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Optimal Electrical Distribution Systems Reinforcement Planning Using Gas Micro Turbines by Dynamic Ant Colony Search Algorithm Salvatore Favuzza, Giorgio Graditi, Mariano Giuseppe Ippolito, and Eleonora Riva Sanseverino

cost of power losses [Euro]; total energy losses evaluated at year [kWh]; cost for buying energy per year [Euro]; energy required by the loads at year [kWh]; revenues from the selling of the heat, per year [Euro]; thermal production at year [thermal kWh]; revenues from the selling of electrical energy, per year [Euro]; yearly objective function (costs – revenues) for a design solution [Euro]; number of years between two interventions; number of interventions in 24 years; distance, in economical terms, between two solutions in the reinforcement plan [Euro]; difference, at year , between the value of of configuration and the of configuration for value of new installations [Euro]; set of configurations that have been identified for the year configuration belongs to; pheromone amount between configurations and ; probability that the th ant moves from solution to solution ; economical impact of the best reinforcement plan [Euro]; year in which new installations have been executed; total number of edges of the th path;

Abstract—Distribution systems management is becoming an increasingly complicated issue due to the introduction of new energy trading strategies and new technologies. In this paper, an optimal reinforcement strategy to provide reliable and economic service to customers in a given time frame is investigated. In the new deregulated energy market and considering the incentives coming from the political and economical fields, it is reasonable to consider distributed generation (DG) as a viable option for systems reinforcement. In the paper, the DG technology is considered as a possible solution for distribution systems capacity problems, along several years. Therefore, compound solutions comprising the installation of both feeders and substations reinforcement and DG integration at different times are considered in the formulation of a minimum cost distribution systems reinforcement strategy problem. An application on a medium size network, hypothesizing a scenario of reinforcement also using as DG gas micro-turbines, is carried out using a novel optimization technique allowing the identification of optimal paths in trees or graphs. The proposed technique is the Dynamic Ant Colony Search algorithm. Index Terms—Cogeneration, distributed generation, gas microturbines, power distribution economics, power distribution planning.

I. NOMENCLATURE A. Variables load at year [kW]; DG systems installation cost [Euro]; maintenance cost per year and for all the DG units [Euro]; electrical energy produced by the DG units at year [kWh]; cables installation cost [Euro]; length of the cable [km]; cables maintenance cost per year [Euro]; MV/LV transformer installation cost [Euro]; maintenance cost per year for all transformers [Euro]; number of transformers;

number of iterations; total profit [Euro]. B. Fixed Parameters

Manuscript received May 31, 2005; revised October 30, 2006. Paper no. TPWRS-000326-2005. S. Favuzza, M. G. Ippolito, and E. Riva Sanseverino are with the Dipartimento di Ingegneria Elettrica, Elettronica e delle Telecomunicazioni, Università di Palermo, 90128 Palermo, Italy (e-mail: [email protected]; [email protected]; [email protected]). G. Graditi is with the Centro Ricerche ENEA, Portici, Napoli, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRS.2007.894861 0885-8950/$25.00 © 2007 IEEE

rate of increase of load; DG fixed installation cost [Euro]; DG variable installation cost per kVA [Euro/kVA]; sizing power of DG unit [kVA]; maintenance cost per year and per kWh [Euro/kWh];



cost per km of the cable for a given capacity [Euro/km]; cost of the transformer with rated power [Euro]; maintenance cost per transformer and per year [Euro]; cost of losses per kWh [Euro/kWh]; buying cost of energy per kWh [Euro/kWh]; unity price of the thermal kWh [Euro/thermal kWh]; ratio between and ; unity price of the electrical kWh [Euro/kWh]; rates for the calculation of the yearly cost; cross-section of the reinforcement cable at ]; the th branch [ actualization rate; parameter weighting the importance of the transition cost from configuration to configuration ; pheromone updating parameter, ruling its decay and its reinforcement; pheromone initialization value which is given to any possible tuple such as ; number of ants constituting the artificial colony; parameter between 0 and 1 ruling the elitism of the algorithm; number of candidate solutions in the following time step; ratio between the selling price of the heat in an hypothesized scenario and its actual market value. II. INTRODUCTION


