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Optimal configuration of power generating systems in isolated island with renewable energy
ARTICLE IN PRESS
Renewable Energy 32 (2007) 1917–1933 www.elsevier.com/locate/renene
Optimal configuration of power generating systems in isolated island with renewable energy Tomonobu Senjyua, Daisuke Hayashia, Atsushi Yonaa, Naomitsu Urasakia, Toshihisa Funabashib, a
Faculty of Engineering, University of the Ryukyus, 1 Senbaru, Nishihara-cho, Nakagami, Okinawa 903-0213, Japan b Meidensha Corporation, 36-2 Nihonbashi Hakozakicho, Chuo-ku, Tokyo 103-8515, Japan Received 2 September 2005; accepted 22 September 2006 Available online 20 February 2007
Abstract In isolated islands, usually diesel generators supply electric power. However, there are problems, e.g., a lack of fossil fuel, environmental pollution etc. So, isolated island, e.g. Miyako island, installs renewable energy power production plants. However, renewable energy power production plants are very costly. This paper presents an optimal configuration of power system in isolated island installing renewable energy power production plants. The generating system consists of diesel generators, wind turbine generators, PV system and batteries. Using the proposed method, operation cost can be reduced about 10% in comparison with diesel generators only from simulation results. r 2007 Elsevier Ltd. All rights reserved. Keywords: Isolated island; Renewable energy; Optimum configuration
1. Introduction Okinawa, which is located in southeast in Japan has about 40 isolated islands. These islands mostly depend on diesel generators for power supply since islands are too far from mainland of Okinawa and areas of islands are so small. Hence diesel generators in isolated island need a transportation cost and an inventory carrying cost of fuel. The generation cost of diesel generators in isolated islands per kWh is very expensive compared with a Corresponding author. Tel.: +81 3 5641 9310; fax: +81 3 5641 7509.
E-mail addresses: [email protected] (T. Senjyu), [email protected] (T. Funabashi). 0960-1481/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2006.09.003
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conventional generation. Since power supply in isolated islands needs a huge cost, reducing the generating cost of diesel generators is very important. On the other hand, the social interest for global environmental concerns and reduction in fossil fuel increase. One of the solutions for these issues is to introduce a renewable energy such as PV system and wind turbine generator which are clean and infinite energy. However, renewable energy sources have demerits that output of renewable energy sources are fluctuated by weather and wind speed, initial cost of facilities is very high, and facilities of renewable energy need regular maintenance cost. Therefore, we evaluate introducing a hybrid generating system in terms of performance and endurance of renewable energy source to obtain availability of renewable energy. We need to reduce both initial and operation costs with optimum configuration. Most of the works reported so far use the hourly average data of isolation, wind speed, and power demand over a few years for simulation [1–3]. But actually, it is near about impossibility that weather conditions are the same everyday. Therefore under the conditions varying every day and every hour, optimum number of facilities using the hourly average data may not be able to supply without outages over a year. Also most of these studies use the iteration method to determine an optimum generating capacity and storage capacity. However, these methods take long time, and it is difficult to adjust their capacities if isolation, wind speed, power demand, rating of each generator, and initial cost of each facility are changed. Therefore in this study, we propose the optimal configuration of power generating systems in isolated island with renewable energy using actual hourly data over a year. The optimization method used in this paper is the Generic Algorithm (GA). The objective function of GA is the total cost which is sum of initial and operation costs per year. By minimizing the total cost, we can achieve an inexpensive and clean electrical power system. In addition, the proposed method can adjust even when data of load, location, and facilities such as PV system and wind turbine generators are changed. 2. Scale of isolated island In this paper, we assume that the isolated islands are Miyako, Kume, and Tokashiki in Okinawa, Japan. Each isolated island data is shown in Table 1, and each plant data is shown in Table 2. In this study, wind speed and isolation data are used at mainland of Okinawa in 1993. Also, power demand data of each island used is derived by multiplying peak power demand ratio to power demand data for mainland Okinawa.
Table 1 Isolated island data Island’s name
Miyako
Kume
Tokashiki
Peak power demand Peak power demand ratio to mainland Okinawa Capacity of diesel generator
50,000 kW 1/25 10,000 kW 4 5000 kW 4 47.0
11,000 kW 1/100 3000 kW 2 1500 kW 4 11.5
3500 kW 1/324 1000 kW 2 500 kW 5 3.65
Operating cost diesel generator (million yen)
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Table 2 Plant data Photovoltaic Initial cost per 1000 m2 Maximum area Life time
1 million yen 127,000 m2 15 years
Wind turbine Rated output power Initial cost Maximum number of equipment Life time
600 kW 2.5 million yen 127 15 years
Diesel generator Fuel cost
20 yen/kWh
Battery Capacity Inverter capacity Initial cost Maximum number of equipment Life time
3000 kW 750 kVA 10 million yen 63 15 years
3. Formulation In this section, we will formulate the problem. The variables used in this study are shown in Table 3. The configuration of a hybrid generating system used in the paper is shown in Fig. 1. This system consists of wind turbine generators, PV system, batteries, and diesel generators. The supply power Ps is sum of the output power of PV system Sp, wind turbine generators Wp, batteries Bp, and diesel generators Dp: Ps ¼ Sp þ W p þ Bp þ Dp ,
(1)
where positive values of Bp mean an operation of discharge and negative values of Bp mean an operation of charge. The total cost Tc is sum of the initial cost Tic and the operation cost Ta as given by the following equation: T c ¼ T ic þ T a .
(2)
The initial cost Tic is sum of initial costs of each facility: T ic ¼ ðS ic þ W ic þ Bic Þ=Y n
(3)
where Sic, Wic, and Bic are the initial cost of PV system, wind turbine generators, and batteries, and Yn is the life time for each equipment, respectively. The operation cost is shown as the following equation: T a ¼ Dp t, where Dp is the total generating power of the diesel generator.
