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Market-driven dynamic transmission expansion planning 1

Market-driven dynamic transmission expansion planning

MarketMarket--driven dynamic transmission driven dynamic transmission expansion planningexpansion planning

Ing. Álvaro Martínez Valle (UMA)Dr. José Antonio Aguado Sánchez (UMA)

Dr. Sebastián de la Torre Fazio (UMA)Dr. Javier Contreras Sanz (UCLM)



ESCUELA TÉCNICA SUPERIOR DE INGENIEROS INDUSTRIALESUNIVERSIDAD DE CASTILLA – LA MANCHA

13071 Ciudad Real, Spain

ESCUELA TÉCNICA SUPERIOR DE INGENIEROS INDUSTRIALESUNIVERSIDAD DE MÁLAGA

29071 Málaga, Spain


MarketMarket--driven transmission expansion planningdriven transmission expansion planning

SummarySummary

Introduction to electrical power systemsIntroduction to electrical power systems

MotivationMotivation

Bibliography searchBibliography search

Dynamic formulation of the expansion algorithm in a competitive marketDynamic formulation of the expansion algorithm in a competitive market

Case studiesCase studies

Conclusions and future workConclusions and future work

2

Modeling of the components of a power system marketModeling of the components of a power system market



TRADITIONAL ENVIRONMENT-

Electricity = Public service

- Vertically integrated utility

- Centralized operation without competition

Minimization of operation costs

COMPETITIVE ENVIRONMENT-

Deregulation of electricity

- Separation of activities:-Generation and trading Free market- Transmission Centrally regulated

- Existence of a wholesale market (spot market)

Maximization of social welfare



SummarySummary







2




OBJECTIVE OF THE WORK

Development of a network planning tool:

- Adaptation to the needs of competitive markets

- Development of dynamic multi-period expansion plans

- Foresight of systems interconnection (multi-area expansion)



SummarySummary







2




Clasification by solving methodologies:- Heuristic methods:

“Transmission system expansion planning using a sigmoid function to handle integer investment variables”, DE OLIVEIRA, E.J.; DA SILVA, I.C.; PEREIRA, J.L.R., y CARNEIRO, S. (2005).

- Methods based on game theory:“An effective transmission network expansion cost allocation based on game theory”, RUIZ, P.A. y CONTRERAS, J. (2008).

- Mathematical optimization methods:

Linear programming:“Transmission network planning using linear programming”, VILLASANA, R.; GARVER, L.L., y SALON, S.J. (1985).

Benders decomposition:“A new Benders decomposition approach to solve power transmission

network design problems”, BINATO, S.; PEREIRA, M.V.F., y GRANVILLE, S. (2001).

Mixed-integer nonlinear programming:“Transmission Expansion Planning in Electricity Markets”, DE LA TORRE, S.; CONEJO, A. J., y CONTRERAS, J. (2008).



SummarySummary







2



Unidad Generadora A

Oferta de Generación A

RED DE TRANSPORTE

Unidad Generadora B

Unidad Generadora C

Demanda A

Demanda B

Demanda C

OPERADOR DEL MERCADO

OPERADOR DEL SISTEMA

Flujo de energía

Flujo de información

Ofertas aceptadas

Datos Liquidación

Oferta de Generación B

Oferta de Generación C

Oferta de Adquisición B

Oferta de Adquisición A

Oferta de Adquisición C

Electricity market modelElectricity market model


ELECTRICITY NETWORK MODELING

-

The electrical network connects nodes with generation units to demand nodes where the energy is consumed

-This work uses a DC model with losses. It is derived from an AC model using several simplificacions:

• Nodal voltage has a unitary p.u value.

• Angle of nodal voltage close to 0.

• Sin of angle close to 0 approximated by its argument.

( ) 1cos0 ss ≅⇒≅ δδ( ) sss sen δδδ ≅⇒≅ 0

-

Description of the network only in terms of active power and nodal phase angles.

Network modelNetwork model

1Vs ≅


ELECTRICITY NETWORK MODELING

LOSSES- Nonlinear expression losses must be linearized to be included in the expansion algorithm:

-

Piecewise linearization by means of L+2 variables:)2 SS 2

s2

ssrsrsrrsrssrsr V(VgcosgVVPPq ++−=+= δ

Network modelNetwork model

Nudo s Nudo r Zsr

12 qsr1

2 qsr


GENERATING COMPANIES MODELINGGENERATING COMPANIES MODELING

Offer strategy: Set of rules or algorithms that a generating company needs to calculate the offers

presented to the market operator.

