Format And Type Fonts CHEMICAL ENGINEERINGTRANSACTIONS VOL. 45, 2015 A publication of The Italian Association of Chemical Engineering www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Sharifah Rafidah Wan Alwi, Jun Yow Yong, Xia Liu Copyright © 2015, AIDIC ServiziS.r.l., ISBN 978-88-95608-36-5; ISSN 2283-9216 DOI: 10.3303/CET1545138 Please cite this article as: Krishna Priya G.S., Bandyopadhyay S., Tan R.R., 2015, Multi-objective pinch analysis with multiple resources, Chemical Engineering Transactions, 45, 823-828 DOI:10.3303/CET1545138 823 Multi-Objective Pinch Analysis with Multiple Resources Govindankutty S. Krishna Priya a , Santanu Bandyopadhyay* a , Raymond R. Tan b a Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India b Chemical Engineering Department, De La Salle University, Manila 2401 Taft Avenue, 0922 Manila, Philippines santanub@iitb.ac.in Pinch Analysis is an optimization technique that has been applied to a wide array of problems ranging from water networks to power systems. In general, Pinch Analysis is applied to single objective optimization problems. A characterizing parameter, called prioritized cost, has been developed to identify a cost optimal solution with multiple resources. In this work, Pinch Analysis is extended to address multi-objective Pinch Analysis problems with multiple resources. This is achieved by assigning a weighting factor to each objective and calculating the prioritized cost based on this variable. As the weighted prioritized cost is a linear function, it is possible to identify key values of the weighting factor where the order of priorities shifts. This greatly reduces the complexity of the problem and makes it possible to identify all the viable resource combinations. The plots of prioritized cost as a function of weighting factor can be obtained for any number of available resources. Using the prioritizing order given by these plots, Pinch Analysis can be extended to solving multi-objective optimization problems. The proposed methodology is demonstrated using the Indian power sector as an example with objectives to simultaneously minimize the capital investment and emission of oxides of nitrogen while keeping the carbon dioxide emission within prescribed limits. 1. Introduction In light of rising electricity demands and a pressing need to curb greenhouse emissions, power system planning with emission targeting is of great relevance. The common objective considered during power system planning is cost minimisation. However, quite often, cost is not the only criterion involved in the selection of an optimal resource. Multi-objective optimisation problems are hence common in power system planning. Pinch Analysis is a method commonly used in power system planning with emission targeting. It was applied to carbon constrained power system planning (Tan and Foo (2007 ), pumped hydel storage to minimize supply demand mismatch (Rozali et al., 2013), a renewable based smart grids (Giaouris et al., 2014), and multi-period optimisation of power systems (Ooi et al., 2014).These problems have largely been single objective formulations aimed at minimizing the cost while meeting an emission limit.While such formulations are of great relevance, the selection of one type of power plant over another is a complex decision which requires satisfying multiple requirements ranging from cost to social acceptability. Hence, there is a need for multi-objective optimisation techniques in the power sector. In this paper, the concept of solving linear multi-objective problems using Pinch Analysis is discussed. Initial framework of this formulation was developed by Tan and Bandyopadhyay (2013). The methodology is extended and then applied to the Indian electricity sector. The multiple objectives considered are cost minimisation and minimisation of oxides of nitrogen (NOx) for a specified energy and emission target. The results obtained are discussed along with the sensitivity of objective function to emission limit. 2. Problem Statement The general problem may be stated as follows. There are existing power plants, and a future energy demand. There are new power plants that may be commissioned. It should be noted that here, similar power plants (say coal power plants) are clubbed together as one. Each new power plant i supplies energy at a given emission factor ( ) and each existing power plant j has an emission factor . Emission factor is the carbon dioxide emitted for each unit of energy generated. The future energy demand is to be met 824 with a specified emission factor ( ). Energy supplied from a new power plant i to the demand is denoted as and that from an existing power plant j is denoted as . It is possible that some existing power plants are not utilised to their full capacity, leading to unutilised energy ( as illustrated in Figure 1. Figure 1: Representation of a typical allocation problem Energy balances for any power plant as well as for the overall system may be expressed as follows: (1) ∑ ∑ (2) (3) Where, is the maximum energy