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Abstract— Photovoltaic (PV) energy generation is becoming an

increasingly prevalent means of producing clean, renewable power. PV is renewable, reliable, and domestically secure. One of the most important components of PV systems is the inverter technology that converts the direct current (DC) power output from the PV panel or array to alternating current (AC) used on both the individual end-user and centralized grid levels. The large variety of inverters share the same general goal: to allow for the most efficient and stable transfer of as much power as possible. One specific means of accomplishing this goal is the inclusion of a Maximum Power Point Tracking (MPPT) DC-DC converter. The purpose of MPPT is to ensure that the PV panel or array is always producing power as near to the knee of its I-V curve as possible. This extracts the maximum amount of power at any given time. In constantly sunny situations, there is little impact on overall performance of a particular MPPT design on the PV system, as only small voltage differences due to the particular construction of each panel effects the overall voltage outputs. However, cloud cover changes the output from a PV panel drastically with reduced solar irradiation causing the current of the solar panel to drop. It is postulated herein that the stability and quality problems created by central MPPT during periods of differing solar irradiation on various panels could be solved with a system of MPPT distributed on each panel. These would then feed collectively to a central inverter. To test these systems, a PSCAD model was developed for both centralized and distributed MPPT systems, and the solar irradiation was randomly varied. This allowed for observation of the stability and quality of the output voltage for each system.

Index Terms—Renewable Energy, Energy Efficiency, Photovoltaic, Solar Irradiation, Inverter, MPPT, Power Electronics

I. INTRODUCTION he purpose of this paper is examine the differences in efficiency, stability, and quality of various forms of power conversion for PV systems. Specifically, the

effects of varying solar irradiation over the panels in an array was observed on two separate modeled systems in order to determine which topology performed better in non-ideal conditions. To do this, two PV converter systems were modeled in the PSCAD simulation software. A PV panel model was developed, which was arranged in a 2 by 2 configuration to form a small solar array model. The DC ______________________________________________

Ansel Barchowsky, Jeffrey Parvin, Gregory Reed, Matthew Korytowski, Brandon Grainger and are with the Department of Electrical & Computer Engineering and the Power & Energy Initiative, in the Swanson School of Engineering at the University of Pittsburgh, Pittsburgh, PA 15210 USA (e-mails: reed5@pitt.edu, anb105@pitt.edu, jpp30@pitt.edu, mjk40@pitt.edu, bmg10@pitt.edu )

output from this array was converted to AC power through two different converter types. The two topologies share a common inverter design, but differ in the deployment of their MPPT systems. In the first model, which most accurately represents most industry configurations, the four panel array was connected to a central MPPT buck converter, which was fed directly into the central inverter. In the second model, each individual panel was given an MPPT buck converter and these were connected in the same configuration as the PV array in model 1. This net output was then fed into the central inverter.

In order to explore the effects of non-ideal lighting conditions on various panels in the array, a clouding model was developed. The function of this model was to randomly and unevenly lower the solar irradiance on the panels in the array. This effectively simulates a cloud or shadow passing over the panel, lowering the source current and output power accordingly. By randomly distributing such "clouds", the ability of each system to handle sudden current and voltage changes was observed. The results were compared in order to determine the proper PV converter layout for situations involving periodic shadowing on various parts of the system.

II. PHOTOVOLTAIC PANEL MODELING As a first step in modeling the converter system as a whole,

a model for the PV panel itself was developed. The purpose of this model was to accurately represent the behavior of a PV panel with equivalent circuit components. Traditionally, this has been accomplished by using a current source with an anti-parallel diode, attempting to model the I-V curve of the PV panel with two linear lines.

