The Phenomenon Of Harmonics Engineering Essay

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The phenomenon of harmonics is not new in power distribution systems, but has not been a problem in the past due to the general absence of a large converter population coupled with an underutilized power grid. Currently, public power utilities are demanding higher power factors and higher utilization of installed transmission and distribution equipment from their customer base. They are backing this demand up by imposing power factor penalty clauses in their contracts, and demanding compliance to recently approved standards that set harmonic limits.

In recent years, harmonic in power system has increased substantially due to the increasing of non linear load. There are a number of electrical devices that are nonlinear line currents. These currents will influence the voltage on a power distribution system and can degrade the voltage waveform enough such that the operation of other electrical apparatus may be impacted.

According to IEEE Std 519-1992 [0], harmonic are sinusoidal voltages or currents having frequencies that are integer multiples of the frequency at which the supply system is designed to operate (termed the fundamental frequency, usually 50 Hz or 60 Hz). Combined with the fundamental voltage or current, harmonics produce waveform distortion. They constitute the major distorting components of the mains voltage and load current waveforms. However, the increasing content of power system inter-harmonics, for example distorting components at frequencies that are not integer multiples of the fundamental, has prompted a need to give them greater attention.

Most countries have in the past developed their own harmonic standards or recommendations, to suit local conditions. However, with growth of global trade, the need for equipment manufactured in one country to comply with standards in another has prompted concerted effort in formulating international standards on harmonics and inter-harmonics.

The rationale is to maintain a globally acceptable electromagnetic environment that co-ordinates the setting of emission and immunity limits. This is achieved using reference levels of electromagnetic disturbance, referred to as compatibility levels. The latter are recognized as the levels of severity which can exist in the relevant environment; therefore all equipment intended to operate in that environment is required to have immunity at least at that of disturbance and, thus, a margin appropriate to the equipment concerned is normally provided between the compatibility and immunity levels.

In determining the appropriate emission limits, the concept of planning level is also used. This is locally specific level of disturbance adopted as a reference for the setting of emission limits form large installations in order to co-ordinate those limits with the limits adopted for equipment intended to be connected to the power system. Again, the planning level is generally lower than the compatibility level by a specific margin that takes into account the structure and electrical characteristics of the local supply network. This margin is necessary to make allowance for possible system resonance and for an upward drift in the levels on the network due to future loads that may be connected where there is no consent required. Such loads include computers and other home and office electronic equipment that contain switched-mode power supplies. In addition there is uncertainty about the impedance of the supply systems and the customers' equipment at harmonic frequencies [4].

2.1 Causes of Harmonics

Harmonic typically appear from device with nonlinear characteristics which derive their input power from a sinusoidal electrical system. In nonlinear systems, the resistance is not a constant and in fact, varies during each sine wave. It occurs because the resistance of the device is not a constant and changes during each sine wave. So, nonlinear device is one in which the current is not proportional to the applied voltage. While the applied voltage is perfectly sinusoidal, the resulting current is distorted. Increasing the voltage by a few percent may cause the current to double and take on a different wave shapes. This, in essence, is the source of harmonics distortion in the power system. Some contributors of reflective harmonics currents are [00]:

Transmission and Distribution system such as transformers, HVDC converters and statistic VAR components.

Industrial Equipment such as AC/DC converters, AC/DC cycloconverters, switching controls, arc furnace and arc welding.

Residential and commercial equipment such as diode rectifier circuit and thyristors controlled loads.

There are other contributors of power system harmonics cause serious problems such as Audio Recorders, Battery chargers, Computer Power Unit (CPU), Copy Machine, Discharge Lighting (fluorescent, mercury, sodium, etc.), Electronic Dimmers, Electronic Ballasts, Elevators, File Servers, Laser Printers, Local Area Network (LAN), Telecommunications Equipment, Uninterrupted Power Supplies (UPS), Variables Frequency Drives (VFD), Video Recorders, Video Display Unit and the Welders [00, 2]

2.2 Harmonics effect on power system equipment

Many type of electrical equipment are sensitive to harmonics, including to transformers, cables, motors, generators and capacitor connected to the same power supply with the devices generating the harmonics. In addition in electronic equipment, electronic displays and lighting may flicker, circuit breaker can trip and computer may fail and metering can give false readings [00, 13, 4]. Each equipment have different effect to harmonics. Table 2.1 shows typical equipment effects to harmonic [30].

