Road Lighting Installation Design to Optimize - IEEE Xplore

EUROCON 2005

Road

Serbia & Montenegro, Belgrade, November 22-24, 2005

Installation Design to Optimize Energy Use by Genetic Algorithms Lighting

A. Covitti, G. Delvecchio (Member, IEEE), F. Neri (Member, IEEE), A. Ripoli and M. Sylos Labini (Member, IEEE) E-S K D1 D2

Abstract - In this paper the Authors suggest a software based on the genetic algorithms to optimize the design of a road lighting installation so as to reduce the use of the energy per year. The method has been applied to a real case.

I. INTRODUCTION

A S is well-known, the designing of a road lighting installation consists in fixing a lighting unit, assuming a possible set of design parameters (such as, height of the lighting unit, inclination of the same unit, overhang of the lighting pole, inter-distance between the poles) and finally in checking whether this set complies with the specifications regarding the road taken into con-

a)

h)

Fig. 1. Surface S relating to a lighting unit for the following arrangements: a) unilateral; b) axial; c) quincuncial bilateral; d) opposite bilateral. * DI is the coefficient of depreciation: it considers the decrease in the initial luminous flux emitted by the lamp (see Tab. 1); * D2 is the coefficient of maintenance: it considers the decrease in the luminous efficiency of the lighting units because of the dirtiness, wear and tear of reflectors (see Tab. 2);

II. THE ROAD LIGHTING INSTALLATION DESIGN AS IT IS USUALLY FORMULATED

If we want to get the desired lighting on the road surface we must calculate the luminous flux ID (lm) emitted by every lighting unit. This can be made thanks to the Total

Flux Method ([5], [6]). The luminous flux is given by:

TABLE 1: DEPRECIATION COEFFICIENT D1 OF THE LAMPS. fluorescent bulb or lowhigh-pressure sopressure sodium lamps dium lamp

fluorescent lamps 0.88

G. Delvecchio is with Universita degli Studi di Bari, Piazza Umberto I 1 - 70100 Bari, Italy (phone +39-080-5714648; fax +39-080-5714655; email: a . A. Covitti, F. Neri, A. Ripoli and M. Sylos Labini are with Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Via E. Orabona 4 - 70125 Bari, Italy (phone +39-080-5427919, +39-347-9016226, +39-320-6154998, +39-080-5963256; fax +39-080-5963410; e-mail:

1-4244-0049-X/05/$20.00 (C2005 IEEE

(1)

where: * E is the average illuminance required by the Standards on the roadway (lux) [7]; * S is the road surface lit up by a lighting unit (m2); * L is the roadway width (m); * d is the inter-distance between the lighting units (m); * c is an appropriate coefficient: c= 12 for the arrangement of the opposite bilateral lighting units; c=1 in all the other cases (see Fig. 1);

Keywords - Genetic algorithms, optimization of energy use, road lighting design optimization.

sideration [1], [2]. However, in this way, the possibility that the design made minimizes the lighting energy consumed every year is not considered at all. To this end the power absorbed by the lighting installation must be minimized. The optimization of the design could be made in the following way: calculation of all the possible combinations of the design parameters above and then choice of the best combination. However, in this way, the computational cost would be very high. To settle this problem the Authors suggest in this paper an optimization software based on the genetic algorithms (see [3], [4]) which quickly finds out the best combination of the design parameters above.

E-c-L-d K D1 D2

0.85

0.95

TABLE 2: MAINTENANCE COEFFICIENT D2 OF THE LIGHTING UNITS. Environment

With dust, fumes, exhalations, etc. Clean atmosphere

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Open

Lighting units

0.65 0.70 0.80 0.85

Close 0.75 0.80 0.85 0.90

.,-

-CL

-A

h)

:aL)

L L

I

Fig. 4. Position of the lighting unit with regard to the roadway: a) overhanging s>0; b) backward s0 (that is, if the lighting unit overhangs the roadway, see Fig. 4a), and s 0 H) if s (t,min, we can go on optimizing the design so as to reduce of the energy absorbed in a year by the lighting installation under examination. As explained previously, if the operation hours are equal, the power absorbed by the lighting installation must be minimized to reduce the energy; that is to say, the number of lighting units must be reduced. To this end it is necessary to maximize the inter-distance d between the various lighting units. From (1) it is possible to get:

K

d

I Road side

IK2 Walk side xEH

Fig. 3. An example of curves to calculate the coefficients K1 and K2; each couple of curves is relative to a value of cc and x is equal to (L-s) or to s, in accordance with (2).

