[ieee 2012 first international conference on renewable energies and vehicular technology (revet) -...

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. PAMI-6, NO. 6, NOVEMBER 1984 Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images STUART GEMAN AND DONALD GEMAN Abstract-We make an analogy between images and statistical me- chanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or motecules in a lattice-like phys- ical system. The assignment of an energy function in the physical sys- tem determines its Gibbs distribution. Because of the Gibbs distribu- tion, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more conve- nient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mecha- nisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution de- fimes another (imaginary) physical system. Gradual temperature reduc- tion in the physical system isolates low energy states ("annealing"), or what is the same thing, the most probable states under the Gibbs dis- tribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel "relaxation" algo- rithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios. Index Terms-Annealing, Gibbs distribution, image restoration, line process, MAP estimate, Markov random field, relaxation, scene model- ing, spatial degradation. I. INTRODUCTION T HE restoration of degraded images is a branch of digital picture processing, closely related to image segmentation and boundary finding, and extensively studied for its evident practical importance as well as theoretical interest. An analy- sis of the major applications and procedures (model-based and otherwise) through approximately 1980 may be found in [47]. There are numerous existing models (see [341) and algorithms and the field is currently very active. Here we adopt a Bayesian approach, and introduce a "hierarchical," stochastic model for the original image, based on the Gibbs distribution, and a new restoration algorithm, based on sto- chastic relaxation and annealing, for computing the maximum a posteriori (MAP) estimate of the original image given the de- graded image. This algorithm is highly parallel and exploits the equivalence between Gibbs distributions and Markov ran- dom fields (MRF). Manuscript received October 7, 1983; revised June 11, 1984. This work was supported in part by ARO Contract DAAG-29-80-K-0006 and in part by the National Science Foundation under Grants MCS-83- 06507 and MCS-80-02940. S. Geman is with the Division of Applied Mathematics, Brown Univer- sity, Providence, RI 02912. D. Geman is with the Department of Mathematics and Statistics, Uni- versity of Massachusetts, Amherst, MA 01003. The essence of our approach to restoration is a stochastic relaxation algorithm which generates a sequence of images that converges in an appropriate sense to the MAP estimate. This sequence evolves by local (and potentially parallel) changes in pixel gray levels and in locations and orientations of boundary elements. Deterministic, iterative-improvement methods gen- erate a sequence of images that monotonically increase the posterior distribution (our "objective function"). In contrast, stochastic relaxation permits changes that decrease the pos- terior distribution as well. These are made on a random basis, the effect of which is to avoid convergence to local maxima. This should not be confused with "probabilistic relaxation" ("relaxation labeling"), which is deterministic; see Section X. The stochastic relaxation algorithm can be informally de- scribed as follows. 1) A local change is made in the image based upon the cur- rent values of pixels and boundary elements in the immediate "neighborhood." This change is random, and is generated by sampling from a local conditional probability distribution. 2) The local conditional distributions are dependent on a global control parameter T called "temperature." At low tem- peratures the local conditional distributions concentrate on states that increase the objective function, whereas at high temperatures the distribution is essentially uniform. The limit- ing cases, T= 0 and T= oo, correspond respectively to greedy algorithms (such as gradient ascent) and undirected (i.e., "purely random") changes. (High temperatures induce a loose coupling between neighboring pixels and a chaotic appearance to the image. At low temperatures the coupling is tighter and the images appear more regular.) 3) Our image restorations avoid local maxima by beginning at high temperatures where many of the stochastic changes will actually decrease the objective function. As the relaxation proceeds, temperature is gradually lowered and the process behaves increasingly like iterative improvement. (This gradual reduction of temperature simulates "annealing," a procedure by which certain chemical systems can be driven to their low energy, highly regular, states.) Our "annealing theorem" prescribes a schedule for lowering temperature which guarantees convergence to the global max- ima of the posterior distribution. In practice, this schedule may be too slow for application, and we use it only as a guide in choosing the functional form of the temperature-time de- pendence. Readers familiar with Monte Carlo methods in sta- tistical physics will recognize our stochastic relaxation algo- rithm as a "heat bath" version of the Metropolis algorithm [421. The idea of introducing temperature and simulating an- 0162-8828/84/1100-0721 $01.00 © 1984 IEEE 72 1

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Page 1: [IEEE 2012 First International Conference on Renewable Energies and Vehicular Technology (REVET) - Nabeul, Tunisia (2012.03.26-2012.03.28)] 2012 First International Conference on Renewable

