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Integration of energy efficiency
and renewable energy
- multiple benefits!
Prof. Peter D. Lund
Aalto University, School of Science
Espoo-Otaniemi, Finland
peter.lund@aalto.fi
23 March 2017
Outline of the lecture
Research results based on following journal papers:
[send an email to peter.lund@aalto.fi if you want a copy of the papers]
1. Salpakari, P. Lund. Optimal and rule-based control strategies for energy flexibility in
buildings with PV. Applied Energy 161 (2016) 425-43.
2. J.Salpakari, J. Mikkola, P.D. Lund. Improved integration of large-scale variable renewable
power in cities through optimal control of DSM and power-to-heat measures. Energy
Conversion and Management 126 (2016)649-661.
3. Peter Lund. Market penetration rates of new energy technologies. Energy Policy 34
(2006), 3317-3326.
4. Peter D. Lund. Energy policy planning near grid parity using a price-driven technology
penetration model. Technological Forecasting & Social Change 90 (2015) 389-399.
Peter Lund 2017
Main contents:
①Enabling large scale local renewable power use through
better integration and flexibility
②Market take-up and adoption of these new technologies
Forthcoming energy transition
Peter Lund 2017
http://www.shell.com/global/future-
energy/scenarios/new-lens-scenarios.html
• Fossil fuels : Today >80%; 22% by 2100 of energy
• Electricity important : future power supply > power demand ?
IEA scenario (2015)
Impacts from much variable
renewable electricity (VRE)
Peter Lund 2017
No VRE
Much VRE
Renewables & energy efficiency
Relevance of EE to large-scale RE schemes:
① Reduces resource requirement (‘less needed’)
② Improves matching of RE (‘more flexibility’)
③ Enables optimizing of RE (‘ better use’)
④ Sectorial integration possible (‘close to end-use’)
Link between energy efficiency (EE) and renewable
energy/electricity (RE) increases towards the end-use:
‘supranational’  national urban (cities) homeowner (building)
Peter Lund 2017
Flexibility approaches for the
energy system transformation
Peter Lund 2017
Cost & magnitude of flexibility
Peter Lund 2017
Ref: Energy Innovation, 2015
Power-to-X (P2X) conversion
for increased flexibility
Peter Lund 2017
Oil
Coal
Peat
Natural gas
Biomass
Waste-to-
energy
Nuclear
Hydro
Wind
Solar power
Heat pumps
Imports
Electricity
Heat
Fuel
Electricity
pool
Heat pool
Fuel pool
House-
holds
Services
Transport
Industry
PRIMARY
ENERGY
NEW
FINAL
ENERGY
OLD FINAL
ENERGY
(BALANCE
NODES)
ADVANCED
CONVERSION
CONVENTIONAL
CONVERSION
DEMAND
Unconverted
CHP
District
heating
CHP
Industrial
Separate
heat
production
Separate
electricity
production
Residential
heat
production
Oil
refineries
P2H
elecheat
P2C
eleccold
P2G
elecgas
P2L
gasbiofuel
Biofuel
biomassbio
-fuel
Electricity
and heat
storage
1 2
ENERGY
SERVICES
Curtailment for increased system
flexibility with RE power
Peter Lund 2017
• Curtailment = Cutting off
• Energy lost with curtailment =
capacity factor (RE≈8-40%) ×
curtailment level × curtailment time
• Utilization= curtailed RE for P2X,
EV & battery charging, etc.
