some iit operations research models for electricity markets · 2008. 10. 8. · – a....
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ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)
Some IIT Operations Research Models for Electricity Markets
INSTITUTO DE INVESTIGACIÓN TECNOLÓGICA
Andrés Ramoshttp://www.iit.upcomillas.es/~aramos/
2IIT Electricity Market Models – Andrés RamosSeptember 2008
Content
� Model development at IIT• More detailed description of some specific models• Brief description of some models
3IIT Electricity Market Models – Andrés RamosSeptember 2008
History• Last 10 years (1998 begins the Spanish electricity market)• Development teams were split and isolated by confidentiality
reasons• This resulted in a rich use of OR techniques
– Mathematical programming (LP, MIP, NLP, MCP, SP, Benders decomposition, Lagrangian Relaxation)
– Simulation (Probabilistic Simulation, Business Dynamics)– Other (Fuzzy)
• “Commercial” grade models used in the Spanish or any other large-scale electric system
4IIT Electricity Market Models – Andrés RamosSeptember 2008
Electricity Produced by Company in Mainland Spain
• Source: OMEL (www.omel.es)
5IIT Electricity Market Models – Andrés RamosSeptember 2008
Electricity Distributed by Company in Mainland Spain
• Year 2006: 231461 GWh
• Source: CNE (www.cne.es)
6IIT Electricity Market Models – Andrés RamosSeptember 2008
Generation Planning Functions
Functions
Scope
Traditional operation functions
New market functions
Short termMedium termLong term
• Fuel management• Annual reservoir and seasonal pumped storage management- Water value assessment
• Investments- Installation- Repowering
• Maintenance• Energy management- Nuclear cycle- Hyperannual reservoirs
• Start-up and shut-down of thermal units
• Pumped storage operation
• Economic dispatch
• Market bids:- Energy
- Power reserve
- Other ancillary services
• Objectives:- Market share
- Price
• Budget planning • Future market bids
• Risk management • Long term contracts:
- Fuel acquisition- Electricity selling
7IIT Electricity Market Models – Andrés RamosSeptember 2008
Iberdrola Endesa Unión Fenosa Gas Natural
E.ON España (antes Viesgo) Red Eléctrica Others
Back Office Long Term Operation Planning
BEST MORSE
Market Equilibrium MOES MPO VALORE MARAPE PLAMER PREMED
Hydro Subsystem MHE
Simulador EXLA
Renewable sources MEMPHIS
Transmission Network SIMUPLUS StarNet SECA
Back Office Medium Term Operation Planning Reliability Indices FLOP
Front Office Short Term Offer Strategies and Operation Planning MAFO SGO GRIMEL
General Perspective of Electricity Market Models
8IIT Electricity Market Models – Andrés RamosSeptember 2008
Content
• Model development at IIT� More detailed description of some specific models
� MOES Stochastic� MHE� Simulador� MAFO
• Brief description of some models
9IIT Electricity Market Models – Andrés RamosSeptember 2008
Hierarchy of Operation Planning ModelsST AR T
E ND
Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l
Hyd ro the rm a lCoo rdina tion M ode l
H yd ro the rm a lC oo rdin a tion M o de l
Stochastic S im ula tion Mode l
Stoch as tic S im ulation Mod e l
M onth l y hyd ro basin and the rm a l p lant p roduction
W eekly hyd ro un it p roduction
D a il y h yd ro un it p roduction
Coh ere nce?
Adj
ustm
ent
Adj
ustm
ent
yes
n o
Un it C om m itm en tO ff er ing S trate g iesU n it Com m itm en t
O ffering Strateg ies
ST AR T
E ND
Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l
Hyd ro the rm a lCoo rdina tion M ode l
H yd ro the rm a lC oo rdin a tion M o de l
Stochastic S im ula tion Mode l
Stoch as tic S im ulation Mod e l
M onth l y hyd ro basin and the rm a l p lant p roduction
W eekly hyd ro un it p roduction
D a il y h yd ro un it p roduction
Coh ere nce?
Adj
ustm
ent
Adj
ustm
ent
yes
n o
Un it C om m itm en tO ff er ing S trate g iesU n it Com m itm en t
O ffering Strateg ies
10IIT Electricity Market Models – Andrés RamosSeptember 2008
MOES Stochastic• Purpose
– Medium-term generation operation– Market equilibrium model– Conjectural variations approach– Implicit elasticity of residual demand function
• Main characteristics– Market equilibrium model based on the complementarity problem (MCP)
• References– J. Cabero, Á. Baíllo, S. Cerisola, M. Ventosa, A. García, F. Perán, G. Relaño, "A Medium-
Term Integrated Risk Management Model for a Hydrothermal Generation Company," IEEE Transactions on Power Systems. vol. 20, no. 3, pp. 1379-1388, August 2005
– J. Cabero, Á. Baíllo, S. Cerisola, M. Ventosa, "Application of benders decomposition to an equilibrium problem," Proceedings of the 15th PSCC, Power Systems Computing Conference. Liege, Belgium, 22-26 Agosto 2005
– M. Ventosa, A. Baíllo, A. Ramos, M. Rivier Electricity Market Modeling Trends Energy Policy Vol. 33 (7) pp. 897-913 May 2005
– A. García-Alcalde, M. Ventosa, M. Rivier, A. Ramos, G. Relaño Fitting Electricity Market Models. A Conjectural Variations Approach 14th Power Systems Computation Conference (PSCC '02) Seville, Spain June 2002
– M. Rivier, M. Ventosa, A. Ramos, F. Martínez-Córcoles and A. Chiarri A Generation Operation Planning Model in Deregulated Electricity Markets based on the ComplementarityProblem in book Complementarity: Applications, Algorithms and Extensions KluwerAcademic Publishers. Dordrecht, The Netherlands. pp. 273-295. 2001
30IIT Electricity Market Models – Andrés RamosSeptember 2008
Optimization problem statement
( )max
0
0
e e
e
j
e
k
z x
h
g
=
≤
( )max
0
0
e e
e
j
e
k
z x
h
g
=
≤
( )max
0
0
e e
e
j
e
k
z x
h
g
=
≤
Electricity Market
Price-m(x)=0
Optimization problemFor company 1
( )1 1
1
1
max
0
0
j
k
z x
h
g
=
≤
Optimization problemFor company A
Optimization problemFor company a
( )max
0
0
a a
a
j
a
k
z x
h
g
=
≤
( )max
0
0
A A
A
j
A
k
z x
h
g
=
≤
31IIT Electricity Market Models – Andrés RamosSeptember 2008
Problem statement for each company
( )max
0
0
e e
e
j
e
k
z x
h
g
=
≤
( )max
0
0
e e
e
j
e
k
z x
h
g
=
≤
( )max
0
0
e e
e
j
e
k
z x
h
g
=
≤
Electricity Market
Price-m(x)=0
Optimization problem
For company 1
( )1 1
1
1
max
0
0
j
k
z x
h
g
=
≤
Optimization problemFor company A
Optimization problemFor company a
( )max
0
0
a a
a
j
a
k
z x
h
g
=
≤
( )max
0
0
A A
A
j
A
k
z x
h
g
=
≤
Objective Function
Maximization of:
Company profit for the problem scope
• Other revenues• CTC’s
• Long term contracts...
