Ground currents in single-phase transformerless photovoltaic systems

PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS

Prog. Photovolt: Res. Appl. 2007; 15:629–650

Published online 4 May 2007 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/pip.761

Applications

*Correspondence to: DCampus Arrosadia, 310yE-mail: uge@unavarra

Copyright # 2007 John

r Eug06 Pa.es

Wil

Ground Currents inSingle-phase TransformerlessPhotovoltaic Systems
Eugenio Gubıa*,y, Pablo Sanchis, Alfredo Ursua, Jesus Lopez and Luis MarroyoDepartment of Electrical and Electronic Engineering, Public University of Navarra, Pamplona, Spain
The relative weight of the energy generated by means of renewable sources is

constantly increasing. Among all these sources, the photovoltaic (PV) systems present

the higher and more stable relative growth. However, the PV system is still too

expensive and a significant effort is being done to increase the efficiency and reduce

the cost. Concerning the PV inverters, this has lead to the elimination of the low

frequency (LF) transformer that has been traditionally included. The LF transformer

provides isolation from the grid but reduces the PV inverter efficiency and increases

its size and cost. However, the elimination of the transformer might generate strong

ground currents, which become now an important design parameter for the PV

inverter. The ground currents are a function of the system stray elements. However,

there is no simple model and procedure to study the common mode behavior of a PV

system, which is required to analyze the ground currents. In this paper, a compre-

hensible model is proposed which provides a better understanding of the common

mode issue in single-phase transformerless PV systems. In addition, a procedure is

developed to analyze the global performance, efficiency, grid current quality, and

common mode behavior of a PV inverter as a function of its particular structure and

modulation technique. Copyright # 2007 John Wiley & Sons, Ltd.

key words: photovoltaic (PV); ground current; transformerless; inverter; common mode

Received 18 November 2006; Revised 15 February 2007

INTRODUCTION

Nowadays, the photovoltaic (PV) energy contribution to the total energy consumed in the world is very

low, due to the relatively high cost of the PV systems in comparison with other energy sources.

However, the solar energy resources are distributed all over and the price of the PV systems is

continuously decreasing. This can make the PV systems one of the future most important renewable energy

sources. In fact, it presents one of the highest and more stable relative growth, up to 20–25% per year.1,2

Lowering the PV systems price and increasing its efficiency is necessary for them to achieve a significant role as

an energy source.

enio Gubıa, Edificio Los Tejos, Dpto. Ingenieria Electrica y Electronica, Universidad Publica de Navarra,mplona, Spain.

ey & Sons, Ltd.

630 E. GUBIA ET AL.

A grid-connected PV system basically consists of a PV generator (set of arrays) and a power conversion stage

(inverter). The inverter makes the generator operate at its maximum power point (MPP) and provides the

necessary power conditioning for the electrical energy to be injected into the grid. The most expensive PV

system element is the generator. However, both due to the research effort in the last years and the increase in the

production of PV arrays, an appreciable decrease of the generator price per kilowatt-peak (kWp) is being

achieved. As a result, the price per watt-peak has decreased from 4�4 to 7�9 USD in 1992 to 2�6 to 3�5 USD at

present.3,4 In the future, this price might go below 1 USD due to the emerging technologies like thin-film

techniques.5 These improvements in the PV generator have made the inverter cost more and more important in

the PV system total price. This has motivated the research on new power conversion structures which lead to a

decrease of the conversion stage cost and an increase of its efficiency. Nowadays, most of the PV systems are

dedicated to the residential market with typical system sizes around 2–10 kW.6 The first residential PV systems

included a single-phase inverter with a low frequency (LF) transformer placed between the power conversion

stage and the grid. This transformer has been required by nearly all the national regulations since it guarantees

galvanic isolation between the grid and the PV systems, thus providing personal protection. Additionally, it also

provides isolation between the PV system and the grid ground, so that, the common mode current results

strongly limited. Furthermore, it ensures that no direct current, which could saturate the distribution transformer,

is injected into the grid. Finally, it can be used to increase the inverter output voltage level.7–9 However, the LF

transformers increase the weight, size and cost of the PV system, and reduce its efficiency. This has encouraged

the scientific research into other transformerless solutions.

An alternative that has been proposed is to replace the LF transformers by high frequency transformers placed

in the dc stage of the inverter.10–13With these conversion structures, galvanic isolation is again achieved between

the PV generator and the grid, whereas no injection of direct current into the grid must be guaranteed by means

of the converter control strategy.14 The high frequency transformers have a reduced weight, size, and cost.

However, the power conversion stage is more complex and, additionally, no valuable improvement is obtained in

the global efficiency of the system.2,15

The technology evolution has made it possible to eliminate the transformer with no impact on the system

characteristics as regards to personal safety and grid integration.7 In addition, the use of a string of PV arrays

allows having MPP voltages which are enough to avoid boosting of voltages in the conversion stage. Therefore,

this stage can now consist of a simple buck inverter, with neither the need of transformer nor boost dc-dc

converter, resulting in a more simple, economical, and efficient conversion stage.2,3 As a consequence,

regulations from some countries, like Germany, allow now the use of transformerless inverters, and others are

considering changing their regulations in the same direction. Therefore, it is quite likely that many of the future

grid-connected PV systems will be transformerless.2

Nevertheless, to evaluate the overall performance of a PV system, in addition to the grid current quality (THD)

and system efficiency, the commonmode behavior has to be considered.When no transformer is used, a galvanic

connection appears between the PVarrays and the grid, that is, between the arrays and the ground. Therefore, the

common mode current injected into the ground is only limited by the converter common mode impedances

(mainly from the EMI filter) and the stray capacitance between the PV generator and the ground. Consequently,

when the inverter generates a varying common-mode voltage, strong leakage currents (common mode currents)

can flow through the great stray capacitance between the PV array and the ground.7,16 To avoid these currents

flowing into the ground, it is necessary to use power conversion stages together with appropriate modulation

techniques that generate no variable common mode voltages. The main difficulty in the analysis of these

transformerless PV systems comes from the lack of a simple model and procedure to study theoretically the

common mode behavior of the system. In this paper a comprehensible model is presented to analyze and

understand the common mode issues in single-phase transformerless PV systems. In addition, this model is

useful to search new conversion structures and modulation techniques for systems of this type. First, the problem

of the common mode in transformerless PV systems is introduced. Next, the system behavior is analyzed in

detail from the common mode point of view. As a result of this analysis, a suitable model is obtained to both

identify the converter elements participating in the ground currents and to evaluate the influence of any

modulation technique. Finally, this model is applied to the analysis of the common mode behavior of the power

converter stages used in three commercial transformerless PV inverters.