ENERGY MANAGEMENT BY COORDINATION CONTROL OF DC BUS VOLTAGE IN PV HYDROGEN SYSTEM

Rihab Jallouli 1, Lotfi Krichen 2 , 1 National Engineering School of Sfax, Advanced Control and Energy Management (ACEM) BP 1173, 3038 Sfax, Tunisia,

e-mail: [email protected] 2 National Engineering School of Sfax, Advanced Control and Energy Management (ACEM) BP 1173, 3038 Sfax, Tunisia,,

e-mail: [email protected]

ABSTRACT

This study aims to the modeling and simulation of a production hybrid source. This source comprises a photovoltaic generator (PV), an alkaline water electrolyzer (ELZ), a storage gas tank, a proton exchange membrane fuel cell (PEMFC), a Super-capacitor bank (SC) and power conditioning unit (PCU) to give different system topologies. Electricity is generated by a PV generator to meet the requirements of a user load. An alkaline high pressure water electrolyzer is powered by the excess energy from the PV generator to produce hydrogen. A proton exchange membrane fuel cell (PEMFC) is used to keep the system’s reliability by working as auxiliary generator when the PV generator energy is deficient. SC bank is used to satisfy the fast load transients and smooth ripples. Power conditioning unit is appropriate for the conversion. To ensure harmony between different components, a power strategy based on PI controllers is used. Besides, detailed numerical scaled simulations are considered to test the performance of the production unit. This accurate analysis may be helpful for evaluating the viability of grid-independent renewable energy systems for remote area.

Index Terms— PV generator, fuel cell, electrolyzer, supercapacitor bank, DC bus voltage.

1. INTRODUCTION

The rising need for energy and the fossil fuel exhaustions lead to increase the price of electricity. That is why many countries search to invest on other renewable alternatives to make up this deficit. Solar radiation is considered among the most renewed renewable energy due to its availability, cleanliness, inexhaustibility and easy maintenance [1]. However, due to its highly intermittence and variation along seasons and days, it is a challenge to operate only with PV energy. To overcome this threshold, many previous studies were connected the renewable unit to a fuel cell as a generation system and an electrolyzer as a storage one [2]. Simulation results showed that PV/PEMFC/ELZ is a feasible system but not an efficient one since the delay make by the hydrogen system to meet a load request. To solve this problem, a SC module is linked to the multi source hybrid system. This device allows fast dynamic energy storage and generation and dynamic PV power fluctuations smoothing [3]. A hydrogen tank is considered

in this hybrid system to store the amount of pressurized hydrogen produced by the ELZ. To ensure harmony between the components of this hybrid system (PV/PEMFC/ELZ/SC), an adequate overall power balancing and energy strategy are necessary to coordinate the time of running of each device. The energy management must ensure not only the availability of energy when demanded but also adjusting the storage level of each energy storage system: short term storage level (SC modules) and long term storage level (hydrogen tank).

2. SYSTEM DESCRIPTION

The block diagram of the proposed hybrid unit is shown in Fig. 1. The power generation/storage devices include a PV solar system as main energy generator, a PEMFC, and an ELZ as backups for generation /storage energy, a hydrogen tank to store the produced hydrogen and a SC module as a fast term unit and energy smoother.

2012 First International Conference on Renewable Energies and Vehicular Technology

978-1-4673-1170-0/12/$31.00 ©2012 IEEE 23

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A classical load requires a smooth constant power. However, a renewable energy device can supply a fluctuant power due to variable climatic conditions. These power fluctuations can be filtered by a fast term level device such as a super-capacitor. This component is used also like a generator and a storage element, if the voltage of the super-capacitor didn’t exceed the thresholds mentioned by the manufacturer [4]. Moreover, the actual photovoltaic profile and the forecasted one are not accurately the same. This difference of energies can be generated by the PEMFC or stored in the ELZ into pressurized hydrogen if the storage pressure in the hydrogen tank isn’t too high or too low. This energy scheme is available only in the ideal case: all the storage devices work in normal norms. Therefore, if the storage levels exceed the boundaries designed by the producer, another control scheme is necessary. The energy management has to ensure the system efficiency, the power availability and adjusting the storage level in all time.

