EFEEA’10 International Symposium on Environment Friendly Energies in Electrical Applications

2-4 November 2010, Ghardaïa, Algeria

Solar panel and battery for street lighting M. Becherif1,2, M. Y. Ayad1, A. Henni3, A. Aboubou4 and M. Wack1 1

SeT Laboratory, UTBM University, 90010 Belfort (cedex), France 2 FC-Lab fuel Cell Laboratory, 90010 Belfort (cedex), France 3 University of Technology of Belfort-Montbéliard, UTBM, 90010 Belfort (cedex), France 4 LMSE Laboratory, Biskra University, 07000, Algeria phone: +33 (0)3 84 58 33 46, fax: +33 (0)3 84 58 34 42, e-mail: [email protected]

Abstract- A street lighting application is designed based on renewable energy sources as photovoltaic solar panel hybridized with a battery. The system is applicable for remote areas or isolated DC loads. The state space model of the whole system is presented. Control strategy has been considered to achieve permanent power supply to the load via the photovoltaic/battery on the power available from the sun. Passivity Based Control is applied to ensure the control aims and the energy management between sources. The stability proof is provided and the simulation using Matlab are concluding. A realistic scenario based on the availability of solar radiation is proposed and the energy assessment is discussed.

problem formulation is stated including the energy management requirements. In this paper, the dynamical model of the Uninterruptible power source part (UPS) of this multi-sources charger is considered with its control strategy and the energy management of the whole device. Then, simulation results are presented. The power circuit is described followed by the Energy management section where the state space model is given and the problem formulation is stated. The control process is described using the Port Hamiltonian method with the proof of the stability. The last three sections concern the simulation, the energy assessment and finally the conclusion is given.

Key words- Photovoltaic; Battery; Passivity based control; Renewable energy; Street lighting.

The figure 1 shows the hybrid structure of a solar panel on the DC bus and a battery connected to the DC bus via a current bidirectional converter, the street light is directly supplied by the DC bus.

I.

INTRODUCTION

Renewable energy sources (solar, wind, fuel cell, etc) are considered as alternative energy sources to conventional fossil fuel energy sources due to the environmental pollution and global warming problems. However, control problems arise due to large variances of output under different insolations or wind speed levels. To overcome this problem, PhotoVoltaic (PV) system can be integrated with other power generators or storage systems such as battery bank and fuel cells [1-4]. In this work, the design and control strategy of an autonomous photovoltaic and battery energy system has been developed and simulations have been performed in order to supply electricity to a DC-load. The photovoltaic module produces electricity to meet requirements of a load. When there is enough solar radiation available, the external load can be powered totally by the photovoltaic source. For a continuous power supplying of the load, a battery bank is used with the photovoltaic module. During the period of low insolation, an auxiliary electricity source is required. All the developed models are based on physical and chemical principles, as well as empirical parameters. The state space model for the whole system is derived. The system control is designed to optimize the input and output currents for different components of the overall system during a period of one day. A realistic operating scenario is proposed and a

Solar panel Street light

Battery

uB

DC bus

Fig. 1: Street light supplied by battery and solar panel II.

PHOTOVOLTAIC AND BATTERIES MODELLING

1. Modeling of the photovoltaic generator The mathematical model associated with a cell is deduced from that of a diode PN junction. It consists on the addition the photovoltaic current Iph (which is proportional to the illumination), and a term modeling the internal phenomena. The electrical equivalent circuit is depicted in figure 2.

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EFEEA’10 International Symposium on Environment Friendly Energies in Electrical Applications

For lighting conditions and temperature data, the characteristics of current-voltage and power voltage P=f(U) shows an operating point at maximum power. The photocurrent is nearly proportional to the light or luminous flux. The following figure shows the influence of illumination on the current and power. The photocurrent created in a photocell is proportional to the surface S of the junction subjected to sunlight.

