HARMONIC STUDY REPORT
Harmonic Study
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CONTENT 1.INTRODUCTION............................................................................................................2 2.BASIC CONCEPT ...........................................................................................................4 3.EFFECT OF HARMONICS ON POWER SYSTEM......................................................7 3.1 MOTORS...............................................................................................................................................7 3.2 TRANSFORMERS................................................................................................................................7 3.3 CAPACITOR BANKS............................................................................................................................8 3.4 CABLES................................................................................................................................................9 3.5 NEUTRAL.............................................................................................................................................9
4.HARMONIC LIMITING STANDARD IEEE 519 – 1992 AT A GLANCE.................11 5.HARMONIC DISTORTION..........................................................................................13 5.1 HARMONIC DISTORTION AT 415 V BUS..........................................................................................13 5.2 HARMONIC DISTORTION AT 33 KV LEVEL......................................................................................13 5.3 CONCLUSIONS
...........................................................................................................................14
6.EFFECT OF HARMONICS ON TRANSFORMERS...................................................15 6.1. AN OVERVIEW OF DIFFERENT STANDARDS FOR TRANSFORMERS HANDLING NONSINUSOIDAL LOAD...................................................................................................................................15 6.2. DERATING CALCULATIONS FOR CENTRAL UTILITY TRANSFORMERS.....................................16
6.2.1 OPERATION PHILOSOPHY..........................................................................16 6.2.2 TRANSFORMER DETAILS...........................................................................17 6.2.3 FACTOR K CALCULATIONS (BS 7821, PART 4)......................................17 6.3 CONCLUSIONS...................................................................................................................................19
7.CAPACITOR BANKS...................................................................................................20 7.1 SYSTEM DETAILS..............................................................................................................................20 7.2 CALCULATION OF RESONANCE FREQUENCY...............................................................................20 7.3 CONCLUSIONS...................................................................................................................................22
1.
INTRODUCTION With increasing use of non-linear loads such as variable frequency drives, UPS, SMPS, electronic ballast etc the power systems are getting highly polluted by harmonics which is leading to premature failures of Harmonic Study
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electrical and electronic equipments as well as nuisance tripping leading to production loss. So it is imperative that a study of power quality of the electrical distribution system of a plant should be made to asses the level of pollution due to harmonics and adequate measures should be taken to control it. The standard which is used to deal with the harmonic limits in the system is IEEE 519-1992. This standard is basically designed for Utilities to frame limits of harmonic distortion by the users of utility power supplies on grid to which they are connected; so a word to word application of this standard to a distribution system in a plant may result in over-design, so a fair amount of approximation is required while applying this standard at industrial plant level and same as been done here.
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2.
BASIC CONCEPT A pure sinusoidal voltage is a conceptual quantity produced by an ideal AC generator built with finely distributed stator and field windings that operate in a uniform magnetic field. Since neither the winding distribution nor the magnetic field are uniform in a working AC machine, voltage waveform distortions are created, and the voltagetime relationship deviates from the pure sine function. The distortion at the point of generation is very small (about 1% to 2%), but nonetheless it exists. Because this is a deviation from a pure sine wave, the deviation is in the form of a periodic function, and by definition, the voltage distortion contains harmonics. When a sinusoidal voltage is applied to a certain type of load, the current drawn by the load is proportional to the voltage and impedance and follows the envelope of the voltage waveform. These loads are referred to as linear-loads (loads where the voltage and current follow one another without any distortion to their pure sine waves). Examples of linear loads are resistive heaters, incandescent lamps, and constant speed induction and synchronous motors. In contrast, some loads cause the current to vary disproportionately with the voltage during each half cycle. These loads are classified as nonlinear loads, and the current and voltage have waveforms that are non-sinusoidal, containing distortions, whereby the 50-Hz waveform has numerous additional waveforms superimposed upon it, creating multiple frequencies within the normal 50-Hz sine wave. The multiple frequencies are harmonics of the fundamental frequency. Normally, current distortions produce voltage distortions. However, when there is a stiff sinusoidal voltage source (when there is a low impedance path from the power source, which has sufficient capacity so that loads placed upon it will not