• Price equation
• Interperiod• Fuel management• Hydro reservoir scheduling
• Intraperiod• Weekly pumping • Operational constraints
Technical constraints
Restricciones del Mercado
Subject to:
33IIT Electricity Market Models – Andrés RamosSeptember 2008
Practical difficulties• Good theoretical statement• However, no solver available to solve such
mathematical problem:– Several optimization problems tied by price variable
• Look for another equivalent mathematical problem– With the same solution values– Numerically solvable
• Several alternatives– Complementarity problem [Ventosa, Hobbs]– Equivalent quadratic problem [Barquín, Hobbs]
34IIT Electricity Market Models – Andrés RamosSeptember 2008
Optimality conditions of company problem
max za (x)
Subject to:
hja (x) = 0 ⊥λj
a
gka (x) ≤ 0 ⊥µk
a
( ), ,a a a a a a
j j k k
j k
x z h gλ µ λ µ= + ⋅ + ⋅∑ ∑L
Lagrange Function
( )
( )
, , 0
, , 0
0 0 0
aa
x a
aa a
ja
j
a a a a
k k k k
xx
x h
g g
λ
λ µ
λ µλ
µ µ
∂∇ = =∂
∂∇ = = =∂
⋅ = ≤ ≤
LL
LL
KKT Optimality
Conditions
35IIT Electricity Market Models – Andrés RamosSeptember 2008
( )
( )
, , 0
, , 0
0 0 0
aa
x a
aa a
ja
j
a a a a
k k k k
xx
x h
g g
λ
λ µ
λ µλ
µ µ
∂∇ = =∂
∂∇ = = =∂
⋅ = ≤ ≤
LL
LL
Mixed complementarity problem
• Set of system of equations plus a complementarity problem
• Generalization of complementarityproblem
System of Equations
Complementarity
Problem
36IIT Electricity Market Models – Andrés RamosSeptember 2008
Electricity Market
Deterministic equivalent complementarity problem
Price-m(y)=0
Optimality conditions of company 1
Optimality conditionsof company A
Optimality conditionsof company a
( )
( )
11
1
11 1
1
1 1 1 1
, , 0
, , 0
0 0 0
x
j
j
k k k k
xx
x h
g g
λ
λ µ
λ µλ
µ µ
∂∇ = =∂
∂∇ = = =∂
⋅ = ≤ ≤
LL
LL
( )
( )
, , 0
, , 0
0 0 0
aa
x a
aa a
ja
j
a a a a
k k k k
xx
x h
g g
λ
λ µ
λ µλ
µ µ
∂∇ = =∂
∂∇ = = =∂
⋅ = ≤ ≤
LL
LaL
( )
( )
, , 0
, , 0
0 0 0
AA
x A
AA A
jA
j
A A A A
k k k k
xx
x h
g g
λ
λ µ
λ µλ
µ µ
∂∇ = =∂
∂∇ = = =∂
⋅ = ≤ ≤
LL
LL
42IIT Electricity Market Models – Andrés RamosSeptember 2008
• This approach is a Cournot model with conjectural variations• Decision variable of each company is total output bid into the
market• In the Cournot model, the optimal output of a company considers
a fixed output from competitors• However, in conjectural variation approach reaction from
competitors is taken into account when the company decides its optimal output
Conjectural variation approach
43IIT Electricity Market Models – Andrés RamosSeptember 2008
• For each agent a different conjectural variation is set
• Therefore, sensitivity of spot price with respect to company output is different from the slope of the inverse demand function
Conjectural variation approach
( ),1 1a
a a
a a
s qV
q qα α
−− ∂ ∂= − ⋅ + = − ⋅ +
∂ ∂
( )0 a as S q qα −= − ⋅ +
,aaV−
45IIT Electricity Market Models – Andrés RamosSeptember 2008
Stochastic optimization problem without risk• Simultaneous agents’ stochastic optimization problems with
price equation
Optimization problem of company a
0 at t t t
a
α= − ⋅∑s S q
( )1max
subject to:
Operation constraints
E ΠΠΠΠ
Optimization problem of company A
Optimization problem of company 1
( )max
subject to:
Operation constraints
aE ΠΠΠΠ ( )max
subject to:
Operation constraints
AE ΠΠΠΠ
50IIT Electricity Market Models – Andrés RamosSeptember 2008
Stochastic equilibrium problem without risk
Optimality conditions of company a
0 at t t t
a
α= − ⋅∑s S q
1 1
0
Operation constraints
Complementarity conditions
i jt t
∂ ∂= =∂ ∂L L
q q
Optimality conditions of company A
Optimality conditions of company 1
A
0
Operation constraints
Complementarity conditions
A
i jt t
∂ ∂= =∂ ∂L L
q q
0
Operation constraints
Complementarity conditions
a a
i jt t
∂ ∂= =∂ ∂L L
q q
52IIT Electricity Market Models – Andrés RamosSeptember 2008
Stochastic optimization problem with risk
AΠ
0 at t t t
a
α= − ⋅∑s S q ( ),l t t l= Ef s s
AΠ1Π aΠ
( )1max
subject to:
Operation constraints
E ΠΠΠΠ ( )max
subject to:
Operation constraints
aE ΠΠΠΠ ( )max
subject to:
Operation constraints
AE ΠΠΠΠ
Optimization problem of company a
Optimization problem of company A
Optimization problem of company 1
53IIT Electricity Market Models – Andrés RamosSeptember 2008
Forward price of electricity
• Risk is limited to a certain value• Forward and expected spot price relation:
( ),l t l tf = E s
l t
, ,sc l tf
( ),sc l tE s
54IIT Electricity Market Models – Andrés RamosSeptember 2008
Futures modeling– Futures’ revenues
– Contract gains and losses computed at maturity
– Transaction costs associated to contracts computed when signed. Piecewise linear approximated
, ,t l t t kl k
l t k t< >
= −∑ ∑ΠΠΠΠ r c
( ) ( ), , , ,s b
l t l t t l t l t= − ⋅ −r f s t t
( ), , ,s b
t k m t k t k mC C′≥ ⋅ +c t + t
f forward prices spot pricets forward salestb forward purchases
C‘ Fixed costC Variable cost
Π Futures’ profitsr Gains/lossesc Transaction cots
55IIT Electricity Market Models – Andrés RamosSeptember 2008
Risk constraint• Risk modeling: CVaR
– For a discrete distribution function
( )1VaR α–
1 – α
Π
( )f Π
( )1CVaR α–
( ) ( ) 11 1
1sc sc
sc
CVaR VaR P zα αα
− − − ⋅ ⋅− ∑Π ΠΠ ΠΠ ΠΠ Π=
( )1 0sc sc scz VaR zα≥ − − Π ≥ΠΠΠΠ
Π Profitz Negative values of ΠP Probabilityα Confidence level
scz
63IIT Electricity Market Models – Andrés RamosSeptember 2008
Stochastic equilibrium problem with risk
0 at t t t
a
α= − ⋅∑s S q ( ),l t t l= Ef s s
AΠ1Π aΠ
Optimality conditions of company a
1 1
0
Operation constraints
Complementarity conditions
i jt t
∂ ∂= =∂ ∂L L
q q
Optimality conditions of company A
Optimality conditions of company 1
A
0
Operation constraints
Complementarity conditions
A
i jt t
∂ ∂= =∂ ∂L L
q q
0
Operation constraints
Complementarity conditions
a a
i jt t
∂ ∂= =∂ ∂L L
q q
106IIT Electricity Market Models – Andrés RamosSeptember 2008
Content
• Model development at IIT� More detailed description of some specific models
� MOES Stochastic� MHE� Simulador� MAFO
• Brief description of some models
107IIT Electricity Market Models – Andrés RamosSeptember 2008
Hierarchy of Operation Planning ModelsST AR T
E ND
Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l
Hyd ro the rm a lCoo rdina tion M ode l
H yd ro the rm a lC oo rdin a tion M o de l
Stochastic S im ula tion Mode l
Stoch as tic S im ulation Mod e l
M onth l y hyd ro basin and the rm a l p lant p roduction
W eekly hyd ro un it p roduction
D a il y h yd ro un it p roduction
Coh ere nce?
Adj
ustm
ent
Adj
ustm
ent
yes
n o
Un it C om m itm en tO ff er ing S trate g iesU n it Com m itm en t
O ffering Strateg ies
ST AR T
E ND
Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l
Hyd ro the rm a lCoo rdina tion M ode l
H yd ro the rm a lC oo rdin a tion M o de l
Stochastic S im ula tion Mode l
Stoch as tic S im ulation Mod e l
M onth l y hyd ro basin and the rm a l p lant p roduction
W eekly hyd ro un it p roduction
D a il y h yd ro un it p roduction
Coh ere nce?
Adj
ustm
ent
Adj
ustm
ent
yes
n o
Un it C om m itm en tO ff er ing S trate g iesU n it Com m itm en t
O ffering Strateg ies
108IIT Electricity Market Models – Andrés RamosSeptember 2008
Keys to success• According to [Labadie, 2004] “the keys to success in
implementation of reservoir system optimization models are:– (1) improving the levels of trust by more interactive of decision
makers in system development;– (2) better “packaging” of these systems; and– (3) improved linkage with simulation models which operators more
readily accept”.
