A 6.5 V/50 kA highfrequency switching power supply (HSPS) system composed of 10 power modules is developed to meet the requirements of copperfoil electrolysis. The power module is composed of a twoleg pulse width modulation (PWM) rectifier and a DC/DC converter. The DC/DC converter adopts two fullwave rectifiers in parallel to enhance the output. For the twoleg PWM rectifier, the ripple of the DClink voltage is derived. A composite control method with a ripple filter is then proposed to effectively improve the performance of the rectifier. To meet the process demand of copperfoil electrolysis, the virtual impedancebased currentsharing control method with load current full feedforward is proposed for nparallel DC/DC converters. The roles of load current feedforward and virtual impedance are analyzed, and the currentsharing control model of the HSPS system is derived. Virtual impedance is used to adjust the currentsharing impedance without changing the equivalent output impedance, which can effectively reduce currentsharing errors. Finally, simulation and experimental results verify the structure and control method.
I. INTRODUCTION
Electronic copper foil is an important raw material in the electronic and electrical industries; it provides the primary substrate and conductive circuits in printed circuit boards
[1]
. The DC power supply is the key device in the production of electrolytic copper foil
[2]
. It must be low in voltage but high in current, with an output current that can be more than 50 kA. The performance of the power supply is directly related to the quality, cost, and efficiency of copperfoil production. This power supply traditionally adopts phasecontrolled thyristor rectifiers, which are composed of thyristors, stepdown transformer, and diode rectifier
[3]
. The power conversion of this power supply is conducted at fundamental frequency. Thus, this power supply has shortcomings, including high power loss, poor control accuracy, and harmonic pollution. Highfrequency switching power supplies (HSPSs) have thus been developed
[4]

[7]
in lowvoltage electrolytic areas. By using highfrequency conversion technology, HSPS can realize efficient power conversion and improve output quality. Compared with the thyristor power supply, HSPS has advantages, including high efficiency, small size, and good flexibility. Nowadays, this power system is increasingly being used in the electrolytic industry.
HSPSs are generally composed of an AC/DC rectifier and a DC/DC converter. The diode uncontrolled rectifier is commonly used as the prerectifier to provide a stable DC source
[7]
. It can produce a certain amount of harmonic currents that can seriously pollute the power system. To improve the quality of HSPS and purify the power grid, power factor correction (PFC) technology is developed to achieve high efficiency and low harmonic rectification
[8]

[10]
. For the threephase PFC, several structures are proposed
[11]

[15]
. The widely used threephase threeleg topology
[13]
can continuously control input current by pulse width modulation (PWM). However, this rectifier topology has six power switches and is unsuitable for low and mediumpower applications. To reduce switch number and power loss, the threephase twoleg topology is investigated and developed
[14]
,
[15]
. However, two capacitors are present in the DClink, and this structure has to control the voltage balance of these capacitors.
The back DC/DC converter of HSPS is composed of a singlephase fullbridge inverter, a diode rectifier, and an output filter. Copperfoil electrolysis is a dynamic engineering process with precision. The equivalent resistance of the load electrolytic solution is very small and easy to vary, which affects the stable operation of power supply. To improve dynamic performance of the DC/DC converter, the load current feedforward method is adopted to improve the antidisturbance ability of load
[16]
,
[17]
. Meanwhile, according to the process requirements of electrolytic copper foil, the power supply output is required to have a high current. Thus, the power supply system will be composed of multiparallel DC/DC converters, and the critical currentsharing issue should be achieved to maintain a reliable and stable operation of the system. Dispersion of the main circuit parameter, nonlinear link, and mismatched regulator are consistently regarded as main factors causing output currentsharing errors. However, other factors that can cause output errors, such as random dead time and voltage loss of switches (diodes), are often overlooked
[18]
. To achieve the currentsharing control of a power supply system, a few methods were proposed, such as droop control, master/slave control, and averagecurrent control
[19]

[21]
.
A few droop control methods based on virtual impedance were recently proposed for the nparallel AC inverters to eliminate the circulating current
[17]

[18]
,
[22]
,
[23]
. These methods generally realize virtual impedance through the inductive current feedback to enhance the equivalent output impedance of the converter, which can inhibit circulating currents. These methods can also be used for DC/DC converters to eliminate currentsharing errors. However, virtual impedance, which is used to increase the equivalent output impedance, can increase output voltage loss. The load harmonic currents can also easily distort output voltage.
