Day-ahead electricity markets - Pierre Pinson\Day-ahead electricity markets" Pierre Pinson Technical...

$: Day-ahead electricity markets - Pierre Pinson\Day-ahead electricity markets" Pierre Pinson Technical University of Denmark. DTU Electrical Engineering - Centre for Electric Power and$
“Day-ahead electricity markets”

Pierre Pinson

Technical University of Denmark.

DTU Electrical Engineering - Centre for Electric Power and Energymail: [email protected] - webpage: www.pierrepinson.com

29 January 2018

31761 - Renewables in Electricity Markets 1

[email protected]

www.pierrepinson.com

As part of the overall context...

By the way... why is this called a day-ahead market?


Learning objectives

Through this lecture and additional study material, it is aimed for the students to be ableto:

1 Describe an electricity pool and its auction mechanism

2 Model and solve day-ahead market clearing

3 Understand differences between zonal and nodal pricing

4 Calculate revenues and payments of market players under different settlementmethods


Outline

1 Different types of electricity exchanges

bilateral contractsauctionsmarket-clearing algorithms

2 Network effects

zonal pricingsplitting and difference between system and area priceextension to nodal pricing

3 Different types of market products

in theoryin practice


1 Different types of electricity exchanges


Bilateral contracts

Bilateral contracts are for a direct exchange of power between a buyer and a seller

They may both be producers and/or consumers

Most likely a broker is involved...

Eventually, the system operator is informed about the trades that occurred


Types of bilateral trading

Customized long-term contracts:

very flexible contracts (basically, you can try to negotiate whatever you want)private transactions (conditions are fully unknown to others)large transactions costslarge amounts of energy, over long periods of times

Over the counter (OTC) trading:

standard contractslower transactions coststypically, smaller amount and short lead times

[Note: To be discussed further in Lecture 2 when introducing intra-day markets]

Electronic trading (already leaning towards the pool concept...):

Based on electronic platform that consistently match supply and offer bidsvirtually no transactions costsvery fast, therefore allowing trading “until the last second”

[Note: To be discussed further in Lecture 5 when introducing intra-day markets]


http://pierrepinson.com/31761/Lectures/31761-lecture2.pdf

http://pierrepinson.com/31761/Lectures/31761-lecture5.pdf

Placing it into perspective...

Bilateral trading may be interesting...

but the pool provides a much more centralized form of system management,which seems to be increasingly preferred in Europe for day-ahead markets.

Example:

Nord Pool Spot is the Europe’s largest power market

505 TWh of energy traded in 2016

Nordic and Baltic day-ahead auction Elspot represents 391 TWh of energy traded

Average system price of 26.91e

In Elspot: 380 buyers/sellers - >2000 orders a day

Let us focus on pools and auctions for now...


Auctions in an electricity pool

All generation bids and consumptionoffers are placed at the same time

No-one knows about others’ bids andoffers

A centralized market-clearing algorithmdecides about bids and offers that areretained

Eventually, the system operator isinformed about the trades that occurred


An example auction setup

Deadline for offers: 29th of January, 12:00 - Delivery period: 30th of January,11:00-12:00

Supply and demand offers include:

Demand: (for a total of 1065 MWh)

Company Supply/Demand id Amount (MWh) Price (e/MWh)CleanRetail Demand D1 250 200

El4You Demand D2 300 110EVcharge Demand D3 120 100QualiWatt Demand D4 80 90IntelliWatt Demand D5 40 85

El4You Demand D6 70 75CleanRetail Demand D7 60 65IntelliWatt Demand D8 45 40QualiWatt Demand D9 30 38IntelliWatt Demand D10 35 31CleanRetail Demand D11 25 24

El4You Demand D12 10 16


An example auction setup

Supply: (for a total of 1435 MWh)

Company Supply/Demand id Amount (MWh) Price (e/MWh)RT R© Supply G1 120 0

WeTrustInWind Supply G2 50 0BlueHydro Supply G3 200 15

RT R© Supply G4 400 30KøbenhavnCHP Supply G5 60 32.5KøbenhavnCHP Supply G6 50 34KøbenhavnCHP Supply G7 60 36

DirtyPower Supply G8 100 37.5DirtyPower Supply G9 70 39DirtyPower Supply G10 50 40

RT R© Supply G11 70 60RT R© Supply G12 45 70

SafePeak Supply G13 50 100SafePeak Supply G14 60 150SafePeak Supply G15 50 200

That is a lot of offers to match... but how?


