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Optimization of Integrated Power Conditioning PV Parameters Ahmed Hassan1, Ahmed Shawky1, Mohamed Orabi1, IEEE Senior Member, Jaber A. Abu Qahouq2, IEEE Senior Member, and Mohamed Z. Youssef3, IEEE Senior Member 1
2
APEARC, Aswan University, Aswan 81542, Egypt Electrical and Computer Eng. Dept., The University of Alabama, Tuscaloosa, Alabama 35487, USA 3 Bombardier Transportation, Kingston, Canada
[email protected]
Abstract - Photovoltaic systems should be managed to produce the maximum power under all operating conditions. The Manager is called Maximum Power Point Tracker MPPT. In this paper, the MPPT manager is attached into each PV cell in order to solve the problems of the PV shadow effect. The ripple correlation control algorithm has been used as the control action of the MPPT. The proposed system borderlines have been studied here. Then, the suitable operating ranges have been defined. Also, the inverse minor loop gain theorem is used to study the stability regions of the system.
Index Terms – Dc-Dc converters; Photovoltaic; Stability; Efficiency.
I.
Boost
converter;
INTRODUCTION
Renewable energy resources become the best ways to reduce the oil, gas demand and its resultant pollution. This energy comes from natural resources such as sunlight, wind, rain, tides and geothermal heat. It has not any exhaust, noise or danger on wildlife. Therefore, nowadays there is an increasing trend globally to increase the renewable resources in electricity production. Photovoltaic systems become widespread among the renewable energy systems, also, a large initial investment and limited life time span of photovoltaic array make it necessary for the customer to extract the maximum power from the PV system. In additional, the latest technologies in semiconductor physics try to optimize the PV system where, nowadays its cost reduced compared with the past and its energy go higher. This makes the PV system to be more attractive where the cost of watt per cell has been decreased. On the other hand, PV system is still facing some problems like partial shading, hotspot effect, mismatching effect, non uniform irradiation effect, and the multi peak phenomenon [1, 2]. A number of PV cells are connected in series and parallel
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to form a solar array to produce the desired voltage and current level. In the series connection when numbers of cells are connected in series. The solar array is adversely affected by non equal illumination and one of these cells is shaded where it may be shaded by neighboring construction; this condition is called partial shading [3-4]. In addition in series connection every cell carries the same current. The partial shading makes the shaded cell produce low photon current or acts as a resistor, so it will consume power instead of generating power. The power consumed in the shaded cell will appear in the form of temperature increasing. The temperature increasing can damage the cell or at least reduce its time life, this problem is called hotspot effect [6-7]. In case of series connection the systems assume that all these cells are identical, but each cell different from the other. Each cell has its own characteristic, so it has a MPP different from the other, this is the mismatching problem. In addition to the mismatching problem there is another problem produces the same action which called the non uniform irradiation problem. This problem means that each cell will receive different irradiation from the other, so its behavior will be different. Nowadays a bypass diode is used to eliminate the shaded panel by connecting in parallel with each other. The bypass diode can protect the shaded panel, but in the other hand it causes the multi peak phenomenon. The multi peak phenomenon means that the P-V characteristic curve has not one peak of power. The MPPT will see the P-V characteristic with multi peak of power. This problem confuses the MPPT operation. Figure 1 shows the I-V characteristics of the PV cell at different levels of shading [3-5]. There are two methods for overcoming the previous PV problems. The first one by eliminating the shaded cell where this decreases the non uniform factor of shading and irradiation and the other method is by controlling each cell alone with a MPPT. The first method is so easy, but it affects the system efficiency and stability. The second method is the
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haardest way, bu ut it can solve all problems of o the PV systtem byy generating po ower from the shaded cell.
Cell_1 Cell_2
Mism matching
Cell_3 Cell_4
Power
Cell_5
convertter to track thhe maximum ppower point of each cell. Where, this control ddepends on thee ripple magniitude in the PV solaar cell voltage, current and poower. Thiss paper is conncerned with the study of the system borders so that the M MPPT is achieved under all coonditions of shadingg and load chaange. This stuudy is very im mportant for selectinng the optim mum loading current for the series connecttion so the maaximum efficiency is achievved and the system can cover a large range oof irradiation. A stability study haas been done ffor the proposeed system usinng the minor loop gaiin theorem.
