Reliability assessment of microgrid with renewable generation and prioritized loads

Reliability Assessment of Microgrid with Renewable Generation and Prioritized Loads Osama Aslam Ansari, Nima Safari, and C. Y. Chung Smart Grid and Renewa ble Energy Technology (SM ART) Lab Department of Electrical and Computer Engi neering University of Saskatchewan Saskatoon, Saskatchewan, Canada {oa.ansari, n.safari, c.y.chun g}@usask.ca Abstract — With the increase in awareness about the climate change, there has been a tremendous shift towards utilizing renewable energy sources (RES). In this regard, smart grid technologies have been presented to facilitate higher penetration of RES. Microgrids are the key components of the smart grids. Microgrids allow integration of various distributed energ y resources (DER) such as the distributed generation (DGs) and energy storage systems (ESSs) into the distribution system and hence remove or delay the need for distribution expansion. One of the crucial requirements for ut ilities is t o ensure that the system reliability is maintained with the inclusion of microgrid topology. Therefore, this paper evaluates the reliability of a microgrid containing prioritized loads and distributed RES through a hybrid analytical-simulation method. The stochasticity of RES introduces complexity to the reliability evaluation. The method takes into account the variability of RES through Monte- Carlo state sampling simulation. The results indicate the reliability enhancement of the overall system in the presence of the microgrid topology. In particular, the highest priority load has the largest improvement in the reliability indices. Furthermore, sensitivity analysis is performed to understand the effects of the failure of microgrid islanding in the case of a fault in the upstream network. Index Terms — Reliability evaluation, microgrids, Monte- Carlo, renewable, distributed generation I. I NTRODUCTION For the last few decades, there has been a n increasing concern about the climate change and depletion of no n-renewable energy sources. Increased public awareness has called for reduction of carbon emissions which are one of the main sources of climate change. This requires gradual yet steady replacement of conventio nal coal-based power plants with environmental-friendly renewable e nergy sources (RES). Smart grid technologies have been developed to facilitate large-scale integration of RE S and to tackle diffe rent challenges associated with it. Mi crogrids are one of the main building blocks of smart gr ids [1]. Microgri ds do not only offer the integration of RES in the distribution system but also provide attractive features such as islanded m ode of operation and higher flexibility. In order to fully understand the cost- benefit analysis of distribution system containing microgrids, it is important to take into acc ount the reliability of the electric supply at the custom ers’ ends. Maintaining system reliability is one of the primary motives of any utility. Signi ficant costs and penalties are incurred as a result of sy stem interruptions. Hence not only the com pany’s reputation but also the financial reasons force utilities to ensure an acce ptable level of system reliability. In this regard, se veral standards have been developed to m ake sure that utilities guarantee the reliable supply of electricity to their customers. In such scenarios, reliability studies become crucial for utilities. Reliability studies can also be c onsidered in distributed energy resou rces (DER) sizing, siting and ope ration, and reinforcement of the crucial elements in distribution network [2], [3], [4]. The inclusion of RES intr oduces complexity in their modeling for reliability studies. Furt hermore, the output of distributed generation (DGs) based on RES are energy lim ited and sporadic in nature. In this case, the priority order of the loads should be considered t o maintain electric supply to the most sensitive loads in the event of insuffici ent generation. In literature, several techniques ha ve been presented to evaluate the reliability at customer load points i n the microgrid a nd of the microgrid as a whole. They ca n be categorized into analytical methods, simulation m ethods and hybrid methods. In [5], a method based