Merit order and equilibrium

Consumption offers are ranked indecreasing price order

Supply offers are ranked inincreasing price order

This defines the merit order

A “magic” point appears: theequilibrium point between supplyand demand...

quantity [MWh]

pric

e [E

uros

/MW

h]

0 500 1000 1500

050

100

150

200

demand

supply


Social welfare and its maximization

Social welfare is defined as the areabetween consumption andgeneration

The equilibrium point is that whichallows to maximize social welfare

Why?

Any buyer is to pay at mostwhat he was ready to pay

Any seller will get at minimumthe price he was ready to sell for

quantity [MWh]

pric

e [E

uros

/MW

h]

social welfare

0 500 1000 1500

050

100

150

200


As an optimization problem

On the supply side:

Set of offers: LG = {Gi , i = 1, . . . ,NG}Maximum quantity for offer Gi : PG

i

Price for offer Gi : λGi

Generation level to optimize social welfare: {yGi , i = 1, . . . ,NG}, 0 ≤ yG

i ≤ PGi

On the demand side:

Set of offers: LD = {Di , i = 1, . . . ,ND}Maximum quantity for offer Di : PD

i

Price for offer Di : λDi

Consumption level optimizing social welfare: {yDi , i = 1, . . . ,ND}, 0 ≤ yD

i ≤ PDi

The social welfare maximization problem can be written as:

max{yDi },{y

Gj }

∑i

λDi y

Di −

∑j

λGj y

Gj

subject to∑j

yGj −

∑i

yDi = 0

0 ≤ yDi ≤ PD

i , i = 1, . . . ,ND

0 ≤ yGj ≤ PG

j , j = 1, . . . ,NG31761 - Renewables in Electricity Markets 14

It is a simple linear program!

One recognize a so-called Linear Program (LP, here in a compact form):

miny

c>y

subject to Ay ≤ b

Aeqy = beq

y ≥ 0

[Note: any such optimization problem can be written as a maximization or minimization problem]

LP problems can be readily solved in

Matlab, for instance with the function linprog,R, with the library/function lp solve,and also obviously in GAMS

But, for e.g. R and Matlab, you need to know how to build relevant vectors andmatrices

And, the solution y∗ will only give you the list of offers (supply and demand)accepted...


Vector and matrices in the objective function

The vector y of optimization variables c of weights in the objective function areconstructed as

y =

yG1

yG2

...yGNG

yD1

yD2

...yDND

, y ∈ R(NG +ND ) c =

λG1

λG2

...λGNG

−λD1

−λD2

...−λD

ND

, c ∈ R(NG +ND )


Vector and matrices defining constraints

For the equality constraint (balance of generation and consumption):

Aeq = [1 . . . 1 − 1 . . . − 1] , Aeq ∈ R(NG +ND ) , beq = 0

For the inequality constraint (i.e., generation and consumption levels within limits):

A =

1. . . 0

11

0. . .

1

, b =

PG1

PG2

...PGNG

PD1

PD2

...PDND

,

with A ∈ R(NG +ND )×(NG +ND ) and b ∈ R(NG +ND )

Do not forget the non-negativity constraints for the elements of y...


Getting the complete market-clearing

By complete market-clearing is meant obtaining

list of offers (supply and demand) accepted and their level, as well as

the price at which the market is cleared, i.e., the so-called market-clearing or systemprice (in, e.g., Nord Pool)

The system price is obtained through the dual of the LP defined before:

maxλ,ν

− b>ν

subject to A>eqλ− A>ν ≤ c

ν ≥ 0

This is also an LP: it can be solved with Matlab, R, GAMS, etc.

