A superstructure model of an isolated power supply system using renewable energy: Development and application to Jeju Island, Korea

Renewable Energy 97 (2016) 177e188

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A superstructure model of an isolated power supply system using renewable energy: Development and application to Jeju Island, Korea Sunghoon Kwon a, 1, Wangyun Won b, 1, Jiyong Kim a, * a b

Department of Energy & Chemical Engineering, Incheon National University, 119, Academy-ro, Yeonsu-gu, Incheon, 406-772, Republic of Korea Plant Research Team, GS Engineering & Construction, 33, Jong-ro, Jongno-gu, Seoul, 110-121, 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 24 August 2015 Received in revised form 29 November 2015 Accepted 19 May 2016

In this study, we aim to develop a superstructure-based optimization model using mixed integer linear programming (MILP) to determine the optimal combination and sizing for a hybrid renewable energy system to be used in an isolated area. The developed model has a three-layered energy structure to reflect the current reality in which energy production and consumption sites are generally separate. A variety of economic factors, including distance between facilities and an installation area, are considered for a more accurate estimation of the total annualized cost. Two types of optimization models, i.e., with and without a battery, are proposed to evaluate the economic and technical effects of a storage device to resolve operation issues caused by intermittent resources. An application case study on Jeju Island, Korea, confirms that the proposed model is suitable for decision making at the planning stage of a renewable energy system. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Renewable energy Optimization Power supply Hybrid energy Sensitivity analysis

1. Introduction The demand for electricity has steadily increased with the growing global economy [1]. Current power production systems rely heavily on fossil fuel, which results in air pollution problems, including greenhouse gas emissions. A wide range of studies have been conducted to address this problem [2], but for a more radical approach, it is essential to develop new energy resources as alternatives to conventional fuel sources and their corresponding energy systems. In particular, renewable energy sources (RES) such as wind and solar radiation have drawn substantial attention as viable options for power production due to their clean properties and high practicability for improving technologies [3,4]. While renewable energy systems provide various advantages, including being eco-friendly and offering a high probability for energy self-sufficiency, the current costs of such systems prevent widespread deployment and, thus, research and development efforts are concentrated on accelerated cost reductions and efficiency improvements [5]. Because the design of a RES-based power supply system involves a number of complicated parameters such as energy resources (e.g., wind, solar, biomass, geothermal), backup

* Corresponding author. E-mail address: [email protected] (J. Kim). 1 S. Kwon and W. Won contributed equally to this work. http://dx.doi.org/10.1016/j.renene.2016.05.074 0960-1481/© 2016 Elsevier Ltd. All rights reserved.

energy systems (e.g., fuel cell, battery, diesel generator), and power conditioning units (e.g., buck/boost converters, battery chargers), numerical modeling and optimization studies can play a crucial role in discovering a new configuration that ensures minimal cost while satisfying the electricity demand [6]. The most popular issues being investigated include integration of RES in a suitable hybrid combination [7e11], optimal selection [12e14], and sizing [15e18] of components. The majority of research reported to-date is somewhat restricted in terms of applicability because it concerns a given location and a specific environmental condition for model development [19]. At the planning stage of RES systems, it is necessary to make an enterprise-level decision on the following important issues: (i) where to install the generation equipment, (ii) what type or what combination of RES should be adopted, and (iii) how many and how large capacity of equipment should be used. To this end, a generalized optimization model is required that can embrace a variety of RES and diverse costs occurred during power supply, including power transmission costs, land reclamation costs, as well as equipment costs. This model should be able to accommodate the fact that commercial equipment is generally provided in an off-theshelf form. Accordingly, the focus of this study has been devising a superstructure-based optimization model of a RES-based power supply system and investigating its performance in an application

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on Jeju Island, Korea. The key feature is the three-layered energy structure that considers the geographical nature of an isolated area. The proposed model can embrace the various types of energy resources and is also able to consider a diversity of economic factors, including distance between production and demand sites and installation area, when calculating the total annualized cost. Two types of optimization models are devised to evaluate the energy storage device in techno-economic analysis, together with power generation equipment. The performance of the developed model is validated through application on Jeju Island. In the case study, the combination of wind turbine and battery results in the lowest cost by benefitting from centralized distribution and efficient utilization of electricity. 2. Optimal design of the power supply system 2.1. Three-layered power supply system Because the RES potentials differ from region to region, the electricity production site may not coincide with the demand area. The three-layered power supply system is depicted in a generalized form in Fig. 1. The supply site (SS) indicates a location with high RES potentials and is assumed to be dedicated to producing electricity without any consumption. The SS makes up an extensive area, and therefore the power generation equipment can be spatially installed throughout the site without limit. The demand site (DS) represents the major power-consuming area. The DS can also produce some electricity via self-generation, but, unlike the SS, the amount of generation is restricted due to spatial limitations. Any extra space, such as building rooftops, is assumed to be utilized for equipment installation, and hence land reclamation is not required in this area [20]. The main facility (MF) is an intermediate facility between the SS and a secondary facility (SF) and can contain energy storage devices. The SS, MF, and SF constitute an energy network. The power shortfall of the MF and SF can be supplemented from the SS and connected MF, respectively. Because the existing power lines are used for the electricity transmission from the SS to MF, no additional cost is required. However, for electric transmission between the MF and SF, new power lines should be installed, and commensurate expenses are incurred if the additional lines are

