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Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan
Applied Energy xxx (2012) xxx–xxx
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan Yen-Haw Chen a, Su-Ying Lu a, Yung-Ruei Chang b, Ta-Tung Lee c, Ming-Che Hu c,⇑ a
Taiwan Institute of Economic Research, Research Division 1, 7F, No. 16-8 Dehuei Street, Jhongshan District, Taipei 104, Taiwan Institute of Nuclear Energy Research, Atomic Energy Council, Taiwan, No. 1000, Wenhua Rd., Jiaan Village, Longtan Township, Taoyuan County 32546, Taiwan c Department of Bioenvironmental Systems Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan b
h i g h l i g h t s " An optimization model of energy supply in microgrid system is formulated. " Optimal energy management strategies are determined. " Sensitivity analyses of storage capacity and energy demand is performed.
a r t i c l e
i n f o
Article history: Received 15 September 2011 Received in revised form 10 September 2012 Accepted 11 September 2012 Available online xxxx Keywords: Microgrid Optimization Sensitivity analysis
a b s t r a c t The purpose of this research is to perform economic analysis, formulate an optimization model, and determine optimal operating strategies for smart microgrid systems. Microgrid systems are electricity supply systems that integrate distributed renewable energy production for local demand. Microgrids are able to reduce transmission losses and improve utilization efficiency of electricity and heat. Further, greenhouse gas emissions are reduced by utilizing an efficient power generation microgrid system. This study presents an energy management model that is used to determine optimal operating strategies with maximum profit for a microgrid system in Taiwan. The smart microgrid system is equipped with energy storage devices, photovoltaic power, and wind power generation systems. Sensitivity analyses of investment in storage capacity and growth in electricity demand are conducted for the smart microgrid model. The results show that appropriate battery capacity should be determined on the basis of both battery efficiency and power supply. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Microgrids are community-level electricity systems that provide diversification and reliability of energy supply, integration of distributed renewable energy, and reduction of transmission losses and greenhouse gas emissions [1–3]. Microgrid systems are able to generate, transmit, distribute, store energy, and satisfy energy demand locally [4–8]. Microgrid systems have been designed and field tested in the UK [9,10]. The UK systems include combined heat and power, renewable energy, boiler generators, and batteries in leisure center, hospital, and hotel applications. The operating strategies of the UK systems were determined by minimizing total cost of investment and operation and maintenance costs. In addition, the New Energy Industrial Technology Development Organization in Japan has built and tested three microgrid systems [11–
⇑ Corresponding author. Tel.: +886 2 33663448; fax: +886 2 23635854. E-mail address: [email protected] (M.-C. Hu).
13]. The Japanese systems contain small, distributed power generators, batteries, and heat storage facilities. Economic and optimization analyses were performed to determine investment and optimal operating strategies of microgrid systems. Microgrids have successfully met expectations and been promoted around the world. In Taiwan, the Institute of Nuclear Energy Research (INER) has installed and field-tested a microgrid system. The INER microgrid comprises a 25 kW wind power generator, a 150 kW wind power generator, a 100 kW solar power generator, fuel cell, and battery storage devices. The energy demand of the INER system is simulated by a combination of two office buildings and a family house with lighting, air condition, and other electrical equipment. Most related studies focus on advanced microgrid control technologies [14–18]. This paper formulates an optimization model for microgrid energy management, and determines its optimal operating strategies. In addition, economic analysis and sensitivity analysis of microgrid systems are conducted. Economic indicators are calculated to determine optimal investment in power generators
0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.09.023
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
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Nomenclature Indices e i t
N
wdi equipment, e = 1, 2, . . . , E node of transmission network, i = 1, 2, . . . , I time period, t = 1, 2, . . . , T
N
bmi gtNi
Coefficients PVCA installed solar power capacity (kW) VCPV variable cost of solar power generation ($/kW h) WDCA installed wind power capacity (kW) variable cost of wind power generation ($/kW h) VCWD BMCA installed biomass power capacity (kW) ERBM CO2 emission rate from biomass electricity generation (kg/kW h) FRBM biomass needed for biomass electricity (kg/kW h) HRBM heat production of biomass power generator (J/kW) RCBM biomass feedstock cost ($/kg) VCBM variable cost of biomass power generation ($/kW h) installed gas turbine power capacity (kW) GTCA ERGT CO2 emission rate from gas turbine electricity generation (kg/kW h) FRGT gas needed for gas turbine electricity (m3/kW h) GT HR heat production of gas turbine power generator (J/kW) RCGT natural gas cost ($/m3) GT VC variable cost of gas turbine power generation ($/kW h) installed fuel cell power capacity (kW) FCCA ERFC CO2 emission rate from fuel cell electricity generation (kg/kW h) FRFC hydrogen needed for fuel cell electricity (m3/kW h) hydrogen cost ($/m3) RCFC FC VC variable cost of fuel cell power generation ($/kW h) BKt hours per block (h) PR electricity price ($/kW h) HEATDe;t heat demand of equipment e at time t (J) ELEDe;t electricity demand of equipment e at time t (kW) Decision variables profit total profit ($) pvNi number of solar power generators in microgrids at node i (dimensionless)
and battery devices, including payback period, present value, and net cash flow of microgrid systems. The optimization model for microgrid energy management is formulated as an integer programming model on the General Algebraic Modeling System (GAMS) and is solved by CPLEX solver. GAMS is a modeling system with efficient optimizers to solve complex and large-scale optimization and mathematical programming problems [19]. CPLEX is one of the most efficient optimizers on GAMS; CPLEX solves large linear programming, integer programming, and quadratic constrained problems. The GAMS and CPLEX outputs are used to inform optimal investment and operating solutions with minimal cost for microgrid systems. Significant contributions of this research are discussed as follows. This paper develops an optimal microgrid management model and determines optimal operation of microgrid systems. Next, the optimization management model is tested for the INER microgrid system in Taiwan. Further, economic analysis and sensitivity analysis of microgrid investment are simulated. The structure of this paper is as follows. Section 2 reviews microgrid-related studies in the literature. The optimization model for microgrid energy management is described in Section 3. In Section 4, a case study of the INER microgrid system in Taiwan is conducted, and eco-
N
fci
N
bti
mi,e pvGEN i;t GEN
wdi;t
GEN
bmi;t
gtGEN i;t GEN
fci;t
elei,t IN
number of wind power generators in microgrids at node i (dimensionless) number of biomass power generators in microgrids at node i (dimensionless) number of gas turbines in microgrids at node i (dimensionless) number of fuel cells in microgrids at node i (dimensionless) number of batteries in microgrids at node i (dimensionless) binary variable (mi,e = 1 if equipment e is turned on; mi,e = 0 otherwise) hourly energy production from solar power at node i at time t (kW) hourly energy production from wind power at node i at time t (kW) hourly energy production from biomass at node i at time t (kW) hourly energy production from gas turbine at node i at time t (kW) hourly energy production from fuel cell at node i at time t (kW) storage capacity of batteries at node i at time t (kW)
elei;t
power input of batteries at node i at time t (kW)
OUT elei;t
power output of batteries at node i at time t (kW) heat stored at time t (J)
heatt IN
heatt
heat input to heat storage at time t (J)
OUT heatt FUEL bmi;t gtFUEL i;t FUEL fci;t EM bmi;t
hourly heat output from heat storage at time t (J)
gtEM i;t EM
fci;t
biomass used at node i at time t (kg) gas used by gas turbine at node i at time t (m3) hydrogen used by fuel cell at node i at time t (m3) carbon dioxide emission of biomass at node i at time t (kg) carbon dioxide emission of gas turbine at node i at time t (kg) carbon dioxide emission of fuel cell at node i at time t (kg)
nomic analysis and uncertainty analysis are performed for the system. The conclusions are discussed in Section 5.
2. Literature review Some previous researchers have performed optimization and economic analysis to determine optimal energy management and capacity investment strategies [20–23]. Optimization modeling was used to schedule optimal installation and operation of a renewable microgrid in an isolated area [24]. Then a mixed-integer linear programming problem was formulated to integrate and manage fuel cell, solar power, wind power generators, and battery storage devices. A dynamic programming model of Distributed Energy Resources (DERs) microgrid systems was formulated [25]. To increase the reliability of power supply, optimal microgrid architectures connecting power generation and load were determined. An economic analysis of distributed energy resources in microgrid systems was performed [26]. A linear programming model and a numerical simulation were developed to determine the optimal operating pattern for a microgrid operating in factory, grocery store, sports center, hotel, office, and hospital applications.
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
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Previous studies have investigated risk and uncertainty associated with microgrid systems. Handschin et al. formulated a stochastic programming model to perform uncertainty analysis [27], in which optimal operation of dispersed generation was decided under conditions of power price uncertainty. Siddiqui and Marnay considered uncertainty in electricity price and natural gas production within the California power market [28]; distributed capacity investment of power generation was analyzed for microgrid systems under uncertainty. Monte Carlo simulation and agent-based simulation methods have been used to investigate the dynamic performance of microgrid systems. Firestone and Marnay built a simulation model for a dynamically adaptable microgrid system [29]. Given technical and financial constraints, the optimal control solution and energy manager (EM) for the microgrid were determined. An agent-based model was established to simulate power-trading strategies between power buyers, sellers, and grid operators [30]. The model assumed that each agent behaved with artificial intelligence in the markets. Interaction among agents and dynamic equilibrium in the market were presented. A fuzzy neural network algorithm was applied to a distributed intelligent energy management system [31]. Optimal power control strategies were determined for a single-phase high-frequency alternating current microgrid. A microsource model was formulated to analyze islanded operation of microgrids [32]. The model discussed control strategies for the feasibility and stability of power supply in the systems. Previous researchers have studied optimal power flow, dynamic agent-based simulation, sensitivity analysis, and economic analysis for microgrids [33–35]. However, this paper integrates optimal energy management, capacity expansion, uncertainty analysis, payback period, and cash flow analysis of the INER microgrid system in Taiwan. An optimization model is formulated; then optimal investment and operating decisions are presented. System performance of the Taiwanese INER microgrid system is measured in the results. 3. Methodology
Solar
Electricity storage
Max profit ¼ Ri;t ½ðPR VCPV Þ BKt pvGEN þ ðPR VCWD Þ i;t GEN
Wind power
Biomass power
Electricity demand
Gas Turbine
Heat demand
Fig. 1. Configuration of the microgrid system.
