Benchmarking of STPP Site Parameters

Benchmarking of site parameters for Solar Thermal Power Plants

ABSTRACT

The need for renewable energy is increasing by the day and arguably solar energy is the most

widely available form of renewable energy. Hence it is essential to be able to identify whether or

not a given location is suitable for setting up a Solar Thermal Power Plant. But comparison is

always a subjective thing and hence there should be established benchmark values with which any

site can be compared. This benchmark values can be considered as analogous to the Carnot cycle in

air standard cycles. The project presents the attempts that have been made to arrive at such

benchmarks for Solar Thermal Power Plant sites. To proceed with this, one first needs to

understand all the ‘Viable’ parameters which affect the decision of site selection. Hence an

exhaustive, complete and non-redundant set of all the parameters that affect the selection was

identified and were categorized into three categories namely, Technical, Social and Economic

factors. These criteria include Sunshine hours in technical factors; Land cost in Economic factors

and Public support in Social factors, etc. After extensive research, a quantitative domain was

assigned to each criterion which was then normalized to obtain the constraints subjected to which

the optimization problem is to be solved. Then the problem was mathematically modelled into an

optimization problem by maximizing or minimizing the criteria as per the requirement. This

optimization problem was solved using Linear Programming Method because all the viable

parameters are mutually independent. Each category was separately evaluated and weights were

assigned using the Sati’s scale and separate objective functions were developed for each category.

The three categories were then compared against each other to obtain weights for the categories and

the final objective function was defined as the summation of the product of these weights and their

respective objective functions. This objective function was optimized subject to the constraints and

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the final result was obtained in the normalized form of the criteria. Hence, the quantitative

conditions for the ideal site were obtained and validated.

Thus by using mathematical modeling and optimization methods, one can determine the

ideal quantitative conditions for obtaining the benchmark values for a solar thermal power plant.

The thus obtained results can be integrated into any of the MCDM methods and therefore can be

used for comparison with the other sites. This methodology can also be used to evaluate the ideal

conditions for any type of problem given that the viable criteria are identified.

CONTENTS

Title page……………………………………………………………….1

Acknowledgements……………………………………………………..2

Certificate…………………………………………………………….....3

Abstract………………………………………………………………....4

Work division...........................................................................................6

1. Introduction…...……………………………………….…………......7

2.Working of Solar Thermal Power Plants……...……………………...8

3. Viable Parameters........………………………………………………9

4. Weights of the Criteria...........………………………………………..10

5. Mathematical Modelling......................................................................13

6. Solving the Mathematical Model.........................................................14

7. Case Study ...........................................................................................16

Summary & Conclusion...…………………………………………..…..18

References…………………………………………………………..…..19

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INTRODUCTION

The demand for energy is ever increasing in the modern-day world and the depletion of the

conventional resources is taking place at an even faster rate. The per annum energy consumption of

the world has hit a record value of 141,852 billion kilowatt hours per annum. The energy

consumption in India alone has increased by 91% in a span of 10 years. These statistics can be seen

in the table that follows:

Hence to meet these ever increasing demands and to be able to supply power

continuously, one has to fall back on the renewable ways of generating energy. Out of the many

such renewable methods that are available for electricity generation, using Solar Thermal Power

Plants for electricity generation is one of the most established methods. Presently, the world’s

largest solar plant is set in Mojave Desert, Palm springs, California. It spreads over 3,800acres of

land and produces 10,000 Mega-watts of solar energy.

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If not in such high quantities, steps should be taken to utilise maximum amount of solar

energy that is available, especially in a developing country like India. But setting up solar plants is

not an easy task as the site identification is a very crucial step which will determine the capacity of

the plant. Hence there must be some standard set of criteria which must be considered and carefully

scrutinised for any given site before building a Solar Thermal Power Plant in that site. Hence it is

very important that one should understand the working of a Solar Thermal Power Plant.

WORKING OF SOLAR THERMAL POWER PLANTS

Solar collectors capture and concentrate sunlight to heat synthetic oil called therminol, which then

heats water to create steam. The steam is piped to an onsite turbine-generator to produce electricity,

which is then transmitted over power lines. On cloudy days, the plant has an auxiliary system which

generates electricity. This can be seen in the picture below:

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From this one can understand that to set up a Solar Thermal Power Plant, not just sunlight

but many other resources like water body availability, grid connection availability,etc have to be

checked. Hence there is a need to identify the ‘Viable’ set of criteria which affect the decision

making.

VIABLE PARAMETERS

Many parameters will affect the selection of a site for Solar Thermal Power Plant set up.

