1. No category

.
Optimal investment strategies
for district heating plants
under prediction uncertainties
for cost parameters
th
International PhD Day of the AAEE Student Chapter
Nikolaus Rab
Energy Economics Group (TU Wien)
Vienna, March
,
.
Overview
Overview
/
.
Overview
An investment model for district heating generation is developed
that particularly concerns prediction uncertainties of cost
parameters. It will be based on three different methods:
. Generation expansion planning.
For cost-optimal power plant investments a linear program is
well-established in energy economics.
. CHP planning.
A simple model for short-term CHP planning is described that will be used to
adapt the standard GEP formulation for district heating investments.
. Risk measures for prediction uncertainties.
The impact of prediction uncertainties on the heat generation costs will be
quantified by risk measures that are widely used in financial mathematics.
Overview
/
.
Methodolgy
Methodolgy
/
.
I. Generation expansion planning
. Hourly generation decisions:
Minimizing the hourly generation costs Vi,h (in Euro/MWh) of the ith power
plant with generation gi,h MWh.
Ot := min
gi,h
Methodolgy
∑
Vi,h gi,h .
i,h
/
.
I. Generation expansion planning
. Hourly generation decisions:
Minimizing the hourly generation costs Vi,h (in Euro/MWh) of the ith power
plant with generation gi,h MWh.
Ot := min
∑
gi,h
Vi,h gi,h .
i,h
. Yearly investment decisions:
Minimizing the yearly fixed costs Fi,t in Euro/kW with binary investment
decisions ni,t while taking operation costs Ot (ni,t ) into account:
min
ni,t
Methodolgy
t
∑∑
Fi,t ni,s + Ot (ni,t )
i,t s=1
/
.
II. CHP planning
The feasible operation
region of a CHP plant with
power generation Gel and
heat generation Gh is
modelled as a convex
polygon with extreme
points (h1 , p1 ), (h2 , p2 ), . . . .
Gel
Gel
(h4 , p4 )
(h3 , p3 )
(h1 , p1 )
(h2 , p2 )
.
Any point in the feasible operation region can be displayed as a
convex combination of those four extreme points j = 1, . . . , 4
resulting in the minimum variable costs:
∑∑
min
λi,j vi,j st . . .
λi,j
Methodolgy
i
Gh
Gh
j∈Ji
/
.
III. Risk measures
For measuring the impact of prediction uncertainties of the cost
parameters (gas, electricity, CO emissions, ...) on the distribution
of the overall heat generation costs risk measures are used. Most
common examples include:
. Volatility risk measure (µ + σ): classic dispersion based risk
measure.
. Value-at-risk (Varα ): maximum costs for heat generation in the
best α% of all possible cases.
. Expected shortfall (ESβ ): average costs for heat generation in
the worst β% of all possible cases.
Methodolgy
/
.
Optimization program (simplified)
. Hourly generation decisions:
The hourly generation costs Oh (ni,t , ω) depend on ω ∈ Ω and are therefore
random variables.
Oh (ni,t , ω) := min
λ
Methodolgy
∑∑(
)
Vi,h,j (ω) − gel
(ω)
s
(ω)
λi,h,j (ω)
h
i,h,j
i∈I j∈Ji
/
.
Optimization program (simplified)
. Hourly generation decisions:
The hourly generation costs Oh (ni,t , ω) depend on ω ∈ Ω and are therefore
random variables.
Oh (ni,t , ω) := min
λ
∑∑(
)
Vi,h,j (ω) − gel
(ω)
s
(ω)
λi,h,j (ω)
h
i,h,j
i∈I j∈Ji
. Yearly investment decisions:
A risk measure R(·) is used to include stochasticity of the hourly generation
∑
costs h Oh (ni,t , ω) into the investment decisions.
min :=
n
Methodolgy
t
∑∑∑
t∈t i∈I s=1

