Demand Flexibility and Demand Response · Price Elasticity and Electricity • Load elasticity...
Transcript of Demand Flexibility and Demand Response · Price Elasticity and Electricity • Load elasticity...
Demand Flexibility and Demand Response
Athanasios Papakonstantinou [email protected] - www.athpap.net
Special group course
Overview of the Lecture
1. Part A: Demand flexibility • Flexible demand , from inelastic to elastic demand • Recap : Stochastic optimization • A “first” two-stage stochastic programming model • A second model : multi period formulation • A third model : flexible demand and more
2. Part B: Demand response
• Basic economic definitions • Discussion on Demand Response • Price elasticity and cross price elasticity • Case studies on DR with cross price elasticity
Break
Lecture Agenda
15 MWh
2 €/MWh 50 MWh
70 €/MWh
80 MWh
45 €/MWh
120 MWh
20 €/MWh
70 MWh
25 €/MWh
Lecture Agenda
Lecture Agenda
Part A: Lecture key points
Two-stage Stochastic programming
How does it work ? – is it “reasonable” ?
Formulation of Multi-period problem
Demand Elasticity : step function
Demand Flexibility
Sources of flexibility : storage, heating, EVs, transmission Lack of flexibility : Wind curtailment WHY? Discussion on supply flexibility has reached its limit WHY? Demand flexibility under-utilised (tons of potential) WHY?
80 MWh
60 €/MWh
50 MWh
20 €/MWh
60 MWh
40 €/MWh
Inelastic Demand
CPH CHP
Amager Wind
Swedish Water
Megaton Nuclear
Stephens Colliery
Norwegian Gas
North Sea Oil
Price in EUR/MWh
Production in MWh
30 MWh
5 €/MWh
100 MWh
6 €/MWh
40 MWh
15 €/MWh
10 MWh, 0.5
15 MWh, 0.3
5 MWh, 0.2
0 €/MWh
Bid: 10.5 MWh
Demand : 260.5 MWh Market clearing : 40 €/MWh
30 MWh
* partially cleared price setter
NordPool Elspot bids
1. Hourly Bids (most common): – Price independent : buy / sell always at any price – Price dependent: Up to 64 intervals – stepwise functions
1. Blocks:
– Buy or sell at a fixed price-volume for successive hours – Accept / reject the whole block (with minor exceptions for
volunteers and for minimum 4 hrs)
2. Flexible Hourly: Big consumers “sell” back
Trade at the Nordic Spot Market (2004) Nord Pool AS
Two-stage stochastic programming
• Day-ahead dispatch improved based on its impact on real-time balancing
• Balancing scenarios drawn from prob. Estimates
• Coupling of trading floors:
min day-ahead costs + E[balancing costs] subject to
Day-ahead market constraints: − Power balance in day-ahead stage − Bounds in energy offers
Operation constraints − Power balance at the balancing stage − Network constraints (if applicable) − Non-negativity
Two-stage stochastic programming
Day-ahead constraints
Operation constraints
Min day-ahead costs + E[balancing costs]
Power balance dual variable
Power balance dual variables
Dual variable of each scenario : real-time revenues on expectation
Single period - inelastic demand
Problem #1: Formulation
Operation constraints 1e-1m Day-ahead constraints 1a-1d
Variables:
1 Win power plant
1 Conventional plant Can provide flexibility
2 Conventional plants Do not provide flexibility
Demand: 170 MW
Problem #1: An example
flexible - inflexible
Problem #1: An example
Scenario Low : p = 0.4, 10 MW
Scenario High : p = 0.6, 50 MW
34 MWh
0 EUR/MWh
110 MWh,
30 EUR/MWh
50 MWh
10 EUR/MWh
* 86 MWh cleared price setter
Note: Conventional day-ahead
Inelastic demand: 170 MW
Operation costs?
10 MWh
0 EUR/MWh
70 MWh,
30 EUR/MWh
50 MWh
10 EUR/MWh
Day-ahead schedule
Problem #1: Solution
Inelastic demand: 170 MW
40 MWh,
35 EUR/MWh
*
10 MWh from wind
G1 exp & flex scheduled in case scenario High happens But G2 is cheaper [ ???]