requested. 2.2. Formulation This section provides the specific formulations of the objective function and constraints that correspond to the three-layered power supply system illustrated in Fig. 1. The developed model utilizes a mixed-integer linear programming (MILP)-based superstructure, as shown in Fig. 2, and calculates the electricity that could be provided to each region and the associated costs according to the location, type, and amount of technological equipment. The optimization model without an energy storage device is first presented, and then correction is made for the case with a storage device. In the following equations, the set or subset for a subscript is generally omitted for simplicity except for the subscript i, which represents the equipment type as it is used for both of the general sets, i.e., I, and its subsets, i.e. IP, IB, IT, and IPB. All of the symbols in the subsequent sections are defined in the Nomenclature section. 2.2.1. Objective function The RES-based optimal power supply system can be identified by minimizing the total annual cost (TAC), which is defined as the sum of total investment cost (TIC) and total operating cost (TOC) for one year, such that

min TAC ¼ TIC þ TOC

(1)

q

where q is a decision variable vector that includes the type and the number of equipment installed in the considered regions as well as the connectivity between the MFs and SFs. TIC and TOC are defined in Eqs. (2) and (6), respectively.

TIC ¼ ICP þ ICT

(2)

ICP and ICT are the investment costs associated with power generation and transmission, respectively, which are written as Eqs. (3) and (4).

ICP ¼

XX g

  CRFi $Ni;g $ ECi þ ICi þ LCi;g ;

i2IPB

(3)

i

where CRFi is a capital recovery factor multiplied to the expenses of power generation equipment i, and Ni,g indicates the number of the

Fig. 1. Three-layered power supply system.

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Fig. 2. Superstructure model of the RES-based power supply system.

equipment i installed in the region g. ECi and ICi represent the equipment and installation costs, respectively, and LCi,g is the land reclamation cost for power generation use, which the value is zero for DS and is non-zero for SS as aforementioned in Section 2.1.

ICT ¼ CRFi $

XX m

Xm/c $Lm/c $TC;

i2IT

(4)

c

where Xm/c is the binary variable that represents the connectivity between MF and SF, and Lm/c indicates the distance between the two above-mentioned facilities in the same administrative district. TC indicates the cost required for the electricity transmission. CRFi multiplied in Eqs. (3) and (4) is to consider only the value actually dissipated at present time by depreciation out of the capital initially invested for the equipment i such that

CRFi ¼

rð1 þ rÞni ; ð1 þ rÞni  1

i2I

(5)

XX g

i

OCi $

2.2.2.1. Energy balance without storage device The energy balance in SS can be written as below

XX s

where r is an interest rate, and ni indicates a lifetime of equipment i [21]. TOC in Eq. (1) includes a variety of costs that are needed to maintain the equipment such as labor and cleaning up costs, etc., and is written as

TOC ¼

2.2.2. Constraints In this section, the constraints that should be satisfied when solving the optimization problem are presented. The energy balances related to power generation, demand, and transmission that should be met at each region are presented first for the case without electric power storing system (battery technology, BT), and then some additional equations and changes in the previously presented balances are discussed for the case that takes the BT into account as a viable option in designing the power system. Several constraints that are modeled to take the assumption described in Section 2.1, e.g. area limitation, direction of electricity flow, etc. are also provided in detail.

X

! Ei;g;t ;

i2IPB

(6)

t

where OCi represents an operating cost of equipment i per unit amount of electricity. The time integration is expressed in a discrete-time form as all the energy is calculated in an hourly manner in this paper e the energy is assumed to be constant for the intermission between every hours.

i

Ei;s;t ¼

XX s

Es/m;t ;

i2IP ;

ct

(7)

m

where Ei,s,t is the amount of electricity produced at time t by using the power generator i installed in SS, and Es/m,t indicates the quantity of electricity that transmitted from SS to MF at time t. Therefore, the left-hand and right-hand sides of the above equation means the total amount of electricity produced at time t at all SSs and the total quantity of power that transmitted from all SSs to MFs at time t, respectively. As aforementioned in Section 2.1, the SSs do not have the power-consuming equipment, and thus all the produced energy should be transported to the MFs. It should be noted that the energy balance in Eq. (7) is expressed in a general form that has multiple SSs so as to be easily utilized and applied to the various off-grid actual circumstances. The energy balance for the MF region without BT can be written as follow:

180

X

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Es/m;t þ

s

X

Ei;m;t  Dm;t þ

X

Em/c;t ;

i2IP ;

U min $

cm; t

c

i

X

BR Ni;m $Si;m;t  Em;t

i

 U max $

(8) In this equation, the left-hand side represents the amount of electricity that is available at a specific MF m, which is the sum of two energy terms e the first represents the energy provided from SSs at time t, and the other one indicates the self-generated energy using the generators equipped in the facility m at time t. The righthand side indicates the amount of power required for the MF m at time t and is composed of two terms, including the self-consumed energy at the facility m at time t and the transmitted energy to the subordinate SFs c at time t. By Eq. (8), the quantity of energy available at the MF m is always greater than or equal to that of the requirement. The following equation represents the energy balance that should be satisfied at each SF region.