(4)
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Photovoltaic Sp Generating power Z Energy conversion efficiency, Spe Generating power per 1 m2 for 1MJ/m2 As Area of panels I Isolation Sic Initial cost Sc Cost per 1 m2 Wind turbine Win Cut-in wind speed Wout Cut-out wind speed Wrp Rated output power Wrs Rated wind speed Wp Generating power x Output coefficient Wic Initial cost Wc Cost per equipment Wn Number of wind turbines Diesel Dp Total generating power Dp1 Rated power of type 1 Dp2 Rated power of type 2 Dn1 Number of running diesel generator 1 Dn2 Number of running diesel generator 2 t Running time of diesel generator Battery Bic Initial cost Bn Number of batteries Be Cost per equipment (3000 kW) Bi Inverter capacity Variable of operation Tc Total cost Tic Total initial cost Ta Operation cost Yn Life time t Running time of diesel generator Ps Power supply Pl Power demand
3.1. PV System Output power of the PV system Sp is expressed as a function of isolation: S p ¼ ZS pe As I,
(5)
where Z, Spe, and I are the energy conversion efficiency, a generating power per 1 m2 for 1 MJ/m2, and an isolation, respectively. Initial cost of solar array panel Sic is proportional
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MPPT
PV arrays
AC
Diesel
DC
Rectifier AC
L o a d
AC
DC
DC
Inverter Wind turbines Battery
Fig. 1. System configuration.
Generating Power Wp [kW]
800
Wrp
400
200
0 0
Win
10 Wrs 15 20 Wind Speed Ws [m/s]
Wout
30
Fig. 2. Characteristic of output power of wind generator.
to number of solar array panels As: Sic ¼ Sc As ,
(6) 2
where Sc is the cost per 1 m of solar array panel. 3.2. Wind turbine generator Output characteristic of wind turbine generator used in this study is shown in Fig. 2. A wind turbine generator needs to consider the cut-in wind speed Win and the cut-out wind speed Wout. If wind speed exceeds the cut-in value, the wind turbine generator starts generating. If wind speed exceeds the rated wind speed Wrp, then it generates constant output, and if the wind speed exceeds the cut-out value, the wind turbine generator stops
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running to protect the generator: Wp ¼ 0 W p ¼ xðW s W in ÞW n W p ¼ W rp W n
9 ðW s oW in ; W s 4W out Þ > = ðW in oW s oW rs Þ > ; ðW oW oW Þ rs
s
(7)
out
where x is the slope between Win and Wrs. Initial cost of the wind turbine generators is proportional to the number of wind turbines Wn: W ic ¼ W c W n ,
(8)
where Wc is a cost per generator of wind turbine generators. 3.3. Diesel generator Two types of diesel generators are used in this study, and their capacities are shown in Table 1. In Table 1, capacity Bp and number of diesel generators are the actual data installed from on Miyako, Kume, and Tokashiki islands. Generating power of diesel generators Dp is expressed as Dp ¼ Dn1 Dp1 þ Dn2 Dp2 ,
(9)
where Dp1 and Dp2 are the rated power of type 1 and 2, and Dn1 and Dn2 are the number of running diesel generators of type 1 and 2, respectively. 3.4. Battery Initial cost of the battery Bic is proportional to the number of batteries Bn: Bic ¼ Be Bn ,
(10)
where Be is the cost per one battery of batteries. Using the above equations, we determine an optimal configuration of renewable generating systems, where total cost is reasonable. We assume that renewable energy generating system does not need operation cost because renewable energy is infinite. 4. Operation strategy Using the above-formulated equations, we will simulate the operation of hybrid generating system for 1 year. Initial cost is accounted for a year, the total initial cost is divided by life time of each facility, where we assume that all life time of facility is 15 years. Diesel generation needs to consider operation cost as fuel cost plus transport cost of fuel. However, we assume that renewable energy generating system does not need operation cost. The output power of PV system and wind turbine generators depend on isolation and wind speed, respectively. Battery is a part of PV system and wind turbine generator. So, it charges or discharges in response to condition of load, PV system and wind turbine generator. Also, if the capacity of battery is short, diesel generator compensates. Hence in
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Fig. 3. Flow chart.
this section, we will describe the operation strategy used in this study. The flow chart of operation is shown in Fig. 3, all the steps are explained below: Step 1: If the power supply from renewable energy is smaller than the power demand, go to Step 2. Alternatively, if the power supply from renewable energy is larger than the power demand, go to Step 3. Step 2: If the remaining capacity of battery is larger than 50%, go to Step 4. Alternatively, if the remaining capacity of battery is smaller than 50%, go to Step 5. Step 3: If the surplus power from renewable energy ( ¼ Sp+WpPl) is smaller than the inverter capacity of battery Bi which can be stored in battery per 1 h, go to Step 6. Alternatively, if the surplus power from renewable energy is larger than the inverter capacity of battery Bi, go to Step 7. Step 4: Minimum number of diesel generators to meet power demand is activated, and the surplus power( ¼ Dp+Sp+WpPl) is stored in the battery. Step 5: If the insufficient power from renewable energy is smaller than the inverter capacity, go to Step 8. Alternatively, if the insufficient power only from renewable energy is larger than the inverter capacity, go to Step 9. Step 6: Charge inverter capacity to battery, and remaining surplus power ( ¼ Sp+WpPlBi) is thrown out. Here, if battery becomes full, charge surplus power until battery becomes full and remaining surplus power is thrown out. Go to Step 10. Step 7: Charge all surplus power in battery. Here, if battery becomes full, charge surplus power until battery become full and remaining surplus power is thrown out. Go to Step 10. Step 8: Discharge the insufficient power from battery. And go to Step 10. Step 9: Discharge within inverter capacity, in addition minimum number of diesel generator to meet power demand are activated. And the surplus power( ¼ Dp+Sp+ Wp+BiPl) is charged in battery.
