GESEP – Ger cia de Especialistas e Siste as El tricos de Pot cia

Título:A grid- o e ted photo oltai s ste ith a a i u po er poi t tra ker usi g passi it - asedo trol applied i a oost o erter

Autores:CUPERTINO, A. F. ; DE RESENDE, J. T. ; PEREIRA, H. A. ; SELEME JUNIOR, S. I.Pu li ado em:

th IEEE/IAS I ter aio al Co fere e o I dustr Appli aio s INDUSCONData da pu li ação:

Citação para a versão pu li ada:CUPERTINO, A. F. ; DE RESENDE, J. T. ; PEREIRA, H. A. ; SELEME JUNIOR, S. I. . A grid- o e tedphoto oltai s ste ith a a i u po er poi t tra ker usi g passi it - ased o trol applied i a

oost o erter. I : th IEEE/IAS I ter aio al Co fere e o I dustr Appli aio s INDUSCON,, Fortaleza. . p. .

A GridConnected Photovoltaic System with a Maximum Power Point Tracker using PassivityBased

Control applied in a Boost Converter

A. F. Cupertino, J. T. de Resende, H. A. Pereira Gerência de Especialistas em Sistemas Elétricos de Potência

Universidade Federal de Viçosa Viçosa, Brasil

allan.cupertino@yahoo.com.br, resende@ufv.br, heverton.pereira@ufv.br

S. I. Seleme Júnior Programa de PósGraduação em Engenharia Elétrica

Universidade Federal de Minas Gerais Belo Horizonte, Brasil seleme@cpdee.ufmg.br

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I. INTRODUCTION

The interest in renewable energy has been driven by a combination of fuel price spikes, climate change concerns, public awareness, and advancements in renewable energy technologies [1]. In this context, the solar photovoltaic (PV) energy has gained prominence for its low environmental impact, long operating time and silent operation.

A significant growth in the installed power on solar photovoltaic systems has occurred. In 2011 its value was of 69.68 GWp, a growth of 76 % with respect to the previous year, as shown in Figure 1. More than 95% of this power is generated by gridconnected systems [2].

The European Photovoltaic Industry Association (EPIA) made a forecast for the installed power of solar photovoltaic energy considering two scenarios, as shown in Figure 2. The first scenario (Moderate) assumes rather pessimistic market behavior with no major reinforcement of existing support mechanisms, or strong decrease/limitation of existing schemes. The second scenario (PolicyDriven) assumes the continuation or introduction of adequate support mechanisms, accompanied by a strong political will consider PV as a major power source in the coming years.

Photovoltaic solar energy is a source that is subject to seasonal weather conditions. The behavior of the photovoltaic panel is something between a current source and a voltage

source such as shown in Figure 3. Furthermore, variations in the incident solar irradiance and temperature have a great impact on the generated power as illustrated in Figure 4.

In application of PVarrays connected to the grid, the voltage generated level should be as steady as possible due its interaction with an existent system. If it does not occur, a protection system can be activated in order to disconnect it from the grid [3].

Figure 1. Growth of the global PV installed power [2].

Figure 2. Forecast until 2016 for solar photovoltaic installed power [2].

2.3 2.8 4.0 5.47.0

9.515.7

22.939.5

69.7

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Inst

aled

Pow

er (

GW

p)

Year

0

100

200

300

2012 2013 2014 2015 2016

Fore

cast

(G

Wp)

Year

Moderate PolicyDriven

The authors would like to thank to CNPQ, FAPEMIG and CAPES for

their assistance and financial support.

Figure 3. Characteristics curves of a solar photovoltaic panel.

(a)

(b)

Figure 4. Effect of incident irradiance (a) and temperature (b) in I x V curves of a solar panel.

There are in the literature several studies about the performance of gridconnected photovoltaic systems. Most of their aims are:

• Control the active and reactive power injected in the grid [4], [5];

• Reduce the current harmonic distortion [5];

• Make the maximum power point tracking (MPPT) of the solar system [4], [5], [6].

