Graph theory

1. Site Selection of Thermal Power Plant using Graph Theory and
Matrix Method (GTMM)
Arnav Sharma
MM-262-2K13
Guided by: Mr. Nikhil Dev
Asst.Prof.
YMCAUST Faridabad

2. Contents
• Introduction
• Guidelines for Site Selection of Thermal Power plants
• Objective of Site Selection of Power Plant Analysis
• Identification of factors for Site Selection of Thermal Power
plant
• Methodology for Graph Theory and Matrix Method
• RI FOR SYSTEMS
• Analysis of site selection
• Conclusion

3. Introduction
In recent years, multi-criteria Decision making methods have been applied to
a great extent in energy and environment modeling. The evaluation of the
alternative locations, and selection of the most suitable and efficient
locations for thermal power plants (TPPs) is also a vital multi-criteria decision
making problem. Location choice for TPP affects the amount of generated
energy, power plant’s productivity, cost of power generation and
transmission, economic development and environment. Selection of
unsuitable location for thermal power plant (TPP) will lead to increased costs,
waste of energy and resources, and increased environmental pollution, which
has a tremendous negative impact on society.

4. Guidelines for Site Selection of
Thermal Power plants
Guidelines of Ministry of Environment and Forests (MoEF), Government of India,
for location selection of Thermal Power plants (TPPs) (Samantaray et al 2004).
• Locations of TPPs are avoided within 25 km of the outer periphery of the
following:
- Metropolitan cities,
- National park and wildlife sanctuaries, and
- Ecologically sensitive areas like tropical forest, biosphere reserve,
important lake and coastal areas rich in coral formation.
• The sites should be chosen in such a way that chimneys of the power plants
do not fall within the approach funnel of the runway of the nearest airport;
• Those sites should be chosen which are at least 500 m away from the flood
plain of river system.
• Location of the sites are avoided in the vicinity(say 10 km) of places of
archaeological, historical, cultural/religious/tourist importance and defense
installations.
• Forest or prime agriculture lands are avoided for setting up of thermal
power houses or ash disposal.

5. Contd.
Guidelines of central electric authority (CEA), Government of India, for
location selection Thermal Power plants (TPPs) (Samantaray et al 2004).
• 1. The choice of location is based on factors like availability of land, water,
coal, construction material, etc.
• 2. Land requirement for TPP is 0.2 km2 per 100 MW.
• 3. The land for housing is taken as 0.4 km2 per project.
• 4. Land requirement for ash pond is about 0.2 km2 per 100 MW.
• 5. Water requirement is about 40 cusecs per 1000 MW.
• 6. Location of thermal power station is avoided in the coal-bearing area.
• 7. Coal transportation is preferred by dedicated marry-go-round rail system.

6. Objective of Site Selection of Power
Plant Analysis
• A power plant affects the environment surroundings during its construction
and operation. These effects are of temporary and permanent nature.
Therefore, it is required to analyze any location before the installation of
power plant. The analysis should take care of all the factors and sub-factors
that affect power plant site selection.
• The objective of this research is to first identify, rank and relate the
important factors and sub factors relevant to the power plant location
selection and provide a framework of relationships amongst factors using
Graph Theory Approach (GTA).

7. Identification of factors for Site Selection
of Thermal Power plant
Factors Sub-factors
Availability of resources Land availability
Water availability
Fuel availability
Skilled manpower availability
Economical impact Land acquisition cost
Investment cost
Operation and maintenance cost
Payback period
Future development limitations
Possibility of Site expansion
Table3.1. Factors and Sub-factors for selection of location of power
plant

8. Environment concern Degradation of local air quality
Land Use Impacts
Dust
Noise
Effect on water bodies
Social concern Job creation
Public acceptance
Number of relocation
Social benefits
Accessibility Road/Rail/Airport accessibility
Transmission grid accessibility
Electricity consumption point
Urban area accessibility