In this paper, a 6.5 V/50 kA HSPS system for electrolytic copper foil is investigated. First, the topology of the HSPS system for copperfoil electrolysis is described in Section II. The model of the threephase twoleg PWM rectifier is analyzed, and the AC ripple of the DClink voltage is derived. A composite control method is then proposed for the PWM rectifier in Section III. For the control of DC/DC power modules, the virtual impedancebased currentsharing control method is proposed and its closedloop control model is derived and analyzed in Section IV. Finally, simulation and experiment are conducted in Sections V and VI respectively, and the industrial application is presented to verify the proposed system.
II. TOPOLOGY OF HSPS SYSTEM FOR ELECTROLYTIC COPPERFOIL
The diagram of copperfoil electrolysis is shown in
Fig. 1
(a). The DC power supply is an important device in the production process of electrolysis. Under the action of DC power supply, Cu
^{2+}
in the CuSO
_{4}
solution is moved to the negative cathode and forms copper foil on the roller surface. According to the demand of highgrade copper foil, the power supply output must have low voltage but high current.
Structure of the power supply for electrolytic copper foil. (a) Structure of the HSPS system. (b) Topology of the power module based on the PWM rectifier.
The HSPS system for electrolytic copper foil is shown in
Fig. 1
. The HSPS system is composed of 10 HSPS modules in parallel, with the output of a single HSPS module at 6.5 V/5 kA. The output capacity of the HSPS system can reach 50 kA. The topology of a single HSPS module is shown in
Fig. 1
(b). The HSPS module is composed of the PWM rectifier and a DC/DC converter. The threephase twoleg PWM rectifier is adopted to reduce the number of switch devices, and thus reduce the cost and power loss of HSPS. The improved HSPS system has the following features:
1) To enhance the output ability of the HSPS module, two fullwave rectifiers are adopted. The inputs of fullwave rectifiers are in series, but their outputs are in parallel. Thus, the current output of the HSPS module can be enhanced and the capacity utilization of power switches can be improved.
2) By adopting the PWM rectifier, the HSPS can achieve flexible control performance, reduce reactive power, and suppress harmonic pollution.
3) As for the currentsharing issue of the HSPS modules, an improved currentsharing control method is proposed. This method can improve the output characteristic of HSPS modules and achieve the currentsharing operation of the system.
v_{Sa}
,
v_{Sb}
,
v_{Sc}
are threephase source voltages, and
i_{Sa}
,
i_{Sb}
,
i_{Sc}
are input currents of the PWM rectifier [
Fig. 1
(b)]. The Cphase source is connected to the midpoint of DClink capacitors by a filter inductor. Thus, the switch devices only bear half of the DClink voltage.
According to the circuit shown in
Fig. 1
(b), the relationship between the voltage and current of the PWM rectifier is as follows:
where
L_{o}
is the input filter inductor. According to the circuit, the following can be obtained:
where
C_{m}
is the capacitance of
C
_{1}
and
C
_{2}
.
v
_{c}
_{1}
and
v
_{c}
_{2}
are the voltages of
C
_{1}
and
v
_{2}
, and
i
_{1}
and
i
_{2}
are the currents of
C
_{1}
and
C
_{2}
respectively. Meanwhile, the following can be obtained:
i_{Sc}
=
i
_{2}

i
_{1}
. Assuming
i_{Sc}
=
I_{m}
sin(
ωt
+
φ
), he following can be obtained:
Assuming Δ
u
=
v_{c}
_{1}

v_{c}
_{2}
. According to Eq. (3), the following can be obtained:
where Δ
e
is the DC component or the DC voltage error of the two capacitors. From Eq. (4), a fundamental AC ripple
ε
occurs in the voltage difference, and the AC component is directly related to
i_{Sc}
. Its amplitude is proportional to the magnitude of
i_{Sc}
, but inversely proportional to
C_{m}
. In the steady state, the DClink voltages of the two capacitors can be expressed as follows:
where
U_{d}
s the DC component of the DClink voltage
u_{dc}
. The voltages of the two DClink capacitors are easily unbalanced and influenced by disturbances and control errors
[24]
. Thus, a voltagebalance (VB) controller is always needed to eliminate DC error Δ
e
. However, traditional VB control directly uses Δ
u
as the control input. Hence, the AC component will be introduced into the innerloop current control. Assuming a proportional controller with a gain
k
is used for the VB control, the output command signal of the VB controller can be obtained as follows:
In general, the control system will add
i
Δ to the current reference of the PWM rectifier. Therefore, an additional instruction
kε
will be added to the current reference. Hence, the normal and stable operation of the PWM rectifier can be seriously affected if
kI_{m}
/(
ωC_{m}
) is large enough.