There are, basically, two topologies for PV gridconnected systems, as shown in Figure 5 and described below:

• Topology 1: The photovoltaic panels are connected directly to the DC bus of the PWM inverter [5], [7], [8];

• Topology 2: The photovoltaic panels are connected in a DC chopper and after to the DC bus with one PWM inverter [4], [6], [9].

The first topology needs more solar panels connected in series and is more sensitive to significant variations in the incident irradiance. Besides, the MPPT algorithm is implemented in the control of the inverter. The second topology can be used for a small number of solar panels and allows a better control of the power.

For the control of the DC chopper, some works use proportionalintegralderivate (PID) controllers [9]. Many of these systems are nonminimum phase, making it difficult to design PID controllers. Furthermore, the use of traditional approaches in the frequency domain considers a linearization around the operation point. All these factors degrade the performance of the controller for large variations in reference values [10].

Some works propose nonlinear control techniques to improve the responses during disturbances [11]. In this context, the passivitybased control (PBC) has presented good results [12], [13], [14].

The control by passivity applied to the dynamic system is based on energy functions. This technique derives a control law allowing the plant to store less energy than it absorbs [15]. The design of PBC consists in modifying the system energy adding damping through the dissipative structure. This approach is valid for a wide range of operation and large signal stability is assured [16], [17].

The application of passivitybased control in DC converters was studied in different works: Using energy functions, Sanders proposed control laws for the PBC [18]. Furthermore, [17] added in the work of Sanders an integral action in order to eliminate the steady state errors. Finally, SiraRamirez proposed works [19], [20], in which the converters were modeled as EulerLagrange (EL) systems to which the PBC concepts were applied.

In this context, the present work shows simulation results of a gridconnected photovoltaic system with a maximum power point tracker (MPPT). A DC boost converter working as MPPT and a PWM inverter connect the system to the grid, as shown in Figure 6. The control of the boost converter is made by PBC. This technique allows obtaining a fast dynamic response and good rejection of disturbances.

(a)

(b)

Figure 5. Topologies of gridconnected solar photovoltaic systems: (a) Topology 1 and (b) Topology 2.

Figure 6. Simulated gridconnected photovoltaic system.

II. METHODOLOGY

The electrical circuit model of the solar panel used in this work is shown in Figure 7. The resistances represent the voltage drop and losses for both the current going to the load () and the reverse leakage current of the diode (), respectively. is a DC current source. In Table I, some parameters reported by solar panels manufacturers are given.

Figure 7. Model of a solar photovoltaic panel.

TABLE I. MAIN PARAMETERS OF A SOLAR PANEL

" #

Maximum Power (W) Maximum Power Voltage (V)

Maximum power current (A)

Open circuit voltage (V)

Short circuit current (A)

Temperature coefficient of (V/K)

Temperature coefficient of (A/K) The equation of the current in the solar panel is:

1 (1)

The variable is calculated as:

∆"# $$%&' (2)

Where is the current in the nominal conditions,

calculated by:

(3)

∆" " "( (T is the solar panel temperature and T* is the nominal solar panel temperature); $ e $%&' are the values of incident solar irradiance and the reference irradiance (W/m²), respectively. The variable / is the temperature coefficient of the short circuit current (A/K).

The reverse leakage current in the diode, I is:

∆"1 2345∆6# 7 8 1 (4)

is the nominal shortcircuit current, is the nominal open circuit voltage and is the coefficient of the open circuit voltage (V/K). The variable 9is the ideality constant of the diode, contained in the range1 : 9 : 1.5. Finally, = is calculated by:

= >" (5)

Where > the Boltzmann’s constant, " is the temperature of the panel (K) and is the electron charge.

An algorithm for adjusting and is proposed in [21]. The method is based on the fact that there exists only one pair ? , A for which the maximum power calculated by the IV model B is equal to the maximum experimental power from the datasheet . Using B in equation (1), one has [21]:

# CBDBD 1E (6)

The interactive process is shown in Figure 8. The initial

values of and are [21]:

FBG 0BG (7)

Figure 8. Algorithm of the method used to adjust the I x V model [21].