Em/c;t þ

X

Ei;c;t  Dc;t ;

i2IP ;

cc; t

(9)

i

The left-hand side of Eq. (9) represents the energy available at the SF c and is written as the sum of two energy terms, i.e. the electricity supplied at time t from the MF m that belongs to the same DS region and the electricity that is self-generated at time t by using all power generation equipment of the SF c. The right-hand side indicates the power demand of the SF c at time t. According to Eq. (9), the available energy of each SF should be greater than or equal to the consumed one, as in MFs. The amount of energy produced by the equipment type i at the region g, i.e. Ei,g,t, is always less than or equal to their maximum capacity, which can be calculated by multiplying the number of equipment i, Ni,g, to the maximum capacity of individual equipment, Pi,g,t, such that

Ei;g;t  Ni;g $Pi;g;t

ci2IP ; g; t

(10)

The above equation about the upper bound of the produced energy is valid for all regions, including SS and DS, and constitutes the complete set of energy balance equations together with Eqs. (7)e(9).

2.2.2.2. Energy balance with storage device As illustrated in Fig. 1, the BT can be installed only in the MF regions. Therefore, the energy balances for the SS and SF regions given in Eqs. (7) and (9) are identically valid even for the case that the BT is considered in the model, and the only energy balance for the MF region in Eq. (8) should be replaced by the following Eq. (8a) to express the energy flow in and out of BT.

X s

Es/m;t þ

X

Ei;m;t 

BF Em;t

 Dm;t

i

þ

X

Em/c;t ;

i2IP ;

cm; t

c

(8a) BF Em;t

In the above equation, is the difference between the amounts of electricity charged to and discharged from BTs in the MF m at time t. It has the positive value when the BTs are charged and is negative for the discharging case. The BT can be charged just in case that the MF has the electricity surplus and can be discharged only when the facility has shortfall in energy. The discharged energy from BT is supplied to the corresponding MF. The BT has lower and upper bounds in its storage capacity according to the status such that

X

Ni;m $Si;m;t ;

i2IB ;

cm; t

i

(11) BR indicates the amount of electricity remaining in the BTs where Em;t installed at the MF m at time t, and Ni,m and Si,m,t represent the number of BTs, which types are i, and the maximum capacity of one individual BT provided in specification, respectively. Umin and Umax indicate the minimum and maximum value of BT utilization factor, respectively, which are determined by the status of BT. In this study, Umin and Umax are set to 10% and 95%, respectively. In this research, the BT is operated in a way that the electricity is charged into BT beforehand for the future use and then is released as needed. It should be noted that the BT is never fully charged and is charged only as much as the energy deficit, which cannot be covered by generators, even in case that the surplus power is enough in the MF. To reflect such behavior of BT in the model, it is vital to define the operation mechanism of BT along the time line. In this paper, a day is divided into two timeslots, including daylight hours (7:00a.m.e7:00p.m.) and night time (7:00p.m.e7:00a.m.) which take 12 h, respectively, and the BT is set to be charged in the right-ahead night time as much as the scarcity for the subsequent daytime. Considering these characteristics of BT, the energy balance for the BTs themselves can be written as

BR

BR

BF

BF Em;k  Em;k1 ¼ Em;k ¼ aEm;t ;

cm; k

(12)

where the index k represents the time in hour multiplied by 12, and a is a time-unit conversion factor. According to Eq. (12), the change in averaged-electricity-residue of BTs before and after 12 h is equal to the quantity of net energy flow in or out of BTs for that time. It is assumed that the BT is gradually charged for 12 h in night time, i.e. BR is increased with uniform gradient e in other words, EBF is Em;t m;t constant for night time hours. 2.2.2.3. Other constraints Eqs. (13) and (14) aim to allow only one type of power generation equipment i to be installed in one specific region g and result in uniform type of equipment in the region.

K min $Yi;g  Ni;g  K max $Yi;g ; X

Yi;g  1;

ci2IPB ; g

i2IPB ; cg

(13) (14)

i

If the above constraints are not considered in the optimization problem, various kinds and capacities of generation equipment can be selected to meet the power demand of the region g, and this would lead to the unrealistic result that few extra-type equipment, which is different from those of dominantly selected type and capacity of equipment, are chosen to cover the small remnant of electricity demand. All the electricity generation and storage equipment require a certain scale of area for their installation. As aforementioned in Section 2.1, all the facilities except the SS have limitations on the installation area, and thus only a few equipment can be adopted in each region. This situation is modeled as

X

Ni;d $Ai  Amax ; d

i2IPB ; cd

(15)

i

As described in Eq. (4), Xm/c is the binary variable that

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181

represents the existence of connection between MF and SF. The variable takes the value one for the case that connection exists and zero otherwise, which can be expressed as an inequality constraint such that

Xm/c  1;

cm; c ðbelongs to mÞ

(16)

There are no limitations on capacity of electricity transmission from SS to MF because the well-equipped existing power lines are used for it. However, the transmission from MF to SF requires the new establishment of the transport equipment and subsequently has a restricted capacity as well as the additional costs. This restriction is modeled by min max Em/c $Xm/c  Em/c;t  Em/c $Xm/c ;

cm; c ðbelongs to mÞ; t (17)

Eq. (18) means that the amount of electricity produced at time t using all generation equipment in the SF c cannot exceed the demand, Dc,t e the power demand of SF cannot be satisfied solely by the self-generation and should be always accompanied by the external supplement of electricity. This equation sets the direction of electricity flow between the MF and SF as the electricity can only flow from the region that has surplus to the region that has scarcity.

