Congestion Management in a Stochastic Dispatch Model for ...helper.ipam.ucla.edu/publications/enec2016/enec2016_12751.pdfNordic market time Delivery hour (e.g. 08:00 -08:59) Elbas

Introduction Model Day-ahead formulations Numerical examples Conclusions References

Congestion Management in a Stochastic DispatchModel for Electricity Markets

Endre Bjørndal1, Mette Bjørndal1, Kjetil Midthun2, Golbon

Zakeri3

Workshop on

Optimization and Equilibrium in Energy Economics

UCLA, January 2016

Supported by the Norwegian Research Council1NHH/SNF2SINTEF3University of Auckland 1 / 33


Congestion management and balancing

Reasons for inadequate congestion handling:

• Congestion within areas not considered (in full)

• «Loop-flow» not included in market clearing

• Inadequate representation of capacity constraints

time

Delivery hour (e.g. 08:00-08:59)

Spot marketwith congestion

avoidance

e.g.

- Nodal pricing

- Zonal pricing

- (Uniform price)

Congestion

alleviation

e.g.

- Counter-purchase

- Re-dispatch auction

- Use of reserves list

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Nordic electricity market

3 / 33


Nordic electricity market

4 / 33


Nord Pool Spot - 2015/01/12, 18-19

DK140.33

DK240.33

SE124.34

SE224.34

SE340.33

SE440.33

NO140.33

NO240.33

NO324.34

NO424.34

NO540.33

FI49.58

EE49.58

LV66.03

LT66.03

DEGB92.99

NLPL

BE

RU

FR CZ

BLR

UKR

LU

EIRE

FRE

5 / 33


Markets associate members of PCR

Markets included in PCR - over 2800 TWh

of yearly consumption

Markets that could join next as

part of an agreed European roadmap

Towards Single European Market:

Next Steps

6 / 33


Nordic market

time

Delivery hour (e.g. 08:00-08:59)

Elbas(Until 1 hour

Before delivery)

‘Feasible trade’

Elspot(12:00)

Zonal pricing

Pre-delivery markets

Markets and systems for: • Real-time balancing (Regulating power

market, and other ancillary services)

Bidding regulating power market (20:00)

Special regulation

using regulating power list

Real-time balancing

using regulating power and

ancillary services

• Congestion alleviation

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Flexibility costs and uncertainty

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Stochastic market clearing

Literature:

Wong and Fuller (2007); Bouard et al. (2005b,a); Pritchardet al. (2010); Khazaei et al. (2012); Morales et al. (2012);Khazaei et al. (2013, 2014a,b); Morales et al. (2014); Zugnoand Conejo (2013) ...

Our paper:

Energy-only stochastic market clearing as in Pritchard et al.(2010)How should the day-ahead part of the market be modeled?

Eects of day-ahead network ow and balance constraints

Compare to a sequential market clearing model with myopicclearing of the day-ahead part of the market

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Outline

1 Introduction

2 Model

3 Day-ahead formulations

4 Numerical examples

5 Conclusions

10 / 33


Model

Day-ahead and real-time generation (≥ 0) and load (≤ 0)

quantities:

xi ∈ C 1

i ∀i ∈ I

Xiω ∈ C 2

i (ω, xi ) ∀i ∈ I , ω ∈ Ω

Upregulation X uiω = maxXiω − xi , 0 or downregulation

X diω = maxxi − Xiω, 0 for exible entities.

11 / 33


Generator cost functions

Gen.

Price

bi

ai

xi

ai + b ixi

X i ω1

Xi ω1

d

bid

ai − aid

X i ω2

Xi ω2

u

biu

aiu − ai

12 / 33


Load benet curves

Con.

Price

bi

ai

− xi

ai + b ixi

− Xi ω1

Xi ω1

u

biu

aiu − ai

− Xi ω2

Xi ω2

d

bid

ai − aid

13 / 33


Objective function

Cost of real-time quantity at day-ahead parameters:

ci (Xiω) = aiXiω + 0.5bi (Xiω)2

Flexibility cost:

ci (xi ,Xiω) =(aui − ai )Xuiω + 0.5(bui − bi )(X u

iω)2

+(ai − adi )X diω + 0.5(bdi − bi )(X d

iω)2

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Stochastic market clearing model

minx,f ,X ,F

E

[∑i∈I

(ci (Xi ) + ci (xi ,Xi )

)](1a)

s.t.

xi ∈ C 1i ∀i ∈ I (1b)

Xiω ∈ C 2i (ω, xi ) ∀i ∈ I , ω ∈ Ω (1c)

τn(f ) +∑i∈I (n)

xi = 0 ∀n ∈ N [πn] (1d)

