Nonsinusoidal Conditions Research Articles

Feasible Evaluation and Implementation of Shunt Active Filter for Harmonic Mitigation in Induction Heating System

This paper proposes a shunt active filter (SAF) for harmonic mitigation and reactive power compensation in an induction heating (IH) system. The high-frequency switching in the resonant inverter of the IH system generates a considerable number of high-frequency harmonics. The latter flow back to the supply side and causes a wide variety of problems. The predominant ones are the deterioration of the power quality, distortion in the grid voltage, and malfunctioning of the protective equipment. These harmonics need to be attenuated as per the IEEE 519-1992 and IEEE 519-2014 standards. To overcome these problems, an SAF based on the modified version of instantaneous power theory was placed between the power supply and the IH equipment. Moreover, the proposed model could work in unbalanced and non-sinusoidal input voltage conditions, as well as dynamic conditions with changing reference currents. The feasibility of the proposed SAF-based IH system was verified by a series of simulation results and a comparative analysis of the THD of the input currents. The power quality issues were successfully addressed, which signifies the ability and effectiveness of the proposed model to mitigate the problems caused by harmonics and enhance the power factors.

A new power calculation method based on time–frequency analysis

The increasing spread of non-linear loads is leading to rising distortion levels of power network signals. As a consequence, voltage and current signals deviate from a pure sinusoidal waveform. Under these conditions, the traditional power calculation method is not appropriate for evaluating electrical power. This study proposes a novel power calculation method based on the discrete Stockwell transform (DST) aimed at offline applications. The proposed approach decomposes the apparent power in power components related to circuit elements. The proposed power components provide a comprehensive power characterization in non-sinusoidal conditions. The proposed method is suitable for non-stationary signals, once the DST provides a magnitude and phase representation of signals at each time instant. The performance and effectiveness of the proposed method are evaluated using synthetic, simulated, and actual signals, including a challenging scenario containing signals with random variations. The results attest to the suitability of the proposed method for analyzing non-sinusoidal signals with non-stationary characteristics.

LOAD NOISE INCREASE OF TRANSFORMERS BY LOAD HARMONICS

Harmonic components in the load-current have a larger impact to the increase of the load noise level of transformers than might be expected from their amplitude. The reasons are (a) the interaction of the harmonics with the large load-current at power frequency, (b) the rising sound radiation efficiency with frequency and (c) the A-weighting filter curve which suppresses sound components at lower frequencies. This paper presents a calculation scheme able to estimate the noise increase and the noise spectrum of electrical transformers for non-sinusoidal load conditions. The proposed calculation scheme is applied to three practical examples

Conservative Power Theory for Harmonic Voltage Responsibility Assignment

Discussions on the different methods for sharing responsibilities regarding harmonic distortions in power grids have received wide attention in the area of power quality. This paper proposes a methodology based on Conservative Power Theory (CPT) for responsibility assignment due to the harmonic voltage distortions present at the point of common coupling. First, a theoretical basis for analyzing the orthogonal current decomposition of CPT under non-sinusoidal conditions is presented. Next, using the frequency domain, a methodology is introduced to separate the contributions of the harmonic voltage distortions in the CPT's orthogonal currents. To illustrate the application of the proposed methodology, it is simulated a real large-scale electrical system composed of an energy utility and three industrial plants connected to the same common coupling point. Finally, the results obtained are compared to other method showing the effectiveness of the proposed approach.

