Grid-Connected Modeling, Control and Simulation of ... - IEEE Xplore

2011 7th International Workshop on Systems, Signal Processing and their Applications (WOSSPA)

Grid-Connected Modeling, Control and Simulation of Singlephase two-Level Photovoltaic Power Generation System Coupled to a Permanent Magnet Synchronous Motor BADOUD Abd Essalam1 and KHEMLICHE Mabrouk1 1

Automatic laboratory, Department of electrical engineering, University of Setif, Mabouda city, 19000, Algeria, [email protected], [email protected]

practically inexhaustible, and interdisciplinary research is continuously developed in order to sustain the improvement of the existing conversion technologies and the development of new ones [2]. These renewable generators are generally coupled with a system of storage ensuring availability continuously of energy. The renewable generator selected for our study is a photovoltaic field (PV) with a system of storage, storage is ensured by batteries. This System called Systems PVBatteries. An accurate PV module electrical model is presented based on the Shockley diode equation. The simple model has a photo-current current source. The second model is a model with two diodes. The method of parameter extraction and model evaluation in MS1 is demonstrated for a typical solar panel, in our case the Module SM110-24. This model is used to investigate the variation of maximum power point with temperature and insolation levels. The Bond Graph methodology provides a particularly formalism to represent the energy transformations in the heterogeneous systems because of its unifying character with respect to the various fields of physics [3], [4], [5] based on the energy exchange between under systems; it is a power transfer . It is very simple to specify on a model Bond Graph the causal relations between the signals associated with the physical magnitudes with the system. Once causality is assigned, we can derive directly from the BG of the very current causal models in the automatic. We present in this Paper, in the first time, an average model Bond Graph of photovoltaic structure, then, since our system is nonlinear, we propose to use a nonlinear technique of control which was well developed during the last decade, this technique of command allows to obtain a linear ordering of the system by holding account of all non the linearity by exploiting of advantage the approach BG in the determination of the expression of the linearizing control.

Abstract – The objective of this work is to have the results concerning the electric characterization and modeling by Bond Graph of the photovoltaic system coupled to a permanent magnet synchronous motor. The modeling of the global system components is developed with the integration of inverter with filter. The model of the solar generating subsystem is particularly developed. It is shown that this model is interesting for analyzing the dynamic behavior of the system and for designing the control strategy. The operating point of a photovoltaic generator that is connected to a permanent magnet synchronous motor is determined by the intersection point of its characteristic curves. In general, this point is not the same as the generator's maximum power point. This difference means losses in the system performance. Other point developed in this paper is presents an improved maximum power point tracking (MPPT) algorithm of a PV system under real climatic conditions. The proposed MPPT is based on the perturbation and observation (P&O) strategy and the variable step method that control the load voltage to ensure optimal operating points of a PV system. Bond Graph Modeling, Photovoltaic Keywords: system, Maximum Power Point Tracking, control, Permanent Magnet Synchronous Motor. I. INTRODUCTION In October 2010, the oil price easily exceeded 80$ per barrel due to the weak US dollar and the imbalance between the increasing demands and deficient supplies. People are paying more and more attention to seek for alternative energy sources that would suffice the modern society in the following high-oil-price era. The work in this paper is associated with some fundamental research in one of the solutions to the energy shortage, photovoltaic. Recent hike in oil prices has resulted in strong stimulation of research into renewable energy because such research can make major contributions to the diversity and security of energy supply, to the economic development and to the clean local environment [1]. Nowadays world pays growing attention to the renewable energy sources, clean and

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II. MODELING OF PHOTOVOLTAIC GENERATION A.

