ARTICLE pubs.acs.org/EF
A Multiperiod Mathematical Model for Integrating Planning and SO2 Mitigation in the Power Generation Sector Mohammed S. Ba-Shammakh* Chemical Engineering Department, King Fahd University of Petroleum & Minerals, P.O. Box 5050, 31261, Dhahran, Saudi Arabia ABSTRACT: The power generation sector contributes directly to SO2 emissions, causing economic and environmental damage. These SO2 emissions come mostly from the combustion of fossil fuels for power generation. A multiperiod mixed-integer nonlinear model for power generation planning with SO2 consideration is presented in this paper. The objective of the model is to determine the optimal mix of energy supply sources and SO2 emission mitigation options that meet a specified electricity demand and SO2 emission targets at minimum cost. The model is written in a general format and it is illustrated in a case study from Ontario Power Generation (OPG), Canada. SO2 emissions from power generation can be reduced through fuel balancing (which is simply to increase production from non-fossil-fuel power plants and decrease production from fossil-fuel power plants), fuel substitution or the use of low sulfur fuels, and conventional flue gas desulfurization. These options were considered in the model and the results, for the case study, show that if no SO2 emissions reduction target is imposed, the model does not tend to apply any of the options considered. However, the model recommends building more power plants to meet the electricity demand for the coming 10 years. The electricity cost increases to ∼8.2 cents/kWh in year 2017. For another case study in which different SO2 reduction targets are considered, the model shows that fuel balancing and fuel switching must be applied immediately in several plants.
’ INTRODUCTION Energy and environment are two essential aspects for high air quality. It is not viable to design and implement energy production without considering the environmental factors. Fossil fuel use, especially in power generation, is responsible for many environmental issues. Emissions from fossil-fuel power plants, such as CO2, SO2, NO2, mercury (Hg), and particulate matters (PM), have had serious adverse impacts on the quality of air. Two main effects of the fossil fuel use in power generation—global warming and acid deposition—have been proven in several studies. Many studies have been conducted on the global warming issue side, dealing with CO2 emissions reduction from fossil-fuel power plants. Compared to that, fewer studies considered the acid deposition issue or SO2 emissions reduction from fossil-fuel power generation, which is the focus of this study.1 The objective of this study is to develop a general multiperiod mathematical model for power generation production planning with SO2 consideration. The model is illustrated in a case study related to Ontario Power Generation (OPG) in Canada. Fossil-fuel-fired power plants are responsible for producing a large percentage of the electricity that is currently being generated around the world. Demand for that electricity is increasing rapidly, and in many parts of the world, steadily growing demand for electricity is heightening the need for additional capacity. Fossil fuels will continue to play a role in the development of many national economies into the future. The fossil fuels currently supplying the major part of the world’s energy will remain in abundant supply into the coming years. Consequently, if an action is not taken, atmospheric levels of SO2 emissions will continue to increase.1 SO2 emissions from power generation are mainly due to the combustion of coal. National standards for SO2 emissions from r 2011 American Chemical Society
coal-fired combustion were introduced in the early 1970s in the United States and Japan. In the 1990s, such environmental regulations became progressively more stringent and more widespread. The trend is expected to continue through the coming years. Emission standards for new and existing coalfired plants have been introduced in many countries. Many countries have adopted or are in the process of adopting legislation limiting their SO2 emissions. In some countries, switching from high- to low-sulfur coal or blending to meet the set targets is satisfactory, for the present time. However, fuel switching, cleaning, and/or blending will be insufficient as regulations are made even stricter. Hence, SO2 removal from the flue gases will become increasingly necessary to meet environmental regulations.2 Four main technology strategies for SO2 emissions control have been pursued by the power generation industry: (1) Tall gas stacks that disperse emissions away from immediate areas; (2) Intermittent controls, which involve routine operational adjustments to reduce power plant SO2 emissions in response to atmospheric conditions; (3) Precombustion reduction of sulfur from fuels; and (4) Removal of SO2 from the post-combustion gas stream. The focus has shifted to post-combustion control technologies as well as fuel switching to lower-sulfur-content fuel. These control technologies, known as flue gas desulfurization (FGD) or scrubbing technologies, involve a post-combustion gas stream with a base reagent (or sorbent) in an absorber to remove SO2.