HE formulation of the optimal reinforcement strategy to provide reliable and economical service to customers is one of the key issues for distribution utilities. When the load reaches a certain level, the system capacity must be adapted to the new requirements of the customers. In this case, it is possible to consider, together with the traditional network reinforcement means such as substation or feeders reinforcement, also other options such as distributed generation (DG) installation. Advances in DG technologies offer a broader class of possible installations, which may become competitive in terms of costs in the next years. When dealing with the problem of distribution systems reinforcement in a deregulated environment, and in the frame of sustainable development issues, a more precise estimate of costs is needed and the investment plan minimizing the total cost must be found. Renewable DG options can be considered as feasible alternatives to feeders and substations reinforcement only in the case they have a back-up system in order to make the output power dispatchable. Other options such as micro-turbines are dispatchable sources and they require small investments along time. Moreover the installation of DG minimizes the investment risk in competitive power markets and avoids or delays making large investments such as new substations.


In [1], the idea of distribution systems reinforcement planning using DG resources is clearly formulated. The authors discuss the possibility to consider DG as a feasible alternative to traditional reinforcement planning. They give an indication on how to formulate this problem in detail. In many other papers, pros and cons of the installation of DG units are considered and all the technical aspects of this problem are examined [2], [3]. Other papers address the formulation and solution of optimization problems involving both sizing and location of DG units. In [4], a method to identify optimal locations of distributed resources to minimize losses, line loadings and reactive power requirements is proposed. The method used to solve the optimization problem is a second order method. In [5], again the problem of optimal sizing and location of DG units is considered. The authors use a genetic-algorithm-based approach considering technical constraints as voltage profile and short-circuit current at the load nodes. In [6], the authors develop a method for generating combination of several construction plans of distribution systems, considering the yearly increase of network loads, but they do not consider the installation of DG units. In this paper, a planning process considering DG units (gas micro-turbines) as well as other conventional options is presented. The issue is a combinatorial optimization problem with non linear objective function and constraints, therefore a heuristic method has been used. The solution algorithm is a modified version of the Ant Colony System (ACS) algorithm called Dynamic Ant Colony Search (DACS). Other authors in the field of power systems use the ACS [7], [8], but the problem size is always limited. The problem considered in the present paper requires the solution of an almost new planning problem at each year (stage). For this reason, a mechanism for substituting new solutions with older ones has been implemented. Reliability and power quality aspects should also be considered within the formulation; as an example the introduction of DG may improve the service continuity. These aspects have not taken into account because current regulations do not allow intentional islanding. More in detail, DG also causes a change of the load conditions during the day in relation with the power output of the dispersed and partially undispatchable sources. When including such sources in the planning process, a modified planning process is required with respect to the economical and technical feasible application of the DG. Suitable simulation models for the new technological components and their inclusion into existing network planning are required for precise calculation of: — changing load-flow conditions in accordance with the load course and the discontinuous character of the DG. The consideration of only peak and weak load is not more suitable. A variation of static scenarios is required to find out the congestions in the network operation and the feasibility of energy management activities from the network point of view; — behavior in the case of faults and dynamic changes of load or topology (dynamic scenarios) which may cause adapted protection concepts and recovery strategies. On the other hand, due to the strategical importance of the faced problem to the long time term chosen in this paper for simulations and to the uncertainty of the many parameters related to all the above cited indices related to the model,



Fig. 1. Possible reinforcement of a generic MV/LV node when the load . creases of


