btp_report_aalekh_srijan_FINAL.pdf

Indian Institute of Technology, Delhi ----------------------------------------------------------------------------------------------------------

Pr. No.:

Thermodynamic Modelling of Advanced Power Systems using Gas Turbine (MED 411)

Srijan Mishra 2010ME10734

Aalekh Sharan 2010ME10641

Professor P.M.V Subbarao

(Supervisor)

Professor Prabal Talukdar

(Examiner)

Department of Mechanical Engineering IITD

May 2014

INTRODUCTION

Gas turbine power and thermal efficiency can be augmented by overspray process which

consists of inlet fogging, wet compression and water/steam injection after compressor. In this

study the inlet fogging process is modeled based on the evaporation of droplets and

numerically solved for transient behavior of air and droplet temperatures and droplet

diameter. The wet compression process model is also solved numerically. The transient

behavior of important variables in wet compression such as droplet diameter, air and droplet

temperature, and evaporation rate is investigated. The effects of system parameters on

variables such as droplet evaporation time, compressor outlet temperature are taken up in this

study. Various schemes of steam injection such as steam injected gas turbine(STIG),

recuperative steam injected gas turbine(RSTIG), humidified air turbine(HAT) and

combination of wet compression and steam injection schemes are studied.

In the first part of the B. Tech project, we improved the calculations by using a droplet

size distribution rather than assuming one size for the inlet fogging and wet compression

process. Also, a preliminary investigation into the efficiency drop due to adding an inlet vane

was investigated. Finally, we investigated the amount of green energy that can be added to a

typical power plant by using renewable energy sources such as solar energy. This work would

be continued provisionally in the second part of the project.

NOMENCLATURE A droplet surface area (m

2)

D droplet diameter (m) f amount of water (kg water/kg dry air) si amount of steam injection (kg steam/ kg dry air)

T air temperature (0C)

Ts droplet temperature (0C)

h specific enthalpy (kJ/kg) cp specific heat capacity (kJ/kg K) wc specific compressor input work (kJ/kg) wt specific turbine output work (kJ/kg) hfg latent heat (kJ/kg) n polytropic index

dw/dT Evaporative rate (kg vap/ kg dry air/0C)

p pressure

Q heat flux (W/m2)

CV calorific value (kJ/kg) TIT turbine inlet temperature GREEK SYMBOLS

density (kg/m3) isentropic index efficiency p polytropic efficiency

SUBSCRIPTS 0 compressor duct inlet condition 1 compressor entry 2 compressor exit/ combustion chamber inlet 3 combustion chamber exit/ gas turbine inlet 4 gas turbine exit

ACRONYMS far fuel air ratio CH4 methane CO2 carbondioxide H2O water O2 oxygen N2 nitrogen WET wet compression STIG steam injected gas turbine RSTIG recuperative steam injected gas turbine HAT humidified air turbine ORC organic rankine cycle

CONCEPT

Gas turbines suffer from both decreasing output power and efficiency as the ambient

temperature increases because the air becomes less dense (which results in less mass flow rate),

and the compressor works harder as ambient temperature increases. It has been found that every

1C rise in ambient temperature reduces gas turbine output power by approximately 0.54-0.9%,

Gas turbine inlet air fog cooling is considered a simple and cost-effective method to increase

power output and often also increase thermal efficiency. Fog cooling is done by spraying micro-

scaled water droplets into gas turbine inlet. The air through evaporation absorbs heat until the air

is saturated before entering the compressor; this is called "saturated fogging". If there are water

droplets remaining after the air flow reaching saturation at the wet bulb temperature, the

remaining droplets will enter the compressor as overspray (or high fogging), which can further

cool the compressor. Fog cooling is gaining popularity due to its low initial and maintenance

costs. Steam injection in gas turbine unit is also well proven technique that improves both the

efficiency and power of the gas turbine and also reduces harmful emissions of NOx into the

atmosphere. At present, the steam injection system for power augmentation and reduction of NOx

is offered by dominant gas turbine companies such as General Electric, Rolls-Royce etc.

Most of the power is produced from gas turbine cycle by heat recovery from exhaust gas,

but still there is a potential in the low temperature exhaust gas to produce power. Now a days,

the major thrust is to use organic rankine cycle for low temperature heat recovery. The

organic Rankine cycle technology has many possible applications, and counts more than 250

identified power plants worldwide. Among them, the possible applications are in geothermal

plant, biomass plant, solar thermal plant and in waste heat recovery system. The major

manufactures in ORC technology are Ormat, Enertime, Turboden, GMK etc.

There is very little work done in combined cycle power plant that constitutes gas turbine

cycle and organic rankine cycle. The present work here is to find the possibility of organic

rankine cycle as an alternative to the steam turbine cycle as a bottoming cycle to gas turbine

combined cycle power plant.

The complete block diagram of the present work is shown in figure-1.1. In the advanced gas

turbine cycle, all the processes in the gas turbine cycles are humidified to have higher net power

output and thermal efficiency as compared to simple gas turbine cycle. Most of the thermal

energy of exhaust gas from gas turbine is utilized in gas turbine cycle itself by using recuperator

or HRSG. The remaining exhaust energy at low temperature (200 to 350 0C in the present work)

is recovered in the organic rankine cycle (ORC) as bottoming cycle. The exhaust of the ORC heat

exchanger is cooled to water dew point temperature (55 to 650C in the present work), therefore

ORC system can be operated without any regenerative heat exchanger. Further, water

is recovered from the exhaust of ORC heat exchanger in the water recovery system and again

send back to gas turbine cycle for water/steam injection.

Figure-1.1 Block diagram of combined advanced gas turbine and organic rankine cycle

OBJECTIVES Thermodynamic analysis of advanced gas turbine cycle (inlet evaporative fog cooling/ wet

compression/ steam injected gas turbine cycle).

Thermodynamic analysis of cycle using a variable droplet size distribution Thermodynamic analysis of above system along with hybridization with a renewable energy

source

Incorporating the above analysis using MATLAB code and NIST-REFPROP software for ORC.

LITERATURE REVIEW INLET COOLING/WET COMPRESSION

Chaker et al.[1 ] provides the results of extensive experimental and theoretical studies

conducted over several years, coupled with practical aspects learned in the implementation of

nearly 500 inlet fogging systems on gas turbines ranging in power from 5 to 250 MW. They

treats the practical aspects of fog nozzle droplet sizing, measurement and testing presenting

the information from a gas turbine fogging perspective. This paper describes the different

measurement techniques available, covers design aspects of nozzles, provides experimental

data on different nozzles and provides recommendations for a standardized nozzle testing

method for gas turbine inlet air fogging.

Santos A.P et al. [2] investigated the two cooling methods (absorption chiller and

evaporative cooling) for different inlet conditions (inlet temperature and relative humidity).

Results show that both methods improve the power output and thermal efficiency. The

evaporative cooling method is limited by ambient wet bulb temperature, representing a

suitable solution at low ambient RH inlet conditions. On the other hand, the absorption chiller

reached a larger temperature drop at different inlet conditions. When the ambient temperature

is extremely high with low relative humidity the chiller is most suitable inlet air cooling

system if exhaust energy is available otherwise evaporative cooling method is more

economical for low RH inlet condition.