109IIT Electricity Market Models – Andrés RamosSeptember 2008
MHE• Purpose
– Determine the optimal yearly operation of all the thermal and hydro power plants
– Medium term stochastic hydrothermal model for a complex multi-reservoir and multi-cascaded hydro subsystem
• Main characteristics– General reservoir system topology– Cost minimization model– Thermal and hydro units considered individually– Nonlinear water head effects modeled for large reservoirs (NLP Problem)– Stochastic nonlinear optimization problem solved directed by a nonlinear
solver given a close initial solution provided by a linear solver• References
– A. Ramos, S. Cerisola, J. M. Latorre, R. Bellido, A. Perea, and C. P. López A Medium Term Hydrothermal Coordination Model by Stochastic Nonlinear Programming Working paper
115IIT Electricity Market Models – Andrés RamosSeptember 2008
Demand• Weekly demand with two load levels (peak and off-peak
each week)
0
10000
20000
30000
40000
1 13 25 37 49 61 73 85 97
Dem
and
[MW
]
116IIT Electricity Market Models – Andrés RamosSeptember 2008
Hydro subsystem• Different modeling approach for hydro reservoirs
depending on:– Owner company– Relevance of the reservoir
• Reservoirs belonging to other companies modeled in energy units [GWh]
• Own reservoirs modeled in water units [hm3, m3/s]• Important reservoirs modeled with water head effects• Very diverse hydro subsystem:
– Hydro reservoir volumes from 0.15 to 2433 hm3
– Hydro plant capacities from 1.5 to 934 MW
118IIT Electricity Market Models – Andrés RamosSeptember 2008
Scenario tree generation• A multivariate scenario tree is obtained by neural gas
clustering technique that simultaneously takes into account the main stochastic series and their spatial and temporal dependencies.
• Very extreme scenarios can be artificially introduced with a very low probability
• Number of scenarios generated enough for medium term operation planning
122IIT Electricity Market Models – Andrés RamosSeptember 2008
Constraints: Generation and load balance
Generation of thermal units
+ Generation of storage hydro units
– Consumption of pumped hydro units
= Demand
Generation of thermal units
+ Generation of storage hydro units
– Consumption of pumped hydro units
= Demand
123IIT Electricity Market Models – Andrés RamosSeptember 2008
Constraints: Minimum and maximum operating hours of thermal units
• Introduced to model:– Unavailability of thermal units– Domestic coal subsidies– CO2 Emission allowances– Capacity payments
• They are not separable by period
minimum ≤ Yearly operation hours of each thermal unit for each scenario ≤ maximum
minimum ≤ Yearly operation hours of each thermal unit for each scenario ≤ maximum
minimum ≤ Average yearly operation hours of each thermal unit ≤ maximum
minimum ≤ Average yearly operation hours of each thermal unit ≤ maximum
124IIT Electricity Market Models – Andrés RamosSeptember 2008
Constraints: Water balance for large reservoirs
Reservoir volume at the beginning of the period
+ Natural inflows
– Spills from this reservoir
+ Spills from upstream reservoirs
+ Turbined water from upstream storage hydro plants
+ Pumped water from downstream pumped hydro plants
– Turbined and pumped water from this reservoir
= Reservoir volume at the end of the period
Reservoir volume at the beginning of the period
+ Natural inflows
– Spills from this reservoir
+ Spills from upstream reservoirs
+ Turbined water from upstream storage hydro plants
+ Pumped water from downstream pumped hydro plants
– Turbined and pumped water from this reservoir
= Reservoir volume at the end of the period
125IIT Electricity Market Models – Andrés RamosSeptember 2008
Constraint: Water head effects• Power generation is the product (nonlinear function) of
the flow and the production function
• Production function PF depends linearly on plant water head
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0 20 40 60 80 100 120
Water head [m]
Pro
duct
ion
func
tion
[MW
/m3/
s]
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0 20 40 60 80 100 120
Water head [m]
Pro
duct
ion
func
tion
[MW
/m3/
s]
P = Q x PFP = Q x PF
PF = α HpPF = α Hp
126IIT Electricity Market Models – Andrés RamosSeptember 2008
Constraint: Volume as a function of the head• Reservoir volume depends quadratically (nonlinearly) on
reservoir water head
0
500
1000
1500
2000
2500
3000
0 20 40 60 80 100 120
Water head [m]
Vol
ume
[hm
3]
0
500
1000
1500
2000
2500
3000
0 20 40 60 80 100 120
Water head [m]
Vol
ume
[hm
3]
V = β + β’ Hr+ β” Hr2V = β + β’ Hr+ β” Hr2
127IIT Electricity Market Models – Andrés RamosSeptember 2008
Constraint: Water heads
Water head of the reservoir = forebay height – reference heightWater head of the reservoir = forebay height – reference height
Water head of the plant = forebay height of the reservoir –tailrace height of the plant
Water head of the plant = forebay height of the reservoir –tailrace height of the plant
Tailrace height of the plant = max [forebay height of downstream reservoir, reference tailrace height of the plant]
Tailrace height of the plant = max [forebay height of downstream reservoir, reference tailrace height of the plant]
128IIT Electricity Market Models – Andrés RamosSeptember 2008
Constraint: operation limits
Reservoir volumes between limits for each hydro reservoirReservoir volumes between limits for each hydro reservoir
Power operation between limits for each unitPower operation between limits for each unit
129IIT Electricity Market Models – Andrés RamosSeptember 2008
Multiobjective function• Thermal plant variable costs
• Penalties introduced in the objective function for softening several additional constraints:
– Final reservoir volumes– Exceeding operating rule curves (minimum and maximum)– Minimum and maximum yearly operation hours of thermal
units
130IIT Electricity Market Models – Andrés RamosSeptember 2008
Model results• Results for each period and load block and for each
scenario– Storage hydro, pumped hydro and thermal plant operation– Reservoir management– Basin and river production– Marginal costs
• Byproduct– Optimal water release tables for different stochastic natural
inflows and reservoir volumes (obtained by stochastic nested Benders’ decomposition) used by a lower level stochastic simulation model
132IIT Electricity Market Models – Andrés RamosSeptember 2008
Solution algorithm• Algorithm:
– Successive LP– Direct solution by a NLP solver
• Very careful implementation– Natural scaling of variables– Use of simple expressions– Initial values and bounds for all the nonlinear variables computed
from the solution provided by linear solver (CPLEX 10.2 IPM)– Nonlinear solvers
– CONOPT 3.14 [Generalized Reduced Gradient Method]– KNITRO 5.1.0 [Interior-Point or an Active-Set Method]– MINOS 5.51 [Project Lagrangian Algorithm]– IPOPT 3.3 [Primal-Dual Interior Point Filter Line Search
Algorithm]– SNOPT 7.2-4 [Sequential Quadratic Programming Algorithm]
136IIT Electricity Market Models – Andrés RamosSeptember 2008
Two-year long case study• Spanish electric system
– 130 thermal units– 3 main basins with 50 hydro reservoirs/plants and 2
pumped storage hydro plants– 12 scenarios
145IIT Electricity Market Models – Andrés RamosSeptember 2008
Content
• Model development at IIT� More detailed description of some specific models
� MOES Stochastic� MHE� Simulador� MAFO
• Brief description of some models
146IIT Electricity Market Models – Andrés RamosSeptember 2008
Hierarchy of Operation Planning ModelsST AR T
E ND
Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l
Hyd ro the rm a lCoo rdina tion M ode l
H yd ro the rm a lC oo rdin a tion M o de l
Stochastic S im ula tion Mode l
Stoch as tic S im ulation Mod e l
M onth l y hyd ro basin and the rm a l p lant p roduction
W eekly hyd ro un it p roduction
D a il y h yd ro un it p roduction
Coh ere nce?
Adj
ustm
ent
Adj
ustm
ent
yes
n o
Un it C om m itm en tO ff er ing S trate g iesU n it Com m itm en t
O ffering Strateg ies
ST AR T
E ND
Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l
Hyd ro the rm a lCoo rdina tion M ode l
H yd ro the rm a lC oo rdin a tion M o de l
Stochastic S im ula tion Mode l
Stoch as tic S im ulation Mod e l
M onth l y hyd ro basin and the rm a l p lant p roduction
W eekly hyd ro un it p roduction
D a il y h yd ro un it p roduction
Coh ere nce?