L in-

the Authors have chosen an approach based on the formulation of different scenarios, each accounting for a set of general hypotheses. Of course, it is possible to choose different DG sources or even to account for prices, demand variations and power quality aspects by adapting the parameters and some procedures of the developed approach. III. PLANNING OF DISTRIBUTION SYSTEMS REINFORCEMENT The identification of a good reinforcement strategy in order to supply reliable and economical service to customers is a huge problem for distribution utilities. Traditionally planners start thinking about new capacity only when the load reaches a certain level and only a few options are considered; these are restricted to substation or feeders reinforcement. This methodology works when the economic environment is stable and the number of technically available options is limited. The new deregulated energy market and the new important issues concerning sustainable development make the environment change rapidly and technology provides new viable options for the task of expanding the systems capacity. In this paper, the problem of identifying the best network reinforcement strategy along a given timeframe is dealt with using a new formulation. The installation of DG units provides new viable options for the task of expanding the system’s capacity, alternative to traditional network-reinforcement methods, such as cables and substation transformers installation. In this formulation, the reinforcement consists in introducing parallel medium voltage (MV) cables and medium voltage/low voltage (MV/LV) transformers. It has been hypothesized, in the considered configuration, that both cables and transformers cannot be overloaded. Both DG units installation at LV level and traditional network reinforcement using new cables and transformers can be adopted at each bus. Generally this problem can be faced in presence of any kind of DG. In particular this work considers the possibility to integrate some units of cogeneration (gas micro-turbine) with the distribution system. Fig. 1 shows a generic MV/LV load node of the considered system. In the figure, OT is the Old Transformer, whereas RT is the Reinforcement Transformer. Therefore the problem, here dealt with, results in a combinatorial optimization problem, where the main objective is that of minimizing the overall cost while meeting some technical constraints such as voltage drops limitation and components current capacity consideration. The overall yearly operational revenue

can be expressed as the summation of different terms. Some are derived from the installation of the elements, others from operational conditions, such as losses, fuel and maintenance costs. In addition, the economical benefit deriving from the selling of the heat, which can also be produced by the micro-turbines, has been considered. Beginning with a suitable formulation of these terms, in the paper a methodology for the dynamic planning of reinforcement actions of networks is proposed. The methodology represents a strategical means to direct the plant’s development in a long-term perspective. According to the strategical value of this approach, the proposed method of planning is based on the construction of different scenarios and, then, on their comparison. To this purpose the planning process must allow to generate various scenarios for the different evolutions of load, of fuel price, of energy price, etc. In what follows, all the terms of the problem are described in detail. In the present formulation of the posed problem, all the loads evolve uniformly with the following exponential law:

(1) There are different economical terms that must be considered. Referring to the symbols indicated in Section I: a) The DG systems installation cost can be expressed as

(2) The sizing of the DG units has been carried out considering that the direction of the power flows cannot change because this would produce a significant modification of the voltage profile. The maintenance cost per year and for all the machines can be evaluated as

(3) b) The cables installation cost can be expressed as

(4) In this application, we have considered underground cables. The maintenance costs per year is evaluated in

(5) c) The MV/LV substation transformer installation cost can be expressed as

(6) The maintenance cost per year and for all transformers is evaluated as



d) Cost of power losses can be expressed as (8) e) Selling and buying terms; the present formulation must consider some selling and buying terms. The first term to be considered is the one expressing the cost for buying energy from the transmission level. Per year, it can be evaluated as (9) Two other terms express the revenues that are included in the process. The first expresses the revenues per year produced by the selling of the heat considering that the units would work fully loaded at all times (10) The second term to be considered expresses the revenues deriving from the selling of electrical energy per year (11) Therefore these two terms, and , must be subtracted to the overall yearly cost related to the installation of distributed generation units. IV. OTHER GENERAL ISSUES An underlying hypothesis formulated in this paper is that the distributor can diversify its activity and also sell heat. In the current liberalized gas and electrical energy market, in wide residential commercial or industrial areas, utilities may offer heat and electrical energy supply contracts at favorable conditions for customers, installing distributed cogeneration units (in particular gas micro-turbines). The integration of these units changes the levels of service continuity at customers. It is very difficult to evaluate these effects in economic terms, effects which vary with the regulation of intentional islanding, of penalty/bonus mechanism for the utilities and with other rules. In general, each country has a proper regulation. For this reason, the proposed methodology does not take into account these aspects. V. THE YEARLY OBJECTIVE FUNCTION The yearly objective function can be obtained as the summation of the different terms above described