on Monte- Carlo simulation to evaluate reliability of an active distribution syste m with multiple microgrids is proposed. It has be en s hown that the inclusion of DGs and storage increases the ove r all reliability of the system. The method discretizes the out put of RES and evaluates probability for each step. In [6 ] and [7], the reliability of a microgrid in islande d mode is evaluate d. In [6], Monte-Carlo simulation is used t o model com ponent failure and component repair and historical data for RES. In [7], fault tree analysis is adopted which can become mathematically involve d for large systems. Since gri d-connected mode of microgrid is not taken into account in both of the papers , the values for the reliability metrics are different from the actual values. Markov modeling is used to evaluate the reliability of m icrogrid with photovoltaic (PV) generation an d energy storage systems (ESSs) in [8]. However the proposed m ethod uses a simple two-state model for PV generati on whic h is in sufficient to incorporate the highly interm ittent nature of PV and ot her RES such as wind energy. In [9], the intermittent nature of PV 2016 IEEE Green Energy and Systems Conference (IGSEC) 978-1-5090-2294-6/16/$31.00 ©2016 IEEE based DGs is ignored by considering that the ESSs are sufficiently sized to make DGs dispatchable. The values of reliability indices can be markedly di fferent if intermittency is taken into account. Some papers suc h as [10] evaluated the reliability indices of a small isolated power system s with RES. However, they do not take into account the abilities of a microgrid such as its different m odes of operation. . In [11], a hybrid model is presented to find out the reliability of a microgrid in the presence of renewable DGs and ES Ss. The method does not consider the prio rity order of t he loads. Also in one of the cases, the method as sumes that battery hel ps intermittent DGs to supply the entire load or a large part of the load. This paper presents a hybrid method c omprising of both analytical and simulati on techniques to evaluate the reliability at customers’ load points in a m icrogrid containing wind and solar power generation and prio ritized loads. State sam pling Monte-Carlo simulati on is combined with the analytical method. Simulation methods take into account the chronolo gy of variation of RES and the p ri ority order of the loads whereas analytical methods conside r th e topol ogy of the network and the failure and repair rates of the networks’ c omponents. The paper is form atted as follows. Section II briefly introduces the microgrid. Section III present s the modeling of wind and PV generation sources fo r t he reliability evaluation. Section IV delves into the proposed method for calculating th e reliability indices of the microgrid. The resul ts are indicated in Section V. Section VI provide s the conclusi on of the work. II. M ICROGRIDS A mic rogrid is a grou p of inte rconnect ed load s, DERs (such as DGs a nd ESSs ), and m anagem ent s ystems that c an oper ate either in gr id connected mode or islanded m ode (Fig . 1). From the ut ility ’s point of vi ew, a m icrogri d appea rs as a sing le controllable en tity that can con sume or supply power dependin g upon the total g eneration and the total lo ad insid e the m icrogri d. The ability of a microgrid to operate in islanded mode increases the reliabi lity of the lo ad points. Th e islanding mod e can occur if there is a fau lt w ithin th e microgrid or in the upstrea m ne twork to which i t is conne cte d. In is lande d mode of operat ion, t he loads de pend u pon the power generat ion of DGs connect ed in th e mi crogrid. In the ca se when DGs are una ble t o supply all of the load, ene rgy m anage ment syst ems ca n voluntarily cu rtail the no n-sensitiv e loads util izing advanced switches and co ntrol strategies. This ensures th at the sensitive loads are not interrupted [1], [4]. III. M ODELING R ENEWABLE E NERGY S OURCES One of the key features of the microgrid topology is its ability to integrate DERs suc h as renewable DGs, dispatchable DGs, ESSs and electric vehicles (EVs) i n a seamless manner . DERs not only provide an alternative to the generation expansion plannin g but also assist in improving the reliability of