τn(Fω)− τn(f ) +∑i∈I (n)

(Xiω − xi ) = 0 ∀n ∈ N, ω ∈ Ω [pωλnω] (1e)

f ∈ U1 (1f)

Fω ∈ U2 ∀ω ∈ Ω (1g)

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Myopic market clearing model - day-ahead part

minx,f

∑i∈I

ci (xi ) (2a)

s.t.

xi ∈ C 1i ∀i ∈ I (2b)

τn(f ) +∑i∈I (n)

xi = 0 ∀n ∈ N [πn] (2c)

f ∈ U1 (2d)

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Myopic market clearing model - real-time part, scenario ω

minXω,Fω

∑i∈I

(ci (Xiω) + ci (xi ,Xiω)

)(3a)

s.t.

Xiω ∈ C 2i (ω, xi ) ∀i ∈ I (3b)

τn(Fω)− τn(f ) +∑i∈I (n)

(Xiω − xi ) = 0 ∀n ∈ N [pωλnω] (3c)

Fω ∈ U2 (3d)

17 / 33


Day-ahead constraints

We assume that U2 represents the network constraints in a DC

load ow model without losses

What should U1 represent?

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Alternative day-ahead network representations

1 Nodal model, i.e., U1 = U2

2 Zonal model

No loop owAggregate ow capacities set by system operator(s)

3 Unconstrained ow, i.e., U1 = R|L|

4 Unconstrained ow and balance

min[v stochnodal , vstochzonal ] ≥ v stochbal ≥ v stochunc

19 / 33


Example 1

ω = 1

130

10

20

10

3−3020

ω = 2

10

20

260

40

3−6020

P(1) = P(2) = 0.5

Real-time quantities Xω are given above

All cost parameters equal zero, except au1

= au2

= 1 and

au3

= 0.25

All lines have identical impedances

Capacity of line (2,3) is 40

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Example 1 - stochastic model

min 0.5 · 1 ·([30− x1]+ + [0− x1]+ + [0− x3]+ + [60− x3]+

)+ 0.5 · 0.25 ·

([−30− x3]+ + [−60− x3]+

)s.t.

x1 + x2 + x3 = 0

− 40 ≤ x2 − x33

≤ 40

21 / 33


Example 1 - optimal day-ahead schedules

x1

−50

0

50 x2−50

0

50

x3

−100

0

100

(30,0,−30)

(30,0,−30)

(0,60,−60)(30,0,−30)

(0,60,−60)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)xnodal = (30,45,−75)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)xnodal = (30,45,−75)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)

xunc = (30,60,−30)

xnodal = (30,45,−75)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)

xunc = (30,60,−30)

xnodal = (30,45,−75)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)

xunc = (30,60,−30)

xnodal = (30,45,−75)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)

xunc = (30,60,−30)

xnodal = (30,45,−75)

(30,0,−30)

(0,60,−60)

xbal = (30,60,−90)

xunc = (30,60,−30)

xnodal = (30,45,−75)

(30,0,−30)

v stochunc = 0

v stochbal = 0.5 · (−30− (−90)) · 0.25+ 0.5 · (−60− (−90)) · 0.25 = 11.25

v stochnodal = 0.5 · (−30− (−75)) · 0.25

+ 0.5 ·[(60− 45) · 1

+ (−60− (−75)) · 0.25]= 15

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Example 2

Node 2: Nuclear + Thermal

Eur

os/M

Wh

MWh/h

000

1000

010

000

1500

0

221010

150150

Node 1: Wind (scen. 2) − Consumption

Eur

os/M

Wh

MWh/h

00

7000

0

150150

b = 0.01

1

2

32000

3000

3000 Node 3: Hydro

Eur

os/M

Wh

MWh/h

000

1500

0

150150150

b = 0.01

23 / 33


Wind scenarios

p1 = 0.2

p2 = 0.5

p3 = 0.3

Wind = 0

Wind = 7000

Wind = 15000

24 / 33


Cost and benet parameters

Entity Node Intercept (a) Slope (b) Flexible? Flex. cost up Flex. cost down

Wind 1 0 0 Partly - -Load 1 150 0.01 Yes bu = 30b -Nucl. 2 2 0 No - -Therm. 2 10 0 Yes au − a = 6 -Hydro 3 0 0.01 Yes bu = 10b -

25 / 33


Example 2 - optimal values, stochastic model

Model Value (1000 es)

Wait-and-see 956.620

Unconstrained 952.500

Balanced 950.808

Nodal 950.542

Zonal (cap1,2,3 = 3000) 938.986

Zonal (cap1,2,3 = 5000) 950.808

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Example 2 - optimal schedules, stochastic model