III. CONTROL METHOD OF TWOLEG PWM RECTIFIER
According to the model of the PWM rectifier, a composite control method that can effectively combine the merits of feedback control with feedforward control to improve system performance is proposed. The proposed control diagram is shown in
Fig. 2
. As for the VB control of the PWM rectifier, a ripple filter is adopted to eliminate the AC ripple and maintain the normal operation of the rectifier.
Composite control diagram of the twoleg PWM rectifier.
Assuming the threephase source voltage and current are as follows:
where
U
,
I
, and
θ
are the amplitude of source voltage, source current, and power factor (PF) angle, respectively. In the steady state, the PF angle
θ
of the threephase rectifier is expected to be 0.
According to the energy balance principle, the system loss of the HSPS is ideally regarded as 0. Thus, the expected amplitude of the threephase source currents can be obtained as follows:
where the load power
P_{L}
=
v_{o}
*
i_{o}
, and
v_{o}
and
i_{o}
are the load voltage and current respectively.
I_{S}
can be regarded as the feedforward command signal. Therefore, the PWM rectifier can track the changes of load power in realtime according to
I_{S}
. To maintain the DClink voltage and compensate for the loss of the power switches, a proportionalintegral (PI) controller is adopted for the voltage outerloop. The output of the voltage controller is
I_{out}
, and thus the sum
I_{m}
=(
I_{S}
+
I_{out}
) can be obtained as shown in
Fig. 2
.
I_{m}
is multiplied by the synchronous signals. Hence, the current reference signals for the PWM rectifier can be obtained as follows:
Assuming the output currents and voltages of PWM rectifier are balanced in the steady state, the sum of threephase source currents is zero because no neutral line exists. Thus, the Cphase expected current can be obtained as follows:
As for the VB control of the PWM rectifier, a PI controller is adopted. According to the discussion above, a fundamental AC ripple
ε
occurs in the voltage difference (
v_{c}
_{1}

v_{c}
_{2}
), which is caused by
i_{Sc}
. According to Eq. (11), the fundamental AC ripple
ε
can be obtained as follows:
ε
can be subtracted from Δ
u
to obtain the DC error Δ
e
and eliminate the AC ripple in Δ
u
(
Fig. 2
). Thus, the pure DC component Δ
e
can be obtained and processed by a PI controller. A command signal Δ
I
for voltage balance can then be obtained. The voltagebalance command Δ
I
can change the input current of the PWM rectifier to intentionally strengthen or weaken the charging of some capacitor. Finally, the dynamic balance of two capacitors can be achieved.
The total reference signals of current innerloop can be obtained as follows:
With the traditional PI controller, tracking ability is limited for the AC signal, and error will occur in the steady state. Thus, a proportional resonant (PR) controller that can effectively improve the control error was proposed
[25]
. The
s
domain of the PR controller is expressed as follows:
where
k_{g}
is the proportional coefficient, and
k_{i}
is the integral coefficient. The PR feedback control can output the dynamic adjustment signals (Δ
d_{a}
,Δ
d_{b}
) (
Fig. 2
).
According to Eq. (1) and the average switch principle of the bipolar PWM, the output voltages of
v_{ao}
and
v_{bo}
can be derived as follows:
where
d_{a}
and
d_{b}
are the duty cycles of the twoleg PWM rectifier, and
d_{a}
and
d_{b}
∈ [0,1] occur. Then, the duty cycles can be expressed as follows:
where
v_{Sbc}
and
v_{Sbc}
are the source line voltages. With the expected currents shown as Eq. (10), according to Eq. (16), the expected duty cycles
d_{aE}
and
d_{bE}
of the twoleg PWM rectifier can be calculated as Eq. (17).