the distribution system to which they are connected [4], [12], [13]. Nevertheless, RES poses different challenges to the operation and planning of the power system . The most significant of these is their intermittent behavior. The ou tput of RES depends on various factors i ncluding weather conditions and geographical location. Moreover, RES have widely different characteristics based on their source of energy, for instance, wind and solar. Hence it is diffic ult to use a general model for all RES or to use the sam e models as utilized for conventiona l generators. RES generators als o have their own failure rates and repair tim e. It has been observed that the unavailability of RES is prim arily because of the unavailability of their e nergy s ource rather than the failure of RES generators [14]. The method presented in this work uses the above observation. In reliability studies invo lving simulatio n tech niques, it is neces sary t o genera te sy nthe tic data for RES power ge nerat ion. The ne xt part s of t his se cti on int roduc es the mod els to ge nera te the data for th is purpose. A. Wind Power Generation Modeling Wind energy is the m ost developed and the fastest growing form of renewable energy. Wind power depends upon different factors including wind speed, wind direction, and geographical locations etc. However, wind power is largely dependent on the wind speed. T herefore, in this paper, the wind power is m odeled using the wind speed. Different distributions such as norm al [15] and Weibull [16] are used to model the wind spee d. In general, two parameter Weibull distribution provides a better fit for m odeling the wind speed [17]. In this paper, the mode l for wind speed distribution function is obtained from [16] which uses Weibull distribution. The cumulative probability distribution for the wind speed v , () w Fv is given as: (/) () 1 k vc w Fv e   (1) where, c is the scale parameter and k is the shape parameter. The values for two parameters are obtained usi ng historical data. They are adopted from [16] and given in Ta ble I. In order to sim ulate the wind speed values for a required duration, the inverse transform ation method is implem ented [18]. Inverse transf ormation method states that if a random variable (in this case v) follows the U [0, 1] uniform Fig. 1. Typical structure of a microgrid 2016 IEEE Green Energy and Systems Conference (IGSEC) distribution, then the random variable X = F -1 (U) has a continuous cum ulative proba bility distribution function F(X) . Using this principle, (1) can be expressed as: 1/ [l n ( 1 ) ] k vc X   (2) where X is a random num ber between 0 and 1. Since X is a random number, (2) ca n be also be expressed as: 1/ [l n ( ) ] k vc X  (3) Using (3), daily values of wind speed ca n be simulated by generating random number X for eac h day. The wind power is obtained from the wind speed by using the WTG power curve shown in Fig. 2. The power c urve expresses the wind power as the function of wind speed a nd is provided by the wind turbine manufacturer. The power curve of WTG is usually characterized by the following param eters: Rated speed ( v rated ) : The speed at whic h the m aximum power can be extracted from the WTG. Rated power ( P rated ) : The maxim um power that ca n be produced by WTG at the rat ed wind speed. Cut-in speed ( v cut-in ) : The minimum wind speed required to produce the power from WTG. Cut-out speed ( v cut-out ) : The maximum speed at which WTG can operate. Usually after this wind speed, the WTG is shut down due to safety reasons . The wind power curve is given as: cut- in 3 rated cut-in rated rated rated cut-out cut-out 00 ab 0 WTG vv vP v v v P Pv v v vv d  °  d ° ® d ° ° d ¯ (4) where, a and b are given as: rated 33 rated cut-in 3 cut-in 33 rated cut-in a b P vv v vv   (5) Using the wind power curve, the simu lated wind power is obtained from the wind speed. The sim ulated wind speed and wind power for one of t he two WTGs is shown in Fi g. 3. Table II provides the data for the two wind turbines. B. Solar Power Generation Modeling With the developm ent of new so lar panels , the penetration of solar power is increasing an d further growth is expected in the near future. Solar power of the solar panels m ainly depends upon the s olar radiation