Nodal model

Real-time adj.Entity Day-head Low Medium High

Wind 0 7000 13800Nucl. 1200Therm. 42 -42 438 -42Hydro 3517 83 -877 -3517Load -4758 -42 -6562 -10242

Total 0 0 0 0

Unconstrained model

Real-time adj.Entity Day-head Low Medium High

Wind 0 7000 14000Nucl. 1000Therm. 800 -800 -800Hydro 4000 -1600 -4000Load -5000 -6200 -10000

Total 800 -800 -800 -800

Power ow - nodal model

1

2000

−4758

2

758

1242

32758 3517

1

2000 (0)

−4800 (−42)

2

800 (42)

1200 (−42)

32800 (42) 3600 (83)

1

2000 (0)

−4320 (438)

2

320 (−438)

1680 (438)

32320 (−438) 2640 (−877)

1

800 (−1200)

−1200 (3558)

2

400 (1158)

1200 (−42)

3400 (−2358) 0 (−3517)

27 / 33


Example 2 - cost and benet eects, stochastic model

Nodal model

Flex. costs (−c)Entity E[−c] Low Medium High E[−c − c]

Wind 0.000 0.000Nucl. -2.400 -2.400Therm. -2.400 -2.630 -3.715Hydro -30.384 -0.313 -30.447Load 987.104 987.104

Total 951.920 -0.313 -2.630 -0.000 950.542

Unconstrained model

Flex. costs (−c)E[−c] Low Medium High E[−c − c]

0.000 0.000-2.000 -2.000-4.000 -4.000-30.400 -30.400988.900 988.900

952.500 0.000 0.000 0.000 952.500

28 / 33


Myopic model

Infeasibility issue, e.g. due to scheduling of non-exible nuclear

in day-ahead market

29 / 33


Myopic / nodal model - eect of day-ahead wind capacity

Wind capacity

Tota

l sur

plus

−46

53.9

950.

3

0 15000

30 / 33


Myopic / balanced model - eect of day-ahead wind capacity

Wind capacity

Tota

l sur

plus

−47

95.9

−28

63.9

0 13600

31 / 33


Conclusions and further research

Too restrictive constraints in the day-ahead stage of a

stochastic market clearing model may hinder exibility and

yield sub-optimal solutions

Examples of such constraints are DC load ow capacitites,

European-style zonal capacities, and even nodal balance

constraints

Further research:

PricingInvestigate relevance for deterministic (sequential) marketclearing models

32 / 33


References

Bouard, F., Galiana, F. D., and Conejo, A. J. (2005a). Market-clearing with stochastic security-part i:formulation. Power Systems, IEEE Transactions on, 20(4):18181826.

Bouard, F., Galiana, F. D., and Conejo, A. J. (2005b). Market-clearing with stochastic security-part ii:Case studies. Power Systems, IEEE Transactions on, 20(4):18271835.

Khazaei, J., Zakeri, G., and Oren, S. (2012). Single and multi-settlement approaches to market clearingmechanisms under demand uncertainty.

Khazaei, J., Zakeri, G., and Oren, S. (2013). Deterministic vs. stochastic settlement approaches tomarket clearing mechanisms under demand uncertainty.

Khazaei, J., Zakeri, G., and Oren, S. S. (2014a). Market clearing mechanisms under uncertainty.

Khazaei, J., Zakeri, G., and Pritchard, G. (2014b). The eects of stochastic market clearing on the costof wind integration: a case of new zealand electricity market. Energy Systems, 5(4):657675.

Morales, J., Conejo, A., Liu, K., and Zhong, J. (2012). Pricing electricity in pools with wind producers.Power Systems, IEEE Transactions on, 27(3):13661376.

Morales, J. M., Zugno, M., Pineda, S., and Pinson, P. (2014). Electricity market clearing with improvedscheduling of stochastic production. European Journal of Operational Research, 235(3):765 774.

Pritchard, G., Zakeri, G., and Philpott, A. (2010). A single-settlement, energy-only electric power marketfor unpredictable and intermittent participants. Operations Research, 58(4-part-2):12101219.

Wong, S. and Fuller, J. D. (2007). Pricing energy and reserves using stochastic optimization in analternative electricity market. Power Systems, IEEE Transactions on, 22(2):631638.

Zugno, M. and Conejo, A. J. (2013). A robust optimization approach to energy and reserve dispatch inelectricity markets. Technical report, Technical University of Denmark.

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Documents

Congestion Management in a Stochastic Dispatch Model for ...helper.ipam.ucla.edu/publications/enec2016/enec2016_12751.pdfNordic market time Delivery hour (e.g. 08:00 -08:59) Elbas