Adj
ustm
ent
Adj
ustm
ent
yes
n o
Un it C om m itm en tO ff er ing S trate g iesU n it Com m itm en t
O ffering Strateg ies
147IIT Electricity Market Models – Andrés RamosSeptember 2008
Simulador• Purpose
– Analyze and test different management strategies of hydro plants– Economic planning of hydro operation:
• Yearly and monthly planning– Update the yearly forecast:
• Operation planning up to the end of the year– Short term detailed operation:
• Detailed operation analysis of floods and droughts, changes in irrigation or recreational activities, etc.
• Main characteristics– Simulation technique– It has been proposed a general simulation method for hydro basins– A three phase method implements the maximize hydro production objective– Object Oriented Programming has been used– A flexible computer application implements this method
• References– J.M. Latorre, S. Cerisola, A. Ramos, R. Bellido, A. Perea Creation of Hydroelectric System
Scheduling by Simulation in the book H. Qudrat-Ullah, J.M. Spector and P. Davidsen (eds.) Complex Decision Making: Theory and Practice pp. 83-96 Springer October 2007 ISBN 9783540736646
– J.M. Latorre, S. Cerisola, A. Ramos, A. Perea, R. Bellido Simulación de cuencas hidráulicasmediante Programación Orientada a Objetos VIII Jornadas Hispano-Lusas de IngenieríaEléctrica Marbella, España Julio 2005
154IIT Electricity Market Models – Andrés RamosSeptember 2008
Data representation (i)
• Basin topology is represented by a graph of nodeswhere each node is an element:
• Connections among nodes are physical junctions through the river.
• This structure induces the use of– Object Oriented Programming
Natural inflow
Reservoir
Hydro plant
155IIT Electricity Market Models – Andrés RamosSeptember 2008
Data representation (ii)• Five types of nodes (objects) are needed:
– Reservoir– Channel– Plant– Inflow point– River junction
• Each node is independently operated although it may require information from other elements
156IIT Electricity Market Models – Andrés RamosSeptember 2008
Data representation (iii)
• Reservoir:– Manages the water
• One or more natural inflows• One outflow
– May have associated:• Minimum outflow• Volume curves that guide its operation:
– Minimum/maximum target curves– Lower/upper guiding curves– Avoiding spillage curve
• Minimum and maximum volume• Optimal water release table (input from long term hydrothermal
models)
157IIT Electricity Market Models – Andrés RamosSeptember 2008
Data representation (iv)
• Channel:– Doesn’t manage the water– Flow transportation between nodes with a limit
158IIT Electricity Market Models – Andrés RamosSeptember 2008
Data representation (v)
• Plant:– Produces electric energy from hydro inflow– Coefficient of efficiency depending linearly on the head– May also pump
159IIT Electricity Market Models – Andrés RamosSeptember 2008
Data representation (vi)
• Natural inflow point:– Introduces water into the system– Uses historical or synthetic inflows
160IIT Electricity Market Models – Andrés RamosSeptember 2008
Data representation (vii)
• River junction:– Groups elements in a river junction– Limits the maximum joint outflow– Management determined in tho steps:
1. Independent initial decision2. Reduction of it following a priority order up to the maximum flow
161IIT Electricity Market Models – Andrés RamosSeptember 2008
Reservoir operation strategies
1. Optimal outflow decision taken from a precalculated optimal water release table depending on:
• Week of the simulated day• Hydrologic index of the basin inflows (type of year)• Volume of the own reservoir• Volume of a reference reservoir
– Table calculated by a long term hydrothermal model– Usually for the main reservoirs of the basin
2. Outflow equals incoming inflow (usually for small reservoirs)
3. Go to minimum target curve (spend as much as possible)
4. Go to maximum target curve (keep water for the future)
163IIT Electricity Market Models – Andrés RamosSeptember 2008
Simulation method (I)
• Main objective:– Maximize hydro production following the reservoir
operation strategies– Other objectives:
• Avoid spillage• Satisfaction of minimum outflow (irrigation)
• Proposed method requires three phases:1. Decides the initial management2. Modifies it to avoid spillage and produce minimum
outflows3. Determines the electricity output for previous inflows
164IIT Electricity Market Models – Andrés RamosSeptember 2008
Simulation method (II) – Phase 1
• Downstream• Each element is individually operated according to its
own operation and strategies• Additional information is collected:
– In reservoirs• Spillage and non served minimum flow• Additional volume to spend or to keep
– In all the elements:• Accumulates those values for the own element and those
located upstream
165IIT Electricity Market Models – Andrés RamosSeptember 2008
Simulation method (III) – Phase 1
Keep
Additional
166IIT Electricity Market Models – Andrés RamosSeptember 2008
Simulation method (III) – Phase 2
• Upstream from the end of the basin • Modifies the Phase 1 operation
– To avoid spillage forces the reservoirs to keep water– To serve a minimum flow increases the production of
reservoirs• Splits the changes proportionally to the capacity of
each element with respect to all the remaining elements located upstream
167IIT Electricity Market Models – Andrés RamosSeptember 2008
Simulation method (IV) – Phase 3
• Determines the plant output– By using a coefficient of efficiency– Depending on the average water head of the day
• Splits the production between peak and off-peak hours:– As much as possible in peak hours– The rest in off-peak hours
169IIT Electricity Market Models – Andrés RamosSeptember 2008
Case study• Application to the Tajus basin belonging to Iberdrola with:
– 9 reservoirs of different sizes– 8 hydro plants– 6 natural inflow points– 27 historical series of daily inflows
174IIT Electricity Market Models – Andrés RamosSeptember 2008
Content
• Model development at IIT� More detailed description of some specific models
� MOES Stochastic� MHE� Simulador� MAFO
• Brief description of some models
175IIT Electricity Market Models – Andrés RamosSeptember 2008
Hierarchy of Operation Planning ModelsST AR T
E ND
Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l
Hyd ro the rm a lCoo rdina tion M ode l
H yd ro the rm a lC oo rdin a tion M o de l
Stochastic S im ula tion Mode l
Stoch as tic S im ulation Mod e l
M onth l y hyd ro basin and the rm a l p lant p roduction
W eekly hyd ro un it p roduction
D a il y h yd ro un it p roduction
Coh ere nce?
Adj
ustm
ent
Adj
ustm
ent
yes
n o
Un it C om m itm en tO ff er ing S trate g iesU n it Com m itm en t
O ffering Strateg ies
ST AR T
E ND
Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l
Hyd ro the rm a lCoo rdina tion M ode l
H yd ro the rm a lC oo rdin a tion M o de l
Stochastic S im ula tion Mode l
Stoch as tic S im ulation Mod e l
M onth l y hyd ro basin and the rm a l p lant p roduction
W eekly hyd ro un it p roduction
D a il y h yd ro un it p roduction
Coh ere nce?
