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Scenarios for a Large Scale Installation of Compact Fluorescent Lamps: Influence on the Power Quality S.A. SUFLIS I.E. CHATZAKIS F.V. TOPALIS M.B. KOSTIC School of Electrical and Computer Engineering School of Electrical Engineering National Technical University of Athens University of Belgrade 9 Iroon Politechniou Str., GR 157 80, Athens Bulevar Revolucije 73, Belgrade GREECE SERBIA AND MONTENEGRO Abstract: - The energy efficiency of the compact fluorescent lamps (CFLs) is the main motivation of the promotion policies to replace the tungsten filament bulbs with them. However, their high harmonic content was always a problem for the power quality of the networks, especially the ones with a considerable share of other non linear loads (computers, TVs, electronic devices etc). That problem cannot be neglected in cases of installations with high lighting load (office buildings, educational facilities, hotels etc). In that case the replacement of incandescent lamps by CFLs may cause problems to the power quality. This paper presents an analysis of the low voltage network of a typical electrical installation of a hotel, where lighting is one of the main loads. The complete network is simulated (up to the transformer) using the impedance network model. The CFLs are simulated using their electrical characteristics (active and reactive power, power factor, harmonic content etc) that have been measured in the Laboratory of Photometry of NTUA. The contribution of CFLs to the total load of the network is determined under different scenarios for the scale of replacement of incandescent lamps. For each scenario, the total harmonic distortion (THD) is calculated at each busbar of the network and then it is compared to the respective THD before the replacement. As expected, some scenarios give a non-negligible harmonic distortion although it is always below the upper limits (IEC, IEEE). However, some scenarios (large-scale replacement) may not be realized due to their high harmonic content that will be added to the distortion by other non-linear loads. That means that in case of networks with high lighting loads, the large-scale installation of CFLs should always be studied before replacing the incandescent lamps. Considering the existence of other non-linear loads, the distortion may exceed the maximum allowed values leading to unacceptable power quality. Key-Words: - Harmonics, Power Quality, Compact Fluorescent Lamps 1 Introduction application of CFLs is the problem with the network The idea of using efficacious and long-aged voltage distortion that arises due to their distorted fluorescent lamps in those applications that were currents which contain a high level of harmonic traditionally the province of inefficacious and short- components even at pure sine wave supply voltage. aged incandescent lamps has resulted in the A large number of papers [7-12] have been development of compact fluorescent lamps (CFLs). published dealing with the behaviour of CFLs under Compact fluorescent lamps with conventional caps various exploitation conditions, i.e. under various were primarily intended for residential and voltage distortions and different root mean square commercial customers. Lasting much longer and (rms) values of the network voltage. CFLs represent consuming much less energy than incandescent the loads with an exceptionally unfavourable current lamps with comparable luminous output, they spectral content under various supply conditions, i.e. represented promising new lamp types. An with very high Total Harmonic Distortion (THD) economic analysis also showed an obvious values. advantage of