II. THE PROPOSED SYSTEM
Vo olt
Figure 1: P-V P curve describiing the mismatchin ng problem.
The ssystem is usingg a MPPT per cell to maximiize each cell output tthen sum the ooutput of the ccells to create the desired output voltage. Figurre 2 show thee shape of thhe proposed system consists of muulti cells, each cell connectedd to a MPPT then thee output term minals connecteed in series w with another one. In thhe proposed syystem each PV V cell is connnected to a convertter with a MPP PT in order to ttrack the maxim mum power point. T The boost connverter is usedd to boost thee input cell voltage as boosting thhis voltage is a target. The sysstem should track thhe maximum power pointt of the cell under the availablle irradiance w with variable load current. A. M MPPT Operation
Figure 2: 2 the block diagraam of the proposed system.
Power (W)
Region 1
Region 2
dP
dP dV
dV
Voltag ge (V) Fig gure 3: P-V curve of a photovoltaic cell.
The proposed system is using the seccond method by coonnecting the PV cell with h a controlled boost converrter opperating as a MPPT. Many y MPPT algorrithms have beeen prresented to exttract the maxim mum power. Ripple R correlation coontrol algorithm m [3] has been n used for controlling the bo oost
A rippple correlatioon control alggorithm [3-4] is used to producee the maximum m power from each PV cell. The MPPT algorithhm depends m mainly on the system ripplees. Figure 3 shows tthe P-V curve of the solar ccell. The maxim mum power point diivides the P-V curve into twoo regions. If thhe operating point iss in region 1, tthe voltage siggnal and the power signal increasee simultaneouusly. But if thhe operating point is in region 22, the voltage signal increases while the power signal decreas es. The system m should operaate as close as possible to the maaximum poweer point [1-3]. Figure 5 shows the algorithhms flow chaart of the riipple correlatiion control algorithhm [3].
B. C Control Circuitt Algorithm The boost converrter circuit, whhich is shownn in Fig. 4 operatess around the maximum ppower point uusing MPP tracker algorithm. Thhis algorithm iss shown in Figg. 6. First a current sensor circuit is used to sensse the inductor current and to produuce a voltage signal (VI) coorresponds to tthe inductor current.. The cell volltage is then m multiplied by the voltage signal ((VI) and produuces a voltagee signal that inndicates the
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output power of the cell. The power signal and the voltage signal are applied to two differentiator circuits in order to identify the location of the operating point on the P-V curve.
duty cycle is determined by the generated DC signal, and then applied to the power MOSFET transistors. In the case of the operating point is in region 2, the output signals of the two differentiator circuits are going to be out of phase. The output signal of the XOR circuit is logic 1. This means that the duty cycle of the signal that drives the power switches should increase in order to get closer to the maximum power point. The output signal of the PWM is not powerful enough to drive the power switches. So the output of the PWM is applied to a gate drive circuit which drives the power MOSFETs, and make sure that the two power switches will not turn on at the same time.
III.
Figure 5: The control circuit algorithm flow chart.
Figure 5: The proposed boost converter circuit.
