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A fuzzy analytic network process model to mitigate the risks associated with offshore wind farms
Accepted Manuscript A fuzzy analytic network process model to mitigate the risks associated with offshore wind farms Mahmood Shafiee PII: DOI: Reference:
S0957-4174(14)00643-5 http://dx.doi.org/10.1016/j.eswa.2014.10.019 ESWA 9621
To appear in:
Expert Systems with Applications
Please cite this article as: Shafiee, M., A fuzzy analytic network process model to mitigate the risks associated with offshore wind farms, Expert Systems with Applications (2014), doi: http://dx.doi.org/10.1016/j.eswa.2014.10.019
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A Fuzzy Analytic Network Process Model to Mitigate the Risks associated with Offshore Wind Farms MAHMOOD SHAFIEE † Centre for Offshore Renewable Energy Engineering Cranfield University, Cranfield, Bedfordshire MK43 0AL, United Kingdom
ABSTRACT
In the offshore renewable energy industry, it is extremely important to reduce the likelihood as well as the magnitude of potential risk events during system’s actual operation. Operational risks (either risk of system failures or environmental risks) may cause catastrophic damages to personnel or infrastructure and result in substantial costs in terms of lost production and emergency maintenance operations. Selection of a suitable strategy for mitigation of the risks associated with offshore renewable energy projects is a very complex and critical task. The aim of this paper is to propose a fuzzy analytic network process (FANP) approach, based on Chang’s extent analysis, in order to select the “most appropriate risk mitigation strategy” for offshore wind farms. Our proposed model consists of four possible alternatives (variation of offshore site layout, improvement of maintenance services, upgrading the monitoring systems, and modification in design of wind turbines) among which the decision maker has to select the best strategy according to four comparison criteria: safety, added value, cost and feasibility. The model is then applied to determine a suitable risk mitigation strategy for an offshore wind farm consisting of 30 wind turbines of 2MW. Finally, the results are compared with those obtained using the crisp AHP and ANP models. Key Words: Risk mitigation; Offshore wind farm; multiple-criteria decision analysis (MCDA); Fuzzy analytic network process (FANP); Operation and maintenance (O&M).
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1. Introduction Offshore wind energy has grown very rapidly in recent years. The cumulative installed capacity of offshore wind power in the European Union (EU) has increased from 532 megawatts (MW) in the year 2003 to 6,600 MW in the end of 2013, which represents an annual growth of about 29% (EWEA, 2014). Along with the growth of the market for offshore wind energy, a particular attention should be paid to operation and maintenance (O&M) as well as reliability and availability of the installed wind power systems. Analysis of field failure data collected from various databases like Elforsk in Sweden (http://www.elforsk.se) show that the availability of onshore wind farms is typically between 95% to 99%, while it is evaluated to be in the range of 60% to 70% for offshore wind farms. Moreover, offshore wind turbines suffer from a higher failure rate compared to their equivalent wind turbines located onshore (Tavner, 2012). The main reason is that offshore wind farms are generally exposed to a wider range of risk events, hazards or damages rather than onshore wind farms. Basically, the risks associated with offshore wind farms can be categorized into two major groups: (i) the risks of system failures (e.g. power outage) and (ii) the environmental risks (natural catastrophes, ship collisions, etc.) (Leung and Yang, 2012). The former is caused by system/component degradation (deterioration) while the latter results from harsh surrounding environments (e.g. extreme weather, wind, wave). Any of these hazards can potentially have a negative impact on wind farm performance if it is not avoided (prevented) in an efficient way. Degradation failures result in substantial costs of repair or replacement and significant losses of power production, and nature events lead to catastrophic safety hazards to personnel and infrastructure. Therefore, there is a critical need to reduce the likelihood as well as the magnitude of potential risk events during system’s actual operation. For this purpose, a risk management plan must be developed and applied to the existing or future offshore wind farms. Risk management is a process focusing on identification and elimination of the hazards that could affect asset performance. This process normally includes several stages like identification, assessment, evaluation, control and monitoring, and mitigation of the risks resulting from a certain hazard (Aven & Vinnem, 2007). Among these stages, the risk identification and assessment area has received a reasonable attention within the wind energy industry. To this end, the following studies should be mentioned: Arabian-Hoseynabadi et al. (2010) proposed a failure mode and effects analysis (FMEA) methodology for prioritization of the failure modes in a 2MW wind turbine system. Kahrobaee and Asgarpoor (2011) developed a risk-based FMEA approach for wind turbines in which the risk priorities of failure modes are determined based on failure probability and the incurred costs. Dinmohammadi and Shafiee (2013) developed a fuzzy-FMEA approach for risk and failure mode analysis of offshore wind turbines when field data is missing or is censored. Sunder and Kesavan (2013) studied the implementation of an FMEA methodology for wind turbines that operate in uncertain wind environments. Shafiee and Dinmohammadi (2014) proposed a mathematical tool for risk and failure mode analysis of wind turbine (both onshore and offshore) taking into account the key economic issues for maintenance (e.g. loss
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of power production, costs of logistics and transport). Wang et al. (2014) developed a fuzzy risk decision-making model based on conditional value at risk (CVaR) method for power systems integrated with large-scale wind farms. In spite of the vast research on risk identification and assessment, only a few methods have been developed for mitigating the risks associated with offshore wind farms. A recently published report by the U.S. Department of Energy (DOE, 2008) recommends enhancing the wind turbine reliability (through prototype testing of components before deployment) to mitigate the failure risks within offshore wind farms. Sjodin et al. (2012) and Griffin (2014) introduce the variation of offshore site placement/layout as a way of reducing the weatherrelated risks. Even though this solution may seem to be infeasible for many renewable energy systems, it can be considered as a practical alternative for small offshore wind projects. The selection of a suitable risk mitigation strategy for offshore wind farms is a very complex and critical task. An appropriate risk mitigation strategy not only avoids the negative consequences of natural events but also results in increased power production and less operation and maintenance (O&M) cost. On the other side, an improper selection of strategies may adversely affect the operating budget and thereby reducing productivity as well as profitability. Risk mitigation strategy selection is considered as a typical multiplecriteria decision analysis (MCDA) problem. In this analysis approach, the decision-makers (i.e., system owners or stakeholders) must decide on the most appropriate strategy among a set of possible alternatives to mitigate the system risks. Moreover, many different goals or comparing criteria (economic, social, environmental, etc.) must be taken into account in evaluating the alternatives. These criteria are often conflicting, i.e., according to a criterion, a given alternative is the best one, while according to another criterion, other alternatives score higher. Thus, each alternative is evaluated with respect to each criterion and then, the evaluation ratings are aggregated to obtain a global evaluation. Finally, the alternatives are prioritized from the best (optimal) to the worst. In recent years, the MCDA approach has been applied to solution of a wide range of decision-making problems within offshore wind energy, including the selection of wind farm location, wind turbine technologies, the most resilient materials to be used, and decommissioning decisions. For a thorough review on the use of MCDA approach in the renewable energy industry, the readers can refer to San-Cristóbal (2012). Some recent publications in the area are briefly reviewed below: Lee et al. (2009) developed an MCDA model based on the analytic hierarchy process (AHP) and the benefits, opportunities, costs and risks (BOCR) methods in order to select a suitable wind farm project. Kang et al. (2011) proposed a comprehensive evaluation model on the basis of interpretive structural modeling (ISM), BOCR and fuzzy analytic network process (FANP) to select a suitable location for wind farms. Al-Yahyai et al. (2012) applied the AHP method to derive wind farm land suitability index and classification under Geographical Information System (GIS) environment. Maity and Chakraborty (2012) applied the FANP approach to select the most appropriate materials for wind turbine blades. Lee et al. (2012) proposed a comprehensive evaluation model based on ISM and FANP to
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select the most suitable wind turbines in a wind farm. In another work, Lee et al. (2014) developed an evaluation model incorporating DEMATEL1 and FANP techniques to select the most suitable wind turbines for installation in a wind farm. Yeh and Huang (2014) presented a DEMATEL-ANP based approach to prioritize the key six factors considered in determining the location of wind farms. Sánchez-Lozano et al. (2014) proposed an MCDA approach based on the ELECTRE-TRI method for selection of wind farm sites in the southeast of Spain. Wu et al. (2014) utilized a fuzzy MCDA approach to select the best plan for wind projects. When looking at the literature, no research is found on the risk mitigation strategy selection for offshore wind projects utilizing the MCDA approach to find out solution. In order to address this issue, we propose an FANP methodology on the basis of Chang’s extent analysis to select the most appropriate risk mitigation strategy for offshore wind farms. The proposed model consists of four possible alternatives (variation of offshore site layout, improvement of maintenance services, upgrading the control and monitoring systems, and modification in design of wind turbine assemblies) among which the decision maker has to select the best strategy acording to four comparison criteria: safety, added value, cost and feasibility. Our findings indicate that “improving the repair and maintenance services” is chosen as the most cost-effective risk mitigation strategy for an offshore wind farm consisting of 30×2MW wind turbines. This paper is organized as follows. Section 2 presents a brief overview of the FANP approach so as to set the background for the main contribution of the paper. In Section 3, a decision model is proposed for risk mitigation strategy selection within offshore wind energy. In Section 4, the implementation of the proposed model is presented and the results are discussed. Finally, the paper is concluded in Section 5. 2. Fuzzy analytic network process (FANP) Among the several existing MCDA techniques, AHP and ANP are the most widely used models. In AHP technique, the problem is modeled in a hierarchical structure where the goal, decision criteria, and alternatives are connected top-to-bottom (see Fig. 1-a). As shown, each element in hierarchy structure is considered to be independent of all the others, and hence, the interactions and feedbacks which might be present in the system are ignored (Saaty, 1994). To overcome this limitation, the ANP technique was introduced by Saaty (1996). The ANP technique is a generalization of the AHP where the hierarchies are replaced by networks enabling to take into account all possible interactions between the clusters and elements within a cluster (see Fig. 1-b). In fact, the ANP technique provides a general framework to deal with decisions without making assumptions about the independence of higher level elements from lower level elements and about the independence of the elements within a level. So, ANP is a coupling of two parts. The first consists of a control hierarchy or 1
DEcision MAking Trial and Evaluation Laboratory
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network of criteria and sub-criteria that control the interactions. The second is a network of influences among the elements and clusters.
“Fig. (No. 1)” In both the AHP and ANP techniques, there is a need for integration of the mathematical model with human experiences. In order to prioritize alternatives, a pairwise comparison must be carried out between all pairs of criteria (or sub-criteria) as well as of alternatives. These pairwise comparisons are done by a group of experts with knowledge in the concerned area. However, there often exists an inherent uncertainty and imprecision with the mapping of the decision-makers’ judgments into crisp values. This uncertainty in the initial stages of the decision-making process limits the chances of getting satisfactory results. For this reason, the fuzzy AHP/ANP approach was developed in which fuzzy linguistic numbers, e.g., ‘‘between three and five times less important’’ are used for uncertain comparison ratios instead of crisp values. In the present study, a triangular fuzzy number (TFN) is used to represent the relative importance of one element over another. A TFN is a special case of fuzzy number with two ~ linear functions on either sides of the peak. It is defined by a triplet N = (l, m, u) as shown in Fig. 2, where l, m, and u are respectively considered as the lower bound, mean bound, and the upper bound.