compact fluorescent lamps compared All these papers pointed to the complexity of the with incandescent ones [1, 2]. As a part of their modelling of CFLs working in real conditions, energy saving strategy, many power utilities were characterized by the non stable rms value of supply promoting the use of CFLs, even offering to voltage and the non stable voltage waveform. Since partially offset their relatively high purchase prices. such a model does not exist yet, the analysis of the The basic problem arising in the mass voltage distortion in the low voltage electrical installation, presented in the previous section, was emission of the equipment with input current not based on the assumption that the current spectral exceeding 16 A per phase. It is obvious that it was content is identical to the maximum permitted particularly difficult to harmonize the limits for self- (Table 1). Note that the values of current harmonics ballasted CFLs with electronic gear, omitted in the of the tested samples in some cases [10] exceeded 1995 edition of this standard. In the valid 2001 these limits. On the contrary, a small number of standard, the maximal current levels, expressed in analyses were published dealing with the influence mA per lamp wattage (valid for wattages not of CFLs to power network wherein they are, i.e. exceeding 25 W), were adopted. They are provided trying to establish their maximal presence not in Table 1. The third column, showing rms current leading to the excessive voltage distortion. of the nth harmonic (In) with respect to rms current In [3] an analysis of the medium voltage network of the fundamental one (I1), was determined on the of 13.8kV was made for three different feeders, each basis of second column and the assumption that the of load of 10MVA. The results showed that 3000 to current fundamental harmonic is equal to the ratio of 4000 residential customers in a 10MVA feeder, all active power and voltage (230V low voltage of them having two or three CFLs per home, would network). cause voltage distortion with THD greater than 5%, Note that the standards allow somewhat higher which is less than the maximum “planning” level of limits for the harmonic current emission [5], under 6.5%, specified by the utilities [4]. During the last the condition that some particular requests are few years some international standards for voltage fulfilled concerning the current change during every distortion [4], as well as for harmonic current period. emission [5], were adopted. That is why it is now possible, using some parameters published in them, Table 1 Maximum permissible harmonic current. to make a real estimation of the influence of CFLs Harmonic order per Watt % of fundamental to the network voltage distortion. Such an analysis, (n) (mA/W) which, in addition, concerns the low voltage 3 3.40 78.20 network (with the greatest harmonic components 5 1.90 43.70 impact), is presented in this paper. An example of a 7 1.00 23.00 typical hotel electrical installation was analyzed, 9 0.50 11.50 where a considerable share of the load of CFLs in 11 0.35 8.05 the total installed load can exist. Note that hotels can 13 0.30 6.90 be considered as good representatives of 15≤n*≤39 3.85/n 88.55/n commercial customers, which also include, offices, *odd harmonics only hospitals, department stores, shopping centres. In general, the voltage distortion problem (its deviation from pure time sine wave function) has 2 Voltage Harmonics become topical with a mass implementation of Voltage harmonic components can be calculated consumers containing power electronic elements using the impedance network model. All cables, (first, input rectifiers). That is