Dc;t 

X

Ei;c;t ;

i2IP ; cc; t

(18)

i

More specifically, by combining Eq. (18) with Eq. (9), we can obtain the following condition which allows electricity transmission only in one direction from MF to its subordinate SFs.

Em/c;t  0;

cm; c ðbelongs to mÞ; t

(19)

It is remarkable that, in case of the transmission between SS and MF, the constraints regarding the transport direction are always satisfied without introducing the explicit equation like Eq. (18) in the model because the SS is only possible to produce the electricity without consumption and therefore the excess fundamentally flows in only one direction, i.e. from SS to MF. Fig. 3. Design and evaluation procedures of the RES-based power supply system.

2.3. Optimization technique and implementation procedure Fig. 3 illustrates the implementation procedure of the proposed RES-based power supply system. The key is the optimal system identification using superstructure-based optimization model described in Section 2.2. The optimization problem is solved by using CPLEX 9.0 in the General Algebraic Modeling System (GAMS), which is a commercial software well-known for its superb capability of solving mixed-integer problems [22]. 3. Application to Jeju Island To validate the effectiveness and usability of the optimization model proposed in Section 2, we applied the model to Jeju Island, Korea. This island is an excellent target area on which to apply the RES-based power supply system because it has abundant RES, such as wind and solar energy, as well as environmental constraints due to a well-developed national park and tourism industry. 3.1. Location and power demand of public service facilities Fig. 4 illustrates the location of the relevant public service facilities in the national park of Jeju. The SS region is located on the west coast of the island, as RES is plentiful in this area. The DS includes Hallasan National Park, with many highly concentrated public facilities, which is the major power-consuming area and is

capable of restrictively producing electric power using RES. The public service facilities, composed of five management offices and twenty-five ancillary buildings such as information centers, shelters, and rescue offices, are equally divided into five administrative districts according to geopolitics; each district is composed of one management office and five affiliated ancillary buildings. These management offices and ancillary buildings correspond to the MF and SF in Fig. 2 during optimization. In Table 1, the spatial information of the MFs and SFs in Jeju is provided. Fig. 5 shows the monthly average power demand data of the MFs. All facilities experience a high demand around summertime, whereas the lowest demand occurs in early spring. This trend is a direct result of the four-season climate of Jeju. During the summer and winter seasons, electricity demand increases due to the excessive use of air conditioners and heaters, respectively, but decrease in the spring in light of favorable weather conditions. Analogous trends can be observed in the demand of SFs. Table 2 lists the monthly average electricity demand of the five SFs within the same administrative district as the fourth MF. The electricity demand sharply increases in the summer months, during which the use of air-conditioning units is concentrated.

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Fig. 4. Location of the public service facilities in Hallansan National Park on Jeju Island, Korea.

Table 1 Spatial information of the main and secondary facilitiesa. MF

Area

SF 1

1 2 3 4 5

140 100 120 100 200

2

3

4

5

Dist.

Area

Dist.

Area

Dist.

Area

Dist.

Area

Dist.

Area

0.06 0.05 3 1.2 0.06

34 35 17 24 61

1.8 1.3 2.4 1.7 0.06

26 37 12 32 54

3 2.4 2.1 3 4.1

28 44 46 22 11

3.1 3.2 3.7 5.3 5.8

48 41 28 21 10

6 4.7 5.8 7 7.3

22 41 25 16 13

a Dist. represents the distance between each SF and its MF [km], and area is represented in m2.

than summer. The solar radiation, which was measured and averaged over the SSs and the five administrative districts, respectively, is stronger at SSs than at other regions in the spring and autumn, but, in contrast to the wind speed, it tends to be much stronger in the summer compared to the winter in all regions. Table 3 summarizes the technical and economical parameters of the power production and storage technologies considered in this study. The WT and PP data were obtained using the System Advisor Model (SAM) [25], which is a type of databank software, and the data for the BT were obtained from the software, named improved Hybrid Optimization by Genetic Algorithm (iHOGA) [26]. The values in Table 3 are represented as per-unit equipment.

Power demand (MWh)

4. Results

5 35

4.1. Effect of energy storage on energy costs

0 30 25 5 20 0 15 5 10 0 5 0

1

2

3

MF1

4

5

6

MF 2

7

8

9 10 11 12

MF3

MF4

MF5

Fig. 5. Monthly-averaged power demand of the main facilities.

3.2. Renewable energy sources Fig. 6 illustrates the monthly averaged data of wind speed and solar radiation, which are the most suitable RES for power generation on Jeju Island [1,23,24]. The wind speed, which was measured 30 m above the ground at SSs, is slightly stronger during winter

4.1.1. Total annual cost Energy storage is a technically and economically important issue in the design and analysis of RES-based energy systems because the amount of produced electricity is autonomously determined depending on the environmental conditions, which can result in dramatic decreases in energy utilization efficiency. Energy deficiencies can occur during daylight hours due to high demand, whereas excess energy can be made available during nighttime hours. Therefore, for a power supply system that consists only of power generation equipment without energy storage devices, the generators tend to be overdesigned, which causes increased expenses, to satisfy the peak hours of power consumption during the daytime. On the contrary, the inclusion of a battery in the power system can prevent the unnecessary increased equipment capacity required to meet peak demand, as surplus electricity can be saved and later distributed as needed. However, the energy storage device itself requires substantial extra costs, and therefore the economics should be carefully scrutinized before application. In this study, as a result of optimization, the required total annual cost given by Eq. (1) for the case without a battery was calculated as $644,110 (or, equivalently, 0.409 $/kWh-supplied), whereas the total annual cost for the case with a battery was