Rational offer strategy:

Offer for which, once determined by the unit the energy amount to produce, the price is equal to the unit’s marginal cost.

pGi

P3P2P1

m3

m2

m1

Ci (pGi)

Pmax

Market modelMarket model


DEMAND MODELING

Stepwise linear elastic demand: The demand bids are accepted by blocks of energy at constant prices, thus, the aggregate demand function is a decreasing (in price)

step-wise

curve.



MARKET MATCHING MODELING

In a deregulated system, the price of electricity is composed of

two terms:

- One term is related to the cost of generation.

- The other term is related to the transmission cost.

Nodal prices or Locational Marginal Prices (LMPs):

•

LMPs represent a market mechanism whose value is a function of the node placement in the network.

• LMPs reflect the marginal costs in time and space.

•

LMPs are obtained as dual variables (Lagrange multipliers) associated with the balance equations of an optimal power flow (OPF).




SummarySummary







2



1)r1()r1(r

t

t

−++⋅

=τ8761000

=σ

Maximize SOCIAL WELFARE

subject to:

• Technical operation constraints

• Economic constraints

• Temporal constraints

Objactive function:Maximize

( ) ( )( )

( )∑ ∑ ∑∑ ∑ ∑∑ ∑∈ ∈ ∈∀

−∈∀ ∈∀ ∈∀

−∈∀ ∈∀

−+

+

−−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

+Y Y L

0

srksrk

)y(C G i0

ibib

D d0

dhdh

y y )k,r,s(yy

yysrk

sr)y(c i b

yy

)y(cG

)y(cG

d hyy

)y(cD

)y(cD)y(c

r1hwK

r1p

r1p

WΩ Ω ΩΩ Ω ΩΩ Ω

σετλλ

Dynamic formulation of the expansion algorithm Dynamic formulation of the expansion algorithm in a competitive marketin a competitive market


