Design and Control of A Low Power DC-AC Converter fed by a Photovoltaic array

F. Belkacem, D. Diallo Member IEEE and G.A. Capolino Fellow IEEE

Centre de Robotique d’Electrotechnique et d’Automatique, University of Picardie “Jules Verne” 7, Rue du Moulin Neuf, 80000 Amiens, France

Phone: +33 3 22 82 76 80 – Fax: + 33 3 22 82 78 22 – E-mail: ddiallo@ieee.org .

Abstract- In this paper, we present a DC-AC converter fed by a PV array for stand alone applications up to 50W. It is dedicated to rural areas in countries having abundant sunshine and where there is no grid connection to the utility network or the power supply is weak as in many underdeveloped countries. Using a single PV array of 50W as typical power, the aim is to have a simple system, robust, free-maintenance and highly efficient for cellar phone adapter e.g. . The design of the structure has led to a double boost for the DC-DC module (400V as output voltage) where a high gain is needed. The DC-AC converter is made of a half-bridge inverter and an (LC) filter tuned for 50Hz. Using simulation packages, we have obtained the power components parameters (inductances, switches and diodes) and set the switching frequency. For control purposes, a linear controller (PID type) is used and a non linear approach using sliding mode are evaluated. Simulation results in terms of robustness and efficiency are promising. Index Terms—DC-DC converter, Boost, inverter, Photovoltaic, PI control, sliding mode

I – Introduction

A photovoltaic conversion system suitable for AC load up to 50 W is proposed. In rural areas far from grid connections or with a weak power network, the system can be used to supply either a passive load or an active load such as air conditioning or single phase motor for irrigation pumps for example [1-2]. The requirements for the conversion system are:

- a high efficiency because of the high cost of PV arrays,

- a stable DC voltage output, - simple, light and free-maintenance.

II - Power system description

The proposed system is shown in block diagram form in Fig. 1. It consists of a DC-DC double boost converter and an inverter.

Fig.1: Full system block diagram

The most common AC loads have a 230V AC nominal voltage. So a 400V DC is required at the output of the DC converter. The PV array used in our application is a PW500 from Photowatt International whose specifications are:

- typical power 50W, - voltage 17,2V, - short circuit current 2.9A ,

- available surface 0.46m2.

Therefore the DC stage must be designed to have a high output to input voltage ratio. This rising of PV voltage from 17.2V to 400V is made by means of two boost type converters. The double boost converter shown in Fig. 2 has finally been adopted [3-5]. The ratio is

1 2

1 11 1

Gα α

= − −

where α1 and α 2 stands respectively for the duty cycle of each power switch Q1 and Q2.

Fig.2 : DC-DC converter Topology

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There is no intermediate storage elements to avoid additional losses and to reduce the weight of the structure. The AC module is built with a half-bridge inverter and an (LC) filter without a transformer. The generation of square-waves is guaranteed by the switching of two MOSFETs Q3 and Q4 alternately. The (LC) filter will select the harmonic (230V-50Hz) to feed the load.

Fig.3: Power converter Topology

The inverter is driven by an open loop PWM. The first studies were conducted under simulation using Pspice® software package. The power components were chosen and the simulation of the double boost converter in open loop configuration has been conducted. The models include components real characteristics to evaluate accurately the efficiency. In the power system, MOSFET switches are used. This type of semiconductors is characterized by high operating voltage (hundreds of volts) and fast switching mode (hundreds of kHz). Diodes are of Schottky type. In the DC stage, power MOSFET IRF640N and Schottky rectifier 16CTQ100 are chosen for the first boost and power MOSFET IRFI820G and diode RURD460 are chosen for the second. Inductances values calculated from the current ripple and switching frequency are set to L1=1mH, RL1=1Ω, L2=1.9mH; RL2=0.5 Ω. In the AC stage, power MOSFET IRFI820G is implemented. The LC filter parameters are chosen from the following relation : The control block is composed of the current mode PWM controllers UC3842A and IC blocks of op-amps which are equivalent to the chosen control algorithm (PI or VSC). After this validation, we have used the Matlab® software to implement the whole system including the control blocks and the converter. The following sections focus on the control of the DC-DC converter.

III – Control System Description

The DC-DC converter state –space or so called topological model is shown in equation (1). It’s non-linear and has two free degrees represented by the switch commands.