Received: November 21, 2010 Revised: February 17, 2011 Published: March 29, 2011 1504
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Energy & Fuels Several studies have been conducted that address the control of SO2 emissions from the power generation sector. Ellison2 gave a broad overview of SO2 emission regulation, as well as an overview of the diverse technologies available for the control and/or removal of SO2 pollutant in coal firing. The logistics and trends in worldwide supply and use of diverse available steam coal resources are reviewed in relation to the need for continuing restraint and reduction in sulfurous emissions. Chaaban et al.3 outlines options for SO2 emissions reduction from power plants. Several mitigation technologies are given to reduce the SO2 emissions, and the most pronounced ones, according to the study, are switching to low-sulfur fuel oil, filtering stack emissions using flue gas desulfurization systems, and shifting to natural gas as an alternative fuel for thermal power plants. Cofala et al.,4 also in the same manner, studied cost-effective control of SO2 emissions in Asia. Shrestha and Marpaung5 studied the supply and demand side effects of power sector planning with demand side management options and SO2 emission constraints in Indonesia. Islas and Grande,6 in their study, also highlighted optimization of alternative options for SO2 emissions control in the Mexican electrical sector. In another paper, they give abatement costs of the SO2 control options given in their first paper for the Mexican electrical sector. Many papers have been published on using multiperiod optimization methods for planning purposes. Iyer et al.7 have developed a multiperiod mixed-integer linear programming (MILP) model for the planning and scheduling of offshore oil field facilities. Maravelias and Grossmann8 developed a complex multiperiod optimization model to address the challenge of planning for the production of a new product in highly regulated industries, such as pharmaceuticals and agrochemicals. Hashim et al.9 and Elkamel et al.10 developed a singleperiod deterministic MINLP optimization model to predict a fleet-wide system configuration that simultaneously satisfies electricity demand and CO2 emission constraints at minimum cost. Ba-Shammakh et al.11 developed a MINLP model for CO2 reduction in power plants, considering increasing power plant efficiency as an option to reduce CO2 emissions. Mirzaesmaeel et al.12 developed a novel deterministic optimization model that considers multiperiod factors and CO2 mitigating technologies to select the optimal mix of energy supply sources that will meet current and future electricity demand and CO2 emission targets, and will minimize the overall cost of electricity. Many other studies that involve energy planning models also have appeared in the literature. Jebaraj and Iniyan13 also presented a comprehensive review of the literature on the various emerging issues related to the energy modeling problem. The objective of this study is to develop a multiperiod optimization model for power generation planning with SO2 mitigation at minimum cost. A case study from Ontario Power Generation (OPG) will be shown as an illustration of the model.
’ MODEL FORMULATION The model is written in a general format that consists of an objective function and a set of constrains. The objective function
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(Z) is to minimize cost of electricity generated and in mathematical format, it can be written as
where the parameters are defined as follows: Z = cost of electricity ($/MW) i = power plant f = fuel type k = SO2 control technology l = load block (base or peak) t = time period (yr) FF = fossil-fuel power plants NFF = non-fossil-fuel power plants FCift = fixed cost of plant i using fuel f during period t ($/MW) Cif = capacity of plant i using fuel f (MW) OCift = operating cost for plant i using fuel f during period t ($/MW) Eiflt = electricity generation from plant i using fuel f for load l during period t (MW) (DL)lt = duration of load block l during period t (h) Rit = retrofit cost for fuel switching for plant i during period t ($/MW) (Tech)i = cost of technology for SO2 reduction in plant i ($/tonne SO2) (SO2)if = SO2 emissions from plant i using fuel f (tonne/ MWh) εikt = percent reduction of SO2 from plant i using technology k during period t (%) Eifkt = electricity generation from plant i using fuel f and technology k during period t (MW) Xift = binary variable (Xift = 1 if a fossil-fuel power plant i is working