Modelling of Microgrid-Renewable Generators Accounting for Power ...

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 28, NO. 4, OCTOBER 2013

Modelling of Microgrid-Renewable Generators Accounting for Power-Output Correlation Stefania Conti, Member, IEEE, and Santi Agatino Rizzo

Abstract—The possibility to operate in islanding mode some portions of a distribution network, after fault occurrence, helps to improve system reliability. In this perspective, it is crucial to estimate the ability of distributed generators (DGs) to meet the local load. A major issue in the adequacy assessment is to take into account the correlation existing among the power outputs of DGs based on the same renewable intermittent primary energy source (sun, wind). This paper presents a new modelling approach to provide the hourly generation models for each type of renewable DGs, by taking into account both power correlation and hardware availability. An interesting aspect of the proposed approach is that it encompasses such correlation, avoiding the analytical calculation of its value. An innovative method to obtain hourly load models is also presented. Finally, a method to evaluate analytically loss of load probability by using the proposed generation and load models is also described. Both the presented method and Monte Carlo simulations (MCS) are applied to the IEEE RBTS-BUS6. Applying the proposed models and analytical method actually enables obtaining benchmark results to test approximated models and/or MCS results. Index Terms—Benchmark testing, correlation, distributed power generation, power system modelling, power system reliability.

I. INTRODUCTION

T

HE “20-20-20” targets of the EU climate and energy package are a reduction in EU greenhouse gas emissions of at least 20% below 1990 levels, 20% of EU energy consumption to come from renewable resources, and a 20% reduction in primary energy use compared with projected levels, to be achieved by improving energy efficiency [1]. To do this, many countries adopt new policies to provide incentives to use renewable energy sources and to increase energy efficiency. Such policies, along with the electricity market liberalization, bring about challenging issues to be faced by the distribution network operators (DNOs). In the last decade, distribution networks have gradually passed from a “passive” system to an “active” one, creating the necessary conditions to implement the network paradigm of smart grids [2]. This is possible by exploiting suitable monitoring and control technologies to minimize the potentially negative impact of a high penetration of distributed generators

Manuscript received June 14, 2012; revised September 17, 2012 and February 07, 2013; accepted March 26, 2013. Date of publication September 12, 2013; date of current version September 19, 2013. Paper no. TPWRD-00617-2012. The authors are with Dipartimento di Ingegneria Elettrica, Elettronica e Informatica (DIEEI), University of Catania, Catania 95125, Italy (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2013.2265606

(DGs) in terms of power-quality (PQ) problems especially related to voltage regulation [3], [4] and protective relays coordination [5], [6]. Actually, smart-grid implementation even means the ability to make DGs and energy storage systems a resource for DNOs to improve system reliability and provide ancillary services. In this perspective, researchers investigate the potential advantages coming from microgrids and multimicrogrids networks [7] implementation and islanding operation of DGs. The possibility to continue supplying loads by means of the local generators is acknowledged as a valuable prospective way to improve reliability [5], [8]–[15], even though DNOs have traditionally been considered preferable, for safety and protection reasons, to disconnect the DGs when a network fault occurs, thus preventing DGs from operating in islanding mode. The distribution network, in which DGs are installed, can be seen as a minicomposite system having characteristics previously associated only with the “second hierarchical level” of a power system (HLII) [16], especially when DGs are necessary to support the network load, which is evidently the case of an islanded microgrid (in the following text, it is simply called an “island”). Hence, the concept of power system adequacy, historically related to the ability of generation to meet the load at the “first hierarchical level” (HLI) [16] can be extended to distribution islands. Then, indices such as loss of load probability (LOLP), loss of load expectation (LOLE), and loss of energy expectation (LOEE) [17] can be used to evaluate the adequacy of local DGs to supply the islands’ load. In the reliability perspective, DGs can generally be grouped into two main types. The power output of one type depends on need and availability of the generation units themselves (e.g., gas and diesel generators). These DGs are, hereafter, referred to as conventional distributed generators (CDGs). The contribution of other types of generators depends, on one hand, on need and hardware availability, and on the other, on the amount of available energy from the intermittent primary source (e.g., sun and wind). These DGs will be referred to as unconventional distributed generators (UDGs) [14], [16]. UDGs’ impact on adequacy has been mainly investigated at HLI by means of Monte Carlo simulations (MCS) and analytical methods [18]–[31]. Over the last few years, adequacy assessment has been carried out for islanded portions of distribution networks too [9], [15], [32]–[36]. A major difficulty in the adequacy assessment in the presence of UDGs is to deal with the power-output correlation among those UDGs that depend on the same fluctuating energy source. In the following text, a set of generators made up of UDGs of the same technologies is called a class (e.g., photovoltaic class and wind class).