Fi,t ni,s + R 
∑∑

Oh (ni,t , ω) ,
t∈T h∈Ht
/
.
Prediction uncertainties
Yearly characteristics (distribution parameters) of all cost data and
the district heating load can be given as a stochastic or
deterministic process. During the numerical evaluation hourly
synthetic profiles are generated based on ARMA-GARCH modelling
for the corresponding yearly distributional parameters.
55
Price [in Euro/MWh]
30
35
40
45
Correlation
0.4
0.6
0.03
Density
0.02
20
30
40
50
Price [in Euro/MWh]
60
20
0.0
10
25
0.2
0.01
0.00
0
Daily seasonal pattern
50
1.0
Auto correlation
0.8
0.04
Distribution
5
Lags
10
15
Time [in hours]
20
Time series characteristics and distribution of the spot electricity price.
Methodolgy
/
.
Results
Results
/
.
100
MW Electricity
200
300
400
500
600
Case study portfolio
0
CHP 1
CHP 2
0
50
100
150
MW Heat
200
250
300
Feasible operation regions of the two CHP plants.
Results
The case study portfolio
comprises two CHP plants
with a maximum heat
generation of
and
MW (range of η el of . % to
% and . % to %).
For peak loads a gas fired
district heating boiler with a
maximum capacity of
MW and a minimum
capacity of . MW is
installed (thermal efficiency
η th of % to %).
/
.
0.010
Case study load
0.008
Density
0.004
0.006
0.002
0.000
The average load for district
heating will be on warm
days with a temperature
above °C at MW, on cold
days with a temperature
below °C at
MW. Peak
loads will be up to
MW.
Temperature > 15°C (67%)
Temperature < 15°C (33%)
0
100
200
300
District heating load [in MW]
400
Density conditional on the outside temperature for the
corresponding district heating load.
Results
/
.
Optimization
Possible additional technologies include heat pumps ( MW each),
electric boilers and solar district heating. For the analysis the
development of some cost parameters is uncertain for two different
cases:
. Case : The gas price has an uncertain development with its
mean remaining at Euro/MWh with a standard deviation of
one Euro/MWh. The spot electricity price rises up to
Euro/MWh in mean (no uncertainties).
. Case : In addition to case also the development of the mean
spot electricity price is uncertain with a standard deviation of
one Euro/MWh.
Results
/
.
Existing generation portfolio
400
Existing portfolio
0
50
100
150
MW
200
250
300
350
Heat plant
CHP 2
CHP 1
0
1000
2000
3000
4000
5000
Time [in hours]
6000
7000
8000
Shares of districting heating supply for the existing generation portfolio for one
reference year.
Results
/
.
... and portfolio a er optimization.
400
Existing portfolio + 100 MW heat pumps
0
50
100
150
MW
200
250
300
350
Heat pumps
Heat plant
CHP 2
0
1000
2000
3000
4000
5000
Time [in hours]
6000
7000
8000
Shares of districting heating supply for the optimized portfolio with
MW
additionally installed heat pumps (optimal for both cases).
Results
/
.
Heat generation costs (Case )
0.12
Case 1
0.00
0.02
0.04
Density
0.06 0.08
0.10
Existing Portfolio
+ 100 MW heat pumps
20
25
30
35
Heat generation costs [in Euro/MWh]
Existing portfolio
+
MW heat pumps
Results
µ
.
.
µ+σ
.
.
40
VaR
.
.
%
ES
%
.
.
/
.
Heat generation costs (Case )
0.12
Case 2
0.00
0.02
0.04
Density
0.06 0.08
0.10
Existing Portfolio
+ 100 MW heat pumps
20
25
30
35
Heat generation costs [in Euro/MWh]
Existing portfolio
+
MW heat pumps
Results
µ
.
.
µ+σ
.
.
40
VaR
.
.
%
ES
.
.
%
/
.
Conclusion
Conclusion
/
.
Concluding remarks
. Uncertain developments of several costs parameters have a
strong influence on the composition of the optimal district
heating generation portfolio.
Conclusion
/
.
Concluding remarks
. Uncertain developments of several costs parameters have a
strong influence on the composition of the optimal district
heating generation portfolio.
. Using only deterministic scenarios neglects the uncertainty
nature of the GEP problem. The resulting scenario specific
portfolios aren’t very useful for investment decisions.
Conclusion
/
.
Concluding remarks
. Uncertain developments of several costs parameters have a
strong influence on the composition of the optimal district
heating generation portfolio.
. Using only deterministic scenarios neglects the uncertainty
nature of the GEP problem. The resulting scenario specific
portfolios aren’t very useful for investment decisions.
. Prediction uncertainties of cost parameters influence the
expected heat generation costs as well as the risk exposure
towards cost parameter changes. Risk measures (in particular
value-at-risk and expected shortfall) allow for a suitable
consideration of these down-side risks.
Conclusion
/
Contact:
. Conclusion.
Nikolaus Rab
[email protected]
Institut für Energiesysteme und Elektrische Antriebe
Energy Economics Group
eeg.tuwien.ac.at