Design and Analysis of a DC/DC/AC Three Phase SolarConverter with Minimized DC Link Capacitance

B. Wittig, W.-T. Franke, F.W. FuchsInstitute of Power Electronics and Electrical Drives

Christian-Albrechts-University of Kiel, D-24143 Kiel, Germany,Phone: +49 (0) 431-880-6104, Email: bw@tf.uni-kiel.de

Keywords<<Energy storage>>, <<Photovoltaic>>, <<Converter control>>, <<Converter circuit>>,<<Renewable energy systems>>

AbstractSolar converters to feed the energy from the solar module into the AC grid consist of a DC/DC and athree phase DC/AC converter decoupled by a capacitor in the DC link which is to be minimized. A cur-rent fed instead of a voltage fed full bridge DC/DC converter is chosen and leads to a higher efficiency.Furthermore undesirable voltage spikes can be avoided by the use of this topology. This paper presentsa control concept without additional sensors to reduce the DC link capacity in solar converters and itsanalysis. Two different analytical methods to determine a minimal DC link capacity are explained. Theproposed control method to reduce the voltage deviation in the DC link can be implemented withoutadditional sensors in most of solar converter applications. It can also be adapted to other DC/AC con-verter applications like converter systems for fuel cells. Laboratory measurements confirm the simulationresults.

IntroductionThe solar energy collected by solar cells is one of the energies which is imputed as one of the mostimportant renewable energies in the future [1]. Besides the development of high powerful solar cells andsolar modules, the development of high efficient and small solar converters with a long life time becomesmore and more important. Additionally it is necessary to use the irradiated solar power efficiently asmuch as possible.In many applications the solar converter is separated into two general components. The first componentis the DC/DC converter which has the main task to ensure the required minimum DC input voltage of thesecond component, the DC/AC converter. The latter has to feed the current into the grid which here is athree phase system as used in medium power applications above 1 to 5 kW [2]. These two componentsare connected by a DC link capacitor to smooth the DC link voltage and to ensure a decoupling of thegrid side from the load side [3]. The structure in principle of this converter type is displayed in Fig. 1.A common used and low priced DC link capacitor is the aluminum-electrolytic capacitor (al-e-capacitor).The disadvantage is the limited life time of this capacitor type. Life time design has to be made carefullyto ensure the guaranteed performance [4].Film capacitors offer higher current ratings and lower power dissipation than al-e-capacitors with similarcapacitance whilst their energy density is lower [5]. Therefore it is preferable to use film capacitors witha small capacity in the DC link instead of al-e-capacitors.Compared to the al-e-capacitors the disadvantages are the low available capacitances in regard to thevolume on the market and the higher costs of high capacitances.Many different control methods which make it possible to reduce the DC link capacity in AC to ACconverters have been published and very good results have been achieved in [3], [6] and [7]. All controlmethods have been adopted in AC/DC/AC converters to feed a three phase induction motor, but none ofthem has considered a DC link of a solar converter for solar cells fed via a DC/DC converter as far as theauthors know.In this paper a simple and easy to implement control scheme is presented where it is possible to minimizethe DC link capacitance in solar converters with a DC/DC and a DC/AC converter. First the topology of

Figure 1: Principle Structure of a common medium power PV generator

the proposed solar converter is presented and measurements for verification of the theory are explained.With a given load step, an application dependent time constant and a maximum voltage deviation aminimum capacitance is calculated. Subsequently the proposed control scheme is explained and formulasfor the determination of the control parameters are derived. Finally simulation and practical results arepresented that confirm the performance of the proposed control method and show the potential of thisminimization method. The results are transferable to other DC/AC converter applications like convertersystems for fuel cells.

Solar Converter Topology and DC Link Design

Converter TopolgyThe circuit diagram of the analysed solar converter is shown in Fig. 2. The first component of the solarconverter is a current fed full bridge DC/DC converter with an internal clamping energy feedback. Incomparison to the voltage fed type this converter topology has the main advantage of a higher efficiency[8].

Figure 2: Proposed topology of the solar converter

In addition during the operation of a voltage fed full bridge converter undesirable oscillations of thereverse voltage of the output rectifiers caused by the parasitic inductivity of the transformer can appear[9], which can result in several kilovolts of overvoltage. In the current fed DC/DC converter theseoscillations are avoided by the clamping capacitor Ccl and the clamping transistor Tcl . The turn-onsignals of the clamping transistor can easily be generated by a simple logic NAND gate.A very important part of the design of the active clamping network is the choice of the clamping transistorTcl because of its anti-parallel body-diode. Choosing a transistor with a high reverse recovery charge Qrrcan lead to high voltage spikes at the turn on and turn off moments of the transistors T1−T4. Using anIGBT with a fast body diode instead of a MOSFET could result in a much better performance.The DC/AC converter, which is connected to the DC link at the input side and to the three phase grid atthe output side is a conventional three phase voltage fed DC/AC inverter. This common used topologycombines high efficiency with simple control structures. This special power circuit does not affect thegenerality of the analysis concerning the DC link capacitance.