0885-8977 © 2013 IEEE

CONTI AND RIZZO: MODELLING OF MICROGRID RENEWABLE GENERATORS

Recent works propose some solutions to evaluate wind speed correlation [37], [38]. Some papers specifically deal with the issue to develop models accounting for wind speed correlation [23]–[26], [30] in order to assess the adequacy in an island more accurately. The main drawbacks of these approaches are one or more of the following: they require a numerical estimation of the correlation; they need a reference site to be appropriately chosen in the correlation assessment procedure; they do not include the hardware availability. Moreover, the use of the developed models is often limited to either analytical methods or MCS only. Then, in order to overcome the limitations of the aforementioned drawbacks, this paper presents a new method to model correlation for a class of UDGs. The proposed modelling approach provides hourly generation models for a class of UDGs supplying an island, taking into account power-output correlation. A new load modelling approach to provide hourly load models is also presented. The hourly approach enables taking into consideration correlation among loads, correlation among different classes of UDGs and, finally, correlation among loads and UDGs [39]. The presented models can be used to assess adequacy by means of both analytical methods and MCS [17]. The application of the proposed models and analytical method actually allows obtaining benchmark results to test approximated models and/or MCS results. Finally, a case study is presented in order to apply analytical and MCS methods. II. DISTRIBUTION RELIABILITY AND ADEQUACY Typical quantities to evaluate distribution system reliability are system average interruption frequency index (SAIFI) and system average interruption duration index (SAIDI) [40]. These indices can be estimated in a probabilistic manner from the annual outage rate and duration , that are, respectively, the number of outages and the total outage time in a year for load point (LP) [17]. An LP is a secondary substation supplying customers. In [14], an innovative generalized systematic approach and an analytical formulation to evaluate the distribution system reliability in a multi-microgrid network environment [7] are proposed, in which the islanded operation of microgrids helps to improve local and overall reliability, thanks to an advanced automation and protection scheme. In order to do this, such an analytical formulation takes into account the adequacy of conventional and renewable DGs (e.g., photovoltaic (PV) or wind generators) by using probabilistic models for loads and generators. In detail, [14] presents an accurate classification of possible scenarios and for each of them, provides the related analytical expressions to assess the LPs’ annual outage rate and duration in the distribution network where islanded operation may be permitted. Such a formulation takes into account the benefits, in terms of annual outage rate and duration reduction, due to the presence of DGs in the network along with the opportunity to operate in islanded mode some portions of the network itself. A probability of adequacy (PoA) is considered, where PoA is the probability that island DGs are able to meet the local load.

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As stated before, traditional adequacy indices applied for generation level (HLI) can be used to evaluate PoA of local DGs in distribution islands. The loss of load probability (LOLP) appears to be the better one to estimate PoA, as follows: (1) LOLP is a measure of the probability that the load will exceed the available generation but does not evaluate the severity of the event. In this paper, the modelling criteria described in Sections III–V are applied to carry out hourly load and generation models that can be applied to evaluate LOLP by using the approach (similar to the one used in [39]) presented in Section VI. Note that a single load model must be carried out for each LP, independently by the island which the LP belongs to. On the other hand, one generation model must be carried out for each class of generators on the entire island, and another generation model must be carried out for the entire set of CDGs of the island.

III. LOAD MODEL The load model is carried out by studying typical days of the periods in which the year has been divided, for example, the four seasons. In detail, the typical days analyzed are “workday” (W) and “holiday” (H, including the days of the weekend). A typical day is represented by means of 24 hourly models. Hence, assuming to divide a year into a number of periods, the load model is represented by means of hourly models. Historical data, in terms of active power absorbed by an LP, are used to create the 24 hourly models for each typical day of all periods in which the year has been divided. Obviously, if the data items related to a specific hour of some day are not available, the hourly model related to that hour can be obtained even so, but it will be less accurate than the other ones, derived by a higher number of items. The hourly model of an LP at hour can be represented by means of several power demand levels linked to their probabilities, similar to the annual load model [14]. It is worth noting that the use of a load hourly model for each LP, permits taking into consideration the power demand correlation among the island’s LPs as well as the correlation between power demand of LPs and power output of different classes of UDGs belonging to the same island, while the annual model lacks in these useful features [39]. Table I shows an example of hourly and annual load model with five levels of power, where: LP; period (e.g., a value between 1 and 4 when the years is divided into the four seasons); type of day (1 stands for W, 2 stands for H); hour (a value between 1 and 24);