These parameters include solar irradiation, wind speed, clearance factor, Land cost, public support,

economic incentives, etc. All these factor should be carefully analysed and arranged together to

form anexhaustive, complete and non-redundant set of criteria. Hence the Viable set of criteria for a

Solar Thermal Power Plant was found out and was further classified into three categories namely,

Technical, Social and Economic Factors. Each criterion is again divided into sub categories as

shown below:

No/: Criteria Min/Max Range (units)

Technical Factors:

A1 Sunshine Hours Max 6 < X1 < 10 (hrs)

A2 Standard Coal Max 2 < X2 < 4 (tons/acre)

A3 Water Availability Min 0 < X3 < 5 (km)

A4 Site Accessibility Min 0 < X4 < 1.5 (km)

A5 Grid Connection Distance Min 0 < X5 < 150 (km)

Economic Factors:

B1 Land Cost Min 968 < X6 < 1210 (10,000/acre)

B2 Subsidies and Incentives Max 5 < X7 < 9 (on a scale of 1 – 9 )

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Social Factors:

C1 Ecological Environmental Influence Min 2 < X8 < 7 (on a scale of 1 – 9 )

C2 Pollutant Emission Reduction Benefits Max 6 < X9 < 9 (on a scale of 1 – 9 )

C3 Public Support Max 5 < X10 < 9 (on a scale of 1 – 9 )

But as can be seen each criteria has its own units and hence there is no uniformity among the

criteria. Hence the criteria must be normalised by using either of the standard normalisation

techniques, namely

Method 3 and 4 can be used when there is a functional value that defined the variable. Also,

Method 2 might result in ‘0’ values when F i(a) takes the minimum value. Hence Method 1 has been

used to normalise the criteria and the normalised values of the criteria are as shown below:

0.6 < C1 < 1

0.625 < C2< 1

0 < C3< 1

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Method 1 Method 2

Method 3 Method 4

0 < C4< 1

0< C5< 1

0.8< C6< 1

0.556 < C7< 1

0.285 < C8< 1

0.667 < C9 < 1

0.556 < C10 < 1

These are the normalised non-dimensional values of the criteria and hence can be compared

against each other. Since apples cannot be compared with oranges, while comparing two criteria we

need to ensure that we can indeed compare them against each other. Hence each set of criteria were

compared against each other separately as explained in the next section.

WEIGHTS OF THE CRITERIA

Sati’s scale is a standard method to assign weights to criteria when compared against each

other. Each set of criteria was compared individually and weights were assigned using this scale to

obtain the weighted matrix. The normalised weights of the criteria were then obtained by

calculating the Eigen vectors of the matrix. To validate the weights that were obtained, Consistency

Ratio (CR) values were obtained for each matrix. Since all the CR values were obtained lesser than

0.1, implies that all the weight values are consistent.

The weighted matrix and the normalised weights obtained for each criteria is as shown

below.

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Table for Technical factors weight calculation:

A1 A2 A3 A4 A5A1 1 5 3 9 3A2 0.2 1 2 2 0.5A3 0.334 0.5 1 2 2A4 0.112 0.5 0.5 1 0.5A5 0.334 2 0.5 2 1

By calculating the Eigen vector values for this matrix we obtain the normalised weights for each

criterion as mentioned below,

W1 = 0.4962

W2 = 0.1389

W3 = 0.1555

W4 = 0.0634

W5 = 0.1460

The Consistency ratio (CR) for this table is obtained as; CR = 0.0815 < 0.1 hence the weights that

are obtained are correct only.

Similarly, The weighted matrix for Social and economic factors are as shown below:

B1 B2

B1 1 5

B2 0.2 1

Therefore we get:

W6 = 0.833

W7 = 0.1667

And CR = 0< 0.1 hence the weights are consistent

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C1 C2 C3

C1 1 0.2 0.334

C2 5 1 5

C3 3 0.2 1

Hence

W8 = 0.1022

W9 = 0.6864

W10 = 0.2114

And CR = 0.0555 < 0.1 and hence these weights are also consistent

MATHEMATICAL MODELLING

All the Viable criteria are independent of each other. Hence the current problem can be

defined as a Linear Programming Problem. Therefore the Objective functions for each set of the

criteria i.e.; Technical, Economic and Social, can be written as shown below

Z1 = C1*W1 + C2*W2 – C3*W3 – C4*W4 – C5*W5

Z2 = - C6*W6 + C7*W7

Z3 = - C8*W8 + C9*W9 + C10*W10

Now to obtain the final weights, each of these criteria is compared against the other using

the same method as was used above and a weighted matrix is obtained. The Eigen vectors of this

matrix are calculated to obtain the final weights Wa ,Wb and Wc.

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Z1 Z2 Z3

Z1 1 5 9

Z2 0.2 1 3

Z3 0.112 0.334 1

Therefore,

Wa = 0.7482

Wb = 0.1804

Wc = 0.0714

CR value is obtained as 0.07 < 0.1, hence even these weights are consistent.

Therefore the final Objective Function can be written as

Z = Wa*Z1 + Wb*Z2 +Wc*Z3

SOLVING THE MATHEMATICAL MODEL

Therefore, on substituting all the weights in the above equation, we obtain Z as a function

of Ci’s as shown below.

Z = 0.3712*C1 + 0.1039*C2 – 0.1163*C3 – 0.0474*C4 – 0.1092*C5 – 0.1502*C6 + 0.0300*C7

- 0.0073*C8 + 0.0490*C9 + 0.0151*C10.

