Analysis of Control Strategies for a 3 Phase 4 Wire

Topology for Transformerless Solar Inverters

W.-Toke Franke, Claudia Kürtz, Friedrich W. Fuchs

Institute of Power Electronics and Electrical Drives

Christian-Albrechts-University of Kiel

Kaiserstr. 2 24143 Kiel, Germany

Phone: +49 431 8806106 Fax: +49 431 8806103

Email: tof@tf.uni-kiel.de, fwf@tf.uni-kiel.de

URL: http://www.tf.uni-kiel.de

Abstract—Three different current control strategies includingP+Resonant controller, PI-controller in dq0-reference frame andhysteresis controller for a three-phase-four-wire solar inverterare investigated and compared concerning their influences onthe leakage current at the solar array, the grid harmonics, thestep response and the resulting power losses in the power devices.

I. INTRODUCTION

During the last years many topologies of solar inverters have

been proposed [1]–[5]. In general, they can be classified into

topologies with and without a transformer. The advantages

of the transformerless topologies are higher efficiency and

less volume which are the reasons to select these topologies

for the marked. However, the lack of the transformer also

leads to some drawbacks: The main problems are the leakage

currents between the solar panel and earth. These leakage

currents are a risk for humans touching the panel.Another

point is that for many solar systems the output voltage of

the solar array is smaller than the required DC link voltage.

The voltage can easily be boosted by a transformer [6]. In

case of a transformerless topology the voltage has typically

to be boosted by a DC-DC converter. Because of the leakage

current at the PV arrays, typically three single phase converters

are connected in parallel to achieve the three phase grid

connection. In case that a three phase topology is applied, it is

essential for low leakage current to connect the midpoint of the

DC link to neutral (earth). Typically, the neutral point clamped

(NPC) and the voltage source inverter with split capacitors and

earthed midpoint are used [4].

In this paper the three phase four wire topology is proposed

and analysed. The fourth wire that connects the midpoint

of the DC-link to neutral leads to three independent phases

which have to be controlled individually. For that purpose,

three different control strategies are proposed and investigated

concerning their influence on grid harmonics, leakage current,

efficiency of the inverter and step response.

The paper is structured as following: In section II the

system is described. In the next section the investigated control

strategies are proposed. In sections IV and V simulation and

experimental results are presented. In the last section there is

a conclusion.

Figure 1. Solar inverter with earthed dc link midpoint

Table IEXEMPLARY ELECTRICAL DATA OF THE PV ARRAY

open circuit voltage 1000 Vmax. MPP voltage 800 VMPP range 500 - 800 Vmax. Power 5 kW

II. SYSTEM DESCRIPTION

The variable output voltage of the PV array is fed to the

grid by the inverter topology given in figure 1. The system is

based on a PV array with the data given in table I. However

the results are also valid for other PV arrays. It consists of

a voltage source inverter (VSI) and a boost converter (BC)

in the DC link to cover the whole voltage range of the solar

array. The MPP tracking is realized by both the BC for low

and by the VSI for high input voltages. The connection to the

grid is realized via an LCL filter. Special about this topology

is the fourth wire which connects the midpoint of the split DC

capacitors with the neutral phase of the grid. The advantage of

the fourth wire is a great reduction of the leakage current at the

PV array that arises due to the variation of the dc link potential

to ground generated by the switching pattern. Assuming that

the grid is y-connected the midpoint of the DC link has four

different potentials to ground during one switching period.

During one of the two zero-states all three phases of the grid

are short circuited by having all upper devices conducting

and the lower ones blocking or vice versa. In this state the

upper or lower rail of the DC link is connected to ground

978-1-4244-6391-6/10/$26.00 ©2010 IEEE 658

so that the midpoint of the DC link is at ±VDC2

. During the

active states one device of each phase is conducting whereas

at least one of them is in the upper half and one is in the lower

half. In case that two upper devices and one lower device are

conducting two phases are switched in parallel and connected

to the upper DC link rail. Thus the voltage drop across the

upper DC link rail of the load is only half of the voltage

drop of the phase that is connected to the lower DC link rail.

That leads to a midpoint voltage of the dc link to ground

of −VDC6

and toVDC

6in case that two devices in the lower

half are conducting. The reduction of the leakage current by

connecting ground and the midpoint of DC link is given by

the factor of CPV2CDC

. However the fourth wire also leads to two

drawbacks. The first is that the DC link voltage has to be 2/√

3

higher than for the system without the fourth wire to deliver

the same grid voltage. The second issue is that the widely used

current control strategy in rotating dq-reference frame is not

feasible since the three phases are independent. In the next

section three suitable current control strategies are proposed

and compared concerning their influence on the efficiency, the

harmonic distortion and leakage current at the PV array to

each other. The LCL filter is designed according to [7].

