UruguayGeneración

energía eléctrica.2012 - 2022

Ruben Chaer rchaer@simsee.org

Director proyecto SimSEE

IIE – FING – UDELAR Asesor – Presidencia de UTE.

Marzo 2013Montevideo – 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.

0

2000

4000

6000

8000

10000

12000

14000

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

GW

h/añ

o

año

Escenario de alto crecimiento

Escenario de bajo crecimiento

Generación esperada por fuente.Escenario de baja integración con Br. (d300)

Variabilidad Eólica.

Oferta Térmica – Uruguay 2012

Proyección del precio del petróleo.Proyección del precio del petróleo.

Hydroelectric Plants

1541 MW

Bonete155MW140 days

Baygorria108MW3 days

Palmar333MW22 days

Salto Grande(50% UY)945MW8 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.

500 MW

70 MW

2000 MW

Generación Distribuida,

Redes e Interconexiones.

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

t

nowt

u dttufailCosttufuelCostnowXFC ,,),(

u is the vector of control variables of the system. (Typically they are the power at the power plants.)

A policy is a function u(X,t) that indicates how to operate the system for each state (X) at each time (t).

The Future Cost associated with the policy u(X,t) is:

The Optimal Dispatch

nowXFCuu

,min

The optimal u is the Optimal Policy.

Programación Dinámica Estocástica.

t

1kxkx

ku

1,' kxCF'CE

kr

''CE 1,'' kxCF

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: posgrado@fing.edu.uy

• INSCRIPCIONES: http://www.fing.edu.uy/ensenanza/cursos

Generación por fuente (VE)

Energía por fuente según hidrología.

2727

Proyección del CAD.

2828

Proyección CAD/MWh

•CAD: costos de combustible, compra CAD: costos de combustible, compra a agentes nacionales e importacionesa agentes nacionales e importaciones

2929

Proyección Costo Marginal.

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 state-space.

• 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”.