Figure 1: I-V curve of a PV panel, with key points marked [1]

A Comparative Study of MPPT Methods for Distributed Photovoltaic Generation

Ansel Barchowsky, Student Member, IEEE; Jeffrey P. Parvin; Gregory F. Reed Member, IEEE; Matthew J. Korytowski, Student Member, IEEE; Brandon M. Grainger, Student

Member, IEEE;

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978-1-4577-2159-5/12/$31.00 ©2011 IEEE

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These lines intersect at the VMP point shown in Figure 1, and while providing a fairly accurate representation, still leave much to be improved upon. Alternatively, a four segment model can be used to more closely model a PV module at the expense of a more complicated design. This design incorporates three diodes with increasing forward voltage drops in parallel with a current source. The two top diodes are set in parallel with two resistors. The effect of this setup is that instead of having two linear lines with one point on the real I-V curve, there are now four linear lines with three points on the I-V curve. [1]

Figure 2: Output of four-segment model of PV panel [2]

These points are as close to VMP, ½VOC, and ½ (Voc + VMP) as possible. This allows for much closer following of the real I-V curve, and a more accurate representation of the I-V characteristics of a photovoltaic array [1].

The four point model was then implemented in PSCAD. This was done by creating a component for the PV panel which contained a variable current source. This allowed for direct control of the source current, which will be discussed later. An extra shunt resistor was put in place to more accurately produce the desired voltage output.

Figure 3: PSCAD implementation of four-segment model

The resistors and diodes were scaled according to equations from the Sandia solar model so as to accurately represent the effect of a real solar panel [3]. This component was then inserted into the overall system to serve as the source for both of the developed models.

III. MAXIMUM POWER POINT TRACKING MODELING Maximum power point tracking, or MPPT, is the automatic

adjustment of the load of a photovoltaic system to achieve the maximum possible power output. PV cells have a complex relationship between current, voltage, and output power, which produces a non-linear output. This output is expressed as the current-voltage characteristic of the PV cell.

Constant fluctuations in external variables such as temperature, irradiance, and shading cause constant shifts of the I-V curve upwards and downwards. A change in temperature will have an inversely proportional effect on output voltage, and a change in irradiance will have a proportional affect on output current [4].

Figure 4: Current and voltage output with varying conditions [4]

As seen here, an increase in temperature will decrease output voltage, while a decrease in sunlight will decrease output current. This means that to maintain the MPP in instances of varying irradiance, a voltage must be found to complement the raised or lowered output current from the panel, in order to produce the maximum amount of power.

For a given I-V characteristic, with temperature and irradiance held constant, there is a single point at the knee of the curve with a current-voltage pair that produces maximum power output. A corresponding Resistance, R=V/I, is the resistance required across the terminals of the PV cell to achieve this maximum power point (MPP). The purpose of the MPPT system is to monitor the power output of the PV system and adjust the resistance to achieve maximum power as the I-V characteristic shifts with changing irradiance and temperature. MPPT systems are connected between the PV array and its load, and are comprised of a control structure which allows them to search for the max power point, as well as a way of varying the resistance across the terminals, for example by varying the duty cycle of a DC/DC converter [5].

For the model presented here, the incremental conductance of MPPT was used. The advantage of this method is over more simplistic methods, such as the Hilltop or Perturb and Disturb methods, is that it allows the array's operating point to be maintained at the MPP instead of oscillating back and forth on either side of it. Incremental conductance is able to find the MPP without a perturbation by using the incremental conductance of the PV array [6]. This is based on the fact that the slope of the PV panel’s power curve is zero at the MPP, shown below:

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This implies:

Figure 5: MPPT equations and power curve [6]

To implement the incremental conductance control method

in PSCAD , a simple DC-DC buck converter was created, with the duty cycle, D being governed by the output from the MPPT controller. The controller itself utilizes various math and logic functions of PSCAD to implement the above equations. The voltage and current from the panel or array, depending on the construction, was sent to the controller, along with the feedback reference voltage from the system. These were then processed through the implemented incremental conductance model to produce D. This duty cycle was used to govern the IGBT in the buck converter shown below, based on the fact that the voltage output varies according to . The setup is shown in Figures 6-8.

Figure 6: DC-DC buck converter for MPPT

Figure 7: Duty cycle calculation for buck converter

Figure 8: Incremental conductance calculation structure

By maintaining the voltage at the peak point of the current curve, the maximum amount of power is always being drawn from the panel model described above. Thus, when the source current is varied as described later in this paper, changing the output voltage of the panel, the duty cycle adjusts accordingly, producing the MPP. This MPPT system was employed in two different topologies in order to test the efficiency of distributed and centralized MPPT under varying levels of irradiance.

