Neutral current compensation in three phase, four wire systems a review

Electric Power Systems Research 86 (2012) 170–180 Contents lists available at SciVerse ScienceDirect Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr Review Neutral current compensation in three-phase, four-wire systems: A review D Sreenivasarao ∗ , Pramod Agarwal, Biswarup Das Electrical Engineering Department, Indian Institute of Technology Roorkee, Roorkee, India a r t i c l e i n f o Article history: Received July 2011 Received in revised form 20 December 2011 Accepted 23 December 2011 Available online 26 January 2012 Keywords: Active power filters (APF) Harmonic elimination Neutral current compensation Power quality Three-phase four-wire distribution system Transformers a b s t r a c t In many residential and office buildings, power is distributed through a three-phase, four-wire (3P4W) systems The non-linear and unbalanced loads in these systems may result in excessive neutral currents, which may potentially damage the neutral conductor and distribution transformer while affecting the safety of the consumers Several techniques have been reported in literature to overcome this problem This paper presents a comprehensive review of neutral current compensation methods, their topologies, and their technical and economical limitations Simulations are also carried out in MATLAB/SIMULINK environment for comparing the existing methods © 2011 Elsevier B.V All rights reserved Contents Introduction Problems of high neutral currents Recommended practices for handling excess neutral currents Passive harmonic filters Synchronous machine as a filter Transformer based topologies 6.1 Zigzag transformer 6.1.1 Operation of zigzag transformer with unbalanced/distorted supply voltages 6.2 Star-delta transformer 6.3 T-connected transformer 6.4 Star-hexagon transformer 6.4.1 Zigzag transformer with single-phase shunt APF 6.4.2 Zigzag transformer with single-phase series APF 6.4.3 Star-delta transformer with single-phase half-bridge PWM APF Three-phase, four-wire active power filters 7.1 Three H-bridge shunt APF topology 7.2 Three-phase, four-wire capacitor midpoint APF topology 7.3 Three-phase, four-wire four-leg APF topology Conclusion References ∗ Corresponding author E-mail address: luckysrinu@gmail.com (D Sreenivasarao) 0378-7796/$ – see front matter © 2011 Elsevier B.V All rights reserved doi:10.1016/j.epsr.2011.12.014 171 171 171 171 172 172 172 172 173 173 173 174 175 175 176 176 176 177 178 178 D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 171 Introduction The three-phase, four-wire (3P4W) electrical distribution systems have been widely employed to deliver electric power to single-phase and/or three-phase loads in manufacturing plants, commercial and residential buildings In these systems singlephase supply to small loads is provided by one of the phase conductors and neutral wires To balance the load on each of the phases, the single-phase loads are evenly distributed to the various floors In practice, these single-phase loads are not completely balanced, thus resulting in a net current flowing through the neutral conductor These are not the only sources for neutral current but there are other sources such as non-linear loads, where even perfectly balanced single-phase non-linear loads on 3P4W system can result in significant neutral current Nonlinear loads, such as power electronic based equipment, have phase currents which are non-sinusoidal and the vector sum of balanced, nonsinusoidal, three-phase currents does not necessarily equal to zero and result current in the neutral conductor [1–4] With sinusoidal load currents, the neutral current depends only on the system unbalance But, in a balanced system with harmonic distorted current waveforms, only the triplen harmonics (i.e with harmonic order multiple of 3) contribute to the neutral current When both harmonic distortion and load current unbalance are simultaneously present, the neutral current may contain all harmonics [1–14] The paper discusses the problems of high neutral currents, recommended practices for handling the excess neutral currents and presents comprehensive review of technical and economical limits for compensating these neutral currents Problems of high neutral currents Unbalanced and non-linear loads on 3P4W system causes excessive neutral current and the problems related to the excessive current in the neutral conductor are: [3,4] • Overloading of distribution feeders and transformers: With four current carrying conductors, the distribution system feeders and transformers may overload and cause additional heat loss • Common mode noise: The voltage difference between neutral and ground causes common mode noise in 3P4W power systems This common mode voltage can result in the malfunction of sensitive electronic equipments • Flat-topping of voltage waveform: The power supplies use the peak voltage of the sine wave to keep the capacitors at full charge, reductions in the peak voltage appear as low voltage to the power supply, even though the rms value of the voltage may be normal • Wiring failure: In old buildings, load growth with passage of time makes size of neutral conductor insufficient and cause wiring failure and poses a fire hazard Recommended practices for handling excess neutral currents The high neutral currents in 3P4W system have detrimental effect on both distribution system and end users The recommended practices and temporary measures recommend by different agencies to reduce/eliminate the neutral current are given below [15–19] • Over sizing of neutral conductor: Over sizing of neutral conductor is an expensive solution, while the overloading of distribution transformer and feeder remains unaddressed [4,16] • Derating of distribution transformer: With non-linear loads, the maximum loading of transformer should be reduced to below its Fig A four branch star connected passive filter rated capacity to avoid overheating the distribution transformer and excessive distortion in output voltage Derating of transformers for three-phase three wire supplies and 3P4W power supplies are similar, yet they have significantly different crest factors and neutral current [4,18] • Separate neutral conductors: Use of separate neutral conductors for non-linear loads to avoid shared neutral conductors is also practiced However, this is almost impossible where loads are widely scattered The above recommended practices are effective temporary measures and have serious drawbacks The only solution for handling these excess neutral current is to incorporate the neutral current compensation devices There are various approaches reported in the literature for compensating neutral currents Passive solutions such as zero sequence harmonic filters, synchronous machine, specially designed transformers and active solutions such as 3P4W active power filters (APF) Details of these methods and their comparisons are given below Passive harmonic filters The filtering of excess neutral current in 3P4W systems was achieved through the use of single-phase passive filters connected between each phase conductor and the neutral wire These passive harmonic filters comprise of passive elements such as inductors, capacitor, and resistors and tuned to a particular harmonic frequency(s) [20–25] A solution for filtering current harmonics in 3P4W networks based on the usage of a four-branch star connected filter topology is depicted in Fig and presented in [23] This topology has four individual