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Step 10: If time t does not reach the end of simulation, increase t ¼ t+1 and go to Step 1. If time t reaches end of simulation, go to End. 5. Simulation results The purposed method in this study is used to determine the optimal configuration of renewable energy with minimum of total cost. In this section, we perform the simulations for Miyako, Kume, and Tokashiki, using data of isolation, wind speed, and power demand for the year 1993. 5.1. GA used in this paper The GA flow chart to optimize the number of each facility is shown in Fig. 4. Also, each individual is represented by binary digits 1 and 0, and a distribution for the number of each facility is shown in Fig. 5. In this study, parameters of GA are selected based on the onepoint crossover and the mutation rate is 0.3. We will describe the optimization flow chart as follows: With the available isolation, wind speed, and power demand data determine the initial set up of each facility at random. Next, operate 1 year, and calculate the operation cost,
Fig. 4. Flow chart of optimization using GA.
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Fig. 5. Individual example of GA.
Total cost [ million yen / year ]
48 47 46 45 44 43 42 0
500
1000
1500 Generation
2000
2500
3000
Fig. 6. Total cost (Miyako).
and the total cost for 1 year which includes the one year operation and initial costs. Determine the facility arrangement using GA, with the fitness function being the total cost. The one-point crossover and the mutation are implemented. And if termination condition is not satisfied, go to Operation of next generation. Alternatively, if the condition is satisfied, simulation is finished, where individual of the most reasonable total cost is the optimum solution. 5.2. Simulation results of optimization We perform simulations for Miyako, Kume, and Tokashiki. Fig. 6 shows the transition of the total cost in Miyako, where the horizontal axis gives the generation and the vertical axis gives the total cost. Fig. 7 shows the transition of the optimal number of facilities in Miyako, where horizontal axis gives the generation of and vertical axis gives the optimal number of facilities. Likewise Fig. 8 shows the transition of the total cost in Kume, and Fig. 9 shows the transition of the optimal number of facilities in Kume. Fig. 10 shows the transition of the total cost in Tokashiki and Fig. 11 shows the transition of the optimal number of facilities in Tokashiki. The above results are tabulated in this table. From Table 4, the optimum number of solar array panels, wind turbine generators, and batteries in Miyako are 0, 61, and 3, respectively. In Kume, they are 0, 16, and 1, and in Tokashiki they are 0, 5, and 0, respectively. Besides, the cut-down cost in Miyako is 4.0 million yen/ year, In Kume it is 0.7 million yen/year, and in Tokashiki it is 0.21 million yen/year. In all the islands, the number of photovoltaic sources is zero since initial cost of PV system is so expensive and energy conversion efficiency is low.
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70
Number of equipment
60 50
Sn Wn
40
Bn
30 20 10 0 0
500
1000
1500
2000
2500
3000
Generation
Fig. 7. Optimal number of facilities (Miyako).
12.0
Total cost [millionyen / year]
11.8 11.6 11.4 11.2 11.0 10.8 0
500
1000
1500
2000
2500
3000
Generation
Fig. 8. Total cost (Kume).
5.3. Cost analysis Next, we will examine the special conditions that the grant rate is introduced for initial costs of PV system and batteries. Here, we assume that the grant rates are 25% and 50% for each case. This simulation results for Miyako, Kume, and Tokashiki are shown in Tables 5, 6, and 7, respectively. From the above results, the number of photovoltaic sources does not increase even though the initial cost of PV system is reduced. Also when the initial cost of battery is reduced, the number of batteries in Miyako and Tokashiki slightly increases, but in Kume it is constant.
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18 16 Number of equipment
14 12 Sn
10
Wn
8
Bn
6 4 2 0 0
500
1000
1500
2000
2500
3000
Generation
Fig. 9. Optimal number of facilities (Kume).
3.70
Total cost [millionyen / year]
3.65 3.60 3.55 3.50 3.45 3.40 0
500
1000
1500
2000
2500
3000
Generation
Fig. 10. Total cost (Tokasiki).
5.4. Operation on optimum configuration We perform power supply simulations for 1 year with an optimum configuration determined by GA. The simulation period is through 1st to 7th January in 1993. The simulation results for Miyako, Kume, and Tokashiki are shown in Figs. 12, 13, and 14, respectively. Fig. 12 shows the simulation results in Miyako. Fig. 12(a) shows the relationship between demand power and supply power, Fig. 12(b) shows the supply power of each facility, Fig. 12(c) shows the charge and discharge of battery, Fig. 12(d) shows the capacity of battery, and Fig. 12(e) shows the disposal of power.
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6
Number of equipment
5 4
Sn Wn
3
Bn 2 1 0 0
500
1000
1500 Generation
2000
2500
3000
Fig. 11. Optimal number of facilities (Tokasiki).
