Fig. 8.3. Controlled three phase power supply, NetWave 30 type, front view [601491]

1 Application 8 EXPERIMENTAL DETERMINATION ON HARMONIC POLLUTION IN POWER GRIDS 8.1. Aim of the application Application aims experimental determination on harmonics pollution of nonlinear consumers operating in balanced power grids. It is referred to the following objectives: 1. Knowing the conducted electromagnetic disturbances test stand structure and functionality, 2. Knowing the harmonics testing procedures according to EN/IEC 6100-3-12 standard, 3. Identification and characterization of category 1 and 2 harmonics sources, 4. Identification of harmonics effects on electric equipments and networks. 8.2. Theoretical issues 8.2.1. Non sinusoidal periodic regime Analysis of operating regimes on electrical circuits, in which currents and voltages are various periodic functions, has a practical significance. In the generation, transmission and distribution electric systems, the variation in time of the voltage and current is not strictly sinusoidal, and the deviation is called distortion or deformation, hence the deforming regime name. The distortion comes from constructive imperfections of generators (not a perfect sinusoidal distribution of magnetic induction in the air gap) and the nonlinearities of the circuit elements (iron core coils, electric ovens, magnetic amplifiers, rectifier diodes, thyristors, etc.). These nonlinear elements, sinusoidal fed, distort the current, which in turn produce non-sinusoidal voltage drops on other circuit elements, either linear or nonlinear. Study of non-sinusoidal periodic regime is important both from the troublesome effects produced in the transmission and distribution of power network, as well as that of the electrical equipments construction. In power systems which operate in deforming regime, the power factor falls, as capacitive reactive power compensation is generally not possible, and additional energy losses occur, there are resonances, producing overvoltage or over-currents, etc. Calculation of linear electric circuits or approximated by linear elements is usually carried out based on Fourier decomposition of network periodic signals (voltages) and by superposition theorem application. Periodic non-sinusoidal currents and voltages are calculated as the sum of currents and voltages produced separately by each harmonic component. Periodic quantities A quantity variable in time whose values are periodically repeated, satisfying the relationship: y(t) = y(t+nT ) (8.1) for any constant T and any value of time t, is called a periodic over time quantity. The lowest (positive) T value, which satisfies the relation (8.1) is called the period.

2 Any periodic function y(t), which satisfy Dirichlet conditions (the period may be divided into a finite number of intervals so that the function is continuous and monotonous on each of them) can be developed (decomposed) in Fourier series, having the form: ()()()tkBtkAAtykkkkωωsincos110⋅+⋅+=∑∑∞=∞= (8.2) where ω is the fundamental pulsation (angular velocity) corresponding to y, the T period of the function: fTωωω22== (8.3) where f is the fundamental frequency. Fourier coefficients are determined by the relations: ()dttfTAT∫=001 (8.4) ()()dttktfTATk∫=0cos2ω (8.5) ()()dttktfTBTk∫=0sin2ω. (8.6) If y(t) has certain symmetry, or antisymmetry properties, it can restrict the range of integration in the above relations. For example: – An alternative function has on a period the mean value equal to 0, A0 = 0; – An even function with the property f(t) = f(-t), has only cosine terms , that is, Bk = 0, and Ak is calculated by the equation ( 8.5 ) ; – An odd function with the property f(t) = -f(-t), has only sine terms , that is, Ak = 0, and Bk is calculated by the equation ( 8.6 ) ; – An alternating symmetric function with the property f(t) = – f(t+T/2), has zero DC component (A0 = 0) and contains only odd order harmonics, whose amplitudes are calculated with relations (8.5) and (8.6), integrating the half period; – If alternate symmetric functions, longer enjoys even or odd properties, only the cosine , sine respectively terms remain, and the interval of integration, for calculating the coefficients is reduced to a quarter of a period: – even function: Bk=0, ()()dttktfTATk∫=4/0cos8ω (8.7) – odd function: Ak=0, ()()dttktfTBTk∫=4/0sin8ω (8.8) Note: In power systems (the strong currents techniques), the vast majority of electromotive forces, voltages and currents curves are alternate symmetrically. Therefore alternate symmetrical curves are called electrotechnic curves. 8.2.2. Non sinusoidal regime indicators The voltage / current wave deformation is characterized by the following indicators: • Distortion coefficient (total harmonic distortion) THD is the ratio, of the actual value of the distorting residue and the effective value of the fundamental, expressed as a percentage: – For the voltage wave