IV. INVERTER DESIGN Inverters form an essential part of any photovoltaic system,

converting the DC power output from the photovoltaic panel or array into AC power for grid distribution or local use. The general tasks that such an inverter must accomplish are twofold. They must convert, as efficiently as possible, AC power to DC power, and they must accomplish this in a way that does not expose the photovoltaic panel or array to damaging amounts of feedback from the grid connection. A wide variety of inverter designs exist, but normally contain many common components. Usually in a full H bridge setup; the transistor elements utilized in the inverter design topology can be IGBTs, MOSFETs, or JFETs.

Figure 9: Standard full H-bridge inverter [7]

They are switched at high-frequencies, ranging up to 20 kHz. This conversion is done after the MPPT converter, taking the output power from that portion of the system and converting to usable AC power. The basic premise is to use sets of transistors paired together and fired in pulses to convert the DC signal into a roughly AC response, in the form of a step function. This highly harmonic signal is then passed through inductors and capacitors in order to filter out as many of the harmonics as possible, resulting in a nearly perfect sinusoidal waveform. The AC power can be stepped up through a transformer for transmission to the grid, or can be used directly at the output voltage for local applications.

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Several key design considerations are involved in the construction of this inverter type. Especially important is the selection of a switching speed and transformer combination. Switching speeds for transistors in this type of layout can range up to the 16-20 kHz range, and as switching speeds are increased, heat losses are introduced in the silicon-based transistors which are employed in almost all current inverters [9]. Novel transistor technologies, such as SiC and GaN transistors, are being developed and show promise for lower losses at higher switching speeds, but have yet to be widely deployed in commercial models [8]. It is therefore important to find the proper switching speed for each converter design in order to maximize efficiency and reduce switching and operating losses.

A simple method for modeling one of the most common commercial inverter topologies will now be presented. The B6 bridge type three-phase inverter is used throughout industry.

Figure 10: Three phase inverter with B6 bridge and boost

converter, center tapped [9]

To create it in PSCAD, IGBTs were used. In this case, they

were connected in sets of two, a set for each phase. Their output was passed through a bank of inductors and capacitors sized to the voltage level of the system. These help remove harmonics on the output waveform of each phase. The switches themselves were controlled by sinusoidal pulse width modulation (SPWM), which utilized comparators operating between a grid frequency sine waveform and a much faster triangle carrier waveform. At the point where the carrier waveform is greater than the sine waveform, the signal governing the top switch in that set changes state. That signal is then inverted for the bottom switch in that set, such that the two are always opposite one-another.

Figure 11: Control structure for SPWM signal generator

These signals were sent to the IGBTs in the inverter bridge setup, causing them to switch at varying frequencies over time. Thus, the portions of the switch schemes with wide pulses formed the positive peaks of the sinusoidal waveform, and the portions with narrow pulses formed the negative peaks. In this way, an AC step function was generated.

Figure 12: Unfiltered inverter output for phase A

This step function was fed through a bank of inductors and capacitors in order to isolate the pure sinusoidal waveform from the unwanted harmonic components of the signal.

Figure 13: Inverter topology with filtering components

A careful balance had to be struck between attempting to create a more ideal sinusoidal form and lowering the output voltage by too large of an amount. In the end, the inductors were set at 0.00125 H and the capacitors at 12.6 µF. The resulting output of this system is a 3-phase AC waveform with very limited harmonics. In theory, a system such as this could be connected to a transformer and stepped up to a grid-level voltage for transmission, or connected directly to a bus or load for local use. In this case, it was connected directly to a load in order to simulate its effects in a local setting.

