Abstract:
Disclosed is a method for the improvement of the line quality in a system, in which a common feeding ( 1 ), via at least one distribution transformer ( 3 ), feeds at least two non-linear loads ( 11 ) drawing non-sinusoidal currents from the common feeding ( 1 ), wherein between the common feeding ( 1 ) and the distribution transformer ( 3 ) there is at least one primary side transformer line ( 2 ) and between the at least one distribution transformer ( 3 ) and the loads ( 11 ) there is at least one lower voltage secondary side transformer line ( 22 ), wherein at least one active filter ( 24 ) attached to at least one lower voltage secondary side transformer line ( 22 ) is used for the attenuation or elimination of higher order harmonics experienced by the common feeding ( 1 ). Furthermore a high power distribution system for use of such a method is disclosed, in particular for the operation of an electrostatic precipitator.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to a method for the improvement of the line quality for power distribution systems distributing to non-linear loads such as transistor based ESP power supplies. It furthermore relates to a distribution system implementing such a method and in particular to the use of such a distribution system for the operation of an electrostatic precipitator unit. 
       PRIOR ART 
       [0002]    With the increasing concern for environmental pollution, the reduction of particle emissions by using Electrostatic Precipitators (ESPs) is a highly important issue for coal fired power plants. ESPs are highly suitable dust collectors. Their design is robust and they are very reliable. Moreover, they are most efficient. Degrees of separation above 99.9% are not unusual. Since, when compared with fabric filters, their operating costs are low and the risk of damage and stoppage owing to functional disorders is considerably smaller, they are a natural choice in many cases. In an ESP, the polluted gas is conducted between electrodes connected to an ESP power supply. Usually, this is a high-voltage transformer with thyristor control on the primary side and a rectifier bridge on the secondary side. This arrangement is connected to the ordinary AC mains and thus is supplied at a frequency, which is 50 or 60 Hz. The power control is performed by varying the firing angles of the thyristors. The smaller the firing delay, i.e. the longer the conducting period, the more current supplied to the ESP and the higher the voltage between the electrodes of the ESP. Modern ESPs are divided into several bus sections for increasing the collection efficiency. Each of these bus sections has its own power supply (PS), which is controlled individually and has a typical output power range of 10-200 kW and an output voltage range of 30-150 kVDC. 
         [0003]    Modern ESP&#39;s power supplies are often based on resonant converters in order to utilize the transformer&#39;s nonidealities and to have soft switching for a wide operation range. One exemplary power supply for ESPs is known from US 2009/0129124. 
       SUMMARY OF THE INVENTION 
       [0004]    Correspondingly, the present invention relates to a method for the improvement of the line quality in a power distribution system, in particular for suppressing higher order harmonics generated by non-linear loads powered by the line at the common feeding. The typical applications are high power applications, so cases where the distribution transformer mentioned further below is rated in the range of 30 kVA-3000 kVA. 
         [0005]    In this method, a common feeding, via at least one distribution transformer, feeds at least two non-linear loads drawing non-sinusoidal currents from the common feeding. Between the common feeding and the distribution transformer there is at least one primary side transformer line and between the at least one distribution transformer and the loads there is at least one lower voltage secondary side transformer line. At least one active filter attached to at least one lower voltage secondary side transformer line is used for the attenuation or elimination of higher order harmonics experienced by the common feeding. In accordance with the invention, the control of the active filters is based on the measurement of a current sensor on the low voltage level (which should be present in each of the low-level circuits, only measurement and taking into account of the current conditions in each of the low voltage level circuits allows appropriate and complete line power quality improvement). This measurement however is preferentially not directly used as will be outlined further below but only after a computational correction taking the attenuation effect of the transformer itself into account. The active filter(s) so to speak correct the conditions on the low-level side via injection. This correction is however not principally aiming at a correction of harmonics on the low-level size, but rather at a correction of the conditions on the primary side. This is achieved in that the active filters inject into the low-level system in a manner which, so to speak backwards via the transformer and taking its effect into account, corrects the conditions on the high voltage side by eliminating the harmonics, which otherwise if present negatively influence the line power quality and also taking into account phase shifts generated by the transformer. Correspondingly therefore, preferably the currents i L     —     n  (where the index n stands for the nth secondary side transformer line) in all lower voltage secondary side transformer lines are measured and used for the control of the active filter. 
         [0006]    As mentioned above said current i L     —     n  (or in case of several secondary side lines, the corresponding set of current values as a function of time in the individual secondary side lines) is not directly used as an input reference for the active filter but from said current, using a computational model of the transformer, the current on the primary side transformer line is calculated, and therefrom, using a computational model of the transformer, the current on the secondary side transformer line is back calculated, and this current is used as input reference to the active filter. 
         [0007]    In case of only one single secondary side line, the input variable for this back and forth calculation is the above-mentioned current value. In case of more than one secondary side line, so in case there are several transformers transforming from one primary side line to several secondary side lines, the input variable for the calculation of the reference value for the active filter (or the plurality of active filters) is the set of all current values measured in the individual secondary side lines. It is to be noted that in such a case if there are several active filters the reference value for each of these active filters preferentially takes into account and is based on each of the current values measured in each of the secondary side lines. 
         [0008]    Interestingly, even if there are two transformers and two secondary side lines, it is not necessary that active filters be present in each of these secondary side lines of the transformer, as long as the currents measured in all secondary side lines are taken as input variables for the active filter. In other words one single active filter is in a position to correct for the effects of each of the secondary side lines on the primary side line. 
         [0009]    For primary current prediction (on the primary side transformer line) one can use for a  12  pulse system the following analytical calculation scheme: 
         [0000]    
       
         
           
             
                
               
                 
                   
                     
                       i 
                       RP 
                     
                   
                 
                 
                   
                     
                       i 
                       SP 
                     
                   
                 
                 
                   
                     
                       i 
                       TP 
                     
                   
                 
               
                
             
             = 
             
               
                 
                   1 
                   
                     n 
                     B 
                   
                 
                  
                 
                   
                      
                     
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           
                             - 
                             1 
                           
                         
                       
                       
                         
                           
                             - 
                             1 
                           
                         
                         
                           1 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           
                             - 
                             1 
                           
                         
                         
                           1 
                         
                       
                     
                      
                   
                   · 
                   
                      
                     
                       
                         
                           
                             i 
                             LR_UB 
                           
                         
                       
                       
                         
                           
                             i 
                             LS_UB 
                           
                         
                       
                       
                         
                           
                             i 
                             LT_UB 
                           
                         
                       
                     
                      
                   
                 
               
               + 
               
                 
                   1 
                   
                     n 
                     A 
                   
                 
                 · 
                 
                    
                   
                     
                       
                         
                           i 
                           LR_UA 
                         
                       
                     
                     
                       
                         
                           i 
                           LS_UA 
                         
                       
                     
                     
                       