1 11 01 01 1

1 1 1 1

011 2 1 1

1 1 1

2 201 2 02 02 2

2 2 2 2

022 02 2 2

2 2 02 2

1 1 +

1 1 1

1 1 1+

1 1 1.

iL LL

L L L

L LL

L L

VdI R I V V udt L L L L

dV I I I udt C C C

dI RV I V V udt L L L L

dV I V I udt C C R C

= − − = − − = − − = − −

(1)

Where u1, u2 are digital control signals. Two main targets are specified for the control block, first of all the control scheme must keep the input current iL1 within the PV array characteristics and second guarantee a stable DC output voltage with a low ripple rate. A Maximum Power Point Tracking strategy [6,7] can be superimposed. With only to control variables and four states, a suitable strategy must be used to manage properly the input inductor current and the output voltage. The inductor current must be kept within a safety margin depending on the PV characteristics. The output voltage must be regulated to its nominal value even in presence of input or load disturbances and parameter variations. We have chosen to use only two sensors: one for the input current and one for the output voltage The following tables show how to obtain the power switch command u2 from u1.

Table I V01min V01 V01max

IL1min u1=1 u1=1 u1=1 IL1 u1=0 u1=X u1=1

IL1max u1=0 u1=0 u1=0

Table II V02min V02 V02max

u1=0 u2=0 u2=0 u2=1 u1=1 u2=1 u2=1 u2=1

For the past few years, many solutions have been proposed for control system design of DC-DC converters using all the linear or non linear available control techniques, classical ones and even fuzzy or ANN [8-10] depending on the applications. To evaluate our converter, we have chosen two techniques: a linear one based on a standard PI and a Variable Structure

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Control (VSC) which seems to be dedicated to the natural switching behavior of the converter. For simulation purposes, the precise topological non linear model is implemented in Simulink PSB toolbox. The PV is approximated by a voltage source, the output current depending on sunshine conditions and load current. In the following curves, the nominal set point is chosen to be : 17.2V-2.9A-50W.

a) Linear approach

The first approach is to use the classical linear analysis to found a suitable controller. Using the average model approach, we can obtain the small signal state space model around equilibrium points defined as follows.

The small state variables are denoted ∆IL1, ∆V01, ∆IL2 and ∆V02:

1 1 1 1 1 1 2 2 2

2 2 2 1 1 1 2 2 2

L L L ref o o o ref L L L ref

o o o ref ref ref

I I I V V V I I I

V V V α α α α α α= ∆ + = ∆ + = ∆ +

= ∆ + = ∆ + = ∆ +

The small state space model is described by the following

equation:

( )

( )

( )

( )

11 1

1 1 1

1 11 1

1 1 11 1

2 2 222

2 2 22 2 2

22

2 2 02

10 0 0

1 10 0 0

11 00

1 1 00 0.

refL o ref

ref L refL L

o o

L L o refrefL

o o

Lref

R VL L L

II IC C CV Vd

I I Vdt RV V LL L L

I

C C R

α

α

α

α

− − − −∆ ∆ − − ∆ ∆ = +

∆ ∆ − − − ∆ ∆

− − −

[ ]

1

2

2

1

1 12

2 2

2

0 00 0

0 0 0 10 00 0

ref

L

oo

L

o

C

IV

VIV

αα

αα

∆ ∆

∆ ∆ ∆ ∆ = + ∆ ∆ ∆

We can then obtain the transfer functions 2

1

oVα

∆∆

, 2

2

oVα

∆∆

and

therefore build the linear controller. The pole placement approach is used to determine the PI controller parameters.

A constant switching frequency is assumed. So the system can be viewed over a period as the combination of four different circuits each of them represented by a set of differential time – invariant equations. If we assume continuous conduction mode, we can show that in our case (high duty cycles and high switching frequency) the continuous small signal model is a good approximation of the discrete small signal model. In figure 4 (a) , one can see the input current wit respect of the PV characteristics. Figures 4(b) and (c) show the voltage regulation performance for the ideal set point and for input voltage disturbances introduced at 0.6s. The controller reveals good robustness properties.