Table 2.1 Equipment Effects of Harmonics

More specifically, the effects of the harmonics can be described in more details as follows [00]:

2.2.1 Effects of Harmonics on Neutral Conductor

Harmonics due to many single phase distorting loads spread across three phases, such as occurs in commercial offices buildings, can give neutral currents exceeding the active line current. When harmonics are absent, the neutral conductor carries very small current, and it has been the practice to rate the neutral for all of or may be for half of the active line current. With excessive levels of harmonics due to single phase loads, there is the risk of overloading the neutral with two possible consequences. Overheating the neutral conductor with loss of the conductor life and possible risk of fire. There have been some claims that high neutral-earth voltages can affect digital equipment and local area network (LANs) if the earthing system is poor.

2.2.2 Effect of Harmonics on Rotating Machines

For both the synchronous and the induction machines, the main problems of the harmonics are increasing on the iron and copper losses, and heating by result of the high current caused by harmonics as a result reducing the efficiency [13]. The harmonics can be a one reason as an introduction of oscillating motor torque and it is usually very small. Also, the high current can cause high noise level in these machines.

2.2.3 Effect of Harmonics on Transformers

In recent papers [10] the authors have shown that there are several issues which are harmonics effect on power system that must considered into evaluation of distribution transformer losses under nonlinear load. Transformers are one of the component and usually the interface between the supply and most nonlinear loads. With the increasing use of nonlinear load the harmonic problem become worse. The increased losses in the transformer due to the harmonic distortion can cause excessive winding loss and abnormal temperature rise. From the result shown that the current harmonic distortion will increase the transformer losses and hence decreased its life expectancy. More detail, the result in increased transformer heating when the load current includes harmonic components [00]:

Rms current. If the transformer is sized only for the KVA requirement of the load, harmonic currents may result in the transformer rms current being higher than its capacity. The increased total rms current results increase conductor losses.

Eddy-current losses. These are induced currents in the transformer caused by the magnetic fluxes. These induced currents flow in the windings, in the core, and in the other connecting bodies subjected to the magnetic field of the transformer and cause additional heating. This component of the transformer losses increases with the square of the frequency of the current causing the eddy current. Therefore, this becomes a very important component of transformer losses for harmonic heating.

Core losses. The increase in core losses in the presence of the harmonics will be dependent on the effect of the harmonics on the applied voltage and the design of the transformer core. Increasing the voltage distortion may increase the eddy currents in the core lamination. The net impact that this will have depends on the thickness of the core laminations and the quality of the core steel. The increase in these losses due to harmonics is generally not as critical as the previous two.

2.2.4 Effect if Harmonics on Lines and Cables

The main problems associated with harmonics are : increased losses and heating, serious damages in the dielectric for capacitor banks and cables, appearance of the corona (the amount of the ionization of the air around the conductor or the transmission line) due to higher peak voltages and corrosion in aluminum cables due to DC current.

In reference [22] harmonic in distribution cable systems can increased ohmic losses and increased operating temperatures. The ampacity of the cable determined by the ohmic losses of cable system and the ability of its surrounding to remove the heat generated where the ohmic losses are dependent upon the presence and magnitude of harmonic current [22].

Furthermore, the higher harmonic frequencies cause a greater degree of heating in conductors because the skin effect increases as a frequency and amplitude increase [00]. The proximity effects exist because the electromagnetic field of cables in proximity can interact with each other, causing the resistance of cables to increase [23].

2.2.5 Effect of Harmonic on Converter Equipment

This equipment can be expressed as switches or On-off equipment because of the switching the current and voltage by some device such as diodes and thyristors. These converters can switch the current so, creating notches in voltage waveforms, which may affect the synchronizing of the other converter equipment. These voltage notches cause misfiring of the thyristors and creating other firing instances of the other thyristors in the equipment.

