Spare parts control strategies for offshore wind farms: A critical review and comparative study

Abstract

Offshore Wind Farm (OWF) downtime causes huge financial loss to the stakeholders. One of the major concerns for them is to reduce the downtime of the offshore wind turbine as much as possible. To do this, inventory managers must keep the required number of spare parts in the inventory. It is important to forecast the type and amount of spare parts ahead of time. The maintenance team tries to figure out failure symptoms to predict the approximate time for failure. This prediction helps to purchase and stock spare parts systematically. There is a trade-off between the ordering cost, holding cost, and shortage cost. Proper inventory planning saves a manager from placing expensive emergency orders and also an extended period of holding spare parts. The desired service level should be determined earlier, based on which spare parts planning is done. In this paper, some prominent spare parts models have been studied, findings have been systematically presented, compared against some key determinant factors, critical analysis has been performed and the applicability of the models has been discussed. More than a 100 research articles on spare parts have been reviewed and major contributions from the most relevant articles in OWF have been presented in this paper. One advanced spare parts modeling reported up to 51% cost reduction compared to traditional spare parts planning. Another integrated spare parts planning reported 27% savings. This critical review aims to suggest some guidelines for the managers and other associates of wind farms about the effective and efficient spare parts management technique from the beginning of the turbine installation to the end of its life cycle.

Keywords

Offshore wind farm spare parts planning and control failure prediction inventory management

Introduction

Concern for renewable energy has been increasing very fast for the last few years. Global warming, climate change, and energy insecurity are some of the reasons. Total renewable energy capacity will increase 50% in 2024 from what was in 2019 (IEA 2019). Because of global ecological disturbance and depletion of fossil fuel, searching for some alternate forms of energy is the primary focus of research nowadays. Renewable energy is going to be one of the largest power sources since it is capable of: being start early, mature development, and superior industrialization. Acheampong (2019) says that carbon emission is the primary cause of global warming. Sarshar et al. (2017) found that coal, oil, gas, and nuclear power plants are the major source of energy.

Wind energy is a sustainable source of power that depends on airflow. Different part of the earth never receives an equal amount of sunlight. This unbalanced heating creates a pressure difference which causes the air to flow for pressure balancing. Wind energy produced 591 GW of electricity in 2018, which is 5% of global powered generation (GWEC, 2019). Wind energy has many attractive features. Two of them are sustainability and cost-efficiency. Since wind is produced by some sustainable everlasting natural action, this source is considered an infinite lifetime source. Secondly, the power generation cost from wind energy is only 2–5 cents/kWh which is one of the lowest (IRENA, 2021). The cost is decreasing with time. In terms of installation and maintenance costs, wind energy is arguably the cheapest form of renewable energy. It has been considered a major source of electricity generation by many countries now. According to the Global Wind Report 2021, the total installed wind energy capacity is now 743 GW, protecting the earth from facing 1.1 billion tons of Carbon-di-Oxide. The year 2020 saw a 53% annual increase in global wind capacity which was the best in the history of global wind energy generation. A total 93 GW of new capacity has been installed (GWEC, 2021a). To handle the worst effect of climate change, this rate should be continued till 2050. According to Anis et al. (2021), “Wind power is abundant, cheap, inexhaustible, available almost everywhere, clean and climate-friendly. No other energy source has all these qualities.”

Offshore Wind Energy (OWE) has significant potential for economic and environmental benefits. One installed, Offshore Wind Farm (OWF) can operate at a low fixed cost in a long-term agreement which reduces the electricity generation cost and increases energy security. It holds the promise to control the volatility of fossil fuel prices. According to the GWEC (2021b), the global installed capacity for wind energy is 743 GW among which offshore has a share is 41.1 GW. Though offshore wind energy is only 18.08% of total global wind energy capacity, it has the biggest growth potential among all forms of renewable energy technology (GWEC, 2021b). Due to land constraints, more wind farms will be installed in the offshore area in the future. Besides, wind speed is higher, robust, and steady in the offshore region which is a precondition of generating sustainable and continuous power. Higher wind speed is very crucial in the wind industry. A little increase in wind speed can increase power generation significantly: a turbine can produce twice as much energy at 15 mph wind as 12 mph wind (BOEM, 2021). Besides, most of the coaster areas are densely populated all over the world. No other energy source can be more feasible than offshore wind in these regions (BOEM, 2021).

Most small or large manufacturing companies have some sort of inventory. The items kept in the inventory are required for frequent operations and maintenance to keep the system running and reduce downtime. Lack of necessary spare parts leads to extended downtime which results in a huge loss of power generation. A proper balance is needed to keep the inventory cost and the shortage cost at the desired level. In the case of OWF, system downtime cost is added to shortage cost. Errors in demand forecasting should be minimized as much as possible. Regular inspection of critical components is necessary to forecast the required spare parts accurately. Over forecasting results in wastage due to overstock and under forecasting leads to extended downtime. Therefore, efficient inventory management is a must to reduce the inventory cost of an OWF.

The motivation of this study is to find an efficient alternative to fossil fuel as an energy source. Since wind is one of the cheapest forms of renewable energy source, experts and investors can concentrate on it. OWF has better prospects than onshore because of its large-scale power generation capacity. As an emerging renewable energy source, many curious researchers are getting attracted to different subject areas of OWF. They are working on different types of operations and maintenance activities, that is, condition-based maintenance, opportunistic maintenance, reliability and risk management, stochastic weather models, cost optimization, scheduling and sequencing of vessel activities, and location/site selection. Though other areas of OWF are being studied pretty much, a very limited number of inventory studies have been conducted on the inventory of OWF. Since wind energy deals with expensive spare parts (like turbine, nacelle, and blades), an efficient inventory system is very crucial in reducing the overall electricity production cost. In this study, the authors are motivated to perform a comparative study among different inventory models to present some inventory guidelines for the managers, investors, and stakeholders and find research gaps to invite other researchers to work on these gaps. Upon completion of the expected tasks, this article could be a novel work in the field of the offshore wind farm spare parts industry.

Few inventory models have been found in the literature, but most of those models did not consider all the crucial factors related to OWF and surroundings. The absence of an organized and systematic inventory model is a major research gap in the field of OWF. Thus, the goal is to reduce inventory costs for OWE. The main objective of this work is to study inventory-related articles, extract different qualitative and quantitative findings, compare the relative benefits and limitations, and finally discuss the applicability of these models to find the most suitable models under various real-life scenarios. The purpose is to provide recommendations about suitable inventory strategies to the involved stakeholders. There are many inventory models in the literature and spare parts models for the OWF are very few.

The subsequent part of the paper is structured as follows: Section 2 presents all the prominent offshore spare parts inventory (SPI) models in detail which includes the models, assumptions, and the methodologies with necessary figures and tables. Section 3 discusses spare parts inventory management and its stages. Section 4 describes several management strategies for spare parts planning, cost functions, tradeoff technique among stockout cost and inventory cost, some specialized tools, and techniques. Section 5 illustrates joint strategies for maintenance tasks and spare parts management (SPM) with required assumptions. Section 6 summarizes some case studies conducted by experts and professionals. Section 7 lists the findings from papers written by the researchers who worked in this area so far. It also illustrates a comparative study table that will give a concrete concept of different SPI models, their characteristics, and their applicability. Finally, Section 8 draws concluding remarks with a hint of future research scope in this area.

Current state of spare parts research

For the last few years, concern for clean and renewable energy has been grown remarkably. In literature, many research-works are highlighting the importance and scope of renewable energy. Sadorsky (2009a, 2009b) shows a correlation between economic growth and the use of renewable energy and illustrated this claim for G7 countries. Salim and Rafiq (2012) showed for Turkey, Indonesia, Brazil, China, India; Chang et al. (2015) for the United Kingdom and France. Few more researchers showed it for other countries (Apergis and Payne, 2010a; Apergis et al., 2010; Apergis and Payne, 2010b, 2011, 2012; Inglesi-Lotz, 2016; Menegaki, 2011).

Röckmann et al. (2017) and Meng et al. (2016) reported that operations and maintenance cost is 1/5th of the total life cycle cost of OWF. The primary goal of maintenance is to reduce downtime (Tusar and Sarker, 2022). Van Horenbeek and Pintelon (2013) showed that assigning a penalty cost in the inventory model can take care of this issue. Ruijters and Stoelinga (2015) introduced Fault Tree Analysis for downtime loss. Penalty cost can be determined using Binary Decision Diagram and Barlow-Proschan measure (Arabian-Hoseynabadi et al., 2010; Deng et al., 2015; Zhu and Kuo, 2014). Stockout penalty cost can be measured by Tamjidzad and Mirmohammadi (2015) and Vu et al. (2016).

