Optimization of Korean energy planning for sustainability considering uncertainties in learning rates and external factors

Energy 44 (2012) 126e134

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Optimization of Korean energy planning for sustainability considering uncertainties in learning rates and external factors Seunghyok Kim a, Jamin Koo a, Chang Jun Lee b, En Sup Yoon a, * a b

School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Seoul, Republic of Korea Samsung Corning Precision Materials Co., Ltd., Asan, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 August 2011 Received in revised form 20 February 2012 Accepted 26 February 2012 Available online 4 April 2012

During the last few decades, energy planning has focused on meeting domestic demand at lower total costs. However, global warming and the shared recognition of it have transformed the problem of energy planning into a more complex task with a greater number of issues to be considered. Since the key issue is to reduce greenhouse effects, governments around the world have begun to make investments in renewable energy systems (e.g., hydro, wind, solar, and/or biomass power). The relatively high costs of renewable energy systems and the uncertain outlook of their rate of diffusion in the market make it difficult to heavily rely on them. The uncertain variations in production cost over time are especially challenging. To handle uncertainties, the concept of the learning rate was adopted in this study so as to compute the costs of energy systems in the future and Monte Carlo simulation was performed. The aim of this study was to optimize plans of conventional and prospective renewable energy systems with respect to production cost. The production cost included capital, fixed, variable, and external costs. For the case study, the energy situation in South Korea was used. The results of the case study where the proposed methodology was applied could provide useful insights economically and strategies of sustainable energy management for ambiguous environments. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Energy planning Renewable energy Optimization Learning rate

1. Introduction Although many countries have struggled to decrease their consumption of energy, world consumption of fossil fuels in generating energy has continuously increasing at the rate of 2% per annum [1]. This continual increase has brought about the depletion of natural resources and the emissions of greenhouse gases, which has resulted in environmental problems, including greenhouse effect. By the Kyoto Protocol, Intergovernmental Panel on Climate Change (IPCC) and Copenhagen climate change conference (COP15), many nations have been required to comply with environmental regulations, especially the reduction of CO2 emissions [2]. Thus renewable energy sources such as hydro, wind, solar and biomass energy have emerged and technologies related to renewable energy systems have been developed. Recently a number of organizations have begun to consider renewable energy systems and their industries as opportunities rather than regulations [3,4]. Korea is no exception; government and companies in Korea have put effort into promoting green technologies [5].

* Corresponding author. E-mail address: [email protected] (E.S. Yoon). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.02.062

Despite the awareness of renewable energy grows, renewable energy systems make up averagely 7e8% of the entire energy supply in Europe [6], and only 2.2% in Korea [5]. The reasons are that the efficiencies of renewable energy systems are still lower than that of conventional energy systems, and the discontinuity of generation can be occurred. Since the availability of renewable energy sources should be broadened to reduce the emissions of greenhouse gases, it is essential that the planning of energy systems be optimized considering multiple constraints that include satisfying energy demands, minimizing production cost and meeting the required and/or permitted greenhouse gas emission levels [7,8]. Previously, a number of methodologies and schemes for energy planning have been studied and proposed for optimal energy planning. In terms of models, schemes have been introduced by the time-stepped energy system optimization model (TESOM) [9], market allocation model (MARKAL) [10e12], energy flow optimization model (EFOM) [7], and inexact community-scale energy model (ICS-EM) [13]. Each model reflects its own characteristics and optimization techniques but does not incorporate recent changes in nature of renewable energy planning, and overall energy sources in large scale. Krukanont considered various uncertainties to analyze the near-term energy planning and suggested several policy regimes but covered limited renewable