Mathematical-physical model To test the characteristics of PV arrays, firstly, we should establish the mathematical-physics model [6,7],

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which reflects the influence of temperature, illumination and other factors on the characteristics of PV arrays. Generally PV cells can be equivalent to the circuit shown in Fig. 1[7]. Based on the analog circuit analysis, Eq. (1) is obtained:

Using a appropriate mathematics-physical model to set up the relation between PV arrays and environmental factors [9]. ΔT = T − Tref S −1 S ref

ΔT =

I

'

V I

'

V

'

oc

' m

(5)

= (1 − cΔT ) ln ( e + bΔS )

(6)

S (1 + aΔT ) Sref

(7)

= Im

= Vm (1 − cΔT ) ln ( e + bΔS )

m

(8)

Where the coefficient a is 0.0025/0C, b is 0.5, c is 0.00288/0C. In order to distinguish the four major parameters in different conditions we definite them respectively as followed: In the standard condition: Isc_ref, Uoc_ref, Im_ref, Um_ref, Sref, Tref .While in actual testing condition: Isc, Voc, Im, Vm, S, T. and predict new condition: I'sc, V'oc, I'm, V'm, S', T'. Take the following steps we can get the characteristic of PV arrays. First, put the actual testing data into the Eq.(7)~(10) , calculate out the parameter in the standard condition I sc S ref (9) I sc _ ref = S (1 + aΔT )

Fig.1. Equivalent diagram of a Model cell statement with diode.

⎡ ⎪⎧ q (V − Rs I ) ⎪⎫ ⎤ I = I ph − I d _ I sc = I ph − I 0 ⎢ exp ⎨ ⎬ − 1⎥ ⎢⎣ ⎩⎪ AKT ⎭⎪ ⎥⎦ V + Rs I − (1) Rsh Where I is the output current of PV arrays, Iph is PV current, Io is the saturated current of the diode. V is the output voltage of PV arrays, Rs is the serial resistance of PV arrays. A is the characteristic factor of the diode. K is the Boerziman constant. T is the temperature of PV arrays. Rsh is the parallel resistance of PV arrays. ⎛ V + Rs I ⎞ Since the expression ⎜ ⎟  I ph and Rs is far ⎝ Rsh ⎠ smaller than the forward continuity resistance, Iph can be approximately equal to Isc [8]. Introduce undetermined coefficient C1 and C2 in Eq.(1) and substitute AKT / q for C1Voc , Io for C2 Isc ,it follows that, ⎛ ⎡ ⎪⎧ V ⎪⎫ ⎤ ⎞ I = I sc − ⎜1 − C1 ⎢ exp ⎨ ⎬ − 1⎥ ⎟ ⎜ ⎩⎪ C2VOC ⎭⎪ ⎦⎥ ⎟⎠ ⎣⎢ ⎝ Among ⎛ 1 − Im ⎞ ⎡ ⎪⎧ −Vm ⎪⎫⎤ C1 = ⎜ ⎟ ⎢exp ⎨ ⎬⎥ ⎪⎩ C2VOC ⎪⎭⎦⎥ ⎝ I sc ⎠ ⎣⎢

(4)

S (1 + aΔT ) Sref

= I sc

sc

(3)

Vco _ ref = I m _ ref = Vm _ ref =

Vco

(10)

(1 − cΔT ) ln ( e + bΔS ) I m Sref

(11)

S (1 + aΔT ) Vco (1 − cΔT ) ln ( e + bΔS )

(12)

Secondly, substitute the parameter above into Eq.(7) to (10) , in this way, four predictive major parameter in new environment is obtained. (13) ΔT ' = T ' − Tref

(2)

ΔS ' =

−1

⎛ V ⎞ ⎡ ⎪⎧1 − I m ⎪⎫⎤ C2 = ⎜ m − 1⎟ ⎢ln ⎨ ⎬⎥ ⎝ Voc − 1 ⎠ ⎢⎣ ⎪⎩ I sc ⎪⎭⎥⎦ A practical simplified model is established. It should be noted from the above expression that we can get the characteristics of PV arrays just with four major parameter which including short-circuit current Isc, open circuit voltage Voc , the circuit Im and voltage Vm at the max power point. Through the model we can we can assess the performance of PV arrays easily and effectively.

I

' sc

V I

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=

' oc

' m

S' −1 Sref

(

)

(

) (

(

)

I sc S ' 1 + aΔT ' S (1 + aΔT )

=

=

(14)

Voc 1 − cΔT ' ln e + bΔS '

(1 − cΔT ) ln ( e + bΔs )

I m S ' 1 + aΔT ' S (1 + aΔT )

(15)

)

(16)

(17)

V B.