Inventory management is one of the core functions of logistics and supply chain management (Konur et al., 2017; Ripanti and Tjahjono, 2019). According to Hu et al. (2015), operations and management support cost is almost 60% of plant life cycle cost, and inventory cost is half of those. Inventory costs are high because the availability of inventory impacts the production directly (Conceição et al., 2015; Zhang and Zeng, 2017). Tatham et al. (2017) argue that inventory management affects the competitiveness of the supply chain. This is why some big companies decorate their inventory system with several hundreds of items (Kennedy et al., 2002; Macchi et al., 2011). Teixeira et al. (2018) showed that an efficient system improves the availability of production. Spare parts management (SPM) is a special section of inventory management that works as a support to defective production systems (Kareem and Lawal, 2015). Tracht et al. (2013) refer that these parts are required immediately when any component of the system fails to minimize downtime and loss of production. Driessen et al. (2014) demonstrate the importance of selecting the appropriate location and number of items. Some other studies on SPM were done by Suryadi (2007), Do Rego and de Mesquita (2011), Moharana and Sarmah (2016), and Ayu Nariswari et al. (2019).

Grouping the spare parts depending on their characteristics is a good way to make the task easier (Hu et al., 2017; Meng, 2000; Roda et al., 2014). Several researchers like Bosnjakovic (2010), Braglia et al. (2004), Roda et al. (2014), and Stoll et al. (2015) classified the items by focusing on existing stock. Apart from this, the ABC method is the most popular spare parts categorization method (Bacchetti and Saccani, 2012). Hu et al. (2018) state that there are two basic options for meeting the initial provisioning: waiting for the demand to appear, storing the item from the very beginning. Time series demand forecasting is not an option where there is not enough historical data (Boylan and Syntetos, 2008). De Felice et al. (2014) and Do Rego and de Mesquita (2015) applied the SPM technique to the automotive industry, Molenaers et al. (2012) in petrochemical, Zeng et al. (2012) to the energy sector, and Zhang and Zeng (2017) at the wind farm.

Downtime might be responsible for a big portion of maintenance, it can be as big as 67% to be precise (Van Houtum and Kranenburg, 2015). Condition monitoring can contribute to reducing downtime (Ahmadi, 2019; Fouladirad and Grall, 2014; Liang and Parlikad, 2015). Saccani et al. (2016) prepared spare parts to demand planning using historical data using simulation. Digiesi et al. (2015) used various terms in the objective function to measure the environmental impact of SPM. Other researchers worked on stocking strategies (Botter and Fortuin, 2000), heterogeneous environment (Barabadi et al., 2021; Chang et al., 2015), heuristic approach (Bülbül et al., 2019), stochastic demand classification (Conceição et al., 2015), uncertain demand (Gu et al., 2015), hybrid approach (Muniz et al., 2021), multiple components (Olde Keizer et al., 2017), binary decision fault tree (Remenyte-Prescott and Andrews, 2008), equivalent equipment exchange (Khademi and Eksioglu, 2018), optimizing spare parts necessity (Eruguz et al., 2018), spare parts demand planning (Kian et al., 2019) based on shelf degradation and without knowing the degradation level (Ghasemi et al., 2007; Moghaddass and Ertekin, 2018).

Optimal spare parts inventory management

Spare parts are important for any Maintenance Repair and Operations (MRO) activities as their unavailability extends machine costs time. Maintenance cost is divided into mainly direct and indirect cost. These direct and indirect cost includes all sorts of cost in between a particular timeline such as: cost of operations, costs for spare parts, technician fees, cost for repair. Total maintenance cost is referred to the average cost per unit uptime (Tracht et al., 2012). According to Schuh et al. (2015), total maintenance cost, $C_{T}$ is comprised of cost of minor damages, $C_{MD}$ ; machine downtime cost, $C_{D}$ ; internal maintenance cost, $C_{I}$ ; cost for service providers, $C_{S}$ ; and some additional costs, $C_{A}$ as follows

C_{T} = C_{MD} + C_{D} + C_{I} + C_{S} + C_{A}

(1)

The first cost component is minor damage which can also be referred to as secondary damage. Secondary damage occurs when a failed component impacts some other components. The second cost component is downtime cost which is lost sales due to machine downtime. The third component is internal maintenance cost consists of material cost, labor cost, transportation cost, etc. The fourth component is service provider cost which is the contract signing cost between service provider and owner.

Machine downtime cost, $C_{D}$ can be written by Schuh et al. (2015) as to

C_{D} = t_{d} f l_{j} p_{v}

(2)

where $t_{d}$ is length of machine breakdown time (hour), $f$ is the feed-in tariff per kWh ($/kWh), $l_{j}$ is the wind turbine power, $p_{v}$ is the percentage of full load per day (%/day). Severe weather conditions can be dealt with proper maintenance planning and SPM. However, high spare parts storage leads to high capital cost. Capital cost for spare parts storage is given by Schuh et al. (2015) as

C_{In} = C_{p} ((r_{inv} + r_{int}) + 1)^{t_{l}}

(3)

$C_{In}$ is the daily SPI cost, $C_{p}$ is the purchasing cost of spare parts, $r_{inv}$ is the inventory rate, $r_{int}$ is the interest rate, and $t_{l}$ is the duration of stocking. Capital cost is a major component of SPI cost which has a tradeoff issue with shortage cost.

Stages of spare parts management (SPM)

SPM can be classified into three stages: demand forecasting, inventory management, and data processing. Data processing means removing the irrelevant data to improve prediction accuracy and grouping the spare parts according to their demand and cost. Spare parts planning starts with demand forecasting. There are two primary groups of demand forecasting: One is the qualitative method which depends on expert opinion and the other one is the quantitative method which worth computations and analysis. Among different types of quantitative demand forecasting time series method is applied if any of the previous demand patterns are expected in future (Croston, 1972; Teunter and Duncan, 2009). The goal of inventory management is to minimize the components of inventory cost, that is, ordering processing cost, holding cost, shortage cost etc. Basten and van Houtum (2014), Kennedy et al. (2002), Muckstadt et al. (2005), and Sherbrooke (2004) have studied all the relevant inventory models and discussed relative advantages and disadvantages of each model.

Replenishment policy

Spare parts manufacturers are usually independent and separated from one another. Therefore, spare parts are to be modeled as single items. However, WT owners prefer batch purchases because of quantity discount. So, $(r, Q)$ replenishment policy is followed where $Q$ is the order quantity and $r$ is the reorder point. If the inventory level at the time of placing order is $CD$ and lead time demand is $LD$ then the number of goods at hand when the order is delivered is $HD$ = $CD - LD$ . If $H D^{S}$ is the steady-state inventory position then the cost of the $(r, Q)$ replenishment policy, $C (r, Q)$ can be calculated as follows (Wang et al., 2018),

C (r, Q) = \frac{k}{Q} + \frac{1}{Q} h . \sum_{j = 0}^{\infty} j . \Pr {H D^{S} = j} + \frac{1}{Q} p . \sum_{j = - \infty}^{- 1} (- j) . \Pr {H D^{S} = j}

(4)

where $k$ is investment cost, $h$ is holding cost, $p$ is stockout penalty cost. Steady state distribution of $CD$ may take the value of ${r + 1, r + 2, \dots \dots \dots, r + Q}$ . Considering the relationship shown in equations (4) and (5) can be rewritten as

\begin{matrix} \arg mi n_{r, Q} C (r, Q) = \frac{K λ}{Q} + \frac{1}{Q} \sum_{y = r + 1}^{r + Q} h \sum_{i = 0}^{y} (y - i) \Pr {DE = i} + \frac{1}{Q} \sum_{y = r + 1}^{r + Q} p \sum_{i = y + 1}^{\infty} (i - y) \\ \Pr {DE = i} \end{matrix}

(5)

where $y$ and $i$ is $CD$ and $LD$ , respectively; $λ$ is demand rate per time during lead time; $K$ is the setup cost per order.

Table 1.

Name and components of cost.