Araimo L et al. [3] has done the analytical study of wet compression. The results show that

an effective intercooling can be achieved through wet compression. Such a cooling brings the

reduction of compressor work and the increase of compressor efficiency. The wet

compression work can even be lower than that of dry air isentropic compression work. The

wet compression technique has great potential to enhance the performance of the gas turbine.

Bracco S et al. [4] examines the effect of wet compression on gas turbine power plants,

particularly analyzing the influence of ambient condition on plant performance. The water

injection (2% overspray) into the compressor intake air increases the power output by 14%

and this value rises to 17% if the fogging effect is also considered. Wet compression process

causes an efficiency gain from .3% to 1.3% as a function of ambient temperature and the

injected water mass flow rate. STEAM INJECTED GAS TURBINE CYCLE

Jonsson M et al. [5] reviews all the possible cases of humidified gas turbine. Gas turbine

with air-water mixtures as the working fluid promise high electrical efficiencies and high

specific power output. Different humidified gas turbine cycles have been proposed, for

example direct water injected cycles, steam injected cycles and evaporative cycles with

humidification towers.

Bouam A et al. [6] have studied the influence of steam injection parameters on injected

steam quantity. To maintain the same thermal efficiency (as on ISO condition) the amount of

steam injected is increased when the steam injection pressure and temperature is decreased

and vice versa with varying ambient temperature. The net effect of steam injection on thermal

efficiency and power output is on increasing trend.

Wang F.J et al. [7] studied the steam injected cycle with inlet air cooling. It is found that

STIG and IAC are well suited for retrofitting project without destroying its original integrity.

In this study, an existing simple cycle generation system was considered as the basic system

and converted into the modified system with either IAC or/and STIG features. The results

show that the system with STIG can have the best generation efficiency improved from

29.3% to 39.9% and thus the shortest payback period, while the system with both STIG and

IAC can achieve the greatest power capacity increased from 52.1 MW to 96.8 MW.

Cheng D.Y [8] introduced CLN technology as an emission control system through

improved steam injection in gas turbine cycle. They claimed that this technology will be the

only money saving control technology to be installed. In addition, it is the only proven

greenhouse gas emission reduction technology available now to meet the 20% reduction

before the targeted date of 2020. Such a retrofit retains the fast start up characteristics of the

simple cycle which is typically used as peaking units or mechanical drive applications for

compressors and pumps for the oil and gas industries.

ORGANIC RANKINE CYCLE Saleh B et al. [9] has done thermodynamic screening of 31 pure component working fluids

for organic Rankine cycles (ORC) is given using BACKONE equation of state. The fluids are

alkanes, fluorinated alkanes, ethers and fluorinated ethers. Thermal efficiencies are presented

for cycles of different types. They used an internal heat exchanger (IHE), in case that the

vapour leaving the turbine is superheated,. The highest thermal efficiencies are obtained for

the high boiling substances with overhanging saturated vapour line in subcritical processes

with an IHE. On the other hand, a pinch analysis for the heat transfer from the heat carrier

with maximum temperature of 120 0C to the working fluid shows that the largest amount of

heat can be transferred to a supercritical fluid and the least to a high-boiling subcritical fluid.

Gao H et al. [10], has done the performance analysis of a supercritical organic Rankine cycle

system driven by exhaust heat using 18 organic working fluids. Several parameters, such as the

net power output, exergy efficiency, expander size parameter (SP), and heat exchanger

requirement of evaporator and the condenser, were used to evaluate the performance of this

recovery cycle and screen the working fluids.

Farnandez F.J et al. [11] used the SpanWagner equation of state for siloxanes, used as

working fluids in high-temperature organic Rankine cycles, is applied in a mathematical

model to solve cycles under several working conditions. The proposed scheme includes a

thermo-oil intermediate heat circuit between the heat source and the organic Rankine cycle to

maintain the thermal stability of organic fluid even if the source temperature is greater than

the thermal stability temperature of the working fluid.The cycle includes an internal heat

exchanger (regenerative cycle), although a non-regenerative scheme is also solved. Simple

linear (MM, MDM) siloxanes in saturated regenerative schemes show good efficiencies and

ensure thermal stability of the working fluid.

Chacartegui R et al. [12] studied low temperature organic rankine cycles as bottoming

cycle in medum and large scale combined cycle power plants. The aim of this work is to use

the alternative cycles with high efficiency heavy duty gas turbine engines with lower exhaust

temperature than in conventional combined cycle gas turbines. Competitive results have been

obtained for toluene and cyclohexane ORC combined cycles, with reasonably high global

efficiencies. WORK DONE AT IIT DELHI ADVANCED GAS TURBINE CYCLE

Sairam A [19] has done detailed thermodynamic analysis of wet compression. They

assume the evaporation rate as constant and study the effect of varying evaporation rate on

wet compression process. The adverse effect of water injection in compressor was also

studied. With water injection, polytropic efficiency of the compressor deteriorates compared

to that of dry compression. Steam injected gas turbine is also discussed. They have

emphasized wet compression with steam-injected gas turbine will produce more power output

at hugh thermal efficiency. ORGANIC RANKINE CYCLE

Hemadri V.B [20] has selected Hexamethyldisiloxane (MM) a linear siloxane as the working fluid for ORC in their work. The thermal efficiencies of both cycles: simple ORC and superheated ORC schemes without regeneration are compared with steam cycle for the same turbine inlet and condenser conditions. The opportunity for regeneration at the turbine exit is observed and studied. The advantage of ORC with regeneration is emphasized depending upon the degree of superheat of the vapor at the turbine exit. They have used the house developed Gibbs energy based property model using generalized PengRobinson (GPR) cubic equation is used to predict the thermodynamic properties. The results obtained from GPR are compared with National Institute of Standards and Technology (NIST) developed REFPROP9.0.

Siddiqui, P[21] has combined all of the above research inputs along with their advantages and

disadvantages to create an integrated advanced combine cycle turbine which powers a

secondary ORC turbine. Industry standard software such as REFPROP has been used to

develop a mathematical model on MATLAB which can predict various flow parameters.

COMPRESSOR INLET COOLING - FOGGING

Compressor inlet fogging is a method of cooling intake air by injecting demineralized

water in the duct through the special atomizing nozzles. The evaporation of droplets results in

a cooling of air and a consequent increase of mass flow rate. When the mass fraction of

injected water is less than the water required for complete evaporation within inlet duct then

the process is considered as low fogging. High fogging generally corresponds to larger liquid

mass fractions, in which case droplet evaporation is not completed within the duct but is

extended into the compressor for wet compression. The effect of cooling of air due to droplet

evaporation is the reduction of compression work.

For a given inlet duct length, several factors such as water injection rate, droplet size

distribution, air velocity and intake air condition affect whether injected water droplets

completely evaporate or not. In this study the inlet fogging process is modeled based on the

evaporation of droplets with the help of heat and mass transfer correlations and

thermodynamic relations. The model is solved numerically to evaluate transient behavior of

droplet diameter, air and droplet temperature for different initial diameter of droplets.

