Optimal Order Strategies on the Day- Ahead Electricity Market - - PowerPoint PPT Presentation

KTH ROYAL INSTITUTE OF TECHNOLOGY

Optimal Order Strategies on the Day- Ahead Electricity Market

Martin Biel 20/9-2017

Outline Background Problem Description Contribution Optimal Strategies Outlook on Future Work

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Outline Background Problem Description Contribution Optimal Strategies Outlook on Future Work

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Background - Motivation

◮ Simulation of hydro power operations → Decision-support

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Background - Motivation

◮ Simulation of hydro power operations → Decision-support

◮ Price forecasts ◮ Irregular power production: solar and wind ◮ Nuclear power phase-out

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Background - Motivation

◮ Simulation of hydro power operations → Decision-support

◮ Price forecasts ◮ Irregular power production: solar and wind ◮ Nuclear power phase-out

◮ Common: Trade-off between accuracy and computation time

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2017 2041

Figure: Simulations of hydro power operations

Background - Aim Provide reliable decision-support in real time

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Background - Aim Provide reliable decision-support in real time

◮ Accurate models ◮ Fast computations

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Background - Aim Provide reliable decision-support in real time

◮ Accurate models

◮ Optimal model reductions

◮ Fast computations

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Background - Aim Provide reliable decision-support in real time

◮ Accurate models

◮ Optimal model reductions

◮ Fast computations

◮ Scalable algorithms that make efficient use of commodity hardware

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Backgound - Approach Stochastic programming for hydro power operations:

◮ Optimal orders on the day-ahead market ◮ Maintenance scheduling ◮ Long-term investments ◮ Wind/solar uncertainties

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Backgound - Approach Stochastic programming for hydro power operations:

◮ Optimal orders on the day-ahead market ◮ Maintenance scheduling ◮ Long-term investments ◮ Wind/solar uncertainties

Improvements

◮ Multiple scenarios → More accurate models ◮ Parallel decomposition → Faster computations

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Backgound - Approach Stochastic programming for hydro power operations:

◮ Optimal orders on the day-ahead market ◮ Maintenance scheduling ◮ Long-term investments ◮ Wind/solar uncertainties

Improvements

◮ Multiple scenarios → More accurate models ◮ Parallel decomposition → Faster computations

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Outline Background Problem Description Contribution Optimal Strategies Outlook on Future Work

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Problem Description - Scandinavian Electricity Market Electricity markets in Scandinavia deregulated since 90s

◮ Norway 1991 ◮ Sweden 1996 ◮ Finland 1998 ◮ Denmark 2000

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Problem Description - Scandinavian Electricity Market Electricity markets in Scandinavia deregulated since 90s

◮ Norway 1991 ◮ Sweden 1996 ◮ Finland 1998 ◮ Denmark 2000

Energy volumes actively traded on a competitive market: Nord Pool

◮ Day-ahead market ◮ Intraday market

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Problem Description - Electricity Market Day- Ahead Actor 1 P1 E1 Actor 2 P2 E2

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Problem Description - Electricity Market Day- Ahead Actor 1 P1 E1 Actor 2 P2 E2 Market closes

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Problem Description - Electricity Market Day- Ahead Actor 1 P1 E1 Actor 2 P2 E2 Market closes Actor 1 Actor 2 Balance responsible PM,E1 Balance responsible PM,E2 Next day

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Problem Description - Electricity Market Day- Ahead Actor 1 P1 E1 Actor 2 P2 E2 Market closes Actor 1 Actor 2 Balance responsible PM,E1 Balance responsible PM,E2 Next day Intraday P E P E

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Problem Description - The Day-Ahead Market Order Types

◮ Single Hourly Order

◮ Price independent ◮ Price Dependent

◮ Block Order

◮ Regular ◮ Linked

◮ Exclusive Group ◮ Flexible Order

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Problem Description - The Day-Ahead Market Order Types

◮ Single Hourly Order

◮ Price independent ◮ Price Dependent

◮ Block Order

◮ Regular ◮ Linked

◮ Exclusive Group ◮ Flexible Order

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Problem Description - Single Order

0.00 203.32 406.63 609.95 813.27

Order Volume [MWh/h]

0.00 17.49 34.97 52.46

Price [EUR/MWh]

Order Curve

Price Independent Order Price Dependent Order

Figure: Single hourly order 10/39

Problem Description - Single Order

0.00 203.32 406.63 609.95 813.27

Order Volume [MWh/h]