' m

=

(

) (

Vm 1 − cΔT ' ln e + bΔS '

(1 − cΔT ) ln ( e + bΔS )

)

A. The mathematical model of the inverter with filter:

(18)

The topology of Grid-Connected Inverters is shown below.

Bond Graph model of the PV

The Shell SM 110-24, a typical 550W PV module, was chosen for modeling. The module has 72 series connected monocrystalline cells. The key specifications are shown in table 1. From the preceding model of the photovoltaic cell, one modeled a photovoltaic module which is composed of 72 cells connected in series. For the Bond Graph representation, the PV generator is then modeled by a flow source Sf = Iph in parallel with two resistors Rdiode and Rsh, the whole followed by a serial resistance Rs. (see figure 2).

Fig.3. The structure of inverter

L = 0.47mH , c = 20μ F , r = 0.9Ω

The transfer function of inverter: 1 1 sc Φ (s) = = 2 1 Lcs + rcs + 1 sL + r + sc

=

(19) 1

−9 2

9.4 Χ 10 s + 1.8 X 10-5 s + 1

After transform : 0.126 z + 0.122 p(z) = 2 z − 1.6606 z + 0.9087 B. Bond Graph model of the inverter with filter:

Fig.2. Bond Graph model of 72 cells (4X18) connected in series;

TABLE I Parameters for Shell SM 110-24 solar panel AT S.T.C Maximum Power Rating, Pmpp Minimum Power Rating, Pmpp Current at MPP , Impp Voltage at MPP , Vmpp

Impp = 3.142A Vmpp= 35V

Short circuit current Open Circuit Voltage , Voc The maximum tension crêt The maximum current crêt The surface of the photovoltaic module

Isc=2.5 A Voc = 35V Vm = 17.39 V Im =2.3 A S=0.351 m2

Pmpp=110W Pmin=104.5W

Fig.4. Bond Graph model of inverter with filter

III. GRID-CONNECTED PV INVERTER

IV. BATTERY MODEL

Grid-Connected Inverter not only converts the direct current generated by photovoltaic cells into alternating current but also connects with the control of the frequency, voltage, current, phase, active and reactive power, etc [10]. So the control of grid connected inverter has always been the focus of the study and the research methods are varied.

Photovoltaic charging system designs a management module specifically for the battery; with the command of CPU dominating module, the management module can take charge of charging management, supplying management, calibrating the battery power and the corresponding protection. With the charging and

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The Bond Graph model of a Permanent Magnet Synchronous motor is presented by figure 6.

discharging characteristic of lithium-ion battery, battery management module charges in phased, when the battery voltage is low, it will charge with a rate of current less than 0.1C; then open the switch to high-rate charge switch will be opened to charge with large current less than 1C; finally, it will enter the floating charging stage. Power management is mainly responsible for monitoring the battery voltage and collecting surplus electricity statistics; when the power fell to 15% and the voltage is lower than a certain threshold. The model corresponding to the battery is shown on figure 5.

Fig.6. Bond Graph model of a Permanent Magnet Synchronous motor

VI. MPPT ALGORITHME As explained previously, an MPPT controller is important for a PV system in order to increase the PV system efficiency. The principle of the proposed MPPT algorithm is to calculate the optimal reference output voltage that ensures the PV system is operated at its MPP. The implementation steps of the MPPT controller can be summarized as follows [13], [14]: Step 1: An initial reference voltage is assumed to be equal to the double of the PV open circuit voltage. Step 2: The PV voltage, the PV current and the load voltage are measured and applied to the MPPT controller as input signals. Step 3: The PV power is calculated at the sample time k as below: Ppv ( k ) = I pv( av ) ( k )V pv ( k ) (21)

Fig.5. Bond Graph model of battery

V. BOND GRAPH MODEL OF A PERMANENT MAGNET SYNCHRONOUS MOTOR For an order in tension of the synchronous motor, the complete model corresponding in the reference mark related to the rotor is obtained by considering the following vectors of state: [[11], [12]

x = [x1

[

x 3 ]T = i d

x2

[

u = [u1

]

iq

]