Table 2 Monthly-averaged electricity demand of the SFs that belong to the same administrative district as MF4 (kWh). SF

1 2 3 4 5

Month 1

2

3

4

5

6

7

8

9

10

11

12

1965 1877 1564 1197 857

1799 1949 1714 1366 1058

2269 2423 2152 1783 1442

2568 2578 2278 1948 1618

3016 2855 2504 2188 1847

3160 2886 2523 2229 1899

3370 3034 2663 3253 2012

3251 3002 2662 2327 1987

2899 2787 2504 2146 1816

2641 2666 2416 2015 1674

2211 2285 2053 1652 1322

2063 1967 1663 1282 941

Solar radiation (kWh/m2/d)

S. Kwon et al. / Renewable Energy 97 (2016) 177e188

8

7.5

7.1

6.8

6.6

6.4

4

5

5.8

6

6.3

6.6

6.8

7

8

9

183

6.9

7.1

7.3

10

11

12

4 2 0 1 SS

2 DS 1

3 DS 2

DS 3

6 DS 4

DS 5

Wind speed in SS (m/s)

Fig. 6. Meteorological data of RES in the supply site and the demand sites.

Table 3 Technical and economic parameters of electricity production and storage equipment. WT1 Power (kW) Operation cost ($1000/kWh) Equipment cost ($1000) Installation cost ($1000) Land reclamation cost ($1000) Required area (m2) Lifetime (yr) a

10 0.62 16.9 1.25 6.63 9 24

WT2 20 1.20 33.9 2.28 10.01 36 24

WT3 50 3.05 84.0 6.69 17.08 100 24

PP1 3 0.11 8.1 1.20 1.23 1 24

PP2 4 0.14 10.8 1.60 1.64 1.5 24

PP3 5 0.17 13.5 2.00 2.05 2 24

BT1

BT2 a

100 0.28 27.7 0.28 0 0 12

BT3 a

200 0.56 55.4 0.56 0 0 12

400a 1.12 110.9 1.12 0 0 12

Capacity (kWh).

computed as $569,460 (or, equivalently, 0.361 $/kWh-supplied), which is a superior figure. These results reveal that an economically more efficient system can be achieved by introducing an energy storage device, despite the accompanying capital and operating expenditures of the battery, as it enables electricity management that is flexible in light of the time-varying availability of RES. 4.1.2. Cost contribution Fig. 7 illustrates the TAC in more detail. We first discuss the cost contribution of the power system with a BT and then analyze the cost contribution of the power system without a BT. As shown in Fig. 7(a) for the case with the BT, only WTs and BTs were selected for constructing the optimal power supply system,

Fig. 7. The cost components of the power supply system (a) with BT and (b) without BT; the numbers in parentheses represents the absolute value of the cost in $1000/ year.

despite the fact that PPs were also considered a viable option for optimization. From the viewpoint of individual DSs, the selfgeneration of electricity by installing PPs at each facility may seem more economically efficient than the generation and provision from SSs with WTs, as there is no land reclamation cost. However, in this case study, a centralized energy production system that manages all supply and demands nodes, in which electricity is mass produced at SSs and then distributed to each DS, and a flexible energy-management using BTs, result in a more energy-efficient system than the distributed energy production system, in which energy is produced at the respective DSs. Even considering land reclamation costs, the centralized operational strategy benefits from economies of scale and can suppress energy waste at each individual demand node by supplying the electricity to the respective regions only as needed. The sum of the energy savings at each region more than makes up for the extra land reclamation costs of the centralized system, and consequently the combination of WTs and BTs was selected by optimization. Note that, for the distributed energy production system, the overproduced electricity at each DS is permitted to be transmitted only in one direction from the MF to its subordinate SFs according to Eq. (18) and is otherwise dissipated. Fig. 7(b) shows that a major part of the TIC, which is taken up by WTs and BTs in the case with the BT, as shown in Fig. 7(a), is replaced by PPs when a BT is not considered in the optimization. This is a result of the power consumption in all of the public service facilities on Jeju Island during daylight hours being far greater than nighttime consumption. Therefore, electricity self-sufficiency due to the installation of PPs, by which the electricity production varies similarly to the pattern of power demand (i.e., increased during the day), of individual facilities at the DSs is economically more efficient in the absence of a buffer against intermittent resource availability. Nonetheless, WTs are still selected in the optimization model to make up for the PPs, which cannot producing electricity during the night, and to reduce energy waste due to local generation at each node by incorporating the centralized production strategy, as in the previous case with the BT.