effect the voltage), one need not be concerned about current distortions producing voltage distortions. Examples of nonlinear loads are battery chargers, electronic ballasts, variable frequency drives, and switching mode power supplies. As Harmonic Study
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nonlinear currents flow through a facility's electrical system and the distribution-transmission lines, additional voltage distortions are produced due to the impedance associated with the electrical network. Thus, as electrical power is generated, distributed, and utilized, voltage and current waveform distortions are produced. Power systems designed to function at the fundamental frequency, which is 50-Hz in India, are prone to unsatisfactory operation and, at times, failure when subjected to voltages and currents that contain substantial harmonic frequency elements. Very often, the operation of electrical equipment may seem normal, but under a certain combination of conditions, the impact of harmonics is enhanced, with damaging results. Thus the harmonics are AC voltages and currents with frequencies that are integer multiples of the fundamental frequency. On a 50-Hz system, this could include 2nd order harmonics (100 Hz), 3rd order harmonics (150 Hz), 4th order harmonics (200 Hz), and so on. Normally, only odd-order harmonics (3rd, 5th, 7th, and 9th) occur on a 3-phase power system. If we observe even-order harmonics on a 3phase system, we more than likely have a defective rectifier in our system. Let us understand this by superimposing the third harmonic and fifth harmonic voltage on perfectly sinusoidal harmonic voltage and resulting harmonically distorted waveform. The figure 1 is the fundamental sinusoidal waveform, figure 2 is the third harmonic and figure 3 is the fifth harmonic waveform. Figure 4 is the resultant distorted wave form.
FIGURE- 1 Perfectly Sinusoidal Waveform. U (t) = U1 Sin (wt)
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= FIGURE- 2 Third Harmonic Waveform. U 3(t) = U3 Sin (3wt)
FIGURE - 4 Resultant Distorted Waveform. U(t) = U1 Sin (wt) + U3 Sin (3wt) + U5 Sin (5wt)
+
FIGURE- 3 Fifth Harmonic Waveform. U 5(t) = U5 Sin (5wt)
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3.
EFFECT OF HARMONICS ON POWER SYSTEM We have seen that a harmonic affected voltage and current consist of voltage and current of multiple frequencies; this gets circulated along the fundamental component in the power system. This presence of current and voltages of multiple frequencies results in increased losses and overloading in the power system, the effects of harmonic on different component of power system are discussed in brief below.
3.1
MOTORS
There is an increasing use of variable frequency drives (VFDs) that power electric motors. Voltage supplied to a motor sets up magnetic fields in the core, which create iron losses in the magnetic frame of the motor. Hysteresis and eddy current losses are part of iron losses that are produced in the core due to the alternating magnetic field. Hysteresis losses are proportional to frequency, and eddy current losses vary as the square of the frequency. Therefore, higher frequency voltage components produce additional losses in the core of AC motors, which in turn, increase the operating temperature of the core and the windings surrounding in the core. Application of nonsinusoidal voltages to motors results in harmonic current circulation in the windings of motors. The net rms current is [I.sub.rms] = [square root of [([I.sub.1]).sup.2] + [([I.sub.2]).sup.2] + [([I.sub.3]).sup.2] +] ..., where the subscripts 1, 2, 3, etc. represent the different harmonic currents. The [I.sub.2]R losses in the motor windings vary as the square of the rms current. Due to skin effect, actual losses would be slightly higher than calculated values. Stray motor losses, which include winding eddy current losses, high frequency rotor and stator surface losses, and tooth pulsation losses, also increase due to harmonic voltages and currents.
3.2 TRANSFORMERS
The harmful effects of harmonic voltages and currents on transformer performance often go unnoticed until an actual failure occurs. In some instances, transformers that have operated satisfactorily for long periods have failed in a relatively short time when plant loads were Harmonic Study
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changed or a facility's electrical system was reconfigured. Changes could include installation of variable frequency drives, electronic ballasts, power factor improvement capacitors, arc furnaces, and the addition or removal of large motors. Application of nonsinusoidal excitation voltages to transformers increases the iron losses in the magnetic core of the transformer in much the same way as in a motor. A more serious effect of harmonic loads served by transformers is due to an increase in winding eddy current losses. Eddy currents are circulating currents in the conductors induced by the sweeping action of the leakage magnetic field on the conductors. Eddy current concentrations are higher at the ends of the transformer windings due to the crowding effect of the leakage magnetic fields at the coil extremities. The eddy current losses increase as the square of the current in the conductor and the square of its frequency. The increase in transformer eddy current loss due to harmonics has a significant effect on the operating temperature of the transformer. Transformers that are required to supply power to nonlinear loads must be de-rated based on the percentages of harmonic components in the load current and the rated winding eddy current loss.