Fair Power Factor Billing Under Unbalanced and Nonsinusoidal Voltage Supply

Utilities apply an additional fee for medium and large customers with low power factors. However, unfair financial charges may occur in installations subjected to voltage unbalance and harmonic distortion. The objective of this paper is to determine the fairest PF definitions and their corresponding measurement algorithms in the case in which a constant impedance load or an induction motor is supplied with unbalanced and nonsinusoidal voltages. Fairness is defined considering that the meter (built based on a particular definition and measurement method) under nonideal supply should lead to very close values as if it was submitted to an ideal balanced sinusoidal supply. We performed computational simulations to emulate several conditions in which a balanced customer (modeled as a constant impedance load or an induction motor) is charged due to a voltage supply no longer balanced and sinusoidal. We also performed experimental tests with an induction motor subjected to a wide range of unbalanced nonsinusoidal supply conditions to ratify the conclusions drawn from the simulations. Based on the simulation results and the experimental tests, we indicate some power factor definitions and measurement methods that are not significantly affected by voltage unbalance and harmonic distortions. These indicated PF definitions provide the fairest billing for conditions with unbalanced nonsinusoidal voltages.

Nonlinear load modeling for analysis of non-sinusoidal conditions in electrical networks based on measurements of harmonic parameters

Non-sinusoidal conditions in electrical networks need to be calculated for their control and development of technical measures to maintain harmonic parameters according to the requirements of regulatory documents. These calculations are impossible without electrical network and nonlinear load models that adequately reflect them in computational programs. Nonlinear load models have been developed for a long time. Some studies present general modeling principles and models of various nonlinear devices. Others consider some nonlinear devices as equivalent nonlinear loads connected to low and medium voltage networks. A whole host of high-power nonlinear electrical equipment is connected to high voltage networks. Modeling nonlinear loads connected to these networks is a problem. Research of measured parameters of harmonic conditions in electrical networks has shown that they are random values. The probabilistic nature is determined by the network configuration, a range of network components, the number of nonlinear loads, wave and frequency properties of the network, harmonic source phase currents, voltage at terminals of nonlinear electrical equipment, changes in operating conditions and load power, and many other factors. Nonlinear loads can only be modeled based on the measurements of parameters of harmonic conditions due to their unpredictability. The paper presents an overview of existing methods for modeling nonlinear loads, a methodological approach to modeling nonlinear loads based on measured parameters, an algorithm for modeling harmonics of active and reactive currents, a computational program algorithm designed to identify distribution functions of measured current harmonics, and modeling results for current harmonics of railway transformers supplying power to electric locomotives.

A Simulation Method for Dynamic Hysteresis and Loss Characteristics of GO Silicon Steel Sheet Under Non-Sinusoidal Excitation

The magnetic property measurementfor grain oriented (GO) silicon steel sheet under non-sinusoidal excitations (DC bias and harmonic) were conducted based on the experimental platform. Based on the Preisach model, the static hysteresis and loss properties were accurately simulated. Furthermore, an improved loss model was proposed by adjusting the statistical parameter of abnormal loss, which depends on the characteristic quantities of DC bias or harmonic excitations. The simulated dynamic hysteresis loops and iron losses under different non-sinusoidal conditions were compared with the measured ones, and thus the accuracy and generality of the improved model proposed in this paper were verified. In addition, the influences of the harmonic and DC-biasing quantities upon the total losses is investigated.

Analysis of Errors in Active Power and Energy Measurements Under Random Harmonic Distortion Conditions

Abstract As harmonic distortion of voltage and current is reality in the power system, the need for accurate measurement of electrical power and energy goes beyond the instruments’ specifications and calibration procedures regarding pure sine wave signals. Several international standards and recommendations provide test signals for examination of electricity meters under non-sinusoidal conditions, however, not all of the test signal parameters’ possible states are faithfully represented in those documents. Because the high order harmonics may possess random amplitudes and phase shifts in relation to components at fundamental frequency, it is important that the meter’s performance is verified with random waveforms as well. The non-linear dependence between the measured power/energy and the phase shifts, both between fundamental and harmonic components, provides additional complexity of such an analysis. Simple test signals, which are in accordance with the standards’ demands and propositions, are used for determination of the measurement error in case of different harmonic distortion parameter change. In order for a general error function for any measurement device to be determined, mathematical modelling, regarding the results from multiple tests, is performed. The mathematical model presents a strong dependence between a single component’s phase shifts and a meter’s error and it provides a systematization of all signal parameters’ influence on the measurement accuracy.