and temperature . The temperature dependency of so lar power is non-linear and introduces com plexity to the modeling. In t his work, solar radiation is utilized to obtain the output power of sola r panels. Historical data of solar radiation is used to fi nd out the probability distribution of solar radiation. The historical data for 5 years is obtained from [19]. It has been sho wn that the beta distribution fits m ore ac curately to solar radiation as compared to gamma and logarit hmic distribution [20]. Therefore in this paper, beta distribution is fitted on the historical data of solar radiation. The probability distribution function of beta distribution is given as: 11 (1 ) () B( , ) xx fx DE DE   (6) where, B in term s of gamma function ( Γ ) is defined as: () ( ) B( , )= () DE DE DE ** * (7) After fitting the beta distribution on historical data, the two parameters for beta distribution obtained from statistics and machine learning toolbox of MATLAB are as follows: 1.03745 1.38279 D E (8) After obtaining the correspond ing proba bility distribution, inverse transformation m ethod is applied. Using t he inverse transformation method, solar ra diation is predicted for the required interval of time. Simi lar to wind power curve, the solar power curve expresses solar power in terms of solar radiation. The expression for outp ut po wer of PV in terms of solar radiation is given as [14]: 2 sn c std c PV sn std std sn std 0 c G PG R GR G PP R G G G PG G  d ° ° ° ° d d ® ° ° ! ° ° ¯ (9) TABLE I W EIBULL D ISTRIBUTION D ATA Parameter Region 1 Region 2 Mean speed (m/s) 7.0 7.5 k 2.62 3.18 c 7.88 8.46 TABLE II W IND T URBINES D ATA Parameter Region 1 Region 2 Rated Power (kW) 2000 1500 Rated speed (m/s) 15 12 Cut-in speed (m/s) 3 3 Cut-out speed (m/s) 25 25 Fig. 2. Wind power curve. 2016 IEEE Green Energy and Systems Conference (IGSEC) where, P PV is solar output power in MW. G is simulated solar radiation in W/m 2 . G std is solar radiation in the standa rd environment. Usually this value is set to 1000 W/m 2 . R c is a certain radiation point set usually to 150 W/m 2 . P sn is the rated output power of solar pa nels. IV. R ELIABILITY E VALUATION M ETHO D A. Reliability Indices For evalu ating the reliability of custo mer load points in a distri bution system , the sys tem a verage i nterrupt ion freq uency index (SAIFI), th e system average in terruption duration ind ex (SAIDI), the custo mer average interruptio n duration index (CAIDI), the energy not supplied (ENS ) and average energy not supplied (AENS) indices are used. These are defined as [21]: SA IF I ii T N N O ¦ (10) SA ID I ii T UN N ¦ (11) SA ID I CA ID I SA IF I (12) ENS ii iL P UL  ¦ (13) ENS AEN S = T N (14) where, i O is the failure rate, U i is the outage time, N i is the number of custom ers, and L i is the total load at load point i. N T is the total number of cust omers in the system . B. Evaluation Method The steps for reliabili ty evaluation are as fo llows: Step 1 . Obtain the cumulative distribution functio ns of wind and solar radiation from their historical data. Step 2 . Use cumulative distribution functions, and the inverse transform ation method t o generate the simulated values of wind speed and sol ar radiation for required number of samples. This requires ge neration of random number X for each sample. Here one sam ple can be considered as one day. Step 3 . Convert the wind speed to wind power using wind power curve (4) – (5) and solar radiation to solar power using (9). Step 4 . At each day, sample the output of all WTGs and PV panels. The com bined output of all RES is compared with the load. In the case if RES cannot supply all of the loads, then the load with highest priority is supplied first followed by t he next load in the priority list and so on. Step 5 . Step 4 is performed for each day of the year. T he number of occurrences at which the load is supplied by RES for each of the load points is c ounted. At the end of year, the probability of RES supplying different load points is calculated. Let RES i P be the probability that RES can supply the load at load point i. This probability value along with the system stochastic data (failure r ate and repair time) are used to obtain the average failure rat e, unavailability and repair tim e at