2.2.6 Effect of Harmonic on Protective Relays

The protective devices such as circuit breaker and fuses are designed to trip out in specific current and voltage and through very specific short time. The presence of the harmonic causes the difference on the voltage and current. So, this can cause failing tripping of these protective equipment. In addition, circuit breaker has some evidence that harmonic distortion of the current can affect the interruption capability of circuit breakers. Their load current can be distorted and low level faults may contain high percentages of distorted load current. High level fault currents will not be influenced by distorted load currents [6].

The authors [7] describes that how harmonics can affect the current sensing ability of thermal magnetic breakers. Its shows when nuisance opening, false sensing, overheating and altered operational characteristics have all been attributed to harmonic-rich current. Specifically, only true RMS - sensing overcurrent devices sized reliable overcurrent protection may be attained. Also, the harmonics can let the relays to operate slower and /or at higher pickup values. Over current and over voltage can cause improper operation for relays. However, this cause the unsuitable tripping time so, causing some serious damages as far as fire occurs.

2.2.7 Effects of Harmonics on Residential and Commercial Equipment

These effects can be observed for some specific important types of equipment. For instance:

Computer: sensitive to threshold voltages of digital circuit. Manufacturers impose limits on-supply-voltage harmonics distortion.

Television: distorted waveforms cause fluctuations in TV picture size and brightness

Converters (rectifiers, inverters): are sensitive to voltage so, misfiring angles for these converters.

2.3 Harmonics Standards

Nowadays, the most widespread standards for harmonic control worldwide are due to IEEE in the U.S. and IEC (International Electrotechnical Commission) in the European Union [13]:

IEEE 519-1992: IEEE Recommended Practices and Requirements for harmonic Control in Electrical Power Systems [0]

IEC 61000 : Electromagnetic compatibility [24]

NFPA 70 (1996 NEC)

These three standards deal separately with two aspects of the problem:

Quantity or level of harmonics or other Power Quality deviations tolerated at different point in their network

Ways to measure or monitor Power Quality deviations and harmonics in a network.

Both standards divide the levels of allowed harmonics into different categories:

IEEE Standard (denoted IEEE Std. 519-1992) is titles "IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems". The main focus of this standard was more suitable stance in which limitations on customers regarding maximum amount of harmonic currents at the connection point with the power utility did not pose a threat for excessive to verify that any remedial measures taken by a customers to reduce harmonic injection into the distribution system would reduce the voltage distortion to tolerable limits [13]. This standard requires verification of harmonic limits at the interface between sources and loads is described as the point of common coupling (PCC) also observance of the design goals will minimize interference between electrical equipment [13,0]. This standard is a revision of an earlier IEEE work published in 1981 covering harmonic control.

The author [10] support the standard which it's recommend for evaluating new harmonic source by measurement and detailed modeling and simulation studies. In addition, it provides several examples to illustrate how this recommendation can be implemented effectively in several practical systems

In IEC harmonic standard set their limits at the utility-customer interface and also set limits for customer equipment benefit to residential installation [13]. The last revision, the IEC harmonic standard 61000-3-2 focused on limiting equipment consumption of harmonics. It's applicable to electrical and electronic equipment having an input current up to and including 16 A per phase, and intended to be connected to public-low-voltage distribution systems [24]. Unlike IEEE-519, IEC considers the harmonic distortion assessment to cover short - and long -term effects [13].

2.3.1 Harmonic Distortion Limits [13]

The rms value of a voltage waveform, considering the distortion produced by harmonic currents, is followed by:

Standardzation of Harmonic Level


Likewise the rms value of a sinusoidal current, taking into account the distortion created by the harmonic source currents, is given by:


For information, total harmonic distortion is a parameter used in IEEE and IEC standards.



The general level of tension harmonics in the supply network at the PCC as the percent of the rated voltage according to IEEE are characterized in Table 2.1[0]:

Table 2.1

Recommended Voltage Distortion for General Systems IEEE 519

Table 2.2 [0] shows the harmonic current limits based on the size of the load to the size of the power system that the load is connected to. It is recommended that load current calculation should be calculated as the average current of the maximum demand for the preceding 12 months. It can be noted in Table 2.2 that as the size of the user load decreases with respect to the size of the system, the percentage harmonic current that the user is allowed to inject into the utility system increases [25].

Table 2.2

The harmonic Current Limits IEEE 519-1992

In table 2.3 present the limits for individual harmonic current for every one of the classified equipment classes [24].