MODELING OF COMPRESSOR INLET FOGGING PROCESS

0

Figure-4.1 Gas Turbine system with inlet fogging process

In this modeling, air is assumed to enter the inlet duct at temperature T0, pressure P0 and

relative humidity RH0. Water is sprayed at very high pressure (7 to 14 MPa) through low vlume

nozzle, in the form of fine droplets into the inlet air stream, with initial droplet diameter D0 at a

ratio of f0 (kg/kg of dry air). It is assumed that the pressure in the inlet duct is constant.

The initial mass of water vapor per unit mass of dry air (specific humidity) can be expressed as follows:

w0 = where, 0 = 0 (t0) = vapor pressure.

In this study, water droplets are assumed to be spherical and monodisperse and they do not

interact with each other during the process. Then, the number of droplets per kg of dry air, N,

can be assumed to be constant after injection till the end of evaporation. The number N (per

unit kg of dry air) can be expressed as

N = constant =

Where, w is the density of water and N is assumed to be constant after injection. When the droplet diameter is D, the total surface area of the liquid droplets per unit mass of

dry air can be expressed as A = 2

The conservation of water mass requires that

f + w = constant

where, f = amount of liquid water per unit kg of dry air w

= amount of water vapor per unit kg of dry air The specific enthalpy of the mixture of dry air, water vapor and liquid water during

compression is expressed as follows

h = ha (T) + whv(T) + f hl(Ts) = constant .. (1) (assuming adiabatic process) where, ha, hv, hl are the specific enthalpy of air, water vapor and liquid water respectively. Also, liquid water depletion rate = water droplet evaporation rate = . (2)

Rate of increase in the internal energy of water droplets = rate of sensible heat flux rate of

latent heat flux required for vaporization fcpw dTdts = A(Qs QL ) = A(Qs hfg I) .. (3)

Where, I is the vapor mass flux away from the droplets, QL is the latent heat flux due to

droplet evaporation, hfg is the specific enthalpy of vaporization and Qs is the sensible heat

flux due to diffusion or convection. We have 3 equations and 3 unknowns (f, T, Ts), that can be solved numerically.

The Stokes model [13] enables formulation of the heat and mass fluxes as follows: Qs = kNuD (T Ts)

03

6 0

0

0.622 0

I = Sh Dv (ps pv ) DRv Ts T

Where, Dv is the mass diffusion coefficient of water vapor in air, Rv is the gas constant of

water vapor, T and Ts are the temperatures of humid air and water droplets respectively. ps is

the saturation pressure of water at Ts. pv is the vapor pressure of air- vapor mixture.

Nusselt number, Nu = 2 + .6 .25 .33 2 Sherwood number, Sh = 2 + .6 .25 .33 2

Since, the droplet readily attains the velocity of air on injection in the duct. Therefore, heat

and mass transfer is largely affected by natural convection. Nusselt number and Sherwood

number are taken as constant in this analysis on the basis of small relative velocities for the

small droplet diameter.

FLOW CHART FOR THE MODELING OF COMPRESSOR INLET FOGGING PROCESS

TRANSIENT BEHAVIOR STUDY OF COMPRESSOR INLET FOGGING

The initial state is taken as p0 = 1.01325 bar, T0 = 35 0C, RH0= 60 %. Droplet temperature

is taken to be equal to the ambient temperature at T0. Air and water droplet temperature and

droplet diameter are computed at any given time, for water droplet initial diameter of 20 m for different water injection ratio ( ratio of water injection rate and critical injection rate ie.

f/fc = 0.8, 0.9, 1, 1.1, 1.2 ) at the inlet duct. f/fc < 1, f/fc = 1 and f/fc > 1 corresponds to low fogging, critical fogging, high fogging respectively. Critical fogging here signifies the water injection rate for given ambient condition at which the temperature at the compressor inlet is the saturation temperature. Low fogging means that the injection rate is lower than critical injection rate. High fogging means that the injection rate is higher than critical injection rate.

It is inferred from figure-4.2 that the droplet size gradually decreases with time. In case of

low fogging (f < fc), the diameter diminishes to zero after finite time. The dry out time

increases with the amount of initial water injection and grows to infinity as f approaches fc. In

case of high fogging (f > fc), the droplets do not evaporate completely but tend to have small

final diameter. The remaining droplets enter into the compressor of gas turbine system and

then wet compression begins there.

The humid air temperature decreases with time as indicated in Figure-4.3, and the only

way to approach the wet bulb temperature (19 0C) asymptotically is to exceed the critical

injection ratio. In all cases, a rapid temperature decrease is followed by a much slower rate of

decrease, which suggests an optimal duct length for complete evaporation. If complete

evaporation is desired, then the duct must be long enough to accommodate the residence

times for low fogging.

Figure-4.2 Transient behavior of water droplet diameter

Figure-4.3 Transient behavior of humid air temperature Figure-4.4 Variation of humid air temperature with the amount of liquid water present in

the duct

The humid air temperature is an almost linearly decreasing function of liquid water

depletion as shown in figure-4.4. The slope of temperature change gets steeper as the water

injection ratio f/fc increases. For the low fogging case, the droplets evaporate completely and

outlet humid air temperature is lower for higher f/fc. In contrast there is no complete droplet

evaporation for the high fogging case and the final humid air temperature is almost constant

and independent of water injection ratio. Issues and Improvements

The issue with this approach is that by taking a uniform droplet size distribution, the end result

can be drastically different than if droplets of various diameters were taken. In this regard, we

were able to use a modified version of the Nukiyama-Tanasawa equation which took only one

parameter(Sauter Mean Diameter) as input in order to create 10 buckets of different drop sizes.

The same simulation was performed for all the buckets in order to get drastically different

results.

PDF of number of droplets

PDF of volume of droplets

1Nukiyama-Tanasawa distribution used

WET COMPRESSION PROCESS MODELING OF THE WET COMPRESSION PROCESS According to Gibbs equation,

Tds = dh dp For an ideal wet compression, it is assumed that the evaporative heat equals to the reversible

heat transfer from air to liquid water,

-hfgdw = Tds where, hfg = Latent heat of vaporization - hfg dw = dh dp - hfg dw = dT 1R RT dpp

dpp = dTT [ 1+ hRfg* dwdT ] Assuming evaporative rate of water droplets varies linearly with temperature, i.e. dwdT = constant, the isentropic relation is obtained as, p vk = C

k = [ + hfg * dw ] k1

R dT

1

If p is the polytropic efficiency of the compressor, it can be shown that T2

T1 = [ p2p1 ](n1)n

Where, n

= p [

+

hfg *

dw ]

n1

R dT

1

This equation shows that the increase of evaporation rate decreases the polytropic index

(k) of wet compression from isentropic process towards the isothermal process (k=1) which

results in reduction of compressor power. This can be seen in the p-v diagram in figure-5.1

[17] as the wet compression process 1- 2 is less steeper than dry compression (1-2). This shows that the work input (i.e. vdp) in infinitesimal stage is lesser in the case of wet

compression process.

Figure-5.1 Fog/overspray cooling process in the compressor (for air only)

Where, Process (1-2) = dry compression when the compressor inlet is at ISO condition.

