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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 1, MARCH 2007 159

Aspects of Relevance in Offshore Wind FarmReliability Assessment

Nicola Barberis Negra, Ole Holmstrøm, Member, IEEE, Birgitte Bak-Jensen, Member, IEEE,and Poul Sorensen, Member, IEEE

Abstract—The worldwide increase of installed wind power ca-pacity demands the inclusion of wind farm (WF) models into powersystem reliability assessment. This paper looks at this issue fromavailable literature, and presents a list of factors that highly in-fluence offshore WF generation. An example of sequential MonteCarlo simulation applied to an offshore WF is described using anew synthetic wind-speed generator. The simulation includes someof the reliability factors highlighted in the paper and their influenceon reliability assessment.

Index Terms—Monte Carlo methods, offshore wind farm, powersystem reliability, wind speed time series.

I. INTRODUCTION

E LECTRICITY has become increasingly important since itsuse in the beginning of the 20th century. Now, it dominates

most human activities in industrialized countries. This relevancehas increased the interest in ensuring a safe and secure electricalsupply at a reasonable cost. Reliability issues gained growingattention at the beginning of the 1950s, and now represent oneof the main considerations when a power system is both plannedand operated.

Definition of reliability depends on the purpose of the analy-sis. As a general definition, the term can be used to indicate theoverall ability of the system to perform its function adequatelyfor the period of time considered under the operating conditionsintended [1].

Reliability evaluation can be considered for a wide range ofsituations. Some typical studies are [2]:

1) reliability assessment of large systems;2) transfer capability studies, where adequacy of selected

transmission solutions is investigated;3) studies of interconnected systems, where the adequacy

is assessed for economic exchange and emergency assis-tance;

4) reliability studies of area supply systems, where reliabilityof smaller systems such as local supply networks andstations is evaluated;

Manuscript received July 12, 2006; revised October 18, 2006. This work is apart of the project, “Offshore wind power—Research related bottlenecks,” andwas supported in part by Danish Research Agency under Grant 2104-04-0005,in part by Elsam Engineering A/S, a part of Dong Energy, and in part by theDanish Academy of Wind Energy (DAWE). Paper no. TEC-00269-2006.

N. Barberis Negra and O. Holmstrøm are with Elsam Engineering A/S,Dong Energy, Fredericia DK-7000, Denmark (e-mail: [email protected];[email protected]).

B. Bak-Jensen is with Aalborg University, Aalborg DK-9100, Denmark(e-mail: [email protected]).

P. Sørensen is with Riso National Laboratory, Roskilde DK-4000, Denmark(e-mail: [email protected]).

Digital Object Identifier 10.1109/TEC.2006.889610

5) identification of system weakness for future reinforce-ment;

6) economic studies, where costs or marginal costs due tochanges in network configuration and loading for variousscenarios are calculated, and then used to forecast produc-tion and establish the costs of external constraints.

Apart from these standard studies, consideration must begiven to power systems’ past 15-year evolution toward astructure different from its previous configuration. Renewablesources and distributed generator installation have created newfactors. These two aspects have introduced some elements, e.g.,variability, availability, “fuel” randomness, and private operatorcontrol of generation, etc. From a reliability point of view theseare new involved challenges that power system owners mustassess to avoid problems during normal system operation [3].

This paper focuses on relevant aspects, highlighted in avail-able literature, that must be considered when evaluating thereliability of wind farms (WF) in offshore environment.

In Section II, some definitions for power system reliabilityassessment are presented. In Section III, the current status ofWF reliability modeling is described. The first part of Section IIIintroduces some available models, then lists relevant aspectsof offshore WF reliability evaluation. In the last section, anassessment example is presented, and a Monte Carlo simulation,which includes some aspects listed in Section III, is performed.

II. POWER SYSTEM RELIABILITY ASSESSMENT

Power system reliability assessment can be performed con-sidering two main system aspects: adequacy and security [2].