“Fig. (No. 2)” The mathematical expression of the membership function of a TFN is described as follows: ⎧ x−l l≤x≤m ⎪m−l; ⎪⎪ u − x . (1) ; μ N~ ( x) = ⎨ m≤ x≤u ⎪u − m otherwise ⎪ 0; ⎪⎩ In what follows, we propose a methodology to determine a suitable risk mitigation strategy for offshore wind farms. To our knowledge, this paper is the first study on the subject area utilizing an FANP approach to find out the solution. 3. Proposed methodology Our proposed methodology for selection of the most appropriate risk mitigation strategy in offshore wind farms, as shown in Fig. 3, includes ten steps. These steps are described in details as following:
“Fig. (No. 3)”
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Step 1. Form a group of decision makers First, a project team must be established to determine and examine the operational hazards and their potential impact on wind farm safety. The project team is often composed of key managers (i.e., power generation manager, head of safety and risk, project finance director) as well as some practitioners from operation and maintenance (O&M). Let K represent the number of team members who participated in interviews. Step 2. Determine the alternative risk mitigation strategies Several alternatives can be taken into account for risk mitigation, but some of them might be technically infeasible to offshore renewable energy. In this paper, four alternative risk mitigation strategies are considered for our application:
A1 : Variation of offshore site layout The ‘layout’ of an offshore wind farm is one of the critical elements influencing the risks associated with natural events (i.e., environmental damages) (Tiusanen et al., 2011). It refers to the arrangement of wind turbines in a wind farm, and typically deals with decisions regarding position of installations with respect to wind and wave direction, distance from the shore, water depth, distance between wind turbines, location of warehouses and capacity of depots. In general, the potential nature events are more likely to happen in cold, icy or remote offshore areas than they are in normal marine environments. According to existing statistics, the power outage caused by unexpected events for deep-water wind farms is 10 to 20% longer than that for wind farms built in shallow waters near the coast (Shafiee, 2014). Therefore, any improvement in offshore site layout will have a substantial effect on harmful outcomes resulting from extreme weather and harsh marine conditions. A 2 : Improvement of maintenance services
The current practice of maintenance for offshore wind farms is reactive response (or failure-based). Under this policy, the maintenance actions are undertaken once a failure is detected in wind turbines. Van Bussel and Schöntag (1997) in Opti-OWECS1 project, and Van Bussel and Henderson (2001) in CA-OWEE2 project report that using reactive response maintenance policy causes frequent stoppages, high repair costs, long waiting and maintenance times, logistics disruption, and severe damages and trouble shooting problems. For this reason, preventive maintenance (PM) policies (including periodic inspections, reliability-centered, risk-based, condition-based, and predictive) are extensively applied to control the rate of degradation failures and avoid costly replacements (Shafiee & Finkelstein, 2014). A well-planned and optimized maintenance policy can effectively reduce the costs associated with operating and repairing wind turbines.
A3 : Upgrading the control and monitoring systems 1 2
Structural and Economic Optimization of Bottom-Mounted Offshore Wind Energy Converters Concerted Action on Offshore Wind Energy in Europe
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One effective way to reduce the likelihood of risk events within the offshore wind energy industry is improving the fault detection capability. This improvement can be achieved by installing a number of high quality and technically advanced sensors at specified locations as well as using new monitoring techniques (such as acoustic emission, ultrasonic testing, strain measurement, radiographic inspection, thermography, and signal processing methods) (Yang et al., 2014).
A4 : Modification in design of wind turbine sub-assemblies The operational risks in offshore wind farms can be reduced by enhancing the reliability of wind turbines through design modification or new design of the systems. The aim of design modification is to minimise the number of failures experienced in wind farms, which results in enormous savings in maintenance and energy costs. The modification in design of sub-assemblies includes reliability growth testing, or adding redundancy to critical components in order to increase the mean-time between failures (MTBF) (Shafiee et al. 2013). Step 3. Identify and calssify the selection criteria In order to evaluate and prioritize the risk mitigation alternatives, the project team must specify a set of comparison criteria. Different decision-makers may have different objectives. In this paper, we first determined a list of criteria based on the review of literature. Then, semi-structured interviews were conducted with project team in order to get a better understanding of their objectives. Finally, four main criteria were selected for consideration in the study. These criteria are described in details as following: C1 : Safety A high level of safety is required for many offshore wind farms, in particular for the ones that are connected to the grid in series. In a serial power grid, any failure in one of the units causes the failure of entire system. The relevant factors describing the safety are: C11 : Technicians safety - A failure of wind turbine and/or a nature event may lead to serious damages to personnel/technicians who work on site. C12 : Power grid safety - A failure of wind turbine and/or a nature event would damage the grid connection equipment and thereby disconnects the wind farm from electricity grid. C2 : Added value The added-value criterion deals with the benefits that may be gained from implementing a particular risk mitigation strategy. This category includes the improvement in terms of power production and fault detection. C21 : Power production - A failure of wind turbine and/or a nature event often leads to substantial production losses. Selecting a suitable strategy for risk mitigation can potentially increase the electricity generated by offshore wind farms.
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C22 : Fault detection - Fault diagnostic and prognostic techniques aim to quickly alert the maintenance engineers where and why faults occur. As a result, the maintenance leadtimes are shortened and the availability of wind farms will improve. C3 : Cost Different risk mitigation alternatives have different expenditure of hardware, software, and personnel training. C31 : Hardware cost - For implementation of risk mitigation strategies, a number of service vessels, support facilities, maintenance tools, monitoring and prognostic sensors, and some computers must be purchased. C32 : Software cost - More expensive and advanced software will be needed if it is decided to upgrade the control and monitoring systems or to modify the design of subassemblies. C33 : Training cost - Risk mitigation actions in offshore wind farms should be started only after sufficient training. C4 : Feasibility The feasibility criterion is divided into acceptance by stakeholders and acceptance by wind farm managers. C41 : Acceptance by stakeholders - Successful implementation of a risk mitigation alternative needs the support and participation of wind farm stakeholders (i.e., financial institutions, insurance companies, owners, and regulatory authorities). C42 : Acceptance by wind farm managers - Wind farm managers often prefer the strategies yielding more return on investment (ROI) and are easy to implement. So, the variation of offshore site layout ( A1 ) and modification in design of wind turbines ( A 4 ) might be suitable options for mid- or long-term investments. Step 4. Identify criteria/alternatives’ interdependence In real-world decision making problems, there often exists a two way relationship between criteria and alternatives and also intra-relationships among criteria. For instance, the relationship between the two criteria safety and cost is such that a risk mitigation strategy with high level of safety would be expected to incur more costs in terms of hardware, software and personnel training. In this study, no interdependency among the risk mitigation alternatives is considered. Step 5. Construct a network model Using criteria, sub-criteria and alternatives, a network model is constructed. Fig. 4 illustrates a network model for the decision problem of selecting a suitable risk mitigation strategy for offshore wind farms. As can be seen, the proposed structure includes three clusters. The first cluster represents the ultimate goal of the problem (i.e., selection of the best risk mitigation
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strategy). The second cluster in the network consists of four main criteria, which are namely, safety, added value, cost, and feasibility. Each criterion is also decomposed into various subcriteria as discussed in step 3. Finally, the third cluster represents the alternative strategies. The relationships among the criteria and sub-criteria are also determined and reflected in the network model.
“Fig. (No. 4)” Step 6. Perform pairwise comparisons using a TFN linguistic scale Team members are asked to perform a series of pairwise comparisons. In this study, the triangular fuzzy numbers are used to represent comparison ratios, i.e., the relative importance of element i over element j for decision-maker k is represented in the form of a~ijk , where (i) a~ijk = (1,1,1) if i = j , and (ii) a~ijk = (l ijk , m ijk , u ijk ) if i ≠ j , for i , j = 1, 2 ,…, n, and k = 1, 2 ,…, K. The reciprocal of a~ijk represents the preference of element j over element i for decision-maker k and is given by: a~
ijk
−1
= (1 / uijk ,1 / mijk ,1 / lijk ) .
(2)
The pairwise comparisons among all criteria (sub-criteria) and alternatives are done following the scale given below in Table 1. This scale has been widely used in the fuzzy MCDA literature (e.g. see Wang et al., 2007; Kumar & Maiti, 2012). The decision maker chooses a linguistic term based on the relative importance of the two elements being considered. Then, the corresponding triangular fuzzy scale is assigned for judgment.
“Table (No. 1)” When all pairwise comparisons are completed at a level, the fuzzy judgment matrix can be established. The fuzzy judgment matrix for decision-maker k, A~k is given by:
~ Ak = {a~ijk }n× n
(1,1,1) (l12 k , m12 k , u12 k ) ⎛ ⎜ (1,1,1) ⎜ (l 21k , m21k , u 21k ) ⎜ . . =⎜ . . ⎜ ⎜ . . ⎜ (l , m , u ) (l , m , u ) n2k n2k n2k ⎝ n1k n1k n1k
... ... ... ... ... ...
(l1nk , m1nk , u1nk ) ⎞ ⎟ (l 2 nk , m2 nk , u 2 nk ) ⎟ ⎟ . ⎟ , for k=1, 2 ,…, K , (3) . ⎟ ⎟ . ⎟ (1,1,1) ⎠
where n is the number of related elements at the level, and (l jik , m jik , u jik ) = (1 / uijk ,1 / mijk ,1 / lijk ) . Step 7. Test the consistency and aggregate the judgment matrices The consistency analysis is an essential part of both FAHP and FANP methods whose aim is to make sure that the judgment results are accurate and reliable. When looking at the literature, only a few studies have addressed the issue of inconsistency checking for fuzzy ~ judgement matrices. According to Buckley (1985), the fuzzy matrix Ak in Eq. (3) is
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consistent if a~ijk ≈ a~ipk ⊗ a~ pjk , for i , j , p = 1, 2 ,…, n, where ≈ denotes fuzzy equal to, and ⊗ is the multiplication operation on fuzzy numbers and is defined by: ( x1 , y1 , z1 ) ⊗ ( x2 , y 2 , z 2 ) = ( x1 x2 , y1 y 2 , z1 z 2 ) .
For judgment matrix which fails the consistency test, the decision maker is asked to revise his/her pairwise comparisons. Once all fuzzy judgement matrices for team members pass the consistency test, an aggregate fuzzy judgment matrix can be established. The aggregate fuzzy judgment matrix for a group of decision makers is given by: ~ A = {a~ij }n×n ; a~ij = (l ij , mij , u ij ) ,
(4)
where l ij , mij and u ij are calculated using the following Equation (Chang et al., 2009): ⎛ K ⎞ l ij = min (l ijk ) , mij = ⎜⎜ ∏ mijk ⎟⎟ k ⎝ k =1 ⎠
1
K
, u ij = max (u ijk ) .
