Scholarly article on topic 'Optimal Control of a Grid Connected Photovoltaic System with Constant Switching Frequency'

Optimal Control of a Grid Connected Photovoltaic System with Constant Switching Frequency Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — S. Lalouni, D. Rekioua

Abstract This paper presents maximum power point tracking (MPPT) algorithms for grid connected photovoltaic system. Due to the instantaneous changing of solar irradiance and temperature, it is desirable to determine the optimal voltage that ensures maximum energy yield. In order to optimize the photovoltaic energy generation, the MPPT is integrated in the inverter control. Perturb & Observ (P&O), Incremental Conductance (Inc Cond) techniques and fuzzy logic controller (FLC) are applied. A comparison shows the effectiveness of the FLC. The maximum power generated by the photovoltaic system is sent to the power grid to be consumed by the nearest customers. A constant switching frequency is used for the current controlled inverter. The main idea of this method is to superpose an adequate triangular signal having the desired switching frequency to the reference current. The new modulated reference current is then compared to the calculated current in hysteresis controller. Simulation results and some experimental ones are presented to prove the feasibility of the studied system.

Academic research paper on topic "Optimal Control of a Grid Connected Photovoltaic System with Constant Switching Frequency"

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Energy Procedía 36 (2013) 189 - 199

TerraGreen 13 International Conference 2013 - Advancements in Renewable Energy

and Clean Environment

Optimal Control of a Grid Connected Photovoltaic System with Constant Switching Frequency

S .Lalouni*, D. Rekioua

Laboratory LTII, Department of Electrical Engineering, University of Bejaia, Algeria

Abstract

This paper presents maximum power point tracking (MPPT) algorithms for grid connected photovoltaic system. Due to the instantaneous changing of solar irradiance and temperature, it is desirable to determine the optimal voltage that ensures maximum energy yield. In order to optimize the photovoltaic energy generation, the MPPT is integrated in the inverter control. Perturb & Observ (P&O), Incremental Conductance (Inc Cond) techniques and fuzzy logic controller (FLC) are applied. A comparison shows the effectiveness of the FLC. The maximum power generated by the photovoltaic system is sent to the power grid to be consumed by the nearest customers. A constant switching frequency is used for the current controlled inverter. The main idea of this method is to superpose an adequate triangular signal having the desired switching frequency to the reference current. The new modulated reference current is then compared to the calculated current in hysteresis controller. Simulation results and some experimental ones are presented to prove the feasibility of the studied system.

© 2013 The Authors. Published by Elsevier Ltd.

Selection and/or peer-review under responsibility of the TerraGreen Academy

Keywords: Photovoltaic systems, MPPT, Fuzzy logic controller (FLC), Constant Switching frequency

Introduction

Photovoltaic energy systems have gained tremendous attention over the past decade as one of the most promising renewable energy sources due to the probable depletion, high costs, and negative environmental impacts of conventional energy sources. Photovoltaic energy is a pollution-free and inexhaustible source. Photovoltaic arrays should be installed in a way that their exposure to the sun is maximized. The power provided by the PV array varies with solar irradiance and temperature. In order to optimize the energy transfer from the PV array to the load, it is necessary to force the working point at the

Corresponding author. Tel/Fax: +21334215006/+21334215005 E-mail address: lalouni_sofia@yahoo.fr.

1876-6102 © 2013 The Authors. Published by Elsevier Ltd.

Selection and/or peer-review under responsibility of the TerraGreen Academy

doi: 10.1016/j.egypro.2013.07.022

maximum power point (MPP) [1, 2]. The first system with MPPT was introduced in 1968 for a space system [3]. Over the years, several MPPT algorithms have been developed and widely adapted to determine the maximum power point [2,4]. The main components of the MPPT circuit are its power stage and the controller. The MPPT control combined to a DC/DC converter, output a signal to change the duty cycle converter to operate at optimal power whatever the environmental conditions and the load change [2]. The simplest topology to be connected to the ac grid is the single-stage inverter where the MPPT control is integrated in the inverter control [5,6].

