A hierarchical cost learning model for developing wind energy infrastructures

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A hierarchical cost learning model for developing wind

energy infrastructures

Amy J.C. Trappey

a,n

, Charles V. Trappey

b

, Penny H.Y. Liu

a

, Lee-Cheng Lin

c

, Jerry J.R. Ou

d

a

Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Taiwan b_{Department of Management Science, National Chiao Tung University, Taiwan}

c

Green Energy and Environment Research Laboratories, Industrial Technology Research Institute, Taiwan d

Bureau of Energy, Ministry of Economic Affairs & Department of Business Administration, Southern Taiwan University, Taiwan

a r t i c l e i n f o

Article history: Received 2 July 2012 Accepted 11 March 2013 Available online 27 March 2013 Keywords:

Wind power Learning curve Hierarchical linear model

a b s t r a c t

Renewable energy has been increasingly promoted and used to substitute non-renewable fossil-fuels, which cause negative effects on the environment. The Taiwan Statute for Renewable Energy Develop-ment has regulated and promoted renewable energy since 2009. A feed-in tariff (FIT) for renewable energy is one of the incentives that the government uses to promote the installation of green power generation facilities. The price of the electricity feed-in tariff is based on the current and future costs of renewable energy generation. When analyzing cost trends for renewable energy installation, many researchers use a single factor cost learning curve model. However, past studies indicate that there are multiple factors affecting the overall cost of installing renewable energy. Hence, this research develops a hierarchical installation cost learning model which considers multiple factors to accurately model and forecast wind energy development. This research uses wind power development data from Taiwan as a case study. We identify the cost factors, evaluate the learning effects, and compare the hierarchical learning curve model to the basic (non-hierarchical) learning curve model. The research results show an improvedﬁt between the hierarchical model and the actual data when compared to the basic learning model. The study also provides new insights between the wind power learning progression of Taiwan and three countries in Europe.

1. Introduction

According to the International Energy Association report (IEA, 2008), the projected world demand for energy will increase 45% between 2006 and 2030 with an average annual growth rate of 1.6%. Oil remains the dominant fuel in the primary energy mix

(IEA, 2008). Further, global climate change remains an important

issue with global average sea levels increasing at an average rate of about 3.1 mm per year from 1993 to 2003 and the annual average Arctic sea ice shelf is shrinking 2.7% per decade since 1973 (IPCC, 2007). In order to help resolve the problem of energy demand and climate change, most of countries have increased their investment in renewable energy. Global investment in renewable energy in

2004 was $22 US billion dollars and reached to $211 US billion dollars in 2010 (REN21, 2011).

Renewable power generation policies have been implemented in 96 countries and represent the most common type of support policy. Two of the most popular policies for governments to stimulate the deployment of renewable energy are the implementation of Renew-able Portfolio Standard (RPS) and Feed-in-Tariffs (FIT). RPS requires electricity supply companies to produce a speciﬁed fraction of their electricity from renewable energy sources and the renewable energy generators sell their electricity back to supply companies. RPS relies almost entirely on the private market for its implementation. Therefore, this approach helps deliver renewable energy at a lower cost, allowing renewable energy to compete with cheaper fossil fuel energy sources. Unlike RPS, FIT offers long-term contracts, which last 15 years to 25 years, where renewable energy producers guarantee to purchase all the generated renewable energy based on the cost of electricity generation. FIT is the most widely implemented policy with at least 61 countries and 26 states or provinces in the world implementing FIT. Ten countries and at least 50 other jurisdictions, including 30 U.S. states and British Columbia have implemented RPS (REN21, 2011). The Taiwan government passed the Statute Contents lists available atScienceDirect

journal homepage:www.elsevier.com/locate/ijpe

Int. J. Production Economics

n_{Correspondence to: Department of Industrial Engineering and Engineering}

Management, National Tsing Hua University, Hsinchu, Taiwan 30013, R.O.C. Tel.:+88635742651; fax: +88535722204.

