Voltage Harmonic Distortion Research Articles

Wireless power transfer system based on LCC/LCL-S variable structure with constant output power

In magnetic coupling wireless power transfer system, the relative position of power transfer coils may change during the operating condition. In order to solve the mutual inductance variation caused by the movement of coils, increase the anti-offset capability of the system to achieve constant power output, a variable structure is proposed in this article. Build the mathematic models of LCC-S and LCL-S structures and analyze the expressions of output power and efficiency in two structures. Design the switching condition, the relationship between coupling coefficient at switching point and parameter setting of capacitor array is obtained with the same input voltage and constant output power. The coupling coefficient range is estimated by output open circuit voltage with a small-voltage input, and the controlling strategy is put forward. Analyze the efficiency of variable structure and build the loss model. It is proved that the switching and input harmonic loss can be reduced by using LCC/LCL-S structure, while the transfer efficiency can be improved through the structure switching between two structures. The simulation results show that the variable structure can effectively reduce the variation range of input voltage and decrease the total harmonic distortion (THD) of input voltage by 46.6%, and keep THD of input current small in a wide range of coupling coefficient.

Impact on the Power Grid Caused via Ultra-Fast Charging Technologies of the Electric Buses Fleet

Battery Electric Buses (BEBs) are considerably integrated into cities worldwide. These buses have a strict schedule; thus, they could be charged in a very short time with a power level up to 600 kW. The high-power systems and short charging times imply special grid operation conditions that should be taken into account. Therefore, it is necessary to consider the influence of their charging infrastructure on the distribution system operation, especially near the charging point. This work presents two Use Cases (UCs) from two demos (Germany and the Netherlands) to investigate the impact of the slow and fast-chargers’ integrations on the power grid and environment. Fast-chargers up to 350 kW based on pantograph technology and slow-chargers up to 50 kW based on Combined Charging System Type 2 (CCS2) are used on the BEB line route and in the depot, respectively. The charging of BEBs with these solutions is studied here to investigate their impact on the grid in terms of power quality. It was found that the voltage variations due to fast-chargers terminal remain much below the EN50160 standard limit values i.e., ±10%. The obtained maximum Total Harmonic Voltage Distortion (THDv) value is 2.7%, with an average value of 1.3%, which is below the limit value of 8%, as per the standard EN 50160. Similarly, the individual harmonic currents were measured. The maximum value of total harmonic current distortion (THDI) is around 25%, with an average value of 3% only. As the average value of THDI is quite low, the harmonic current pollution is not a big concern for the installation at this time.

Electromagnetic Compatibility of Compensating Devices and Converters of an Adjustable Electric Drive in Electrical Networks of Industrial Enterprises

The problems of reactive power compensation and improving the quality of electrical energy in the power supply systems of industrial enterprises are inseparable. Their relevance is due to the widespread use of electric receivers that consume reactive power and distort the quality of electrical energy in the network, as well as the implementation of new technologies, systems and equipment into production that make increased demands on the quality of electrical energy consumed. An important characteristic of the quality of electrical energy rationed by GOST 32144–2013 is the non-sinusoidal voltage. The main reason for the non-sinusoidal voltage in the electrical networks of industrial enterprises is the use of electrical equipment with a nonlinear voltage characteristic, which is a source of conductive electromagnetic interference, in particular: adjustable DC and AC electric drives, uninterruptible power supplies of electric receivers, electric welding equipment, electric arc furnaces, induction heating installations, gas-discharge radiation sources. Due to the nonlinearity of the current-voltage characteristics, the above devices consume a non-sinusoidal current from the network, which causes harmonic distortion of the supply voltage, including the fundamental harmonic component and higher harmonic components that are multiples of the fundamental frequency. Non-sinusoidal voltage, in turn, causes additional losses of power and energy in the elements of the electrical network, causes overheating and accelerated aging of the insulation of electrical equipment, reducing its operational reliability and reducing service life, worsens the accuracy of electrical measurements, causes malfunctions in automation systems, telemechanics, relay protection, electronic systems and communications. Non-sinusoidal voltage significantly complicates the compensation of reactive power in the electrical network. Compensating devices are made on the basis of capacitors, whose electrical parameters (resistance, power, current) depend on both the magnitude of the supply voltage and its harmonic composition. The present article identifies problems and proposes solutions in terms of reactive power compensation and improving the quality of electrical energy in electrical networks containing thyristor voltage converters and frequency converters used in adjustable electric drive installations of industrial enterprises.