λ and ν are sets of Lagrange multipliers associated to all equality and inequalityconstraints:

λ = λS

ν = [νG1 . . . νGNGνD1 . . . νDND

]>

[Note: basics of optimization for application in electricity markets are given in:

JM Morales, A Conejo, H Madsen, P Pinson, M Zugno (2014). Integration Renewables in Electricity Markets: Operational Problems. Springer (link)]


http://pierrepinson.com/31761/Literature/reninmarkets-appB.pdf

More specifically for the market-clearing problem

Only one equality constraint:

∑i

yDi −

∑j

yGj = 0

for which the associated Lagrange multiplier λS represents the system price

And ND + NG inequality constraints:

0 ≤ yDi ≤ PD

i , i = 1, . . . ,ND , 0 ≤ yGj ≤ PG

j , j = 1, . . . ,NG

for which the associated Lagrange multipliers νDi and νGj represents the unitary benefits for the

various demand and supply offers if the market is cleared at λS

The resulting LP writes:

maxλS ,{νDi },{ν

Gj }

−∑j

νGj PGj −

∑i

νDi PDi

subject to λS − νGj ≤ λGj , j = 1, . . . ,NG

− λS − νDi ≤ −λDi , i = 1, . . . ,ND

νGj ≥ 0, j = 1, . . . ,NG , νDi ≥ 0, i = 1, . . . ,ND

[To retrieve the dual LP, one may want to follow the steps described in: S Lahaie (2008) How to take the Dual of a Linear Program. (link)]


http://pierrepinson.com/31761/Literature/lahaie2008-lpprimer.pdf

Let’s also write it as a compact linear program!

As for the primal LP allowing to obtain the dispatch for market participants on bothsupply and demand side, we write here the dual LP in a compact form:

maxy

c>y

subject to Ay ≤ b

y ≥ 0

The next 2 slides describe how to build the assemble the relevant vectors andmatrices in the above LP...

Then, it can be solved with Matlab, R, GAMS, etc.

And, the solution y∗ will give you the unit benefits for each and every marketparticipant, as well as the equilibrium price...

[NB: Most optimization functions and tools readily give you the solution of dual problemswhen solving the primal ones! E.g., see documentation of linprog in Matlab]


Vector and matrices in the objective function

The vector y of optimization variables c of weights in the objective function areconstructed as

y =

νG1νG2...νGNG

νD1νD2...νDND

λS

, y ∈ R(NG +ND+1) c =

−PG1

−PG2

...−PG

NG

−PD1

−PD2

...−PD

ND

0

, c ∈ R(NG +ND+1)


Vector and matrices defining constraints

No equality constraint!

For the inequality constraint:

A =

−1 1. . . 0

...−1 1

−1 −1

0. . .

...−1 −1

, b =

λG1

λG2

...λGNG

−λD1

−λD2

...−λD

ND

,

with A ∈ R(NG +ND )×(NG +ND ) and b ∈ R(NG +ND )


Application to our simple auction example

Solving the primal LP for selecting the supply and demand offers yields:

Total Energy: 995 MWhSupply side - accepted: {G1, . . . ,G8} (but only 55 MWh for G8)Supply side - rejected: {G9, . . . ,G15}Demand side - accepted: {D1, . . . ,D9}Demand side - rejected: {D10, . . . ,D12}

Solving the dual LP gives:

the system price: 37.5 e/MWhUnitary benefits on the demand and supply sides:

Supply id. Unitary benefit (e/MWh) Demand id. Unitary benefit (e/MWh)G1 37.5 D1 162.5G2 37.5 D2 72.5G3 22.5 D3 62.5G4 7.5 D4 52.5G5 5 D5 47.5G6 3.5 D6 37.5G7 1.5 D7 27.5G8 0 D8 2.5

D9 0.5


Settlement process

After offers are selected and the system price determined, comes the settlementprocess...

In short:

who should pay what?

who should should get paid, and what amount?

Any opinion?


Settlement: pay-as-bid

The first settlement option is the so-called pay-as-bid one.

Method:

Consumption side: if λDi ≥ λS , consumer i pays λDi for any unit of energy to be

consumedSupply side: if λGj ≤ λ

S , supplier j is paid λDj for any unit of energy produced

Example (continued):

Consumption side:

D1 pays 250× 200 = 50.000eD2 pays 300× 110 = 33.000eD3 pays 120× 100 = 12.000e, etc.

Supply side:

G1 receives 120× 0 = 0e(!!)G2 receives 50× 0 = 0e(!!)G3 receives 200× 15 = 3.000e, etc.

