Optimal Design of Single-Tuned Passive Filters to Minimize Harmonic Loss Factor

Transcription

1 Middle-East Journal of Scientific Researc (): 49-55, 04 SSN DOS Publications, 04 DO: 0.589/idosi.mejsr Optimal Design of Single-Tuned Passive Filters to Minimize Harmonic Loss Factor Murat Eran Balci and Selçuk Sakar Department of Electrical and Electronics Engineering, Balikesir University, Balikesir, Turkey Department of Electrical and Electronics Engineering, Gediz University, zmir, Turkey Abstract: Transformers are conventionally designed for operation under sinusoidal load currents wit supply voltage-frequency. Te non-sinusoidal or armonically distorted currents drawn by non-linear loads lead to excessive winding losses and overeating of te transformers. Tese adverse effects result in loss of useful life of te transformers. To prevent te excessive winding losses, te transformers sould be loaded at less tan teir rated loading capacity under non-sinusoidal load current conditions. n EEE standard C57.0, te loading capacity of te transformer, wic is dedicated to supply a non-linear load, is determined in terms of te armonic loss factor (F HL). Te same standard also figured out tat te loading capacity of a transformer is inversely proportional to te F HL index of te supplied non-sinusoidal current. Te main purpose of tis paper is to employ te passive filters for imization of te loading capacity of te transformers under non-linear load conditions. Tus, an optimal passive filter design approac is proposed regarding minimization of F HL. Wit respect to EEE standard 59, voltage total armonic distortion (THDV), current total armonic distortion (THD) and displacement power factor (DPF) are considered as tree constraints for te proposed approac. Numerical results are presented to sow tat te proposed approac provides iger loading capacity of te transformers wen compared wit te traditional filter design approac based on minimization of THD. Key words: Harmonics Non-linear loads Transformer loading capacity Passive filters NTRODUCTON determined in Underwriters Laboratories (UL) standard 56 [4] and EEE standard C57.0 [5, 6]. n UL std. Transformers are conventionally designed for 56, derating ratio is expressed in terms of K-factor for operation under sinusoidal load currents wit supply dry-type transformers. Te determination of te derating voltage-frequency. However, te non-linear loads, wic ratio, wic is recommended by EEE std. C57.0, is ave armonically distorted or non-sinusoidal current based on F HL index. EEE standard metod covers bot wave sapes, are largely proliferated in te modern dry-type and liquid filled transformers. n addition, two industrial power systems [, ]. Tus, in te literature, standards clearly concluded tat te transformer s great interests ave been focused on te effects of te loading capacity is inversely proportional to K-factor armonics on te transformers [3-3]. t is seen from tese and F HL indices. studies tat non-sinusoidal currents cause excessive n parallel wit tese standards, transformer winding losses, wic result in overeating and useful life production companies started to design te transformers, reduction of te transformers. Tese studies also employ wic are dedicated to supply te non-linear loads suc an effective tecnique, widely called as derating [9, 3-5, as adjustable speed drives, power rectifiers and inverters, 7-9], to prevent te excessive winding losses related etc., by considering te rated powers and F HL or K-factor wit te current armonics. Derating is te intentional values of te loads [7-9]. reduction in loading capacity of a transformer, wic is On te oter and, it is reported in [30] tat te dedicated to supply a non-linear load. n addition to studies focused on te optimal filter design aim to acieve tat, derating ratio (permissible loading capacity) of a many combinations of five goals suc as () minimization transformer under non-linear load conditions is of current total armonic distortion (THD), (ii) Corresponding Autor: Murat Eran Balci, Department of Electrical and Electronics Engineering, Balikesir University, Balikesir, Turkey. 49