(1-2) = dry compression when compressor inlet temperature is higher than ISO condition

(1-1) = inlet fog cooling

(1-2) = dry compression for low fogging and critical fogging cases. (1-2) = wet compression for high fogging case

In order to evaluate the effect of evaporation rate of water droplet dw/dT (kg water

vapor per unit kg of dry air/ 0C), the study of wet compression process is done by numerical

analysis of heat and mass transfer model as was done in chapter-3 for inlet fogging process.

The only difference in the modeling of wet compression analysis is that there is continuous

pressure variation and enthalpy variation through out wet compression process.

The pressure variation can be expressed by the parameter of compression rate, C defined by

C =

1 dp [14]

p dt

It is assumed that C has a constant value that depends on compressor speed, which

implies an exponential form for pressure variation w.r.t time. This relation provides an

acceptable pressure distribution inside a compressor. An average value of C may be used to

characterize actual compressors. Then the pressure varies as

p = p1 exp(C t)

The enthalpy variation can be expressed by using polytropic efficiency of compressor as

follows cp = vdpdh Compressor input work per unit kg of dry air:

wc, wet = (ha2 ha1) + w1 (hv2 hv1) + (w2 w1) (hv2 hv1) When the amount of water completely evaporated, then dry compression begins, and

temperature and work input can be determined for this as usual.

wc, dry = (ha3 ha2) + w2 (hv3 hv2)

wc = wc, wet + wc, dry

where, stae-1 = property at the start of compression

stae-2 = property at the end of evaporation and

state-3 = property at the end of compression

TRANSIENT BEHAVIOR STUDY OF WET COMPRESSION

The behavior of the non-equilibrium wet-compression process depends on operational

parameters such as the water injection ratio f1, the pressure ratio rp, the initial diameter of the

droplets D1, the compression rate C, the polytropic compression efficiency and the ambient

conditions. Parameters are computed at inlet pressure p1 of 1 atm, inlet temperature T1 of

150C, inlet relative humidity RH1 of 60% (ISO condition), compression rate C = 200 s

-1, and

polytropic efficiency = 91%. Transient behavior study w.r.t various droplet diameter:

Figure-5.2 shows the transient behavior of the mass of liquid droplets with time for water

injection ratio of f1= 5%. It can be seen from the figure that once water droplets are injected

at the compressor inlet, the mass of the liquid droplets decreases monotonically as

evaporation continues until the evaporation is completed. The droplet temperature increases obeying the steady energy balance, after an abrupt initial

transient behavior, which can be seen in Figure-5.3. Figure-5.4 shows that the humid air

temperature increases with time, as pressure increases. The slope increases with droplet

diameter, for the same injection ratio. After complete evaporation, the humid air temperature

increases at a higher rate than during evaporation. Yet, the temperature is lower than that for

dry compression. It can be seen from Figure-5.5 that the temperature difference between the

humid air and droplets decreases as the diameter of the droplets decreases. Improvements: We used the Nukiyama-Tanasawa model again to evaluate the drop sizes in 10 buckets. The

resulting graph was an amalgamation of the graphs calculated by P. Siddiqui.

Figure-5.2 Liquid water fraction transient behavior for various droplet diameter (f1 =5 %)

Figure-5.3 Water droplet temperature transient behavior for various droplet diameter (f1

=5 %)

Figure-5.4 Humid air temp transient behavior for various droplet diameter (f1 =5 %)

Figure-5.5 Temperature difference between humid air and water droplet for various droplet

diameter (f1 =5 %) Transient behaviors w.r.t various water injection rate:

Figure-5.6 shows the transient behavior of the mass of liquid droplets with time for

various water injection rate. The evaporation completion time increases as the water injection

ratio increases. Hence, liquid water may remain at the compressor outlet that can be observed

for high water injection ratios.

Figure-5.7 shows that the humid air temperature increases at a lesser rate during

evaporation and faster after completion of evaporation. The final humid air temperature is

lower for higher injection ratios. Figure-5.8 shows that humid air and droplet temperature

difference increases with time and its magnitude is higher for lower injection ratio values.

This graph then reflects the fact that, whereas humid air temperatures are a strong function of

the injection ratio, liquid temperatures depend only weakly on it as shown in figure-5.9.

Figure-5.6 Liquid water fraction transient behavior for various water injection ratio (D1

=10 micron)

Figure-5.7 Humid air temp transient behavior for various water injection ratio (D1

=10 micron)

Figure-5.8 Temperature difference between humid air and water droplet for various water

injection ratio (D1 =10 micron)

Figure-5.9 water droplet temperature transient behavior for various water injection ratio

(D1 =10 micron)

Compressor outlet temperature and input work:

Figure-5.10 shows the variation of compressor outlet temperature and compressor input

work as a function of compression ratio, for various values of the water injection ratio. It is

evident that compressor outlet temperature increases with compression ratio, however, the

increase rate is lower than for dry compression. When the compression ratio is greater than

the value at which injected water droplets are completely evaporated, the compressor outlet

temperature approaches the same value for a given water injection ratio.

Figure-5.10 compressor exit temperature wrt pressure ratio (D1 =10 micron)

Figure-5.11 shows the variation of compression work as a function of compression ratio,

with injection ratio as parameter. It can be seen from the figure that the compression work

increases with compression ratio, its rate of increase can be lowered by evaporation.

Figure-5.11 compressor input work wrt pressure ratio (D1 =10 micron)

Synthesis of Inlet Fogging and Wet Compression The two methods used here are synthesized in order to create a complete model. By carefully

adjusting the parameters and the water injection rate, we can arrive at a critical ratio of water

droplets remaining after the end of the wet compression process. Ideally, all the water should

evaporate, but in practice, the larger droplets will remain as it will take much longer to

evaporate them due to a smaller surface area to volume ratio.

Analysis of potential solar energy available at typical power plants

An empirical study was done in order to determine the typical solar energy available at power

plants in India. To do this, a combination of Google maps and an online tool for area

calculation was used. This was combined with the data on solar insolation by latitude to give

an indication of the potential energy augmentation possible by various technologies. Total Conventional Total recoverable Recoverable

Name of plant annualized power Area(km^2) area energy

Anpara Thermal Power Station 1385.5 4.916 4.907 215.908

Faridabad Thermal Power Plant 365.5 0.134 0.124 5.456

Guru Nanak Dev Thermal Plant 374 2.38 2.308 101.552

Kolaghat Power Plant 1071 1.728 1.712 75.328

Korba Power Plant 2210 2.5 2.487 109.428

Kota Power Plant 1054 1.715 1.685 74.14

Narora Power Plant 374 5.484 5.211 229.284

Panipat Thermal Power Plant 374 4.107 3.92 172.48

Raichur Power Plant 1462 4.485 4.199 184.756

Rajiv Gandhi Power Plant 510 2.349 2.015 88.66 Table 1:Recoverable solar energy of various Indian power plants

The recoverable area was found by subtracting the non recoverable areas from the total power

plant area. For example, the area occupied by cooling towers cannot be used for solar co-

generation.