When the system operates in region 1, the output signals of the two differentiators are in phase. The outputs of the two differentiator circuits are applied to an XOR circuit. The output of the XOR will be logic 0. This means that the duty cycle of the signal that drives the power switches should be decreased to reach the maximum power point. Then the output of the XOR circuit is applied to an integrator circuit that produces the average value of the input signal, which indicates the location of the operating point. The output signal of the XOR circuit is compared to a generated saw tooth signal in order to produce a train of pulses. Then, the
BORDER STUDY OF THE PROPOSED SYSTEM
The MPPT should track the cell maximum power under all environmental conditions employing the converter circuit. The main affected conditions on the delivered power from any PV cell are the received irradiation, temperature and loading condition. These parameters determine the actual delivered power. As the target system is a series connection for the power conditioning converters as shown in Fig. 2, thus their passing (loading) current should be the same. Note that this current is representing the current fed inverter. Therefore, this current value is designed based on the study of the borders of the system. Lower received irradiation can limit the available obtained current at the output and so limit the overall system operation. Where, it can force the proposed system to operate at defined regions. By another way, the proposed converter circuit is a boost converter to increases the output voltage. This means that the input current of the converter circuit (delivered from the cell) should be higher than the output current (load current). Therefore, the cell must deliver a current higher than the load current. On the other hand, at high load current the duty cycle cannot track the MPP especially in lower irradiation as the cell current decreases with low received irradiation. This issue called load limitation. A border studding has done for the system in order to identify the optimum load current that the system can deliver under the irradiation change. From the previous discussion it is clear that the system cannot operate in a very wide range of irradiation change with achieving MPPT. As a result the duty cycle cannot manage the converter and track the MPP under low irradiations with high load current. Figure 7 shows the duty cycle versus the load current at different irradiations. It is shown that, at high load current there is a limitation on the irradiation where the system cannot operate at lower level irradiation (e.g. at i = 4A the possibe irriadition where the and the system system can operate will equal to IR = cannot operate at lower irradiation). This limitation may
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deecrease the reliability of overall system. On the other haand, att low load curreent the irradiattion level rangee can increase but b thhis make a limiitation on the duty d cycle(e.g. at i = 1A the syystem will op perate on a wide w range of irradiation IR R= 25 50: 1000W/m m . However, the t duty cyclee range decreassed too (0.25: 0.5). This T means thee optimization of the duty cy ycle raange and the bo oost converter topology t will be b minimized. Efficiency is another imporrtant parameteer that affects the syystem border study. High effficiency meanss higher delivered poower to the loaad which is a taarget for all thee customers in the m market. Thereffore, the designer should design a high effficiency systeem with widee range of load current. This T m makes a big chaallenge to calcculate the optim mum load currrent off the proposed d system on a wide w range of irradiations leevel w with high efficiiency. Figure 8 shows the efficiency and the duuty cycle with load current att different irrad diation levels. It shows that the optimum load l current sh hould take caree of effficiency, irrad diation level an nd duty cycle. First, F at light lo oad cuurrent the duty cycle will be high h and this decays d the overrall effficiency where the boost co onverter efficieency decreasess at hiigh duty cycle. But on the oth her hand the sy ystem will operrate onn a wide range of irradiation.
Figuure 7: Duty cycle vvs. load cuurent at different irradiatioon levels.
Second, at hiigh load the efficiency of th he overall systtem w will be high. But B on the han nd there are liimitations on the irrradiation. Thiss means the opttimum value of o the load currrent m must be in betw ween to take the advantages of o high efficien ncy annd wide rangee of irradiation level. Thereefore the overrall syystem can cover a high leevel of irradiiation with high effficiency. This means for thee proposed system the optimu um vaalue of load current varies between b 1A and a 1.5A. Wheere, thhis range comb bines between high efficiency y and wide ran nge off irradiation lev vel. I_cell
Figure 8: The total efficienncy (ƞ) and the dutyy cycle (D) with thhe load current at diffferent irradiation level (IR).
To poweer switches Current sensor
G_Drive
V_cell
Multiplieer
Diffrentiator
Zo
Zin XOR
Inttegrator
Diffrentiator
Figure F 6: The block k diagram of MPP PT.
Toi i o
PWM
Gdo d ZL
iin Gdid
Gio iin
Figgure 9: The repressentation of the currrent to voltage coonverter.
io
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IV.
STABILITY STU UDY OF THE PRO OPOSED SYSTEM M
The main diffference betweeen the boarderr and the stabillity stu tudy is that the boarder lines describe the raange at which the duuty cycle can manage the system in orrder to track the m maximum poweer point. Howeever, stability study determin nes thhe defined parrameters for keeping k the system tacking the M MPPT. The PV V cell can be represented r as a current sou urce w with output imp pedance so thaat the input sou urce of the bo oost coonverter is a cu urrent source. The T load can bee represented as a a cuurrent source as a the convertter output will be connected d in seeries with the other o converterrs. As a result the converter is i a cuurrent to voltag ge converter ass mentioned in n [8]. The typee of thhe converter can c be changeed from voltag ge to current by appplying properr feedback conttrol or by forcing the output by coonnecting a voltage source which repressents the parallel coonnection of th he output. Figurre 9 shows the representation n of thhe current to vo oltage converter without inclluding the sou urce im mpedance.