Copyright # 2007 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2007; 15:629–650

DOI: 10.1002/pip

Figure 1. Scheme of a single-phase PV system

GROUND CURRENTS IN PV SYSTEMS 631

SYSTEM DESCRIPTION

A grid-connected PV system consists basically of a PV generator (set of arrays) and a power conversion stage

(inverter). Figure 1 shows a generic PV system, which is going to be precisely studied to analyze the common

mode issue in PV systems.

Points ‘1’ and ‘2’ correspond to the power converter outputs. Typically, the converter is a voltage controlled

source, and therefore, a short-circuit condition appears whenever it is directly connected to other voltage source

like the grid. Consequently, the line inductor (L) is required to control the current injected into the grid. The

inverter includes also the LF transformer and the EMI filter. In a PV system the inverter has a double objective.

On one hand, it must control the voltage of the PV generator, VPV, so that the operating point of the PV generator

be always as close as possible to the MPP. On the other hand, it has to inject the energy extracted from the PV

generator into the grid by means of injecting a sinusoidal current, igrid, with unity power factor.17

Another aspect to be considered in grid connected PV systems is the current flowing through the connection

between the grid and the ground as a consequence of the normal operation of the PV system. This current has

negative effects concerning the electromagnetic compatibility (EMC) and, if it is very strong, the integrity of the

system as well. To study both the quality of the current injected to the grid and the leakage current into the

ground, it is very useful to describe the system behavior with the help of the commonmode and differential mode

concepts.

The commonmode of any circuit output voltage is the average value of the voltages between the outputs and a

common reference. For this system, it is very convenient to use the negative terminal of the dc bus, point N, as

the common reference. Therefore, the common mode voltage of the converter, vcm, is:

vcm ¼ v1N þ v2N

2(1)

The differential mode output voltage, vdm, is defined as the voltage between both converter outputs:

vdm ¼ v1N � v2N ¼ v12 (2)

From Equations (1) and (2) the voltage between the converter outputs and the N point can be expressed as:

v1N ¼ vdm2þ vcm

v2N ¼ � vdm2þ vcm

(3)

Concerning the converter output currents, they can also be expressed in terms of their common and

differential mode components. The common mode current at the full bridge (FB) output is defined as:

icm ¼ i1 þ i2 (4)


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632 E. GUBIA ET AL.

The differential mode current is:

idm ¼ i1 � i2

2(5)

From Equations (4) and (5) the current at the converter outputs can be written as:

i1 ¼ idm þ icm2

i1 ¼ �idm þ icm2

(6)

From Figure 1 and Equation (4), it is clear that the ground current corresponds to the common mode current,

icm. Therefore, icm needs a continuous path from the ground to the converter. Concerning the differential mode

component, it leaves one of the FB legs and returns through the other. The current flowing into the grid, if a 1:1

ratio for the line transformer is considered, can be expressed in the following way:

igrid ¼ i1 ¼ idm þ icm

2(7)

The model of a PV system shown in Figure 1 does not include any path for the ground current to flow back to the

FB converter. Then, the current icm is zero. Under these conditions, the only current injected into the grid

corresponds to the differential mode component idm. The dynamics of this component is a function of the voltage

applied across the line inductor L, which can be controlled by means of the voltage vdm generated by the converter:

digrid

dt¼ didm

dt¼ vdm � vgrid

L(8)

Therefore, the differential mode voltage controls the current injected into the grid. The instantaneous value of

vdm depends on the voltages at the points 1 and 2. Quite often the converter consists of a set of switches and

behaves as a voltage source that can only generate discrete values of the output voltage. These values are called

output levels. The voltage levels that can be generated by the converter depend on its structure. The conversion

structures are then classified in two-, three- or more level converters. At present, the most commonly used

converters in PV systems are the three-level converters.

The level of the converter output voltage is set by the conduction state of the converter switches. By means of

Pulse Width Modulation (PWM) techniques, during a very short time called switching period (TS), a particular

sequence of the output converter levels is selected, and then a specific average value for vdm inside the �VPV to

VPV range can be obtained. The switching frequency ( fs¼ 1/Ts) is typically selected around tens of kHz for

single-phase PV systems. As a consequence, the converter can vary the average value of vdm fast enough to

control the current injected into the grid, with a small high frequency ripple. To keep the current controlled

during the whole grid period, the voltage at the dc bus, VPV, has to be higher than the maximum of the grid

voltage. A minimum value for this voltage of around 350V is necessary in 230V grid systems.

From the point of view of the spectral components, vdm exhibits a fundamental component at the grid

frequency and high frequency harmonics whose amplitudes are a function of the vector sequence generated by

the corresponding modulation technique. The fundamental component of the current injected into the grid, and

with it the energy injected into the grid, is controlled by means of the fundamental component of vdm. There are

multiple modulation techniques (‘sequences’) that produce the same fundamental component for vdm but with

different high frequency harmonics. Once the vector sequence and the grid voltage are known, the grid current

can be directly calculated by means of Equation (8). Therefore, it is easy to evaluate the quality of the

modulation technique from the point of view of the current THD.

The higher the switching frequency is, the higher the quality of the converter output current is. However, the

losses increase with the switching frequency and then the converter efficiency reduces. Energy losses in

the converter are due to the conduction energy losses caused by the flow of the current through the switches and

the switching energy losses caused by the turn on and off process of the switches. Therefore, when the

performance of a converter that operates with a particular modulation technique is evaluated, both features,

current quality and efficiency, have to be considered.


