STEPSA Stochastic Top-down Electricity

Price Simulator

Martin Peat

Motivation

• 70% of NZ electricity provided by hydro-generation, so normal changes in price primarily result from fluctuations in demand or hydro-generation capacity

• Hydro-generation capacity is dependent on reservoir level so our model should reflect this

• Tool for price takers who:– Procure and contract electricity– Manage small hydro reservoirs

• Single reservoir optimisation (HERO paper)– Driven by price duration curves– Need to relate PDC to market state– Build a market state that depends on storage using STEPS

Background of Model

• EPOC presentations by James Tipping of a top-down model for Hydro Storage Levels and Spot Prices

• Tipping has an innovative valuation water as a function of storage level

• Revisit the model for the purpose of small reservoir optimisation

• Build application to keep track of the model

Tipping, J. (2004) Incorporating Storage Levels into a Model for New Zealand Spot Prices, EPOC Winter Workshop 2004

Tipping, J. (2005) A Model for New Zealand Hydro Storage Levels and Spot Prices, EPOC Winter Workshop 2005

Benmore Weekly Price Series

Escribano Model

• As proposed by Escribano et al (2002)

• Deterministic component– Captures trend and seasonality– based on storage level (Tipping 2004)

• Stochastic component– Autoregressive– Volatility

ttt XfP~

ttt volatilityXX 1

)1,1(GARCH

Escribano, A., Pena, J., Villaplana, P. (2002) Modelling Electricity Prices: International Evidence, Working paper 02-27, Universidad Carlos III de Madrid

Tipping’s Model

• Daily average prices at Benmore

• Two components proposed by Tipping– Water value model– Water release model

• Model can run independently

• Tipping (2004) uses “water value” as deterministic component, based on the residual storage between the current storage level and the 10th percentile of storage levels over the past 25 years

Water Value Model

• Tipping (2004) uses “water value” as deterministic component, based on the residual storage between the current storage level and the 10th percentile of storage levels over the past 25 years

Water Value Model

• Tipping (2004) uses “water value” as deterministic component, based on the residual storage between the current storage level and the 10th percentile of storage levels over the past 25 years

Water Value Model

• Tipping (2004) uses “water value” as deterministic component, based on the residual storage between the current storage level and the 10th percentile of storage levels over the past 25 years

• Take storage level from COMITfree website

Water Value Model

Water Value Model

• Storage difference used in modified Water Value model

– parameters c, w, x, y vary with time in the form:

)(e tRSLyxtt wcWVf

-1000

0

1000

2000

3000 010

2030

4050

60

0

50

100

150

200

250

300

350

400

WeekRSL

Wat

er V

alue

Ct

Bt

Ap )52

2sin()52

2cos(

• This gives continuity and prevents jumps in prices between seasons

Release Model

• STEPS weekly release model, based on Tipping’s daily model

• Minimum release, β0, considers:– Generation required as demand is not met without

using some hydro-generation– Environmental factors– Capacity constraints– Contracts

+ )ln( + )ln( + )ln( 3210 tt IWVRelease

Model Fitting

• Parameters for the price and release models were estimated using historical data– Benmore spot prices (1999-2007)– Inflow, release and storage sequences

obtained from M-co (1926-2007)

• Least squares method used to fit both models

Fitted to BEN Price Series

Simulating Price Trajectories

• Price Trajectories are calculated given an initial storage level and some inflow sequence:

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ttt

ttt

tt

tt

RISS

IWVfR

XWVP

RSLfWV

SfRSL

1

),(

~)(

)(

Back-casting PDC 1999-2008

Simulation: Jan 2001

Simulation: Jan 2006• Risk Analysis

Simulation: Sep 2007

Simulation: Sep 2005

Simulation: May 2006

Simulation: Feb 2003

Simulation: Dec 2007

2008 High’s

Graph of dec 07- aug 2008

Separation of prices

Simulation: Aug 2008

Pt

Pt~

Model Enhancement

• Selecting inflow sequences based on current year conditions to narrow confidence interval

• Build model using South Island storage• Complete implementation of initial price correction• Maximum likelihood estimator for parameters• Test poisson jumps from the Escribano model

Uses

• Analysis of historical events• Assessing effects of constraints on release and storage

levels• Generation and Demand side tool for price takers• Planning hedge contracts• Optimisation of hydro-electric reservoir (HERO)

– Using forecast to create price duration curves– Building market state based on curves, thus based on storage

Conclusions

• Weakness is when price separation occurs due to market and network structure

• Strength of the model is in the simplicity

• Model can run as stand alone application

• STEPS LIVE forecasthttp://epoc.esc.auckland.ac.nz:8000/steps.html