                         
                           i 
                           LT_UA 
                         
                       
                     
                   
                    
                 
               
             
           
         
       
     
         [0010]    For the active filter references adjustment (currents without the harmonics which the 12 pulse transformer could mitigate):
       For the AF installed on the low voltage side of the transformer with lagged voltage:       
 
         [0000]    
       
         
           
             
                
               
                 
                   
                     
                       i 
                       LR_UB 
                       * 
                     
                   
                 
                 
                   
                     
                       i 
                       LS_UB 
                       * 
                     
                   
                 
                 
                   
                     
                       i 
                       LT_UB 
                       * 
                     
                   
                 
               
                
             
             = 
             
               
                 
                   
                     k 
                     1 
                   
                    
                   
                     n 
                     B 
                   
                 
                 3 
               
                
               
                 
                    
                   
                     
                       
                         1 
                       
                       
                         
                           - 
                           1 
                         
                       
                       
                         0 
                       
                     
                     
                       
                         0 
                       
                       
                         1 
                       
                       
                         
                           - 
                           1 
                         
                       
                     
                     
                       
                         
                           - 
                           1 
                         
                       
                       
                         0 
                       
                       
                         1 
                       
                     
                   
                    
                 
                 · 
                 
                    
                   
                     
                       
                         
                           i 
                           RP 
                         
                       
                     
                     
                       
                         
                           i 
                           SP 
                         
                       
                     
                     
                       
                         
                           i 
                           TP 
                         
                       
                     
                   
                    
                 
               
             
           
         
       
       
         
           
             For the AF installed on the low voltage side of the transformer with lead voltage: 
           
         
       
     
         [0000]    
       
         
           
             
                
               
                 
                   
                     
                       i 
                       LR_UA 
                       * 
                     
                   
                 
                 
                   
                     
                       i 
                       LS_UA 
                       * 
                     
                   
                 
                 
                   
                     
                       i 
                       LT_UA 
                       * 
                     
                   
                 
               
                
             
             = 
             
               
                 k 
                 2 
               
                
               
                 
                   n 
                   A 
                 
                 · 
                 
                    
                   
                     
                       
                         
                           i 
                           RP 
                         
                       
                     
                     
                       
                         
                           i 
                           SP 
                         
                       
                     
                     
                       
                         
                           i 
                           TP 
                         
                       
                     
                   
                    
                 
               
             
           
         
       
       
         
           
             To enable that all active filters installed in each low voltage side of the distribution transformers process similar harmonic amplitudes k 1  and k 2  are given below: 
           
         
       
     
         [0000]    
       
         
           
             
                 
             
              
             
               
                 k 
                 1 
               
               = 
               
                 
                   
                     
                       n 
                       A 
                     
                     
                       
                         n 
                         A 
                       
                       + 
                       
                         ? 
                       
                     
                   
                    
                   
                       
                   
                    
                   
                     k 
                     2 
                   
                 
                 = 
                 
                   ? 
                 
               
             
           
         
       
       
         
           
             
               ? 
             
              
             
               indicates text missing or illegible when filed 
             
           
         
       
     
         [0014]    —For the active filter installed on the lagged voltage transformer: 
         [0000]        k   1 =1  k   2 =0       For the active filter installed on the lead voltage transformer:         
         [0000]        k   1 =0  k   1 =1 
         [0000]    wherein:
   i Rp , i Sp , i Tp , are the predicted MV (medium voltage) side line currents;   i LR     —     UA , i LS     —     UA , i LT     —     UA  are the currents drained by the load installed on the lead transformer (counter clockwise);   i LR     —     UB , i LS     —     UB , i LT     —     UB  are the currents drained by the load installed on the lagged transformer;   n A  is the turns ratio of the lead transformer;   n B  is the turns ratio of the lagged transformer;   i LR     —     UA *, i LS     —     UA *, i LT     —     UA * are the adjusted current references for active filter installed on the lead transformer (counter clockwise);   i LR     —     UB *, i LS     —     UB *, i LT     —     UB * are the adjusted current references for active filter installed on the lagged transformer (counter clockwise);   k 1 , k 2  are the coefficients for adjustment of the current amplitudes on the low voltage side of the transformers.   
 