(5)
k
Step 8. Calculate priority weights using Chang’s fuzzy extent analysis The aggregate fuzzy judgment matrix in Eq. (4) can now be used to calculate the crisp priority vector. For this purpose, the fuzzy extent analysis proposed in Chang (1992, 1996) is used. The steps of this analysis are described below. i. Calculate the value of “fuzzy synthetic extent” for element i (= 1, 2 ,…,n), as defined by following Equation: ⎛ ~ S i ≡ (l i , m i , u i ) = ⎜ ⎜ ⎝
n
∑ a~
ij
j =1
⎞ ⎡ ⎟⊗⎢ ⎟ ⎢ p =1 ⎠ ⎣ n
n
∑ ∑ a~
pj
j =1
⎤ ⎥ ⎦⎥
−1
⎛ ⎜ ⎜ ≈⎜ ⎜ ⎜ ⎝
n
∑
n
∑
l ij
j =1
n
,
n
∑u
j =1
n
⎞ ⎟ ⎟ j =1 , n n ⎟, l kj ⎟ ⎟ p =1 j =1 ⎠ n
m ij
n
ij
(6)
∑∑u ∑∑m ∑∑ kj
p =1 j =1
kj
p =1 j =1
where l ij , m ij and u ij are given by Eq. (5). ~
~
ii. Calculate the degree of possibility of Si ≡ (li , mi , ui ) ≥ S j ≡ (l j , m j , u j ) for two elements i and j using the Eq. (7): ⎧ ⎪ mi ≥ m j 1 ⎪⎪ ~ ~ (7) V (Si ≥ S j ) = ⎨ l j ≥ ui . 0 ⎪ ui − l j ⎪ otherwise ⎪⎩ (u i − mi ) + ( m j − l j ) ~ ~ As shown in Fig. 5, the value of V ( S i ≥ S j ) represents the ordinate of the highest
intersection point between two fuzzy membership functions μ S~i (.) and μ S~j (.) .
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“Fig. (No. 5)” iii. Compute the degree of possibility of S~i to be greater than all the other n − 1 TFNs, that is,
~ ~ ~ ~ ~ ~ d ( S i ) ≡ V ( S i ≥ S1 ,..., S i −1 , S i +1 ,..., S n ) , ~ ~ = min V ( S i ≥ S j ) , for j = 1, 2 ,…, n , j ≠ i . j
(8)
iv. Obtain the normalized priority vector W = ( w1 , w2 ,..., wn ) T of the fuzzy judgement matrix ~ A , where wi is given by: ~ d (S i ) , i = 1, 2 ,…, n . (9) wi = n ~ ∑ d (S j ) j =1
Step 9. Compute supermatrix and limit supermatrix The supermatrix represents the influence priority of an element on the left of the matrix on an element at the top of the matrix with respect to a particular control criterion (Saaty, 1996). The supermatrix is actually a partitioned matrix where each matrix segment represents a relationship among two nodes (components or clusters) in the network. To form a supermatrix, the priority vectors (obtained in Step 8) are entered in the appropriate columns based on the flow of influence from one cluster to another, or from a cluster to itself as in the loop. If there exists no relationship between two elements, the corresponding entry in the supermatrix is zero. Since there usually is interdependency among clusters in a network, the columns of a supermatrix may sum to more than one. In this case, the supermatrix must be transformed into a weighted supermatrix. This process involves multiplying every node in a cluster of the intial supermatrix by the weight of the cluster, which has been established by pairwise comparison among the clusters. Each column in the weighted supermatrix has a sum of one, and thus the matrix is stochastic. To achieve a convergence on the importance weights, the weighted supermatrix is raised to the power of 2k + 1, where k is an arbitrarily large number, and this new matrix is called the limit supermatrix. Therefore, the matrix will be limited, and gradually the consolidation of the interdependency and relative weighs will be derived. Step 10. Select the best strategy and compare the results with crisp techniques The MCDA approach deals with the problem of choosing the best alternative, that is, the one with the highest degree of satisfaction for all the relevant criteria. In our proposed model, the best risk mitigation strategy is the alternative with the highest value in its row of the limiting supermatrix. After finding out the best alternative, the results can be compared with those obtained using crisp AHP and ANP models.
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4. Application and results In this Section, the proposed model is applied to determine a suitable risk mitigation strategy for an offshore wind farm consisting of 30 wind turbines of 2MW. A schematic layout of the wind farm is shown in Fig. 6.
“Fig. (No. 6)” By interviewing the wind farm owner, it is concluded that the criteria and sub-criteria in Section 3 can be accepted. Therefore, the network scheme presented in Figure 4 is used for this study. In the following steps of the decision-making process, fuzzy comparison matrices are constructed according to the judgments of the wind farm owner. The fuzzy judgment matrix for the four criteria with respect to the overall goal is shown in Table 2. Here, the linguistic terms and corresponding fuzzy intervals given in Table 1 were used for comparison ratios.
“Table (No. 2)” Next, Chang’s extent analysis is applied to determine the priority weights of the four criteria. First of all, we calculate the fuzzy synthetic extent values by using Eq. (6): ~ ~ S1 = ( 0 .167 , 0 .370 , 0 .745 ) ; S 2 = ( 0 . 086 , 0 . 168 , 0 . 373 ) ;
~ ~ S 3 = (0.167 , 0.317 , 0.596 ) ; S 4 = ( 0 .077 , 0 .145 , 0 .298 ) . ~
~
Then, the values of V ( S i ≥ S j ) are obtained from Eq. (7) as follows: ~ ~ V ( S1 ≥ S 2 ) = 1 ~ ~ V ( S 2 ≥ S1 ) = 0.504
~ ~ V ( S 3 ≥ S1 ) = 0.890 ~ ~ V ( S 4 ≥ S1 ) = 0.368
~ ~ V ( S1 ≥ S3 ) = 1 ~ ~ V ( S 2 ≥ S 3 ) = 0.579 ~ ~ V ( S3 ≥ S 2 ) = 1 ~ ~ V ( S 4 ≥ S 2 ) = 0.902
~ ~ V ( S1 ≥ S 4 ) = 1 ~ ~ V (S2 ≥ S4 ) = 1 ~ ~ V ( S3 ≥ S 4 ) = 1 ~ ~ V ( S 4 ≥ S3 ) = 0.432
Afterwards, the non-normalized weights of four criteria are calculated using Eq. (8): ~ ~ ~ ~ d ( S1 ) = 1 ; d ( S 2 ) = 0.504 ; d ( S3 ) = 0.890 ; d ( S 4 ) = 0.368 .
Finally, we obtain the normalized weights of four criteria by using Eq. (9): w1 = 0.362 (Safety); w2 = 0.183 (Added value); w3 = 0.322 (Cost); w4 = 0.133 (Feasibility).
As can be seen, in evaluation of the risk mitigation strategies for offshore wind farms, the greatest weight is given to safety criterion. This is perhaps in due consideration of the huge impact of operational hazards on grid safety. Now, all sub-criteria are compared at the second level in terms of corresponding main criteria and the related judgment matrices are constructed. The Chang’s priority weights for sub-criteria with respect to main criteria are given as follows:
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w11 = 0 .684 (Technicians safety), w12 = 0 .316 (Grid safety); w21 = 0 .692 (Power production), w 22 = 0 .308 (Fault detection);
w31 = 0.401 (Hardware cost), w32 = 0.367 (Software cost), w33 = 0.232 (Training cost); w 41 = 0 .692 (Acceptance by stakeholders), w42 = 0 .308 (Acceptance by wind farm managers).
In addition, the amount of interdependency among sub-criteria or in fact the amount of sub-criteria impacts on each other was measured. The priority weights of sub-criteria against each other are addressed in Table 3.
“Table (No. 3)” Similar to Table 2, fuzzy intervals and Chang’s priority weights for the alternative risk mitigation strategies with respect to sub-criteria were obtained. These estimated priority weights are shown in Table 4.
“Table (No. 4)” Finally, the priority weights for the sub-criteria regarding risk mitigation alternatives are determined. Table 5 represents the estimated priority weights of each sub-criterion against four risk mitigation strategies.
“Table (No. 5)” The priority vectors obtained through paired comparisons are placed in the appropriate columns to form the supermatrix. Table 6 represents the supermatrix for this problem. As can be seen, four out of five sections of supermatrix have been completed using the priority weights of criteria, sub-criteria and alternatives as presented in Tables (3)–(5). The zero elements in the supermatrix show the independency among the variables in the rows and columns.
“Table (No. 6)” Later, the supermatrix is transformed into a weighted matrix. The transformation process involves multiplying the supermatrix by the cluster matrix, so that the priorities of the clusters can be taken into account in the decision making process. Finally, the weighted supermatrix is transformed into the limit supermatrix to make the distribution of the vector values meaningful to decision makers. The limit supermatrix is shown in Table 7.
“Table (No. 7)” The final priority of the four risk mitigation alternatives is represented in Table 8.
“Table (No. 8)” As shown, “improvement of maintenance services” is chosen as the best risk mitigation strategy within the offshore wind farm, followed by “upgrading the control and monitoring
13
systems”. This result shows the importance of a well-planned maintenance policy and an efficient condition monitoring system in reduction of the risks associated with offshore wind projects. Some comparisons are also made between the results obtained using the proposed FANP methodology and our earlier study using the crisp AHP and ANP models in Shafiee & Kolios (2014). The results of comparisions are shown in Table 9.
“Table (No. 9)” The AHP and ANP models have been implemented in ‘Expert Choice’ and ‘Super Decisions’ software, respectively (see http://experchoice.com & http://www.superdecisions.com). From Table 9, we can find out that the alternatives’ rankings obtained from the proposed model and the crisp ANP are similar to each other, but different from those using the crisp AHP method. However, in the proposed approach the decision makers were more comfortable to express their preferences in the form of fuzzy intervals rather than in the form of single numeric values. Moreover, the proposed model was better able to deal with the interdependent decision networks as it can take into account all possible dependencies between decision elements. 5. Conclusions and topics for future research In the current study, a multiple-criteria decision analysis (MCDA) approach using combined fuzzy set theory and analytic network process (ANP) was proposed to select the most appropriate risk mitigation strategy for offshore wind farms. To the best of our knowledge, this research was the first study utilizing the fuzzy ANP approach to find out solution. The proposed model was able to take into account all possible dependencies among selection criteria as well as between alternatives and selection criteria. Taking into account these interdependencies among decision elements provides more realistic solutions than the crisp AHP model which ignores such interdependencies. This study also overcame the shortcoming of traditional ANP approach by using fuzzy linguistic variables for comparison ratios, instead of using crisp values. The use of fuzzy intervals for priority judgments allows decision-makers to incorporate both objective and subjective considerations in the evaluation process. For the purpose of clearly illustrating the analysis approach, our model was applied to determine a suitable risk mitigation strategy for an offshore wind farm consisting of 30×2MW wind turbines. Finally, among the considered alternatives for risk mitigation, improving the repair and maintenance services was chosen to be the most cost-effective solution, followed by upgrading the control and monitoring systems. There is a wide scope for future research in the area of risk mitigation for renewable energy projects (either onshore or offshore). We here present some of the possible extensions: (a) In this study, we confined our analysis to only four alternatives. However, several other alternatives (e.g. using new materials with improved mechanical properties, outsourcing the operation and repair services) could also be taken into consideration.
