This study proposes a coupled inductor method for the parallel operation of a power conditioning system (PCS). When primary and secondary currents flow in the same direction in a coupled inductor, total flux and inductance are cancelled; when currents flow in opposite directions, each flux becomes an individual inductor. These characteristics are applied in the parallel operation of a PCS. To connect at a grid code, abnormal current, which is barred under the grid connection code, is blocked by using a coupled inductor. A design based on the capacity and current duration time of a PCS is verified through hardware implementation. Experiment results show the effectiveness of variance reduction.
I. INTRODUCTION
Power conditioning systems (PCSs) have been widely implemented in new and renewable energy systems in recent years. In particular, they are used in new renewable energy sources, such as solar cells, fuel cell generation, and batteries, all of which must convert DC source power into AC output.
The inverter input voltage in a PCS is always higher than the peak grid voltage. However, most current and prospectively utilized energy sources provide a lowvoltage DC output. A onestage PCS consists of an inverter and a transformer. This system can achieve galvanic isolation and solve output voltage difference by implementing a specific turn ratio. Although using a transformer has several advantages, transformerless systems have recently gained preference in residential solar PCS applications. Nevertheless, specific issues with respect to high efficiency and low cost must be addressed. Without a transformer, a twostage PCS can convert an energy source to a higher voltage DC before changing it into AC for grid tie applications (
Fig. 1
)
[1]
,
[2]
. The first stage of this process is the boost stage, which requires using a stepup DC–DC converter with a lowvoltage DC input. The second stage involves using a DC–AC inverter to implement grid connection. The twostage PCS exhibits high efficiency and consumes a relatively small amount of space, which makes it commercially preferable
[3]
,
[4]
.
Twostage tranformerless PCS diagram.
To add capacity to a PCS, additional power electronic systems, which require additional AC power, can be built into the PCS within a parallel structure; most of such systems have separate DC and connected AC sides
[5]

[8]
. A multiunit system is operated synchronously in parallel, with each unit having its own controller. Therefore, the components of a parallel PCS do not always operate at exactly the same time. Connecting inverters in parallel can cause a zerosequence circulating current, which can damage system or power sources
[7]