Does that look like a good system?

Let’s play a game then... to show what can go wrong.


Settlement: pay-as-bid

The first settlement option is the so-called pay-as-bid one.

Method:

Consumption side: if λDi ≥ λS , consumer i pays λDi for any unit of energy to be


S , supplier j is paid λDj for any unit of energy produced


Consumption side:

D1 pays 250× 200 = 50.000eD2 pays 300× 110 = 33.000eD3 pays 120× 100 = 12.000e, etc.

Supply side:

G1 receives 120× 0 = 0e(!!)G2 receives 50× 0 = 0e(!!)G3 receives 200× 15 = 3.000e, etc.

Does that look like a good system?

Let’s play a game then... to show what can go wrong.31761 - Renewables in Electricity Markets 26

Settlement: uniform pricing

The second settlement option is the so-called uniform pricing one.

Method:

Consumption side: if λDi ≥ λS , consumer i pays λS for any unit of energy to be


S , supplier j is paid λS for any unit of energy produced


Consumption side:

D1 pays 250× 37.5 = 9.375eD2 pays 300× 37.5 = 11.250eD3 pays 120× 37.5 = 4.500e, etc.

Supply side:

G1 receives 120× 37.5 = 4.500e(!!)G2 receives 50× 37.5 = 1.875e(!!)G3 receives 200× 37.5 = 7.500e, etc.

Does that look like a better system?


2 Network effects


The transmission “problem”

Remember there is a network involved, and power has to flow...

This was not represented so far in our market description!


Approaches to representing network constraints

There are basically two philosophies, developed on both sides of the Atlantic:

USEurope

Europe US

System Operator TSO ISOMarket Operator Ind. Market Operator ISO

Offers Market products Unit capabilitiesClearing Supply-demand equilibrium UCED problem

Prices Zonal Nodal

TSO: Transmission System OperatorISO: Independent System OperatorUCED: Unit Commitment and Economic Dispatch


Illustration of Zonal and Nodal pricing

Scandinavia (Zonal):

Go visit: http://nordpoolgroup.com (marketdata, map)

Midwest US (Nodal):

Go visit: https://www.misoenergy.org


http://nordpoolgroup.com

https://www.misoenergy.org/markets-and-operations/real-time-displays

From system to area prices

Let us revisit our previous example,

considering two areas: DTU-West and DTU-Eastwith a transmission capacity of 40 MW

Demand: (for a total of 1065 MWh)

Company id Amount (MWh) Price (e/MWh) AreaCleanRetail D1 250 200 DTU-West

El4You D2 300 110 DTU-EastEVcharge D3 120 100 DTU-WestQualiWatt D4 80 90 DTU-EastIntelliWatt D5 40 85 DTU-West

El4You D6 70 75 DTU-WestCleanRetail D7 60 65 DTU-EastIntelliWatt D8 45 40 DTU-WestQualiWatt D9 30 38 DTU-WestIntelliWatt D10 35 31 DTU-EastCleanRetail D11 25 24 DTU-East

El4You D12 10 16 DTU-East


And supply...

Supply: (for a total of 1435 MWh)

Company id Amount (MWh) Price (e/MWh) AreaRT R© G1 120 0 DTU-West

WeTrustInWind G2 50 0 DTU-EastBlueHydro G3 200 15 DTU-West

RT R© G4 400 30 DTU-EastKøbenhavnCHP G5 60 32.5 DTU-WestKøbenhavnCHP G6 50 34 DTU-EastKøbenhavnCHP G7 60 36 DTU-West

DirtyPower G8 100 37.5 DTU-WestDirtyPower G9 70 39 DTU-WestDirtyPower G10 50 40 DTU-West

RT R© G11 70 60 DTU-EastRT R© G12 45 70 DTU-West

SafePeak G13 50 100 DTU-EastSafePeak G14 60 150 DTU-EastSafePeak G15 50 200 DTU-East


Localizing the previous market-clearing results

Following previous market clearing results, one obtains

DTU-West:

Supply side: {G1,G3,G5,G7,G8} (but only 55 MWh for G8) - Total: 495 MWhDemand side: {D1,D3,D5,D6,D8,D9} - Total: 555 MWh

→ Deficit of 60 MWh

DTU-East:

Supply side: {G2,G4,G6} - Total: 500 MWhDemand side: {D2,D4,D7} - Total: 440 MWh

→ Surplus of 60 MWh

BUT, only 40 MWh can flow through the interconnection!