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(b) Some other MCDA techniques such as TOPSIS 1 could be utilized to find the solution. (c) The selection of an appropriate risk mitigation strategy is a group decision making problem and cannot be performed on an individual basis. Different team members may demonstrate different opinions because of their different expertise and backgrounds. The diversity of team members’ information will be considered in our future research. (d) Investigating the impact of risk mitigation strategies on performance of the wind farm, in terms of reduction in operating expense (OPEX) is also an interesting topic for the future research. Acknowledgements The author gratefully acknowledges the support provided by the management of the wind farm during field visits and data collection. The author would also like to thank Dr. A. Kolios for his valuable comments during the early preparation stage of this manuscript. References Al-Yahyai, S., Charabi, Y., Gastli, A., & Al-Badi, A. (2012). Wind farm land suitability indexing using multicriteria analysis. Renewable Energy, 44, 80–87. Arabian-Hoseynabadi, H., Oraee, H., & Tavner, P.J. (2010). Failure modes and effects analysis (FMEA) for wind turbines. International Journal of Electrical Power & Energy Systems, 32, 817–824. Aven, T., & Vinnem, J-E. (2007). Risk management with applications from the offshore petroleum industry. Springer Series in Reliability Engineering, Springer, London. ISBN 978-1-84628-653-7. Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 17, 233–247. Chang, D.Y. (1992). Extent analysis and synthetic decision, optimization techniques and applications. Vol. 1, Singapore: World Scientific, p. 352. Chang, D.Y. (1996). Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95(3), 649–655. Chang, C.-W., Wu, C.-R., & Lin, H.-L. (2009). Applying fuzzy hierarchy multiple attributes to construct an expert decision making process. Expert Systems with Applications, 36, 7363–7368. Dinmohammadi, F. & Shafiee, M. (2013). A fuzzy-FMEA risk assessment approach for offshore wind turbines. International Journal of Prognostics and Health Management, 4, 1–10. DOE (Department of Energy) (2008). 20% wind energy by 2030: increasing wind energy’s contribution to U.S. electricity supply. Chapter 2: Wind turbine technology. pp. 23–60. EWEA (European Wind Energy Association) (2013). Wind in Power: European Statistics; Published in February 2014. Available online: http://www.ewea.org/statistics/. Griffin, D.A. (2014). Mitigating project risks for offshore wind. Offshore wind China Conference & Exhibition, Shanghai, China, June 4–6. Kahrobaee, S., & Asgarpoor, S. (2011). Risk-based failure mode and effect analysis for wind turbines (RBFMEA). In Proceedings of the North American Power Symposium (NAPS), Boston, USA, August 4–6, pp. 1–7. Kang, H-Y., Hung, M-C., Pearn, W.L., Lee, A.H.I., Kang, M-S. (2011). An integrated multi-criteria decision making model for evaluating wind farm performance. Energies, 4, 2002–2026.
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Goal External relationship Internal relationship
Factors Feedbacks Sub-factors
×××
×××
Alternatives
(a)
(b)
Figure 1. (a) AHP structure (b) ANP structure (adapted from Sevkli et al., 2012).
μ N~ ( x)
1 ~ N
l
m
u
x
Figure 2. A triangular fuzzy number (TFN).
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Start
Form a group of decision-makers
Determine the alternative risk mitigation strategies Identify and calssify the selection criteria Identify criteria/alternatives’ interdependence
Construct a network model
Perform pairwise comparisons using a TFN linguistic scale Revise the judgements reject
Test the consistency accept
Aggregate the judgement matrices
Calculate priority weights using Chang’s extent analysis Compute super-matrix and limit super matrix Select the best strategy and compare the results with crisp techniques Stop
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Figure 3. FANP methodology applied to risk mitigation strategy selection. Goal Risk Mitigation Strategy Selection
Criteria Safety
Added value
Cost
Feasibility
C1: Safety
C2: Added value
C3: Cost
C4: Feasibility
C11: Technicians
C21: Power
C31:Hardware HardwareCost Cost
C41: Acceptance by
Safety
Production
C12: Power Grid
C22: Fault
Safety
Detection
Stakeholders
C32: Software Cost C42: Acceptance by Wind Farm Managers
C33: Training Cost
Alternatives A1
A2
A4
A3
A1: variation of offshore site layout; A2: improvement of maintenance services; A3: upgrading the control and monitoring systems; A4: modification in design of wind turbine sub-assemblies.
Figure 4. A network model for risk mitigation strategy selection in offshore wind farms. μ (x)
1 ~ Sj
~ Si
~ ~ V (Si ≥ S j )
li
mi lj
ui ~
uj
mj ~
Figure 5. Degree of possibility of S i ≡ (l i , mi , u i ) ≥ S j ≡ (l j , m j , u j )
20
Figure 6. Offshore wind farm considered in this study.
21
Table 1. Triangular fuzzy scale used in our FANP approach. Linguistic scale for importance
Triangular fuzzy scale
About equal
(1/2 , 1 , 2)
About x times more important a
( x-1 , x , x+1 )
About x times less important
(1/(x+1) , 1/x , 1/(x-1) )
Between y and z times more important b
( y , (y+z)/2 , z)
Between y and z times less important
(1/z, 2/(y+z) , 1/y )
a x = 2,3,…,9. b y , z =1,2,…,9, y < z.
Table 2. Fuzzy judgment matrix for the four criteria with respect to the overall goal Goal
C1
C2
C3
C4
C1 C2 C3
(1 , 1 , 1)
(1 , 2 , 3)
(1/2 , 1 , 2)
(2 , 3 , 4)
(1/3 , 1/2 , 1)
(1 , 1 , 1)
(1/2 , 2/3 , 1)
(1/2 , 1 , 2)
C4
(1/2 , 1 , 2)
(1 , 3/2 , 2)
(1 , 1 , 1)
(2 , 5/2 , 3)
(1/4 , 1/3 , 1/2)
(1/2 , 1 , 2)
(1/3 , 2/5 , 1/2)
(1 , 1 , 1)
Table 3. Chang’s priority weights of sub-criteria against each other. Sub-criteria C11
C12
C21
C22
C31
C32
C33
C41
C42
C11
0.000
0.000
0.500
0.500
0.500
0.500
0.692
0.500
0.500
C12
0.000
0.000
0.500
0.500
0.500
0.500
0.308
0.500
0.500
C21
0.500
0.500
0.000
0.000
0.692
0.308
0.500
0.500
0.684
C22
0.500
0.500
0.000
0.000
0.308
0.692
0.500
0.500
0.316
C31
0.334
0.334
0.334
0.334
0.000
0.000
0.000
0.334
0.334
C32
0.333
0.333
0.333
0.333
0.000
0.000
0.000
0.333
0.333
C33
0.333
0.333
0.333
0.333
0.000
0.000
0.000
0.333
0.333
C41
0.500
0.500
0.500
0.500
0.692
0.684
0.500
0.000
0.000
C42
0.500
0.500
0.500
0.500
0.308
0.316
0.500
0.000
0.000
22
Table 4. Chang’s priority weights of alternatives with respect to sub-criteria. Sub-criteria C11
C12
C21
C22
C31
C32
C33
C41
C42
A1
0.069
0.236
0.133
0.066
0.076
0.287
0.311
0.066
0.133
A2
0.339
0.339
0.362
0.285
0.517
0.302
0.295
0.566
0.362
A3
0.356
0.356
0.322
0.566
0.089
0.201
0.229
0.285
0.322
A4
0.236
0.069
0.183
0.083
0.318
0.210
0.165
0.083
0.183
Table 5. Chang’s priority weights of sub-criteria with respect to alternatives. Alternative strategies Sub-criteria
A1
A2
A3
A4
C11
0.500
0.500
0.500
0.500
C12
0.500
0.500
0.500
0.500
C21
0.692
0.692
0.308
0.692
C22
0.308
0.308
0.692
0.308
C31
0.723
0.560
0.464
0.238
C32
0.262
0.233
0.298
0.464
C33
0.015
0.206
0.238
0.298
C41
0.692
0.500
0.684
0.692
C42
0.308
0.500
0.316
0.308
Table 6. (unweighted) Super-matrix for the risk mitigation strategy selection. Alternatives
Alternatives
Criteria
Criteria C1
Cluster node level
C2
Goal C3
C4
A1
A2
A3
A4
C11
C12
C21
C22
C31
C32
C33
C41
C42
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
0.069 0.339 0.356 0.236
0.236 0.339 0.356 0.069
0.133 0.362 0.322 0.183
0.066 0.285 0.566 0.083
0.076 0.517 0.089 0.318
0.287 0.302 0.201 0.210
0.311 0.295 0.229 0.165
0.066 0.566 0.285 0.083
0.133 0.362 0.322 0.183
0.000 0.000 0.000
C11 C12
0.500 0.500
0.500 0.500
0.500 0.500
0.500 0.500
0.000 0.000
0.000 0.000
0.500 0.500
0.500 0.500
0.500 0.500
0.500 0.500
0.692 0.308
0.500 0.500
0.500 0.500
0.248 0.114
C21 C22
0.692 0.308
0.692 0.308
0.308 0.692
0.692 0.308
0.500 0.500
0.500 0.500
0.000 0.000
0.000 0.000
0.692 0.308
0.308 0.692
0.500 0.500
0.500 0.500
0.684 0.316
0.127 0.056
C31 C32 C33
0.723 0.262 0.015
0.560 0.233 0.206
0.464 0.298 0.238
0.238 0.464 0.298
0.334 0.333 0.333
0.334 0.333 0.333
0.334 0.333 0.333
0.334 0.333 0.333
0.000 0.000 0.000
0.000 0.000 0.000
0.000 0.000 0.000
0.334 0.333 0.333
0.334 0.333 0.333
0.129 0.118 0.075
C41
0.692
0.500
0.684
0.692
0.500
0.500
0.500
0.500
0.692
0.684
0.500
0.000
0.000
0.092
A1 A2 A3 A4
0.000
C1
C2
C3
C4
23
C42 Goal
0.308
0.500
0.316
0.308
0.500
0.500
0.500
0.500
0.308
0.316
0.500
0.000
0.000
0.041
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Table 7. Limit super-matrix for the risk mitigation strategy selection. Alternatives Cluster node level Alternatives
Criteria
Criteria C1
C2
Goal C3
C4
A1
A2
A3
A4
C11
C12
C21
C22
A1
A2
A3
A4
C11
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.057 0.031
C11 C12
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
C21 C22
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
C31 C32 C33
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
C41 C42
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
A1 A2 A3 A4
0.027 0.065
C1
C2
C3
C4
Goal
Table 8. Priority weights of the four risk mitigation strategies. Risk mitigation strategy
Priority (normalized limiting values)
A 2 : Improvement of maintenance services
0.361
A 3 : Upgrading the control and monitoring systems
0.317
A 4 : Modification in design of wind turbine sub-assemblies
0.172
A1 : Variation of offshore site layout
0.150
Table 9. The results of comparisons. Model
Alternative Rankings
Fuzzy ANP
A 2 > A 3 > A 4 > A1
ANP
A 2 > A 3 > A 4 > A1
AHP
A 2 ≈ A 3 > A 4 ≈ A1
24
RESEARCH HIGHLIGHTS
A fuzzy ANP approach based on Chang’s extent analysis for “risk mitigation strategy selection”;
To select the most appropriate risk mitigation strategy for offshore wind farms;
To apply the model to an offshore wind farm consisting of 30×2MW wind turbines;
To compare the results with the crisp AHP and ANP models.