No merit order !!!
Problem #1: Solution
*
Day-ahead scheduled based on exp. real-time outcomes
Point in coupling of trading floors i.e. total costs count
DA price = 30 EUR G1 bid (gen. cost) 35 EUR
But !!! Low operation costs !!!
Scenario Low : p = 0.4, 10 MW
Scenario High : p = 0.6, 50 MW
Bid 10 MWh Balance
Surplus: 40 MWh
Problem #1: Solution Real-time expected dispatch
Low : Nothing happens
High: Buy 40 MWh of down-regulation
Flexibility induces risk Check that Down Reg = 40 MWh
Another issue : LMPs and duals γ / p
Low : 14.6 / 0.4 = 36.5 High : 15.4 / 0.6 = 25.67
These prices do not represent physical characteristics of PES
Problem #2: Formulation
Day-ahead constraints
Operation constraints
Multi period – inelastic demand
Min Σ day-ahead costs & reserve + ΣE[balancing costs]
Problem #2: An example
Problem #2: An example
Problem #2: Solution
*
Problem #2: Solution
Wind Spillage
$
Multi period – elastic demand
Problem #3: Formulation
Min Σday-ahead costs & reserve+ ΣE[balancing costs] - Σday-
ahead flex demand utilities + ΣE[balancing flex demand]
More notation :
down / up regulation consumption :
down reg: surplus in supply – load increase up reg: deficit in supply – load curtailment
consumers
: utilities (reverse cost)
Multi period – elastic demand
Problem #3: Formulation
Day-ahead constraints
Operation constraints
Add to day-ahead constraint (a) for l consumers:
Add to balancing constraint (e)
for l consumers
Load balance Load regulation
+
Multi period - inelastic demand
Problem #3: Formulation
Load balance
Load regulation
definition of flex demand per scenario
the maximum load increase and drop rates (eq. ramping constraints)
change in scheduled load (day-ahead) bound by max and min demand levels
Part A: Lecture key points
Definitions: Elasticity / cross price elasticity
Demand Response : Useful or not?
DR and electricity markets
Impact of DR
Demand Response
Demand response : natural extension of demand flexibility (aspect of demand side management – other examples? )
Smart meters : allow real-time billing
Benefits of demand response: • Increase economic efficiency • Decongests networks (alleviates costly investment) • Support renewables sources of energy
Denmark: Support RES
Supply consistently exceeds demand DR : shifts load to bridge supply – demand gaps
Load and wind generation on 2014 Xmas week [Larsen, E. PhD Thesis]
Types of Demand Response
1. Volume based contracts : constrain electrical consumption • Static : cap on consumption complex: consumer must be aware of consumption profiles loss of autonomy / privacy (disclose consumption habits) • Dynamic : hourly caps on consumption Additional burden on complexity / lack of privacy Higher reward
2. Price based contracts : price triggers changes in consumption • Static : fixed tariffs for specific periods e.g. night electricity simple, consumer in control, no privacy issues, low risk/reward • Dynamic : hourly tariffs depending on wholesale prices complex, no privacy issues (automated), higher risk/reward
Types of Demand Response
3. Direct load control : • Consumer cedes control of specific appliances to a third party
Appliances turn on / off remotely • No price risk / no volume risk • Complete lack of autonomy and privacy Disclose information on specific appliances • Variable rewards depending on control Buzzword : prosumer
4. Indirect load control • Price based (more privacy – more risk)
Source and more information
Important Definitions
1. Price Elasticity: defines a load’s sensitivity on price changes e.g. a small increase on the price will lower demand. But how much?
Elastic demand : % in price results in larger % change in demand Inelastic demand : (the opposite)
Negative elasticity : the more expensive the product the lower the demand – what about positive elasticity? Alternative name: own-elasticity WHY?
price demand
Ratio of the relative change in demand to the relative change in price
Important Definitions
2. Cross-price Elasticity (in economics) : the % increase in
demand in item i is a result in % increase in price of j e.g. the elasticity of the demand of coffee would be smaller if there was tea shortage (people will by coffee even if its expensive if there is not tea)
3. Complementary vs substitute items: price for one
commodity increases, demand for both drops (negative cross elasticity) vs the opposite e.g. printers and ink cartridges vs coffee and tea
Demand Response : Does it make sense?