(12) where and are the rates for the calculation of the yearly cost depending on the presumed lifetime and the interest rate. The constraints concern voltage drop within limits and current


below branches capacity. Another constraint is related to the requirement of full loads supply. A single solution is coded into a string having two times the number of branch elements, so that each couple of elements is related to one branch and to its ending bus. The solution string is therefore a vector composed as follows: (13) Each of these elements can vary in a discrete fashion among a set of possible available sizes. The optimization problem here dealt with is then a combinatorial maximization problem, therefore the fitness can be expressed as the inverse of the cost function (12). In [9], the authors have focused their attention on the definition of the minimum cost reinforcement plan with a simplified objective function and renewables installations which were not dispatchable; the Evolutionary Parallel Tabu Search algorithm was suitable for static combinatorial optimization. In this paper, the authors propose a more efficient formulation including dispatchable units and a novel dynamic design strategy. It is aimed at the optimization of the expansion strategy of a distribution system through a discrete number of interventions within a time frame of 24 years with reference to a load increase in the served area. The problem is combinatorial and nonlinear and has been dealt with by means of a dynamic version of the ACS algorithm. VI. THE DYNAMIC ANT COLONY SEARCH ALGORITHM The ACS algorithm, proposed by Dorigo and Gambardella [10], is an algorithm simulating the behavior of natural ant colonies. The algorithm uses a set of agents which cooperate for the research of new solutions acting simultaneously. This algorithm has been applied to different problems in engineering, in particular to those applications where a length measure must be optimized such as in the Travelling Salesman Problem, (TSP)1. This algorithm has rarely been applied for optimization strategy problems. However there are some papers regarding this aspect for different engineering fields [11], [12]. The key to the application of the ACS to a new problem is to identify an appropriate representation for the problem, namely an appropriate “spatialization”. The latter can be attained by means of a graph representation (when possible) of the considered engineering problem. Any solution must also be represented by means of a tour through the edges of the graph. Besides, a suitable expression of the distance between any two nodes of the graph must also be determined. Then the probabilistic interaction among the artificial ants mediated by the pheromone trial deposited on the graph edges will generate good, and often optimal, problem solutions. In the application here proposed, the different reinforced configurations of the electrical system at different years (with the relevant load factor) represent the nodes of the graph, the distances between them are transition costs, suitably actualized in order to make them comparable at year zero. The transition costs are the installation costs to 1The TSP is the problem of finding, given a finite number of “cities” along with the cost of travel between each pair of them, the cheapest way of visiting all the cities and returning to the starting point.



expand the system from the current configuration to another to be reached in the following time. The problem of identifying the best reinforcement strategy of distribution systems is essentially a minimum cost tour problem, but there is not a unique set of points to be visited for a single solution, there are indeed infinite possible paths through different points. The basic difference with traditional ACS is that the algorithm dynamically creates new candidate solutions and eliminates unpromising search directions. In this way, at each year a number of candidate solutions is identified; these are the analogue of the cities that have to be visited in the TSP. It is realistic to assume that utilities do not operate each year but they carry out years. A solution strategy is interventions only every therefore a “tour”’ comprising all the system’s configurations intervals of between year zero and year 24 with years; the cost of a strategy is the summation of the transition costs in the considered time horizon. The distance between two solutions, namely between configuration , related to year () and configuration related to year , is given by defined as follows:

(14) Configuration that has to substitute the starting configura: tion is identified by means of the following law, if (15) is a random number and is a paramwhere eter allowing to regulate the elitism of the algorithm, namely to establish a compromise between exploration and exploitation is very close to the unity, it of the search space. Indeed, if is highly possible that the random parameter is lower than and therefore that configuration is the maximum of the func). tion ( configuration is chosen following the probabilistic If law:

(16) The probability that the th ant moves towards a configuration of the same year must be zero, whereas a biased law has been used to select the “city” towards which the ant shall move. The local updating, to prevent premature convergence and simulate the natural phenomenon of evaporation of the pheromone, is executed on the traveled paths by means of the function (17) Global updating is executed when all ants have completed an entire tour for exploration and it is aimed at the reinforcement of belonging to the best the pheromone of those transitions tour, namely to the minimum cost strategy, in the last iteration.

