A Novel Topology and Control Strategy forMaximum Power Point Trackers and Multi-String

Grid-Connected PV InvertersS. Ali Khajehoddin∗, Alireza Bakhshai ‡ , and Praveen Jain §

∗khajeddin@ieee.org, ‡ alireza.bakhshai@queensu.ca, § praveen.jain@queensu.caEnergy and Power Electronics Applied Research Laboratory (ePEARL)

ECE Department, Queen’s University, Kingston, Canada

Abstract— The number of grid-connected photovoltaic (PV)systems is increasing noticeably. However, the high initial cost ofsuch systems impedes their wide spread commercialization. Thispaper presents a new multi-string grid-connected converter topol-ogy and a simplified control strategy with a minimum number ofcomponents that considerably lowers the initial investment andincreases the life time of the system. The proposed system consistsof two stages. The first stage is a new robust maximum powerpoint (MPP) tracker circuit that can rapidly follow the givenreference signal of the MPP under any irradiation or temperaturecondition. This stage also decouples the output power pulsationfrom the input power generation to minimize the deviation fromthe MPP. The multi-string topology enables the circuit to extractthe maximum available power from each string independently forpartially shaded conditions. The second stage is a current sourceinverter using a modified modulation strategy to inject a currentwith minimum harmonic components into the grid at unitypower factor. Simulation results are provided to demonstratethe performance of the converter and to prove the validity of theproposed control system.

I. INTRODUCTION

Grid-connected PV systems consist of two major parts:PV arrays to convert irradiation to electrical energy, anda converter to feed the energy into the grid. The PV cellconfigurations fall into four groups, [1]: centralized, string,multi-string and AC-module and AC-cell technologies, see Fig.1(a). All approaches have advantages and disadvantages [1],[2]; and will compromise various attributes such as harmonicrejection capability, simplicity, efficiency, flexibility, reliability,safety, modularity and cost. The centralized topology is thebest for high power applications because the input powerlevel can be increased and it only utilizes one inverter whichincreases the conversion efficiency. However, the technologysuffers from severe limitations. Since there are significantamount of high voltage DC wiring between PV modulesand the inverter the system design demands expensive DCswitches and special isolations, safety and protection circuits.Due to a centralized MPPT, partial shading or any mismatchbetween the PV modules cause significant drop in the outputpower generation. For medium power applications, the mostsuitable configuration seems to be the string or multi-stringtechnologies, [3], where one or more strings of PV cells areconnected to a single inverter, Fig. 1(b). Unlike the centralizedconfiguration, this type of configuration enables independent

(a) (b)

Fig. 1. (a) PV systems categorized by different PV cell configurations andinverter types, (b) Multi-string converter configurations.

Maximum Power Point Tracking (MPPT) for all strings whichmight be installed in different sizes and orientations. This alsoincreases the overall efficiency under special circumstanceslike partial shadowing. Therefore, the topology offers theflexibility to optimize the number of strings and convertersfor the specific application power level to increase the overallefficiency and to reduce the losses.

Since the PV array characteristic is highly nonlinear, themaximum power point tracking (MPPT) of PV arrays becomesrather challenging. The MPPT systems usually consists of twoparts; an MPP tracker hardware, and an algorithm. The MPPtracker alters the input resistance of the converter seen fromthe output terminal of the PV cells that results in a change ofthe operating point. MPPT algorithms [4] calculate the bestoperating point available based on the current irradiation andtemperature of the PV cells and provide the reference point

978-1-4244-1874-9/08/$25.00 ©2008 IEEE 173

1d

pv

Cf2

i

V

Fig. 2. Maximum Power Point Tracker control circuit.

for the MPP tracker hardware.

Another MPP tracker task is to decouple the output powerpulsation from the input power generation. This pulsation isspecifically a troublesome issue in single-phase grid-connectedsystems, where the instantaneous output power oscillates attwice the grid frequency. The oscillation results in a deviationfrom the optimum operating point [2], [5]. This problem isusually resolved by a big electrolytic capacitor in the rangeof mF at the PV terminals, which in turn decreases thelifetime and increases the volume, weight and cost of theconverter. To avoid the electrolytic capacitor, authors in [6], [7]proposed auxiliary circuits which draw constant current fromthe input and generate a high DC voltage at the middle stageto supply the pulsation required at the output. Authors in [8]proposed another auxiliary circuit with a transformer and fewpassive and active components to avoid oscillation. However,such solutions are designed for low power applications, andhave complex hardware and control systems, which make theoverall system expensive.