Table 4 Simulation result Scale of power demand
Large
Medium
Small
Name of island Photovoltaic (m2) Wind turbine Battery Total cost (million yen) Operating cost for diesel generators only Cut down cost
Miyako 0 61 3 43.0 47.0 4.0
Kume 0 16 1 10.8 11.5 0.7
Tokashiki 0 5 0 3.44 3.65 0.21
Table 5 Simulation result (Miyako) The grant rate (PV: Battery)
Photo-voltaic (m2)
Wind turbine
Battery
Total cost
0%: 0% 0%:25% 0%:50% 25%:0% 25%:25% 25%:50% 50%:0% 50%:25% 50%:50%
0 0 0 0 0 0 1000 2000 1000
61 55 55 60 55 54 59 55 55
3 4 4 3 4 4 3 4 4
43.0 42.4 41.8 43.0 42.4 41.8 43.0 42.4 41.8
From Fig. 12(a), the power demand exceeds the power supply all the time. Also from Fig. 12(b), we can verify that when the power supply from renewable energy is large, the power supply from diesel generator is small. Conversely, when the power supply from
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Table 6 Simulation result (Kume) The grant rate (PV: Battery)
Photo-voltaic (m2)
Wind turbine
Battery
Total cost
0%: 0% 0%:25% 0%:50% 25%: 0% 25%:25% 25%:50% 50%: 0% 50%:25% 50%:50%
0 0 0 0 0 0 0 0 0
16 15 13 13 15 13 14 15 14
1 1 1 1 1 1 1 1 1
10.8 10.7 10.5 10.8 10.7 10.5 10.8 10.7 10.5
The grant rate (PV: Battery)
Photo-voltaic (m2)
Wind turbine
Battery
Total cost
0%: 0% 0%:25% 0%:50% 25%:0% 25%:25% 25%:50% 50%:0% 50%:25% 50%:50%
0 0 0 0 0 1000 0 0 0
5 5 4 6 4 5 5 6 3
0 0 1 0 0 1 0 0 1
3.44 3.44 3.35 3.46 3.46 3.37 3.44 3.46 3.38
Table 7 Simulation result (Tokasiki)
renewable energy is small, the power supply from diesel generator is large. Fig. 12(c) shows that when the power supply is larger than the power demand, the surplus power is stored in battery. Conversely, when the power supply is smaller than the power demand, insufficient power is supplied from battery. Also if the surplus power exceeds the inverter capacity, the surplus power exceeding the inverter capacity is thrown out. From Fig. 12(e), when the power supply from the renewable is huge, a lot of disposal power is generated. From Fig. 12(d), we can verify that battery is charged and discharged in the vicinity of 50% of the capacity of battery. The capacity of battery can never be below 25%, because if the capacity of battery reduces below 25%, life time of battery becomes very short. Therefore we never allow it to be below 25% to keep life time of battery to be long. Fig. 13 shows simulation results of Kume. Fig. 13(a) shows the relationship between demand power and supply power, Fig. 13(b) shows the supply power of each facility, Fig. 13(c) shows the charge and discharge of battery, Fig. 13(d) shows the capacity of battery, and Fig. 13(e) shows the disposal of power. In Miyako, the power demand exceeds the power supply all the time. And when the power supply from renewable energy is large, the power supply from diesel generator is small. Also battery is charged and discharged in the vicinity of 50% of the capacity of battery, and the capacity of battery is never below 25%.
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Generating Power PsPl [kW]
a
30.000 Ps
25.000
Pl
20.000 15.000 10.000 0
Generating Power DpWp [kW]
b
20
40
60
80 Time [h]
100
120
140
160
140
160
30.000 Dp
Wp 20.000 10.000 0 0
Supply Power Bp[kW]
c
Capacity Bc[kW]
40
60
80
100
120
Time [h] 2400 1200 0 −1200 −2400
d
20
0
20
40
60
80 100 Time [h]
0
20
40
60
80
120
140
160
11.250 9.000 6.750 4.500 2.250 0
Dispose power Pwt [kW]
e
100
120
140
160
Time [h] 12.000 9.000 6.000 3.000 0 0
20
40
60
80
100
120
140
160
Time [h]
Fig. 12. Operation in Miyako in January 1993. (a) Demand and supply power, (b) supply power of each facility, (c) charge and discharge of battery, (d) capacity of battery and (e) disposal of power.
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Generating Power Ps Pl [kW]
a
8.000 7.000 6.000 5.000 4.000 3.000 2.000
Ps
0
Generating Power Dp Wp[kW]
b
20
40
1931
Pl
60
80
100
120
140
160
Time [h] 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0
Wp
0
20
40
60
80
Dp
100
120
140
160
100
120
140
160
100
120
140
Time [h] Supply Power Bp[kW]
c
750 500 250 0 −250 −500 −750 0
20
40
60
80 Time [h]
Capacity Bc [kW]
d
3.750 3.000 2.250 1.500 750 0 0
20
40
60
80
160
Time [h] Dispose power Pwt [kW]
e
3.000 2.500 2.000 1.500 1.000 500 0 0
20
40
60
80
100
120
140
160
Time [h]
Fig. 13. Operation in Kume in Jannuary 1993. (a) Demand and supply power, (b) supply power of each facility, (c) charge and discharge of battery, (d) capacity of battery and (e) disposal of power.
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Generating Power PsPl[kW]
a
2.500 Pl
Ps 2.000 1.500 1.000 500 0
20
40
60
80
100
120
140
160
Time [h] Generating Power WpDp[kW]
b
2.500 Wp
2.000
Dp
1.500 1.000 500 0 0
20
40
60
80
100
120
140
160
Time [h] Dispose power Pwt [kW]
c
1.000 750 500 250 0 0
20
40
60
80
100
120
140
160
Time [h]
Fig. 14. Operation in Tokashiki in January 1993. (a) Demand and supply power, (b) supply power of each facility and (c) disposal of power.
Fig. 14 shows the simulation results in Tokashiki. Fig. 14(a) shows the relationship between demand power and supply power, Fig. 14(b) shows the supply power of each facility, and Fig. 14(c) shows the disposal of power. As for as Miyako and Kume, in these areas the power demand exceeds the power supply all the time, and when the power supply from renewable energy is large, the power supply from diesel generator is small. But since Tokashiki has no battery, the ratio of disposal power is large as compared to other islands. 6. Conclusions In this paper, we present the optimal configuration of power generating systems in isolated islands with renewable energy using GA. To use the proposed method, we can determine the optimum number of solar array panels, wind turbine generators, and batteries. Also we could verify that cutting-cost of the total cost is achieved for 1 year power supply simulations for each isolated island. In addition, the proposed strategy will be able to adjust when isolation, wind speed, power demand, rating of each generator, and
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initial cost of each facility are changed. Hence the proposed strategy can be applied for marking decision of the various optimum configurations. Acknowledgment A part of the financial support of TOSTEM Foundation for Construction Materials Industry Promotion is gratefully acknowledged. References [1] Borowy BS, Salmeh ZM. Methodology for optimally sizing the combination of battery bank and PV array in a wind/PV hybrid system. IEEE Trans Energy Convers 1996;11(2):367–75. [2] Chadid R, Rahman S. Unit sizing and control of hybrid wind–solar power system. IEEE Trans Energy Convers 1997;12(1):79–84. [3] Kellogg WK, Nehrir MH, Venkataramanan G, Gerez V. Generation unit sizing and cost analysis for stand-alone wind, photovoltaic, and hybrid wind/PV system. IEEE Trans Energy Convers 1998;13(1):70–5.