3.3
CAPACITOR BANKS
Many industrial and commercial electrical systems have capacitors installed to offset the effect of low power factor. Most capacitors are designed to operate at a maximum of 110% of rated voltage and at 135% of their KVAR ratings. In a power system characterized by large voltage or current harmonics, these limitations are frequently exceeded, resulting in capacitor bank failures. Since capacitive reactance is inversely proportional to frequency, unfiltered harmonic currents in the power system find their way into capacitor banks, these banks act like a sink, attracting harmonic currents, thereby becoming overloaded. A more serious condition, with potential for substantial damage, occurs as a result of harmonic resonance. Resonant conditions are created when the inductive and capacitive reactance become equal in an electrical system. Resonance in a power system may be classified as series or parallel resonance, depending on the configuration of the resonance circuit. Series resonance produces voltage amplification and parallel resonance causes current multiplication within an electrical Harmonic Study Done By - VT Page 8 of 22
system. In a harmonic rich environment, both types of resonance are present. During resonant conditions, if the amplitude of the offending frequency is large, considerable damage to capacitor banks would result. And, there is a high probability that other electrical equipment on the system would also be damaged.
3.4 CABLES
The flow of normal 50-Hz current in a cable produces [I.sup.2]R losses and current distortion introduces additional losses in the conductor. Also, the effective resistance of the cable increases with frequency due to skin effect, where unequal flux linkages across the cross section of the cable causes the AC current to flow on the outer periphery of the conductor, higher the frequency of the AC current, the greater this tendency. Because of both the fundamental and the
harmonic currents that can flow in a conductor, it is important to make sure a cable is rated for the proper current flow.
3.5 NEUTRAL In a three phase system the voltage waveform from each phase to the neutral star point is displaced by 120 ° so that, when each phase is equally loaded, the combined current in neutral is zero. When the loads are not balanced only net out of balance current flows in the neutral. In the past, installers (with the approval of standard authorities) have taken advantage of the fact by installing half sized neutral conductors. However, although the fundamental component cancels out but harmonic components do not -in fact those that are an odd multiple of three times the fundamental, the triple-N (triplen) harmonics, add in the neutral. Case studies in high harmonic affected commercial buildings generally show neutral currents between 150 % and 210 % of the phase current often in half sized neutral conductors. This results in overloading and overheating of neutral and often failure of neutral.
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4.
HARMONIC LIMITING STANDARD IEEE 519 – 1992 AT A GLANCE. IEEE 519 was introduced in 1983 and was more recently revised in 1992. It was intended to provide direction on dealing with harmonic introduced by static converters and non-linear loads. The standard is basically prepared to set standard for limitation of harmonic distortion by the users of utility power supplies on grid to which they are connected, it is also widely used to define harmonic limiting standards inside the plant due to absence of any other relevant harmonic limiting standard for the systems, however use of this standard inside the plant makes it very stringent for the user. Terms Pertaining to IEEE 519-1992
5.
1. PCC: Point of common coupling is defined as the point where non-linear loads are connected to main bus. 2. ISC: Short circuit current of the bus under consideration. 3. IL: 15 or 30 minute (average) maximum demand current. 4. TDD: Total demand distortion. TDD is identical to THD except IL (as defined previously) is used instead of the fundamental current component. Ih: Individual harmonic current component. It may be noted that there are no limits recommended for individual loads like V.F.Ds etc but only for the overall system. The limits specified may however, be discretionally to various P.C.Cs to understand the impact the existing level of harmonics may have on other loads on the common bus. The point of analysis (POA) can be chosen as per the guidelines with specific aim in view. IEEE 519-1992 recommends different limits on Individual Harmonics (Ih) and Total Demand Distortion (THD), depending on the ISC/IL ratio. ISC isthe short circuit current at the PCC, and IL is the maximum demand load current (fundamental) at the PCC. More current distortion is allowed at higher ISC/IL ratios, since voltage distortion decreases as the ratio increases. IEEE 519-1992 classifies systems in three categories viz. Special Application, General System & Dedicated System to set limit for voltage THD. Table 1 below specifies the harmonic current limits at PCC.