why in the course of conductors and power transformers can be the last decade a considerable effort was invested to substituted by equivalent impedances (most often provide, through the international standards, some the serial impedance is used). A capacitor is recommendations for harmonic distortion limits, modelled by capacitance between the node being one of the most important power quality corresponding to bus-bars where the capacitor is factors. connected and the reference potential node. The On one hand, the standards protect the customers loads (such as resistive loads, induction motors etc) from the consequences of the bad-quality voltage, are not shown in the impedance network model by prescribing the maximal permitted values of because they do not affect considerably the voltage individual harmonics and of the total harmonic values. However, this is not valid in the cases when distortion of the supply voltage. Reference [4] the capacitors for fundamental harmonic reactive contains the data for low, medium, high and ultra energy compensation exist. Non-linear loads are high voltage systems. most frequently modelled as higher harmonic On the other hand, the standards protect the current generator. Note that the equivalent power utilities (i.e. electric power network), impedance model is made for each harmonic forbidding too high current harmonic components separately. produced by the consumers. IEC Standard [5] The cables, conductors and transformers are provides the limits for the harmonic current modelled as elements with a constant resistance R and constant inductance L. In such a way, for the nth CFLs so that to use them in the simulation program, harmonic they are substituted by the impedance: many samples of CFLs were tested in the laboratory in order to determine their odd order harmonic Zn=R+jnωL=R+jn2πfL, f=50Hz spectrum. Such lamps do not produce even order The values of R and L correspond to the direct harmonic currents. The nominal power of the CFLs sequence impedance for the harmonics of order n = that is widely used in the hotel is 20W. It must be 5, 7, 11, 13, 17, 19 etc, while they correspond to also noticed that the phase difference between the zero sequence impedance for the harmonics n = 3, 9, supply voltage waveform and the fundamental 15 etc. More accurate calculations require to take current waveform of the tested lamps is negligible. into account the skin effect, which increases with However, the power factor is very low (0.4-0.5) due the increase of the harmonic order. However, this to the considerable harmonic content of current. The exceeds the needs of the analysis of this paper. measured values of the current harmonics of this The modelling of a non-linear load by an ideal CFL are presented in Table 3. All data from the current generator [6] is based on the assumption that measurements are properly used as input in the the spectral current content is not affected by the simulation model in order to estimate the influence voltage distortion. In the case of some consumers, of CFLs to the network voltage distortion. where very high values of higher harmonic components in the supply voltage could be Table 3 Harmonics of a 20W CFL anticipated, the model of the consumer could be Harmonic Normalized extended by impedance parallel with the ideal order amplitude current generator. (%) 3 92 5 72 3 Description of the Network 7 53 A low-voltage electrical installation of a hotel, 9 45 representing a typical commercial customer, was 11 43 analyzed. The nominal voltage of the transformer that supplies the hotel is 20 kV/400V, the nominal 13 40 power is 1000 kVA and its standard connection is 15 33 Dyn11. The