The Impact of Intermittent Renewable Energy
Sources on Wholesale Electricity Prices
Prof. Dr. Felix Müsgens, Thomas Möbius
USAEE-Conference
Pittsburgh, October 27, 2015
Motivation
 How will intermittent renewable energy sources (RES) influence
wholesale electricity prices, and in particular price volatility?
 Relevant for
– Traders
• risk premia
• structural changes peak/off-peak
– Regulators
• increasing zero variable cost generation
• peak load pricing and capacity mechanisms
– Investors
• how to finance investment?
Brandenburg University of Technology – Felix Müsgens
2
Outline and Methodology
 Stylized Analysis:
– Two thermal technologies (base and peak load)
– Exogenous RES capacity changes
– Dynamic effects (i. e. start-up costs and minimum load requirements)
– Uncertainty of RES feed-in
• investment planning
• start-up and dispatch decisions
– Implemented with linear optimization electricity market model
• endogenous optimization of base/peak capacity investments and
base/peak/wind dispatch (depending on availability factors)
• model computes green-field full cost electricity market equilibria
• electricity price equals marginal of demand constraint (shadow price)
Brandenburg University of Technology – Felix Müsgens
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Outline and Methodology
 Stylized Analysis:
– Two thermal technologies (base and peak load)
– Exogenous RES capacity changes
– Dynamic effects (i. e. start-up costs and minimum load requirements)
– Uncertainty of RES feed-in
• Investment planning
• start-up and dispatch decisions
– Load duration curve
– Perfect foresight
– Implemented with linear optimization electricity market model
• endogenous optimization of base/peak capacity investments and
base/peak/wind dispatch (depending on availability factors)
• model computes (green-field) full cost electricity market equilibria, electricity
price equals marginal of demand constraint.
Brandenburg University of Technology – Felix Müsgens
4
Insights from Textbook (Power System) Economics
 Two thermal technologies (base load and peak load)
– Characteristics: 𝑉𝐶 𝐵 , 𝑉𝐶 𝑃 , 𝐹𝐶 𝐵 , 𝐹𝐶 𝑃 , 𝑉𝐶 𝐵 < 𝑉𝐶 𝑃 , 𝐹𝐶 𝐵 > 𝐹𝐶 𝑃
 Only three price levels occur
𝑆
𝑃
𝑃
– 1 hour with 𝑝 (equal to 𝑉𝐶 + 𝐹𝐶 )
–
𝑛𝑃 − 1 hours with 𝑝𝑃 (equal 𝑉𝐶 𝑃 )
[MW]
no wind generation
X
– 𝑛𝐵 hours with 𝑝𝐵 (equal to 𝑉𝐶 𝐵 )
 𝑛𝑃 solves 𝐹𝐶 𝑃 + 𝑛𝑃 ∗ 𝑉𝐶 𝑃 = 𝐹𝐶 𝐵 + 𝑛𝑃 ∗ 𝑉𝐶 𝐵 ,
𝑛𝐵 = 8,760 − 𝑛𝑃
 Appearance of RES
– 𝑉𝐶
𝑅𝐸𝑆
, 𝑉𝐶
𝑅𝐸𝑆
< 𝑉𝐶
𝐵
[MW]
no RES generation
RES generation
X
Y
𝑛𝑃
Brandenburg University of Technology – Felix Müsgens
t
𝑛𝑃
t
5
Results – Textbook
 Installing wind capacity leads to:
– Variation in installed thermal capacities (usually more peak, less base)
– However, identical number of hours for each price level with and without
wind
– Hence, identical variance:
𝑉𝑎𝑟 =
1
∗ 𝑛𝐵 𝑝𝐵 − 𝑝
8760
2
+ 𝑛𝑃 − 1 𝑝𝑃 − 𝑝
2
+ 𝑝𝑆 − 𝑝
2
 Result:
𝑛𝑤
𝑤𝑤
– 𝑉𝑎𝑟𝑡𝑏
= 𝑉𝑎𝑟𝑡𝑏
Brandenburg University of Technology – Felix Müsgens
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Outline and Methodology
 Stylized Analysis:
– Two thermal technologies (base and peak load)
– Exogenous RES capacity changes
– Dynamic effects (i. e. start-up costs and minimum load requirements)
– Uncertainty of RES feed-in
• Investment planning
• start-up and dispatch decisions
– Load duration curve
– Perfect foresight
– Implemented with linear optimization electricity market model
• endogenous optimization of base/peak capacity investments and
base/peak/wind dispatch (depending on availability factors)
• model computes (green-field) full cost electricity market equilibria, electricity
price equals marginal of demand constraint.