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the blue and green lines in Fig. 8 is exactly equal to the decrement in the red line, and the BT returns to its original minimum-charged status (see Eq. (11)) before the end of each daylight period, i.e., by 7:00 p.m., as mentioned in Section 2.2.2. In Fig. 8(d), the BT is maintained at the minimum-charged status throughout the day, as the electricity demand does not exceed the power production of the WTs. As shown in Fig. 8(e) to (h), in case without a BT, the peak demands during daylight hours are covered by the relatively small

4.1.3. Transient behavior The hourly data for the amount of electricity generated, stored, and consumed over all regions for the two cases illustrated in Fig. 7 are depicted in Fig. 8. Considering the results of the case with a BT, the BT is gradually charged using the electricity surplus during the night and is discharged when the electricity demand exceeds the power supplied by the WTs. The amount of electricity released from the BT exactly matches the electricity deficiency during the day; the area between

Spring

Amount of electricity

600

With BT Nighttime

Daylight hours

Without BT (a)

Nighttime

Daylight hours

(e)

500 400 300 200 100 0

Summer

Amount of electricity

600

(b)

(f)

(c)

(g )

(d)

(h )

500 400 300 200 100 0

Autumn

Amount of electricity

600 500 400 300 200 100 0

Winter

Amount of electricity

600 500 400 300 200 100 0

1 3 5 7 9 11 13 15 17 19 21 23 Time (hr)

1 3 5 7 9 11 13 15 17 19 21 23 Time (hr)

Electricity residue (charged) in BT(kWh)

Electricity generated by PP (kW)

Electricity generated by WT (kW)

Electricity consumed (demand) (kW)

Fig. 8. The hourly data on the amount of electricity; the row represents the seasonal change (representative days are chosen for each season) and the column indicates the configuration changes; each data is the sum of the electricity that is generated/consumed/stored in all regions.

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number of WTs with the help of the PPs, as the patterns of power generation by the PPs are analogous to the pattern of power consumption. Because the PPs cannot produce electricity during the night, electricity demand during this time is entirely satisfied by the WTs.

reference case. Remarkably, among the three types of WTs, only WT3 is selected due to its high cost-effectiveness per unit of electricity.

4.2. Sensitivity analyses for equipment costs

4.2.2. Changes in PP costs Table 4 shows that the 20% decline in PP cost does not affect the design and cost of the power system, but as the price further decreases below a certain level, the proportion of WTs and BTs in the optimal configuration is sharply diminished and substituted with PPs. As depicted in Fig. 9(b), PPs were determined to be installed only in the DSs, despite the fact that the average solar radiation at the SSs is better than in other regions (see Fig. 6). This is due to a large land reclamation cost required at the SSs. In addition, the majority of PPs were favored to be installed at MFs rather than at SFs, among the DSs, as the energy utilization efficiency depends on the directionality of the electricity flow. In this study, the energy efficiency is improved as the power generation equipment is located in higherlevel regions due to the constraint allowing only one-way electricity flow from the SSs to SFs via intermediate MFs. If the electricity is produced in high-level regions, the individual demand facilities can be supplied electricity based on their energy requirements, without energy waste possibly occurring from overcapacity by way of self-generation at the respective facilities, and thus MFs are preferred to SFs when PPs are adopted in the optimization model. As shown in Table 3, the three types of PPs have the same unit cost of electricity generation. However, because only one type of power production equipment is acceptable for use in each region due to Eqs. (13) and (14), PP1 and PP2, which have relatively low capacities and thus are likely to produce only a small excess of electricity after satisfying the power demand, are preferred. For this reason, PP3 was not selected in any of the optimization cases.

The effects of technical enhancements on the structure and economy of the power supply system were investigated. The sensitivity analyses were conducted only for the case with the BT, which was identified as more energy-efficient than the case without the BT, as discussed in Section 4.1. The analyses were carried out by re-optimizing the result against the sequential decrease in equipment costs given in Table 3, from 0% to 80% at intervals of 20%. The results are summarized in Fig. 9 and Table 4, and a detailed description is given in the following sections. 4.2.1. Changes in WT costs As shown in Fig. 9, the TAC gradually decreased as the efficiency of the WTs increased. According to Table 4, the structure of the power system remains unchanged until the equipment cost decreases to 60%. However, if the WT cost decreases to 80%, the power system is structured such that the electricity is produced and distributed entirely by the WT, whereas the BT is no longer used. In the reference case, the BT was chosen for the optimization model to save energy, which is associated with flexible energy management between high and low cycles of energy demand during a day, and the resulting energy savings were greater than the extra cost of adding the BT. However, the advantage of the BT is no longer applicable for the case of the 80% decrease in WT cost, as the unit price of generation is quite cheap, and the waste of energy during the night is negligible compared to the extra cost of the BT. The price competitiveness of PPs is further undermined as the price of WTs decreases, and hence PPs are not introduced as in the

569 530

500

600

(a) 413

400

382

300 200

512

448

(b) 396

400 300 200

0

0 Ref.

569

500

-20 -40 -60 -80 Change in WT cost (%) 553

534

504

Ref.

600

(c) 485

TAC ($1,000/yr)

TAC ($1,000/yr)

569

100

100

600

569

500

479

TAC ($1,000/yr)

TAC ($1,000/yr)

600

400 300 200 100

569

-20 -40 -60 Change in PP cost (%)

-80

(d)

530

500

466 390

400

289

300 200 100 0

0 Ref.

-20 -40 -60 Change in BT cost (%) WT in SS

Ref.

-80

-20

-40

-60

-80

Change in WT and PP costs (%) PP in MF

BT

Trans.

PP in SF

Fig. 9. Sensitivity analysis for equipment costs; (a) WT, (b) PP, (c) BT, and (d) WT and PP.