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TABLE I EXAMPLE OF HOURLY AND ANNUAL LOAD MODEL FOR AN LP

TABLE III EXAMPLE OF HOURLY MODEL FOR AN LP CARRIED OUT BY APPLYING THE PROPOSED PROCEDURE

TABLE II EXAMPLE OF HOURLY MODEL FOR AN LP , CONSIDERING HOURLY PEAK

Fig. 1. Procedure to subdivide the ordered historical data items when their number is not a multiple of the levels’ number of the hourly model.

probability that LP absorbs active power equal to level , at hour , in day of period (superscript stands for “Load”); probability that LP absorbs an active power equal to level during the year. The drawback of such an approach, as highlighted by Table I, is obviously to provide a probability equal to zero for many levels due to the low data dispersion. In fact, the historical data related to a specific hour of a typical day are close to each other, especially when a high number of periods is considered (e.g., the 12 months of the year). By using the percentage of the hourly peak related to hour , instead of the annual peak, into the model does not permit overcoming this negative aspect. In this case, such an approach provides a probability equal to zero for the lower levels (i.e., 1,2,3 ) and a probability greater than zero for the higher ones, as shown in Table II. A procedure to obtain an hourly model is proposed in order to overcome this drawback. In detail, for an LP , the hourly model related to hour of a typical day for period , is obtained by means of the following procedure (referred to as “load modelling procedure”). 1) The collected historical data (i.e., the values of active power absorbed by the LP at hour in all days of type belonging to ) are sorted in ascending order. 2) The number of levels of the hourly model is defined as and the number of data items collected is defined as . The ordered data are subdivided into sets. The first values will belong to the first set, the second will belong to the second set and so on; finally, the last values belong to the th set. Indeed, data belong to each set only if is a multiple of (if is not, some procedures are presented in the following text to subdivide the data). 3) The mean value is computed for each set and such a value is linked to a level. In detail, the mean value of the first

set is linked to level 1, the mean value of the second set is linked to level 2, and so on, so that the mean value of the last set is linked to level . 4) The hourly model is represented by the percentage of these mean values with respect to the annual peak. The probability linked to each level is equal to the number of data items in the related set divided by . Note that, each probability is equal to when is a multiple of . Otherwise, each probability is equal to or and, obviously (2) Table III shows an example of an hourly model carried out using the proposed approach, when the data items number is a multiple of the levels number of the model. When is not a multiple of , two approaches can be followed: 1) some data are removed or duplicated to obtain a multiple of ; 2) some specific procedure must be applied to subdivide the data into the sets. In the first case, some data can be removed (or duplicated) either randomly or by considering the boundary values (i.e., the lowest and greatest ones in the set). In the latter case, a procedure to subdivide the ordered data can be the one shown in Fig. 1. IV. GENERATION MODEL OF UDGS The generation model for a class of UDGs is carried out by studying a typical day of each period in which the year has been divided. Obviously, differently by the load model, no distinction is made between W and H days to create the generation model.


On the other hand, a typical day will be represented by 24 hourly models, similar to the modelling procedure applied to the load. Hence, assuming to divide a year into periods, the generation model is represented by means of hourly models. The power output of UDGs belonging to the same class and connected to the feeders supplied by the same primary substation is correlated owing to the relatively small geographic distance between the generators. Of course, the smaller the distance between two UDGs of the same type, the greater the correlation. The fact is even more evident in an islanded microgrid because of its reduced extension. Correlation between load power demand and UDGs power output is taken into account by using a hourly approach [39]. On the other hand, this is not enough in order to consider power output correlation among UDGs that depend on the same fluctuating energy source (i.e., a class of UDGs). In fact, to do this, an appropriate procedure is required. The modelling procedure proposed in this paper takes into account the correlation of UDGs power output for a given class, , also by considering their availability probability. One generation model is carried out for each class. The following procedure (called “generation modelling procedure”) is applied to obtain such a hourly model for hour of a period . 1) Simultaneous power outputs of the UDGs belonging to a class are put together in the same set. For example, assuming to know historical data spanning over four years (from 2006 to 2009) for a class made up by 3 PV generators (where is the number of UDGs in class ), considering 10, 12, and 5 (i.e., May), there are 4 (years) 31 (days of May) sets 124), each one made up by three data items (each data item is the power produced by one of the aforementioned PV generators). Then, a set is made up by the power output of each generator on the May 1, 2006; another power output of each generator on May 2, 2006, and so on; finally, the last set is made up by the power output of each generator on May 31, 2009. 2) The CAPT, here defined as the complementary of capacity outage probability table (COPT, see [17, Ch. 2, Table 2.6]) is applied to each set. To obtain CAPT for powers’ set , first, each UDG is represented by means of a two-state model (state 1 means “available generator”, state 0 means “not available generator”). Then,. each state combination is considered, thus obtaining powers, , with the . Table IV shows an example of related probability, CAPT for a set ( , and ) of a class made by 3 UDGs ( , and , where FOR stands for forced outage rate [17]). For example, in row 4 of Table IV, is obtained by summing up and , while is given by the product of by by . 3) Then, by applying the CAPT to each set, a number of power values equal to is obtained. A procedure similar to the “load modelling” one is applied to these powers to develop the hourly model. The power