Hints: price elasticity in electricity Consumption patterns
Discussion: Demand Response
Price Elasticity and Electricity
• Price Elasticity in Electricity, does it really exist? Economists may argue against it [1]
• Engineers think otherwise - case studies: 1. EcoGrid EU 2. Impact on investment
• Short term vs long term e.g. consumers’ choice and electric heating* now vs district heating in the future * positive elasticity and DR
• Advances in technology (smart meters) [1] The real-time price elasticity of electricity
Price Elasticity and Electricity
• Load elasticity ratio : 1/price elasticity
: ratio of price to demand response
• Cross-price elasticity in the context of electricity market: how sensitive demand is in price changes before or after a fixed point
e.g. if there is (forecasted) high price in 17:00 – 18:00, consumption will react before and after that period
: demand response (DR)
Case study #1: EcoGrid EU
Source: Ecogrid – Overall Evaluation and Conclusion
Case study #1: EcoGrid EU
Bornholm island : connected to DK2 28,000 customers EcoGrid test: price-responsive control 1950+ test installations
Consumption profile
• Thermal modelling of a house: comfort levels, heat, insulation
• Controlled appliances : heat pumps etc
Formulation of the optimization problem:
Day-ahead market
max customer utility – generation cost
Case study #1: EcoGrid EU
Reservation price : highest supply bid in the market
Formulation of the optimization problem:
Real-time market
max customer utility – generation cost
Case study #1: EcoGrid EU
Imbalance
Formulation of the optimization problem
Infeasibility issues in the conventional setup Supply and demand profiles cannot be met
Introduce further constraints to make model more realistic:
• Multi-period setup • Supply: Ramping constraints, on-off schedule, specific
generation (i.e. thermal) • Demand: Inter-temporal parameters (i.e. flexibility)
New constraints : MILP (mixed integer LP) / MIQCP (mixed integer quadratic constraint programming)
Case study #1: EcoGrid EU
Adjusting real-time market to include cross-elasticity:
Case study #1: EcoGrid EU
cross-elasticity matrix replaces single dimensional a
Cross elasticity captures inter-temporal constraints Increases social welfare + “checks and balances” Parameters theta and alpha:
θ : Finite Impulse Response (shifts in thermostatic load)
α : cross elasticity matrix
Case study #1: EcoGrid EU
Case study #1: EcoGrid EU
Source: DR in a market environment Emil Larsen PhD Thesis
Case study #2: Investment Planning
Basic model in long-term investment planning
Generation constraints
Min Σ investment costs + ΣΣt generation cost + Σt wind curtailment cost
• Balancing constraint : Supply = demand • Generation up to capacity • Imbalances (up – down regulation) ~ wind • Storage (pumped hydro) • Maintenance off-time • Technical constraints (ramp time/rates, on-
off etc • Export / import
Source: De Jonghe et al, Optimal Generation Mix With Short-Term Demand Response and Wind Penetration
Case study #2: Investment Planning
• Time delay (lag) in consumption e.g. fridges, washing machines
• Hourly reaction to price signals
• Basic model fails to incorporate DR : minimizing costs is too simple (i.e. benefit of consumption ?)
• New model : Minimizing the cost of meeting a particular demand (in the given time period) while accounting for demand response to prices
… s.t. max of social welfare (market clearing)
Case study #2: Investment Planning
Key is the replacement of demand in balancing constraint : Complementarity program model structure
Max supply and demand surpluses
Suppliers and consumers maximize their profits s.t …
Case study #2: Investment Planning
• Complementarity model solves a system of constraints incl. market participants 1st order optimality conditions (KKTs)
Historical wind data from Denmark
4h time windows
Consumers foreknowledge of hourly prices
Filling the gaps and “shaving” the peaks is DR
DTU Findit
For additional reading
• Material in Chapter 5
• “Sources” and references in slides