0.00 17.49 34.97 52.46

Price [EUR/MWh]

Order Curve

Price Independent Order Price Dependent Order Trading Outcome

Figure: Interpolated energy volume for a given market price 10/39

15 Hour

Block Order

36.85 [EUR/MWh] 3.37 [MWh/h]

Figure: Block order between 00:00-15:00

15

Hour

21.52 28.47 35.42 42.37

Price [EUR/MWh]

Block Order

36.85 [EUR/MWh] 3.37 [MWh/h]

Rejected Order Market price

Figure: Rejected after market price settlement

15

Hour

25.07 27.29 29.51 31.73 33.95 36.17 38.40 40.62 42.84 45.06 47.28 49.50

Price [EUR/MWh]

Block Order

36.85 [EUR/MWh] 3.37 [MWh/h]

Accepted Order Market price

Figure: Accepted after market price settlement

Problem Description - Optimal Order Strategies

◮ Optimal orders given price forecasts ◮ Price taking hydro power producer ◮ Next day production governed by hydroelectric model

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Outline Background Problem Description Contribution Model Framework Stochastic Day-Ahead Model Optimization Algorithms Optimal Strategies Outlook on Future Work

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Outline Background Problem Description Contribution Model Framework Stochastic Day-Ahead Model Optimization Algorithms Optimal Strategies Outlook on Future Work

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Contribution - Model Framework Data

◮ Physical data of Swedish hydro power stations

◮ Topologies ◮ Capacitites ◮ Flow times

◮ Financial data from Nord Pool

◮ historic prices

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Contribution - Model Framework Data

◮ Physical data of Swedish hydro power stations

◮ Topologies ◮ Capacitites ◮ Flow times

◮ Financial data from Nord Pool

◮ historic prices

Julia: JuMP + StructJuMP

◮ Domain-specific modeling language for mathematical optimization ◮ Optimization models can be processed programatically

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HydroModels.jl

# Variables # ======================================================== @variable ( internalmodel , xt_d [ i = model . bids , t = model . hours ] >= 0) @variable ( internalmodel , yt [ t = model . hours ] >= 0) @variable ( internalmodel ,H[ t = model . hours ] >= 0) # Define

• bjective

# ======================================================== @objective ( internalmodel , Max, n e t _ p r o f i t + value_of_stored_water ) # Constraints # ======================================================== # Load balance @constraint ( internalmodel , loadbalance [ s = model . scenarios , t = model . hours ] , yt [ s , t ] + sum( yb [ s , b ] for b = f i n d (A− >in ( t ,A) , model . hours_per_block ) ) − H[ s , t ] == z_up [ s , t ] − z_do [ s , t ] )

HydroModels.jl

# Variables # ======================================================== @variable ( internalmodel , xt_d [ i = model . bids , t = model . hours ] >= 0) @variable ( internalmodel , yt [ t = model . hours ] >= 0) @variable ( internalmodel ,H[ t = model . hours ] >= 0) # Define

• bjective

# ======================================================== @objective ( internalmodel , Max, n e t _ p r o f i t + value_of_stored_water ) # Constraints # ======================================================== # Load balance @constraint ( internalmodel , loadbalance [ s = model . scenarios , t = model . hours ] , yt [ s , t ] + sum( yb [ s , b ] for b = f i n d (A− >in ( t ,A) , model . hours_per_block ) ) − H[ s , t ] == z_up [ s , t ] − z_do [ s , t ] )

+

HydroModels.jl

# Variables # ======================================================== @variable ( internalmodel , xt_d [ i = model . bids , t = model . hours ] >= 0) @variable ( internalmodel , yt [ t = model . hours ] >= 0) @variable ( internalmodel ,H[ t = model . hours ] >= 0) # Define

• bjective

# ======================================================== @objective ( internalmodel , Max, n e t _ p r o f i t + value_of_stored_water ) # Constraints # ======================================================== # Load balance @constraint ( internalmodel , loadbalance [ s = model . scenarios , t = model . hours ] , yt [ s , t ] + sum( yb [ s , b ] for b = f i n d (A− >in ( t ,A) , model . hours_per_block ) ) − H[ s , t ] == z_up [ s , t ] − z_do [ s , t ] )

+ =

data = HydroModelData ( " data / plantdata . csv " , " data / spotpricedata . csv " ) dayahead = DayAheadModel ( data ,5 , " Ljusnan " ) plan ! ( dayahead )

