A mixed-integer non-linear programming model for ... - Semantic Scholar

254

Int. J. Environment and Pollution, Vol. 29, Nos. 1/2/3, 2007

A mixed-integer non-linear programming model for CO2 emission reduction in the power generation sector M. Ba-Shammakh, A. Elkamel*, P. Douglas and E. Croiset Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] *Corresponding author Abstract: Electricity generation is considered to be one of the main contributing sources to the air pollution problem. It is, therefore, important to develop and implement effective control strategies to prevent the expected abrupt increase in emissions from this sector. Any control strategy must be suitable for local implementation and must also be economically viable. The main objective of this paper is to present optimisation models that can be used to determine the most cost effective strategy or combination of strategies to reduce CO2 emissions to a specific level. Optimisation results for an existing network of power plants show that it may be possible to reduce CO2 emissions by increasing power plant efficiency through a variety of adjustments in the plants. These include fuel balancing, fuel switching, and the implementation of improvement technologies to existing power plants to increase their thermal efficiency. Keywords: air pollution during electricity generation; carbon dioxide emission reduction; non-linear programming model; power plant efficiency. Reference to this paper should be made as follows: Ba-Shammakh, M., Elkamel, A., Douglas, P. and Croiset, E. (2007) ‘A mixed-integer non-linear programming model for CO2 emission reduction in the power generation sector’, Int. J. Environment and Pollution, Vol. 29, Nos. 1/2/3, pp.254–273. Biographical notes: Mohammed Ba-Shammakh is a PhD Candidate at the University of Waterloo (Department of Chemical Engineering) and is currently working in the area of optimal air pollution control as applied to chemical processes. He got his MS as well as his BS in Chemical Engineering from King Fahd University of Petroleum and Minerals in Saudi Arabia. Ali Elkamel is an Associate Professor of Chemical Engineering at the University of Waterloo. Prior to joining the University of Waterloo, he served at Purdue University, Procter and Gamble, Kuwait University, and the University of Wisconsin. His research has focused on the applications of systems engineering and optimisation techniques to pollution problems and sustainable development.

Copyright © 2007 Inderscience Enterprises Ltd.

A mixed-integer non-linear programming model

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Peter Douglas is a Professor of Chemical Engineering at the University of Waterloo. He specialises in process modelling, simulation, control and optimisation. He has been a visiting Professor at the University of Queensland (Brisbane, Australia), University Teknologi Malaysia (Kuala Lumpur, Malaysia) and King Mongkut’s University of Technology Thonburi (Bangkok, Thailand). He has consulted on a worldwide basis for clients such as DuPont, Shell, IBM, Goodyear, Alcan, CANMET, Government of Canada, and National Science and Technology Development Agency of Thailand. Eric Croiset is an Associate Professor of Chemical Engineering at the University of Waterloo. He does research on control of emissions from combustion sources, air pollution control technology and reaction engineering. His current research is on the capture of CO2 from power plants and on hydrogen production from methane and ethanol. He joined the University of Waterloo in 1999 as an Assistant Professor. Prior to his appointment, he worked at CANMET (Natural Resources Canada) on advanced coal and natural gas combustion techniques to facilitate CO2 capture from flue gas.

1

Introduction

Global warming has been the subject of considerable public debate over recent years. Concern over the potential effect of CO2 emission from electricity generation on the global climate change is a key issue for the future of power generation worldwide. Fossil fuel power generation plants are being challenged to comply with the Kyoto Protocol developed by the United Nations Framework Convention and Climate Change (UNFCCC). Canada actively participated in the UNFCCC and signed the Kyoto Protocol in 1997. In the Protocol, Canada agreed to reduce its net GHG emissions by 6% from 1990 levels by the period 2008–2012 (Canada Energy Outlook, 2002). In 2002, Canadians contributed about 731 megatonnes of CO2 equivalent (Mt CO2 eq) of GHGs to the atmosphere, an increase of 2.1% over the 716 Mt recorded in the year 2001. CO2 Emissions are (as of 2002) slightly above the 2000 figure of 725 Mt, an increase of about 1%. Approximately 74% of total GHG emissions in 2002 resulted from the combustion of fossil fuels, (Canada Energy Outlook, 2002). Ontario Power Generation (OPG), the main electricity producer in Ontario, is one of the largest electricity generators in North America. OPG currently operates approximately 74% of the available generation capacity in Ontario. About 35% of OPG electricity is produced through combustion of fossil fuels, same percentage from nuclear, 29% from hydroelectricity and the remaining 1% comes from renewable or green energy sources, such as wind turbines. As of December 31, 2003, OPG’s electricity generating portfolio had a total in-service capacity of 22,777 megawatts (MW), generating about 109.1 TWh of electricity and emitting approximately 36.5 million tonnes (Mt) of CO2, mainly from coal fired power plants, (Canada Energy Outlook, 2002). CO2 reduction strategies for the electric sector may include one or more of the following options: increasing power plant efficiency, fuel balancing, fuel switching, using renewable energy (i.e., solar and wind turbines) and CO2 capture and sequestration. In this paper, we will focus on three possible options to reduce CO2 emission by a certain target while maintaining the electricity to the grid at nominal levels. The options being considered are increasing power plant efficiency, fuel balancing and fuel switching.