Type of costs	Components of cost
Machine downtime cost	Sales loss, the opportunity cost of feeding into the grid
Internal maintenance cost	Maintenance, raw material supply, tools, spare parts, depreciation
Secondary damage cost	Cost of a unit destroyed by a failed unit

Failure mode and effect analysis (FMEA)

There are several critical components with a short lead time. Corrective maintenance is often restricted by weather and logistic restriction for those components. In those cases, an enriched SPI system helps to come out with a solution. Ferdinand et al. (2018) tried to find out optimum spare parts inventory level based on Failure Mode and Effect Analysis (FMEA). They used the key terms: lost capacity, repair difficulty, and failure probability to calculate the risk priority number (RPN). The risk level of critical components has been significantly reduced by their systematic approach. Generally, risk management means identifying the hazard of a system, preventing or at least controlling it to keep it to a minimal level. In this case, risk indicated the failure of energy supply to the grid and the resultant economic impact of it. RPN is a product of lost capacity value (LCV), repair complexing value (RCV), and failure probability value (FPV) as follow,

RPN = (LCV) (RCV) (FPV)

(6)

The availability level of the system can be given as

avail . = 1 - \frac{T_{dt}}{T_{ot}} \frac{C_{lost}}{C_{total}}

(7)

where $T_{dt}$ is expected downtime, $T_{ot}$ is the total operating time, $C_{lost}$ is lost capacity, and $C_{total}$ is total capacity. Lost revenue, $R_{Lost}$ is also calculated by Ferdinand et al. (2018) like RPN and availability level as follows,

R_{Lost} = \frac{T_{dt}}{8750} p_{fail} C_{lost} T_{ot} {\bar{T}}_{FL} k_{R}

(8)

where $p_{fail}$ failure probability, ${\bar{T}}_{FL}$ mean yearly full load hours, $k_{R}$ feed in tariff. RPN values for different risk level is defined in Table 3 based on the data from Ferdinand et al. (2018).

The Risk Priority Number (RPN) increases with the risk level. For low-risk level, RPN value is less than 20. Medium risk level starts from 21 and continues all the way to 80. High risk level starts from 81 and continues till 200. If a spare part is at high-risk level, arrangement to change that spare part is made immediately. For low-level components, it is permissible to wait until any other component reaches its high RPN.

Spare parts inventory optimization

Ferdinand et al. (2018) calculated Risk Priority Number (RPN) and $R_{Lost}$ values for two different cases. For the first case, spare parts availability can ensure faster repair from the breakdown stage. Lost revenues for those spare parts are indicated by $R_{Lost, SP}$ . For the second case, availability of spare parts cannot guarantee faster recovery as other preparation for the repair needs more time than the lead time of the spare parts. Lost revenues for those spare parts are indicated by $R_{Lost, No SP}$ . Spare parts inventory is optimized using linear optimization (LO). The objective is to minimize the lost energy, LE

LE = \sum_{i = 1}^{n} R_{Lost, SP} (i) - R_{Lost, No SP} (i)

(9)

Subject to

C_{SPI} = \sum_{i = 1}^{n} c_{i} m \leq Budget

(10)

Where $C_{SPI}$ is the cost for optimized spare parts list, $c_{i}$ the cost of the spare part, and $m$ is the number of purchased parts for a component. For this optimization problem, the aimed availability was 99.50% and the budget was 1% of the investment cost.

Four different scenarios have been studied by Ferdinand et al. (2018). The scenarios are: No spare parts, Minimum, Pareto, and the Optimum. Table 4 (Source: Ferdinand et al., 2018) shows that the availability for “No spare parts” scenario is 95.03% and no investment is required for spare parts inventory. The percentage of high-risk components is as high as 8%. Both the low risk and medium risk components are 46% each.

Table 2.

Details of LCV, RCV, and FPV Ferdinand et al. (2008).

LCV scenarios			RCV scenarios			Component FPV
Failure impact	Capacitylost	LCVranking	Repair scenario	Time (T)	RCVranking	Failurescenario	Failureprob., p	FPV
Zero	0 MW	0	Remote reset	<= 6 hours	1	Rare	p ≤ 0.0001	1
Minimum	0–5 MW	1	Onsite reset	7–24 hours	2	Seldom	0.0001 ≤ p < 0.001	2
Small	6–25 MW	2	Small repair	2–19 days	3	Often	0.001 ≤ p < 0.01	3
Medium	26–100 MW	3	Complex repair	20–45 days	5	Frequent	0.01 ≤ p < 0.1	4
Heavy	101–200 MW	4	Large corrective	>45 days	6	Very frequent	p ≥ 0.1	5
Extreme	>200 MW	5

Table 3.

Different risk groups.

Range of RPN	Risk level
[1, 20]	Low
[21, 80]	Medium
[81, 200]	High

Table 4.

Availability and risk group percentages.

	No spare parts	Minimum (%)	Pareto (%)	Optimum (%)
Budget	NA	0.15	0.35	1
Availability	95.03%	99.13	99.38	99.51
High risk	8%	1	1	1
Medium risk	46%	50	33	27
Low risk	46%	49	66	72

For the “Minimum” spare parts scenario, the budget is 0.15% of the total investment, and availability is increased to 99.13%. Share of medium risk and low risk has been increased by 4% and 3%, respectively. To make that happen share of high risk has been reduced by 4 + 3 = 7%. For the “Pareto” scenario, availability is further increased to 99.38% for the budget of 0.35%. Seventeen percent of components have been added to low risk from medium risk. Finally, the “Optimum” scenario which incurs 1% budget of the total investment and availability is 99.51%.

Figure 1 shows pie charts of the percentage of components in different risk groups analyzed by Ferdinand et al. (2018). According to the experts and practitioners, the Pareto scenario seems to be the best option for the manager of OWF (Ferdinand et al., 2018).

Figure 1.

Distribution of risk groups for four different groups.

Availability of spare parts

The availability of spare parts is one of the main determinants of maintenance waiting time duration. Shortage of necessary spare parts can drive to huge downtime loss while excess inventory level leads to excessive operating cost. There are two basic and common inventory policies: periodic and continuous review. Usually, demands are consistent and stable for the main components of a wind turbine, that is, gearbox, turbine, rotor, blade etc. The inventory policy $(r, R)$ can be used in this case where, $r$ is the reorder level, and $R$ is the order up to level (Figure 2). In the figure, when the inventory level goes below $s$ then an order is made with an order size of ( $R$ - $s$ ). Those points of time are A, C, and E in the figure. The gap between A & B, C & D, and E & F are the lead times.

Figure 2.

Schematic diagram of inventory policy.

Management strategies for spare parts planning

Power production cost from wind farm projects are very high because of excessive downtime cost. Proper operations and management (O&M) and spare parts inventory planning can reduce this cost significantly (Martin and Ramsey, 2009; Nguyen et al., 2017). It is possible to reduce this huge cost using some systematic approaches. Wang et al. (2018) used Fault Tree (FT), Binary Decision Diagram (BDD), and Barlow-Proschan (BP) to figure out the systematic dependence among the critical components and assigned penalty cost over each of those.

Spare parts are used when regular parts are failed or damaged. Spare parts can be either repairable or consumable. In this section, we discuss only about the repairable spare parts. In most cases, repairable spare parts are expensive and sophisticated (Biedermann, 2008). Purchasing costs for these spare parts are high. Inventory costs are expected to keep as low as possible. The goal of spare parts management is to balance inventory cost and downtime cost. Spare parts failure prediction accuracy is the key to reduce inventory level (Liao and Rausch, 2010; Vaughan, 2005; Wang and Syntetos, 2011). Figure 3 shows how spare parts planning depends on logistics restrictions and resource availability. The core logistics activities are procurement and warehousing.

Figure 3.

Model for spare parts planning (Modified from Tracht et al., 2013).

Maintenance is triggered by three facts: component condition, maintenance site condition, and failure mode results. When a component is on the verge of failure, maintenance activity is triggered. But, often the rough weather condition restricts reaching out to the site. In those cases, maintenance has to wait for better weather.