25
S0957-4174(14)00643-5 http://dx.doi.org/10.1016/j.eswa.2014.10.019 ESWA 9621
To appear in:
Expert Systems with Applications
Please cite this article as: Shafiee, M., A fuzzy analytic network process model to mitigate the risks associated with offshore wind farms, Expert Systems with Applications (2014), doi: http://dx.doi.org/10.1016/j.eswa.2014.10.019
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A Fuzzy Analytic Network Process Model to Mitigate the Risks associated with Offshore Wind Farms MAHMOOD SHAFIEE † Centre for Offshore Renewable Energy Engineering Cranfield University, Cranfield, Bedfordshire MK43 0AL, United Kingdom
ABSTRACT
In the offshore renewable energy industry, it is extremely important to reduce the likelihood as well as the magnitude of potential risk events during system’s actual operation. Operational risks (either risk of system failures or environmental risks) may cause catastrophic damages to personnel or infrastructure and result in substantial costs in terms of lost production and emergency maintenance operations. Selection of a suitable strategy for mitigation of the risks associated with offshore renewable energy projects is a very complex and critical task. The aim of this paper is to propose a fuzzy analytic network process (FANP) approach, based on Chang’s extent analysis, in order to select the “most appropriate risk mitigation strategy” for offshore wind farms. Our proposed model consists of four possible alternatives (variation of offshore site layout, improvement of maintenance services, upgrading the monitoring systems, and modification in design of wind turbines) among which the decision maker has to select the best strategy according to four comparison criteria: safety, added value, cost and feasibility. The model is then applied to determine a suitable risk mitigation strategy for an offshore wind farm consisting of 30 wind turbines of 2MW. Finally, the results are compared with those obtained using the crisp AHP and ANP models. Key Words: Risk mitigation; Offshore wind farm; multiple-criteria decision analysis (MCDA); Fuzzy analytic network process (FANP); Operation and maintenance (O&M).
†
Tel: +44 1234 750111, email: [email protected]
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1. Introduction Offshore wind energy has grown very rapidly in recent years. The cumulative installed capacity of offshore wind power in the European Union (EU) has increased from 532 megawatts (MW) in the year 2003 to 6,600 MW in the end of 2013, which represents an annual growth of about 29% (EWEA, 2014). Along with the growth of the market for offshore wind energy, a particular attention should be paid to operation and maintenance (O&M) as well as reliability and availability of the installed wind power systems. Analysis of field failure data collected from various databases like Elforsk in Sweden (http://www.elforsk.se) show that the availability of onshore wind farms is typically between 95% to 99%, while it is evaluated to be in the range of 60% to 70% for offshore wind farms. Moreover, offshore wind turbines suffer from a higher failure rate compared to their equivalent wind turbines located onshore (Tavner, 2012). The main reason is that offshore wind farms are generally exposed to a wider range of risk events, hazards or damages rather than onshore wind farms. Basically, the risks associated with offshore wind farms can be categorized into two major groups: (i) the risks of system failures (e.g. power outage) and (ii) the environmental risks (natural catastrophes, ship collisions, etc.) (Leung and Yang, 2012). The former is caused by system/component degradation (deterioration) while the latter results from harsh surrounding environments (e.g. extreme weather, wind, wave). Any of these hazards can potentially have a negative impact on wind farm performance if it is not avoided (prevented) in an efficient way. Degradation failures result in substantial costs of repair or replacement and significant losses of power production, and nature events lead to catastrophic safety hazards to personnel and infrastructure. Therefore, there is a critical need to reduce the likelihood as well as the magnitude of potential risk events during system’s actual operation. For this purpose, a risk management plan must be developed and applied to the existing or future offshore wind farms. Risk management is a process focusing on identification and elimination of the hazards that could affect asset performance. This process normally includes several stages like identification, assessment, evaluation, control and monitoring, and mitigation of the risks resulting from a certain hazard (Aven & Vinnem, 2007). Among these stages, the risk identification and assessment area has received a reasonable attention within the wind energy industry. To this end, the following studies should be mentioned: Arabian-Hoseynabadi et al. (2010) proposed a failure mode and effects analysis (FMEA) methodology for prioritization of the failure modes in a 2MW wind turbine system. Kahrobaee and Asgarpoor (2011) developed a risk-based FMEA approach for wind turbines in which the risk priorities of failure modes are determined based on failure probability and the incurred costs. Dinmohammadi and Shafiee (2013) developed a fuzzy-FMEA approach for risk and failure mode analysis of offshore wind turbines when field data is missing or is censored. Sunder and Kesavan (2013) studied the implementation of an FMEA methodology for wind turbines that operate in uncertain wind environments. Shafiee and Dinmohammadi (2014) proposed a mathematical tool for risk and failure mode analysis of wind turbine (both onshore and offshore) taking into account the key economic issues for maintenance (e.g. loss
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of power production, costs of logistics and transport). Wang et al. (2014) developed a fuzzy risk decision-making model based on conditional value at risk (CVaR) method for power systems integrated with large-scale wind farms. In spite of the vast research on risk identification and assessment, only a few methods have been developed for mitigating the risks associated with offshore wind farms. A recently published report by the U.S. Department of Energy (DOE, 2008) recommends enhancing the wind turbine reliability (through prototype testing of components before deployment) to mitigate the failure risks within offshore wind farms. Sjodin et al. (2012) and Griffin (2014) introduce the variation of offshore site placement/layout as a way of reducing the weatherrelated risks. Even though this solution may seem to be infeasible for many renewable energy systems, it can be considered as a practical alternative for small offshore wind projects. The selection of a suitable risk mitigation strategy for offshore wind farms is a very complex and critical task. An appropriate risk mitigation strategy not only avoids the negative consequences of natural events but also results in increased power production and less operation and maintenance (O&M) cost. On the other side, an improper selection of strategies may adversely affect the operating budget and thereby reducing productivity as well as profitability. Risk mitigation strategy selection is considered as a typical multiplecriteria decision analysis (MCDA) problem. In this analysis approach, the decision-makers (i.e., system owners or stakeholders) must decide on the most appropriate strategy among a set of possible alternatives to mitigate the system risks. Moreover, many different goals or comparing criteria (economic, social, environmental, etc.) must be taken into account in evaluating the alternatives. These criteria are often conflicting, i.e., according to a criterion, a given alternative is the best one, while according to another criterion, other alternatives score higher. Thus, each alternative is evaluated with respect to each criterion and then, the evaluation ratings are aggregated to obtain a global evaluation. Finally, the alternatives are prioritized from the best (optimal) to the worst. In recent years, the MCDA approach has been applied to solution of a wide range of decision-making problems within offshore wind energy, including the selection of wind farm location, wind turbine technologies, the most resilient materials to be used, and decommissioning decisions. For a thorough review on the use of MCDA approach in the renewable energy industry, the readers can refer to San-Cristóbal (2012). Some recent publications in the area are briefly reviewed below: Lee et al. (2009) developed an MCDA model based on the analytic hierarchy process (AHP) and the benefits, opportunities, costs and risks (BOCR) methods in order to select a suitable wind farm project. Kang et al. (2011) proposed a comprehensive evaluation model on the basis of interpretive structural modeling (ISM), BOCR and fuzzy analytic network process (FANP) to select a suitable location for wind farms. Al-Yahyai et al. (2012) applied the AHP method to derive wind farm land suitability index and classification under Geographical Information System (GIS) environment. Maity and Chakraborty (2012) applied the FANP approach to select the most appropriate materials for wind turbine blades. Lee et al. (2012) proposed a comprehensive evaluation model based on ISM and FANP to
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select the most suitable wind turbines in a wind farm. In another work, Lee et al. (2014) developed an evaluation model incorporating DEMATEL1 and FANP techniques to select the most suitable wind turbines for installation in a wind farm. Yeh and Huang (2014) presented a DEMATEL-ANP based approach to prioritize the key six factors considered in determining the location of wind farms. Sánchez-Lozano et al. (2014) proposed an MCDA approach based on the ELECTRE-TRI method for selection of wind farm sites in the southeast of Spain. Wu et al. (2014) utilized a fuzzy MCDA approach to select the best plan for wind projects. When looking at the literature, no research is found on the risk mitigation strategy selection for offshore wind projects utilizing the MCDA approach to find out solution. In order to address this issue, we propose an FANP methodology on the basis of Chang’s extent analysis to select the most appropriate risk mitigation strategy for offshore wind farms. The proposed model consists of four possible alternatives (variation of offshore site layout, improvement of maintenance services, upgrading the control and monitoring systems, and modification in design of wind turbine assemblies) among which the decision maker has to select the best strategy acording to four comparison criteria: safety, added value, cost and feasibility. Our findings indicate that “improving the repair and maintenance services” is chosen as the most cost-effective risk mitigation strategy for an offshore wind farm consisting of 30×2MW wind turbines. This paper is organized as follows. Section 2 presents a brief overview of the FANP approach so as to set the background for the main contribution of the paper. In Section 3, a decision model is proposed for risk mitigation strategy selection within offshore wind energy. In Section 4, the implementation of the proposed model is presented and the results are discussed. Finally, the paper is concluded in Section 5. 2. Fuzzy analytic network process (FANP) Among the several existing MCDA techniques, AHP and ANP are the most widely used models. In AHP technique, the problem is modeled in a hierarchical structure where the goal, decision criteria, and alternatives are connected top-to-bottom (see Fig. 1-a). As shown, each element in hierarchy structure is considered to be independent of all the others, and hence, the interactions and feedbacks which might be present in the system are ignored (Saaty, 1994). To overcome this limitation, the ANP technique was introduced by Saaty (1996). The ANP technique is a generalization of the AHP where the hierarchies are replaced by networks enabling to take into account all possible interactions between the clusters and elements within a cluster (see Fig. 1-b). In fact, the ANP technique provides a general framework to deal with decisions without making assumptions about the independence of higher level elements from lower level elements and about the independence of the elements within a level. So, ANP is a coupling of two parts. The first consists of a control hierarchy or 1
DEcision MAking Trial and Evaluation Laboratory
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network of criteria and sub-criteria that control the interactions. The second is a network of influences among the elements and clusters.
“Fig. (No. 1)” In both the AHP and ANP techniques, there is a need for integration of the mathematical model with human experiences. In order to prioritize alternatives, a pairwise comparison must be carried out between all pairs of criteria (or sub-criteria) as well as of alternatives. These pairwise comparisons are done by a group of experts with knowledge in the concerned area. However, there often exists an inherent uncertainty and imprecision with the mapping of the decision-makers’ judgments into crisp values. This uncertainty in the initial stages of the decision-making process limits the chances of getting satisfactory results. For this reason, the fuzzy AHP/ANP approach was developed in which fuzzy linguistic numbers, e.g., ‘‘between three and five times less important’’ are used for uncertain comparison ratios instead of crisp values. In the present study, a triangular fuzzy number (TFN) is used to represent the relative importance of one element over another. A TFN is a special case of fuzzy number with two ~ linear functions on either sides of the peak. It is defined by a triplet N = (l, m, u) as shown in Fig. 2, where l, m, and u are respectively considered as the lower bound, mean bound, and the upper bound.