Outline Background Problem Description Contribution Model Framework Stochastic Day-Ahead Model Optimization Algorithms Optimal Strategies Outlook on Future Work

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Contribution - Stochastic Day-Ahead Model maximize Profit + Water Value − Balance Cost subject to Day-Ahead Orders Physical Limitations Economic/Legal Limitations

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Contribution - Stochastic Day-Ahead Model Day-Ahead Orders - x ∈ X

◮ Indices t ∈ T := {1, . . . , 24}, b ∈ B := {b = (ta, . . . , tb) : ti ∈ T} ◮ Price independent: xi t ≥ 0 ◮ Price dependent: 0 ≤ xd i,t ≤ xd i,t+1 ◮ Block: xb j,b ≥ 0

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Contribution - Stochastic Day-Ahead Model Day-Ahead Orders - x ∈ X

◮ Indices t ∈ T := {1, . . . , 24}, b ∈ B := {b = (ta, . . . , tb) : ti ∈ T} ◮ Price independent: xi t ≥ 0 ◮ Price dependent: 0 ≤ xd i,t ≤ xd i,t+1 ◮ Block: xb j,b ≥ 0

Scenario Outcomes - y ∈ Y(x, ξ) yt = xi

t + ρξ t − pi

pi+1 − pi xd

i+1,t + pi+1 − ρξ t

pi+1 − pi xd

i,t,

pi ≤ ρξ

t ≤ pi+1

yb =

¯ j(b)

• j=1

xj,b, ¯ j(b) = max

• i : pi ≤ 1

|b|

• t∈b

ρξ

t

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Contribution - Stochastic Day-Ahead Model Next Day Production - h ∈ H(y)

◮ Indices p ∈ P := {All power stations operable by the producer} ◮ Water discharge/spillage: 0 ≤ Qp,t ≤ Qp, Sp,t ≥ 0 ◮ Reservoir content: 0 ≤ Mp,t ≤ Mp ◮ Energy production: Hp,t ≥ 0 ◮ Local inflow/outflow: Vp ◮ Power imbalances: z+ t , z− t ≥ 0

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Contribution - Stochastic Day-Ahead Model Next Day Production - h ∈ H(y)

◮ Indices p ∈ P := {All power stations operable by the producer} ◮ Water discharge/spillage: 0 ≤ Qp,t ≤ Qp, Sp,t ≥ 0 ◮ Reservoir content: 0 ≤ Mp,t ≤ Mp ◮ Energy production: Hp,t ≥ 0 ◮ Local inflow/outflow: Vp ◮ Power imbalances: z+ t , z− t ≥ 0

Load Balance L(y, h) : yt +

• b∈B:t∈b

yb −

• p

Ht = z+

t − z− t

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Qp,t [HE] Hp,t [MWh]

Hp,t =

1 Q p,t,1

Hp,t =

2 Q p,t,2

Hp,t =

3 Q p,t,3

Figure: Piecewise linear production equivalent

Contribution - Stochastic Day-Ahead Model Hydro power production

Qp,t [HE] Hp,t [MWh]

Hp,t = 1 Q p,t,1 Hp,t = 2 Q p,t,2 Hp,t = 3 Q p,t,3

Figure: Piecewise linear production equivalent

→ Hp,t =

• s

µp,sQp,t,s

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Contribution - Stochastic Day-Ahead Model Hydro power production

Qp,t [HE] Hp,t [MWh]

Hp,t = 1 Q p,t,1 Hp,t = 2 Q p,t,2 Hp,t = 3 Q p,t,3

Figure: Piecewise linear production equivalent

→ Hp,t =

• s

µp,sQp,t,s Hydrological balance Mp,t = Mp,t−1 − Qp,t − Sp,t +

• pq∈Qu

Qpq,t−τpq +

• ps∈Su

Sps,t−τps + Vp

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Contribution - Stochastic Day-Ahead Model Water value W(h) = λf

• p

Mp,24

• pq∈Qd,s

µpq,s

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Contribution - Stochastic Day-Ahead Model Water value W(h) = λf

• p

Mp,24

• pq∈Qd,s

µpq,s Profit Π(y) =

• t

ρξ

t yt +

• b

|b|¯ ρξ

byb −

• t

(λ+

t z+ t − λ− t z− t )

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Contribution - Stochastic Day-Ahead Model Water value W(h) = λf

• p

Mp,24

• pq∈Qd,s

µpq,s Profit Π(y) =

• t

ρξ

t yt +

• b

|b|¯ ρξ

byb −

• t

(λ+

t z+ t − λ− t z− t )