In this way, the pheromone of the transitions belonging to the best tour is increased whereas the pheromone of other transitions is decreased. It is performed using the function global best tour (18) is the economical impact of the best strategy which where has been identified in the last iteration (the “length” within the DACS algorithm); it is defined as

(19) Note that when equals the total number of edges of the considered path, the ant has reached the target configuration and the strategy is complete, therefore (19) gives the cost of the entire strategy actualized at the starting year. In the traditional ACS algorithm, a number of ants starts exploring the search space which is constituted by a finite number of points. Then they gradually converge towards the best path. When the search space of the faced problem is intrinsically of finite type, as in the TSP, the original ACS algorithm works quite well. When instead the search space is large and a “spatialization” (discretization or reduction of the search space dimension) of the problem is required, the above cited approach may be no more valuable. Indeed, it is well known that in these cases, trying to reduce the search space dimensions may bring to misleading results. Real ants indeed move randomly before finding the optimal way from their nest to the food. They do not have discrete points in the search space through which they move. This happens especially at the beginning. After some time, the ants go one after the other towards the food, because of the mechanism of the pheromone release. This is the idea behind the DACS algorithm. Using the DACS algorithm the search tree is indeed created by the search agents. In this representation of the problem, the depth of the tree is the timing at which the interventions over the distribution system are carried out, see Fig. 2. So the maximum depth of the tree, , is fixed by the user. Since the overall time frame in which the strategy is designed is also fixed, the number of years between one intervention and is also known. The basic hypothesis is that the other components are installed in order to face the load increase relevant to the following time interval and at the beginning of the same time interval. Each branch of the tree represents the move later; it is weighted with the cost of from one year to the possible installation of new components or with the cost of the yearly amortization expense. The algorithm starts with the generation of a given number of candidate solutions, , each of which is created accordingly with a given percentage of penetration of the DG units. In this way, in the first created solution, all the nodes of the system are equipped with installations with rated power between ; in the second solution, the units will have rated 0 and and , and so on. power randomly chosen between and are chosen Since the power flows can never invert, in order to never exceed the power required by the loads at the


Fig. 2. Dynamic tree representing the different strategies, p


2 [0; T].

starting year. The data structure used to represent the search tree is a dynamic tree, thus it is well possible to choose different at each step of the strategy. Of course, this would produce an increase in the complexity of the problem that would require at each time step also to generate solutions referring to different elementary time intervals. Further studies will address existing paths it can still this issue. When the ant finds new solutions with different DG penetrations and generate it will again activate the selection using expressions (15) and (16). If an existing path is selected, the pheromone trace is modified according to (17); if instead a new trace is selected, the worst, in terms of pheromone and cost, among the old paths is selected and eliminated, together with the branches and nodes downstream, and replaced with the chosen new trace. The pheromone trace is then modified according to (17). At the end of the generation, all the ants have gone through the 24 years and probably have generated a number of new nodes. The maximum possible number of nodes of the dynamic tree , where is the number of containing the traces is of order . is variable and can be set by the user. intervals of It defines the precision with which the algorithm can work out a solution. On the other hand, the opportunity to generate a new set of solutions at each step gives some confidence about finding the solution with appropriate diversification. Also is variable and can be set by the user, but it is a design variable since the timing with which interventions can be carried out on the system is also a design choice. In Fig. 3, the flowchart of the DACS is is the ants counter. reported, where At the end of this section, it is useful to remark that the dynamic nature of the proposed algorithm seems suitable to study dynamic scenarios in a long-term perspective. Indeed the optimization process produces a series of reinforcement actions: any action is operated at the beginning of a subperiod ( -years). When a generic subperiod ends, it is possible to repeat the application of planning procedure, starting from more accurate previsions of evolution of load, of fuel price, and so on. VII. APPLICATIONS The studied system is a radial power distribution network with 20 kV of rated voltage. It has 23 branches and 23 load nodes as depicted in Fig. 4. Each load node is represented in Fig. 1. The reinforcement strategy is carried out in a time frame of 24 years and with interventions that can be carried out every

Fig. 3. Flowchart of DACS.