V. CENTRAL INVERTER WITH CENTRAL MPPT CONVERTER The first of two models designed for testing, the ‘central

inverter with central MPPT converter’ system takes each of the components described above and combines them into one single system. Four of the PV panel components were combined into two sets of two panels in series, which were then connected together in parallel, forming a two by two array. The output from this array was fed into the MPPT DC-DC buck converter. This in turn was connected to the inverter and passed through the filtering to produce the AC output. The complete system can be seen in Figure 14. Note that rather than modeling the four panels a one-component array, they were left as individual panels. This allowed each panel’s source current to be varied individually, as would be the case with a real-world array. In doing so, a

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comparison was created between this model and the following model with distributed MPPT, based on each systems reaction to changing irradiance. Monitors were placed on the system for the output current, voltage, and power.

VI. CENTRAL INVERTER WITH DISTRIBUTED MPPT CONVERTERS

The second of two models designed for testing, the ‘central inverter with distributed MPPT converters’ system was extremely similar to the one presented above, with one crucial difference. The central MPPT model took the four panels and connected them in a two by two array before feeding them into a central buck converter. In this second model, each panel had its own MPPT buck converter connected to its output. These outputs, already at the MPP of each individual panel, were fed together in the same series/parallel arrangement as the panels in the first model. The output from this array of MPPT controlled PV panels was then fed into the same central inverter as above. As above, this output was fed through the filtering bank of capacitors and inductors and then to a small load. The complete system can be seen in Figure 15, above. As above, each panel’s source current can be varied independently. It was predicted that because of the distributed nature of the MPPT, this system would be better suited to handling the changes in current created by the variation of the irradiance. With monitors again placed on the current, voltage and power outputs from the system, the performance of each system could be observed and compared in order to determine the more ideal performance.

VII. “CLOUD” GENERATION MODEL To drive the changes in the source current of each individual

solar panel, a “cloud” generation model was developed. This model simulated the reduction in irradiance to a PV panel under clouded or shadowed conditions by varying the source current of the panels over time. In PSCAD, this was accomplished by first creating a user-controlled weather controller. The controller allowed the user to select from four weather conditions: Sunny, Mostly Sunny, Mostly Cloudy, and Cloudy, which corresponded to the integers 4 through 1 respectively. A randomizing system was constructed, connecting an impulse generator at 1Hz to four separate random number generators, one for each PV panel. The numbers generated by these were compared with the weather index selected by the user by means of comparators. If the random number generated was greater than the weather index, a “cloud” was created for that second over the panel. Clouds took the form of a scaled reduction in the source current of the panel. The difference between the random number and the weather index was found, divided by ten, and subtracted from one. This weather factor was then multiplied by the base source current for the PV panel, reducing by a scaled factor proportional to the intensity of cloud cover at that moment. Thus, at the start of every second in the simulation, a new cloud had a chance of being generated over each of the panels, reducing their output. The result was a set of changing inputs to each system’s MPPT controls. This allowed for observation of the outputs of each system under changing irradiance, and comparison of the effectiveness of the responses of each system.

Figure 14: Topology for central MPPT system

Figure 15: Topology for distributed MPPT system

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VIII. RESULTS By applying the cloud generator to each model at different

weather indexes, the two systems were observed and compared. The output voltage for each system is shown below. The results here represent the best and worst case performance of each system – i.e., a weather index of four and a weather index of one.

Figure 16: Output voltage for central MPPT, sunny case

Figure 17: Output voltage for distributed MPPT, sunny case

Representing a weather index of four or a sunny situation, these waveforms from both systems behave almost exactly the same. They both handle the small fluctuations in source current with minimal amounts of disturbance to the system and produce even waveforms as a result. The oscillations that appear to exist in the centers of each waveform are a result of graphical limitations within the PSCAD software, and are not apparent upon closer examination of the waveform, as shown in the following section. From these two waveforms, it can be concluded that under sunny conditions, the difference between the two systems is minimal if it exists at all. Due to the increased cost of the distributed MPPT system, this makes the central MPPT system a better choice if placed in an environment where near constant sunlight is expected. In such an environment, a central MPPT system would be able to react to subtle changes in sunlight throughout the day, without negative performance issues incurred from sporadic clouding.

The next case shows each system operating at a weather index of one, or a cloudy day. In this case, each panel was almost constantly clouded to some varying extent, leading to much greater variation in the output current of each panel. The results of this situation for each system can be seen in Figures 18 and 19.