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M. Ba-Shammakh, A. Elkamel, P. Douglas and E. Croiset

Increasing power plant efficiency is one option to reduce CO2 emission by implementing improvement technologies to an existing power plant to increase its thermal efficiency. Fuel balancing is the optimal adjustment of the operation of generating stations to reduce CO2 emission without making structural changes to the fleet. Finally, fuel switching is the switching from carbon intensive fuels, e.g., coal to less intensive fuels e.g., nuclear, hydro-electricity, renewable or natural gas and involves structural changes to the fleet. The basic problem to be addressed in this paper can be stated as follows, “given a number of power plants emitting CO2 to the environment, find the best portfolio of strategies to meet electricity demand at minimum cost, while reducing CO2 emissions to a specific target.”

The objective of this paper is to develop an optimisation model that can be employed to find the best strategy or combination of strategies that should be implemented to reduce CO2 emissions from power generation. Recently, several papers have been published which addressed the cost effectiveness of CO2 control strategies. Yamaji et al. (1993) presented a study on the effectiveness of CO2 emission control strategies in Japan. They considered applying a CO2 tax as one control option. Wu et al. (1994) analysed the characteristics of China’s CO2 emissions from the energy sector and proposed several options for mitigating the CO2 emissions on a large scale, such as strengthening energy conservation, introducing energy-efficient technologies into the energy system, speeding up non-fossil fuels development and importing oil and natural gas as substitute for coal. They evaluated the effectiveness of the different CO2 mitigation options but they did not employ any optimisation techniques. Rovere et al. (1994) summarised a cost benefit analysis based on applying alternative energy strategies, such as increasing hydroelectric power for abatement of carbon emissions in Brazil. Elmahgary et al. (1994) considered a case study in Egypt to mitigate CO2 emissions from the energy sector. They considered several technologies including energy conservation, fuel switching and use of renewable energy to decrease CO2 emissions. The impact of energy conservation measures on the economy of the country was found to be positive. Zhou et al. (2004) developed an expert system to assist power plant decision makers in selecting an economical and efficient pollution control system that meets new stringent emission standards. A fuzzy relation model and a Gaussian dispersion model were integrated into the expert system. Genchi et al. (2002) developed a prototype model for designing regional energy supply systems. Their model calculates a regional energy demand and then recommends a most effective combination of 11 different power supply systems to meet required CO2 emission targets with minimum cost. The new energy system, to be installed, included co-generation systems, garbage incineration and solar energy. Linares and Romero (2000) proposed a methodology that combines several multi-criteria methods to address electricity planning problems within a realistic context. This approach was applied to an electricity planning scenario in Spain with a planning horizon set for the year 2030. The model included the following objectives: •

total cost

•

CO2

•

SO2

•

NOx emissions as well as the amount of radioactive waste produced.


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Mavrotas et al. (1999) developed a mixed integer Multiple Objective Linear Programming (MOLP) model applied to the Greek electricity generation sector for identifying the number and output of each type of power units needed to satisfy the expected electricity demand in the future. Antunes et al. (2004) presented a multiple objective mixed integer linear programming model for power generation expansion planning that allows the consideration of modular expansion capacity values of supply side options. Climaco et al. (1995) developed new techniques that incorporate MOLP and Demand-Side Management (DSM). The techniques were able to determine the minimum expansion cost by changing the levels and forms of the electricity use by the consumers and generating alternatives from the supply side. The model also considered the emissions caused by the electricity production. Noonan and Giglio (1977) studied and developed an optimisation program for planning investments in electricity generating systems. The optimisation program determined the mix of plant types, sizes of the individual plants to be installed and the allocation of installed capacity to minimise total discounted cost while meeting the system’s forecasted demand for electricity. This problem is referred to as the Generation Planning Problem (GPP). In order to comply with the variation in electricity demand, the electricity demand to be met was described by the Load Duration Curve (LDC). The mathematical model was solved using Benders’ Decomposition Method (BDM) and it was applied to New England Generation Planning Task Force. Yokoyama et al. (2002) formulated a mixed integer linear programming model for the structural design problem to determine an optimal structure of energy supply system to match energy demand requirement, by expressing the selection and on/off status of operation of equipment by binary variables and capacities and load allocation of equipment by continuous variables. The effect of equipment performance characteristics on their capacities as well as capital cost, were incorporated into the optimisation model. The objective was to minimise annual capital cost, and was evaluated as the sum of the annualised capital and operational costs of energy purchased. Bai and Wei (1996) developed a linear programming model to evaluate the effectiveness of possible CO2 mitigation options for the electric sector. The options considered were fuel alternatives, energy conservation, reduced peak production and improved electric efficiency. The results indicated that energy conservation can significantly reduce CO2 emissions only when combined with reduced peak production and improved electric efficiency. More recently, Hashim et al. (2005) considered the problem of reducing CO2 emissions from a fleet of generating stations consisting of coal, natural gas, nuclear, hydroelectric, and renewable energy. The problem was formulated as a Mixed Integer Linear Program (MILP) and implemented in GAMS. Two carbon dioxide mitigation options were considered in their study: fuel balancing and fuel switching. The optimisation results showed that fuel balancing can contribute to the reduction of the amount of CO2 emissions by up to about 3%. Beyond 3% reductions, more stringent measures that include fuel switching and plant retrofitting have to be employed. Improving power plant efficiency was not considered in their study. Efficiency improvements techniques in power plants can range from boiler maintenance and cleaning to improved combustion control. These are discussed in more details in the next section.

