Techno-economic evaluation of energy technologies under … · 6 6 KIT –Universität des Landes Baden25.09.2009-Württemberg und Prof. Fichtner, Lehrstuhl für Energiewirtschaft,

KIT – Universität des Landes Baden-Württemberg und

nationales Großforschungszentrum in der Helmholtz-Gemeinschaft www.kit.edu

INSTITUT FÜR INDUSTRIEBETRIEBSLEHRE UND INDUSTRIELLE PRODUKTION (IIP)

Lehrstuhl für Energiewirtschaft (Prof. Fichtner)

Techno-economic evaluation of energy technologies under

uncertainty based on stochastic dynamic programming

Dresden, 27.04.2012

Dogan Keles

Prof. Fichtner, Lehrstuhl für Energiewirtschaft, IIP2 25.09.20092KIT – Universität des Landes Baden-Württemberg und

nationales Großforschungszentrum in der Helmholtz-Gemeinschaft Lehrstuhl für Energiewirtschaft, IIP

• Background

• Modeling overview – stochastic optimization in electricity

markets

• Optimization strategies for evaluating energy storage

power plans under uncertainty

• Evaluation of CAES plants under different dispatch

strategies

• Conclusions

• Outlook: Evalutaion of wind+CAES systems

Agenda



Time

Ele

ctr

icit

y P

ric

es

Background

• High uncertainties in energy markets due to

liberalization and structural changes

• Electricity prices have become very volatile

Stochastic simulation to capture the

uncertainties

• Volatile feed-in of renewable electricity into grid

• Electricity production is not correlated to

demand

• Electricity surplus or scarcity due to volatile

production

Need for energy storage (plants)

Evaluation under uncertainty using

stochastic optimization



Introduction - stochastic optimization in electricity

markets

State 1.1

(root)

State 2.1

State 2.2

p 1.1-2.1

p 1.1-2.2

State 3.1

(leave)

State 3.2

(leave)

p 2.1-3.1

p 2.1-3.2

State 3.3

(leave)p 2.2-3.3

p 2.2-3.2

Stage 3Stage 2Stage 1

, , ,

, , 0

, ,

min

(1 ) ( )

, ,

t

t

t EL

s t s u t s

t T s S

EL

u t s t t

u U

EL

u t s u

r pr C X

X D s S t t T

X Cap

Optimization of power plant dispatch and expansion:

• Overall optimization over all scenarios

(or scenario tree) instead of individual

optimization of the scenarios

• The optimization result corresponds to

the expected value of all scenarios



Scenario generation and reduction

Analytic scenario generation regarding an uncertain

parameter:

• Determining the expected value E(xt) and

• Determining the standard deviation σ

t-3 t-2 t-1 t

E(xt)

} +Δx

} - Δ x

po

pu

pmpm

po

pu

dupx

/2


markets



Scenario generation and reduction

Simulative scenario generation and reduction:

• Generation of a large number of scenarios (e.g. 1000) using a stochastic

process (= series of drawings of a random variable)

• Reduction to a tree with transition probabilities

...

...

...

t0 t0+1 t0+2 T-1 T

min max min max

, , , , 1 ', 1 ', 1

, ', 1 min max

, , ,

| , ,

| ,

l t s t s t l t s t s t

s t s t

l t s t s t

card l p p p p p pPr

card l p p p

ps

t0 t0+1 .... T-1 T


markets



Optimization strategies for the evaluation of

energy storage technologies

Maximization of contribution margin of

energy production and storage technologies:

optimization model

spot market reserve market

simulated

power prices

economic

parameter

technical

parameter

• optimized annual

contribution margin

• bids on spot and reserve

market

• full load hours of plant

(-components)src: http://schwarmkraft.at, www.eti-brandenburg.de



• Method: stochastic

dynamic programming

(SDP)

• Considering price

uncertainty using a

stochastic szenario tree

possible adjustment of

plant dispatch to

changes in price

expectations

Dynamic

optimization of

plant dispatch

Optimization strategies

Overall optimization

of annual contribution

margin

• Calculation of the

optimal annual

contribution margin

under perfect price

foresight

Monte Carlo (MC)-

simulation over 1000

price paths

„Simple strategy“

under uncertainty

• At night (0-8:00 a.m.)

pumping to reservoir,

during the day: generation

• Only if the spread between

charging and discharging

electricity prices is > 0

• Daily margins are added

up through a stoch. tree

for price uncertainty to

yield the annual return

Optimization strategies for the evaluation of

energy storage technologies



d0 d1 d2 D-1 D=365

*

, ,d D ps sbCF , ,

*

1 , ', endd ps sbd D ps sb S

CF

1,ps dPr

, ', 1ps d ps dTpr

ps

Reduction of simulated electricity price paths to

form a recombining tree

• Optimization: Backward

computation via

stochastic dynamic

programming (SDP)

• Objective: Maximizing

daily pay-offs CF*

• Clustering of the simulated price paths pd,h,s into price clusters ps:

Algortihm for clustering and calculation of transition probabilities

for d=1:D

[Centers(psi),ID] = kmeans (pd,h,s,, #cluster, city block distance)

Prob(psi) = #s(ID = i) / #price simulation

TrProb(d,psi,psj) = #s(ID(d) = i) & #s(ID(d+1) = j) / #s(ID(d) = i)

end

Figure: Scenario lattice generated from price simulations



Stochastic dynamic programming using

recombining trees

Indices

ps … Price scenarios

sb … Initial storage state

d ...D days in model horizon

h… hours

ts… time slices

Variables/parameters

CF*dD optimal contribution margin from d until D

p prices(electricty, fuel, certificates)