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Figure 2. PV system schematic including the most significant stray elements


Till now the common mode current has not been taken into account since, apparently, no path exists for it to

flow. In real PV systems, stray capacitance appears that provide electrical paths for the ground current, which is

the common mode current icm. Certainly, the value of the common mode current is a function of the common

mode voltage. However, the value of icm cannot be directly deduced from the value of vcm, since icm is influenced

by other voltage sources and elements like the system parasitic elements. Figure 2 shows a more detailed scheme

of the PV system including the most important stray elements, modeled as capacitors and inductors, which

influence the ground current dynamics. In this figure,CPVg represents the stray capacitance between the PVarray

and the ground. This capacitance is distributed over the PV generator surface. Some authors propose to model

CPVg as two capacitors connected to the first one between the positive PV generator terminal and the ground, and

second between the negative and the ground.18 Nevertheless, modeling with just one capacitor is accurately

enough to evaluate the PV generator influence on the commonmode. The value of this capacitorCPVg is affected

by the installation characteristics (ground nature, humidity, connection to the converter, etc.). C1g and C2g

represent the stray capacitances between the ground and the outputs points of the converter. Their values are a

function of the switches and the connection between them and the heat-sink, and the heat-sink to the ground.

ZGcGg is the series impedance between the ground connection points of the converter and the grid. This series

impedance is mainly due to the ground stray inductance lGcGg. Zp and Zn are the series impedances, also mainly

inductive, of the phase and neutral conductors, respectively. Finally, Ct is the stray capacitance between the

transformer windings.

As it can be noted in Figure 2, the common mode current icm can flow through the system thanks to the stray

capacitances in the LF transformer. These capacitances are in the order of hundreds of picofarads and then they

exhibit a high impedance in the low and medium frequency range (<50 kHz). As a consequence, the common

mode current associated to the low and medium frequency harmonics of vcm is going to be strongly reduced. The

EMI filter has to filter only the high frequency components of vcm, so the filter size is considerably small.

Therefore, if a transformer is used, the common mode has no significant weight in the selection of the power

converter and its modulation technique.

COMMON MODE MODEL OF THE SYSTEM

The voltage between the outputs of the converter and point N, v1N, and v2N, are imposed by the switches

modulation sequence. Therefore, both outputs can be studied as controlled voltage sources connected to the

negative terminal of the dc bus (N point). The pulses rise and fall times are around tens to hundreds of

nanoseconds and they are determined, mainly, by the switch characteristics. If the converter of Figure 2 is

substituted by these voltage sources, the model of Figure 3 is obtained. The line inductor has been split in two


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Figure 3. Model for a PV system with voltage source converter

634 E. GUBIA ET AL.

parts, namely L1 (the part connected to the phase) and L2 (the part connected to the neutral). The differential

mode current, idm, always flows through the whole line inductor L1þ L2. Therefore it is of no relevance if this

inductor is connected to either the phase or the neutral conductor, or even split into two parts connected to both

of them. However, half of the common mode current flows through the phase conductor and the other half

through the neutral conductor. Therefore the position of the line inductor will affect the common mode current.

With the aim of studying the influence of the line inductor position, this inductor is split in the model of Figure 3

into L1 and L2. This circuit makes it possible to analyze both the differential and the common modes.

In order to develop a more suitable model for the analysis of the common mode, some further work has to be

done on the circuit of Figure 3. First, the model shown in Figure 3 is now represented in Figure 4 in terms of the

differential and common mode voltages vdm and vcm. As no simplification has been introduced in the model, the

circuit of Figure 4 remains valid to analyze both the common and the differential modes of the system. However,

it is very complicate to evaluate the influence of the modulation techniques over the common mode behavior,

which determines the size of the EMI filter inductor. With that aim, a simplified model, limited to the common

mode, is derived from the one of Figure 4. As a previous step, and in order to make the deriving of the equivalent

circuits between points A–B and C–A easier, the differential mode sources appear duplicated in the model of

Figure 5 as well as the points 1 and 2.

The voltage across stray capacitance between the PV generator and ground presents a LF component due to

the grid.18 However, the grid is a LF voltage source (50–60Hz) and its output impedance is much smaller

compared with both the line inductor L and the EMI filter common mode inductor Lcm. Consequently, the grid

influence on the common mode current will be neglected from now on. By introducing the equivalent circuits

between points A–B and C–A in the model of Figure 5, the model of Figure 6 is obtained. This model can only be

applied for the analysis of the common mode.

The developed model includes obviously the voltage source vcm, but also two additional voltages sources, vs1and vs2. These voltage sources are due to the asymmetries in the differential mode impedances, that is, in the line

impedances and in the stray capacitances between the switches and ground. Therefore, even if the converter does

not generate any common mode voltage, it is possible to have common mode currents when there is some

asymmetry in the value of the mentioned impedances. Most of the times, the two converter outputs are

physically symmetric, and then it can be assumed that the stray capacitances of the switches are similar.

Therefore vs2 will be close to zero. Anyway, even when that symmetry is not found, the influence of vs2 on the

common mode current for the low and medium frequency range is expected to be much less significant than the

one of the sources vs1 and vcm. This is due to the low value of C1g and C2g, in the range of tens to hundreds of

picofarads compared with CPVg. If the contribution of this circuit branch is neglected, the circuit of Figure 7 is

finally obtained. The main advantage of this simple circuit is the possibility to easily evaluate and understand the

influence of any modulation technique and line inductor placement in the common mode current. An immediate

conclusion is that when the voltage vtcm, which will be referred as total common mode voltage, does not vary, no


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Figure 4. PV system model in terms of the converter differential and common mode voltages


common mode current will then flow through the circuit. This is due to the presence of capacitor CPVg, which

remains charged at the voltage vtcm.

ANALYSIS OF A TRANSFORMERLESS PV SYSTEM BASEDON THE FULL BRIDGE CONVERTER

The FB converter is a well-known three-level structure that provides a good trade-off between complexity and

performance. The FB converter consists of two legs, each one with two controlled transistors, usually IGBTs,

and two diodes. Figure 8 shows a transformerless PV system based on this converter.