This paper introduces a new hardware configuration anda novel control strategy which uses a minimum number ofcomponents with optimized values. The proposed topologyboth decouples the output power pulsations from the inputpower generation and independently extracts maximum avail-able power from each PV string. This circuit specifically avoidthe usage of large electrolytic capacitors, which is a majorfactor in limiting the circuit life time. A unique feature of theproposed topology is that the MPP tracker is not limited tolow-power applications. Since the PV array has a multi-stringconfiguration, all the aforementioned benefits of this topologyare inherited. Simulation results show a good robustness anddecoupling performance for medium-power systems (such asresidential applications). The proposed converter configurationis a multi-string buck-boost current source inverter in which

(a)

(b)

Fig. 3. (a) PV module current, voltage and power waveforms during threeswitching cycles, (c) MPP tracker typical output waveforms during two gridcycles.

the output voltage can be greater or smaller than the input PVmodules voltage levels which accepts a wide range of inputvoltage variations. Unlike the voltage source topologies, theproposed converter directly generates and feeds the desiredcurrent into the grid using a modified PWM technique. Thetracking capabilities and system responses for different tem-perature and irradiation are investigated through simulationsthat verify the theoretical concepts.

II. MAXIMUM POWER POINT TRACKER CIRCUIT DESIGN

AND PRINCIPLE OF OPERATION

Fig. 2 illustrates the schematic diagram of the power circuitof the proposed MPP tracker and its control strategy. Althoughthe power circuit resembles the topology of a buck converter,the proposed MPP tracker utilizes the main switch to regulatethe input capacitor voltage. Controlling the input voltageenables the converter to displace the power pulsation frominput terminal through the control, and not as traditionallydone by bulky input capacitors. It is important to note that thissubstantial removal of the input voltage oscillations stabilizesthe input operating point resulting in a high efficiency conver-sion with much smaller capacitors. With the help of any MPPtracking algorithm, this topology with its control strategy canalways absorb the maximum power available from the PV cellsindependent from the output voltage and current. This poweris delivered to the next stage and as it will be explained later,the output current and voltage of this stage are controlled andinduced by the next stage.

174

Fig. 4. The proposed grid-connected inverter with MPP tracker.

A. Dc and AC Loads

Fig. 3(a) shows a snapshot of the input voltage, currentand power waveforms. It is clear that the MPP is trackedsince during both rise time and fall time of the PV voltage,output power has a maximum. Fig. 3(b) illustrates the MPPtracker’s output power and current when a voltage source(Vinv = k + A sin ωt) is connected to the output. It can beobserved that when the output voltage increases the outputcurrent tends to decrease to feed the constant input powerto the output. As a result, the output voltage forms the outputcurrent such that the average output power equals the extractedpower from the PV. This MPP tracker can also be used withdc load and if a resistive load is connected to the output, aslong as the induced output voltage Vout =

√PinRload, is less

than the input voltage (buck topology), the output power willbe constant for all loads.

B. Control Strategy for Maximum Power Point Tracker Circuit

The input capacitor voltage control can be briefly explainedas follows. The capacitor voltage is maintained between twoupper and lower levels. The upper level, V ref

pv , is obtainedfrom the MPPT algorithm. The lower level is calculated insuch a way that under worst conditions, i.e. MPP, the switchingfrequency and the voltage ripple do not exceed certain values.When the input capacitor voltage exceeds the upper level, themain switch turns on, and the capacitor is discharged. Theswitch remains on until the capacitor voltage hits the lowerlimit. Since the level of the input voltage is proportional to thepower generation, by controlling the input voltage the powerfed to the circuit is controlled.

To limit the switching frequency, the lower limit is not takenas a constant value. Instead it is a function of the desiredfrequency f d and the PV current level. The lower limit canbe found as follows:

Δ Q = C Δ Vpv = ipvtoff ⇒ Δ Vpv =ipv

2C1fd(1)

For C1 = 20 μF, f d = 20KHz, imaxpv = 4A , the PV

voltage variation is Δ Vpv = 5V . It is clear from (1) thatin obtaining a desired PV voltage variation, there is a tradeoff between the switching frequency and the capacitor value.Utilization factor is a parameter that indicates the loss dueto the deviation form the MPP, [2]. For example, calculationsshow that to reach %98 utilization ratio, the voltage rippleshould be less than Δ Vpv = %8.5V MPP

pv . Therefore, in thedesign procedure the optimum voltage of the PV cell at thelowest operating temperature is selected for V MPP

pv , which isthe largest possible PV output voltage. Based on this value theΔ Vpv is calculated. If the parameters are chosen in this way,the proposed control scheme satisfies Δ Vpv < %8.5V MPP

pv

for all temperatures. Besides, according to (1), when theirradiation level decreases (decrease of ipv), the Δ Vpv alsodecreases which will guarantee the aforementioned conditionfor all irradiation and temperature levels and thus, the circuitalways operates below the selected desired frequency.