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2


Power plant efficiency improvement

Several studies have been conducted in order to increase power plant efficiency and, as a consequence, decrease CO2 emissions. The thermal efficiency of a plant can be defined as a percentage determined by the ratio of electrical energy output to the fuel energy input. Increased plant efficiency means that less coal is burned (producing less CO2) for the same power output (Audus, 1993). Improved efficiency in any power plant can produce noticeable reductions in CO2 emissions: typically, a 1% gain in efficiency reduces CO2 output by 2% (Torrens and Stenzel, 2001). Boiler efficiency in any power plant is a function of size, capacity factor, the fuel fired, operating and ambient conditions and unit design. Existing coal boilers, operating today, use mostly subcritical or in some cases supercritical steam cycles. A supercritical steam cycle operates above the water critical temperature (374°C) and critical pressure (221 bar) where water can exist only in the gaseous phase. Subcritical systems historically have achieved thermal efficiencies (HHV) of 34–36%. Supercritical systems can achieve thermal efficiencies 3–5% higher than subcritical systems (US Department of Energy, 2001). There are various measures that can be used to increase power plant efficiency relative to current design. Increasing the steam pressure and temperature can increase the efficiency by nearly 2%. Controlling the excess air is an important function in boiler operation and reducing the excess air ratio from 25% to 15% can bring a small increase of about 1% in efficiency. Controlling the excess air is an important issue since too much air will cool the furnace and carry away useful heat and too little air will lead to incomplete combustion. Using a second reheat stage can add another 1% and decreasing the condenser pressure can further increase efficiency. Table 1 shows some actions that can be employed to improve the efficiency of coal power plants (Audus, 1993). Table 1

Some actions for efficiency improvement

Action

Efficiency improvement (%)

Restore plant to design conditions Boiler chemical cleaning

0.84

Reinstate any feedheaters out of service

0.46

Refurbish feedheaters

0.84

Reduce steam leaks

1.0

Reduce turbine gland leakage

0.84

Change to operational settings Low excess air operation

1.22

Improved combustion control

0.84

Retrofit improvements Extra airheater surface in the boiler

2.1

Install new high efficiency turbine blades

0.98

Install variable speed drives

1.97

Install on-line condenser cleaning system

0.84

Install new cooling tower film back

1.97


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For a number of the initiatives listed in Table 1, the gain in efficiency stated would appear to be optimistic. For example, low excess air operation might bring slightly more than 1% gain in efficiency. One other efficiency improvement measure where the nominated gain would appear to be optimistic is for the improvement of the cooling tower performance by the inclusion of a film pack. A potential improvement of 1.97% has been reported. In order to achieve this improvement, a reduction in condenser pressure of 3.5 kPa would be required which in turn would necessitate an 8°C reduction in cooling water temperature. A film pack is capable of reducing the water temperature by only some 3°C. In order to advance the practical options for efficiency improvement, a soundly based techno-economic engineering study would need to be undertaken for each station (US Department of Energy, 2001). Wisconsin Electric Power Company (WEPCO) in the USA has implemented a number of actions to improve the efficiency at five coal power plants (US Department of Energy, 2001). Some of which are already included in Table 1. These plants are namely Oak Creek, Pleasant Prairie, Port Washington, Presque Isle and Valley. At Oak Creek for example, the efficiency improved by 3.9%. Projects that contributed to efficiency improvements include variable speed drives on the forced and induced draft fans, reduced air in-leakage and feed water heater replacements. At the Pleasant Prairie power plant, the efficiency improved by 3.2%. This improvement came from variable pressure operation, unit and equipment performance monitoring, reduced air in-leakage and installation of variable speed drives. Additional projects may include operation at lower cooling water tower temperatures to improve condenser vacuum and variable speed drives on boiler fans and other large motors. At the Port Washington power plant, the efficiency improved by 11%. This improvement was the result of a major plant renovation project, which included the refurbishment or replacement of most major plant equipment. The result of the project was a restoration of the units to their original capacity and improved efficiency. At the Presque Isle power plant, the efficiency improved by 4%. Some actions that contributed to improvements include reduced air in-leakage, reduced excess boiler O2, boiler chemical cleaning, CO2 monitors on the boiler, improved turbine pressure and updated or additional instrumentation. At the Valley power plant, the efficiency improved by 2.3% due to last row turbine blade replacement, variable speed drives for the forced and induced draft fans and reduced air in-leakage. Several power plants in different countries have implemented improvement technologies for increasing power plant efficiency. For example, OPG was involved in a project to help Jordan to improve the efficiency of its oil fuelled electricity generating units (Jordan Central Electricity, 2000). In 2000, the project was completed and the total emissions savings resulting from the project estimated over a three year period was 141,983 Mg of carbon dioxide (Jordan Central Electricity, 2000). If deep reduction in CO2 from generating stations is required, CO2 capture and sequestration technologies must be employed. CO2 capture processes separate CO2 from the flue gas for subsequent transportation and or sequestration. Some types of CO2 capture technologies (based on both chemical and physical absorption) are well established and have been in use for several decades. The majority of chemical-based methods rely on scrubbing systems that utilise amine solutions to remove CO2 from exhaust gases. Amine scrubbers have already been applied to coal-fired industrial process and power stations (International Energy Agency, 2003). In most cases, the systems used are similar in concept and configuration and usually employ a regenerable amine, such as

