Post on 11-Apr-2018
“Day-ahead electricity markets”
Pierre Pinson
Technical University of Denmark.
DTU Electrical Engineering - Centre for Electric Power and Energymail: ppin@dtu.dk - webpage: www.pierrepinson.com
29 January 2018
31761 - Renewables in Electricity Markets 1
As part of the overall context...
By the way... why is this called a day-ahead market?
31761 - Renewables in Electricity Markets 2
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
31761 - Renewables in Electricity Markets 3
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
31761 - Renewables in Electricity Markets 4
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
31761 - Renewables in Electricity Markets 6
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]
31761 - Renewables in Electricity Markets 7
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...
31761 - Renewables in Electricity Markets 8
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
31761 - Renewables in Electricity Markets 9
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
31761 - Renewables in Electricity Markets 10
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?
31761 - Renewables in Electricity Markets 11
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
31761 - Renewables in Electricity Markets 12
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
31761 - Renewables in Electricity Markets 13
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...
31761 - Renewables in Electricity Markets 15
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 )
31761 - Renewables in Electricity Markets 16
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...
31761 - Renewables in Electricity Markets 17
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)]
31761 - Renewables in Electricity Markets 18
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)]
31761 - Renewables in Electricity Markets 19
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]
31761 - Renewables in Electricity Markets 20
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)
31761 - Renewables in Electricity Markets 21
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 )
31761 - Renewables in Electricity Markets 22
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
31761 - Renewables in Electricity Markets 23
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?
31761 - Renewables in Electricity Markets 24
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.
31761 - Renewables in Electricity Markets 25
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.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
consumedSupply side: if λGj ≤ λ
S , supplier j is paid λS for any unit of energy produced
Example (continued):
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?
31761 - Renewables in Electricity Markets 27
The transmission “problem”
Remember there is a network involved, and power has to flow...
This was not represented so far in our market description!
31761 - Renewables in Electricity Markets 29
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
31761 - Renewables in Electricity Markets 30
Illustration of Zonal and Nodal pricing
Scandinavia (Zonal):
Go visit: http://nordpoolgroup.com (marketdata, map)
Midwest US (Nodal):
Go visit: https://www.misoenergy.org
31761 - Renewables in Electricity Markets 31
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
31761 - Renewables in Electricity Markets 32
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
31761 - Renewables in Electricity Markets 33
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!
31761 - Renewables in Electricity Markets 34
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
31761 - Renewables in Electricity Markets 35
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
31761 - Renewables in Electricity Markets 36
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:
Supply side: {G1,G3,G5,G7,G8} (but only 75 MWh for G8) - Total: 515 MWhDemand side: {D1,D3,D5,D6,D8,D9} - Total: 555 MWh
→ 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?
31761 - Renewables in Electricity Markets 37
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...
31761 - Renewables in Electricity Markets 38
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
31761 - Renewables in Electricity Markets 39
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
31761 - Renewables in Electricity Markets 40
Results for our auction example
For the 2 zones...
DTU-West:
Supply side: {G1,G3,G5,G7,G8} (but only 75 MWh for G8) - Total: 515 MWhDemand side: {D1,D3,D5,D6,D8,D9} - Total: 555 MWh
→ 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
31761 - Renewables in Electricity Markets 41
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)]
31761 - Renewables in Electricity Markets 42
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?
31761 - Renewables in Electricity Markets 44
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.
31761 - Renewables in Electricity Markets 45
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?
31761 - Renewables in Electricity Markets 46
Some of the more advanced products (2)
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)
31761 - Renewables in Electricity Markets 47
Some of the more advanced products (2)
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)
31761 - Renewables in Electricity Markets 48
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
31761 - Renewables in Electricity Markets 50
Thanks for your attention! - Contact: ppin@dtu.dk - web: pierrepinson.com
31761 - Renewables in Electricity Markets 51
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