Market split: Import-Export approach

Due to transmission constraints, the market has to split and becomes two markets

quantity [MWh]

pric

e [E

uros

/MW

h]

0 500 1000 1500

050

100

150

200

demand

supply

→

DTU-West

quantity [MWh]

pric

e [E

uros

/MW

h]

0 500

050

100

150

200

DTU-East

quantity [MWh]

pric

e [E

uros

/MW

h]

0 500

050

100

150

200

In practice:

2 market zones with their own supply-demand equilibriumextra (price-independent) consumption/generation offers representing the transmissionfrom one zone to the next to be added


Adding transmission-related offers

Extra supply in the high price area(40 MWh coming from DTU-East)

quantity [MWh]

pric

e [E

uros

/MW

h]

● ●

0 500

050

100

150

200

Extra consumption in the low pricearea (40 MWh for DTU-West)

quantity [MWh]

pric

e [E

uros

/MW

h]

● ●

0 500

050

100

150

200

Power ought to flow from a low price area to a high price area


Results for each zone

The same type of LP problems as introduced before is solved

for each zone individually,with the extra consumption/generation offers representing the amount of energytransmitted

That eventually yields

DTU-West:


→ Zonal price: 37.5 e

DTU-East:

Supply side: {G2,G4,G6} (but only 30 MWh for G6) - Total: 480 MWhDemand side: {D2,D4,D7} - Total: 440 MWh

→ Zonal price: 34 e

A few questions at this stage:

What is the impact on the settlement?Do you think it would generalize well for more than 2 zones?


Market split: Flow-based coupling

Instead of boldly splitting the market, one could instead acknowledge how powerflows...

our system with 2 zonescan be modelled as a 2-bussystem,

loads and generators areassociated to the relevantbus

DC power flow can beassumed to simplifythings...


Formulating the market clearing

The network-constrained social welfare maximization problem can be written as:

max{yDi },{y

Gi }

∑i

λDi y

Di −

∑j

λGj y

Gj

subject to∑i

yD,Westi −

∑j

yG ,Westj = B∆δ

∑i

yD,Easti −

∑j

yG ,Eastj = −B∆δ

0 ≤ yDi ≤ PD

i , i = 1, . . . ,ND

0 ≤ yGj ≤ PG

j , j = 1, . . . ,NG

− 40 ≤ B∆δ ≤ 40

where:

B is the absolute value of susceptance (physical constant) of the interconnection betweenDTU-West and DTU-East

∆δ is the difference of voltage angles between the 2 buses

→ B∆δ represents the signed power flow from DTU-West to DTU-East


Obtaining the zonal prices

As for the case of a single zone, the dual LP allows to obtains market-clearing prices

These 2 prices corresponds to the Lagrange multipliers for the 2 equality constraints(i.e., balance equations):

max{yDi },{y

Gi }

∑i

λDi y

Di −

∑j

λGj y

Gj

subject to∑i

yD,Westi −

∑j

yG ,Westj = B∆δ : λS,West

∑i

yD,Easti −

∑j

yG ,Eastj = −B∆δ : λS,East

0 ≤ yDi ≤ PD

i , i = 1, . . . ,ND

0 ≤ yGj ≤ PG

j , j = 1, . . . ,NG

− 40 ≤ B∆δ ≤ 40


Results for our auction example

For the 2 zones...

DTU-West:


→ Zonal price: 37.5 e

DTU-East:

Supply side: {G2,G4,G6} (but only 30 MWh for G6) - Total: 480 MWhDemand side: {D2,D4,D7} - Total: 440 MWh

→ Zonal price: 34 e

The dispatch and prices are the same as before, though...

one relies on a rigorous optimize problem that acknowledge how power flows on thenetwork,it should readily scale to more than 2 zones


Final extension to nodal pricing

In a US-like setup, each node of the power system is to be seen as an area...

