HERBS - HYDRO ELECTRIC RESERVOIR BIDDING

SYSTEMFaisal WahidAndy Philpott

Anthony Downward

2011 - Graduated in operations research at Engineering Science, University of Auckland Final year project: Investigating the operational effects of

Tekapo A and B asset transfer

2012 - Worked as Trading Analyst for Mighty River Power

Currently pursuing a PhD with Gaspard Monge Program for optimisation and operations research (PGMO) , Meridian Energy and EDF

River Optimisation: short term hydro scheduling under uncertainty

ACKNOWLEDGEMENTS

Professor Andy Philpott – EPOC Dr. Anthony Downward – EPOC Andrew Kerr – Meridian Dr. Anes Dallagi – EDF Professor Frederic Bonnans - INRIA

FRENCH BALANCING MARKET

HYDRO-BIDDING

?Price

Quantity

HYDRO BIDDING PROBLEM

Producing optimal supply/offer curves for hydropower producers

Integrates hydropower production and market exchange

PRESENTATION OUTLINE

HERBS formulation (single reservoir)Simple exampleChallengesOpportunitiesDiscussion

FORMULATION – SINGLE STAGE Market price modelled by discrete states Market clearing price is a random variable Each state has a price interval

Price States = Each price intervals has an average price

Each average price has associated probability

Quantity variables for each price state

FORMULATION – SINGLE STAGE

𝒑𝟏

𝒑𝟐

𝒑𝟑

𝝅𝟑

𝝅𝟐

𝝅𝟏

𝒒𝟏 𝒒𝟐 𝒒𝟑≤ ≤

Max Price($/MW)

Quantity (MW’s)

FORMULATION – SINGLE STAGE

Maximising expected profit Max

Conservation of reservoir storage

Storage bounds

Monotonic offers

FORMULATION – TWO STAGE

0

1

2

3

1

2

3

Stage 1 Stage 2Stage 0

𝒙𝟎 𝑸𝟏(𝝅)

𝑸𝟐(𝝅)𝒙𝟏𝟏=𝒙𝟎−𝒒𝟏

𝟏

𝒙𝟐𝟏=𝒙𝟎−𝒒𝟐

𝟏

𝒙𝟑𝟏=𝒙𝟎−𝒒𝟑

𝟏𝒙𝟑𝟐=𝒙𝟑

𝟏−𝒒𝟑𝟐

𝒙𝟐𝟐=𝒙𝟐

𝟏−𝒒𝟐𝟐

𝒙𝟏𝟐=𝒙𝟏

𝟏−𝒒𝟏𝟐

EXAMPLE #1

Stage 0 Stage 1 Stage 2

0

30707070

70303030

70303030

State (i) Probability Cumulative Probability

1 $ 70.00 0.2 0.2

2 $ 100.00 0.6 0.8

3 $ 130.00 0.2 1

𝝅=$𝟏𝟎𝟎

𝒙𝟎=𝟏𝟎𝟎 𝒒=𝟕𝟎

COMPARISON WITH EVP

Stage 0 Stage 1 Stage 2

0

30707070

70303030

70303030

Stage 0 Stage 1 Stage 2

0

50505050

50505050

50505050

Max Max

EVP HERBS

EXAMPLE #2

Stage 0 Stage 1 Stage 2

0

30707070

30707070

70303030

State (i) Probability Cumulative Probability

1 $ 70.00 0.2 0.2

2 $ 80.00 0.6 0.8

3 $ 130.00 0.2 1

𝝅=$𝟖𝟖

𝒙𝟎=𝟏𝟎𝟎 𝒒=𝟕𝟎

CHALLENGES

Curse of dimensionalitySimulating stochastic pricesImplementing large river chainsSolution integrity

OPPORTUNITIES

Effects of gate closuresUnintuitive offer strategies Outer approximation (i.e. SDDP,

DOASA)Stochastic dynamic programming

Thank YouQuestions?