Brandenburg University of Technology – Felix Müsgens
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Equivalent (Simple) Electricity Market Model
 Objective Function
min 𝑇𝐶 =
𝑣𝑐𝑖 ∗ 𝐺𝑖,𝑡
Variable generation costs
𝑖,𝑡
+
𝑖𝑐𝑖 ∗ 𝐷𝑖
Annualized investment costs
𝑖
 s. t.
0 ≤ 𝐺𝑖,𝑡 ≤ 𝐷𝑖 ∗ 𝑎𝑓𝑖
0 ≤ 𝐺"𝑊𝑖𝑛𝑑",𝑡 ≤ 𝑝𝑓𝑡 ∗ cap"𝑊𝑖𝑛𝑑"
𝐺𝑖,𝑡 = 𝑑𝑒𝑚𝑡
Lower/upper limit for generation
∀ 𝑖, 𝑡
∀𝑡
∀𝑡
Wind feed-in
Energy balance – market clearing
𝑖
 Parameters:
– Peak tech: OCGT, base tech: hard coal (numbers: appendix)
– Wind: 0, 35 and 70 GW, availability factors from Germany
– Hourly load profile: Germany
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Results
 Simplest model formulation
Price Variance
Wind Curtailment
[GWh per year]
0 GW Wind
35 GW Wind
70 GW Wind
286,000
286,000
286,024
0
0
199
 Variance increases with further increasing wind capacity?
 Wind curtailment appears at 70 GW wind capacity!
Brandenburg University of Technology – Felix Müsgens
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Results –
Textbook with Wind Curtailment
 Curtailment price occurs: 𝑝𝐶 = 𝑉𝐶 𝑊
 For moderate wind increase
– Decreasing amount of base load hours: 𝑛𝐵 ′ + 𝐶 = 𝑛𝐵 ,
𝐶 equals number of hours with negative residual load.
[MW]
no wind generation
high wind generation
X
Y
t
PeakLoad
1
′
𝑉𝑎𝑟 =
∗ 𝑛𝐵 𝑝𝐵 − 𝑝
8760
BaseLoad
2
+ 𝑛𝐶 𝑝𝐶 − 𝑝
Brandenburg University of Technology – Felix Müsgens
Curtailment
2
+ 𝑛𝑃 − 1 𝑝𝑃 − 𝑝
2
+ 𝑝𝑆 − 𝑝
2
10
Outline and Methodology
 Stylized Analysis:
– Two thermal technologies (base and peak load)
– Exogenous RES capacity changes
– Dynamic effects (i. e. start-up costs and minimum load requirements)
– Uncertainty of RES feed-in
• Investment planning
• start-up and dispatch decisions
– Load duration curve
– Perfect foresight
– Implemented with linear optimization electricity market model
• endogenous optimization of base/peak capacity investments and
base/peak/wind dispatch (depending on availability factors)
• model computes (green-field) full cost electricity market equilibria, electricity
price equals marginal of demand constraint.
Brandenburg University of Technology – Felix Müsgens
11
Model Extensions – Intertemporal Constraints
 Objective Function
min 𝑇𝐶 =
Variable generation costs
𝑣𝑐𝑖 ∗ 𝐺𝑖,𝑡
𝑖,𝑡
+
𝑖𝑐𝑖 ∗ 𝐷𝑖
Annualized investment costs
𝑠𝑐𝑖 ∗ 𝑆𝑈𝑖,𝑡
Start-up Costs
𝑖
+
𝑆𝑈
𝑃𝑖,𝑡
[MWel]
𝐺𝑖,𝑡
𝑖,𝑡
𝑆𝑈
𝑃𝑖,𝑡
− 𝐺𝑖,𝑡 ∗ 𝑧𝑖
+
Costs at partial load
𝑆𝑈
𝑃𝑖,𝑡
* 𝑔𝑖𝑚𝑖𝑛
𝑖,𝑡
[hour]
 Upper bound constraint
𝑆𝑈
0 ≤ 𝐺𝑖,𝑡 ≤ 𝑃𝑖,𝑡
 Lower bound constraint
∀ 𝑖, 𝑡
Brandenburg University of Technology – Felix Müsgens
𝑆𝑈
𝑃𝑖,𝑡
∗ 𝑔𝑖𝑚𝑖𝑛 ≤ 𝐺𝑖,𝑡
∀ 𝑖, 𝑡
12
Model Extensions – Intertemporal Constraints
 Activating start-up costs
𝑆𝑈
𝑆𝑈
𝑃𝑖,𝑡
− 𝑃𝑖,𝑡−1
≤ 𝑆𝑈𝑖,𝑡
∀ 𝑖, 𝑡
 Upper limit for started capacity
𝑆𝑈
0 ≤ 𝑃𝑖,𝑡
≤ 𝐷𝑖 ∗ 𝑎𝑓𝑖
∀ 𝑖, 𝑡
 Wind feed-in
0 ≤ 𝐺"𝑊𝑖𝑛𝑑",𝑡 ≤ 𝑝𝑓𝑡 ∗ cap"𝑊𝑖𝑛𝑑"
∀𝑡
 Energy Balance - Clearing the market in every time period