The current I in the output of the cell is then Written: e .( U − R S I ) ⎛ ⎞ U + R SI I = I ph − I s ⎜ exp( ) − 1⎟ − KT R sh ⎝ ⎠ Consider Id (the output diode current):

2-4 November 2010, Ghardaïa, Algeria

(1)

e ( U − R S I) ⎞ ⎛ I d = I s ⎜ exp( ) − 1⎟ , KT ⎠ ⎝ kT Where = VT representing the thermal potential (25mV at e 20 ° C)

3 T=25°C E=1000W/m 2

2.5

E=800W/ m2

I (A)

2

E=600W/ m 2

1.5

E= 400W/m

1

E= 200W/m

0.5

2

2

Fig. 2: equivalent circuit of a photocell 0 0

5

10

15

20

25

V (v)

The diode models the behavior of the cell in darkness. The generation of current is modeled by the current Iph representing the degree of illumination. Finally, the internal losses are modeled by the two resistances (a shunt and serial resistances): - Serial resistance Rs: models the ohmic losses of material. - Shunt resistance Rsh: models the stray currents passing through the cell. - (Rs.I) can generally be neglected comparing to U, the following simplified model is then obtained:

I = I ph

⎛ qU ⎞ U − I s ⎜ e kT − 1 ⎟ − ⎜ ⎟ R sh ⎝ ⎠

Fig.4 Effect of illumination on the characteristic currentvoltage 50 E=200:200:1000W/m

45

2

T=25°C Trajectory of the optimal power

40

2 E=1000W/m

35 30 P (w) 25 20

(2)

15 10

As the shunt resistance is much higher than the series resistance, one can still neglect the current deflected in Rsh:

E=200W/m 2 5 0

I = I

ph

⎛ − Is⎜e ⎜ ⎝

qU kT

⎞ − 1⎟ ⎟ ⎠

0

5

10

15

20

25

V (v)

(3)

Fig.5 Effect of illumination on the characteristic powervoltage

Figure 3 corresponds to the simplified model:

2. Modeling of battery Many electrical equivalent circuits of battery are found in literature [6-7]. Batteries are presented with overview of some much utilized circuits to model the steady and transient behavior. The Thevenin’s circuit is one of the most basic circuits used to study the transient behavior of battery. This model is shown in figure 6.

Fig. 3: Simplified equivalent circuit Note that in this paper, we consider the PV model of the equation (2) then the shunt resistance is taken in account.

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EFEEA’10 International Symposium on Environment Friendly Energies in Electrical Applications

2-4 November 2010, Ghardaïa, Algeria

The PV used model is the one given by equation (2). The battery is modeled as a voltage source of emf eb (9V) in series with a resistance rb carrying a current ib. The output battery voltage EB is given by

EB = eB − rBiB

Fig. 6: Thevenin’s model

The battery converter is controlled with u b ∈ [0,1] , u b = 1 ⇔ Tb is Off An average continuous model for the DC-DC converter is considered.

It uses a series resistor (Rseries) and a RC parallel network (Rtransient and Ctransient) to predict the response of the battery to transient load events at a particular state of charge by assuming a constant open circuit voltage [Voc(SOC1)].

The following state vector of the whole system is chosen: T x = [U i B ]

⎧ x x ⎤ 1 ⎡ µx2 + I ph − Is eax1 −1 − 1 − 1 ⎥ ⎪x&1 = ⎢ ⎪ CDC ⎣ Rsh RL ⎦ ⎨ 1 ⎪ x&2 = [− µx1 + eB − rB x2 ] ⎪⎩ LB

(

Fig.7: Circuit showing battery emf and internal resistance Rinternal III.

STRUCTURE OF THE HYBRID SOURCES

µ = 1 − u B , and a =

RSH

U

PV

CDC RL

2. Operating scenario • It is assumed in this scenario that the illumination is available for 50% of the time and completely absent during the rest of the time. • Simulations will be conducted over a period of 12s. • The period of the illumination is from 0s to 3s (and then decreases until it disappears at 3.4s), restart again at 6s (to the maximum illumination at 6.4s) until 9s (where it declines to disappear at 9.4s). • The lamp is lit before the disappearance of the light and is off a long time after the return of the illumination. Thus, it is lit from 2.5s to 7s and from 8.5s to 12s. The lamp is therefore turned on 2/3 of the total time. • For the duration of the illumination, the energy produced by the PV is completely absorbed by the battery. Upon ignition of the lamp energy produced by PV is used entirely to feed the load. In this case the battery is not used. • Since the disappearance of the illumination, the battery is progressively taking over the charge to power aided in transient peaks. The battery yields subsequently relay to the PV from the re-emergence of the illumination.