         [0024]    Alternatively the transformer model can be performed using a harmonic detection method such as FFT, DFTT, RDFT or the like, as will be detailed further below. 
         [0025]    According to a preferred embodiment of the proposed method and in order to take into account the specifics of the transformer(s), in addition to the above current values measured in each of the individual secondary side lines furthermore synchronization voltages u sync     —     n  can be measured on the lower voltage secondary side transformer line and can be used to calculate the voltage rms values on the secondary side transformer line. Again as in the case of the measured current values, preferably these voltages are measured in all individually secondary side lines and are taken into account for each of the active filters. 
         [0026]    According to yet another preferred embodiment, the distribution transformer is a 12 pulse transformer. This may preferably be selected from the group of Ddn, Dyn, Dzn, Ydn, Yyn, Yzn, with n selected from 0, 1, 5, 6, or 11, or in case of several transformers, combinations thereof. 
         [0027]    For a situation where two distribution transformers are present, preferably both are arranged as a  12  pulse transformer, which are transforming from the primary side of the transformer line to two lower voltage secondary side transformer lines. In this case preferentially the 12 pulse transformers are selected from the group Dd 0 -Dy 1 , Dy 1 -Dz 2 , Yd 1 -Dd 0 , Dz 0 -Dy 1 . 
         [0028]    According to another preferred embodiment, at least two distribution transformers, preferably 12 pulse transformers, are transforming from the primary side of the transformer line to at least two lower voltage secondary side transformer lines, and in at least two lower voltage secondary side transformer lines active filters are located, and preferably each lower voltage secondary side transformer line is equipped with an active filter controlled by reference signals calculated based on measurements in each and every lower voltage secondary side transformer line. 
         [0029]    Preferentially, the non-linear load is a transistor based power supply element, e.g. for continuous or pulsed operation, including a switched full bridge inverter, preferably a power supply for an electrostatic precipitator. In this case typically a transistor based power supply element comprises an input rectifier and a transistor based full bridge inverter, optionally followed by a resonant tank and/or a transformer unit and/or an output rectifier, wherein preferably on the input side of the full bridge inverter and/or on its output side smoothing inductors are arranged. However the method is principally suitable for any kind of non-linear load. 
         [0030]    The active filter control strategy in principle can be a conventional control strategy because the necessary correction for the behaviour of the transformer is already taken into account by the above-mentioned back and forth computational methods. The control strategy is nevertheless preferably selected from the group of dq-frame, PQtheory, Fryze currents, generalized integrators, frequency domain strategies, in particular DFT, RDFT and FFT. The present invention furthermore relates to a high power distribution system with a common feeding which, via at least one distribution transformer feeds at least two non-linear loads drawing non-sinusoidal currents from the common feeding, wherein between the common feeding and the distribution transformer there is a primary side of the transformer line and between the at least one distribution transformer and the loads there is at least one lower voltage secondary side of the transformer line, and wherein at least one active filter is attached to at least one lower voltage secondary side of the transformer line for the attenuation or elimination of higher order harmonics experienced by the common feeding. 
         [0031]    Furthermore according to a preferred embodiment, the proposed distribution system is provided with at least one sensor in at least one lower voltage secondary side of the transformer line sensing the current in said line, which is used for the control of the active filter. Preferably computational means are provided using said current and a computational model of the transformer is implemented in these means to calculate the current on the primary side of the transformer line, and therefrom, using a computational model of the transformer, the current on the secondary side of the transformer line, and this current is then input reference to the active filter(s), optionally taking into account synchronization voltages measured via further (all the same) sensors on the lower voltage secondary side of the transformer line to calculate the voltage rms values on the secondary side of the transformers. 
         [0032]    Preferentially, the distribution transformer is a  12  pulse transformer, such as selected from the group of Ddn, Dyn, Dzn, Ydn, Yyn, Yzn, with n selected from 0, 1, 5, 6, or 11, or in case of several transformers combinations thereof. Preferably two distribution transformers are present, typically arranged as a 12 pulse transformer by proper selection, transforming from the primary side of the transformer line to two lower voltage secondary side of the transformer lines, wherein the 12 pulse transformers are selected from the group Dd 0 -Dy 1 , Dy 1 -Dz 2 , Yd 1 -Dd 0 , Dz 0 -Dy 1 . There are 26 commercial configurations of three-phase transformer standardized by IEC (all 6 pulses), which can be selected to provide phase shift between primary and secondary windings as a multiple of 30 degrees. In the case where two commercial distribution transformers fed by the same grid are selected with 30 degrees phase-shift, they constitute a  12  pulse system. 
         [0033]    Furthermore the present invention relates to an electrostatic precipitator unit comprising a distribution system as outlined above and/or using a method as outlined above. 
         [0034]    Last but not least the present invention relates to the use of a method as outlined above and/or a distribution system as outlined above for powering a set of non-linear loads such as for the operation of an electrostatic precipitator unit with at least two, preferably at least six, more preferably at least 12 or 24 power supplies with transistor based full bridge inverter elements. 
         [0035]    Further embodiments of the invention are laid down in the dependent claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0036]    Preferred embodiments of the invention are described in the following with reference to the drawings, which are for the purpose of illustrating the present preferred embodiments of the invention and not for the purpose of limiting the same. In the drawings, 
           [0037]      FIG. 1  shows typical commercial ESP power supplies with: (a) ac-side smoothing inductor; and (b) dc-side smoothing inductor; 
           [0038]      FIG. 2  shows a typical ESP system electrical installation; 
           [0039]      FIG. 3  shows an ESP system using multi-pulse and active filter systems: (a) System using two active filters; and (b) System using one active filter; 
           [0040]      FIG. 4  shows a proposed ESP system control strategy 
           [0041]      FIG. 5  shows in a) and b) the transformer current model, where n represents the transformer turns ratio, wherein i L     —     1  represents i L,R     —     UA , i L,S     —     UA  and i L,T     —     ua  and wherein i L     —     2  represents i L,R     —     UB , i L,S     —     UB  and i L,T     —     UB ; for the case where 2 active filters are used (c.f.  FIG. 3(   a )), k 1 =k 2 =0.5; for only one active filter installed on the Dd 0  transformer secondary side (c.f.  FIG. 3(   b )), k 1 =0 and k 2 =1; and for only one active filter installed on the Dy 1  transformer secondary side, k 1 =1 and k 2 =0, and in c) it shows a schematic of a selective harmonic detection method; 
           [0042]      FIG. 6  shows an ESP system comprising a  12  pulse system and two active filters; the gray shaded background diodes of the active filter are SiC Schottky diodes; for the simulation for validating the theory, the gray active filter and the Dd 0  transformer are not employed (cf. experimental section); 
           [0043]      FIG. 7  shows an highly dynamic loading analysis: (a) System&#39;s line current; (b) Mains&#39; voltage; (c) ESP power supply B&#39;s line currents; (d) Active filter B&#39;s line currents; (e) ESP Power supply A&#39;s line currents; and (f) Active filter A&#39;s line currents; 
           [0044]      FIG. 8  shows a transformers unbalanced loading analysis: (a) Mains voltage; (b) Line currents&#39; Loci diagram; (c) System&#39;s line current and harmonic analysis; (d) ESP power supply B and Active filter B&#39;s line currents; (e) ESP Power supply A and Active filter A&#39;s line currents, wherein in the bar graphs of d) and e) at each harmonic the left side bar represents the non linear load current harmonic, the center bar represents the current generated by the active filters  24 , and the right side bar represents the current harmonics in the secondary side of the two transformers; 
           [0045]      FIG. 9  shows the situation for transformers with asymmetric parameters: (a) Line currents; (b) Single phase&#39;s load current for Unit A and B; and (c) Single phase active filter&#39;s currents for Unit A and B; 
           [0046]      FIG. 10  shows the situation for transformers with asymmetric parameters and adjusted transformer model: (a) Model&#39;s current predicted; (b) Line currents for the multi-pulse system without active filter; 
           [0047]      FIG. 11  shows a transformers unbalanced loading analysis: (a) Line Currents and harmonic analysis; (b) ESP power supply A&#39;s line current and active filter&#39;s current analysis; and (c) ESP power supply B&#39;s line current and harmonic analysis, wherein in the bar graphs of d) and e) at each harmonic the left side bar represents the non linear load current harmonic, the center bar represents the current generated by the active filters  24 , and the right side bar represents the current harmonics in the secondary side of the two transformers; 
           [0048]      FIG. 12  shows a  12  pulse system transformers unbalanced loading analysis: (a)  12  pulse system configuration; (b)  3  phases line currents and voltage; (c) Dd 0  and Dy 1  transformer&#39;s primary current and equivalent line current; and (c) Line current harmonic analysis; 
           [0049]      FIG. 13  shows alternatives for positioning the active filter for typical ESP systems; 
           [0050]      FIG. 14  shows a realistic MV/LV Dy 1  oil power transformer frequency dependent model; 
           [0051]      FIG. 15  shows an ESP system&#39;s performance evaluation against transformer asymmetries and parasitic variations: (a) Line current harmonic analysis for symmetric Dd 0  transformer and for changing Dy 1  transformer&#39;s turns ratio asymmetries between windings for one active filter solution and (b) for two active filter solutions; (c) Line current harmonic analysis for both symmetric Dd 0  and Dy 1  transformers, but with changing Dy 1  transformer&#39;s turns ratio for one active filter solution and (d) for two active filter solutions; (e) The influence of the transformer&#39;s parasitic variation (leakage inductance and windings resistance) against the system&#39;s 5th and 7th current harmonics mitigation performance for or one active filter solution and (f) for two active filter solutions; and 
           [0052]      FIG. 16  shows in a) experimental results for a balanced  12  pulse system: mains voltage ( 48 ); line current ( 49 );  12  pulse current without compensation ( 50 ); and active filter current ( 51 ); in b) experimental results for unbalanced  12  pulse system: mains voltage ( 48 ); line current ( 49 );  12  pulse current without compensation ( 50 ); and active filter current ( 51 ); in c) experimental results: line currents for unbalanced 12 pulse system; in d) experimental results: 12 pulse currents for unbalanced 12 pulse system; and in e) experimental results: active filter compensation currents for unbalanced 12 pulse system. 
       
