\Day-ahead electricity markets" Pierre Pinson Technical University of Denmark . DTU Electrical Engineering - Centre for Electric Power and Energy mail: [email protected]- webpage: www.pierrepinson.com 29 January 2018 31761 - Renewables in Electricity Markets 1
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Day-ahead electricity markets - Pierre Pinson\Day-ahead electricity markets" Pierre Pinson Technical University of Denmark. DTU Electrical Engineering - Centre for Electric Power and
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“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
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
1 Different types of electricity exchanges
31761 - Renewables in Electricity Markets 5
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]
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:
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
Thanks for your attention! - Contact: [email protected] - 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