Load

Battery

µ Fig. 8. Hybrid structure of PV and battery sources. The structure is the hybridization of the figure 8 consists of a PV panel, the resistive load representing the street light, a DC bus (capacity on the bus), and a battery connected to the bus via the DC-DC current bidirectional converter.

Fig. 9. Structure of the battery and the DC-DC converter 1

q >0 kT

1. Problem Formulation The control objective is to ensure a desired constant voltage Vd of 12V on the DC bus and to manage the energy between the solar source and the battery for the phases of charge / discharge and the lamp supplying.

I Id

(4)

with

As shown in Fig. 8, this hybridization of solar panels is done with a PV panel with a power of 50 W and a battery.

IPH

)

This problem is solved using recent techniques based on energy issues such as passivity-based control [10-11].

SOC: State Of Charge

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EFEEA’10 International Symposium on Environment Friendly Energies in Electrical Applications

3.

1 ⎧ ⎪⎪ x&1 = C [µx2 + I − I L ] DC ⎨ 1 ⎪x&2 = [− µx1 + eB − rB x2 ] ⎪⎩ LB 1 ⎧& ⎪⎪x1 = 0 = C [µx2 + I − I L ] DC ⎨ 1 ⎪ x&2 = [− µx1 + eB − rB x2 ] ⎪⎩ LB

Stability study

A. Equilibrium Let denotes x as the equilibrium state of the state vector x . The first objective of the DC-DC converter is to assure a desired voltage at the DC bus. Hence, we chose the following equilibrium value for the control signal (this value is the duty ratio value at the equilibrium allowing to have the voltage Vd at the DC bus), where Vd is the desired (and constant) DC bus voltage, e µ= b Vd After some simple calculation, we find the following for the equilibrium.

µ x2 = I L − I

1 ~ ⎧ ~& ⎪⎪ x1 = C [µx2 + x2 (µ − µ )] DC ⎨ 1 ~ & ⎪x2 = [− µ~ x1 − x1(µ − µ ) − rB ~ x2 ] ⎪⎩ LB

In order to have a PCH form for the closed loop system and to proof the stability the following choice for the control vector is done: (11) µ=µ

(6) L b } is a diagonal matrix.

In the following, the closed loop Port-Controlled Hamiltonian (PCH) representation is given [10]. The desired closed loop energy function is: 1 T ~ Hd = ~ x Qx (7) 2

DC 1

b

The closed loop dynamics is, then: µ ⎤ ⎡ ⎢ 0 LBCDC ⎥ ~ ⎥∇H x& = ⎢ − rB ⎥ d ⎢ −µ ⎢⎣ LBCDC L2B ⎥⎦

(12)

~ x& = [J − R]∇H d

(13)

Where J (µ ) = −J (µ ) is a skew symmetric matrix defining the interconnection between the state space and R = R T ≥ 0 is symmetric positive semi definite matrix defining the Damping of the system. The derivative of the desired energy function (7) along the trajectories of (12) is non positive. Proof: & & = ∇H T ~ H d dx T

Where ~ x = x − x is the new state space defining the error between the state x and its equilibrium value x . The gradient of the desired energy function is: ∇H = [C ~ x L ~ x ]T d

(10)

The dynamic of the error is given by the following: µ ⎤ ⎤ ⎡ x2 ⎡ ⎢ C (µ − µ ) ⎥ ⎢ 0 ⎥ L C ~ B DC ⎥ ⎥∇H + ⎢ DC x& = ⎢ − rB ⎥ d ⎢ x1 ⎥ ⎢ −µ ( ) µ µ − − ⎢⎣ LBCDC ⎥⎦ ⎢⎣ LB L2B ⎥⎦

B. Control and stability proof Let H be the energy function of the system:

Where Q = diag{C DC

(9)

I and IL can not be evaluated at the equilibrium and treated as constant values since that the illumination is variable (consequently I is variable) and the charge can be variable (switching on and off, consequently IL is variable). (8)-(9) gives the dynamic of the error

T

1 T x Qx 2

(8)

From the first equation of (9) we can write:

⎡ ⎤ Vd (5) ( I L − I )⎥ x = ⎢Vd eB ⎣ ⎦ x I L = 1 is the Load current and I is the bounded PV output RL current. The value of the current battery at the equilibrium depends on the values of the load current and the PV output current. Then, if the PV current is equal to the load current then iB=0, if iPV is less then iL then iB will compensates the feed the load and finally if iPV is greater than iL then iB becomes negative and the battery is recharged by the excess produced PV current. The choice of these equilibrium values allows to manage the energy between the different sources in addition to the DC bus voltage control.