Fig. 4. Test system.

years. The yearly rate of increase of the loads, , is 0.03. The minimum rated power of DG micro-turbines installa, is 50 kVA. The Authors have assumed that coeffitions, cients and have the same value (7%). The runs have been carried out using the parameters and the values reported in Tables I and II. The DACS parameters are taken from the literature on ACS and if they are varied within a small range they do not produce





significant variation in the attained results. The only parameters really influencing convergence and calculation times are the number of ants and the branching factor. Choosing larger numbers for these parameters gives a more stable solution, but sometimes due to the discrete nature of variables (available size of DG units, cables and transformers), it turns to be unjustified in terms of calculation times as compared to the limited improvement obtainable. Several runs have been carried out considering different scenarios. Each of these is characterized by a different value of the parameter which indicates the ratio between the selling price of the heat in the hypothesized scenario and its actual market value (in Italy 0.066 Euro/kWh). Figs. 5 and 6 show the results of the executed simulations in the different scenarios : in terms of total DG power installed and of profit

Fig. 5. Total DG power installed for different timings of the reinforcement and different values of .


(20) Fig. 6. Profit from the installation of micro-turbines for different timings of the reinforcement and different values of .

where is the yearly objective function, at year , expressed in (12). As it can be observed no installation of DG units is below or equal to 0.7. is suggested when the parameter Other values instead suggest some installations with an entity that depends on the considered scenario in terms of the chosen values. For values of timing of the interventions and of the below or equal 0.7, the optimization procedure does not suggest any installation of DG units and proposes traditional reinforcement means for the considered system. For fixed the rated power of DG units to be installed varies with the adopted number of interventions along the considered timeframe. In particular, for values of around 0.8, the gas micro-turbines installation is favorable above all for strategies based on few numbers of interventions (in particular 3 8 as shown in Fig. 5); this indeed makes stronger the influence of the revenues coming from the selling of the heat for a larger time frame. Quite interesting are also the results shown in Fig. 6. It is evident that decreases, the total profit also decreases up to (for as ) the minimum value (about 78 MEuro) which is attained executing the reinforcement only with traditional means. , the courses show a certain dependency on the For chosen timing, with maximum values when the number of interventions is four and six in 24 years. The proposed procedure, in terms of alternative development of distribution systems, allowing the penetration of DG micro-turbines, determines a more



rational usage of the primary energy sources thanks to the contemporaneous fruitful employment of heat and electrical energy. Some other runs have been carried out in order to test the efficiency of the proposed algorithm as compared to an evolutionary algorithm. Robustness and better results are the features characterizing the proposed approach. Table III reports the results of 20 runs, in terms of average value and standard deviation , over a reinforcement plan with four interventions of profit every six years by using the evolutionary parallel tabu search (EPTS) [8], a genetic algorithm (GA) and DACS. In these runs, . As it can be observed, standard deviation is worst for EPTS and GA, whereas it is considerably better for DACS. The average value of the attained overall profit ( ) is still better for DACS, whereas GA and EPTS get lower values. Finally the


average number of function evaluations to attain the above reported results is around 2000 for DACS, around 800 000 for EPTS and around 10 000 for GA. The reason for these results resides in the difficulty to detect the linkage between the high fitness solutions substrings for a traditional GA or even for a more effective EPTS, when the problem has a dynamic nature and thus requires a dynamic solution approach. VIII. CONCLUSIONS In this paper, the problem of the reinforcement of distribution systems considering different scenarios and using DG units, in particular gas micro-turbines, instead of traditional means, such as cables and transformers, has been studied. The comparison has been carried out trying to correctly evaluate the two possible alternatives also considering the possibility to couple them together in the same system. The results put into evidence that the installation and maintenance costs of the DG units are economically interesting as compared to traditional means because they give the opportunity to produce heat. The problem presents a large number of mixed-integer variables and is a typical dynamic optimization problem. For this reason, the authors have set up a modified version of the Ant Colony Search optimization which can be used for dynamic optimization problems. The algorithm has proved to be robust and able to deal with large search spaces since it dynamically creates the search routes, such as real ants do. The algorithm is also a valuable tool to solve the same problem using different DG sources such as biomass, photovoltaic systems, as well as fuel cells or even a combination of these, and to make comparisons in order to find out general guidelines for the installation of DG sources and renewables in existing networks. It is also easily possible to change the times of interventions or even make these parameters optimization variables. The algorithm can easily be modified to push the research towards exploration or towards exploitation by tuning the parameters. REFERENCES [1] R. C. Dugan, T. E. McDermott, and G. J. Ball, “Planning for distributed generation,” IEEE Ind. Applic. Mag., vol. 7, no. 2, pp. 80–88, Mar./Apr. 2001. [2] W. Sweet, “Networking assets,” IEEE Spectrum, vol. 38, no. 1, pp. 84–88, Jan. 2001. [3] L. Philipson, “Distributed and dispersed generation: Addressing the spectrum of consumer needs,” in Proc. IEEE Power Engineering Society Summer Meeting, 2000, Jul. 16–20, 2000, vol. 3, pp. 1663–1665. [4] N. S. Rau and Y.-H. Wan, “Optimum location of resources in distributed planning,” IEEE Trans. Power Syst., vol. 9, no. 4, pp. 2014–2020, Nov. 1994. [5] G. Carpinelli, G. Celli, F. Pilo, and A. Russo, “Distributed generation siting and sizing under uncertainty,” in Proc. IEEE Porto Power Tech 2001, Porto, Portugal, Sep. 10–13, 2001.