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TABLE IV EXAMPLE OF CAPACITY AVAILABLE PROBABILITY TABLE

TABLE V EXAMPLE OF HOURLY MODEL FOR A CLASS

values are sorted in ascending order and for each of them the associated probability, that is, the one in the CAPT, is stored. 4) The ordered power values are subdivided into sets (note that, these sets are not those considered so far in points 1, 2 and 3 for the generation modelling procedure, but are similar to those of point 2 of the load modelling procedure). The first values will belong to the first set, the subsequent values will belong to the second set and so on; finally, the last set (which is the th one) is made up by the last values. When is not a multiple of , the procedure shown in Fig. 1 is applied to subdivide the power values. 5) The mean value is computed for each set and such a value is linked to a level. The stored probabilities related to the powers belonging to a set (see step 3) are summed up and the resulting value is divided by . Then, the result is the probability linked to the set (i.e., to the related level). 6) The hourly model is represented by the percentage of these mean values with respect to the sum of the rated powers of the UDGs belonging to the class. The probability linked to each level is equal to the one of point 5. Table V shows an example of hourly model with five levels for the UDGs of a class . V. CONVENTIONAL GENERATION MODEL The power output of a CDG only depends on need and the availability of the unit itself. The basic generating unit parameter used in static capacity evaluation is the probability of finding the unit on forced outage at some distant time in the future. In power system applications, this probability is known as the unit forced outage rate (FOR) (i.e., FOR is a measure of the unit unavailability probability) [17]. Such a quantity does not depend on the amount of the primary energy source available. Then, each CDG can be modelled independently by the other ones. The simplest generation model

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TABLE VI EXAMPLE OF GENERATION MODEL FOR A CDG

TABLE VII EXAMPLE OF AN HOURLY MODEL FOR AN LP

for a CDG is the two-state model, as reported in Table VI [14], where is the probability of generating a power output equal to the one corresponding to level . In the previous section, a procedure has been described to develop a single model for each class of UDGs. Such a procedure takes into account the correlation among the values of the energy source in the area of a distribution island. On the other hand, even though, as said before, the available power output of each CDG is not correlated, it is useful to consider a single model for the whole set of CDGs in order to highlight the contribution on adequacy of the overall CGDs set. For this reason, a single generation model is obtained for the local conventional generators by applying the CAPT to their rated power as in Table IV.

probability that the whole load is equal to level in period , day , hour , during islanding operation of microgrid (in other words, it is the probability related to one of the aforementioned combinations); probability that the whole available generation (CDGs and UDGs) is less than load level in period and hour , during islanding operation of microgrid (in other words, it is the probability of loss of load and its value can be obtained directly from the capacity outage probability table [17] obtained by combining all generation models); number of generation combinations for which the whole available generation is less than load level considering the DGs of island ;

VI. LOLP EVALUATION LOLP has been computed similar to [39], with the difference that the considered load model is not given by a single load value for each hour. In details, in this paper, all load combinations and the related probability for each hour have been considered. Then, the hourly LOLP is computed as

probability related to one ( th) of the aforementioned combinations

.

is obtained by means of

Finally, LOLP for island

(3) (5) (4) where where island; number of load combinations, considering the hourly load model at hour in a day of period for the LPs belonging to island (e.g., consider 5 LPs, respectively, two of which described by a hourly load model with 4 levels, one described by a hourly load model with 7 levels, and the remaining two described by a hourly load model with 10 levels: then , where equality holds when no pair of combinations provide the same load); can be considered as the number of levels of a hourly load model for the island;

number of days in period ; number of days in period ; number of days in the analyzed year (365 or 366); LOLP of island

in period .