Deriving Eq. (17) is based on the switch model of the PWM rectifier; the model Eq. (17) can directly control the rectifier output the corresponding voltage to obtain the expected current. Hence, the expected duty cycles
d_{aE}
and
d_{bE}
can be used as the feedforward control signals to realize a rapid response for current control.
Finally, the total duty cycles
d_{a}
and
d_{b}
of the PWM rectifier can be calculated by superimposing the outputs of feedback control with the feedforward control. Thus, the control system of the PWM rectifier effectively combines the closeloop tracking performance of the feedback control with the rapid response of the feedforward control, which can effectively improve the operation performance of the system.
IV. CONTROL METHOD OF DC/DC CONVERTER
The equivalent model of single DC/DC converter is shown in
Fig. 3
.
L
and
C
are the parameters of output filter, and
R
is the equivalent series resistance corresponding to the loss.
Equivalent model of single DC/DC converter.
Given that copperfoil electrolysis is a dynamic engineering process, the solution in the electrolytic tank is prone to fluctuations. Hence, the equivalent resistance of load easily varies, which will affect the stable operation of the power supply. The load current is considered a disturbance because the load varies. The control system of the single DC/DC converter in
s
domain is established (
Fig. 4
).
Control diagram with load current feedforward.
In
Fig. 4
,
F_{i}
is the load current feedforward function, and
H_{i}
and
H_{v}
are the feedback links that can be considered a first filter 1/(
τ_{C}s
+1), where
τ_{C}
is the time constant of the filter.
G_{i}
and
G_{v}
are the current and voltage controllers respectively. Here,
G_{i}
is a proportional controller with a gain
k_{c}
, while,
G_{v}
is a PI controller with the expression
k_{p}
[1+1/(
T_{i}s
)], where
k_{p}
and
T_{i}
are the gain and integral coefficient respectively.
k_{m}
is the gain of the DC/DC converter, and it is
U_{d}
/(2
n
), where
n
is the turn ratio of the transformer.
F_{m}
is 1/
V_{m}
, and
V_{m}
is the amplitude of the carrier wave.
The output voltage of the HSPS can be expressed as
According to
Fig. 4
, the following can be obtained:
where
A
(
s
) =
H_{v}G_{v}G_{i}k_{m}F_{m}
+
H_{i}G_{i}k_{m}F_{m}Cs
+ (
Ls
+
R
)
Cs
+ 1.
To suppress the output voltage fluctuations caused by load changes and increase the voltage output ability of power supply, a load current full feedforward method is adopted as shown in Eqs. (18) and (19). This method is used to control the equivalent output impedance
Z
_{o}
approach to 0, which can suppress the adverse effect of load changes. Therefore, when
Z
_{o}
is set as 0, the following can be derived:
Given that
τ_{C}
is small and
R
<<
G_{i}k_{m}F_{m}
, to facilitate the implementation of the controller, Eq. (20) can be simplified as follows:
According to the control and circuit parameters of the DC/DC converter (
Table I
), the Bode diagram of
Z
_{o}
is shown in
Fig. 5
. When
F_{i}
= 0, the load current feedforward method is not used. After using the load current feedforward method (
F_{i}
= 1)
[17]
, the gain of equivalent output impedance
Z
_{o}
decreases in the lowfrequency band. Then, using the proposed full feedforward function, the gain of
Z
_{o}
is attenuated greatly in the lowfrequency range. Thus, this method can effectively enhance the ability of load antidisturbance and increase the voltage output capacity of the power supply.
PARAMETERS OF THE HSPS
Bode diagram of equivalent inner impedance Z_{o}
The power supply system for electrolytic copper foil is composed of multiparallel power modules. Given the differences in system parameters of each power module, currentsharing error will be produced. According to
[18]
, the output voltage
u
of converter can be expressed as follows:
where
D
is the normal duty ratio of the converter,
U_{Se}
is the voltage drop of switches (diodes) and,
D_{d}
and
D_{off}
are the loss of duty ratio caused by the dead time and softswitching respectively, which are important factors that cause output voltage errors. In
Fig. 6
,
u_{e}
is the offset voltage caused by
U_{Se}
,
D_{d}
, and
D_{off}
. To achieve the currentsharing control, a control method based on the virtual resistor is proposed.