Adj
ustm
ent
Adj
ustm
ent
yes
n o
Un it C om m itm en tO ff er ing S trate g iesU n it Com m itm en t
O ffering Strateg ies
176IIT Electricity Market Models – Andrés RamosSeptember 2008
MAFO• Purpose
– Short-term generation operation– Strategic Unit Commitment development of offering strategies– Daily and adjustment markets
• Main characteristics– Decomposition techniques (Benders, Lagrangean relaxation)
• References– A. Baillo, S. Cerisola, J. Fernandez-Lopez, A. Ramos Stochastic Power Generation
Unit Commitment in Electricity Markets: A Novel Formulation and A Comparison of Solution Methods Operations Research (accepted) JCR impact factor 1.234 (2006)
– J.M. Fernandez-Lopez, Á. Baíllo, S. Cerisola, R. Bellido, "Building optimal offer curves for an electricity spot market: a mixed-integer programming approach," Proceedings of the 15th PSCC, Power Systems Computing Conference. Liege, Belgium, 22-26 Agosto 2005
– Á. Baíllo, M. Ventosa, M. Rivier, A. Ramos, "Optimal offering strategies for generation companies operating in electricity spot markets," IEEE Transactions on Power Systems. vol. 19, no. 2, pp. 745-753, May 2004
– A. Baíllo, M. Ventosa, M. Rivier, A. Ramos, G. Relaño Bidding in a Day-Ahead Electricity Market: A Comparison of Decomposition Techniques 14th Power Systems Computation Conference (PSCC '02) Seville, Spain June 2002
– A. Baíllo, M. Ventosa, A. Ramos, M. Rivier, A. Canseco Strategic unit commitment for generation companies in deregulated electricity markets in book The Next Generation of Electric Power Unit Commitment Models Kluwer Academic Publishers Boston, MA, USA pp. 227-248 2001
177IIT Electricity Market Models – Andrés RamosSeptember 2008
Curva esperada de demanda residual
0
20
40
60
80
100
120
6000 8000 10000 12000 14000 16000 18000
Energía (MWh)
Pre
cio
(€/M
Wh)
Modeling short term uncertainty: multistage approach
• Generation company doesndoesn’’t knowt know the residual demand residual demand curve for each hour:
178IIT Electricity Market Models – Andrés RamosSeptember 2008
Curva esperada de demanda residual
0
20
40
60
80
100
120
6000 8000 10000 12000 14000 16000 18000
Energía (MWh)
Pre
cio
(€/M
Wh)
Modeling short term uncertainty: multistage approach
• Explicit recognition of uncertainty justifies the importance of offering strategies:
Posibles curvas de demanda residual
0
20
40
60
80
100
120
6000 8000 10000 12000 14000 16000 18000
Energía (MWh)
Pre
cio
(€/M
Wh)
179IIT Electricity Market Models – Andrés RamosSeptember 2008
Selling offers have to build an increasing curve
Offering curve between two possible realizations of residual demand curve
is irrelevant
Company decisions are reduced to chose selling output for each residual demand
Modeling short term uncertainty: multistage approach
•• Hypothesis:Hypothesis: probability distributionprobability distribution of residualresidual demand demand curve has finitefinite supportsupport:
Number of possible realizations of residual demand curve is finite
Cantidad
Precio
( )1p q
1q 2q
( )2p q
3q
( )3p q
186IIT Electricity Market Models – Andrés RamosSeptember 2008
•• Solution in two phases:Solution in two phases:– Stochastic unit commitment
– Optimal offering strategies under uncertainty.•• StructureStructure of these problems.•• Possible decomposition techniques:Possible decomposition techniques:
– Benders.– Lagrangian relaxation.
Solution problem strategy
187IIT Electricity Market Models – Andrés RamosSeptember 2008
•• Scope of short term decisionsScope of short term decisions is one weekone week:– Startup and shutdown planning: unit commitmentunit commitment.– Daily hydro scheduling: hydrothermal coordinationhydrothermal coordination.
• This weekly problem can be seen as a sequence of sequence of twotwo--stage stochastic problemsstage stochastic problems, one for each day of the week.
First problem: weekly stochastic multistage planning
188IIT Electricity Market Models – Andrés RamosSeptember 2008
First problem: weekly stochastic multistage planning
Ofertas para el mercado diario
Casación mercado
diario
Distribución de probabilidad discreta del mercado diario
Ofertas para el mercado de ajustes
Casación mercado ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
Día 1
Ofertas para el mercado diario
Casación mercado
diario
Distribución de probabilidad discreta del mercado diario
Ofertas para el mercado de ajustes
Casación mercado ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
Día 2
Ofertas para el mercado diario
Casación mercado
diario
Distribución de probabilidad discreta del mercado diario
Ofertas para el mercado de ajustes
Casación mercado ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
Día 7
189IIT Electricity Market Models – Andrés RamosSeptember 2008
Ofertas para el mercado diario
Casación mercado
diario
Distribución de probabilidad discreta del mercado diario
Ofertas para el mercado de ajustes
Casación mercado ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
Día 1
Ofertas para el mercado diario
Casación mercado
diario
Distribución de probabilidad discreta del mercado diario
Ofertas para el mercado de ajustes
Casación mercado ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
Día 2
Ofertas para el mercado diario
Casación mercado
diario
Distribución de probabilidad discreta del mercado diario
Ofertas para el mercado de ajustes
Casación mercado ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
Día 7
First problem: detail for each day of the week
Ofertas para el mercado diario
Casación mercado
diario
Distribución de probabilidad discreta del mercado diario
Ofertas para el mercado de ajustes
Casación mercado ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
Día 2
Ofertas para el mercado diario
Casación mercado
diario
Distribución de probabilidad discreta del mercado diario
Ofertas para el mercado de ajustes
Casación mercado ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
Día 2
205IIT Electricity Market Models – Andrés RamosSeptember 2008
Second problem: two-stage problem of offering strategies
Ofertas para el mercado diario
Casación del mercado diario
Distribución de probabilidad discreta para el mercado diario
Ofertas para el mercado de ajustes
Casación del mercado de
ajustes
Resultado esperado para el mercado de ajustes
Programa de generación
209IIT Electricity Market Models – Andrés RamosSeptember 2008
Solution technique:Benders decomposition
Subproblem: Adjustment market (resource) and generation planning
Marginal costs associated to
offers.
Daily market offers
Master problem: Daily market.
Decide offers: quantities and prices.
215IIT Electricity Market Models – Andrés RamosSeptember 2008
Content
• Model development at IIT• More detailed description of some specific models
� Brief description of some models
216IIT Electricity Market Models – Andrés RamosSeptember 2008
BEST• Purpose
– Assessment of investments in generation assets and other strategic decisions • Main characteristics
– Long-term scope (20-30 years)– System-dynamics based simulation (Business Dynamics)– Includes a detailed representation of agents’ market behavior based on
endogenously-computed conjectured price variation– Includes a detailed representation of decisions evaluation based on Merton-Black-
Scholes theory • References
– E. Centeno, J. Barquín, A. López-Peña, J.J. Sánchez, "Effects of gas-production constraints on generation expansion," 16th Power Systems Computation Conference - PSCC 08. Glasgow, Scotland, 14-18 Julio 2008
– J.J. Sánchez, J. Barquín, E. Centeno, "Fighting market power by auctioning generation: A system dynamics approach," INFORMS Annual Meeting 2007. Seattle, USA, 4-7 Noviembre2007
– J.J. Sánchez, J. Barquín, E. Centeno, A. López-Peña, "System dynamics models for generation expansion planning in a competitive framework: Oligopoly and market power representation," Twenty-Fifth International System Dynamics Conference. Boston, Massachusetts, USA, 29 Julio-2 Agosto 2007
217IIT Electricity Market Models – Andrés RamosSeptember 2008
BEST
AVAILABLEPOWER PLANTS
ELECTRICITYPRICE
POWERPRODUCTION
PRICEFORECASTING
POWERPRODUCTIONFORECASTING
NEW POWERPLANTS
DEMAND
Building
ForecastingDecision
Market
• Overall structure
218IIT Electricity Market Models – Andrés RamosSeptember 2008
MORSE (+EQUITEC)• Purpose
– MORSE: Simplified model of the electricity Spanish sector, for strategic long term analysis (regulatory policies, agent structure evolution, technological improvements, etc.)
• Main characteristics– Set of excel modules for conventional calculations, data input and output, and
reporting– Includes EQUITEC, which is a quadratic optimization GAMS module to solve the
equilibrium market, with the following features:• Generation is aggregated at a technology level: less details allows for more complex
complementary algorithms, such as multiple scenario evaluation for statistic results, iterative conjecture determination, etc.
• Conjectural variation Cournot market model• Algorithm for robust conjecture determination assuming robustness against demand
scenarios and linear behaviors around the equilibrium point.
– Long term purposes– Additional goal optimization module for relevant input determination (such as
tariffs for zero deficit)
219IIT Electricity Market Models – Andrés RamosSeptember 2008
MORSE (+EQUITEC) architecture
Liberalized clients energy, for agents and distrib zones
Agents: conjectures,
power, technologies,
contracts, etc.
Sector final
balance
Other incomes
(coogeneration,
transmission, distrib,
international
exchanges, …)
Sector balance
Clients
Load
Insular
compensation
Peninsular s.
Non dispatched
energies (hydrau, coogen, internation
exchanges, ….)
Generation(technologies)
load levels demand
EQUITEC
(GAMS)
Regulated business
(trams, distrib)
Fuels
Lib clients energy for agent, distrib
Sector incomes, from
lib. and tarifs clients
Prod. cost for each
technology
Insular syst.