star-connected passive branches (three phase-branches and one neutral branch) The impedance of the phase branches of the filter are identical and different from neutral branch The phase branches are tuned to the positive/negativesequence harmonics such as 5th, 7th and/or 11th, 13th and the neutral branch is tuned to 3rd and/or 9th Passive solutions, albeit simple, are bulky and expensive Also, the sensitivity of the components to temperature and aging can result in ineffective filtering as the critical frequencies and the quality factor drifts Another bigger problem is the possibility of exciting a resonance condition with the ac system impedance, which can worsen the situation [24,25] 172 D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 Fig Schematic diagram for neutral current compensation with synchronous machine Synchronous machine as a filter Simultaneous absorption all the zero-sequence harmonic currents of the neutral wire using a synchronous machine has been proposed in [26] If the zero-sequence impedance of the synchronous machine is sufficiently smaller than that of the power source, then the synchronous machine would allow the absorption of the zero-sequence harmonic currents This can be done by selecting the coil pitch of the armature winding as 2/3 As a result, the zero-sequence reactance of the synchronous machine reaches minimum value The only limiting factor of the zero-sequence harmonics is armature resistance of the synchronous machine Hence, it is possible to absorb all the zero-sequence harmonic currents by the synchronous machine Fig shows the basic system in which the synchronous machine is used for absorbing the zero-sequence harmonic currents In this method the synchronous machine is connected in shunt between the utility and nonlinear load The neutral point of the armature winding of synchronous machine is connected to the neutral line through a switch A buffer reactor is installed on the utility side of the neutral line so that the harmonic compensation characteristics not depend on the impedance of the utility side This method does not require any additional controller and the synchronous machine can be operated as a synchronous condenser to control the reactive power in distribution systems and/or operate as a motor or generator set However, its compensation characteristics depend on zero-sequence impedance of the synchronous machine and buffer reactor The high initial and maintenance cost of the synchronous machine limits its application The passive neutral current compensation technique using different transformer topologies can reduce/eliminates the neutral current to a great extent Transformer based topologies The neutral current compensation for a 3P4W distribution system using different transformer topologies have been analysed by different researchers Some of the important transformer topologies are discussed below: 6.1 Zigzag transformer In past the zigzag transformer was used for creating a neutral, thereby converting a three-phase, three-wire (3P3W) distribution system to a 3P4W system [27] But, the use of zigzag transformer is articulated to reduce the neutral current in 3P4W system [27–37] The schematic diagram of the basic topology is illustrated in Fig In this method the zigzag transformer is connected in parallel to the load, and it is connected as close as possible to the load A zigzag transformer consists of three single-phase transformers with the turn ratio of 1:1 Therefore, the input currents flowing into the Fig A zigzag transformer for reducing the neutral current in 3P4W systems primary windings is equal to the output currents flowing out from secondary windings Then, the three-phase currents flowing into three transformers must be equal Hence, ideally the zigzag transformer can be regarded as open-circuit for the positive-sequence and the negative-sequence currents [31] Then, the current flowing through the zigzag transformer is only the zero-sequence component But in practice the impedance offered for the zero-sequence currents is a function of the zero-sequence impedances of the utility system, zigzag transformer and the neutral conductor [31] However, the impedance of the utility system, the zigzag transformer and the neutral conductor are very small in most practical cases [31] So a large value of the zero-sequence currents will circulate between zigzag transformer and load The rating of the zigzag transformer depends on the amount of load imbalance and harmonic content To reduce the neutral current of utility side furthermore it is advised to insert an inductor (Zn ) in the neutral conductor of the utility side in order to split the current into two paths, one to the distribution transformer and the other to the zigzag transformer [27,31] 6.1.1 Operation of zigzag transformer with unbalanced/distorted supply voltages In case of an unbalanced and/or distorted system voltage, then a zero-sequence voltage also exists This zero-sequence voltage generates a fundamental zero-sequence current flowing through the three-phase utility conductors, zigzag transformer and utility neutral conductor However, the impedance of the utility system, the zigzag transformer and the neutral conductor are very small in most of the 3P4W distribution power systems Hence, there is a significant neutral current flow into the zigzag transformer and this neutral current adversely affect the performance of the zigzag transformer This excess neutral current may result in the burn-down of the zigzag transformer, the neutral conductor and the distribution power transformer [31] To alleviate this problem, the zigzag transformer is not recommended in unbalanced and/or distorted voltage of 3P4W distribution power system except an inductor (Zn ) is inserted in the neutral conductor of the utility side [31] The inserted inductor serves three purposes: Increases the attenuation rate by spiriting more neutral current towards zigzag transformer [27,31] Reduce the undesired increase of the neutral current if the system voltage is unbalanced and/or distorted [31] Reduces the fault current in case of a line-to-neutral fault [27] The attenuation of this neutral current is a function of the inserted inductor If a large inductor is inserted a better compensation is achieved [27] The effect of buffer reactor (Zn ) on the performance of zigzag transformer topology, simulations are carried out in MATLAB/SIMULINK environment The summary of D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 173 Table The performance of the zigzag transformer based compensator with different values of inserted inductors Source neutral current without compensator (rms, A) Source neutral current after compensation with inserted inductor (Zn) (rms, A) 19.3 No inductor 10.3 mH 6.2 mH 5.0 mH 3.6 mH 1.8 10 mH 1.1 the simulated results are tabulated in Table From the table it is observed that the source neutral current decreases with the increase in the buffer reactor and improves the performance of zigzag transformer However, insertion of additional inductor may result in the neutral voltage variation [31] Many electrical facilities use the neutral line as the referred ground, the neutral voltage variation or raising the neutral voltage of the load side may cause shut down or abnormal operation of the electric facilities in the load side Therefore, this method can reduce the neutral current to a large extent but it will not completely compensate the same 6.2 Star-delta transformer In this method a star-delta