III. CURRENT CONTROL STRATEGIES

The current control strategies can be divided into linear

and non-linear approaches. Since the investigated topologies

consist of a three phase four wire system, the most promising

linear control schemes are the control in dq0-reference frame

and the resonant control, where every phase is controlled

individually. As a non-linear control technique the hysteresis

controller is investigated. For both linear control strategies the

same method for generating the PWM pulses can be applied.

In contrast the hysteresis control delivers directly the pulse

pattern.

A. PI Current Control in dq0-Reference Frame

The standard PI controller in the form of

GPI = KP +KI ·1

s(1)

has an infinite open loop gain at 0 Hz. For that reason the

steady state error can only be eliminated for DC signals. On

account of this the AC signals have to be transferred into DC

signals in a rotating reference frame by(

idiqi0

)

=

√

2

3

(

cosθ sinθ 0

−sinθ cosθ 0

0 0 1

)

(

1 − 12

− 12

0√

32

−√

32

1√2

1√2

1√2

)

(

i1i2i3

)

(2)

After the PI control block the signal is inverse transferred for

the PWM generation by

(

i1i2i3

)

=

√

2

3

(

1 0 1

2√

2

− 12

√3

21

2√

2

− 12

−√

32

1

2√

2

)

(

cosθ −sinθ 0

sinθ cosθ 0

0 0 1

)(

idiqi0

)

. (3)

Figure 2 shows the control structure. The DC link voltage is

controlled by a PI controller. The output of the DC link voltage

controller is the d-component for the current controller. The

q- and 0-component are set to zero for this investigations. The

inverter states are generated by a sine-triangular PWM.

DC

DC

1

2

3

C1

C2

C3

G1

G2

G3

f1-3

DC1

DC2

0d q

d

q

0

Figure 2. Control structure of the PI current controller in dq0 referenceframe

Figure 3. P-resonant controller

Figure 4. Frequency response characteristic of the open loop p-resonantcontroller

B. Resonant Control

The resonant controller is a generalized PI controller that is

able to control not only DC but also AC variables. Figure 3

shows the structure of the resonant controller according to [3],

[8]–[10]. In addition to a forward integrator there is another

integrator in the feedback loop. The transfer function is given

by

GPR = KP +KI ·s

s2 +ω20

. (4)

Figure 4 shows the bode diagram of the resonant controller

for a resonance frequency of 50Hz. At 50Hz there is an

infinite open loop gain and thus it is able to eliminate the

steady state error at this frequency. If ω would be zero the

resonant controller has the same structure as the well known

PI controller.

659

Figure 5. Functionality of the hysteresis control

1

3

2 3

2

1

Figure 6. Control structure of the hysteresis controller

The control structure is similar to that of the PI control in

dq0-reference frame in figure 2. Only the current PI controller

is substituted by the P-resonant controller and therefore the

output signal of the voltage controller is transferred into the

abc-reference frame. The outputs of the current controller can

now directly be transferred to the PWM unit.

C. Hysteresis Control

In this investigation a standard hysteresis controller with

variable frequency is used. Therefore for each phase a toler-

ance band of a given amplitude 2h is allocated around the

phase current. If the phase current exceeds the tolerance band

the converter switches its state into the opposite direction. This

functionality can be seen in figure 5. Since the amplitude of the

tolerance band is given and because the sinusoidal grid voltage

leads to a variable counter voltage and thus to a variable

gradient of the current, the switching frequency depends on the

actual value of the grid voltage. To achieve the same average

switching frequency fs,av in the nominal operating point as

for the other control strategies the magnitude of the tolerance

band h is adjusted by [11]:

2h =VDC

4 ·LC · fs,av

(

1−M2

n

2

)

(5)

There Mn is the modulation index in the nominal operating

point.

IV. SIMULATION RESULTS AND COMPARISON

All three control strategies have been investigated by simu-

lation with MATLAB Simulink and Plecs. The power circuit

is implemented in Plecs for a detailed analysis of the leakage

current and power losses. For the simulation the same param-

eters are used as for the experimental setup, given in table

II.

Figure 7. Leakage current reduction by connecting the midpoint to earth(top), leakage current with the fourth wire connencted (bottom)

A. Leakage Currents

Before comparing the different control methods to each

other a simulation shall clarify, how the leakage currents

are reduced by the split DC capacitors C3 = C4 = 1000µF.