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0053]    Nowadays, modern ESP&#39;s power supplies often employ three-phase diode bridge rectifiers as a front-end converter due to its simplicity, reliability and low cost. 
         [0054]    A high frequency three phase power supply  11  for powering one individual bus section in a setup according to  FIG. 2  described below is illustrated in  FIG. 1 . On the input side the power supply  11  is connected to the mains  1  and first comprises an input rectifier  12 . At the output side of the input rectifier  12  a direct current (DC) is provided and between the levels there is located a DC link capacitor  18 . This direct voltage is then fed trough a full bridge inverter  13  with a number of correspondingly fired transistors. The alternating current on the output side of the full bridge inverter  13  enters a resonant tank  14  and then a transformer unit  16 , the resonant circuit given by a series arrangement of a capacitor  19  and an inductor  20  followed in the transformer unit  16  by a transformer  21 . On the output side the unit  16  is coupled to an output rectifier  15  the output side of which is then coupled to the electrodes of the electrostatic precipitators  5 . For pulsed operation of such a power supply the full bridge inverter is operated in pulsed mode, continuous operation is possible as well 
         [0055]    A modern ESP power supply uses six-pulse diode bridge rectifiers with ac or dc-side smoothing inductors as front-end converter due their simplicity, reliability and low cost as illustrated in  FIG. 1   a  for a smoothing inductor  17  on the alternating current site and in  FIG. 1   b  for a DC side smoothing inductor  23 . 
         [0056]    However, such power supplies draw non-sinusoidal currents from the source, deteriorating the mains power quality. This system presents current harmonics of the order n=(6.i±1), where i is an integer greater than or equal to one. 
         [0057]    So the main drawback of this concept is that diode rectifiers inject significant current harmonics into the power system which can cause overloading of nearby shunt capacitors or a distortion of the mains voltage at the point of common coupling. Therefore, simple rectifiers do not meet the IEEE 519 guidelines concerning input current harmonics. 
         [0058]    Especially in pulsed operation, a significantly unbalanced loading of the mains phases could occur. Accordingly, the concept employed today bears the risk of causing severe problems such as malfunction of other equipment fed by the same mains, audible noise, increased losses of transformers, generators and power lines, electric resonances in the mains, and mechanical oscillations in generators. 
         [0059]      FIG. 2  shows a typical ESP installation with several sequential bus sections driven by 24 power supplies. The electrostatic precipitator  5  comprises an inlet side trough which a gas flow  4  loaded with particles, e.g. coal dust, enters the ESP. The ESP has an inlet field  6 , followed by middle fields  7  and is terminated by an outlet field  8 , the outlet of which is connected to a stack  9  through which the cleaned exhaust gas  10  exits to the environment. Each of the fields  6 - 8  has four cells or rows of individually powered precipitator systems, and to this end e.g. 24 power supplies (PS) are provided for the energisation of the precipitators. The power supplies are energized via the mains  1 , which via a low or medium voltage line  2  and distribution transformers  3  and low voltage level lines  22  connects to the individual power supplies. In other words the totality of the power supplies is connected to the same mains system  1  and if these power supplies or at least a fraction thereof are operated in pulsed mode the load on the main can be heavily unbalanced. 
         [0060]    In such a setup, 3-phase transformers providing phase shift between the voltages of the primary and secondary windings are employed to feed the ESP&#39;s power supplies in a three-wire system. Therefore, a multi-pulse system can be built by selecting suitable distribution transformers, where the simplicity and reliability of ESP power supplies are preserved. However, the performance of a multi-pulse system strongly depends on the load balance between the secondary sides of the transformers, which can be difficult to achieve in an ESP system, since the ESP bus section loading characteristics can vary considerably. 
         [0061]    As shown in  FIG. 3 , to further improve the line quality, ensuring agreement with harmonic guide lines, active filters  24  can be employed; however, they need to cope with the high dynamic loading of the ESP system. Moreover, the location of the active filters  24  plays an important role in the total efficiency of the system and cost of this active solution, i.e. if one installs the active filter  24  in the low or medium-voltage level  2  (primary side of the transformer  3 ) high voltage rating integrated gated bipolar transistors IGBTs and insulated transducers are required. 
         [0062]    This document relates to a highly efficient ESP system configuration schematically illustrated in  FIG. 3 , which complies with harmonic guidelines. Therein, distribution transformers are chosen to build a multi-pulse system  3  and active filters  24  are installed on the low voltage side  22  of the transformer  3  in order to use standard, low cost IGBTs and circuit components, which also enable a higher switching frequency/efficiency. The active filters  24  are mainly intended for high order harmonic-current-mitigation (&gt;7th harmonic), and for balancing the 5th and 7th current harmonics, which can be effectively eliminated by the multi-pulse system. In fact, the active filter(s)  24  compensate the line current harmonics on the medium voltage side that the 12 pulse system shown in  FIG. 3  cannot fully compensate. The ESP system becomes highly efficient because the active structures (active filters  24 ), only process about 20% of the total system power. 
         [0063]    The presented system configuration becomes feasible due to the proposed mathematical model of the distribution transformer  3  which quickly predicts and adjusts the line current on the LV or MV side  2  as the active filter&#39;s  24  current reference, by only sensing the currents of the ESP power supplies on the transformers&#39; LV side  22 . Due to the fact that just small calculations are necessary, delays on the reference signal processing are minimized, and control strategies, which are commonly used in active filter solutions, can be adapted without degrading the active filter overall performance. 
         [0064]    As illustrated in  FIG. 3   a ) such a setup may comprise one individual active filter  24  on each of two parallel low voltage level secondary sides  22  of the transformer  3 . In the alternative however it may also only comprise one active filter in one of the low-level circuits  22  as illustrated in  FIG. 3   b ). 
         [0065]    The control of the active filters  24  is based on the measurement of a current sensor  25  on the low voltage level (which in any case must be present in each of the low-level circuits  22 , only measurement and taking into account of the current conditions in each of the low voltage level circuits allows appropriate line power quality improvement), which measurement however is not directly used as will be outlined further below but only after a computational correction taking the effect of the transformer  3  into account. The active filter  24  so to speak corrects the conditions on the low-level side  22  via injection by a line  27 . This correction is however not principally aiming at a correction of harmonics on the low-level side  22 , but rather at a correction of the conditions on the primary side  2 . This is achieved in that the active filters inject into the low-level system in a manner which, so to speak backwards via the transformer  3  and taking its effect into account, corrects the conditions on the high voltage side  2  by eliminating the harmonics which otherwise if present negatively influence the line power quality. Using the proposed method also the phase shifts generated by the transformer are taken into account. 
         [0066]    In order to improve the line power quality of an ESP system, this invention thus proposes a highly efficient system configuration comprising two parts:
       A multi-pulse system  3 , which can be built by proper selection of distribution transformers in a typical ESP electrical installation (see  FIG. 2 ). The main objective of this system is to eliminate mainly the 5th and 7th harmonics (but also higher harmonics such as the 17th, the 19th, etc) of the line current on the transformer&#39;s low or medium voltage side  2  (primary side of the transformers).   Active Filters  24  intended for high order harmonic-current-mitigation (&gt;7th harmonic), and for balancing the 5th and 7th current harmonics, which can then be effectively eliminated by the multi-pulse system  3  in cases where the transformers&#39; loading are unbalanced. The active filters  24  are installed on the low voltage transformer side in order to use standard low cost IGBTs and circuit components with better loss characteristics.       
 