2 Middle-East J. Sci. Res., (): 49-55, 04 minimization of voltage total armonic distortion (THDV), (iii) imization of power factor, (iv) minimization of te filter s loss, (v) minimization of te filter s investment cost. Terefore, it can be concluded tat te passive armonic filters are not employed as equipment for imization of te transformer s loading capacity under non-sinusoidal current conditions in te literature. Consequently, in tis paper, te passive armonic filters are designed for minimization of F HL index or imization of transformer loading capacity under nonsinusoidal current conditions. Displacement power factor (DPF), THD and THDV limits recommended by EEE std. 59 [3] are considered as tree constraints in te optimal filter design process. For te typical industrial power system, wic is used as an exemplary system in several optimal filter design studies [30, 3-35], te proposed approac is comparatively evaluated wit respect to te traditional optimal filter design approac based on te minimization of THD ().Te numerical results sow tat te proposed approac provides iger loading capacity of te transformer under a non-sinusoidal load current condition wen compared wit te traditional one. Tis is an important finding for effective utilization of transformers in te non-sinusoidal power systems. Linear and non - linear loads Utility side s Tevenin equivalent PCC Consumer s transformer Single tunedlc filter Load bus Fig. : One line diagram of te typical industrial power system. Modeling of te Typical ndustrial Power System: Te one line diagram of te typical industrial power system is sown in Figure, wic consists of a consumer wit tree-pase linear and non-linear loads, a single-tuned LC filter connected to load bus and te consumer s transformer. Fig. : Single-pase equivalent circuit of te typical n order to state te current, voltage and power industrial power system. expressions for te system, its single-pase equivalent circuit (given in Figure ) can practically be used. were X tr is te winding s fundamental armonic Tis practical solution is valid due to te fact tat te inductive reactance, R dc and R ec denote te winding s dc system is balanced. n te figure, a linear impedance resistance and te winding s equivalent resistance ( RL + jx ) and a constant current source per armonic corresponding to te eddy-current loss, respectively. L ( L ) denote te linear and non-linear load model Using te superposition principle, te current and voltage expressions can be written for te single-pase equivalent circuit as follows: parameters [36], wic are referred to te primary side of te transformer. On te oter and, utility side is modelled as Tevenin equivalent voltage source ( V S ) and Tevenin equivalent impedance ( Z S ) for eac armonic number. Te consumer s transformer is modelled using its sort circuit impedance, wic is referred to its primary side: Tr = dc + ec + Tr Z R R jx () VS Z = + FL Z + Z + Z Z + Z + Z S Tr FL S Tr FL V = VS Z S were Z FL is te parallel equivalent of te load s t t armonic impedance ( RL + jx ) and armonic L impedance of te single-tuned passive filter L () (3) 50

3 Middle-East J. Sci. Res., (): 49-55, 04, wic are referred to te primary X Z j X CF F = LF side of te transformer. Note tat as; Z FL XCF j X LF ( RL + jx L ) ZF RL + jx L ZFL = = ( ZF + RL + jx L ) X j X CF LF + RL + jx L THDV = V V THD = P = V cos S = V can be expressed Te subscript ( _ ) denotes pasor values of te respective voltage, current and impedances. Considering te voltage and current armonics, wic are found from and, THDV and THD can be calculated as follows: n addition, one can express fundamental armonic active powers (P ) and fundamental armonic apparent powers (S )at eac-pase of te PCC as below: Tus, te displacement power factor (DPF) can be found in terms of P and S : (4) (5) (6) (7) (8) S % = 3V pu pu 00 R () were V R(pu), P LL-R(pu) and P EC-R(pu) are pu values of te rated line - to-line voltage, winding rated loss and winding eddy-current rated loss of te transformer, respectively. One can see from -tat F HL, (pu) and S are, pu and 00% under rated sinusoidal current condition. n addition, F HL>, (pu)<pu and S <00% will be observed if te current as a non-sinusoidal wave sape. Te proposed and traditional optimal passive filter design approaces will be formulated and solved regarding te detailed model of te typical industrial power system in te next sections. Formulation of Optimal Filter Design Problem: As mentioned above, te passive armonic filters can be employed for imization of te transformer s loading capacity under non-sinusoidal load current conditions. To acieve tis goal, minimization of F HL indexes used as an objective function for te optimal passive filter design problem. THD and THDV indices are considered as two constraints in te optimization problem due to te fact tat bot indices are taken under limitation by EEE std. 59 for several levels of te supply voltage and sort circuit power of te power systems. On te oter and, te same standard recommended tat a lagging DPF is necessary wit a value between 95% and 00%. Tus, DPF is a tird constraint of te optimization problem. After defining te objective function and constraints, optimal design problem of te single-tuned passive filter becomes: P DPF = = cos S Finally, for te system, te F index, wic is placed HL in EEE std.c57.0, can be calculated as follows: (9) Minimize F X, X Subject to HL ( LF CF ) THD( X, X ) THD LF CF MAX (3) (4) F HL = (0) THDV ( X, X ) THDV LF CF MAX DPF( X, X ) 00% LF CF (5) (6) By means of te calculated value, te permissible current capacity ( ( pu) ) and permissible loading capacity ( (%) ) of te transformer can be determined: ( pu) S PLL R pu + PEC R pu = = + PEC R pu + PEC R pu () DPF( X, X ) 95% LF CF (7) were eq. (3) is te objective function of te proposed optimal filter design problem and eq. (4)-(7) are te inequality constraints of te proposed optimal filter design problem. n te inequality constraints, THD MAX and THDV MAX are te imum allowable THD and THDV values, wic are determined in EEE standard 59. 5