Balance de potencia

Flujos de potencia sin pérdidas

Linealización de las pérdidas

Flujos de potencia máximos

Technical operation constraints


;p]q21f[p

sD

ds

Ls

G

id

)y(cD

)y(csrk

)k,r(

)y(csrk

i

)y(cG ∑∑∑

∈∈∀∈

=+−ΨΨΨ

)()( :y,)(, yc

sYyCN ycs λΩ∈∀Ω∈∀Ω∈∀

;max)(maxsrk

ysrk

ycsrksrk

ysrk pwfpw ≤≤−

;)1()()1( )()()()(

MwbfMw yc

srkyc

sryc

srsrk

ycsrky

srk −≤−+≤−− −+ δδ

Y)y(CL y,)y(c,)k,r,s( ΩΩΩ ∈∀∈∀∈∀


;pwq0 maxsrk

ysrk

)y(csrk ≤≤

;M)w1()()(g

q0 2ysrk

)y(csr

L

1sr

srk

)y(csrk −≤+−≤ ∑

=

lll

δα

;)(1

)()()( ∑=

−+ =+L

ycsr

ycsr

ycsr

l

lδδδ

;)()()()( −+ −=− ycsr

ycsr

ycr

ycs δδδδ



Y)y(CL y,)y(c,)r,s( ΩΩΩ ∈∀∈∀∈∀


;pq21f max

srk)y(c

srk)y(c

srk ≤+

;pq21f max

srk)y(c

srk)y(c

srk ≤+−




Technical operation constraints


Máxima potencia generada ofertada

Máxima potencia de demanda ofertada

Límites para las variables de fase

Fijación de variables para líneas existentes

;pp0 yG

)y(cG ibib

≤≤

;pp0 )ymax(G

)y(cG ii

≤≤

;)()( ycG

b

ycG i

i

ibpp =∑

Ω∈∀

Y)y(CGi y,)y(c,i;b ΩΩΩΩ ∈∀∈∀∈∀∈∀

Y)y(CG y,)y(c,i ΩΩΩ ∈∀∈∀∈∀

Y)y(CG y,)y(c,i ΩΩΩ ∈∀∈∀∈∀

;0 )()( ycD

ycD dhdh

pp ≤≤

;)()( ycD

h

ycD d

d

dhpp =∑

Ω∈∀

Y)y(CdD y,)y(c,h,d ΩΩΩΩ ∈∀∈∀∈∀∈∀

Y)y(CD y,)y(c,d ΩΩΩ ∈∀∈∀∈∀

;0)( =ycsδ

;0 ,0 )()( ≥≥ −+ ycsr

ycsr δδ

;0)()( ≥lycsrδ

;)1()()( Mwysrksr

ycsr −+Δ≤ δδ l

Y)y(C y,)y(c ΩΩ ∈∀∈∀s: nudo de referencia


Y)y(CL y,)y(c,,L,1 ,)r,s( ΩΩΩ ∈∀∈∀=∈∀ Kl

Y)y(CL y,)y(c,,L,1,)k,r,s( ΩΩΩ ∈∀∈∀=∈∀ Kl

l6sr ⋅=

πδΔ

;1=ysrkw

YLL y,\)k,r,s( ΩΩΩ ∈∀∈∀ +


Economic constraints


Límite de inversión

Temporal constraints

Relación lógica

NO construcción en los 3 primeros años

Definición de la variable de amortización

Definición de variables binarias

( )( ) MAX

y )k,r,s(yy

yysrk

sr Ir1

hwK

Y L

0

srksrk ≤+

−∑ ∑∈ ∈∀

−+Ω Ω

τ

;1 ysrk

ysrk

ysrk aww =− −

YLy,)k,r,s( ΩΩ ∈∀∈∀ +

;0w)y,y,y(y )k,r,s(

ysrk

321 L

=∑ ∑∈ ∈∀ +Ω

};1,0{h,a ysrk

ysrk ∈ YL

y,)k,r,s( ΩΩ ∈∀∈∀ +

};1,0{wysrk ∈ YL y,)k,r,s( ΩΩ ∈∀∈∀

;MaT1w2TMa ysrk

1ysrk

ysrk

ysrk

ysrk ≤−+−≤− −

;M)a1(1w2TM)a1( ysrk

ysrk

ysrk

ysrk −≤+−≤−−

;Mh)1IRP(TM)h1( ysrksr

ysrk

ysrk ≤+−≤−−

;0hYy

ysrk =∑

∈Ω

[ ] ( )[ ]4IRPY/y,)k,r,s( srYL +≥∈∀∈∀ + ΩΩ

[ ] ( )[ ]4IRPY/y,)k,r,s( srYL +≥∈∀∈∀ + ΩΩ

[ ] ( )[ ]4IRPY/y,)k,r,s( srYL +≥∈∀∈∀ + ΩΩ

[ ] ( )[ ]4IRPY/)k,r,s( srL+<∈∀ +Ω

Yy,)k,r,s()a1(T1w2T Lysrk

1ysrk

ysrk

ysrk ∈∀∈∀−+−= +

− Ω


System metrics

∑ ∑

∑ ∑

∈ ∈∀

∈ ∈∀=

Y L

Y L

max

y )k,r,s(

ysrk

maxsrk

y )k,r,s(

)y(csrk

s wp

p

i

Ω Ω

Ω Ω

λ

λλΩ

Ni Ns

s

c

∑∈∀

−=

Y

WY )y(Cy )y(c

)y(c)y(cs

s

∑ ∑∈∀ ∈∀

⎟⎟⎠

⎞⎜⎜⎝

⎛

=Ω Ω

λ

λ

NNs

s∑∈∀= Ω

λλ

Investment evaluation parameters

( )( )∑ ∑

∈ ∈∀−

+ +

−−

=

Y L

0

srksrk

y )k,r,s(yy

yysrk

sr

0*

1

r1

hwKSWSW

Ω Ω

τμ


( )( )∑ ∑

∈ ∈∀−

+ +

−−

=

Y L

0

srksrk

y )k,r,s(yy

yysrk

sr

0*

3

r1

hwKCSCS

Ω Ω

τμ

( )( )∑ ∑

∈ ∈∀−

+ +

−−

=

Y L

0

srksrk

y )k,r,s(yy

yysrk

sr

0*

2

r1

hwKGSGS

Ω Ω

τμ

( )( )∑ ∑

∈ ∈∀−

+ +

−−

=

Y L

0

srksrk

y )k,r,s(yy

yysrk

sr

0*

4

r1

hwKMSMS

Ω Ω

τμ



E s tu d i o d e l a n e c e s id a d d e e x p a n s ió n

O P F d e l S i s t e m a

A n á l i s i s d e Í n d i c e s

i s

P r o p o s i c i ó n d e l í n e a s c a n d id a t a s

A p l i c a c ió n d e l a l g o r i t m o d e e x p a n s ió n

¿ N e c e s i d a d d e e x p a n s ió n d e l s i s t e m a ?