Cost function with relaxation

Tracht et al. (2013) showed that the sum of all operating cost, $C$ is the summation of inventory cost, $C_{i}$ ; total maintenance cost, $C_{m}$ and capital commitment cost, $C_{acc} (wt)$ as follows

C = C_{i} + C_{m} + C_{acc} (wt)

(11)

Inventory cost, $C_{i}$ is a function of stock keeping cost (overhead), $C_{so}$ ; capital commitment interest rate, $R_{icc}$ ; stock keeping cost ratio, $C_{sdr}$ ; stock quantity, $S_{q}$ ; the number of exchange of spare parts under preventive maintenance, $x_{pm}$ ; spare parts cost, $C_{sp}$ and the downtime, $T_{d}$ as follows

C_{i} = C_{so} + (R_{icc} + C_{sdr}) (S_{q} - x_{pm}) C_{sp} \frac{T_{d}}{365}

(12)

The second term next to equal sign of equation (13) is total maintenance cost, $C_{m}$ which can be split as

C_{m} = x_{cm} C_{cm} + x_{pm} C_{pm}

(13)

where $x_{cm}$ is number of exchanges of spare parts under corrective maintenance; $C_{cm}$ and $C_{pm}$ are the cost of preventive and corrective maintenance, respectively. Both of the two quantities consist of spare parts cost, $C_{sp}$ ; maintenance technician cost, $C_{mt}$ ; transport resources cost, $C_{tr}$ ; downtime cost, $C_{d}$ ; capital commitment cost, $C_{acc}$ like below

C_{cm} = C_{sp} + C_{mt} + C_{tr} + C_{d} + C_{acc} (t_{ce})

(14)

C_{pm} = C_{sp} + C_{mt} + C_{tr} + C_{d} + C_{acc} (t_{pe})

(15)

where $t_{ce}$ and $t_{pe}$ are the points of time when preventive and corrective functions take place, respectively.

Functionality of the model, $F_{fn}$ is defined by Tracht et al. (2013) as product of $A_{mt}$ , $A_{sp}$ , $A_{tr}$ which are availability of maintenance technician, spare parts and transport resources, respectively; along with wind turbine accessibility, $A_{ta}$ as follows,

F_{fn} = A_{mt} A_{sp} A_{tr} A_{ta}

(16)

Though each of the four terms on the right side of equation (16) takes binary value: either $0$ or $1$ . But, due to binary relaxation assumption, these four terms might have any value between $0$ to $1$ . Total downtime, $T_{d}$ is equal to mean time to repair $T_{mttr}$ if $F_{fn}$ = $1$ , but $T_{d}$ is the summation of the time of non-feasibility $T_{nf}$ and mean time to repair $T_{mttr}$ if $F_{fn}$ =0. Equations (17) and (18) show these below,

T_{d} (F_{fn} = 1) = T_{mttr}

(17)

T_{d} (F_{fn} = 0) = T_{nf} + T_{mttr}

(18)

Downtime cost, $C_{d}$ can be written as the product of total downtime, $T_{d}$ ; lost full load hours during the downtime, $h_{flh}$ ; amount of feed-in tariff, $f_{ft}$ ; and the power of the wind turbine, $W_{pt}$ as follows,

C_{d} = T_{d} h_{flh} f_{ft} W_{pt}

(19)

Capital commitment cost, $C_{acc}$ can be calculated from cost of investment, $C_{inv}$ ; capital commitment interest rate, $R_{icc}$ ; and life span of wind turbine, $T_{lt}$ ; and $t$ is the point time when the cost is calculated;

C_{acc} = C_{inv} (1 + R_{icc})^{(T_{lt} - t)} - C_{inv}

(20)

Tradeoff between inventory and stockout costs

Several things are considered to predict failure of critical components. Sensors are located in the critical components to get the signal. For example, rough weather and irregular wind speed increase turbine failure cost. The main task is to compare excess stock-keeping cost and shortage cost in order to find the cost optimal quantity. Schuh et al. (2015) has done it in three following steps shown in Figure 4. The steps are: (a) system analysis, (b) demand forecast and failure prediction, and (c) inventory planning. First of all, all the critical technical components are identified. Then spare parts are classified in terms of demand and procurement cost. Demand patterns can be predicted by analyzing the historical data.

Figure 4.

Approach for inventory planning.

If $F (x)$ and $F (x + t)$ is the instant failure probability at $x$ and $x + t$ time, respectively, then the failure probability of an individual component during a time period $x$ to $t$ is given as

Fx (t) = \frac{F (x + t) - F (x)}{1 - F (x)}

(21)

Mean failure probability of any component $\bar{F} x (t)$ is summation of all components’ failure rate starting from component 1 to component $n$ divided by the number of components $n$ as, $\bar{F} x (t)$ = $\frac{1}{n} \sum_{i = 1}^{n} Fx (t)_{i}$ . Demand during lead time is expressed by a random variable, $X$ . Probability of $X$ is less than or equal to any particular value $x$ is given as:

P (X \leq x) = \sum_{m = 0}^{x} (\begin{matrix} n \\ m \end{matrix}) \bar{F} x {(t)}^{m} (1 - \bar{F} x (t))^{n - m}

(22)

here $m$ is the spare parts demand in number. It is possible to find the surplus or stock out probability using equation (22) and eventually possible to calculate the downtime or the inventory cost. Minimum total inventory cost is calculated by Schuh et al. (2015) as follows,

c_{t} = (\sum_{m = S}^{\infty} (m - S) p_{m}) c_{d} + (\sum_{m = 0}^{\infty} (S - m) p_{m}) c_{i}

(23)

where $S$ is the stock amount in pieces, $p_{m}$ is the probability of occurrence, $c_{d}$ and $c_{t}$ is the downtime and inventory cost per spare parts per day, respectively. Another important parameter here is the ratio factor, $η = \frac{K_{i}}{K_{d}}$ which is the ratio between total daily inventory cost, $K_{i}$ and the total daily downtime cost.

Proportional hazard model (PHM)

Failure data analysis is an important function of spare parts planning. It is essential to predict the failure time precisely so that the desired spare parts are in hand when needed. There are some popular ways to perform failure data analysis. Cox (1972) proposed a Proportional hazard model (PHM) to analyze failure data. PHM is a semiparametric model capable to analyze failure data when there is no defined failure data. Let, $h_{0} (t)$ be the baseline hazard function; $z_{1}$ , $z_{2}$ , $z_{3}$ , …, $z_{m}$ are the covariate function and $α_{1}$ , $α_{2}$ , $, \dots, α_{m}$ are the regression coefficient then the modified hazard function $h (t; z)$ is given by

h (t; z) = \exp (α_{1} z_{1} + α_{2} z_{2} + \dots + α_{m} z_{m}) h_{0} (t)

(24)

Weibull hazard rate is used instead of baseline hazard function for modeling mechanical wear as follows:

h_{0} (t) = \frac{β}{T} (\frac{t}{T})^{β - 1}

(25)

where $β$ is the shape parameter and $T$ is scale parameter. This model is used in medical science, but it has been used in technical fields also. Lanza et al. (2009) discuss various Weibull models for technical reliability analysis. Some researchers used PHM for spare parts failure prediction as well (Vlok et al., 2002; Wang, 2007).

Fault tree analysis (FTA)

Wind Turbine (WT) system failure is the result of cumulative or sequential failures. A good way to build an FT is using AND and OR logic gates. A typical FT is given shown in Figure 5. The total system failure is denoted by T which is also called top event (TE); $M_{1}, \dots \dots ., M_{6}$ denote the subsystem failure; $A, . . . . . ., E$ are defined as the basic events; state variables for basic events are $e_{1}, \dots \dots ., e_{6},$ respectively. Interdependency among these failures are shown in Table 5. Minimum Cut Sets (unique combination of components failures leading to the system failure) are also determined.

Figure 5.

A typical logic FT.

Table 5.

Determination of minimum cut sets (MCSs).

Computational process	Minimum cut sets
$M_{5}$ = $D + E$	${A, B} {C, D} {A, D, E} {B, C, E}$
$M_{6}$ = $C + E$
$M_{3}$ = $M_{5} C = (D + E) C = DC + EC$
$M_{4}$ = $D M_{6} = D (C + E) = DC + DE$
$M_{1}$ = $M_{3}$ + $A = DC + EC + A$
$M_{2}$ = $M_{4}$ + $B = DC + DE + B$
$T$ = $M_{1} M_{2} = (DC + EC + A) (DC + EC + A)$

Both Figure 5 and Table 5 are modified from Wang et al. (2018) which are all about determination of interdependencies using fault tree analysis. Subsystem $M_{5}$ consists of component $D$ and $E$ which are connected with an “or” gate with $M_{5}$ . It does mean that subsystem $M_{5}$ works if anyone of these two components works. But, in case of subsystem $M_{3}$ , the scenario is different. Both, the subsystem $M_{5}$ and the component $C$ have to be in working condition to keep $M_{3}$ active. That means subsystem $M_{3}$ can work under two conditions: (i) both $D$ and $C$ are working, or (ii) both $E$ and $C$ are working (Table 5).