Fuel cell
Heat storage
GEN
BKt wdi;t þ ðPR VCBM Þ BKt bmi;t FUEL
ðRCBM Þ bmi;t
þ ðPR VCGT Þ BKt gtGEN i;t GEN
ðRCGT Þ gtFUEL þ ðPR VCFC Þ BKt fci;t i;t FUEL
ðRCFC Þ fci;t ðICBM BT
ðIC
N bmi Þ
N bti Þ
N
ðICPV pvNi Þ ðICWD wdi Þ
ðICGT gtNi Þ ðICFC
N fci Þ
ð1Þ
Constraints upon the microgrid operating system are examined in the following stage. Assuming multiple generators are installed within the microgrid system, capacity constraints of electricity generators are addressed in Eqs. (2)–(6).
pvNi PVCA P pvGEN i;t
Microgrid systems contain distributed energy generators and storage devices, including gas turbine, fuel cell, wind power, solar power, biopower generators, battery, and heat storage technologies [36–41]. This section first plots the scope of microgrid system (see Fig. 1). Then an optimization model of the energy management system for the studied microgrid is introduced. The decision GEN GEN GEN GEN variables include pvGEN (kW), reprei;t , wdi;t , bmi;t , gti;t , and fci;t senting electricity generation of photovoltaic, wind, biomass, gas turbine, and fuel cell generators in node i at time t. In addition, BKt is the number of hours at time t; PR ($/kW h) and VC ($/ kW h) represent electricity price and production cost, respectively.
power
The objective function maximizes total profit which is equal to electricity power revenue minus generation cost. The profit earned from power generation in photovoltaic, wind, biomass, gas turbine, and fuel cell components of the grid are represented as GEN ðPR VCPV Þ BKt pvGEN ðPR VCWD Þ BKt wdi;t , ðPR i;t , GEN BM GT GEN VC Þ BKt bmi;t , ðPR VC Þ BKt gti;t , ðPR VCFC Þ GEN FUEL FUEL BKt fci;t . Further, bmi;t , gtFUEL , and fci;t represent biomass i;t feedstock consumption for biomass power, natural gas consumption for gas turbine operation, and hydrogen consumption for fuel cell in node i at time t, respectively. Biomass feedstock cost, natural gas cost, and hydrogen cost are RCBM, RCGT, and RCFC. Hence, FUEL FUEL ðRCBM Þ bmt , ðRCGT Þ gtFUEL , and ðRCFC Þ fct represent total t fuel cost terms for biomass feedstock, natural gas, and hydrogen, respectively. Moreover, the size of the microgrid system is important for decision making. Hence, capacity expansion of renewable energy generators and storage facilities are considered within the N N N N optimization function. pvNi , wdi , bmi , gtNi , fci , and bti represent the number of photovoltaic, wind, bioenergy, gas turbine, fuel cell generators, and batteries at node i, respectively. Incorporating the above stages, the optimal microgrid size to produce maximum profit is determined via
8i; t
N
GEN
8i; t
ð3Þ
N
GEN
8i; t
ð4Þ
wdi WDCA P wdi;t bmi BMCA P bmi;t gtNi GTCA P gtGEN i;t N
ð2Þ
GEN
fci FCCA P fci;t
8i; t 8i; t
ð5Þ ð6Þ
mi,e denotes a binary decision variable of equipment e at node i that is available for consumer use; mi,e is 1 if equipment e in node i is turned on, but is otherwise 0. Power net inflow of node i at time t is denoted by yit. Then, the mass balance constraint of electric power is formulated in Eq. (7). The mass balance constraint of Eq. (8) describes that heat production from bioenergy and gas turbines is equal to total heat demand at node i. Power system operation constraints are also considered, including both of Kirchhoff’s laws. In the model, power system operation constraints are considered for direct current (DC) and alternating current (AC). In DC systems, power flows in a constant direction and, in AC systems, the flow of electric charge periodically reverses direction. In the following, two types of transmission capacity constraints are introduced. First, Kirchhoff’s Current and Voltage Laws can be simulated via DC approximation [42–44]. The transmission constraints of a linearized DC electric network are built as follows. Define PTDFik as power transmission distribution factors of node i through interface k of the transmission network. In addition, the
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx
upper and lower bounds of transmission capacity of interface k are TC1k and TC2k, respectively. Accordingly, [PTDFik yit] is power transmission through interface k, and the transmission capacity constraints are established in Eqs. (9) and (10). On the other hand, AC is predominant form of electricity transmitted and distributed to customers. To analyze delivery capacity, sinusoidal functions of AC power current and voltage are considered: v k ðtÞ ¼ V mk ðcos xt þ hVk Þ and ik ðtÞ ¼ Imk ðcos xt þ hIk Þ [45]. Eqs. (11), (12) determine the power transmission in a microgrid network and then transmission capacity constraints are formulated in Eqs. (13), (14). i Xh GEN GEN GEN IN OUT mi;e ELEDe;i;t pvGEN wdi;t bmi;t gtGEN fci;t þ elei;t elei;t ¼ yit i;t i;t
8i; t
e
ð7Þ Xh
i GEN IN OUT HRGT gtGEN þ heati;t heati;t ¼ 0 8t mi;e HEATDe;i;t HRBM bmi;t i;t
i;e
ð8Þ
Ri ½PTDFik yit 6 TC1k 8k; t Ri ½PTDFik yit 6 TC2k
ð9Þ
8k; t
ð10Þ
pk ðtÞ ¼ v k ðtÞ ik ðtÞ m V I ¼ Vm k I k ðcos xt þ hk Þ ðcos xt þ hk Þ
pk ¼ ð1=TÞ
Z
T
o
m V I pk ðtÞdt ¼ ð1=2Þ V m k I k cosðhk hk Þ
8k
pk 6 TC1k pk 6 TC2k
ð11Þ ð12Þ ð13Þ
8k
ð14Þ
Fuel consumptions of power generators are calculated in Eqs. (15)–(17). The carbon dioxide emission rates for biomass, gas turbine, and fuel cell generators are represented by ERBM, ERGT, and ERFC [kg/kW h], and total emissions of carbon dioxide are estimated in Eqs. (18)–(20). FUEL
bmi;t
GEN
¼ FRBM BKt bmi;t
gtFUEL ¼ FRGT BKt gtGEN i;t i;t FUEL
fci;t
GEN
¼ FRFC BKt fci;t
EM
8i; t
8i; t
ð17Þ
GEN
EM
GEN
ðfci;t Þ ¼ ERFC BKt fci;t
ð16Þ
8i; t
ðbmi;t Þ ¼ ERBM BKt bmi;t GT ðgtEM BKt gtGEN i;t Þ ¼ ER i;t
ð15Þ
8i; t
ð18Þ
8i; t
ð19Þ
8i; t
ð20Þ
Eq. (21) defines me as a zero–one binary variable. In addition, Eq. (21) defines gtN, fcN, bmN, pvN, and wdN to be integer variables. Non-negativity constraints of decision variables are listed in Eqs. (22)–(24).