S. Kim et al. / Energy 44 (2012) 126e134

energy systems [14]. Evaluating feasibility various renewable energy systems have also been introduced. Viebahn compared costs and the contributions of carbon capture and storage (CCS) technologies and renewable energy systems in the long-term [15]. Chatzimouratidis and Kaya evaluated some energy systems under several criteria with weights obtained by an analytical hierarchy process (AHP) [16,17]. Krey incorporated uncertain energy prices into energy systems by including a stochastic risk function [18]. Similarly, Streimikiene conducted a long-term assessment of new electricity generation technologies for CO2 price scenarios [19], and Koo studied scenario-based economic evaluation of renewable energy systems considering carbon capture and storage (CCS) and varying fuel prices [2]. Despite the recent works, energy planning needs to reflect the integration in terms of uncertainties in prices of fuel price for energy generation, expansion of carbon dioxide trading, and change of learning rates with various models to obtain optimal solution, because the governments which are interested in energy planning want to evaluate energy systems in many ways for robustness. While some previous works provided estimates of variables separately [20,21], we suggest that the proposed method should apply the future prospects on cost and learning effect. Based on the previous works, a modified model can be introduced with supplementary information. The supplementary information discussed in the proposed method includes not only cost estimates at the present level but also prospects for the future. The uncertainties in the future situations will be considered with respect to the types of energy systems, and the proposed method presents several major uncertainties related to energy systems e the learning rate of the technologies, fuel prices, and carbon prices. The major uncertainties will affect the competitiveness of energy systems. The effects of learning rate and prices of an energy system may be unique attributes; we cannot anticipate exactly [22e24]. Thus, we have to estimate the unpredictable values. This study aims to integrate various uncertainties in growth rate scenarios and apply Monte Carlo simulation for handling uncertainties. The proposed method constructs the production and CO2 emission trading costs as an objective function, which allows for economic evaluation of conventional and renewable energy systems taking into consideration the uncertainties. As a result, the optimal capacities of energy systems to be added can be obtained. The rest of this paper is organized as follows. In Section 2, the brief descriptions on the problem, learning rates, and other uncertainties are provided. Section 3 presents the proposed model including the objective function and constraints. Section 4 discusses the results of the proposed method applied to a Korean case. Section 5 concludes this study. 2. Model formulation The model is defined to reflect the integration of uncertainties in this section. As mentioned, the previous model needs to be modified by the supplementary information such as learning rate and prices. That makes our model consider the prospect for the future as well as estimation at the present level. The uncertainties are considered by Monte Carlo simulation to achieve robust optimization. Since the using of random input from sampling turns the model into a stochastic model, the inclusion of uncertainties would be reflected to decision-making that decides which energy system should be installed.

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optimize energy planning that included renewable energy systems. According to the method commonly practiced for economic evaluation, the total cost of the production can be expressed as the summation of the capital, fixed, variable, and external costs. Each cost can be calculated as follows [2,7,25,26]. Nt X

Capital cost ¼

Fixed cost ¼

Nt X

Variable cost ¼

External cost ¼

In this study, energy system refers to power plants that generate electricity using a certain energy source. The aim of this study was to evaluate the production costs of possible energy supplies and

KCIt

þ dÞt

1

t t ¼ 1 ð1 þ dÞ Nt X

KFCt

1

t t ¼ 1 ð1 þ dÞ Nt X

1

t t ¼ 1 ð1 þ dÞ

(1)

(2)

Ct PFt rs

(3)

Ct PCt Rs

(4)

where Nt denotes the total years from 2011 to 2030; d is the discount rate; KC is the initial unit capital cost of the energy system; It is the capacity of the energy system installed in year t; KF is the unit fixed cost of the energy system in 2011; here, the unit fixed cost includes the operation and maintenance cost that are not dependent on the capacities. Ct is the cumulative capacity of the energy system in year t. Variable cost refers to expenses that change in proportion to the activity of a business; here, we assumed that the variable cost is limited to buying fuel. Thus, the variable cost is dependent on fuel price only, and PFt is the required fuel price to operate the energy system in year t; r is the conversion ratio from the TOE to the MWh; s is the capacity factor for the energy system, which represents the fraction of actual output produced over the maximum output achievable during a period of time. Lastly PCt is carbon price in year t; R is the emission rate with capacity Ct for the energy system. 2.2. Learning effects The basic concept of learning is cost reductions as the result of learning-by-doing. It means that the performance improves as capacity or a product expands [22]. Learning can also be regarded as the cost-reducing effect in each energy system that might be used in economics to describe improvement in productivity [27]. The learning process can also be seen as a fundamental human characteristic. A person engaged in a task will improve his/her performance with experience and technological development. Many studies present that the cost reduction is dependent on the industry, region, and time. Especially for renewable system, empirical studies show that learning is influenced by cumulative capacity, Ct [27,28]. The cumulative capacity can be defined as following equation.