ΩT

f(x) =

⎡ f(x ) ⎤ ⎢ 1 ⎥ ⎢ ⎥ ⎢ f(x 2 ) ⎥ ⎢ ⎥ ⎢ f(x ) ⎥ ⎢⎣ 3 ⎥⎦

⎡g g=⎢ 1 ⎣0

=

⎡ L ⎢ − R x1 + p q x 2 x 3 ⎢ L Ld d ⎢ ⎢ ⎢ L Φ ⎢ − p d x1x 3 − R x 2 − p f x 3 ⎢ Lq Lq Lq ⎢ ⎢ ⎢ Φ ⎢ p(L d − L q ) x1x 2 + p f x 2 − f x 3 − ⎢ J J J ⎢⎣⎢

0 g2

⎡ 1 T ⎢L 0⎤ ⎢ d ⎥ =⎢ 0⎦ ⎢0 ⎣⎢

0 1 Lq

Step 4: The PV current and PV power samples are delayed by a switching period. Step 5: The PV current and PV power errors are calculated as follows: ⎪⎧ΔI = I pv ( k ) − I pv ( k − 1 ) (22) ⎨ ⎪⎩ΔP = Ppv ( k ) − Ppv ( k − 1 ) Step 6: The reference voltage Vref (k) is calculated as below: Vref ( k ) = V0 ( k ) + ΔVref , (23)

(20)

u 2 ]T = v d v q T This model is governed by: x = f(x) + gu Where the vector fields F and G are given by:

(5)

Cr J

⎤ 0⎥ ⎥ ⎥ 0⎥ ⎦⎥

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦⎥

where ΔV ref the perturbation voltage is given by ΔV ref = sin gn( ΔPΔI )V step (24) where Vstep is the perturbation step. Step 7: The load voltage error is calculated as below: ΔV0 ( k ) = V ref ( k ) − V0 ( k ) (25)

T

(6)

The load voltage error is then controlled by a PI controller to generate a required duty cycle d and a 20

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A number of discrete data points are shown on the curves in figures 8 and 9. These are points taken directly from the manufacturer’s published curves, and shows excellent correspondence to the model. The I-V characteristic from the model is shown in figure 8.

kHz fixed frequency PWM is applied to the driver of the IGBT. Step 8: The previous steps are repeated until reaching the PV optimal operating points. It is worth noting that the fixed Vstep in the P&O algorithm is changed in this work to a variable Vstep in order to improve the MPPT efficiency. Vstep is varied according to the PV power slope as follows: (i) Vstep is increased if the power slope is high; (ii) Vstep is decreased if power slope remains constant. It is concluded that the variable perturbation step method can decrease the oscillation in the PV operating points. It is important to calculate the trigger frequency of the MPPT algorithm accurately in order to allow the PV system to reach a steady state under variations of reference voltages. The trigger frequency is set to be equal to the exponential damping frequency ¾d, i.e., the magnitude of the real part of the system poles, which is given by 4 4 = (26) ts = ζwn σd Where ts is the settling time of the system, ζ the damping ratio, and !n the natural frequency. In this research, the MPPT algorithm is triggered at a frequency of 7 Hz.

Figure 8 shows the power-voltage relationship of the solar panel. The power curves are obtained from the product of the I-V curves as shown in figure 9. The maximum power obtained for an insolation of 100% can be seen from the figure to be very close to 110W. This validates the maximum power value ( Pmpp ) as stated on the solar panel data sheet.

Fig.9. P-V characteristics of the Photovoltaic system for five different levels of insolation

Fig.7. MPPT controller

C. RESULTS AND DISCUTIONS

A.

simulation results of the PV module

The output of the MS1 function is shown for various irradiation levels using different current values Fig. 8 and 9.

Fig. 10. Torque-Speed Curve of motor driven by PV System.

Fig.11. Universal Motor input Voltage Vs Current at no load

Fig. 8. Current-voltage Characteristics of the PV system.