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monoethanolamine (MEA) as the working solvent. Depending on the particular application and type of flue gas being treated, such systems can recover up to 98% of the CO2 present and produce a CO2 stream of up to 99% purity. Recently, however, more advanced amines have been developed, for instance by Mitsubishi Heavy Industries (MHI), and are now being applied commercially (International Energy Agency, 2003). Such new amines are claimed to suffer less degradation and to have lower consumption rates and energy requirements than conventional MEA-based solvents (International Energy Agency, 2003). A number of physical absorption technologies are also in use, generally applied to systems operating at higher pressures. These rely on a range of solvents that include methanol and propylene carbonate. Alternative capture technologies that may also be applicable to coal-fired power plants in the longer term include systems based on the application of specialised separation membranes and cryogenic technologies. However, the major shortcoming for the application to CO2 capture processes in fossil fuel power plants is the large energy requirements (International Energy Agency, 2003). The main objective of this paper is to present a mathematical programming model for the reduction of CO2 emissions from a network of power plants. Various CO2 emission reduction strategies will be considered in the model. These include efficiency improvement actions, fuel balancing, and fuel switching. However, CO2 capture processes are not included in this study. The remainder of this paper is organised as follows: first, the superstructure representation of the different CO2 reduction strategies considered in this study will be illustrated. A mathematical model will then be introduced. The model is a Mixed Integer Non Linear Program (MINLP); an exact linearisation strategy will be employed to reduce the model to an MILP. Finally, a case study based on OPG will be illustrated and the results for reducing CO2 emissions while meeting electricity demand will be presented.

3

Methodological approach

3.1 Superstructure representation The superstructure representing a power generation energy supply system from different types of power plants is shown in Figure 1. Different types of power plants generate electricity and inject it into the grid directly. It is assumed that only the coal and natural gas plants generate CO2 and there are no CO2 capture processes on any existing power plants. Figure 2 shows the fuel balancing where CO2 emissions are decreased by increasing the load of existing non-fossil fuel power plants and decreasing the load of existing fossil fuel power plants. The goal here is to determine the optimal load for each power plant in order to maintain electricity to the grid and reduce the CO2 emissions at the same time. Figure 3 illustrates the fuel switching option which involves switching from the fuel used in a particular power plant to a less carbon intensive fuel, typically from coal to natural gas. Finally, Figure 4 shows the incorporation of possible improvement technologies that can be implemented in power plants to increase the thermal efficiency or in other words to decrease the CO2 emissions while maintaining the same electricity to the grid; here we have focused our attention on coal based generating stations only.

A mixed-integer non-linear programming model Figure 1

Superstructure for power plants

Figure 2

Superstructure for fuel balancing

Figure 3

Superstructure for fuel switching

261

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Figure 4

Superstructure for efficiency improvement

3.2 Mathematical model The model consists of an objective function to be minimised and equality and inequality constraints which need to be satisfied at the solution. The objective function can be written as: Min Z =

∑∑ C E i∈F

ij

ij

j

Cost of electricity generation from fossil fuel power plant

+

∑ Ci Ei

i∈NF

Cost of electricity generation from non-fossil fuel power plant

+

∑∑ R

X ij +

i∈F

ij

j

Retrofit cost for switching from coal to natural gas

∑∑ C

ik Yik i k

(1)

Cost of applying technology for effeciency improvement

where Z: F: NF: i: j: k: Cij: Ci : Cik: Eij: Ei: Rij: Xij: Yik:

Annualised capital and operating cost of the fleet of power stations. Fossil power stations includes coal and natural gas. Non-Fossil power stations includes nuclear, hydroelectric and wind turbine. Power plant. Type of fuel (coal or natural gas). Technology applied to increase power plant efficiency. Cost of electricity generation if fuel j is used on fossil power plant i ($/MWh). Cost of electricity generation for non fossil fuel power plants i ($/MWh). Cost of applying improvement technology k in plant i ($/yr). Electricity generated from ith power plant if fuel j is used (MWh/yr). Electricity generated from ith non-fossil power plants (MWh/yr). Retrofit cost to switch from coal to natural gas generating stations ($/yr). Binary variable either to switch plant i to natural gas or not. Binary variable either to implement improvement technology k in plant i or not.

