Demand Flexibility and Demand Response

Athanasios Papakonstantinou athpapa@elektro.dtu.dk - 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