Therefore, a simulation test with and without earthed midpoint

is done for a parasitic solar array capacity of 150nF for 1kW

according to [5]. The results are given in figure 7 for the

P+resonant controller, where the fourth wire is connected at

50 ms to ground. However the results look similar for the

other control strategies. Without the fourth wire the leakage

currents rise up to a value of 5A whereas it is reduced to about

1.5mA (Fig. 7 bottom) when the fourth wire is connected to

the midpoint of the split capacitor. The current ripple is 20

kHz.

B. Influence on Grid Harmonics

To clarify the influence of the proposed control strategies

on grid harmonics the resulting grid currents have been ana-

lyzed. For this purpose a sinusoidal reference voltage replaces

the grid in simulation. In the case that an ideal sinusoidal

waveform is used no harmonics greater than 0.1% show up.

Figure 8 shows the harmonic spectrum when a non ideal

sinusoidal waveform is utilized. Here on each of the third, fifth

and seventh harmonic a disturbance of 1.5% is superimposed.

The red stems describe the maximum allowed harmonics

concerning DIN VDE 0126-1-1. The P-resonant control per-

forms similar to the PI control in dq0-reference frame. Both

control methods slightly amplify the given harmonics. No

other harmonic numbers appear. With the hysteresis control the

given harmonics are attenuated but other harmonic numbers

are added even though they are only insignificant.

C. Step Response for Optimal Control Parameters

Figure 9 displays the step responses to a step of the DC

link power. Here, the d-component of the output current is

depicted, whereas the value is normalized to 1. Therefore

the output currents are transferred in dq0-reference frame

for measurement reasons. Comparing the time period until

the system is in steady state, both the PI controller in dq0-

reference frame as well as the P+resonant controller take 4ms

660

a) b) c)

Figure 8. Harmonics current spectrum with a disturbed grid voltage (1.5 % of the 3rd, 5th and 7th added) for a) PI controller in dq0 reference frame; b)P-resonant controller; c) hysteresis controller

0.01 0.015 0.02 0.025 0.03−0.5

0

0.5

1

1.5

t in s

0.01 0.015 0.02 0.025 0.03−0.5

0

0.5

1

1.5

t in s

Figure 9. Step responses top: PI control in dq0 reference frame, middle:P+resonant, bottom: hysteresis

due to the LCL filter. Applying the hysteresis controller the

overshoot subsides after approximately 1.5ms. After that there

is some ringing for another 4ms. The faster step response

results in a higher overshoot of the current of 55%. Whereas

the p-resonant controller only has 25% and the PI control in

dq0-reference frame has even less with 22%.

D. Power losses and Efficiency

To demonstrate the efficiency of the analyzed control struc-

tures it is simulated at different input power. Therefore the DC

link voltage is kept constant at 800V and the input current is

adjusted between 0.625 A and 6.25 A. The examined power

losses are the conducting and switching power losses of the

IGBTs and diodes. They were simulated by means of a thermal

simulation in Plecs. Therefore the switching and conducting

losses were measured on a real device at different temper-

Figure 10. Efficiency of the inverter with different control strategies

atures, blocking voltages and currents [12]. After that, these

results have been implemented in the Plecs model. The results

are presented in figure 10 and show promising values between

94,5% and 97.6% depending on the current and control

strategy. The highest efficiency is achieved by the hysteresis

controller since the highest switching frequency occurs when

the magnitude of sinusoidal output current is at its minimum.

For the maximum current only low switching frequencies

occur. The two linear control methods show very similar

efficiencies because both lead to the same PWM-pattern. Due

to the constant switching frequency their efficiency is lower

than for the hysteresis control. Here, some improvements may

be achieved by applying a discontinuous PWM method by

injecting the third harmonic. This will lead to a 50% reduction

of the switching losses since the highest current carrying IGBT

is turned on permanently for 1/6 switching period [13].

V. EXPERIMENT RESULTS

For the experimental results a three phase four wire VSI

inverter has been built up on PCB (figure 11). The focus

was on a circuit with lowest stray inductances to enable high

switching frequencies and short turn-on and turn-off times.

The output filter is an LCL filter designed concerning to [7].

The input voltage is delivered by a solar simulator that is on

the one hand able to produce a fixed DC voltage and on the

other hand can deliver a current and voltage according to a

given V/I-characteristic of a solar array. The control of the

inverter is realized on a TriCore µ-controller from Infineon

Technologies. The significant parameters of the experimental

setup are given in table II.

