Dynamics of supplychain and market volatility of networks

1
Dynamics of supply-chain and market volatility of
networks
WP5
Fernanda Strozzi Cattaneo University-LIUC Italy
2
WP5 Tasks overview
Coupling models Task5.5
EWDS of Blackouts T5.4
Electricity price Model T5.1
Interaction Risk T5.6
Electric power Model T5.1
Supply chain Model T5.1, T5.5
Correlation(T5.2) Analysis(T5.3)
Energy spot prices Volatility
Blackouts Volatility
Redworks to be presented
3
D5.3 (M24) Correlation analysis between
electricity prices and faults in electricity grid
in the Nordic countries

• Contents
• Data provision
• Data treatment
• Correlation analysis
• Linear correlation coefficient
• Cross Correlation function
• Cross Recurrence Plots
• Principal Component Analysis
• Conclusions

4
Data provision

• Monthly Disturbances
• Monthly Total Consumption
• http//www.nordel.org
• Monthly Electricity prices
• http//www.nordpool.com
• in Denmark, Finland, Norway and Sweden
• from January 2000 until December 2006

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Data provision

• Nordel is the collaboration organisation of the
  Transmission System Operators (TSOs) ( Denmark,
  Finland, Iceland, Norway and Sweden).
• Nord Pool is the Nordic Power Exchange Market
• Norway(1993), Sweden(1996), Finland (1997),
• W Denmark (1999), E Denmark (2000), Kontek
  (2005)

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Data provision

• Nordel annual report
• Disturbance is an outage, forced or
  unintended disconnection or failed reconnection
  as a results of faults in the power grid
• A disturbance may consist of a single fault but
  it can also contain many faults, typically
  consisting of an initial fault followed by some
  secondary faults.
• The grid considered is the 100-400kV network

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Data treatment
Disturbances
Electricity prices
Total Consumption
Denmark(), Finland(), Norway(.-) and Sweden(-).
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Data treatment
Detrended data
Trends
Volatilities
First differences
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Data treatment
W3, s3
W3, s1
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Linear Correlation Coefficient
The linear Correlation Coefficient r between
x(i) and y(i) for i1..N with mean mx and my
Correlation matrix. w1, s1, yellow if
rgt0.7071 (r2gt0.5) confidence level of 95
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Linear Correlation Coefficient
r values between Std (for VS, VD, VT) and the
mean (for the others time series), rgt0.7071
(r2gt0.5), confidence level of 95
12
Cross Correlation Function
w2,s1
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Cross Recurrence plot, (Marwan, 2007)
CRP is a bivariate extension of RP and is a tool
to analyse the dependencies between two
different time systems by comparing their states
(Marvan and Kurths, 2002). It can be considered
as a generalization of the linear
cross-correlation function (Marwan et al. 2007).

where i1, , n, j1, m the CRP matrix is
defined by
x(t)
y(t)
t
t
time for y(t)
x(t) y(t)
no embedding
t
time for x(t)
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Cross Recurrence plot quantification
Laminarity
Determinism
Recurrence
Lines diagonally oriented
They represent segments of both trajectories
running parallel for some time. Frequency and
length of these lines are related to the
similarity between the two dynamical systems not
always detected by cross correlation
function. One trajectory? main black diagonal
(LOI) If the values of the second trajectory are
modified ?LOI becomes LOS
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Cross Recurrence plot quantification Line Of
Synchronization (LOS)
t-20.012 e0.01

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LOS calculation for electricity prices,
disturbances and Total Consumption
w2,s1, e0.5

Sfd
Tfd

D
D
Q80.40
Q64.32
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LOS Algorithm
1. Find the recurrence point next to the
origin 2. Find the next point by looking for
recurrence points in a squared window of size
w2, If the edge of the window find a recurrence
point we go to step 3, else we iteratively
increase the size of the window. 3. If there are
subsequent recurrence points in y-direction
(x-direction), the size w of the window is
iteratively increased in y-direction
(x-direction) until a predefined size or until
no new recurrent points are met. When a new
recurrence point is found we return to step 2
LOS Quality
Nt is the number of targeted points Ng the number
of gap points. The larger is Q the better is LOS
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LOS calculation in CRP between Disturbances and
the other time series. Only the CRP with at least
a part of the LOS parallel to the main diagonal
is considered.
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Principal Component Analysis
Principal Component Analysis how many
independent variables
Principal Factor Models Which are the
independent variables and how we have to use them
to build the model
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Principal Component Analysis

• The data have very different mean and
  variances?Correlation matrix
• Eigenvectors? loadings
• Corresponding eigenvalues?
• Percent of variance explained on that direction
  100eigenvalue/sum(eigenvalues)
• Percent of variance ?
• Cumulative sum of variance explained