mi;e is a zero—one binary variable 8e; i N
N
N
pvNi ; wdi ; bmi ; gtNi ; fci are positive integer variables 8i GEN
GEN
GEN
GEN pvGEN i;t ; wdi;t ; bmi;t ; gti;t ; fci;t IN
OUT
heatt ; heatt ; heatt
IN
ð21Þ
P 0 8i; t
ð22Þ
OUT
ð23Þ
; elei;t ; elei;t ; elei;t
P 0 8i; t
FUEL
FUEL
EM
EM
EM bmi;t ; gtFUEL 8i; t i;t ; fci;t ; bmi;t ; gti;t ; fci;t P 0
ð24Þ
A Taiwanese microgrid system was constructed by the Institute of Nuclear Energy Research (INER); it has a 25 kW wind power generator, a 150 kW wind power generator, a 100 kW High Concentration Photovoltaic generator, a 2 kW fuel cell generator, and a battery device for power storage. The case study measured the electricity generation of solar and wind power. The INER microgrid system also simulated electricity demand by establishing power demand for two office buildings and a family house. The installation costs for a 100 kW high-concentration photovoltaic generator, a 150 kW wind power generator, and a 25 kW wind power generator are approximately 10, 15, and 6 million NTD, respectively. In this study, the lifespan of the generators is assumed to be 20 years. The supply of INER microgrid illustrated that the 150 kW wind power generator produces about 60–70 kW in the morning and 50–75 kW in the afternoon. The 25 kW wind generator produced 7–11 kW and 8–13 kW in the morning and afternoon peaks, respectively. The data illustrated maximum wind power generation at hours 6–9 and 16–20 for both 150 kW and 25 kW wind generators. Alternatively, an HCPV power generator produced 10– 40 kW electricity at hours 9–16. The demand data demonstrated peak demand of 25–30 kW at hours 9–17. In this basic demand case, the microgrid system with renewable energy generators was able to meet electricity demand with the exception of hours 10 and 23. To analyze the sensitivity of demand growth in microgrid systems, the study examined three scenarios characterized by basic power demand, double demand, and triple demand. Data on power generation and demand were analyzed in the microgrid optimization model. The optimization model seeks maximal profit of power trading between the microgrid and the primary electricity grid; the profit is equal to power sale revenue minus power purchase cost. The case study is conducted and the outcome is discussed in the following section. 4. Results and discussion This section presents a case study of the Taiwanese INER microgrid system. First, the optimization models of the microgrids are analyzed by the CPLEX solver on the GAMS platform. Then, sensitivity analyses of battery capacity and electricity demand are examined. Further, payback period and cash flow of microgrid investment are discussed. The effect of different electricity storage capacities on Taiwanese INER microgrid systems is illustrated in this research. First, scenarios with battery capacities of 10 kW, 20 kW, 30 kW, 40 kW, and 50 kW were compared to the scenario without any battery capacity. Next, sensitivity analyses of battery capacities were tested for different demand growth scenarios including basic-demand, double-demand, and triple-demand scenarios. Hence, the extent of battery utilization for each scenario is measured by indicators including total power output of battery, total power input of battery, electricity storage capacity of battery, and battery utilization rate. Battery utilization rate is equal to power output divided by battery capacity (i.e., total electricity output/battery capacity). Moreover, electricity trading between the main electricity network and the microgrid is estimated. The impact of battery storage capacities for the basic demand, double demand, and triple demand scenarios are compared. Tables 1–3 show the battery performance, including average storage, power charge, power discharge, battery utilization (=output/capacity), electricity sale, electricity purchase, electricity demand, and total profit of the microgrid system. In Table 1, it is assumed that the system has a basic demand, and so total profit increases from 1742.0 NTD (no battery) to 1754.9 NTD (50 kW battery case) where NTD is New Taiwan Dollar
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx Table 1 Results of basic demand scenario in the microgrid for summer scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 2.0 4.8 5.3 5.8 8.3
0.0 30.0 35.8 45.8 56.6 66.6
0.0 30.0 35.8 45.8 56.6 66.6
– 299.7 179.2 152.8 141.6 133.3
643.6 621.4 611.4 601.4 591.4 585.0
58.6 36.4 26.4 16.4 6.4 0.0
493.6 493.6 493.6 493.6 493.6 493.6
1742.0 1746.8 1749.0 1751.2 1753.4 1754.9
The generation of solar power and wind power are 210 and 869 kW h, respectively.
Table 2 Results of double demand scenario in the microgrid for summer scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 5.0 9.2 14.2 17.6 20.0
0.0 20.3 40.3 60.3 80.3 79.1
0.0 20.3 40.3 60.3 80.3 79.1
– 203.2 201.6 201.1 200.8 158.1
439.2 419.2 399.2 380.5 370.5 360.5
347.8 327.8 307.8 289.1 279.1 269.1
987.1 987.1 987.1 987.1 987.1 987.1
197.7 202.1 206.5 210.6 212.8 215.0
Table 3 Results of triple demand scenario in the microgrid for summer scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 3.8 2.0 12.2 14.8 21.7
0.0 20.0 40.0 60.0 80.0 119.2
0.0 20.0 40.0 60.0 80.0 119.2
– 200.0 200.0 200.0 200.0 238.4
371.3 351.3 331.3 311.3 291.3 271.3
773.4 753.4 733.4 713.4 693.4 673.4
1480.7 1480.7 1480.7 1480.7 1480.7 1480.7
1376.6 1372.2 1367.8 1363.4 1359.0 1354.6
and the exchange rate of US dollar (USD) is about 30–33 NTD/USD. Electricity trading, including sale and purchase from outside the microgrid system, diminished by 58.6 kW h. Additionally, Table 2 shows that total profit increased from 197.7 NTD (no battery) to 215.0 NTD (50 kW battery) for double demand scenarios. Total profit increased from 1376.6 NTD (no battery) to 1354.6 NTD (50 kW battery) for triple demand scenarios, as illustrated in Table 3. Additionally, power trading fell by 78.7 kW h (=from 347.8 to 269.1 kW h) and 100 kW h (=from 773.4 to 673.4 kW h) in Tables 2 and 3, respectively. In conclusion, increased battery capacity had the effect of increasing total profit and reducing trade between the microgrid and primary electricity grid systems. It is clear that larger batteries enable greater local storage and subsequent usage of power generated within the microgrid. Nevertheless, battery utilization rate (=battery output/battery capacity) was cut by 166.4% (=from 299.7% to 133.3%) and 45.1% (=from 203.2% to 158.1%) under the basic demand scenario in Table 1, and the double demand scenario in Table 2, respectively. Table 3 illustrates that battery utilization rate increased by 38.4% (=from 238.4% to 200.0%). According to the previous observation, larger battery capacity reduced the need to purchase power from sources outside the microgrid, and thereby yielded greater profit; however, battery utilization rate (=output/capacity) was low. Conversely, lower bat-
tery capacity produced less profit due to higher power purchase costs; however, high utilization rate of infrastructure was obtained. The tradeoff between total profit and efficiency is demonstrated in Tables 1–3. Following this, the sensitivity analysis of electricity demand was estimated. In the scenario with no battery capacity, growth in demand resulted in reduced profit, from 1742.0 NTD in the basic demand case to 197.7 NTD in the double demand case, and 1376.6 NTD for triple demand. For the 10 kW battery case, electricity demand increased while profit reduced to 1746.8 NTD under basic demand, 202.1 NTD for double demand, and 1372.2 NTD for triple demand. For the 20 kW battery case, increased demand led to reduced profit in the three demand scenarios, of 1749.0 NTD, 206.5 NTD, and 1367.8 NTD, respectively. Profit was reduced because the additional demand was serviced by purchasing electricity from the national grid. Figs. 2 and 3 present the battery storage dynamics and battery discharge dynamics, respectively, for the basic demand scenario. Battery utilization was analyzed using a 10-kW battery case with 299.7% battery efficiency (highest) in the basic demand scenario. The lowest utilization rate of 200% occurred in the triple demand scenario. In the triple demand scenario, battery efficiency increased from 179.2% (10 kW) to 200% for the 20 kW battery case.
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
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Power sale in no battery scenario
Basic demand (Case 1.1) 200% demand (Case 1.2) 300% demand (Case 1.3)
Power (kWh)
120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (hr)
Fig. 6. Sale of electric power in the microgrid (no battery case). Fig. 2. Dynamics of electricity storage in the battery.
Power purchase in no battery scenario
Basic demand (Case 1.1) 200% demand (Case 1.2) 300% demand (Case 1.3)
Power (kWh)
120 100 80 60 40 20 0
0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (hr) Fig. 7. Purchase of electric power in the microgrid (no battery case). Fig. 3. Dynamics of electricity discharge in the battery.
Power sale in 10 kW battery scenario
Basic demand (Case 2.1) 200% demand (Case 2.2) 300% demand (Case 2.3)
Power (kWh)
120 100 80 60 40 20 0
0 1 2 3
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (hr) Fig. 4. Sale of electric power in the microgrid (10 kW battery case).
Power purchase in 10 kW battery scenario
Basic demand (Case 2.1) 200% demand (Case 2.2) 300% demand (Case 2.3)
Power (kWh)
120 100 80 60 40 20 0
0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (hr) Fig. 5. Purchase of electric power in the microgrid (10 kW battery case).
The reason for this occurrence is explained as follows: Under basic demand, the 10 kW battery is charged a total of three times per 24 h at hours 9, 13, and 20, when power demand is higher than power supply in the microgrid. However, for the cases of double and triple demand, the lack of surplus power within the microgrid
meant that the 10 kW battery was only charged a total of twice per day, at hours 8 and 18, respectively. Note that the basic demand case was capable of utilizing the battery one more time, at hour 13, owing to lower demand and associated extra power, which was used to charge the battery at hour 11. Therefore, the basic demand scenario provided higher battery efficiency (299%) compared to that of the higher demand scenarios (203% and 200%). The effect of battery capacities is tested and the outcomes show that smaller batteries are utilized more often. The 20 kW batteries were charged twice per 24 h for different demand scenarios. The basic demand case exhibited low demand during hours 13–24 and, accordingly, did not need to charge the battery before hour 12. Therefore, for the basic demand, a 20 kW battery scenario had a battery efficiency of 179.2%. It was also observed that power stayed in the batteries longer in the basic- and double demand scenarios, as batteries were able to meet demand for a longer period in lower-demand scenarios. Conversely, under the triple demand scenario, the battery was depleted quickly at hours 9 and 22. Similarly, the results for 30 kW, 40 kW and 50 kW battery scenarios are compared in Figs. 2 and 3. Fig. 4 shows power sales for basic-, double-, and triple-demand cases utilizing a 10-kW battery scenario. Three curves exhibit two major sale peaks at hours 2–8 and 18–20. Note that the basic demand scenario produced surplus power for sale at hour 9; however, this did not occur for double demand and triple demand scenarios, as the power generated at hour 9 was used to charge the batteries. Further, an extra sale peak was observed at hour 14 for basic demand, as this case was characterized by lower demand, which yielded surplus electricity. Fig. 5 plots power purchases for the three demand cases under a 10 kW battery scenario. Two purchase peaks were recorded at hours 10 and 15. The basic demand scenario with 10 kW battery exhibits one peak less (at hour 15) compared to the other two cases because the system produced sufficient energy to supply basic demand at hour 15. For comparison, Figs. 6 and 7 display power sale and purchase under a no-battery scenario; curves for sensitivity analyses of power
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
7
Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx Table 4 Results of basic demand scenario in the microgrid for winter scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 1.4 3.4 3.7 4.1 5.8
0.0 21.0 25.1 32.1 39.6 46.6
0.0 21.0 25.1 32.1 39.6 46.6
– 209.8 125.4 106.9 99.1 93.3
450.5 435.0 428.0 421.0 414.0 409.5
41.0 25.5 18.5 11.5 4.5 0.0
345.5 345.5 345.5 345.5 345.5 345.5
1219.4 1222.8 1224.3 1225.9 1227.4 1228.4
The generation of solar power and wind power are 147 and 608 kW h, respectively.