         [0069]    As illustrated in  FIG. 3 , both systems comprise two medium voltage/low voltage distribution transformers  3  configured as a multi-pulse system (Dd 0  and Dy 1  in this example) feeding two typical commercially available ESP power supplies  11  (see also  FIG. 1 ) and shunt active filters  24  installed on the low voltage side of the transformer  3 . As can be observed, there is the possibility of using one ( FIG. 3   b ) or more active filter structures  24  ( FIG. 3   a ). The selection of one or more active filters  24  and of their design is mainly dependent on the necessary amount of reactive power the active filter  24  needs to handle in order to provide high line power quality, which is about 20% of the total system power in case of 2 active filters  24  (see  FIG. 3   a ). 
         [0070]    In order to enable the active filter operation on the low voltage side of the transformer, the active filters units  24  need to predict or directly sense the current on the transformer&#39;s  3  low or medium voltage side  2 . Thereby, a special adjustment in a typical active filter  24  current reference generation strategy is proposed to avoid measurements on the low or medium voltage transformer side  2  as shown in  FIGS. 4 and 5 . The basic idea is that all the active filters  24  equally compensate the harmonics, which could not be eliminated by the multi-pulse transformer  3 . Thereby, instead of using directly the ESP power supply currents i L     —     1  as reference for the active filters  24 , as would be done by a traditional harmonic detection method, the proposed control strategy uses the current generated by a mathematical model of the transformer  3 . This model predicts the line currents in the transformer medium voltage side  2  by sensing the ESP power supplies currents i L     —     1  in the low voltage side  22  of the transformer (see also  FIG. 5 ). These currents i L     —     1  carry the information of the harmonics that need to be filtered (harmonics that the transformers  3  could not fully compensate). By adjusting proportionally the predicted currents to the low voltage side  22  of the transformer  3  according to the transformer turn ratio and configuration, the reference of each active filter  24  will be the same, but includes the transformer waveform phase-shift (30 degree in the 12 pulse system case). 
         [0071]    Summarizing, the main functions of the transformer model are:
       1) Mathematically subtract from the measured current k 1  the harmonics which the multi-pulse transformer would eliminate; and   2) To adjust the current reference according to the transformer side, where the active filter  24  is located, with proper phase shift and magnitude.       
 
         [0074]    It is important to mention that the current model of the transformer  3  is also valid for other 12 pulse system configurations, such as Dy 1 -Dz 2 , Yd 1 -Dd 0 , Dz 0 -Dy 1 , etc. For other cases, the new transformer, which has the lead secondary voltage (counterclockwise orientation), takes the role of the Dd 0  transformer and the lagged one takes the position of the Dy 1  transformer in the current model. 
         [0075]    For the primary current prediction (on the primary side transformer line) and the active filter references adjust the above explained analytical calculation scheme can be used. 
         [0076]    Due to the fact that only small calculations are necessary, delays on the reference signal processing are minimized and control strategies, which are commonly used in active filter  24  solutions, can be adapted without degrading the active filter  24  overall performance. 
         [0077]    The active filter  24  control strategy used here was the dq-frame (see also B. Kaku et al., IEEE Proceedings, electric power applications, Vol. 144, pp 182-190, 1997); however other strategies such as PQ-theory, Fryze currents, generalized integrators, frequency domain strategies (DFT, RDFT and FFT), etc, could also be employed. In addition, the synchronization voltages u Sync     —     1  and U Sync     —     2  can further be used to adjust asymmetries on the transformer windings coupling, by modifying the model&#39;s transformer turns ratio n for each single phase. 
         [0078]    As mentioned above, there are alternative ways to perform the transformer current model, e.g. by using a harmonic detection method such as FFT, DFT, RDFT, etc: 
         [0079]    So alternatively, e.g. selective harmonic detection methods, such as FFT, DFT, RDFT, etc, can be used to adjust the active filter current reference as shown in  FIG. 5   c . By calculating the amplitude and phase of the currents drained by the non-linear load  5  on the low voltage side  22  of each distribution transformer  3 , mainly the fundamental, the 5th and 7th harmonics, the loading unbalance between the secondary  2  of the 12 pulse system can be determined. By using the expressions shown in  FIG. 5   c  and as given below, the remaining 45th and 47th current harmonics on the primary side of the transformer can be determined. The current references of the installed active filters  24  are then adjusted according to the system characteristics and expressions shown in  FIG. 5   c : 
         [0000]    
       
         
           
             
               Δ5 
                
               
                   
               
                
               th 
             
             = 
             
               
                  
                 
                   
                     X 
                     
                       5 
                        
                       
                           
                       
                        
                       
                         th 
                          
                         _ 
                       
                        
                       1 
                     
                   
                   
                     n 
                     a 
                   
                 
                  
               
               - 
               
                  
                 
                   
                     
                       √ 
                       3 
                     
                      
                     
                         
                     
                      
                     
                       X 
                       
                         5 
                          
                         
                             
                         
                          
                         
                           th 
                            
                           _ 
                         
                          
                         2 
                       
                     
                   
                   
                     n 
                     b 
                   
                 
                  
               
             
           
         
       
       
         
           
             
               Δ7 
                
               
                   
               
                
               th 
             
             = 
             
               
                  
                 
                   
                     X 
                     
                       7 
                        
                       
                           
                       
                        
                       
                         th 
                          
                         _ 
                       
                        
                       1 
                     
                   
                   
                     n 
                     a 
                   
                 
                  
               
               - 
               
                  
                 
                   
                     
                       √ 
                       3 
                     
                      
                     
                         
                     
                      
                     