Total energy and energy profile
Energy for load levels Technologies data: fuel
costs, availability, etc.
Peninsular s.
Insular syst.
Prices, productions,
incomes, costs, margins
Market results, prods, prices,
incomes, costs, etc
% liberalized clients for
agents and zones
network loads
Total load,
profiles, load
levels
Extra cost for
regulatory
purposes
Peninsular s.
Insular syst.
Data for ancilllary and
security of supply incomes
estimation
Macro variables (brent, Api2, etc.)
Insular syst.
Peninsular s.
Contracts for hedging
Peninsular s.
Insular syst.
Tolls, tarifs
Contracts
Peninsular s.
Insular syst.
Energy prices and
energy contract prices
Total
ancilllary and
security of supply
prices
Transmission and
distribution data
Excel optimaser for
Input data coherence
%’s lib
% lib for
agents,
zones
220IIT Electricity Market Models – Andrés RamosSeptember 2008
• Iterative conjecture determination – equivalent to slopes bidding curves determination– Klemperer based method is being used with linear bidding curves– Equilibrium is solved for two different demand scenarios – Slopes bidding curves are iteratively adjusted until convergence to
the final slopes
MORSE: EQUITEC conjecture determination
( ) ( )( ) ( ) { }
( ) ( ) { }∑
∑
∈∀=
∈∀⋅+=
≠E
e
e
e
ee
e
ee
DP
ePPCM
21
21
'
'
,
,,1
εεεεε
εεεεα
εελ
Equilibrium equations for both demand scenarios
( ) ( )( ) ( ) e
PP eee ∀
−−
=12
12
ελελεεα
Iterative adjustment of bidding slopes0,eα
0,eα
D
( )1εD
( )2εD
( )11ελ( )
12ελ
( )11εeP
( )12εeP
Energy
Price
1,eα
Aggregated supply function at iteration 1
221IIT Electricity Market Models – Andrés RamosSeptember 2008
Valore• Purpose
– Oligolopolistic electricity markets simulation
• Main characteristics– Based on quadratic optimization– Medium-term
• Detailed physical assets modeling• Stochastic optimization (i.e. water inflows)• Network constraints (explicit and implicit transmission auctions)
• References– J. Barquín, M. Vázquez, Cournot Equilibrium Calculation in Power Networks: An
Optimization Approach With Price Response Computation, IEEE Trans. on Power Systems, 23, no. 2, 317-326, May, 2008
– J. Barquín, E. Centeno, J. Reneses , Stochastic Market Equilibrium Model For Generation Planning, Probability in the Engineering and Informational Sciences, 19, 533-546, August, 2005
222IIT Electricity Market Models – Andrés RamosSeptember 2008
Valore Deterministic equilibrium
• In equilibrium, for each company (utility) u, marginal cost and marginal revenue must be equal
• The theory is explained in the single period case, but it is straightforward to generalize it to include inter-temporal constraints (as in the example case).
u uMC MR=
223IIT Electricity Market Models – Andrés RamosSeptember 2008
Valore Deterministic equilibrium
• Marginal revenue has two components:– 1 additional MW-h earns the market price .– But because of the greater production, market price decreases
an amount . The price fall impacts on all the energy sold in the market, that we assume to be the total generation.
λ
uθ
u uuR PM λ θ= −
Conjectural Response
224IIT Electricity Market Models – Andrés RamosSeptember 2008
Valore Deterministic equilibrium• All together
0
0
u
u
u
u
u
uu P
MRMC
DD
P D
MR θλα
λ== −
= −
=∑
225IIT Electricity Market Models – Andrés RamosSeptember 2008
Valore Deterministic equilibrium• It is easy to check that previous equations are just the
optimality conditions of problem
– Demand utility:
– Effective cost:
( )( ) ( ),
.
min
s.t :
uu
u
u
u
u
P DUP
P D
C D
λ
−
=
∑
∑
( )2
0
0
1
2D
DD DU
α
= −
( ) ( ) 2
2u uu
uu uC P PCP
θ= +
Price is the multiplier
226IIT Electricity Market Models – Andrés RamosSeptember 2008
Fuzzy Valore
• Purpose– Proposing an electricity market model based on the conjectural-price-
response equilibrium when uncertainty of RDC is modeled using the possibility theory
• Main characteristics– Compute robust Cournot equilibrium by using possibilistic VAR for
medium term analysis– Determine possibility distributions of main outputs (prices and incomes)– Novel variational inequalities (VI) algorithms with global and proved
convergence that iteratively solve quadratic programming (QP) models• References
– F.A. Campos, J. Villar, J. Barquín, J. Reneses, “Variational inequalities for solving possibilistic risk-averse electricity market equilibrium," IET Gener. Transm. Distrib.vol. 2, no. 5, pp. 632-645, Sep 2008
– F.A. Campos, J. Villar, J. Barquín, J. Ruipérez, "Robust mixed strategies in fuzzy non-cooperative Nash games," Engineering Optimization. vol. 40, no. 5, pp. 459-474, May 2008
– F.A. Campos, J. Villar, J. Barquín, "Application of possibility theory to robust Cournot equilibriums in electricity market," Probability in the Engineering and Informational Sciences. vol. 19, no. 4, pp. 519-531, October 2005
227IIT Electricity Market Models – Andrés RamosSeptember 2008
Fuzzy Valore Possible RDC and uncertainty reduction
1
0
( )eµπ
(pe,λe)
pe
λe
Price
Power
10
( )eλπ
Posible RDC for each agent
λ(Pe,µµµµe)=λe+µµµµe·(pe-Pe)
µµµµ1e µµµµ2
e µµµµ3e
Slope µµµµe
µµµµ4e
Possibility
Possibility 1
UncertaintyUncertainty reductionreductionusingusing possibilisticpossibilistic VARVAR
Price
Power
(De,λe)EquilibriumEquilibriumconditionsconditions
( ) ( )
( )D
PD
ePPCM
E
e
e
eeeeee
λλ
αλµαλ
=
=
∀⋅+=
∑=1
00 ,,
SlopeSlope expectedexpectedRDC:RDC:
notnot constantconstant !!!!!!
ExpectedExpected RDC: RDC: PercentilPercentil
228IIT Electricity Market Models – Andrés RamosSeptember 2008
Fuzzy Valore Equilibrium resolution
Proposed resolution:
““VI algorithm that solve at each iteration an approximated VI proVI algorithm that solve at each iteration an approximated VI problem and a blem and a additional projection oneadditional projection one””
• The approximated VI problem is solved with a QP similar to Valore:
• The projection problem is also solved with a QP:
( ) ( ){ }PPPPMinArgPkTk
XP
k −−=∈
+1
( ) ( )
PDas
PPDUPPCaMin
T
kE
e
e
k
eeXPD
1..
2,,
2
1
0,
=
−⋅+−∑=∈
αα
PenalizationPenalizationDemandDemand utilityutilityAmpliatedAmpliated CostsCosts
229IIT Electricity Market Models – Andrés RamosSeptember 2008
Fuzzy Valore Possibility distributions of Incomes
Average and variance of incomes
5
7
9
11
13
15
17
19
21
Ene Feb Mar Abr May Jun Jul Ago Sep Oct Nov Dic
Monh
Inco
mes
(M€)
Possibilitic
Deterministic
Lesser variance withpossibilistic approach:RobustRobust EquilibriumEquilibrium
Main results:
230IIT Electricity Market Models – Andrés RamosSeptember 2008
EXLA• Purpose
– Optimal planning of hydroelectric reservoirs in the mid-term• Main characteristics
– Deterministic & stochastic approach– Profit-based & demand-based– LP in a iterative under-relaxed process, MILP or QPC– Mid-term: weekly periods, with load blocks.– Very detailed representation of hydro systems peculiarities– Used by Endesa to manage their reservoirs in the Spanish system.