Table 5 Results of double demand scenario in the microgrid for winter scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 3.5 6.5 10.0 12.3 14.0
0.0 14.2 28.2 42.2 56.2 55.3
0.0 14.2 28.2 42.2 56.2 55.3
– 142.2 141.1 140.7 140.6 110.7
307.5 293.5 279.5 266.4 259.4 252.4
243.5 229.5 215.5 202.4 195.4 188.4
691.0 691.0 691.0 691.0 691.0 691.0
138.4 141.5 144.5 147.4 149.0 150.5
Table 6 Results of triple demand scenario in the microgrid for winter scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 2.6 1.4 8.5 10.4 15.2
0.0 14.0 28.0 42.0 56.0 83.4
0.0 14.0 28.0 42.0 56.0 83.4
– 140.0 140.0 140.0 140.0 166.9
259.9 245.9 231.9 217.9 203.9 189.9
541.4 527.4 513.4 499.4 485.4 471.4
1036.5 1036.5 1036.5 1036.5 1036.5 1036.5
963.6 960.5 957.5 954.4 951.3 948.2
demand are plotted in the figures. The above results relate to the operation of microgrids in summer. However, renewable energy and load vary between summer and winter seasons. Hence, the results for winter are also simulated in Tables 4–6. Further, yearlong operation is simulated to analyze uncertain and seasonal variation affecting microgrid operation. Table 7 calculates annual profit of the microgrid system (NTD/year). The results show that greater storage provides flexible operating strategies with higher annual profit. In addition, sensitivity analyses are conducted of renewable energy generation, power load for consumer, and a combined scenario (see Tables 8–10). Heat production from combined heat and power generation (gas turbine and biopower generation) are mentioned in the previous section. Potential heat production is simulated as shown in Table 11. Payback period (also known as break-even time) is an economic indicator representing the number years required to achieve return on investment. To examine the payback period of investment in a microgrid system, a uniform series profit is related to present investment as follows. Given a series of uniform annual profits, finding present equivalent value can be expressed functionally as
P ¼ A ½ð1 þ iÞN 1=½i ð1 þ iÞN
ð25Þ
where P, A, i, and N are present capital investment, annual income, interest rate, and payback period, respectively. Rearranging Eq. (25) yields payback period in Eq. (26). Assuming a 1% interest rate and battery installation cost of 14 million NTD, the result shows that the payback period for the battery is about 30 years. However, the useful lifespan of present battery technology is a maximum of 20 years. Hence, battery installation is not profitable while fixed installation cost of storage devices is considered.
N ¼ logð1þiÞ ½A=ðA P iÞ
ð26Þ
Table 7 Annual profit of the microgrid system (NTD/year). Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Annual profit (NTD/year) 100% demand
200% demand
300% demand
540,704 542,218 542,901 543,583 544,266 544,705
61,358 62,724 64,090 65,370 66,052 66,735
427,297 425,932 424,566 423,200 421,834 420,469
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx
Table 8 Sensitivity analysis for the energy supply uncertainty scenario (kW). Results
Supply uncertainty
Battery size 10 kW
20 kW
30 kW
40 kW
50 kW
Battery storage (kW)
High Med Low
0 0 0
94.1 120.0 118.7
112.4 231.5 152.9
202.2 501.2 363.4
200.6 438.4 451.6
601.3 314.5 584.5
Battery input (kW)
High Med Low
0 0 0
20.0 20.0 20.0
38.9 40.0 49.5
48.9 60.0 75.1
98.9 80.0 80.0
104.5 100.0 100.0
Battery output (kW)
High Med Low
0 0 0
20.0 20.0 20.0
38.9 40.0 49.5
48.9 60.0 75.1
98.9 80.0 80.0
104.5 100.0 100.0
Power sold (kW)
High Med Low
103.5 371.3 658.9
83.5 351.3 638.9
64.6 331.3 618.9
54.6 311.3 598.9
44.6 291.3 578.9
34.6 271.3 565.8
Power purchase (kW)
High Med Low
1044.9 773.4 521.8
1024.9 753.4 501.8
1006.0 733.4 481.8
996.0 713.4 461.8
986.0 693.4 441.8
976.0 673.4 428.7
0 kW
Table 9 Sensitivity analysis for the energy demand uncertainty scenario (kW). Results
Demand uncertainty
Battery size 0 kW
10 kW
20 kW
30 kW
40 kW
50 kW
Battery storage (kW)
High Med Low
0 0 0
101.6 90.0 70.0
131.8 211.5 200.0
327.4 521.7 275.7
393.5 438.4 285.7
496.4 383.7 386.4
Battery input (kW)
High Med Low
0 0 0
32.2 20.0 20.0
65.7 40.0 40.0
110.9 66.0 60.0
169.6 80.0 80.0
83.2 100.0 100.0
Battery output (kW)
High Med Low
0 0 0
32.2 20.0 20.0
65.7 40.0 40.0
110.9 66.0 60.0
169.6 80.0 80.0
83.2 100.0 100.0
Power sold (kW)
High Med Low
511.8 371.3 287.4
491.8 351.3 267.4
475.5 331.3 247.4
465.5 311.3 227.4
455.5 291.3 207.4
445.5 271.3 187.4
Power purchase (kW)
High Med Low
173.6 773.4 1429.9
153.6 753.4 1409.9
137.3 733.4 1389.9
127.3 713.4 1369.9
117.3 693.4 1349.9
107.3 673.4 1329.9
Table 10 Sensitivity analysis for the combination (demand and supply uncertainty) case (kW). Results
Demand and supply uncertainty
Battery size 0 kW
10 kW
20 kW
30 kW
40 kW
50 kW
Battery storage (kW)
High Med Low
0 0 0
166.3 100.0 60.0
150.7 198.1 138.3
268.5 485.2 267.1
326.0 438.4 266.4
496.4 421.7 327.2
Battery input (kW)
High Med Low
0 0 0
20.0 20.0 20.0
40.0 40.0 40.0
97.1 60.0 60.0
124.6 80.0 80.0
113.9 100.0 100.0
Battery output (kW)
High Med Low
0 0 0
20.0 20.0 20.0
40.0 40.0 40.0
97.1 60.0 60.0
124.6 80.0 80.0
113.9 100.0 100.0
Power sold (kW)
High Med Low
185.6 371.3 556.9
165.6 351.3 536.9
145.6 331.3 516.9
128.8 311.3 496.9
118.8 291.3 476.9
108.8 271.3 456.9
Power purchase (kW)
High Med Low
386.7 773.4 1160.1
366.7 753.4 1140.1
346.7 733.4 1120.1
329.9 713.4 1100.1
319.9 693.4 1080.1
309.9 673.4 1060.1
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx Table 11 Simulation of potential heat production in microgrid (GJ). Scenario
Basic demand (GJ)
Double demand (GJ)
Triple demand (GJ)
10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
186.4
126.4
124.4
222.9
250.8
248.8
285.1
375.2
373.2
352.2
499.6
497.6
414.4
491.8
741.5
Accordingly, annual net present value changes within the system can be calculated on an annual basis. The result shows that the present value of profit in the first ten years, the second ten years, and the third ten years are 5,114,504 NTD, 4,630,094 NTD, and 4,191,564 NTD, respectively. Hence, the net present value changes of the system reduce to 8,885,496 NTD (10 years), 4,225,401 NTD (20 years), and 63,838 NTD (30 years), respectively.
5. Conclusions Microgrid systems are distributed energy production systems intended to increase local use of renewable energy and power supply reliability, and to lower transmission loss and carbon dioxide emissions. The objective of this research was to construct an optimization model for microgrid energy management, which is essential to smart microgrid systems. The operating framework was tested on a smart microgrid system currently being developed at the Institute of Nuclear Energy Research, Taiwan. The optimization model of microgrid energy management was established and solved by GAMS/PATH. Uncertainty of electricity demand was simulated and sensitivity analysis of battery capacity was conducted. In the results, greater battery storage capacity requires greater investment, and so installation of additional storage devices might not profitable while high fixed cost is considered. Optimal battery size should be determined based on demand and supply of the microgrid system. In this research, economic analysis was conducted and an energy management model was developed. In addition, sensitivity analysis was used to examine various scenarios for investment in local power generators and storage capacity. Potential future studies include multi-criteria optimization of carbon dioxide reduction, cost minimization, and energy maximization. Further, risk management is an important consideration, including uncertainty analysis of environmental policy, energy policy, energy supply, and energy demand.
Acknowledgments This research was funded by the National Science Council of Taiwan under Grants NSC 100-2313-B-002-056, NSC 100-3113-E009-003-CC2, and NSC 101-3113-E-009-001-CC2. The authors wish to thank the editors and anonymous referees for their thoughtful comments and suggestions. The authors are responsible for the opinions expressed and any errors.