E S T A D O A C T U A L D E L S I S T E M A

A n á l i s i s d e r e s u l t a d o s +P a r á m e t r o s d e e v a lu a c ió n d e l a i n v e r s ió n

¿ P la n a c e p t a d o ? C a m b i o d e p a r á m e t r o s

P l a n d e e x p a n s i ó n d e f i n i t i v o

S I

N O

S I

N O

i c



SummarySummary







2



Mainland Spanish network (SEPE)

5

D4

D5G1

3

6

1

2

4

D1

D2

D3

G8-10

G2-7

Garver 6-bussystem

G1

1 2

G2 G3

7

34

5

6

8

9 10

1211

13

14

15

16

17

18

19 20

21

22

23

24

G4G6

G5

G7

G8

G9

G10

G11

D1 D2 D7

D3 D4 D5D6

D8

D9 D10

D11

D12D13

D14

D15

D16 D17

138 kV

230 kV

IEEE-24 RTS

Case StudiesCase Studies


Case study 1: 6Case study 1: 6--bus Garver systembus Garver system

5

D4

D5G1

3

6

1

2

4

D1

D2

D3

G5-10

G2-4

System features:

- 4 scenarios of demand:

-

5 demand units (piecewise elastic linear offers split into 5 blocks).

-

10 generating units (linear production costs, single-block offer).

System metrics

ic

= 0.2275 is

= 0.6343

- Insufficient installed generation capacity.

- Reduced satisfied demand level.

-

Installation of new generating units at node 6 to meet demand increase.

Scenario Relative weight Demand coefficient

1 0.4120 0.47

2 0.3297 0.85

3 0.1592 1.20

4 0.0991 1.70



Año 2019Año 2013Año 2011

D5G1

D1

5

D4

3

6

1

2

4

D2

D3

G5-10

G2-4

5

D4

D5G1

3

6

1

2

4

D1

D2

D3

G5-10

G2-4

Total investment cost: 76.44 M€.

System metrics

ic

= 0.2275 is

= 0.6343

ic

= 0.0930 is

= 0.7017


( ) ( )( )

( )∑ ∑ ∑∑ ∑ ∑∑ ∑∈ ∈ ∈∀

−∈∀ ∈∀ ∈∀

−∈∀ ∈∀

−+

+

−−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

+Y Y L

0

srksrk

)y(C G i0

ibib

D d0

dhdh

y y )k,r,s(yy

yysrk

sr)y(c i b

yy

)y(cG

)y(cG

d hyy

)y(cD

)y(cD)y(c

r1hwK

r1p

r1p

WΩ Ω ΩΩ Ω ΩΩ Ω

σετλλ

Año 2019Año 2013Año 2011

D5G1

D1

5

D4

3

6

1

2

4

D2

D3

G5-10

G2-4


Running time: 5.26 hours 1.63 hours

Priority listcorridor

line ε Δbenefit (%)from to

2 6 1 3 27.27

2 6 2 2 39.67

4 6 1 1 42.11

2 6 3 0.5 38.15

4 6 2 0.25 31.78

1 5 2 0.2 27.05

3 5 2 0.13 21.89

4 6 3 0.1 13.95


Case study 2: IEEECase study 2: IEEE--24 RTS24 RTS

G1

1 2

G2 G3

7

34

5

6

8

9 10

1211

13

14

15

16

17

18

19 20

21

22

23

24

G4G6

G5

G7

G8

G9

G10

G11

D1 D2 D7

D3 D4 D5D6

D8

D9 D10

D11

D12D13

D14

D15

D16 D17

138 kV

230 kV

IEEE-24 RTS

-

Standard model developed by the IEEE Power Engineering Society.

-

17 demand units with piecewise bids split into 3 blocks.

-

11 generating units with piecewise offers split into 4 blocks.

-

Network with two voltage levels: 138 kV and 230 kV.

- 34 lines connecting 24 buses.

- 4 demand scenarios.

- New lines construction costs: • 20 M€

(138 kV).

• 40 M€

(230 kV).