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Figure 11. Experimental solar converter setup: PCB of the converter,measurement unit and LCL filter bottom

Table IIPARAMETERS OF THE EXPERIMENTAL SETUP

Input voltage 500 - 1000 V

Input power 5000 W

DC-link Capacitance 660 µF

Semiconductors IKW08T120

Switching frequency 20 kHz

Converter side inductor three powder cores 2.6 mH

Grid side inductor laminated steel 0.5 mH

Filter capacitor 4.4 µF

A. Leakage Currents

Figures 12, 13 and 14 show the leakage current through

a 450 nF capacitor connected to ground for the control in

dq0-reference frame, the P+resonant control and the hysteresis

control, respectively. The output current in each phase is 5

Arms. The leakage current consists of a ringing of 200 mA for

operating with the linear control strategies and about 100 mA

for the hysteresis controller. The rms values are 78.8 mA, 81.3

mA and 43.1 mA, respectively and therefore well below the

allowed 300 mA concerning VDE 0126-14-2. Compared to

the simulation results the leakage current is significant higher.

The reason is that in the simulation ideal capacitors for the

DC link are applied. For the experimental test the DC link

consists of electrolyte capacitors with not negligible parasitic

inductances and resistances, while for CPV a film capacitor

with much lower parasitic effects is used. This leads to higher

equalizing current through this path. It is expected that for real

solar arrays the leakage current is lower.

B. Harmonic spectrum

The measured harmonic spectra for the three control strate-

gies are given in figure 15. It is obvious that the spectra for the

current control in dq-reference frame and with the P+resonant

controller have a similar appearance, since the same switching

frequency, grid filter and pwm modulation are applied. The

THD values are calculated to 3.074 % and 2.966 % for the

current control in dq0 reference frame and for P+resonant

controller, respectively. For the hysteresis controller for most

frequencies the spectrum is smaller as for the other two control

strategies, even though the current has much higher ringing as

shown in figure 14. This is caused by the fact that the ringing

Figure 12. Solar inverter, control in dq reference frame: DC-link voltage100 V/div (Ch 1), AC contents of the voltage across CPV (Ch 2) grid current5A/div (Ch 3) and leakage currents 200 mA/div (Ch 4)

Figure 13. Solar inverter, P+resonant controller: DC-link voltage 100 V/div(Ch 1), AC contents of the voltage across CPV (Ch 2) grid current 5A/div (Ch3) and leakage currents 200 mA/div (Ch 4)

has switching frequency that is between 2.5 kHz and 30 kHz

and therefore not visible in the first 40 harmonics. The THD

is calculated to 1.2 % for the first 40 harmonics and to 7.7 %

for the total spectrum.

C. Efficiency

The measured power losses for all proposed control strate-

gies are shown in figure 16. The efficiency is calculated from

the measured input and output power of the inverter that

is done by the DEWETRON 2010. Its power accuracy is

Figure 14. Solar inverter, Hysteresis controller: DC-link voltage 100 V/div(Ch 1), AC contents of the voltage across CPV (Ch 2) grid current 5A/div (Ch3) and leakage currents 200 mA/div (Ch 4)

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Figure 15. Harmonic current spectra of the investigated control strategies

Figure 16. Measured efficiencies with DEWE2010

determined to about 0.5 %. For both linear strategies the same

results are achieved, since they lead to the same switching

pattern. Due to the IGBTs with their current independent

forward voltage drop and fix power losses caused by balancing

resistors for the DC link capacitors, the efficiency is reduced

for very low input power but increases up to 2.5 kW. After

that it starts to decrease slightly. For the hysteresis controller

the grid filter was changed to an L-filter with 4.5 mH, due

to the ringing of the output current. Using damping resistors

would lead to lower efficiency compared to the larger L-

filter. The power losses for the hysteresis control depend very

much on the input power. The spectrum has shown that the

average switching frequency increases with the reduction of

the modulation index, leading to increasing switching losses.

This also approves (5). For the input power above 2.5 kW

the average switching frequency is already reduced to 5 kHz.

This explains the better efficiency of the hysteresis controller

compared to the other controllers.

VI. CONCLUSION

Three different current control strategies (P+Resonant, PI

in dq0-reference frame and hysteresis controller) for a three

phase four wire solar inverter have been investigated. A special

attention was given to the leakage current at the solar array and

the resulting power losses as well as on the harmonic distortion

of the grid current. The leakage current is reduced effectively

by the earthed midpoint of the DC-link capacitors for all three

control strategies. It could be concluded that the hysteresis

controller leads to the lowest losses but depicts a wide har-

monic spectrum due to the variable switching frequency. The

behavior of the PI controller in dq0 reference frame and the

P+Resonant controller show very similar results. Regarding the

processing power of the µ-controller the P+Resonant controller

has some advantages compared to the PI controller due to

lack of the dq0-transformation. The switching losses for the

linear control strategies can be reduced by applying loss

optimized modulation strategies, which however will lead to

higher harmonics in the grid current.

ACKNOWLEDGMENT

This work is sponsored by the Rainer Lemoine Stiftung

(RLS).

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