Figure 18: Output voltage for central MPPT, cloudy case

Figure 19: Output voltage for distributed MPPT, cloudy case

In these two cases, there are vastly different performance results when compared to the sunny case. Here the voltage waveform changes frequently and sometimes drastically. In Figure 18, the central MPPT system, the jumps in voltage are much greater and are not smoothed as well as in the distributed MPPT system, the output of which is shown in Figure 19. The distributed MPPT system responds better to changes in the source current of its panels, with each panel controlling its power output independently, resulting in a smoother waveform. This translates to improved system stability, as keeping a consistent output protects the other components of the system from voltage spikes. It also produces a higher quality of power, as the waveform is not oscillating over time. Additionally, the waveform in the central MPPT case appears jagged. This jaggedness does not appear in the waveform of the distributed MPPT system. A closer examination of this phenomenon can be seen in Figure 21 below:

Figure 20: Close up of cloudy case central and distributed MPPT

voltage output

As can be clearly seen here, the central MPPT system

oscillates between periods of the waveform in the cloudy case. This implies that the MPPT controller is having difficulty locating the MPP during the quick changes to the source current from the panels. The distributed MPPT controller, on the other hand, is consistently at the same voltage between periods. This is not be confused with the changes in voltage that are seen as the source current changes on the second. These waveforms are of the flat area of the output seen between 3.5 and 3.75 seconds into the simulation.

This shows that not only is the distributed MPPT better at reacting smoothly to the overall changes in output from the more varied irradiance, but also maintains a more consistent waveform, taking less time to find the MPP after a sudden change. In the cloudy case, therefore, it is clear that the distributed MPPT system is superior in terms of output quality and stability.

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IX. CONCLUSION Models for a photovoltaic panel, a MPPT controller and

DC-DC buck converter, inverter, and cloud generation were developed. Using these components, two systems were developed: the first with a centralized MPPT system and the second with MPPT systems distributed to each panel in the array. For each system, a best case and worst case weather scenario was run, varying the source current of each panel according to the output of the cloud generator model. The performance of each system was observed and compared. In the sunny weather case, both systems adjusted equally well to the small changes in source current that occurred. Thus, because of the lower cost of the centralized MPPT system, it was determined to be superior for situations in which near constant sunlight could be expected. In the cloudy weather case, the distributed MPPT system vastly outperformed the centralized MPPT system, showing a much smother reaction to the frequent sudden changes in source current, as well as a more stable waveform. From these results it was concluded that the distributed MPPT system would be better for any location that could not guarantee near constant sunlight.

X. ACKNOWLEDGEMENTS We would like to express our thanks for the number of

people and organizations that made this paper possible. Firstly, we would like to thank Emmanuel Taylor and Raghav Khanna for their invaluable advice and the huge amount of knowledge they provided us with. Additionally, we would like to thank the Mascaro Center for Sustainable Innovation at the University of Pittsburgh. Without their enthusiastic funding and support for undergraduate research, and their vision for a more sustainable planet, none of this would have been possible. In addition, funding from ABB and Commonwealth of Pennsylvania – Ben Franklin Technology Development Authority has helped to make this work possible and is greatly appreciated.

XI. REFERENCES [1] King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic Array Performance Model. [2] Campbell, R.C.; "A Circuit-based Photovoltaic Array Model for Power System Studies," Power Symposium, 2007. NAPS '07. 39th North American , pp.97-101, Sept. 30 2007-Oct. 2 2007. [3] Sandia National Laboratories. Sandia's Photovoltaic Research & Development Database. [4] Gupta, R.; Gupta, G.; Kastwar, D.; Hussain, A.; Ranjan, H.; "Modeling and design of MPPT controller for a PV module using PSCAD/EMTDC," Innovative Smart Grid Technologies Conference Europe (ISGT Europe), 2010 IEEE PES , vol., no., pp.1-6, 11-13 Oct. 2010 [5] V. Salas, E. Olias, A. Barrado, A. Lazaro, Review of the maximum power point tracking algorithms for stand-alone photovoltaic systems, Solar Energy Materials and Solar Cells, Volume 90, Issue 11, 6 July 2006, Pages 1555-1578, ISSN 0927-0248, DOI: 10.1016/j.solmat.2005.10.023. [6] Hohm, D.P.; Ropp, M.E.; "Comparative study of maximum power point tracking algorithms using an experimental, programmable, maximum power point tracking test bed," Photovoltaic Specialists Conference, 2000. Conference Record of the Twenty-Eighth IEEE , vol., no., pp.1699-1702, 2000 [7] Araujo, S.V.; Zacharias, P.; Mallwitz, R.; "Highly Efficient Single-Phase Transformerless Inverters for Grid-Connected Photovoltaic Systems," Industrial Electronics, IEEE Transactions on , vol.57, no.9, pp.3118-3128, Sept. 2010