Ct ¼ C0 þ

Nt X

It

(5)

t¼1

Reflecting the concept of learning effect, the total cost of each energy system over its life time can be modified as following equation.

Total cost ¼

" Nt X t ¼1

2.1. Definition of production costs

1

t ¼ 1 ð1

1 ð1 þ dÞt #

þ PCt Rst Þ



 Ct at ðKCIt Þ þ Ct ðKF þ PFt rst C0 (6)

C0 stands for the initial capacity at the base year, at corresponds to learning effect term at year t. The learning effect is restricted to

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S. Kim et al. / Energy 44 (2012) 126e134

capital since the fixed, variable, and external costs do not depend on factors of experiences: the prices of fuel do not decrease with accumulated capacity, and the emission rate is assumed to remain unchanged throughout the studied period. And ae,t depends on the particular energy system of interest, and can be expressed by following equation [25].

ae;t

Table 2 Mean and standard deviation of fuel prices for electricity generation of each energy sources [$/MWh].

Mean Std.

Coal

Oil

Natural gas

Nuclear

Hydro

Wind

Solar

Biomass

28 3

49 5

39 5

13 1

0a 0

0a 0

0a 0

24 5

a In hydro, wind, solar power, fuel price for electricity generation is assumed to be zero.

  be;t ln 1  100 ¼ ln2

(7)

Here, be,t indicates the learning rate for the energy system of interest each at time t. Reliable estimates of learning rate are important if meaningful projections of cost reduction are to be sought under the application of the learning effect [27]. Here, a dispute may occur; the differences between regional and global learning rates. Although the regional learning rate may not be same as the global learning rate, Korean effort can reflect the global movement to some degree because Korea is one of the countries that a lot of researches have been done in various energy systems. Thus, we assume that the regional learning rate is same as the global learning rate in this case. We are to adopt the learning rates from previous works [27,28]. For the reliable estimation of learning rate, the value is sampled using by Monte Carlo method and reestimated every year. The method requires a model in order to use properly, and we adopt Eq. (7) instead of modeling the learning curves from the complicated techniques, Although many studies analyzing learning curves and/or learning rates have been done; these studies are profound and have a massive amount of information, in this study, the detailed theories on the prediction and estimation of learning curves for various energy systems have been omitted for the sake of brevity. If readers are interested in those works, the readers can refer to following works [29]. The mean and standard deviation values for Monte Carlo simulation in this study can be adopted by [25,30e33] (Table 1).

evaluation will be represented as histograms. Also we can see the distribution of values of feasible total cost, and the result can offer more reliable implications in the uncertain future. 3. Mathematical programming of the proposed model 3.1. Structure of the problem Fig. 1 shows the structure of the problem for the proposed methodology based on previous works [13,25]. Although there are many renewable energy sources, which have been developed in Korea, it is assumed that four representative and potential ones will be adopted in this paper. The generated energy is utilized by industries, transportation, residences, commerce, and public use. In addition, we assume that there will be emission allowance trading with foreign countries. 3.2. Objective function The objective function for the proposed model can be expressed as the sum of the modified cost functions as described in Section 2. The CO2 trading term is added.

min Total cost ¼

2.3. Fuel and carbon prices for handling uncertainties As mentioned, the uncertain variables to be treated are the fuel prices and the carbon cost besides learning rates. The fuel price (Table 2) and the carbon cost (Table 3) are generated by Monte Carlo sampling [34,35]. These values are renewed every year in the same way as learning rate. 2.4. Monte Carlo simulation Monte Carlo simulation is a method for iteratively evaluating a deterministic model using sets of random numbers as inputs and for analyzing uncertainty propagation. The goal is to determine how random variation and lack of knowledge of the system are modeled. Since the learning rate, fuel price, and carbon cost are hard to model accurately, this method can be an efficient approach to estimate uncertain variables stated in this study [36,37]. The key to Monte Carlo method is generating the set of random inputs, which are uncertain variables in this study [38]. The uncertain variables are assumed to follow normal distribution. Related values are listed in Tables 1e3 All values of each energy system are updated every year t. The number of the generated sample and function evaluation are set as 10,000. The results generated from the Table 1 Mean and standard deviation of learning rates of energy systems (%).