H=

2-4 November 2010, Ghardaïa, Algeria

2

In order to write the error dynamic, let us define first the equations at the equilibrium. (4) can be written as

H& d = ∇H dT J∇H d − ∇H dT R∇H d H& d = −∇H dT R∇H d ⇔ H& d ≤ 0

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EFEEA’10 International Symposium on Environment Friendly Energies in Electrical Applications

We recall that J is a skew symmetric matrix then for all vector X ⇔ X T JX = 0 . Hence, the derivative of the desired energy function (7) (which plays the role of the Lyapunov function) along the trajectories of (12) and the proposed control (11) is negative semi definite. Consequently, the origin of the closed loop dynamics (11) is globally2 stable.

I(A)

4 2 0

0

2

4

6 t(s)

8

10

12

0

2

4

6 t(s)

8

10

12

0

2

4

6 t(s)

8

10

12

iB(A)

10 0 -10

4.

2-4 November 2010, Ghardaïa, Algeria

Simulation results 5 iL(A)

The simulation parameters are the following: PV

0

Q (C) 1,602.10-19

Rsh (Ω) 1k

K (eV) 8,62.10-5

T (°K) 25+273

Is (A) 100.10-9

P (W) 50

Fig. 10 PV, battery and load currents Battery 50 PL(W)

eB (V) 9

rB (Ω) 5.10-2

Fig. 9 shows the DC link voltage and its reference, and the battery voltage. Fig. 10 presents the load, PV and battery currents. During the day light, the battery is recharging (current of -5A), the sign “-“ corresponds to the charge of battery while the “+” corresponds to a discharge mode. When the lamp is switched on, battery feeds (rapidly) the load and the battery current becomes positive. The battery discharges continuously until the night period. When PV generates energy and the lamp is turned off, battery is recharged again from PV. Fig. 11 shows the PV, load and battery powers. This figure is very interesting; we can see the load power, the generated PV power and the battery power with discharge and recharge phases.

0

2

4

6 t(s)

8

10

12

0

2

4

6 t(s)

8

10

12

Vd & U(V)

8

10

12

0

2

4

6 t(s)

8

10

12

0

2

4

6 t(s)

8

10

12

PB(W) PPV(W)

0 -50

Fig. 11 PV, battery and load powers Fig. 12 shows the turn on and off switching of the street light lamp. One can see that the lamp is turned on before the complete disappearance of natural light and is turned off after the presence of sunlight (this scenario is realistic and is used in all street light application). Fig. 12 shows the PV current, corresponding to the turn on and off of the street light lamp. It illustrates the presence and the absence of sunlight illumination, this illumination changes progressively. One can see in the Fig. 9, that the DC bus voltage (which is the voltage applied to the lamp) that the controller act to regulated this voltage to its reference (Vd=12V). There is quasi no steady state error (there is a zoom in).

9.05 EB(V)

6 t(s)

50

9.1

9 8.95 8.9

4

0 -100

12

0

2

100

12.5

11.5

0

Fig. 9 DC link voltage, battery voltage 2 The desired energy function (7) is radially unbounded then the stability is global.

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EFEEA’10 International Symposium on Environment Friendly Energies in Electrical Applications

V.

2-4 November 2010, Ghardaïa, Algeria

CONCLUSION

4

In this paper, a modeling and the control principles of DC hybrid source systems, composed of a photovoltaic source and battery have been presented. The state space model is given for the whole structure. Considering the chosen scenario, energy supplied by the battery is recovered by PV during periods of illumination. For hybrid structures, passivity-based control principle has been applied. A very simple controller was designed using no sensors. The choice of the equilibrium points allows the management of the energy between the different sources and the load. The stability proof is provided. A simulation of the proposed controllers was presented. These results give a good functioning and a correctly attempt objectives. The proposed hybrid structure and the control law are suitable for stand alone application and for isolated area and desert regions.