Table 2.3

Harmonic Current Limits for Different Equipment Classes

2.3.2 Factors Influencing the Development of Standards [26]

To develop a harmonic standards, it's has the following issues

Description and characterization of the phenomenon

Major source of harmonic problems

Impact on other equipment and on the power system

Mathematical description of the phenomenon using indices or statistical analysis to provide a quantitive assessment of its significance

Measurement techniques and guidelines

Emission limits for different types and classes of equipment

Immunity or tolerance level of different types of equipment

Testing methods and procedures for compliance with the limits

Mitigation guidelines

2.4 Harmonic Reference Impedance

If the power system appears to a very low impedance (for instance, to a harmonic source) at the resonant frequency, then this condition is termed series resonance, Likewise, if the system appears to be a very high impedance at the resonant frequency, the this condition is termed parallel resonance. In either case, if the resonant frequency of the power system happens to be close to one of the frequency generated by a harmonic source in the system, the result may be the flow of high harmonic currents ( or the appearance of high harmonic voltage) [12].

Although a system resonance condition does not produce harmonic currents or voltages, small currents (voltages) generated by a harmonic source in the power system can be amplified significantly by a resonance condition.

2.5 Harmonic Monitoring

By finding several of reference, we can know experience for harmonic monitoring. The monitoring involved simultaneous measurements of the three-phase harmonic current and voltage from the residential, commercial, and industrial load sectors. To installed the power line monitor at a site, there have an assessment to finished like listing of the installed loads, a description of the power supply installation, an evaluation of the wiring quality, assessment of on-site standby generating facilities, and establishment of an approximate schedule of daily and weekly load connections and their operation [8]. In power quality monitoring, there have two key considerations like instrument hardware and the software capability for data collection and analysis [9]. It's essential for determining the optimum configuration for a comprehensive monitoring system.

Below are the examples of the several issues when looking at power quality monitoring hardware [9]:

Backup of data collected even when the power fails.

Enclosure - depends on portable or permanent application

Sampling rate - is it fast enough for RMS, transients, energy and harmonics measurement?

Ease of use, set up and programming

Processing power - how much data is reduced by instrument?

Communications -current state of the art uses Ethernet, TCP/IP

In order to design a solution for a harmonics problem, we have to execute the following steps:

Monitor the network according to the standard

Measure the specific branch that is suspected to be the cause of the problem or the specific branch that is suffering from problems.

Analyze the results of both steps 1 & 2 to achieve a unique conclusion with a clear recommendation for a solution

According to the Model chosen to represent the network, make the proper calculation for obtaining a realistic representation of the ohmic resistance values of the network components or branches to avoid unwanted resonance effects (that can be disastrous)

Following the implementation of the solution, monitor again the network to compare the expected result to the real one and adjust the elements that require adjustments.

As described above and according to many articles and books related to all aspects of the Harmonics subject, there are two main obstacles while dealing with Harmonic problems:

Know and be able to use existing standards and rules

Be able to create a relevant model representing the monitored network during the monitoring stage and after adding new elements to the network.

2.6 Harmonic Events and Statistic

In reference [27] present that the examiners effect of harmonic distortion on power transformers on local university in southern Peninsular Malaysia. The first case is at the computer centre building and the second case being the office and lecture hall buildings. Difference that the number of computers connected to the first case is much higher than that of the second case. However, each building include personal computers, fluorescent lamps, air conditioners, printers, photocopy machines and LCD projectors. From the result, show that it is not sufficient to apply the standard IEC 61000 for the both cases; there will still be a loss of life at a higher loading because the lifespan will be maintained only at 90% of the load. In their simulation results of the harmonic effects on transformers show that higher the loads, the lower will be the life of transformer due to current harmonics generated by the electrical device.

Similarly, this paper [28] also present the investigation on power quality report at Electrical & Electronic Engineering department building in University Science Malaysia for three phase four- wire system. This investigation carried out based on power system harmonic for distribution and transmission systems monitoring. Difference between the both cases, the first case being when the building is connected with load and without students during semester break. For the case no. 2, the study is carried out with loads and there were student attending lecturer, tutorials, laboratory session and etc. From the results, show that pf become worse after office hour, and the measure maximum neutral currents is Case no. 1 higher with Case no. 2. Also, these papers have been monitor harmonic levels and total harmonic distortion for the power distribution system.