When the upper IGBT of one leg is ON, the lower one has to be OFF in order to avoid short-circuiting of the

dc-bus, and vice versa. Table I list the four possible combinations corresponding to the allowable conduction

states of the FB switches. Conduction states for T2 and T4 are the complementary states of T1 and T3,

respectively. There are only three levels, that is, three different instantaneous values, for the differential mode

voltage (0, VPV, and �VPV). From now on, the four combinations will be referred to by means of their associate

vectors (0N, N, P, 0P).The conduction states of the switches determine the voltage vdm but do not provide enough information for the

analysis of the PV system common mode behavior. From the model of Figure 7 it is clear that voltage vtcm has to

be evaluated. This voltage is a function of the voltage sources vcm and vs1. The common mode voltage vcm can be

derived directly from the vectors in Table I, whereas the voltage vs1 depends also on the asymmetry in the value

of the inductors L1 and L2. Therefore, in order to deal with the common mode it is necessary to evaluate the total


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Figure 5. Intermediate step before obtaining the simplified common mode model

636 E. GUBIA ET AL.

common mode voltage for each combination of L1 and L2. Although there are obviously infinite combinations,

only the two most interesting cases are here considered. Results for both cases are shown in Tables II and III.

These tables present the values of vdm and vtcm for each case and allow to analyze and develop modulations

techniques for a transformerless PV system with FB structure.

Figure 6. Model for the common mode

Figure 7. Final model for the common mode


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Figure 8. Transformerless PV system with a full bridge converter


Case 1: whole line inductor placed in the phase conductor (L2! 0 and L1! L)

This is the most simple and commonly used choice for the line inductor placement. In practice, it is not possible

to eliminate all the inductance from the neutral conductor due to the conductor stray inductance (Figure 8).

Therefore, in the model of Figure 7, the parallel impedance due to L1 and the stray inductance will be

approximately equal to the neutral stray inductance (in the order of hundreds of nH to few mH). Table II presents

the values corresponding to vdm and vtcm, which are the key to derive or analyze any modulation technique.

Table I. Output voltages and vectors of the full bridge converter

Vector T1 T3 v1N v2N vdm¼ v1N � v2N

0N OFF OFF 0 0 0

N OFF ON 0 VPV �VPV

P ON OFF VPV 0 VPV

0P ON ON VPV VPV 0

Table II. Main inverter voltages, full bridge converter and L1¼ L (L2¼ 0)

Vector vdm vcm ¼ v1Nþv2N2

vs1 ¼ vdm � 12

� �vtcm¼ vs1þ vcm

0N 0 0 �0 �0

N �VPV VPV/2 �VPV/2 �VPV

P VPV VPV/2 ��VPV/2 �0

0P 0 VPV �0 �VPV

Table III. Main inverter voltages, full bridge converter, and L1¼ L2¼ L/2

Vector vdm vcm ¼ v1Nþv2N2

vs1 ¼ vdm � 0 vtcm¼ vs1þ vcm

0N 0 0 �0 �0

N �VPV VPV/2 �0 �VPV/2

P VPV VPV/2 �0 �VPV/2

0P 0 VPV �0 �VPV


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638 E. GUBIA ET AL.

Case 2: line inductor split into two identical parts (L1¼ L2¼ L/2)

An alternative to case 1 that seems very interesting is to divide symmetrically the line inductor L between the phase

and the neutral conductors so as the voltage vs1 becomes zero. Table III lists the values of vdm, and vtcm for this case.

With Tables II and III it is possible to analyze a particular modulation technique or to derive new ones, in

terms of the differential and the common mode issues. Regardless of the modulation technique considered, the

controllability of the grid current imposes that the fundamental component of vdm exhibits a sinusoidal shape at

the grid frequency. To simplify the notation, from now on the positive half cycle of the fundamental component

of vdm will be referred to as the positive half cycle of vdm. A similar notation will be followed by the negative

counterpart. Concerning the common mode current, it is clear from the model of Figure 7 that the key aspect is

that the voltage vtcm remains always constant, no matter what the value is. Then, we have to check these

conditions in both Tables II and III, in order to analyze or derive any modulation technique.

Firstly, the Unipolar modulation technique (UPWM) is examined to evaluate its suitability for transformerless

PV systems. This technique is the most extended modulation technique implemented in FB converters. The

UPWM uses the three levels achievable at the converter outputs, which are VPV, 0, and �VPV. There are several

ways to implement the UPWM. The traditional one consists of dividing the time for the 0 level in two identical

times, each one for each null vector 0N and 0P. In this case, the positive half cycle of vdm is obtained with vectors

0P, P, and 0N. The negative half cycle is generated by means of vectors N, 0N, and 0P. According to Table I, in

order to implement the sequence 0p, P, 0N, P both legs have to be modulated by means of a complementary duty

cycle (conduction time of the upper switch with respect to the switching period). In addition, the switching

orders have to be synchronized so as to obtain an output frequency fo, in vdm, that doubles the switching

frequency (Figure 9). This last feature is very valuable as it improves the trade-off between switching energy

losses and current quality (THD), so that, higher efficiency for the PV system can be achieved. The efficiency is a

key parameter of a power conversion stage and therefore, it is going to be considered and compared among all

the structures analyzed in this paper. With the UPWM, the output current flows always through two IGBTs or

one IGBTand one diode, that is, the conduction energy losses in the converter are due to the conduction losses of

two power semiconductors. The converter switching energy losses are due to two IGBTs and two diodes

modulating at half the output frequency and with a voltage of VPV.

Figure 9. Waveforms with the UPWM technique when the line inductor is symmetrically split


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To analyze the common mode behavior, Tables II and III have to be examined. In Table II, the line inductor is

connected to the phase conductor. In this case, vtcm shows four voltage steps with amplitude equal to VPV during

each switching period. In the other case (Table III), the line inductor is symmetrically split between the phase

and the neutral conductors. Again, there are four voltage steps in vtcm, although now the amplitude is limited to

VPV/2. When the line inductor is split between the phase and the neutral conductors, the voltage waveform of

vtcm corresponding to the positive half cycle of vdm is depicted in Figure 9.