Power quality improvement of distribution systems asymmetry caused by power disturbances based on particle swarm optimization-artificial neural network

With an increase of non-linear load in today’s electrical power systems, the rate of power quality drops and the voltage source and frequency deteriorate if not properly compensated with an appropriate device. Filters are most common techniques that employed to overcome this problem and improving power quality. In this paper an improved optimization technique of filter applies to the power system is based on a particle swarm optimization with using artificial neural network technique applied to the unified power flow quality conditioner (PSO-ANN UPQC). Design particle swarm optimization and artificial neural network together result in a very high performance of flexible AC transmission lines (FACTs) controller and it implements to the system to compensate all types of power quality disturbances. This technique is very powerful for minimization of total harmonic distortion of source voltages and currents as a limit permitted by IEEE-519. The work creates a power system model in MATLAB/Simulink program to investigate our proposed optimization technique for improving control circuit of filters. The work also has measured all power quality disturbances of the electrical arc furnace of steel factory and suggests this technique of filter to improve the power quality.

Validation of photovoltaics powered UPQC using ANFIS controller in a standard microgrid test environment

The power quality improvement becomes one of the important tasks while using microgrid as main power supply. Because the microgrid is combination of renewable energy resources. The renewable energy resources are intermittent in power supply and at the peak loading condition it has to supply the required power. So, the power quality problems may increase in that time. Out of all power quality issues the voltage drop and harmonic distortion is considered as the most serious one. In recent years unified power quality conditioner (UPQC) is emerged as most promising device which compensates both utility as well as customer side power quality disturbances in effective way. The compensating potentiality used in the UPQC is limited by the use of DC link voltage regulation and the conventional proportional integral (PI) controller. In this paper the compensating potentiality of the UPQC device is controlled by an adaptive neuro fuzzy inference system (ANFIS) control and it is powered from the available photovoltaics (PV) power generation. The effect of adding an intelligent UPQC is tested in the standard IEEE-14bus environment. MATLAB 2017b is used here for testing and plotting the simulation results.

A Novel Nearest Level Modulation Method with Increased Output Voltage Quality for Modular Multilevel Converter Topology

The modular multilevel converter (MMC) topology is gaining more interest because of its modular design, high efficiency, and scalable voltage levels in medium- and high-power industrial applications, where the nearest level modulation (NLM) method is frequently preferred. In this paper, a novel NLM method is proposed with increased output voltage quality for MMC topology. In conventional NLM (C-NLM), output voltage is obtained as N + 1 levels, where N is the number of submodules (SMs) per arm. The output voltage is increased to 2N + 1 levels by the proposed NLM method without using any additional SMs. The proposed NLM method is based on the offset term injection, which is optimally determined in terms of the best output performance of MMC. Also, trapezoidal reference signal is used instead of sinusoidal reference, which provides better output voltage quality and controls the modulation process. The proposed NLM method presents simple implementation as in the C-NLM, and it is implemented to the upper and lower arms of the MMC; then, arm voltages are successfully controlled. Furthermore, output voltage returns the value of zero in the C-NLM process for low-modulation-ratio applications in relatively small amount of SM usage of MMC design. However, the proposed NLM method gives promising results instead of zero voltage. In order to validate the superior performance of the proposed NLM method, a comparative study is presented with C-NLM and third-harmonic injected NLM method in terms of total harmonic distortion (THD) and magnitude of the output voltage and current. THD of output waveforms of MMC is significantly reduced, and DC voltage utilization is remarkably increased, thanks to the proposed NLM method. In addition, capacitor voltage balancing for the proposed NLM method is accomplished to keep the capacitor voltage of each SM of MMC constant. Simulation results are presented to verify the effectiveness of the proposed NLM method under various case studies. Finally, experimental validation is carried out using a field programmable gate array (FPGA)-based hardware implementation on the laboratory prototype to show the applicability of the proposed NLM method.