Perturb and Observ. (P&O) method which is based on iterative algorithms to track continuously the MPP through the current and voltage measurement of the PV module is presented in [4]. Most control schemes use the P&O technique because it is easy to implement [7-9] but the oscillation problem is unavoidable. Incremental Conductance method presented in [5] requires complex control circuit. The two last strategies have some disadvantages such as high cost, difficulty, complexity and instability. Intelligent based control schemes MPPT have been introduced (fuzzy logic, neural network). The fuzzy controller improves control robustness, it does not need exact mathematical models, it can handle non-linearity and this control gives robust performance under parameters and load variation [7; 10-16].

In this paper, we present a control structure of the grid connected photovoltaic system. The MPPT control is integrated in the inverter control. The P&O, the Inc Cond and FLC techniques are applied to the studied system and a comparison is made. The energy generated by the grid photovoltaic system is sent to the power grid. This is accomplished through an efficient DC/AC conversion where the MPPT is integrated in the inverter control which ensures the control of the active and reactive power level injected to the grid. The inverter is operated at unity power factor. Current control based on hysteresis algorithm is used. This control is very simple, has robust current control performance with good stability, very fast response, inherent ability to control peak current and easy to implement [17, 18]. But, this method has the drawbacks of variable switching frequency, heavy interference, harmonic content around switching side band and irregularity of the modulation pulse position [18, 19]. These drawbacks result in high current ripples and acoustic noise. To overcome these undesirable drawbacks, this paper presents a modulated hysteresis control [20]. The principle is to superpose an adequate triangular signal having the desired switching frequency to the reference current. The new modulated reference current is then compared to the calculated current in hysteresis controller. The results obtained from simulation are presented.

2. System description

To be connected to the AC grid, the most popular way is to be connected with a single-stage system. The system that has been studied consists of photovoltaic arrays with a peak power of 11,2kW connected through a DC bus to a three-phase DC/AC inverter that is connected to an ideal grid through an L filter.

3. Modeling of the proposed system

3.1 Model of PV Array

In literature, there are several mathematical models that describe the operation and behavior of the photovoltaic generator [21]. In Ref [22], a simplified model is presented. It predicts with success the performance of single crystal and polycrystalline PV arrays. The PV array current Ipv obeys to the expression:

Ipv = Ic •{! - Q[exp(C2 v;v ) -1]} (1)

Where, Ci= 0.01175 is determined experimentally in STC conditions [22] and the coefficients C2, C3 and m are defined as:

C =—m~

2 vm oc

C3 = ln

C = ln

ISc (1 + Q) -1„

C, Is,

1 + C1

C ~ / V

3 /ln mpp

C _ 4 _ / _ Voc _

With Vmpp voltage at maximum power point; Voc open circuit voltage; Impp current at maximum power point; Isc short circuit current. The parameters determination is achieved with the standard test conditions (STC). Eq. 1 is only applicable at one particular irradiance level G and cell temperature T, at (STC) (Gref=1000 W/m2, Tref=25 °C). When irradiance and temperature vary, the parameters change according to the following equations, where a^ is the current temperature coefficient and poc the voltage temperature coefficient and (AT=T-Tref)

AI = a

V ref J

AV =-B AT - R AI

pv r^oc s pv

The new values of the photovoltaic voltage and the current are given by:

V = V + ^ V

Pv, new Pv Pv

pv, ne'w

The reference of maximum power operating point Pmax is determined for different solar insulation levels (G) using polynomial approximation. It is represented by a six order polynomial, assuming constant cell temperature.

Pref = 0.114*10-

G -0.422* 10 G5 + 0.716* 10 G4 - 0.462* 10~4G3 + 0.0203G2 + 6.61G

The solar cell is modeled and simulated using Matlab software. The experimental and simulation are based on the data sheet of Siemens SM110-24 photovoltaic panel [2]. The curves Ppv(Vpv) and Ipv(Vpv) of the photovoltaic panel are carried out by varying the load's resistance. The characteristics PPV (VPV) and IPV (VPV) of one 110W photovoltaic panel, are presented in Fig.1 for the same operating conditions (G=753W/m2, T=35.7°C; G=628W/m2, T=33°C; G=530W/m2, T=28.9°C). From these characteristics, the non-linear nature of the PV array is apparent. An MPPT algorithm must be incorporated to force the system to always operate at the MPP. This paper presents a comparative study between (P&O, Inc Cond and FLC).