Objective Q(y, h, ξ) = W(h) + Π(y)

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Contribution - Stochastic Day-Ahead Model Complete Model min Eξ [Q(y, h, ξ)] s.t. x ∈ X y ∈ Y(x, ξ) h ∈ H(y) L(y, h) = 0

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Outline Background Problem Description Contribution Model Framework Stochastic Day-Ahead Model Optimization Algorithms Optimal Strategies Outlook on Future Work

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Contribution - Optimization Algorithms Benders decomposition for stochastic programming

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Contribution - Optimization Algorithms Benders decomposition for stochastic programming

◮ L-Shaped [Van Slyke,Wets]

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Contribution - Optimization Algorithms Benders decomposition for stochastic programming

◮ L-Shaped [Van Slyke,Wets] ◮ Regularized Decomposition [Ruszczy´

nski]

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Contribution - Optimization Algorithms Benders decomposition for stochastic programming

◮ L-Shaped [Van Slyke,Wets] ◮ Regularized Decomposition [Ruszczy´

nski]

◮ Trust-Region L-Shaped [Linderoth,Wright]

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Contribution - Optimization Algorithms Benders decomposition for stochastic programming

◮ L-Shaped [Van Slyke,Wets] ◮ Regularized Decomposition [Ruszczy´

nski]

◮ Trust-Region L-Shaped [Linderoth,Wright]

LShaped.jl ls = LShapedSolver(model,x0) rls = RegularizedLShapedSolver(model,x0) trls = TrustRegionLShapedSolver(model,x0)

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Contribution - Parallel Optimization Algorithms The algorithms are cutting-plane methods:

◮ Solve subproblems and generate cutting-planes ◮ Update and resolve a master problem

min cTx + Eξ

• min

y∈Y(x) Q(y, ξ)

• min

cTx +

n

• i=1

θi s.t. x ∈ X → s.t. x ∈ X ∂Qix + θi = qi

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Contribution - Parallel Optimization Algorithms The algorithms are cutting-plane methods:

◮ Solve subproblems and generate cutting-planes ◮ Update and resolve a master problem

min cTx + Eξ

• min

y∈Y(x) Q(y, ξ)

• min

cTx +

n

• i=1

θi s.t. x ∈ X → s.t. x ∈ X ∂Qix + θi = qi Readily extendable to asynchronous variants

◮ Master problem is solved on a master node ◮ Subproblems are distributed among workers

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Contribution - Parallel Optimization Algorithms Idea to exploit structure and make use of commodity hardware

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Contribution - Parallel Optimization Algorithms Idea to exploit structure and make use of commodity hardware

◮ Linear subproblems have the same underlying matrix structure

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Contribution - Parallel Optimization Algorithms Idea to exploit structure and make use of commodity hardware

◮ Linear subproblems have the same underlying matrix structure

◮ LU factorize once and store on GPU ◮ Reuse for efficient linear solves during simplex iterations

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Contribution - Summary

◮ HydroModels.jl

◮ Possible to extend to other models of hydro power operations

◮ Day-Ahead Model

◮ Optimization formulation ◮ Visualization tools

◮ LShaped.jl

◮ 3 fully implemented serial L-Shaped variants ◮ 1 parallel implementation (work in progress)

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Contribution - Summary

◮ HydroModels.jl

◮ Possible to extend to other models of hydro power operations ◮ Modular

◮ Day-Ahead Model

◮ Optimization formulation ◮ Visualization tools

◮ LShaped.jl

◮ 3 fully implemented serial L-Shaped variants ◮ 1 parallel implementation (work in progress) ◮ Modular

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Outline Background Problem Description Contribution Optimal Strategies Example 1: Ljusnan Example 2: All rivers Outlook on Future Work

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Outline Background Problem Description Contribution Optimal Strategies Example 1: Ljusnan Example 2: All rivers Outlook on Future Work

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50 100 km

LJUSNAN

Teckenförklaring: Regleringsdamm Kraftverk

Figure: Courtesy of VRF (http://www.vattenreglering.se/)

Example 1: Ljusnan

◮ 21 power stations ◮ 5 price curves from historic data

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Example 1: Ljusnan

◮ 21 power stations ◮ 5 price curves from historic data

Day-Ahead model with:

◮ 9305 linear constraints ◮ 18274 variables

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Example 1: Single Order

0.00 203.32 406.63 609.95 813.27

Order Volume [MWh/h]