To understand better the magnitude of the common mode EMI issue, it is interesting to have a look at the

system behavior when no EMI filter (Lcm and Ccm) is included. Without the EMI filter, every voltage step in vtcmoriginates a fast transient that depends on both the conductor and the ground stray inductances (ls), and CPVg.

Capacitor CPVg will reach quickly the steady state with the same voltage than vtcm. Therefore, when the UPWM

is implemented the voltage across CPVg will result in voltage steps with a magnitude of either VPVor VPV/2. Due

to the low damping provided by the losses in the conductors and the high resonant frequency, which is much

higher than the switching frequency, the peak of the common mode current icm can be calculated for the whole

line inductor in the phase conductor as:

Ip cm � VPVffiffiffiffiffilsCbg

q (9)

By evaluating in Equation (9) for a 5 kW PV system, and taking CPVg¼ 50 nF, VPV¼ 350Vand a total stray

inductance ls of 4mH, the current peak Ip_cm results to be around 40A. In a real PV system, the EMI filter will

reduce this magnitude in several orders if the core of the common mode inductor does not saturate. The size

required by the common mode inductor of the EMI filter to withstand the voltage vtcm generated in

transformerless PV systems with UPWM FB converter, without going into saturation, results very high. This is

the reason why this modulation technique is not adequate for transformerless PV Systems.

Now, Tables II and III are going to be examined with the aim of finding a more suitable modulation technique

for transformerless PV systems. From Table II, it can be appreciated that for the positive half cycle of vdm,

vectors 0N and P can be used, then the voltage vtcm remains constant and equal to 0V. For the negative half cycle

of vdm, vectors 0P and N can be selected. Therefore, voltage vtcm remains also constant but now equal to VPV.

With this modulation technique, during each half cycle the voltage vtcm do not experiment any variation. Then,

capacitorCPVg (see Figure 7) remains at constant voltage and no common mode current appears. From Table I, it

can be seen that the practical implementation of this modulation technique consists of modulating one of the FB

legs at the grid frequency and the other at the switching frequency. This technique, called Hybrid Pulse Width

Modulation (HPWM), was proposed with the aim of improving the FB efficiency, since it allows using switches

with lower conduction losses in the leg modulated at grid frequency. 19 But in the switching period in which vdmalternates from one half cycle to the other, a voltage step, with amplitude equal to VPV, takes place in vtcm. As it

has been evaluated in Equation (9), the ground current will show a strong peak unless the EMI filter includes a

common mode inductor big enough to withstand the voltage steps in vtcm. Therefore, this modulation technique

also exhibits the same important drawback as the UPWM in transformerless PV systems based on the FB

converter.

Table II does not offer any other valuable option. From Table III, that is, when the line inductor is

symmetrically split between the phase and the line conductors, it can be seen that using only vectors P andN it is

possible to obtain both the positive and negative half cycles of vdm. At the same time, there is no variation in the

value of vtcm, remaining constant and equal to VPV/2. Therefore, this modulation technique seems to have

interesting properties for transformerless PV systems. From Table I, the practical implementation of this

technique can be derived. This modulation technique modulates both legs of the FB converter by means of

switching the upper (lower) IGBT of a leg simultaneously with the lower (upper) IGBT of the other leg at the

output frequency. Therefore, the output frequency results to be the same as the switching frequency. In fact, this

technique is the well-known Bipolar modulation technique. The main waveforms for the positive half cycle of

vdm are depicted in Figure 10.


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Figure 10. Main voltage waveforms with Bipolar modulation (line inductor symmetrically split)

640 E. GUBIA ET AL.

The Bipolar modulation with the line inductor split between the phase and the neutral conductors exhibits

excellent characteristics considering the conducted EMI. Nevertheless, it is worth to mention that a small

common mode current always flows through the ground due to:

� I

Co

mbalance in the value of the parasitic capacities C1g and C2g.

� I
mbalance in the value of the line impedances L1 and L2. The impedance of the grid takes part in this
imbalance.

� L
ack of synchronism in the switching of the two legs of the FB (imbalance in the switches behavior, delays in
the switching drivers, etc.).

These three reasons force an EMI filter to be included. In fact, the third one could lead to a high content of

electromagnetic interferences in the high frequency range, requiring a value of Lcm similar to the one required

with the UPWM modulation. Nevertheless, and considering the three reasons, the integral of the voltage across

Lcm will be always very small, and therefore the size of Lcm will be much smaller than in the UPWM technique.

As it was pointed out, the overall performance of the inverter has to include the common mode issue but also

the efficiency and the quality of the current injected into the grid. The last two characteristics are related to the

differential mode voltage. It can be noted in Figure 10 that the output frequency is equal to the switching

frequency. Therefore, to reach the same output frequency than the one obtained with the UPWM, the switching

frequency has to double. Even then, the ripple of the current injected into the grid will be higher than the one

obtained with the UPWM, as the voltage steps of vdm are of 2VPV. With regard to the efficiency, during each

switching period there are two IGBTs and two diodes modulating at the output frequency. Therefore, the

switching energy losses double those of the UPWM for the same output frequency. Concerning the conduction

losses, these will be similar. In the Bipolar technique, there are two IGBTs or two diodes conducting the output

current, that is, two semiconductors, the same as in the UPWM. Consequently, the trade-off between efficiency

and current quality reached by the Bipolar modulation technique is worse than that obtained with the UPWM.

pyright # 2007 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2007; 15:629–650

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TRANSFORMERLESS PV SYSTEM WITH THREE-LEVEL HALFBRIDGE CONVERTER

The Bipolar modulation technique with a FB converter shows excellent common mode behavior but, in

comparison with the UPWM, it shows a lower trade-off between current quality and efficiency. This has

motivated a research effort on other converters. A power converter structure that inherently generates a

non-variable common-mode voltage is the half bridge family of inverters, with two, three, or more levels.3,7,20 In

Figure 11, a transformerless PV system that includes a three-level half bridge converter is depicted. This

converter consists of four IGBT and six diodes, that is, two more diodes than the FB converter. In addition to its

excellent common mode behavior, it also shows very valuable features with regard to both the differential mode

(it offers three levels for the output voltage) and the efficiency (the switches have to withstand half the dc bus

voltage, 2VPV).