Energy mix at various powerplants using solar thermal

3000

2500

2000

1500

1000

500

0 Anpara Faridabad Guru Nanak Kolaghat Korba Kota Power Narora Panipat Raichur Rajiv Gandhi

Thermal Thermal Dev Power Plant Power Plant Plant Power Plant Thermal Power Plant Power Plant

Power Power Plant Thermal Power Plant

Station Plant

Non-renewable

Renewable

2Energy mix at various power plants On an average, it was found that 13.6% of existing capacity can be either augmented or replaced by solar power.

Project Progress

The simulation of the system was completed using the Nukiyama Tanasawa equation.

Optimization was done to ensure adequate number of water droplets remained for the wet compression stage.

Also, progress was made into the second phase of the project scheduled for next semester, i.e., investigating the renewable energy potential of existing conventional power plants.

The methodology for an optimized integration of RE technologies into Indias power plant portfolio is

shown at Figure 1.

In a first step, within a resource and site assessment for utility-scale PV, onshore wind power and

Concentrating Solar Power (CSP), technology specific hot spots for the most promising RE

technologies in India are identified using a Geographic Information System (GIS). Thereby, the

technology specific hot spots are identified by applying a site-ranking process with respect to the

availability of the primary energy source (wind speed, solar radiation) as well as to the distance to

demand centers and infrastructure (substations, transmission lines, major streets, etc.). At each site,

information about the hourly availability of the respective resource, the hourly ambient temperature

and the maximal installable capacity are assessed. With this information representative hourly

generation profiles of each technology at the respective sites are calculated. This information serves,

together with detailed information about power demand and supply in Jordan and related techno-

economic data, as input for the capacity expansion and replacement optimization model ReMix-

MENA.

The results of the capacity expansion optimization (base case scenario) are shown in Figure 2. As

can be observed, RE technologies are already competitive in the short term in Jordan. Until the end of

the optimization time-frame in the year 2022 about 2200 MW of CSP, 2100 MW of utility-scale PV,

1000 MW of onshore wind power and 1800 MW of conventional capacity is installed. The share of

power generation by RE technologies is increased from about 0.3 % in 2012 to more than 47 % in

2022, whereby Jordan becomes significantly more independent from fossil fuels and the related risk

of cost escalation. In Figure 4, the development of the average specific generation costs of the base

case scenario is compared with a fossil fuel scenario (investments only in

conventionaltechnologies) and a fluctuating RE scenario (no investments in CSP units). As can be

observed, the optimization shows that a well balanced mix of all available RE technologies and some

conventional generation technologies according to the base case scenario is the least cost option for

Jordan to meet future power demand.

The future challenges for Jordans electricity authorities have become obvious in the last years.

Reliable electricity supply at reasonable prices is a key factor for India in order to ensure the future

economic development. The paper at hand describes how a well balanced mix of renewable and

conventional power generation technologies can ensure to keep up with Jordans strong increasing

electricity demand and to get simultaneously more independent from fossil fuel imports whereby the

escalation of future electricity generation costs can be significantly absorbed. It shows that CSP,

utility-scale PV and onshore wind power, due to the excellent solar and wind resources, are already

competitive today in certain load segments of Jordans electricity sector. Each of these technologies

has characteristics which determine the application within the electricity system. PV and wind power

can be used as cheap fossil fuel saver. The CSP technology, as a dispatchable and renewable power

generation technology, can deliver strongly required firm and flexible power generation capacity and -

due to its constant generation costs - has a significant advantage over fossil-fuel based technologies.

However, even though the analysis has shown that RE technologies are competitive in India in the

short-term and the large-scale introduction is favorable for economic reasons, suitable market

conditions still have to be implemented in order to trigger investments in renewable power generation

projects. Providing security about future revenues is the easiest way to attract private investors and to

bring down generation costs of RE technologies. One possibility is the introduction of technology

specific international insured long-term power purchased agreements whereby project risks can be

brought down to an AAA level.

Several models have been developed to identify the optimal combinations of renewable and

conventional resources on a large scale. Short et al. (2003) divide the United States into 356 wind

regions, and model the cost-e cient installations and operation of wind farms and conventional

generators from 2000 through 2050. DeCarolis and Keith (2006) develop an optimization model for

one investment period in 2020 based on 5 years of hourly wind and load data. Considering the

assumed costs of wind turbines, the simulation indicates that supplying 50 % of the electricity demand

by wind power adds about 1-2 ct/kWh to the costs of electricity generation. Neuho et al. (2008) divide

the United Kingdom into 7 regions and optimize investments and dispatch choices for new and

existing natural gas, coal and wind generators during four 5-year investment periods. The SWITCH

model at the University of California, Berkeley (Fripp, 2008) concentrates on California and

optimizes the combination of more than 229 wind, 464 solar sites and con-ventional resources

considering investment and operational costs. Heide et al. (2010) model the optimal mix of wind and

PV capacities for Europe by minimizing needed storage capacities subject to the constraint that all

renewable energy is used (independent of total system costs). In case of supplying 100 % electricity

by wind and solar technologies, the optimal mix is found to be 55 % wind and 45 % solar power

generation. The DIMENSION model of the Institute of Energy Economics at the University of

Cologne (EWI, 2011) simulates in 5-year time steps the cost-e cient European capacity development

and dispatch for twelve typical days of conventional, renewable and storage technologies until 2050.

Di erent regional conditions for RES-E capacites are considered by modeling 47 wind onshore, 42

wind o shore and 38 solar regions. Due to modeling deterministic feed-in structures and average full

load hours of wind and solar technologies, all of these models neglect the uncertainty about the hourly

availability of renewable energy.

Methodologies incorporating uncertainty in optimization models were developed by Dantzig (1955).

They were applied to electricity generation planning problems to analyze the impact of demand

uncertainty for the rst time in the 1980s (Murphy et al., 1982; Modiano, 1987). A broad overview of

di erent stochastic modeling approaches for electricity markets is given in Most and Keles (2010).

The economic value of wind power, taking into account the volatility of wind velocity, was analyzed

by Beenstock (1995). The method is based on the intuition that one can immunize the output of a

wind turbine against uctuations in wind speed by investing in back-up capacities and the costs of

necessary back-up investments may be regarded as the costs of wind volatility. Papaefthymiou et al.

(2006) present a Monte-Carlo simulation technique to model the extremes of stochastic wind

generation in power systems by sampling wind turbines with similar generation patterns. Swider and

Weber (2006) apply a stochastic fundamental electricity market

model to estimate the integration costs of wind due to the changed system operation and investments

in Germany. The simulation indicates that the value of uctuating renewables is overestimated applying

a static, deterministic model. In particular, investment planning under uncertainty considering power

plant outages and uctuating renewable feed-in was analyzed in Sun et al. (2008). By applying a

stochastic mixed-integer optimization model for power plant investment planning to the German

electricity market, Sun et al. (2008) show how ignoring short term uncertainties signi cantly

undervalues the needed operational exibility and can result in insu cient investments. However, in

these models the deployment of RES-E capacities is not part of the optimization problem and

therefore the optimal mix of conventional, nuclear, storage and renewable technologies in high RES-E

scenarios was not determined.

In this paper, we present a stochastic investment and dispatch optimization model for electricity

markets that accounts for the uncertain feed-in of wind and solar technologies to determine the

optimal mix of conventional, renewable and storage capacities for di erent European RES-E targets.