3. MODELING AND CONTROL OF THE SYSTEM COMPONENTS

3.1. Modeling and control of the PV generator

The PV generator is modeled using an empirical model. The most empirical used model is the one with a diode [5]. The output current of a PV panel is described by the following equation:

(1)

Fig.2 shows the organization of the power conditioning unit. We can see a causal link between the photovoltaic voltage Upv and the chopper’s duty ratio mpv. The control scheme is obtained by inverting this link in order to control Upv.

Figure 2. Modeling and control scheme of the PV generator

3.2 PEMFC modeling and control

A fuel cell is a power generator which takes hydrogen and oxygen as inputs to produce electricity and water as outputs. The fuel cell voltage is the combination of four pertinent voltages as:

(2)

All those voltages are well explained in [6].

Figure 1. Diagram of the hybrid system components

IL.pv_ref IC.pv_ref Upv_ref

IL.pv

Upv

Upv

Ipv

Cho

ke f

ilter

+- -

+

Cap

acito

r

++

IL.pv

Um-pv

GS Ta

PV panel

MPPT

Upv

DC bus

Im.pv

Udc

+-

Cho

pper

PI

PI

Hydrogen tank

Interface with the

load

Load demand

PV panel

SC

Electrolyzer

Fuel cell

Energy management

unit

Ipv mpv-ref

Um.pv-ref PI

mpv

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Page 3: [IEEE 2012 First International Conference on Renewable Energies and Vehicular Technology (REVET) - Nabeul, Tunisia (2012.03.26-2012.03.28)] 2012 First International Conference on Renewable

(2) Fig. 3 illustrates the modeling and control equations of a fuel cell system. We can see a causal link between the fuel cell current Ifc and the chopper’s duty ratio mfc as described in the following equations:

(3)

where is the bus voltage, is the modulated

current of the fuel cell and is the modulated voltage of a fuel cell.

Figure 3. Modeling and control scheme of the FC

3.3 Modeling and control of the super-capacitor

A super-capacitor module is used to ensure fast-dynamic energy storage for elevated power requirement. For the common energy applications, the model of Zubieta and Bonert [8] can be used. This model supposes the super-capacitor as a voltage source which has the filter current ISC as input and the voltage USC as output. It takes into account an equivalent capacitor CSC associated to a series resistor (ESR) and an equivalent parallel resistance (EPR). Fig. 4 shows the equivalent electrical circuit of a super-capacitor unit.

Figure 4. Electrical equivalent model of a SC

The output voltage of a super-capacitor is expressed as:

(4)

where is the initial value of a super-capacitor voltage. The SC bank power is obtained by associating SCs units in series and in parallel. The number of serial SCs (ns) determines the bank voltage while the number of parallel SCs (np) gives the full capacitance. The super-capacitor resistance and capacitance are given by:

(5)

(6)

The modeling of the Super capacitor bank is presented in detail as below (Fig.5). The energy supervision is detailed with the required control equations.

Figure 5. Modeling and control scheme of a SC

3.4 Modeling and control of the electrolyzer

An electrolyzer is a reversible fuel cell. This device uses water and electricity to produce hydrogen and oxygen [7]. The ELZ is modeled by its voltage expression as:

(7)

The different equations which impose the modeling and the control of an electrolyzer system are described in Fig. 6.

msc_ref

Umsc_ref

Usc_ref

Isc_ref

Udc Um-sc

Im-sc Isc

Isc

Usc DC bus

Energy manage

ment +- ++

SC

Cho

ke f

ilter

Chopper

PI

mfc

Umfc_ref

Ufc_ref

Pfc_ref

Ifc_ref

Udc Um-fc

Im-fc Ifc

Ifc

Ufc DC bus FC

PH2 PO2 TFC

Energy manag-ement

+- +

+

Cho

ke f

ilter

PI

Cho

pper

EPR

ESR

CSC

Psc_ref

25

Page 4: [IEEE 2012 First International Conference on Renewable Energies and Vehicular Technology (REVET) - Nabeul, Tunisia (2012.03.26-2012.03.28)] 2012 First International Conference on Renewable

Figure 6. Modeling and control scheme of the electrolyzer

4. ENERGY MANAGEMENT STRATEGY

The different sources are linked to the DC bus through different power converters (Fig.1) [9]. Thus, four types of sources are used in the hybrid power system: - the renewable energy system: photovoltaic generator (PV); - the fast-dynamic energy storage device: super-capacitor (SC); - the long-term energy storage units: fuel cell (FC) and an electrolyzer system (ELZ); - the load. In order to make the autonomy between the different hybrid power system elements, the modeling and the control of each source should be accurately studied, as well as the overall energy management strategies. Several control strategies have been presented for the power management of the hybrid power system in many applications. These methods are based on the evolution of the system state [10], on the neural control or the fuzzy control one [11] [12]. In this study, the energy control is ensured by the regulation of the DC bus voltage.