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Contents lists available at SciVerse ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan Yen-Haw Chen a, Su-Ying Lu a, Yung-Ruei Chang b, Ta-Tung Lee c, Ming-Che Hu c,⇑ a
Taiwan Institute of Economic Research, Research Division 1, 7F, No. 16-8 Dehuei Street, Jhongshan District, Taipei 104, Taiwan Institute of Nuclear Energy Research, Atomic Energy Council, Taiwan, No. 1000, Wenhua Rd., Jiaan Village, Longtan Township, Taoyuan County 32546, Taiwan c Department of Bioenvironmental Systems Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan b
h i g h l i g h t s " An optimization model of energy supply in microgrid system is formulated. " Optimal energy management strategies are determined. " Sensitivity analyses of storage capacity and energy demand is performed.
a r t i c l e
i n f o
Article history: Received 15 September 2011 Received in revised form 10 September 2012 Accepted 11 September 2012 Available online xxxx Keywords: Microgrid Optimization Sensitivity analysis
a b s t r a c t The purpose of this research is to perform economic analysis, formulate an optimization model, and determine optimal operating strategies for smart microgrid systems. Microgrid systems are electricity supply systems that integrate distributed renewable energy production for local demand. Microgrids are able to reduce transmission losses and improve utilization efficiency of electricity and heat. Further, greenhouse gas emissions are reduced by utilizing an efficient power generation microgrid system. This study presents an energy management model that is used to determine optimal operating strategies with maximum profit for a microgrid system in Taiwan. The smart microgrid system is equipped with energy storage devices, photovoltaic power, and wind power generation systems. Sensitivity analyses of investment in storage capacity and growth in electricity demand are conducted for the smart microgrid model. The results show that appropriate battery capacity should be determined on the basis of both battery efficiency and power supply. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Microgrids are community-level electricity systems that provide diversification and reliability of energy supply, integration of distributed renewable energy, and reduction of transmission losses and greenhouse gas emissions [1–3]. Microgrid systems are able to generate, transmit, distribute, store energy, and satisfy energy demand locally [4–8]. Microgrid systems have been designed and field tested in the UK [9,10]. The UK systems include combined heat and power, renewable energy, boiler generators, and batteries in leisure center, hospital, and hotel applications. The operating strategies of the UK systems were determined by minimizing total cost of investment and operation and maintenance costs. In addition, the New Energy Industrial Technology Development Organization in Japan has built and tested three microgrid systems [11–
⇑ Corresponding author. Tel.: +886 2 33663448; fax: +886 2 23635854. E-mail address: [email protected] (M.-C. Hu).
13]. The Japanese systems contain small, distributed power generators, batteries, and heat storage facilities. Economic and optimization analyses were performed to determine investment and optimal operating strategies of microgrid systems. Microgrids have successfully met expectations and been promoted around the world. In Taiwan, the Institute of Nuclear Energy Research (INER) has installed and field-tested a microgrid system. The INER microgrid comprises a 25 kW wind power generator, a 150 kW wind power generator, a 100 kW solar power generator, fuel cell, and battery storage devices. The energy demand of the INER system is simulated by a combination of two office buildings and a family house with lighting, air condition, and other electrical equipment. Most related studies focus on advanced microgrid control technologies [14–18]. This paper formulates an optimization model for microgrid energy management, and determines its optimal operating strategies. In addition, economic analysis and sensitivity analysis of microgrid systems are conducted. Economic indicators are calculated to determine optimal investment in power generators
0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.09.023
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx
Nomenclature Indices e i t
N
wdi equipment, e = 1, 2, . . . , E node of transmission network, i = 1, 2, . . . , I time period, t = 1, 2, . . . , T
N
bmi gtNi
Coefficients PVCA installed solar power capacity (kW) VCPV variable cost of solar power generation ($/kW h) WDCA installed wind power capacity (kW) variable cost of wind power generation ($/kW h) VCWD BMCA installed biomass power capacity (kW) ERBM CO2 emission rate from biomass electricity generation (kg/kW h) FRBM biomass needed for biomass electricity (kg/kW h) HRBM heat production of biomass power generator (J/kW) RCBM biomass feedstock cost ($/kg) VCBM variable cost of biomass power generation ($/kW h) installed gas turbine power capacity (kW) GTCA ERGT CO2 emission rate from gas turbine electricity generation (kg/kW h) FRGT gas needed for gas turbine electricity (m3/kW h) GT HR heat production of gas turbine power generator (J/kW) RCGT natural gas cost ($/m3) GT VC variable cost of gas turbine power generation ($/kW h) installed fuel cell power capacity (kW) FCCA ERFC CO2 emission rate from fuel cell electricity generation (kg/kW h) FRFC hydrogen needed for fuel cell electricity (m3/kW h) hydrogen cost ($/m3) RCFC FC VC variable cost of fuel cell power generation ($/kW h) BKt hours per block (h) PR electricity price ($/kW h) HEATDe;t heat demand of equipment e at time t (J) ELEDe;t electricity demand of equipment e at time t (kW) Decision variables profit total profit ($) pvNi number of solar power generators in microgrids at node i (dimensionless)
and battery devices, including payback period, present value, and net cash flow of microgrid systems. The optimization model for microgrid energy management is formulated as an integer programming model on the General Algebraic Modeling System (GAMS) and is solved by CPLEX solver. GAMS is a modeling system with efficient optimizers to solve complex and large-scale optimization and mathematical programming problems [19]. CPLEX is one of the most efficient optimizers on GAMS; CPLEX solves large linear programming, integer programming, and quadratic constrained problems. The GAMS and CPLEX outputs are used to inform optimal investment and operating solutions with minimal cost for microgrid systems. Significant contributions of this research are discussed as follows. This paper develops an optimal microgrid management model and determines optimal operation of microgrid systems. Next, the optimization management model is tested for the INER microgrid system in Taiwan. Further, economic analysis and sensitivity analysis of microgrid investment are simulated. The structure of this paper is as follows. Section 2 reviews microgrid-related studies in the literature. The optimization model for microgrid energy management is described in Section 3. In Section 4, a case study of the INER microgrid system in Taiwan is conducted, and eco-
N
fci
N
bti
mi,e pvGEN i;t GEN
wdi;t
GEN
bmi;t
gtGEN i;t GEN
fci;t
elei,t IN
number of wind power generators in microgrids at node i (dimensionless) number of biomass power generators in microgrids at node i (dimensionless) number of gas turbines in microgrids at node i (dimensionless) number of fuel cells in microgrids at node i (dimensionless) number of batteries in microgrids at node i (dimensionless) binary variable (mi,e = 1 if equipment e is turned on; mi,e = 0 otherwise) hourly energy production from solar power at node i at time t (kW) hourly energy production from wind power at node i at time t (kW) hourly energy production from biomass at node i at time t (kW) hourly energy production from gas turbine at node i at time t (kW) hourly energy production from fuel cell at node i at time t (kW) storage capacity of batteries at node i at time t (kW)
elei;t
power input of batteries at node i at time t (kW)
OUT elei;t
power output of batteries at node i at time t (kW) heat stored at time t (J)
heatt IN
heatt
heat input to heat storage at time t (J)
OUT heatt FUEL bmi;t gtFUEL i;t FUEL fci;t EM bmi;t
hourly heat output from heat storage at time t (J)
gtEM i;t EM
fci;t
biomass used at node i at time t (kg) gas used by gas turbine at node i at time t (m3) hydrogen used by fuel cell at node i at time t (m3) carbon dioxide emission of biomass at node i at time t (kg) carbon dioxide emission of gas turbine at node i at time t (kg) carbon dioxide emission of fuel cell at node i at time t (kg)
nomic analysis and uncertainty analysis are performed for the system. The conclusions are discussed in Section 5.
2. Literature review Some previous researchers have performed optimization and economic analysis to determine optimal energy management and capacity investment strategies [20–23]. Optimization modeling was used to schedule optimal installation and operation of a renewable microgrid in an isolated area [24]. Then a mixed-integer linear programming problem was formulated to integrate and manage fuel cell, solar power, wind power generators, and battery storage devices. A dynamic programming model of Distributed Energy Resources (DERs) microgrid systems was formulated [25]. To increase the reliability of power supply, optimal microgrid architectures connecting power generation and load were determined. An economic analysis of distributed energy resources in microgrid systems was performed [26]. A linear programming model and a numerical simulation were developed to determine the optimal operating pattern for a microgrid operating in factory, grocery store, sports center, hotel, office, and hospital applications.
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx
Previous studies have investigated risk and uncertainty associated with microgrid systems. Handschin et al. formulated a stochastic programming model to perform uncertainty analysis [27], in which optimal operation of dispersed generation was decided under conditions of power price uncertainty. Siddiqui and Marnay considered uncertainty in electricity price and natural gas production within the California power market [28]; distributed capacity investment of power generation was analyzed for microgrid systems under uncertainty. Monte Carlo simulation and agent-based simulation methods have been used to investigate the dynamic performance of microgrid systems. Firestone and Marnay built a simulation model for a dynamically adaptable microgrid system [29]. Given technical and financial constraints, the optimal control solution and energy manager (EM) for the microgrid were determined. An agent-based model was established to simulate power-trading strategies between power buyers, sellers, and grid operators [30]. The model assumed that each agent behaved with artificial intelligence in the markets. Interaction among agents and dynamic equilibrium in the market were presented. A fuzzy neural network algorithm was applied to a distributed intelligent energy management system [31]. Optimal power control strategies were determined for a single-phase high-frequency alternating current microgrid. A microsource model was formulated to analyze islanded operation of microgrids [32]. The model discussed control strategies for the feasibility and stability of power supply in the systems. Previous researchers have studied optimal power flow, dynamic agent-based simulation, sensitivity analysis, and economic analysis for microgrids [33–35]. However, this paper integrates optimal energy management, capacity expansion, uncertainty analysis, payback period, and cash flow analysis of the INER microgrid system in Taiwan. An optimization model is formulated; then optimal investment and operating decisions are presented. System performance of the Taiwanese INER microgrid system is measured in the results. 3. Methodology
Solar
Electricity storage
Max profit ¼ Ri;t ½ðPR VCPV Þ BKt pvGEN þ ðPR VCWD Þ i;t GEN
Wind power
Biomass power
Electricity demand
Gas Turbine
Heat demand
Fig. 1. Configuration of the microgrid system.