To our knowledge, a stochastic electricity market model with as much detail concerning the di erent

local RES-E conditions and the uncertain feed-in of uctuating renewables has not appeared before.

The di erence between the stochastic model results and the deterministic solution based on averages in

wind speeds and solar radiation can be interpreted as the impact of the stochastic availability of wind

and solar power.

3. Generation of combined wind and solar feed-in structures

Wind and solar technologies are meant to produce a large share of the future electricity demand.

However, the availability of these technologies depends on local weather conditions and therefore

weather character-istics must be considered when optimizing the future electricity mix. Regional

weather characteristics lead to di erent local RES-E conditions throughout Europe (higher solar

radiation in Southern Europe and stronger winds in Northern Europe), to stochastic amounts of yearly

generated electricity of wind and solar sites as well as to positive or negative correlations between the

availabilty in di erent regions or between technologies. In this section, we describe the characteristics

of wind speeds and solar radiation in Europe (subsection 3.1), a bootstrap approach to create

consistent regional wind and solar feed-in structures and a heuristic to select representative feed-in

structures as input parameters for the stochastic optimization model (subsection 3.2).

3.1. Empirical data for wind speeds and solar radiation in Europe

The description of wind speed (subsection 3.1.1) and solar radiation (subsection 3.1.2) characteristics

for di erent regions throughout Europe is based on hourly wind speed and solar radiation data from

EuroWind for the years 2006-2010 and includes an analysis of the regional correlations between wind

speeds (and solar radiation) in Europe as well as the correlation between wind and solar power

(subsection 3.1.3). The hourly wind speed data in 30 meters above ground and solar radiation for 64

European regions the years 2006-2010 provide a deep insight of the characteristics of regional wind

speed and solar radiation in Europe as well as the correlation between wind speed and solar

radiation.5 In the following the di erent conditions throughout Europe are discussed for some of the

selected regions. The numerical data for all regions can be found in Appendix B.

3.1.1. Characteristics of wind speeds

Wind speed distributions re ect that in most regions strong winds are rare and that moderate winds

occur most often. Due to seasonal characteristics the average wind speed is usually higher in winter

and autumn as in the summer months. Table 2 shows summarizing statistics for some of the selected

wind regions in Europe. As wind speeds are usually higher in Northern Europe, the average wind

speed in 30 meters was 6.74 m/s in Northern Ireland compared to 3.59 m/s in Southern Italy for the

years 2006-2010. Higher wind speeds often result in a higher variance as can be seen by comparing

the variance of the wind speed in the Southern part of the Iberian Peninsula (9.02) and o shore wind in

the United Kingdom (18.81). Due to generally short distances between European regions the same

general weather situations occur. Hence, the hourly wind speeds in Europe are to some extent

correlated. Table 3 shows the Pearson correlation factors for some of the selected wind regions in

Europe. This sample shows that closer regions have a stronger correlation, e.g. 0.587 between on- and

o shore wind in the United Kingdom. However, some wind regions in Europe are not or negatively

correlated (e.g. United Kingdom and Iberian Peninsula).

Table 2: Summarizing statistics for some of the selected wind regions

UK-W (on) IB-S (on) DE-C (on) PL-N (on) IT-S (on) UK-N (o ) IB-W (o )

Mean [m/s] 6.74 4.80 4.89 6.33 3.59 8.82 5.03

- summer [m/s] 5.95 4.40 4.38 5.49 3.44 7.45 4.52

- winter [m/s] 7.65 5.03 5.47 7.22 3.67 10.26 5.30

Median [m/s] 6.28 4.12 4.54 5.92 3.10 8.28 4.27

Variance 10.48 9.02 5.51 9.24 4.34 18.81 10.23

10%-Quantil 2.97 1.73 2.18 2.80 1.42 3.55 1.71

90%-Quantil 11.15 8.90 8.13 10.36 6.48 14.85 9.60

Meteorological data for 242 measure stations of the German Weather Service for the years 2000-2010

and the European solar radiation from Satel-Light for the years 1996-2000 con rms the listed

characteristics in the dataset from EuroWind.

6

Table 3: Correlation matrix for some of the selected wind regions (full table in the Appendix B)

UK-W (on) IB-S (on) DE-C (on) PL-N (on) IT-S (on) UK-N (o ) IB-W (o )

UK-W (on) 1

IB-S (on) -0.026 1

DE-C (on) 0.204 -0.031 1

PL-N (on) 0.143 -0.014 0.289 1

IT-S (on) 0.085 0.137 0.171 0.029 1

UK-N (o ) 0.587 -0.053 0.298 0.178 -0.002 1

IB-W (o ) -0.025 0.922 -0.024 -0.006 0.239 -0.039 1

IT-W (o ) 0.027 0.365 0.096 0.003 0.327 0.028 0.303

The values in Table 2 and Table 3 represent the average of several years. However, as weather

situations di er between years, the yearly average wind speed varies as well. Table 4 depicts the yearly

average wind speed for the years 2006 to 2010. The average wind speed in the United Kingdom in

2008 was signi cantly higher with 7.26 m/s than the 5.93 m/s in 2010. Even considering the small

dataset, the di erence of more than 1 m/s represents about 20 % of the average over the ve years.

Similar to the yearly average wind speed, the correlation between wind regions di ers as well. The

Pearson correlation factor for wind in the United Kingdom of 0.58 in 2006 indicates a rather strong

correlation but with 0.45 in 2010 the correlation can also be lower. Naturally, data for ve years does

not represent the long term average of wind speeds as it does not capture the variance between years

su cienctly.

Table 4: Di erence between wind years: 2006-2010

UK-W (on) IB-S (on) DE-C (on) PL-N (on) IT-S (on) UK-N (o ) IB-W (o )

Mean [m/s]

2006 6.90 4.49 4.86 6.07 3.49 8.80 4.81

2007 6.73 4.72 5.35 6.74 3.50 9.04 4.95

2008 7.26 4.94 5.08 6.66 3.63 9.54 5.19

2009 6.89 4.75 4.81 6.15 3.69 8.97 4.97

2010 5.93 5.11 4.34 6.03 3.61 7.74 5.26

Based on the described wind characteristics three aspects in ucence the optimal electricity mix: First,

from a system perspective it might be cost-e cient to focus on the best European sites i.e. with the

highest full load hours on average. The data suggests that on average more than twice as much

electricity can be produced from the same turbine in Ireland than in Italy. As installation costs are

similar over Europe, levelized electricity costs for wind power are about 50 percent lower in Northern

Europe as in Southern Europe at relatively similar conditions. Second, in particular in electricity

systems with a high share of uctuating RES-E generation a distribution of wind turbines might be

cost-e cient as the hourly European-wide total power generation from wind turbines would be more

stable. Third, the optimal electricity mix has to consider an uncertainty about the yearly availabilty of

wind power - resulting from high as well as low wind years. Hence, there should exist an optimum

between focusing on the best sites and a distribution throughout Europe.