9. Methodology for Graph Theory and
Matrix Method
Graph theory is a logical and systematic approach useful for modeling and
analyzing various kinds of systems and problems in many fields of science and
technology. If the graph/digraph is complex, it becomes difficult to analyze it
visually. Quick analysis may be carried out by logical and systematic computer
programming tool through the use of the matrix method. It is a three stage
integrated systems approach.
• Modeling of system and subsystem in terms of nodes and edges for
structural representation in the form of directed graph (digraph) which is
suitable for visual analysis and gives a better understanding of
interrelationships among system and subsystems.
• Digraph representation is converted to matrix form, which is suitable for
computational analysis. Value of each element in the matrix is assigned
based upon inheritance of system or subsystem and their
interdependency.
• Matrix model is solved and results in the expression form called as
permanent function. After quantification of each term of permanent
function, result is represented in term of a single numerical index which is
the indication of system performance

10. System Digraph
• A system digraph is prepared to represent the selection factors of the site
selection of thermal power plant in terms of nodes and edges. Let nodes
represent selection factors and edges represent their interactions. It
represents factors (Di’s) through its nodes and dependence of factors
(dij’s) through its edges. Di indicates the inheritance of factors and dij
indicates degree of dependence of jth factor on ith factor. In the digraph
dij is represented as a directed edge from node i to node j. The digraph
permits to show the proposed factors and interactions between factors.
• In particular five factors identified form the System digraph. The five
factors – Availability of resources (D1), Economical impact (D2),
Environment Concern (D3), Social Concern (D4), and Accessibility and
interactions amongst them are shown in Figure

12. MATRIX REPRESENTATION
(a) System Structural Adjacency Matrix
Let a general case of a system, for example, a SSPP having N systems be
considered leading to adjacency matrix (0, 1) of order NXN and dij
representing the connectivity between system i and j such as dij =1, if system i
is connected to the system j, (in the graph, this is represented by an edge (dij)
between node i and j) and is equal to zero, otherwise. Thus dii = 0 for all i, as
no system is connected to itself in case of combined cycle power plant.

13. (b) Characteristic System Matrix
The presence of different systems of the SSPP is realized by defining a
characteristic system structure matrix that is
Bc= {DI-Ac}
Where I is the identity matrix and D is the characteristic of systems,
representing its characteristic structural features. This matrix for system
Diagraph of SSPP is expressed as:

14. (c) Variable Characteristic System Matrix (VCSM)
A variable characteristic system structure matrix Za is defined taking into
account the distinct characteristic of systems and their interconnection defined
in the system structure graph. For System Diagraph the VCSM Za= [Dc - Fc] is
written as:

15. (d) Variable Permanent System Matrix (VPSM)
The negative signs in equation indicate subtraction of information about dyads,
loops of systems, or system attributes which will not project a true picture of
the SSPP under analysis. For realistic understanding and characterization, a
permanent function is proposed and no negative sign will appear in the
expression. Application of the permanent concept will thus lead to a better
appreciation of the complete structure, in general

16. Variable permanent system function
The permanent function of VPSM is called the variable permanent System
function and is abbreviated as VPF-e. It is used to calculate the index. The
index value indicates the suitability of site.
The quantified values of Di and dij in the expression results in the form of an
index called as SSPP suitability Index in the present case. The main features
are as follows
• This index is quantitative representation of site selection of thermal power
plant (SSPP) and a mean to evaluate the effect of five systems and
interdependency on site selection of thermal power plant.

17. • By changing the value of inheritance (Di) and interdependency (dij), index
value is changed. A comparison in between the index values for different Di
and dij is helpful to study the effect or importance of different systems.
• Index value may be used for the comparison of site selection of thermal
power plant under varying sets of inheritance of systems.
The value of the permanent function can be calculated with the help of
computer programming tool.

19. Digraph at System Level

22. Matrix Representation of Diagraph at
System Level
The Variable Permanent sub-system Matrix (VPSSM) for five systems, for a
general case with N sub-system, is represented as:
It may be noted that above matrix represents inherent values of the sub-system
that is Di’s (i = 1, 2 …, N) and the interaction amongst sub-system is dij’s (i, j =
1, 2 …, N and i ≠ j). Variable Permanent sub-system Matrix (abbreviated as
VPMSystem) for each system Diagraph is developed.