The objective is to minimise Z the total annualised cost of operating a fleet of generating stations while satisfying the electricity demand and specified CO2 reduction targets. The first term in equation (1) above represents the cost associated with electricity generated from fossil power plants whereas the second term shows the cost for electricity generated from non-fossil power plants. The third term represents the retrofit cost if the


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fuel is to be switched from coal to natural gas; there is no retrofit cost for non-fossil power plants. The last term is the cost associated with applying technologies on fossil fuel power plants for efficiency improvement.

4

Constraints

Power demand satisfaction The electricity generated from all power plants must be equal to or greater than the demand (D).

∑∑ E i∈F

ij

j

+

∑E

i∈NF

i

≥ D.

(2)

Fuel selection or plant shut down For each fossil fuel power plant i, the plant either operates with a given fuel or is shut down. For this reason, a binary variable is introduced to represent the type of fuel used in a given fossil fuel plant. Xij = 1 if fuel j is used in plant i otherwise it is 0.

∑X

≤ 1 ∀i ∈ F .

ij

(3)

j

Upper bound on operational changes The adjusted electricity generated from each power plant should be less than or equal to a certain percentage higher than current production. Eij ≤ (1 + ri ) Eicurrent X ij

Ei ≤ (1 + ri ) Eicurrent

∀i ∈ F

∀i ∈ NF .

(4) (5)

This constraint set requires that the electricity produced from any plant i should not exceed the current electricity produced from the same plant by ri which is the maximum increase in the base load due to operational constraints. Lower bound on operational changes 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. The electricity generated from each power plant must be greater than some minimum ( Eimin ), otherwise the plant will be shut down. Eij ≥ Eimin X ij Ei ≥ E

min i

∀i ∈ F

∀i ∈ NF .

(6)

Emission constraints The CO2 emissions from electricity generation must satisfy a CO2 reduction target. Different technologies, k, to increase the power plant efficiency are implemented in the mathematical model. It is assumed that the effects of these technologies is additive. If this is not the case, then different sets or combinations of technologies can be defined as a single composite technology with a proper corresponding overall efficiency.

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∑∑ CO i∈F

j

CO 2ij =

2 ij

   1 − ∑ ε ik Yik  Eij ≤ (1 − %CO 2 )CO 2 k  

(7)

0.03667(%C / HHV)

(8)

ηik

where (CO2)ij: %CO2: CO2: %C: HHV: ηik: εik: Yik:

CO2 emission from coal plant i (million tones per year). Reduction target. CO2 emission (million tonnes per year). Carbon percentage for a given fuel. Higher heating value for the fuel (MJ/tonne). Efficiency of power plant i if technology k is implemented. Gain in efficiency associated with applying technology k in coal power plant i. Binary variable defined earlier.

The CO2 emission from each power plant, if technology k is chosen, must be within certain reduction target. Technology selection A binary variable (Yik) is introduced in the model to represent whether technology k for efficiency improvement should be implemented in power plant i or not.

∑Y

ik

+ Card( K ) × X ijεng ≤ Card( K ) ∀i ∈ F .

(9)

k

Where Card(K) is cardinality of the set of technologies k. This constraint imposes the fact that no improvement technology should be implemented in a plant that is to be switched from coal to natural gas. Non-negativity constraints The electricity produced from all power plants must be greater than zero. Eij ≥ 0 and

Ei ≥ 0.

(10)

The previous mathematical model was developed based on the following assumptions: •

the process units are modelled at a low level of detail and treated as black boxes to simplify the excessively large scale problem that would otherwise exist

•

the nominal amount of electricity generated is fixed

•

the electricity price is constant

•

the supply and price of fuels (coal and natural gas) are constant

•

all coal fired power plants use Canadian Eastern Bituminous coal with 78% carbon and a higher heating value of 6000 MJ per tonne

•

no efficiency improvement technologies are currently being implemented.


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The resulting model is formulated as a MINLP because of a constraint set where there is a multiplication of a decision variable (Eij) and a binary variable (Yik) in the CO2 emissions term. The model has been linearised and proved to have the same optimum as the original one; the linearisation and proof are given in the Appendix.

5

Case study

The model was applied to the existing fleet of OPG’s power plants to determine the best strategy for OPG to reduce the amount of CO2 at a minimum cost. The options being considered are fuel balancing, fuel switching and implementing efficiency improvement technologies. OPG operates currently six fossil fuel power plants (Ci=1–6): five running on coal and one on natural gas, 69 hydroelectric (Hi=1–69), three nuclear (Ni=1–3) and one wind turbine (Ai=1). In 2003, OPG had a total installed capacity of 13,765 MWe and emitted about 36.5 Mt of CO2, mainly from fossil fuel power plants. There are 27 fossil fuel boilers at the six fossil-fuel stations: four boilers at Lambton (L1–L4), eight boilers at Nanticoke (N1–N8), one boiler at Atikokan (A1), eight boilers at Lakeview (LV1–LV8), four boilers at Lennox (L1–L4), and two boilers at Thunder Bay (TB1–TB2). Currently, the four boilers at Lennox are running on natural gas. Table 2 shows a general view of OPG fossil fuel generating stations. Since non fossil fuel power plants are assumed not to emit CO2, the main focus is on electricity generated from the fossil fuel power plants. The operational costs for nuclear, hydroelectric, and wind turbine were estimated to be $32, $5, and $4/MWh, respectively. The nominal conditions for OPG’s existing fleet of power plants are (Hashim et al., 2005): •

total electricity generation: 13,765 MWe

•

total CO2 emissions: 36.57 × 106 tonne/yr

•

total operational cost: 2.808 × 109 $/yr.