4.1 DC bus modeling

In the studied PV energy conversion system, all power exchanges are performed via the DC bus and have an impact on the DC bus voltage. In this hybrid power system, five energy sources are associated to the DC coupling via power converters as shown in Fig.6.

Where: : the power in the DC bus capacitor; : the power generated by the photovoltaic

generator;

: the power generated by the fuel cell system;

: the power generated/extracteded by the super capacitor;

: the power extracted by the electrolyzer; : the power extracted by the load.

So the DC-bus voltage as expressed in the following equation should be adapted with the different sources.

Figure 7. Power’s sharing in DC bus

(9)

So the instant power scale management is very significant for the stability of the system and should be well achieved to adjust the DC-bus voltage. In fact, hydrogen systems (the fuel cell and the electrolyzer) are the main energy buffers because of enough energy availability. For efficiency reasons, the fuel cell and the electrolyzer should work at different time. The operating of the fuel cell or the electrolyzer depends on the sign of However, due to their slow dynamics, fuel cell and electrolyzer are unable to response on fast energy transitions. The super-capacitors are not manufactured for a long-term energy medium because of their limited storage capacities. However, they represent a fast power

(8)

+

+

+

-

-

Ppv

Pfc

Psc

Pel

PL

Pdc

IL.el_ref

IC.el_ref Pel ref

Uel_r

IL.el

Uel

Uel

Iel

ELZ

PH2 PO2 Tel C

hoke

filte

r

Energy management

+ - PI + +

Cap

acito

r

+ - PI + +Umel_ref

IL.el

Um-el

DC bus

Im.el

Udc

mel-ref

Chopper

26

Page 5: [IEEE 2012 First International Conference on Renewable Energies and Vehicular Technology (REVET) - Nabeul, Tunisia (2012.03.26-2012.03.28)] 2012 First International Conference on Renewable

dynamic and can supply fast power peaks. They are used as backup’s power system of the fuel cell and the electrolyzer to ensure energy lack during fast transitions.

5. SIMULATION RESULTS AND DISCUSSION

The energy management strategy test should be performed for a long time range. However, because the fast dynamics of the super-capacitor ones which should

be performed in minutes or even seconds scale instantaneous power flow supply is considered for the load demand and photovoltaic power. Simulation results have been obtained using Matlab-Simulink software. To proof of the efficiency of the control strategy, radiation profile represented in Fig.8 is applied. The forecasted electrical power demand is given in Fig. 9. The measured photovoltaic power of the generator is depicted in Fig. 10.

0 50 100 150 200 250 3000

100

200

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400

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1000

Time (s)

Gs

(W/m

²)

0 50 100 150 200 250 300

0

200

400

600

800

1000

1200

Time (s)P

L (W

)

Figure 8. Solar irradiation Figure 9. Load profile

0 50 100 150 200 250 3000

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Time (s)

Pp

v (W

)

0 50 100 150 200 250 300

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

1200

Time (s)

Pp

v-P

L (

W)

Figure 10. Photovoltaic power Figure 11. Difference of powers

With the proposed power balancing strategies, the super-capacitor voltage (Fig. 15) has not varied much since the super-capacitor ensure the power difference during the first 5seconds only, thanks to the help of the

long-term energy storage system. For the long term energy demand, the fuel cell and the electrolyzer should make the balance between the demanded power and the delivered one as depicted in Fig. 12 and 13.

