capacitor sizes found by neglecting the harmonic components may result in unacceptable voltage distortion levels     

通用瞬时功率定义及广义谐波理论

传统功率理论无法对非正弦电路中的功率现象加以解释,现有的瞬时功率理论的物理意义又都不够明确。针对这一问题,该文提出了一种基于最小传输能量损失的有功及无功功率定义,给出了数学模型及简化解。该定义物理意义明确,能够与传统正弦电路功率理论、弗兰芝（Fryze）单相无功理论和赤木泰文（H.Akagi）三相无功理论相统一。在该定义体系中,单相电路与三相电路的有功、无功确定原则是一致的。该文还提出了一种广义谐波理论,该理论所定义的谐波不仅具有传统的傅立叶谐波的两两正交的优点,而且可以直观地衡量负载的非线性程度,并将谐波理论与本文所提功率理论相统一。     

自然采样SPWM逆变电源的谐波分析及抑制策略

在借鉴国内外相关研究的基础上,对电太源型自然采样正弦脉宽调制（SPWM）逆变器输出电压、电流的谐波及其产生规律进行了较为详尽的分析,并从工程实际出发给出了3种谐波抑制策略：选择合适的载波频率,以消除低次和某些奇次谐波;精确实现先定的载波频率,以避免异步调制中出现的偶次谐波;注入适当的谐波分量,以在不加大输出谐波含量的情况下提高电压利用率。最后,把以上谐波抑制策略应用于35kVA客车空调逆变电源,并给出了实验结果。     

电力系统中非正弦波功率体系的研究

研究了非正弦波系统的能量转换，着重研究了畸变功率在能量转换中的作用，并提出了新的功率体系。     

基于半不变量及最大熵的概率谐波潮流算法

针对电力系统中谐波分布的不确定性,提出了一种结合半不变量、线性化谐波潮流方程以及最大熵模型的概率谐波潮流算法。首先,根据谐波电流的样本获取高阶矩和半不变量等数字特征,根据电网基础数据构建谐波潮流方程并在基准运行点处线性化,计算谐波电压数字特征,进而建立最大熵模型拟合其概率分布。所提方法具有计算量小、编程简单、结果客观准确等优点。最后,使用所提方法在4节点系统上与卷积法比较,以及在IEEE 57节点系统上与蒙特卡洛法比较,均验证了该方法的有效性。