• References– R. Moraga, J. García-González, E. Parrilla, S. Nogales, "Modeling a nonlinear
water transfer between two reservoirs in a midterm hydroelectric scheduling tool," Water Resources Research. vol. 43, no. 4-W04499, pp. 1-11, April 2007
– J. García-González, R. Moraga, S. Nogales, A. Saiz-Chicharro, "Gestión óptima de los embalses en el medio-largo plazo bajo la perspectiva," Anales de Mecánica y Electricidad. vol. LXXXII, no. IV, pp. 18-27, July 2005
231IIT Electricity Market Models – Andrés RamosSeptember 2008
Resultados agregados� producción de cada UGH� evolución de las reservas
Resultados detallados� producciones por central� caudales turbinados por central� caudales vertidos� políticas de desembalse� evolución de cotas� identificación de riesgo de vertidos, etc...
Emb-Camarasa
Cen-Camarasa
Cen-Talarn
Emb-Talarn
Cen-Terradets
Emb-Rialb
Cen-Rialb
Cen-Gavet
Cen-Lorenzo
Cen-Termens
Cen-Balaguer
Cen-Lleida
Emb-Presaler
Emb-Seros
Cen-Seros
Emb-Terradets
Emb-Oliana
Cen-Oliana
TalarnTalarnD
Gavet
Terradets
Camarasa
Olinana
Rialb
Urgell
LorenzoAux_Urgell
Cu_Com
Termens
Fontanet
Nog
Seros
Emb-Camarasa
Cen-Camarasa
Cen-Terradets
Emb-Rialb
Cen-Rialb
Cen-Gavet
Cen-Lorenzo
Emb-Terradets
Emb-Oliana
Cen-Oliana
Terradets
Camarasa
Olinana
Rialb
Urgell
LorenzoAux_Urgell
Cu_Com
Datos físicos [Hm3],[m3/s]
� topología de los subsistemas� caudales de aportaciones� servidumbres� curvas de garantía� consignas de cotas de los embalses� datos estáticos de emb. y cen., etc...
Modelo equivalente [MWh],[MW]� producible� potencia fluyente� reservas máximas y mínimas� reservas iniciales� energías máximas y mínimas, etc...
Modelo de coordinación
hidrotérmica de medio plazo
EXLA
232IIT Electricity Market Models – Andrés RamosSeptember 2008
SGO: Intelligent Electricity Market Information System • Purpose
– Electricity market set of tools for strategic market analysis and optimal bids generation, applied to the Spanish Electricity Market.
• Main characteristics– First versions running for Endesa since 2000, it includes:
• Oracle Database• Market analysis tools for past bids competitors analysis using data
mining techniques (Matlab)• Generation resources determination tools based on linear and heuristic
optimization techniques (C, Gams)• Optimal bidding strategies: competitors patterns, scenarios
generations, optimal bidding strategies determination, genetic algorithms (C, Matlab, Excel)
• Reporting tools (Excel)– Short term, day ahead
233IIT Electricity Market Models – Andrés RamosSeptember 2008
SGO architecture
SGO-BDORACLE
SGO-BDORACLE
SGO-DataSGO-Data
Thermal unitsre-dispatch
Thermal unitsre-dispatch
Hidraulic unitsre-dispatch
Hidraulic unitsre-dispatch
Pumping unitsre-dispatch
Pumping unitsre-dispatch
Data Files
SGO-Market-1SGO-Market-1
SGO-Market-2SGO-Market-2
SGO-Market-3SGO-Market-3
SGO-LoaderSGO-Loader
DLL-LOADDLL-LOAD
SGO-AutoloaderSGO-Autoloader
SGO-ReportsSGO-Reports
SGO-AnalysisSGO-Analysis
OPTIMIZER
...
SGO-ExpertSGO-Expert
234IIT Electricity Market Models – Andrés RamosSeptember 2008
SGO-Analysis example
Day
s
Hours
0 5 10 150
20
40
60
80
100
120
140
Precio (Pta/kW)
Ba
nda
NO
RM
ALI
ZA
DA
(%
)
Curv as de of erta de reserv a secundaria de la competencia de Endesa
0 5 10 150
20
40
60
80
100
120
140
Precio (Pta/kW)
Ba
nda
NO
RM
ALI
ZA
DA
(%
)
Curv as de of erta de reserv a secundaria de la competencia de Endesa
235IIT Electricity Market Models – Andrés RamosSeptember 2008
SGO: Intelligent Electricity Market Information System
• References– J. Villar, A. Muñoz, E.F. Sánchez-Úbeda, A. Mateo, M. Casado, F.A. Campos, J.
Maté, E. Centeno, S. Rubio, J.J. Marcos, R. González, "SGO: Management information system for strategic bidding in electrical markets," IEEE Power Tech. Conference, POM6-394. Porto, Portugal, September 2001
– E.F. Sánchez-Úbeda, A. Muñoz, J. Villar, "Minería y visualización de datos del mercado eléctrico español," Inteligencia Artificial - Revista Iberoamericana de Inteligencia Artificial . vol. 10, no. 29, pp. 79-88, May 2006
– A. Mateo, E.F. Sánchez-Úbeda, A. Muñoz, J. Villar, A. Saiz-Chicharro, J.T. Abarca, E. Losada, "Strategic bidding under uncertainty using genetic algorithms," PMAPS2000: 6th International Conference on Probabilistic Methods Applied to Power Systems. Funchal, Madeira, Portugal, September 25-28, 2000
– J. García-González, A. Muñoz, F.A. Campos, J. Villar, "Connecting the intraday energy and reserve markets by an optimal redispatch," IEEE Transactions on Power Systems. vol. 22, no. 4, pp. 2220-2231, November 2007
– E. Centeno, B. Vitoriano, F.A. Campos, A. Muñoz, J. Villar, E.F. Sánchez-Úbeda, "A goal programming model for rescheduling of generation power in deregulated markets," Annals of Operations Research. vol. 120, no. , pp. 45-57, April 2003
236IIT Electricity Market Models – Andrés RamosSeptember 2008
MARAPE• Purpose
– Risk identification, analysis and management– Risk and rate-of-return measures– Medium-term contracting decisions
• Main characteristics– Strategic Probabilistic Simulation– ELDC convolution– Time series, GARCH
• References– C. Batlle, J. Barquín, "A strategic production costing model for electricity market
price analysis," IEEE Transactions on Power Systems. vol. 20, no. 1, pp. 67-74, February 2005
– C. Batlle, J. Barquín, "Fuel prices scenario generation based on a multivariate GARCH model for risk analysis in a wholesale electricity market," International Journal of Electrical Power & Energy Systems. vol. 26, no. 4, pp. 273-280, May 2004
237IIT Electricity Market Models – Andrés RamosSeptember 2008
PLAMER• Purpose
– Compute medium term market prices and agents’ output applying liberalized market equilibrium conditions
– Evaluate the impact of incorporating new bidding units– Analyze electricity market regulatory changes
• Main characteristics– Model with quadratic objective function, linear constraints, binary variables.– Minimum load of bidding units– Different scenarios of fuel prices– Hydro reserves management by agent– Pumped storage units– CO2 emission costs– Medium term scope (2 years)– Results disaggregated by weeks, periods and load levels
• References– López de Haro, S., Sánchez Martín, P., de la Hoz Ardiz, J.E.. y Fernández Caro, J.,
“Estimating conjectural variations for electricity market model”, European Journal of Operations Research, Vol. 181, Issue 3, 16, Septiembre 2007, Pages 1322-1338
238IIT Electricity Market Models – Andrés RamosSeptember 2008
GRIMEL• Purpose
– Strategic bidding model that optimizes the electrical resources (energy and ancillary services) of a generation company
• Main characteristics– Short term stochastic optimization model (MIP)– The same model is used to obtain the optimal bid for the daily energy
market, secondary reserve and intradaily markets in Spain– Used in the Spanish electricity market by a medium size generation
company– The strategy of the rest of the agents is modeled by the residual demand
curve• Forecasted using decision trees
– High degree of modeling in the units• For instance, models each physical unit of a pumping generator and is
able to obtain simultaneously its sell and buy bid• References
– A. Ugedo, E. Lobato, A. Franco, L. Rouco, “Strategic bidding in Sequential Electricity Markets”, IEE Generation, Transmission and Distribution, Julio, vol. 153 (4), pp. 431-442, 2006
– A. Ugedo, E. Lobato, A. Franco, L. Rouco, J. Fernández-Caro, J. de-Benito, J. Chofre, J.de la Hoz “Stochastic Model of Residual Demand Curves with Decision Trees”. 2003 PES General Meeting, Toronto, Canada, 2003.