DL

KDl D2 EcL

(3)

Once the lighting unit is chosen and once size and kind of road are known, the parameters DL, E, c, L, D1, and D2 are consequently fixed. In (3) the only parameter that is useful for maximizing d is the coefficient of utilization K which must be maximized, too. According to formulas (2) this coefficient depends on the parameters H, s and ac. Then, fixing at first the lighting units to take into consid-

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eration for the design, and indicating with A the progressive number associated with each of them (1 for the first unit, 2 for the second one, and so on), the question consists in finding the combination or the set of the four parameters (A, H, s, ca) in correspondence with which the inter-distance d turns out to be the greatest one (dmax) insofar as lighting design specifications allow. As said in Section I, the best choice could be made by calculating, for example, all the possible combinations of (A, H, s, ca): but, in this way, the computational cost should be high. To settle this problem the Authors suggest an optimization software based on the genetic algorithms which finds out the best combination. IV. THE PROPOSED METHOD BASED ON THE GENETIC ALGORITHMS

We wish to find the combination of the four parameters (A, H, s, ca) which maximize the inter-distance d. To this end every combination can be considered as an individual Ind (A, H, s, ca) having four genes which are made up of the parameters A, H, s, a, respectively. These values are discrete since A is an integer number and the parameters H, s, oc are defined in a discrete way by the Standards. For example, the combination (2, 10, 0.5, 15) is an individual having the numbers 2, 10, 0.5, 15 as genes; this combination considers the second lighting unit put at H 10 m, with overhang s = 0.5 m and angle of inclination c = 15°. The choice of the number of individuals Nind constituting the initial population has been made by the Authors by the following empiric formula:

Nind = No. of individuals of the initial population (4) = max(4 N, 30) This formula assures us that the convergence times of the algorithm improve. In (4) N stands for the maximum number among the values of A, H, s, ca, the number of these values being, as already said above, discrete. For example, if the number of possible values of A, H, s, oc is 2, 25, 5, 9, respectively, then N= max(2, 25, 5, 9) = 25. So formula (4) gives: max(4 N, 30) = 100. Then the process goes on with various iterations and in each of them the individuals of the population generate other individuals through the cross-over technique; some of them undergo a mutation, too. As is well-known, the cross-over technique allows the exchange of genes between two individuals (parents) to generate a new individual. In this way the individuals of the "procreating" population generate a second population called "offspring" population. The crossover technique has been carried out by means of the "discrete recombination" function which consists in the following [9]. Once two future parents are chosen at random the "discrete recombination" function generates a random vector of bits called mask. The genes of the first child (child,) are those of the first parent if the corresponding bits of mask are equal to 1; while they are those of the second parent if the corresponding bits of mask are equal to 0. The opposite is done to determine the genes of the second child (child2). For example, ifpl = [a b c d] and

P2 = [1 2 3 4] are the parents, and if the random vector of bits is mask= [11 0 0], then the children will be: child, = [a b 3 4], child2= [I 2 c d]. It is also well-known that mutation consists in changing at random a gene of the individual. In the approach proposed a cross-over rate equal to 1, and a mutation rate of 0.1 have been adopted, that is to say at each iteration all the individuals of the "procreating" population undergo cross-over, whereas only 10% of individuals undergo mutation. In each iteration, after cross-over and mutation have taken place, the objective function to be maximized as well as the fitness function are calculated for each individual. The objective function associated with each individual is: * d calculated by means of (3), if the lighting specifications (such as, uniformity of lighting, disability glare, discomfort glare, etc. -see [5], [6]-) are fulfilled by the combination (or individual) considered. These specifications are fixed by the Standards (see [7], [8]). * zero, if the lighting specifications are not fulfilled. The fitness function shows if the individual is fit to represent the solution of the problem. The function used is the Ranking Function [9]: at each iteration all the individuals constituting the "procreating" and "offspring" are all put back in order: in decreasing order of d, and in increasing order of H, s, and ac. Thus, d being equal, the software chooses the combination that has, in the order, a smaller H, s and a. In fact, the pole and straddle cost depends on these parameters. Fitness is a function of the individual rank, that is of its position in the list above [9]; that's why the fittest individual will have rank 1 (the best individual), the next one 2, and so on. According to this function, at each iteration, the Nind best individuals between "procreating" and "offspring" are chosen, whereas the worst ones are rejected. The best individuals are the ones which give big inter-distances d (see Fig. 5). As the iterations proceed, the population evolves until the solution of the problem is reached. The algorithm stops either when a pre-arranged number of iterations is

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Fig. 5. The block diagram of the genetic algorithm.

reached, or when the combination that maximizes d (i.e. the best individual) remains unchanged in the various iterations for a pre-arranged number of iterations (stop criterions). Fig. 5 shows the block diagram of the whole algorithm proposed.

binations really evaluated by the algorithm) in 1.35 seconds. The saving of computation has been S)% = 91.02, where Sc% has been defined by the Authors as follows:

(5)

Sc% I 00 [(Ncomb Neval GA) / Ncomb] =

-

Table 3 shows the optimization results regarding the two lighting units X and Y.