Study of the need for expansion

System metrics

ic

= 0.26 is

= 0.73

LMPs Congested lines and met

demand

02468

1012141618

2008

2010

2012

2014

2016

2018

2020

2022

Años del horizonte temporalN

º de

líne

as s

atur

adas

-100

100

300

500

700

900

1100

1300

Dem

anda

med

ia(M

W)

Líneas Sat. en E1Líneas Sat. en E2Líneas Sat. en E3Líneas Sat. en E4Demanda media(MW)

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Nudo

Prec

io n

odal

(€/M

Wh)

Expansion planningExpansion planning Priority listPriority list



Priority list

OrderCorridor

Line ε Δbenefit (%)from to

1 1 5 2 1.70 1.02

2 20 23 2 1.60 2.73

3 1 5 3 1.50 3.48

4 2 4 2 1.20 3.82

5 2 4 3 1.00 3.84

6 2 6 2 0.85 3.69

7 20 23 3 0.80 3.21

8 2 6 3 0.60 2.77

9 18 21 2 0.36 1.09

10 16 17 2

0.32 -4.2911 16 19 2

12 17 22 2

13 3 9 2 0.25 -5.26

14 17 22 3 0.23 -7.30

15 7 8 2 0.22 -8.32



G6

G5

G7

G8

G9

G10

G11

D9 D10

D11

D12D13

D14

D15

D16 D17

Año 2011Año 2014Año 2019

G1

1 2

G2 G3

7

34

5

6

8

9 10

D1 D2 D7

D3 D4 D5D6

D8

1211

13

14

15

16

17

18

19 20

21

22

23

24

G4

Multiperiod expansion plan

(15 years)

Multiperiod expansion plan

(15 years)

P.N.

CorridorLine Come into

service yearfrom to

1 5 2 2011

1 5 3 2011

2 4 2 2011

2 4 3 2011

2 6 2 2011

20 23 2 2011

20 23 3 2011

2 6 3 2014

18 21 2 2019



Expansion results

System metrics

ic

= 0.26 is

= 0.73

ic

= 0.22 is

= 0.77

0

500

1000

1500

2008

2010

2012

2014

2016

2018

2020

2022

Años del horizonte de planificación

Pote

ncia

(MW

)

0

5

10

15

20

%

Demanda antes de expandir Demanda después de expandirIncremento de demanda

GeneratorsCosts: 1983.55

Benefit: 693.73 ΔBenefit: 12.2%Incomes: 2677.28

DemandsPayments: 3286.89

Benefit: 1093.93 ΔBenefit: 12.8%Utility: 4380.82

Transmision planner Benefit: 609.61 ΔBenefit: 12.8%

Social welfare 2272.33 ΔBenefit: 6.8%



Sensitivity analysis w.r.t. changes in the system growth rateSensitivity analysis w.r.t. changes in the system growth rate

G1

1 2

G2 G3

7

34

5

6

8

9 10

D1 D2 D7

D3 D4 D5D6

D8

1211

13

14

15

16

17

18

19 20

21

22

23

24

G4G6

G5

G7

G8

G9

G10

G11

D9 D10

D11

D12D13

D14

D15

D16 D17

Sistema 1,1

109

8

6

5

43

7

G3G2

21

G1

Sistema 2,1

D17D16

D15

D14D13

D12

D11

D10D9

G11

G10

G9

G8

G7

G5

G6G4

24

23

22

21

2019

18

17

16

15

14

13

11 12

D8

D6D5D4D3

D7D2D1

D17D16

D15

D14D13

D12

D10D9

G11

G10

G9

G8

G7

G5

G6G4

24

23

22

21

2019

18

17

16

15

14

13

11 12

D8

D6D5D4D3

D7D2D1

109

8

6

5

43

7

G3G2

21

G1

Caso base

15

14

13

11 12

D8

D6D5D4D3

D7D2D1

109

8

6

5

43

7

G3G2

21

G1

Sistema 4,1

D17D16

D15

D14D13

D12

D11

D10D9

G11

G10

G9

G8

G7

G5

G6G4

24

23

22

21

2019

18

17

16

G1

1 2

G2 G3

7

34

5

6

8

9 10

D1 D2 D7

D3 D4 D5D6

D8

1211

13

14

15

16

17

18

19 20

21

22

23

24

G4G6

G5

G7

G8

G9

G10

G11

D9 D10

D11

D12D13

D14

D15

D16 D17

Sistema 5,1

Año 2021

Año 2018Año 2015

Año 2013

Año 2019

Año 2014

Año 2011

Año 2022

Año 2012


Sensitivity analysis w.r.t. changes in the discount rateSensitivity analysis w.r.t. changes in the discount rate