239IIT Electricity Market Models – Andrés RamosSeptember 2008
GRIMEL• Overview
Thermal units
Hydro units
Pump storage units
Market data Strategic parameters
Residual demand curves’ estimationExplanatory variables
STOCHASTIC
OPTIMIZATION
Market
bid curves
construccion
240IIT Electricity Market Models – Andrés RamosSeptember 2008
GRIMEL• Modes of operation
– MD: obtains the strategy and bid curve for daily market– BS: obtains the strategy and bid curve for secondary reserve, taking
into account results of the previous daily energy market– MI: obtains the strategy and bid curve for each intradaily market,
taking into account results of previous energy markets and secondary reserve market
– The same model is valid for each market
241IIT Electricity Market Models – Andrés RamosSeptember 2008
GRIMEL
THE SAME MODEL IS VALID FOR ALL MARKETSTHE SAME MODEL IS VALID FOR ALL MARKETS
MDMD
M
O
D
E
( )1 1
1 1md mi 1
md mi mi
g ,h ,scmig ,h ,esc ,esc g ,h ,s g ,h ,scmicmdqt qt qt dt= + −
,
max
, , ,, _0 g h g g hg h sc hbs POPs ve qtb≤ ≤ ⋅ −δ
, ,
min
, ,, _0 gg h scb hs g hh gPOb Pe qtb v≤ ≤ − ⋅δ
Decision
variable to
obtain bid
in actual
market
BSBS
MIMI
Decision
variable of
future
markets
Parameters
known
( )1 1
md mi 1 1 1
md mi mi
g ,h ,esc ,esc g ,hg ,h ,scmd ,scmi g ,h ,scmiqt qt dtqt= + −
,
max
, , ,, _0 g h g g hg h sc hbs POPs ve qtb≤ ≤ ⋅ −δ
, ,
min
, ,, _0 gg h scb hs g hh gPOb Pe qtb v≤ ≤ − ⋅δ
( )1 1
md mi 1 1 1
md mi mi
g ,h ,esc ,esc g ,hg ,h ,scmd ,scmi g ,h ,scmiqt qt dtqt= + −
max
, ,, , , _0 g h scbs g h g h g hbs POP ve qt≤ ≤ ⋅ −δ
min
, ,,, ,_0 gg h sc hbs g h g hbb POPve qt≤ ≤ − ⋅δ
242IIT Electricity Market Models – Andrés RamosSeptember 2008
GRIMEL
Modo de estrategia de oferta:
• Modo MD• Modo BS• Modo MIx
Definición de índices y parámetros
Carga de índices
Carga de parámetrosValidación de parámetros
Modelo de mercado
Modelo del parque generador
Ejecución del modo seleccionado
Identificación variables holgura
Alarmas parámetros
Alarmas infactibilidades
Generación salidas con resultados
Módulo de construcción de ofertas según el formato requerido por el mercado
Fijar variables según resultados reales de mercados anteriores
Modelo térmico
Modelo hidráulico
Modelo bombeo
PROGRAMMING STRUCTURE OF THE ORIGINAL MODELPROGRAMMING STRUCTURE OF THE ORIGINAL MODEL
Model
Adaptation to each
mode and solver
Infeasibility
detectionResults
Bids adapted to the required format
243IIT Electricity Market Models – Andrés RamosSeptember 2008
MEMPHIS• Purpose
– Determine the impact of a large scale penetration of renewable energy sources in the electric system operation
• Main characteristics– Chronological simulation
• References– A. Ramos, L. Olmos, J. M. Latorre, I. Pérez-Arriaga Modeling
Medium Term Hydroelectric System Penetration with Large-scale Penetration of Intermittent Generation XIV Congreso Latino IberoAmericano de Investigación de Operaciones (CLAIO 2008) Cartagena de Indias, Colombia September 2008
244IIT Electricity Market Models – Andrés RamosSeptember 2008
SIMUPLUS• Purpose
– Evaluation of potential network investments in regulated and liberalized electric markets
– Analysis of additional investments by sensitivities– Study the security of supply due to failures in generation or transmission elements
• Main characteristics– Medium and long term– Linear optimization– Simulation of availability of generation or transmission elements – Simulation of agents’ bids– Hydro scheduling in regulated markets– Scenarios for hydro inflows and fuel prices– Transmission network DC load flow with ohmic losses– N-1 preventive security criterion– Long term scope– Disaggregation by weeks, periods and load levels
245IIT Electricity Market Models – Andrés RamosSeptember 2008
SIMUPLUS• References
Sánchez-Martín, P., Ramos, A. y Alonso, J.F., “Probabilistic Midterm
Transmission Planning in a Liberalized Market”, IEEE Transactions on
Power Systems, Vol. 20, nº 4, Noviembre 2005, pp. 2135-2142
246IIT Electricity Market Models – Andrés RamosSeptember 2008
PREMED• Purpose
– Forecast marginal costs and electricity prices in the mid-term• Main characteristics
– PreMed is an hybrid model that combines two different approaches: fundamental and quantitative.
• Fundamental: cost-based dispatch model (LP) used to obtain the theoretical marginal cost in a perfect competition situation and the theoretical optimal schedule of the system. It is also used to estimate future marginal cost s(input for the quantitative model in the forecasting)
• Quantitative: the difference between historic prices and obtained marginal cost (markup) is adjusted by means of statistical techniques (multivariate regression, time series and Neural Networks).
• References– J. García-González, J. Barquín Gil, P. Dueñas, “A hybrid approach for modeling
electricity price series in the medium-term.” 16th Power Systems Computation Conference (PSCC'08) Glasgow, Scotland, July 14-18, 2008.
PreMed
247IIT Electricity Market Models – Andrés RamosSeptember 2008
... 2008-09
Estimation of historical marginal
costs
Market simulation(optimization)
Market simulation(optimization)
Estimation of future marginal costs and productions
Statistical analysis(regression + time seris +NN)
Historical data
Prices
Hypothesis about demand, fuel costs, hydro inflows, …
2004 2007
248IIT Electricity Market Models – Andrés RamosSeptember 2008
StarNet• Purpose
– Determines the system operation variables that minimize variablecosts for a defined time scope. It determines the unit commitment binary variables and furthermore the unit output and power flow through the network.
– Short and medium-term generation operation– Nodal prices, nodal factors.
• Main characteristics– Generalized unit commitment– Hydro scheduling– Transmission network DC load flow with losses
• References– M. Rey, A. Ramos, P. Sánchez Martín, F. Martínez Córcoles, V. Martín
Corrochano Modelado de las pérdidas óhmicas de transporte en modelosde explotación generación/red a medio plazo V Jornadas Hispano-Lusasde Ingeniería Eléctrica 2: 885-891 Salamanca, España Julio 1997
– http://www.iit.upcomillas.es/~aramos/starnet.htm
249IIT Electricity Market Models – Andrés RamosSeptember 2008
SECA• Purpose
– Evaluation of capacity bids for exchange between areas– Price determination for transmission capacity auctions for different time
scopes– Hydrothermal multiarea dispatch with transmission network
• Main characteristics– Mixed integer linear model– Hydro scheduling– Scenarios for hydro inflows and fuel prices– Minimum load of thermal units– Pumped hydro units– Transmission network DC load flow– Medium term scope with disaggregation in months and load levels
• References– P. Sánchez, A. Campos Marginalistic Bidding for Cross Border Transmission
Capacity XIV Congreso Latino Ibero Americano de Investigación de Operaciones(CLAIO 2008) Cartagena de Indias, Colombia September 2008
250IIT Electricity Market Models – Andrés RamosSeptember 2008
FLOP• Purpose
– Compute reliability indexes:• Expected Energy Non Served (EENS)• Loss Of Load Probability (LOLP)
– Determine firm capacity of any unit.• Main characteristics
– Probabilistic simulation– ELDC convolution– Excel based
• Reference– http://www.iit.upcomillas.es/~aramos/flop.htm
ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)
Some IIT Operations Research Models for Electricity Markets
INSTITUTO DE INVESTIGACIÓN TECNOLÓGICA
Andrés Ramoshttp://www.iit.upcomillas.es/~aramos/