[10]
. To avoid this phenomenon, some applications use a transformer to implement an isolation approach
[11]
,
[12]
. Chen et al.
[14]
proposed using a triport transformer in standalone PCSs, such as uninterruptible power systems, to prevent circulating currents through phasedifference compensation. When connecting commercial products to the grid, a multiwinding transformer is used to prevent circulating currents
[15]
. However, transformertype systems have several disadvantages, as discussed earlier. Moreover, parallel systems are expensive and bulky. Given that converters are added in parallel to a system, such approaches become practically unaffordable. Therefore, adopting transformerless systems whenever possible in multiunit applications is advantageous. For example, interphase inductors are used in parallel offgrid inverters
[10]
and additional coupled inductors are used in offgrid inverters
[16]
and motor drives
[7]
. A coupled inductor differs from transformers and interphase inductors, that is, under ideal circumstances, the voltage drop of a coupled inductor is zero when the sum of the magneto motive force drops around the loop
[17]
. Although Liu et al.
[15]
proposed a voltage control method for parallel circulation current suppression, their method is unsuitable for use in all situations.
A gridconnected PCS controller receives phase data from the mother grid and generates an output phase. However, a tiny controller time gap exists in this process, which causes circulating currents and instantaneous surges and dips in the initial current.
Fig. 2
illustrates several utility waveform distortions that can affect power quality. Some distortions originate in power electronics, whereas some surges and dips arise from initial interconnection characteristics and high speed “dv/dt” and “di/dt” events
[18]
,
[19]
. Several regulatory standards specify the interconnection requirements of distributed generation units in power systems, including IEEE Standards 15472003, 1547.22008, and 1547.12005 and IEC 61727. Furthermore, electromagnetic compatibility is regulated under interconnection electric load regulation standards IEC 2009, 950, and 6100032, 2005.
Utility waveform distortions.
This study aims to propose a coupled inductorbased interconnection surge elimination method that can be adopted in a gridconnected PCS. The proposed method has several advantages. First, circulation current is suppressed. Second, PCS reconnection condition, which is governed under the newly enacted international grid code, is smoothly obtained. The analysis and experiment results obtained from two 3 kW PCSs are presented in this study to validate the proposed coupled inductor method.
II. PARALLEL PCS OPERATION AND DESIGN
 A. Structure of the Coupled Inductor
The coupled inductor has two windings: the primary and secondary windings, which are shown in
Fig. 3
. When primary and secondary currents flow in the same direction, total flux in the core has the opposite polarity, which causes its cancellation. Total flux indicates the sum of each selfinductance and mutual inductance.
Structure of the coupled inductor.
When currents flow in opposite directions, however, each generated flux functions as an individual inductor. When combined, these fluxes generate a total flux that is greater than either individual flux. The impedance of the coupled inductor is reduced when the output vectors of the parallel inverters are perfectly synchronized. However, a transient difference in the outputs leads to a high inductance that blocks the instantaneous inrush current.
 B. Coupled Inductor in Parallel PCS
Fig. 4
shows two PCSs connected with a coupled inductor. Each PCS is equivalent to an ideal voltage source, namely,
Vpcs1
and
Vpcs2
, with equivalent output impedances
Lpcs1
and
Lpcs2
, respectively. A load is connected between the coupled PCSs and the grid, with the PCSs controlling the connection of a renewable source to the grid. As shown in
Fig. 4
, all the currents are theoretically supplied by the two PCSs.
Equivalent circuit of the coupled inductor in parallel PCS.
According to magnetic coupled circuit theory, the inductance voltage is given by
In an ideal case, the PCS output voltage and load voltage are equal, that is, the two PCSs generate the same current. Accordingly, the mutual inductance is the same as the selfinductance. Consequently, the voltage drop is zero because of the additional coupled inductor.
 C. Analysis of the Circulation Current
During daytime, photovoltaic (PV) sources feed power into the AC grid through the PCS. The voltages of the parallel PCS system shown in
Fig. 4
can be expressed as follows:
In the parallel system, the current from one PCS can flow to the other instead of to the grid when a PCS output voltage vector difference occurs. The vector of the circulation current is defined as follows
[15]
,
[22]
:
In Equation (5),
n
is the number of parallel PCS. The difference between the two PCSs is equivalent to the voltage vector as follows:
The circulation current in the system can be given as follows
[15]
:
By setting the output impedances of the two PCSs to the same value, Equation (7) can be simplified into
Considering that the circulation current is determined by the voltage vector and the output impedances, additional inductance can reduce the circulation current even if a voltage vector difference occurs.
 D. Design of the Coupled Inductor
The inductance of the coupled inductor must be designed to decrease the instantaneous surge in the circulation current. Such design concept should consider the worstcase condition that occurs at peak current and a phase difference of 180° when the PCS is reconnected after failure. In this case, the current becomes an impulse that is several microseconds long.
Fig. 5
shows the waveform of the surge current (the right side of the figure expands the time axis of the left side). The area of current waveform
A’
can be expressed as follows:
Waveform of the surge current.
where
x
is given by
By using Equation (10), Equation (9) can be rewritten as follows:
By substituting the short surge current duration
t_{1}
= 2
a
and
I_{peak}
=
b
into Equation (11), the area of the surge current waveform is obtained as follows:
where
k
is the ratio of the square impulse to the surge current, which is defined differently in the current study from that in a previous work
[23]
. By using the ratio
derived from Equation (12), we can obtain highly accurate results.
The presence of the additional inductor increases the duration of the surge pulse. The relationship between the original duration
t_{1}
and the increased duration
t_{2}
can be expressed as follows:
As mentioned earlier, voltage phase difference affects the current, which is obtained as follows:
Each inductance of the coupled inductor pair can then be obtained as follows:
PCS peak current is determined by the capacity of the system, for example, the peak current for a 3 kW system is approximately 18 A at a grid condition of 220 V
_{RMS}
. In this case, surge current duration (
t_{1}
) is 0.05 ms. To decrease current, this duration can be extended to 5 ms (that is, to
t_{2}
). Accordingly, inductance
L_{C1}
can be obtained as follows:
L_{C1}
is the inductance of only one of the coupled inductor pair. A double inductance is considered when designing a coupled inductor.
 E. Coupled Inductor Geometry and Material Design
Soft magnetic material cores, which allow great PCS compactness and low weight, are widely used in power conversion applications. The core loss factor is an important factor in an energy transfer system. Although metal powder materials have the most favorable core loss factors
[20]
, cost should be considered for the purpose of mass production. To decrease cost, improved Si steel “JNHFCore” is chosen for the inductor core material used in this study. Unlike conventional Si steel, which contains 3.5% or less Si, the chosen material has a Si content of 6.5%, which minimizes core loss and maximizes permeability. Table I lists the inductor design parameters of the fabricated PCSs. The volume of an inductor is related to the area product
A_{p}
, which is the product of the window area
W_{a}
and the core cross section
A_{c}
, as shown in
Fig. 6
. The area product can be obtained from the inductance, material factors, and apparent power as follows
[21]
:
Left: Core outline that shows the window area (W_{a} = F ⋅ G) and core cross section (A_{c} = D ⋅ E); right: photo of the coupled inductor.
DESIGN PARAMETERS OF THE COUPLED INDUCTOR
DESIGN PARAMETERS OF THE COUPLED INDUCTOR
Apparent power should have sufficient margins if an airgap does not exist in the inductor. The number of inductor turns is obtained from the following equation
[21]
:
Given an inductor core volume of 60 cm
^{3}
and a total turn ratio of 96 turns, the magnetic inductance of the inductor is calculated to be 3.8 mH for a single inductor (
L_{C1}
) and 1.48 mH for the coupled inductor (
L_{C2}
).
III. EXPERIMENT AND RESULTS
Fig. 7
shows a circuit that consists of parallelPCSs with the proposed coupled inductor. For the experiment, a singlephase gridconnected PCS is fabricated with PV modules and a DC source used as input sources. The capacity is 3 kW, which is popular in residential models.
Experimental circuit of gridconnected PCSs.
Given that the series voltage of a typical solar module is lower than the minimum DClink voltage, a twostage PCS topology is selected for the test.
Fig. 8
shows a photograph of the two 3 kW PCS prototypes, in which the first stage boosts the voltage and the second stage inverts AC to connect with a 220 V
_{RMS}
single phase. These prototypes have the same topologies. Both control boards consist of a gate driver, a signal conditioning circuit, and a 32 bit digital signal processor with interface circuitries. To measure input and output voltages as well as input current, a closedlooptype Hall effect LV20P voltage sensor and LA50P current sensor (LEM, Beijing, China) are employed. In the power circuit, all switching devices are insulatedgate bipolar transistor SKM100GB128D. The inductance of the output filter is 4 mH. In a gridtied situation, the quality of a distributed source is important, and instantaneous surge must be compensated for by, for example, a coupled inductor, such as the one assessed in this experiment. The outofphase situation at the point of common coupling (PCC) is PCS reconnection after failure.
Figs. 9
and
10
compare the output current performances under reconnection at 5 A/div and a voltage slewrate of 100 V/div, respectively. The waveform in
Fig. 9
shows the reconnection of PCS2 while operating PCS1. The PCS2 current turns off and then reconnects over a total of 9 s. In
Fig. 9
(a), the surge current attains a peak of 31.5 A, during which the reconnected current is not zero. Hence, power increases instantaneously to a high level, and PCC voltage is altered. After the coupled inductor is installed, the circulating current is significantly reduced, as shown in
Fig. 9
(b). The surge currents are reduced by 4.3 A and lasted for only 4 ms.
Fig. 10
compares the experimental results with opposite reconnection. When PCS1 is reconnected, the surge current reaches 39.3 A, as shown in
Fig. 10
(a).
Fig. 10
(b) shows the experimental results obtained when the coupled inductor is installed. In this case, surge currents are reduced by 9.9 A. Operation during reconnection is similar to that prior to coupled inductor installation.
Gridconnected 3 kW PCS prototype.
Waveforms of i_{PCS1}, i_{PCS2}, v_{grid}, and i_{PCS_total} in parallel PCSs.
Output current waveforms of i_{PCS1} and i_{PCS2} in parallel PCSs with opposite reconnection.
IV. CONCLUSIONS
A coupled inductor connection for parallel PCS operation is proposed to achieve high output performance. The significant results of our assessment are summarized as follows.