• Advantage = Sizing of RE >> Self-
use limit of power (as RE surplus can
be curtailed)
• Active curtailment= RE power
could provide very fast power ramp-
up and ramp-down
• Power-to-thermal: surplus or curtailed
RE converted to thermal energy; P2H=heat
• Heat (resistance, heat pump) or cooling
(refrigeration cycle)
 η (resistance) ≈100%
 COP (heat pump) ≈300%
Power-to-thermal strategy
• Coupled to thermal
demand/storage
• The building could also
function as ’thermal’
storage
Rationale of P2H (Power-to-Heat)
EU-27 household
final energy
67%
15%
14%
4%
Space heating
Appl&Light
Hot water
Cooking
1. Thermal energy (heat, cooling) dominate final
energy use in built environment
• >50% of final energy use in cities
• Up to 80% of EU-27 household final energy
2. With a high RE share of power, marginal value of
electricity < marginal value of heat
3. Thermal storage is proven and cheap (~$5-
25/kWh), from short-term small size to long-term
large-size (max. unit ~1-2GWh, 100-200 MW),
from centralized to decentralized schemes
4. P2H decreases price volatility at high RE shares
and allows to integrate more RE
Peter Lund 2017
Case 1. Large wind scheme with
P2H for urban use: Case Helsinki
Peter Lund 2017
Power and heat demand &
plants in Helsinki
1GWel ;1.3GWth,CHP ; 2.0GWth,peak
(coal, gas); district heating
Big wind scheme:
Results: cross-sectoral integration
2. Wind with P2H ≤ Power + Heat demand 1349 MW wind power
= 60% of electricity per year (2% of heat)Ref: Lund, P. : Large-scale urban renewable electricity schemes - integration and interfacing aspects. Energy Conversion and Management, 2012
1. Wind ≤ Power demand  max. 486 MW wind power
= 20-25% % of yearly electricity in Helsinki
Peter Lund 2017
1349 MW
486 MW
1
2
(’worst day’ Feb 6)
Wind
power
Heat
Elec
(1 year)
Case 2: Improved flexibility
through DSM + P2H + Storage
Peter Lund 2017
• Helsinki case as above, but in
addition:
 Solar + Wind
 DSM+Storage
• Control strategies for flexibility:
a) load and supply matching b)
link to electricity market +
investments
Fig Electricity load in Helsinki with shiftable components (DSM). The
duration that a load can shift its consumption is indicated in the legend
Improved flexibility with large-scale variable renewable power in cities through optimal demand side management and
power-to-heat conversion
Energy Conversion and Management, Volume 126, 2016, 649–661
http://dx.doi.org/10.1016/j.enconman.2016.08.041
Shiftable loads 35-350
MW, or 7-50% of hourly
power demand
Power profile + shiftable loads
Peter Lund 2017
Electricity demand
http://dx.doiorg/10.1016/j.enconman.2016.08.041
Surplus VRE
production
Peter Lund 2017
• DSM enables more
VRE (wind and PV)
• P2H very effective
(cross-sectorial
integration to
increase flexibility)
Improved
integration
due to DSM
Baseline (topmost surface)
No surplus (VRE<Load)
Improved
integration
due to P2H
http://dx.doi.org/10.1016/j.enconman.2016.08.041
Cash-flow when linked to spot
electricity market
Peter Lund 2017
Baseline
1
2 3
4
Case 3: Flexibility in 1 building +
PV
Peter Lund 2017
• Same as above, but 1 house+PV
• Optimization: minimize variable
costs & maximize self-use of PV
• 13–25% savings in electricity bill with cost-optimal control (1h-based price)
• 8–88% decrease in electricity fed into the grid
Peter Lund 2017
Market take-up of new
technologies (diffusion)
”Diffusion is a process in which the innovation is distributed to
members of the social system through different channels having
different threshold for adoption of new innovations” (Rogers)
• Key elements of diffusion of innovations
– Innovation; Communication channel; Time; Social system; Adopters
• The diffusion process explains the penetration of a new
technology to the market over time
time
Innovation Communication
channels
Social
system
Peter Lund 2017
Decision making process linked to
technology diffusion or adoption
Knowledge
Communication channels
Diffusion of
innovation
Social system
Previous experience
Needs/problems
Norms of the society
Degree of innovation
Personal
character:
Social status
Personality
Communication
behaviour
Innovation
characteristics:
Compatibility with values
Advantages?
Prev. experiences,needs?
How complex to use?
How easy to try? Visibility?