Analysis of modified plug-in electric vehicle charger controller with grid support functionalities.

Power quality issues, which are mainly due to power electronic devices that are invariably used not only in domestic sector but also industries, still persist despite various mitigation strategies. The slow but steady invasion of Electric vehicles or Plug-in Electric Vehicles (PEVs) in recent years, in the automobile sector, adds woes to the power quality issues further. Majority of the charging systems presently available for charging PEVs are unidirectional and so supports Grid to Vehicle (G2V) mode only as the bidirectional integration of those vehicles into the grid is still a big challenge. However, Vehicle to Grid (V2G) support mode also deserves an equal importance as the PEV charger with V2G mode of operation is capable of supporting grid functionalities also, on need basis, which largely depends on the power circuit topology and controller topology it uses. Hence, in this work an improved controller topology has been designed and developed to alleviate the burdens on the grid. Support for active power demand, voltage swell and sag mitigation, in addition to catering its prime objective of charging the batteries are focused. A Second Order Generalized Integrator Phase Locked Loop (SOGI-PLL) based controller has been developed and implemented in the proposed work to improve the transient response, apart from controlling the steady-state oscillations of the grid to which it is connected to. A single phase non-isolated bidirectional PEV charger with proposed control topology has been simulated in MATLAB-Simulink for vehicle support and grid support mode of operations. The simulation proves the satisfactory operation of the proposed charger in the four quarters of active power and reactive power (PQ) plane, thus complies the design objectives of bidirectional power flow. The results obtained from the simulation show improved performance in terms of DC link voltage overshoot, steady-state oscillations, overall efficiency, voltage and current Total Harmonic Distortions (THD)

Performance Analysis of Modular Multilevel Converter with NPC Sub-Modules in Photovoltaic Grid-Integration

In this article, a three-phase modular multilevel converter (MMC) with three-level neutral point clamped converter (NPC) sub-modules (SMs) along with the placement of transformers in place of arm inductors is proposed for PV grid integration. Compared to the traditional MMCs, the proposed configuration reduces the voltage and power rating for the switches and the requirement of a high capacitor bank. In order to analyze the performance of the proposed converter arrangement, we have implemented four pulse width modulation schemes, such as Sine PWM with phase-level shifted carrier (SPWMLSC), Sine PWM with a phase-shifted carrier (SPWMPSC), Sine with the third harmonic injected level-shifted carrier (STHILSC), and Sine with the third harmonic injected phase-shifted carrier (STHIPSC). The proposed converter was simulated in the MATLAB/Simulink platform. Under normal and faulty operation, the results were presented with their performance indices of voltage and current harmonic distortion and sub-module capacitor voltage ripples at various modulation indices.

Accuracy assessment of frequency-domain models for harmonic analysis of residential type photovoltaic-distributed generation units

Since Photovoltaic-Based Distributed Generation Units (PV-DGUs) have power electronic interfaces for their grid integration, they can cause harmonic pollution in the system. Thus, the harmonic analysis is required to determine the system’s harmonic constrained PV-DGU hosting capacity and proper planning of the harmonic mitigation devices and PV-DGUs. The accuracy of the harmonic analysis highly depends on the validity of the system equipment models. Accessible literature shows that there is not a report on accuracy assessment of the PV-DGU frequency-domain harmonic models. In this paper, firstly, for numerous distorted grid voltage conditions, the current harmonic distortion nature of the single-phase transformerless two-level H-bridge residential type on-grid PV inverter is examined in an experimental test system. Secondly, for current harmonic analysis of the examined PV inverter, the accuracy of the widely known frequency-domain models is statistically analyzed under numerous distorted grid voltages. For the accuracy assessment of the models, the measurements obtained from an experimental test system are considered as reference values. Finally, to investigate the effect of the models on the voltage harmonic distortion results of the harmonic analysis, the harmonic penetration analysis algorithm is integrated with the models, and it is simulated for IEEE 33 bus test system.