3.2 MPPT Control Algorithms

The output power induced in the photovoltaic modules depends on solar irradiance and temperature of the solar cells. The PV array has a unique (MPP) that can supply maximum power to the load. The locus

of this point has a non-linear variation with solar irradiance and the cell temperature. Usually the MPPT controls a DC/DC converter [13, 16] that is generally placed between the PV array and the inverter. DC/DC converter maintains the output voltage at its optimal value for extracting maximum power. With an appropriate sizing of the PV array, the DC/DC converter can be avoided, due to the relatively small changes in the optimum voltage in operating condition and moving the MPPT to the inverter. This will save one stage in the system and therefore will increase simplicity and efficiency.

The P&O method measures the derivative of power (dPpv) and the derivative of voltage (dVpv) to determine the movement of the operating point. If the sign of (dPpv/dVpv) is positive, the perturbation of the operating voltage should be in the same direction of the increment. However, it is negative, the system operating point obtained moves away from the MPPT and the operating voltage should be in the opposite direction of the increment. The Incremental Conductance method can track the maximum power point voltage accurately than P&O method, by comparing the Incremental Conductance and instantaneous conductance of a PV array, and to make its decision (to increase or decrease the reference voltage). These methods are iterative based on the increase or the decrease value of the control variable according to a certain time period to be fixed arbitrarily.

Experimental Simulationn

G=753 W/m2, T=35.7°C G=530 W/m2, T=2B.9°C G=628 W/m2, T=33°C

Fig.1. Experimental and simulation curves PPV (VPV) and IPV (VPV).

Each one of these methods presents disadvantages such as oscillations around the operating point at a steady state and convergence slowness, which cause in a way or other losses in power. Recently fuzzy logic controllers have been introduced in the tracking of the MPP in PV systems [2, 13]. The fuzzy controllers improve control robustness and have advantages over conventional ones; they can be summarized in the following way: they do not need exact mathematical models; they can work with vague inputs and are adaptive. Based on their heuristic nature and fuzzy rule tables, these methods use

different parameters to predict the maximum power output [2,15,16]. However, choosing fuzzy parameters to yield optimum operating point and a good control system depends on the experience of designer [23]. The fuzzy logic controller measures the PV array characteristics and then perturbs the operating voltage by an optimal increment (AVpvref) and the resulting PV power change. The power variation (APpv) is either in the positive direction or in the negative one. The value of (APpv) can also be small or large. From these inferences, the reference photovoltaic voltage variation (AVpv,ref) is increased or decreased in a small or respectively large way in the direction which makes it possible to increase the power Ppv. The fuzzy logic controller structure is shown in Fig. 2. The inputs (APpv and AVpv) and output (AVpvref) variables are expressed in terms of linguistic variables (such as BN (Big Negative), MN (Medium Negative), SN (Small Negative), Z (Zero), SP (Small Positive), MP (Medium Positive), and BP (Big Positive)). They are triangular and have seven fuzzy subsets. The value of inputs and output are normalized by a scaling factor. In this system the input scaling factor has been designed such that inputs and output values are between (-1 and 1). The control rules are indicated in Table.1. The fuzzy inference is carried out by using Mamdani's method [23], and the defuzzification uses the centre of gravity to compute the output of this FLC which is the reference photovoltaic voltage variation.

Fig. 2. Structure of MPPT fuzzy controller.

Table.1 Fuzzy rule table [2].