R_{v}
is the virtual resistor, which is the control gain of currentsharing loop.
i_{av}
is the average output current of multiparallel power modules.
i_{h}
is the currentsharing error. According to
Fig. 6
, the following can be obtained:
Currentsharing control method of the DC/DC converter.
where
Z
_{h}
can be defined as the currentsharing impedance. The currentsharing control will retain the stability of the closedloop control system and the value of the equivalent output impedance
Z
_{o}
. Thus, this implementation method of virtual impedance is through the feedback of currentsharing error, which offers better performance than the method through the feedback of inductive current. Assuming
G_{u}
,
Z
_{o}
,
G
_{e}
, and
Z
_{h}
are similar for mparallel power modules, the output voltage expression of jth power module can be obtained as follows:
Then, according to Eq. (24), the following can be obtained:
m
is the number of power modules. If Eq. (24) is subtracted from Eq. (25), the following can be obtained:
Then, the following can be derived:
In practice, the voltage references given for power modules are generally similar, that is, the value of the first term in Eq. (27) is approximately 0. However, the offset voltage
u
_{ej}
of each power module varies with different parameters of switches and dead time. This phenomenon is the major factor causing currentsharing error. In the case of highpower operation in particular, given that the system impedance is small, a small bias voltage will produce a large currentsharing error. The smaller the
Z
_{o}
, the poorer the inhibitory effect on
i
_{h}
, as shown in Eq. (27). Therefore, in the case that
Z
_{o}
is determined, selecting the virtual resistance
R
_{v}
to decay the gain of
G
_{e}
/
Z
_{o}
+
Z
_{h}
) can be reasonable. Thus, the currentsharing error caused by the offset voltage error can be eliminated through this method. According to Eqs. (23) and (19), the following can be obtained:
According to Eq. (28) and the parameters of DC/DC converter (
Table I
), the Bode diagram of
G
_{e}
/
Z
_{o}
+
Z
_{h}
) is shown in
Fig. 7
. When the virtual resistor is set as 0, the gain of
G
_{e}
/(
Z
_{o}
+
Z
_{h}
) s large in the lowfrequency band. Hence, a small bias voltage will generate a significant currentsharing error. When the virtual resistance is 5, the gain of
G
_{e}
/(
Z
_{o}
+
Z
_{h}
) is attenuated substantially. Thus, the currentsharing error in lowfrequency range will be greatly reduced. With increasing virtual resistance, the currentsharing impedance
Z
_{h}
can be effectively increased, which can attenuate the gain of
G
_{e}
/(
Z
_{o}
+
Z
_{h}
) Here, the value of
R
_{v}
is selected as 10. In summary, the control system has an inhibitory effect on both DC and harmonic bias voltage, and the virtual resistance
R
_{v}
has a significant suppression effect on the lowfrequency bias voltage.
Bode diagram of G_{e}/(Z_{o}+Z_{h})
V. SIMULATIONS
To verify that the proposed system is feasible, the simulation model is established by using PSIM6 software (
Fig. 1
). The design of the HSPS system is as follows: AC line voltage is 220 V/50 Hz, and output of the HSPS module is DC 5 kA/6.5 V for copperfoil electrolysis. The DClink voltage of the PWM rectifier is set to 700 V, and the turn ratio of the transformer is 40:1. The switching frequencies
f
_{s}
of the PWM rectifier and fullbridge inverter are 10 and 20 kHz respectively. The amplitude of carrier wave
V
_{m}
= 10. A resistor (
R
_{d}
= 6.5/5 k) is used to simulate the load. The other circuit parameters of the HSPS are shown in
Table I
.
The load is switched into the system at 0.4 s, and the output voltage reference is linearly given from 0 V at 0.4 s to 6.5 V at 0.6 s.
Fig. 8
(a) shows the output voltage and current waveforms of the power module. The output voltage “Vo” of the DC/DC converter almost linearly increases with the reference “uref.” Thus, the output voltage can fast track to the reference without vibration. In the steady state, the output voltage and current of DC/DC converter are stable at the expected value [
Fig. 8
(a)].
Fig. 8
(b) shows the dynamic current and voltage waveforms of the PWM rectifier. With increasing output voltage and current, the load power increases. Hence, the input currents of the PWM rectifier also rapidly increase with increasing output power. Meanwhile, the AC voltage ripples of the DClink capacitors also increase with increasing Cphase input current of the PWM rectifier [
Fig. 8
(b)].