2.7 Harmonic Analysis

The use of loads with nonlinear characteristics, such as arc furnace, result in harmonic voltage and current generation. Of the many types of arcing devices on the power system today, arc furnaces may be the most notorious harmonic producers because they have grwat capacity lumped together on one place. It has been found that the arc at the electrode is basically a voltage clamp with a trapezoidal shape waveform is shown.

Under unbalanced conditions of electrode arcing, there could be significant amount of third harmonics and its multiples.

Harmonic analysis is considered in many industrial facilities. There are three major reasons for interest in harmonic analysis application [11]:

The number and size of harmonic producing devices on the plant electrical system is increasing. The most important category of these harmonic sources is power electronic devices such as rectifiers, inverters, and adjustable speed drives. Arc furnaces technology is improving and steel melt shops are incorporating ladle arc refineries

Shunt capacitor banks are being applied in greater numbers for power factor control. Capacitors do not produce harmonics, but they create resonant conditions which can magnify harmonics voltages and currents produced by other devices.

System loads are becoming more sensitive to harmonic distortion. Electronic controls often require clean waveform for synchronization and control. Increased harmonics duty affects motors and transformers causing excessive heating. Capacitor banks can experience failures or nuisance fuse blowing due to harmonic resonance conditions.

Harmonic power system analysis basically requires the same type of information as that required for the analysis of the system under steady-state conditions. The exception to this is the harmonic current source, which must be represented through solid-state switching to recreate the operation of power converters or through appropriate models to represent magnetic core saturation and are devices. A precise representation of the power system elements will be necessary if an accurate prediction of harmonic response is required.

The propagation of harmonic currents is influenced by a number of factor that relate the offending and affecting parties because the two play a major role in the propagation mode of the harmonic currents in the power system. The waveform distortion produced by a strong harmonic source, for example, may still be tolerable to the power system if its dominant harmonic is farther away from natural resonant points in the system. Conversely, a small harmonic source may give rise to large waveform distortion if any of its characteristic harmonics coincides with a resonant frequency in the system, as was illustrated.

The growing need to conduct harmonic analyses in electrical power systems makes in convenient to review the fundamental principles that govern the flow of harmonic currents. In the process, we must look at relevant aspects like the importance of linear loads as harmonic distortion attenuation elements. It will be important to find the interaction between the different elements of the circuit in relation to the establishment of parallel resonance points. Ascertaining the relationship between the total harmonic distortion level and the voltage notching caused during the operation of thyristors or any other electronic switching devices in power converters is also important.

Power Frequency Vs Harmonic Current Propagation

It is important to highlight that 60-Hz power flow studies are centered in the steady - state solution of electric network to establish optimum operating conditions for a given network to satisfy generation and load requirements. A load flow study will investigate system steady-state load performance under normal operating conditions. Power sources including electric company substations and distributed generation are involved. All significantly system loads encompassing resistive and inductive elements, capacitor banks associated with power factor, voltage profile, and harmonic filters are involved in load flow analysis.

Source equivalent model are often, assumed, especially in extended networks. Eventually, industrial installations require through representations, particularly when detailed characteristics of distributed generation or network topology are desired. A load flow study is usually carried out in power system analysis to determine voltage, current, and power quantities under steady-=state operation.

The reasons for conducting a power flow study are diverse:

Determine the flow of active and reactive power required for estimation of power losses.

Assess the requirements of reactive power compensation

Estimate voltage profile along the feeders, particularly at remote locations, under heavy load conditions. This helps utilities to define corrective actions to compensate sagging voltage profiles along the feeders and maintain voltage within limits stipulated by voltage regulation policies.

Assess loadbility limits of distribution systems under different operation scenarios, which can call for the need of resizing conductors and or/transformers. Overload feeder sector and transformers contribute to increased losses.

Harmonic flow studies, in contrast, are conducted to determine the propagation of current components of current components of frequency other than the fundamental and the resultant distortion of the voltage waveform. The aim of these studies, among other, is:

Determine individual and total harmonic distortion levels produced by non-linear loads at the location of harmonic sources and at the distribution substation.