Renewable Energy 32 (2007) 1917–1933 www.elsevier.com/locate/renene
Optimal configuration of power generating systems in isolated island with renewable energy Tomonobu Senjyua, Daisuke Hayashia, Atsushi Yonaa, Naomitsu Urasakia, Toshihisa Funabashib, a
Faculty of Engineering, University of the Ryukyus, 1 Senbaru, Nishihara-cho, Nakagami, Okinawa 903-0213, Japan b Meidensha Corporation, 36-2 Nihonbashi Hakozakicho, Chuo-ku, Tokyo 103-8515, Japan Received 2 September 2005; accepted 22 September 2006 Available online 20 February 2007
Abstract In isolated islands, usually diesel generators supply electric power. However, there are problems, e.g., a lack of fossil fuel, environmental pollution etc. So, isolated island, e.g. Miyako island, installs renewable energy power production plants. However, renewable energy power production plants are very costly. This paper presents an optimal configuration of power system in isolated island installing renewable energy power production plants. The generating system consists of diesel generators, wind turbine generators, PV system and batteries. Using the proposed method, operation cost can be reduced about 10% in comparison with diesel generators only from simulation results. r 2007 Elsevier Ltd. All rights reserved. Keywords: Isolated island; Renewable energy; Optimum configuration
1. Introduction Okinawa, which is located in southeast in Japan has about 40 isolated islands. These islands mostly depend on diesel generators for power supply since islands are too far from mainland of Okinawa and areas of islands are so small. Hence diesel generators in isolated island need a transportation cost and an inventory carrying cost of fuel. The generation cost of diesel generators in isolated islands per kWh is very expensive compared with a Corresponding author. Tel.: +81 3 5641 9310; fax: +81 3 5641 7509.
E-mail addresses: [email protected] (T. Senjyu), [email protected] (T. Funabashi). 0960-1481/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2006.09.003
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conventional generation. Since power supply in isolated islands needs a huge cost, reducing the generating cost of diesel generators is very important. On the other hand, the social interest for global environmental concerns and reduction in fossil fuel increase. One of the solutions for these issues is to introduce a renewable energy such as PV system and wind turbine generator which are clean and infinite energy. However, renewable energy sources have demerits that output of renewable energy sources are fluctuated by weather and wind speed, initial cost of facilities is very high, and facilities of renewable energy need regular maintenance cost. Therefore, we evaluate introducing a hybrid generating system in terms of performance and endurance of renewable energy source to obtain availability of renewable energy. We need to reduce both initial and operation costs with optimum configuration. Most of the works reported so far use the hourly average data of isolation, wind speed, and power demand over a few years for simulation [1–3]. But actually, it is near about impossibility that weather conditions are the same everyday. Therefore under the conditions varying every day and every hour, optimum number of facilities using the hourly average data may not be able to supply without outages over a year. Also most of these studies use the iteration method to determine an optimum generating capacity and storage capacity. However, these methods take long time, and it is difficult to adjust their capacities if isolation, wind speed, power demand, rating of each generator, and initial cost of each facility are changed. Therefore in this study, we propose the optimal configuration of power generating systems in isolated island with renewable energy using actual hourly data over a year. The optimization method used in this paper is the Generic Algorithm (GA). The objective function of GA is the total cost which is sum of initial and operation costs per year. By minimizing the total cost, we can achieve an inexpensive and clean electrical power system. In addition, the proposed method can adjust even when data of load, location, and facilities such as PV system and wind turbine generators are changed. 2. Scale of isolated island In this paper, we assume that the isolated islands are Miyako, Kume, and Tokashiki in Okinawa, Japan. Each isolated island data is shown in Table 1, and each plant data is shown in Table 2. In this study, wind speed and isolation data are used at mainland of Okinawa in 1993. Also, power demand data of each island used is derived by multiplying peak power demand ratio to power demand data for mainland Okinawa.
Table 1 Isolated island data Island’s name
Miyako
Kume
Tokashiki
Peak power demand Peak power demand ratio to mainland Okinawa Capacity of diesel generator
50,000 kW 1/25 10,000 kW 4 5000 kW 4 47.0
11,000 kW 1/100 3000 kW 2 1500 kW 4 11.5
3500 kW 1/324 1000 kW 2 500 kW 5 3.65
Operating cost diesel generator (million yen)
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Table 2 Plant data Photovoltaic Initial cost per 1000 m2 Maximum area Life time
1 million yen 127,000 m2 15 years
Wind turbine Rated output power Initial cost Maximum number of equipment Life time
600 kW 2.5 million yen 127 15 years
Diesel generator Fuel cost
20 yen/kWh
Battery Capacity Inverter capacity Initial cost Maximum number of equipment Life time
3000 kW 750 kVA 10 million yen 63 15 years
3. Formulation In this section, we will formulate the problem. The variables used in this study are shown in Table 3. The configuration of a hybrid generating system used in the paper is shown in Fig. 1. This system consists of wind turbine generators, PV system, batteries, and diesel generators. The supply power Ps is sum of the output power of PV system Sp, wind turbine generators Wp, batteries Bp, and diesel generators Dp: Ps ¼ Sp þ W p þ Bp þ Dp ,
(1)
where positive values of Bp mean an operation of discharge and negative values of Bp mean an operation of charge. The total cost Tc is sum of the initial cost Tic and the operation cost Ta as given by the following equation: T c ¼ T ic þ T a .
(2)
The initial cost Tic is sum of initial costs of each facility: T ic ¼ ðS ic þ W ic þ Bic Þ=Y n
(3)
where Sic, Wic, and Bic are the initial cost of PV system, wind turbine generators, and batteries, and Yn is the life time for each equipment, respectively. The operation cost is shown as the following equation: T a ¼ Dp t, where Dp is the total generating power of the diesel generator.