To analyze this system, new tables, equivalent to Tables I–III, have to be derived. As it can be appreciated in

Figure 11, output 2 is permanently connected to the midpoint of the PV generator voltage, while output 1

corresponds to a switching leg that modulates in order to provide control over the vdm voltage. This converter

offers three levels for the output voltage. Voltage VPV can be reached when T1 and T2 are on. In that case T3

and T4 have to be turned OFF to avoid short circuits. 0 V is reached if T2 and T3 are switched ON, and then T1

and T4 OFF. Finally, voltage�VPVappears if T3 and T4 are switched ON, being then T1 and T2 OFF. From these

considerations the possible modulation states are listed in Table IV. Tables Vand VI list the values of vdm and vtcmfor the two options in the placement of the line inductor. Table V corresponds to case in which the whole line

inductor is in the phase conductor and Table VI to the case in which the line inductor is symmetrically split in

both conductors.

When the line inductor is split between the neutral and the phase conductors (Table VI), it can be seen that

there is no way to modulate the positive and the negative half cycles of vdm without having also a variable vtcmwaveform. However, if the whole line inductor is connected to the phase conductor (Table V), it is clear that

whatever the vector is selected, the voltage vtcm remains constant and equal to VPV. This is an improvement

compared to the FB converter with the Bipolar technique, where only two levels were possible. Therefore, the

modulation technique has to be designed to achieve the best differential mode characteristics. With that aim, the

key points amounts to two. One is to generate an output voltage, vdm, with the lowest ripple and highest output

frequency to get the lowest THD in the current injected into the grid. The other one is to achieve this high output

frequency with the lowest switching frequency, in order to have as low switching losses as possible. To reduce

the vdm ripple, vectors 0 and P are used for the positive half cycle of vdm, and vectors 0 and N for the negative.

From Table IV, it can be directly concluded that during the positive half cycle of vdm T2 remains always ON and

only T1 and T3 modulate at the switching frequency. A similar situation results for the negative half cycle. The

waveforms that correspond to this modulation are shown in Figure 12.

Figure 11. Transformerless PV system with three-level half bridge converter


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Table IV. Output voltages and vectors of the three-level half bridge converter

Vector T1 T2 T3 T4 v1N v2N vdm¼ v1N� v2N

N OFF OFF ON ON 0 VPV �VPV

P ON ON OFF OFF 2VPV VPV VPV

0 OFF ON ON OFF VPV VPV 0

Table V. Main inverter voltages, three-level half bridge converter and L1¼ L (L2¼ 0)

Vector vdm vcm vs1 vtcm¼ vs1þ vcm


P VPV 3VPV/2 ��VPV/2 �VPV

0 0 VPV 0 VPV

642 E. GUBIA ET AL.

The total switching energy losses for this structure are due to the switching of one IGBT and one diode at the

output frequency and with a voltage equal to VPV. In order to achieve the same output frequency than the FB

converter modulated with UPWM, it is necessary that the switching frequency doubles the one of the FB with

UPWM. In doing so, the same switching losses will be achieved in both converters. Regarding the conduction

losses, it can be noted that in this structure the output current flows through two IGBT or one IGBT and one

diode, so the conduction losses are also similar to those of the FB structure. It can be concluded that, in a

transformerless PV system, the modulation technique described for this three-level converter with the whole line

inductor in the switching leg results in a better performance than the FB with UPWM. The output current THD

and efficiency are similar but now no varying total common mode voltage is generated.

However, the dc bus voltage has to be twice the required one with the FB topology since the amplitude of the

vdm fundamental component, imposed mainly by the grid voltage amplitude, has to be the same. This is achieved

by means of connecting in series more PVarrays or using dc/dc power stages that boost the dc bus voltage. If a

dc/dc converter is included, the configuration of the PV generator can be the same as that one used with a FB

converter. However, the energy losses in the dc/dc stage reduce the overall efficiency of the PV system.

TRANSFORMERLESS PV SYSTEM BASED ON THE FULL BRIDGE WITHAC-BYPASS CONVERTER

In Figure 13, a transformerless PV system including this conversion structure, called Highly Efficient Reliable

Inverter Concept (HERIC) inverter,16 is depicted. The power converter consists now of a FB structure with the

possibility of short-circuiting their outputs (ac-bypass) without using the FB switches. The ac-bypass is achieved

by means of transistors T5 and T6 and their diodes in anti-parallel. This converter includes six IGBTs and six

diodes, that is, two diodes and two IGBTs more than the FB converter and two IGBTs more than the three-level

half bridge converter.

Table VI. Main inverter voltages, three-level half bridge converter and L1¼ L2¼ L/2



P VPV 3VPV/2 �0 �3VPV/2

0 0 VPV 0 VPV


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Figure 12. Modulation waveforms for the three-level half bridge converter


In order to analyze the performance of this converter, the equivalent to Table I (permitted conduction states),

Table II (output voltage waveforms when the line inductor is in the phase conductor) and Table III (output

voltagewaveforms when the line inductor is split between the phase and the neutral conductors) have to be again

developed. To obtain the equivalent to Table I, it is necessary to identify the permitted conducting states of the

converter switches. In order to avoid short circuits, the forbidden combinations for the switches in the ON state

are T1–T2, T3–T4, T1–T6–T4, T3–T5–T2. Table VII lists the available states for the converter switches.

Table VII is exactly the same as Table I except for vectors 01 and 02. To evaluate the common mode behavior,

it is necessary to know the common mode voltage generated by the converter. This requires to know v1N and v2N.