Fuel cell
Heat storage
GEN
BKt wdi;t þ ðPR VCBM Þ BKt bmi;t FUEL
ðRCBM Þ bmi;t
þ ðPR VCGT Þ BKt gtGEN i;t GEN
ðRCGT Þ gtFUEL þ ðPR VCFC Þ BKt fci;t i;t FUEL
ðRCFC Þ fci;t ðICBM BT
ðIC
N bmi Þ
N bti Þ
N
ðICPV pvNi Þ ðICWD wdi Þ
ðICGT gtNi Þ ðICFC
N fci Þ
ð1Þ
Constraints upon the microgrid operating system are examined in the following stage. Assuming multiple generators are installed within the microgrid system, capacity constraints of electricity generators are addressed in Eqs. (2)–(6).
pvNi PVCA P pvGEN i;t
Microgrid systems contain distributed energy generators and storage devices, including gas turbine, fuel cell, wind power, solar power, biopower generators, battery, and heat storage technologies [36–41]. This section first plots the scope of microgrid system (see Fig. 1). Then an optimization model of the energy management system for the studied microgrid is introduced. The decision GEN GEN GEN GEN variables include pvGEN (kW), reprei;t , wdi;t , bmi;t , gti;t , and fci;t senting electricity generation of photovoltaic, wind, biomass, gas turbine, and fuel cell generators in node i at time t. In addition, BKt is the number of hours at time t; PR ($/kW h) and VC ($/ kW h) represent electricity price and production cost, respectively.
power
The objective function maximizes total profit which is equal to electricity power revenue minus generation cost. The profit earned from power generation in photovoltaic, wind, biomass, gas turbine, and fuel cell components of the grid are represented as GEN ðPR VCPV Þ BKt pvGEN ðPR VCWD Þ BKt wdi;t , ðPR i;t , GEN BM GT GEN VC Þ BKt bmi;t , ðPR VC Þ BKt gti;t , ðPR VCFC Þ GEN FUEL FUEL BKt fci;t . Further, bmi;t , gtFUEL , and fci;t represent biomass i;t feedstock consumption for biomass power, natural gas consumption for gas turbine operation, and hydrogen consumption for fuel cell in node i at time t, respectively. Biomass feedstock cost, natural gas cost, and hydrogen cost are RCBM, RCGT, and RCFC. Hence, FUEL FUEL ðRCBM Þ bmt , ðRCGT Þ gtFUEL , and ðRCFC Þ fct represent total t fuel cost terms for biomass feedstock, natural gas, and hydrogen, respectively. Moreover, the size of the microgrid system is important for decision making. Hence, capacity expansion of renewable energy generators and storage facilities are considered within the N N N N optimization function. pvNi , wdi , bmi , gtNi , fci , and bti represent the number of photovoltaic, wind, bioenergy, gas turbine, fuel cell generators, and batteries at node i, respectively. Incorporating the above stages, the optimal microgrid size to produce maximum profit is determined via
8i; t
N
GEN
8i; t
ð3Þ
N
GEN
8i; t
ð4Þ
wdi WDCA P wdi;t bmi BMCA P bmi;t gtNi GTCA P gtGEN i;t N
ð2Þ
GEN
fci FCCA P fci;t
8i; t 8i; t
ð5Þ ð6Þ
mi,e denotes a binary decision variable of equipment e at node i that is available for consumer use; mi,e is 1 if equipment e in node i is turned on, but is otherwise 0. Power net inflow of node i at time t is denoted by yit. Then, the mass balance constraint of electric power is formulated in Eq. (7). The mass balance constraint of Eq. (8) describes that heat production from bioenergy and gas turbines is equal to total heat demand at node i. Power system operation constraints are also considered, including both of Kirchhoff’s laws. In the model, power system operation constraints are considered for direct current (DC) and alternating current (AC). In DC systems, power flows in a constant direction and, in AC systems, the flow of electric charge periodically reverses direction. In the following, two types of transmission capacity constraints are introduced. First, Kirchhoff’s Current and Voltage Laws can be simulated via DC approximation [42–44]. The transmission constraints of a linearized DC electric network are built as follows. Define PTDFik as power transmission distribution factors of node i through interface k of the transmission network. In addition, the
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx
upper and lower bounds of transmission capacity of interface k are TC1k and TC2k, respectively. Accordingly, [PTDFik yit] is power transmission through interface k, and the transmission capacity constraints are established in Eqs. (9) and (10). On the other hand, AC is predominant form of electricity transmitted and distributed to customers. To analyze delivery capacity, sinusoidal functions of AC power current and voltage are considered: v k ðtÞ ¼ V mk ðcos xt þ hVk Þ and ik ðtÞ ¼ Imk ðcos xt þ hIk Þ [45]. Eqs. (11), (12) determine the power transmission in a microgrid network and then transmission capacity constraints are formulated in Eqs. (13), (14). i Xh GEN GEN GEN IN OUT mi;e ELEDe;i;t pvGEN wdi;t bmi;t gtGEN fci;t þ elei;t elei;t ¼ yit i;t i;t
8i; t
e
ð7Þ Xh
i GEN IN OUT HRGT gtGEN þ heati;t heati;t ¼ 0 8t mi;e HEATDe;i;t HRBM bmi;t i;t
i;e
ð8Þ
Ri ½PTDFik yit 6 TC1k 8k; t Ri ½PTDFik yit 6 TC2k
ð9Þ
8k; t
ð10Þ
pk ðtÞ ¼ v k ðtÞ ik ðtÞ m V I ¼ Vm k I k ðcos xt þ hk Þ ðcos xt þ hk Þ
pk ¼ ð1=TÞ
Z
T
o
m V I pk ðtÞdt ¼ ð1=2Þ V m k I k cosðhk hk Þ
8k
pk 6 TC1k pk 6 TC2k
ð11Þ ð12Þ ð13Þ
8k
ð14Þ
Fuel consumptions of power generators are calculated in Eqs. (15)–(17). The carbon dioxide emission rates for biomass, gas turbine, and fuel cell generators are represented by ERBM, ERGT, and ERFC [kg/kW h], and total emissions of carbon dioxide are estimated in Eqs. (18)–(20). FUEL
bmi;t
GEN
¼ FRBM BKt bmi;t
gtFUEL ¼ FRGT BKt gtGEN i;t i;t FUEL
fci;t
GEN
¼ FRFC BKt fci;t
EM
8i; t
8i; t
ð17Þ
GEN
EM
GEN
ðfci;t Þ ¼ ERFC BKt fci;t
ð16Þ
8i; t
ðbmi;t Þ ¼ ERBM BKt bmi;t GT ðgtEM BKt gtGEN i;t Þ ¼ ER i;t
ð15Þ
8i; t
ð18Þ
8i; t
ð19Þ
8i; t
ð20Þ
Eq. (21) defines me as a zero–one binary variable. In addition, Eq. (21) defines gtN, fcN, bmN, pvN, and wdN to be integer variables. Non-negativity constraints of decision variables are listed in Eqs. (22)–(24).
mi;e is a zero—one binary variable 8e; i N
N
N
pvNi ; wdi ; bmi ; gtNi ; fci are positive integer variables 8i GEN
GEN
GEN
GEN pvGEN i;t ; wdi;t ; bmi;t ; gti;t ; fci;t IN
OUT
heatt ; heatt ; heatt
IN
ð21Þ
P 0 8i; t
ð22Þ
OUT
ð23Þ
; elei;t ; elei;t ; elei;t
P 0 8i; t
FUEL
FUEL
EM
EM
EM bmi;t ; gtFUEL 8i; t i;t ; fci;t ; bmi;t ; gti;t ; fci;t P 0
ð24Þ
A Taiwanese microgrid system was constructed by the Institute of Nuclear Energy Research (INER); it has a 25 kW wind power generator, a 150 kW wind power generator, a 100 kW High Concentration Photovoltaic generator, a 2 kW fuel cell generator, and a battery device for power storage. The case study measured the electricity generation of solar and wind power. The INER microgrid system also simulated electricity demand by establishing power demand for two office buildings and a family house. The installation costs for a 100 kW high-concentration photovoltaic generator, a 150 kW wind power generator, and a 25 kW wind power generator are approximately 10, 15, and 6 million NTD, respectively. In this study, the lifespan of the generators is assumed to be 20 years. The supply of INER microgrid illustrated that the 150 kW wind power generator produces about 60–70 kW in the morning and 50–75 kW in the afternoon. The 25 kW wind generator produced 7–11 kW and 8–13 kW in the morning and afternoon peaks, respectively. The data illustrated maximum wind power generation at hours 6–9 and 16–20 for both 150 kW and 25 kW wind generators. Alternatively, an HCPV power generator produced 10– 40 kW electricity at hours 9–16. The demand data demonstrated peak demand of 25–30 kW at hours 9–17. In this basic demand case, the microgrid system with renewable energy generators was able to meet electricity demand with the exception of hours 10 and 23. To analyze the sensitivity of demand growth in microgrid systems, the study examined three scenarios characterized by basic power demand, double demand, and triple demand. Data on power generation and demand were analyzed in the microgrid optimization model. The optimization model seeks maximal profit of power trading between the microgrid and the primary electricity grid; the profit is equal to power sale revenue minus power purchase cost. The case study is conducted and the outcome is discussed in the following section. 4. Results and discussion This section presents a case study of the Taiwanese INER microgrid system. First, the optimization models of the microgrids are analyzed by the CPLEX solver on the GAMS platform. Then, sensitivity analyses of battery capacity and electricity demand are examined. Further, payback period and cash flow of microgrid investment are discussed. The effect of different electricity storage capacities on Taiwanese INER microgrid systems is illustrated in this research. First, scenarios with battery capacities of 10 kW, 20 kW, 30 kW, 40 kW, and 50 kW were compared to the scenario without any battery capacity. Next, sensitivity analyses of battery capacities were tested for different demand growth scenarios including basic-demand, double-demand, and triple-demand scenarios. Hence, the extent of battery utilization for each scenario is measured by indicators including total power output of battery, total power input of battery, electricity storage capacity of battery, and battery utilization rate. Battery utilization rate is equal to power output divided by battery capacity (i.e., total electricity output/battery capacity). Moreover, electricity trading between the main electricity network and the microgrid is estimated. The impact of battery storage capacities for the basic demand, double demand, and triple demand scenarios are compared. Tables 1–3 show the battery performance, including average storage, power charge, power discharge, battery utilization (=output/capacity), electricity sale, electricity purchase, electricity demand, and total profit of the microgrid system. In Table 1, it is assumed that the system has a basic demand, and so total profit increases from 1742.0 NTD (no battery) to 1754.9 NTD (50 kW battery case) where NTD is New Taiwan Dollar
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx Table 1 Results of basic demand scenario in the microgrid for summer scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 2.0 4.8 5.3 5.8 8.3
0.0 30.0 35.8 45.8 56.6 66.6
0.0 30.0 35.8 45.8 56.6 66.6
– 299.7 179.2 152.8 141.6 133.3
643.6 621.4 611.4 601.4 591.4 585.0
58.6 36.4 26.4 16.4 6.4 0.0
493.6 493.6 493.6 493.6 493.6 493.6
1742.0 1746.8 1749.0 1751.2 1753.4 1754.9
The generation of solar power and wind power are 210 and 869 kW h, respectively.
