Highpower threelevel voltagesource converters are widely utilized in highperformance AC drive systems. In several ultrapower instances, the harmonics on the grid side should be reduced through multiple rectifications. A combined harmonic elimination method that includes a dual primaryside seriesconnected winding transformer and selective harmonic elimination pulsewidth modulation is proposed to eliminate loworder current harmonics on the primary and secondary sides of transformers. Through an analysis of the harmonic influence caused by dead time and DC magnetic bias, a synthetic compensation control strategy is presented to minimize the gridside harmonics in the dual primary side seriesconnected winding transformer application. Both simulation and experimental results demonstrate that the proposed control strategy can significantly reduce the converter input current harmonics and eliminates the DC magnetic bias in the transformer.
I. INTRODUCTION
Active rectifiers that can feed back the breaking energy to the grid are commonly employed in highpower drive systems, such as metallurgical rolling mills and mines. In mediumvoltage applications, active rectifiers often adopt a threelevel neutralpointclamped topology with the merits of high voltage and low harmonics. However, in this case, the converter must be controlled with low switching frequency considering the switching losses. The reduction in current harmonics with a low switching frequency is an important issue in the design of highpower converter systems.
The modulation methods and control strategies
[1]

[8]
of threelevel converters have long been a research issue. Many scholars have exerted fruitful efforts to reduce gridside harmonics significantly. Most of them focused on modulation strategy and system design and implemented comprehensive optimization. The specific harmonicseliminating modulation strategy [selective harmonic elimination pulsewidth modulation (SHEPWM)] is a preferable modulation method at low switching frequency with low grid current total harmonic distortion (THD). A type of threelevel SHEPWM strategy was presented in
[9]
. The strategy can realize balance in neutral voltage. A certain minimum harmonic modulation strategy that can achieve the most optimal harmonic modulation ratio in the entire scope was also proposed in
[10]
. These studies focused on the theory analysis of a single aspect of the SHEPWM strategy under ideal conditions.
In practical applications, for the design of a gridside system, the structure of the transformer directly affects the gridside harmonics. For example, the splittype pulse transformer, which is widely utilized in urban rail transit power systems, can effectively eliminate the primaryside current harmonics of the transformer.
[11]
,
[12]
proposed a threelevel harmonic optimal modulation strategy based on a 12pulse rectifier transformer integrated with a dual main circuit structure. This strategy can realize low harmonics in the transformer primary side with low switching frequency. A multipletandem transformer winding structure was described in
[13]
,
[14]
. This structure is mainly utilized for highvoltage DC power systems and static synchronous compensators. However, the working principle, advantages, and output current harmonic characteristics of the system on the grid side were not analyzed comprehensively.
The dead time of a highpower device influences the control precision and voltage harmonic distribution in the converter output valveside fundamental wave. In addition to several nonideal factors, such as the influence of grid voltage harmonics and the difference in device switch characteristic and control system error, the magnetic bias in the transformer windings caused by the DC component of the pulsewidth modulation (PWM) converter output voltage
[15]

[18]
also leads to gridside current distortion and affects the gridside current harmonics.
[19]

[21]
discussed the influence of dead time and compensation strategies; space vector PWM was used in detail.
[22]