cross sections and the parameters 17 25 (resistance and inductance) of the cables and the 19 21 conductors (internal distribution lines), are shown in 21 18 Table 2. THD 158 Table 2 The low voltage network parameters. S (mm2) R (Ω/km) X (Ω/km) 4 Simulation All the electrical characteristics of the network (i.e. 1.5 11.90500 0.115 transformer, distribution lines and load) have to be 2.5 7.14290 0.110 accurately simulated in order to obtain reliable 4.0 4.46430 0.107 results. The simulation of the electric network is 10.0 1.78570 0.094 performed using the PSCAD v3.0.6 software. 25.0 0.71429 0.086 The essential parameters describing the transformer, the cables and the conductors Ten cables (25 mm2 each) supply the consumers, (resistance and inductance) are determined using which they have equal loads, located in the hotel their values for the fundamental harmonic. rooms and corridors (3-phase network). The length The elements are modelled by serial impedances. of the 10th cable is 60 m and the length of the same The magnetizing current of the transformer was cross section cables (1, 2, …, 9) is 5 m shorter than neglected. This is a usual approximation [3], whose the length of the (+1)st cable. Two cables (10 mm2 adoption introduces a negligible error. each) supply the consumers, which they have equal The sources of the harmonics (CFLs) are defined loads, situated in other parts of the hotel (1-phase according to the adopted lamp wattage and the network). The length of the 1st cable is 50 m and the current limits given in the second column of Table length of the 2nd cable is 30 m. 1. It is adopted that the currents of the current In order to obtain real and reliable data generators are in phase for every harmonic (the concerning the exact current harmonic content of influence of this approximation is also negligible). The calculation is made under the assumption CFLs amounts to 122kW. This power corresponds that except CFLs there no other non-linear loads. to 12.2% of the rated transformer power. The entire linear load is observed as a load with 4th scenario: 90% of 75W incandescent lamps are PF=cosφ=0.85 and its equivalent impedance is replaced with 20W CFLs. The total active power of connected directly to the transformer low-voltage CFLs amounts to 146.4kW that corresponds to busbars. This approximation is justified because the 14.64% of the rated transformer power. impedances of particular linear loads are Laboratory measurements showed that the CFLs considerably greater than those of their supplying of 20W have the same maintained luminous flux cables. This impedance is significant in the with the replaced incandescent ones of 75W. calculations of the voltage distortion if there exists the fundamental harmonic reactive energy compensation. The load reactance for the nth 5 Results harmonic is calculated as the load reactance for the The calculation results at all electric network buses, fundamental harmonic multiplied by the harmonic where from the consumers are supplied, for all order n. Though in the case of rotating electrical scenarios are given in Tables 4-7. The most machines the adoption of this assumption introduces significant conclusions derived for all the examined an error [13], it is usually used in the analyses of scenarios are also presented and discussed as this type. The linear load is so selected that the sum follows. of its active power and the total active power of CFLs amounts to 610kW. st Table 4 Voltage THD (%) for the 1 scenario A detailed point of view of the proposed simulation is described in Fig. 1. Bus Phase A Phase B Phase C 1 1.042 1.040 1.017 2 1.060 - - 3 1.102 1.100 1.077 3 X 150 W 3 X 150 W 4 1.110 1.108 1.086 430117 430117 430117 430117 430117 430117 5 1.111 1.109 1.087 0. 