“Fig. (No. 2)” The mathematical expression of the membership function of a TFN is described as follows: ⎧ x−l l≤x≤m ⎪m−l; ⎪⎪ u − x . (1) ; μ N~ ( x) = ⎨ m≤ x≤u ⎪u − m otherwise ⎪ 0; ⎪⎩ In what follows, we propose a methodology to determine a suitable risk mitigation strategy for offshore wind farms. To our knowledge, this paper is the first study on the subject area utilizing an FANP approach to find out the solution. 3. Proposed methodology Our proposed methodology for selection of the most appropriate risk mitigation strategy in offshore wind farms, as shown in Fig. 3, includes ten steps. These steps are described in details as following:
“Fig. (No. 3)”
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Step 1. Form a group of decision makers First, a project team must be established to determine and examine the operational hazards and their potential impact on wind farm safety. The project team is often composed of key managers (i.e., power generation manager, head of safety and risk, project finance director) as well as some practitioners from operation and maintenance (O&M). Let K represent the number of team members who participated in interviews. Step 2. Determine the alternative risk mitigation strategies Several alternatives can be taken into account for risk mitigation, but some of them might be technically infeasible to offshore renewable energy. In this paper, four alternative risk mitigation strategies are considered for our application:
A1 : Variation of offshore site layout The ‘layout’ of an offshore wind farm is one of the critical elements influencing the risks associated with natural events (i.e., environmental damages) (Tiusanen et al., 2011). It refers to the arrangement of wind turbines in a wind farm, and typically deals with decisions regarding position of installations with respect to wind and wave direction, distance from the shore, water depth, distance between wind turbines, location of warehouses and capacity of depots. In general, the potential nature events are more likely to happen in cold, icy or remote offshore areas than they are in normal marine environments. According to existing statistics, the power outage caused by unexpected events for deep-water wind farms is 10 to 20% longer than that for wind farms built in shallow waters near the coast (Shafiee, 2014). Therefore, any improvement in offshore site layout will have a substantial effect on harmful outcomes resulting from extreme weather and harsh marine conditions. A 2 : Improvement of maintenance services
The current practice of maintenance for offshore wind farms is reactive response (or failure-based). Under this policy, the maintenance actions are undertaken once a failure is detected in wind turbines. Van Bussel and Schöntag (1997) in Opti-OWECS1 project, and Van Bussel and Henderson (2001) in CA-OWEE2 project report that using reactive response maintenance policy causes frequent stoppages, high repair costs, long waiting and maintenance times, logistics disruption, and severe damages and trouble shooting problems. For this reason, preventive maintenance (PM) policies (including periodic inspections, reliability-centered, risk-based, condition-based, and predictive) are extensively applied to control the rate of degradation failures and avoid costly replacements (Shafiee & Finkelstein, 2014). A well-planned and optimized maintenance policy can effectively reduce the costs associated with operating and repairing wind turbines.
A3 : Upgrading the control and monitoring systems 1 2
Structural and Economic Optimization of Bottom-Mounted Offshore Wind Energy Converters Concerted Action on Offshore Wind Energy in Europe
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One effective way to reduce the likelihood of risk events within the offshore wind energy industry is improving the fault detection capability. This improvement can be achieved by installing a number of high quality and technically advanced sensors at specified locations as well as using new monitoring techniques (such as acoustic emission, ultrasonic testing, strain measurement, radiographic inspection, thermography, and signal processing methods) (Yang et al., 2014).
A4 : Modification in design of wind turbine sub-assemblies The operational risks in offshore wind farms can be reduced by enhancing the reliability of wind turbines through design modification or new design of the systems. The aim of design modification is to minimise the number of failures experienced in wind farms, which results in enormous savings in maintenance and energy costs. The modification in design of sub-assemblies includes reliability growth testing, or adding redundancy to critical components in order to increase the mean-time between failures (MTBF) (Shafiee et al. 2013). Step 3. Identify and calssify the selection criteria In order to evaluate and prioritize the risk mitigation alternatives, the project team must specify a set of comparison criteria. Different decision-makers may have different objectives. In this paper, we first determined a list of criteria based on the review of literature. Then, semi-structured interviews were conducted with project team in order to get a better understanding of their objectives. Finally, four main criteria were selected for consideration in the study. These criteria are described in details as following: C1 : Safety A high level of safety is required for many offshore wind farms, in particular for the ones that are connected to the grid in series. In a serial power grid, any failure in one of the units causes the failure of entire system. The relevant factors describing the safety are: C11 : Technicians safety - A failure of wind turbine and/or a nature event may lead to serious damages to personnel/technicians who work on site. C12 : Power grid safety - A failure of wind turbine and/or a nature event would damage the grid connection equipment and thereby disconnects the wind farm from electricity grid. C2 : Added value The added-value criterion deals with the benefits that may be gained from implementing a particular risk mitigation strategy. This category includes the improvement in terms of power production and fault detection. C21 : Power production - A failure of wind turbine and/or a nature event often leads to substantial production losses. Selecting a suitable strategy for risk mitigation can potentially increase the electricity generated by offshore wind farms.
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C22 : Fault detection - Fault diagnostic and prognostic techniques aim to quickly alert the maintenance engineers where and why faults occur. As a result, the maintenance leadtimes are shortened and the availability of wind farms will improve. C3 : Cost Different risk mitigation alternatives have different expenditure of hardware, software, and personnel training. C31 : Hardware cost - For implementation of risk mitigation strategies, a number of service vessels, support facilities, maintenance tools, monitoring and prognostic sensors, and some computers must be purchased. C32 : Software cost - More expensive and advanced software will be needed if it is decided to upgrade the control and monitoring systems or to modify the design of subassemblies. C33 : Training cost - Risk mitigation actions in offshore wind farms should be started only after sufficient training. C4 : Feasibility The feasibility criterion is divided into acceptance by stakeholders and acceptance by wind farm managers. C41 : Acceptance by stakeholders - Successful implementation of a risk mitigation alternative needs the support and participation of wind farm stakeholders (i.e., financial institutions, insurance companies, owners, and regulatory authorities). C42 : Acceptance by wind farm managers - Wind farm managers often prefer the strategies yielding more return on investment (ROI) and are easy to implement. So, the variation of offshore site layout ( A1 ) and modification in design of wind turbines ( A 4 ) might be suitable options for mid- or long-term investments. Step 4. Identify criteria/alternatives’ interdependence In real-world decision making problems, there often exists a two way relationship between criteria and alternatives and also intra-relationships among criteria. For instance, the relationship between the two criteria safety and cost is such that a risk mitigation strategy with high level of safety would be expected to incur more costs in terms of hardware, software and personnel training. In this study, no interdependency among the risk mitigation alternatives is considered. Step 5. Construct a network model Using criteria, sub-criteria and alternatives, a network model is constructed. Fig. 4 illustrates a network model for the decision problem of selecting a suitable risk mitigation strategy for offshore wind farms. As can be seen, the proposed structure includes three clusters. The first cluster represents the ultimate goal of the problem (i.e., selection of the best risk mitigation
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strategy). The second cluster in the network consists of four main criteria, which are namely, safety, added value, cost, and feasibility. Each criterion is also decomposed into various subcriteria as discussed in step 3. Finally, the third cluster represents the alternative strategies. The relationships among the criteria and sub-criteria are also determined and reflected in the network model.
“Fig. (No. 4)” Step 6. Perform pairwise comparisons using a TFN linguistic scale Team members are asked to perform a series of pairwise comparisons. In this study, the triangular fuzzy numbers are used to represent comparison ratios, i.e., the relative importance of element i over element j for decision-maker k is represented in the form of a~ijk , where (i) a~ijk = (1,1,1) if i = j , and (ii) a~ijk = (l ijk , m ijk , u ijk ) if i ≠ j , for i , j = 1, 2 ,…, n, and k = 1, 2 ,…, K. The reciprocal of a~ijk represents the preference of element j over element i for decision-maker k and is given by: a~
ijk
−1
= (1 / uijk ,1 / mijk ,1 / lijk ) .
(2)
The pairwise comparisons among all criteria (sub-criteria) and alternatives are done following the scale given below in Table 1. This scale has been widely used in the fuzzy MCDA literature (e.g. see Wang et al., 2007; Kumar & Maiti, 2012). The decision maker chooses a linguistic term based on the relative importance of the two elements being considered. Then, the corresponding triangular fuzzy scale is assigned for judgment.
“Table (No. 1)” When all pairwise comparisons are completed at a level, the fuzzy judgment matrix can be established. The fuzzy judgment matrix for decision-maker k, A~k is given by:
~ Ak = {a~ijk }n× n
(1,1,1) (l12 k , m12 k , u12 k ) ⎛ ⎜ (1,1,1) ⎜ (l 21k , m21k , u 21k ) ⎜ . . =⎜ . . ⎜ ⎜ . . ⎜ (l , m , u ) (l , m , u ) n2k n2k n2k ⎝ n1k n1k n1k
... ... ... ... ... ...
(l1nk , m1nk , u1nk ) ⎞ ⎟ (l 2 nk , m2 nk , u 2 nk ) ⎟ ⎟ . ⎟ , for k=1, 2 ,…, K , (3) . ⎟ ⎟ . ⎟ (1,1,1) ⎠
where n is the number of related elements at the level, and (l jik , m jik , u jik ) = (1 / uijk ,1 / mijk ,1 / lijk ) . Step 7. Test the consistency and aggregate the judgment matrices The consistency analysis is an essential part of both FAHP and FANP methods whose aim is to make sure that the judgment results are accurate and reliable. When looking at the literature, only a few studies have addressed the issue of inconsistency checking for fuzzy ~ judgement matrices. According to Buckley (1985), the fuzzy matrix Ak in Eq. (3) is
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consistent if a~ijk ≈ a~ipk ⊗ a~ pjk , for i , j , p = 1, 2 ,…, n, where ≈ denotes fuzzy equal to, and ⊗ is the multiplication operation on fuzzy numbers and is defined by: ( x1 , y1 , z1 ) ⊗ ( x2 , y 2 , z 2 ) = ( x1 x2 , y1 y 2 , z1 z 2 ) .
For judgment matrix which fails the consistency test, the decision maker is asked to revise his/her pairwise comparisons. Once all fuzzy judgement matrices for team members pass the consistency test, an aggregate fuzzy judgment matrix can be established. The aggregate fuzzy judgment matrix for a group of decision makers is given by: ~ A = {a~ij }n×n ; a~ij = (l ij , mij , u ij ) ,
(4)
where l ij , mij and u ij are calculated using the following Equation (Chang et al., 2009): ⎛ K ⎞ l ij = min (l ijk ) , mij = ⎜⎜ ∏ mijk ⎟⎟ k ⎝ k =1 ⎠
1
K
, u ij = max (u ijk ) .
