Modelling the NSW Electricity
Supply Curve
Prof Michael Sherris and Calvin Kwok
Background
AU National Electricity Market
„ Australian electricity market was deregulated in late
1998
„ Prior the deregulation . . .
Background
AU National Electricity Market
„ After the deregulation . . .
„ Retail price is pre-agreed
„ Wholesale price (spot price) is determined by the
aggregate supply & demand every 30 minutes
Background
NSW Electricity Pool
„ Prior each 30-minute trading interval . . . (each day is
divided into 48 trading intervals)
Vol. (MWh)
Price ($/MWh)
<50 <100 <200 <400 <800
12
30
50
800 2000
Background
NSW Supply Stack
01 Jan 02 (05:00 – 05:30):
Regional Demand = 5,322MWh
Spot Price = $11.19/MWh
Background
NSW Supply Stack
Background
Pros & Cons
„ Pro:
ƒ Competitive price settings
„ Cons:
ƒ Volatility
ƒ Price spikes
ƒ Modelling challenges
„ Example
ƒ On 23 June 2003, the half-hourly spot price in NSW
jumped from $52/MWh to $7,948/MWh in 30 minutes
and came back to $1,609/MWh after an hour
Background
NSW Electricity Spot Price
Spot Price Modelling
General Problems
„ Most widely used models are Brownian motion
based models
„ Problems with Brownian motion based models:
ƒ Unstable parameters due to insufficient price
information
ƒ Occurrence & magnitude of jumps in these models
are random (do not agree with empirical observations)
„ Better way to model the spot price is by modelling
the underlying aggregate supply and aggregate
demand separately
Spot Price Modelling
General Problems
„ Aggregate demand is highly predictable and many
models have been proposed
„ Periodic patterns in supply function is difficult to be
detected
„ Proposed models for supply function tend to be
very complicated or market specific
ƒ Modelling the bidding strategies (i.e. game theory)
ƒ Genc and Reynolds (2004), Anderson and Philpott
(2002), Supatgiat et al (2001), Wolfram (1998) and
Green and Newbery (1992)
ƒ Fitting with exponential functions
ƒ Skantze et al (2000)
ƒ Transformation of cost function to supply function
ƒ Eydeland and Wolyneic (2002)
Cost Fn vs. Supply Fn
Supply
Cost
Objectives
„ To develop a simple and practical model for the
NSW half-hourly aggregate supply function
„ To apply our supply model on spot price modelling
NSW Supply Stack
General Characteristics
„ Start from a negative price
D
„ Non-decreasing function
„ “S-shape” characterised by
B, C, D & E
„ Segment CD is the
steepest - price is very
sensitive to the change in
demand
B
A
C
E
NSW Supply Stack
The Horizontal Coord. of B - E
„ Let (V(i),P(i)) be the coordinates of B, C, D & E and
plotting the V(i)’s . . .
10000
Volume (MWh)
9000
8000
7000
6000
5000
4000
Mo n
T ue
Wed
T hu
VB
Fri
VC
Sa t
VD
Sun
Mo n
VE
12000
11000
Volume (MWh)
10000
9000
8000
7000
6000
5000
4000
3000
No v02
De c02
Ja n03
Fe b03
Ma r03
Ap r03
Ma y03
Jun03
Jul03
Aug03
Se p03
O ct03
No v03
The Model
General Procedures
„ Identifying B to E from the past supply stacks
ƒ B is the first point where the supply stack is above $0
ƒ E is the end point of the stack
ƒ C & D are where the “smooth function” bends
„ Modelling the coordinates of B to E i.e. (V(i), P(i))’s
„ Simulating B to E
„ Interpolating the simulated points to construct
forecasts of the supply stacks
The Model
Identifying C & D
„ Draw a line joining B & E
min d
„ Compute the closest
distance, d from each
point on the stack to the
line
max d
B
E
D
C
The Model
Modelling the V(i)’s
„ Recall V(B), V(C), V(D) & V(E) exhibit daily, weekly and
yearly patterns
„ Multi-equation regression approach:
ƒ Divide each consecutive time series of V(i) half-hour by
half-hour
ƒ Let h be the h-th half-hour interval of each trading day. For
h = 1, 2, . . ., 48 and i = B, C, D, E,
i,1
i,2 
V h,t   h V h,t   h
i
E
i,6
 h
i,3 
MON t   h
i,7
i,4 
TUEt   h
i,8
FRI t   h SATt   h
i,10
i,11 
 h
cos 2t   h
sin
365
i,13
i,14 
 h
sin 4t   h
cos
365
WED t   h
i,5 
THU t
i,9
SUN t   h PUBLICHOLIDAY t
2t   i,12  cos 4t
h
365
365
8t   i,15  sin 8t  e i
h
h,t
365
365
ƒ Each group of 48 sub-series is estimated using seemingly
unrelated regression (SUR).
The Model
Modelling the P(i) ’s
„ Assumptions:
ƒ P(B) = 0
ƒ P(E) = 10,000
„ We fit the following model to P(C) and P(D):
i 
Pt

i
P t−1
with probability q
P t−1  ΔP i
with probability 1 − q
i
The Model
Reconstructing the Stacks
„ Monotone piecewise cubic interpolation
ƒ Fritsch and Carlson (1980)
ƒ Similar to cubic spline except
ƒ Cubic spline produces a smoother result (2nd derivative
is continuous)
ƒ Cubic spline does not guarantee monotonicity
ƒ Captures roughly the overall curvatures and the
monotonicity of the supply stack
Simulation Results
„ Sample period for estimating the models: 11 April
2002 to 31 October 2003
„ For testing: 1 November 2003 to 7 November 2003
Simulation Results
Supply Stacks
Actual supply stacks
(1 November 2003)
Simulated supply stacks
Simulation Results
Spot Prices
Actual (Theoretical) Price
Simulated Price
Simulation Results
Spot Prices
Simulated Spot Price for 1 - 7 November 2003
10000
9000
8000
Price ($/MWh)
7000
6000
5000
4000
3000
2000
1000
0
0
50
100
150
200
Hour
250
300
350
Conclusions & Summary
„ A model for modelling the NSW aggregate supply
function
„ Can be used for detection of regular bidding
patterns which could be difficult to be detected
otherwise
„ Can be used in conjunction with any demand model
to produce forecasts of NSW electricity spot price