3.1.2. Characteristics of solar radiation

Global radiation depends on the location, daytime, season and local weather conditions. Hence, the

yearly radiation in Southern Europe is higher than in Northern Europe and the average solar radiation

is generally higher in summer than winter. The times of sunrise and sunset also depend on the season

and hence the duration of daily solar radiation varies throughout the year. Regional weather

conditions such as cloudiness or wind signi cantly in uence the solar radiation. Table 5 shows

summarizing statistics for some of the analyzed solar regions in Europe. Due to the same general

weather conditions in Europe, solar radiation in di erent European regions is correlated on an hourly

basis. Table 6 shows the Pearson correlation factors for some of the selected solar regions in Europe

(only daytime hours). Due to the distinguished solar structure with a peak at midday, the Pearson

factors are rather high. This sample shows that some regions have a stronger correlation, e.g. 0.730

between Southern France and Southern Italy compared to 0.643 between Poland and the United

Kingdom.

Table 5: Summarizing statistics for some of the selected solar regions

UK-C IB-SFR-S DE-C SK-S PL-N IT-S

Mean [W/m2] 139 228 191 138 138 152 214

- summer [W/m2] 231 314 283 233 247 250 309

- winter [W/m2] 75 172 130 70 61 81 150

Maximum [W/m2] 953 1,021 997 909 834 886 976

Variance 44,884 88,594 68,087 44,537 43,124 48,356 75,138

90%-Quantil 490 746 575 496 497 534 690

Table 6: Correlation matrix for some of the selected solar regions - daytime (full table in Appendix B)

UK-C IB-S FR-S DE-C SK-S PL-N IT-S

UK-C 1

IB-S 0.709 1

FR-S 0.717 0.783 1

DE-C 0.707 0.654 0.688 1

SK-S 0.715 0.646 0.713 0.763 1

PL-N 0.643 0.584 0.603 0.714 0.746 1

IT-S 0.653 0.670 0.730 0.683 0.728 0.703 1

The values in Table 5 and Table 6 represent the average of several years. However, the yearly average

solar radiation varies between the years. Table 7 depicts the yearly average solar radiation for the

years 2007 to 2010. Average solar radiation of 222 W/m2 in Italy in 2008 was signi cantly higher than

the 206 W/m2 in 2010. Even considering the small dataset, the di erence of more than 16 W/m2

represents about 7 % of the average over the four years. Similar to the yearly average solar radiation,

the correlation between solar regions di ers as well. The Pearson correlation factor between the hourly

solar radiation in Southern France and Southern Italy of 0.86 in 2008 indicates a strong correlation but

with 0.80 in 2007 the correlation can also be lower in a speci c year. Naturally, data for four years

does not represent the long term average of solar radiation as it does not capture the variance between

years.

Table 7: Di erence between solar years: 2007-2010

UK-C IB-S FR-S DE-C SK-S PL-N IT-S

Mean [W/m2]

2007 134 228 195 133 135 154 213

2008 136 231 185 141 141 149 222

2009 143 231 196 137 141 156 213

2010 144 223 190 143 133 149 206

The optimal regional allocation of solar technologies follows the same concept as for wind turbines.

Due to better conditions solar technologies might be cost-e cient in Southern rather than in Northern

Europe. However, a large deployment of solar technologies in one region might lead to a very

unbalanced availability of solar power in the system. A regional concentration might also need signi

cant grid extensions from solar sites to large load centers.

3.1.3. Correlation of wind speeds and solar radiation

Solar radiation and wind speeds are in uenced by similar local weather characteristics such as air

pressure, sunshine, degree of cloudiness or rain. As higher wind speeds usually occur when the sky is

cloudy and sunshine is low, wind speed and solar radiation are to some extent negatively correlated.

Table 8 shows the correlation factors between wind speed and solar radiation for the years 2006-2010

at daytime. The data re ects that solar radiation and wind speed within the same region are negatively

correlated with a Pearson correlation factor between -0.004 in Iberian Peninsula (north) and -0.231 in

the United Kingdom (central).

Table 8: Correlation matrix of wind and solar radiation for some selected regions - daytime

Wind

UK-C IB-N IB-S FR-S DE-C PL-N CZ-C IT-N

Solar UK-C -0.053 -0.187 -0.195 -0.098 -0.137 -0.008 0.065

-0.230

IB-N -0.176 -0.045 -0.200 -0.163 -0.043 -0.090 0.013 0.069

IB-S -0.158 -0.057 -0.140 -0.096 0.018 -0.093 0.045 0.043

FR-S -0.164 -0.107 -0.192 -0.231 -0.040 -0.076 0.026 0.026

DE-C -0.209 -0.070 -0.211 -0.232 -0.228 -0.150 -0.148 0.011

PL-N -0.195 -0.105 -0.182 -0.190 -0.124 -0.141 -0.156 -0.032

CZ-C -0.196 -0.086 -0.195 -0.191 -0.184 -0.159 -0.198 -0.004

IT-N -0.189 -0.139 -0.219 -0.248 -0.102 -0.104 -0.069 -0.147

However, the extent of the negative correlation between the availability of wind and solar power di ers

between years. Table 9 depicts the di erent correlation factors for hourly wind speed and solar

radiation for the years 2007 to 2010. As can be seen for the example of Poland the Pearson correlation

factors vary between -0.077 (2009) and -0.188 (2008) among these years.

Table 9: Extent of the negative correlation between wind and solar for the years 2007-2010 - daytime

UK-C IB-N FR-S DE-C PL-N CZ-C IT-N

2007 0.035 -0.146 -0.278 -0.162 -0.233 -0.224

-0.186

2008 -0.241 -0.021 -0.214 -0.196 -0.188 -0.243 -0.205

2009 -0.221 -0.108 -0.290 -0.215 -0.077 -0.106 -0.289

2010 -0.270 -0.083 -0.284 -0.212 -0.135 -0.206 -0.353

3.2. Extraction of feed-in structures from the data

In subsection 3.1, the characteristics of wind and solar availability for Europe were discussed and their

in uence on the optimal electricity mix indicated. On the one hand long term average wind speed and

solar power as well as average correlations are important for the determination of the optimal

electricity mix. On the other hand characteristics such as the yearly availability or correlations can

signi cantly vary between years and the optimal electricity mix can only be determined by accounting

for these variations.

As the empirical data of combined wind and solar availability is available for ve years for this

analysis, we only have an indication about the variance for yearly full load hours for each region and

for the yearly correlation between regions or technologies. Therefore, we use a bootstrapping

approach to estimate the variance of yearly full load hours as well as the correlations between regions

and technologies. A selection of the created possible feed-in structures are used as input data for the

optimization model. The bootstrap approach is a resampling method which can be used to assess the

properties of a distribution underlying a sample and the parameters of interest that are derived from

this distribution (Efron, 1979). As a necessary condition for the bootstrap method, the original data

needs to re ect the underlying distribution. This leads to two critical assumtions for this analysis: First,

we assume that the hourly data for wind speeds and solar radiation of ve years represents the full

spectrum of possible weather situations. Second, as we create consistent wind and solar structures for

a future year, we need to assume that weather conditions will stay similar as today. It is clear that the

data does not contain all possible weather situations in Europe but it can be assumed that ve years of

hourly wind speed and solar radiation give a broad spectrum. Taking into account the e ects of climate

change on stochastic regional solar and wind availabilities in energy optimization models clearly

remains a challenge, but is beyond the scope of this paper.