G8

G9

G10

G11

D9 D10

D11

D12D13

D14

D15

D16 D17

Sistema i=14%

G1

1 2

G2 G3

7

34

5

6

8

9 10

D1 D2 D7

D3 D4 D5D6

D8

1211

13

14

15

16

17

18

19 20

21

22

23

24

G4G6

G5

G7

Sistema i=12%

D17D16

D15

D14D13

D12

D11

D10D9

G11

G10

G9

G8

G7

G5

G6G4

24

23

22

21

2019

18

17

16

15

14

13

11 12

D8

D6D5D4D3

D7D2D1

109

8

6

5

43

7

G3G2

21

G1

D17D16

D15

D14D13

D12

D10D9

G11

G10

G9

G8

G7

G5

G6G4

24

23

22

21

2019

18

17

16

15

14

13

11 12

D8

D6D5D4D3

D7D2D1

109

8

6

5

43

7

G3G2

21

G1

Caso base

D4 D5D6

D8

1211

13

14

15

16

17

18

19 20

21

22

23

24

G4G6

G5

G7

G8

G9

G10

G11

D9 D10

D11

D12D13

D14

D15

D16 D17

Sistema i=6%

G1

1 2

G2 G3

7

34

5

6

8

9 10

D1 D2 D7

D3

24

23

22

21

2019

18

17

16

15

14

13

11 12

D8

D6D5D4D3

D7D2D1

109

8

6

5

43

7

G3G2

21

G1

Sistema i=8%

D17D16

D15

D14D13

D12

D11

D10D9

G11

G10

G9

G8

G7

G5

G6G4

Año 2012

Año 2022

Año 2011

Año 2014

Año 2019

Año 2013

Año 2016Año 2018

Año 2021


Case study 3: SEPECase study 3: SEPE

SEPE model:SEPE model:

-

400kV network.

- 86 buses.

- 168 lines.


GENERATION

- The main 6 generation technologies in Spain have been modeled.

- Total installed power considered: 65374.2 MW

(96% demand met).

Carbon

Fuel/gas

Nuclear

Ciclo combinado

Eólica

Hidroeléctrica



DEMAND

-The overall demand of SEPE has been grouped in demand units connected to different nodes of the network.

- Each demand unit has been modeled as piecewise elastic linear demand with a single block.

- Demand behavior characterized by 4 demand scenarios:

Low demand.

Low-medium demand.

Medium-high demand.

High demand.


E1

54,39Precio (€/MWh)

Pot. (MW)571,7 680,3 Pot. (MW)

Precio (€/MWh)54,39

E2

788,9 Pot. (MW)


E3

903,3 Pot. (MW)


E4

D11055


INTERNATIONAL EXCHANGES

- SEPE is connected to three countries: Portugal, Morocco and France.

-

Interconnections are modeled as generations or demands as a function of the import/export balance:

France: 2 generators (600 MW).Portugal and Morocco: 4 demands (1240 MW).



PARAMETERS

- Time horizon: 10 years.

- Set of candidates made up of 34 lines:

23 lines parallel to the existing ones (obtained from static simulation).

11 lines for new corridors (obtained from LMP analysis).

Electric parameters: R = 0.000015 pu/km; X = 0.00015 pu/km; pmax = 10.00 pu.

- Cost proportional to the length of the line (600,000 €/km).

- Line amortization period: 25 years.

- Financial interest rate: 10%.

- Growth rate of the system (generation and demand): 3.1%.

- Growth rate of the offer and bid prices (sales and purchases): 5%.

SEPE model implemented in GAMS 21.7, using the solver Cplex 9.0.