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The THD of Voltage specified for “General Systems” in IEEE 519-1992 is 5%. If THD for current complies with this standard then no need to calculate TDD.
Table 1 - Harmonic Distortion Limits as per IEEE 519-1992.
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5.
HARMONIC DISTORTION 5.1
Sr. No
HARMONIC DISTORTION AT 415 V BUS
Feeder /Drive
1
Trafo 1 (MLTP A) 2 Trafo 2 (MLTP A 3 Trafo 3 (MLTP A 4 MDB 3 5 MDB 1 6 UPS 1 7 UPS 2 TABLE 2
ISC (kA)
ISC / IL
TDD (%) Permitte d
TDD (%) Actual
Distortion
100
115
15
12.85
100
64
12
4.70
100
99
12
2.12
100 100 10 10
598 170.6 1221 2778
15 15 20 20
13.13 12.4 19.34 19.6
SAFE SAFE SAFE SAFE
SAFE SAFE SAFE
(Refer Annexure A for detail data.)
Sr. No
Feeder /Drive
1 2 3 4 5 6 7 8
Printing 1 Printing 2 Biscuit 1 Biscuit 2 Soap 1 Soap 2 Snacks Cream & Shampoo TABLE 3
ISC (kA)
ISC / IL
TDD (%) Permitte d
TDD(%) Actual
Distortion
100 100 100 100 100 100 100 100
164 266 233 605 143 132 140 540
15 15 15 15 15 15 15 15
8.5 6.8 20.35 21.4 18 12.45 16.85 13.9
SAFE SAFE UNSAFE UNSAFE UNSAFE SAFE UNSAFE SAFE
(Refer Annexure A for detail data.)
5.2
Sr. No
HARMONIC DISTORTION AT 33 KV LEVEL
Feeder /Drive
1
33 KV Incomer TABLE 4
ISC (kA)
ISC / IL
TDD (%) Permitte d
TDD (%) Actual
Distortion
26.2
757.74
15
8
SAFE
(Refer Annexure A for detail data.)
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5.3
CONCLUSIONS
1. The more serious voltage harmonic distortion level (THD) at all buses is well below the safe limit of 5 %. (Refer Annexure A) 2. The current distortion level at 33 KV bus is under safe limits. 3. The current harmonic distortion on 415 bus (Main LT Panel) is under safe limits. 4. The current harmonic injection from PCC of Division indicates that the harmonic distortion at the PCC of Printing, Soap PCC 2 and Cream & Shampoo PCC are at safe level. 5. The current harmonic injection from PCC of Division indicates that the harmonic distortion at both the PCC of Biscuit, PCC of Snacks, Soap PCC 1 are unhealthy level with a th predominance of 5 and 7th harmonic; so a detailed harmonic analysis is required and suitable harmonic mitigation measures should be taken thereafter. 6. The TDD of both Lighting UPS of Utility are alarmingly closed to limits, this high TDD should be discussed with OEM to identify the reason.
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6.
EFFECT OF HARMONICS ON TRANSFORMERS 6.1. AN OVERVIEW OF DIFFERENT STANDARDS FOR TRANSFORMERS HANDLING NON-SINUSOIDAL LOAD REF. STANDARD
FORMULA
REMARK 1.
K-Factor; UL-1561, UL1562 (Underwriter Laboratories)
Where Ih = Individual Harmonic component IR= Rated RMS load current of transformer. h = The harmonic order
First the K-factor of the nonsinusoidal load which the proposed transformer has to feed is calculated. 2. Then a transformer of K-Factor rating above the K-Factor rating of the load is chosen, typical K-Factor rating of transformers is 1,4,9,13,20,30,40,50. 3. This is used when choosing new transformers; the K-Factor transformers have tolerance in their design to accommodate the losses due to harmonics.
1.