Accept or
Reject
Persuasion Decision Realization Verification
Peter Lund 2017
Diffusion Model
)0(
)0(1
0
f
f
a
−
=
)(
0
0
1
1
)( tt
ea
tf −⋅−
⋅+
= β
Classical diffusion equation also so-called
epidemic model
(f=market share, β=adoption rate, t=time)
Bass model: influence of internal (q) and
external (p) information
Other models: Gompertz, Mansfield,
Nonsymmetric models
Diffusion equation/model describes the adoption of the new
technology over time, e.g. change of the market share
Peter Lund 2017
Analyzing the diffusion equation
Importance of parameter β [%/year]
• β = adoption rate or penetration rate of the new technology
• Steepness of the penetration depends on the β; affected by attributes of innovation
(e.g. price), type of decision (e.g. collective or authority), communication channel
(e.g. media), social system (e.g. norms), promotion efforts
)(
0
0
1
1
)( tt
ea
tf −⋅−
⋅+
= βS-curve
)0(
)0(1
0
f
f
a
−
=
Results from diffusion models
Peter Lund 2017
Effectiveness of policy measures in transforming the
energy system. Energy Policy 35 (2007) 627-639
Market penetration rates of new energy
technologies. Energy Policy 34 (2006), 3317-3326
Peter Lund 2017
Modelling diffusion of innovations and
decision making with two choices
• Binary choice model (BCM) describes the choice between technologies A and B
(e.g. substitution of old with new)
• Probability to purchase the new product A is P (logit probability); C=price=direct
cost + other costs (e.g. behavioral factors, inconvenience costs) σ=arb. parameter;
• BCM could be extended to other factors as well; replace C with a vector of factors
0 %
20 %
40 %
60 %
80 %
100 %
-50 -30 -10 10 30 50
Probabilityofpreferences
Price difference (€/MWh)
Technology A
Technology B
B cheaper than A A cheaper than B
Importance of financial support to
market penetration and shares
Peter Lund 2017
1. Price affects market penetration
(both potential and decisions)
2. Above grid parity (old cheaper than
new), fast penetration requires
“over-subsidization”
3. At grid-parity (new≈old), support
necessary to gain a market share
4. Clearly below grid-parity (new
cheaper than old) no support
5. Dynamic energy policy support
important, i.e. adjusting the support
levels over time as new technology
gets cheaper
Energy policy planning near grid parity using a price-
driven technology penetration model. Technological
Forecasting & Social Change 90(2015)389-399.
0,0 %
0,5 %
1,0 %
1,5 %
2,0 %
0,01 % 0,10 % 1,00 % 10,00 %
Growthinmakertshare(dfi/yr)
Market share (fi)
GLO Nuclear 1966-2011
GLO PV 1978-2012
GLO Wind 1982-2012
GER Wind 1990-2012
GER PV 1990-2012
USA NG 1994-2011
USA NG 5-year avg
Price ratio: 0.1
Price ratio: 0.2
Price ratio: 0.3
Price ratio: 0.5
Extras
Peter Lund 2017
Example: Curtailing solar power
in Finland
0%
20%
40%
60%
80%
100%
0% 50% 100%
Reductioninsolaryield
Power cut-off limit (% of nominal PV power
installed)
Peter Lund 2017
Helsinki Wind+CHP+DH base case
(simple integration, P2H=elec.boiler)
Peter Lund 2017
25%
55%
62% 10%0%
1%
Wind power share:
Technical simulation 1-hour steps over 1 yr; no overflow of power from the city
Self-use limit
power heat
yearly demand
Present
Effects on remaining power system
from VRE
Peter Lund 2017
A
Optimal and rule-based control strategies for
energy flexibility in buildings with PV (2)
Peter Lund 2017
• 8–88% decrease in electricity fed into the grid
• 13–25% savings in electricity bill with cost-optimal control (1h-based price)
Other findings with
improved flexibility
Peter Lund 2017
1. Reference: RE power limited to self-use of electricity
2. Power-to-Thermal (P2T) strategy: RE is oversized, surplus converted
into thermal energy (heat or/and cold)
RE of yearly electricity demand
1.RE coupled to power
system and limited to
self-use of power
2. RE coupled to both
power and thermal system
through P2H
Shanghai (China)
Solar PV
25% 54-58%
(+116-132%)
Helsinki (Finland)
Wind Power
25% 55-62%
(+120-148%)
Delhi (India)
Solar PV
22% 50-52%
(+127-136%)
Similar results for Conception (Chile) and Dhahran (Saudi-Arabia)
Social behaviour and decisions
• Consumer interface and decisions (e.g. Daniel Kahneman)
Peter Lund 2017
Peter Lund 2017
Analyzing the diffusion equation
Importance of parameter β [%/year]
• β = adoption rate or penetration rate of the new technology
• Steepness of the penetration depends on the β; affected by attributes of innovation
(e.g. price), type of decision (e.g. collective or authority), communication channel
(e.g. media), social system (e.g. norms), promotion efforts
What else can we see from
the diffusion curve?
• Denote α= βt0+ln (a0) 
• Inflexion point, maximum at t= α/β (f=50%)
• Relative market growth (%/yr)
Year-to-year growth starts to decline
when market share grows !
)(
0
0
1
1
)( tt
ea
tf −⋅−
⋅+
= β
S-curve
How does ‘price’ influence market
penetration of energy technologies ?