each load point at the end of the year using the following equation: RES up RES up up (1 ) (1 ) i ij i ij j P Ur P r OO O OO     ¦ ¦ (15) where, i O and U i are the failure rate and unavailability at load point i, respectively , up O and up r are the failure rate and repair time of upstream network, respectively, and j O and r j are the failure rate and repair tim e of microgrid network c omponents, respectively that results in int erruption at load point i . Step 6 . Afterwards, the system indices SAIFI, SAIDI, CAIDI, ENS and AENS are ca lculated using (10) – (14). Step 7 . Steps 4-6 are repeated for each year until the variation in system indices is less than the specified t olerance or maximum num ber of iterations is reached. In (15), each expression consists of two terms. The first term arises from the stochastic data of the net work components. The second term is derived from the followin g conditional probability equation. ( | RES can supply ) +( | RES c ann ot supp ly ) ( 1 ) i RES i RES P P OO O u u (16) In the first part of above expression, in the case of failure in the upstream network, if RES can supply th e load point i , the failure in the upstream network will not result in any interruption at that load point. He nce, the (16) reduces to: RES up (1 ) i P OO  u (17) The P i RES calculated through simulation takes into account the intermittency and variability of RES. During a sample, if RES generation is greater tha n the load, t he excess generat ion would be curtailed. V. C ASE S TUDY AND R ESULTS A. Test System The proposed meth od is applied to a modified v ersion of the di stri bution syst em conne cte d to bus 5 of the R oy Bi llinton Fig. 3. Simulated wind speed and wind power for WT A 2016 IEEE Green Energy and Systems Conference (IGSEC) Test S yst em (RBT S) [21] . The ad vanta ges of usi ng the RBTS incl ude the ava ila bility of st ochas tic data for netw ork components, and manageab le system size. The test system is shown in Fig. 4. Table III provides the assumed load data fo r the system. For this syste m, in the case of a fault in a feed er section, assume 4 for an instance, the management system acts so as to reduce interruptio n duration for the custo mers. In this case, firstly F1 wo uld open and then isolating switch es connected to section 4 wou ld open to isolate the faulty secti on from the rest o f the netwo rk. Then F1 and norma lly ope n (N/O) swit ch woul d close to rest ore the supply to rest of the cust ome rs. In th is si tuati on, LP3 a nd LP 4 woul d be interrupted until section 4 is repaired completely whereas , the othe r load points woul d be i nterrupt ed for t he durat ion equal to the sw itching time o f F1, N/O and isolatin g switches. As mentioned earlier, a priority list is constr ucted to serve the most sensitiv e load first in th e case of islanded mode of operation resulting from fail ure in the upstream netwo rk. In this case it is ass umed t hat gove rnm ent loa d (LP9) ha s t he highest prio rity followed by office lo ads (LP3) and then hou se loads (LP 4). On t he ot her ha nd, com merc ial l oads (LP2) are assumed to have th e lowest priority. Following four cases are studied t o consider the effects of DGs on reliability of m icrogrid. Case 1 : Without DGs. Case 2 : With 4 WTGs as DGs. Case 3 : With 2 WTGs and 2 PV panels as DGs. Case 4 : Case 3 with variable load . The rat ings for the WTG and PV panel s are gi ven in t able IV. These ratings are selected considering th at the capacity factor s of DGs based on RES a re quite low. Henc e the combined rate d power of all D Gs is higher th an the tota l load in the m icrogri d. The failure rates and repair times of the test syste m are given in [21]. The failu re rate and the rep air time of u pstream networ k are a ssum ed to be 0.5 f/yr and 10 h ours, res pect ivel y. The swit ching time and repai r time ar e assum ed to be 3.5 ho urs and 30 hours, respectivel y. These assumed values ar e frequently used in the literatu re. The maximum number of samples is set t o 100,000. Th e variable load model is obtai ned from [21]. B. Results The application of the meth od on four cases in dicates that the presence o f DGs in the microgrid increa ses the overall relia bility of the syst em. Althou gh the value s of SA IFI do no t change significan tly, there is a n oticeable change in SAIDI an d ENS values. An improvement of 20% is ob served in the valu es of ENS from case 1 to cas e 4. F urtherm ore, the improv ement is expected to b e higher for larger systems. The results for each of the load p oints are shown in Table V. Tab le VI shows the system indices fo r all four cases from which it should be inferred that the ov erall system reliabili ty has i mproved. Th e decrease in unav ailability and failure rate for the highest priority load (LP9) is significan t as compared to the o ther load points. Fig . 