transformer used for the reduction of neutral current in 3P4W system [38,39] is shown in Fig Normally a limb core construction is used in the star winding of the transformer, because the zero sequence flux in the three legs does not add to zero as in the positive sequence case Instead, the sum of these fluxes must seek a path through the air or through the transformer tank, either of which presents a large reluctance The result is a low zero sequence excitation impedance Hence, the star connected primary winding of the transformer offers a low impedance path for the zero sequence currents The delta connected secondary winding provides a path for the induced zero sequence currents to circulate [39] The main disadvantage of this topology is that its compensation characteristics are depends on the impedance of the transformer, location and source voltage [31] However, this method can reduce only the neural current to a large extent but it will not completely compensate the same 6.3 T-connected transformer In this method a T-connected transformer is used for the reduction of neutral current in 3P4W systems [40] Here the T-connected transformer is connected in parallel and as close as possible to the load Fig shows the schematic diagram of the T-connected transformer for neutral current compensation in 3P4W system The T-connected transformer consists of two single-phase transformers (one two-winding and one three-winding) arranged in a T-connection [40] This arrangement has the advantage of using standard two single-phase transformers; consequently, the cores Fig A star-delta transformer for reducing the neutral current in 3P4W systems Fig A T-connected transformer for reducing the neutral current in 3P4W systems are economical to build and easy to assemble Accordingly, the transformer is small in floor space, low in height, and with a lower weight than any of the other types of transformers available [41–43] With proper selection of winding arrangements, the Tconnected transformer can be regarded as open-circuit for the positive and negative sequence currents Hence, the current flowing through the T-connected transformer is only the zero-sequence component [40] But in practice the impedance offered for the zerosequence current is a function of the zero-sequence impedances of the utility system, T-connected transformer and the neutral conductor The rating of the T-connected transformer depends on the amount of load imbalance and harmonic content [40] Similar to the zigzag transformer, its compensation characteristics are depends on the impedance of the transformer, location and source voltage [31] However, this method can reduce only the neural current to a large extent but not completely compensate the same 6.4 Star-hexagon transformer A star-hexagon transformer can also be used for the reduction of neutral current in 3P4W systems [44,45] Fig shows the schematic diagram of star-hexagon transformer configuration for neutral current compensation in 3P4W system A star-hexagon transformer is constructed from three single-phase three-winding Fig A star-hexagon transformer for reducing the neutral current in 3P4W systems 73.28 55.73 53.46 26.80 68.39 52.78 55.44 20.19 73.21 55.00 45.21 34.21 70.10 56.42 49.08 27.21 16.98 53.52 30.31 32.19 46.39 37.55 55.87 43.67 46.21 35.70 58.21 45.42 36.43 45.09 48.68 50.23 39.07 40.97 54.75 51.21 35.08 53.39 53.56 21.91 60.11 48.22 53.61 25.22 55.92 45.67 50.61 22.70 55.62 53.90 42.34 30.11 60.70 54.72 46.10 28.09 31.71 51.25 31.35 14.59 37.89 49.88 41.17 50.13 34.76 46.79 34.22 46.99 28.21 40.60 48.31 52.32 30.44 44.68 44.73 57.59 13.53 55.79 52.07 32.45 12.01 56.79 45.99 50.80 Isc Isb 53.13 48.56 48.12 27.46 Isa Isn 8.98 54.76 44.11 51.67 Isc Isb 50.19 45.34 49.44 23.43 Isa Isn 11.13 60.92 42.10 51.18 Isc Isb 50.02 53.67 45.21 26.79 Isa Isn 9.30 56.92 39.98 52.13 Isc Isb 52.92 50.67 49.44 19.79 Isa Isn Isc Isb 19.42 17.71 With star-delta connected transformer (Fig 4) With only zigzag (Fig 3) Isa 35.36 33.03 Source currents after compensation (rms, A) 6.4.1 Zigzag transformer with single-phase shunt APF Fig shows a filter scheme for compensation of neutral current in 3P4W system [28,29] In this hybrid filter topology a single phase APF is connected in between the neutral conductor of the utility and the neutral point of the zigzag transformer The single phase APF is controlled in such a way that, it produces the desired compensating current These compensating currents are injected through the neutral of the zigzag transformer DC voltage is maintained across the capacitor of the single-phase APF by using a separate single-phase transformer with a diode rectifier bridge of a very low kilo-Volt Ampere (kVA) rating [28] Rating of the single-phase APF is very small; this is due a low voltage between the transformer neutral and the utility neutral The low kVA rating of the inverters also reduces cost as well as power losses and the generated Electromagnetic Interference (EMI) However, this will not be the Source currents before compensation (rms, A) Several hybrid approaches are reported in literature and are given below [28,29,32,33,39] Utility voltage conditions The compensator effectiveness is independent of the zerosequence impedance of the transformer and its installation location It greatly reduces the size of the active power filter (APF) Table The performance of the transformer based compensators under different voltage conditions The comparison of the neutral current compensation methods in 3P4W systems with different transformer configurations are given in Table The kVA rating of the transformer is primarily decided by the amount of the neutral current The kVA rating of the transformer is calculated by considering the product of the rms values of the voltage and current associated with each of its windings It is observed from Table that, zigzag transformer approach requires least kVA rating but it may require three single-phase transformers with turn’s ratio of 1:1 The T-connected transformer requires only two single-phase transformers and also its rating is nearly equal to the zigzag transformer and far less than star/delta transformer However, the transformer based methods can reduce the neural current to a large extent but it will not completely compensate the same Complete compensation of neutral current is achieved by using a hybrid filter The main advantages of these hybrid filters are: [28,29] 52.92 50.63 • Under ideal source voltage conditions, transformer attenuates the neutral current to a large extent but it will not completely eliminate the same • When source voltage having unbalance and/or distortions, it causes significant rise in the neutral and line currents When both harmonic distortion and unbalance are simultaneously present in the source voltage, then the raise in the neutral current is stringent 53.42 32.21 With T-connected transformer (Fig 5) With star-hexagon transformer (Fig 6) transformers In this method the star connected primary provides a low impedance path for the zero-sequence harmonic currents The hexagon connected secondary winding provides a path for the induced zero sequence currents to circulate [44–46] Similar to the zigzag transformer, its compensation characteristics depend on the impedance of the transformer, location and source voltage [31] However, this method can reduce only the zero-sequence harmonic current to a large extent but it will not completely compensate the same The compensation characteristics of transformer based methods depend