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Page 6: [IEEE 2012 First International Conference on Renewable Energies and Vehicular Technology (REVET) - Nabeul, Tunisia (2012.03.26-2012.03.28)] 2012 First International Conference on Renewable

0 50 100 150 200 250 3000

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Time (s)

PF

C (W

)

0 50 100 150 200 250 3000

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Time (s)

P E

lz (

W)

Figure 12. Fuel cell power Figure 13. Electrolyzer power

0 50 100 150 200 250 300

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-500

0

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Time (s)

PS

C (

W)

0 50 100 150 200 250 300

103

103.5

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Time (s)

VS

C (

V)

Figure 14. Super-capacitor power Figure 15. Super-capacitor voltage

0 50 100 150 200 250 30015

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Pst

o (

Ba

r)

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399.4

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400.8

401

Time (s)

Ud

c (V

)

Figure 16. Storage pressure Figure 17. DC bus voltage

As illustrated in Fig. 16 the storage tank is in suitable rates, it is not undercharged or overcharged, so the whole system works in normal mode. The balance between the different currents enables us to obtain a constant DC bus voltage at 400 V as

represented in Fig. 17, which shows the efficiency of the control strategy.

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Page 7: [IEEE 2012 First International Conference on Renewable Energies and Vehicular Technology (REVET) - Nabeul, Tunisia (2012.03.26-2012.03.28)] 2012 First International Conference on Renewable

6. CONCLUSION

In this paper, the modeling and the control of a photovoltaic generator associated to a SC module as a fast dynamic storage system and to a hydrogen system as a long term storage device have been presented. The main aim of this work was to control the DC bus voltage by sharing the power’s level between the different power sources. Simulation results showed the performance of the proposed system and the efficiency of applied control strategies. This system can deal with other circumstances, i.e the empty/full mode of the fast storage system (super-capacitor) or the empty/full mode of long storage system (the hydrogen tank). Those modes will be discussed in further studies.

REFERENCES

[1] J-Kwon M, Nam K-H and Kwon B-H. ‘’Photovoltaic power conditioning system with line connection’’. IEEE Trans Ind Elec; vol.53, no.1048, pp 54. 2006 [2] El-Shatter Th,F, Eskandar MN and El-Hagry MT. ‘’Hybrid PV/fuel cell system design and simulation’’. Renew Energy; vol. 27 no.3:pp 479–85. 2002 [3] Phatiphat Thounthong, Viboon Chunkag, Panarit Sethakul, Suwat Sikkabut, Serge Pierfederici and Bernard Davat. ‘’Energy management of fuel cell/solar cell/supercapacitor hybrid power source.’’ Journal of Power Sources, vol.196 pp 313–324. 2011 [4] Y. Ates, O. Erdinc, M. Uzunoglu and B. Vural. ‘’Energy management of an FC/UC hybrid vehicular power system using a combined neural network-wavelet transform based strategy’’. International journal of hydrogen energy , vol 35,pp 774–783. 2010. [5] R. Maouedj, A. Deliou and B. Benyoucef. ‘’Modélisation et simulation des performances d’une cellule photovoltaïque’’in Proc. CERE 2006, Hammamet, Tunisia, 06-08 November 2006, CD ROM. [6] R. Jallouli, L. Krichen, B. François and A. Ouali. ‘’Modelling and Control of an Optimized PV Array with Hydrogen System Comprising a PEMFC and an Electrolyzer’’. International Journal of Electrical and Power Engineering , vol 1 pp 264-273,2007. [7] Tao ZHOU, Bruno FRANCOIS, Mohamed el hadi LEBBAL and Stéphane LECOEUCHE.

‘’Modeling and Control Design of Hydrogen Production Process by Using a Causal Ordering Graph for Wind Energy Conversion System’’ in Proc. IEEE International Symposium on Industrial Electronics. Vigo, Spain, ( 2007), CD ROM. [8] L. Zubieta, R. Bonert. ‘’Charactererization of double-layer capacitors for power electronics applications’’. IEEE transaction on Industry Applications. vol.36, pp 199-205.2000. [9] T. Zhou, D. Lu, H. Fakham, B. Francois. ‘’Power flow control in different time scales for a wind/hydrogen/super-capacitors based active hybrid power system’’.in Proc EPE-PEMC’08, Poznan (2008), CD-ROM. [10] M.Y. Ayad and al. ‘’Voltage regulated hybrid DC power source using super-capacitors as energy storage device. Energy Conversion and Management’’,Vol. 48,pp 2196-2202,2007. [11] A. hajizadeh and M.A. Golkar. ‘’Intelligent power management strategy of hybrid distributed generation system. . Electrical Power and Energy System’’ pp.783-795. 2007 . [12] J. Moreno, M.E.Ortuzar and J.W.Dixon. ‘’Energy-management system for a hybrid electric vehicle, using ultracapacitors and neural networks’’. IEEE transactions on Industrial Electronics. Vol.53. pp 614-623. 2006.

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