0. 0. 0. 0. 0. 759. 759. 759. 759. 759. 759. 6 1.063 - - 69 69 69 69 69 69 nd Table 5 Voltage THD (%) for the 2 scenario Bus Phase A Phase B Phase C 1 2.084 2.081 2.034 2 2.118 - - 3 2.197 2.193 2.147 39E- 2. 006 39E- 2. 006 03815 0. 03815 0. Va5 Va 4 2.212 2.208 2.162 39E- 2. 006 39E- 2. 006 03815 0. 03815 0. Vb5 Vb 39E- 2. 006 39E- 2. 006 0. 03815 2. 39E-006 0. 03815 39E- 2. 006 Vc5 Vc 5 2.214 2.210 2.164 03815 0. 03815 0. 6 2.122 - - Fig. 1 Part of the electric network (the current rd sources represent the harmonic content of CFLs) Table 6 Voltage THD (%) for the 3 scenario Bus Phase A Phase B Phase C The electric network of the hotel, after the 1 3.233 3.228 3.152 addition of the harmonic current of CFLs is fully 2 3.279 - - described in Fig. 2 at the end of this paper. 3 3.396 3.390 3.316 The following four scenarios for the hotel are 4 3.416 3.410 3.335 simulated and examined in this paper. 5 3.419 3.413 3.339 1st scenario: 25% of 75W incandescent lamps are 6 3.284 - - replaced with 20W CFLs. The total active power of th CFLs amounts to 40.67kW. This power corresponds Table 7 Voltage THD (%) for the 4 scenario to 4.067% of the rated transformer power. Bus Phase A Phase B Phase C 2nd scenario: 50% of 75W incandescent lamps 1 3.980 3.980 3.884 are replaced with 20W CFLs. The total active power 2 4.077 - - of CFLs amounts to 81.33kW that corresponds to 3 4.171 4.172 4.077 8.133% of the rated transformer power. 4 4.191 4.193 4.098 3rd scenario: 75% of 75W incandescent lamps are 5 4.195 4.197 4.102 replaced with 20W CFLs. The total active power of 6 4.092 - - Given that the rest hotel network loads were 6: Assessment of emission limits for distorting considered linear one comes to the conclusion that loads in MV and HV power systems - Basic the each time calculated voltage THD factor is the EMC publication, 1996. least possibly expected, when replacing [5] IEC 61000-3-2, Electromagnetic compatibility incandescent lamps with CFLs. This also means that (EMC) - Part 3-2: Limits - Limits for harmonic even in that ideal case (absence of non-linear loads) current emissions (equipment input current <= CFLs do not increase the voltage THD factor up to 16A per phase), 2001. the acceptable limit of 5% because the circulating [6] Cahier technique Merlin Gerin No. 152, currents are very low. Harmonics in industrial networks, 1998. The harmonic distortion problem is a complex [7] M. Etezadi-Amodi, T. Florence, Power factor one, especially in low-voltage distribution networks. and harmonic distortion characteristics of In such cases, every significant change of load energy efficient lamps, IEEE Transactions on synthesis to achieve energy saving must be Power Delivery, Vol.4, No.3, 1989, pp. 1965- thoroughly studied. Otherwise problems like 1969. unacceptable harmonic distortion may rise. [8] F.V. Topalis, Efficiency of energy saving lamps and harmonic distortion in distribution system, IEEE Transactions on Power Delivery, 6 Conclusion Vol.8, No.4, 1993, pp. 2038-2042. This paper considers the problem of voltage [9] E.E. Hammer, Effects of changing line voltage harmonic distortion in commercial low-voltage with various fluorescent systems, IEEE networks with a significant participation of CFLs Transactions on Industry Application, Vol.24, with electronic gear, which is an important No.4, 1988, pp. 692-699. parameter for energy saving strategies. The use of [10] F.V. Topalis, I.F. Gonos and M.B. Kostic, energy saving technologies, i.e. CFLs in order to Effects of changing line voltage on the decrease the power consumption in this category of harmonic current of compact