IPH(A )

3 2 1 0 -1

0

2

4

6 t(s)

8

10

12

1

Lam p O N /O F F

0.8

OFF

OFF

ON

ON

0.6 0.4 0.2 0

0

2

4

6 t(s)

8

10

12

Fig. 12 Operating Scenario IV.

References

ENERGY ASSESSMENT

Despite the modeling and the control of this system, a contribution of this paper consists on the following energy assessment. Using the obtained simulation, an extrapolation of the functioning is done to reach a 24 hours functioning. Upon the described scenario, the different energies are calculated: Consider EL, EPV, EBch and EBdisch as the load, PV, the battery charge and discharge energies. H=hours.

[1] K. Ro, and S. Rahman, “Two-loop controller for maximizing performance of a grid-connected photovoltaic-fuel cell hybrid power plant”, IEEE Trans Energy Conversion 1998; 13(3); pp. 276-281. [2] J.Appelbaum, “Photovoltaics Energy Conversion”, Syllabus, KU Leuven 2001 [3] M. Becherif, M. Y. Ayad, A. Henni, M. Wack, A. Aboubou "Control of Fuel Cell, Batteries and Solar Hybrid Power Source", Proceeding IEEE-ICREGA'10-- March 8th-10th Dubai [4] A. Rufer, D. Hotellier and P. Barrade, “A Supercapacitor-Based Energy-Storage Substation for Voltage - Compensation in Weak Transportation Networks,” IEEE Trans. Power Delivery, vol. 19, no. 2, April 2004, pp. 629-636. [5] Y. Sukamongkol, S. Chungpaibulpatana and W. Ongsakul, “A simulation model for predicting the performance of a solar photovoltaic system with alternating current loads”, Renewable Energy 27(2002); pp. 237-258. [6] M. Chen; A. Gabriel; Rincon-Mora. (2006). Accurate Electrical Battery Model Capable of Predicting Runtime and I–V Performance. . IEEE Trans. Energy Convers, Vol. 21, No.2, pp.504-511 June 2006. [7] Z.M. Salameh; M.A. Casacca & W.A. Lynch (1992). A mathematical model for lead-acid batteries, IEEE Trans. Energy Convers., vol. 7, no. 1, pp. 93–98, Mar. 1992. [8] M. Y. Ayad, M. Becherif, A. Henni, A. Aboubou, M. Wack, S. Laghrouche “ Passivity Based Control applied to DC hybrid power source using Fuel cell and Supercapacitors”, Energy Conversion and Management, Volume 51, Issue 7, July 2010, Pages 1468-1475, Elsevier publisher. [9] M. Becherif, M. Y. Ayad, A. Henni, M. Wack and A. Aboubou “Unit Power Factor Converter To Charge Embarked Supercapacitors”11CHLIE: 11th International SpanishPortugues Conference on Electrical Engineering. 1 -4 of July, 2009. Saragosa-Spain. [10] M. Becherif and E. Mendes, “Stability and Robustness of Disturbed-Port Controlled Hamiltonian Systems with Dissipation”, 16th IFAC World Congress 2005. [11] M. Becherif, R. Ortega, E. Mendes and S. Lee, “Passivity-based control of a doubly-fed induction generator interconnected with an induction motor”, 42nd Conf. on Decision and Contr., pp.5657-5662, Maui, Hawai USA 2003.

1) Street light lamp: EL = 767 WH, Functioning time = 2/3 of the whole time (16H) 2) Photovoltaic: EPV = 594 WH Functioning time = ½ of the whole time (12H) 3) Battery: EBch = -383 WH EBdisch = 556 WH Functioning time as generator = 53% (12H50) Functioning time as receptor = 33% (8H) The excess of the stored energy in the battery can be used if illumination duration is less then the one considered in this simulation. Considering the chosen scenario, 70% of the battery energy can be recovered by the PV to recharge the battery during periods of daylight. This amount can be increased (until 100%) if the street light is equipped with a dark sensor allowing the adjustment of the lamp switch ON and OFF with the light illumination.

6