Study of the need of expansion

System metrics

ic

= 0.0428 is

= 0.2394

0

10000

20000

30000

40000

50000

60000

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Años del horizonte temporal

MW

Escenario 1Escenario 2Escenario 3Escenario 4Media ponderada

Met demand

0123456789

10

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017


Nº

de lí

neas

sat

urad

as

Escenario 1

Escenario 2

Escenario 3

Escenario 4

Congested lines


Application of the expansion programApplication of the expansion program


201120122013

20152014

2017



Expansion results

SEPE antes de expandir

0

2

4

6

8

10

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017


Nº

de lí

neas

sat

urad

as

Escenario 1

Escenario 2

Escenario 3

Escenario 4

SEPE expandido

0

2

4

6

8

10

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017


Nº

de lí

neas

sat

urad

as

Escenario 1

Escenario 2

Escenario 3

Escenario 4

System metrics

ic

= 0.0428 is

= 0.2394

ic

= 0.0357 is

= 0.2432


50

55

60

65

70

75

N1100

0N11

025

N1105

0N11

075

N1202

0N12

045

N1207

0N13

001

N1302

5N13

045

N1307

5N14

010

N1405

0 N14

065

N1409

0N15

001

N1501

5N15

030

Nudos del SEPE

Prec

ios

noda

les

(€/M

Wh)

Antes de la expansión Después de la expansión


Expansion results

05000

100001500020000250003000035000400004500050000

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

Años del horizonte de planificación

MW

0

1

2

3

4

5

6

7

8

%

Demanda antes de expandir

Demanda despúes de expandir

Incremento de demanda

Demand coverage

2,64

0,28

8,13

-5,77-8

-6

-4

-2

0

2

4

6

8

10

Investment evaluation parameters

Some computational features:-

2-processor computer (with 8 cores) at 3.0 GHz and 16 GB of RAM under Linux O.S.

- 211,118 equations (23 blocks).

- 125,741

variables (3,380 binary variables).

- 432,389 seconds (≈

5 days).

1μ 2μ 3μ4μ



Case study 4: Multiarea 6Case study 4: Multiarea 6--bus Garver systembus Garver system

- New supranational electrical networks interrelated with each other.

- Examples:

EU electricity market (UCTE).

Australian market.

Mercosur (Argentina, Brazil, Paraguay and Uruguay).

Central America electricity market.

U.S. Regional Transmission Organizations.

- Fundamental driver Economics:

• Exploitation of economical mutually beneficial transactions between

systems.

• Increased safety and cost reduction by interconnecting systems.

NEED TO CONSIDER THE INFLUENCE OF INTERCONNECTIONS BETWEEN SYSTEMS

Multiarea expansionMultiarea expansion


D4

3

6

1

2

4

D2

D3

G5-10

G2-4

G2-7

G8-10

D3

D2

4

2

1

6

3

G1D5

D4

5

Sistema 2

Sistema 1

D1

D5G1

D1

5




5

D4

D5G1

3

6

1

2

4

D2

D3

G8-10

G2-7

G2-4

G5-10

D3

D2

4

2

1

6

3

D4

5

D1G1

D5

D1

Año 2021Año 2012Año 2013

Año 2015Año 2011Año 2019

Sistema 1

Sistema 2

Independent expansionsIndependent expansions

0.67 0.740.63 0.70Evolution of is

0.24 0.110.23 0.09Evolution of IC

0.960.75μ4

2.612.64μ3

0.450.27μ2

4.023.67μ1Evaluationinvestmentparameters

868.13685.80Social welfare (M€)

89.7776.44Investment in expansion (M€)

76Nº of lines built

System 2System 1

0.67 0.740.63 0.70Evolution of is

0.24 0.110.23 0.09Evolution of IC

0.960.75μ4

2.612.64μ3

0.450.27μ2

4.023.67μ1Evaluationinvestmentparameters

868.13685.80Social welfare (M€)

89.7776.44Investment in expansion (M€)


System 2System 1



Año 2022Año 2021Año 2020Año 2019

Año 2011

Año 2013

Año 2018

G2-7

G8-10

D3

D2

4

2

1

6

3

G1D5

D4

5

G2-7

G8-10

D3

D2

D1

4

2

1

6

3

G1D5

D4

5

Sistema 1

Sistema 2

Año 2012

Año 2016

D1

Año 2014

Expansion of the interconnected system (I)

Expansion of the interconnected system (I)

0.71 0.750.67 0.760.68 0.73Evolution of is

0.22 0.100.24 0.110.20 0.09Evolution of IC

0.281.37-1.19μ4

2.552.672.39μ3

0.600.420.84μ2

3.434.462.04μ1Investmentevaluationparameters

1614.48762.86851.62Social welfare (M€)

155.5789.6365.94Investment in expansion(M€)