Vectors 01 and 02 are a special condition of the converter because all the FB stage switches are in this case turned

OFF. Due to this, the values of v1N and v2N cannot be evaluated since the dc bus negative point is theoretically

disconnected from the converter outputs. In practice, the converter switches exhibit a stray capacitance across

theirs power terminals. This capacitance allows deducing the FB output voltage when all the FB switches are

Figure 13. Transformerless PV system with a full bridge converter with ac-bypass


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Table VII. Output voltages and vectors of the HERIC converter

Vector T1 T2 T3 T4 T5 T6 v1N v2N vdm¼ v1N� v2N

N OFF ON ON OFF OFF OFF 0 VPV �VPV

P ON OFF OFF ON OFF OFF VPV 0 VPV

0N OFF ON OFF ON OFF OFF 0 0 0

0P ON OFF ON OFF OFF OFF VPV VPV 0

01 igrid> 0 OFF OFF OFF OFF ON OFF — — 0

02 igrid< 0 OFF OFF OFF OFF OFF ON — — 0

644 E. GUBIA ET AL.

OFF. During the turn-off process the output current has to leave the FB and go into the ac-bypass. As the outputs

are short-circuited by the ac-bypass, the final voltage of v1N and v2N has to be the same. Assuming that the stray

capacitances of the FB switches are similar, the whole turn-off process of the FB will be symmetrical. Therefore

the variation of the voltage in both legs would be the same. In that case, the vcm voltage results equal to half the dc

bus, that is, VPV/2. Now, the corresponding tables for vdm and vtcm as a function of the line inductor placement

can be easily derived. Table VIII corresponds to the case in which the whole line inductor is placed in the phase

conductor, and Table IX to the case in which the line inductor is symmetrically split in both conductors.

If vectors 01 and 02 are not used, the analysis is exactly the same as the one of the FB converter. Therefore,

only the improvements that can be achieved when modulating with vectors 01 and 02 are considered. Vectors Pand 01 are selected during the positive half cycle of vdm. In this half cycle, the output current igrid is positive since

the power factor is close to 1. VectorsN and 02 are selected for generating the negative half cycle of vdm. Looking

at Tables VIII and IX, it can be directly seen that only when the line inductor is symmetrically split between the

phase and the neutral conductors this modulation strategy avoids the variation in the voltage vtcm. Therefore an

excellent performance will be achieved from the common mode point of view. From Table VII, the modulation

strategy for the converter switches can be derived. During the positive half cycle, transistors T1 and T4 drive the

flowing of the output current when vector P is applied. When applying vector 01, the output current flows

through T5 and the diode in parallel with T6. Therefore vdm shows a pulse of VPV volts. Transistor T5 can be ON

during the whole positive half cycle of vdm, since the diode in parallel with T6 prevents the bridge from being

short circuited when T1 and T4 are ON. For the negative half cycle of vdm, vectors N and 02 are used. Therefore,

Table VIII. Main inverter voltages, HERIC converter and L1¼ L (L2¼ 0)



P VPV VPV/2 ��VPV/2 �0

0N 0 0 0 0

0P 0 VPV 0 VPV

01 0 �VPV/2 0 �VPV/2

02 0 �VPV/2 0 �VPV/2

Table IX. Main inverter voltages, HERIC converter and L1¼ L2¼ L/2



P VPV VPV/2 �0 �VPV/2

0N 0 0 0 0

0P 0 VPV 0 VPV

01 0 �VPV/2 0 �VPV/2

02 0 �VPV/2 0 �VPV/2


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Figure 14. Modulation waveforms for the full bridge converter with ac-bypass


the structure operates as a three-level converter with the output frequency equal to the switching frequency and

with a total common mode voltage constant and equal to VPV/2. The main voltage waveforms for the half

positive cycle are shown in Figure 14.

In comparison with the FB converter with UPWM, the FB with ac-bypass converter has to switch at double

frequency to achieve the same output frequency and vdm waveform. In this converter two IGBTs modulate at the

output frequency but with half the dc bus voltage (VPV/2) and one diode modulates at the output frequency with

VPV. Therefore the switching losses are similar to those of the FB with UPWM for the same output frequency.

With regard to the conduction losses, the output current flows through two IGBTs or through one IGBTand one

diode, that is, two semiconductors. Therefore conduction losses will be also similar for both converters. As a

conclusion, in transformerless PV systems, the FB with ac-bypass improves the performance of the FB.

Additionally, it presents as good performance as the three-level half bridge structure but requires only half of the

dc bus voltage. As a drawback, it can be pointed out that it is the structure that requires more switches.

Finally, Table X summarizes the main theoretical results of the analysis developed along Sections 4, 5, and 6

for the PV conversion stages considered. The output frequency and the value for the line inductor are the same in

all the cases.

Table X. Summary of the analysed conversion stages

Conversion stage Line inductor

placement

Number of

switches

dc bus

voltage

Energy losses Current ripple EMI inductor

sizeConduction Switching

FBþUPWM L1¼L 8 Ref Ref Ref Ref Very high

FBþHUPWM L1¼L 8 Similar Slightly better Similar Similar Very high

FBþBPWM L1¼ L2¼ L/2 8 Similar Similar Double Double Small

Three-level half bridge L1¼L 10 Double Similar Similar Similar Small

HERIC L1¼ L2¼ L/2 12 Similar Similar Similar Similar Small


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646 E. GUBIA ET AL.

EXPERIMENTAL RESULTS

The influence of the modulation technique on the ground current is firstly shown by means of a transformerless

PV system with a FB converter modulated with the Unipolar and Bipolar modulations techniques. After that, the

performance of three commercial transformerless PV systems, including the three converters studied in this

paper, is examined.

The transformerless PV system with FB converter is a 5 kW system for connection to a 230V grid. The stray

capacitance between the PV generator CPVg and the ground is around 45 nF. The selected output frequency is

16 kHz, which means a switching frequency of 8 kHz in the case of the UPWM and 16 kHz for the Bipolar

modulation technique. The line inductor L has an inductance of 3mH and is symmetrically split between the

phase and the neutral conductors. To design the EMI filter, the cut-off frequency due to both the common mode

inductance of the filter, Lcm, and CPVg is selected to be around 4�5 kHz (almost a quarter the switching

frequency), which means a value of 25mH. The EMI filter includes also two 10 nF capacitors, Ccm, to reduce the

high frequency components of the current injected into the grid. Themagnetic core of the EMI inductor begins to

saturate with a magnetizing current of around 100mA.