Table 2 Results of double demand scenario in the microgrid for summer scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 5.0 9.2 14.2 17.6 20.0
0.0 20.3 40.3 60.3 80.3 79.1
0.0 20.3 40.3 60.3 80.3 79.1
– 203.2 201.6 201.1 200.8 158.1
439.2 419.2 399.2 380.5 370.5 360.5
347.8 327.8 307.8 289.1 279.1 269.1
987.1 987.1 987.1 987.1 987.1 987.1
197.7 202.1 206.5 210.6 212.8 215.0
Table 3 Results of triple demand scenario in the microgrid for summer scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 3.8 2.0 12.2 14.8 21.7
0.0 20.0 40.0 60.0 80.0 119.2
0.0 20.0 40.0 60.0 80.0 119.2
– 200.0 200.0 200.0 200.0 238.4
371.3 351.3 331.3 311.3 291.3 271.3
773.4 753.4 733.4 713.4 693.4 673.4
1480.7 1480.7 1480.7 1480.7 1480.7 1480.7
1376.6 1372.2 1367.8 1363.4 1359.0 1354.6
and the exchange rate of US dollar (USD) is about 30–33 NTD/USD. Electricity trading, including sale and purchase from outside the microgrid system, diminished by 58.6 kW h. Additionally, Table 2 shows that total profit increased from 197.7 NTD (no battery) to 215.0 NTD (50 kW battery) for double demand scenarios. Total profit increased from 1376.6 NTD (no battery) to 1354.6 NTD (50 kW battery) for triple demand scenarios, as illustrated in Table 3. Additionally, power trading fell by 78.7 kW h (=from 347.8 to 269.1 kW h) and 100 kW h (=from 773.4 to 673.4 kW h) in Tables 2 and 3, respectively. In conclusion, increased battery capacity had the effect of increasing total profit and reducing trade between the microgrid and primary electricity grid systems. It is clear that larger batteries enable greater local storage and subsequent usage of power generated within the microgrid. Nevertheless, battery utilization rate (=battery output/battery capacity) was cut by 166.4% (=from 299.7% to 133.3%) and 45.1% (=from 203.2% to 158.1%) under the basic demand scenario in Table 1, and the double demand scenario in Table 2, respectively. Table 3 illustrates that battery utilization rate increased by 38.4% (=from 238.4% to 200.0%). According to the previous observation, larger battery capacity reduced the need to purchase power from sources outside the microgrid, and thereby yielded greater profit; however, battery utilization rate (=output/capacity) was low. Conversely, lower bat-
tery capacity produced less profit due to higher power purchase costs; however, high utilization rate of infrastructure was obtained. The tradeoff between total profit and efficiency is demonstrated in Tables 1–3. Following this, the sensitivity analysis of electricity demand was estimated. In the scenario with no battery capacity, growth in demand resulted in reduced profit, from 1742.0 NTD in the basic demand case to 197.7 NTD in the double demand case, and 1376.6 NTD for triple demand. For the 10 kW battery case, electricity demand increased while profit reduced to 1746.8 NTD under basic demand, 202.1 NTD for double demand, and 1372.2 NTD for triple demand. For the 20 kW battery case, increased demand led to reduced profit in the three demand scenarios, of 1749.0 NTD, 206.5 NTD, and 1367.8 NTD, respectively. Profit was reduced because the additional demand was serviced by purchasing electricity from the national grid. Figs. 2 and 3 present the battery storage dynamics and battery discharge dynamics, respectively, for the basic demand scenario. Battery utilization was analyzed using a 10-kW battery case with 299.7% battery efficiency (highest) in the basic demand scenario. The lowest utilization rate of 200% occurred in the triple demand scenario. In the triple demand scenario, battery efficiency increased from 179.2% (10 kW) to 200% for the 20 kW battery case.
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx
Power sale in no battery scenario
Basic demand (Case 1.1) 200% demand (Case 1.2) 300% demand (Case 1.3)
Power (kWh)
120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (hr)
Fig. 6. Sale of electric power in the microgrid (no battery case). Fig. 2. Dynamics of electricity storage in the battery.
Power purchase in no battery scenario
Basic demand (Case 1.1) 200% demand (Case 1.2) 300% demand (Case 1.3)
Power (kWh)
120 100 80 60 40 20 0
0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (hr) Fig. 7. Purchase of electric power in the microgrid (no battery case). Fig. 3. Dynamics of electricity discharge in the battery.
Power sale in 10 kW battery scenario
Basic demand (Case 2.1) 200% demand (Case 2.2) 300% demand (Case 2.3)
Power (kWh)
120 100 80 60 40 20 0
0 1 2 3
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (hr) Fig. 4. Sale of electric power in the microgrid (10 kW battery case).
Power purchase in 10 kW battery scenario
Basic demand (Case 2.1) 200% demand (Case 2.2) 300% demand (Case 2.3)
Power (kWh)
120 100 80 60 40 20 0
0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (hr) Fig. 5. Purchase of electric power in the microgrid (10 kW battery case).
The reason for this occurrence is explained as follows: Under basic demand, the 10 kW battery is charged a total of three times per 24 h at hours 9, 13, and 20, when power demand is higher than power supply in the microgrid. However, for the cases of double and triple demand, the lack of surplus power within the microgrid
meant that the 10 kW battery was only charged a total of twice per day, at hours 8 and 18, respectively. Note that the basic demand case was capable of utilizing the battery one more time, at hour 13, owing to lower demand and associated extra power, which was used to charge the battery at hour 11. Therefore, the basic demand scenario provided higher battery efficiency (299%) compared to that of the higher demand scenarios (203% and 200%). The effect of battery capacities is tested and the outcomes show that smaller batteries are utilized more often. The 20 kW batteries were charged twice per 24 h for different demand scenarios. The basic demand case exhibited low demand during hours 13–24 and, accordingly, did not need to charge the battery before hour 12. Therefore, for the basic demand, a 20 kW battery scenario had a battery efficiency of 179.2%. It was also observed that power stayed in the batteries longer in the basic- and double demand scenarios, as batteries were able to meet demand for a longer period in lower-demand scenarios. Conversely, under the triple demand scenario, the battery was depleted quickly at hours 9 and 22. Similarly, the results for 30 kW, 40 kW and 50 kW battery scenarios are compared in Figs. 2 and 3. Fig. 4 shows power sales for basic-, double-, and triple-demand cases utilizing a 10-kW battery scenario. Three curves exhibit two major sale peaks at hours 2–8 and 18–20. Note that the basic demand scenario produced surplus power for sale at hour 9; however, this did not occur for double demand and triple demand scenarios, as the power generated at hour 9 was used to charge the batteries. Further, an extra sale peak was observed at hour 14 for basic demand, as this case was characterized by lower demand, which yielded surplus electricity. Fig. 5 plots power purchases for the three demand cases under a 10 kW battery scenario. Two purchase peaks were recorded at hours 10 and 15. The basic demand scenario with 10 kW battery exhibits one peak less (at hour 15) compared to the other two cases because the system produced sufficient energy to supply basic demand at hour 15. For comparison, Figs. 6 and 7 display power sale and purchase under a no-battery scenario; curves for sensitivity analyses of power
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx Table 4 Results of basic demand scenario in the microgrid for winter scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 1.4 3.4 3.7 4.1 5.8
0.0 21.0 25.1 32.1 39.6 46.6
0.0 21.0 25.1 32.1 39.6 46.6
– 209.8 125.4 106.9 99.1 93.3
450.5 435.0 428.0 421.0 414.0 409.5
41.0 25.5 18.5 11.5 4.5 0.0
345.5 345.5 345.5 345.5 345.5 345.5
1219.4 1222.8 1224.3 1225.9 1227.4 1228.4
The generation of solar power and wind power are 147 and 608 kW h, respectively.