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Table 4 Effect of changes in equipment costs on the optimal configuration of the power supply system. Equipment

Referencea WT

PP

BT

WT&PP

a b

Cost changes (%)

0 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80

Number of equipmentb SS

MF

WT3

BT1

BT2

BT3

PP1

PP2

PP1

PP2

20 20 20 20 32 20 9 9 9 20 20 20 20 20 10 9 10

3 3 3 3 0 3 0 0 0 3 3 4 5 3 0 0 0

2 2 2 2 0 2 1 1 0 2 2 3 2 2 1 0 0

4 4 4 4 0 4 0 0 1 4 4 3 3 4 0 1 0

0 0 0 0 0 0 96 100 100 0 0 0 0 0 0 96 95

0 0 0 0 0 0 60 60 79 0 0 0 0 0 137 60 57

0 0 0 0 0 0 28 25 25 0 0 0 0 0 0 23 25

0 0 0 0 0 0 51 47 31 0 0 0 0 0 51 51 17

Related section

Related figure

Section 4.2 Section 4.2.1

Fig. 9 Fig. 9(a)

Section 4.2.2

Fig. 9(b)

Section 4.2.3

Fig. 9(c)

Section 4.2.4

Fig. 9(d)

SF

The reference case was obtained based on the original data in Table 3 without any cost modification. WT1, WT2, PP1, PP2, and PP3 in SS and PP3 in DS were not selected in all cases although they were considered a viable option during optimization.

4.2.3. Changes in BT costs The BT improves the energy utilization efficiency by enabling the excess power that is generated during the night to be used during daylight hours, under the condition that the amount of power produced is determined autonomously depending on environmental factors. However, it should not be overlooked that the BT is merely incidental equipment (i.e., it is not imperative) as it cannot produce or consume electricity on its own. Therefore, the result that the overall configuration remains unchanged against the decline in BT price, as presented in Table 4, and the consequence that the decrease in the TAC is equal to the decrease in the EC of the BT, as illustrated in Fig. 9(c), are predictable.

4.2.4. Concurrent changes in WT and PP costs We simultaneously changed the EC of the three types each of WTs and PPs presented in Table 3 and examined the effect of such a price change on the optimal structure and the cost of the RES-based power supply system. Table 4 shows that the configuration is not changed by the 20% EC decrease and, as a result, is structured the same as that of the reference case via the optimization. Nonetheless, as depicted in Fig. 9(d), the TAC for this case is slightly reduced, not due to the structure change, but simply to the drop in the EC of the WTs, similar to the case shown in Fig. 9(a) for the 20% WT price reduction. In Fig. 9(d), as the ECs of the WTs and PPs further decrease below 40%, the proportion of WTs and BTs dwindle to less than half of the original value of the reference case and is substituted by PPs, similar to the sole PP price decrease case shown in Fig. 9(b). Many of the WTs and BTs are replaced by PPs despite the decrease in the WT price and the PP cost because the hybrid system that uses various types of RES is able to effectively overcome RES volatility and, hence, is more energy-efficient than a singleRES-based power generation system. In particular, in the case of the decrease in WT and PP costs of 80%, it is remarkable that the power supply system is designed with only WTs and PPs by introducing one additional WT3 to replace the BT, unlike the case of the decrease in the sole PP cost of 80% in Fig. 9(b). This indicates that the overproduction strategy is more cost-effective than the flexible energy management strategy that uses a BT, at least in this case.

4.3. Sensitivity analyses for renewable energy sources The structural and economic effects of the environmental changes that entail the changes in RES quality to the optimal design of power supply systems were investigated. In the sensitivity analyses, RES contributions corresponding to 40%, -20%, 20%, and 40% of the reference case, as given in Fig. 6, were considered simultaneously in all regions. The results are summarized in Fig. 10 and Table 5.

4.3.1. Variation of wind speed As shown in Fig. 10(a), the TAC varied inversely to the wind speed. The power system is continually structured based entirely on WTs and BTs against the 20% decrease in wind speed due to the high cost-efficiency of the centralized power production strategy. However, as the wind speed is further decreased to 40%, much of the power that was originally covered by the WTs in the reference case is complemented by the PPs located at the DSs. In addition, for a 40% decrease in wind speed, the number of BTs drastically declines along with the WTs because the PPs can meet the extensive power demand during daylight hours, as the power generation pattern of PPs is similar to the pattern of power consumption.

4.3.2. Variation of solar radiation Fig. 10(b) illustrates the effect of variations in solar radiation on the optimal configuration of the power supply system. Decreases in solar radiation can lead to small changes in the type and location of BTs but does not affect the overall power production system or the TAC. This is because the deterioration in solar radiation reinforces the benefit of combined WTs and BTs, as such a combination is economically optimal based on the reference case. On the contrary, the improvement in solar radiation intensifies the price competitiveness of PPs, and thus PPs are selected in the optimization. However, PPs cannot completely replace WTs in the considered range of increased solar radiation, as the power demand in some administrative districts cannot be satisfied solely by local PPs, the number of PPs installed in such regions is restricted by the spatial constraint given by Eq. (15), and PPs cannot generate electricity during nighttime.

S. Kwon et al. / Renewable Energy 97 (2016) 177e188

800

600

(a)

700

(b)

500

600

TAC ($1,000/year)

TAC ($1,000/year)

187

500 400 300 200 100

400 300 200 100 0

0 -40

-20 0 20 Variation of wind speed(%) WT in SS

-40

40

PP in MF

BT

-20 0 20 40 Variation of solar radiation(%)

Trans.