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The main aim of this research is to develop an MPPT controller for a PV system to obtain maximum power with weather fluctuations. Bond Graph models of a PV panel, battery and a inverter with filter are introduced. A P&O strategy with the variable step method has been adopted for implementing the MPPT algorithm. REFERENCES [1] M. Arif Hasan, K. Sumathy, Photovoltaic thermal module concepts and their performance analysis: A review, Renewable and Sustainable Energy Reviews, RSER-911; No. of Pages 15, Article in press. [2] ***, Promotion and growth of renewable energy sources and systems, Final Report, European Project PROGRESS, Ctrc. No. TREN/D1/42-2005/S07.56988. http://ec.europa.eu/energy/renewables/studies/doc/renewab les/2008_03_progress.pdf, December 2009. [3] Fatma Soltani, Noureddine Debbache, Integration of Converter Losses in the Modelling of Hybrid PhotovoltaicWind Generating System, European Journal of Scientific Research ISSN 1450-216X Vol.21 No.4 (2008), pp.707718. [4] M. Vergé, D. Jaume. Modélisation structurée des systèmes avec les Bond Graphs, Editions Technip, (2004). [5] W. Borutzky, Bond graphs A Methodology for Modelling Multidisciplinary Dynamic Systems, volume FS-14 of Frontiers in Simulation, SCS Publishing House, Erlangen, San Diego, 2004, ISBN 3-936150-33-8. [6] Gnter.Ryot (1991). “PV use of solar energy”. Yu Shijie、 He Huiruo translate， Hefei University of Technology [7] Su Jianghui,Yu Shijie and Zhao Wei (2001). “An investigation on engineering analytical model of silicon cells”. Acta Energiae Solaris Sinica, Vol. 22 [8] Mehm et Akbaba ， IsaQmaber and Adel Kemal (1998). “Matching of Separately Excited DC Motors to Photovoltaic Generators for Maximum Power Output”. Solar Energy, Vol. 63, No. 6, pp.375-385. [9] Han Yu (2006). “Research and design for solar energy arrays simulation”. Zhejiang University. [10] R. Marino, S. Peresada, P. Valigi, “Adaptative inputOutput Linearizing Control of Induction Motors”. IEEE Transcations on Automatic Control, vol.38, No. 2, pp. 208-221, February 1993. [11] Thomas J. Vyncke, René K. Boel and Jan A.A. Melkebeek, « Direct Torque Control of Permanent Magnet Synchronous Motors – An Overview », 3rd IEEE Benelux Young Researchers Symposium in Electrical Power Engineering, 27-28 April 2006, GHENT, BELGIUM [12] Zhou Xuesong,Song Daichun,Ma Youjie, Cheng Deshu, Grid-connected control and simulation of single-phase two-level photovoltaic power generation system based on Repetitive control, 2010 International Conference on Measuring Technology and Mechatronics Automation. DOI 10.1109/ICMTMA.2010.307 [13] F. Liu, Y. Kang, Y. Zhang, and S. Duan. Comparison of P&O and hill climbing MPPT methods for grid-connected PV converter, IEEE Industrial Electronics and Applications, 2008, pp. 804-807. [14] A.J. Mahdi, W. H. Tang and Q.H. Wu, Improvement of a MPPT Algorithm for PV Systems and Its experimental validation, International Conference on Renewable Energies and Power Quality (ICREPQ’10) Granada (Spain), 23th to 25th March, 2010.

Fig. 12. Universal Motor input Voltage Vs Speed at no load

Fig. 13. P-V characteristics with a Load

Fig. 14. Power Vs time during battery discharge test; showing power delivered to load over time

III. CONCLUSIONS A unified method for modeling of photovoltaic systems using bond graph energy-flow modeling. This modeling technique has been developed for simulation of photovoltaic system using MS1 environment. By using the bond graph formalism it is possible to combine linear and nonlinear circuits. Our study brought on the analysis of the photovoltaic systems intended for the insulated dwelling. Generally, this study brought the element necessary for the setting in devotement: it is likely to improve very quickly and with the help of an optimal cost the productivity and living conditions of the dwelling geographically dispersed.

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