A Transformerless AC-AC Converter with Improved Power Quality Employed to Step-Down Power Frequency at Output

Variable voltage and frequency are required to govern the torque-speed characteristics of many industrial drive systems. Traditionally, this is achieved with a power converting system implemented with multistage converters. This technology is based on rectifying AC power into DC and then DC into AC with an inverter circuit. The power quality concerns of both conversion stages are tackled by selecting high switching frequency PWM control and harmonics mitigation filters. Also, using a bulky DC-link capacitor is one of the big sources of low system reliability, so this approach increases the conversion losses, circuit, and control complications. The frequency step-down conversion is very attractive with direct AC-AC converters as it has a simple control and circuit structure, but these converters face poor power quality challenges once the output frequency is decreased with respect to an input. In these converters, the total harmonic distortion (THD) of the output voltage becomes very poor once the output frequency is reduced. The problem of high THD of the output is addressed in the power converting circuits implemented with line frequency multi-winding transformers. The required number of output winding and switching devices (diodes and thyristors) increases once the value of the output frequency is decreased. This will increase the overall volume, cost, and losses. The use of a bulky and costly line frequency transformer may be eliminated if AC voltage controllers have non-inverted and inverted voltage buck capabilities, such existing topologies either have complex control schemes or require a large number of operating devices. Therefore, in this research article, a new transformerless frequency step-down converter employing fewer devices is proposed. This approach is realized with a high-frequency controlled rectifier for the required voltage stabilization and a low-frequency inverter bridge for frequency control. Its validation is supported by the results attained from Simulink and practical-based prototypes.

Repetitive Predictive Control for Current Control of Grid-Connected Inverter Under Distorted Voltage Conditions

A repetitive predictive control for grid-connected inverter current control scheme is presented in this paper under voltage harmonic distortion in the stationary reference frame. Predictive control is an approach that uses a receding horizon to achieve the optimal track for the reference. In this approach, the repetitive controller behavior is added to the predictive control to increase its performance under distorted voltage conditions. In addition, to apply the controller in the generation system, controller is designed from the perspectives of the power system. The controller is designed considering the state-space model in the stationary reference frame. The controller performance was verified using a laboratory experimental setup under distorted grid voltage condition. Experimental results confirm that the proposed controller can effectively suppress harmonics under both normal operation and distorted grid voltage conditions, and also satisfy the requirements stipulated in IEEE Std. 1547.2-2008.

Development and implementation of a voltage harmonic elimination method for the single-phase inverter operating with nonlinear load

Single-phase inverters are widely used in power conversion systems. When operating with linear loads, these inverters produce regulated quasi-sinusoidal output voltages. When feeding nonlinear loads, they absorb non-sinusoidal (distorted) currents and the inverter's output voltage deteriorates - it contains high levels of harmonics. This paper presents a method to reduce the harmonics in the output voltage. The control strategy is based on selective harmonic elimination - the method eliminates some of the low order harmonics of the output voltage. The method uses stationary reference frame voltage and current controllers. The voltage controller regulates the fundamental and eliminates certain harmonics using a modulation-demodulation technique. In the paper, the 3rd, 5th and 7th harmonics are eliminated. However, the scheme can be expanded to eliminate more higher-order harmonics. It is shown that the control proposed, significantly reduces the total harmonic distortion of the inverter's output voltage, from 5.8% to 1.64% (at full load).

Harmonic Mitigation by Optimal Allocation of Tuned Passive Filter in Distribution System

The purpose of this work is to determine the appropriate allocation of a single tuned passive filter “STPF” in a real distribution network at Tala city to prevent harmonic distortion caused by nonlinear loads. This design will cover the ideal filter parameter as well as the best filter position. The filter design is based on single and multi-objective functions that optimize the cost of the proposed filters, real power losses, total harmonic distortion “THD,” and individual harmonic distortion “IHD”. Upper and lower limitations for filter parameters, quality factor, voltage and harmonic distortion limits are determined using inequality constraints. This will be done under the equality constraint of power balance. The challenge of optimization is solved using two modern algorithms, jellyfish optimization technique “JFOT” and arithmetic optimization algorithm “AOA”, in which the placements of the filters and their parameters are selected. IEEE 33-bus radial system and an actual system as a part of the Egyptian network at Tala city are used for demonstrating the results obtained by the proposed techniques. The results reveal that the system’s harmonic distortion of current and voltage is reduced less than the limitations of the IEEE 519 standards.