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5345742&isnumber=5545545 [8] Guerra, Alberto and Jason Zhang. GaN Power Devices for Microinverters. Power Electronics Europe, Issue 4 2010, Page 28-31. [9] Burger, B.; Kranzer, D.; "Extreme high efficiency PV-power converters," Power Electronics and Applications, 2009. EPE '09. 13th European Conference on , vol., no., pp.1-13, 8-10 Sept. 2009 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5279115&isnumber=5278662

XII. BIOGRAPHIES Ansel Barchowsky (S’2011) is currently in his fourth year in the Electrical Engineering program at the University of Pittsburgh. He plans to pursue a concentration in electric power, as well as a certificate in nuclear power. He is also a member of the undergraduate research program at the Mascaro Center for Sustainable Innovation. He plans on beginning PhD studies in Electrical Engineering beginning in the fall of 2012. Jeffrey Parvin is a Chancellor's Scholar at the University of Pittsburgh, finishing dual Bachelor's degrees in Electrical Engineering and Economics. His current research interests include maximum power point tracking, energy harvesting, and wireless sensor networks. He is planning on continuing his education with a PhD in Electrical Engineering beginning in the fall of 2012.

Gregory F. Reed (M’1985) is the Director of the Power and Energy Initiative in the Swanson School of Engineering, Associate Director of the Center for Energy, and Associate Professor in the Electrical and Computer Engineering Department at the University of Pittsburgh. He has over 25 years of electric power industry experience, including utility, manufacturing, and consulting at Consolidated Edison Co. of NY, Mitsubishi Electric, and KEMA Inc. Reed received his B.S. in Electrical Engineering from Gannon University, Erie PA; his M. Eng. in ElectricPower Engineering from Rensselaer Polytechnic Institute, Troy NY; and his Ph.D. in Electrical Engineering from the University of Pittsburgh, Pittsburgh PA. He is a member of the IEEE Power & Energy Society and Industrial Applications Society, and a member of ASEE.

Matthew J. Korytowski (S’2006) was born in Erie, Pennsylvania. Attending the University of Pittsburgh in Pittsburgh, Pennsylvania, he received a Bachelor’s Degree in Electrical Engineering with a Concentration in Electric Power in 2009. He is pursuing a MS degree in electrical engineering also at the University of Pittsburgh. Matthew is currently focused on research in power electronics and renewable energy integration. He interned at Nayak Corporation performing work in PSCAD on power system simulations and modeling of renewable generation. Mr. Korytowski is a student member of the IEEE Power & Energy Society and the Power Electronics Society.

Brandon M. Grainger (S’2006) was born in Pittsburgh, Pennsylvania. Currently, he is finishing his Master’s degree in electrical engineering from the University of Pittsburgh with a concentration in electric power engineering and plans to further pursue his Ph.D. in electrical engineering specializing in high and medium voltage power electronic applications. From April 2008 to April 2009, Brandon interned for Mitsubishi Electric Power Products, Inc and, during the summer of 2010, with ABB Corporate Research Center in Raleigh, NC. Brandon’s research interests are in power electronic technologies including HVDC and FACTS devices, power electronic converter design, motor drives and power electronic applications suitable for renewable integration. He is a student member of the IEEE Power & Energy Society, Power Electronics Society, and Industrial Electronics Society.