PP in SF

Fig. 10. Sensitivity analysis for the RES potential; (a) wind speed and (b) solar radiation.

Table 5 Effect of variation of RES potential on the optimal configuration of power supply system. RES

Changes (%)

a

Reference Wind speed

Solar radiation

a b

0 40 20 þ20 þ40 40 20 þ20 þ40

Number of equipmentb SS

MF

WT3

BT1

BT2

BT3

PP1

PP2

PP3

PP1

PP2

PP3

20 15 25 17 14 20 20 20 10

3 0 4 6 9 2 16 17 0

2 0 2 1 2 8 1 0 0

4 1 3 3 2 1 1 1 1

0 100 0 0 0 0 0 0 0

0 60 0 0 0 0 0 0 24

0 0 0 0 0 0 0 0 60

0 23 0 0 0 0 0 0 3

0 49 0 0 0 0 0 0 31

0 0 0 0 0 0 0 0 2

Related section

Related figure

Section 4.3 Section 4.3.1

Fig. 10 Fig. 10(a)

Section 4.3.2

Fig. 10(b)

SF

This case was calculated based on the original RES conditions without any modification. WT1, WT2, PP1, PP2, and PP3 in SS were not selected in all cases although they were considered a viable option during optimization.

5. Conclusions and discussion In this paper, a superstructure model using MILP was proposed to determine the optimal configuration of a RES-based power supply system in an isolated area. The optimization model has a three-layered energy structure to consider the reality that energy production and consumption sites are generally separated. Diverse economic factors such as transmission and reclamation costs were considered for more accurate evaluation of total annualized cost. The model was suggested in two types, i.e., with and without a BT, to investigate the effect of an energy storage device on the energy efficiency of a power supply system. In a considered case study of Jeju Island, the power supply system with a BT was revealed to be more economical than the system without a BT, despite the accompanying capital and operating expenditures of the BT. This was because the BT enables us to flexibly manage the energy supply between high and low cycles of energy demand during a day. In a base case, the electricity generation and provision from SS with WTs was preferred over selfgeneration with PPs at each facility, mainly due to the benefit from economies of scale and the efficient distribution of electricity. However, in-depth sensitivity analyses showed that the optimal structure of the power supply system can be changed according to the technical enhancement and the changes in RES potentials. In all cases, the proposed model could successfully determine the optimal configuration to ensure minimal cost while satisfying electricity demands. It should be noted that the optimization model proposed in this study may not be directly applicable to some specific regions where the topographic conditions are not in accordance with the assumptions introduced in model development, e.g. limitless area of

SS and the use of existing power lines for electricity transmission from SS to MF. If this is the case, the model is should be modified to incorporate the geographical conditions before being applied. Acknowledgement This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2058904). Nomenclature

Sets i2I g2G t2T

equipment (electricity production/storage/transmission) regions (supply site/main facility/secondary facility) time

Subsets IP IB IT IPB s2GS m2GM c2GC d2GD

equipment for electricity production, IP⊂I equipment for electricity storage, IB⊂I equipment for electricity transmission, IT⊂I IPB¼IP∪IB regions of supply site, GS⊂G regions of main facility, GM⊂G regions of secondary facility, GC⊂G regions of demand site, GD¼GM∪GC

Parameters Ai installation area of equipment i (m2) Amax available area in demand site d (m2) d

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CRFi Dm,t Dc,t min Em/c

capital recovery factor of equipment i power demand of main facility m at time t (kW) power demand of secondary facility c at time t (kW) minimum allowable electricity transmission between main and secondary facility (kW) max Em/c maximum allowable electricity transmission between main and secondary facility (kW) Kmin arbitrary small number used in Eq. (13) Kmax arbitrary large number used in Eq. (13) Lm / c distance between main and secondary facilities (km) ni life time of equipment i (yr) OCi operating cost of equipment i ($/kWh) Pi,g,t maximum capacity of one individual generation equipment i in region g at time t (kW) r interest rate Si,m,t maximum capacity of one individual storage equipment i in main facility m at time t (kW) TC equipment cost for electricity transmission per unit length ($/km) Umin minimum battery utilization factor Umax maximum battery utilization factor Continuous variables Ei,g,t electricity produced by equipment i in region g at time t (kW) Ei,s,t electricity produced by equipment i in supply site s at time t (kW) Ei,m,t electricity produced by equipment i in main facility m at time t (kW) Ei,c,t electricity produced by equipment i in secondary facility c at time t (kW) E s/ m,t electricity transmitted from supply site s to main facility m at time t (kW) Em / c,t electricity transmitted from main facility m to secondary facility c at time t (kW) BF Em;t net electricity flow in or out of battery in main facility m at time t (kW) BR Em;t electricity charged in battery in main facility m at time t (kWh) BF

Em;k BR

Em;k ICP ICT Ni,g Ni,m TAC TIC TOC

net electricity flow in or out of battery in main facility m for 12 h (kW) averaged electricity residue in battery in main facility m for 12 h (kWh) investment cost associated with electricity production (kW) investment cost associated with electricity transmission (kW) number of equipment i in region g number of equipment i in main facility m total annual cost ($/yr) total investment cost ($/yr) total operating cost ($/yr)

Binary variables Xm / c connectivity between main and secondary facilities Yi,g existence of equipment i in region g References [1] J. Kim, I. Moon, The role of hydrogen in the road transportation sector for a

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