For a system with K nodes, the network-constrained social welfare maximizationmarket-clearing writes:

max{yDi },{y

Gi }

∑i

λDi y

Di −

∑j

λGj y

Gj

subject to∑i

yD,ki −

∑j

yG ,kj =

∑l∈Lk

Bkl(δk − δl), k = 1, . . . ,K : λS,k

0 ≤ yDi ≤ PD

i , i = 1, . . . ,ND

0 ≤ yGj ≤ PG

j , j = 1, . . . ,NG

− Ckl ≤ Bkl(δk − δl) ≤ Ckl , k, l ∈ LN

where

LN is the set of nodes, Lk the set of nodes connected to node k

Bkl are the line suseptances, (δk − δl ) the phase angle differences

λS,k are the K nodal prices

[More on Locational Marginal Pricing: Enerdynamics (2012). Locational marginal Pricing. Electricity Markets Dynamics online course (video - 3’26 mins)]


https://www.youtube.com/watch?v=sSSa93S4v8M

3 Different types of market products (a quick tour...)


From simple to more advanced products

So far, we only considered the most basic market product, i.e., a quantity of energyfor a single time unit

An electricity market based on such a simple market product may not function verywell...

why?


From simple to more advanced products

So far, we only considered the most basic market product, i.e., a quantity of energyfor a single time unit

An electricity market based on such a simple market product may not function verywell...

why?

Since operational constraints, and flexibility, need to be somewhatrepresented!!

These may include

minimum and maximum generation levels

minimum up and down time

ramping constraints

varying costs

flexibility in generation and consumption

etc.


Some of the more advanced products (1)

Stepwise offer curves:

Different potential energy blocks atdifferent prices

Can reflect for (e.g., supply side)

minimum and maximumgeneration levels

varying generation costs

Also relevant on the demand side

quantity [MWh]

pric

e [E

uros

/MW

h]

0 5 10 15 20 25 30 35 40 45 50 55

2030

4050

6070

It is straightforward to extend market-clearing algorithms... do you see how?



Block offer: Let me offer to generate/consume X MWh, uniformly distributedover N consecutive time units

→ Allow to account for: (i) minimum up/down time; and (ii) minimum/maximum

generation levels and varying costs to a lesser extent

Flexible offer: Let me offer to generate/consume X MWh over any single timeunit of the day

→ Allow to account for: flexibility in generation and consumption (e.g., industrial

processes)

It is NOT straightforward to extend market-clearing algorithms... do you see how?

This is since:

all market time units have to be considered altogether

integer variables have to used for the various on/off states

→ one needs to formulate a Mixed Integer Linear Program (MILP)


Questions / discussion


For you to do...

Before the next session on Monday 5 February 2018

For those who want to know more about wholesale markets:

Alberto Pototschnig (2013). Electricity Markets: The Wholesale Markets. Youtube video

For those who need a refresh on linear programming:

Optimization Methods in Management Science / Operations Research (2013). Introduction to LPformulations. MIT OpenCourseWare (link to slides)

For those who need a refresh on linear programming and duality:

Thomas S. Ferguson (????). Linear Programming - A Concise Introduction. Electronic text


https://www.youtube.com/watch?v=2jQiPHBoF5o

http://ocw.mit.edu/courses/sloan-school-of-management/15-053-optimization-methods-in-management-science-spring-2013/tutorials/MIT15_053S13_tut01.pdf

http://www.math.ucla.edu/~tom/LP.pdf

Thanks for your attention! - Contact: [email protected] - web: pierrepinson.com


Appendix

For a fixed and inflexible demand D, the market-clearing becomes:

min{yGj }

∑j

λGj y

Gj

subject to∑j

yGj = D

0 ≤ yGj ≤ PG

j , j = 1, . . . ,NG

Though, since overall supply might happen to be less than demand, one adds acomponent reflecting the value of lost load τ , for the part of the load δD not served:

min{yGj ,δD}

(∑j

λGj y

Gj

)+ τδD

subject to∑j

yGj + δD = D

0 ≤ yGj ≤ PG

j , j = 1, . . . ,NG

0 ≤ δD ≤ D

τ is usually set to a high value, e.g., τ = 1000e/MWh31761 - Renewables in Electricity Markets 52

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