Peter Lund 2017
• Binary choice model
• Growth mainly self-financed
• Influence of support
E.g. at low market share, Y2Y growth
of a new technology:
dVi /Vi ≈ [a1 +a2] × Cold/Cnew
Vi =volume or capacity
C =cost of technology
a1= yearly growth of power demand
a2= replacement rate of old capacity
Model verification

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Integration of energy efficiency and renewable energy - multiple benefits!

  • 1. Integration of energy efficiency and renewable energy - multiple benefits! Prof. Peter D. Lund Aalto University, School of Science Espoo-Otaniemi, Finland peter.lund@aalto.fi 23 March 2017
  • 2. Outline of the lecture Research results based on following journal papers: [send an email to peter.lund@aalto.fi if you want a copy of the papers] 1. Salpakari, P. Lund. Optimal and rule-based control strategies for energy flexibility in buildings with PV. Applied Energy 161 (2016) 425-43. 2. J.Salpakari, J. Mikkola, P.D. Lund. Improved integration of large-scale variable renewable power in cities through optimal control of DSM and power-to-heat measures. Energy Conversion and Management 126 (2016)649-661. 3. Peter Lund. Market penetration rates of new energy technologies. Energy Policy 34 (2006), 3317-3326. 4. Peter D. Lund. Energy policy planning near grid parity using a price-driven technology penetration model. Technological Forecasting & Social Change 90 (2015) 389-399. Peter Lund 2017 Main contents: ①Enabling large scale local renewable power use through better integration and flexibility ②Market take-up and adoption of these new technologies
  • 3. Forthcoming energy transition Peter Lund 2017 http://www.shell.com/global/future- energy/scenarios/new-lens-scenarios.html • Fossil fuels : Today >80%; 22% by 2100 of energy • Electricity important : future power supply > power demand ? IEA scenario (2015)
  • 4. Impacts from much variable renewable electricity (VRE) Peter Lund 2017 No VRE Much VRE
  • 5. Renewables & energy efficiency Relevance of EE to large-scale RE schemes: ① Reduces resource requirement (‘less needed’) ② Improves matching of RE (‘more flexibility’) ③ Enables optimizing of RE (‘ better use’) ④ Sectorial integration possible (‘close to end-use’) Link between energy efficiency (EE) and renewable energy/electricity (RE) increases towards the end-use: ‘supranational’  national urban (cities) homeowner (building) Peter Lund 2017
  • 6. Flexibility approaches for the energy system transformation Peter Lund 2017
  • 7. Cost & magnitude of flexibility Peter Lund 2017 Ref: Energy Innovation, 2015
  • 8. Power-to-X (P2X) conversion for increased flexibility Peter Lund 2017 Oil Coal Peat Natural gas Biomass Waste-to- energy Nuclear Hydro Wind Solar power Heat pumps Imports Electricity Heat Fuel Electricity pool Heat pool Fuel pool House- holds Services Transport Industry PRIMARY ENERGY NEW FINAL ENERGY OLD FINAL ENERGY (BALANCE NODES) ADVANCED CONVERSION CONVENTIONAL CONVERSION DEMAND Unconverted CHP District heating CHP Industrial Separate heat production Separate electricity production Residential heat production Oil refineries P2H elecheat P2C eleccold P2G elecgas P2L gasbiofuel Biofuel biomassbio -fuel Electricity and heat storage 1 2 ENERGY SERVICES
  • 9. Curtailment for increased system flexibility with RE power Peter Lund 2017 • Curtailment = Cutting off • Energy lost with curtailment = capacity factor (RE≈8-40%) × curtailment level × curtailment time • Utilization= curtailed RE for P2X, EV & battery charging, etc. • Advantage = Sizing of RE >> Self- use limit of power (as RE surplus can be curtailed) • Active curtailment= RE power could provide very fast power ramp- up and ramp-down
  • 10. • Power-to-thermal: surplus or curtailed RE converted to thermal energy; P2H=heat • Heat (resistance, heat pump) or cooling (refrigeration cycle)  η (resistance) ≈100%  COP (heat pump) ≈300% Power-to-thermal strategy • Coupled to thermal demand/storage • The building could also function as ’thermal’ storage
  • 11. Rationale of P2H (Power-to-Heat) EU-27 household final energy 67% 15% 14% 4% Space heating Appl&Light Hot water Cooking 1. Thermal energy (heat, cooling) dominate final energy use in built environment • >50% of final energy use in cities • Up to 80% of EU-27 household final energy 2. With a high RE share of power, marginal value of electricity < marginal value of heat 3. Thermal storage is proven and cheap (~$5- 25/kWh), from short-term small size to long-term large-size (max. unit ~1-2GWh, 100-200 MW), from centralized to decentralized schemes 4. P2H decreases price volatility at high RE shares and allows to integrate more RE Peter Lund 2017