System adequacy, which is mainly used in power systemplanning, is an indicator of sufficient system facilities to satisfyfuture consumer demand or system operational constraints [4].System security, which may be used in both power system plan-ning and operation, is a measure of the system’s ability to re-spond to dynamic and transient disturbances arising within thesystem [4]. This paper focuses on the adequacy issue.

In order to analyze a power system for any purpose, it canbe divided into three functional zones: generation, transmission,and distribution. The three zones can be combined to create threehierarchical levels that provide a basic framework for powersystem adequacy evaluation [4], [5].

Hierarchical level I (HLI) assessment, usually termed as “gen-erating capacity reliability evaluation,” mainly concerns assess-ing the installed generating capacity to satisfy the perceivedsystem load and to perform necessary corrective/preventivemaintenance at an acceptable risk level. The effects of trans-mission networks and distribution facilities are neglected.

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160 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 1, MARCH 2007

Hierarchical level II (HLII) analysis, usually called a “com-posite system reliability evaluation” or “bulk power system reli-ability evaluation,” considers generation and transmission sys-tems. HLII adequacy evaluation techniques consider assessingboth generation and transmission facilities for their ability tosupply adequate, dependable, and suitable electrical energy atbulk power load points.

Hierarchical level III (HLIII) analysis that is called “com-plete power system reliability evaluation,” includes all threefunctional zones, starting with generation and terminating at in-dividual consumer load points. The objective of an HLIII studyis to obtain suitable adequacy indices at actual consumer loadpoints.

This power system structure is still useful, but two new aspectsmust be considered in the analysis [3]: power system planningthat is influenced by economic competition between generationowners, and power system operation that is influenced by powerfluctuations due to embedded generation. These two factorsmust be considered and need special consideration when powersystem reliability is assessed.

Reliability calculation may be performed considering deter-ministic and probabilistic approaches [5].

Deterministic techniques are still used today for general stud-ies, and in the past, were the practical application, when re-liability became a relevant power system analysis issue, i.e.,worst-case scenarios analysis. However, to apply deterministictechniques, the system had to be artificially constrained into afixed set of values, which have no uncertainty or variability. Themain drawback of deterministic techniques is that they do notassess the system’s stochastic behavior (i.e., forced outages ofsystem components and uncertainty of customer demand) [5].

Probability methods were developed later, and can providemore meaningful information for design, resource planning, andresource allocation since they consider probability aspects of asystem. Two main approaches can be considered for probabilitymethods [5].

1) Analytical methods: The system is represented by mathe-matical models, and where direct analytical solutions eval-uate a priori reliability indices from the models.

2) Monte Carlo simulation: This estimates a posteriori reli-ability indices by simulating the system’s actual randombehavior, either randomly or sequentially.

Both techniques have advantages and disadvantages and maybe very powerful with the proper application. The main advan-tage of the analytical approach is its relative compactness thatcan be enhanced by suitable approximations, and can simplifyso much, such that it gives unrealistic results. Monte Carlo sim-ulation may be preferable for [4]:

� models with nonexponential time distributions;� characterization of peaking units;� definition of distributions function of output indices;� use of time dependent on chronological issues.Monte Carlo simulation usually requires more computational

time, but might be more suitable for analysis with a high levelof stochastic phenomenon.

Both techniques may be used for static capacity adequacy orfrequency and duration (F&D) studies. F&D analysis provides

information on both occurrence frequency and duration of insuf-ficient capacity condition, whereas, the static approach evaluatesexpected results as a number of days or as unsupplied energywhen the load exceeds production. The terminology presentedis for analytical methods; in Monte Carlo simulation, the firstanalysis is called random or nonchronological approach, andthe second one is called sequential or chronological approach.