Global system

System 2System 1

0.71 0.750.67 0.760.68 0.73Evolution of is

0.22 0.100.24 0.110.20 0.09Evolution of IC

0.281.37-1.19μ4

2.552.672.39μ3

0.600.420.84μ2

3.434.462.04μ1Investmentevaluationparameters

1614.48762.86851.62Social welfare (M€)



Global system

System 2System 1


Año 2015

D1

Año 2016

Año 2012

Sistema 2

Sistema 1

5

D4

D5G1

3

6

1

2

4

D1

D2

D3

G8-10

G2-7

5

D4

D5G1

3

6

1

2

4

D2

D3

G8-10

G2-7

Año 2018

Año 2013

Año 2011Año 2019Año 2020Año 2021Año 2022

Expansion of the interconnected system (II)

Expansion of the interconnected system (II)


0.71 0.740.67 0.740.68 0.72Evolution of is

0.22 0.100.24 0.100.20 0.08Evolution of IC

0.090.92-0.88μ4

2.372.562.30μ3

0.790.770.86μ2

3.244.252.27μ1Nvestmentevaluationparameters

1614.72741.97877.90Social welfare (M€)



Global System

System 2System 1

0.71 0.740.67 0.740.68 0.72Evolution of is

0.22 0.100.24 0.100.20 0.08Evolution of IC

0.090.92-0.88μ4

2.372.562.30μ3

0.790.770.86μ2

3.244.252.27μ1Nvestmentevaluationparameters

1614.72741.97877.90Social welfare (M€)



Global System

System 2System 1


Multiarea expansionMultiarea expansion

-System composed of 72 buses and

107 lines.

- 33 generating units.

- 51 demand units.

-

3 IEEE-24 RTS with the same topology but different generation and demand values.

-

New lines to interconnect systems are allowed.

G1

12

G2G3

7

34

5

6

8

910

12 11

13

14

15

16

17

18

1920

21

22

23

24

G4G6

G5

G7

G8

G9

G10

G11

D1D2D7

D3D4D5D6

D8

D9D10

D11

D12D13

D14

D15

D16D17

SISTEMA 3

D17D16

D15

D14D13

D12

D11

D10D9

D8

D6D5D4D3

D7D2D1

G11

G10

G9

G8

G7

G5

G6G4

24

23

22

21

2019

18

17

16

15

14

13

11 12

109

8

6

5

43

7

G3G2

21

G1

G1

1 2

G2 G3

7

3

4

5

6

8

9 10

1211

13

14

15

16

17

18

19 20

21

22

23

24

G4G6

G5

G7

G8

G9

G10

G11

D1 D2 D7

D3 D4 D5D6

D8

D9 D10

D11

D12D13

D14

D15

D16 D17

SISTEMA 1SISTEMA 2

Case study 5: Multiarea IEEECase study 5: Multiarea IEEE--24 RTS24 RTS


Interconnected systemsInterconnected systems

Independent systemsIndependent systems

Case study 5: Multiarea IEEECase study 5: Multiarea IEEE--24 RTS24 RTS



SummarySummary







2



A planning algorithm has been designed to develop multiperiod expansion plans including both classic technical operation constraints and new realistic economic and financial constraints.

Implementation of different demand scenarios to characterize the behavior of each year of the planning horizon.

The influence of interconnections between electrical networks has been analyzed related to the individual system expansions (as compared an overall multi-area expansion)

The developed tool has beeen proven useful and robust as tested

with realistic cases.

ConclusionsConclusions


Introduction of safety and reliability criteria.

Demand forecasting.

Connection of GAMS with friendly visual interfaces (PowerWorld).

Development of a decentralized multi-area expansion algorithm based on Lagrangian relaxation techniques.

Future workFuture work


Market-driven dynamic transmission expansion planning

MarketMarket--driven dynamic transmission driven dynamic transmission expansion planningexpansion planning





ESCUELA TÉCNICA SUPERIOR DE INGENIEROS INDUSTRIALESUNIVERSIDAD DE CASTILLA – LA MANCHA

13071 Ciudad Real, Spain

INFORMS 2009 Annual Meeting, San Diego, 11-14 October, 2009

ESCUELA TÉCNICA SUPERIOR DE INGENIEROS INDUSTRIALESUNIVERSIDAD DE MÁLAGA

29071 Málaga, Spain

market market-driven dynamic transmission expansion planning … · market-driven dynamic...

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