  • 12. Case 1. Large wind scheme with P2H for urban use: Case Helsinki Peter Lund 2017 Power and heat demand & plants in Helsinki 1GWel ;1.3GWth,CHP ; 2.0GWth,peak (coal, gas); district heating Big wind scheme:
  • 13. Results: cross-sectoral integration 2. Wind with P2H ≤ Power + Heat demand 1349 MW wind power = 60% of electricity per year (2% of heat)Ref: Lund, P. : Large-scale urban renewable electricity schemes - integration and interfacing aspects. Energy Conversion and Management, 2012 1. Wind ≤ Power demand  max. 486 MW wind power = 20-25% % of yearly electricity in Helsinki Peter Lund 2017 1349 MW 486 MW 1 2 (’worst day’ Feb 6) Wind power Heat Elec (1 year)
  • 14. Case 2: Improved flexibility through DSM + P2H + Storage Peter Lund 2017 • Helsinki case as above, but in addition:  Solar + Wind  DSM+Storage • Control strategies for flexibility: a) load and supply matching b) link to electricity market + investments
  • 15. Fig Electricity load in Helsinki with shiftable components (DSM). The duration that a load can shift its consumption is indicated in the legend Improved flexibility with large-scale variable renewable power in cities through optimal demand side management and power-to-heat conversion Energy Conversion and Management, Volume 126, 2016, 649–661 http://dx.doi.org/10.1016/j.enconman.2016.08.041 Shiftable loads 35-350 MW, or 7-50% of hourly power demand Power profile + shiftable loads Peter Lund 2017 Electricity demand
  • 16. http://dx.doiorg/10.1016/j.enconman.2016.08.041 Surplus VRE production Peter Lund 2017 • DSM enables more VRE (wind and PV) • P2H very effective (cross-sectorial integration to increase flexibility) Improved integration due to DSM Baseline (topmost surface) No surplus (VRE<Load) Improved integration due to P2H
  • 17. http://dx.doi.org/10.1016/j.enconman.2016.08.041 Cash-flow when linked to spot electricity market Peter Lund 2017 Baseline 1 2 3 4
  • 18. Case 3: Flexibility in 1 building + PV Peter Lund 2017 • Same as above, but 1 house+PV • Optimization: minimize variable costs & maximize self-use of PV • 13–25% savings in electricity bill with cost-optimal control (1h-based price) • 8–88% decrease in electricity fed into the grid
  • 19. Peter Lund 2017 Market take-up of new technologies (diffusion) ”Diffusion is a process in which the innovation is distributed to members of the social system through different channels having different threshold for adoption of new innovations” (Rogers) • Key elements of diffusion of innovations – Innovation; Communication channel; Time; Social system; Adopters • The diffusion process explains the penetration of a new technology to the market over time time Innovation Communication channels Social system
  • 20. Peter Lund 2017 Decision making process linked to technology diffusion or adoption Knowledge Communication channels Diffusion of innovation Social system Previous experience Needs/problems Norms of the society Degree of innovation Personal character: Social status Personality Communication behaviour Innovation characteristics: Compatibility with values Advantages? Prev. experiences,needs? How complex to use? How easy to try? Visibility? Accept or Reject Persuasion Decision Realization Verification
  • 21. Peter Lund 2017 Diffusion Model )0( )0(1 0 f f a − = )( 0 0 1 1 )( tt ea tf −⋅− ⋅+ = β Classical diffusion equation also so-called epidemic model (f=market share, β=adoption rate, t=time) Bass model: influence of internal (q) and external (p) information Other models: Gompertz, Mansfield, Nonsymmetric models Diffusion equation/model describes the adoption of the new technology over time, e.g. change of the market share
  • 22. Peter Lund 2017 Analyzing the diffusion equation Importance of parameter β [%/year] • β = adoption rate or penetration rate of the new technology • Steepness of the penetration depends on the β; affected by attributes of innovation (e.g. price), type of decision (e.g. collective or authority), communication channel (e.g. media), social system (e.g. norms), promotion efforts )( 0 0 1 1 )( tt ea tf −⋅− ⋅+ = βS-curve )0( )0(1 0 f f a − =