FHL, Harmonic Loss Factor; IEEE C57.1101998
REF. STANDARD
Harmonic Study
Ih= Individual Harmonic Component. I1=Fundamental Component; IRMS can also be used as FHL depends on harmonic distribution and not on relative magnitude. Ih / I1= This quantity can be directly computed from the harmonic measuring meters. FORMULA
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FHL is used to take into account the increase in eddy current losses in the windings and other stray losses in tank, core of transformers due to harmonics. 2. Based on these new stray losses, the full load current carrying capacity of dry type transformer is de-rated and the full load current as well as top oil temperature rise for liquid filled transformer is derated. 3. The std. is applicable for designing REMARK
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new transformer as well as to de-rate transformers under use; to de-rate the transformer under use, different parameters are required from certified test reports particularly those which are mentioned in appendix of IEEE Std. C57.12.90.1993 or IEEE Std C57.12.91-1995. Factor K BS 7821, Part 4.
1. Above two std. were American practice and this one is European practice. N q 2 [1+(e/1+e)( I1/I) (∑ n=1 n 2. This also takes in account the 2 0 .5 ( In/I) )] eddy current loss in winding e = Eddy current loss at due to harmonics. fundamental 3. It directly gives a de-rating frequency divided by loss factor for transformers which due to are in use. DC current equivalent to RMS 4. Transformer is de-rated by value of sinusoidal current. factor 1 / K I1 = Fundamental component of Here also as the current. transformers are in use, I = RMS value of current we have used Factor K to including all determine the de-rating of harmonics the transformers. th n = n order harmonic. K=
q = Exponential constant dependent on type of winding and frequency. q = 1.7, for rectangular and round cross sectional conductor. q = 1.5, for low voltage winding. Estimation of Extra Losses due to Harmonics; IEC 61378-1
This std. deal with converter transformers and takes into account the effect of harmonics on the losses of transformers.
Table - 5; Transformer De-Rating Standards
6.2. DERATING CALCULATIONS FOR CENTRAL UTILITY TRANSFORMERS. 6.2.1 OPERATION PHILOSOPHY I. The Central Utility has 3 Nos. of transformers, each supplying individually to each sections of MLTP. Depending on the load, Harmonic Study
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only one transformer can feed to two or three sections of MLTP or only two transformers can feed entire MLTP. II. Due to fault level considerations, none of the transformers are paralleled. III. To achieve energy saving any two of transformers are loaded and one transformer remains OFF. IV. So the harmonic distribution of any or all three sections can be applied to all of the transformers. 6.2.2 TRANSFORMER DETAILS Name TR-1 TR-2 TR-3 TABLE 6
KVA Rating 3500 3500 3500
Vector Group Dyn11 Dyn11 Dyn11
Voltage Ratio 33/0.433 KV 33/0.433 KV 33/0.433 KV
Leakage Impedance 10.15% 10.17% 10.06%
Full Load LT Current 4666.9 A 4666.9 A 4666.9 A
For the purpose of Factor K calculation, we can safely assume for all three transformers that eddy current losses are 10% of resistive losses. Therefore for Factor K Calculation, from Table 3, value of e for all three transformer can be assumed as 0.1 and q = 1.7 as rectangular conductors are used. 6.2.3
FACTOR K CALCULATIONS (BS 7821, PART 4) Harmonic distribution for all three buses of MLTP was taken (see Annexure A). For all three transformer, k = 0.1 and q = 1.7. From Table - 2 Factor K = [1+ (e/1+e) (I1/I) 2 (∑Nn=1 nq (In/I) 2)] 0 .5
a.
Factor K for Transformer 1 & 2 The Harmonic Distribution of load (Annexure A, Item No -24) on TR 2 (Load of MLTP Sec 1 & 2) and from Table 2
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Harmonic Order, n 1
In/I1
(In/I1)2
nq
nq (In/I1)2
1
1 0.00004 9 0.00025 6 0.00028 9 0.00000 9 0.00016 9 0.00002 5 0.00000 1
1
1
6.47300784
0.000317177
15.42584657
0.003949017
27.33170144
0.007898862
41.8998305
0.000377098
58.93422336
0.009959884
78.28953236
0.001957238
99.85162577
0.0000998516
3
0.007
5
0.016
7
0.017
9
0.003
11
0.013
13
0.005
15
0.001
∑
n=1
15
1.024559128
nq(In/I1)2
I1 = 1839 A, I = 1949 A
Factor K = [1+ (e/1+e) (I1/I) 2 (∑Nn=1 nq (In/I) 2)] 0 .5, Factor K = 1.03997, TR-2 to be de-rated by 1 / K = 0.9615 = 96.15 %. Transformer 1 should also be de-rated by same factor (96.15%) as during measurement load of MLTP Sec 1 & Sec 2 was on TR-2 which is also load of TR - 1( MLTP Sec 1 & Sec 2). b.