Determine harmonic resonant frequencies at capacitor bank locations.

Assess the increased losses due to harmonic currents and take action when they approach thresholds that can have an impact on equipment lifetime.

Specify design characteristic of harmonic filters that can permit the reduction of harmonic distortion levels within recommended limits. This is particularly important when severe harmonic distortion produced by certain customer loads penetrates into adjacent customers installations.

Properly define size of capacitor banks so that the resultant parallel peak impedance stays away from characteristic harmonic of harmonic-producing nonlinear loads.

Figure below shows voltage and current waveforms for cases when (a) voltage is in phase with current; (b) voltage leads current; and (c) current leads voltage involving a power factor equal to 0.7.These results obtained in a typical load flow

Voltage in phase with current

Voltage leading current

Figure 3: Voltage and current waveforms in a typical load flow calculation. (a) Voltage in phase with current. (b) Voltage leading current. (c) Current leading voltage

2.8 Harmonic mitigation techniques

There are many solutions to prevent damage due to harmonic. Typically, these solutions can be categorized into three classes:

Solutions in the manufacturing process itself

Solutions between the process and the public electric grid

Solutions in the grid

Many mitigation techniques have been proposed and implemented to maintain the harmonic voltages and current within recommend levels:

High power quality equipment design

Harmonics cancelation

Dedicated line or transformer

Optimal placement and sizing of capacitor banks

Derating of power system devices

Harmonic filters (passive, active, hybrid) and custom power devices such as active power line conditioners (APLC's) and unified or universal power quality conditioners (UPQC's).

More specifically, the mitigation techniques can be described in more details as follows:

2.8.1 High Power Quality Equipment Design

The use of nonlinear and electronic-based devices in steadily increasing and it is estimated that they will constitute more than 70% of power loading by year 2010 [4]. Therefore, the designers and product manufacturers increased effort to produce devices that generate lower current distortion, and for end -users to select and purchase high power quality devices. These actions have already been started in many countries, as reflected by improvements in fluorescent actions lamp ballast [31], efficiency energy saving lamps [32], improved PWM adjustable-speed drive controls [34], high power quality battery chargers [33], switch mode power supplies uninterruptible power source [35].

2.8.2 Harmonic Cancellation

There are some relatively simple techniques that use transformer connections to employ phase-shifting for the purpose of harmonic cancellation, including [4, 36]:

Delta-delta and delta-wye transformer (or multiple phase shifting transformers) for supplying harmonic producing loads in parallel (resulting in twelve-pulse rectifiers) to eliminate the 5th and 7th harmonic components.

Transformers with delta connection to trap and prevent triplen (zero-sequence) harmonics from entering power systems

Transformers with zigzag connection for cancellation of certain harmonics and to compensate load imbalances,

Other phase-shifting techniques to cancel higher harmonic orders, if required

Canceling effects due to diversity have been discovered

2.8.3 Dedicated Line or transformer

Interharmonics (e.g., cause by induction motor drives) are examples of problems that can be reduced at the terminals of a sensitive load by a dedicated transformer. They can also attenuate capacitor switching and lighting transients coming from the utility system and prevent nuisance tripping of adjustable-speed drives and other equipment. Isolate transformers do not totally eliminate voltage sags or swells. However, due to inherent large impedance, their between PC and the source of disturbance (e.g., system fault) will lead to relatively shallow sags.

2.8.4 Optimal Placement and Sizing of Capacitor banks

It is well know that proper placement and sizing of shunt capacitor banks in distorted networks can result in reactive power compensation, improved voltage regulation, power factor correction, and power/energy loss reduction [37]. The capacitor placement problem consists of determining the optimal numbers, types, locations, and sizes of capacitor banks such that minimum yearly cost due to peal power/energy losses and cost of capacitor is achieved, while the operational constraints are maintained within required limits.

Most of reported techniques for capacitor placement assume sinusoidal operating conditions. These methods include nonlinear programming, and near global methods (genetic algorithms, simulated annealing, tabu search, artificial neural networks, and fuzzy theory) [38-42].