The hourly load models of LPs reported in Tables III and VII are used in order to obtain an example of the hourly load model for an island with two LPs, whose annual peak load is, respectively, 800 and 600 kW. Table VIII shows how to obtain the hourly load model for an island by considering the hourly load model for the LPs belonging to the island itself. Note that , , and are, respectively, the load power


TABLE VIII EXAMPLE—LPS’ HOURLY LOAD MODELS COMBINATION HOURLY LOAD MODEL FOR THE ISLAND

TO

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OBTAIN AN

TABLE IX EXAMPLE OF HOURLY MODEL FOR ISLAND

Fig. 2. RBTS-BUS6.

example, rows 3 and 6, as well as 4 and 7, have to be combined together). VII. CASE STUDY

of , , and islanded microgrid at level , in period , day , and hour . Each row in Table VIII is obtained by combining the power and probability of the hourly load models of the LPs. For example, row 7 is related to level 2 for LP1 and level 3 for LP2: the value of is obtained by summing the power of levels 2 for LP1 to the power of level 3 for LP2; the value of is obtained by multiplying the probabilities associated with the aforementioned levels. Finally, Table IX shows the hourly model for island , obtained from Table VIII, by associating a level with each power level with its probability and, in the case of multiple rows with the same power, by summing up the probabilities associated with the same values of power in order to obtain the resulting probability for each power value that defines a level of the hourly model for island (as for the considered

The load and generation modelling described in the previous sections has been applied to the RBTS-BUS6 network [41] shown in Fig. 2, in which conventional and renewable DGs have been added. The elements of the primary substation bounded by the dashed line are considered fully reliable. In the network representation, a node indicates a point (bus) where customers and/or generators are connected. A branch represents the electrical equipments connecting two nodes. Obviously, a node connecting customers is an LP. Moreover, in the following, island indicates the autonomous microgrid that is disconnected from the main distribution network by opening the switch installed in branch . Finally, a PoA equal to one (then an LOLP equal to zero) is considered when a normally open switch (NOS) is installed downstream from switch . This is due to the ability to transfer the load after NOS closure thanks to the availability of an alternative energy path (tie-line); then, the load is met by the capacity of the main feeder, notwithstanding the capacity of the local generators [14]. For

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TABLE X TYPE, CAPACITY, AND FOR OF THE DGS ADDED TO THE NETWORK

TABLE XI LOLP FOR EACH PERIOD AND ANNUAL VALUE FOR ALL POTENTIAL ISLANDS OF THE MODIFIED RBTS-BUS6

Fig. 3. Island 29—LOLP variation with the number of simulations.

TABLE XII SAIFI AND SAIDI CALCULATION FOR EACH FEEDER AND FOR RBTS-BUS6

TABLE XIII ITERATIONS) FOR ALL LOLP ASSESSMENT BY MEANS OF RANDOM MCS ( POTENTIAL ISLANDS OF THE MODIFIED RBTS-BUS6

this reason DGs’ data related to feeders F1 and F2 are not reported in Table X since there is no need for islanding in these feeders (LOLP is equal to 0). Historical data provided by Enel Distribuzione S.p.A. has been considered to develop hourly load and generation models. In detail, for each LP, the historical data of the utility’s secondary substation that better matches LP’s type and load level (in terms of mean and peak load) reported in [41] have been chosen to apply the proposed load modelling procedure. The UDGs added to the network are modelled by using generation historical data of wind generators, also provided by Enel Distribuzione S.p.A. The year has been divided into four periods (seasons) and in all periods: • for each LP, 24 hourly load models with 5 levels for both type of day are developed;



• for each UDG class, 24 hourly generation models with 10 levels are developed. Type, capacity, and FOR of each DG affecting the PoA are reported in Table X. Table XI reports the LOLP value for each period and the usual overall annual (2012) value for all potential islands of the modified RBTS-BUS6. Table XII shows SAIFI and SAIDI computed both in case islanding operation is allowed and in case it is not, considering branches’ data reported in [42].


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Fig. 8. Island 59—LOLP variation with the number of simulations. Fig. 6. Island 45—LOLP variation with the number of simulations.

Fig. 9. Island 53—LOLP variation with the number of simulations. Fig. 7. Island 50—LOLP variation with the number of simulations.