Dynamic waveforms. (a) Output waveforms of the DC/DC converter. (b) Waveforms of the PWM rectifier.
To confirm the proposed ripple filter for the VB control, a comparison simulation is conducted.
Fig. 9
(a) shows the detected voltage difference and voltage ripple “um” calculated by using Eq. (12) in the steady state. The voltage ripple “um” is nearly similar to the detected voltage difference, and their amplitude is approximately 43 V.
Comparison of waveforms for the ripple filter. (a) Voltage difference of DClink capacitors. (b) Waveforms without ripple filter. (c) Waveforms with ripple filter.
A fundamental ripple caused by the Cphase current of the PWM rectifier occurs in the voltage difference. If the voltage ripple is not eliminated, then this ripple will be processed by the VB controller and added to the current instructions of the PWM rectifier. With the current innerloop control, the voltage ripple will generate a corresponding current in the input currents of the PWM rectifier. Thus, the PWM rectifier will be out of normal operation [
Fig. 9
(b)]. If the control system adopts the ripple filter proposed in this paper, it can eliminate the fundamental ripple in the voltage difference without adding a lowpass filter, and the VB controller can then eliminate the DC error of voltage difference. In the steady state, the PWM rectifier can operate normally, and the input currents are balanced at 93.5 A [
Fig. 9
(c)]. The PF of the PWM rectifier is 0.99, and total harmonic distortion (THD) of the current is 3.2%. Thus, the proposed HSPS can effectively reduce harmonic currents and improve power quality of the system.
A simulation is conducted (
Fig. 10
) to confirm the performance of the proposed control method with feedforward control. A disturbance of 0.05 Ω, which is in parallel with the load, is switched into the system at 0.7 s and switched off at 0.71 s.
Dynamic waveforms with a disturbance of 0.05 Ω: (a) waveforms of the DC/DC converter, (b) waveforms of the PWM rectifier.
As the disturbance is switched into the system, the output voltage and current of the HSPS suddenly change. However, with the proposed control method, the output current can rapidly attenuate to the steadystate value within 0.02 s [
Fig. 10
(a)]. As the load changes, the output power also varies, which can result in fluctuations of the DClink voltage and input current of the PWM rectifier. Given that the PWM rectifier adopts the proposed method, two kinds of feedforward control signals exist. One is the feedforward of load power, by which it can immediately calculate the current instructions according to Eqs. (9) and (10) for current controller. The other is the feedforward of duty cycles calculated from Eq. (17). Thus, the control system can rapidly obtain the expected duty cycles of the PWM rectifier, which can cause it to output the expected AC voltages to rapidly generate the corresponding currents [
Fig. 10
(b)].
To present the results of other conditions, a disturbance of 0.025 Ω is switched into the system at 0.8 s and switched off at 0.9 s. The results are shown in
Fig. 11
.
Dynamic waveforms with a disturbance of 0.025 Ω: (a) waveforms of the DC/DC converter, (b) waveforms of the PWM rectifier.
When the disturbance occurs, the output voltage falls down or ascends suddenly [
Fig. 11
(a)]. With the proposed feedforward control method of DC/DC converter, the output voltage increases or descends rapidly to track the reference without vibrations. In general, DClink capacitors can be considered a large inertia link. As the output load power changes severely, the DClink voltage will fluctuate. With the proposed control method, the PWM rectifier can rapidly regulate the output voltage and current to charge or discharge the capacitors and maintain a stable voltage [
Fig. 11
(b)].
To verify the currentsharing control method of the DC/DC converter based on virtual resistance, dead time is used to simulate the parameter difference of the HSPS modules. The dead time of one HSPS module is set as 1 us, whereas the other is set as 3 us. The other circuit and control parameters of HSPS module are similar. The openloop output voltages of two power modules and their spectrum when the duty ratio is set to 0.8 are shown in
Fig. 12
.
Openloop output voltages with different dead time: (a) output voltages, (b) spectrum of the output voltages.
Dead time can cause the loss of output voltage (
Fig. 12
). The larger the dead time, the greater the output voltage loss. In the spectrum of output voltages, a 0.2 V DC offset voltage occurs between them which will generate a nonnegligible currentsharing error.