Therefore, the relationship of the system failure with the basic events can be given as

T = e_{1} e_{2} + e_{3} e_{4} + e_{1} e_{4} e_{5} + e_{2} e_{3} e_{5}

(26)

Joint optimizations

SPI planning is an important part of inventory management. Most research start with a given demand for spare parts and with unlimited number of available spare parts (Olde Keizer et al., 2017). Assumptions for 100% spare parts availability is not optimal (Zahedi-Hosseini et al., 2017). Spare parts planning and maintenance activity are very much related to each other’s to be taken care of simultaneously (Wang, 2012). Integration of spare parts and maintenance management has become popular among researchers. Tracht et al. (2013) presented an approach for inventory and spare parts planning considering some restrictions related to offshore wind engineering. Bousdekis et al. (2017) showed a proactive decision model. Zhang and Zeng (2017) also proposed a joint model for safety policy and preventive maintenance considering spare parts for a complex multiunit structure. It is observed that spare parts management combined with condition-based maintenance or opportunistic maintenance are the most prominent inventory and maintenance strategies. Current maintenance strategy is mainly focused on maintenance itself with an immutable maintenance schedule. But there is a lot of uncertainty associated with it. All the maintenance resources are assumed to be present all the time which is not the case. Very few maintenance models have been developed where spare parts uncertainty is considered. Zhang et al. (2019) proposed a model for inventory cost $C_{inv}$ that is given below

C_{inv} = \sum_{t = 1}^{T} \sum_{j = 1}^{n} λ_{j^{*}} (C_{o} + C_{j}^{p} * (S_{j} - q_{j}^{t}) + \sum_{k = 1} C_{j}^{h} * q_{j}^{t} * (t_{j}^{k} - t_{j}^{k - 1})) * (1 + r)^{- y}

(27)

where $T$ is the life cycle, $n$ is the considered number of wind turbine component, $C_{o}$ is the ordering cost, $r$ is the inflation (often termed as discount) rate, and $y$ is operation period in years. $C_{j}^{p}$ , $S_{j}$ , $C_{j}^{h}$ , $q_{j}^{t}$ , $t_{j}^{k}$ and $t_{j}^{k - 1}$ are the procurement cost, the maximum stock level, per unit holding cost, amount of stock, $k^{th}$ reorder time for component $j$ , respectively.

Joint opportunistic maintenance and spare parts management

A system is considered which has $n$ similar critical units. Each unit undergoes through Wiener deterioration process. The proposed Reasonable and Useful Lifetime (RUL) policy by Cai et al. (2017) is described in the following:

Each unit will be subject to periodic inspection at $t_{k} = k . T (k \in N)$ , where $T$ is the inspection interval. Exceptions might occur for the units which have a potential failure state as per the previous inspection. Compared to the inspection interval, the inspection time is negligible. The inspected deterioration stages of unit $i$ is $i = 1, 2, \dots \dots, n$ at time $t_{k}$ is noted as $X_{i}^{t_{k}}$ .

CM (corrective maintenance) is done for unit $i$ when $X_{i}^{t_{k}}$ is greater than functional failure threshold, $L_{f}$ . In other words, functional maintenance triggers when the deterioration stage exceeds the functional threshold. When $X_{i}^{t_{k}}$ is less than $L_{f}$ but less than $L_{p}$ (potential failure threshold), PM (preventive maintenance) is done. After performing CM/PM the unit becomes as good as a new unit. When $X_{i}^{t_{k}}$ is less than $L_{p}$ , the unit $i$ is allowed to keep working and the RUL is predicted at definite point of time ( ${RUL}_{i}^{t_{k}}$ ). This is shown in the form of list in Table 6.

Table 6.

Required actions based on deterioration stage.

Deterioration stage	Action
$X_{i}^{t_{k}}$ > $L_{f}$	CM is implemented
$L_{p}$ < $X_{i}^{t_{k}}$ < $L_{f}$	PM is implemented
$X_{i}^{t_{k}}$ < $L_{p}$	No CM/PM is needed, only ${RUL}_{i}^{t_{k}}$ is updated

If ${RUL}_{i}^{t_{k}}$ is less than the appointment threshold, $t_{b}$ ; one spare parts from the stock is appointed for unit i. Therefore, the number of available spare parts in stock, $N_{a - spare}^{t_{k}}$ reduces by 1. The time when unit i starts operating after inspection and PM/CM, is denoted by $t_{k}^{+}$ , and its deterioration stage is expressed by $X_{i}^{t_{k}^{+}}$ .

3. Once inventory level falls below safety stock level, $s$ ; an order is placed. Ordering cost is $C_{0}$ and lead time is $t_{l}$ = $l . T$ where $l$ is any natural number. No new order is made during the lead time period.

4. In case of spare parts shortage, the units on the verge of failure would keep working while the units under functional failing unit would stop working. Shortage cost/unit/time is $c_{d}$ .

5. The unit under functional stage gets priority for maintenance once the parts are delivered. The remaining spare parts are kept in the stock. Holding cost is $c_{k}$ per unit per spare parts.

As an illustration of joint strategy, a typical system with two critical units is shown in Figure 6 (Modified from Cai et al., 2017). Here, maximum inventory level, $S = 3$ ; safety inventory level, $s = 1$ ; lead time, $t_{l}$ = $3 T$ .

$X_{1}^{t_{1}}$ , $X_{2}^{t_{1}}$ < $L_{p}$ and ${RUL}_{1}^{t_{1}}$ , ${RUL}_{2}^{t_{1}}$ > $t_{b}$ happens at time $t_{1}$ . In another word, deterioration levels for units 1 and 2 are less than the potential failure threshold, and $RUL$ for unit 1 and 2 are greater than appointment threshold. So, no maintenance or appointment is required.

At time $t_{2}$ , ${RUL}_{2}^{t_{2}}$ < $t_{b}$ . So, unit 2 requires 1 spare part to be appointed from the stock. Therefore, the number of spare parts appointed is, $N_{app}^{t_{2}}$ =1. The number of available spare parts at time $t_{2}$ , $N_{a - spare}^{t_{2}}$ decreases from 3 to 2. However, the total number of spare parts, $N_{stock}^{t_{2}}$ does not change.

At time $t_{3}$ , ${RUL}_{1}^{t_{1}}$ < $t_{b}$ . So, unit 1 requires 1 spare part to be appointed from the stock. Therefore, the number of spare parts appointed is, $N_{app}^{t_{3}}$ = $N_{app}^{t_{2}} + 1 = 2$ and $N_{a - spare}^{t_{3}}$ = $1$ . So, an order for $N_{order}^{t_{3}}$ = $2$ has been placed.

At time $t_{4}$ , $X_{2}^{t_{4}}$ is larger than $L_{f}$ , so CM is applied on unit 2. $N_{stock}^{t_{4}}$ decreases by $1$ and takes the value of 2, $N_{app}^{t_{4}}$ = $N_{app}^{t_{3}}$ – 1 = $1$ and $N_{a - spare}^{4}$ = $N_{stock}^{t_{4}}$ - $N_{app}^{t_{4}}$ = $2 - 1 = 1$ .

At time $t_{5}$ , $L_{p}$ < $X_{1}^{t_{5}}$ < $L_{f}$ , so PM is applied on unit 1. $N_{stock}^{t_{5}}$ decreases by $1$ and takes the value of 1, $N_{app}^{t_{5}}$ = $N_{app}^{t_{3}}$ – $1$ =0 and $N_{a - spare}^{5}$ = $N_{stock}^{t_{5}}$ - $N_{app}^{t_{5}}$ = $1 - 0 = 1$ .

At time $t_{6}$ , the order is supposed to be shipped. So, $N_{a - spare}^{6}$ = $N_{stock}^{t_{6}}$ = $3$ .

Figure 6.

A system of two units under joint decision process (Adapted from Cai et al., 2017).

In this study Cai et al. (2017) proposed a joint optimization method in which they introduced an appointment policy for the first time. The appointment policy helps to predict the RUL of the parts to place an early order which eventually minimizes the inventory and maintenance cost. The results showed that they were not only able to minimize the cost but also the likelihood of shortage. The model was 45.36% cost efficient compared to the traditional separate optimization methods. Cost was even further reduced from joint optimization when joint optimization with appointment policy was used (4.24%).