Reliability assessment results are usually expressed by indicesthat attribute values to the aspects of the analyzed power system.Indices, which have been defined for different HL analyses areclassified into [5] absolute indices that are evaluated before andafter consideration of design or operating changes, or relativeindices that are calculated with past system performance andwith no assessment of the future. Another classification thatfits HLII analysis distinguishes between bus and global systemindices [2].

Given these definitions, this paper describes current proba-bilistic approaches for reliability adequacy assessment of off-shore WF. An example of simulation that may be used for bothHLI and HLII analysis is presented.

III. WF RELIABILITY MODELING

A. Current Available Reliability Models for WF

A WF poses special difficulties in the analysis of the adequacyof generating system capacity. Wind energy is intermittent andnondispatchable, because wind speed (WS) is highly variableand site-specific. Each wind park’s wind turbine (WT) has noindependent capacity distribution, and is dependent on the sameprimary energy source. Other problems are related to the non-linear relationship between WT output power and WS [4].

The reported research on modeling wind power generationrefers mainly to probabilistic methods, both analytical and sim-ulation. Older studies refer to the analytical solution with a staticapproach [6]–[8]. Chowdhury [9] adapts a standard load modifi-cation approach to adequacy assessment of wind energy’s powersystem generating capacity.

Zhao et al. [10] defines an offshore WF reliability model thatcan provide output power information and that can be used foroptimization analysis. The model emphasizes the WF designincluding components (i.e., WTs, transformers, cables, buses,and converters) and different system configurations. The modelevaluates the probability that a certain percentage of wind powercannot be sent to the grid system due to component failures.Since the model focuses on generation and transmission systemreliability, WS variability’s effect is weakened in the evaluation,and is only considered as an occurrence probability.

The most evident static analytical solution deficiency is thatinformation might be lost since chronological characteristics ofWS and its effects on wind power output are compacted in aprobability table.

Sayas and Allan’s F&D analytical method [11] for generat-ing WF reliability assessment accounts for wind’s stochastic andchronological nature, WT’s failure and repair rates, WT’s outputcurves, wind spatial correlation, and wake effects. Failure andrepair rates assume different values for normal or extreme WSconditions. WF internal grid and preventive maintenance are

BARBERIS NEGRA et al.: ASPECTS OF RELEVANCE IN OFFSHORE WIND FARM RELIABILITY ASSESSMENT 161

neglected. This very detailed model accounts for many reliabil-ity evaluation aspects, but may require greater computationaltime and huge memory storage when large numbers of WT andWS states are considered.

Finally, in [12], probabilistic reliability calculations areperformed for an offshore WF using NEPLAN software. Thissystem analysis combines an analytical approach and a failure-effect analysis. The analysis considers the entire grid sys-tem, including cable, WT, and offshore component failures.The results highlight components, which influence most WFgeneration, and include some sensitivity analysis of relevantparameters.

Simulation approaches for reliability assessment have beenconsidered in the last years. Models for a random Monte Carlomethod are presented in [13]. This paper accounts for con-ventional generating units, small combined power plants, andchronology (assumes the load’s seasonal, weekly, and daily cy-cles). In [14], a nonsequential Monte Carlo method is presented,where many grouped WFs are modeled based on weekly cumu-lative power function. In many other studies, a sequential MonteCarlo approach is considered to appreciate the chronological na-ture of the system [3], [15].

Ubeda and Garcia [15] describes a wind generation modelfor an electric energy system’s stochastic simulation, based on asequential approach. The wind generation model is divided intothree components (models of WS, WT, and WF). Hourly mea-surements, hub height variations, WF wake effects, a two-statemodel for each WT’s forced outage, and correlation betweenWSs of different WFs are included. Forced outages of the WF’sinternal grid and different WS installation and scheduled out-ages are neglected.

A WT model based on a sliding window technique is pre-sented in [16]. An effective forced-outage rate for wind plants(EFORW) is calculated after defining a window of hours beforeand after the current hour. EFORW measures the statistical ex-pectation that the WF will not achieve a given output level over aspecified time period. With this value, the WF is then convolvedin the standard capacity outage table. This approach accountsfor WS variability and can include each WT availability.