Mean Std.

  Ce;t ae;t  KCe Ie;t þ Ce;t ðKFe t C e;0 e¼1 t ¼1 ð1 þ dÞ   þ PFe;t rse þ PCt Re se  PCt VTt Ne X Nt X

1



Ie;t ¼ argmin ðTotal costÞ

(8)

ce;t

The subscript e indicates the type of energy sources. In Eq. (8), Ne indicates 8 (1: coal, 2: oil, 3: natural gas, 4: nuclear power, 5: hydro power, 6: wind power, 7: solar, and 8: biomass). Ce,0 denotes the initial capacity of each energy system. VTt is the amount of CO2 emissions treated in year t. At this point, the objective function is formulated as a nonlinear optimization because the learning effect term is nonlinear. And the uncertain variables such as learning effect (ae,t), fuel price (PFe,t), and CO2 cost (PCe,t) are sampled using by Monte Carlo simulation. Then the sampled values are applied to objective function, and the optimization results reflect a robust handling of uncertainties. 3.3. Constraints 3.3.1. Size limits on renewable energy sources Renewable energy systems like hydro, wind, and solar energy cannot be constructed infinitely. Thus the size limit, SLe, is set for the potential of the renewable energy sources. Since the biomass

Table 3 Mean and standard deviation of CO2 prices ($/tCO2).

Coal

Oil

Natural gas

Nuclear

Hydro

Wind

Solar

Biomass

6.25 2.4

2.5 1.5

10.6 9.2

5.9 0.1

3.8 1.9

13.1 5.2

28.2 6.6

15 0.3

CO2 price Mean Standard deviation

48.7 8.9

S. Kim et al. / Energy 44 (2012) 126e134

129

Foreign Systems CO2 emission trade Energy Sources

Main Electricity Usage

Users

Lighting

Industry

Coal

Conventional Energy Sources

Oil Natural Gas

Transport Nuclear power

Air Conditioning & Heating

Hydro power

Renewable Energy Sources

Residence & Commerce

Wind power

Others

Solar power

Public & Etc. Biomass Fig. 1. Structure of the proposed model.

Table 4 The values of energy demand, growth rate, level of energy target, loss factor and discount rate.

Industry Transport Residence & Commerce Public & etc.

Energy demand [TOE]

Energy growth rate

Energy supply target level

Loss factor

Discount rate

47,081,000 196,000 36,547,000

0.01 (Low) 0.02 (Normal) 0.03 (High)

1.1

0.06

0.05

Energy Capital Fixed cost CO2 emission Initial Size limit Capacity sources cost [$/MW] [$/MW] rate [t/MW] capacity [MW] factor [h] [MW]

4,084,000

can usually be derived from timber, agriculture, and food processing waste; thus we need not restrict the size of this energy system. Eq. (9) indicates the size limits of each energy system.

P

Nt P

hydro t ¼ 1 Nt P P wind t ¼ 1 Nt P P solar t ¼ 1

Table 6 The values of capital cost, emission rate, initial capacity, size limit and capacity factor.

Coal Oil Natural Gas Nuclear Hydro Wind Solar Biomass

1,218,750 603,750 765,000

237.5 78 125

1965 1496 1154

18,678 6128 10,049

e e e

6132 6132 6132

1,987,500 3,029,000 1,567,000 5,223,000 2,089,000

375 910 310 210 760

631 234 127 57 793

17,932 351 50 32 e

e 1709 1408.4 127,392 e

6132 4380 1314 1314 4380

Nt Xn Ne X Nt  o X X jr ð1 þ kÞCe;t se;t ð1 þ gÞt VDuser;t 

Ie;t þ Chydro;0  SLhydro

t ¼ 1 user

Ie;t þ Cwind;0  SLwind

(9)

Ie;t þ Csolar;0  SLsolar

The value of SLe is based on the natural and technological conditions of the particular geographic region of interest such as Korea. 3.3.2. Energy demand The energy planning should be able to satisfy the energy demand.

