Transcript
Applications Ground Currents inSingle-phase Transformerless Photovoltaic Systems Eugenio Gubı´a* , y , Pablo Sanchis, Alfredo Ursu´a, Jesu´s Lo´pez and Luis Marroyo Department 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 tooexpensive 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 increasesits 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 PVinverter 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 N owadays, the photovoltaic (PV) energy contribution to the total energy consumed in the world is verylow, 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 iscontinuously decreasing. This can make the PV systems one of the future most important renewable energysources. 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 asan energy source. PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS Prog. Photovolt: Res. Appl. 2007; 15 :629–650Published online 4 May 2007 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/pip.761*Correspondence to: Dr Eugenio Gubı´a, Edificio Los Tejos, Dpto. Ingenieria Electrica y Electronica, Universidad Publica de Navarra,Campus Arrosadia, 31006 Pamplona, Spain. y E-mail:
[email protected] # 2007 John Wiley & Sons, Ltd. 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 thenecessary power conditioning for the electrical energy to be injected into the grid. The most expensive PVsystem element is the generator. However, both due to the research effort in the last years and the increase in theproduction of PV arrays, an appreciable decrease of the generator price per kilowatt-peak (kWp) is beingachieved. 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 atpresent. 3,4 In the future, this price might go below 1 USD due to the emerging technologies like thin-filmtechniques. 5 These improvements in the PV generator have made the inverter cost more and more important inthe PV system total price. This has motivated the research on new power conversion structures which lead to adecrease of the conversion stage cost and an increase of its efficiency. Nowadays, most of the PV systems arededicated to the residential market with typical system sizes around 2–10kW. 6 The first residential PV systemsincluded a single-phase inverter with a low frequency (LF) transformer placed between the power conversionstage and the grid. This transformer has been required by nearly all the national regulations since it guaranteesgalvanic isolation between the grid and the PV systems, thus providing personal protection. Additionally, it alsoprovides isolation between the PV system and the grid ground, so that, the common mode current resultsstronglylimited.Furthermore,itensuresthatnodirectcurrent,whichcouldsaturatethedistributiontransformer,is injected into the grid. Finally, it can be used to increase the inverter output voltage level. 7–9 However, the LFtransformers increase the weight, size and cost of the PV system, and reduce its efficiency. This has encouragedthe scientific research into other transformerless solutions.An alternativethat has been proposed isto replace the LF transformers by high frequencytransformers placedinthedcstageoftheinverter. 10–13 Withtheseconversionstructures,galvanicisolationisagainachievedbetweenthe PV generator and the grid, whereas no injection of direct current into the grid must be guaranteed by meansof the converter control strategy. 14 The high frequency transformers have a reduced weight, size, and cost.However,thepowerconversionstageismorecomplexand,additionally,novaluableimprovement isobtainedinthe global efficiency of the system. 2,15 The technology evolution has made it possible to eliminate the transformer with no impact on the systemcharacteristics as regards to personal safety and grid integration. 7 In addition, the use of a string of PVarraysallows 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-dcconverter, 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 areconsidering changing their regulations in the same direction. Therefore, it is quite likely that many of the futuregrid-connected PV systems will be transformerless. 2 Nevertheless,toevaluatetheoverallperformanceofaPVsystem,inadditiontothegridcurrentquality(THD)andsystemefficiency,thecommonmodebehaviorhastobeconsidered.Whennotransformerisused,agalvanicconnection appears betweenthePVarrays andthegrid,thatis,betweenthearraysandtheground.Therefore, thecommon 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 PVarray and the ground. 