on source voltage conditions Effects of source voltage on the performance of transformer based topologies have been investigated in MATLAB/SIMULINK environment The summary of the simulated results are given in Table 2, and observations are as under: Isn D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 Ideal Amplitude unbalance (50% sag in Phase A) Phase unbalance (20◦ , −120◦ & −240◦ ) Amplitude & phase unbalance Distorted (15% 3th & 10% 5th order harmonics) Distorted & unbalanced (amplitude & phase) 174 D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 175 Table Comparison of neutral current compensation methods in three-phase, four-wire system with different transformer configurations [37,40,46] Transformer type Zigzag (Fig 3) Star-delta (Fig 4) T-connected (Fig 5) Star-hexagon (Fig 6) Number of transformers required to build (single-phase two-winding) (three-phase two-winding) (single-phase three-winding and single-phase two-winding) (single-phase three-winding) Vl V √l Vl V √l : √ : 3 Vl V √ and 2l In V √l Winding voltages (Vl = line-to-line voltage) Primary winding current (In = neutral current) Transformer rating Is it a standard transformer? Space requirement Induce circulating currents in the secondary winding Effectiveness of neutral current compensation (based on simulation study under ideal utility voltage from Table 2) Cost of the compensator : Vl In In Vl In V √l : = 0.333Vl In Vl In √ = 0.577Vl In √ 3 + : Vl Vl In = 0.359Vl In No Lowest No : V √l : V √l In Vl In √ = 0.577Vl In No Low No Yes High Yes No Highest Yes Better than star-delta and star-hexagon Good Better than star-delta and star-hexagon Good Low High Lowest Highest case under transient as well as abnormal unbalanced utility voltage conditions Under these conditions, an appropriate Metal Oxide Varistors (MOV) must be used to protect the single-phase inverter and zigzag transformer [29] 6.4.2 Zigzag transformer with single-phase series APF Fig shows a filter scheme for compensation of neutral current in 3P4W system [32,33] In this type of hybrid filter topology, a zigzag transformer is connected in parallel with the load and a single-phase pulse-width-modulation (PWM) APF is connected in series with the neutral conductor Proper operation of PWM APF increases the effectiveness of circulation of the neutral current of the load via the zigzag transformer The DC capacitor of the PWM APF is recovered by drawing real power from the utility or from an external supply [32] This series connection of the PWM APF results in significant reduction in kVA rating of the inverter [32] This is because, only the currents other than zero-sequence (the zero-sequence will flow through the zigzag transformer) could only flow through the inverter [32] A bypass switch (S) is placed in parallel with the active power filter and will be operated in case of inverter failure or under abnormal utility conditions [28] Fig A hybrid approach for compensation of neutral current: a zigzag transformer with single-phase shunt APF Fig A hybrid approach for compensation of neutral current: a zigzag transformer with single-phase series APF 6.4.3 Star-delta transformer with single-phase half-bridge PWM APF Fig shows a hybrid topology with star-delta transformer [39] In this method a single-phase half-bridge PWM APF is connected to the neutral of the transformer primary and neutral conductor A Fig A hybrid approach for compensation of neutral current: a star-delta transformer with single-phase APF 176 D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 three-phase diode bridge rectifier is connected to the delta winding to provide the necessary real power to maintain the dc voltage across the capacitors of the single-phase half-bridge PWM APF Proper switching signals are used to control the PWM APF in such a way that it produces the desired current to compensate the neutral current This harmonic current is injected through the neutral of the transformer The above mentioned methods are used only for neural current compensation Compensation of neutral current along with elimination of phase harmonic currents can be done by incorporating a three-phase, three-wire APF to the zigzag transformer [28,29,34–36] These approaches greatly reduce the rating of the active filter The main reason for the reduction in the APF rating is due to the separation of the zero-sequence currents from the positive and negative-sequence currents to be compensated [28] Fig 10 The three H-bridge shunt APF topology Three-phase, four-wire active power filters Now-a-days, power-electronics-based compensators such as Distribution STATic COMpensator (D-STATCOM), Dynamic Voltage Restorer (DVR), Solid State Fault Current Limiter (SSFCL), Active Power Filter (APF), and Solid State Transfer Switch (SSTC) have been used to overcome the power quality problems [47] These power electronic based compensators will solve the power quality problems by injecting voltage or current referring to the amount of reference voltage or current of the distribution system [3,47] Among these solutions, APF are specially designed to 3P4W systems for compensating neutral current along with necessary compensation features of the three-phase, three-wire APFs [48,49] These compensators can compensate not only the neutral current, but also compensate harmonics from the positive- and negative-sequence components of the load current Three different topologies are available for 3P4W systems and are given below [48–55,103] Three H-bridge shunt APF topology 3P4W capacitor midpoint (or split-capacitor) APF topology 3P4W four-leg APF topology 7.1 Three H-bridge shunt APF topology Fig 10 shows the three H-bridge shunt APF topology It consists of three single-phase full bridge (H-bridge) voltage source inverters with a common self supporting DC bus [50] Here all 12 switching devices are used to realise the 3P4W shunt APF system These Hbridge inverters are connected to the 3P4W system by using three single-phase isolation transformers Considering the structural advantage of this topology, the control can be done either as a three-phase unit or three separate single-phase units An independent phase control approach based on single-phase instantaneous reactive power theory is presented in [80,81] In this topology the maximum voltage that appears across each H-bridge is the single-phase voltage and not the three-phase voltage, as in the case of split capacitor or four-leg topology √ [51,52] This result into a reduction of DC bus voltage by a factor of Thus the reference DC bus voltage needed for proper operation of shunt √ APF also reduces by a maximum factor of 3, this reduces the rating of inverter But, the main disadvantage of this topology is the increased number of switching devices 7.2 Three-phase, four-wire capacitor midpoint APF topology The first one uses three H-bridge voltage source inverters and these H-bridge are connected through isolation transformers The capacitor midpoint topology and four-leg topologies are looking similar The fundamental difference between these two topologies is the number of power semiconductor devices and the connection of the neutral wire The other possible 3P4W topologies such as combination of capacitor midpoint and four-leg topology [53] and the method proposed in [54] In the later method the neutral conductor of the utility is directly connected to the positive or negative terminal of the DC bus The performance of the 3P4W APFs depend on the control algorithm i.e the extraction of the current