(4)
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Photovoltaic Sp Generating power Z Energy conversion efficiency, Spe Generating power per 1 m2 for 1MJ/m2 As Area of panels I Isolation Sic Initial cost Sc Cost per 1 m2 Wind turbine Win Cut-in wind speed Wout Cut-out wind speed Wrp Rated output power Wrs Rated wind speed Wp Generating power x Output coefficient Wic Initial cost Wc Cost per equipment Wn Number of wind turbines Diesel Dp Total generating power Dp1 Rated power of type 1 Dp2 Rated power of type 2 Dn1 Number of running diesel generator 1 Dn2 Number of running diesel generator 2 t Running time of diesel generator Battery Bic Initial cost Bn Number of batteries Be Cost per equipment (3000 kW) Bi Inverter capacity Variable of operation Tc Total cost Tic Total initial cost Ta Operation cost Yn Life time t Running time of diesel generator Ps Power supply Pl Power demand
3.1. PV System Output power of the PV system Sp is expressed as a function of isolation: S p ¼ ZS pe As I,
(5)
where Z, Spe, and I are the energy conversion efficiency, a generating power per 1 m2 for 1 MJ/m2, and an isolation, respectively. Initial cost of solar array panel Sic is proportional
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MPPT
PV arrays
AC
Diesel
DC
Rectifier AC
L o a d
AC
DC
DC
Inverter Wind turbines Battery
Fig. 1. System configuration.
Generating Power Wp [kW]
800
Wrp
400
200
0 0
Win
10 Wrs 15 20 Wind Speed Ws [m/s]
Wout
30
Fig. 2. Characteristic of output power of wind generator.
to number of solar array panels As: Sic ¼ Sc As ,
(6) 2
where Sc is the cost per 1 m of solar array panel. 3.2. Wind turbine generator Output characteristic of wind turbine generator used in this study is shown in Fig. 2. A wind turbine generator needs to consider the cut-in wind speed Win and the cut-out wind speed Wout. If wind speed exceeds the cut-in value, the wind turbine generator starts generating. If wind speed exceeds the rated wind speed Wrp, then it generates constant output, and if the wind speed exceeds the cut-out value, the wind turbine generator stops
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running to protect the generator: Wp ¼ 0 W p ¼ xðW s W in ÞW n W p ¼ W rp W n
9 ðW s oW in ; W s 4W out Þ > = ðW in oW s oW rs Þ > ; ðW oW oW Þ rs
s
(7)
out
where x is the slope between Win and Wrs. Initial cost of the wind turbine generators is proportional to the number of wind turbines Wn: W ic ¼ W c W n ,
(8)
where Wc is a cost per generator of wind turbine generators. 3.3. Diesel generator Two types of diesel generators are used in this study, and their capacities are shown in Table 1. In Table 1, capacity Bp and number of diesel generators are the actual data installed from on Miyako, Kume, and Tokashiki islands. Generating power of diesel generators Dp is expressed as Dp ¼ Dn1 Dp1 þ Dn2 Dp2 ,
(9)
where Dp1 and Dp2 are the rated power of type 1 and 2, and Dn1 and Dn2 are the number of running diesel generators of type 1 and 2, respectively. 3.4. Battery Initial cost of the battery Bic is proportional to the number of batteries Bn: Bic ¼ Be Bn ,
(10)
where Be is the cost per one battery of batteries. Using the above equations, we determine an optimal configuration of renewable generating systems, where total cost is reasonable. We assume that renewable energy generating system does not need operation cost because renewable energy is infinite. 4. Operation strategy Using the above-formulated equations, we will simulate the operation of hybrid generating system for 1 year. Initial cost is accounted for a year, the total initial cost is divided by life time of each facility, where we assume that all life time of facility is 15 years. Diesel generation needs to consider operation cost as fuel cost plus transport cost of fuel. However, we assume that renewable energy generating system does not need operation cost. The output power of PV system and wind turbine generators depend on isolation and wind speed, respectively. Battery is a part of PV system and wind turbine generator. So, it charges or discharges in response to condition of load, PV system and wind turbine generator. Also, if the capacity of battery is short, diesel generator compensates. Hence in
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Fig. 3. Flow chart.
this section, we will describe the operation strategy used in this study. The flow chart of operation is shown in Fig. 3, all the steps are explained below: Step 1: If the power supply from renewable energy is smaller than the power demand, go to Step 2. Alternatively, if the power supply from renewable energy is larger than the power demand, go to Step 3. Step 2: If the remaining capacity of battery is larger than 50%, go to Step 4. Alternatively, if the remaining capacity of battery is smaller than 50%, go to Step 5. Step 3: If the surplus power from renewable energy ( ¼ Sp+WpPl) is smaller than the inverter capacity of battery Bi which can be stored in battery per 1 h, go to Step 6. Alternatively, if the surplus power from renewable energy is larger than the inverter capacity of battery Bi, go to Step 7. Step 4: Minimum number of diesel generators to meet power demand is activated, and the surplus power( ¼ Dp+Sp+WpPl) is stored in the battery. Step 5: If the insufficient power from renewable energy is smaller than the inverter capacity, go to Step 8. Alternatively, if the insufficient power only from renewable energy is larger than the inverter capacity, go to Step 9. Step 6: Charge inverter capacity to battery, and remaining surplus power ( ¼ Sp+WpPlBi) is thrown out. Here, if battery becomes full, charge surplus power until battery becomes full and remaining surplus power is thrown out. Go to Step 10. Step 7: Charge all surplus power in battery. Here, if battery becomes full, charge surplus power until battery become full and remaining surplus power is thrown out. Go to Step 10. Step 8: Discharge the insufficient power from battery. And go to Step 10. Step 9: Discharge within inverter capacity, in addition minimum number of diesel generator to meet power demand are activated. And the surplus power( ¼ Dp+Sp+ Wp+BiPl) is charged in battery.
