STEPS
A 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 topdown 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)
~
Pt  ft  X t
• Deterministic component
– Captures trend and seasonality
– based on storage level (Tipping 2004)
• Stochastic component
X t  X t 1  volatilityt
– Autoregressive
– Volatility
GARCH (1,1)
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
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
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
• Storage difference used in modified Water Value model
f t  WVt  c  w e x ( y  RSLt )
– parameters c, w, x, y vary with time in the form:
p  A cos( 2
t
t
)  B sin( 2 )  C
52
52
• This gives continuity and
prevents jumps in prices
between seasons
Water Value
400
350
300
250
200
150
100
50
0
-1000
0
1000
RSL
2000
3000
0
10
20
30
40
Week
50
60
Release Model
• STEPS weekly release model, based on
Tipping’s daily model
ln( Release   0 )  1 +  2ln( WVt ) + 3ln( I t ) + 
• Minimum release, β0, considers:
– Generation required as demand is not met without
using some hydro-generation
– Environmental factors
– Capacity constraints
– Contracts
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:
RSLt  f ( S t )
WVt  f ( RSLt )
~
Pt  WVt  X t
Rt  f (WVt , I t )
S t 1  S t  I t  Rt
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
Relative Storage Level
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 forecast
http://epoc.esc.auckland.ac.nz:8000/steps.html