Definitions of Power Quantities in the IEEE Std 1459-2010

The paper deals with the definitions of electrical power to quantify the flow of electrical energy in single-phase and three-phase circuits under sinusoidal, nonsinusoidal, balanced and unbalanced conditions recommended for the instrumentation design by the current IEEE standard. These definitions were adopted not by consensus but by balloting. They are based on concepts strongly contested by some eminent researchers. According to the author of the article, this determines the expected lack of practical impact of the standard.

Investigation of the Effects of DC Bias on Single-Phase Shell Type Transformers Using Frequency-Dependent Reluctance-Based Model

In this article, a reluctance-based model is developed for time-efficient analysis of shell type single-phase power transformers under the direct current (dc) bias conditions. Unlike other reluctance-based transformer models in the literature, the developed one considers frequency dependent nature of the winding resistances. This is important especially for accurate determination of losses and maximum loading capability (MLC) of the transformers under dc bias and non-sinusoidal conditions. In addition to that, by using the developed model, three different MLC determination approaches, which are based on the rated primary side current, rated total loss and rated primary winding loss, are examined for dc bias conditions. These novel examination results clearly point out that among three approaches the rated primary winding loss-based one should be preferred for the safe operation of the transformers in the systems with dc bias.

Contemporary electric energy meters testing under simulated nonsinusoidal field conditions

Contemporary electric energy meters testing under simulated nonsinusoidal field conditions

Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

Traditional electrical power theories and one of their most important concepts—apparent power—are still a source of debate, because they present several flaws that misinterpret the power-transfer and energy-balance phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been introduced to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, electrical power theories for single-phase systems based on GA were revisited. Several drawbacks and inconsistencies of previous works were identified, and some amendments were introduced. An alternative expression is presented for the electric power in the geometric domain. Its norm is compatible with the traditional apparent power defined as the product of the RMS voltage and current. The use of this expression simplifies calculations such as those required for current decomposition. This proposal is valid even for distorted currents and voltages. Concepts are presented in a simple way so that a strong background on GA is not required. The paper included some examples and experimental results in which measurements from a utility supply were analysed.

Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.

Active power losses and energy efficiency analysis of HPS lamps with electromagnetic control gear and electronic ballast under the sinusoidal and nonsinusoidal condition

Active power losses and energy efficiency analysis of HPS lamps with electromagnetic control gear and electronic ballast under the sinusoidal and nonsinusoidal condition

Non-Linear Load Characterisation Using Orthogonal Apparent Power Decompositions

There is no generally accepted definition for apparent power components in circuits with non-sinusoidal conditions. The decomposition of apparent power has been the subject of many discussions and is still an open topic. Over the years, a number of apparent power decompositions have been proposed and analysed, usually in the context of compensation. These analyses were performed by means of simulations or by calculating quantities using measurements on a simple test circuit. Here, we present a unique system capable of simultaneous apparent power decompositions for non-sinusoidal conditions in real-time. The system can calculate power components related to various power decompositions. The system’s capabilities are demonstrated on non-linear load characterization.

An optimal transmission line power control under non‐sinusoidal conditions using static synchronous series compensator

In view of the growing load demand in developing countries, overloading in existing transmission lines is a major concern. In addition to the voltage drop due to overloading, the proliferation of non-linear loads in recent years distort the shape of sinusoidal voltage. Stable transmission of power through a transmission line under such condition is a challenge. In the presence of harmonics, control of transmittable power using static synchronous series compensator needs additional efforts, where increased power demand can be fulfilled by taking into consideration various other parameters. If an attempt is made to increase transmittable power through a transmission line using SSSC, power loss, the magnitude of voltage and its shape deteriorate in the presence of non-linear loads. Thus, the trade-off between transmittable power, transmission loss and voltage quality is tackled by optimal control of the compensator. In this study, a novel optimal control of SSSC is proposed with the objective of minimising transmission loss by maintaining the voltage within the limits while enhancing the transmittable power under non-sinusoidal conditions. A two-machine model of power system with 400 kV transmission line with parameters as per standards issued by the Central Electricity Authority is considered for validation of the algorithm using MATLAB platform and results are presented.