Assumptions for joint optimization

The goal of joint optimization is to minimize both the maintenance and the inventory cost for total life cycle. Some common assumptions for inventory and maintenance model are (Ramli et al., 2016):

There are four major components in a turbine system. They are rotor, gearbox, generator, and bearing. Failure patterns of all of these components are individual and follow the Weibull distribution.

Three maintenance actions are considered: preventive, corrective, and opportunistic maintenance. To make it simple, only replacement is allowed. Spare parts are needed to make that happen.

Lead time is very small (negligible) and no failure is allowed during the lead time.

Absence of spare parts at the time of failure and maintenance results in excess lead time and downtime cost.

Forecasting and estimation of parameters

There are some periods with no demand for spare parts in offshore wind turbine system. Demand prediction can be done by the exponential method or Croston’s algorithm (Rabe et al., 2008). In their case studies, Schuh et al. (2015) worked with stator which is a component of the turbine. They found no linear trend in their demand data so they used simple exponential smoothing technique. The result they got is given in Table 7. We see from Table 7 that the point estimate for the rotor is 0.63 which is rounded up to 1. The most optimistic forecasting makes it 2 at 95% confidence interval.

Table 7.

Result of exponential smoothing technique.

Point forecast	Forecast confidence level: 0.77		Forecast confidence level: 0.95
	Lower limit	Upper limit	Lower limit	Upper limit
0.63 (1) part	−0.40 (0) parts	1.65 (2) parts	−1.05 (0) parts	2.30 (2) parts

They also calculated Weibull parameters values using maximum likelihood method from the lifetime demand data. Their analysis suggested that the most significant correlation was between the lifetime of the parts and the temperature of stator 2. They found a positive coefficient between the two: meaning that the higher the temperature, the sooner the end of life for the spare parts. During their simulation time, the temperature exceeded the threshold temperature 40 times. They calculated failure probability for every corresponding unit and took the mean of those. Finally, they compared the demand forecasting result obtained from three different methods: exponential smoothing, probabilistic method (maximum likelihood) and Combined method/Weibull PHM shown in Table 8.

Table 8.

Summary of parameter estimations for Weibull PHM (Schuh et al., 2015).

Method	Point forecast	Confidence level of forecast
		Lower limit (0.77)	Upper limit (0.95)
Exponential smoothing	0.63 (1) part	1.65 (2) parts	2.30 (2) parts
Probabilistic method	0.64 (1) part	—	—
Combined method (WPHM)	—	1 part	2 parts

The combined method seems promising as it can compensate for the missing demand data with the lifetime data and the condition monitoring information. It can also analyze the cost benefit scenario of stock outs and excess inventory. Schuh et al. (2015) showed that the optimal inventory level for wind energy system depends on two factors: the mean failure probability, $\bar{F} x (t)$ and the $η$ where, $η$ = daily inventory cost/daily downtime cost. They performed a simulation for 20 critical components for $η$ values of 0.25, 0.50, 0.75, and 1. They observed that for all four cases, the optimal stock level increases with the increase of failure probability but this relationship is linear only when $η$ = 1. There are several for higher component failure probability, for example lower reliability, unfriendly weather factors, higher wind speeds due to hurricanes, tornados, cyclones etc. For a given $\bar{F} x (t)$ value if the inventory cost is much lower than the downtime cost (say, $η$ = 1/4), stock optimal stock level increases (Table 9).

Table 9.

Cost optimal stock level versus failure probability for different ratio factors, $η$ (Schuh et al., 2015).

Average failure prob.	Cost minimal stock level
	1/4	1/2	3/4	1/1
0.00	0	0	0	0
0.05	2	1	1	1
0.10	3	2	2	2
0.15	4	4	3	3
0.20	5	5	4	4
0.25	7	6	5	5
0.30	8	7	6	6
0.35	9	8	7	7
0.40	10	9	8	8

Life cycle inventory analysis

Life cycle of a windfarm starts from planning, designing, manufacturing, installation, operations and maintenance, and disposal of the full system. Lee and Tzeng (2008) analyzed the life cycle of wind energy in Taiwan. They divided their study into three sections: feasibility study and primary assessment, inventory analysis for entire life cycle, and payback period calculation. Figure 7 (Modified from Lee and Tzeng, 2008) shows the full life cycle of an offshore wind farm in a single look. Starting from material acquisition, there are other steps like: manufacturing, turbine installation, operation and maintenance, and finally dismantling and disposal. There are some common bulk inventories for wind system: metal, concrete, sand, petrochemicals, glass. All of these are taken as input materials. The output elements are CO₂ and other greenhouse gases. The functional unit is defined according to the power generation capacity in kWh unit.

Figure 7.

Life cycle inventory analysis.

Lee and Tzeng (2008) studied the inventory characteristics of three wind turbine systems installed in Taiwan. The location of the wind farms is: Mailiao, Penghu Island, and Chunfong which has a capacity of 660, 600, and 1750 KW, respectively. Inventory for material requirements shown in Table 10 is reported by Lee and Tzeng (2008) from the literature (Khan et al., 2005; Schleisner, 2000; Voorspools et al., 2000). Among tower, nacelle, rotor, and base; base is the heaviest having approximately 80% of the total weight. Energy consumption by wind turbine material is estimated by “factor of energy input” or popularly known “embodied energy.” For an example, energy consumption for Aluminum is 0.019 Giga Joule per kg of material that has been used (Schleisner, 2000). The energy consumption rate for cement and steel is 4 and 7.87 MJ/Kg, respectively.

Table 10.

Characteristics of three selected wind power systems and material requirements.

		Chunfong (NW)	Jhontun (Penghu)	Mailiao (SW)
Wind farm characteristics	Turbine system	Vestas (V-66)	Enercon (E-40)	Vestas (V-47)
	Power capacity	1.75 MW	0.6 MW	0.66 MW
	Rotor dia.	60	43.7	47
	Tower ht.	60	46	45
	Rotor wt.	23	8.27	7.2
	Nacelle wt.	57	19.77	20.4
	Tower wt.	100	31.27	36.45
	Base wt.	500	220	240
	Total wt.	680	279.31	304.05
Inventory of materials (kg)	Steel	155,027	63,677	69,317
	Aluminum	3623	1488	1620
	Copper	3590	1474	1605
	Sands	3794	1558	1696
	Glass	5589	2296	2499
	Plastics	5745	2360	2569
	Petroleum products	2011	826	899
	Others	1535	631	686
	Concrete	546,636	224,531	244,419

dia.: diameter; ht: height (unit is meter); wt.: weight (unit is tons).

The life cycle energy input is summarized in Table 11 based on the data given by Lee and Tzeng (2008). Input energy is categorized step by step, such as: installation stage energy consumption, energy consumption during operation and maintenance (roughly 1% of total electricity yield), required energy to dismantle the system. A large portion (almost 50%) of input energy is used for manufacturing of wind turbines. CO₂ is also a matter of concern here. Total life cycle CO₂ emission can be divided into three kinds. Manufacturing, installation, and dismantling emits 90.5%, 7.7%, and 1.8%, respectively. Amount of CO₂ emission is 3.6 g/kWh.

Table 11.

Life cycle energy inputs for selected wind power systems.

Life cycle stage energy input in GJ	Chunfong	Jhontun	Mailiao
Turbine manufacture	3898	3202	3486
Foundation construction	3608	2964	3226
System installation	877	827	847
O&M	75	62	67
Dismantling	150	123	134
Total/combined
Total life-cycle energy input (GJ)	23,547
Total electricity generated (kWh)	455,741,660
Energy input intensity (MJ/kWh)	0.05

Lee and Tzeng (2008) shows the number of resources required to generate 1 kWh of energy: steel 1.6 g, plastic 0.068 g, glass 0.067 g, sands 0.045 g, copper 0.043 g, aluminum 0.043 g, petrochemicals 0.024 g, and others 0.018 g. They also calculated payback period as follows

Payback period = \frac{life cycle energy input (2.5 GWh)}{net electricity generated (22.6 GWh / year)} = 0.11 year = 1.3 month

(28)

It is very optimistic payback period since the usual payback period is usually 3.1–7.8 months. It is needless to mention that investors always prefer to invest in such a project which has a low payback period. Since an offshore wind farm is a project of billion dollars, the payback period is a good determinant of investment feasibility.