E-mail addresses: [email protected] (A.J.C. Trappey), [email protected] (C.V. Trappey),

[email protected] (P.H.Y. Liu),

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for Renewable Energy Development in 2009 and used FIT as the incentive policy to promote investment in renewable energy. The goal of the statute is to increase the installed capacity of renewable energy to 8000 MW over the next 20 years.

Wind power has become the fastest growing source of renewable energy. According to the REN 21 Report (REN21, 2012), global wind capacity increased by 20% (from 198 GW in 2010 to 238 GW in 2011) which is more than any other renewable technology. Over 68 count-ries have added more than 10 MW of reported capacity, with 22 of these countries passing the 1 GW level during 2011. Taiwan is an island with an extensive coastal region. The Taiwan potential for wind energy can be developed by 3000 MW and is considered the most suitable for development than other renewable energies (Liou, 2010). The government regularly revises FIT prices for new installations in order to ensure economic efﬁciency and to minimize windfall proﬁts for renewable energy installers. In other words, the government reduces FIT prices if renewable energies reach mature development and stable installation costs. Thus, for countries with the potential for developing wind energy and adopting FIT policies, understanding the trend between the relationships of wind energy costs and wind energy production and utilization is important. Learning curves offer important strategic implications for industrial production (Chand and

Sethi, 1990). Product output are depicted by a production cost curve

and its variation with output level. Previous studies (McDonald and

Schrattenholzer, 2001;Ibenholt, 2002) utilized the learning curve to

analyze the relationship between wind power generation cost and the accumulated wind power production. The empirical results help governments and power plant installers understand the installation cost changes and trends for wind-power electricity production. Nonetheless, these studies usually adopt a single factor learning curve model to describe the cost trend. Some researchers note that single factor learning curve models provide a weak explanation of the causal effects and may bias the estimation of cost trends (Nemet, 2006;Yu

et al., 2011). Therefore, this study develops a hierarchical cost learning

curve model to interpret the cost trends of a wind power facility. The purpose is to discover the multiple factors that signi_{ﬁcantly impact} the relationship between wind cost and accumulated wind produc-tion. The results provide information for policy makers to improve the design of wind energy systems and to optimize wind energy development.

This research paper is organized as follows. Section 2 is a literature review which introduces learning curves and the hier-archical linear model.Sections 3and4describe the methodology and present a case study, respectively. For the case study, the learning curve is used to compare theﬁtness of hierarchical model with general learning curve model. The progression rate is compared with similar studies conducted in Denmark, Germany and the United Kingdom. Section 5 provides a conclusion and overview of the research results and contribution.

2. Literature review

In this section, the concepts of basic and hierarchical linear curve models and the related research literatures are reviewed. 2.1. Basic learning curves and related literature

A learning curve offers a means of analyzing past cost devel-opment that had been adapted to analyze future cost develdevel-opment

(Neij, 2008). The curve shows the relation between accumulated

production quantity or experience and unit production time or cost for a given activity or product. The learning curve effect

(Fig. 1) depicts that as the total production quantity (in units)

doubles, the cost per unit declines by a constant percentage (Jaber

and El Saadany, 2011). Wright (1936) was one of the ﬁrst

researchers to describe and apply the learning effect. By observing the aircraft industry, he proposed a mathematical model to describe the declining trend of required labor hours needed to produce one unit of product at a constant rate. Learning curves have been widely applied and each application typically has a unique learning rate. The usefulness of learning curves was demonstrated during World War II as a very effective means for predicting the cost and time for constructing ships and aircraft (Yelle, 1979).