fluorescent lamps, networks may result in unacceptable distortions in Proceedings International Conference on the network line voltage. It is obvious that a Power and Energy Systems, Las Vegas, U.S.A., limitation, as a percentage of the rated transformer 1999, pp. 24-27. power, is to be taken into account when designing [11] C. Ming-Tong, F. Che-Ming, Characteristics of the entire lighting in the buildings of this type. In fluorescent lamps under abnormal system order to achieve and maintain the desired power voltage conditions, Electric Power System quality and performance, appropriate suggestions Research, Vol.41, 1997, pp. 99-107. should be given to the consumers concerning the [12] F.V. Topalis, I.F. Gonos, G.A. Vokas, load quality and quantity that will not increase the Arbitrary waveform generator for harmonic THD of line voltage beyond the accepted limits. distortion tests on compact fluorescent lamps, Measurement, Journal of the International Measurement Confederation, Vol.30, No.4, References: 2001, pp. 257-267. [1] F.V. Topalis, M.B. Kostic, Z. Radakovic, [13] F. Gagliardi, U. De Martinus, G. Fusco, D. Advantages and disadvantages of the use of Lauria, Interaction between non-linear loads compact fluorescent lamps with electronic gear, and synchronous generators, European Lighting Research and Technology, Vol.34, Transactions on Electric Power, Vol.2, No.5, 2002, pp. 279-288. 1992, pp. 279-283. [2] R. Arseneau, M. Ouellette, The effects of supply harmonics on the performance of compact fluorescent lamps, IEEE Transactions on Power Delivery, Vol.8, No.2, 1993, pp. 473- 479. [3] D.J. Pileggi, E.M. Gulachenski, C.E. Root, T.J. Gentile, A. E. Emanuel, The effect of modern compact fluorescent lights on voltage distortion, IEEE Transactions on Power Delivery, Vol.8, No.3, 1993, pp. 1451-1459. [4] IEC/TR3 61000-3-6, Electromagnetic compatibility (EMC) - Part 3: Limits - Section A A A 0E- 1. 010 A 11E- 4. 006 5. 7 M 1 [ VA] Va1 a I 012945 0. 003226 0. B B B 0E- 1. 010 B #1 #2 11E- 4. 006 7 5. Vb1 b I 1. 010 0E- 000 W 3 X 20. C 0 20. 0. 402 C C C 0. 012945 0. 003226 Vc1 c I 11E- 4. 006 7 5. 012945 0. 003226 0. B A Pow er 4.11E-006 012945 0. Q P 000 W 5. 250 W R =0 A B C 48E- 5. 006 7 5. 012904 01726 0. 003226 0. 25807 48E- 5. 006 7 5. 0. 0. 0. 0. 0. 0. 0. 0. 455. 000 W 3 X 20. 22. 0. 0. 05178 05178 05178 05178 0648 0648 01726 0. 003226 0. 108 108 79 005 005 005 005 005 005 82 006 006 48E- 5. 006 7 5. 643E- 643E- 643E- 643E- 497E- 497E- 98E- 98E- 430117 0. 01726 0. 003226 0. 8. 8. 1. 1. 1. 1. 1. 1. 48E- 5. 006 Vc5 69 759. 01726 0. 3 X 150 W 430117 0. Vb5 69 759. 430117 0. 85E- 6. 006 7 5. Va5 69 759. 021575 0. 003226 0. 0. 0. 0. 0. 03815 03815 03815 03815 85E- 6. 006 7 5. 006 006 006 006 000 W 3 X 20. 39E- 39E- 39E- 39E- 021575 0. 003226 0. 2. 2. 2. 2. 85E- 6. 006 7 5. 021575 0. 003226 0. 430117 0. 099E- 1. 005 6.85E-006 69 759. 4341 0. V6 021575 0. 099E- 1. 005 3 X 150 W 430117 0. 4341 0. 69 759. 22E- 8. 006 7 5. 0. 430117 4750 W 02589 0. 003226 0. 69 759. 0. 0. 0. 0. 22E- 8. 006 7 5. 03815 03815 03815 03815 000 W 3 X 20. 006 006 006 006 013583 02589 0. 003226 0. 39E- 39E- 39E- 39E- 22E- 8. 006 7 5. 0. 2. 2. 2. 2. 23. 02589 0. 003226 0. 99 22E- 8. 006 430117 0. 02589 0. 69 759. 3 X 150 W 430117 0. 59E- 9. 006 7 5. 69 759. 030205 0. 003226 0. 430117 0. 59E- 9. 006 7 5. 000 W 3 X 20. 69 759. 030205 0. 003226 0. 0. 0. 0. 0. 03815 03815 03815 03815 59E- 9. 006 7 5. 006 006 006 006 LO W VO LTAG E NETW O R K O F 39E- 39E- 39E- 39E- 030205 0. 003226 0. 9.59E-006 2. 2. 2. 2. AL A C O M M ER C I C USTO M ER 030205 0. 0. 430117 O SC ENAR I O F R EPLAC EM ENT 69 759. NC 75 % C FL - 25 % I 096E- 1. 005 7 5. V2 3 X 150 W 430117 0. 03452 0. 