To verify the performance of the proposed currentsharing control based on virtual resistance, a simulation comparison is conducted (
Fig. 13
). At the first time, the dead time of twoparallel power modules is set as 1 us, and they share with the load. The dead time of one HSPS module is changed to 3 us at 0.8 s to compare the dynamic currentsharing control performance.
Output waveforms of the two HSPSs with two different control methods. (a) Waveforms with traditional dualloop control method. (b) Waveforms with the proposed control method.
Fig. 13
(a) shows the dynamic output voltage and current waveforms of the two HSPSs with traditional dualloop control method with currentsharing control loop. Before the dead time disturbance, the output voltage is stable at 6.5 V and the output currents of the two HSPSs are stable at the expected value of 5 kA. When the dead time is the same, almost no currentsharing error occurs (io1≈io2). As the dead time disturbance occurs at 0.8 s, a dynamic adjustment process with a few vibrations will occur before the system stabilizes. In the steady state, a currentsharing error of 77 A occurs for the output currents of the two HSPSs.
The waveforms when using the proposed control method with the deadtime disturbances at 0.8 s are shown in
Fig. 13
(b). Given that the currentsharing control loop can rapidly regulate the output voltages of the two HSPSs, the output vibrations can be effectively suppressed and rapidly go into the steady state. According to the analysis above, with the closedloop control of virtual resistance, the gain of currentsharing impedance
Z
_{h}
can increase to effectively attenuate the gain
G
_{e}
/(
Z
_{o}
+
Z
_{h}
). This method can greatly reduce the currentsharing error caused by the offset voltage. In the steady state, the currentsharing error of the HSPS modules is almost 0 [
Fig. 13
(b)]. Thus, the proposed control method can effectively improve the currentsharing performance of the HSPS system.
VI. EXPERIMENT AND INDUSTRIAL APPLICATION
To verify the feasibility of the structure and the proposed control method, an industrial prototype of 220 V HSPS system is developed. For highprecision electronic copper project, the output of DC power supply must be 6.5 V/50 kA. Therefore, an HSPS system composed of 10 parallel 6.5 V/5 kA HSPS modules (
Fig. 1
) is developed. The design and circuit parameters of the HSPS module are listed above.
Each HSPS module adopts a TMS320F2812 as the digital signal processor (DSP), which is used to detect signals, execute algorithm, and generate the PWM drive signals for the IGBTs of the PWM rectifier and fullbridge inverter. The physical implementation diagram of the HSPS is shown in
Fig. 14
(a). The Aphase voltage is processed by the zerocrossing comparison circuit, and then the rising edge of output square wave is used to trigger an interruption by event manager A (EVA) of DSP. Thus, the current phaseangle of the PWM rectifier can be initialized in every grid period. The physical photos of the device are shown in
Figs. 14
(b) to
14
(d). The field experimental waveforms with the proposed control method are shown in
Figs. 15
to
16
.
Implementation figures of the HSPS system. (a) Physical implementation diagram. (b) Physical photo of system. (c) Highfrequency transformer. (d) DSP control board.
Experimental waveforms. (a) Threephase input currents. (b) DClink voltages. (c) Output DCvoltage of system. (d) Output DCcurrents.
Experimental waveforms for currentsharing. (a) Output currents with traditional dualloop control. (b) Output currents with the proposed currentsharing control.
The input currents of the HSPS module are stable at 94.3 A [
Fig. 15
(a)]. The voltages of the DClink capacitors are stable at 350 V [
Fig. 15
(b)]. The current waveforms are smooth with a THD of 4.3%, and the PF of the PWM rectifier is about 0.98. The power quality of the system is effectively improved compared with the uncontrolled rectifier. In the steady state, the load voltage is stable at 6.5 V [
Fig. 15
(c)], and the output currents of any two modules in the HSPS system are stable at about 5 kA [
Fig. 15
(d)].
An experimental comparison is conducted to further verify the proposed currentsharing control method. The experimental condition is similar to that in
Fig. 13
.
As the dead time of one HSPS module changes, a currentsharing error occurs using the traditional dualloop control method [
Fig. 16
(a)]. When using the proposed currentsharing control method based on virtual resistance, the currentsharing error is greatly reduced [
Fig. 16
(b)]. These experimental results are similar to those in
Fig. 13
. Given the dispersion of circuit parameters (
L
,
C
, and
R
) of the prototype, the currentsharing error is not 0 in the steady state.
