Birbhum, , India
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1.1 POWER FACTOR Power factor is defined as the cosine of the angle between voltage and current in an ac circuit. There is generally a phase difference between voltage and current in an ac circuit. cos is called the power factor of the circuit. If the circuit is inductive, the current lags behind the voltage and power factor is referred to as lagging. However, in a capacitive circuit, current leads the voltage and the power factor is said to be leading. In a circuit, for an input voltage V and a line current I, VIcos the active or real power in watts or kW. VIsin - the reactive power in VAR or kVAR. VI- the apparent power in VA or kVA. Power Factor gives a measure of how effective the real power utilization of the system is. It is a measure of distortion of the line voltage and the line current and the phase shift between them. Power FactorReal powerAverage/Apparent power Where, the apparent power is defined as the product of rms value of voltage and current. 2 P a g e LINEAR SYSTEMS In a linear system, the load draws purely sinusoidal current and voltage, the current and voltage, hence the power factor is determined only by the phase difference between voltage and current. i.e. PFcos POWER ELECTRONIC SYSTEMS In power electronic system, due to the non-linear behaviour of the active switching power devices, the phase angle representation alone is not valid. A non linear load draws typical distorted line current from the line. The PF of distorted waveforms is calculated as below The fourier representation for line current is and line voltage vs are given by, is IDC Isnsinnt vsVDC Vsnsinnt The line current is non-sinusoidal when the load is nonlinear. For sinusoidal voltage and non- sinusoidal current the PF can be expressed as Where, cosF is the displacement factor of the voltage and current. Kp is the purity factor or the distortion factor. 1,0, coscoscos ,1 11 prmsrmsp P rms rms rmsrms rmsrms KIIK K I I IV IV PF 3 P a g e Figure1.1 Input current of a single phase bridge rectifier 2 a Waveforms b harmonics spectrum Another important parameter that measures the percentage of distortion is known as the current total harmonic distortion THDi which is defined as follows Hence the relation between Kp and THDi is rms n rmsn i I I THD ,1 2 2 , 21 1 i P THD K 4 P a g e 1.2 HARMONICS Switching converters of all types produce harmonics because of the non-linear relationship between the voltage and current across the switching device. Harmonics are also produced by conventional equipment including 1 Power generation equipmentslot harmonics. 2 Induuction motorssaturated magnetics. 3 Transformers overexcitation leading to saturtation 4 Magnetic-ballast fluorescent lamps arcing and 5 AC electric arc furnances. All these devices cause harmonic currents to flow and some devices, actually, directly produce voltage harmonics.2 1.3 AFFECTS OF HARMONICS ON POWER QUALITY The contaminative harmonics can decline power quality and affect system performance in several ways 1 Conductor loss and iron loss in transformers increase due to harmonics decreases the transmission efficiency and causes thermal problems. 2 The odd harmonics in a three phase system overload of the unprotected neutral conductor. 3 High peak harmonic currents may cause automatic relay protection devices to mistrigger. 4 Excessive current in the neutral conductor of three-phase four-wire systems, caused by odd triple-n current harmonics triple-n 3rd, 9th, 15th, etc.. This 5 P a g e leads to overheating of the neutral conductor and tripping of the protective relay. 5 Telephone interference and errors in metering equipment 6 The line rms current harmonics do not deliver any real power in watts to the load, resulting in inefficient use of equipment capacityi.e. low power factor. 7 Harmonics could cause other problems such as electromagnetic interference to interrupt communication, degrading reliability of electrical equipment, increasing product defective ratio, insulation failure, audible noise etc..2 1.4 THE PROBLEM OF POWER FACTOR IN SINGLE PHASE LINE COMMUTATED RECTIFIERS Classical line commutated rectifiers suffer from the following disadvantages 1 They produce a lagging displacement factor w.r.t the voltage of the utility. 2 They generate a considerable amount of input current harmonics. These aspects negatively influence both power factor and power quality. The massive use of single-phase power converters has increased the problems of power quality in electrical systems. 6 P a g e Figure 1.2 Single phase rectifier a circuit b waveforms of input voltage and current2 1.5 STANDARDS FOR HARMONICS IN SINGLE PHASE RECTIFIERS The relevance of the problems originated by harmonics in single-phase line-commutated rectifiers has motivated some agencies to introduce some restrictions to these converters. Standardization activities in this area have been carried out for many years. As early as 1982, the International Electro-technical Committee-IEC published its standard IEC 555-2, which was also adopted in 1987 as European standard EN 60555-2, by the European Committee for Electro- technical Standardization - CENELEC. Standard IEC 555-2 has been replaced in 1995 by standard IEC 1000-3-2 1, also adopted by CENELEC as European standard EN 61000-3-2. 7 P a g e Figure 1.3 Input current harmonics produced by a single-phase diode bridge rectifier compared against IEC standards2 Standard IEC 1000-3-2 1. It applies to equipment with a rated current up to and including 16Arms per phase which is to be connected to 50Hz or 60 Hz, 220-240Vrms single-phase or 380-415Vrms three-phase mains. 2. Electrical equipments are categorized into four classesA, B, C, and D, for which specific limits are set for the harmonic content of the line current. 3. These limits do not apply for the equipment with rated power less than 75W, other than lighting equipment 8 P a g e CLASS-A It includes balanced three-phase equipments, household appliances, excluding the equipment identified as class-D. Equipment not specified in one of the other three classes should be considered as class-A equipment. CLASS-B It includes portable tools, and non-professional arc welding equipment. Class-A Balanced 3F equipment Portable tool No No Special shape and 75 1000 15.0 7.0 6.0 2.5 1.4 20 TDD Total Demand Distortion is the harmonic current distortion in of a maximum demand load current Standard IEC 1000-3-2 sets limits on the harmonic content of the current but does not specifically regulate the purity factor Kp or the total harmonic distortion of the line current THDi The values of Kp and THDi for which compliance with IEC 1000-3-2 is achieved depend on the power level. For low power level, even a relatively distorted line current may comply with the 12 P a g e standard. In addition to this, it can be seen that the distortion factor Kp of a waveform with a moderate THDi is close to unity e.g. Kp0.989 for THDi15. The following statements can be made regarding power factor 1. A high power factor can be achieved even with a substantial harmonic content. The power factor PF is not significantly degraded by harmonics, unless their amplitude is quite large low Kp, very large THDi. 2. Low harmonic content does not guarantee high power factor Kp close to unity, but low cosF. 3. As PF and THD are related to distortion and displacement factors, hence improvement in power factor i.e. power factor correction PFC also implies harmonic reduction

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