components for compensation Control schemes for the three-phase, three-wire active power filers [56–62] are not directly applicable here and require additional considerations in the control circuitry for the compensation of the neutral current To achieve this there are various control schemes are reported in the literature and some of these are instantaneous reactive power (IRP) theory, instantaneous compensation, instantaneous symmetrical components, synchronous reference frame (SRF) theory, computation based on per phase basis, Adaline based control algorithm and scheme based on neural network etc [63–80] The rest of the details of the previously mentioned topologies are given below: The capacitor midpoint APF topology utilizes the standard three-phase conventional inverter where the dc capacitor is split and the neutral wire is directly connected to the electrical midpoint of the capacitors through an optional inductance [51,52] The split capacitors allow load neutral current to flow through one of the dc capacitors Cdc1 , Cdc2 and return to the ac neural wire Fig 11 shows the capacitor midpoint APF topology used in 3P4W systems Fig 11 The 3P4W capacitor midpoint topology D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 Fig 12 The 3P4W four-leg topology One of the serious problems with this topology is voltage unbalance between the capacitors [49] This is due to the direct flow of the neutral current through one of the capacitors, causing voltage variations among them There are two possible ways to balance the capacitors: By adjusting the switching of the inverter (such as dynamic hysteresis controller) [49,82–89] This approach requires additional control circuitry By using additional power electronic switching circuitry (such as choppers) [90] This approach increases the cost when compared with the former one 7.3 Three-phase, four-wire four-leg APF topology Fig 12 shows the four-leg APF topology used in 3P4W systems [51,52] In this topology three of the switch legs are connected to the three phase conductors through a series inductance while the fourth switch leg is connected to the neutral conductor with an optional inductor This topology is most suitable for compensation of high neutral currents [48] Despite having higher number of switching devices this topology outweighed the split capacitor topology by number of factors [48,49,51,52] Better controllability: In this topology only one dc-bus voltage needs to be regulated, as opposed to two in the capacitor midpoint topology This significantly simplifies the control circuitry with better controllability [48] 177 Lower dc voltage and current requirement: This topology requires a lower dc-bus voltage and capacitor current with it [51,52] High order harmonics in dc side current: The dc side current in three H-bridge and capacitor midpoint topology must handle the low order harmonics These low order harmonics contribute to significant ripple on the dc-bus voltage But in four leg topology, the dc side current has only higher order harmonics and will not contribute to significant ripple on the dc-bus voltage [51,52] The main disadvantage of this topology is the difficulty in control of the four-leg inverter The conventional voltage or current controlled methods [91] are not directly applicable here and require special consideration Several modulation methods for the four-leg converter have been suggested in [92–101] Among these methods, the carrier-based pulse width modulation (PWM) methods are heuristic and can be easily applied to four-leg converters [92,93] Nevertheless, the space vector PWM (SVPWM) is very interesting because it offers significant flexibility to optimize switching waveforms and it is well suited for digital implementation [94–98] Mathematical modelling of the four-leg inverter is given in [102] 3P4W APFs may use simple 2-level inverter structures with high switching frequency or multilevel inverter topologies with relatively low switching frequency [104,105] However, currently there is tough competition for high-power medium-voltage applications between the use of classic power converter topologies using high-voltage semiconductors and new converter topologies using medium-voltage devices Multilevel inverters built using mature medium-voltage semiconductors are competing in development race with classic power converters using high-voltage semiconductors Nowadays, multilevel inverters are a good solution for high power applications due to the fact that they can achieve high power using mature medium-power semiconductor technology [105] The comparison of 3P4W APFs are given in Table The significant factor that may decide the selection of these topologies is the overall cost involved to realise the 3P4W APF Owing to the topological advantage of three H-bridge topology, the required reference √ DC bus voltage for APF is reduced maximum by a factor of The high cost of three H-bridge topology owing to an increased number of semiconductor devices can be counterbalanced by reduction in voltage rating of the devices, and thus making this topology suitable for high-voltage and high power application For low-to-mediumpower applications, the low cost of capacitor midpoint topology can Table Comparison of three-phase, four-wire system active power filters [51,52] [103] Active filter topology Three H-bridge (Fig 10) Capacitor midpoint (Fig 11) Four-leg APF (Fig 12) Number of switching devices (2-level inverter) Number of capacitors Additional sensor requirement 12 None One extra DC bus voltage sensor (total two) One extra current sensor DC-Side Voltage (Vl =line-to-line voltage) ≥ ≥ ≥ DC-side current harmonics Need of coupling transformer Control over neutral current Effectiveness of neutral current compensation Lower order harmonics Necessary Indirect Better performance than capacitor midpoint Lower order harmonics Not necessary Indirect May degrade with high neutral currents Overall cost Main advantage High Reduced dc voltage requirement More number of switching devices Low Least number of switching devices Capacitor unbalance problem due to voltage difference across two capacitors Suitable for low to medium power applications Main disadvantage Application and topology selection 2/3Vl Suitable for high voltage, medium to high power applications Suitable for compensating high neutral currents √ V 0.87 l √ 2Vl Higher order harmonics only Not necessary Direct (using 4th leg) Better performance than capacitor midpoint and three H-bridge Moderate Better controllability More number of switching devices Suitable for low to medium power applications Suitable for compensating high neutral currents 178 D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 Table Comparison of neutral current compensation techniques in three-phase, four-wire systems Features Type of solution Transformer based solutions Basic principle Effectiveness of neutral current compensation Operation under unbalanced and/or distorted utility voltage conditions Phase harmonic compensation, reactive power compensation and flicker mitigation Rating of the compensator Robustness of compensator Effect of location on compensating characteristics Effect of source impedance on compensating characteristics Effect of buffer reactor (Zn) on compensating characteristics Design of compensator Cost of the compensator Application and topology selection Three-phase, four-wire active power filters Provides low impedance path for zero-sequence harmonics currents Depending upon the selection of