As a rst step we generate 2000 di erent feed-in structures based on the provided wind speed and solar

radiation data for the years 2006 to 2010 (subsection 3.2.1). Ideally, all these could be used as input

parameters in the stochastic optimization model considering their relative probability. Due to

computational contraints for the optimization problem we will select representative feed-in structures

for wind and solar technologies throughout Europe (subsection 3.2.2).

3.2.1. Bootstrap approach to generate combined wind and solar feed-in strucures

To account for the above described seasonal characteristics for wind and solar availability, we divide

the dataset in two blocks: months from April to August as spring and summer; months from

September to March as autumn and winter. We randomly pick 30 days of consistent wind and solar

radiation data over all regions in three day-blocks from the dataset and repeat this 2000 times.6 By

taking blocks rather than single hours, typical hourly changes and daily structures of wind speeds and

solar radiation are re ected. Another advantage of picking blocks rather than single days is that

common general weather situations such as a storm traveling from Western to Eastern Europe are to

some extent considered. Naturally, due to picking three day blocks common weather situations which

last for more than three days are not re ected in the bootstrapped data.7 The possible feed-in of wind

power and PV sites in di erent regions in Europe is computed based on the hourly wind speed and

solar radiation of the 30 days (720 hours) as well as the technical parameters of wind and solar

technologies. Future state-of-the-art wind and solar technologies are assumed to have the technical

properties shown in Table 10.

As solar radiation is zero at night, the change from one block to another does not induce an unrealistic

change of solar radiation at midnight. The situation is di erent for wind speeds and therefore we

average wind speeds for the hours between 21 pm to 3 am to smooth the break around midnight. We

nd that taking the moving average of four hours leads to a realistic change of wind speeds.

Table 10: Assumed state-of-the-art wind and solar technologies

Technology Capacity [MW] E ciency [%] Area [km2] Height [m] Radius [m]

Wind turbine 8 80 0.423 140 65

PV ground 1 14

PV roof 0.005 14

To scale wind speeds from 30 meters to the assumed turbine height, the standard logarithmic

conversion is used. The conversion of wind speeds in reference height to turbine height are

computated by a scaling factor which is a function of turbine height, reference height and the

roughness parameter of the region. The roughness parameter takes the di erent surface conditions into

account.8

The power generation of wind turbines is calculated as a ratio of the installed capacity of the speci c

wind turbine.9 Power output is a function of air density, rotor area, power coe cient, wind speed and e

ciency. A typical power curve for wind turbines (pitch control) is assumed with no generation at wind

speeds lower than 3 m/s and a shutdown at more than 25 m/s to avoid damages. The power generation

by the assumed state-of-the-art photovoltaic system is computed based on the net e ciency, the surface

area and solar radiation. This implies standard con gurations of PV systems directed towards the

South and

with an angle of 30 degrees in order to achieve the highest yearly energy output.

Pel(reg; tech; h; s) = 1=Pnom(tech) 1=2r2(tech) v3(reg; h; s) total (2)

Pel(reg; tech; h; s) = 1=Pnom(tech) total(tech) A(tech) radiation(reg; h; s) (3)

The resulting regional wind speed and solar radiation structures have the characteristics shown in

Table 11. When comparing the wind speed and solar radiation to the original data re ected in Table 2

and 5, we nd similar wind speed and solar radiation characteristics. Hence, we argue that this

approach provides consistent feed-in structures of wind and solar technologies for several European

regions.

8Alternatively, the Hellmann height conversion formula could be used to scale wind speeds to di erent

heights:

v(h; s) = vrefh(h; s) [ refhh ] Hell . Typical Hellman coe cients Hell are in the range of 0.06 to 0.60

(Hsu, 1988).

9As we use a linear optimization model, any linear combination of technologies can be realized.

Therefore all capacities are normalized to 1 MW units.

Table 11: Summarizing statistics for created wind speeds and solar radiation for some of the selected

regions

Wind [m/s] UK-W (on) IB-S (on) DE-C (on) PL-N (on) IT-S (on) UK-N (o )

IB-W (o )

Mean 6.8 4.9 5.0 6.6 5.2 9.0 5.1

Median 6.3 4.2 4.7 6.2 4.5 8.5 4.3

Variance 10.9 9.6 5.9 9.7 8.9 18.9 10.9

Solar [W/m2] UK-C IB-S FR-S DE-C SK-S PL-N IT-S

Mean 131 222 184 132 130 146 209

Median 21 55 38 23 22 33 69

Variance 41,327 85,413 65,041 42,059 40,716 45,471 72,042

Figure 1 depicts the distribution of full load hours for two solar (Southern part of the Iberian Peninsula

and Northern Germany) and two wind regions (Central France and Central part of the United

Kingdom) in the 2000 created scenarios. The full load hours of wind as well as solar technologies di

er between the years and are normally distributed. However, the variance is signi cantly larger for

wind than for solar

generation.10

4% 12%

pr obability (wind) [%] 3% 9% probability (solar) [%]

2% 6%

1% 3%

0% 0%

Wind on - FR-C (left) Wind on - UK-C (left) Solar - IB-S (right) Solar - DE-N (right)

Figure 1: Distribution of full load hours in two wind and two solar regions in the 2000 scenarios

3.2.2. Heuristic to select representative feed-in structures

Due to computational constraints not all 2000 created feed-in structures can be used as input data in

the stochastic electricity market model. Therefore, representative feed-in structures are selected which

are

10As the estimation of yearly full load hours is based on resampling 30 instead of 365 days, it is

possible that the variance of full load hours is overestimated. To account for a possible

overestimation, we exclude the 10 % quantil on each side.

For this purpose, we de ne an indicating value for the yearly availability of wind power and an

indicating value for the yearly availability of solar power in Europe.

The importance of a speci c wind or solar site for an electricity system is mainly de ned by the area

potential and the expected power generation (full load hours). Therefore, we de ne the indicating

values as the average availability of the most important wind (solar) sites in Europe in terms of these

two factors. For wind power, we calculate the average full load hours of onshore wind in the Northern

part of the United Kingdom, Germany, the Iberian Peninsula and Poland and wind sites at the atlantic

coast of France as well as o shore wind at Norway's coastline. For solar power, we select the Southern

part of Italy, the Iberian Peninsula, France and Germany. From the distribution of the indicating

values, we pick ten feed-in structures with the following characteristics: S1 extremly low wind year;

S2 low wind year; S3 average wind year; S4 high wind year; S5 extremly high wind year; S6

extremely low solar year; S7 low solar year; S8 average solar year; S9 high solar year; S10 extremly

high solar year. Table 12 shows the full load hours in the selected scenarios. Apart from the yearly

amount of electricity generation the selected feed-in structures consider di erent hourly correlations

between regions and between technologies (wind and PV).

The bounds (lowest and highest full load hours) for each category are chosen such that the probability

for the extreme scenarios amounts to 2.5 %, for the low and high scenario to 10 % and the average

scenario to 25 %. As the probablility for an extremely high wind year is lower than an average wind

year, the dierent dispatches in the stochastic optimization model are weighted by the specific

probability factor as also shown in Table 12.

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