B. Relevant Factors of Influence

Based on available literature, the following aspects forwind generation’s realistic reliability assessment are clearlyimportant:

1) WS simulation;2) wake effects;3) WT technology;4) offshore environment;5) different WSs in the installation site;6) power collection grid in the wind park;7) correlation of output power for different WTs;8) grid connection configuration;9) hub height variations.Each of these aspects will be individually analyzed in the

following sections.

1) Simulation of WS: The most relevant aspects for reliabil-ity assessment are WS variability and randomness. A set of WSmeasurements is required for both probability approaches.

Statistical information from the set of measurements (e.g.,probability, occurrence frequency, etc) is extrapolated to de-scribe the phenomenon, and analyzed from a WS probabilitytable. Depending on the topology of analysis (static or F&D),the amount of required information varies, as shown in [9]–[11].

In the Monte Carlo simulation, random and sequential ap-proach must be distinguished. In the random approach, a simpleWS probability table may be sufficient to obtain the randomvalues of the necessary WS. In the sequential approach, eachsample (i.e., in an year) needs a new random WS time seriesobtained from, and representative of, real measurements. Dif-ferent solutions have been defined for this purpose. The Uni-versity of Saskatchewan’s [3] time-series model is based onan autoregressive moving average (ARMA), which considersdifferent orders of the function to fit wind measurement datain the most suitable way. Other WS time series have been de-veloped based on Markov chains. At Colorado’s National Re-newable Energy Laboratory (NREL), a WS simulation tool isbased on a state-transition matrix with wind data from a singleyear [17]. The Chalmers University model includes two windconditions, (above and below the yearly mean) and the hubheight [18]. Ubeda and Garcia [15] considers an hourly WSmodel based on the Weibull distribution and a Markov transi-tion matrix. Another approach is presented in Section IV of thispaper.

2) Wake Effects: WT spatial arrangement influences outputpower. Wake effects reduce total WF output to a fraction of whatwould be obtained if each WT stood alone. In available litera-ture, this seems to be considered mainly in more detailed models([11] and [15]) and is included as an efficiency coefficient as-sumed equal to 90%–95% of the total WF production [15].

3) WT Technology: The choice of WT technology is one ofthe main tasks for planning new WFs. The choice of technologyand its components depends on available state of the art, andinfluences some parameter values in the analysis (mainly fail-ure/repair rate and maintenance). Reliability evaluation used tomodel a WF, considerations for possible WT technologies, andconcepts for offshore installation can be found in [19]–[21].

The WT availability model, which is independent of technol-ogy, is usually defined as a machine either at full service or outof service (two-state model). Preventive outages are not addedto most of the considered models since maintenance may bescheduled during low-wind periods [11] and may be performedin a short time due to the relatively simple machines used inWFs [15].

4) Offshore Environment: Little data are available for main-tenance and failure/repair rates for offshore WTs due to theirrelatively new development. An evaluation of this issue hasbeen performed in the DOWEC project, and presented in [19]and [22]. Data for onshore WF failures and maintenance inGermany, Denmark, and USA are collected in these papers.Figures for availability are shown, which consider different WTconcepts, future evolution, and necessary offshore installationimprovements.


A similar approach is presented in [23], where onshore WFinstallation figures are adjusted to offshore conditions. The ana-lyzed figures are failure rate and mean-time-to-failure (MTTR),and the influence of marine and electrical environment on themis considered. In [23], comments refer to main electrical com-ponents of offshore WF collection grids (breakers, cables, andtransformers), while WT failures are not considered at all.

All three references ([19], [22], and [23]) consider the fol-lowing as relevant aspects for offshore installations.

� MTTR can greatly increase during bad weather (e.g., win-ter), because the time to reach and repair a failed componentis related to the bad-weather window’s length.