) (10)

e¼1 t ¼1

In Eq. (10), VDuser,t denotes the energy demand from each user. To estimate the future energy demand, g and j are introduced. g indicates the energy demand growth rate and j the level of energy supply target. In this study, three scenarios of demand growth rate are applied to cover the energy fluctuation. Additionally, the level of energy supply target can be regarded as a buffer [2]. j is determined as 1.1, which means 10% buffer of target in this study. In right-hand side,k denotes the loss factor, mainly due to the transmission loss and internal use of electricity in the energy systems. Those values for case study are shown in Table 4 [39,40]. Each energy demand values are based on the Korean case.

Table 5 Estimated target amount of CO2 emission from 2011 to 2030 [Mt]. t

2011

2012

2013

2014

2015

2016

2017

2018

2019

2020

ETt

289

281.2

273.4

265.6

257.8

250.0

242.2

234.4

226.6

218.8

t

2021

2022

2023

2024

2025

2026

2027

2028

2029

2030

ETt

211.0

203.2

195.4

187.6

179.8

172.0

164.2

156.4

148.6

140.0

130

S. Kim et al. / Energy 44 (2012) 126e134

Fig. 2. Result of Monte Carlo sampling: (a) the fluctuation of average total cost and (b) the distribution of total cost.

S. Kim et al. / Energy 44 (2012) 126e134

The Korean government seeks to rely less on fossil fuels in supplying the necessary energy by expanding the renewable energy portfolio to 11 percent by 2030 [39,41]. Thus the lower limit of the energy supplied by renewable energy systems should be considered as follows. Nt 8 X X

! Ie;t þ Ce;0

 se;t  0:11 

e¼5 t¼1

Ne X Nt X

! Ie;t þ Ce;0

 se;t

e¼1 t¼1

(11) 3.3.3. CO2 emissions trading In external cost, there is a term, VTt, which is the amount of CO2 emissions traded. CO2 may be tradable to achieve the CO2 emission target. A positive value of VTt value implies that the amount of CO2 emitted is lower than the target level; it allows the government to sell and the total cost can be reduced. Conversely, a negative VTt, which means CO2 emission is not satisfied with the target can increase the total cost.

VTt ¼ ETt 

Ne  X  Ce;t Re se ; ct

(12)

e¼1

ETt indicates the emission target in year t. Some researches were studied CO2 emission in various scenarios [42e45] but, in this study, the value of the emission target by 2030 can be obtained in reports prepared by the Korean Ministry of Knowledge and Economy [39]. It is assumed that the value for each year is calculated with linear interpolation for simplicity. Table 5 shows the values. 4. Case study 4.1. Case description Korea has been a big importer of fossil fuels. Its dependency on overseas energy sources is about 97%, ranking fourth in global petroleum import. Since Korea imports raw materials and reexports high value-added products, the dependency on energy sources is inevitable for consecutive growth. Due to the consecutive growth, the amount of fuel for domestic uses is increasing and

131

national annual average temperature has continued to grow. Hence Korean government has the interest in CO2 emission reduction as well as renewable energy systems. Consequently a strategy for energy planning will be crucial for the Korean energy supply and demand balance. In this section, the proposed model is applied to the Korean energy situation, and the results show the applicability and effectiveness of the proposed model. The exemplary case is based on data related to Korean energy situations [30]. In addition to the aforementioned data listed in Tables 1e5, the additional data for solving the problem are shown in Table 6. The values can be obtained by many sources [39,46e49]. The capacity factor may vary with many disturbances, but the values are determined as constant in this study. 4.2. Results and discussion According to the Monte Carlo simulation, the total costs are around 1.887  1011, 2.557  1011, and 3.647  1011 [$] through scenarios. The dispersed total costs indicate that the uncertain variables, especially CO2 emission cost and learning rate, have a considerable impact on total cost (Fig. 2). A considerable portion of total cost distribution is within 5% and 95% confidence intervals. Also, we can see how sensitive the uncertain variables are to total cost using Monte Carlo simulation. Among three uncertain variables, two variables are fixed and the one variable is to be perturbed. In this way, the sensitivity of each uncertain variable can be obtained (Fig. 3). The number of the generated sample and function evaluation were set as 1000. In this figure, each standard variation of results is 1.612  107, 2.036  108, and 1.766  105. It indicates that the fluctuation of carbon price contributes considerably to that of the total cost. It will be helpful to interpret the results. Since the carbon price is the most sensitive parameter, a decision maker should monitor the fluctuation of carbon price for installation of energy systems; if the carbon price is stable, the decision of installation can be made more reliably and not be affected by fluctuation. However, the carbon price applies to all over the energy systems as an independent term. The learning rate should be interpreted as an essential factor having a characteristic of each energy system for reliable solution. The solutions of the case study, which were the capacities of each energy system to be added over the specified periods, are

Fig. 3. Sensitivity analysis of each uncertain variable.