For the modeling of the Boost converter it will be assumed that the control strategy of the inverter guarantees that the DC bus voltage is approximately constant. According to [22] it is possible to linearize the I x V curve of the solar panel around the maximum power point. Thus, the solar panel can be modeled as a voltage source in series with a resistance. For this reason, the dynamics of the converter can be modeled as in Figure 9. The EulerLagrange model of this converter is given as: IJKL MNJ JOK PJ M1 QOJ (8)

Where:

IJ RS 00 TU ;NJ R 0 11 0U ;J C0 00 1 W E ;

PJ CP W0 E ; J RXY0 UandK RKZK[U. The variables KZ and K[ represent the inductor current and

capacitor voltage, respectively. The symbol Q represents the duty cycle.

Figure 9. Boost converter model.

The desired values for the average inductor current and average capacitor voltage are respectively the panel current and voltage on maximum power point. The vector of averaged dynamic error is defined by:

KM]O ^KZM]OK[M]O_ ^KZM]O KZ`M]OK[M]O K[`M]O_ (9)

As KM]O KM]O K`M]O withK`M]O aKZ`M]O K[`M]Ob6

the desired state, it can be obtained that: IJKL MNJ JOK PJ M1 QOJ aIJKL` MNJ JOK`b (10)

The design of the PBC consists in modifying the system

energy by adding damping through the dissipative structure [16]. This modification is accomplished through the addition, in closed loop, of a dissipative term that emulates a resistor connected in series with the inductor, denoted byZ. This strategy is denominated indirect control, or series control. The addition of the dissipative term is:

ZX RZ 00 0U (11)

and the new dissipative structure is given as:

X` CZ 00 1 W E (12)

Given a desired J` MJ ZXO, it is possible to verify

the following change in the dynamic averaged error equation: IJKL MNJ J`OK PJ M1 QOJ aIJKL` MNJ JOK` ZXKb (13)

The energy adjustment of the system is obtained doing: PJ M1 QOJ aIJKL` MNJ JOK` ZXKb 0 (14)

In this circumstance, the error equation will be:

IJKL MNJ JOK 0 (15)

The desired energy in terms of the error can be modeled

byc`:

c` 12 K6IJK e 0; ∀K g 0 (16)

c` is a Lyapunov function candidate for (15). The time derivative of (16) along the paths (15) results in: cL`M]O : K6J` K : hc`M]O i 0M∀K g 0O (17)

Where h is strictly positive and constant. The condition

(17) is ensured for (15), and satisfied if: PJ M1 QOJ aIJKL` MNJ JOK` ZXKb (18)

Accomplishing some algebraic manipulations, the result is:

jklkmKL[` P K[` KZ`T Q 1 aK[` ZMKZ KZ`O SKLZ`bXY

(19)

The equations in (19) are the expressions of the control

law. To avoid the influence of parasite elements, reference [17] proposed an integral action, as:

Q(= Q n MK[ K[`Oo]= (20)

Equation (20) gives the duty cycle of the converter for the

control of the input voltage. The variables Z and are parameters of the controller.

For the inverter modeling, a balanced threephase system is assumed, and only the positive sequence control is considered. The expressions of the active and reactive power injected to the grid are:

p 32 rr#s 32 r r# (21)

Where M , rO are the direct and quadrature components of

the grid voltage. M , rO are the direct and quadrature components of the current injected by the inverter.

Using the grid voltage angle as orientation, results in r 0. Thus, the active power is defined only by the direct axis current and the reactive power is defined by the quadrature

axis current. Therefore, it is possible to obtain an independent control law for the two axes.

A synchronism technique is necessary to connect the system to the grid, made by a Phase Locked Loop (PLL) circuit. This structure estimates the grid voltage angle for the control of the inverter. In this work a Synchronous Reference Frame – PLL (SRFPLL) was used, shown in Figure 10. The PI control is adjusted in order to obtain a fast response and good filtering.