DC Link DesignAn easy to use method to appreciate a minimal capacity of the capacitor bank is given in [10]. Thismethod of calculating a minimal capacity of the DC link capacitor depends on the expected maximuminput power step and the definition of a limit of allowed voltage deviation. A widely-used limit is a

deviation of ten percent of the DC link voltage at any step-on and step-off load response. The expectedmaximum input power step is equal to the solar panel power at the maximum power point (MPP). Thetime constant Tr stands for the control delay of the DC/DC converter and for instance a value of aboutfive to ten modulation periods is a good choice [10], [11].This method starts with the energy ∆W which is estimated as:

∆W =∫ Tr

0∆Pmax ·dt = ∆Pmax ·Tr (1)

The stored energy of the capacitor can be written as follows:

W =12·Cd ·V 2

d (2)

The variation of the stored energy in the capacitor also depends on the DC link voltage Vd , the DC linkvoltage deviation ∆Vd and the capacity Cd and can estimated as:

∆W =12·Cd · (Vd +∆Vd)2− 1

2·Cd ·V 2

d (3)

The combination of the equations (1) and (3) leads to the expression of the minimal capacity Cd,min:

Cd,min ≥Tr ·∆Pmax

(Vd∆Vd + 12 ∆V 2

d )(4)

Another method to appreciate the minimal DC link capacity is given in [11], where the exchanged energy∆W by the capacitor bank is estimated as follows:

∆W =Tr ·∆Pmax

2(5)

The voltage deviation is given by:

∆Vd =∆W

CdVd(6)

Finally this leads to another equation of the minimal capacity Cd,min:

Cd,min ≥Tr ·∆Pmax

(2 ·Vd∆Vd)(7)

Comparing the equations (4) and (7) and assuming a DC link voltage deviation ∆Vd of commonly usedten percent, it can be seen, that the appreciation of [10] delivers nearly twice the values of the minimumcapacity than the appreciation of [11].

DC/AC Converter Control

Conventional Voltage Oriented Control of the DC/AC ConverterA conventional voltage oriented control in the dq-reference frame is chosen to control the DC/AC con-verter. Thereby the regulated line currents are DC quantities in steady state. This control strategy pro-vides a fast transient response and the elimination of the steady state error [12].Fig. 3 shows the equivalent circuit of the grid connected DC/AC converter.The equations of the grid and the DC link can be expressed in the grid voltage oriented d,q-frame asfollows:

Figure 3: Equivalent circuit of the grid connected DC/AC converter in the grid voltage oriented rotating referenceframe

vd,qL = R · id,q

L +L · did,qL

dt+ jωLLid,q

L + vd,qG (8)

Cdddt

vd = id1− id2 (9)

Assuming that the DC link voltage vd is kept constant (vd = Vd,0), the decoupled continuous equationsof the DC link voltage and the line current can be written as:

ddt

iLdiLq

vd

=

−RL 0 0

0 −RL 0

32

vLdVd,0

1Cd

0 0

iLdiLq

vd

+ . . .

. . .+

1L 0 00 1

L 00 0 − 1

Cd

vLd− vGdvLq− vGq

id2

(10)

This leads to the simple decoupled and linearized line side converter system as shown in Fig. 4.

Figure 4: Decoupled and linearized line side converter system

Fig. 5 illustrates the block diagram of the proposed control structure. The current controller consists of aPI-controller with an anti-windup, which is designed for continuous mode by the ’modulus optimum’ toget a good reference reaction of the current control loop [13]. The q-component of the reference currentsignal is set to zero.The superimposed DC link voltage controller, which also consists of a PI-controller with an anti-windup,generates the reference signal of the d-component of the line current. This continuous mode voltagecontroller is designed by the ’symmetrical optimum’ to get a good disturbance reaction [13].

Figure 5: Block diagram of the control structure

Additional Feed Forward Control of the DC/AC ConverterThe conventional voltage oriented control is now expanded by a simple feed forward control to reducethe DC link voltage deviation. First of all the derivation of the feed forward control factor K f starts withthe output power PL of the solar converter, which can be written as:

PL = 3VLILcosϕ≈ 3VLIL (11)

The output power PL can also be expressed as a function of the DC/AC converter input power Pd and theefficiency factor of the DC/AC converter η1:

PL = Pd ·η1 = Vd · Id1 ·η1 (12)

With the assumption that Id1 equals Id2, the line current IL depends on the DC/DC converter outputcurrent Id2:

IL =Vdη1

3VLId2 (13)

With the knowledge of the efficiency factor η2 of the DC/DC converter the output power of the DC/DCconverter Pd can be expressed as:

Pd = Id2Vd = Pscη2 = IscVscη2 (14)

Finally a simple linear relation by the feed forward factor K f between the line current IL and the inputpower of the solar converter Psc is given in equation (15).

IL =η1η2

3VLIscVsc =

η1η2

3VLPsc = K f Psc (15)

The advantage of this kind of feed forward control is the availability of the sense signals of Isc and Uscin most of the solar converter applications in case of the MPP-tracking. There is no additional sensornecessary and the accessibility of the DC link is no problem anymore. This control method is alsotransferable to converter systems for fuel cells.A further advantage of the feed forward control by the input current Isc instead of the DC link currentId2, as described in [11], is the fact, that Isc is a DC quantity without high AC disturbances, which on thecontrary the DC link current Id2 consists of a DC part and an AC part in order of a few magnitudes of theswitching frequency of the grid side DC/AC converter. Therefore implementing a feed forward controlby the DC link current leads to the necessity of a current filter and therefore to another control delay.