1) Parallel PCS operation differs from the operation of a single system. Given that the total system is influenced by the abnormal operation of a single PCS, the output phase will not be synchronized with the grid and the resulting circulation current can damage the PCS.

2) The design guide for our coupled inductor is based on PCS capacity and circulation current duration time.

3) The sum of the output surge is reduced by 87% by introducing the coupled inductor. Reduction in surge during reconnection is demonstrated.
In our experimental assessment, parallel singlephase 3 kW PCSs are fabricated and tested in various situations to demonstrate the performance of the proposed method. The results indicate that the coupled inductor produces a circulation current compensation of 87%, which suggests that its use in improving performance is justified. However, one drawback in implementing the proposed system arises from the fact that adding an additional inductor tends to increase the size and cost of a system. To mitigate these factors, further efforts can be directed toward improving the compensation control method during vector difference duration. Reflection in the output impedance variation in the inverter current controller gain improves current quality during that time.
Acknowledgements
This paper was supported by Konkuk University in 2013.
BIO
JungMuk Choe was born in Seoul, Korea. He received his B.S., M.S., and Ph.D. in Electrical Engineering from Konkuk University, Seoul, Korea in 2006, 2008, and 2014, respectively. He was a researcher for LSIS, Korea from 2008 to 2009. He is currently a postdoctoral researcher at Virginia Tech, Blacksburg, VA, USA. His research interests include modeling and control power converters.
ByengJoo Byen was born in Seoul, Korea. He received his B.S. and M.S. in 2011 and 2013, respectively. He is currently pursuing his Ph.D. in Power Electronics at Konkuk University, Seoul, Korea. His research interests include electric vehicle chargers and DC distribution technology related to intelligent grids.
GyuHa Choewas born in Pusan, Korea. He received his B.S., M.S., and Ph.D. from Seoul National University, Seoul, Korea in 1978, 1980, and 1986, respectively. Since 1980, he has been with the Department of Electrical Engineering, Konkuk University, Seoul, Korea where he is currently a professor and the director of the Energy Electronics Research Center. Dr. Choe was the President (2007–2008) of the Korean Institute of Power Electronics. His research interests are in the fields of harmonic cancellation and active power filtering, PWM control for AC voltage regulators and inverter welding machines, PCS design of Brown’s gas generation, photovoltaic and fuelcell generation, various technologies related to DC distribution, and electric vehicle charging with smart grids.
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