(a)

(b) (c)

Fig.4 : DC – DC converter signals with PI controller

The efficiency of the DC-AC converter is evaluated near 83%.

b) VCS approach The second approach is to use the Variable Control Structure namely the sliding mode technique to drive the converter. The inherent robustness [11,12] and the simple implementation of the controller makes it an attractive technique. The sliding surface is chosen as a weighted mean of the state errors as follows f(x) = k1∆IL1 + k2∆V02 Where [k1 k2] is the gain vector which must be properly selected to guarantee convergence of f(x) toward zero. The controller structure is depicted in Fig.5.

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Fig.5 : Sliding-mode control

The results shown in Fig. 6 validate the sliding mode controller. The efficiency obtained is rather the same than with the PI controller.

(a) input current

(b) output voltage

Fig.6 : DC – DC converter signals with sliding mode controller We have also noticed a good robustness of the output voltage against input voltage variations due to environmental conditions and also against parameter uncertainties.

V – Conclusion

In this paper, we present a DC-AC converter fed by one PV array for stand alone applications up to 50W. It is dedicated to rural areas where there is no grid connection to the utility network. The aim is to have a simple system, robust, free-maintenance and highly efficient. The design of the structure has led to a double boost for the DC-DC module where a high gain is needed (400V DC) without any storage element. The DC-AC converter is a half-bridge inverter and an (LC) filter tuned for 50Hz. The first step of the work was to design carefully the power components so as to obtain weak losses and therefore a high efficiency. This has been done using Pspice® software package. The second one was to find the suitable control method to implement. A comparison has been made between

a standard PI controller and a sliding mode controller .using only two state variables. The results obtained show that the PI controller is a solution to reach our goal despite the non linearity of the converter. This is mainly due to the fact that in our application the linear model is accurate enough. The total efficiency of the DC –AC converter evaluated in simulation (with real components characteristic) is near 80%. So this solution may be attractive because of the absence of an intermediate storage element.

VI – References

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2. J.A. Gow, C.D. Manning, ”Photovoltaic converter system suitable for use in small scale stand-alone or grid connected applications”, IEE Proc-Elecr. Power Appl., Vol. 147, No.6, pp 535-543, November 2000.

3. Maksimovic, D.; Cuk, S., “General properties and Synthesis of PWM DC to DC Converters”, PESC’89 Record , 20th Annual IEEE, 26-29 june 1989,Pages:515-525 vol.2.

4. Maksimovic, D.; Cuk, S., “Switching converters with wide DC conversion range” Power Electronics, IEEE Transactions on, volume: 6, Issue:1, Jan. 1991, pages: 151-157.

5. Huber, L.; Jovanovic, M.M., “A Design approach for server power supplies for networking applications” APEC 2000,15th Annual IEEE, volume 2, 6-10 Feb. 2000, pages 1163-1169.

6. Brambilla, A. and all, “New approach to photovoltaic arrays maximum power point tracking” PESC’99. 30th Annual IEEE, Volume:2, 1999, pages : 632 – 637 vol.2.

7. De Broe, A.M. and all; “A peak Power Tracker for small wind turbines in battery charging applications” Energy Conversion, IEEE Transactions on, volume: 14, Issue : 4, Dec. 1999, pages: 1630-1635.

8. Garofalo, F.and all; “Control of DC-DC Converters with Linear Optimal Feedback and Nonlinear Feedforward” Power Electronics, IEEE Transactions on, volume: 9, N°:6, Nov. 1994, pages: 607-614.

9. Mattavelli, P.; Rossetto,L.; Spiazzi,G. ; “Small-Signal Analysis of DC-DC Converters with Sliding Mode Control” Power Electronics, IEEE Transactions on, volume: 12, N°:1, Jan. 1997, pages: 96-102.

10. Mattavelli, P.;Rossetto, L.; Spiazzi,G. ;Tenti, P. ; “General - Purpose Fuzzy Controller for DC-DC Converters” Power Electronics, IEEE Transactions on, volume: 12, N°:1, Jan. 1997, pages: 79-86.

11. Utkin, V. “Variable Structure Systems with Sliding modes”, IEEE Transactions on Automatic Conrol, Vol. AC-22, N°2, April 1977, pages: 212-222

12. Slotine, J.J.E; Li, W. ; “ Applied Non Linear Control” Prentice Hall, Englewoods Cliffs, New Jersey 1991

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