003226 0. 69 759. 096E- 1. 005 7 5. 0. 430117 000 W 3 X 20. 03452 0. 003226 0. 69 759. 0. 0. 0. 0. 096E- 1. 005 7 5. 03815 03815 03815 03815 nt TH D poi 1 006 006 006 006 03452 0. 003226 0. THD Va1 THD Vb1 THD Vc1 1.096E-005 39E- 39E- 39E- 39E- 03452 0. 2. 2. 2. 2. % % % 0 100 0 100 0 100 430117 0. 759. 69 233 3. 228 3. 152 3. 232E- 1. 005 7 5. 3 X 150 W 430117 0. nt TH D poi 2 038835 0. 003226 0. 759. 69 THD V2 232E- 1. 005 7 5. 0. 430117 000 W 3 X 20. 038835 0. 003226 0. % 69 759. 0 100 0. 0. 0. 0. 232E- 1. 005 7 5. 03815 03815 03815 03815 279 3. 006 006 006 006 038835 0. 003226 0. 232E- 1. 005 39E- 39E- 39E- 39E- nt TH D poi 3 038835 0. 2. 2. 2. 2. THD Va3 THD Vb3 THD Vc3 430117 0. % % % 369E- 1. 005 7 5. 69 759. 0 100 0 100 0 100 04315 0. 003226 0. 3 X 150 W 430117 0. 3. 396 39 3. 316 3. 369E- 1. 005 7 5. 69 759. 000 W 3 X 20. nt TH D poi 4 04315 0. 003226 0. 430117 0. THD Va4 THD Vb4 THD Vc4 369E- 1. 005 7 5. 69 759. 0. 0. 0. 0. 03815 03815 03815 03815 04315 0. 003226 0. % % % 1.369E-005 006 006 006 006 0 100 0 100 0 100 39E- 39E- 39E- 39E- 04315 0. 416 3. 41 3. 335 3. 2. 2. 2. 2. nt TH D poi 5 430117 0. THD Va5 THD Vb5 THD Vc5 1. 506E-005 5. 7 69 759. 047465 0. 003226 0. 3 X 150 W 0. 430117 % % % 506E- 1. 005 7 5. 0 100 0 100 0 100 000 W 3 X 20. 69 759. 047465 0. 003226 0. 419 3. 413 3. 339 3. 430117 0. 506E- 1. 005 7 5. 759. 69 nt TH D poi 6 047465 0. 003226 0. 0. 0. 0. 0. 506E- 1. 005 03815 03815 03815 03815 THD V6 006 006 006 006 047465 0. 39E- 39E- 39E- 39E- % 0 100 2. 2. 2. 2. Va3 284 3. 430117 0. Vb3 69 759. M ag 15 M ag 15 al Tot al Tot (15) (15) Vc3 FFT m Har oni c FFT m Har oni c 3 X 150 W 430117 0. st ton D i or i st ton D i or i Ph 15 Ph 15 (15) ndi dual I vi (15) ndi dual I vi 69 759. Va1 Va4 0 Hz] F = 50. [ dc F = 50. [ 0 Hz] dc 430117 0. 69 759. M ag 15 M ag 15 0. 0. 0. 0. (15) al Tot (15) al Tot 03815 03815 03815 03815 FFT m Har oni c FFT m Har oni c st ton D i or i st ton D i or i 006 006 006 006 Ph 15 Ph 15 (15) ndi dual I vi (15) ndi dual I vi 39E- 39E- 39E- 39E- Vb1 Vb4 dc dc 2. 2. 2. 2. 0 Hz] F = 50. [ 0 Hz] F = 50. [ 33 6. 003584 0. M ag 15 M ag 15 430117 0. al Tot al Tot (15) m Har oni c (15) m Har oni c FFT FFT 33 6. st ton D i or i st ton D i or i 69 759. Ph 15 Ph 15 000 W 3 X 18. ndi dual I vi ndi dual I vi Vc1 (15) Vc4 (15) 003584 0. 3 X 150 W 430117 0. dc dc 0 Hz] F = 50. [ 0 Hz] F = 50. [ 33 6. 69 759. 003584 0. M ag 15 M ag 15 430117 0. al Tot al Tot (15) m Har oni c (15) m Har oni c FFT FFT Ph st ton D i or i 15 Ph st ton D i or i 15 69 759. 0. 0. 0. 0. (15) ndi dual I vi (15) ndi dual I vi 03815 03815 03815 03815 V2 Va5 006 006 006 006 dc dc 0 Hz] F = 50. [ 0 Hz] F = 50. [ 39E- 39E- 39E- 39E- M ag 15 M ag 15 2. 2. 2. 2. 452E- 2. 005 227. 91 (15) Tot al (15) Tot al FFT m Har oni c FFT m Har oni c Ph st ton D i or i 15 Ph st ton D i or i 15 6097 0. Va4 0. 129035 ndi dual I vi ndi dual I vi 430117 0. (15) (15) Va3 Vb5 452E- 2. 005 91 227. dc dc 69 759. 0 Hz] F = 50. [ 0 Hz] F = 50. [ 3 X 500 W 6097 0. Vb4 129035 0. 3 X 150 W 430117 0. M ag 15 M ag 15 452E- 2. 005 227. 91 al Tot Tot al (15) m Har oni c (15) m Har oni c 69 759. FFT FFT Ph st ton D i or i 15 Ph st ton D i or i 15 6097 0. Vc4 0. 129035 ndi dual I vi ndi dual I vi 430117 0. 452E- 2. 005 Vb3 (15) Vc5 (15) 759. 69 6097 0. dc dc 0. 0. 0. 0. 0 Hz] F = 50. [ 0 Hz] F = 50. [ 03815 03815 03815 03815 006 006 006 006 M ag 15 M ag 15 al Tot al Tot (15) (15) 39E- 39E- 39E- 39E- FFT m Har oni c FFT m Har oni c Ph st ton D i or i 15 Ph st ton D i or i 15 2. 2. 2. 2. ndi dual I vi ndi dual I vi Vc3 (15) V6 (15) dc dc 0 Hz] F = 50. [ 0 Hz] F = 50. [ Fig. 2 Simulation of the electric network (the current sources represent the harmonic content of CFLs)