[24]
proposed several control strategies to inhibit magnetic bias, but they focused on carrier modulation and square wave modulation strategies. In lowswitchingfrequency applications, the dead time effect of SHEPWM for threelevel converters and the corresponding magnetic bias compensation methodology have not been reported to date.
A combined harmonic elimination method that includes a dual primaryside seriesconnected winding transformer and SHEPWM is introduced in this study to eliminate the loworder harmonics of the primaryside and secondaryside currents of the transformer. The effects of dead time and magnetic bias are analyzed in principle. A synthetic compensation control strategy (SHEPWMSC) is then proposed to minimize the gridside harmonics in the dual primaryside seriesconnected winding transformer application. Finally, experiments are conducted on the dual primary seriesconnected winding transformers based on threelevel integrated gate communicated thyristor (IGCT) converters. Both simulation and experimental results show that the proposed control strategy can eliminate
order harmonics and below and can further reduce grid harmonics by dead time and magnetic bias compensation.
II. COMBINED HARMONIC ELIMINATION
As an important system component, the structure and design parameters of the transformer directly determine the converter performance level in the system design. The multipleprimaryside seriesconnected winding transformer, as a special transformer structure, is mainly utilized in highpower systems
[25
–
27]
. Compared with the multiplesplit winding transformer, a lower shortcircuit impedance of the multipleprimaryside seriesconnected winding transformer can be designed but with the same current THD. Thus, the transformer size can be reduced. The secondaryside current of the split winding transformer contains abundant harmonics when connected to a highpower converter. However, the primary current harmonic can be at a low level by carrierphase shifting or transformer wind shifting. The structure of the primaryside seriesconnected winding transformer reveals that the current harmonic level is similar in both windings; only the amplitude differs. After applying a certain control strategy, the current harmonic on both sides can be at a low level. The waveform factor is optimized, and capacity is fully maximized.
A schematic of a dual seriesconnected winding transformer is shown in
Fig. 1
. The primary and secondary windings of dual transformers are connected in star (Y) and delta (Δ) forms. The dual secondary windings are connected separately to the as sides of PWM converters. Transformer leakage inductors are utilized as the input inductors. The voltages/currents in the dual secondary windings have a 30° phase shift.
Schematic of the transformer.
In
Fig. 1
, a, b, and c are the three input phases of the converter.
V
_{1ab}
,
V
_{1bc}
are the line voltages on the grid side.
V_{2ab}
,
V_{2bc}
are the line voltages of the secondary Yconnected winding.
V_{3ab}
,
V_{3bc}
are the line voltages of the secondary Δconnected winding.
U_{ab}
,
U_{bc}
are the primaryside line voltages inducted from the secondary winding.
i_{1a}
,
i_{1b}
,
i_{1c}
are the Phase A, B, and C primary side currents,
i_{2a}
is the Phase A current of the secondary Yconnected winding,
i_{3a}
is the Phase A current of the secondary Δconnected winding, and
L_{1}
and
r_{1}
are the equivalent impendence of the transformer winding.
We let the turn ratios of the primary and secondary windings be
k_{1}
and
k_{2}
to guarantee the consistency of the two secondary voltages. The turn ratios of the two windings satisfy the relationship
Given the special structure of the transformer, a strong coupling relationship exists within the windings. The output voltages of PWM rectifiers connected to the dual secondary windings have the same magnitude but a 30° phase shift to maintain current and voltage sharing within the windings. By analyzing the output line voltages of the dual converters, we can rewrite the inverter output voltage as follows:
where
is the amplitude of each harmonic in line voltage and
φ_{n}
is the initial phase of each harmonic in Yconnected winding line voltage.
Therefore,
where
k
=1,2,3……,
U_{ab}
is the primaryside Line AB voltage inducted from the secondary winding.
As indicated by Equ. 2, the primaryside line voltage
U_{ab}
inducted from the secondary PWM voltage of the transformer only contains 12
k
±1 (
k
=1,2,3……)order harmonic components. When using SHEPWM,
where
M
is the modulation ratio and
α_{k}
is the switching angle in a quarter of a switching cycle.