� Failure rate may increase due to marine conditions, or toan installation site’s closeness to a sailing route.

� Component quality should be improved in order to com-pensate the two above-mentioned problems.

5) Different WS in the Area of Installation: Wind conditionsare usually defined by a unique set of measurements where theWF is installed. In reality, the WS varies in the area around itsaverage value as a function of time and space, so the outputpower of each running WT at each considered time is not equalto the others. This problem increases as the size of the areaincreases, and can become a relevant issue for large offshoreWFs [11], [23], and [24].

The available literature on reliability evaluation takes thisproblem into account only in [11], while in [15], it is assumedto be negligible, since the hourly mean-value averages the short-term variations that occur during the considered hour.

To evaluate this issue, several publications analyze the gen-eral problem with aggregated models of extended-area, largeWF output power. For instance, in [24], an aggregated model isgenerated for WT power curve and WS time series, which ac-counts for the area dimension and the statistical data of availableWS measurements.

6) Power Collection Grid in the Wind Park: WF power col-lection system availability is relevant to reliability assessmentfor an increased site size. This aspect was neglected in earlyoffshore WF reliability modeling, but interest has grown in re-cent publications [10], [12], [23], and [25]. An example in [25]uses a sequential Monte Carlo simulation to evaluate WF reli-ability with three possible internal cablings. Collected data foravailable technology and cable faults showed a preferred con-figuration and the importance of redundancy. WT failure ratesare not considered in the analysis. HLII analysis is used, dueto the large number of considered transmission components.As previously mentioned Zhao et al. [10] consider the wholewind park electrical grid as obtaining information on WF outputpower from an analytical approach, while Sannino et al. [23]compare three offshore WF’s collection grids, including cables,breakers, switches, and nacelle transformers, but neglects WTfailure, the offshore transformer, and uses a probability tableto define the WS. Underbrink et al. [12] evaluates grid compo-nent’s individual influence on system reliability.

7) Correlation of Output Power for Different WTs: Correla-tions between WS conditions and therefore WT output powersmust be considered if the assessment includes WFs from differ-ent locations. The closer the WFs, the more relevant the corre-

lation that has to be considered. This issue is presented in [13]for three WFs and in [15] for a generic number of elements.

8) Grid Connection Configuration: Different configurationsfor power transmission to the shore can be considered for anoffshore WF. Some possible solutions are presented in [26]including heating ventilation and air conditioning system high-voltage alternating current (HVAC) and high-voltage direct cur-rent (HVDC) solutions. However, all currently installed offshoreWF use ac transmission for the connection to the grid.

9) Hub Height Variations: WS measurements to evaluate in-stallation site wind conditions are obtained at a certain referencealtitude, and must be scaled to hub height [15]. This aspect isusually considered using the standard logarithmic wind profiledescribed in [20, pp. 114–115].

C. Reliability Indices

As previously mentioned, a generic reliability assessment canevaluate a set of indices that represent interesting aspects of thesystem. When a WF is included in the reliability evaluation, itsgeneration can be evaluated by the following indices, as definedin [11], [10], and [15].

1) Installed wind power (IWP) is the sum of the nominalpower of all the WTs in the WF.

2) Installed wind energy (IWE) is the product of installedcapacity and the number of hours in the period.

3) Expected available wind energy (EAWE) is the sum ofenergies that all installed WTs produce in the period (nocomponent failures are considered here).

4) Expected generated wind energy with WT failure (EG-WEWTF) is the sum of energies that all installed WTsproduce in the period including WT failures.

5) Expected generated wind energy (EGWE) is the sum ofenergies that all effectively available (due to componentfailures) WTs produce in the period.

6) Capacity factor (CF) is the ratio of EGWE to IWE.7) Generation ratio (GR) is the ratio of the power delivered

to the point of common coupling (PCC) to the powerinjection generated by the WF (i.e., available power dueto the current WS).