Factor K for Transformer 3 The Harmonic Distribution of load (Annexure A, Item No -25) on TR 2 (Load of MLTP Sec 1 & 2) and from Table 2 Harmonic Order, n 1
(In/I1)2
In/I1 1
3
0.002
5
0.02
7
0.004
9
0
11
0.002
13
0.003
15
0
∑
n=1
15
1 0.00000 4 0.0004 0.00001 6 0 0.00000 4 0.00000 9 0
nq(In/I1)2
nq
nq (In/I1)2 1
1
6.47300784
0.00003
15.42584657
0.00617034
27.33170144
0.00043731
41.8998305
0
58.93422336
0.00023574
78.28953236
0.00070461
99.85162577
0 1.00757388
I1 = 1944 A, I = 1957 A
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Factor K = [1+ (e/1+e) (I1/I) 2 (∑Nn=1 nq (In/I) 2)] 0 .5, Factor K = 1.04421, TR-3 to be de-rated by 1 / K = 0.9576 = 95.76 %. c.
Factor K When Load of All Three Sections of MLTP is on Single Transformer. The Harmonic Distribution of load (Annexure A, Item No -26) when all three section of MLTP are loaded on single transformer and from Table 2 Harmonic Order, n 1 3 5 7 9 11 13 15
In/I1 1 0.002 0.002 0.003 0 0.003 0.004 0
∑
n=1
15
(In/I1)2
nq
1 0.000004 0.000004 0.000009 0 0.000009 0.000016 0
1 6.47300784 15.42584657 27.33170144 41.8998305 58.93422336 78.28953236 99.85162577
nq(In/I1)2
nq (In/I1)2 1 0.000025892 0.000061703 0.000245985 0 0.000530408 0.001252633 0 1.002116621
I1 = 3856 A, I = 3888 A
Factor K = [1+ (e/1+e) (I1/I) 2 (∑Nn=1 nq (In/I) 2)] 0 .5, Factor K = 1.04384, Transformer to be de-rated by 1 / K = 0.957699 = 95.8 %. 6.3
CONCLUSIONS
1. There is not much significant harmonic loading on all the transformers consequently de-rating is not so significant. 2. For current load, the transformers should be de-rated as transformer 1 & 2 (TR-1 & TR-2) by 96%, transformer 3 (TR-3) by 95%. 3. When all three sections of load are given on any of the single transformer, the transformer should be de-rated by 95%.
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7.
CAPACITOR BANKS As discussed in sec 3.3, harmonics can result in resonance by making the inductive reactance of the system equal to effective capacitance of the p.f. correction capacitor banks at a certain frequency. To avoid this situation, the resonance frequency of the system is calculated and reactors are connected in series with the capacitor banks to from a detuned circuit which will shift the resonance frequency of the system to a safe value. 7.1 SYSTEM DETAILS
1. There are 8 Nos. of Automatic Power Factor Correction Panels connected to MLTP in Central Utility. Their distribution in 3 sections of MLTP and rating are given in the table below. MLTP BUS MLTP BUS A (Section 1, TR 1) MLTP BUS B (Section 2, TR 2) MLTP BUS C (Section 3, TR 3) TABLE 7
Number of APFC Panels 3 2 3
KVAR RATING 503.91 510.63 510.63 510.63 510.63 510.63 507.63 510.63
2. The capacitors installed in the banks are rated for 525 V and capacitors are effectively de-rated for use at 415V. 3. The above mentioned banks are formed by combination of banks of 25.2 KVAR, 50.39 KVAR and 53.75 KVAR. Each of these banks is connected with 7% detuned filter reactor. 4. Each of these banks are controlled by two APFC Relays, one is operative when load of that particular section of MLTP is on transformer and other relay is operational when load is on DGs. 7.2 CALCULATION OF RESONANCE FREQUENCY
The effective capacitance of these capacitor banks can form resonance circuit with the inductance of the winding of the transformer to which they are connected. So given below is the sample calculation for Harmonic Study Done By - VT Page 20 of 22
finding inductance of transformer winding and capacitance of APFC Capacitor banks to find out the resonance frequency. a. CALCULATION FOR INDUCTANCE OF TRANSFORMER Given a transformer with line voltage on LT side VLL, phase voltage on LT side VPH, leakage impedance Z, phase current on LT side IPH and vector group Dyn11; therefore VPH = VLL / 1.7312. Inductive Reactance of Transformer winding, XL = Z * (VPH / IPH). Therefore Inductance of the transformer winding, L (in Henry) = XL / 2∏F Taking transformer data from Table 6, the inductances of three transformer are here under in Table 8. TRAFO TR-1 TR-2 TR-3
VLL 433 V 433 V 433 V
IPH
Z (%)
4666.9 A 4666.9 A 4666.9 A
10.15 10.17 10.06
VPH 250 V 250 V 250 V
Freq (Hz)
50 50 50
XL (Ohms) 0.005437228 0.005447942 0.005389016
L (mH) 0.017300271 0.017334361 0.01714687
TABLE 8
b.