Figures 15 and 16 depict the most significant waveforms obtained for each modulation technique. These

waveforms are the voltages of the FB legs, V_1N (channel 1) and V_2N (channel 2), the voltage across the

Figure 15. Common mode inductor saturation phenomena in a transformerless PV system with full bridge converter and

UPWM. Current scale: 2A/div


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Figure 16. Waveforms for the PV system with full bridge converter and Bipolar modulation. Current scale: 100mA/div


common mode inductor V_Lcm (channel 3), and the common mode current i_cm (channel 4). The voltage scale

is 250V/div for all the voltage waveforms. The current scale varies to better depict the saturation phenomenon.

To begin with the experimental study, the UPWM technique is first analyzed. It can be seen in Figure 16 that

when one of the converter outputs changes, the common mode inductor strongly limits the common mode

current rising until it becomes saturated. Once the saturation point is reached, the inductor loses its ability to

withstand the voltage and a high frequency common mode current peak of near 5A appears. To avoid this effect,

a common mode inductor is required with a higher saturation limit, which implies a much bigger size. When the

Bipolar modulation is implemented, it can be appreciated (Figure 17) that the voltage across the EMI filter

inductor is not significant and, therefore, the common mode current is almost null. The small quasi-sinusoidal

wave that can be appreciated in the common mode current is due to the imbalances described in Section 4. The

current scale is 100mA/div to appreciate more precisely the current waveform. These results are in agreement

with the analysis for the FB inverter common mode behavior.

The Bipolar technique shows the best performance with regard to the common mode behavior, but its

efficiency is lower than the one achieved by the UPWM. Any converter for a transformerless PV system has to be

evaluated considering not only the common mode behavior but also the efficiency and the output current THD.

Now, the overall performance of three commercial inverters will be examined. The main characteristics of each

inverter are listed in Table XI.


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Figure 17. Basic structure of the Sunny Boy 5000TL inverter

648 E. GUBIA ET AL.

It can be noted that all the structures combine the modulation technique and the inductor placement which

avoid the variation in the total common mode voltage vtcm. This is an example of the common mode current

importance in transformerless systems. The Kaco BluePlanet inverter includes a power stage that consists of a

FB converter with Bipolar modulation. The line inductor, of around 3mH, is split between the neutral and the

phase conductors. Its value is the highest of all the inverters, in order to lower the output current THD without

increasing the output frequency, which would imply higher switching losses. The Sunny Boy 5000TL inverter

has a three-level half bridge converter and a whole line inductor of around 2mH connected in the phase

conductor. As the voltage required by a half bridge converter is double that of the FB structure, the Sunny Boy

incorporates a previous power stage for boosting the dc boost voltage. With this option, it avoids connecting in

series more PV arrays. This stage consists of three boost converters connected in parallel (Figure 17).

The common mode behavior of the commercial inverters was tested and found that all of them offer excellent

behavior. Now, their efficiency is evaluated. The output power of a PV system is inherently variable because it

depends on the solar irradiance. It is then meaningful to evaluate the efficiency considering the conditions of

irradiation, as it is done by the European Efficiency (heuro). This parameter provides a mean to evaluate the

global efficiency of a commercial PV inverter for central Europe typical irradiation conditions. The European

Efficiency is calculated as 16:

heuro ¼ 0 � 03h5% þ 0 � 06h10% þ 0 � 13h20% þ 0 � 1h30% þ 0 � 48h50% þ 0:2h100%

The European Efficiency for each inverter in terms of the PV generator voltage is depicted in Figure 18. As the

output frequency is almost the same for the three inverters, its efficiency is very close. Since the switching losses

increase with the dc bus voltage, the inverters offer a lower efficiency when the dc bus voltage increases except

for the Sunny Boy 5000TL. The Sunny Boy 5000TL inverter is based on a half bridge three-level converter and

the dc bus voltage is always constant and close to 700V. When the PV generator voltage is lower than the dc bus

Table XI. Characteristics of three commercial inverters

Inverter Converter Line inductor placement Output

frequency

Switching

frequency

Rated dc

bus voltage

Kaco BluePlanet Full bridge

(with Bipolar modulation)

1.5mH (phase conductor) 18 kHz 18 kHz 350V

1.5mH (neutral conductor)

Sunways NT6000 Full bridge with ac-bypass

(HERIC)

1mH (phase conductor) 16 kHz 16 kHz 350V

1mH (neutral conductor)

Sunny Boy 5000TL Three-level half bridge 2mH (phase conductor) 16 kHz 16 kHz 700V


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Figure 18. European efficiency achieved by three commercial inverters


voltage, the boost converter has to elevate the voltage. For the same output power, the lower the voltage of the PV

generator is, the higher the current in the boost stage is. As a consequence, the conduction and switching losses

are higher with low voltages. As a result, the Sunny Boy 5000TL inverter efficiency increases when the PV

generator voltage increases.

CONCLUSIONS

When no transformer is included in a PV system, the common mode behavior appears as a very important issue.

As a consequence, a new scenery appears in the power conversion stage design and in the modulation strategy

selection. Both the current sources and the impedances affecting the shape and value of the common mode

currents are complicated to be identified directly from the power stage structure. In this paper, a comprehensible

model has been developed allowing the analysis of the common mode of single-phase PV systems. From this

model, it is clear that the line inductor placement together with the particular modulation technique determine

the PV inverter common mode behavior. In addition, a systematic procedure has been developed which makes it

easier to analyze the global performance (efficiency, THD of the current injected to the grid and common mode

behavior) achieved by a particular single-phase PV inverter. The procedure has been applied to examine the most

suitable modulation technique and line inductor placement for three different transformerless PV inverters. The

model and procedure developed in this paper can be used in the research on new inverters.

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Ground currents in single-phase transformerless photovoltaic systems

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