Table 2

Ontario Power Generation fossil fuel generating stations Installed capacity Number (MW) of units

CO2 emission Annual capacity Operational rate factor cost ($/MWh) (tonne/MWh)

Generating station

Fuel

Lambton1 (L1)

Coal

500

2

0.75

25

0.9384

Lambton2 (L2)

Coal

500

2

0.5

34

0.9386

Nanticoke 1 (N1)

Coal

500

2

0.75

30

0.9300

Nanticoke2 (N2)

Coal

500

6

0.61

30

0.9300

Atikokan (A)

Coal

215

1

0.44

30

1.0230

Lakeview (LV)

Coal

142

8

0.25

35

0.9765

Lennox (LN)

Natural gas

535

4

0.15

50–70

0.6510

155

2

0.55

30

1.0230

Thunder Bay (TB) Coal

Figure 5 shows the existing OPG fossil fuel power plants (27 boilers) and their associated electricity generation.

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Figure 5

Electricity generated from OPG power plants (27 boilers)

Three options to reduce CO2 emission considered here are fuel balancing, fuel switching and efficiency improvement technologies for coal power plants. The efficiency improvement technologies being considered in this study are: install variable speed drive, with 1.5% efficiency improvement, and install high efficiency turbine blades with about 1% increase in efficiency. The actual cost for these technologies depends on the boiler capacity; estimates were obtained from WEPCO (Wisconsin Electric Power Company, 2005) and they are $2,000,000 and $5,000,000 respectively for 500 MW power plant capacity. The cost for each technology is amortised with a 20-year lifetime and a 10% annual interest.

6

Results and discussion

The linearised model discussed earlier was coded into GAMS and solved using the MILP solver. The optimisation 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 CO2 emissions. The overall effect of the adjustments in the capacity factors is to reduce the overall CO2 emissions. The results show that all non fossil fuel power plants have to operate with 1% (maximum allowable value) higher than the nominal 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 about 10% which is the maximum allowable lower limit or the plant should be shut down. This result may seem to be counter intuitive since the Lennox generating station is fuelled 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 reduction in CO2 emissions is accomplished by increasing slightly the capacity factor of the non-fossil fuel generating stations (hydro-electric, nuclear and wind) and by decreasing significantly the capacity factor of Lennox. The capacity factors of the other fossil fuel plants were increased by only a small increment.


267

Figure 6 shows the optimisation results for the case of a 1% CO2 reduction target. For this case, no fuel switching is needed. In other words, the objective can be obtained by adjusting the operation of existing boilers e.g., increasing load from existing non-fossil power plants and decreasing load from some existing fossil power plants (fuel balancing). The results show that the capacity factors for all four natural gas boilers have been reduced by 34% and two coal fired boilers (LV4 and LV7) by 34% and 60%, respectively. No efficiency improvement technologies were recommended. Therefore, a 1% CO2 reduction target can be achieved by fuel balancing only. Figure 6

Electricity generation strategy for 1% CO2 reduction

In order to achieve more than a 1% CO2 reduction, it was found that fuel switching must be implemented. This involves fleet changes from coal to natural gas. As seen in Figure 7, the optimisation results show, that in order to achieve a 5% CO2 reduction while maintaining the electricity to the grid at minimum cost, the capacity factor of one of the natural gas boilers at Lennox (LN4) needs to be increased by 2%, and the only boiler at Atikokan, two boilers at Thunder Bay and one boiler, (LV5), at Lakeview power plant need to be switched from coal to natural gas. The capacity factors for the non-fossil fuel generating stations should be increased by 1%. The results also showed that the capacity factor of three boilers (LV6, LV7 and LV8) at Lakeview power plant should be decreased by about 40%. The model showed also that only one efficiency improvement technology (install variable speed drive) should be applied to the Nanticoke power plant and to three other boilers (L1, L3 and L4) at Lambton power plant. Higher CO2 reduction targets require more coal boilers to be switched to natural gas. For a 10% reduction (see Figure 8) the results show that larger boilers – two boilers (L1 and L2) at Lambton, two boilers (LV5 and LV8) at Lakeview and one boiler (TB2) at Thunder Bay power plants – should be switched to natural gas. The electricity generation from all non-fossil fuel power plants has also been increased by 1%. The capacity of two boilers (LV1 and LV4) at Lakeview power plant should be decreased by 60% and 30% respectively. The optimiser considered to install variable speed drive technology for efficiency improvement on two boilers (L3 and L4) at Lambton power plant and on all boilers except (N2) at the Nanticoke power plant.