V. AN EXAMPLE OF DESIGNING The method has been applied to the design of a new road lighting installation in the place of the existing one (see Fig. 6). This is an installation of the ENEA (National Agency of Alternative Energy) centre of Trisaia (Rotondella, near Matera), which is in the South of Italy. The input data are: * arrangement of the lighting units: unilateral (see Fig. 1); * lamp: 150 W (qDL = 130000 lm) high-pressure sodiumvapour lamp; * average illuminance required: E= 14 lux; * roadway width: L = 7 m.

TABLE 3: COMPARISON BETWEEN TWO DIFFERENT LIGHTING UNITS EQUIPPED WITH THE SAME LAMP.

Lighting Unit

x Y

The following ranges have been assigned to the four variables A, H, s, and oc (see Fig. 2 and Fig. 4): * A = 1, 2, which means that only two lighting units (later indicated with X and Y ) of two different manufacturers have been considered for the design optimization; each lighting unit has the above lamp; * H= (3 :15) m, step 0.5 m (for a total of 25 values); * s =(0 2) m, step 0.5 m (for a total of 5 values); * c = 00 200, step 2.50 (for a total of 9 values).

H [m] 10

11

s [m] 0.5

1.5

a

[deg] 15 10

dm,a

[m] 36.5

49.5

As you can see, design data (DL, E, c, L, D1, D2) being equal, the best solution dmax is clearly different in the two cases. In particular, with the unit Y, dmax is greater than 350% compared to unit X, and so also the energy consumed by the lighting installation with the Y lamp in the year is also reduced by 35%. Obviously the choice of a greater inter-distance d also involves the reduction in the initial cost for installation and maintenance [10]. VI. CONCLUSIONS The Authors have carried out a method to find a combination of parameters which optimizes an objective function by means of genetic algorithms. It is completely general and allows considerable savings of energy consumed in a year. The method has been applied to a real case. A big number of simulations has been carried out by the Authors on both different kinds of roads and different lighting units. From them it is possible to conclude that the best designs, from an energy saving point of view, are often obtained when the heights of the lighting poles are lower than those generally used. Therefore it is incorrect to think that the higher a lighting unit is more parts of the road are lit up. REFERENCES [1] L. Di Fraia, "Planunssoftwre fur okonomisch optimierte strabenbeleuchtungen", Elektropraktiker, Berlin, 1996. [2] L. Di Fraia, "Road lighting optimization: influence of the luminaire optic", in Proc. 8th European Lighting Conference, Amsterdam, May 1997. [3] M.Mitchell, Introduction to Genetic Algorithms. Boston (USA), MIT press, 1996. [4] S. W. Mahfoud, Niching Methods, T. Back, D. B. Fogel, Z. Michalewicz eds., Evolutionary Computation 2. Bristol and Philadelphia, IOP, 2000. [5] V. Cataliotti, G. Morana, Impianti elettrici di illuminazione. Italy: Dario Flaccovio Editore, 1997. [6] V. Carrescia, Illuminazione esterna. Italy: Ed. TNE, 2004. [7] UNI Requisiti illuminotecnici delle strade con traffico motorizzato, Norma UNI 10439, 2001. [8] UNI Requisiti per la limitazione della dispersione verso l'alto del flusso luminoso, Norma UNI 10819, 1999. [9] A. Chipperfield, P. Fleming, H. Pohlheim e C. Fonseca, "Genetic Algorithm Toolbox for use with MATLAB", version 1.2 of the User' s Guide, Department of Automatic Control and System Engineering, University of Sheffield. [10] A. Covitti, G. Delvecchio, D. Marinelli, F. Neri, M. Sylos Labini, "Algorithm of Optimization for the Maintenance of Roads Illumination with Verifies of the Analysis Costs-Benefits", in Proc. International Lighting Symposium - SINAIA 2004, Sinaia, Romania, 2004,

Fig. 6. Road lighting installation now existing at the ENEA centre of Trisaia (Rotondella, near Matera), Italy.

According to these values the possible combinations are equal to Ncomb = 2250. In other terms, if we wanted to optimize the design by means of the traditional method, we should have to process a number of combinations equal to Ncomb = 2250. On the contrary, the genetic algorithms method here proposed has made a number of evaluations which can be considered, on average, to be equal to Nevai GA= 202 (this value being the average of all the com-

pp.28-37.

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