The learning curve can be applied to describe effects of groups as well as individual performance, e.g., a group comprising direct and indirect labor. Technological or skill progresses are considered types of learning. The industrial learning curve can be used to model the improved skill of an individual by repetition of simple opera-tions. It can also be used to describe more complex systems, such as group efforts of people on production lines and others in supportive positions, all working to progressively improve a common task

(Jaber and Bonney, 1999). Learning curves are described by the

following equation (Berndt, 1991): Ct¼ C1ntαeut

where Ctrepresents the unit production cost at time t and C1is the

ﬁrst unit production cost. ntIs the production quantities

accumu-lated to time t,α is the learning index, utis the stochastic term, and

eut _{is the error term following a normal distribution.}

A reliable learning curve model is a useful tool for the planning and control of operations. The predictions of future performance are more reliable, the use of resources are better planned, the sequen-cing of operations are more precise, and the cost of future produc-tion are more accurately estimated when learning effects are taken into consideration (Andrade et al., 1999). Plaza and Rohlf (2008)

focused on the relationship between the capabilities of a project team and consulting-cost management. They proposed a model based on learning curves to study the impact of training on project cost and duration. In order to further de_{ﬁne production ramp-up,}

Terwiesch and Bohn (2001) modeled the complex dynamics of a

new product's ramp-up by providing concrete values for the cost and beneﬁts of learning efforts. Speciﬁcally relevant to this research, there are research papers which apply learning curves to renewable energy production. Wang et al. (2011) simulated wind energy industry development in China using a logistic learning curve model.

Ibenholt (2002)constructed learning curves of wind power

produc-tion costs in three countries, i.e., Denmark, Germany and United Kingdom. He compared the aerodynamic conditions and renewable energy policies which affect the costs and utilizations of wind power in these countries.Neij (2008)presented an analytical framework, which was based on an assessment of available experience curves. The analysis was complemented with a bottom-up analysis of sources of cost reductions and expert assessments of long-term

Production cost/per unit

Quantity

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analysis of future costs for developing new technologies of green electricity generation.Qiu and Anadon (2012)used bidding data for wind power projects from 2003 to 2007 in China and applied learning curve models to predict development costs.

For most studies related to energy production learning curves, a one-factor learning curve model was applied. Thus, only the relation between the production cost and the production quantity (the accumulated capacity when used in renewable energy) was modeled. In addition to the learning effect generated from experi-ence,Nemet (2006)considered that other observable factors played important roles in decreasing production costs. He identiﬁed seven factors that affect photovoltaic module costs and found that plant size, module efﬁciency, and the cost of silicon are critical factors that impact the production cost of solar power. More importantly, the accumulated production quantity, which is usually represented by the learning experience curve, weakly explains decreasing costs.

Yu et al. (2011)also noted that the one factor learning curve model

only explains cost declines in the initial development stage of a new technology and cannot fully describe the cost changes caused by other factors such as key material (input) prices.Ibenholt (2002)

also indicated that the connection between wind power electricity production cost and accumulated production quantity may be in_{fluenced by factors such as R&D investment, policy measures,} changes in input material prices (e.g., steel), competition in the market, economies of scale, and other technology specific variables. The relationship among these factors and wind power production quantity and cost are often discussed and planned in a nested and hierarchical fashion. Thus, this paper incorporates the hierarchical linear model concept as a cost learning curve model to include multiple factors that significantly influence cost changes.

2.2. Hierarchical linear model (HLM) and related literature Hierarchical linear models are a statistical model of parameters that vary at more than one level. These models are generalizations of linear models, which can be extended to non-linear models. HLM is appropriate for research where the data are described in a nested structure, such as students in a class where within a cohort there may be many varying factors such as weight, sex, and height. HLM is applied frequently in the educational domain, since itﬁts the classical nested structure of student and faculty populations (Wen and Chiou, 2011). To estimate the likelihood of success of students,Cyrenne and

Chan (2012) track the performance of university students and

analyze with a least squares dummy variable model and a hierarch-ical linear model.Perry et al. (2007) applied HLM and regression techniques to explore the effects of teacher practices in promoting student academic achievement, behavioral adjustment, and feelings of competence. Other areas such as sociology and consumer science have also applied HLM as a method to understand attitudes, motiva-tions, and behaviors.Gentry and Martineau (2010)describe HLM as an example of a multilevel methodological approach to examine changes over time in the evaluation of human resource team leader-ship development. Addressing the multilevel relation among time variance, disposable income, and U.S. entertainment consumption,

Chen (2012)adopted a hierarchical linear model to determine that

time variance and disposable income are positively related to entertainment expenditures over different entertainment categories. As reported byWen (2006), HLM applications have also been used in biostatistics and economics.