5 shows pictorially th e improvement in the reliability at LP9 . The results also in dicate that the r eliability indices for the most non -sensitive lo ad does n ot change significantly. C. Sensitivity Analysis The successful islanded operation o f the microgrid in the case of upst ream failure depe nds up on suc ce ssful o pera tion of the i sola ting swi tch. T his i solati on ope rati on usua lly has a high probab ility of success. In previo us scen arios, this probab ility was taken to be un ity i.e. the island ing operation is always successful. A sen sitivity analysis is performed to observe the effects of the probab ility of switchin g on system indices. Scena rio 3 i s con sider ed aga in an d the pro babi lity of succ ess ful isola tion is va ried from 100% t o 0%. The result s for all four cases are shown in Tab le VI. As expected, the results indicate TABLE III L OAD D ATA Load Point Load Level (kW) Type of Load No. of Customers LP2 1000 Commercial 100 LP3 3000 Office loads 300 LP4 1000 House loads 250 LP9 500 Governmental 50 TABLE IV R ENEWABLE DG S D ATA Type Location Rated Power (kW) WTG 1 LP7 2000 WTG 2 LP10 1500 PV 1 LP1 2000 PV 2 LP8 2000 TABLE V R ELIABILITY I NDICES FOR A LL L OAD P OINTS LP Index Case 1 Case 2 Case 3 Case 4 LP2 λ (f/yr) 0.726 0.720 0.721 0.715 r (hr) 11.042 11.051 11.049 11.059 U (hr/yr) 8.017 7.957 7.975 7.908 LP3 λ (f/yr) 0.726 0.669 0.657 0.635 r (hr) 10.823 10.893 10.906 10.941 U (hr/yr) 7.858 7.293 7.135 6.954 LP4 λ (f/yr) 0.726 0.696 0.706 0.692 r (hr) 10.093 10.098 10.096 10.098 U (hr/yr) 7.328 7.035 7.135 6.990 LP9 λ (f/yr) 0.656 0.248 0.247 0.291 r (hr) 10.554 11.468 11.469 11.251 U (hr/yr) 6.924 2.844 2.841 3.274 Fig. 4. Modified Bus 5 of RBTS [21] 2016 IEEE Green Energy and Systems Conference (IGSEC) that the d ecrease in probability of successful ly i sla nding, reduces the reliabilit y of the system. There is a decrease of 9.72% i n the va lue o f SAIDI i f prob abi lity of succ essful isla nding de crea ses from 1 to 0. VI. C ONCLUSION In this wor k, reli abilit y evalua tion of a microgri d conta ining wind and sola r ene rgy sou rces was pe rform ed. The s tocha sti c nature of wind and so lar energy introd uces complexity in the reliability eval uation methods. This sto chastic nature is deal t through state -sampling si mulation whereas, an alytical meth ods are applied to e valuate the rel iab ility metrics. The prio rity order of the load s is also taken into acco unt through simulat ion. The studi es indi cate d that i ntegr ation of inte rmit tent wi nd and s olar energy sources in microgrid increase the reliab ility indices of the system. In particular, the most sensit ive load h as the largest increase in its reliability. It was also highli ghted that th e reliability of th e system decreases with decrease in reliability of the islan ding operation. For future stud ies, dispatchable D Gs and ESSs can be inc luded in the syste m to understand their effects on the reliabil ity indices of the syste m. ESSs in particular, can affect the reliabili ty of the system as they can store e xcess renewabl e ener gy duri ng lo w-demand periods and can sup ply dur ing hi gh-dem and peri ods. Fo r a mor e acc urate evaluation, h ourly variations of RES gen eration can be utilized . Moreove r, reli abilit y cost /worth a nalysis can be pe rform ed. A CKNOWLEDGMENT This work was supported by the Na tural Sciences and Enginee ring R esearch Counc il (NSE RC) of Canada . R EFERENCES [1] N. Hatziargyriou, H. Asano, R. Ir avani and C. Marnay, "Microgrids: An overview of ongoing research, de velopment, and demonstration projects," IEEE Power and Energy Mag ., pp. 1488-1505, Aug. 2007. [2] S. A. Arefifar