0.00 17.49 34.97 52.46

Price [EUR/MWh]

Order Curve

Price Independent Order Price Dependent Order

Figure: Single order during the first hour 27/39

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

Hour

0.00 17.49 34.97 52.46 69.94

Price [EUR/MWh]

Single Orders

0.0 23.33 93.50 0.0 38.73 0.0 79.33 0.0 88.86 0.0 112.9 25.20 0.0 33.43 0.0 667.1 0.0 250.9 717.5 613.6 0.0 99.07 0.0 730.9 728.8 0.0 264.4 0.0 474.6 0.0 731.4 11.50 0.0 723.2 275.0 0.0 455.4 588.9 0.0 135.2 554.6 0.0 142.8 0.0 710.8 247.6 0.0 93.13 0.0 50.86 0.0 0.0 246.1 0.0 368.9 0.0 17.05 Independent Volume [MWh] Dependent Volumes [Mwh]

Figure: All single orders in optimal strategy

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

Hour

0.00 10.11 20.21 30.32 40.43 50.53 60.64 70.74

Price [EUR/MWh]

Single Orders

38.62 37.68 77.19 86.36 110.0 25.20 32.69 662.1 717.5 613.6 98.88 744.7 728.8 13.94 264.4 474.6 731.4 11.50 723.2 275.0 455.4 588.9 141.5 554.6 179.6 709.4 247.6 93.13 50.86 60.30 246.1 366.1 16.77 Independent Volume [MWh] Dependent Volumes [Mwh]

Accepted Orders Rejected Orders Market price

Figure: Single order outcome of optimal strategy, for a given price curve

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

Block Orders

19.37 369.4 19.37 253.6 36.85 3.37 36.85 0.59 36.85 16.71 36.85 3.30 36.85 7.56 36.85 0.31 36.85 0.83 36.85 6.50 36.85 4.96 Price [EUR/MWh] Volume [MWh/h]

Figure: All block orders in optimal strategy

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

Hour

21.73 24.46 27.18 29.91 32.64 35.36 38.09 40.82 43.54 46.27 49.00

Price [EUR/MWh]

Block Orders

42.06 369.4 41.25 253.6 37.11 0.59 45.80 3.30 44.23 7.56 39.29 0.31 39.13 0.83 36.92 6.50 37.80 4.96 Price [EUR/MWh] Volume [MWh/h]

Accepted Orders Rejected Orders Market price

Figure: Block order outcome of optimal strategy, for a given price curve

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

Hour

0.33 86.33 172.33 258.34 344.34 430.34 516.34 602.34 688.34

Energy Volume [MWh]

H Hmax H_2 H_3 H_4 H_5

Figure: Energy production in all scenarios

Outline Background Problem Description Contribution Optimal Strategies Example 1: Ljusnan Example 2: All rivers Outlook on Future Work

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Example 2: All rivers

◮ 257 power stations ◮ 20 price curves from historic data

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Example 2: All rivers

◮ 257 power stations ◮ 20 price curves from historic data

Day-Ahead model with:

◮ 376700 linear constraints ◮ 748043 variables

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

Hour

0.00 29.85 59.69 89.54

Price [EUR/MWh]

Single Orders

0.0 1.21e+04 0.0 3.11e+03 0.0 2.17e+03 0.0 2.80e+03 0.0 1.10e+04 0.0 1.38e+04 0.0 478.3 1.34e+04 0.0 1.07e+04 1.33e+04 0.0 9.00e+03 1.37e+04 0.0 9.62e+03 1.31e+04 0.0 3.35e+03 1.41e+04 0.0 1.47e+04 0.0 1.48e+04 0.0 1.43e+04 0.0 1.42e+04 0.0 5.18e+03 1.38e+04 0.0 1.41e+04 0.0 4.31e+03 1.40e+04 0.0 1.14e+04 1.33e+04 0.0 8.58e+03 1.32e+04 0.0 1.32e+04 0.0 1.24e+04 0.0 1.04e+04 0.0 2.47e+03 Independent Volume [MWh] Dependent Volumes [Mwh]

Figure: All single orders in optimal strategy

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

Block Orders

4.49 500.0 4.49 500.0 4.49 487.5 34.34 487.7 34.34 500.0 34.34 500.0 64.19 500.0 64.19 500.0 64.19 494.9 64.19 500.0 64.19 500.0 64.19 500.0 64.19 500.0 Price [EUR/MWh] Volume [MWh/h]