\APpv AV„>\ BN MN SN Z SP MP BP

BN BP BP MP Z MN BN BN

MN BP MP SP Z SN MN BN

SN MP SP SP Z SN SN MN

Z BN MN SN Z SP MP BP

SP MN SN SN Z SP SP MP

MP BN MN SN Z SP MP BP

BP BN BN MN Z MP BP BP

The reference voltage Vpvref is calculated according to the following equation, where AVpv[k] and Vpv[k-1] are the reference photovoltaic voltage variation at sampled times (k) and the voltage of the photovoltaic generator at sampled times (k-1). Vpvref[k] is the instant of reference voltage. Vpv,f [K ] = Vpv[k-1] + AVpVrr<f [k ] ' (9)

The grid side inverter has six IGBTs as switching devices. The inverter must act as a power controller between the DC link and the grid [6]. The energy provided by the photovoltaic generator is applied to the inverter and transmitted to the grid. The role of this inverter is to ensure the control of the active and reactive power injected to the grid which is characterized by an ideal grid voltage and frequency of 50 Hz.

4. Proposed Control Strategy

The control structure of the grid connected photovoltaic system is given by the Fig.3. The current control is based on modulated hysteresis control to impose a constant switching frequency. These technical is used for solve the problems of variable switching frequency of the classical hysteresis algorithm which produce harmonic around switching side band and irregularity of the modulation pulse position.

P = P - P

ref pv c

ref- y d

ld _ ref

q _ ref

^ref-Y q

Qref - Vd

As explained previously, the FLC optimises the reference voltage (Vpv,ref) for maximum power tracking. This voltage represents the input reference of the PI controller, which performs the DC bus voltage. The reference power (Pref) represents the amount of active power produced by the photovoltaic generator interfaced to the main utility through the inverter, and Pc the power of capacitor Cpv; while Qref represents amount of reactive power desired to be injected into or absorbed from the main utility. In the present case, the inverter is operating at unity power factor (Qref=0) therefore no reactive power is exchanged and the total power extracted from the PV generator is injected to the grid. The references current idref and iqref are given by eq.11.

PV Generator

Inverter

Rf, Lf

|Sc fsb \

Voltage ^^-»g)—,

Qr_ref=0 -

Fig.3. Proposed Control structure.

The modulated hysteresis current control technique is used, it permit a constant switching frequency in the inverter. This control consists to add to the reference current iref a triangular signal itr, with frequency

ftr and amplitude A^. The frequency f^ must be choosing equal to desired switching frequency of the

semiconductor.

1 mod = lref + 1 tr (12)

With iref the reference current, itr is the triangular signal, imod is the modulated reference current.

............;...................:.....f

Ttr = 1/ftr

Fig. 4. Determination of the switches states

The hysteresis controller is defined by its band width BH which borders iref*. In this way, the upper and the lower limit shown in Fig. 4 are obtained. The switches states are determined by the intersection points between the measured current im and the obtained limits. The switching strategy is a function of the reference current waveform. The desired switching period will be equal to the period of the triangular signal Ttr.

In order to impose the switching frequency, the measured current variation during a half period Ttr/2 should not exceed the difference between the maximum of the upper limit and the minimum of the lower one. In the case where the measured current will have only two intersections with the hysteresis band limits during every half period Ttr/2 of the triangular signal, these points determinate the switching times of the voltage inverter. Atr and Bh can be calculated by the following equation [20]:

di i = (*^ ( H-ALBA=4ja±M=4.MA+BJ (13)

dt J_ (T r / 2) Tr/2 Tr ■'*' " tJ

5. Numerical simulation

The proposed system is composed of photovoltaic generator made of 6 strings of 17 series connected each, connected in parallel. This gives a total peak power around 11.2kW with a photovoltaic voltage of 595V in STC condition. All modules are considered to be identical and to work in the same conditions of temperature and irradiance. Various simulations evaluate the performances of the system. The different parts of the system are modelled by separated blocks then related in a coherent way, while the MPPT is controlled by (P&O, Inc Cond and FLC). The inverter current is controlled by using a modulated hysteresis controller. The triangular signal amplitude is Atr=2.1 with frequency 5 kHz and the hysteresis band width is fixed to BH =0.1. Fig. 5 present solar panels voltage for the different MPPT controllers (P&O, Inc Cond and FLC). The results of Fig.5 show that the fuzzy logic controller gives us a fast response since it reaches its optimal value at 0.112 s compared to (P&O and Inc Cond) methods which required respectively 0.184s and 0.192s to track the MPP and presents oscillations around the operating point at a steady state. The FLC allows reduction not only in the convergence time to track the MPP, but also in the fluctuation of power in steady state, as it is clearly presented in Fig. 5(b).