Table 5 Results of double demand scenario in the microgrid for winter scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 3.5 6.5 10.0 12.3 14.0
0.0 14.2 28.2 42.2 56.2 55.3
0.0 14.2 28.2 42.2 56.2 55.3
– 142.2 141.1 140.7 140.6 110.7
307.5 293.5 279.5 266.4 259.4 252.4
243.5 229.5 215.5 202.4 195.4 188.4
691.0 691.0 691.0 691.0 691.0 691.0
138.4 141.5 144.5 147.4 149.0 150.5
Table 6 Results of triple demand scenario in the microgrid for winter scenario. Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Battery
Power trading
Average storage (kW h)
Power charge (kW h)
Power discharge (kW h)
Battery utilization (=output/capacity) (%)
Total sale (kW h)
Total purchase (kW h)
Total demand (kW h)
Total profit (NTD)
0.0 2.6 1.4 8.5 10.4 15.2
0.0 14.0 28.0 42.0 56.0 83.4
0.0 14.0 28.0 42.0 56.0 83.4
– 140.0 140.0 140.0 140.0 166.9
259.9 245.9 231.9 217.9 203.9 189.9
541.4 527.4 513.4 499.4 485.4 471.4
1036.5 1036.5 1036.5 1036.5 1036.5 1036.5
963.6 960.5 957.5 954.4 951.3 948.2
demand are plotted in the figures. The above results relate to the operation of microgrids in summer. However, renewable energy and load vary between summer and winter seasons. Hence, the results for winter are also simulated in Tables 4–6. Further, yearlong operation is simulated to analyze uncertain and seasonal variation affecting microgrid operation. Table 7 calculates annual profit of the microgrid system (NTD/year). The results show that greater storage provides flexible operating strategies with higher annual profit. In addition, sensitivity analyses are conducted of renewable energy generation, power load for consumer, and a combined scenario (see Tables 8–10). Heat production from combined heat and power generation (gas turbine and biopower generation) are mentioned in the previous section. Potential heat production is simulated as shown in Table 11. Payback period (also known as break-even time) is an economic indicator representing the number years required to achieve return on investment. To examine the payback period of investment in a microgrid system, a uniform series profit is related to present investment as follows. Given a series of uniform annual profits, finding present equivalent value can be expressed functionally as
P ¼ A ½ð1 þ iÞN 1=½i ð1 þ iÞN
ð25Þ
where P, A, i, and N are present capital investment, annual income, interest rate, and payback period, respectively. Rearranging Eq. (25) yields payback period in Eq. (26). Assuming a 1% interest rate and battery installation cost of 14 million NTD, the result shows that the payback period for the battery is about 30 years. However, the useful lifespan of present battery technology is a maximum of 20 years. Hence, battery installation is not profitable while fixed installation cost of storage devices is considered.
N ¼ logð1þiÞ ½A=ðA P iÞ
ð26Þ
Table 7 Annual profit of the microgrid system (NTD/year). Case
0 kW battery 10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
Annual profit (NTD/year) 100% demand
200% demand
300% demand
540,704 542,218 542,901 543,583 544,266 544,705
61,358 62,724 64,090 65,370 66,052 66,735
427,297 425,932 424,566 423,200 421,834 420,469
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
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Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx
Table 8 Sensitivity analysis for the energy supply uncertainty scenario (kW). Results
Supply uncertainty
Battery size 10 kW
20 kW
30 kW
40 kW
50 kW
Battery storage (kW)
High Med Low
0 0 0
94.1 120.0 118.7
112.4 231.5 152.9
202.2 501.2 363.4
200.6 438.4 451.6
601.3 314.5 584.5
Battery input (kW)
High Med Low
0 0 0
20.0 20.0 20.0
38.9 40.0 49.5
48.9 60.0 75.1
98.9 80.0 80.0
104.5 100.0 100.0
Battery output (kW)
High Med Low
0 0 0
20.0 20.0 20.0
38.9 40.0 49.5
48.9 60.0 75.1
98.9 80.0 80.0
104.5 100.0 100.0
Power sold (kW)
High Med Low
103.5 371.3 658.9
83.5 351.3 638.9
64.6 331.3 618.9
54.6 311.3 598.9
44.6 291.3 578.9
34.6 271.3 565.8
Power purchase (kW)
High Med Low
1044.9 773.4 521.8
1024.9 753.4 501.8
1006.0 733.4 481.8
996.0 713.4 461.8
986.0 693.4 441.8
976.0 673.4 428.7
0 kW
Table 9 Sensitivity analysis for the energy demand uncertainty scenario (kW). Results
Demand uncertainty
Battery size 0 kW
10 kW
20 kW
30 kW
40 kW
50 kW
Battery storage (kW)
High Med Low
0 0 0
101.6 90.0 70.0
131.8 211.5 200.0
327.4 521.7 275.7
393.5 438.4 285.7
496.4 383.7 386.4
Battery input (kW)
High Med Low
0 0 0
32.2 20.0 20.0
65.7 40.0 40.0
110.9 66.0 60.0
169.6 80.0 80.0
83.2 100.0 100.0
Battery output (kW)
High Med Low
0 0 0
32.2 20.0 20.0
65.7 40.0 40.0
110.9 66.0 60.0
169.6 80.0 80.0
83.2 100.0 100.0
Power sold (kW)
High Med Low
511.8 371.3 287.4
491.8 351.3 267.4
475.5 331.3 247.4
465.5 311.3 227.4
455.5 291.3 207.4
445.5 271.3 187.4
Power purchase (kW)
High Med Low
173.6 773.4 1429.9
153.6 753.4 1409.9
137.3 733.4 1389.9
127.3 713.4 1369.9
117.3 693.4 1349.9
107.3 673.4 1329.9
Table 10 Sensitivity analysis for the combination (demand and supply uncertainty) case (kW). Results
Demand and supply uncertainty
Battery size 0 kW
10 kW
20 kW
30 kW
40 kW
50 kW
Battery storage (kW)
High Med Low
0 0 0
166.3 100.0 60.0
150.7 198.1 138.3
268.5 485.2 267.1
326.0 438.4 266.4
496.4 421.7 327.2
Battery input (kW)
High Med Low
0 0 0
20.0 20.0 20.0
40.0 40.0 40.0
97.1 60.0 60.0
124.6 80.0 80.0
113.9 100.0 100.0
Battery output (kW)
High Med Low
0 0 0
20.0 20.0 20.0
40.0 40.0 40.0
97.1 60.0 60.0
124.6 80.0 80.0
113.9 100.0 100.0
Power sold (kW)
High Med Low
185.6 371.3 556.9
165.6 351.3 536.9
145.6 331.3 516.9
128.8 311.3 496.9
118.8 291.3 476.9
108.8 271.3 456.9
Power purchase (kW)
High Med Low
386.7 773.4 1160.1
366.7 753.4 1140.1
346.7 733.4 1120.1
329.9 713.4 1100.1
319.9 693.4 1080.1
309.9 673.4 1060.1
Please cite this article in press as: Chen Y-H et al. Economic analysis and optimal energy management models for microgrid systems: A case study in Taiwan. Appl Energy (2012), http://dx.doi.org/10.1016/j.apenergy.2012.09.023
Y.-H. Chen et al. / Applied Energy xxx (2012) xxx–xxx Table 11 Simulation of potential heat production in microgrid (GJ). Scenario
Basic demand (GJ)
Double demand (GJ)
Triple demand (GJ)
10 kW battery 20 kW battery 30 kW battery 40 kW battery 50 kW battery
186.4
126.4
124.4
222.9
250.8
248.8
285.1
375.2
373.2
352.2
499.6
497.6
414.4
491.8
741.5
Accordingly, annual net present value changes within the system can be calculated on an annual basis. The result shows that the present value of profit in the first ten years, the second ten years, and the third ten years are 5,114,504 NTD, 4,630,094 NTD, and 4,191,564 NTD, respectively. Hence, the net present value changes of the system reduce to 8,885,496 NTD (10 years), 4,225,401 NTD (20 years), and 63,838 NTD (30 years), respectively.
5. Conclusions Microgrid systems are distributed energy production systems intended to increase local use of renewable energy and power supply reliability, and to lower transmission loss and carbon dioxide emissions. The objective of this research was to construct an optimization model for microgrid energy management, which is essential to smart microgrid systems. The operating framework was tested on a smart microgrid system currently being developed at the Institute of Nuclear Energy Research, Taiwan. The optimization model of microgrid energy management was established and solved by GAMS/PATH. Uncertainty of electricity demand was simulated and sensitivity analysis of battery capacity was conducted. In the results, greater battery storage capacity requires greater investment, and so installation of additional storage devices might not profitable while high fixed cost is considered. Optimal battery size should be determined based on demand and supply of the microgrid system. In this research, economic analysis was conducted and an energy management model was developed. In addition, sensitivity analysis was used to examine various scenarios for investment in local power generators and storage capacity. Potential future studies include multi-criteria optimization of carbon dioxide reduction, cost minimization, and energy maximization. Further, risk management is an important consideration, including uncertainty analysis of environmental policy, energy policy, energy supply, and energy demand.
Acknowledgments This research was funded by the National Science Council of Taiwan under Grants NSC 100-2313-B-002-056, NSC 100-3113-E009-003-CC2, and NSC 101-3113-E-009-001-CC2. The authors wish to thank the editors and anonymous referees for their thoughtful comments and suggestions. The authors are responsible for the opinions expressed and any errors.
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