HLM was first developed by Lindley and Smith (1972). In general, the model of HLM can be classified as the full model, the intercept model, and the coefficient model (Table 1).

For the full model, level 1 is the basic structure of HLM, which denotes the relation between the dependent variable Yijand the

explanatory variable Xij. In level 2, two dependent variables are

derived as the intercept (β0j) and coefﬁcient (β1j) of the linear

model in level 1. Both are inﬂuenced by the explanatory variable Zj.

By the values of parameters_γ00,γ01,γ10andγ11in level 2 equations

indicate the degree that Zjinteracts with the variablesβ0jandβ1j

can be determined.ɛij, u0j and u1j are the error terms for both

models in level 1and level 2. For the intercept model, Zj

deter-minesβ0jwhich is the intercept in level 1. While in the coefﬁcient

model, the coefﬁcient β1jof level 1 is estimated by Zjin level 2.

Gill (2005) explains that HLM has several advantages over

standard linear models. Their arguments include that hierarchical models are ideal tools for identifying and measuring structural relationships that fall at different levels of the data generating procedure with virtually no limit to the dimension of their hierarchy. Hierarchical models also directly express the exchangeability of units, whereas nonhierarchical models applied to multilevel data typically underestimates the variance. Finally, hierarchical models facilitate the testing of hypotheses across different levels of analysis, whereas nonhierarchical models can be nested within hierarchical models, allowing a likelihood or Bayes factor test of the validity of the proposed hierarchical structure.

3. Methodology

In order to build a hierarchical learning curve of the cost of installing wind power in Taiwan, we collect relevant data and use statistic software tofit the model (Fig. 2). Residual analysis is used to confirm the fitness of the hierarchical learning curve model and compare the model to the basic learning curve model. Finally, the study compares the learning effect of Taiwan wind power installa-tion with the cases of Denmark, Germany and the United Kingdom described byIbenholt (2002).

Table 1 HLM model types.

Type Level 1 Level 2

Full model Yij¼ β0jþ β1jXijþ εij β0j¼ γ00þ γ01Zjþ u0j β1j¼ γ10þ γ11Zjþ u1j Intercept model Yij¼ β0jþ β1jXijþ εij β0j¼ γ00þ γ01Zjþ u0j Coefﬁcient model Yij¼ β0jþ β1jXijþ εij β1j¼ γ10þ γ11Zjþ u1j

Construct hierarchical learning

curve model

Collect relevant data

Use PASW Statistic 18 to find

suitable model

Compare the learning effect

with other countries

Compare the proposed model

with general learning curve

model

Fig. 2. Constructing a hierarchical learning curve of wind power installation in Taiwan.

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The data was checked to determine whether the learning curve factors would interfere with the relationship between accumu-lated wind energy capacity and wind power installation costs. This study utilizes the coefﬁcient models to construct the hier-archical learning curve model of installing wind power in Taiwan and the detailed data analysis is presented inSection 4. The model, as shown in Eqs.(1) and (2), assumes thatβ0and β1haveﬁxed

effects.

Level 1: C ¼ β0Xβ1ε ð1Þ

Level 2: β1¼ γ0þ γ1Z1þ γ2Z2þ ⋯ þ γmZmþ δ ð2Þ

natural logarithms are used to estimate parameters and Eqs.