                       X 
                       
                         7 
                          
                         
                             
                         
                          
                         
                           th 
                            
                           _ 
                         
                          
                         2 
                       
                     
                   
                   
                     n 
                     b 
                   
                 
                  
               
             
           
         
       
       
         
           
             
               i 
               
                 
                   L 
                    
                   _ 
                 
                  
                 1 
               
               * 
             
             = 
             
               
                 i 
                 
                   
                     L 
                      
                     _ 
                   
                    
                   1 
                 
               
               - 
               
                 ( 
                 
                   
                     i 
                     
                       
                         L 
                          
                         _ 
                       
                        
                       1 
                        
                       
                           
                       
                        
                       
                         st 
                          
                         _ 
                       
                        
                       1 
                     
                   
                   + 
                   
                     i 
                     
                       
                         L 
                          
                         _ 
                       
                        
                       5 
                        
                       
                           
                       
                        
                       th_ 
                        
                       1 
                     
                   
                   + 
                   
                     i 
                     
                       
                         L 
                          
                         _ 
                       
                        
                       7 
                        
                       
                           
                       
                        
                       
                         th 
                          
                         _ 
                       
                        
                       1 
                     
                   
                   - 
                   
                     
                       k 
                       2 
                     
                      
                     
                       
                         n 
                         a 
                       
                        
                       
                         ( 
                         
                           
                             Δ5 
                              
                             
                                 
                             
                              
                             th 
                           
                           + 
                           
                             Δ7 
                              
                             
                                 
                             
                              
                             th 
                           
                         
                         ) 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               i 
               
                 
                   L 
                    
                   _ 
                 
                  
                 2 
               
               * 
             
             = 
             
               
                 i 
                 
                   
                     L 
                      
                     _ 
                   
                    
                   2 
                 
               
               - 
               
                 ( 
                 
                   
                     i 
                     
                       
                         L 
                          
                         _ 
                       
                        
                       1 
                        
                       
                           
                       
                        
                       
                         st 
                          
                         _ 
                       
                        
                       2 
                     
                   
                   + 
                   
                     i 
                     
                       
                         L 
                          
                         _ 
                       
                        
                       5 
                        
                       
                           
                       
                        
                       th_ 
                        
                       2 
                     
                   
                   + 
                   
                     i 
                     
                       
                         L 
                          
                         _ 
                       
                        
                       7 
                        
                       
                           
                       
                        
                       
                         th 
                          
                         _ 
                       
                        
                       2 
                     
                   
                   + 
                   
                     
                       
                         
                           k 
                           1 
                         
                          
                         
                           n 
                           b 
                         
                       
                       
                         √ 
                         3 
                       
                     
                      
                     
                       ( 
                       
                         
                           Δ5 
                            
                           
                               
                           
                            
                           th 
                         
                         + 
                         
                           Δ7 
                            
                           
                               
                           
                            
                           th 
                         
                       
                       ) 
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             Δ5 
              
             
                 
             
              
             th 
              
             
                 
             
              
             and 
              
             
                 
             
              
             Δ7 
              
             
                 
             
              
             th 
              
             
                 
             
              
             respect 
              
             
                 
             
              
             the 
              
             
                 
             
              
             transformer 
              
             
                 
             
              
             phase 
              
             
                 
             
              
             shift 
           
         
       
     
         [0080]    To enable that all active filters  24  installed in each low voltage side  22  of the distribution transformers  3  process similar harmonic amplitudes k 1  and k 2  are given below: 
         [0000]    
       
         
           
             
                 
             
              
             
               
                 k 
                 1 
               
               = 
               
                 
                   
                     
                       
                         n 
                         A 
                       
                        
                       
                           
                       
                     
                     
                       
                         
                           n 
                           A 
                         
                         + 
                         
                           ? 
                         
                       
                        
                       
                           
                       
                     
                   
                    
                   
                       
                   
                    
                   
                     k 
                     2 
                   
                 
                 = 
                 
                   ? 
                 
               
             
           
         
       
       
         
           
             
               ? 
             
              
             
               indicates text missing or illegible when filed 
             
           
         
       
     
         [0081]    for one active filter installed on the lagged voltage transformer: 
         [0000]        k   2 =1  k   2 =0 
         [0082]    for one active filter installed on the lead voltage transformer: 
         [0000]        k   1 =0  k   2 =1 
         [0083]    For a  12  pulse systems typically n B =n A √3. 
         [0084]    In order to verify the proposed study, the following simulations were performed for the ESP system depicted in  FIG. 6 :
       a) The system performance for highly dynamic ESP loading, where two active filters  24  are installed on the secondary side  22  of the 12 pulse system  3  with ac-side smoothing inductor  17  ESP power supplies  11 , are shown in  FIG. 7 . As one can observe, the active filters  24  could effectively compensate the current harmonics and the system draws sinusoidal current from the mains (see  FIG. 7(   a )). Although the two transformers  3  process different amounts of power (see  FIGS. 7(   c ) and  7 ( e )), the active filters  24  process the same amount of reactive power (see  FIGS. 7(   d ) and  7 ( f )).   b) The current harmonic analysis for the case where the transformers operate with unbalanced loading is shown in  FIG. 8 . Here, one can observe that the mains currents have sinusoidal waveform (see  FIG. 8(   c ), also the loci diagram in  FIG. 8(   b )), and the current harmonics generated by the active filters  24  are of the same amplitude (center bars at each harmonic in the bar diagrams on the right side of  FIGS. 8   c, d  and  e ). The current harmonics on the secondary side  22  of the two transformers  3  are of the same amplitude (right side bars at each harmonic in the bar diagrams on the right side of  FIGS. 8   c, d  and  e ), which helps the transformer to effectively compensate the 5th and 7th harmonics.   c) The proposed system behaviour for the case where transformer parameters are asymmetric is shown in  FIG. 9 . Here, the transformer turns ratio and the leakage inductances for each transformer&#39;s windings are set to be asymmetric (Dd 0 : nR=1.03 (L φR =100 μF), nS=0.99 (L φS =350 μF), nT=1.02 (L φT =50 μF); Dy 1 : R=1.732 (L φR =80 μF), nS=1.698 (L φS =200 μF), nT=1.767 (L φT =400 μF)). As one can observe, the system using the ideal model of the transformer for generating the current references has good performance for this test condition. Thus, the effort to obtain a more accurate transformer model is not justified.   d) In order to verify the characteristic of the mathematical model adjustment over transformer asymmetries on the transformer&#39;s windings turns ratio, one can simulate the case where the transformer&#39;s windings are set to be: Dd 0 : nR=1.0, nS=1, nT=1.0; and Dy 1 : nR=1.05√3, nS=√3, nT=0.87√3. Here, the proposed control determines the transformer&#39;s asymmetries on the single phase windings&#39; turns ratio n by calculating the voltage rms value on the secondary side of the transformers (u Sync     —     1  and u Sync     —     2 ).  FIG. 10  shows both the model predicted current on the primary side of the transformer (see  FIG. 10(   a )) and the obtained multi-pulse system currents (see  FIG. 10(   b )). As one can observe, the predicted currents are very similar to the simulated one, validating the model adjust strategy.   e) The 12 pulse system is now feeding two ESP power supplies  11  with dc-side smoothing inductors  17  with one active filter  24  connected to the Dd 0  transformer&#39;s secondary side  22 . The current harmonic analyses, for the case where the transformers operate with unbalanced loading are shown in  FIG. 11 . One can observe that the mains currents have sinusoidal waveform (see  FIG. 11(   a )). Note that the current harmonics in the secondary side of the two transformers are of the same amplitude (right side bars at each harmonic in the bar diagrams on the right side of  FIGS. 11   b  and  c ), which helps the transformer to effectively compensate the 5th and 7th harmonics.       
 