A LCL filter was used to reduce the harmonics generated by IGBT’s switching. Its topology is shown in Figure 11. The design of this component is presented in [23]. The modulation strategy used was the sinusoidal pulsewidth modulation (SPWM).

Figure 10. SRFPLL blocks diagram.

Figure 11. LCL filter structure.

In order to write the dynamic equations of the system, it will be assumed that in the fundamental frequencyω*, the LCL filter can be approximated for a L filter whose inductance is the sum of the inductances LZ andLv. The dynamics of the grid side can be written as:

wx ∙ zx S ∙ ozxo] x (22)

Where vx is the vector of inverter output voltage, Vx is the

vector of grid voltage, ıx is the vector of filter current, S S S1 and 1. Extracting the components o and of (22), results in:

w` ∙ ` S ∙ o`o] ( ∙ S ∙ r (23)

wr ∙ r S ∙ oro] ( ∙ S ∙ ` r (24)

The terms ( ∙ S ∙ r and ( ∙ S ∙ ` are

compensated by a feedforward action. By applying the

Laplace transform to the compensated system, the transfer function of the inverter is given as:

$MO w`MO`MO wrMOrMO 1S (25)

Where the inputs are the voltages w` and wr and the

outputs are the currents ` and r. The DC bus dynamics is given as:

T oXYo] X= ` (26)

The application of the Laplace transform to (26) results in: TXY X=MO ` MO (27)

The term X=is a disturbance in the control (see Fig. 6).

It is assumed in this work that the DC bus loop is sufficiently fast, as to eliminate the perturbation term. For this reason, the DC bus transfer function will be:

$` MO XYMO` MO 1T (28)

Where the input is the current ` MO and the output, the dc

bus voltage, XY.

The control loops of the inverter are shown in Figure 12 . Externally, there is the reactive power loop that controls the power factor and the loop to regulate the DC bus voltage. The current control loops use proportional controllers and the external loops use proportionalintegral controllers. The controller gains were adjusted by the poles allocation method.

Figure 12. Control loops of the inverter.

It was simulated in ®, version , a photovoltaic system of 4.8 kWp. The solar array consists of 100 panels, in a connection of 20 panels in series and 5 blocks in parallel.

The parameters of the solar panel (model SM 48KSM, manufactured by Kyocera) are shown in Table II. The value of the resistances was calculated by the adjust algorithm, and the obtained values was:

0.1558Ω 115.0317Ω (29)

The parameters of the boost converter, of the inverter and

of the LCL filter are shown in Table III.

TABLE II. ELECTRICAL PERFORMANCE OF SM 48KSM UNDER STANDARD TEST CONDITIONS(*STC)

" $ 48 18.6 2.59 22.1 2.89 0.070/ 1.66/ *STC: Irradiance1000/[, AM1.5 spectrum, module temperature 25 °C.

TABLE III. PARAMETERS OF THE CONVERTER AND INVERTER

% & '

( 2,9> 10 kHzX 20>cK SZ 7.5 mHS 15c S' 20 µHT 330Q T' 13 µFTXY 0.2 mF ` 2.5

In a real system, it is necessary to inform the value of the

voltage and current in the maximum power point using a given algorithm. This algorithm is not presented here. For the simulations, the values of voltage and current in the maximum power point were supposed to be known. The objective here is only the fast dynamic response of the passivity based control. It must be observed that the speed of the algorithm of MPPT tends to degrade the response of the PBC controller, because of the time to stabilize the reference.

III. RESULTS

The variation of solar irradiance is shown in Figure 13. This change represents the shadow made by a cloud, for example. The three phase injected current is shown in Figure 14. It can be observed that the inverter’s control regulate the amplitude of the current in function of the generated power. Besides, as shown by Figure 15, the amplitude of the harmonics is in accordance to the !""" # $ %& !$ $ ' ()* &(IEEE Std 9292000). This fact shows the appropriate design of the LCL filter.