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S. Kim et al. / Energy 44 (2012) 126e134

Table 7 The mean values of added capacities of energy sources [MW]. Coal, oil, natural gas

Nuclear

Energy growth rate

La

Na

Ha

L

N

H

L

N

H

L

N

H

L

N

H

L

2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 Added capacity

e e e e e e e e e e e e e e e e e e e e e

e e e e e e e e e e e e e e e e e e e e e

e e e e e e e e e e e e e e e e e e e e e

4281.5 574.1 579.8 e 591.5 e e e e e e e 640.5 e 653.3 307.8 e e 580.3 e 8208.7

4849.9 1159.5 1182.7 1206.3 1230.5 e e e e e e e e e e 1529.9 1560.5 139.1 1623.6 1656.0 16138

5418.3 1756.3 1809.0 1863.2 1919.1 e e e e e e e e e e 2656.5 2736.2 1365.7 2902.9

e e e e e e e e e e e e e e e e 784.1

22427

784.1

e e e e e e e e e e e e e e e e e 1709 e e 1709

e e e e e e e e e e e e e e e e e 1709 e e 1709

e e e e e e e e e e e e e e e 1408.4 e e e e 1408.4

e e e e e e e e e e e e e e e e e e e e e

e e e e e e e e e e e e e e e e e e e 1408.4 1408.4

e e e e e e e e e e e e e 2587.5 e e e e e e 2587.5

e e e e e e e e e e e e e e e e e e e e e

e e e e e e e e e e e e e e e e e e e 10551.4 10551.4

e e e 688.9 e 702.8 709.8 716.9 724.1 731.3 738.6 746.0 e e e e e 791.9 e e 6550.4

a

Hydro

Wind

Solar

Biomass N

e e e e e 1476.5 1506.1 1536.2 1566.9 1598.3 1630.2 1662.8 1696.1 1730.0 1764.6

16,167.7

H

e e e e e 2325.5 2395.3 2467.2 2541.2 2617.4 2695.9 2776.8 2860.1 2945.9 3034.3 e e e e e 26,659.7

L: Low, N: Normal, H: High energy grow rate.

shown in Table 7. The mean values of capacities of energy system are listed. The result indicates that nuclear, solar, and biomass energy system should be mainly installed until 2030 while all conventional energy systems need no longer to be installed. Though some novel technologies such as Integrated Gasification Combined Cycle (IGCC), Integrated Gasification Fuel Cell (IGFC), and Advanced Ultra Supercritical power plant are emerging, these are confined to retrofitting conventional energy systems, and will not affect the cost reduction of new construction favorably. This study accounts for newly added capacities of energy sources. This study conducts the economic evaluation using three scenarios, including CO2 emission trading. In the case with a low

energy demand growth rate, nuclear energy with 12583 MW, biomass energy with 3598 MW, and solar energy with 8931 MW should be added in the order of the added capacity. In the normal growth rate case, nuclear energy with 32088 MW, solar energy with 11040 MW, and biomass energy with 2413 MW will minimize the total cost while satisfying the energy demand and meeting the target emission reduction scheme. Lastly, in the high growth rate case, nuclear energy with 48,149 MW, biomass energy with 15,177 MW, and solar energy with 12,739 MW should be added. Fig. 4 indicates nuclear energy will play an important role when the energy demand increases. Overall the nuclear, solar, and biomass

35000.0 60000.0

50000.0

Nuclear Hydro Wind Solar Biomass

Low case Normal case High case

30000.0 25000.0

40000.0

20000.0 30000.0

15000.0 10000.0

20000.0

5000.0

10000.0

0.0 0.0 Low case

Normal case

Fig. 4. The amount to be added in each scenario.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

High case Fig. 5. Cumulative capacities of renewable energy systems (hydro, wind, solar, and biomass energy).