X,S variables: plant dispatch,

storage states

Tpr transition probabilities

1/μg gas heat ratio

EF emission factor

CAF compressed air factor

Objective function: cumulated cash flows CF from day d until D:

, ,

24

, , , , , ,

1

, , , , ,

*

( , ) ( 1, ') 1 , ','

( ) ( )

max ,...

endd ps sb

spot reserve

d ps sb h d ps sb ts

h

spot

d D ps sb d ps sb h

d ps d ps d D ps sb Sps PS

CF X CF X

CF X

Tpr CF

CF on the

spot marketCF on the

reserve market

Expected cash flows d+1 until D



1 1

* *

, , ,max ps d d D ps sbsb

ps PS

DB Pr CF

Calculation of the annual contribution margins based on the occurence

probabilities Prps,d1 of the price clusters on the first day d1 and the cumulated

CFs from d1 until D:

Constraints:

, , , , , , 1 , , , , , ,

min , , , , , , max

, , , , , ,

, , , , , ,

0, 0

1

4

comp turb

d ps sb h d ps sb h d ps sb h d ps sb h

turb turb reserve turb

d ps sb h d ps sb ts

reserve turb

d ps sb ts d ps sb h

reserve

d ps sb ts d ps sb h

S S X CAF X

X X X X

X X h ts

X S h ts

storage level change during day d

market consistency

reserve market contraint

time-coupled restriction PSpsSsbS psd

end

sbpsd d 'max',1,,

Stochastic dynamic programming using

recombining trees



Case study: Evaluating a diabatic CAES power plant

Input data:

specific investment 625 €/KW

Operation and 9000 €/MWCapTurb

maintenance

• Discount rate 5-10%

• Turbine power 90 - 250 MW

• Compressor power 70 - 50 MW

• Economic lifetime 25 Jahre

• Compressed air factor 0,66 (MWhin/MWhout,el)

• Gas usage rate 1,13(MWhin,g/MWhout,el)

• Overall efficiency 0,56

• Storage capacity 1000 MWhout,el

Further input data:

simulated electricity prices for

the base year 2010 on the basis

of the 2006-2010 historic data

Historic gas, carbon

certificate, and reserve power

prices



Results on the spot market

Perfect / MCSimple

StrategySDP

Annual contribution margin 15,4 million € 10,1 million € 14,2 million €

Net present value (i = 5%) 29,1 million € -45,6 million € 12,2 million €

Net present value(i = 10%) -36,9 million € -85,0 million € -47,8 million €

Internal rate of return i 6,8 % 1,8 % 5,8 %

Annual spot market revenue 49,2 million € 22,3 million € 55,6 million €

Annual costs 33,8 million € 12,2 million € 41,4 million €

Full load hours turbine 3199 h 1459 h 3770 h

Full load hours compressor 3519 h 1604 h 4147 h

Computation time ~8h (1000 Sz.)~few seconds.

(10 clusters)

~2h (10

clusters)



Results on the spot and minutes reserve market

Perfect / MC SDP

Contribution margin 18,3 million € 17,7 million €

Net present value (i = 5%) 70,1 million € 61,5 million €

Net present value (i = 10%) -19,2 million € -16,0 million €

Internal rate of return i 9,1 % 8,6 %

Spotmarkterlöse p.a. 41,6 million € 45,2 million €

Annual spot market revenue 4,5 million € 5,6 million €

Annual costs 27,8 million € 33,2 million €

Full load hours turbine/spot 2647 h 3009 h

Full load hours compressor 2911 h 3309 h

Dispatch hours reserve market 2735 h 3603 h

Computation time ~8h (1000 sz.) ~2h (10 Price cl.)



Results – NPV comparison

-100

-50

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10

NP

V in

mil

lio

n€

Discount rate in %

MC_Spot

Einfache_Spot

SDP_Spot

MC_SpotReserve

SDP_SpotReserve

-100

-50

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10

MC_Spot

Einfache_Spot

SDP_Spot

MC_SpotReserve

SDP_SpotReserve

Economic lifetime 25 years Economic lifetime 20 years

• Bidding strategy only on the spot market does not yield a satisfactory

internal rate of return

• Given an economic lifetime of 25 years, the IRR of 8,6% (SDP strategy)

is acceptable, but i* falls below 8% at T = 20 years.



Summary

SDP is a suitable method for evaluating energy storage technologies under

uncertainty

Optimization of the annual return under perfect foresight and MC simulation over

1000 price paths results in an upper limit for the economic value

Dispatch strategy using SDP yields results close to this limit (ca. 92% or 96% of the upper

limit when bidding on both markets)

Simple strategy performs significantly worse (only 66% of the upper limit)

Following the SDP strategy, the storage plant has more operating hours

(compared to the „simple strategy“)

Trading on both spot and reserve markets leads to a significant increase in

profitability of CAES plants

Future research: modeling further uncertainties, e.g. fuel and reserve power prices

and mapping the correlation to spot market prices



Outlook

Evaluation of wind-CAES systems

• Idea: Incentives = Higher capacity payments or market premium for wind parks

based on higher availbility of wind power at peak times

• only if operation of CAES plant is adjusted to wind power availability

• No incentives to shift wind

production to peak load times

each component can act as

single utility on energy markets

Value (wind+CAES) = Earnings on spot + reserve market + extra premium

Value (wind+CAES) = value(wind) + value(CAES)



Thank you!

Questions / Remarks?

Documents

Techno-economic evaluation of energy technologies under … · 6 6 KIT –Universität des Landes Baden25.09.2009-Württemberg und Prof. Fichtner, Lehrstuhl für Energiewirtschaft,