  • 23. Results from diffusion models Peter Lund 2017 Effectiveness of policy measures in transforming the energy system. Energy Policy 35 (2007) 627-639 Market penetration rates of new energy technologies. Energy Policy 34 (2006), 3317-3326
  • 24. Peter Lund 2017 Modelling diffusion of innovations and decision making with two choices • Binary choice model (BCM) describes the choice between technologies A and B (e.g. substitution of old with new) • Probability to purchase the new product A is P (logit probability); C=price=direct cost + other costs (e.g. behavioral factors, inconvenience costs) σ=arb. parameter; • BCM could be extended to other factors as well; replace C with a vector of factors 0 % 20 % 40 % 60 % 80 % 100 % -50 -30 -10 10 30 50 Probabilityofpreferences Price difference (€/MWh) Technology A Technology B B cheaper than A A cheaper than B
  • 25. Importance of financial support to market penetration and shares Peter Lund 2017 1. Price affects market penetration (both potential and decisions) 2. Above grid parity (old cheaper than new), fast penetration requires “over-subsidization” 3. At grid-parity (new≈old), support necessary to gain a market share 4. Clearly below grid-parity (new cheaper than old) no support 5. Dynamic energy policy support important, i.e. adjusting the support levels over time as new technology gets cheaper Energy policy planning near grid parity using a price- driven technology penetration model. Technological Forecasting & Social Change 90(2015)389-399. 0,0 % 0,5 % 1,0 % 1,5 % 2,0 % 0,01 % 0,10 % 1,00 % 10,00 % Growthinmakertshare(dfi/yr) Market share (fi) GLO Nuclear 1966-2011 GLO PV 1978-2012 GLO Wind 1982-2012 GER Wind 1990-2012 GER PV 1990-2012 USA NG 1994-2011 USA NG 5-year avg Price ratio: 0.1 Price ratio: 0.2 Price ratio: 0.3 Price ratio: 0.5
  • 27. Example: Curtailing solar power in Finland 0% 20% 40% 60% 80% 100% 0% 50% 100% Reductioninsolaryield Power cut-off limit (% of nominal PV power installed) Peter Lund 2017
  • 28. Helsinki Wind+CHP+DH base case (simple integration, P2H=elec.boiler) Peter Lund 2017 25% 55% 62% 10%0% 1% Wind power share: Technical simulation 1-hour steps over 1 yr; no overflow of power from the city Self-use limit power heat yearly demand Present
  • 29. Effects on remaining power system from VRE Peter Lund 2017 A
  • 30. Optimal and rule-based control strategies for energy flexibility in buildings with PV (2) Peter Lund 2017 • 8–88% decrease in electricity fed into the grid • 13–25% savings in electricity bill with cost-optimal control (1h-based price)
  • 31. Other findings with improved flexibility Peter Lund 2017 1. Reference: RE power limited to self-use of electricity 2. Power-to-Thermal (P2T) strategy: RE is oversized, surplus converted into thermal energy (heat or/and cold) RE of yearly electricity demand 1.RE coupled to power system and limited to self-use of power 2. RE coupled to both power and thermal system through P2H Shanghai (China) Solar PV 25% 54-58% (+116-132%) Helsinki (Finland) Wind Power 25% 55-62% (+120-148%) Delhi (India) Solar PV 22% 50-52% (+127-136%) Similar results for Conception (Chile) and Dhahran (Saudi-Arabia)
  • 32. Social behaviour and decisions • Consumer interface and decisions (e.g. Daniel Kahneman) Peter Lund 2017
  • 33. Peter Lund 2017 Analyzing the diffusion equation Importance of parameter β [%/year] • β = adoption rate or penetration rate of the new technology • Steepness of the penetration depends on the β; affected by attributes of innovation (e.g. price), type of decision (e.g. collective or authority), communication channel (e.g. media), social system (e.g. norms), promotion efforts What else can we see from the diffusion curve? • Denote α= βt0+ln (a0)  • Inflexion point, maximum at t= α/β (f=50%) • Relative market growth (%/yr) Year-to-year growth starts to decline when market share grows ! )( 0 0 1 1 )( tt ea tf −⋅− ⋅+ = β S-curve
  • 34. How does ‘price’ influence market penetration of energy technologies ? Peter Lund 2017 • Binary choice model • Growth mainly self-financed • Influence of support E.g. at low market share, Y2Y growth of a new technology: dVi /Vi ≈ [a1 +a2] × Cold/Cnew Vi =volume or capacity C =cost of technology a1= yearly growth of power demand a2= replacement rate of old capacity Model verification