4 Middle-East J. Sci. Res., (): 49-55, 04 On te oter and, te optimal filter design studies traditionally aim to minimize THD. Tese studies consider te same constraints wit te proposed optimal design approac. Terefore, te traditional optimal filter design approac can be described as: Minimize THD X, X LF CF (8) Subject to Te inequality constraints presented in eq. (4)-(7). Bot optimization problems are solved by means of Grid Searc Metod (GSM),wic is one of te oldest and te most reliable optimization tecniques [37]. GSM searces all feasible X LF and X CF values for finding optimal solution. t sould be underlined tat te traditional optimal filter design approac does not aim to imize te loading capacity of te transformers under non-linear load conditions. Terefore, te proposed filter design approac as an advantage on te effective utilization of te transformers wit respect to te traditional one. Exemplary Cases: n tis section, several exemplary cases are presented to analyze te performances of te proposed and traditional optimal filter design approaces. A typical industrial power system, wic is given in Figure, is used for te simulations of te exemplary cases. Fundamental frequency supply voltage and sort circuit power of te typical industrial power system are predetermined as 6.3 kv (line - to-line) and 0 MVA. n te typical industrial power system s single-pase equivalent circuit (illustrated in Figure ), te impedance parameters are R S=0.089, X S=0.89, R L=3.67, X L=3, R dc=0.04, R =0.04 ec and X =0.88 Tr. Fundamental frequency line - to-neutral source voltage (V S) and fundamental frequency line current ( ) are 3637 V and 84 A. Tese values are defined as base voltage and base current values. For te first exemplary case (case ), pu values of te voltage source and current source armonics are presented in Table. For te voltage source and current source armonics presented in Table, te THDV, THD, F HL, DPF and P values at te PCCbus are calculated as.80%, 5%, 7.05, 70.50% and 409kW, respectively. According to te recommendations placed in EEE std. 59, THDV and THD levels of te simulated system do not exceed 5% and 5%, respectively. n addition, te loading capacity of te transformer (S ) as a very low value, wic is calculated as 69% for F HL=7.05. Table : Pu values of te voltage source and current source armonics for case VS ( pu) L ( pu) Table : Te results obtained by te proposed and traditional optimal filter design approaces for case. F HL minimization THD minimization (proposed approac) (traditional approac) XLF XCF THD 3.50%.30% THDV.%.35% DPF 99.99% 99.99% S 86.35% 84.6% For tese conditions, two different optimal filter designs are determined by considering te proposed and traditional approaces (Table ).Te values of te power quality indices (THDV, THD, F HL and DPF) and te transformer s loading capacities (S ), wic are acieved wit bot optimal filter designs, are also given in Table. t can clearly be seen from tis table tat te proposed design approac provides lower F value (.84) and HL iger S value (86.35%) wen compared wit te traditional design approac (F HL=3.34, S =84.6%). Tus, it can be figured out tat tedifference ( S ) of te S values, wic are attained by te proposed and traditional filter designs, is about.%.on te oter and, te proposed one does not acieve te minimum THD (.30%), wic is obtained by te traditionalone. Note tat bot approaces meet THD and THDV limits of te EEE std. 59. Tey also attain te same DPF value(99.99%). n addition to te above mentioned results, to evaluate te performances of te proposed and traditional approaces under te igly distorted current conditions, bot approaces are implemented witout considering THDV and THD constraints for case -6.For case -6, wic ave te current source armonics given in Table 3, Table 4 presents te THD, THDV and F HL values at te PCC bus and te loading capacity (S ) of te transformer. For tese cases, te results of te proposed and traditional optimal design approaces are given in Table 5 and 6. One can see from tese tables tat tey can provide very different F HL values, particularly in te 5