If the switching frequency is T (T is odd) times of the power frequency (50 Hz), the 12
k
±1
harmonics can be eliminated in Line AB voltage. Accordingly,
where
and
U_{dc}
is the DC link voltage.
Line BC voltage
U_{dc}
inducted from the secondary winding is similar to that in Equ. 4.
For the primary current, the equation can be written as
where
i_{1a}
is the Phase A primaryside current,
i_{1b}
is the Phase B primaryside current,
V
_{1ab}
is the Line AB voltage on the grid side, and
V
_{1bc}
is the Line BC voltage on the grid side.
If the grid voltage is ideal, the primaryside phase current
i_{1}
from the above equations only contains
harmonics, and the secondary phase current can be written as
Therefore, the secondary winding phase currents
i_{2a}
and
i_{3a}
of the transformer contain
order harmonics, from which the current harmonics on each side of the transformer can be eliminated. The waveform coefficient of the converter input current is improved, which is friendly to the grid.
III. DEAD TIME AND MAGNETIC BIAS
 A. Influence of Dead Time
Dead time г must be inserted in the complementary pulse trigger signal to guarantee that the same phase switch can reliably turn off to prevent the shootthrough phenomenon. Owing to the characteristic of the turnon and turnoff snubber circuit, highpower semiconductor devices (such as IGCT) need longer dead time. Therefore, the effect of dead time remains severe although switching frequency is low.
Highpower electric drive converters always operate in unit power factor. When the motor operates in motor mode, current and voltage have the same phase on the grid side. When the motor operates in generator mode, current and voltage have an opposite phase. The dead time effects on the phase voltage of the converter when using SHEPWM are shown in
Fig. 2
. In
Fig. 2
(a), the system works as a rectifier, and dead time leads to a wide pulse width of the ideal phase voltage level. In
Fig. 2
(b), the system works as an inverter, and dead time leads to a narrow pulse width of the ideal phase voltage level.
Effect of dead time on phase voltage.
The actual output voltage of the converter is as follows:
where
is the actual phase voltage,
U_{po}
is the ideal phase voltage,
U_{gain}
is the voltage gain caused by dead time,
U_{lose}
is the voltage loss caused by dead time, and
i
is the input current on the grid side.
Under the condition of the rectifier mode, with the effect of dead time as an example, after Fourier transform for the periodic function, we obtain
Where
Given that
U_{gain}
(
t
) is an odd function, no evenorder harmonic components exist in it. For SHEPWM, by substituting Equ. 3 into Equ. 5, we can calculate the harmonic amplitudes as
The harmonic phase is provided by
If the switch frequency is 350 Hz, it works in a normal modulation scope (0.675<
M
<0.934). We net
n
=11, 13, 23, 25, 35, 37 in Equ. 5. The converter works in the rectifier state, and the dead time effects on each harmonic are shown in
Fig. 3
.
Dead time effects.
In
Fig. 3
(a),
p
is the proportion of harmonic amplitude and half voltage and
M
is the modulation ratio. Given that the dead time is fixed, the effects of dead time on each harmonic amplitude of phase voltage are different. In the normal modulation ratio, the
23rd
harmonic that should be eliminated is up to 6% of a half bridge voltage amplitude, the
37th
harmonic reaches 4%, and the others increase at different degrees.
By Equ. 6, along with the increase in dead time, the harmonic amplitudes in every phase voltage increase. With the
37th
harmonic as an example, as shown in
Fig. 3
(b), harmonic amplitude increases with dead time. When the dead time reaches 90 μs, the
37th
harmonic’s amplitude can reach 6.5% of the half bridge voltage, which results in increased current harmonic on the grid side
 B. Influence of Magnetic Bias
For highpower threelevel converters, the input inductor on the grid side is generally equivalent to the leakage inductor of transformers. A singlephase model of a transformer is shown in
Fig. 4
. The transformer secondary side is usually directly connected to the converter valve side. Thus, PWM voltage directly imposes on the transformer secondary side. Owing to the sampling bias of the control system, delay characteristics, power grid voltage harmonics, and semiconductor voltage drop, the PWM voltage on the valve side contains a DC component, which causes the transformer core to become saturated over a long period and leads to current distortion on the transformer secondary side.
Singlephase model of a transformer.
L_{m}
and
r_{m}