transformer, these currents may circulate in the secondary winding of the transformer or may circulate between load and transformer Compensates only zero-sequence harmonics (complete compensation is possible with addition of 1-␸ APF) Degrades and causes uneven raise of neutral and line currents (but with addition of 1-␸ APF this problem can be alleviated to some extent) Not possible (possible only with addition of three-phase, three-wire compensator) Compensate by injecting equal-but-opposite compensating current Very less (low kVA rating of the compensator reduces cost, power losses and the generated electromagnetic interference) High because of passive compensation Dependent Very high Dependent Independent (dependent only when load impedance is less than source impedance) No buffer reactor is required Dependent (but no buffer reactor is required with addition of 1-␸ APF) Less complex Less Suitable for high voltage, medium to high power applications Not suitable with unbalanced and/or distorted utilities voltages be selected For better performance at moderate cost, the four-leg topology could be a best option for low-to-medium-power applications The merits and demerits of transformer based topologies and 3P4W APFs are given in Table The application of transformers for reduction of neutral current is advantageous due to reduced rating, passive compensation, rugged, low cost, easy installation and less complex over active compensation techniques But, its compensation characteristics are strongly dependent on system impedance and utility voltage conditions The 3P4W APF helps to achieve other controllable objectives such as reactive power compensation, flicker mitigation, voltage sag/swell reduction and also their compensation characteristics are independent of system impedance However, for 3P4W APFs requires large rating inverter Conclusion In this paper, causes, problems, recommendations and mitigation techniques of excess neutral current have been investigated for 3P4W distribution systems Neutral current in these systems has serious drawbacks and the only solution for handling these currents is to incorporate the neutral current compensation devices within the distribution system Passive harmonic filters for neutral current compensation are bulky and may cause resonance with system impedance The transformer based methods can reduce the neutral current to a large extent but, it will not completely compensate the same and also its compensation characteristics are depends on zero-sequence impedance of the transformer and the utility voltage conditions For complete compensation, a hybrid approach is must However, the application of transformers for reduction of neutral current has an advantage due to passive compensation, ruggedness, and less complexity over the active compensation techniques Among all transformer based methods, zigzag transformer approach has least kVA rating The 3P4W APFs are specially designed for neutral current compensation and harmonic elimination in line-currents The commercial success of these filters is due to their acceptable cost, Completely compensates neutral current Degrades (with proper design of controller this problem can be alleviated to some extent) Possible (this is the native feature of 3P4W APFs) Less Independent Complex High Suitable for low to medium power applications coupled with desirable technical features such as extremely fast response time, flexibility of control, continuous operation with virtually no maintenance and simultaneously other controllable objectives can be achievable However, the large rating of the inverter is main drawback of these topologies The rating of these 3P4W APF can be greatly reduced by replacing with a hybrid filter topology which consists of a 3P3W APF, a special transformer (such as zigzag) and a single-phase APF References [1] J Arrillaga, N.R Watson, Power System Harmonics, 2nd edition, John Wiley & Sons Ltd., 2003 [2] R.C Dugan, M.F McGranaghan, H.W Beaty, Electric Power Systems Quality, 2nd edition, McGraw-Hill, New York, 2006 [3] A Moreno-Munoz, Power Quality: Mitigation Technologies in a Distributed Environment, Springer-Verlag limited, London, 2007 [4] T.M Gruzs, A survey of neutral currents in three-phase computer power systems, IEEE Trans Ind Appl 26 (4) (1990) 719–725 [5] A.-C Liew, Excessive neutral currents in three-phase fluorescent lighting circuits, IEEE Trans Ind Appl 25 (4) (1989) 776–782 [6] H.O Aintablian, H.W Hill Jr., Harmonic currents generated by personal computers and their effects on the distribution system neutral current, in: Conf IEEE Ind Appl., vol 2, October, 1993, pp 1483–1495 [7] D.O Koval, C Carter, Power quality characteristics of computer loads, IEEE Trans Ind Appl 33 (3) (1997) 613–621 [8] J.C Balda, A.R Oliva, D.W McNabb, R.D Richardson, Measurements of neutral currents and voltages on a distribution feeder, IEEE Trans Power Deliv 12 (4) (1997) 1799–1804 [9] A Capasso, R Lamedica, A Prudenzi, Experimental characterization of personal computers harmonic impact on power quality, Comput Stand Interfaces 21 (1999) 321–333 [10] D.P Manjure, E.B Makram, Impact of unbalance on power system harmonics, in: Proc 10th Int Conf Harmonics and Quality of Power, vol 1, October 6–9, 2002, pp 328–333 [11] D Maheswaran, A Kalyanasundaram, S Kameshwaran, Power quality issues in a distribution network impact of neutral current due to nonlinear loads, in: Proc of India Int Conf on Power Electronics, December, 2006, pp 150–155 [12] J.A Pomilio, S.M Deckmann, Characterization and compensation of harmonics and reactive power of residential and commercial loads, IEEE Trans Power Deliv 22 (2) (2007) 1049–1055 [13] Nonlinear loads mean trouble, EC&M, pp 83–90, March 1988 [14] S Mohamadian, A Shoulaie, Comprehensive definitions for evaluating harmonic distortion and unbalanced conditions in three and four-wire threephase systems based on IEEE standard 1459, IEEE Trans Power Deliv 26 (3) (2011) 174–1782 D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 [15] IEEE Recommended Practices and Requirements for Harmonics Control in Electric Power Systems, IEEE Standard, vol 519, 1992 [16] A Hiranandani, Calculation of cable ampacities including the effects of harmonics, IEEE Ind Appl Mag (2) (1998) 42–51 [17] CBEMA Information Letter, CBEMA, ESC-3 Committee, CBEMA, 311 First St., N.W., Suite 500, Washington, DC 20001 [18] Recommended Practice For Establishing Transformer Capability When Supplying Nonsinusoidal Load Currents, ANSI/IEEE C57.110-1986, IEEE, Inc., New York, NY, 1986, 10017 [19] J.P Nelson, The grounding of power systems above 600 volts: a practical view point, in: Proc IEEE/IAS, 2003, pp 13–22 [20] F.Z Peng, Harmonic sources and filtering approaches, IEEE Trans Ind Appl (2001) 18–25 [21] F.Z Peng, G.J Su, A series LC filter for harmonic compensation of ac drives, in: Proc IEEE Power Electron Specialist Conf., 1999, pp 213–218 [22] S Senini, P.J Wolfs, Hybrid active filter for harmonically unbalanced three phase three wire railway traction loads, IEEE Trans Power Electron 15 (4) (2000) 702–710 [23] P Rodriguez, J Ignacio Candela, A Luna, L Asiminoaei, R Teodorescu, F Blaabjerg, Current harmonics cancellation in three-phase, four-wire systems by using a four-branch star filtering topology, IEEE Trans Power Electron 24 (8) (2009) 1939–1950 [24] J.C Das, Passive filters – potentialities and limitations, IEEE Trans Ind Appl 40 (2004) 232–241 [25] C.J Wu, J.C Chiang, S.S Yen, C.J Liao, J.S Yang, T.Y Guo, Investigation and mitigation of harmonic amplification problems caused by single-tuned filters, IEEE Trans Power Deliv 13 (3) (1998) 800–806 [26] T Fukami, T Onchi, N Naoe, R Hanaoka, Compensation for neutral current harmonics in a three-phase, four-wire system by a synchronous machine, IEEE Trans Ind Appl 38 (2002) 1232–1236 [27] P.P Khera, Application of zig-zag transformers for reducing harmonics in the neutral conductor of low voltage distribution system, in: Proc IEEE/IAS, vol 2, 1990, pp 1092–1096 [28] G Kamath, N Mohan, A novel, reduced rating active filter for 3-phase, 4-wire loads, in: Proc IEEE APEC’94, vol 2, 1994, pp 936–940 [29] G Kamath, N Mohan, V.D Albertson, Hardware implementation of a novel, reduced rating active filter for 3-phase, 4-wire loads, in: Proc IEEE APEC’95, vol 2, 1995, pp 984–989 [30] R Apolonio, J.C de Oliveira, A.B de Vasconcellos, Three-phase electromagnetic filter for zero sequence harmonics, in: Proc IEEE Int Conf Harmonic and Quality of Power, 2004, pp 613–618 [31] H.