Simulation and Experimental ResultsThe proposed control method is simulated and tested in the laboratory. The electrical parameters ofthe simulated system and the laboratory setup are listed in Table I. For theoretical analysis the systemwas simulated with MATLAB from Mathworks and the electrical system was modeled with Plecs fromPlexim GmbH.

Table I: Electrical parameters of the system used in simulation and laboratory

Grid voltage (phase voltage) VG 75VGrid and filter resistance R 0.5Ω

Grid and filter inductance L 4mHDC link voltage Vd 400VDC link capacitance Cd 33µFClamping Capacity Ccl 70µFRated input power Psc 2kWInput Power Step ∆Psc 1.4kWPower factor cosϕ ≈ 1Switching frequency of the dc/dc converter fs,1 20kHzSwitching frequency of the dc/ac converter fs,2 5kHz

For determination of the minimal DC link capacity equation (4) is used for following calculation. Witha voltage deviation ∆Vd of ten percent of the DC link voltage Vd , a step-on and step-off input powerresponse of ∆PSC = 1.4kW and a time constant Tr = 8 · 1/ fs,1 = 400µs, the minimal DC link capacityCd,min is about 33µF. In Fig. 7 and Fig. 8 the simulation and experimental results of the response to thestep-on and step-off input power ∆PSC are illustrated.

Figure 6: Input setup of the solar converter for simulation and experimental analysis

Instead of a solar module (PV in Fig. 2) a voltage source V0 and a resistor Ri are used at the input ofthe solar converter as shown in Fig. 6. A power step for dynamic analysis is done by a fast changing ofthe DC/DC converter duty ratio. In this way the voltage difference between V0 and Vsc across the inputresistor Ri leads to an adjustable current isc.The step-on input power response leads to a fast rise of the input current isc. The higher duty ratio of theDC/DC converter affects a longer simultaneous duty cycle of the transistors T1−T4 and therefore leadsto a drop of the input voltage Vsc of the solar converter. Due to the power step the DC link voltage Vdstarts to increase.Since the DC/DC converter duty cycle is fix and the DC link voltage starts to rise, the clamping capacitorvoltage Vcl and the solar converter input voltage Vsc are also forced to rise. This leads to an temporary

Figure 7: Simulation results of the step-on and step-off input power response a) without feed forward control, b)with feed forward control

Figure 8: Experimental results of step-on and step-off load response a) without feed forward control, b) with feedforward controlCH 1: line current (5A/div); CH 2: solar converter input current (5A/div);CH 3: DC link voltage (100V/div); CH 4: solar converter input voltage (100V/div)

decreasing voltage difference between V0 and Vsc and therefore to a temporary decreasing input currentisc, which can be seen in Fig. 8 at the channels 2, 3 and 4.At the step-off response of the input power the input current rise is affected similarly. This effect is alsobeen decreased by reducing the DC link voltage deviation.In Fig. 7 and 8 it is clearly recognizable, that the voltage deviation is much smaller in the case with thefeed forward control. Regarding the solar converter input current isc, it can be seen, that the feed forwardcontrol improves the command action of the control loop significantly.In Table II the voltage deviations in simulation and experiment are shown which verify the superiorperformance of the system with feed forward control. A relative good approximation between the sim-ulation and experimental results can be achieved in case of the voltage oriented control without feedforward control. Applying the proposed feed forward control the results at the laboratory setup differ alittle from the simulation results.The dimensioning of the minimal capacity by equation (4) has been proven to be adequate and togetherwith the feed forward control leads to an acceptable reduction of the DC link voltage deviation below tenpercent of the DC link voltage.

Table II: Simulation and Experimental Voltage Deviations

∆Vd [%] ∆Vd [V]Simulation ResultsWithout Feed Forward Control -13,5 ... +20,1 -54,1 ... +79,9With Feed Forward Control -5,6 ... +8,5 -22,0 ... +34,1

Experimental ResultsWithout Feed Forward Control -13,4 ... +18,1 -53,8 ... +72,2With Feed Forward Control -9,9 ... +8,3 -39,7 ... +33,0

ConclusionA DC/DC/AC three phase solar converter with a control method to reduce the DC link capacity has beenpresented and analysed. Firstly the solar converter topology has been introduced and the advantagesof the choice of the current fed DC/DC converter with internal clamping energy feedback have beenexplained. The determination of the minimal DC link capacity has been described and a minimizedcapacitance has been chosen. Thus a favourable film capacitor can be used. A control of the DC/DCand voltage oriented control of the DC/AC converter are designed. In addition the control of the DC/ACconverter is expanded by a simple feed forward control. This expanded control structure has been im-plemented and verified by simulation and experimental results. The results have shown an acceptableperformance when applying the control method to the system with reduced capacitance.

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