         [0090]    As can be observed in  FIGS. 7 to 11 , the proposed transformer model can be used to adjust the current reference of typical active filter controls, without degrading its performance even in cases where the parameters of the transformer are asymmetric (see  FIGS. 7 and 9 ). To have an enhanced performance when the transformer parameters are highly asymmetric, the synchronization voltages u Sync     —     1  and u Sync     —     2  can be used to calculate the voltage&#39;s rms value on the secondary side of the transformers in order to perform adjustments on the proposed mathematical model (see  FIG. 10 ). 
         [0091]    The proposed transformer&#39;s model can be used in a multi-pulse system configuration with either one or more active filters (see  FIGS. 8 and 11 ). For single active filter solution, all the reactive power, which the multi-pulse system  3  could not eliminate, will be processed by this converter. For the multiple active filter solution, all the reactive power is equally shared between the active filters. Moreover, the proposed strategy can be used for ESP systems, comprising power supplies either in configuration with dc- or ac-side smoothing inductors (see  FIGS. 8 and 11 ). 
         [0092]    Note that if the 12 pulse system total loading is equally shared by the two transformers as proposed in  FIG. 12(   a ), the system naturally has the 5th and 7th harmonics balanced (see  FIGS. 12(   b ),  12 ( c ) and  12 ( d )). In this configuration the power processed by an installed active filter  24  is reduced, because it only processes &gt;7th current harmonics. However, to employ this solution, one can consider an increment in the total installation cost, which would be mainly originated from the necessity of more power cabling. 
         [0093]    An ESP system, which complies with harmonic guide lines by utilizing the combination of multi-pulse systems and active filter solutions can be arranged as described in the following:
       a) The active filter solution  24  is directly connected to the medium voltage side  2  of the multi-pulse transformer  3  as shown in  FIG. 13(   a ). In this configuration, medium-voltage semiconductors/sensors are required, which increases the cost of the active filter solution  24 . Moreover, switches for high voltage and relatively low current results in poor utilization of the semiconductor.   b) In order to overcome the drawbacks of the configuration depicted in  FIG. 13  ( a ), one can use an external MV/LV transformer  45  to feed the active filter  24  as illustrated in  FIG. 13(   b ). In this case, better utilization of the active filter semiconductors can be achieved; however, one additional MV/LV transformer  45 , which processes the same amount of power as the active filter  24 , is required increasing the cost of the system.   c) In order to reduce the power processed by both the active filter  24  and the additional transformer  45  proposed in  FIG. 13(   b ), a hybrid filter solution can be used as shown in  FIG. 13(   c ). In this case, good utilization of the semiconductors and a more efficient system can be achieved (less power processed by the active filter); however, high voltage rating passive elements  46  are required. Moreover, in the case of unbalanced loading on the secondary windings of the multi-pulse transformer, the system would not fully compensate the line&#39;s 5th and 7th currents harmonics, and additional 5th and 7th harmonic passive filters could be necessary.   d) A system configuration with a special MV/LV transformer  3  is shown in  FIG. 13  ( d ). In this case, the active filter  24  is installed on the low voltage side  22  of the transformer  3 , but the additional cost of the special distribution transformer  3  would be very high.   e) A system with active filters  24  directly installed on the low voltage side  22  of the transformer is shown in  FIG. 13(   e ). In this case, there is the possibility of using either only one active filter structure  24  or one active filter  24  for each secondary windings of the transformer. The active filters  24  are intended for high order harmonic-current-mitigation (&gt;7th harmonic), and for balancing the 5th and 7th current harmonics, which can be effectively eliminated by the multi-pulse system  3  in cases where the transformers&#39; loading are unbalanced. Due to the fact that the active filters  24  are installed on the low voltage transformer side  22 , IGBTs and circuit components with better loss and insulation characteristics are used.   f) A system with active filters  24  directly installed on the low voltage side of the transformer together with a multi-pulse system  3  built with autotransformers and non-linear loads  44 , which can be ESP power supplies  11 , are shown in  FIG. 13(   f ). In this case, there is no need for MV/LV transformers configured as multi-pulse system; however, an autotransformer processing of about 20% of the ESP loading power will be required (high cost). Typical commercial available active filters can be employed.       
 
         [0100]    As can be observed in  FIG. 5 , the proposed active filter reference current generation strategy does not consider the parasitic character or asymmetries of the system&#39;s transformers. In order to analyse the parasitic effect on the system performance employing the proposed ideal transformer current model, the frequency dependent model of a MV/LV oil power transformer presented by B. Kaku et al., IEEE Proceedings, electric power applications, Vol. 144, pp 182-190, 1997 is considered for evaluation (c.f.  FIG. 14 ). Simulations of the system depicted in  FIG. 6 , assuming an ideal Dd 0  transformer and a realistic Dy 1  transformer, were performed as described in the following:
       a) The influence of the transformer&#39;s turns ratio asymmetries between the secondary windings of the realistic Dy 1  transformer on the system&#39;s 5th and 7th current harmonics mitigation is investigated. A graph plotting the remaining 5th and 7th current harmonics (in percentage of the fundamental component) on the system&#39;s MV side in dependent on the maximum percentage of turns ratio variation between the Dy 1  transformer&#39;s secondary windings is depicted in  FIG. 15  ( FIG. 15(   a ) for one AF and  15 ( b ) for two AF solutions). As can be observed, the system line quality is preserved even for a highly asymmetric transformer. Moreover, the current mitigation performance for the one or two active filter solution is very similar.   b) Both Dd 0  and Dy 1  transformers are considered with symmetric phase characteristics (for each transformer the secondary windings have similar parasitic and turns ratio values); however the turns ratio of the Dy 1  transformer varies proportionally to the theoretical value for a  12  pulse system ((Δn+1)n√3). Here, the transformer current reference model is not adjusted.  FIGS. 15(   c ) and  15 ( d ) show the 5th and 7th line current harmonic mitigation performance as percentage of the fundamental component for one AF and two AF solutions, respectively. As can be observed, the proposed transformer model generates an error on the active filter reference signals, which can degrade the systems mitigation performance. To overcome this drawback, the synchronization voltages u Sync     —     1  and u Sync     —     2  can be used to calculate the voltage rms values on the secondary side  22  of the transformers to perform the necessary adjustment on the reference mathematical model (see also  FIG. 10) .   c) The influence of the transformer&#39;s parasitic variation (leakage inductance and windings resistance) against the system&#39;s 5th and 7th current harmonics mitigation performance is investigated. The variation on the transformer&#39;s parasitic character is executed symmetrically in each one of the Dyl&#39;s realistic phases parameters as (Δ+1)Lσ and (Δ+1)Rσ.  FIGS. 15  ( e ) and  15 ( f ) present the results obtained with this experimentation for one active filter  24  and two active filter  24  solutions, respectively. As one can observe, the system line quality is preserved even for a high parasitic components values of the transformer.       
 
