Uruguay
Generación
energía eléctrica.
2012 - 2022
Ruben Chaer
[email protected]
Director proyecto SimSEE
IIE – FING – UDELAR
Asesor – Presidencia de UTE.
Marzo 2013
Montevideo – Uruguay.
Indice.
• Características del Sistema.
- Demanda.
- Oferta Térmica.
- Oferta Hidroeléctrica.
- Interconexiones.
• Operación óptima de un sistema dinámico.
- Modelado estocástico.
- Política de Operación.
- Valor de la Optimización.
Proyección de la demanda.
14000
Escenario de alto
crecimiento
12000
8000
Escenario de bajo
crecimiento
6000
4000
2000
2016
2015
2014
2013
2012
2011
2010
2009
2008
año
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
0
1995
GWh/año
10000
Generación esperada por fuente.
Escenario de baja integración con Br. (d300)
Variabilidad Eólica.
Oferta Térmica – Uruguay 2012
Proyección del precio del petróleo.
Salto Grande
(50% UY)
945MW
8 days
Palmar
333MW
22 days
Baygorria
108MW
3 days
Hydroelectric
Plants
1541 MW
Bonete
155MW
140 days
Expansión futura: No quedan grandes proyectos por realizar. Posibilidad de
generación distribuida en mini y micro aprovechamientos 200 MW. ???
Centrales de bombeo distribuidas ??? 300 – 1000 MW
Variabilidad de la generación
Hidráulica.
Licitaciones Eólica
Integración Regional
• 2000 MW con Argentina.
• 70 MW con Brasil
• + 500 MW con Brasil en construcción para
fines de 2013.
Generación Distribuida,
Redes e Interconexiones.
70 MW
500 MW
2000 MW
Optimización de la Operación.
El Jardín de las Delicias. EL BOSCO 1450-1516
Operación de
sistemas con
ALMACENES
• Problema de optimización
complejo por el vínculo
temporal.
Using the stocked resource.
• The complexity comes from
the fact that we are leading
with systems with reservoirs.
• The problem is not only how
much to use of each of the
stocks but also when to use
them.
operation costs
• FUEL consumption at the
fuel fired power plants.
• IMPORTS
• FAILURE in supplying
energy to the system load.
present vs. future costs
• The use of stocked water today
potentially increases the cost of stages
in the future. The preservation of water
today for a later use may reduce the
cost of some stages in the future, but
really increases the cost today due to
the additional fuel based generation.
• The problem is to find a policy of use
of the stocked resources that results in
an equilibrium between present and
future costs.
operation policy
A policy is a function u(X,t) that indicates
how to operate the system for each state
(X) at each time (t).
u is the vector of control variables of the
system. (Typically they are the power at
the power plants.)
The Future Cost associated with the policy u(X,t) is:
t  
FCu ( X , now) 
  fuelCost u, t   failCost u, t  dt
t  now
The Optimal Dispatch
min FCu  X , now
u
The optimal u is the Optimal Policy.
Programación Dinámica Estocástica.
rk
xk 1
xk
CE ''
CE '


CF x , k  1
CF x '' , k  1
'
t
uk
Valor de la Optimización.
Plataforma SimSEE
• 2005-2007 Proyecto PDT 47/12 BID-CONICYT.
Creación de la Plataforma.
• 2009 Proyecto ANII-FSE-19. Mejoras. La más
importante implantación de OddFace y modelado
de red eléctrica.
• 2013 Proyecto ANII-FSE-2011-1-6552. Modelado
de Renovables. Creación de versión 10-minutal,
modelo estocástico de radiación solar, etc. (En
Curso).
Curso SimSEE
• Del 2/Abril/2013 al 28/Mayo/2013
Horario y Salón: Martes y Jueves de 9 a
12 en el Laboratorio de Software del
IIE.
• INFORMES: [email protected]
• INSCRIPCIONES:
http://www.fing.edu.uy/ensenanza/cursos
Generación por fuente (VE)
Energía por fuente según
hidrología.
Proyección del CAD.
27
•CAD: costos de combustible, compra
CAD/MWh
a agentesProyección
nacionales
e importaciones
28
Proyección Costo Marginal.
29
Matriz eléctrica 2015
Two well known strategies
to face this optimization
problem
• Stochastic Dynamic
Programming (SDP)
• Stochastic Dual Dynamic
Programming (SDDP).
Stochastic Dynamic Programming
(SDP)
• The SDP computes the cost function
from the future back to the present.
• To proceed with the calculus, a
discretization, both in time and space,
is defined for each of the state
variables of the system.
• This leads to the well known
Bellman’s ”curse of dimensionality”
that turns the SDP not applicable when
the number of state variables increases.
SDP Curse of Dimensionality
SDDP vs. the Curse of dimensionality.
• The SDDP leads with the dimension of the
state space using Benders cuts to
approximate the cost function for each
time step by hyper-planes in the statespace.
• The approximation is carried out in
successive sweeps of the stages forward,
computing the cost of a feasible solution
and backward computing the cost of the
relaxation.
• If stochastic inputs are present, the process
opens on a tree of approximations that
may suffer of a sort of “curse of
dimensionality”.
• Very good method for large system with
large number of reservoirs, using main
values for stochastic inputs.
SDDP vs. convexity
• If the cost function and the constrains are convex,
we obtain the exact solution. Without convexity,
we have a gap, “the duality gap”.
• When the production costs of the fuel fired units
are considered constant, the resulting cost
functions are convex, linear, so the overall
production cost is also convex and the method is
applicable. When a more detailed production cost
function is considered, a minimum operation point
appears resulting in a non convex function.
• If the system is great enough the duality gap is
irrelevant. But in small systems, where the power
of a unit is greater than 10% of the power of the
demand the duality gap may be relevant.
• Very good method for large system with
large number of reservoirs, using main
values for stochastic inputs.
we choose classical SDP
• The daily maximum of the power demand in
Uruguay is about 1300MW.
• The greatest thermal unit in the system has a
power of 125MW, so the system is very small and
some care must be taken with dual optimization
techniques.
• The 60% of the energy comes from one hydro
plant an so the stochastic modeling of the water
inflows is important.
• It is also true that classical SDP method are more
suitable for distributed programming and with the
permanent increasing of the power of computers at
lower prices, it is foreseeable that SDP method
can be implemented in spite of ”the curse of
dimensionality”.