Figure 16 shows the variables of solar panel (voltage and current) and the DC bus voltage. The passivity based control allows the solar panel to work in the maximum power point. Thus, the fast dynamic response of the control improves the

efficiency of the generation. Figure 17 (b) shows the active and reactive power. The active power injected in the grid is very close to the generated value. The difference is due to the internal losses in the system. The reactive power oscillates around zero giving a power factor close to one.

Figure 13. Solar irradiance on solar photovoltaic panels.

Figure 14. Three phase injected currents.

Figure 15. Current harmonic spectrum in phase A.

Figure 16. Voltage and current of the solar panel and DC bus voltage.

Figure 17. Generated and injected power.

IV. CONCLUSIONS

The analysis and study of the insertion of solar photovoltaic panels in power networks is important in order to increase the market competitiveness of this source.

The presented results show that the PBC applied to the converter allows the panel to work in the maximum power point with fast dynamic response, improving the efficiency of the gridconnected system. Besides, the control of the inverter connects the system to the grid with high efficiency and with low harmonic distortion.

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ACKNOWLEDGMENT

The authors would like to thank to CNPQ, FAPEMIG and CAPES for their assistance and financial support.

REFERENCES

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[10] SIRARAMIREZ, H.; ORTEGA, R. PassivityBased Controllers for the Stabilization of DCtoDC Power Converters. 34th Conference on Decision & Control, New Orleans, p. 34713476, December 1995.

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[13] BECHERIF, M.; AYAD, M. Y.; HISSEL, D. Modelling and control study of two hybrid structures for street lighting. IEEE International Symposium on Industrial Electronics, Gdansk, p. 22152221, Junho 2011.

[14] MU, K.; MA, X.; ZHU, D. A New Nonlinear Control Strategy for ThreePhase Photovoltaic GridConnected Inverter. International Conference on Eletronic & Mechanical Engineering and Information Technology, Harbin, p. 46114614, 2011.

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[16] JELTSEMA, D.; SCHERPEN, J. M. A. Tuning of PassivityPreserving Controllers for Switched Mode Power Converters. IEEE Transactions on Automatic Control, v. 49, p. 13331334, Agosto 2004.

[17] LEYVA, R. et al. Passivitybased integral control of a boost converter for largesignal stability. IEE Proceedings. Control Theory and Applications, v. 153, p. 139146, Março 2006.

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BIOGRAPHIES

& was born in Visconde do Rio Branco, Brazil. He is student of Electrical Engineering at Federal University of Viçosa, Viçosa, Brazil. Currently is integrant of GESEP, where develop works about power electronics applied in renewable energy systems. His research interests include solar photovoltaic, wind energy, control applied on power electronics and grid integration of dispersed generation.

()*+ received M.S. degrees in electrical engineering from the Federal University of Itajubá (UNIFEI), Itajubá, Brazil, in 1994, and P.H. degree in electrical engineering from the Federal University of Uberlândia (UFU), in 1999. He is currently Professor at Federal University of Viçosa, Brazil. His research interests include modeling of electric machines, power systems and renewable energy.

#'#(. received the B.S. degree in electrical engineering from the Escola Politecnica (USP), Sao Paulo, Brazil, in 1977, the M.S. degree in electrical engineering from the Federal University of Santa Catarina, Florianópolis, Brazil, in 1985, and the Ph.D. degree in control and automation from the Institut National Polytechnique de Grenoble (INPG),Grenoble, France, in 1994. He spent a sabbatical leave with the Power Electronics Group,

University of California, Berkeley, in 2002. He is currently an Associate Professor with the Department of Electronic Engineering, Federal University of Minas Gerais, Belo Horizonte, Brazil. His research interests are electrical drives, control applied to power electrics and electromechanic systems.

, " was born in São Miguel do Anta, Brazil, in 1984. He received the B.S. degree in electrical engineering from the Federal University of Viçosa (UFV),Viçosa, Brazil, in 2007, the M.S. degree in electrical engineering from the Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil, in 2009, and currently is Ph.D. student from the Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil. He is currently an

Assistant Professor with the Department of Electric Engineering, Federal University of Viçosa, Brazil. His research interests are wind power, solar energy and power quality.