An Improved Equilibrium Optimizer for Optimal Placement of Distributed Generators in Distribution Systems considering Harmonic Distortion Limits

This paper proposes an improved equilibrium optimizer (IEO) for determining optimal location and effective size of distributed generation units (DGUs) in the distribution systems in order to minimize the total power loss on distribution branches, investment cost, and operation and maintenance cost. In a good obtained solution, limits of voltage, current, and harmonic flows are also seriously considered, exactly satisfying predetermined ranges. Especially, individual harmonic distortion (IHD) and total harmonic distortion (THD) of bus voltage must fall into IEEE Std. 519. The proposed IEO is developed from the original equilibrium optimizer (EO), which was motivated by control volume mass balance models. This novel algorithm can effectively expand the search area and avoid the premature convergence to low‐quality solution spaces. With the determined solutions from IEO, not only are the voltages well improved but also the harmonics are mitigated from the violated values down to the allowable values of IEEE Std. 519. Moreover, the total power loss is significantly reduced from 0.2110 MW to 0.0815 MW, 0.2245 MW to 0.07197 MW, and 0.3161 MW to 0.1515 MW for IEEE 33‐bus, IEEE 69‐bus, and IEEE 85‐bus radial distribution systems, respectively. Not only that, the total cost of DGUs is also more economical and consumes only $3.4753 million, $3.2840 million, and $3.0593 million corresponding to the three systems for a 20‐year planning period. The performance of the proposed algorithm is compared to three other implemented methods consisting of artificial bee colony (ABC) algorithm, salp swarm algorithm (SSA), and EO and eight previously published methods for the three test systems. The comparisons of results imply that IEO is better than other methods in terms of performance, stability, and convergence characteristics.

Heterodyne Controlled Matrix Converter as a Direct Frequency Reduction Method for Microturbine Generators (MTG)

In this paper a control method for a matrix converter (MC) based on the heterodyne concept from the communication field is presented. The method is used to convert the high frequency of a microturbine generator’s (MTG) output voltage to the utility grid’s frequency. In this control method a frequency modulation (FM) of the MC’s switching frequency is achieved using a DQ0 analysis of the converter’s filtered output voltage with the utility grid’s frequency as a reference. After filtration, the MC achieves a conversion to the reference frequency with a minimal total harmonic distortion (THD) of the output voltage while using a low switching frequency. In addition, the proposed method decouples the output frequency, phase angle and voltage amplitude, which allows them to be controlled separately. This significantly simplifies the required control, and enables a robust and low-cost design. The theoretical analysis, simulation and experimental results of the method are reported.

Minimization of DC-Link Capacitance and Improved Operational Performance of a 5-Level Hybrid Multilevel DC-Link Inverter

This study analyzes a single-phase hybrid multilevel dc-link (MLDCL) inverter, in which a dc-link with two capacitors is integrated into a single dc source. When controlled under the conventional modulation scheme, the MLDCL inverter synthesizes a five-level output voltage. As the capacitor-voltage balancing depends on the fundamental period, the output voltage may contain unsolicited low-order harmonics. Moreover, in the conventional scheme, this inverter requires large dc-link capacitors. To avoid these problems, the present paper develops a simple phase-shifted pulse-width modulation scheme based on redundant switching states, which controls the MLDCL inverter and balances the capacitor voltage within each carrier period. The proposed modulation scheme also minimizes the dc-link capacitance by a factor of the frequency modulation ratio while reducing the total harmonic distortion of the output voltage and current. Unlike the conventional method, the proposed scheme considerably reduces the capacitor-voltage ripples and can be regulated by increasing the carrier frequency, thereby reducing the voltage stress on the switches and improving the reliability of the inverter. The feasibility of the proposed scheme over the conventional scheme is confirmed in a comparative study. Finally, the steady-state and dynamic performances of the proposed strategy are demonstrated in simulations and validated in experiments.