𝐺𝑖,𝑡 = 𝑑𝑒𝑚𝑡
∀𝑡
𝑖
 Electricity price estimator: marginal of energy balance constraint
Brandenburg University of Technology – Felix Müsgens
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Results
 Extended Model - Intertemporal Constraints
Without
intertemporal
constraints
With
intertemporal
constraints
Price Variance
Wind Curtailment
[GWh per year]
Price Variance
Wind Curtailment
[GWh per year]
0 GW Wind
35 GW Wind
70 GW Wind
286,000
286,000
286,024
0
0
199
286,762
286,774
286,814
0
0
213
 Intertemporal constraints generally lead to a higher price variance
 Slight increase up from the first 35 GW wind capacity is visible
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14
Outline and Methodology
 Stylized Analysis:
– Two thermal technologies (base and peak load)
– Exogenous RES capacity changes
– Dynamic effects (i. e. start-up costs and minimum load requirements)
– Uncertainty of RES feed-in
• Investment planning
• start-up and dispatch decisions
– Load duration curve
– Perfect foresight
– Implemented with linear optimization electricity market model
• endogenous optimization of base/peak capacity investments and
base/peak/wind dispatch (depending on availability factors)
• model computes (green-field) full cost electricity market equilibria, electricity
price equals marginal of demand constraint.
Brandenburg University of Technology – Felix Müsgens
15
Results – Volatility under Uncertainty
– Long term uncertainty due to a set
of different ‘wind years’
2010
2011
+ 10%
± 0
- 10%
• One global investment decision
with identical installed capacities for
all wind years and short term
deviations.
2012
– Short term uncertainty with a strong
impact at the start-up decision
2013
2014
‚Investment
Decision‘
long term
variation of
‚wind years‘
+ 10%
± 0
- 10%
short term wind
variation –
influences the unit
commitment
Brandenburg University of Technology – Felix Müsgens
• Started capacity is fixed at the
second stage of the scenario
tree, but has to hold for all
variations at the third stage
 Integrated ‘single stage’
electricity market model
16
Model Extensions – Uncertainty
 Objective Function
– Set extension for ‘wind years’ (𝑦) and wind realization scenario (𝑤𝑟)
– Scaling of startup and investment costs by likelihoods 𝜌 𝑦 and 𝜌𝑤𝑟 which do not
vary within its set
min 𝑇𝐶 =
𝑣𝑐𝑖 ∗ 𝐺𝑖,𝑦,𝑤𝑟,𝑡
Variable generation costs
𝑖,𝑦,𝑤𝑟,𝑡
𝑆𝑈
𝑃𝑖,𝑦,𝑡
− 𝐺𝑖,𝑦,𝑤𝑟,𝑡 ∗ 𝑧𝑖
+
Costs at partial load
𝑖,𝑦,𝑤𝑟,𝑡
+
+
1
∗
𝜌𝑤𝑟
𝑠𝑐𝑖 ∗ 𝑆𝑈𝑖,𝑦,𝑡
Start-up Costs
𝑖,𝑦,𝑡
1
∗
𝜌 𝑦 ∗ 𝜌𝑤𝑟
𝑖𝑐𝑖 ∗ 𝐷𝑖
Annualized investment costs
𝑖
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Model Extensions – Uncertainty
 s. t. following constraints
– Lower/upper limit for generation
𝑆𝑈
𝑆𝑈
𝑃𝑖,𝑦,𝑡
∗ 𝑔𝑖𝑚𝑖𝑛 ≤ 𝐺𝑖,𝑦,𝑤𝑟,𝑡 ≤ 𝑃𝑖,𝑦,𝑡
∀ 𝑖 ∈ 𝐼\"Wind", 𝑦, 𝑤𝑟, 𝑡
– Activating start-up costs
𝑆𝑈
𝑆𝑈
𝑃𝑖,𝑦,𝑡
− 𝑃𝑖,𝑦,𝑡−1
≤ 𝑆𝑈𝑖,𝑦,𝑡
∀ 𝑖, 𝑡