with fuel f during period t; Xift = 0 otherwise) Yit = binary variable (Yit = 1 if a non-fossil-fuel power plant i is working with fuel f during period t; Yit = 0 otherwise) Jit = binary variable (Jit = 1 if power plant i is built during period t; Jit = 0 otherwise) Zifkt = binary variable (Zifkt = 1 if power plant i is working with fuel f using technology k for SO2 reduction during period t; Zifkt = 0 otherwise) Mit = binary variable; (Mit = 1 if fossil fuel power plant i undergoes fuel switching during period t; Mit = 0 otherwise) The first two terms in the objective function are fixed cost for current fossil-fuel and non-fossil-fuel power plants, respectively, followed by two terms for the operating cost for the set of plants (fossil-fuel and non-fossil-fuel). Then, a term for switching is included with a binary variable M, which is set to be 0 if no switching is carried out and 1 in the case of switching to a lesssulfur fuel. Then, two terms for fixed and operating cost for new power plants are included in the objective function. The last two terms are mainly for the cost associated with applying technologies for SO2 reduction if needed for current and new power plants. 1505
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The constraints of the model are as follows:
Table 1. OPG Fossil Fuel Power Plants
Power Demand Constraints. The total power generation
power plant
from all existing fossil-fuel and non-fossil-fuel power plants, in addition to new power plants, should be greater than the total power demand in all periods and years of the planning horizon considered. In mathematical format, it can be written as
∑ ∑ Eiflt ðDLÞlt þ i ∈∑NFF Eilt ðDLÞlt þ i ∈∑new Enew ilt ðDLÞlt g Dlt
capacity (MW)
SO2 emissions (tonnes/yr)
Atikokan
211
837
Lambton
1920
6191
Lenoxx (natural gas)
2100
571
Nanticoke
3640
21 480
306
421
Thunder Bay
i ∈ FF f
ð2Þ Fuel Selection or Plant Shutdown. For each fossil-fuel power plant i, the plant either operates with a given fuel or is shut down at a certain period of time during the time horizon considered. For this reason, a binary variable is introduced to represent the type of fuel used in a given fossil fuel plant. Xift = 1 if fuel f is used in plant i at time t; otherwise, Xift = 0.
∑f Xift e 1
" i ∈ FF, " t
SO2 Emissions. The total SO2 emissions from current and new power plants must be less than a certain limit. The first term represents the SO2 emissions from existing power plants that might include installation of a technology k to achieve the limit. A binary variable Z is introduced to represent the existence (or nonexistence) of the reduction technology k. The second term involves SO2 emissions from new power plants.
∑ ∑½ð∑f ðSO2Þif Eift ðDLÞlt Þð1 - ∑k εikt Zikt Þ þ
ð3Þ
i ∈ FF l
∑
Since fuel switching of a coal power plant can occur only once during the time horizon considered, another constraint must be included:
∑t Mit e 1
" i ∈ FF
ð4Þ
Maximum Capacity for Existing Power Plants. This constraint set requires that the electricity produced from any plant i with load l should not exceed the maximum capacity of the plant at any time. The first constraint is for fossil-fuel power plants, while the second is for non-fossil-fuel power plants. A binary variable is introduced in each constraint to represent its existence (or nonexistence) at any time t.
∑l Eiflt e Emax if Xift ∑l Eilt e Emax i Yit
" i ∈ NFF
ð5Þ
" i ∈ FF " i ∈ NFF
ð6Þ
Capacity for New Plants. The multiperiod nature of the model requires consideration of the construction time for new power plants. For new power plants, no power can be supplied to the grid unless the construction of the new power plant has been completed. To achieve this, the following constraint has been formulated to ensure that, during the construction phase of a new power plant, no electricity generating capacity is available:
Enit e Cmax i ð1 - Jit Þ
∑t Jit e 1
" i ∈ new, " t
" i ∈ new
ð7Þ
ðSO2 Þni Enilt ðDLÞlt e ðSO2 Þlimit, t
ð8Þ
Selection of SO2 Reduction Technology. This constraint basically ensures that, if an existing power plant is shut down, no SO2 control technology should be installed.
∑f Xift g ∑k Zikt
" i, " t
ð9Þ
Furthermore, only one control technology can be installed for a given power plant i during time period t:
∑k Zikt e 1
" i ∈ FF
Minimum Capacity for Existing Power Plants. These constraints introduce a lower bound for each power plant, and the plant production must be at least equal to this lower limit, or, otherwise, the plant should be shut down and a binary variable is introduced to represent that at any time t.