and Y. A. I. Moh amed, "DG mix, reactive sources and energy storage units for optimizing m icrogrid reliability and supply security," IEEE Trans. Smart Grid , vol. 5, no. 4, pp. 1835-1844, Jul. 2014. [3] S. Bahramirad, W. Reder and A. Khodaei, "Relia bility-constrained optimal sizing of energy storage system in a microgrid," IEEE Trans. Smart Grid , vol. 3, no. 4, pp. 2056-2062, Dec. 2012. [4] N. Z. Xu and C. Y. Chung, "R eliability evaluation of distribution systems including vehicle-to-ho me and vehicle-to-grid," IEEE Trans. Power Syst. , vol. 31, no. 1, pp. 759-768, Jan. 2016. [5] Z. Bie, P. Zhan g, G. Li et al., "Reliability evaluation of active distribution systems including microgrids," IEEE Trans. Power Syst ., vol. 27, no. 4, pp. 2342-2350, Nov. 2012. [6] S. Kennedy and M. M. Marden, "R eliability of islanded microgrids with stochastic generation and prioritized load," in 2009 IEEE Bucharest PowerTech , pp. 1-7, Bucharest, Jun.-Jul. 2009. [7] Z. Li, Y. Yuan and F. Li, "E valuat ing the reliability of islanded microgrid in an emergency mode," in 2010 45th Int. Universities Power Eng. Conf. (UPEC) , pp. 1-5, Cardiff, Aug.-Sep. 2010. [8] T. Tuffaha and M. AlMuhaini, "R eliability assessment of a microgrid distribution system with pv and storage," in 2015 Int. Symp. Smart Elec. Distr. Syst. Technol. , pp. 195-199, Vienna, Sep. 2015. [9] I. S. Bae and J. O. Ki m, "R eliability evaluation of customers in a microgrid," IEEE Trans. Power Syst., vol. 23, no. 3, pp. 1416-1422, Aug. 2008. [10] 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. [11] C. L. T. Borges, and M. Costa, "Reliability assess ment of microgrids with renewable generation by an hybrid model," in 2015 IEEE Eindhoven PowerTech , pp. 1-6, Eindhoven, Jun.-Jul. 2015. [12] P. M. Costa and M. A. Matos, "R eliability of distribution networks with microgrids," in 2005 IEEE Russia Power Tech , pp. 1-7, Jun. 2005. [13] M. Fotuhi-Firuzabad, and A. Rajabi -Ghahnavie, "An analytical method to consider DG impacts on distri bution system reliability", in 2005 IEEE/PES Transmission & Distribution Conf. & Expo.: Asia & Pacific , pp. 1-6, Dalian, 2005. [14] J. Park, W. Liang, A. A. El -Keib et al., "A probablistic reliability evaluation of a power system including solar/photovoltaic cell generator," in 2009 IEEE Power and Energy Society General Meeting , pp. 1-6, Calgary, Jul. 2009. [15] R. Karki, P. Hu and R. Billinton, "A simplified wind power generation model for reliability evaluation," IEEE Trans. Energy Convers ., vol. 21, no. 2, pp. 533-540, Jun. 2006. [16] A. P. Leite, C. L. T. Borges and D. M. Falcao, "Probabilistic wind farms generation model for reliability studies applied to Brazilian sites," IEEE Trans. Power Syst ., vol. 21, no. 4, pp. 1493-1501, Nov. 2006. [17] T. P. Chang, “Estimation of wind energy potential using different probability density functions,” Applied Energy, Elsevier, vol. 88, no. 5, pp. 1848-1856, May 2011. [18] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems, 2nd ed. New York, NY, USA: Plenum, 1996. [19] NASA Atmospheric Science Data Center [Online]. https://eosweb.larc.nasa.gov/sse/RETScreen/. [20] Z. Qin, W. Li, and X. Xiong, "Incorporating multiple correlations among wind speeds, photovoltaic powers and bus loads in composite system reliability evaluation," Applied Energy , Elsevier, vol. 110, pp. 285-294, Oct. 2013. [21] R. Billinton and S. Jonnavithula, "A test system for teaching overall power system reliability assessment," IEEE Tra ns. Power Syst ., vol. 11, no. 4, pp. 1670-1676, Nov. 1996. TABLE VI R ELIABILITY I NDICES FOR THE M ICROGRID Case SAIFI (int/yr cust) SAIDI (hr/ yr cust.) CAIDI (hr/int cust) ENS (kWh/yr) AENS (kWh/yr cust.) Case 1 0.721 7.624 10.57 42381 60.544 Case 2 0.656 6.979 10.63 38304 54.714 Case 3 0.653 6.967 10.63 37965 54.220 Case 4 0.642 6.844 10.65 33821 48.315 TABLE VII S ENSITIVITY A NALYSIS Probability of islanding success SAIFI (int/yr cust) SAIDI (hr/ yr cust.) CAIDI (hr/int cust) ENS (kWh/yr) AENS (kWh/ yr cust.) 1 0.653 6.949 10.63 37960 54.22 0.75 0.670 7.118 10.62 39062 55.80 0.5 0.687 7.286 10.60 40164 57.37 0.25 0.704 7.456 10.89 41273 58.96 0 0.721 7.625 10.58 42381 60.54 Fig. 5. Reliability indices for load points 9 for different cases. 2016 IEEE Green Energy and Systems Conference (IGSEC)