According to newly developed investigation based on fuzzy and genetic algorithms, proper placement and sizing of capacitor banks in power systems with nonlinear loads can prevention of harmonic parallel resonances, as well as improved power quality [41, 42].

2.8.5 Derating of Power System Devices

Power system components must be derated when supplying harmonic loads. Commercial buildings have drawn the most attention in recent years due to the increasing use of nonlinear loads. According to the IEEE dictionary, derating is defined as "the intentional reduction of stress /strength ratio (e.g., real or apparent power) in the application of an item (e.g. cables, transformer, electrical machines), usually for the purpose of reducing the occurrence of stress-related failure (e.g. reduction of lifetime due to increased temperature beyond rated temperature)."

There are several techniques for determining the derating factors (functions) of appliances for non-sinusoidal operating conditions including:

From tables in standards and published research (e.g. ANSI/IEEE StdC57.110 for transformer derating)

From measured (or computed) losses

By determining the K-factor and

Based on the Fhl-factor

2.8.6 Harmonic Filters, APLCS, and UPQCs

Harmonics filters are generally divided into passive, active and hybrid filters. It's only can compensate for harmonic currents and/ or harmonic voltages at the installed bus and do not consider the power quality of other buses [3]. Hybrid structures combine of active filters with passive filters. Passive filters use passive components such as resistors, inductors, and capacitors to reduce the overall filter rating and improve its performance [2]. Active filters are classified into single-phase active filters and three-phase active filters [43].

2.9 Economics evaluation on harmonic affects

The quality of power can have a direct economic impact on utilities, customer and specific equipment. The economic effects of harmonics are shorter equipment lifetime reduced energy efficiency and a susceptibility to nuisance tripping. Shorter equipment lifetime can be very expensive. Equipment such as transformers is usually expected to last for 30 and 40 years and having to replace it in 7 to 10 years can have serious financial consequences [14]. The cost of avoidance is relatively small, requiring only good installation practice and proper equipment selection. Installing cables that are one to two sizes greater than the calculated minimum reduces losses and operating costs at very little increase in initial cost.

Many papers can be found dealing with the cost of energy losses and premature aging [15, 16, 17, 18, 19] but practically no contribution refers to the misoperation cost. The effects of the voltage and current distortion on the equipment that can be economically quantified are the energy losses, the premature aging and the misoperation [20]. The evaluation of the cost to the electric utility to contend with the harmonic pollution is the first contributions [18, 19]. The costs include the total active power losses values as well as the capital invested in the design and construction of filtering system and the cost due to premature aging cost of the equipment recognized as potential additional cost but it was not include in this cost estimation. In [16, 17] the cost due to harmonic was extended to take into account also the premature aging of the equipment and the operating cost. A simplified approached base on closed form relation was proposed to evaluate the above quantities but it can apply when considering only one group of nonlinear load is the main cause of the harmonic pollution. The operating costs are referred to the cause of incremental energy losses cause by harmonic flow in each component but the incremental cost of demand lost are not taken into account. The aging costs are referred to incremental of investment cost cause by premature aging of components due to harmonic pollution. The procedure steps needed to compute the cost of energy losses can be found in [15, 18, 19] for a distribution system and in [16, 17] for the industrial system also referring the probabilistic scenario.

To evaluate the cost of the additional energy losses and the aging cost arising for the system life period it is required the knowledge of system operating conditions in the study period network configurations and a typical duration of system states, the knowledge of type, operating conditions and absorbed power level of linear and nonlinear loads, the knowledge of life models of equipment and components to estimate the failure times of their electrical insulation and the assignment of the buying costs of the components together with their variation rate [21]. For estimating the aging costs in presence of statistically characterized harmonics the procedure is described in [16, 17] referring to cases in which the thermal stress is prevailing.

The system operating costs and the aging costs increase with the harmonic pollution and with a law dependent on the type and on the size of equipment [20]. In particular the aging costs can assume not negligible values of high levels of harmonic pollution also in case of only the thermal stress. For a practical quantification of the misoperation cost, it can be also introduced the concept of "mission-quality" of the equipment, for example the quality of the equipment performance that can be compromises by harmonics that, together with a measurable "quality performance figure", can allow the computation of the misoperation economical damage [20].