– Lower/upper limit for started capacity
𝑆𝑈
0 ≤ 𝑃𝑖,𝑦,𝑡
≤ 𝐷𝑖 ∗ 𝑎𝑓𝑖
∀ 𝑖, 𝑡
– Wind feed-in
0 ≤ 𝐺"𝑊𝑖𝑛𝑑",𝑦,𝑤𝑟,𝑡 ≤ 𝑝𝑓𝑦,𝑤𝑟,𝑡 ∗ cap"𝑊𝑖𝑛𝑑"
∀ 𝑦, 𝑤𝑟, 𝑡
– Energy Balance - Clearing the market in every time period
𝐺𝑖,𝑦,𝑤𝑟,𝑡 = 𝑑𝑒𝑚𝑦,𝑤𝑟,𝑡
∀ 𝑦, 𝑤𝑟, 𝑡
𝑖
 Electricity price estimator: marginal of energy balance constraint
Brandenburg University of Technology – Felix Müsgens
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Results – Volatility under Uncertainty
Without
intertemporal
constraints
With
intertemporal
constraints
Price Variance
Wind Curtailment
[GWh per year]
Price Variance
Wind Curtailment
[GWh per year]
With
Price Variance
intertemporal
constraints Wind Curtailment
Under uncertainty
[GWh per year]
0 GW Wind
35 GW Wind
70 GW Wind
286,000
286,000
286,024
0
0
199
286,762
286,774
286,814
0
0
213
286,762
4,282,914
4,282,976
0
0
297
 Generally higher values due to lower likelihood for the occurrence of the scarcity
hour and thus, a significantly higher value for the scarcity price
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Conclusion
 In all considered market equilibria, market prices cover (and must
cover) full costs of all thermal technologies. This is true regardless of
the amount of wind energy in the system.
 Price volatility increases with additional renewable energy sources
(RES) capacity.
 Driving factors are
– RES curtailment
– Changes in residual load profile in combination with thermal inflexibility
– Uncertainty of RES generation
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Thank you very much!
Questions?
Methodology
 Stylized system with two thermal technologies and one intermittent RES technology
–
Base-Load Technology: High fix and low variable costs
–
Peak-Load Technology : Low fix and high variable costs
Technology
Annual
fixed costs
[€/MW*a]
𝒊𝒄𝒊
Variable
production
costs [€/MWh]
𝒗𝒄𝒊
Start-up
costs
[€/ΔMW]
𝒔𝒄𝒊
Minimal load
[%]
𝒈𝒎𝒊𝒏
𝒊
Efficiency loss at
minimum load
[%-pt]
Base Load
132,000
34
105
40
6
Peak Load
56,000
70
40
20
22
Wind
-
0
0
0
0
 Variable wind generation as the only intermittent RES
–
Wind capacities exogenously implemented
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Backup I
 Comparison of resulting investment decision with and without
considering uncertainty at different wind levels
 Uncertain wind realization encourages a higher share of peak load plants
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23
Backup II – Basic Model
 Objective Function
min 𝑇𝐶 =
𝑆𝑈
𝑃𝑖,𝑡
− 𝐺𝑖,𝑡 ∗ 𝑧𝑖 +
𝑣𝑐𝑖 ∗ 𝐺𝑖,𝑡 + 𝑠𝑐𝑖 ∗ 𝑆𝑈𝑖,𝑡 +
𝑖,𝑡
𝑖,𝑡
𝑖
[MW]
𝑧𝑖 = ∆𝑣𝑐𝑖 ∗ 𝑔𝑖𝑚𝑖𝑛
𝑖𝑐𝑖 ∗ 𝐷𝑖
𝑆𝑈
𝑃𝑖,𝑡
𝐺𝑖,𝑡
1 − 𝑔𝑖𝑚𝑖𝑛
𝑆𝑈
𝑃𝑖,𝑡
* 𝑔𝑖𝑚𝑖𝑛
𝑆𝑈
𝑆𝑈
𝑃𝑖,𝑡
− 𝑃𝑖,𝑡−1
≤ 𝑆𝑈𝑖,𝑡
–
∀ 𝑖, 𝑡
[hour]
Operating at partial load is causing lower efficiency rates and thus, higher variable costs
Brandenburg University of Technology – Felix Müsgens
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