From Table XI it can be noted that the LOLP for island 59 is equal to the FOR of the CDG connected to node 60 since the annual peak load of the island is less than the generator rated power. This means that a high PoA (0.98) is obtained for such an island. On the other hand, the benefits deriving from operating island 31 and 50 autonomously is negligible owing to the lack of CDGs in these islands. The results shown in Table XII highlight that system reliability increases when islanding mode of operation is allowed for portions of the distribution network, depending on the network topology and generators’ features. The SAIFI index does not change in feeders 1, 2, and 3 because no circuit breaker (CB), with the exception of the one in the primary substation, is present, and then islanding does not reduce interruption frequency. Finally, the assumption to consider LOLP equal to zero for feeders 1 and 2 implies that there is no difference between the two values of SAIDI computed when islanding mode of operation is allowed and when it is not. Finally, MCS has been carried out in order to assess the values of LOLP for all potential islands of the modified RBTS-BUS6. In particular, random simulations [17] have been performed. Table XIII shows the values obtained after iterations, along with accuracy (in terms of number of significant figures coinciding with those obtained by the analytical method) and time

consumption. Figs. 3–8 show MCS results in term of LOLP variation with number of simulations and the analytical value (straight line). VIII. CONCLUSION This paper presented a new method to model renewable DGs by using historical data related to their power output. The proposed modelling approach provides hourly generation models that encompass power-output correlation among renewable DGs depending on the same intermittent energy source. Moreover, an innovative approach to develop an hourly load model is also presented. Hourly models take correlation among loads into consideration, among different types of renewable DGs and, finally, between loads and renewable DGs. A method to analytically evaluate LOLP by using the proposed models is also described. Both the presented method and MCS are applied to the IEEE RBTS-BUS6. Traditionally, the primary energy source (wind or sun) is first modelled, then the power output is obtained by means of nonlinear functions (referred to as power performance curves), that is, functional relations between the energy source and the corresponding power output. The main advantage of the energy source modelling approach is that it does not depend on a specific generator, and then it is more general than the one proposed in this paper, as the former one provides a wider application

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field (e.g., optimal location of generators at the planning stage of power systems). On the other hand, the traditional approach is affected by the approximation degree of the power performance curves, while the proposed one overcomes this drawback by using historical power-output values. Then, the proposed approach is more suitable for distribution adequacy evaluation. Another advantage of the proposed method used to model the power output of a class of UDGs is that it accounts for power correlation without calculating its value. Finally, it is worth noting that adequacy assessment was carried out by using the proposed modelling approach and analytical calculation (i.e., by considering a complete enumeration of all possible operating conditions) needs a heavy computational effort, but it provides very accurate results [43] that can also be considered as a benchmark to test approximated models and/or MCS. ACKNOWLEDGMENT The authors would like to thank E. Distribuzione S.p.A. for supplying the data required for the presented study. REFERENCES [1] The EU climate and energy 2020 package. [Online]. Available: http://ec.europa.eu/clima/policies/package/index_en.htm [2] X. Fang, S. Misra, G. Xue, and D. Yang, “Smart grid—,The new and improved power grid: A survey,” IEEE Commun. Surveys Tutorials, vol. 14, no. 4, pp. 944–980, 4th quarter 2012. [3] S. Conti, S. Raiti, G. Tina, and U. Vagliasindi, “Integration of multiple PV units in urban power distribution systems,” Solar Energy, vol. 75, pp. 87–94, 2003. [4] D. Moneta, P. Mora, S. Conti, and S. A. Rizzo, “Advanced voltage regulation system for MV networks with DG: Prospective technical and economic performances,” presented at the Int. Symp. Elect. Power Syst. Future—Integrating Supergrids and Microgrids CIGRÈ, Bologna, Italy, Sep. 13–15, 2011. [5] A. Pregelj, M. Begovic, A. Rohatgi, and D. Novosel, “On optimization of reliability of distributed generation-enhanced feeders,” in Proc. 36th Annu. Hawaii Int. Conf. Syst. Sci., Big Island, HI, USA, Jan. 6–9, 2003. [6] S. Conti, “Analysis of distribution network protection issues in presence of dispersed generation,” Elect. Power Syst. Res. J., vol. 79, no. 1, pp. 49–56, Jan. 2009. [7] N. J. Gil and J. A. P. Lopes, “Hierarchical frequency control scheme for islanded multi-microgrids operation,” in Proc. IEEE PowerTech, Lausanne, Switzerland, Jul. 1–5, 2007, pp. 473–478. [8] F. Li and N. Sabir, “Monte Carlo simulation to evaluate the reliability improvement with DG connected to distribution systems,” presented at the 8th WSEAS Int. Conf. Elect. Power Syst., High Voltages, Elect. Mach., Venice, Italy, Nov. 21–23, 2008. [9] M. Fotuhi-Firuzabad and A. Rajabi-Ghahnavie, “An analytical method to consider DG impacts on distribution system reliability,” presented at the IEEE/PES Transm. Distrib. Conf. Exhibit.: Asia and Pacific, Dalian, China, Aug. 18, 2005. [10] H. Falaghi and M.-R. Haghifam, “Distributed generation impacts on electric distribution systems reliability: Sensitivity analysis,” presented at the Int. Conf. Comput. Tool EUROCON, Belgrade, Serbia, Nov. 22–24, 2005. [11] J. Antikainen and S. Repo, “Possibilities to improve reliability of distribution network by intended island operation,” Int. J. Innovations Energy Syst. Power, vol. 2, no. 1, pp. 22–28, 2009. [12] A. Pregelj, M. Begovic’, and A. Rohatgi, “Recloser allocation for improved reliability of DG-enhanced distribution networks,” IEEE Trans. Power Syst., vol. 21, no. 3, pp. 1442–1449, Aug. 2006. [13] W. S. Andrade, C. L. T. Borges, and D. M. Falcao, “Integrated reliability evaluation of distribution and sub-transmission systems incorporating distributed generation,” presented at the IEEE/Power Eng. Soc. Power Syst. Conf. Expo., Seattle, WA, USA, Mar. 15–18, 2009.