are the magnetizing impedance of the transformer.
Magnetic induction intensity B(
t
) can be written as
where
U_{1}
is the voltage on the valve side of the converter,
N_{1}
is the number of turns on the secondary side of the transformer, and
S
is the effective crosssectional area of the transformer core.
We let
where
U_{AC}
represents the AC component of the converter voltage on the valve side and
U_{DC}
is the DC component.
Hence,
From Equ. 7, when
U_{DC}
=0, the V–S area is equal to the forward and reverse pulse as well as the maximum operating magnetic induction intensity, as shown in
Fig. 5
. The magnetic core operating point moves along the hysteresis loop symmetrically and without biasing. In several cases, if
U_{DC}
>0, the V–S area of the positive pulse is larger than that of the reverse pulse and the maximum magnetic induction intensity. The hysteresis loop in the entire pulse cycle transfers to the first quadrant and thus results in biasing.
Transformer DC bias magnetic saturation.
In the subsequent cycle, when the time difference ceases to increase, the bias does not increase either. However, the bias cannot be eliminated automatically. When the magnetic bias increases sequentially, the magnetic core saturates, and the nonlinearity of the magnetic curve increases. The magnetizing current increases rapidly and leads to transformer saturation eventually, which then causes a sharp increase in current through the transformer. This part of sharpincreased current is superimposed on the secondary side of the transformer current and causes current distortion and deterioration of the gridside harmonic. The analysis of the DC component is similar, and no additional details are provided.
In a threephase transformer, any DC component existing in line voltage leads to magnetic bias corresponding to the two phases of the transformer and causes serious current distortion.
The waveform of the gridside input current when magnetic bias saturation occurs is shown in
Fig. 6
(a). Converter threephase current distortion occurs periodically at the wave crest and trough, where a sharp current slew rate di/dt results in overvoltage and damages the devices severely in extreme situations.
Transformer magnetic bias saturation.
Fig. 6
(a) presents the converter threephase input currents.
Fig. 6
(b) shows the fast Fourier transform analysis of Phase A current. According to
Fig. 6
(b), transformer magnetic bias saturation brings considerable loworder current harmonics to the grid, especially evenorder harmonics. Asymmetric evenorder harmonics are introduced to the modulation wave by feedback control, which increases the DC component in the modulation wave. This increase leads to further asymmetry of the output pulse in the control system. Therefore, once the transformer magnetic bias saturates, positive feedback may be caused by the asymmetric evenorder harmonics in the output current, which enhance the transformer magnetic bias in turn.
IV. PROPOSED CONTROL STRATEGY
Given the special structure of the transformer, a strong coupling relationship exists within windings. Voltage and current sharing must be maintained within windings. Particularly in highvoltage cases, dead time and magnetic bias exert significant effects on the system. Therefore, traditional multiple current loop and inverter control are unsuitable for this system. In this section, a synthetic compensation control strategy called SHEPWMSC that includes combined harmonic elimination, dead time, and magnetic bias compensation is proposed to minimize the harmonics with dual seriesconnected winding transformers. The structure of the proposed control strategy is shown in
Fig. 7
.
Proposed control structure.
In an ideal transformer model, the secondaryside phase current is proportional to the primaryside phase current, and any change in one current will affect the other current. Unlike the traditional multiplesplit transformer winding that is decoupled, the secondary windings of the dual primaryside seriesconnected winding transformer have a strong coupling relationship. The dual winding inducted to the primary voltage and current should present strict equilibrium. Otherwise, the primary winding voltage will become unbalanced. Consequently, traditional utility voltage outer loop and independent current inner loop control are no longer feasible. In an ideal condition, the secondaryside currents
i_{2}
and
i_{3}
have the same controlled quantity. Taking the dual current into threephase average
dq