It should be noticed that many aspects relevant to offshore WFreliability assessment have not been considered all together inthe available models. In the Section IV, a small example of howto include some of them in offshore WF reliability assessmentis presented.

IV. EXAMPLE OF SIMULATION

A sequential Monte Carlo simulation is used for the reliabilityassessment of an offshore WF. Due to the limited statistic infor-mation about offshore WF reliability issues, any presented resultis a qualitative conclusion to show the function of a simulationtool for reliability assessment.

The used approach is a standard Monte Carlo simulation thatincludes:

� random generation of the yearly WS time series;� WT failures;� internal grid failures;


TABLE ICOMPONENT DATA FOR RELIABILITY EVALUATION

� connector to shore failures;� influence of offshore environment.The simulation is performed with the following steps:1) definition of WF layout and component data;2) calculation of the WS probability table;3) then, for each sampled year the following is carried out:

a) calculation of a synthetic WS time series;b) random definition of each component’s hourly avail-

ability;c) then, the following is carried out on hourly basis;

i) definition of the “effectively” available WT;ii) evaluation of the WF output power;

iii) calculation of WF indices.d) evaluation of the result accuracies;

4) calculation of the final indices by average.The framework above is the standard Monte Carlo simulation,

therefore, only some points will be explained in detail in thefollowing section. In item 3.c.i, “effectively” means that theWT is connected to the PCC at the current hour, and if available,produces energy. In addition, the availability of each component(3.c.ii) is calculated considering some data as listed in Table Iand ssuming an exponential distribution for both failure andrepair states.

Regarding point (3.d), the simulation is performed until astable accuracy of 0,2% is achieved. That criterion is based onthe evaluation of the coefficient of variation [27] calculated forall the system indices. The index with the highest value is chosenand compared to a reference tolerance. In the presented study,the most critical index is EGWE.

The WS data are obtained from a seven-year measurement,recorded at the Horns Rev location, in the North Sea close to theDanish coast. The data are recorded as 10-min averages fromMay 14, 1999 to May 13, 2006. The data should total 368208,but available data was 339492 due to some equipment failures.

A. WS Time Series

To assess the WF’s reliability with a sequential Monte Carlosimulation, a defined wind-speed-time series with the step ofinterest (e.g., 1 h) must be input to evaluate the WF generationduring each sample. A newly developed synthetic WS generatorused in this paper is described below.

First, the set of measured WS data is divided into states (steplength equal to 1 m/s) and some statistics are extrapolated foreach state [11]. This data are the state probability, the state-occurrence frequency, and the state-transition rates to up anddown states. The following assumptions have been made [11].

1) The WS model is statistically stationary, i.e., the stochasticbehavior of the WS is same at all points of time irrespectiveof the point of time being considered.

2) The distribution of residence times is based on a birth- anddeath-Markov process, and the distribution is exponentialin a given state of the process.

3) The probability of a transition from a given WS stateto another state is directly proportional to the long-termaverage probability of existence of the new state.

4) Transitions between WS states occur independently ontransitions between WT states.

5) From a given WS state, only the case of transitions toimmediately adjacent states is considered (if some transi-tions occur between nonadjacent WS states, the residencetime duration is estimated by a linear proportion of thesampling time).

After obtaining the table, it is possible to calculate the syn-thetic WS time series. In order to preserve some seasonal char-acteristics of the WS measurements, one table for each monthof the year is calculated and used to define the WS time series.

The current WS can reside in one of the different mutuallyexclusive states presented in the WS probability table. Afterresiding in the current state for a certain amount of time, thecurrent WS moves to one of the two adjacent states (if at a thevery first or the very last current state of the table, there existsonly one adjacent state). Since the phenomenon can be describedby an exponential distribution [4], [11] and the transition ratesof each state are known, it is possible to calculate the time serieswith the following steps.

1) Initialization of the WS vector ws(h) = ws1 and the timevariable t(h) = 0. In the case presented here, the initialWS value is chosen close to the average WS of the mea-surements (9 m/s).