25. Permanent Function of Diagraph at
System Level
Permanent function of VPSSM is called Variable Permanent Sub-System
Function, abbreviated as VPF-ss and for matrix is written in sigma form in
expression

26. RI FOR SYSTEMS
RI for each system is the ratio of real time by to Maximum. If system is
operating at its best then RI is one otherwise it will be lesser than one because
no system can perform better than its maximum value.

27. Analysis of site selection
For this purpose, some numerical values of all parameters and
their interdependencies are required i.e. the value of all terms of
VPMSSPP The value of diagonal elements in VPMSSPP, i.e., the
value of all five systems D1, D2, D3, D4 and D5 are evaluated by
applying GTA for Sub-system of the respective system.
• Various system categories affecting the SSPP are identified
• A digraph is developed for these five systems
• Sub-System are identified for each category
• Digraphs for each system have been developed.
• At system level, Tables are used to determine numerical values
for inheritance of parameters and their interactions. The
VPSSM for five systems are corresponding to equations from
and after quantification they are as written below:

29. • The value of permanent function for each category is calculated using a
computer programmed developed in language C++. The values of
permanent function of different systems are written as under

30. • Now for example after some years availability of water is decreased and
inheritance of is 5 in place 6, then expression for availability of water will
become

31. • If all the systems of SSPP are working at their maximum efficiency, which
is the ideal case, then VPSM for SSPP system
• In actual life, for selecting location of power plant it is impossible to get
everything in one place. A lot many factors come into play when deciding
where to install the plant.
• Corresponding to these, the quantified values of inheritance for Availability
of resources, Economic impact, Environment Concern, Social Concern and
Accessibility is obtained and these are 6,7,6,7,9 respectively

32. For the decrease in Availability of water RI for Availability of resources is 0.859.
Therefore, corresponding to above expression is

33. • Value of permanent function during Site selection is 37125 and for the real
time case is 33173. Value of relative SSPP comes out to be 34.41%. From
the GTA it came out that with decrease in Availability of Water, relative is
decreased from 38.51% to 34.41%.
• Site Selection of Thermal Power Plant calculated with the help of GTA
depends upon the inheritance and interdependencies of systems and Sub-
System. By carrying out similar analysis, the index for different Location
can be obtained.

34. CONCLUSION
In the present work GTA is selected with a view that it is qualitative
cum quantitative method. The GTA developed for selection analysis
can be used for reliability, maintainability, availability and cost analysis
also. A common guiding principle provided by GTA is helpful to
develop an index integrating all the factors to be analyzed for proper
site selection. In the present analysis SSPP is divided into five systems.
If at some stage management personals found it suitable then number of
subdivisions may be increased and analysis may be carried out with
same GTA methodology. In the present work RI is calculated for
analysis at system and subsystem level. If the number of subsystems is
changed, even then index will remain in-between 0-1. If the concept of
RI is not used then index value is dependent on the number of
subsystem and parameters. Therefore, it is convenient to handle the
score obtained by the methodology developed in the present work. RI
may be used for the following analysis.

35. • Index may be used to evaluate the real time situation and it may be used to
compare with the maximum index value. From this weak parameters may
be identified .
• Suitability of two or more real life operating power plants may be
compared with the help of index.
• If any suggestion is given by some manufacturer for the improvement in
the plant then some quantitative results may be calculated to check whether
the improvement is beneficial or not.
In the era of competition, early decision with the help of some mathematical
method with logical reasoning is helpful to make the presence in global
market. A complex and large system such as site selection of thermal power
plant require analyzing large number of factors to achieve the goal of
organization. For this purpose the methodology developed in this section may
be helpful to take the organization one step forward.