III. MULTI-STRING CURRENT SOURCE INVERTER DESIGN

AND PRINCIPLE OF OPERATION

Fig. 4 demonstrates the power circuit diagram of the pro-posed multi-string inverter. The power circuit consists of twostages and two strings of PV modules. The first stage consistsof parallel MPP trackers connected to PV strings and thesecond stage is a grid-connected current source inverter. C f

and Lf form a low pass filter to eliminate the output currenthigh frequency components. To understand the principle ofoperation, first assume that the inverter is fed by a dc currentsource and it uses a Pulse Width Modulation (PWM) scheme[9] that modulates a sinusoidal reference waveform to generatesinusoidal output current. As a result of the PWM strategy thevoltage induced at the input port of the inverter will be themodulated grid voltage that is full-wave rectified. However,in Fig. 4 the inverter stage is connected to the MPP trackerwhich is not a constant current source. Thus, the input currentof the inverter changes according to the induced voltage as

175

L

dc

L

i

i

∏ ∏ ∏

( ) A

1in2peak

grid

21in

peakgrid

1in

L2P

V

P

V

P++

( ) B

2in2peak

grid

22in

peakgrid

2in

L2P

V

P

V

P++

∏

Fig. 5. Control system block diagram of the multi-string inverter.

discussed in Section II-A. As a matter of fact, the oscillationinduced in the inductor current is inevitable because, the inputpower generation is kept constant by the MPP tracker circuitbut the output power oscillates at a twice grid frequency (willbe proved in the next section) and thus, the power oscillationhas to be supplied from an energy storage component like theinductors of the MPP tracker circuits. Therefore, the PWMtechnique must be modified to generate a pure sinusoidalwaveform based on the oscillatory input current source. Todo this, first the inductor current is formulated. Then, thereference signal to the PWM modulator is modified so thatit regulates and controls the dc component of the inductorcurrent, iL, and prevents the double frequency harmoniccomponent of iL from appearing in the output ac current.

A. Inductor DC Current Regulation

Assume that the converter is lossless (Pin = P avgo ) and

the output filter energy storage is negligible. Also, at thisstage assume that there is only one PV string connected tothe circuit. Therefore, the only energy storage component isLA. As discussed in Section II, the MPP tracker circuit willextract constant power from the PV modules. Assuming thatthe inverter generates a current in phase with the grid voltage,the output power can be derived as follows:

io(t) = Io sin(ωt), vo(t) = Vo sin(ωt) ⇒

po(t) =12VoIo(1 − cos(2ωt)) ⇒

Pin = P avgo =

12π

∫ 2πω

0

po(t)dt =12VoIo (2)

At t = ± π4ω , we have po(t) = Pin, and if t ∈ (− π

4ω , π4ω ),

the input power will be greater than the output power. There-fore, for this period of time the inductor LA will be charged

from ILAmin to ILAmax:

12LAI2

LAmax − 12LAI2

LAmin =∫ π

4ω

− π4ω

(Pin − po(t))dt =Pin

ω(3)

⇒ Δ ILA =Pin

2ωLAILA

, ILA =ILAmin + ILAmax

2(4)

Since the inductor current is equal to its dc value at t=0, usinga similar procedure described above the inductor current as afunction of t can be derived as follows:

iLA(t) =√

I2

LA+

12ωLA

VoIo sin 2ωt (5)

The control concept of the inductor dc component using themodulation index can be explained as follows. By reducingthe modulation index the output current reduces temporarily.Consequently, the output power decreases and the differenceenergy will be stored in the inductor which in turn increasesits dc value. As a result, the output current increases up tothe point that the average power injected into the grid equalsthe input power. To reduce the conduction losses, the inductordc current can be simply minimized by the modulation index.Equations (4) and (5) show that the oscillation of the inductorcurrent depends on the input power, the inductor value, and theinductor dc current. Thus, as the inductor dc current decreases,Δ IL increases, which eventually results in a discontinuousmode of operation where the output current becomes distorted.To avoid this mode of operation, the minimum of the inductorcurrent should be higher than the maximum output currentbecause the output converter is a voltage boost or step downcurrent source inverter. Thus, the following inequality has tobe satisfied:

ILdc − Δ IL ≥ Io =2Pin

Vo⇒ (6)

ILdc ≥ Pin

Vo+

√P 2

in

V 2o

+Pin

2ωL(7)

Fig. 6 shows the case when the reference current is too lowand the grid current is distorted. Since the minimum possible

176

inductor current is desired, the equality is used in the controllerloop to generate a reference signal for the inductor dc current,as shown in Fig. 5. To form the feedback loop, first the dcinductor value is measured and then the error signal is fedinto a PI controller. The output of the PI controller adjusts theamplitude of the output current reference signal.