3 ()%,100140221001⋅∑==⋅=UnnUUdUuTHD (8.9) where dU- voltage distorting residue; 1U- effective value of the fundamental – For the current curve: ()%,100140221001⋅∑==⋅=InnIIdIiTHD (8.10) where dI- current distorting residue; 1I- effective value of the fundamental. • The distorting residue – is the wave that comes from a given periodic waveform by the fundamental harmonic suppression. – Voltage distorting residue effective value: ∑==4022nnUdU (8.11) where nU- n order harmonic voltages ( 2 to 40 ). – Current distorting residue effective value: ∑==4022nnIdI (8.12) where nI- n order harmonic currents ( 2 to 40 ). 8.3. Harmonics sources identification and characterisation Consider the case of a star three phase balanced receivers with neutral, supplied from a three phase balanced network (Fig. 8.1).
Fig .8.1. Three phase balanced voltage network which supplies a star balanced consumer with neutral conductor Known phase impedance of the receiver: 321ZZZ== (8.13) and the supply network phase voltages : fUU=10 10220UaU⋅= (8.14) 1030UaU⋅=

4 ()001102101010210302010=⋅=++⋅=⋅+⋅+=++UaaUUaUaUUUU (8.15) 3020100302010UUUUUU+=−⇒=++ According to neutral point potential theorem: ∑+∑⋅=KYNYKUKYNU00 (8.16) ()03210132130201013213032021010=+++⋅=+++++⋅=+++⋅+⋅+⋅=NYYYYYNYYYYUUUYNYYYYUYUYUYNU 00=NU (8.17) In a symmetrical balanced network, single phase currents can be written using the Fourier transform. Neutral current is the sum of the three phases currents, IN=IR+IS+IT. In these equations, for phase angles, the same reference is used: ()()()()…5sin3sinsin553311++++++=ϕωϕωϕωtItItItiR (8.18) ()…325sin323sin32sin553311+⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛−+⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛−+⎟⎠⎞⎜⎝⎛+−=ϕπωϕπωϕπωtItItItiS(8.19) ()…325sin323sin32sin553311+⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛++⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛++⎟⎠⎞⎜⎝⎛++=ϕπωϕπωϕπωtItItItiT(8.20) ()()…3sin333++⋅=ϕωtItiN (8.21) It can be seen that the first order harmonics (i = 6k +1, where i is the order of harmonics and k = 1, 2 , 3 … ) form a direct phase currents system, harmonics of order three (i = 6k+3 ) form a zero sequence and fifth order harmonics (i = 6k +5 ) an inverse system. According to Fortescue’s theorem, any system (non symmetrical and unbalanced) can be written as the sum of the three symmetric systems, positive, negative and zero sequence. In (8.21), Fortescue's theorem applies to single-phase harmonics of order i. ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⋅⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡TiSiRiiiiIIIaaaaIII222101111131 (8.22) In the neutral cable, the sum of positive sequence component is equal to zero, and negative sequence components is equal to zero too, (1 + a + a2 = 0), only the sum of zero-sequence component is different from zero. ()()iiiiNiIIIaaIaaI0022123311=++++++= (8.23) The neutral current consists only of zero sequence component of the phase currents. For a symmetrical balanced power network, these zero sequence component correspond to third order harmonics. From equation (8.22) we have: ()TiSiRiTiSiRiiNiIIIIIIII++=++⋅⋅==31330 (8.24) Assuming RijeRiIRiIϕ⋅=, SijeSiISiIϕ⋅=,TijeTiITiIϕ⋅= (8.25) It result: NiI is given by: ()()TiTiSiSiRiRiiTTiSiSiRiRiNiIIIjIIIIϕϕϕϕϕϕsinsinsincoscoscos,⋅+⋅+⋅+⋅+⋅+⋅= (8.26)