fter obtaining the open loop transfer The next step aft functionn with the looad impedancee is to includee the input impedannce Z which rrepresents the P PV cell output impedance. Figure 11 shows the representationn of the currennt to voltage convertter with includding the sourcee impedance. T The same as doe in ((2), to includee the effect of the source im mpedance by replacinng the input cuurrent by; i
_
= i +
(4)
The theoreticcal formulation n derived baseed on the nam med traansfer function H and Z parameters p wh hich valid mo odel baased analytical transfer functiion. − −
=
(1)
Figure 10: T The open loop TF of the converter.
iin
(ee.g. Z is the transfer functio on from V an nd i ),
Eqquation (1) doees not include the load imped dance. To inclu ude thhe load impedance i is repllaced by (2) to get (3). =
−
(2)
Gdo d
Toi i o
Z = (JwL + R (2D − 1) + DR D −D R ) R ,R are the t on resistancces of the two MOSFETs M T=D G = −I (V + 2R + R +R ) G = I 1 Z = JwC
Zo
Zin
W Where:
_
io
+
−
+
= −
+
ZL
Zs
iinss
Gdi d
i os
Gio iin
Figure 111: The representaation of the currentt to voltage converrter including the looad and source im mpedances.
If the T TF between V
and i
is Z
= Z + T G
,
so by iincluding the input impedannce accordingg to (4) itis ( ) convertted to = , aand the otheer TFs are ( )
_
multipliied by the term m of (1 −
( ) =
(3)
Figure 10 sho ows the Transfe fer Function (T TF) block diagrram p boost converrter which inclludes i , i and a off the open loop d as input sign nals into the control. c Easier the independ dent soources are inpu uts and the dep pendant sourcees are outputs, so thhe output signals are V and V V.
).
i (s) + −
+
−
i (s) +
+
+
+
d(s)
+
(5)
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The next step after getting the open loop transfer function with the load impedance and the source impedance is to get the closed loop TF. Figure 12 shows the feedback of the converter which sensing the input voltage then comparing it with the reference voltage which comes from the MPPT to is the gain of the sensor. The error get the error signal. to get the duty signal is the input of the compensator cycle which controls the converter input voltage equal to the reference voltage. In order to get the closed loop TF, the duty cycle d(s) is replaced by ( )=(
( )
−
)
(6)
Equation (5) can be rearranged to be in the form of; ( )=
( ) + ( ) + ( )
(7)
converter and the output impedance of the PV cell. In addition these impedances can be measured experimentally using a frequency analyzer and then comparing them together to know the stability regions. V.
CONCLUSION
In this paper, a border study of a MPPT has been presented in order to know the suitable operating regions at which the duty cycle can manage the converter to do its purpose. The regions of maximum and minimum efficiency have been defined in order to select the point of optimum efficiency which can cover optimum irradiation ranges. The parameters of the stability are also defined from the stability study of the PV cell and the converter impedances. The inverse minor loop gain theorem has been used to perform the stability study in this paper.
So input voltage equation is obtained as; ( )=
( )+
( )+
(8)
The inverse minor loop gain is the suitable technique to study the stability of the system from the relation between the input and the output impedance of impedance of the converter Z the source (PV cell) [9-10]. From the previous equations the stability regions can be determined from the term (1 + Z Z ) which makes the equation undefined if it equal zero. Z The condition at which this term is equal zero is Z = and Z are equal in magnitude −1 which means that Z with 180 difference in phase.
ACKNOWLEDGMENT This work is sponsored in part by the Egyptian Science and Technology Development Funds (STDF) under STDF project # 1954 and in part by the U.S. - Egypt Science and Technology Joint Fund in cooperation with U.S. Department of Agriculture (USDA) under USDA Project # 58-3148-0204. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the funding agencies.
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[2]
[3]
[4] [5] Figure 12: The converter with the closed loop feedback. [6]
The main conclusion is that the stability regions can be determined by equations of the input impedance of the
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