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Loadings for w1, s1
Principal Component Analysis
PC1 PC2 PC3 PC4 PC5
PC6 PC7 PC8 PC9 PC10 PC11
PC12
0.1801 -0.4014 -0.2349 -0.4308 0.0655
-0.2196 -0.2880 -0.6285 0.1153 -0.1032
0.1062 0.0023 -0.3934 -0.1531 0.2379
0.0802 -0.3920 -0.1733 -0.1521 0.1371
0.6040 -0.2497 0.3226 0.0436
0.2872 0.0083 0.1344 -0.2054 0.6711
0.2206 0.0899 0.2632 0.4220 -0.0910
0.3051 0.0378 0.1018 -0.4453 -0.3041
-0.3593 -0.1610 -0.1850 -0.0466 0.6879
-0.0987 0.1073 -0.1129 -0.0156 -0.2924
-0.1836 0.3101 -0.1076 0.1262 0.5012
-0.6616 0.0590 -0.1768 0.1009 -0.1439
-0.0518 0.1527 -0.0640 0.2032 0.4514
0.3460 -0.6499 -0.3977 0.1075 -0.0781
0.0744 -0.0624 -0.0133 0.2213
-0.4827 0.0824 0.3576 -0.0895 0.2244
0.1905 -0.1379 0.3781 0.5055 -0.2666
0.0098 -0.3963 -0.2527 0.1831 -0.1117
0.3116 -0.1412 0.3549 -0.0538 0.0358
-0.3832 -0.5822 0.0093 0.2760 0.0306
0.5399 -0.2630 -0.1996 -0.1090 0.1178
-0.0161 -0.0529 0.0168 -0.0135
-0.7023 0.2610 -0.4511 0.0570 0.3734
-0.0783 0.2393 0.0953 0.0227 -0.3546
-0.5614 0.2681 -0.0044 -0.4144 -0.2761
0.1856 -0.0793 0.1824 -0.1403 0.3181
-0.0775 -0.3328 0.4165 0.5145
0.0476 0.2985 0.0421 0.5203 -0.2574
-0.2139 -0.0787 0.0375 -0.0069 -0.1150
0.0149 -0.0860 0.7056
S D T Sdt Ddt Tdt Sfd Dfd Tfd VS VD VT
?
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Principal Component Analysis
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Conclusions

• Linear Correlation Coefficient
• For near all the windows w and time shifts s we
  found a
• high linear correlation between D and T or their
  modified versions.
• Exception w1, s1.
• For w12 s12 a new correlation appears between
  VD, Sdt(0.8138)

Cross Recurrence Plot (LOS) We can detect
windows and shifts to increase linear
correlation D-S -0.2692?0.6304 D-Sfd 0.0702?
0.5466
Principal Component Analysis 2-3 variables ? at
least 50 variance explained More than 3
variables ? at least 90 variance explained
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LIUC Colaborations

• Qeen Mary (Physica A)
• JRC (Physica A, Physica D)
• COLB (under discussion)
• MASA (defined)

LIUC Gender Action

• 2 female PhD students started to work on
• Models of Supply Chain
• Ranking Risk in Supply Chain
• 1 female student for the final project

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Conferences DISSEMINATION 1_ Analysis of
complex systems by means of mathematical and
simulation methods (Noè, Rossi) . International
Conference on applied simulation and modeling,
Corfù (June 2008) 2_ Quantifying and ranking
risks. IPMA world congress Rome 9-11 Nov 2008.
Colicchia, Sivonen, Noè, Strozzi. 3_Application
of RQA to Financial Time Series, F. Strozzi, J.M.
Zaldivar, J. Zbilut, Second International
workshop on Recurrence Plot, Siena, 10-12
September 2007. Reports -Application of
non-linear time series analysis techniques to the
Nordic spot electricity market F. Strozzi,
E.Gutiérrez, C. Noè, T. Rossi, M.Serati and
J.M.Zaldívar. LIUC Paper 200, october 2007
-Deliverables D5.1, D5.2 Papers 1_Time series
analysis and long range correlations of Nordic
spot electricity market data, H.Erzgraber, F.
Strozzi, J.M. Zaldivar, H.Touchette, E.
Gutierrez, D.K.Arrowsmith,  submitted to Physica
A 2_ Measuring volatility in the Nordic spot
electricity market using Recurrence
Quantification Analysis. F. Strozzi,
E.Gutiérrez, C. Noè, T. Rossi, M.Serati and J.M.
Zaldívar . Accepted in EPJ Special Topics. 3_ A
supply chain as a serie of filter or
amplificators of the bullwhip effect . Caloiero,
G., Strozzi, F., Zaldívar, J.M., 2007.
International Journal of Production Economics
(Accepted). 4_Control and on-line optimization
of one level supply chain, F. Strozzi, C.Noè,
J.M. Zaldivar, submitted to IJPE, 2008