When there is more than one string connected to the circuit,the output power equals to the sum of the input powers. Thus,the output current can be decomposed into two componentscorresponding to each string (io(t) = io1(t) + io2(t)). How-ever, the charging and discharging of each inductor solelydepends on the difference between the power generated bya string and the power injected to the system from that string.Therefore, (2),(4) and (5) hold true for all string numberj, if io, po, Pin and LA are substituted by ioj, poj , Pinj andLX . If the inequality (6) is satisfied for each string for anycondition, the sum of the inductors’ currents will be largerthan the maximum output current. As a result, the controlstrategy shown in Fig. 5 regulates the dc inductor current ofall strings. One of the advantages of the proposed multi-stringtopology is that the output power oscillation is not suppliedonly by one inductor; in fact all strings contribute to thepower oscillation. As a result, with more strings, the currentoscillation on each inductor is reduced and smaller inductorscan be used. Moreover, because of smaller oscillations, (5)results in smaller dc reference for inductors’ currents whichin turn reduces the conduction losses.

B. Harmonic Cancelation Method

As shown in (5), the inductor current oscillates arounda dc value at twice the grid frequency. Conventional PWMtechniques assume a constant dc input current and thus, anyharmonic of the input source will be reflected to the modulatedoutput current. This problem can be avoided by introducing acompensation factor as shown in Fig. 5. When the oscillatoryinverter input dc current increases, the compensator decreasesthe modulation index proportionally, as shown in Fig. 7. As aresult, an increase in the dc current value is compensated by areduction in the modulation pulse width and vice versa. Thistype of compensation prevents the oscillatory harmonics fromappearing at the output current because the energy transfer tothe output will be equivalent to the case where the inductorcurrent was a constant dc with no oscillation. Fig. 6 show thatthe output current has been fully compensated and containsno harmonic component at twice the grid frequency.

IV. SIMULATION RESULTS

To demonstrate the impact of the irradiance level, inputvoltage level and partial shading on the performance of thesystem, a simulation is setup according to Table I, and theresults are shown in Fig. 7. The system is initially started withstring #2 partially shaded with %40 of the full irradiationlevel and string #1 at the full power. At t=0.2 (Sec) bothstrings are partially shaded and %15 of the full irradiationlevel is applied and the system response is obtained. At t=0.3(Sec) the temperature of the cells are increased so that the

TABLE I

SIMULATION PARAMETERS

Parameters Values

CPV 1, CPV 2 20 μFCf 2 μF

LA,LB 2000 μHLf 1000 μH

CSI fs 10 KHzFirst stage fmax

s 20 KHzGrid voltage 110 V

Grid frequency 60 HzPV String MPP 1.1KW

output voltage of the pv cells are decreased from 150V to80V, which is less than the grid voltage. At t=0.4 (Sec) bothstrings are exposed to full irradiance and it can be seen thatafter any change, the controller stabilizes the output currentfast enough. However, the maximum input power extractionis almost instantaneous which is because of the MPP trackercircuit and its fast dynamic response.

V. CONCLUSION

This paper introduces a new two stage grid-connectedphotovoltaic converter topology and control strategy. It isshown that the first stage performs both Maximum PowerPoint Tracking (MPPT) and decoupling for each string in-dependently using a minimum number of components withoptimized values. The second stage is a current source inverteremploying a modified modulation technique that injects acurrent with low total harmonic distortion into the grid. Thesimulation results verify and validates the performance of thesystem.

REFERENCES

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[7] S. B. Kjaer and F. Blaabjerg, “Design optimization of a single phaseinverter for photovoltaic applications,” Power Electronics Specialist Con-ference, PESC ’03. IEEE 34th Annual, vol. 3, pp. 1183–1190, Jun. 2003.

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Fig. 6. The effect of different sections of the proposed controller on the output grid current.

Fig. 7. Different waveforms of the proposed converter for various irradiation and pv voltage levels.

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