2) For the ith generic step, random numbers Ui1 and Ui

2 aregenerated in the interval (0,1), one for the up transitionrate and one for the down-transition rate.

3) Calculation of the time to up (TTU) and time to down(TTD) for the current state by means of equations

TTUi =hyear

λupln (U i

1) (1)

TTDi =hyear

λdownln (U i

2) (2)

where hyear is the length of the simulation period ex-pressed in hours (i.e., one year, hyear is 8760 hours), λup

is the up-transition rate and λdown is the down-transitionrate of state WSi. The smallest of the two values calcu-lated from (1) and (2) defines the current WS movementto and duration in the current state (e.g., if TTU < TTD,it is assumed that the current WS goes to the upper stateafter TTU seconds).

4) Update of the two vectors, such that

ti = ti−1 + TTUi (3)

ws(ti−1 : ti) = wsi−1 + 1 (4)

where (ti−1 : ti) means between time ti−1 and ti (assum-ing that WS moves up from the current state). If ti be-longs to the same hour of ti−1, the WS ws(ti−1 : ti) is not


Fig. 1. WS time series. (a) Original measurements (year 2004), (b) syntheticWS time series based on yearly WS probability table, and (c) synthetic WS timeseries based on 12-monthly WS probability table.

recorded in the WS vector since the wind enters and leavesthe current state during the same hour.

5) Repetition of steps 2–4 until t is equal to the hyear.A WS time series is thus obtained, and can be used for further

calculations in the Monte Carlo simulation. The main advantageof this approach is that it accounts for the random variationof WS, and allows for a more realistic simulation. The maindrawback is the long computation to calculate the time seriesat every sampled year, but that can be shortened by definingand storing a set of synthetic WS time series in advance (beforesimulation), and calling for them during computation. Since theywill not be calculated yearly, computation time will be sensiblyreduced.

In Fig. 1, three WS time series can be compared: 1) theWS time series in year 2004; 2) a randomly simulated WStime series based on a yearly WS probability table; and 3) arandomly simulated WS time series based on the 12 monthlyWS probability tables. Fig. 1(a) and (c) have similar seasonalbehavior (high WS for first and last quarters, low WS in themiddle months). Fig. 1(b) has a complete random characteristicduring the year, with high and low WS averages distributed allaround the year. This shows why WS seasonal characteristicsmust be included in a sequential analysis to preserve informationabout the WS curve, and shows why a monthly probability tablecan be a useful tool for this purpose.

B. Results of the Simulation

The offshore WF has 25 WTs rated at 3 MW, 25 cables,and three connectors to shore. Data for the WT availabilityare obtained from [19] and [22]; data for cables and connectorscome from [23]. The layout of the WF is presented in Fig. 2 (“x”indicates a WT, a line represents a cable or connector), whilecomponent data (failure rate and mean time to failure MTTR)are shown in Table I. The MTTR for cables and connectors is

Fig. 2. WF layout used for the simulation.

TABLE IICALCULATED RELIABILITY INDICES

chosen as an average between summer and winter hypotheticalvalues.

It is assumed that cables connecting WTs have the sameelectrical characteristic and length (700 m), and that connectorsto shore (between nodes 26–29, 27–29, and 28–29) have thesame electrical characteristic and a 10 km length.

Simulation results are presented in Table II, including time ofthe simulation, accuracy of the results, and required number ofsamples.

A broad range of indices can be calculated to assess the WFgeneration. Also, as shown in [28], the distribution function ofeach index is known, and can be studied to predict the behaviorof indices of interest.

The inclusion of cable and connector failures influences theWF generation. Comparing indices 4 and 5, a difference in thevalues is due to the above-mentioned components’ inclusionor noninclusion. These components should be included in theanalysis to obtain more realistic results.