750 600 450 300

150 □

_ 1— _C c Cond

- p - In

0.4 0.6

Fig.5 waveform of solar panel voltage, (a). Transient state (b). Steady state.

In order to validate the performances of the studies MPPT based fuzzy logic controller; we proceeded by observing the tracking of the MPP during the grid connection operation. The PV characteristics using FLC and the theoretical PV array characteristics are illustrated in Fig. 6 for variations in solar radiation level and temperature. The FLC can drive quickly the system to the new MPP when an abrupt change of the MPP occurs. Figures 7-8 shows the waveform of PV voltage and power, under the proposed controllers for three insulation levels G =1000, 750 and 500W/m2. The system effectiveness can be evaluated by comparing between the extracted power using FLC and the reference maximum power that can be generated given from Eq.8 as it is shown in Fig.8 (b).

G=753 W/m2, T=35.7°C G=628 W/m2, T=33°C

G=530 W/m2,

1000 750 500 250 0

Fig. 6 Characteristics of a PV array for different irradiance and temperature, (a). Ppv(Vpv), (b). Ppv(Ipv).

700 BOO

4 , > B

(a) (b)

Fig. 7. (a) Solar radiance, (b). Photovoltaic voltage.

12000 10000 g 0000 □I gi 6000 4000 CL 2000 : : : :

Fig. 8 (a). Photovoltaic power and power injected to grid, (b). Comparison between reference power and the photovoltaic power.

400 600

G (W/m2) (b)

300 1000

Fig.9 voltage at the output of the inverter (a). With modulated hysteresis control, (b). With classical hysteresis control

I pv (A)

Figures 9-10 shows a zoom of the output inverter's voltage and current in grid side, with modulated hysteresis control and classical hysteresis control. The last control shows irregularity of the modulation pulse position. The grid current has a constant frequency of 50Hz, it is observed that the modulated hysteresis current control gives a smooth current shape and a low total harmonic distortion.

The grid current total harmonic distortions are shown in Fig. 11. The THD decreases when the insulation levels increase. The results reveal that, modulated hysteresis current controller gives less THD (3.97%) of grid current at standard test condition compared to classical hysteresis current controller (5.21%). As it can be seen in (Fig.10(c)), voltage and current are in phase which means that the maximum of power extracted from the PV array can pass into the grid and system operates at unity power factor (Qref=0) with no reactive power exchange. Then, the system can provide energy to a utility grid with low harmonics compared to the classical control one.

............\J

1.02 Its)

1.02 I [ = )

Fig.10. Current injected into the grid (a). With modulated hysteresis control, ( b). With classical hysteresis control, (c).Wave form of

voltage and current in grid side.

—Jt— Classical hysteresis control Q Moduleted hysteresis control

*- - -

□□ 200 300 400 500 BOO 700 800 900 1000 G (W/rn1) (a)

Classical hysteresis control Moduleted hysteresis control ----

......

... ..... .....

100 200 300 400 500 BOO 700 800 900 1000 G (Wrn1) (b)

Fig.11. (a) Total harmonic distortion of grid current, (b).Fundamental of grid current.

5. Conclusion

An optimal operation of a grid connected photovoltaic system was presented in this paper. It is based on fuzzy logic theory, where the MPPT is integrated in the inverter control. A fast and steady fuzzy logic MPPT controller is used, it adjust appropriately the optimal increment's magnitude of voltage required for reached the optimum operating voltage. It makes it possible to find the MPP in a shorter time runs compared to the conventional method (P&O and Inc Cond) regardless of the weather variations. The current control is based on modulated hysteresis control to impose a constant switching frequency, these technical is used to solve the problems of variable switching frequency of the classical hysteresis algorithm. The results reveal that, modulated hysteresis current controller gives less THD of grid current compared to the classical controller. The grid PV system is continuously operating at the MPP and the system can provide energy to the utility grid with low harmonics and unit power factor.

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