[6] T. Asakura, T. Yura, N. Hayashi, and Y. Fukuyama, “Long-term distribution network expansion planning considering multiple construction plans,” in Proc. Power Systems Technology (PowerCon 2000), 2000, vol. 2, pp. 1101–1106. [7] J.-H. Teng and Y.-H. Liu, “A novel ACS-based optimum switch relocation method,” IEEE Trans. Power Syst., vol. 18, no. 1, pp. 113–120, Feb. 2003. [8] J. G. Vlachogiannis, N. D. Hatziargyriou, and K. Y. Lee, “Ant colony system-based algorithm for constrained load flow problem,” IEEE Trans. Power Syst., vol. 20, no. 3, pp. 1241–1249, Aug. 2005. [9] A. Augugliaro, L. Dusonchet, M. G. Ippolito, and E. R. Sanseverino, “An optimal reinforcement strategy for distribution utilities with distributed generation using an evolutionary parallel tabu search approach,” in Proc. Int. Conf. PMAPS 2002, Naples, Italy, Jun. 2002. [10] M. Dorigo and L. M. Gambardella, “Ant Colony System: A cooperative learning approach to the Traveling salesman problem,” IEEE Trans. Evol. Comput., vol. 1, pp. 53–66, Apr. 1997. [11] S.-J. Huang, “Enhancement of hydroelectric generation scheduling using ant colony system based optimization approaches, energy conversion,” IEEE Trans. Energy Convers., vol. 16, no. 3, pp. 296–301, Sep. 2001. [12] I.-K. Yu, C. S. Chou, and Y. H. Song, “Application of the ant colony search algorithm to short-term generation scheduling problem of thermal units,” in Power System Technology, Proc. Int. Conf. POWERCON ’98, 1998, vol. 1, pp. 552–556. Salvatore Favuzza received the doctoral degree and the Ph.D. degree in electrical engineering from the University of Palermo, Palermo, Italy, in 1996 and 2000, respectively. Since 2002, he has been a Researcher at the Department of Electrical Engineering, University of Palermo. His main research interests include power systems analysis, optimal planning, and the design and control of electrical distribution systems.

Giorgio Graditi received the doctoral degree and the Ph.D. degree in electrical engineering from the University of Palermo, Palermo, Italy, in 1999 and 2005, respectively. Since 2001, he has been a Researcher at the Italian National Agency for New Technologies, Energy and Environment (ENEA), Napoli, Italy. His main research interests include PV power systems applications, energy system conversion, and the design of electrical distribution systems.

Mariano Giuseppe Ippolito received the doctoral degree and the Ph.D. degree in electrical engineering from the University of Palermo, Palermo, Italy, in 1990 and 1994, respectively. From 1995 to 2001, he was a Researcher with the Department of Electrical Engineering, University of Palermo, where he is now an Associate Professor of Power Systems. His main research interests include power systems analysis, optimal planning, design and control of electrical distribution systems, and power quality.

Eleonora Riva Sanseverino received the doctoral degree and the Ph.D. degree in electrical engineering from the University of Palermo, Palermo, Italy, in 1995 and 2000, respectively. From 2001 to 2002, he was a Researcher in the field of computer systems and computer networks at the National Council of Research. She is now an Associate Professor of Power Systems at the University of Palermo. Her main research interests include optimization methods for electrical distribution systems’ design, operation, and planning.

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