∑l Eiflt e Emin if Xift ∑l Eilt e Emin i Yit
i ∈ new
" i, " t
ð10Þ
’ CASE STUDY The model developed in this study is illustrated in a case study applied to Ontario Power Generation (OPG) for a time horizon of 10 years from 2010 to 2020. OPG is responsible for ∼70% of the electricity generation in the province of Ontario, Canada. Sources of electricity include nuclear, fossil fuel, hydroelectric, and wind. As of the beginning of this year, OPG’s electricity generating portfolio had a total in-service capacity of 21 729 MW, which consisted of • five fossil-fueled generating stations, with a capacity of 8177 MW; • three nuclear generating stations, with a capacity of 6606 MW; • 65 hydroelectric generating stations, with a capacity of 6944 MW; and • two wind power turbines, with a capacity of 2 MW. Since fossil fuel power plants are the contributors to SO2 emissions, they will be the focus of this study. Other power generation plants do not emit SO2 emissions. As indicated above, currently, there are five power plants, with SO2 emissions totalling 29 500 tonnes/yr. The emissions for each plant, along with its capacity, is given in Table 1 with Lenoxx power plant, which the only plant that is running with natural gas.1 The developed model is programmed and implemented in the GAMS package. 1506
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Figure 1. Forecasted annual electricity demand for Ontario.
Figure 2. Forecasted peak load demand for Ontario.
Table 2. Economical and Operational Parameters for Various Power Plants1 nuclear
PC
NGCC
IGCC
capacity (MW)
1500
450
500
500
fixed O&M cost ($/MW)
11 160
57 300
16 000
72 500
capital cost ($/MW)
2 415 100
1 775 000
750 000
2 215 000
capacity factor SO2 emissions
0.9 0
0.75 0.0011
0.85 0
0.85 8.8 10-5
7
5
3
5
(tonnes SO2/MWh) construction time (yrs)
The table clearly shows that Nanticoke is the major contributor to SO2 emissions; it accounts for ∼73% of the total SO2 emissions. The annual electricity demand and peak demand for Ontario are forecasted for a time horizon of 10 years, from 2010 to 2020. In this study, a simple forecasting model is developed to predict the annual electricity demand and peak load demand for the coming 10 years. These are shown in Figures 1 and 2, respectively. To meet future demand, new power plants must be built. The case study discussed in this paper will examine the use of the following supply sources to meet future demand: • nuclear, • pulverized coal combustion (PC), • natural gas combined cycle (NGCC), and • integrated gasification combined cycle (IGCC) The economical and operational parameters for the listed power plants are given in Table 2. This paper uses coal and natural gas price forecasts from the National Energy Board (NEB).14
NEB’s coal prices are measured as delivered prices to industrial consumers in 1986 Canadian dollars per GJ of coal. NEB projects coal prices to decline by 1% until year 2015, after which time the coal prices are expected to remain constant. It is assumed that there are no significant resource constraints on coal production. Also, continuing efficiency improvements such as mergers in the transportation industry are assumed. Similarly, this paper uses the National Energy Board’s (NEB) natural gas price forecasts. It is based on two scenarios: a SupplyPush (SP) case and a Techno-Vert (TV) case. The SP scenario is based on an assumption that technology advances gradually and that there is limited action on the environment in Canada. The TV scenario is based on the assumption that technology advances occur more rapidly and that Canadians take broad action on the environment. The heightened concern for the environment is assumed to result in an increasing demand for cleaner fuels and advances in technology. The natural gas prices are forecasted to decrease after this year for both SP and TV scenarios. It may be a result of the assumption that LNG terminals come on stream after 2010. The model and case studies presented in this paper assume the following: • Three SO2 reduction options considered in this paper: (1) fuel balancing, (2) fuel switching, and (3) SO2 control technology. Fuel balancing involves increasing production from non-fossil-fuel power plants and reduce production from fossil fuel power plants. Fuel switching involves a switch to lower-sulfur-content fuels, such as natural gas. In SO2 control technology, a control technology is installed to mitigate SO2 emission, such as flue gas desulfurization technology, which is considered in this study. • All existing nuclear units in Ontario will be refurbished before their end-of-service dates. The time required to refurbish a single unit is assumed to be two years. During the refurbishment process, the unit being refurbished will be shut down and, consequently, no electricity can be produced from that unit. • No new renewable supply sources are realized within the time horizon of the case studies presented in this paper.