(1) and (2)are combined into Eq.(3).

ln C¼ ln β0þ γ0ln Xþ γ1Z1ln Xþ ⋯ þ γnZnln Xþ ln ε ð3Þ

where C and X separately denote the wind power installation costs and accumulated installed wind power capacity, respectively. Z1,

Z2,…, Znare considered as the variables that may interfere with

the relationship between the cost and the accumulated installed wind-power capacity. The estimated parameters contain the intercept (lnβ0), the learning index γ0, and the interference

coefﬁcients γ1,…, γn.

4. The cost learning curve of installing wind power

In order to reduce emission of carbon dioxide and promote development of renewable energy, Taiwan passed the Statute for Renewable Energy Development in 2009. The electricity purchase program, which is related to the installation cost, is a critical incentive encouraging people to install renewable energy. This research used wind power installation in Taiwan as a case study to collect data and demonstrate the building of hierarchical cost learning curve model.

4.1. Hierarchical learning curve cost model—the Taiwan wind power sector case

For the Taiwan learning curve cost model for installing wind power, we consider the relation between cumulative capacity, the installation costs and other variables which may impact costs. The above-mentioned factors, except changes in input prices, are not easily quantiﬁed. Steel cost plays a key role on the increase or decrease in wind power installation costs. International oil prices also drive renewable energy demand. Thus, the global steel price index and the oil price are used as variables Z1 and Z2 in our

model. The reference installation cost (C, in the unit of€/kW) used in the research is based on the report published by theEuropean

Wind Energy Association (2009). Since offshore wind power has

not yet developed in Taiwan, we only use the historical data of onshore installation costs in the case study. The cumulative capacity and oil price from 2000 to 2010 was collected from the Taiwan Bureau of Energy (Bureau of Energy, 2011, 2012). The global steel index was sourced from the CRU (2012), which publishes annual data in mining, metals, and fertilizers. The global steel price index (Z1) and the oil price (Z2) are the inputs of level

2 model and Eq.(3)is expressed as follows:

ln C_{¼ lnβ}0þ γ0ln Xþ γ1Z1ln Xþ γ2Z2ln Xþ ln ε ð4Þ

we use PASW Statistic 18 (IBM, 2012) to estimate the parameters and the statistical report is shown inTable 2.

Table 2 shows that the relationship between wind power

installation costs and the accumulated wind power installed capacity is signiﬁcant and positive. The steel price has a signiﬁcant and positive effect, which interferes with the relationship between the cost of installing wind power and the accumulated installed

capacity. The oil price has a signiﬁcant but negative effect. Thus, decreasing oil prices strongly affects the relationship between the installation costs and the accumulated installed wind power capacities.

Progression rate (PR) explains the rate of the increase or decline in cost, determining the percentage of cost that will likely occur when cumulative capacity is doubled (Ibenholt, 2002). The PR is calculated using Eq.(5).

PR¼ 2α _ð5Þ

where α represents the learning index (α is equal to γ0 in this

study). Therefore, the learning index of Taiwan is 0.156 and PR is 111.4%. The value PR (¼111.4%) shows that the cost of installing wind power in Taiwan will increase 111.4% from the former level when the cumulative installed wind power capacity is doubled. 4.2. Comparison of learning curve models

The traditional basic model is compared with the hierarchical model since the basic learning curve model does not contain interfering and nesting effects. The basic learning curve only considers cumulative capacity X, which may inﬂuence the esti-mated learning index. The estiesti-mated basic cost learning curve is shown in Eq.(6).

ln C¼ 6:677 þ ð0:079Þln X ð6Þ

by comparing the costs estimated by the two models in a period of 10 years (2001–2010) with the actual installation costs, the results show that the hierarchical learning curve better describes the ﬂuctuation of costs.Fig. 3depicts the log values of costs (in€/kW) from 2001 to 2010 estimated by the basic model and the hierarchical model, with the corresponding real data as reference.

Table 3 indicates that the hierarchical model is a betterﬁt with

much higher values on both R2_{and adjusted R}2_{. The learning index}

for the basic model is 0.079 and the resulting PR is 105.6%.Table 4

shows the different learning indexes and PR values when using the hierarchical and basic learning curve models. The PR calculated using the hierarchical learning curve is higher than the basic

Table 2

The output table generated by PASW Statistic 18.