-L Jou, J.-C Wu, K.-D Wu, W.-J Chiang, Y.-H Chen, Analysis of zig-zag transformer applying in the three-phase, four-wire distribution power system, IEEE Trans Power Deliv 20 (2) (2005) 1168–1173 [32] S Choi, M Jang, A reduced-rating hybrid filter to suppress neutral current harmonics in three-phase, four-wire systems, IEEE Trans Ind Electron Lett 51 (2004) 927–930 [33] S Choi, M Jang, Analysis and control of a single-phase-inverter – zigzagtransformer hybrid neutral-current suppressor in three-phase four-wire systems, IEEE Trans Ind Electron 54 (2007) 2201–2208 [34] H.-L Jou, K.-D Wu, J.-C Wu, W.-J Chiang, A three-phase, four-wire power filter comprising a three-phase three-wire active filter and a zig-zag transformer, IEEE Trans Power Electron 23 (1) (2008) 252–259 [35] B Singh, P Jayaprakash, T.R Somayajulu, D.P Kothari, Reduced rating VSC with a zig-zag transformer for current compensation in a threephase, four-wire distribution system, IEEE Trans Power Deliv 24 (1) (2009) 249–259 [36] B Singh, P Jayaprakash, S Kumar, D.P Kothari, Implementation of neuralnetwork-controlled three-leg VSC and a transformer as three-phase four-wire DSTATCOM, IEEE Trans Ind Appl 47 (4) (2011) 1892–1901 [37] B Singh, P Jayaprakash, D.P Kothari, Magnetics for neutral current compensation in three-phase four-wire distribution system, in: Conf PEDES, 2010, pp 1–7 [38] I.J Pitel, P Enjeti, Active harmonic power filter apparatus and method, US Patent US 5,568,371, 22nd October, 1996 [39] P.N Enjeti, W Shireen, P Packebush, I.J Pitel, Analysis and design of a new active power filter to cancel neutral current harmonics in three-phase, fourwire electric distribution systems, IEEE Trans Ind Appl 30 (1994) 1565–1572 [40] B Singh, P Jayaprakash, D.P Kothari, A T-connected transformer and threeleg VSC based DSTATCOM for power quality improvement, IEEE Trans Power Electron 23 (6) (2008) 2710–2718 [41] E.W Manning, The T-connected 3-phase transformer, Trans AIEE Power Appl Syst 77 (1958) 1021–1023 [42] B.A Cogbill, J.A Hetrick, Analysis of T–T connections of two single phase transformers, IEEE Trans Power App Syst PAS 87 (2) (1968) 388–394 [43] G Olivier, R Cojocaru, A Lefèvre, Analytical model of a T-connected threephase transformer, Math Comput Simul 63 (2003) 407–419 [44] P Jayaprakash, B Singh, D.P Kothari, Three-phase 4-wire DSTATCOM based on H-bridge VSC with a star/hexagon transformer for power quality improvement, in: IEEE Region 10 Colloquium and the Third Int Conf on Ind and Inf Systems, 2008, pp 1–6 [45] B Singh, P Jayaprakash, D.P Kothari, Three leg VSC with a star-hexagon transformer based DSTATCOM for power quality improvement in three-phase, four-wire distribution system, Int J Emerg Electr Power Syst (8) (2008) [46] B Singh, S Gairola, A Chandra, K Al-Haddad, Power quality improvements in isolated twelve pulse AC–DC converters using delta/double polygon [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] 179 transformer, in: IEEE Power Electron Spec Conf (PESC’07), June, 2007, pp 2848–2853 N.G Hingorani, Introducing custom power, in: IEEE Spectrum, June, 1995, pp 41–48 B Singh, K Al-Haddad, A Chandra, A review of active power filters for power quality improvement, IEEE Trans Ind Electron 45 (5) (1999) 960–971 H Akagi, E.H Watanabe, M Aredes, Instantaneous Power Theory and Applications to Power Conditioning, Wiley, Hoboken, NJ, 2007 F.Z Peng, H Akagi, A Nabae, A novel harmonic power filter, in: PESC’88, April, 1988, pp 1151–1158 C.A Quinn, N Mohan, Active filtering of harmonic currents in three-phase, four-wire systems with three-phase and single-phase nonlinear loads, in: Proc IEEE APEC’92, 1992, pp 829–835 C.A Quinn, N Mohan, H Mehta, A four-wire, current-controlled converter provides harmonic neutralization in three-phase, four-wire systems, in: Proc IEEE APEC, 1993, pp 841–846 P Salmeron, J.C Montano, J.R Vazquiez, A Perez, Compensation in nonsinusoidal, unbalanced three-phase, four-wire systems with active power-line conditioner, IEEE Trans Power Electron 19 (4) (2004) 1968–1974 H.L Jou, K.D Wu, J.C Wu, C.H Li, M.S Huang, Novel power converter topology for three-phase, four-wire hybrid power filter, IET Power Electron (1) (2008) 164–173 F.R Quintela, J.M.G Arévalo, R.C Redondo, N.R Melchor, Four-wire threephase load balancing with static VAr compensators, Electr Power Energ Syst 33 (2011) 562–568 B Singh, J Solanki, A comparison of control algorithms for DSTATCOM, IEEE Trans Ind Electron 56 (7) (2009) 2738–2745 H Akagi, Y Kanazawa, A Nabae, Instantaneous reactive power comprising switching devices without energy storage components, IEEE Trans Ind Appl 20 (3) (1984) 625–630 M Kale, E Ozdemir, Harmonic and reactive power compensation with shunt active power filter under non-ideal mains voltage, Electr Power Syst Res 77 (2005) 363–370 S.J Huang, et al., A study of three-phase active power filters under non-ideal mains voltages, Electr Power Syst Res 49 (1999) 125–137 S Saad, L Zellouma, Fuzzy logic controller for three-level shunt active filter compensating harmonics and reactive power, Electr Power Syst Res 79 (2009) 1337–1341 A Bhattacharya, C Chakraborty, A shunt active power filter with enhanced performance using ANN-based predictive and adaptive controllers, IEEE Trans Ind Electron 58 (2) (2011) 421–428 R.R Pereira, C.H da Silva, L.E.B da Silva, G Lambert-Torres, J.O.P Pinto, New strategies for application of adaptive filters in active power filters, IEEE Trans Ind Electron 47 (3) (2011) 1136–1141 M Aredes, J Hafner, K Heumann, Three-phase, four-wire shunt active filter control strategies, IEEE Trans Power Electron 12 (2) (1997) 311–318 M.I.M Montero, E.R Cadaval, F.B González, Comparison of control strategies for shunt active power filters in three-phase, four-wire systems, IEEE Trans Power Electron 22 (1) (2007) 229–236 A Chandra, B Singh, B.N Singh, K Al-Haddad, An improved control algorithm of shunt active filter for voltage regulation, harmonic elimination, power-factor correction, and balancing of nonlinear loads, IEEE Trans Power Electron 15 (3) (2000) 495–507 ˜ R Grinó, R Cardoner, R Costa-Castelló, E Fossas, Digital repetitive control of a three-phase, four-wire shunt active filter, IEEE Trans Ind Electron 54 (3) (2007) 1495–1503 V Khadkikar, A Chandra, A novel structure for three-phase, four-wire distribution system utilizing unified power quality conditioner (UPQC), IEEE Trans Ind Appl 45 (5) (2009) 1897–1902 H Akagi, S Ogasawara, H Kim, The theory of instantaneous power in threephase, four-wire systems: a comprehensive