’ RESULTS AND DISCUSSIONS The model discussed earlier was coded into GAMS and solved using a MINLP solver. Two case studies are illustrated: the first represents a base case with no SO2 reduction, and the second case study involves different SO2 reduction targets. The base case 1507
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Table 3. Base Casea
a
The symbol “X” marks the year in which a new plant must be built; the shaded areas represent the years during which the plant is under construction.
Table 4. 10% SO2 Reductiona plant Lambton Nantikoke Atikokan Thunder Bay Lennox (NG)
2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 X X X
The symbol “X” denotes the years in which that power plant is operated using natural gas.
a
Figure 3. Electricity cost for entire period.
represents a scenario in which no SO2 emission limit is imposed on the power generation. It also assumes that the phase-out of coal power plants is not enforced by the policy makers and the existing nuclear power plants will be refurbished based on their estimated end-of-service dates. Table 3 shows the results for this case study, and it gives the starting year and type of plants to be built during the time horizon considered with no SO2 reduction. The table clearly shows that, for the base case with no SO2 restrictions, one new PC power plant, four NGCC power plants, and one nuclear power plant must be built to meet electricity demand. The model chooses to keep all coal, natural gas, nuclear, hydroelectric, and wind power stations operational throughout the study period from 2010 to 2020. No fuel switching was implemented on existing coal power plants, since there was no limit on SO2 emissions for the base case. Since continuing to operate with coal is less expensive than a switch to natural gas, a choice was made for the model not to switch any of the plants to operate with natural gas. In addition, there is a cost associated with switching, and the optimization model did not select that option, because of its cost, and no restriction on SO2 emissions in the base case was imposed in the model. Even though PC power plants have lower fuel costs than that of NGCC power plants, the model chose to build four new NGCC power plants and only one new PC power plant. This may be due to the lower capital cost of building a new NGCC unit, despite the fuel costs associated with the use of natural gas. The results also show that all non-fossil-fuel power plants must operate with a 2% (maximum allowable value)-higher-thannominal capacity factor. The only plant for which the capacity factor decreases is the Lennox generating station (natural gas), in which the capacity factor decreased by ∼5%, which is the maximum allowable lower limit, or the plant should be shut down. This result may seem to be counterintuitive, since the Lennox generating station is fueled by natural gas. However, the reason why the capacity factor of Lennox must be decreased is because this plant uses the most expensive fuel in OPG’s fleet.
The capacity factor of the other fossil fuel plants was increased by only a small increment to meet demand. The cost of electricity, shown in Figure 3, varies throughout the period considered from 2010 to 2020. The electricity cost ranges from 6.5 cents/kWh in 2010 to a maximum of 8.2 cents/ kWh in 2017. The variability associated with electricity cost in any year is dependent on all factors that are considered in the total expenditure for that year. For example, the high electricity cost observed in year 2017 is due a large amount of capital spent on fuel, construction of new power plants, and refurbishment of nuclear units, relative to how much electricity is generated. This figure also shows that, since no plants were chosen to be built in the year 2015, the cost of electricity decreases slightly. For the second case study, different SO2 reduction targets are imposed in the model. The optimization results show that changing the electricity generated from the Nanticoke generating station (the largest coal power plant in Ontario) will have a large impact on the SO2 emissions. The overall effect of the adjustments in the capacity factors is to reduce the overall SO2 emissions. For 10% reduction, for example, fuel switching was implemented at Nanticoke, Atikokan, and Thunder Bay during the years 2012, 2016, and 2017, respectively. Table 4 shows the coal power plants that have been switched to operate with natural gas. Bold “X” in the table represents the years during which that power plant is operated using natural gas. The results show that no control technologies need to be installed to achieve this reduction target for the coming seven years. However, the flue gas desulfurization technology must be installed during the year 2018 for the Lambton plant. This is due to increasing power demand and SO2 emissions associated with that. For a 25% reduction target, the results show that the Nanticoke plant must immediately operate with natural gas. Other power plants will continue to run with the same fuel, knowing that the Nanticoke is the largest contributor to SO2 emissions. The production from the Lennox plant must be reduced by 10% to lower the cost of electricity production. This is done because this plant operates with natural gas. For a higher reduction target, such as 50%, all coal power plants must be switched to operate with natural gas. Figure 4 shows the power allocated from each source from year 2010 to 2020. 1508
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Figure 4. Case study II: power allocation for years 2010 and 2020.