transformation and making feedback control with instantaneous average current will transform the inner current closedloop output quantity into a threephase modulation wave. After phase shift, a dual gridside converter module control pulse is generated. This pulse can ensure strict equalization between dual windings. The sampling signal of voltage and current on the grid side must pass through a filter to reduce the adverse influence of the gridside harmonics in voltage and current feedback on control performance. Through a control diagram, the DC voltage is controlled by active current
I_{d}
, and the power factor is controlled by reactive current
I_{q}
. When the reactive current is 0, the system works in unit power factor.
The primaryside and secondaryside currents only contain
order harmonics by using combined harmonic elimination. As for dead time and magnetic bias compensation, no details are provided in this paper in consideration of limitations in space.
V. SIMULATION RESULTS
A simulation model is built in Matlab to validate the proposed control strategy. The transformer parameters are as follows: the capacity is 13.6 MVA, dual primaryside seriesconnected winding is adopted, the valveside windings are Yconnected and Δconnected with their shortcircuit impedances (12%), and the output voltage of the valveside windings is 3.16 kV. The DClink voltage is 4840 V. The switching frequency is 350 Hz, and the dead time is 60 μs (depending on the characteristics of IGCT and the snubber circuit).
The threephase output current waveforms of the Yconnected winding with SPWM, SHEPWMDC (SHEPWM with magnetic bias compensation), and SHEPWMSC are shown in
Fig. 8
. Their 12
n
±1 (
n
=1,2,3) harmonic values are listed in
Table I
. The SPWM technique presents much larger
11th
and
13th
output current harmonic values than SHEPWMDC and SHEPWMSC. The amplitude of each harmonic component of SHEPWMSC is smaller than the others.
Output current waveforms of the Y winding.
OUTPUT CURRENT HARMONIC VALUE OF Y WINDING (FUNDAMENTAL WAVEFORM VALUE 2600A) WITH SPWM, SHEPWMDC, AND SHEPWMSC
OUTPUT CURRENT HARMONIC VALUE OF Y WINDING (FUNDAMENTAL WAVEFORM VALUE 2600A) WITH SPWM, SHEPWMDC, AND SHEPWMSC
Control system sampling errors, data transmission delay, device characteristics, and other factors result in a DC offset in the converter output voltage. The influence of the DC offset on the transformer magnetic bias hardware in the loop simulations with dSPACE is verified.
Fig. 9
shows a diagram of the hardwareinloop setup of the threelevel mediumvoltage transmission system. The setup is built in crate, and a digital signal processor and a fieldprogrammable gate array are used to achieve the control algorithm. The transformer, electric motor, converter, power grid, and complete set of transmission system mathematical models are built with dSPACE.
Hardwareinloop setup of the threelevel mediumvoltage transmission system.
The magnetic fluxexciting current of the transformer characteristic curve is shown in
Fig. 10
. When magnetic flux is located in the rated area, the exciting current of the transformer is far below the rated current. Once magnetic flux is saturated, the exciting current of the transformer would increase sharply, which generates output current distortion.
Magnetic fluxexciting current of the transformer characteristic curve.
Fig. 11
(a) shows the Yconnected winding exciting current waveforms using SHEPWM without compensation. The winding exciting current mutates because of flux saturation, and its peak value reaches 300 A. The output current is distorted because of the exciting current effect, as shown in
Fig. 11
(b).
Yconnected winding exciting current and output current with SHEPWM without compensation.
With the SHEPWMSC technique, the Yconnected winding exciting current peak value is 2.5 A, which is 0.1% of the rated value without mutation presented in
Fig. 12
(a). Its output current has no distortion in
Fig. 12
(b). The transformer operates in a regular scope.
Yconnected winding exciting current and output current with SHEPWMSC.
Comparative analysis of
Figs. 11
and
12
shows that the DC component of PWM voltage is restrained when the SHEPWMSC scheme is employed. The transformer magnetic flux is not saturated, and the output current exhibits no distortion.
VI. EXPERIMENTAL RESULTS
Experiments are conducted in a practical engineering application to validate the control strategy (
Fig. 13
). The two threelevel IGCT converters have a common DC bus drive and two synchronous motors. The motorrated power is 5 MW, and the overload is 200%.
Application environment.
The main technical parameters of the application are as follows:

1) transformer output voltage: 3.16 kV

2) switching frequency: 350 Hz

3) DClink voltage: 4840 V

4) dead time: 60 μs

5) shortcircuit impedance of the transformer: 7.5%
where
i_{a1}
is the Yconnected winding Phase A output current and
i_{a2}
is the Δconnected winding Phase A output current.
Fig. 14
shows the output current of transformer secondary windings with SPWM in a heavy load case. The Phase A current of the Δconnected winding is 30° greater than the Phase A current of the Yconnected winding. The current peak value is 2000 A. According to Yconnected winding current
i_{a1}
, a 400 A ripple in the current peak will affect the capacity utilization of the converter in heavyload conditions.
Phase A output current of secondary windings with SPWM.
Figs. 15
(a) and
15
(b) show that the transformer output current is severely mutated under noload and heavyload conditions when SHEPWM without compensation is used. The ripple peak value reaches 350 A. In view of threephase equilibrium, the other two phases are affected as well.
i_{b}
and
i_{c}
in
Fig. 15
(a) mutate simultaneously, which indicates that the DC component of output line voltage
U_{bc}
generates magnetic bias in Phases B and C. Therefore, the exciting current increases sharply. In
Fig. 15
(b), Phase C current mutation emerges at the fundamental wave peak point.
Output current.
The triggered convert overcurrent protection is probably an adverse factor for conversion reliability and safety operation in heavyload conditions.
The output current of Yconnected winding with the SHEPWMDC control scheme is shown in
Fig. 15
(c). The peak value of the input current of the converter reaches 2500 A. No mutation occurs in the heavyload case. Compared with
Fig. 15
(b), the wave coefficient is improved, and the current ripple is reduced.
The output current of Yconnected winding with the SHEPWMSC control scheme is shown in
Fig. 10
(d). The 12n±1(n=1, 2, 3)order current harmonic amplitudes with SPWM, SHEPWMDC, and SHEPWMSC are shown in
Table II
. With SPWM, the converted input current 11th, 13th, 23rd harmonics are greater than those with SHEPWMDC and SHEPWMSC. Its 11th harmonic amplitude is 126.55 A, which is 10.1 times that of SHEPWMDC and 18.6 times that of SHEPWMSC. The size of each harmonic component with SHEPWMSC is the smallest among all the sizes of harmonic components. Similar results are obtained in the simulation.
CURRENT HARMONIC AMPLITUDES WITH SPWM, SHEPWMDC, AND SHEPWMSC
CURRENT HARMONIC AMPLITUDES WITH SPWM, SHEPWMDC, AND SHEPWMSC
VII. CONCLUSION
In a mediumvoltage highpower converter, gridside harmonics are affected by several key factors. Through an analysis of these factors, a gridfriendly control strategy was developed.

1) A combined harmonic elimination method that includes a dual primaryside seriesconnected winding transformer and the SHEPWM scheme was introduced to eliminateorder harmonics and those below the transformer primaryside and secondaryside currents.

2) A synthetic compensation control strategy for threelevel mediumvoltage highpower converters was proposed to eliminate the gridside current distortion resulting from dead time and DC magnetic bias in lowswitchingfrequency application.
The simulation and experimental results validate the control strategy. Compared with the SPWM method, the proposed SHEPWMSC method reduces the 11th, 13th, and 23rd current harmonics to 5.38%, 2.85%, and 20.31%, respectively. The secondaryside line current THD is improved from 8.62% to 2.21% at a rated operating condition.
Acknowledgements
This paper was supported in part by the National Science Foundation of China under grants 61473314 and 61403425 and by the National Science Foundation of China through the Science Foundation of Innovation Research Group under grant 61321003.
BIO
Jing Shang was born in Sichuan Province, China, in 1977. He received his B.Sc. degree in mechanical engineering in 2000 and his M.Sc. degree in electric system and automation in 2003 from Southwest Jiaotong University, China. He is currently working toward his Ph.D. degree at the School of Information Science and Engineering, Central South University, Changsha, China. His current research interests include control methods for highpower converters and optimal pulsewidth modulation techniques.
Xiaohong Nian was born in Gansu, China, in 1965. He received his B.Sc., M.Sc., and Ph.D. degrees from Northwest Normal University, Shandong University, and Peking University in 1985, 1992, and 2004, respectively. He was a research fellow at the Institute of Zhuzhou Electric Locomotive from 2004 to 2008. He is currently a professor and an editor at Converter Technology & Electric Traction. His research interests are coordinated control and optimization of complicated multiagent systems, converter technology, and drive control.
Tao Chen was born in Hunan, China, in 1983. He received his B.Sc. and M.Sc. degrees in electrical engineering from Southwest Jiaotong University, Chengdu, China, in 2006 and 2009, respectively. He is currently with CRRC Zhuzhou Institute Co., Ltd., Hunan, China. His main research interests include control strategies in grid side and electric power quality.
Zhenyu Ma was born in Hunan, China, in 1977. He received his M.Eng. degree in computer engineering from Central South University, Changsha, China, in 2007 and his Ph.D. degree in electrical engineering and electronics from Loughborough University, Leicestershire, U.K., in 2012. He worked for Power Systems Warehouse, U.K., from October 2011 to January 2013. He is currently with CRRC Zhuzhou Institute Co., Ltd., Hunan, China. His main research interests include power electronics, highpower converters, and renewable energy, particularly wind power systems.
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