5 From the above equation, one can calculate the amplitude of NiI and the i order harmonics phase angle Niϕ in the neutral cable. NiI amplitude for the i order harmonic, in neutral cable, is shown in equation (8.27). ()()2sinsinsin2coscoscosTiTiISiSiIRiRiIjTiTiISiSiIRiRiINiIϕϕϕϕϕϕ⋅+⋅+⋅+⋅+⋅+⋅= (8.27) In the case in which the amplitudes of the harmonics of order i in the neutral, TiSiRiIII,, are i order current harmonics in R, S, T phases, Riϕ, Siϕ, Tiϕ, are i order harmonics R, S, T phase angles. The i order harmonic, Niϕ, phase angle in neutral current is: ()()⎟⎟⎠⎞⎜⎜⎝⎛=NiINiIarctgNiReImϕ (8.28) If amplitudes and phase angles of harmonics in phase currents are known, the harmonic content of the neutral current can be calculated using the relations (8.27) and (8.28). 8. 4. Conducted disturbances (harmonics and flicker) test bench Simulation of three phase receivers having star balanced linear and nonlinear loads, with / without neutral, which are fed from three phase symmetrical networks, is made in the stand of the Laboratory of Advanced Electrical Systems Transilvania University of Brasov. Depending on the system configuration is possible to test mono and three-phase equipment.
Fig.8.2. Connecting the harmonics and flicker testing stand equipments Harmonics and flicker testing stand consist of: – Controlled power supply – Three phase digital power analyzer, DPA 503N type, – Flicker-meter – Three phase impedance – The Computer system.

6 8.4.1. Controlled power supply The controlled three phase power supply, NetWave 30 type, 30 kVA power, generates voltages with different waveforms for harmonics and flicker immunity tests. The power supply software allows setting of the voltages and frequency nominal values and supply current limit. The power supply is a multifunctional one and can be used for other applications too.
Fig. 8.3. Controlled three phase power supply, NetWave 30 type, front view
Fig. 8.4. Controlled three phase power supply, NetWave 30 type, rear view 8.4.2. Three phase digital power analyzer, DPA 503N type Three phase digital power analyzer, DPA 503N type, and flicker three phase impedance, are rack mounted, as in Fig. 8.5.

7
Fig. 8.5. Three phase digital power analyzer, DPA 503N type, flicker-meter and three phase impedance Three phase digital power analyzer DPA 503N allows phase current and voltage measurement and harmonics and flicker data calculation, according to actual standards. To supply the EUT, it is made the following electric scheme, containing the power supply and DPA.
Fig. 8.6. Electric scheme, for the power supply and DPA, rear view Three phase electric schema will be in Fig. 8.8. To assess the wiring size for the voltage and the current maximum accepted value. EUT output gives the following electric connections: – mono phase 16 A oulet system – three phase 16 A oulet system – three phase 32 A oulet system. 8.4.3. The three phase flicker impedance The three phase flicker impedance, AIF 503N32 type, is a 32 A three phase impedance, which is automatically coupled and has two internal flicker impedance for tests according to IEC 61000-3-11 standard. An automatic interrupter shorts flicker impedance when harmonics measurements are done.

8 8.4.4. The Computer system The Computer system uses “Dpa.control” software to control, measure and process harmonics and flicker data. The “Netware.control” software allows multifunctional three phase power supply parameters control and command.

Fig. 8.7. The system to analyze 8.5. Experimental determinations 8.5.1. The mounting electric schema The mains has 400/230 V, 50 Hz. The receivers are 25 W, 40 W, 60 W and 100 W incandescent light bulbs and three of 160 W Hg bulbs, used to emphasize the effect of nonlinear receivers on neutral loading. In this laboratory test the three phase star linear and nonnlinear balanced receivers will be studied and the phase loading is performed as in Table 8.1. The receiver supply sine wave voltage is provided by the 30 kVA three phase controlled power supply NetWave 30. Tabelul 8.1.Three phase resistive linear and nonlinear receiver phase loading No exp. PR [W] PS [W] PS [W] 1 3×100+1×60+1×40=400 3×100+1×60+1×40= 400 3×100+1×60+1×40= 400 2 1×160+2×100+1×40= 400 1×160+2×100+1×40=400 1×160+2×100+1×40= 400 3 3×160+1×25= 505 5×100= 500 5×100= 500 For every three phase consumer the connection to power supply is made in two ways: – with neutral (Fig.8.8); – without neutral (Fig.8.9).

9 Case a: connection with neutral

Fig. 8.8. Electric schema for a star balanced with neutral three phase consumer and neutral conductor Case b: connection without neutral
Fig. 8.9. Electric schema for a star balanced without neutral three phase receiver 8.5.2. Working equipments – Controlled three phase power supply NetWave – Digital three phase power analyzer, DPA 503N