(5)
k
Step 8. Calculate priority weights using Chang’s fuzzy extent analysis The aggregate fuzzy judgment matrix in Eq. (4) can now be used to calculate the crisp priority vector. For this purpose, the fuzzy extent analysis proposed in Chang (1992, 1996) is used. The steps of this analysis are described below. i. Calculate the value of “fuzzy synthetic extent” for element i (= 1, 2 ,…,n), as defined by following Equation: ⎛ ~ S i ≡ (l i , m i , u i ) = ⎜ ⎜ ⎝
n
∑ a~
ij
j =1
⎞ ⎡ ⎟⊗⎢ ⎟ ⎢ p =1 ⎠ ⎣ n
n
∑ ∑ a~
pj
j =1
⎤ ⎥ ⎦⎥
−1
⎛ ⎜ ⎜ ≈⎜ ⎜ ⎜ ⎝
n
∑
n
∑
l ij
j =1
n
,
n
∑u
j =1
n
⎞ ⎟ ⎟ j =1 , n n ⎟, l kj ⎟ ⎟ p =1 j =1 ⎠ n
m ij
n
ij
(6)
∑∑u ∑∑m ∑∑ kj
p =1 j =1
kj
p =1 j =1
where l ij , m ij and u ij are given by Eq. (5). ~
~
ii. Calculate the degree of possibility of Si ≡ (li , mi , ui ) ≥ S j ≡ (l j , m j , u j ) for two elements i and j using the Eq. (7): ⎧ ⎪ mi ≥ m j 1 ⎪⎪ ~ ~ (7) V (Si ≥ S j ) = ⎨ l j ≥ ui . 0 ⎪ ui − l j ⎪ otherwise ⎪⎩ (u i − mi ) + ( m j − l j ) ~ ~ As shown in Fig. 5, the value of V ( S i ≥ S j ) represents the ordinate of the highest
intersection point between two fuzzy membership functions μ S~i (.) and μ S~j (.) .
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“Fig. (No. 5)” iii. Compute the degree of possibility of S~i to be greater than all the other n − 1 TFNs, that is,
~ ~ ~ ~ ~ ~ d ( S i ) ≡ V ( S i ≥ S1 ,..., S i −1 , S i +1 ,..., S n ) , ~ ~ = min V ( S i ≥ S j ) , for j = 1, 2 ,…, n , j ≠ i . j
(8)
iv. Obtain the normalized priority vector W = ( w1 , w2 ,..., wn ) T of the fuzzy judgement matrix ~ A , where wi is given by: ~ d (S i ) , i = 1, 2 ,…, n . (9) wi = n ~ ∑ d (S j ) j =1
Step 9. Compute supermatrix and limit supermatrix The supermatrix represents the influence priority of an element on the left of the matrix on an element at the top of the matrix with respect to a particular control criterion (Saaty, 1996). The supermatrix is actually a partitioned matrix where each matrix segment represents a relationship among two nodes (components or clusters) in the network. To form a supermatrix, the priority vectors (obtained in Step 8) are entered in the appropriate columns based on the flow of influence from one cluster to another, or from a cluster to itself as in the loop. If there exists no relationship between two elements, the corresponding entry in the supermatrix is zero. Since there usually is interdependency among clusters in a network, the columns of a supermatrix may sum to more than one. In this case, the supermatrix must be transformed into a weighted supermatrix. This process involves multiplying every node in a cluster of the intial supermatrix by the weight of the cluster, which has been established by pairwise comparison among the clusters. Each column in the weighted supermatrix has a sum of one, and thus the matrix is stochastic. To achieve a convergence on the importance weights, the weighted supermatrix is raised to the power of 2k + 1, where k is an arbitrarily large number, and this new matrix is called the limit supermatrix. Therefore, the matrix will be limited, and gradually the consolidation of the interdependency and relative weighs will be derived. Step 10. Select the best strategy and compare the results with crisp techniques The MCDA approach deals with the problem of choosing the best alternative, that is, the one with the highest degree of satisfaction for all the relevant criteria. In our proposed model, the best risk mitigation strategy is the alternative with the highest value in its row of the limiting supermatrix. After finding out the best alternative, the results can be compared with those obtained using crisp AHP and ANP models.
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4. Application and results In this Section, the proposed model is applied to determine a suitable risk mitigation strategy for an offshore wind farm consisting of 30 wind turbines of 2MW. A schematic layout of the wind farm is shown in Fig. 6.
“Fig. (No. 6)” By interviewing the wind farm owner, it is concluded that the criteria and sub-criteria in Section 3 can be accepted. Therefore, the network scheme presented in Figure 4 is used for this study. In the following steps of the decision-making process, fuzzy comparison matrices are constructed according to the judgments of the wind farm owner. The fuzzy judgment matrix for the four criteria with respect to the overall goal is shown in Table 2. Here, the linguistic terms and corresponding fuzzy intervals given in Table 1 were used for comparison ratios.
“Table (No. 2)” Next, Chang’s extent analysis is applied to determine the priority weights of the four criteria. First of all, we calculate the fuzzy synthetic extent values by using Eq. (6): ~ ~ S1 = ( 0 .167 , 0 .370 , 0 .745 ) ; S 2 = ( 0 . 086 , 0 . 168 , 0 . 373 ) ;
~ ~ S 3 = (0.167 , 0.317 , 0.596 ) ; S 4 = ( 0 .077 , 0 .145 , 0 .298 ) . ~
~
Then, the values of V ( S i ≥ S j ) are obtained from Eq. (7) as follows: ~ ~ V ( S1 ≥ S 2 ) = 1 ~ ~ V ( S 2 ≥ S1 ) = 0.504
~ ~ V ( S 3 ≥ S1 ) = 0.890 ~ ~ V ( S 4 ≥ S1 ) = 0.368
~ ~ V ( S1 ≥ S3 ) = 1 ~ ~ V ( S 2 ≥ S 3 ) = 0.579 ~ ~ V ( S3 ≥ S 2 ) = 1 ~ ~ V ( S 4 ≥ S 2 ) = 0.902
~ ~ V ( S1 ≥ S 4 ) = 1 ~ ~ V (S2 ≥ S4 ) = 1 ~ ~ V ( S3 ≥ S 4 ) = 1 ~ ~ V ( S 4 ≥ S3 ) = 0.432
Afterwards, the non-normalized weights of four criteria are calculated using Eq. (8): ~ ~ ~ ~ d ( S1 ) = 1 ; d ( S 2 ) = 0.504 ; d ( S3 ) = 0.890 ; d ( S 4 ) = 0.368 .
Finally, we obtain the normalized weights of four criteria by using Eq. (9): w1 = 0.362 (Safety); w2 = 0.183 (Added value); w3 = 0.322 (Cost); w4 = 0.133 (Feasibility).
As can be seen, in evaluation of the risk mitigation strategies for offshore wind farms, the greatest weight is given to safety criterion. This is perhaps in due consideration of the huge impact of operational hazards on grid safety. Now, all sub-criteria are compared at the second level in terms of corresponding main criteria and the related judgment matrices are constructed. The Chang’s priority weights for sub-criteria with respect to main criteria are given as follows:
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w11 = 0 .684 (Technicians safety), w12 = 0 .316 (Grid safety); w21 = 0 .692 (Power production), w 22 = 0 .308 (Fault detection);
w31 = 0.401 (Hardware cost), w32 = 0.367 (Software cost), w33 = 0.232 (Training cost); w 41 = 0 .692 (Acceptance by stakeholders), w42 = 0 .308 (Acceptance by wind farm managers).
In addition, the amount of interdependency among sub-criteria or in fact the amount of sub-criteria impacts on each other was measured. The priority weights of sub-criteria against each other are addressed in Table 3.
“Table (No. 3)” Similar to Table 2, fuzzy intervals and Chang’s priority weights for the alternative risk mitigation strategies with respect to sub-criteria were obtained. These estimated priority weights are shown in Table 4.
“Table (No. 4)” Finally, the priority weights for the sub-criteria regarding risk mitigation alternatives are determined. Table 5 represents the estimated priority weights of each sub-criterion against four risk mitigation strategies.
“Table (No. 5)” The priority vectors obtained through paired comparisons are placed in the appropriate columns to form the supermatrix. Table 6 represents the supermatrix for this problem. As can be seen, four out of five sections of supermatrix have been completed using the priority weights of criteria, sub-criteria and alternatives as presented in Tables (3)–(5). The zero elements in the supermatrix show the independency among the variables in the rows and columns.
“Table (No. 6)” Later, the supermatrix is transformed into a weighted matrix. The transformation process involves multiplying the supermatrix by the cluster matrix, so that the priorities of the clusters can be taken into account in the decision making process. Finally, the weighted supermatrix is transformed into the limit supermatrix to make the distribution of the vector values meaningful to decision makers. The limit supermatrix is shown in Table 7.
“Table (No. 7)” The final priority of the four risk mitigation alternatives is represented in Table 8.
“Table (No. 8)” As shown, “improvement of maintenance services” is chosen as the best risk mitigation strategy within the offshore wind farm, followed by “upgrading the control and monitoring
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systems”. This result shows the importance of a well-planned maintenance policy and an efficient condition monitoring system in reduction of the risks associated with offshore wind projects. Some comparisons are also made between the results obtained using the proposed FANP methodology and our earlier study using the crisp AHP and ANP models in Shafiee & Kolios (2014). The results of comparisions are shown in Table 9.
“Table (No. 9)” The AHP and ANP models have been implemented in ‘Expert Choice’ and ‘Super Decisions’ software, respectively (see http://experchoice.com & http://www.superdecisions.com). From Table 9, we can find out that the alternatives’ rankings obtained from the proposed model and the crisp ANP are similar to each other, but different from those using the crisp AHP method. However, in the proposed approach the decision makers were more comfortable to express their preferences in the form of fuzzy intervals rather than in the form of single numeric values. Moreover, the proposed model was better able to deal with the interdependent decision networks as it can take into account all possible dependencies between decision elements. 5. Conclusions and topics for future research In the current study, a multiple-criteria decision analysis (MCDA) approach using combined fuzzy set theory and analytic network process (ANP) was proposed to select the most appropriate risk mitigation strategy for offshore wind farms. To the best of our knowledge, this research was the first study utilizing the fuzzy ANP approach to find out solution. The proposed model was able to take into account all possible dependencies among selection criteria as well as between alternatives and selection criteria. Taking into account these interdependencies among decision elements provides more realistic solutions than the crisp AHP model which ignores such interdependencies. This study also overcame the shortcoming of traditional ANP approach by using fuzzy linguistic variables for comparison ratios, instead of using crisp values. The use of fuzzy intervals for priority judgments allows decision-makers to incorporate both objective and subjective considerations in the evaluation process. For the purpose of clearly illustrating the analysis approach, our model was applied to determine a suitable risk mitigation strategy for an offshore wind farm consisting of 30×2MW wind turbines. Finally, among the considered alternatives for risk mitigation, improving the repair and maintenance services was chosen to be the most cost-effective solution, followed by upgrading the control and monitoring systems. There is a wide scope for future research in the area of risk mitigation for renewable energy projects (either onshore or offshore). We here present some of the possible extensions: (a) In this study, we confined our analysis to only four alternatives. However, several other alternatives (e.g. using new materials with improved mechanical properties, outsourcing the operation and repair services) could also be taken into consideration.