[14] S. Conti, R. Nicolosi, and S. A. Rizzo, “Generalized systematic approach to assess distribution system reliability with renewable distributed generators and microgrids,” IEEE Trans. Power Del., vol. 27, no. 1, pp. 261–270, Jan. 2012. [15] Y. M. Atwa and E. F. El-Saadany, “Reliability evaluation for distribution system with renewable distributed generation during islanded mode of operation,” IEEE Trans. Power Syst., vol. 24, no. 2, pp. 572–581, Apr. 2009. [16] R. Allan and R. Billinton, “Probabilistic assessment of power systems,” Proc. IEEE, vol. 88, no. 2, pp. 140–162, Apr. 2000. [17] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems, 2nd ed. New York: Premium, 1996. [18] G. Desrochers, M. Blanchard, and S. Sud, “A Monte-Carlo simulation method for the economic assessment of the contribution of wind energy to power systems,” IEEE Trans. Energy Convers., vol. EC-1, no. 4, pp. 50–56, Mar. 1986. [19] R. Billinton and L. Gan, “Wind power modeling and application in generating adequacy assessment,” in Proc. IEEE Commun., Comput. Power Modern Environment WESCANEX, May 17–18, 1993, pp. 100–106. [20] R. Billinton, H. Chen, and R. Ghajar, “A sequential simulation technique for adequacy evaluation of generating systems including wind energy,” IEEE Trans. Energy Convers., vol. 11, no. 4, pp. 728–734, Dec. 1996. [21] R. Billinton, H. Chen, and R. Ghajar, “Time-series models for reliability evaluation of power systems including wind energy,” Microelectron. Rel., vol. 36, no. 9, pp. 1253–1261, 1996. [22] R. Billinton and G. Bay, “Generating capacity adequacy associated with wind energy,” IEEE Trans. Energy Convers., vol. 19, no. 3, pp. 641–646, Sep. 2004. [23] Y. Gao and R. Billinton, “Adequacy assessment of generating systems containing wind power considering wind speed correlation,” IET Renew. Power Gen., vol. 3, no. 2, pp. 217–226, 2009. [24] R. Billinton, Y. Gao, and R. Karki, “Composite system adequacy assessment incorporating large-scale wind energy conversion systems considering wind speed correlation,” IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1375–1382, Aug. 2009. [25] W. Wangdee and R. Billinton, “Considering load-carrying capability and wind speed correlation of WECS in generation adequacy assessment,” IEEE Trans. Energy Convers., vol. 21, no. 3, pp. 734–741, Sep. 2006. [26] F. Vallée, G. Brunieau, M. Pirlot, O. Deblecker, and J. Lobry, “Optimal wind clustering methodology for adequacy evaluation in system generation studies using nonsequential Monte Carlo simulation,” IEEE Trans. Power Syst., vol. 26, no. 4, pp. 2173–2184, Nov. 2011. [27] P. Giorsetto and K. F. Utsurogi, “Development of a new procedure for relaibility modeling of wind turbine generators,” IEEE Trans. Power App. Syst., vol. PAS-102, no. 1, pp. 134–143, Jan. 1983. [28] C. Singh and A. Lago-Gonzalez, “Reliability modeling of generation systems including unconventional energy sources,” IEEE Trans. Power App. Syst., vol. PAS-104, no. 5, pp. 1049–1056, May 1985. [29] C. Singh and Y. Kim, “An efficient technique for reliability analysis of power systems including time dependent sources,” IEEE Trans. Power Syst., vol. 3, no. 3, pp. 1090–1096, Aug. 1988. [30] S. H. Karaki, B. A. Salim, and R. B. Chedid, “Probabilistic model of a two-site wind energy conversion system,” IEEE Trans. Energy Convers., vol. 17, no. 4, pp. 530–536, Dec. 2002. [31] R. Billinton and Y. Gao, “Multistate wind energy conversion system models for adequacy assessment of generating systems incorporating wind energy,” IEEE Trans. Energy Convers., vol. 23, no. 1, pp. 163–170, Mar. 2008. [32] R. Billinton and R. Karki, “Maintaining supply reliability of small isolated power systems using renewable energy,” Proc. Inst. Elect. Eng., Gen. Transm. Distrib., vol. 148, no. 6, pp. 530–534, 2001. [33] R. Karki and R. Billinton, “Reliability/cost implications of PV and wind energy utilization in small isolated power systems,” IEEE Trans. Energy Convers., vol. 16, no. 4, pp. 368–373, Dec. 2001. [34] R. Billinton and R. Karki, “Capacity expansion of small isolated power systems using PV and wind energy,” IEEE Trans. Power Syst., vol. 16, no. 4, pp. 892–897, Dec. 2001. [35] Y. M. Atwa, E. F. El-Saadany, and A.-C. Guise, “Supply adequacy assessment of distribution system including wind-based DG during different modes of operation,” IEEE Trans. Power Syst., vol. 25, no. 1, pp. 78–86, Feb. 2010. [36] Y. M. Atwa, E. F. El-Saadany, M. M. A. Salama, R. Seethapathy, M. Essam, and S. Conti, “Adequacy evaluation of distribution system including wind/solar DG during different modes of operation,” IEEE Trans. Power Syst., vol. 26, no. 4, pp. 1945–1952, Nov. 2011.