CALCULATION FOR EFFECTIVE CAPACITANCE OF CAPACITOR BANKS.
Similarly to find out effective capacitance of capacitor banks; If per phase voltage applied to capacitor bank with KVAR rating S connected in delta is VPH, line voltage is VLL, line current to the bank is IL-CAP, phase current to the capacitor bank is IPH-CAP, capacitive reactance of the bank is XC and the effective capacitance of the bank is C, then IL-CAP = S / (1.732 * VLL); IPH-CAP = IL-CAP / 1.732; XC = VPH / IPH-CAP; C = 1 / (2∏F XC); Resonance Frequency, FRES = 1 / [2∏(LC)0.5]
So from Table 6, 7, 8 and above formulae, the resonance frequency when the different combinations of capacitor banks Harmonic Study
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are operating in parallel to their respective transformers is given below in Table 9 in page 23. It is considered that all the banks are operating at rated capacity and the combinations of banks like operation of single bank, two banks and all three banks in corresponding bus are considered.
TABLE 9 TRAFO
KVAR
IL-CAP
IPH-CAP
(AMPS)
(AMPS)
XC (OHMS
C
L
(F)
(mH)
0.005447 0.010897 0.010822 0.005375 0.016269 0.005447 0.010897 0.005447 0.005415 0.010897 0.010862 0.016312
0.0173 0.0173 0.0173 0.0173 0.0173 0.01731 0.01731 0.0171 0.0171 0.0171 0.0171 0.0171
)
TR 1
TR2
TR3
510.63 1021.6 1014.54 503.91 1525.17 510.63 1021.6 510.63 507.63 1021.6 1018.26 1529.23
710.41 1421.30 1411.47 701.06 2121.89 710.41 1421.30 710.41 706.24 1421.30 1416.65 2127.54
410.17 820.61 814.94 404.77 1225.11 410.17 820.61 410.17 407.76 820.61 817.93 1228.37
0.58 0.29 0.29 0.59 0.20 0.58 0.29 0.58 0.59 0.29 0.29 0.20
FRES (Hz) 518.27 366.41 367.68 521.71 299.88 518.12 366.30 521.29 522.83 368.55 369.15 301.23
Harmonic Order Corresponding to FRES 10.4 7.3 7.4 10.4 6.0 10.4 7.3 10.4 10.5 7.4 7.4 6.0
7.3 CONCLUSIONS
1. 2.
3.
The 5th harmonic is the predominant harmonic at the incoming of the APFC panels. (Annexure A; Item 3 to 10). From Table 9, we can conclude that 10th, 7th and 6th harmonic components can cause resonance. From harmonic spectrum in Annexure A, it is clear that these harmonics are not present in significant amount. All the capacitor banks are connected in series with detuned reactor of filter factor of 7%. This 7% detuned reactor will shift the resonance frequency to 189 Hz which is closer to 3rd harmonic component. So choice of 7% detuned filter seems to be adequate as the 5th harmonic is predominant here.
Harmonic Study
Done By - VT
Page 22 of 22