268


Figure 7


Figure 8


As greater CO2 targets are required, the optimiser will choose more fuel switching options. For a 30% reduction, the results show that only two boilers (L3 and L4) at Lambton, one boiler (N3) at Nanticoke and the whole Lakeview power plants should continue to operate with coal and the other remaining boilers should be switched to natural gas (Figure 9). The electricity generation from all non fossil fuel power plants should be increased by 1%. However, the electricity generation from coal boilers (LV7 and LV8) should be reduced by 30% and 60%, respectively. The optimiser recommended to install variable speed drives for efficiency improvement at only two boilers, one (L4) at Lambton and another one (N3) at Nanticoke power plant.


269


Figure 9

A summary of the results is shown in Table 3 with selection of technologies and whether the boiler needs to be switched to natural gas or not. The full black circles represent coal boilers while open circles represent natural gas boilers. Switching is represented by open squares and k1 and k2 represents the installation of efficiency improvement technologies, variable speed drives and high efficiency turbine blades, respectively. Table 4 shows the cost and CO2 emission for each reduction target with the cost of CO2 avoided. It is shown that OPG could save money at 1% CO2 reduction since the cost of CO2 avoided is negative. This can be achieved as mentioned earlier by only increasing the capacity factor of non fossil fuel power plants and decreasing the capacity factor of the natural gas power plant without structural change to the fleet. Increasing the reduction target will lead to a higher cost of CO2 avoided since it involves structural change such as switch some of the coal power plants to natural gas. Table 3

A summary of optimisation results 5% CO2 reduction

1% CO2 reduction

10% CO2 reduction

30% CO2 reduction

Plant Base

S

k1

k2

S

k1

k2

S

k1

k2

S

k1

k2

L1

●

●

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○

●

□

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□

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○

□

○

○

L2

●

●

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○

●

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○

□

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○

□

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○

L3

●

●

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●

□

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●

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○

L4

●

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●

□

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●

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●

□

○

N1

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□

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●

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□

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N2

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N3

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□

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□

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N4

●

●

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●

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●

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□

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○

270


Table 3

A summary of optimisation results (continued) 5% CO2 reduction

1% CO2 reduction

10% CO2 reduction

30% CO2 reduction

Plant Base

S

k1

k2

S

k1

k2

S

k1

k2

S

k1

k2

N5

●

●

○

○

●

□

○

●

□

○

□

○

○

N6

●

●

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●

□

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●

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□

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N7

●

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●

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□

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N8

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□

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A1

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LV1

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LV2

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LV3

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LV4

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LV5

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LV6

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LV7

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LV8

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LN1

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LN2

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LN3

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LN4

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TB1

●

●

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□

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○

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□

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TB2

●

●

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○

●: Coal. ○: Natural gas. □: Switch to NG. k1: Install variable speed drive. k2: Install high efficiency turbine blades. Table 4

Cost of CO2 emission and cost of CO2 avoided at different reduction targets Cost (109 $/yr)

CO2 emission (Mt/yr)

Cost of CO2 avoided ($/tonne CO2 avoided)

1

2.771

36.08

–88.1

5

2.817

34.74

5.0

10

2.886

32.91

21.7

30

3.167

25.59

33.0

Reduction target (%)

7

Conclusions

The optimisation of CO2 emissions from the Ontario power grid was studied. In our calculations, a linearised MINLP model was used and was implemented in GAMS.


271

The reduction options considered were fuel switching, fuel balancing and technologies for power plant efficiency improvement. The results indicate that applying several strategies for increasing the power plant efficiency is an effective way for reducing CO2 emissions. The optimisation results show that overall CO2 emissions can be reduced by 1% by adjusting OPG’s current operational level without having to change the fleet structure (fuel balancing). Fuel balancing also results in a reduction of operating costs by about 1.5%. However, if CO2 emissions are to be reduced further (e.g., by >6%, Canada’s Kyoto target), it will be necessary to employ structural changes such as fuel switching. Fuel switching involving structural changes to the fleet has been considered as the best option for CO2 reduction, especially if the reduction target is 10% or above. Applying technologies for efficiency improvement is an attractive option to reduce CO2 emissions, especially at small reduction targets such as around 5%. The constant fuel price and supply needs to be investigated. Coal supplies are extensive and its price is stable. However, Canadian natural gas supplies are declining and are predicted to last for another decade. This will lead to increased prices and price volatility.