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(b) Some other MCDA techniques such as TOPSIS 1 could be utilized to find the solution. (c) The selection of an appropriate risk mitigation strategy is a group decision making problem and cannot be performed on an individual basis. Different team members may demonstrate different opinions because of their different expertise and backgrounds. The diversity of team members’ information will be considered in our future research. (d) Investigating the impact of risk mitigation strategies on performance of the wind farm, in terms of reduction in operating expense (OPEX) is also an interesting topic for the future research. Acknowledgements The author gratefully acknowledges the support provided by the management of the wind farm during field visits and data collection. The author would also like to thank Dr. A. Kolios for his valuable comments during the early preparation stage of this manuscript. References Al-Yahyai, S., Charabi, Y., Gastli, A., & Al-Badi, A. (2012). Wind farm land suitability indexing using multicriteria analysis. Renewable Energy, 44, 80–87. Arabian-Hoseynabadi, H., Oraee, H., & Tavner, P.J. (2010). Failure modes and effects analysis (FMEA) for wind turbines. International Journal of Electrical Power & Energy Systems, 32, 817–824. Aven, T., & Vinnem, J-E. (2007). Risk management with applications from the offshore petroleum industry. Springer Series in Reliability Engineering, Springer, London. ISBN 978-1-84628-653-7. Buckley, J. J. (1985). Fuzzy hierarchical analysis. Fuzzy Sets and Systems, 17, 233–247. Chang, D.Y. (1992). Extent analysis and synthetic decision, optimization techniques and applications. Vol. 1, Singapore: World Scientific, p. 352. Chang, D.Y. (1996). Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95(3), 649–655. Chang, C.-W., Wu, C.-R., & Lin, H.-L. (2009). Applying fuzzy hierarchy multiple attributes to construct an expert decision making process. Expert Systems with Applications, 36, 7363–7368. Dinmohammadi, F. & Shafiee, M. (2013). A fuzzy-FMEA risk assessment approach for offshore wind turbines. International Journal of Prognostics and Health Management, 4, 1–10. DOE (Department of Energy) (2008). 20% wind energy by 2030: increasing wind energy’s contribution to U.S. electricity supply. Chapter 2: Wind turbine technology. pp. 23–60. EWEA (European Wind Energy Association) (2013). Wind in Power: European Statistics; Published in February 2014. Available online: http://www.ewea.org/statistics/. Griffin, D.A. (2014). Mitigating project risks for offshore wind. Offshore wind China Conference & Exhibition, Shanghai, China, June 4–6. Kahrobaee, S., & Asgarpoor, S. (2011). Risk-based failure mode and effect analysis for wind turbines (RBFMEA). In Proceedings of the North American Power Symposium (NAPS), Boston, USA, August 4–6, pp. 1–7. Kang, H-Y., Hung, M-C., Pearn, W.L., Lee, A.H.I., Kang, M-S. (2011). An integrated multi-criteria decision making model for evaluating wind farm performance. Energies, 4, 2002–2026.
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Goal External relationship Internal relationship
Factors Feedbacks Sub-factors
×××
×××
Alternatives
(a)
(b)
Figure 1. (a) AHP structure (b) ANP structure (adapted from Sevkli et al., 2012).
μ N~ ( x)
1 ~ N
l
m
u
x
Figure 2. A triangular fuzzy number (TFN).
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Start
Form a group of decision-makers
Determine the alternative risk mitigation strategies Identify and calssify the selection criteria Identify criteria/alternatives’ interdependence
Construct a network model
Perform pairwise comparisons using a TFN linguistic scale Revise the judgements reject
Test the consistency accept
Aggregate the judgement matrices
Calculate priority weights using Chang’s extent analysis Compute super-matrix and limit super matrix Select the best strategy and compare the results with crisp techniques Stop
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Figure 3. FANP methodology applied to risk mitigation strategy selection. Goal Risk Mitigation Strategy Selection
Criteria Safety
Added value
Cost
Feasibility
C1: Safety
C2: Added value
C3: Cost
C4: Feasibility
C11: Technicians
C21: Power
C31:Hardware HardwareCost Cost
C41: Acceptance by
Safety
Production
C12: Power Grid
C22: Fault
Safety
Detection
Stakeholders
C32: Software Cost C42: Acceptance by Wind Farm Managers
C33: Training Cost
Alternatives A1
A2
A4
A3
A1: variation of offshore site layout; A2: improvement of maintenance services; A3: upgrading the control and monitoring systems; A4: modification in design of wind turbine sub-assemblies.
Figure 4. A network model for risk mitigation strategy selection in offshore wind farms. μ (x)
1 ~ Sj
~ Si
~ ~ V (Si ≥ S j )
li
mi lj
ui ~
uj
mj ~
Figure 5. Degree of possibility of S i ≡ (l i , mi , u i ) ≥ S j ≡ (l j , m j , u j )
20
Figure 6. Offshore wind farm considered in this study.
21
Table 1. Triangular fuzzy scale used in our FANP approach. Linguistic scale for importance
Triangular fuzzy scale
About equal
(1/2 , 1 , 2)
About x times more important a
( x-1 , x , x+1 )
About x times less important
(1/(x+1) , 1/x , 1/(x-1) )
Between y and z times more important b
( y , (y+z)/2 , z)
Between y and z times less important
(1/z, 2/(y+z) , 1/y )
a x = 2,3,…,9. b y , z =1,2,…,9, y < z.
Table 2. Fuzzy judgment matrix for the four criteria with respect to the overall goal Goal
C1
C2
C3
C4
C1 C2 C3
(1 , 1 , 1)
(1 , 2 , 3)
(1/2 , 1 , 2)
(2 , 3 , 4)
(1/3 , 1/2 , 1)
(1 , 1 , 1)
(1/2 , 2/3 , 1)
(1/2 , 1 , 2)
C4
(1/2 , 1 , 2)
(1 , 3/2 , 2)
(1 , 1 , 1)
(2 , 5/2 , 3)
(1/4 , 1/3 , 1/2)
(1/2 , 1 , 2)
(1/3 , 2/5 , 1/2)
(1 , 1 , 1)
Table 3. Chang’s priority weights of sub-criteria against each other. Sub-criteria C11
C12
C21
C22
C31
C32
C33
C41
C42
C11
0.000
0.000
0.500
0.500
0.500
0.500
0.692
0.500
0.500
C12
0.000
0.000
0.500
0.500
0.500
0.500
0.308
0.500
0.500
C21
0.500
0.500
0.000
0.000
0.692
0.308
0.500
0.500
0.684
C22
0.500
0.500
0.000
0.000
0.308
0.692
0.500
0.500
0.316
C31
0.334
0.334
0.334
0.334
0.000
0.000
0.000
0.334
0.334
C32
0.333
0.333
0.333
0.333
0.000
0.000
0.000
0.333
0.333
C33
0.333
0.333
0.333
0.333
0.000
0.000
0.000
0.333
0.333
C41
0.500
0.500
0.500
0.500
0.692
0.684
0.500
0.000
0.000
C42
0.500
0.500
0.500
0.500
0.308
0.316
0.500
0.000
0.000
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Table 4. Chang’s priority weights of alternatives with respect to sub-criteria. Sub-criteria C11
C12
C21
C22
C31
C32
C33
C41
C42
A1
0.069
0.236
0.133
0.066
0.076
0.287
0.311
0.066
0.133
A2
0.339
0.339
0.362
0.285
0.517
0.302
0.295
0.566
0.362
A3
0.356
0.356
0.322
0.566
0.089
0.201
0.229
0.285
0.322
A4
0.236
0.069
0.183
0.083
0.318
0.210
0.165
0.083
0.183
Table 5. Chang’s priority weights of sub-criteria with respect to alternatives. Alternative strategies Sub-criteria
A1
A2
A3
A4
C11
0.500
0.500
0.500
0.500
C12
0.500
0.500
0.500
0.500
C21
0.692
0.692
0.308
0.692
C22
0.308
0.308
0.692
0.308
C31
0.723
0.560
0.464
0.238
C32
0.262
0.233
0.298
0.464
C33
0.015
0.206
0.238
0.298
C41
0.692
0.500
0.684
0.692
C42
0.308
0.500
0.316
0.308
Table 6. (unweighted) Super-matrix for the risk mitigation strategy selection. Alternatives
Alternatives
Criteria
Criteria C1
Cluster node level
C2
Goal C3
C4
A1
A2
A3
A4
C11
C12
C21
C22
C31
C32
C33
C41
C42
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000
0.069 0.339 0.356 0.236
0.236 0.339 0.356 0.069
0.133 0.362 0.322 0.183
0.066 0.285 0.566 0.083
0.076 0.517 0.089 0.318
0.287 0.302 0.201 0.210
0.311 0.295 0.229 0.165
0.066 0.566 0.285 0.083
0.133 0.362 0.322 0.183
0.000 0.000 0.000
C11 C12
0.500 0.500
0.500 0.500
0.500 0.500
0.500 0.500
0.000 0.000
0.000 0.000
0.500 0.500
0.500 0.500
0.500 0.500
0.500 0.500
0.692 0.308
0.500 0.500
0.500 0.500
0.248 0.114
C21 C22
0.692 0.308
0.692 0.308
0.308 0.692
0.692 0.308
0.500 0.500
0.500 0.500
0.000 0.000
0.000 0.000
0.692 0.308
0.308 0.692
0.500 0.500
0.500 0.500
0.684 0.316
0.127 0.056
C31 C32 C33
0.723 0.262 0.015
0.560 0.233 0.206
0.464 0.298 0.238
0.238 0.464 0.298
0.334 0.333 0.333
0.334 0.333 0.333
0.334 0.333 0.333
0.334 0.333 0.333
0.000 0.000 0.000
0.000 0.000 0.000
0.000 0.000 0.000
0.334 0.333 0.333
0.334 0.333 0.333
0.129 0.118 0.075
C41
0.692
0.500
0.684
0.692
0.500
0.500
0.500
0.500
0.692
0.684
0.500
0.000
0.000
0.092
A1 A2 A3 A4
0.000
C1
C2
C3
C4
23
C42 Goal
0.308
0.500
0.316
0.308
0.500
0.500
0.500
0.500
0.308
0.316
0.500
0.000
0.000
0.041
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Table 7. Limit super-matrix for the risk mitigation strategy selection. Alternatives Cluster node level Alternatives
Criteria
Criteria C1
C2
Goal C3
C4
A1
A2
A3
A4
C11
C12
C21
C22
A1
A2
A3
A4
C11
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.027 0.065 0.057 0.031
0.057 0.031
C11 C12
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
0.144 0.121
C21 C22
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
0.099 0.082
C31 C32 C33
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
0.091 0.082 0.080
C41 C42
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.067 0.054
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
A1 A2 A3 A4
0.027 0.065
C1
C2
C3
C4
Goal
Table 8. Priority weights of the four risk mitigation strategies. Risk mitigation strategy
Priority (normalized limiting values)
A 2 : Improvement of maintenance services
0.361
A 3 : Upgrading the control and monitoring systems
0.317
A 4 : Modification in design of wind turbine sub-assemblies
0.172
A1 : Variation of offshore site layout
0.150
Table 9. The results of comparisons. Model
Alternative Rankings
Fuzzy ANP
A 2 > A 3 > A 4 > A1
ANP
A 2 > A 3 > A 4 > A1
AHP
A 2 ≈ A 3 > A 4 ≈ A1
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RESEARCH HIGHLIGHTS
A fuzzy ANP approach based on Chang’s extent analysis for “risk mitigation strategy selection”;
To select the most appropriate risk mitigation strategy for offshore wind farms;
To apply the model to an offshore wind farm consisting of 30×2MW wind turbines;
To compare the results with the crisp AHP and ANP models.
25