Figure: All block orders in optimal strategy

0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Hour

0.00 16.29 32.57 48.86 65.15 81.43

Price [EUR/MWh]

Single Orders

1.18e+04 3.04e+03 2.13e+03 2.73e+03 1.08e+04 1.36e+04 1.27e+04 1.33e+04 1.37e+04 1.31e+04 1.41e+04 1.47e+04 1.48e+04 1.43e+04 1.42e+04 1.38e+04 1.41e+04 1.41e+04 1.33e+04 1.32e+04 1.32e+04 1.24e+04 1.04e+04 2.44e+03 Independent Volume [MWh] Dependent Volumes [Mwh] Accepted Orders Rejected Orders Market price

0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Hour

0.00 15.44 30.89 46.33 61.78 77.22 92.67

Price [EUR/MWh]

Single Orders

1.15e+04 2.96e+03 2.07e+03 2.65e+03 1.04e+04 1.31e+04 2.01e+03 1.12e+04 1.03e+04 1.08e+04 7.30e+03 1.42e+04 1.42e+04 1.37e+04 1.36e+04 6.73e+03 1.35e+04 5.90e+03 1.18e+04 9.38e+03 1.26e+04 1.19e+04 9.92e+03 2.34e+03 Independent Volume [MWh] Dependent Volumes [Mwh] Accepted Orders Rejected Orders Market price

0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Hour

0.00 16.03 32.05 48.08 64.11 80.14

Price [EUR/MWh]

Single Orders

1.19e+04 3.05e+03 2.13e+03 2.74e+03 1.08e+04 1.36e+04 1.31e+04 1.33e+04 1.37e+04 1.31e+04 1.41e+04 1.47e+04 1.48e+04 1.43e+04 1.42e+04 1.38e+04 1.41e+04 1.41e+04 1.33e+04 1.32e+04 1.32e+04 1.23e+04 1.03e+04 2.43e+03 Independent Volume [MWh] Dependent Volumes [Mwh] Accepted Orders Rejected Orders Market price

0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Hour

0.00 16.59 33.19 49.78 66.37 82.97

Price [EUR/MWh]

Single Orders

1.20e+04 3.08e+03 2.15e+03 2.76e+03 1.09e+04 1.37e+04 1.34e+04 1.33e+04 1.37e+04 1.31e+04 1.41e+04 1.47e+04 1.48e+04 1.43e+04 1.42e+04 1.38e+04 1.41e+04 1.44e+04 1.33e+04 1.32e+04 1.32e+04 1.24e+04 1.04e+04 2.45e+03 Independent Volume [MWh] Dependent Volumes [Mwh] Accepted Orders Rejected Orders Market price

Figure: Single order outcomes of optimal strategy, for 4 different price curves

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

Hour

21.73 24.46 27.18 29.91 32.64 35.36 38.09 40.82 43.54 46.27 49.00 51.72 54.45 57.17 59.90 62.63 65.35 68.08

Price [EUR/MWh]

Block Orders

37.87 500.0 37.20 500.0 40.75 487.5 Price [EUR/MWh] Volume [MWh/h] Accepted Orders Rejected Orders Market price

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

Hour

28.26 31.60 34.94 38.28 41.62 44.96 48.30 51.64 54.98 58.32 61.66 65.00 68.34

Price [EUR/MWh]

Block Orders

46.98 500.0 50.12 500.0 49.40 487.5 34.41 487.7 Price [EUR/MWh] Volume [MWh/h] Accepted Orders Rejected Orders Market price

Figure: Block order outcomes of optimal strategy, for two given price curves

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

Hour

1569.29 3291.63 5013.98 6736.32 8458.67 10181.02 11903.36 13625.71

Energy Volume [MWh]

Figure: Energy production in all scenarios

Outline Background Problem Description Contribution Optimal Strategies Outlook on Future Work

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Future Work Model framework Day-Ahead Model Optimization Algorithms

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Future Work Model framework

◮ Implement more models of hydro power operations

Day-Ahead Model Optimization Algorithms

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Future Work Model framework

◮ Implement more models of hydro power operations

Day-Ahead Model

◮ Generate price curves from statistic model ◮ Allow varying order prices

Optimization Algorithms

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Future Work Model framework

◮ Implement more models of hydro power operations

Day-Ahead Model

◮ Generate price curves from statistic model ◮ Allow varying order prices

Optimization Algorithms

◮ Finish parallel variants ◮ Evaluate on day-ahead model

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