Therefore Z has tobe maximised subject to the constraints of C1, C2 etc.

On maximising, the values of Ci’s were obtained and these values were de-normalised to obtain the

corresponding Quantitative values. The obtained optimal solution is as shown below:

C1 = 1 X1 = 10 hrs

C2 = 1 X2 = 4 tons/acre

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C3 = 0 X3 = 0 km

C4 = 0 X4 = 0 km

C5 = 0 X5 = 0 km

C6 = 0.8 X6 = 968 ten thousands/acre

C7 = 1 X7 = 9 (on a scale of 1 – 9)

C8 = 0.285 X8 = 2 (on a scale of 1 – 9)

C9 = 1 X9 = 9 (on a scale of 1 – 9)

C10 = 1 X10 = 9 (on a scale of 1 – 9)

And the maximum value of Z at these values is Z =0.447.

Therefore a benchmark value has been set for Z as 0.447 and can be compared with Z values

obtained for the other sites when the required data is available and the relative efficiency of that site

can be calculated.

CASE STUDY

Quantitative data corresponding to four Solar Thermal Power Plant sites were obtained and the

value of Z corresponding to these two sites was calculated. These Z values were then compared to

the benchmark values of Z to determine the relative efficiency of these sites.

These Z values can also be compared with each other and the site with the maximum Z

values is considered as the more suitable site.

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Site 1 Site 2 Site 3 Site 4

Sunshine Hours ( C1 ) 0.9 0.9 0.9 0.9

Standard Coal Savings ( C2 ) 0.6 0.6 0.6 0.6

Water availability ( C3 ) 0.6 0.6 0.9 0.5

Site accessibility ( C4 ) 0.2 0.2 0.4 0.3

Grid connection distance ( C5 ) 0.6 0.8 0.9 0.4

Land cost ( C6 ) 0.97 0.87 0.9 0.92

Subsidies and Incentives ( C7 ) 0.87 0.69 0.69 0.7

Ecological Environmental influence ( C8 ) 0.4 0.4 0.4 0.4

Pollutant Emission Reduction Benefits ( C9 ) 0.72 0.72 0.75 0.75

Public Support ( C10 ) 0.4 0.7 0.7 0.6

The data is substituted in the maximization function Z and the following values of Z are obtained

For Site 1, Z1= 0.2071

For Site 2, Z2= 0.1774

For Site 3, Z3= 0.1271

For Site 4, Z4= 0.2297

Thus when arranged in a decreasing order

Z4 > Z1 > Z2 > Z3

Relative closeness to the Ideal site for each of the Selected sites can be evaluated by the following

formula,

Carnot value of the site= (Z value obtained for the site) / (Z value of the ideal site)*100

Therfore the carnot values of the Sites are

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Carnot value of site 1= (0.2071/0.447)*100 = 46.33%




Thus the maxiumcarnot value among the given sites is obtained as 51.39%.

Hence, among the given sites the most ideal location for the allotment of solar Thermal

Power Plant is Site-4, followed by Site-1 and the least suitable sie for installation is Site-3.

Summary & Conclusions

The importance of Renewable energy is increasing everday. The search for extracting or obtaining

the maximum energy and utilization of minimum resources leads to the need for the current site

evaluation method.

The Solar thermal plant sites are evaluated based on the exhaustive criterion sets defined

according to the need of the Solar thermal Plant. The criterion are given set limits for range and

then are normalized to fit the maximisation function. These criteria are compared against each other

in a pair wise comparision matrix within their category and weights are assigned to them with

respect to their category. Then the categories are again compared among themselves with pair wise

comparision matrix and the values of the weights are assigned to them. Thus the final weight

matrix is defined. The Consistency ratios are identified for the individual categories and as a whole

andit was found that the deviations were under 0.1, thus are consistent and weights can be used for

further evaluation of sites.

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The function to evaluate the sites based on the criteria and their weights is written and the

values to be maximum are added while those to be minimum are subtracted. This maximisation

function is solved for the ideal site values..

Ideal site value is obtained by following optimization techniques and ideal Z value of the

site is found. Where Z is the normalized value of the site under evaluation. The site data of the

proposed sites are taken and were substituted in the Z function to find the Z values of the individual

sites. The thus obtained values are analysed to find their carnot value of the respective sites. The

sites satisfying the minimum criteria is first filtered according to the requirement and the best

possible site is known for the Z value or the carnot values.

REFERENCES

http://en.wikipedia.org/wiki/World_energy_consumption

http://time.com/3723592/inside-the-worlds-largest-solar-power-plant/

http://www.nexteraenergyresources.com/what/solar_works.shtml

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http://www.nexteraenergyresources.com/what/solar_works.shtml

http://time.com/3723592/inside-the-worlds-largest-solar-power-plant/

http://en.wikipedia.org/wiki/World_energy_consumption

Benchmarking of STPP Site Parameters

Documents

solar energy

viable parameters

viable criteria

optimization problem

ideal site

economic factors

social factors

benchmark values