Performance improvement of the shunt active power filter using a novel adaptive filtering approach

This paper introduces an efficient control approach to enhance harmonics mitigation performance of the shunt active power filter (SAPF). This approach is based on adaptive filters favored by their built-in automatic parameters adaptation capability. The proposed filter, which uses a variable leaky least mean square (VLLMS) adaptation, is applied with a modified instantaneous power PQ theory. This enhances its dynamic performance over the use of conventional time-invariant filters, and overcomes its limitations in the presence of nonsinusoidal voltage conditions. The studied SAPF model is simulated in MATLAB/SIMULINK with combinations of nonlinear and unbalanced loads. Simulation results indicate a significant improvement in the transient response to less than a quarter of a cycle in its worst case, on top of additional improvements in the steady-state THD value. Moreover, the algorithm?s computation efficiency evaluated in an embedded hardware prototype has given a fast execution time of 1.4µs.

A Harmonic Compensation Method Using a Lock-In Amplifier under Non-Sinusoidal Grid Conditions for Single Phase Grid Connected Inverters

The power quality of grid-connected inverters (GCIs) is attracting a lot of attention as the number of distributed generation systems with renewable energy sources are increased. It is well known that the harmonics present in the grid have a lot of detrimental effects on the equipment and devices connected to a power system network such as heating and derating. These effects lead to problems in terms of safety and lifespan. Therefore, harmonic standards such as IEEE 519 and P1547 suggest that GCIs should achieve total harmonic distortion (THD) of the output current that is less than 5%. However, it is not easy to achieve the current THD of GCIs that is less than 5% with only an output filter under distorted grid conditions. In this paper, a harmonic compensation method using a lock-in amplifier (LIA) is proposed. Due to the outstanding performance of the LIA, accurate information of the harmonics can be obtained. This information is used to eliminate the harmonics by the simple PI controller. To demonstrate the superiority of the proposed method, it is applied to a 5 kW single phase GCI connected to the real grid. The results obtained are compared with those of the conventional harmonic compensation methods.

Adaptive Power Factor Regulation Under Asymmetrical and Non-Sinusoidal Grid Condition With Distributed Energy Resource

Active and reactive power regulation, unbalanced current compensation, and harmonic current mitigation are the most significant functionalities typically embedded to a three-phase multifunctional grid-connected inverter. However, a vital control feature minimally addressed in the literature is the capability to adjust the grid power factor to the minimum value required by standards or grid codes. Hence, this paper presents an adaptive compensation approach to perform dynamic power factor regulation under varying power demand and unpredictable energy generation, also withstanding non-ideal voltage conditions. To demonstrate such an approach, a global power factor definition is first introduced, being validated upon bidirectional power flow conditions and under unbalanced and distorted voltages. Secondly, a simple algorithm is devised to attain scaling coefficients used on compensation purposes, allowing to instantaneously weigh up reference control signals to track a desired grid-side power factor value. As a result, the strategy can be used to retrofit the controllers of grid-connected inverters with little effort, limiting distribution losses and improving power quality. Simulations and analyses of a representative real study case are conducted to illustrate how the proposed approach copes with unpredictable distributed energy resources and variable load demands. Moreover, experimental results considering a grid-connected inverter prototype are shown to validate the feasibility of the control approach to real-life implementations.

Calibration of Electrical Instruments Under Nonsinusoidal Conditions at NRC Canada

The paper describes the recent development of a system for calibration of electrical instruments with harmonics measurement capability, such as revenue meters and power analyzers, under nonsinusoidal test conditions at National Research Council (NRC) Canada. The improvements implemented with respect to an earlier NRC calibration system are aimed at increasing the calibration accuracy in a wider frequency range.