available from new power plants (maximum potential). Total unutilised energy (waste) may be expressed as: ∑ (4) Total new installed capacity requirement: ∑ (5) By taking an overall summation, it can be seen that Existing power plant j=1, EF1 Existing power plant j, EFj New resource i=1, EF1 New resource i, EFi Energy Demand, Fd,EFd Unutilised Energy Existing power plant j=Ns, EFNs New resource i=Nr, EFNr fij, EFsi fi, EFi fjw 825 [∑ ] (6) ∑ (7) the cumulative sum of all existing power plants and future demands is constant. In addition to all this, the required emission target should also be met. ∑ ∑ (8) As setting up a power plant is cost intensive, it is important to minimise the capital investment while meeting the emission and energy targets. In addition to carbon dioxide, power plants emit a large number of other gases which are harmful to the environment. It is important to minimise these as well. As an example, NOx is considered here. The objective is to simultaneously minimise the cost and NOx emission. The variables are capacity factors of existing plants and capacity of new plants. Here, the emission target is denoted by . The problem can be formulated as: ∑ (9) Where is the total number of new power plants and is the cost function containing a component of capital cost and one of NOx emission. The constraints are as follows: ∑ ∑ (10) ∑ ∑ (11) The energy produced by the power plant is obtained by multiplying installed capacity by capacity factor ( ) and total time. (12) Pi is the added installed capacity of the source. The emission from source is obtained by multiplying energy generated by emission factor: (13) Similarly, capital cost is a function of type of resource and installed capacity: (14) (15) Where is the objective function pertaining to capital minimisation and corresponds to NOx emission. As all the constraints as well as the objective functions are linear, this is a multi-objective linear programming problem. The bi-objective problem practically converges to determination of optimal points that satisfies both these objectives simultaneously. To determine these points, the concept of weighted objective can be adopted; for linear systems, this summation always results in a Pareto optimal solution. Assuming a weight w for total cost energy supply and a weight of (1 – w) for the total energy invested, a single objective (C) can be formulated. (16) 826 To get the entire Pareto optimal front, weight w can be varied between 0 and 1. On the other hand, a Pareto optimal point can also be generated keeping one the objective fixed and solving the formulation to optimize the other objective. The procedure is repeated multiple times in order to get all optimal points. Given the objective function, it is possible to identify the prioritising order of resources available. The method for identifying prioritised cost is discussed in Krishna Priya and Bandyopadhyay (2013). Using the same technique, the prioritised cost of plant i in this case can be identified as: (17) The prioritised cost allows for identifying a prioritising order. In short, it says that a resource (power plant) needs to be considered only if its prioritised cost is lower than that of all resources with a lower emission factor. This method is illustrated next using the Indian power sector as an example. 3. Case study: Indian power sector Overall, India’s need for power is growing at a prodigious rate, annual electricity generation and consumption in India has increased by about 64 % between 1997 and 2007, and its projected rate of increase (estimated at as much as 8 - 10 % annually, through the year 2020) for electricity consumption is one of the highest in the world (ICLEI South Asia, 2007). The 17 th electric power survey published by the central electricity authority (CEA, 2007) predicts India’s annual electricity consumption to be 1,900 TWh by 2020. While increasing power production capacity is of prime importance, it is equally important to reduce the overall emission from power sector. It is safe to assume that total emission will have to be reduced by around 20 % of present value by 2020. For the purpose of this project, the target has been set to 703 Mt of CO2 which is a 25 % reduction from that of 2007. It is important to note that CO2 is not the only dangerous emission caused by the power industry. In order to illustrate the suggested method, minimising NOx emission is considered as an additional objective here. The data of resources available is listed in table 1. In order to clearly illustrate the variation of prioritised cost, convenient units have been chosen. Table 1: Future power sources Resource Limit (GW) Operating Capacity factor Tonnes of CO2/ MWh e NOx (100 g/MWh) f Cost (10 6 Rs/MW) Coal NA 0.72 d 1.08 43.4 40 g Nuclear 10.00 b 0.82 b 0.02 0 52 g Hydro 148.70 a 0.50 a 0 0 70 a Wind 47 c 0.14 c 0 0 50 h Biomass 19.50 c 0.70 c 0.15 22 30 h Small Hydro 15 c 0.50 c 0 0 125 i Solar NA c 0.20 c 0 0 200 h Coal with CCS NA 0.9 0.1 43.4 52 g Compiled from data available on a- NHPC (2012); b- NPCIL (2012), c- MNRE (2008); d- NTPC (2012); e-Tan et al. (2009); f-Mittal et al. (2012); g-CEA (2004); h-Banerjee et al. (2006); i-Nouni et al. (2008) Based on the data available, the prioritized cost of various power sources is plotted against the weighting factor (Figure 2). The points of intersection of these lines specify the weighting factor at which the priorities of power sources may change. This change will also depend on the emission factor of the power sources involved. A new power source is viable only if its prioritized cost is lower than that of all other sources with lower emission factor. The prioritized cost of coal power plants is significantly higher than that of others and is not shown in the plot. It can be seen that at lower values of weighting factor, the resources with low NOx emission like solar energy and hydroelectric power play a part in the final energy mix. However, as the weightage for cost minimization increases, this comes down, and new coal power plants with carbon capture units take over. From Figure 2, it can be seen that up to a weighting factor ‘P’ renewable such as hydroelectric and wind power plants have lower prioritised cost along with nuclear energy. As expected, the energy mix obtained at low values of weightage reflects this observation. It should be noted that, as the unrestricted resource, solar energy supplies a large portion of the load. However, at a weighting factor ‘O’, coal power plants with carbon capture becomes more viable than solar energy, and as it is not a limited resource, plays an important part in the mix. Beyond point ‘P’ the mix is stable. It should be noted that not 827 all intersection points alter the mix. For example, at weightage ‘Q’, biomass becomes more viable than nuclear energy. However, as both these resources are limited, they are both used exhaustively. Figure 2: Prioritised costs of various energy sources Figure 3: Pareto optimal front and variation in energy mix at key points Figure 4: Sensitivity of Pareto optimal front and overall cost to emission limit The Pareto optimal front here is a plot of capital cost vs. NOx emission. It is found to be a piecewise linear plot with three key points corresponding to solution at weighting factors corresponding to regions between 0 and ‘O’, ‘O’ and ‘P’ and the region beyond ‘P’. The variation in the mix of new power plants is sho wn in Figure 3. It shows the three possible energy mixes along with the Pareto optimal front of the system. It can clearly be seen that as the weightage for cost minimization increases, the resources migrate from renewables to fossil fuels (coal power plants with carbon capture units). It is also seen that some fraction of existing coal power plants are being shut down to meet the constraints. The fraction of coal power plants shutdown varies from 23 % when weighting factor is zero to 35 % when the weighting factor is one. The emission limit of the system is varied and the variation of overall cost function across the range of weighting factors was studied. Figure 4 gives the variation of cost function as weighting factor and emission limits are varies. For most values of weighting factor, the overall cost increases as the emission Coal with CCS Nuclear Hydel SHP Solar Wind Biomass 0 50 100 150 0.00 0.20 0.40 0.60 0.80 1.00 1.20 P ri o ri ti s e d C o s t Weighting Factor O P Q 0 200,000 400,000 600,000 200,000 400,000 600,000 C o s t (T ri ll io n R s .) NOx emission (Million kg) 0 200,000 400,000 600,000 200,000 400,000 600,000 800,000 C o s t (T ri ll io n R s .) NOx Emission (Million kg) Standard emission 0.8*Standard emission 1.2*Standard emission 200 300 400 500 600 700 800 0 0.5 1 V a l. o f O b je c ti v e ( × 1 0 8 ) Weighting Factor Nuclear 4 %; Hydel 51 %, SHP 5 % Wind 4 % Solar 36 % Nuclear 4 %; Hydel 48 %, Biomass 10 % Coal with CCS 38 % Nuclear 4 %; Biomass 10 % Coal with CCS 86 % 828 limit is made more stringent. However, it is seen that these curves intersect at lower values of weighting factor. This leads to some interesting conclusions. At lower values of weighting factor, trying to achieve a lower carbon dioxide emission limit is more economical than relaxing the emission limit. This is largely because the resources with low carbon emission (i.e., renewables) also have a low NOx emission. 4. Conclusion In this paper, a linear, multi-objective optimization problem is solved using the concept of Pinch Analysis. It is shown that available energy sources can be prioritized using their emission factors and prioritized costs. The method is applied to the Indian power sector and the results obtained are discussed. In addition, a sensitivity analysis is carried out to study the system behaviour with variation in emission limit. It is observed that in general, as emission limit becomes more stringent, the optimal value of overall cost function increases. However, it may be more economical to achieve lower emission targets if the weighting on NOx emission is also high. 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