7,16 To avoid these currentsflowing into the ground, it is necessary to use power conversion stages together with appropriate modulationtechniques that generate no variable common mode voltages. The main difficulty in the analysis of thesetransformerless PV systems comes from the lack of a simple model and procedure to study theoretically thecommon mode behavior of the system. In this paper a comprehensible model is presented to analyze andunderstand the common mode issues in single-phase transformerless PV systems. In addition, this model isusefultosearchnewconversionstructuresandmodulationtechniques forsystemsofthistype.First,theproblemof the common mode in transformerless PV systems is introduced. Next, the system behavior is analyzed indetail from the common mode point of view. As a result of this analysis, a suitable model is obtained to bothidentify the converter elements participating in the ground currents and to evaluate the influence of anymodulation technique. Finally, this model is applied to the analysis of the common mode behavior of the powerconverter stages used in three commercial transformerless PV inverters. Copyright # 2007 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2007; 15 :629–650DOI: 10.1002/pip 630 E. GUBI ´ A ET AL. 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 commonmode issue in PV systems.Points ‘1’ and ‘2’ correspond to the power converter outputs. Typically, the converter is a voltage controlledsource, and therefore, a short-circuit condition appears whenever it is directly connected to other voltage sourcelike the grid. Consequently, the line inductor ( L ) is required to control the current injected into the grid. Theinverter 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 thevoltage of the PV generator, V PV , so that the operating point of the PV generatorbe always as close as possible to the MPP. On the other hand, it has to inject the energy extracted from the PVgenerator into the grid by means of injecting a sinusoidal current, i grid , with unity power factor. 17 Another aspect to be considered in grid connected PV systems is the current flowing through the connectionbetween the grid and the ground as a consequence of the normal operation of the PV system. This current hasnegativeeffects concerning the electromagnetic compatibility (EMC) and, ifit is very strong, the integrity of thesystem as well. To study both the quality of the current injected to the grid and the leakage current into theground,itisveryusefultodescribethesystembehaviorwiththehelpofthecommonmodeanddifferentialmodeconcepts.Thecommonmode of anycircuitoutput voltage isthe averagevalue ofthevoltagesbetweenthe outputsand acommon reference. For this system, it is very convenient to use the negative terminal of the dc bus, point N, asthe common reference. Therefore, the common mode voltage of the converter, v cm , is: v cm ¼ v 1N þ v 2N 2(1)The differential mode output voltage, v dm , is defined as the voltage between both converter outputs: v dm ¼ v 1N v 2N ¼ v 12 (2)From Equations (1) and (2) the voltage between the converter outputs and the N point can be expressed as: v 1N ¼ v dm 2 þ v cm v 2N ¼ v dm 2 þ v cm (3)Concerning the converter output currents, they can also be expressed in terms of their common anddifferential mode components. The common mode current at the full bridge (FB) output is defined as: i cm ¼ i 1 þ i 2 (4) Figure 1. Scheme of a single-phase PV system Copyright # 2007 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2007; 15 :629–650DOI: 10.1002/pip GROUND CURRENTS IN PV SYSTEMS 631 The differential mode current is: i dm ¼ i 1 i 2 2 (5)From Equations (4) and (5) the current at the converter outputs can be written as: i 1 ¼ i dm þ i cm 2 i 1 ¼ i dm þ i cm 2 (6)From Figure 1 and Equation (4), it is clear that the ground current corresponds to the common mode current, i cm . Therefore, i cm needs a continuous path from the ground to the converter. Concerning the differential modecomponent, it leaves one of the FB legs and returns through the other. The current flowing into the grid, if a 1:1ratio for the line transformer is considered, can be expressed in the following way: i grid ¼ i 1 ¼ i dm þ i cm 2 (7)The modelof a PV system shown inFigure 1does notincludeanypathforthegroundcurrent to flow backto theFB converter. Then, the current i cm is zero. Under these conditions, the only current injected into the gridcorresponds to the differential mode component i dm . The dynamics of this component is a function of the voltageappliedacross the lineinductor L , which can becontrolled bymeansof thevoltage v dm generated bythe converter:d i grid d t ¼ d i dm d t ¼ v dm v grid L (8)Therefore, the differential modevoltage controls the current injected into the grid. The instantaneous value of v dm depends on the voltages at the points 1 and 2. Quite often the converter consists of a set of switches andbehaves as a voltage source that can only generate discrete values of the output voltage. These values are calledoutput levels. The voltage levels that can be generated by the converter depend on its structure. The conversionstructures are then classified in two-, three- or more level converters. At present, the most commonly usedconverters 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 ( T S ), a particularsequence of the output converter levels is selected, and then a specific average value for v dm inside the V PV to V PV range can be obtained. The switching