This figure clearly shows that, by the year 2020, no power would be generated from coal power plants and production from natural gas power plants increases from 10% in this year to 27% by year 2020. The power production from renewable sources decreases from 33% in 2010 to 28% in 2020, since this study did not consider renewable supply sources. The NGCC takes a portion in the year 2020 knowing that it does not emit SO2 emissions. Currently, there is no power supply from NGCC and the study recommends building NGCC plants during the period from 2010 to 2020. This is done to meet the electricity demand and satisfy the SO2 reduction for the second case study. The supply from nuclear power plants increases slightly from 30% to 33% in year 2020. The utilization of coal power plants decreases significantly after the year 2010. The decrease in power production from coal plants is due to the SO2 emissions restrictions imposed on the power generation sector. To reduce SO2 emissions to target levels, the model chose to reduce the use of coal power plants and, instead, utilize low- or zero-sulfur-content fuel.
’ CONCLUSIONS This study achieved the objective of developing a multiperiod mixed-integer nonlinear programming (MINLP) model that is able to realize the optimal mix of energy supply sources that meet current and future electricity demand for a time horizon of 10 years, SO2 emission targets, and lower the overall electricity cost. The model was applied to the Ontario Power Generation set of power plants. The annual energy and peak demand were forecasted for the coming 10 years. The SO2 emissions from power generation could be minimized by different alternatives, and three of them were considered in this study: fuel balancing, fuel switching to lower-sulfur-content fuels, and application of SO2 control technologies such as flue gas desulfurization technology. Two case studies were considered. The first did not impose any SO2 reduction target, in which the model did not recommend any of the three options to reduce SO2 emissions. The model also chose to build four new NGCC power plants and only one new PC to meet the electricity demand. The electricity cost increases from 6.5 cents/kWh to 8.2 cents/kWh during the period from 2010 to 2020.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The author would like to thank King Fahd University of Petroleum & Minerals for their support of this study. ’ REFERENCES (1) Ontario Power Generation (OPG). www.opg.com, retrieved Aug. 14, 2010. (2) Ellison, W. Radiat. Phys. Chem. 1995, 45 (6), 1003–1011. (3) Chaaban, F.; Mezher, T.; Ouwayjan, M. Electr. Power Energy Syst. 2004, 26, 57–63. (4) Cofala, J.; Amann, M.; Gyarfas, F.; Schoepp, W.; Boudri, J.; Hordijk, L.; Kroez, C.; Junfeng, L.; Lin, D. J. Environ. Manage. 2004, 72, 149–161. (5) Shrestha, R. M.; Marpaung, C. O. P. Energy Policy 2005, 33, 815–825. (6) Islas, J.; Grande, G. Appl. Energy 2008, 85, 80–94. (7) Iyer, R.; Grossmann, I.; Vasantharajan, S.; Cullick, A. Ind. Eng. Chem. Res. 1998, 37, 1380–1397. (8) Maravelias, C.; Grossmann, I. Ind. Eng. Chem. Res. 2001, 40, 6147–6164. (9) Hashim, H.; Douglas, P.; Elkamel, A.; Croiset, E. Ind. Eng. Chem. Res. 2005, 44, 879–890. (10) Elkamel, A.; Hashim, H.; Douglas, P.; Croiset, E. AIChE J. 2009, 55 (12), 3168–3190. (11) Ba-Shammakh, M.; Elkamel, A.; Douglas, P.; Croiset, E. Int. J. Environ. Pollut. 2007, 29 (1-3), 254–273. (12) Mirzaesmaeeli, H.; Elkamel, A.; Douglas, P.; Croiset, E.; Gupta, M. J. Environ. Manage. 2010, 91, 1063–1070. (13) Jebaraj, S.; Iniyan, S. Renewable Sustainable Energy Rev. 2006, 10, 281–311. (14) National Energy Board (NEB), www.neb.gc.ca, retrieved Sept. 5, 2010.
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