Model Coefﬁcient Standard error t

Intercept 6.475n _0.104 _62.461

Cumulative capacity 0.156n _0.049 _3.167 Steel price cumulative capacity 0.001nn _0.000 _2.446 Oil price cumulative capacity −0.003nn

0.001 −2.805 n_po0.001. nn_po0.05. 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 ln C

Basic model Hierarchical Model Real data Unit of C:€/kW Fig. 3. The costs estimated by the hierarchical and basic models, compared to historical costs.

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learning curve. If the basic cost learning curve is applied which considers the cumulative capacity as the only inﬂuencing factor, then the future wind power installation costs in Taiwan will likely be over projected.

4.3. Comparing the learning index and PR with other countries According to the research reports published byIbenholt (2002)

and ISET (2000), the progression rates (PRs) of the wind power

installations in Denmark, Germany and the United Kingdom are 92–93% (1984–1999), 92% (1990–1998), and 75% (1991–1999) respectively. A lower PR shows that doubling the cumulative capacity will decrease cost faster. The PR value of UK is the lowest among three countries, yet Denmark and Germany have no significant difference in the same period of time. For the renew-able energy development, the United Kingdom has adopted RPS as its policy. The tender system, which is used to set the price, enhances the competition between wind power generators and leads to installation cost reductions. However, according to some reports (Ibenholt, 2002), a lower PR value may also reflect the hampering of diffusion because of a competitive andfierce market. Unlike the United Kingdom, Denmark and Germany both use FIT as the renewable energy development policy which creates stable conditions for installing wind power generators and increases the cumulative capacity (Ibenholt, 2002). Taiwan's development of renewable energy has occurred much later in comparison to these three countries. Taiwan's government did not pass the Statute for Renewable Energy Development until 2009 and has only recently implemented FIT as its renewable energy development approach. With a less matured wind power market and a lower level of accumulated wind power capacity, Taiwan's PR (¼111.4%) repre-sents that the installation costs will increase to 111.4% of the previous costs if installation capacity is doubled. Taiwan has the highest PR comparing to the three countries since the market has not reached an equivalent scale of economy where the learning effect can impact the installation costs. In addition, due to an oligopoly in the Taiwan power generation market, the market is dominated by a small number of firms that cannot efficiently develop wind power and benefit fully from the learning effect.

5. Conclusions

Countries are actively developing renewable energy and wind power is one of the most potential sources of renewable energy. Previous studies constructed the level-1 basic (general) wind learning curve model, which biases the estimated learning index. This paper proposes a hierarchical cost learning curve model for wind power and uses the accumulated wind power installation in Taiwan as a case study. This study includes two price variables, the

steel price index and the oil price, to construct a hierarchical cost learning curve model for wind power. The research shows that both the steel price index and the oil price have signiﬁcant effects on the relationship between the wind power installation costs and accumulated wind power installation capacity. When the steel price index increases and the oil price decreases, then wind energy development is obstructed and policy makers must provide sub-sidies or raise wind tariffs to stimulate wind energy investment. In addition, by comparing the basic learning curve model, the cost estimated by the hierarchical model provides a better R2 _and

adjusted R2 _{and shows that the} _{ﬁtness of hierarchical learning}

curve is superior to the basic learning curve.

The present research uses the hierarchical cost learning curve model to explore the effects of steel and oil prices on the relationship between the installation costs of wind power facilities and accumulated wind power production. The research provides opportunities for researchers and policy makers to apply the advanced learning curve modeling techniques to the new areas of renewable energy sector, e.g., offshore wind, solar, geothermal heat, ocean tides, to provide reliable and effective strategic development and incentive plans.

Acknowledgments

This research is partially supported by the National Science Council and the Industrial Technology Research Institute in Taiwan. References

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Table 3 R2

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Adj. R2

80.6 64.4

Table 4

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