The errors of output currents (expected value: 5 kA) of the 10 HSPS modules with the proposed control method are shown in
Table II
. The maximum error is 24 A and less than 0.5%. Thus, the output of the HSPS modules is almost current sharing, and the system can operate stably by using the proposed control method. This proposed HSPS system can achieve highquality rectification and highcurrent output to meet the requirements of electrolysis.
ERRORS OF OUTPUT CURRENT OF 10 HSPS MODULES
ERRORS OF OUTPUT CURRENT OF 10 HSPS MODULES
The proposed HSPS technology and its device have been successfully installed on the industrial production line of an 18 μm electrolytic copper foil in Jiangxi Copper Group, Southeast China. Compared with the traditional thyristor power supply, the efficiency is increased from 75% to 90% and the output current error is reduced from 2% to 0.5%. Given that the control performance of HSPS system is effectively enhanced, the quality of an 18 μm copper foil is greatly improved and the rate of the finished products is increased by 10%.
VII. CONCLUSION
To meet the requirements of copperfoil electrolysis, a 6.5 V/50 kA HSPS system based on PWM rectifier is investigated. As for the VB control of the PWM rectifier, a ripple filter method is proposed to eliminate the AC ripple. According to the model of the PWM rectifier, a composite control method is proposed to improve the control performance of the system. To meet the process requirements of electrolysis, a control method with load current full feedforward is proposed for DC/DC converters, which can decay the equivalent output impedance
Z
_{o}
to enhance the antidisturbance ability. Aiming at currentsharing of a multiparallel system, a currentsharing control method based on virtual resistance is proposed. This method can adjust the currentsharing impedance
Z
_{h}
by virtual resistance to damp the gain of
G
_{e}
/(
Z
_{o}
+
Z
_{h}
) without changing the system stability. This method can effectively decay the currentsharing error of power modules caused by the offset voltage.
Acknowledgements
This work was supported by the Program for New Century Excellent Talents in University (No.NCET100367) and the Hunan Provincial Natural Science Foundation of China (No.11JJ2023)
BIO
An Luo was born on July 21, 1957 in Changsha, China. He received his B.S. and M.S. degrees in 1982 and 1986 respectively from Hunan University, Changsha, China, and his Ph.D. degree in 1993 from Zhejiang University, Zhejiang, China. Between 1996 and 2002, he was a Professor at the Central South University. In 2003, he became a Professor at Hunan University, where he is currently involved in research on power conversion system, harmonics suppression and reactive power compensation, and electric power saving. He has published more than 300 journal and conference articles. He also serves as Chief of the Hunan Electric Science and Application Laboratory. Dr. Luo is a recipient of the 2006 National Scientific and Technological Awards of China and the 2010 National Scientific and Technological Awards of China. He currently serves as the Associate Board Chairperson of the Hunan Society for Electrical Engineering.
Fujun Ma was born on April 1985 in Hunan, China. He received his B.S. degree in 2004 from the College of Electrical and Information Engineering, Hunan University, Changsha, China. Since 2009, he has been working toward his Ph.D. degree in Electrical Engineering at Hunan University, Changsha, China. He is currently an assistant Professor at Hunan University. His research interests include power quality managing technique of electrified railway, electric power saving, reactive power compensation, and active power filters.
Qiaopo Xiong was born on December 3, 1988 in Nanchang, China. He received his B.S. degree in 2009 from the School of Information Science and Engineering at Central South University, Changsha, China, and his Ph.D. degree in 2014 from the College of Electrical and Information Engineering at Hunan University, Changsha, China. He is currently an Associate Research Engineer in the 722th Research Institute of CSIC, Wuhan, Hubei, China. His research interests include VSC highvoltage direct current system, static var compensator, and modular multilevel system design.
Zhixing He was born on August 12, 1989 in Hunan, China. He received his B.S. degree in 2011 from the College of Information Science and Engineering at Central South University, Changsha, China. He is currently working toward his Ph.D. degree at the College of Electrical and Information Engineering, Hunan University. His research interests include highpower industry power supply, static var compensator, and modular multilevel system design.
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