Case studies

As has been said earlier that the combined optimization of inventory and maintenance is a very popular research topic nowadays. Cai et al. (2017) suggested an appointment policy for spare parts to ensure lower inventory level with no shortage. Eventually, they proposed a combined inventory and preventive maintenance model. Monte Carlo Simulation (MCS) and genetic algorithm have been applied to determine optimum safety stock, order up to level, appointment threshold, and probable failure frequency. Joint optimization and separate optimization were applied in a case study. Joint optimization produced better result in terms of cost.

Case study on a typical wind park

A practical case has been studied by Tracht et al. (2013) in a windfarm with 100 turbines. The other parameter values are given in Table 12 (Data adopted from Tracht et al., 2013). Life span was assumed to be 10 years.

Table 12.

The parameter values of the case study.

Parameter	Value	Parameter	Value
$W_{pt}$	6700 hp	$C_{tr}$	180,300 $/day
$f_{ft}$	0.134 $/hp	$C_{mt}$	13,400 $/day
$T_{lt}$	20 years	$C_{sp}$	1,072,800 $
$T_{\lg}$	10 years	$T_{mttr}$	8 days
$k_{s}$	2	$R_{icc}$	0.03/year
n	100	$C_{so}$	134,100 $/year
$T_{d}$	150–270 days	$C_{sd}$	0.005/year

During the days of non-feasibility, technicians cannot be sent for maintenance. Therefore, the inventory remains idle for a long time. So, it is good idea to perform preventive maintenance before non-feasibility days begins. If the number of non-feasibility days increases, mean spare parts demand ( $μ$ ) also increases. Table 13 (Source: Tracht et al., 2013) shows the accumulated inventory levels for different number of non-feasibility days for 97% expected service level.

Table 13.

Inventory scenario for 97% service level.

Days of non-feasibility	$μ$ of demand	Inventory level (pcs.)	Expected service level (%)
150	2.82	7	0.97
180	3.54	8	0.97
210	4.25	9	0.97
240	4.96	10	0.97
270	5.68	11	0.97

It has been observed that considering the days of non-feasibility before procuring spare parts reduces the inventory levels significantly.

Case study on “Reliawind Project”

A case study is performed at European Union’s “Reliawind Project” presented by Márquez et al. (2016). Failure probabilities are calculated from 369 WT’s historical data for 1-year period. Numerical result of importance parameters of the case study is given in Table 14. For Basic Event (BE) $A$ , highest order quantity $Q$ is observed among the six BEs. Because the ordering cost $K$ is the highest, and also the holding cost $h$ is not too high. Though ordering cost $K$ is second highest for $B$ but the holding cost $h$ is the highest which is responsible for a small order size of 12. For BE of $C$ , the ordering cost is second smallest, so it is feasible to order at a small lot of 7. Demand during lead time, $λ$ is highest for event $D$ , therefore it is expected to have a large order size of 29. Likewise, order size of event $E$ is also as large as 27. Lastly, the Basic Event $F$ which has the lowest ordering cost and the lowest demand during the lead time. For these reasons, it has the smallest order quantity of 3.

Table 14.

Numerical result of the case study (Adapted from Wang et al., 2018).

BE	Failure prob.	BP importance	Penalty cost	$λ$	$K$	p	h	L	$(r, Q)$
A	0.0137	0.3104	5617	0.0137	5000	5617	1.2	8	(0,31)
B	0.0110	0.2483	4493	0.0110	4000	4493	5	8	(0,12)
C	0.0055	0.1241	2246	0.0055	500	2246	0.8	7	(0,7)
D	0.0822	0.1276	2308	0.0822	2500	2308	1	2	(0,29)
E	0.0685	0.1275	2308	0.0685	2500	2308	1	2	(0,27)
F	0.0027	0.0621	1123	0.0027	200	1123	0.5	4	(0,3)

Case study on a Chinese wind farm

Zhang et al. (2019) showed a case study on a wind farm in China with 10 wind turbines for a life cycle of 20 years. Figures 8 to 11 were drawn to show the effects of maintenance reliability threshold, reorder point, order up to level and wind speed threshold on the combined opportunistic cost and the inventory cost based on the data provided by Zhang et al. (2019).

Figure 8.

Effect of maintenance reliability threshold on joint optimization cost.

Figure 9.

Effect of reorder point on joint optimization cost.

Figure 10.

Effect of maximum stock level on joint optimization cost.

Figure 11.

Effect of wind speed threshold on joint optimization cost.

Figure 8 shows that inventory cost remains almost the same for the reliability of 0.90–0.99, but after that the inventory cost increases by approximately 25%. The relationship of opportunistic maintenance threshold with combined cost is interesting. Cost remains almost the same for the reliability range of 0.90–0.95 but decreases after that up to 99% reliability and then jumps after that till 100% reliability. Wind turbine reliability threshold is a previously set quantity based on available and collected data.

Combined cost for maintenance and inventory is less sensitive to reorder level than maintenance reliability threshold (Figure 9). With the increase of the reorder stock level, the inventory cost increases but the maintenance cost decreases. Increase in inventory cost and decrease in maintenance cost nullify each other. That’s why the combined cost doesn’t change much with the increase in reorder stock level.

Maximum stock level is more influential than reorder stock level as Figure 10 shows. Maintenance cost doesn’t change too much with the increase of maximum stock level but the inventory cost increases significantly. So, the total cost increases with the increase of maximum stock level. Maximum stock level depends on the amount of initial investment and the size of the capital.

Figure 11 illustrates that total maintenance and inventory cost varies remarkably with wind speed threshold. For low wind speed thresholds, the total cost is higher which decreases sharply with the increase of the wind speed. It continues up to wind threshold level of 7 before it becomes pretty much stable.

Findings and comparative study

Based on the study and analysis of the articles on spare parts planning on OWF, a similarity has been noticed among the approaches taken by different individual researchers. The critical components are the matter of interest and the first task is to identify those. Failure of any critical component might be the reason for the failure of the entire wind farm structure. An OWF manager replaces the failed critical component before the failure or at least as soon as it fails. Suitable and measurable key performance indices (KPI) to be selected based on which the failure time would be predicted. Once the failure time has been predicted, order for the spare parts has been placed so that it is delivered just-in-time. To reduce the downtime, the manager should give special attention to the parts having longer lead times. Figure 12 shows this series of tasks sequentially:

Figure 12.

Sequential steps of spare parts planning.

Offshore wind farm spare parts planning is a multidimensional task which accumulates a number of factors: availability, profitability, probability of stockout, and reliability. These factors are often conflicting. One of the important issues regarding spare parts planning is determining the type and number of spare parts to be held in the stock. This decision directly impacts the amount of downtime of the system. A clear understanding of the failure pattern and the reliability function is a must to predict the spare parts demand precisely. The first and foremost job is to classify spare parts in few categories based on criticality of the item (Molenaers et al., 2012) or top-down methodology (Duchessi et al., 1988). In case of predictable demand, experts recommend just-in-time spare parts policy. Few other relevant models and findings from these models have been illustrated in Table 15.

Table 15.

Findings from state-of-the-art spare parts models at a glance.

Author	Model	Action	Results/findings
Barabadi et al. (2021)	Spare-part prediction using frailty model	Homogeneous Poisson process was applied for spare parts production	Ignoring the unobservable risk factor might lead to unrealistic estimation for spare parts.
Ruiz et al. (2021)	Bayesian degradation modeling for spare parts management	Stochastic dynamic program had been formulated to reduce the expected spare parts cost	Optimal time between delayed downtime and spare parts order quantity have been found.
Qin et al. (2020)	A stochastic model for flexible spare parts planning	Large scale problems were solved by Bender’s decomposition algorithm	Proposed algorithm showed faster convergence than traditional branch-and-bound algorithm.
Andersson and Jonsson (2018)	Causal based forecasting model	Product-in-use big data for spare parts planning	Eight interventions have been presented that improve the spare parts demand planning significantly.
Zhu et al. (2020)	Spare parts modeling using advanced demand information (ADI)	On-condition maintenance policy which is a form of CBM	Up to 51% cost reduction compared to traditional time series spare parts inventory control.
Li et al. (2017)	Stochastic programing model for MRO spare parts	Two step model formation regarding uncertain production time and storage cost	Equivalent deterministic model was derived using Lagrange interpolating polynomial.
Rahimi-Ghahroodi et al. (2017)	Integrated planning for spare parts and service engineers	The model was constructed as a queuing network and solved heuristically	Integrated planning resulted in up to 27% cost savings than discrete optimization.
Gu et al. (2015)	Two non-linear models for impending spare parts demand prediction	General Algebraic Modeling System (GAMS) and iteration method were used	The models could effectively reduce spare parts cost by up to 98.03%.