approach, in: Proc IEEE IAS Annu Meeting, 1999, pp 431–439 M Aredes, E.H Watanabe, New control algorithms for series and shunt threephase, four-wire active power filters, IEEE Trans Power Deliv 11 (3) (1995) 1649–1656 B.N Singh, P Rastgoufard, B Singh, A Chandra, K.A Haddad, Design, simulation and implementation of three pole/four pole topologies for active filters, Inst Electr Eng Proc Electr Power Appl 151 (4) (2004) 467–476 M Ucar, E Ozdemir, Control of a 3-phase 4-leg active power filter under nonideal mains voltage condition, Electr Power Syst Res 78 (2008) 58–73 P Salmerón, R.S Herrera, Instantaneous reactive power theory – a general approach to poly-phase systems, Electr Power Syst Res 79 (2009) 1263–1270 ˜ J.C Montano, Reviewing concepts of instantaneous and average compensations in polyphase systems, IEEE Trans Ind Electron 58 (1) (2011) 213–220 C Madtharad, S Premrudeepreechacharn, Active power filter for three-phase four-wire electric systems using neural networks, Electr Power Syst Res 60 (2002) 179–192 B Singh, P Jayaprakash, D.P Kothari, New control approach for capacitor supported DSTATCOM in three-phase four wire distribution system under non-ideal supply voltage conditions based on synchronous reference frame theory, Electr Power Energ Syst 33 (2011) 1109–1117 B Singh, K Al-Haddad, A Chandra, Harmonic elimination, reactive power compensation and load balancing in three-phase, four-wire electric distribution systems supplying non-linear loads, Electr Power Syst Res 44 (1998) 93–100 180 D Sreenivasarao et al / Electric Power Systems Research 86 (2012) 170–180 [77] M.C Benhabib, S Saadate, New control approach for four-wire active power filter based on the use of synchronous reference frame, Electr Power Syst Res 73 (2005) 353–362 [78] S Orts-Grau, F.J Gimeno-Sales, A Abellán-García, S Seguí-Chilet, J.C AlfonsoGil, Improved shunt active power compensator for IEEE standard 1459 compliance, IEEE Trans Power Deliv 25 (4) (2010) 2692–2701 [79] P Salmeron, S.P Litran, A control strategy for hybrid power filter to compensate four-wires three-phase systems, IEEE Trans Power Electron 25 (7) (2010) 1923–1931 [80] V Khadkikar, A Chandra, An independent control approach for three-phase, four-wire shunt active filter based on three H-bridge topology under unbalanced load conditions, in: Power Electron Spec Conf., August, 2008, pp 4643–4649 [81] M.T Haque, Single-phase PQ theory, in: Proc Annu Conf IEEE Power Electron Spc (PESC’02), vol 4, June, 2002, pp 1815–1820 [82] C.S Ma, T.J Kim, D.W Kang, D.S Hyun, A simple control strategy for balancing the DC-link voltage of neutral-point-clamped inverter at low modulation index, in: Proc IECON, November 2–6, 2003, pp 2167–2172 [83] A Shukla, A Ghosh, A Joshi, Control schemes for DC capacitor equalization in diode-clamped multilevel invertervoltages based DSTATCOM, IEEE Trans Power Deliv 23 (2) (2008) 1139–1149 [84] A Shukla, A Ghosh, A Joshi, Improved multilevel hysteresis current regulation and capacitor voltage balancing schemes for flying capacitor multilevel inverter, IEEE Trans Power Electron 23 (2) (2008) 518–529 [85] D.W Kang, B.K Lee, J.H Jeon, T.J Kim, D.S Hyun, A symmetric carrier technique of CRPWM for voltage balance method of flying-capacitor multilevel inverter, IEEE Trans Ind Electron 52 (3) (2005) 879–888 [86] M.P Kazmierkowski, L Malesani, Current control techniques for three-phase voltage-source PWM converters: a survey, IEEE Trans Ind Electron 45 (5) (1998) 691–703 [87] M.K Mishra, A Joshi, A Ghosh, Control for equalization of capacitor voltages in neutral clamped shunt compensator, IEEE Trans Power Deliv 18 (2) (2003) 538–544 [88] J.A Barrena, L Marroyo, M.A.R Vidal, J.R.T Apraiz, Individual voltage balancing strategy for PWM cascaded H-bridge converter based STATCOM, IEEE Trans Ind Electron 55 (1) (2008) 21–29 [89] N.-Y Dai, M.-C Wong, F Ng, Y.-D Han, A FPGA-based generalized pulse width modulator for three-leg center-split and four-leg voltage source inverters, IEEE Trans Power Electron 23 (3) (2008) 1472–1484 [90] S Srikanthan, M.K Mishra, DC capacitor voltage equalization in neutral clamped inverters for DSTATCOM application, IEEE Trans Ind Electron 57 (8) (2010) 2768–2775 [91] D.G Holmes, T.A Lipo, Pulse Width Modulation for Power Converters, Wiley, Hoboken, NJ, 2003 [92] J.-H Kim, S.-K Sul, A carrier-based PWM method for three phase four-leg voltage source converters, IEEE Trans Power Electron 19 (1) (2004) 66–75 [93] J Kim, S Sul, N Enjeti, A carrier-based PWM method with optimal switching sequence for a multilevel four-leg voltage-source inverter, IEEE Trans Ind Appl 44 (4) (2008) 1239–1248 [94] F Wang, Sine-triangle versus space-vector modulation for three-level PWM voltage-source inverters, IEEE Trans Ind Appl 38 (2) (2002) 500–506 [95] R Zhang, V.H Prasad, D Boroyevich, Three-dimensional space vector modulation for four-leg voltage source converters, IEEE Trans Power Electron 17 (3) (2002) 314–326 [96] M.A Perales, M.M Prats, R Portillo, J.L Mora, J.I Leon, L.G Franquelo, Threedimensional space vector modulation in ABC coordinates for four-leg voltage source converters, IEEE Power Electron Lett (4) (2003) 104–109 [97] C Liu, J Lai, F.C Lee, D Chen, R Zhang, Common-mode components comparison for different SVM schemes in three-phase four-legged converter, in: Proc 3rd Int Conf Power Electron Motion Control, vol 2, August 15–18, 2000, pp 633–638 [98] O Lopez, J Alvarez, J Doval-Gandoy, F Freijedo, A Lago, C.M Penalver, Fourdimensional space vector PWM algorithm for multilevel four-leg converters, in: Conf IECON’08, November, 2008, pp 3252–3259 [99] P Lohia, M.K Mishra, K Karthikeyan, K Vasudevan, A minimally switched control algorithm for three-phase four-leg VSI topology to compensate unbalanced and nonlinear load, IEEE Trans Power Electron 23 (4) (2008) 1935–1944 [100] G Dong, O Ojo, Current regulation in four-leg voltage-source converters, IEEE Trans Ind Electron 54 (4) (2007) 2095–2105 [101] Vincent George, M.K Mishra, Design and analysis of user-defined constant switching frequency current-control-based four-leg DSTATCOM, IEEE Trans Power Electron 24 (9) (2009) 2148–2158 [102] S Srikanthan, M.K Mishra, Modeling of a four-leg inverter based DSTATCOM for load compensation, in: Int Conf on Power System Technology, 2010, pp 1–6 [103] V Khadkikar, A Chandra, B Singh, Digital signal processor implementation and performance evaluation of split capacitor, four-leg and three H-bridgebased three-phase four-wire shunt active filters, IET Power Electron (4) (2011) 463–470 [104] J Rodriguez, J Lai, F.Z Peng, Multilevel inverters: a survey of topologies, controls, and applications, IEEE Trans Ind Electron 49 (4) (2002) 724–738 [105] S Kouro, M Malinowski, K Gopa Kumar, J Pou, L.G Franquelo, B Wu, J Rodriguez, M.A Perez, J.I Leon, Recent advances and industrial applications of multilevel converters, IEEE Trans Ind Electron 57 (8) (2010) 2553–2578  ... the neutral of the transformer primary and neutral conductor A Fig A hybrid approach for compensation of neutral current: a star-delta transformer with single-phase APF 176 D Sreenivasarao et al... Singh, K Al-Haddad, A Chandra, Harmonic elimination, reactive power compensation and load balancing in three- phase, four- wire electric distribution systems supplying non-linear loads, Electr Power... (single-phase three- winding and single-phase two-winding) (single-phase three- winding) Vl V √l Vl V √l : √ : 3 Vl V √ and 2l In V √l Winding voltages (Vl = line-to-line voltage) Primary winding current