36. REFERENCES
• Ahmad S and Tahar Razman M (2014), “Selection of renewable energy sources for sustainable
Development of electricity generation system using analytic hierarchy process: A case of Malaysia”,
www.elsevier.com/locate/renene, Renewable Energy 63, pp. 458-466.
• Barda OH, Dupuis J and Lencioni P (1990), “Multi-criteria location of thermal power plants”, European
Journal of Operational Research, pp. 332-46.
• Brown PA and Gibson DF (1972), “A quantified model for facility site selection: An application to a multi-
facility location problem”, AIIE Transactions, Vol. 4, pp. 1–10.
• Choudhary D and Shankar R (2012), “An STEEP-fuzzy AHP-TOPSIS framework for evaluation and
selection of thermal power plant location: A case study from India”, www.elsevier.com/locate/energy.
• Cavallaro F and Ciraolo L(2005), “A multi criteria approach to evaluate wind energy plants on an Italian
island”, Energy Policy 33,pp.235-44.
• Chou SY (2008), “A fuzzy simple additive weighting system under group decision-making for facility
location selection with objective/subjective attributes”, European Journal of Operational Research, Vol.
189, pp. 132–145.
• Dev N, Samsher, Kachhwaha SS and Attri R (2014a), “GTA modeling of combined cycle power plant
efficiency analysis”, Ain Shams Eng J4, pp. 273–84.
• Dev, N., Samsher, Kachhwaha, S. S. and Attri, R., (2014b), "Development of Reliability Index for
Combined Cycle Power Plant using graph theoretic approach",Ain Shams Engg. J., 5(1), pp. 193-203.
• Faisal MN, Banwet DK, Shankar R (2007) Supply chain agility: analysing the enablers. Int J Agile Syst
Manag 2(1):76–91
• Gandhi OP and Agrawal VP (1992), “FMEA-a digraph and matrix approach”, Reliab Eng Syst Saf 35, pp.
147–158.
• Gandhi OP, Agrawal VP and Shishodia KS (1991), “Reliability analysis and evaluation of systems”,Reliab
Eng Syst Saf 32, pp. 283–305.
• Mohan M, Gandhi OP and Agrawal VP (2004), “Maintenance strategy for a coal-based steam power plant
equipment—a graph theoretic approach”, In: Proceedings of the institution of mechanical engineers—Part
A. Journal of Power and Energy 218, pp. 619–636

37. • Mohan M, Gandhi OP and Agrawal VP (2006), “Real time efficiency index of a steam power plant: a
systems approach”, In: Proceedings of the institution of mechanical engineers—Part A. Journal of Power
and Energy 220, pp. 103–131.
• Mohan M, Gandhi OP and Agrawal VP (2008), “Real-time reliability index of a steam power plant: a
systems approach”, In: Proceedings of the institution of mechanical engineers—Part A. Journal of Power
and Energy 222, pp. 355–369.
• Mohan M, Gandhi OP and Agrawal VP (2007), “Real-time commercial availability index of a steam power
plant—graph theory and matrix method”, In: Proceedings of the institution of mechanical engineers—Part
A. Journal of Power and Energy 221, pp. 885–898.
• Nag P.K (2011), “Power Plant engineering”, Laxmi Publications, pp. 96.
• Kaya T and Kahraman C (2010), “Multi-criteria renewable energy planning using an integrated fuzzy
VIKOR & AHP methodology: The case of Istanbul”,www.elsevier.com/locate/energy Energy 35, pp. 2517-
2527.
• Samantaray AK, Singh NP and Mukherjee TK (2004), “Evaluation of potential pit-head sites for coal-based
thermal power stations based on site-suitability index (SSI) using geospatial information”, Int J Sustain
Manuf 3(1), pp. 32–40.
• Wani MF and Gandhi OP (1999), “Development of maintainability index for mechanical systems”, Reliab
Eng Syst Saf 65, pp. 259–270.
• Xu G, Tian W, Qian L and ZhangX (2007), “A novel conflict reassignment method based on grey relational
analysis (GRA)”, Pattern Recognit Lett 28(15), pp. 2080–2087.
• Yun-na W, Narenmandula and Yi-li Han (2012), ‘’Study on the Site Selection of Nuclear Power Plants
Based on Optimized Fuzzy Comprehensive Evaluation’’, CISME Vol. 2 Issue 6, pp. 35-38.
• Zhang L (2014), “Modelling policy decision of sustainable energy strategies for Nanjing city: A fuzzy
integral approach”, www.elsevier.com/locate/renene, Renewable Energy 62, pp. 197-203.

38. THANK YOU