An organized review has been conducted over the OWF spare parts models. There is no universal model which fits every situation. Every model has some unique characteristics, specifications, and applicability. OWF managers always try to find the best match for their projects. While matching the wind farm conditions with the existing models, the managers consider maintenance factors, inventory factors, logistics factors, wind farm specifications (site location and size), and some other factors. A single model usually cannot consider all of these factors. But, most of these factors are present in any OWF. For example: Zhu et al. (2020) implemented spare parts modeling using advanced demand information (ADI) which proved to be effective technique for spare parts demand forecasting. This is suitable for condition-based maintenance. This technique might not be for opportunistic or risk-based maintenance is adopted. Before implementing a model, managers decide which factors must be present there depending on the specification of the corresponding wind farm. Table 16 shows some models considering these factors.

Table 16.

Comparison among several OWF spare parts models based on some key criteria.^*

		Schuh et al.(2015)	Wang et al.(2018)	Ferdinand et al. (2018)	Tracht et al.(2013)	Zhang et al.(2018)	Lee and Tzeng (2008)		Cai et al. (2017)		Koçağa and Şen (2007)		Arvesen et al. (2018)		Lütjen and Karimi (2012)		Dahane et al. (2017)
Maintenancefactors	Maintenancepolicy	CBM	CBM	RBM	PM	OM	X		CBM		X		PM		X		CBM
	Type of model	Cost optimalmodel	Maint. strategy opt.	FMEA inv.analysis	Restrictivemaint. condt.	Stochasticinv. mgt.	Life cycle inv.analysis		Jointoptimization		Demandmodel		LCA		Installationmodel		Correctivemaintenance
	Inspection policy	CMS	CMS	CM	CMS	X	X		CMS		X		X		X
	Cost for inspection	Yes	Yes	Yes	X	X	X		Yes		X		X		X		Yes
	Cost of operations	Yes	Yes	Yes	X	X	X		Yes		X		Yes		Yes		Yes
Inventory factors	Inventory policy	Continuousreview	Continuousreview	X	Periodic	Periodic	X		X		X		X		Periodic		X
	No. of units	Multiple items	Multiple items	Multipleitems	Single	Multiple items	X		Multiple items		X		X		Single item		Single item
	Slow/fast item	Slow	Fast	X	X	X	X		X		X		X		Fast		X
	Cheap/expensive	Expensive	X	Expensive	X	X	X		X		X		X		X		Expensive
	Ordering cost	No	Yes	X	X	Yes	X		Yes		X		X		Yes		X
	Shortage cost	Stock-out cost	Penalty cost	X	Stockout cost	Stock out cost	X		Shortage cost		X		X		Shortage Cost		X
Logistics factors	Lead time	Low	X	Low	Low	Negligible	X		Considered		High/low		X		Low		X
	Transportation speed	Faster	X	Faster	Faster	X	X		X		X		X		X		X
	Multi-echelon	X	X	X	Single- echelon	Multi-echelon	X		X		Single-echelon		X		Single-echelon		X
	Emergency orders	No	X	Taken	X	Taken	X		X		Taken		X		X		X
Specifications	Site	Onshore	Offshore	Offshore	Offshore	Offshore	Offshore		Offshore			Offshore		Offshore		Offshore
	Size	Medium	Small	Medium	Large	Small	Large		Medium		Small		Large		Small		Small
	Location	Germany	China	X	Germany	China	Taiwan		China		Turkey		Norway		Norway		France
Other Factors	Weather factor	Considered	Considered	Considered	Considered	Considered	X		No		X		Considered		Considered		Considered
	Failure data	Used	FTA	RPN	Used	X	X		Used		Used		Used		X		Used
	Demand data	Used	No	X	Used	Used		Used		Used		Used		Used		Used

^*As far as the size of the wind farm is concerned: Small is under 11 kW capacity, Medium is 0.1–1 MW, and Large is over 1 MW capacity.

Table 16 compares the results of 11 relevant articles on spare parts control strategies for OWF. We have chosen some criterion to examine the performance of each of them. But, we see that there is no model which satisfies all of our criteria. Schuh et al. (2015) model fits best with our evaluation criteria but still does not 100% match. So, a manager has to decide about the most relevant factors for his project from all the available terms, conditions and the criterion.

Recommendation and conclusion

In this article, the authors summarized most of the prominent spare parts models regarding offshore wind farms. Findings from these models are presented in tabular form. The key factors of the models are illustrated from comparative perspectives. The applicability has been discussed as well. Though a lot of subjects related to OFW spare parts planning have been included in this review article, there are some limitations of this study. The offshore wind farm industry is still in its initial state. So, there are not enough spare parts models in the literature regarding OWF. Along with the available OWF models, the authors selected some relevant models from other fields which applies to OWF.

Managerial implications

Based on the research performed by the authors while writing this article, some managerial implications can be drawn. Managers feel immense pressure to maintain effective spare parts management. There is always a fear of paying extra for holding excessive spare parts which is a motivation to keep the inventory level as low as possible. On the other hand, there is fear of downtime because of spare parts shortage. A manager had to work between this dilemma all the time. Here, some recommendations are made to minimize this uncertainty.

Strategy selection: Managers should always implement predictive strategy rather than responsive strategy. Even after imposing predictive approach, there might be some cases where response tasks may require but the company should not rely on a responsive strategy. Critical components of OWF need to be identified, failure data would be collected regarding those components, proper statistical analysis to be done to predict the failure time precisely.

Efficient ordering process: Once the failure time for critical components is known, it is necessary to place the order ahead of time to avoid paying extra money for an emergency order. An efficient ordering process is the key here. A standard ordering process needs to be developed to make the task easier and faster.

Reviewing inventory from time to time: Taking a spare part from the inventory does not necessarily mean to order for another part immediately. If failure data does not suggest, a manager can restrain ordering for that spare parts. Inventory for spare parts for different critical components should be reviewed from time to time and matched with demand data to check if the wind farm is holding any excess spare parts.

Aware of long lead time: Some spare parts might have longer lead times. If those parts are not critical then it is fine to opt out but managers must stay aware of the critical components with longer lead times. It incurs huge production loss if the wind farm is down for a long time because of spare parts shortage. It is better to be conservative in case of spare parts that have longer lead time.

Newly installed system: There is a common misconception that newly installed turbines in OWF do not require spare parts. This is not true always. Minimal inventory should be kept for immature failure of the critical components. Historical failure data might help to decide this issue.

Reverse logistics: Supply chain sustainability is a burning topic nowadays. Reverse logistics deal with dismantling, consolidation and remanufacturing of the full structure or some parts of it. Since wind turbine is a huge structure, concept of reverse logistics can be applied successfully.

Multi-echelon inventory system: Implementing multi-echelon inventory system for OWF spare parts might reduce the overall inventory level and increase availability at the same time. Most of the models in the literature consider single echelon optimization problems which often cannot optimize the overall inventory level across different echelons or stages.

Demand modeling: Most of the researchers use Poisson process which is a stationary stochastic process. But, the demand for OWF spare parts is mostly lumpy, intermittent and cannot maintain steady-state conditions all the time. In these cases, non-stationary stochastic process performs better.

Future research

Since OWF spare parts management is a growing field of study, many researchers are curious about it. There is huge scope for future researchers to work on different sections of OWF spare parts planning. Future researchers can use big data in condition monitoring by telematics enabled turbines. Since telematics has been used successfully in various fields like GPS tracking technology, communication among vehicle fleets, weather tracking, remote monitoring of equipment; it is time to use this technology steadily for wind farm projects as well. Future researchers can also use robust optimization to reduce the range of uncertain parameters in offshore wind farm spare parts planning. Robust optimization has been successfully used in many other fields of operations management. Most of the spare parts models consider single spare parts, future research may concentrate on modeling multiple spare parts at a time. Besides, classical optimization methods can handle an inventory system only with a few items. But, the Supervisory control and data acquisition (SCADA) system and the installed sensors generate tons of data which is difficult to process using classical optimization techniques. Future researchers can implement Big data analytics for superior performance in predictive modeling and optimization in these cases.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Md Imran Hasan Tusar

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