10 – Three phase flicker impedance, AIF 503N32 – The EUT is an electric light bulbs device – h – Hg incandescent bulbs, with parameters shown in Table 8.1. 8.5.3. Work procedure – a visual mounting correctness is made – according to no.I experiment the DLI light bulbs are mounted and supplied with a sine wave voltage – according to no.II experiment the DLI light bulbs are mounted and supplied with a sine wave voltage – according to no.III experiment the DLI light bulbs are mounted and supplied with a sine wave voltage – measurement are made and the data are written in Table 8.2, 8.3, 8.4 and 8.5. 8.5.4. Data processing – the neutral current value IN from Case I is compared for the three experiments – the voltage value UNO from Case II is compared for the three experiments – the neutral influence in three phase low voltage electrical networks is studied – the receivers nonlinearity effect on consumer phase voltages is studied. Case 1. Experimental tests for linear and nonlinear balanced receivers with neutral The experimental tests are presented in Table 8.2 and Table 8.3. Table 8.2. Receiver’s phase voltages, currents and neutral current- three phase star balanced resistive receiver with neutral No. Exp. U1N [V] U2N [V] U3N [V] I1 [A] I2 [A] I3 [A] IN [A] 1 2 3 Table 8.3. Voltage and current harmonics induced by the receiver’s nonlinearity No. exp. n/ φ U1N [V] U2N [V] U3N [V] I1 [A] I2 [A] I3 [A] IN [A] 1 1 3 5 7 9 11 THD [%] φ 2 1

11 3 5 7 9 THD [%] φ 3 1 3 5 7 9 THD [%] φ Harmonic pollution is present in 2 and 3 experiment which has nonlinear receivers. It is noticed that the third order harmonics as well as the other triple order harmonics (sixth etc.) are added and though the neutral is crossed by this resulted current. Case 2. Experimental tests for linear and nonlinear balanced receivers without neutral The receivers are 25 W, 40 W, 60 W and 100 W incandescent light bulbs, plus other three Hg 160 W light bulbs used to show the nonlinearity receiver effect on neutral load. The phases load way is shown in Table 8.1. Experimental tests are presented in Table 8.4 and Table 8.5. Table 8.4. Receiver’s phase voltages, currents and neutral displacement voltage – three phase star balanced resistive receiver with neutral No. Crt. U1N [V] U2N [V] U3N [V] I1 [A] I2 [A] I3 [A] IN [A] UN0 [V] 1 2 3 Table 8.5. Voltage and current harmonics induced by the receiver’s nonlinearity No. exp. n/ φ U1N [V] U2N [V] U3N [V] I1 [A] I2 [A] I3 [A] 1 1 3 5 7 2 THD [%] φ 1

12 3 5 7 9 11 THD [%] φ 3 1 3 5 7 9 11 13 THD [%] φ 8.6. Issues to be studied 1. The total current and voltage distortion factor. 2. Harmonics influence on the neutral current and neutral displacement voltage value. 3. Harmonics influence on the power quality. 4. The importance of neutral in three phase low voltage networks. References 1. C. Golovanov, M. Albu, Probleme moderne de măsurare în electroenergetică, București, Ed. Tehnică, 2001, pp. 467 – 508. 2. A. Baggini, Handbook of power quality, ed. John Wiley & Sons Ltd, 2008, pp. 163 – 185. 3. L. Dumitru, C. Dumitru, Bazele electroenergeticii, București, 2004 4. G. Chicco, P. Postolache, C. Toader, (2007) Analysis of three-phase systems with neutral under distorted and unbalanced conditions in the symmetrical component-based framework, IEEE transactions on power delivery, 22(1), 674-683. 5. I. Lepădat, C. Mihai, E. Helerea, “Unbalance in electrical networks as indicator of power quality” The 12th International Conference of Scientific Papaers, Scientific Research and Education in the Air Force–AFASES 2010, ISBN: 978-973-8415-76-8 Brasov – România, pp. 512 – 517. 6. G. Chicco, P. Postolache, C. Toader, “Analysis of three-phase systems with neutral under distorted and unbalanced conditions in the symmetrical component-based framework”, IEEE Transactions on Power Delivery, 22(1), 2007, pp. 674-683. 7. F. Batrinu, G. Chicco, A. O. Ciortea, R. Porumb, P. Postolache, F. Spertino and C. Toader, “Experimental Evaluation of Unbalance and Distortion Indicators in Three-Phase Svstems with Neutral”, Power Tech, 2007 IEEE Lausanne, 1-5 July 2007, pp. 1486-1491. 8. T. Zheng, E. B. Makram, and A. A. Girgis, “Evaluating power system unbalance in the presence of harmonic distortion,” IEEE Trans. Power Del., vol. 18, no. 2, Apr., 2003, pp. 393–397.