5 Table 3: Pu values of te current source armonics for case -6 ( pu) L Case Case 3 Case 4 Case 5 Case Table 4: For case -6, te THD, THDV and values at te PCC bus and te loading capacity of te transformer. Case Case 3 Case 4 Case 5 Case 6 THDV 3.5% 3.73% 4.0% 4.70% 5.7% THD 30% 35% 40% 45% 50% S 6.08% 56.7% 5.3% 48.47% 45.3% Table 5: For case -6, te results acieved by te optimal passive filter, wic is designed according to te proposed approac witout considering THD and THDV constraints. Case Case 3 Case 4 Case 5 Case 6 XLF XCF THD 8.0%.35% 4.60% 8.0% 3.98% THDV.0%.35%.50%.66%.83% DPF 99.99% 99.99% 99.99% 99.99% 99.99% S 8.44% 78.49% 74.63% 7.08% 67.64% Table 6: For case -6, te results acieved by te optimal passive filter, wic is designed according to te traditional approac witout considering THD and THDV constraints. Case Case 3 Case 4 Case 5 Case 6 XLF XCF THD 3.% 5.5% 7.30% 9.40%.37% THDV.46%.65%.8%.00%.9% Middle-East J. Sci. Res., (): 49-55, V, t DPF 99.99% 99.99% 99.99% 99.99% 99.99% : armonic voltage and current rms values, S 79.38% 74.98% 70.94% 67.0% 63.% Fig. 3: Calculated S values for five THD levels between 30% and 50%. conditions were tere is a igly distorted load current. Figure 3 sows tat te difference ( S ) of te S values acieved by te proposed and traditional design approaces increases from 3.06% to 4.5% for te interval of THD between 30% and 50%. V, CONCLUSON Tis paper addresses tat te passive armonic filters can be employed to imize te loading capacity of te transformer supplying a non-sinusoidal load current. To acieve tis goal, minimization of F HL index sould be taken into account as an objective in te optimal passive filter design problem. Numerical results sow tat te proposed optimal design approac is valid for te typical industrial power systems. t is also clearly seen from te results tat te proposed design approac provides iger loading capacity of te transformer, wic is dedicated to supply a non-sinusoidal load current, wen compared wit te traditional design approac based on THD minimization. n addition, te proposed approac as a considerably important advantage on te effective utilization of transformers in te industrial power systems wit igly distorted currents. ACKNOWLEDGEMENTS Tis work is supported by Turkis Republic Ministry of Science, ndustry and Tecnology and BEST Transformers Company under te project number of 0008.STZ.0-. Nomenclature: t : armonic voltage and current pasors, t : Pase angle difference between armonic voltage and current, DPF : Displacement power factor, THD : Current total armonic distortion, THDV : Voltage total armonic distortion, P : Fundamental armonic active power, S : Fundamental armonic apparent power, F HL : Harmonic loss factor, P LL-R : Transformer s winding rated loss, P EC-R : Transformer s winding eddy-current rated loss, : RMS current capacity of a dry type transformer under non-linear load conditions, S : Loading capacity of a dry type transformer under non-linear load conditions.

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