[37] D. A. Bechrakis and P. D. Sparis, “Correlation of wind speed between neighboring measuring stations,” IEEE Trans. Energy Convers., vol. 19, no. 2, pp. 400–406, Jun. 2004. [38] D. Villanueva, A. Feijóo, and J. L. Pazos, “Simulation of correlated wind speed data for economic dispatch evaluation,” IEEE Trans. Sustain. Energy, vol. 3, no. 1, pp. 142–149, Jan. 2012. [39] C. Singh and A. Lago-Gonzalez, “Reliability modeling of generation systems including unconventional energy sources,” IEEE Trans. Power App. Syst., vol. PAS-104, no. 5, pp. 1049–1056, May 1985. [40] IEEE Guide for Electric Power Distribution Reliability Indices, IEEE Standard 1366-2003, May 2004. [41] R. Billinton and S. Jonnavithula, “A test system for teaching overall power system reliability assessment,” IEEE Trans. Power Syst., vol. 4, no. 4, pp. 1670–1676, Nov. 1996. [42] R. N. Allan, R. Billinton, L. Goel, I. Sjarrief, and K. S. So, “A reliability test system for educational purposes-basic distribution system data and results,” IEEE Trans. Power Syst., vol. 6, no. 2, pp. 813–820, May 1991. [43] J. C. O. Mello, M. V. F. Pereira, and A. M. Leite da Silva, “Evaluation of reliability worth in composite systems based on pseudo-sequential Monte Carlo simulation,” IEEE Trans. Power Syst., vol. 9, no. 3, pp. 1318–1326, Aug. 1994. Stefania Conti (M’13) received the Ph.D. degree in electrical engineering from the University of Catania, Catania, Italy, in 2001. She became a professional engineer with the University of Catania in 1997. In 2002, she became Assistant Professor in the Department of Electrical, Electronics and Computer Engineering, University of Catania, where she is Aggregate Professor of “Power Systems Dynamics and Control.” Her research interests include power systems reliability, control and protection, integration of distributed

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generation with distribution networks and smart grids, autonomous and nonautonomous operation of microgrids, and optimization techniques applied to electrical power systems. Dr. Conti is a member of the councillors’ board of Catania Association of Italian Electrical, Electronics, Automation, Information Technology and Telecommunication Engineers (AEIT) branch since 2010. She has been a member of the Association of Engineers of Catania since 1997, AEIT since 2002, IEEE Power and Energy Society since 1997, and IEEE Industrial Electronics Society since 2010.

Santi Agatino Rizzo received the Ph.D. degree in electrical engineering from the University of Catania, Catania, Italy, in 2010. Currently, he is a Research Fellow with the Department of Electrical, Electronics and Computer Engineering, University of Catania. His research interests include evolutionary algorithms, optimal control and management of autonomous and nonautonomous microgrids, reliability analysis of distribution networks with and without DERs, smart grids, and numerical methods for electromagnetic-field computation.