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Step 10: If time t does not reach the end of simulation, increase t ¼ t+1 and go to Step 1. If time t reaches end of simulation, go to End. 5. Simulation results The purposed method in this study is used to determine the optimal configuration of renewable energy with minimum of total cost. In this section, we perform the simulations for Miyako, Kume, and Tokashiki, using data of isolation, wind speed, and power demand for the year 1993. 5.1. GA used in this paper The GA flow chart to optimize the number of each facility is shown in Fig. 4. Also, each individual is represented by binary digits 1 and 0, and a distribution for the number of each facility is shown in Fig. 5. In this study, parameters of GA are selected based on the onepoint crossover and the mutation rate is 0.3. We will describe the optimization flow chart as follows: With the available isolation, wind speed, and power demand data determine the initial set up of each facility at random. Next, operate 1 year, and calculate the operation cost,
Fig. 4. Flow chart of optimization using GA.
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Fig. 5. Individual example of GA.
Total cost [ million yen / year ]
48 47 46 45 44 43 42 0
500
1000
1500 Generation
2000
2500
3000
Fig. 6. Total cost (Miyako).
and the total cost for 1 year which includes the one year operation and initial costs. Determine the facility arrangement using GA, with the fitness function being the total cost. The one-point crossover and the mutation are implemented. And if termination condition is not satisfied, go to Operation of next generation. Alternatively, if the condition is satisfied, simulation is finished, where individual of the most reasonable total cost is the optimum solution. 5.2. Simulation results of optimization We perform simulations for Miyako, Kume, and Tokashiki. Fig. 6 shows the transition of the total cost in Miyako, where the horizontal axis gives the generation and the vertical axis gives the total cost. Fig. 7 shows the transition of the optimal number of facilities in Miyako, where horizontal axis gives the generation of and vertical axis gives the optimal number of facilities. Likewise Fig. 8 shows the transition of the total cost in Kume, and Fig. 9 shows the transition of the optimal number of facilities in Kume. Fig. 10 shows the transition of the total cost in Tokashiki and Fig. 11 shows the transition of the optimal number of facilities in Tokashiki. The above results are tabulated in this table. From Table 4, the optimum number of solar array panels, wind turbine generators, and batteries in Miyako are 0, 61, and 3, respectively. In Kume, they are 0, 16, and 1, and in Tokashiki they are 0, 5, and 0, respectively. Besides, the cut-down cost in Miyako is 4.0 million yen/ year, In Kume it is 0.7 million yen/year, and in Tokashiki it is 0.21 million yen/year. In all the islands, the number of photovoltaic sources is zero since initial cost of PV system is so expensive and energy conversion efficiency is low.
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70
Number of equipment
60 50
Sn Wn
40
Bn
30 20 10 0 0
500
1000
1500
2000
2500
3000
Generation
Fig. 7. Optimal number of facilities (Miyako).
12.0
Total cost [millionyen / year]
11.8 11.6 11.4 11.2 11.0 10.8 0
500
1000
1500
2000
2500
3000
Generation
Fig. 8. Total cost (Kume).
5.3. Cost analysis Next, we will examine the special conditions that the grant rate is introduced for initial costs of PV system and batteries. Here, we assume that the grant rates are 25% and 50% for each case. This simulation results for Miyako, Kume, and Tokashiki are shown in Tables 5, 6, and 7, respectively. From the above results, the number of photovoltaic sources does not increase even though the initial cost of PV system is reduced. Also when the initial cost of battery is reduced, the number of batteries in Miyako and Tokashiki slightly increases, but in Kume it is constant.
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18 16 Number of equipment
14 12 Sn
10
Wn
8
Bn
6 4 2 0 0
500
1000
1500
2000
2500
3000
Generation
Fig. 9. Optimal number of facilities (Kume).
3.70
Total cost [millionyen / year]
3.65 3.60 3.55 3.50 3.45 3.40 0
500
1000
1500
2000
2500
3000
Generation
Fig. 10. Total cost (Tokasiki).
5.4. Operation on optimum configuration We perform power supply simulations for 1 year with an optimum configuration determined by GA. The simulation period is through 1st to 7th January in 1993. The simulation results for Miyako, Kume, and Tokashiki are shown in Figs. 12, 13, and 14, respectively. Fig. 12 shows the simulation results in Miyako. Fig. 12(a) shows the relationship between demand power and supply power, Fig. 12(b) shows the supply power of each facility, Fig. 12(c) shows the charge and discharge of battery, Fig. 12(d) shows the capacity of battery, and Fig. 12(e) shows the disposal of power.
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6
Number of equipment
5 4
Sn Wn
3
Bn 2 1 0 0
500
1000
1500 Generation
2000
2500
3000
Fig. 11. Optimal number of facilities (Tokasiki).