Index GR represents WF generation with respect to compo-nent availability, and its low value compared to the standardunits’. This can be explained considering the assumed valuesfor each WT’s availability in Table I. Assumed values mightbe higher than for a realistic installation (not yet available foroffshore installations) and this leads to a pessimistic estimationof the whole generation of WF.


Simulation time and sample number have large values, whichmight even increase if the analysis is extended to an HLI orHLII study. For these cases, the Monte Carlo simulation mustbe improved to reduce the computation time [27].

V. CONCLUSION

The evaluation of a power system’s reliability when includinglarge amounts of wind energy is relevant to avoid problems inelectrical energy delivery. Many solutions have been presentedto assess WF reliability, but all lack the inclusion of all relevantaspects.

Based on available literature, this paper describes a set of ap-proaches used for WF reliability calculations. It highlights nineaspects that influence offshore installation reliability. A MonteCarlo simulation example shows how some of these factors in-fluence the evaluation. A standard offshore WF configurationis used, and indices for evaluating system production are cal-culated. These demonstrate that evaluation must account forconnection grid failures, and must use a tool to represent WSvariability and randomness. The Monte Carlo simulation mustbe optimized to reduce required time and sample numbers.

Future developments of the presented simulation will includethe aspects that have been left out here, and the whole modelwill be used to assess HLI and HLII analyses reliability whenconnecting a large offshore WF to a transmission grid, withsome loads, and other generation units that are conventionaland renewable.

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Nicola Barberis Negra received the M.Sc. degree inelectrical engineering from the Polytechnic of Turin,Turin, Italy, in 2005. He is currently working towardthe Ph.D. degree at Elsam Engineering A/S, DongEnergy, Fredericia, Denmark.

His current research interests include power sys-tem reliability with a particular focus on offshorewind farm (WF) installations.


Ole Holmstrøm (M’02) received the B.Sc. degreein electrical engineering from The Danish Engineer-ing from Academy, Lingby, Denmark, in 1980. He iscurrently a Senior Engineer with Elsam EngineeringA/S, Dong Energy, Fredericia, Denmark. He has com-prehensive experience in general electrical engineer-ing and various disciplines in the analysis of electricalpower systems. He has specialized in the analysis ofpower systems using various software tools, includ-ing advanced computer modeling and dynamic andtransient simulations. His research intersts include

design of wind farms (WFs), analysis of WF grid connection, the developmentof advanced dynamic models of wind turbines, the impact of wind power onpower systems, capacity to power quality, and transient stability.

Birgitte Bak-Jensen (M’89–M’91–S’91–M’92) re-ceived the M.Sc. degree in electrical engineering, andthe Ph.D. degree in modeling of high voltage com-ponents, from the Institute of Energy Technology,Aalborg University, Aalborg, Denmark, in 1986 and1992, respcetively.

From 1986 to 1988, she was an Electrical De-sign Engineer with Electrolux Elmotor A/S, Aalborg,Denmark. Since August 1988, she has been an Asso-ciate Professor at the Institute of Energy Technology,Aalborg University. Her current research interests in-

clude modeling and diagnosis of electrical components, power quality and sta-bility in power systems, and integrating dispersed generation to the networkgrid. She has participated in many projects concerning wind turbines and theirconnection to the grid.

Poul Sorensen (M’04) was born in Kolding,Denmark, on June 16, 1958. He received the M.Sc.degree from the Technical University of Denmark,Lyngby, Denmark, in 1987.

Since October 1987, he has been with the WindEnergy Department of Riso National Laboratory,Roshkilde, Denmark, where he is currently a SeniorScientist and a Project Manager. His research hasbeen concerned with integration of wind power intothe power system. He was a member of the Interna-tional Electrotechnical Commission (IEC) working

group preparing IEC 61400–21, and is currently a member of the maintenanceteam MT21. He is also a member of the International Ergonomics Association(IEA) annex XXI on “Dynamic models of wind farms for power system studies.”

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