Transition of energy system by regulating of Power Quality for efficiency improvements

The supply of electrical energy is of importance for the value creation of most industrialized nations. Ultimately, electrical energy is able to provide the appropriate useful energy at the point of need with virtually no emissions. This aspect plays a greater role today than ever before. When using electrical energy as a clean and sustainable energy source, it is important to note that there can be significant losses in the transmission of electrical energy between the point of generation and the point of use. These transmission losses are caused, among other reasons, by line losses due to power quality deviating from the ideal value. In principle, any deviation from the nominal values of the supply voltage listed in EN 50160 (such as voltage level, frequency or harmonic distortion) leads to an increase in transmission losses. Thus, compliance with the power quality parameters is desirable from all perspectives of (economic, ecological, social) sustainability. Especially with reference to SDGs 7, 8 and 12, a supply voltage that complies with the specified parameters is important. Unfortunately, no incentives currently exist for minimizing deviations in power quality parameters and the transmission losses they cause. Goal should be to implement a transition of energy system that provides incentives to increase the transmission efficiency of electricity. One possibility for this is the unbundling of the guarantee of the power quality parameters on a separate market. Regulatory framework conditions must be adapted for sustainable improvements in energy transmission at all levels. Nevertheless, the economic viability of power quality based business models is difficult. A promising solution is to reintroduce a supplementary factor as an extension of the equation of the incentive based regulation. The vision of the business model explained in the paper is to contribute to the efficient operation of the power grid by avoiding the propagation of harmonics through the use of compensation equipment, this is a new approach that has not yet been investigated.

Modeling and Simulation of New PWM Techniques for Hybrid 7-Level Inverters Using Simplified Switching Table

Nowadays, Cascade H-bridge (CHB) multi-level inverters (MLI) have many applications in the fields of electric drive control, high-power energy control, medium-voltage power grids, and popularization in the conversion of renewable energy power. In order to improve the quality of MLI to meet today's needs while reducing costs, it is necessary to have new methods to improve the working efficiency of the converter. Therefore, this paper presents a novel PWM control for single-phase cascaded hybrid 7-level inverter using simplified switching table (SST). The SST table converts switching states of the traditional multi-level inverter to the switching state of the hybrid cascaded inverter. The SST table is effectively designed to reduce the number of switching when performing output voltage control, thus improving the converter's working efficiency. The PWM method using proposed SST has the advantage of simple implementation, utilizing the traditional Sin-PWM techniques without re-calculating the control function or changing the carrier waveforms. The effectiveness of the proposed method will be evaluated through the voltage and current harmonic distortion factors when applying level shift carrier arrangements (LS-PWM) and speed control application of 3-phase asynchronous motor. Furthermore, in order to prove the advantage of the PWM technique using the proposed SST, the power loss of the 7-level hybrid cascaded inverter is also calculated and compared with traditional seven-level inverter and 3-level inverter. The analysis and modeling results of the 7-level hybrid inverter control are verified and evaluated using MATLAB SIMILINK and PLECS software.

Solar PV-Fed Multilevel Inverter With Series Compensator for Power Quality Improvement in Grid-Connected Systems

Power quality difficulties arise as a result of Renewable Energy Sources (RES) integrating with the grid. Voltage swell, sag, and harmonic distortion occur on the grid due to power quality issues, which have an impact on customers. An inexpensive series compensator, like the Dynamic Voltage Restorer (DVR), is the best solution for overcoming the aforementioned problems. In this article, a solar PV integrated DVR with a novel multilevel inverter is introduced to address the power quality issues in the grid. The main objective of the proposed work is to develop a DVR integrated with a 23-level multilevel inverter to enhance the power quality. In addition, an improved INC-MPPT technique is designed for the boost converter for maximum energy extraction from the solar PV modules. Despite numerous benefits of multilevel inverters, there exist several reliability challenges such as fewer component counts and reduced THD. The suggested topology can able to generate 23 levels of output voltage with asymmetrical DC sources. The MLI has several advantages such as a reduction in the overall component count, cost and size of the inverter. Additionally, a detailed mathematical analysis is presented for the rotating dq reference frame control. The dynamic performance of the DVR is evaluated with a balanced load and implemented experimentally. Simulation results of the proposed system are carried out using MATLAB/Simulink. The proposed system is implemented using a dSPACE controller with a laboratory hardware prototype and OPAL-RT real-time simulator setup as well. The results show that the design of the proposed system is more effective at compensating for voltage sag and improves the power quality significantly. The THD obtained at the grid side is lower, which is under IEEE standards.

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.