Table 4 Simulation result Scale of power demand
Large
Medium
Small
Name of island Photovoltaic (m2) Wind turbine Battery Total cost (million yen) Operating cost for diesel generators only Cut down cost
Miyako 0 61 3 43.0 47.0 4.0
Kume 0 16 1 10.8 11.5 0.7
Tokashiki 0 5 0 3.44 3.65 0.21
Table 5 Simulation result (Miyako) The grant rate (PV: Battery)
Photo-voltaic (m2)
Wind turbine
Battery
Total cost
0%: 0% 0%:25% 0%:50% 25%:0% 25%:25% 25%:50% 50%:0% 50%:25% 50%:50%
0 0 0 0 0 0 1000 2000 1000
61 55 55 60 55 54 59 55 55
3 4 4 3 4 4 3 4 4
43.0 42.4 41.8 43.0 42.4 41.8 43.0 42.4 41.8
From Fig. 12(a), the power demand exceeds the power supply all the time. Also from Fig. 12(b), we can verify that when the power supply from renewable energy is large, the power supply from diesel generator is small. Conversely, when the power supply from
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Table 6 Simulation result (Kume) The grant rate (PV: Battery)
Photo-voltaic (m2)
Wind turbine
Battery
Total cost
0%: 0% 0%:25% 0%:50% 25%: 0% 25%:25% 25%:50% 50%: 0% 50%:25% 50%:50%
0 0 0 0 0 0 0 0 0
16 15 13 13 15 13 14 15 14
1 1 1 1 1 1 1 1 1
10.8 10.7 10.5 10.8 10.7 10.5 10.8 10.7 10.5
The grant rate (PV: Battery)
Photo-voltaic (m2)
Wind turbine
Battery
Total cost
0%: 0% 0%:25% 0%:50% 25%:0% 25%:25% 25%:50% 50%:0% 50%:25% 50%:50%
0 0 0 0 0 1000 0 0 0
5 5 4 6 4 5 5 6 3
0 0 1 0 0 1 0 0 1
3.44 3.44 3.35 3.46 3.46 3.37 3.44 3.46 3.38
Table 7 Simulation result (Tokasiki)
renewable energy is small, the power supply from diesel generator is large. Fig. 12(c) shows that when the power supply is larger than the power demand, the surplus power is stored in battery. Conversely, when the power supply is smaller than the power demand, insufficient power is supplied from battery. Also if the surplus power exceeds the inverter capacity, the surplus power exceeding the inverter capacity is thrown out. From Fig. 12(e), when the power supply from the renewable is huge, a lot of disposal power is generated. From Fig. 12(d), we can verify that battery is charged and discharged in the vicinity of 50% of the capacity of battery. The capacity of battery can never be below 25%, because if the capacity of battery reduces below 25%, life time of battery becomes very short. Therefore we never allow it to be below 25% to keep life time of battery to be long. Fig. 13 shows simulation results of Kume. Fig. 13(a) shows the relationship between demand power and supply power, Fig. 13(b) shows the supply power of each facility, Fig. 13(c) shows the charge and discharge of battery, Fig. 13(d) shows the capacity of battery, and Fig. 13(e) shows the disposal of power. In Miyako, the power demand exceeds the power supply all the time. And when the power supply from renewable energy is large, the power supply from diesel generator is small. Also battery is charged and discharged in the vicinity of 50% of the capacity of battery, and the capacity of battery is never below 25%.
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Generating Power PsPl [kW]
a
30.000 Ps
25.000
Pl
20.000 15.000 10.000 0
Generating Power DpWp [kW]
b
20
40
60
80 Time [h]
100
120
140
160
140
160
30.000 Dp
Wp 20.000 10.000 0 0
Supply Power Bp[kW]
c
Capacity Bc[kW]
40
60
80
100
120
Time [h] 2400 1200 0 −1200 −2400
d
20
0
20
40
60
80 100 Time [h]
0
20
40
60
80
120
140
160
11.250 9.000 6.750 4.500 2.250 0
Dispose power Pwt [kW]
e
100
120
140
160
Time [h] 12.000 9.000 6.000 3.000 0 0
20
40
60
80
100
120
140
160
Time [h]
Fig. 12. Operation in Miyako in January 1993. (a) Demand and supply power, (b) supply power of each facility, (c) charge and discharge of battery, (d) capacity of battery and (e) disposal of power.
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Generating Power Ps Pl [kW]
a
8.000 7.000 6.000 5.000 4.000 3.000 2.000
Ps
0
Generating Power Dp Wp[kW]
b
20
40
1931
Pl
60
80
100
120
140
160
Time [h] 7.000 6.000 5.000 4.000 3.000 2.000 1.000 0
Wp
0
20
40
60
80
Dp
100
120
140
160
100
120
140
160
100
120
140
Time [h] Supply Power Bp[kW]
c
750 500 250 0 −250 −500 −750 0
20
40
60
80 Time [h]
Capacity Bc [kW]
d
3.750 3.000 2.250 1.500 750 0 0
20
40
60
80
160
Time [h] Dispose power Pwt [kW]
e
3.000 2.500 2.000 1.500 1.000 500 0 0
20
40
60
80
100
120
140
160
Time [h]
Fig. 13. Operation in Kume in Jannuary 1993. (a) Demand and supply power, (b) supply power of each facility, (c) charge and discharge of battery, (d) capacity of battery and (e) disposal of power.
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Generating Power PsPl[kW]
a
2.500 Pl
Ps 2.000 1.500 1.000 500 0
20
40
60
80
100
120
140
160
Time [h] Generating Power WpDp[kW]
b
2.500 Wp
2.000
Dp
1.500 1.000 500 0 0
20
40
60
80
100
120
140
160
Time [h] Dispose power Pwt [kW]
c
1.000 750 500 250 0 0
20
40
60
80
100
120
140
160
Time [h]
Fig. 14. Operation in Tokashiki in January 1993. (a) Demand and supply power, (b) supply power of each facility and (c) disposal of power.
Fig. 14 shows the simulation results in Tokashiki. Fig. 14(a) shows the relationship between demand power and supply power, Fig. 14(b) shows the supply power of each facility, and Fig. 14(c) shows the disposal of power. As for as Miyako and Kume, in these areas the power demand exceeds the power supply all the time, and when the power supply from renewable energy is large, the power supply from diesel generator is small. But since Tokashiki has no battery, the ratio of disposal power is large as compared to other islands. 6. Conclusions In this paper, we present the optimal configuration of power generating systems in isolated islands with renewable energy using GA. To use the proposed method, we can determine the optimum number of solar array panels, wind turbine generators, and batteries. Also we could verify that cutting-cost of the total cost is achieved for 1 year power supply simulations for each isolated island. In addition, the proposed strategy will be able to adjust when isolation, wind speed, power demand, rating of each generator, and
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initial cost of each facility are changed. Hence the proposed strategy can be applied for marking decision of the various optimum configurations. Acknowledgment A part of the financial support of TOSTEM Foundation for Construction Materials Industry Promotion is gratefully acknowledged. References [1] Borowy BS, Salmeh ZM. Methodology for optimally sizing the combination of battery bank and PV array in a wind/PV hybrid system. IEEE Trans Energy Convers 1996;11(2):367–75. [2] Chadid R, Rahman S. Unit sizing and control of hybrid wind–solar power system. IEEE Trans Energy Convers 1997;12(1):79–84. [3] Kellogg WK, Nehrir MH, Venkataramanan G, Gerez V. Generation unit sizing and cost analysis for stand-alone wind, photovoltaic, and hybrid wind/PV system. IEEE Trans Energy Convers 1998;13(1):70–5.