         [0104]    The line quality improvement achieved with the proposed ESP system is also verified experimentally. So in order to validate the proposed transformer model the circuit set-up shown in  FIG. 6  was set up. The transformer utilized to phase shift the primary to the secondary windings by 30 degrees is a Dy 1  type transformer with turns ratio of √3:1. An 12 kVAr active filter is added on the Dd 0  transformer secondary side to mitigate the remaining harmonics of the constructed  12  pulse system. The test set-up circuit diagram is shown in  FIG. 6  however the Dd 0  transformer is not employed and only one active filter is used. 
         [0105]    Results are given in  FIG. 16   a )- e ).  FIG. 16   a  shows the case where the 12 pulse transformers have balanced loading, and for this reason the active filter processes only high order harmonics (&gt;7th harmonics).  FIG. 16   b  to  FIG. 16   e  present the experimental waveforms for the unbalanced  12  pulse system. 
         [0106]    As can be noted in  FIG. 16 , the ESP system can comply with harmonic guidelines as the drained line currents have sinusoidal shape. Therefore, the proposed transformer current active filter controls, without degrading the system performance even in cases where the parameters of the 12 pulse transformer are asymmetric. 
         [0107]    As shown in  FIG. 16 , the shunt active filter could efficiently compensate the current harmonics with order higher than the 7th order. In addition, it adjusted the 5th and 7th harmonics on the Dd 0  secondary side to be of the same amplitude as the ones on the Dy 1  secondary side. In this way, the 12 pulse system could eliminate the 5th and 7th harmonics, and the studied ESP system drained close to sinusoidal shaped line currents. 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 LIST OF REFERENCE SIGNS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                  1 
                 mains, common feeding 
               
               
                   
                  2 
                 low or medium voltage level 
               
               
                   
                   
                 line, primary side of the 
               
               
                   
                   
                 transformers 
               
               
                   
                  3 
                 distribution transformer, 12 
               
               
                   
                   
                 pulse system 
               
               
                   
                  4 
                 gas flow loaded with 
               
               
                   
                   
                 particles, e.g. coal dust 
               
               
                   
                  5 
                 electrostatic precipitator 
               
               
                   
                  6 
                 inlet field 
               
               
                   
                  7 
                 middle fields 
               
               
                   
                  8 
                 outlet field 
               
               
                   
                  9 
                 stack 
               
               
                   
                 10 
                 cleaned exhaust gas 
               
               
                   
                 11 
                 power supply 
               
               
                   
                 12 
                 input rectifier 
               
               
                   
                 13 
                 full bridge inverter 
               
               
                   
                 14 
                 resonant tank 
               
               
                   
                 15 
                 output rectifier 
               
               
                   
                 16 
                 transformer and non idealities 
               
               
                   
                 17 
                 AC side smoothing inductor 
               
               
                   
                 18 
                 DC link capacitor 
               
               
                   
                 19 
                 capacitor in series 
               
               
                   
                 20 
                 inductor in series 
               
               
                   
                 21 
                 transformer 
               
               
                   
                 22 
                 low voltage level, secondary 
               
               
                   
                   
                 side of the transformer 
               
               
                   
                 23 
                 DC side smoothing inductor 
               
               
                   
                 24 
                 active filter 
               
               
                   
                 25 
                 current sensor on low voltage 
               
               
                   
                   
                 level, active filter current 
               
               
                   
                   
                 reference 
               
               
                   
                 26 
                 voltage sensor on low voltage 
               
               
                   
                   
                 level 
               
               
                   
                 27 
                 active filter line 
               
               
                   
                 28 
                 primary current prediction 
               
               
                   
                 29 
                 secondary current adjusted 
               
               
                   
                   
                 reference, final input 
               
               
                   
                   
                 reference for active filter 
               
               
                   
                 30 
                 space vector modulation 
               
               
                   
                 31 
                 transformer current model 
               
               
                   
                 32 
                 ideal transformer model 
               
               
                   
                 33 
                 low pass filter 
               
               
                   
                 36 
                 ΔΔ transformer 
               
               
                   
                 37 
                 ΔY transformer 
               
               
                   
                 38 
                 direct connected on the 
               
               
                   
                   
                 medium voltage side 
               
               
                   
                 39 
                 connected on the medium 
               
               
                   
                   
                 voltage side by a transformer 
               
               
                   
                 40 
                 hybrid filter connected on the 
               
               
                   
                   
                 medium voltage side 
               
               
                   
                 41 
                 extra windings on the low 
               
               
                   
                   
                 voltage side 
               
               
                   
                 42 
                 active filter connected in each 
               
               
                   
                   
                 secondary winding 
               
               
                   
                 43 
                 active filter connected in each 
               
               
                   
                   
                 secondary windings and 
               
               
                   
                   
                 autotransformer 
               
               
                   
                 44 
                 nonlinear load 
               
               
                   
                 45 
                 transformer for active filter 
               
               
                   
                 46 
                 high pass filter for 11th, 13th 
               
               
                   
                   
                 order of harmonic 
               
               
                   
                 47 
                 extra winding on the low 
               
               
                   
                   
                 voltage side 
               
               
                   
                 48 
                 mains voltage 
               
               
                   
                 49 
                 line current 
               
               
                   
                 50 
                 12 pulse current without 
               
               
                   
                   
                 compensation 
               
               
                   
                 51 
                 active filter current 
               
               
                   
                 CH 
                 current harmonic (% of 
               
               
                   
                   
                 fundamental) 
               
               
                   
                 ESP 
                 electrostatic precipitator 
               
               
                   
                 OH 
                 order of harmonic 
               
               
                   
                 PLL 
                 phase locked loop 
               
               
                   
                 PS1 
                 power supply 1 
               
               
                   
                 PS2 
                 power supply 2 
               
               
                   
                 . . . 
               
               
                   
                 PSn − 1 
                 power supply n − 1 
               
               
                   
                 PSn 
                 power supply n