frequency ( f s ¼ 1/ T s ) is typically selected around tens of kHz forsingle-phase PV systems. As a consequence, the converter can vary the average value of v dm fast enough tocontrol the current injected into the grid, with a small high frequency ripple. To keep the current controlledduring the whole grid period, the voltage at the dc bus, V PV , has to be higher than the maximum of the gridvoltage. A minimum value for this voltage of around 350V is necessary in 230V grid systems.From the point of view of the spectral components, v dm exhibits a fundamental component at the gridfrequency and high frequency harmonics whose amplitudes are a function of the vector sequence generated bythe corresponding modulation technique. The fundamental component of the current injected into the grid, andwith it the energy injected into the grid, is controlled by means of the fundamental component of v dm . There aremultiple modulation techniques (‘sequences’) that produce the same fundamental component for v dm but withdifferent high frequency harmonics. Once the vector sequence and the grid voltage are known, the grid currentcan be directly calculated by means of Equation (8). Therefore, it is easy to evaluate the quality of themodulation 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, thelosses increase with the switching frequency and then the converter efficiency reduces. Energy losses inthe converter are due to the conduction energy losses caused by the flow of the current through the switches andthe switching energy losses caused by the turn on and off process of the switches. Therefore, when theperformance of a converter that operates with a particular modulation technique is evaluated, both features,current quality and efficiency, have to be considered. Copyright # 2007 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2007; 15 :629–650DOI: 10.1002/pip 632 E. GUBI ´ A ET AL. Till now the common mode current has not been taken into account since, apparently, no path exists for it toflow. In real PV systems, stray capacitance appears that provide electrical paths for the ground current, which isthe common mode current i cm . Certainly, the value of the common mode current is a function of the commonmodevoltage.However,thevalue of i cm cannot bedirectly deducedfrom thevalue of v cm ,since i cm isinfluencedbyothervoltagesources andelementslikethesystemparasiticelements.Figure2showsamoredetailedschemeof the PV system including the most important stray elements, modeled as capacitors and inductors, whichinfluencethegroundcurrentdynamics.Inthisfigure, C PVg representsthestraycapacitancebetweenthePVarrayand the ground. This capacitance is distributed over the PV generator surface. Some authors propose to model C PVg astwo capacitors connected tothefirstonebetweenthe positivePVgeneratorterminal andtheground,andsecond between the negative and the ground. 18 Nevertheless, modeling with just one capacitor is accuratelyenough toevaluatethe PVgeneratorinfluenceon the commonmode. Thevalue of thiscapacitor C PVg isaffectedby the installation characteristics (ground nature, humidity, connection to the converter, etc.). C 1g and C 2g represent the stray capacitances between the ground and the outputs points of the converter. Their values are afunction of the switches and the connection between them and the heat-sink, and the heat-sink to the ground. Z GcGg is the series impedance between the ground connection points of the converter and the grid. This seriesimpedance is mainly due to the ground stray inductance l GcGg . Z p and Z n are the series impedances, also mainlyinductive, of the phase and neutral conductors, respectively. Finally, C t is the stray capacitance between thetransformer windings.As it can be noted in Figure 2, the common mode current i cm can flow through the system thanks to the straycapacitances in the LF transformer. These capacitances are in the order of hundreds of picofarads and then theyexhibit a high impedance in the low and medium frequency range ( < 50kHz). As a consequence, the commonmode current associated tothe low and medium frequencyharmonicsof v cm isgoing to be strongly reduced.TheEMI filter has to filter only the high frequency components of v cm , 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 powerconverter and its modulation technique. COMMON MODE MODEL OF THE SYSTEM The voltage between the outputs of the converter and point N, v 1N , and v 2N , are imposed by the switchesmodulation sequence. Therefore, both outputs can be studied as controlled voltage sources connected to thenegative 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 issubstituted by these voltage sources, the model of Figure 3 is obtained. The line inductor has been split in two Figure 2. PV system schematic including the most significant stray elements Copyright # 2007 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2007; 15 :629–650DOI: 10.1002/pip GROUND CURRENTS IN PV SYSTEMS 633