S. Kim et al. / Energy 44 (2012) 126e134

133

Fig. 6. The proportion of energy sources in 2011 and 2030.

energy will make considerable contributions to the energy supply in the future due to their being not affected by uncertain fuel and carbon prices; although they have high capital and fixed cost, they seem to be enough to compensate. On the other hand, the conventional energy systems are unfavorable to be added because they are more sensitive to learning rate and CO2 emission cost. The hydro and wind energy have disadvantages in terms of size limit and energy efficiency as well as learning rate despite they are advantageous to CO2 emission. There may be some opinions on the contribution of nuclear energy system; it may sound absurd that high security risk inherent in nuclear energy should be endured. But Korea relies on imports for 97% of the energy sources and above 30% of the total electricity generation is dependent on a nuclear power already. Thus Korean government reported that it would not change the nuclear energy policy which plans constructions of twelve new nuclear power plants [48]. The matters of security and risk should be viewed from a different standpoint. It is shown that the solar energy can play a role in the future by virtue of its high learning rate and low CO2 emission; since the hydro and wind energy have strict size limit, they are not selected. From the model equations, we can see that the learning effect term is crucial in lowering the capital and fixed costs of energy systems. Thus, it implies that keeping the conditions that are exogenous to learning effect high is required. Allocating more budgets in R&D and strengthening the knowledge stock may support in successful reduction of capital and fixed costs via learning effects. And the low amount of CO2 emission will bring about the stable cost variation of installation. This may offer the reliable strategy for decision makers. Lastly, a few valuable and optimistic insights can be obtained. It is shown that the cumulative capacities of renewable energy systems are increasing gradually (Fig. 5). Fig. 6 shows the proportion of the energy systems in 2011 and 2030. While the proportion of renewable energy sources in 2011 is just 0.9% in the total supply, it increases to about 16.5%, 13.7% and 22.9% in the case of low, normal, and high energy growth rate. As the amount of energy

demand increases, renewable energy systems will be a solution to satisfy the abatement of CO2 emission. This satisfies one of the goals of the Korean National Energy Plan, which is to make renewable energy sources provide at least 11% of the total energy supply by the year 2030 [50]. 5. Conclusions In this paper, a method for evaluating costs of energy systems including CO2 trading was proposed and applied to Korean energy situation. The proposed method presented the optimization taking into consideration the uncertainties in the learning rates and external factors such as fuel and CO2 prices. To handle uncertainties, Monte Carlo simulation was performed; the method can be one of useful methods to estimate unpredictable variables instead of complicate analysis. The concept of the learning effect was introduced to provide the cost reduction of capital cost of the energy systems. Fuel price and CO2 emission cost were defined as the variable and external cost in the future, and the possibility of CO2 trading was considered as one of the external factors. For robustness, three representative future scenarios in energy growth rate were adopted, and the randomly sampled learning rates, fuel price, and CO2 emission cost were applied. In applying the method to a Korean case, several economic factors were determined as deterministic values. The results of the case study provide several directions for Korean energy planning. The results imply that renewable energy systems, especially solar and biomass energy, are essential for satisfying the increasing energy demand in the future. From the sensitivity analysis of the uncertain variables, being unaffected by volatilities in carbon price and having a high learning rate allow energy systems to be installed over the next two decades. Because the results reflect the realistic Korean energy situation and satisfy the official target of the renewable energy system, it can be of value to decision makers who are planning energy system. Based on the proposed method, a decision maker can improve the model through supplementary information and more realistic data.

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Acknowledgments This work was supported by Brain Korea 21 Program (BK21) and Automation and Systems Research Institute (ASRI) at Seoul National University. Nomenclature Symbols total years (2011e2030) [y] Nt d discount rate [e] C cumulative capacity [MW] a learning effect [e] KC capital cost [$/MW] I installed capacity KF fixed cost [$/MW] PF fuel price [$] r conversion ratio from TOE to MWh [e] s capacity factor [h] PC CO2 price [$/tCO2] R emission rate [t/MW] VT amount of CO2 emission [t] b learning rate [e] SL size limit [MW] j level of energy supply target [e] g energy demand growth rate [e] k loss factor of [e] VD energy demand [TOE] ET CO2 emission target [t]

[16]

[17]

[18] [19]

[20] [21] [22]

[23]

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