References Antunes, C., Martins, A. and Brito, I. (2004) ‘A multiple objective mixed integer linear programming model for power generation expansion planning’, Energy, Vol. 29, pp.613–627. Audus, H. (1993) Greenhouse Gas Releases from Fossil Fuel Power Stations, IEA Greenhouse Gas R&D Program, UK. Bai, H. and Wei, J. (1996) ‘The CO2 mitigation options for the electric sector’, Energy Policy, Vol. 24, pp.221–228. Canada Energy Outlook (2002) http://www.nrcan.gc.ca/es/ener2002/online/html. Climaco, J., Antunes, C.H., Martins, A.G. and Almeida, A.T. (1995) ‘A multiple objective linear programming model for power generation expansion planning’, International Journal of Energy Research, Vol. 19, pp.419–432. Electric Power Company (WEPCO) (2005) Wisconsin, USA, Personal Communication. Elmahgary, Y., Ibrahim, A., Shama, A., Hassan, A., Rifai, M., Selim, M., Higazi, A., Amin, A., Bedewi, F. and Korkor, H. (1994) ‘Costs of CO2 abatement in Egypt using both bottom-up and top-down approaches’, Energy Policy, Vol. 22, No. 11, pp.935–946. Genchi, Y., Saitoh, K., Arashi, N. and Inaba, A. (2002) ‘Assessment of CO2 emissions reduction potential by using an optimisation model for regional energy supply systems’, Paper B5-6 presented at the Sixth International Conference on Greenhouse Gas Control Technologies, Kyoto International Conference Hall, Japan, October 1–4. Hashim, H., Douglas P.L., Elkamel A. and Croiset, E. (2005) ‘Optimization model for energy planning with CO2 emission considerations’, Industrial and Engineering Chemistry Research, Vol. 44, No. 4, pp.879–890. International Energy Agency (2003) Control and Minimization of Coal-fired Power Plant Emissions, Technical Reports, France. Jordan Central Electricity (2000) Efficiency Improvements in Power Plants, project 82. Linares, P. and Romero, C. (2000) ‘A multiple criteria decision making approach for electricity planning in Spain: economic versus environmental objectives’, J. Operational Research Society, Vol. 51, pp.736–743.

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Mavrotas, G., Diakoulaki, D. and Papayannakis, L. (1999) ‘An energy planning approach based on mixed 0-1 multiple objective linear programming’, International Transactions in Operational Research, Vol. 6, pp.231–244. Noonan, F. and Giglio, R.J. (1977) ‘Planning electric power generation: a linear mixed integer model employing benders decomposition’, Management Science, Vol. 23, pp.946–956. Rovere, L., Leget, L. and Miguez, J. (1994) ‘Alternatives energy strategies for abatement of carbon emissions in Brazil’, Energy Policy, Vol. 22, No. 11, pp.914–924. Torrens, I. and Stenzel, W. (2001) Industry Perspectives on Increasing the Efficiency of Coal Fired Power Generation, International Energy Agency, http://www.iea.org. US Department of Energy (2001) Review of Potential Efficiency Improvements at Coal Fired Power Plants, http://www.energy.gov/engine/content.do. Wu, Z., Jiankun, H., Zhang, A., Xu, Q., Zhang, S. and Jayant, S. (1994) ‘A macro-assessment of technology options for CO2 mitigation in China’s energy system’, Energy Policy, Vol. 22, No. 11, pp.907–913. Yamaji, K., Matsuhashi, R., Nagata, Y. and Kaya, Y. (1993) ‘A study on economic measures for CO2 reduction in Japan’, Energy Policy, Vol. 21, No. 2, pp.123–132. Yokoyama, R., Hasegawa, Y. and Ito, K. (2002) ‘A MILP decomposition approach to large scale optimization in structural design of energy supply systems’, Energy Conversion and Management, Vol. 43, pp.771–790. Zhou, Q., Huang, G. and Chan, C. (2004) ‘Development of an intelligent decision support system for air pollution control at coal fired power plants’, Expert Systems with Applications, Vol. 26, pp.335–356.

Appendix The emission constraint (8) is the one that causes non-linearity to the model. The non-linear term is:

∑∑ CO i∈F

j

2 ij

   1 − ∑ ε ik Yik  Eij . k  

(1A)

Non-linearity is due to the product (YikEij) Let γ ijk = Yik Eij (non-linear term).

(2A)

The term can be linearised by adding these constraints to the model: 0 ≤ γ ijk ≤ Eij

(3A)

Eij − Eijmax (1 − Yik ) ≤ γ ijk ≤ Eijmax Yik

(4A)

where Eijmax is a maximum upper bound on Eij. Proof: From equation (2A), we want to show that γijk = 0 if Yik = 0 and γijk = Eij if Yik = 1. Case 1: (no technology is selected) Yik = 0.


273

Since γijk = YikEij (from equation 2A), Then, γijk = 0. Equation (3A) becomes: 0 ≤ γ ijk ≤ Eij .

(5A)

And equation (4A) becomes: Eij − Eijmax ≤ γ ijk ≤ 0.

(6A)

From equations (5A) and (6A), γijk will be chosen to be zero. Case 2: (technology is selected)

γik = 1. Since γijk = YikEij (from equation 2A), Then, γijk = Eij Equation (3A) becomes: 0 ≤ γ ijk ≤ Eij .

(7A)

And equation (4A) becomes: Eij ≤ γ ijk ≤ Eijmax .

From equations (7A) and (8A), γijk is set equal to Eij. Summary Adding the two constraints (equation 3A and 4A) to the model will lead to:

γijk = 0 if Yik = 0 and γijk = Eij if Yik = 1.

(8A)