Transcript Slide 1
ANALYSING AND COMPARING ELECTRICITY SPOT PRICES
MSc. Student: HACA (GHICA) Andreea Valentina
Supervisor: Professor MOISA ALTAR
2007
Goals
Analyzes the dynamic of the spot price for electricity on three European exchanges Present the relevant factors that influence the price, such as long term mean, seasonality and mean reverting Captures the intra-day correlation between the hours for Romanian market to see the if the peak hour imposed are relevant.
Content
Description of Romanian Power Market Operator Day Ahead Market price model Base load index results Peak load index results Hourly spot price model: Romanian evidence Conclusion
Romanian Power Market Operator (OPCOM)
The Romanian electricity market was fully liberalized from 1 July 2007 OPCOM was established in 2000 – mandatory spot market In 2005 the new day ahead market (DAM) system was launched DAM is a voluntary market administrated by OPCOM In near future OPCOM will take the roll of Central Counterparty for DAM
Day ahead model price
Lucia and Schwartz (2002) establish the base for analyzing electricity spot prices The behavior of spot price (P t ) is described by two components.
1. Deterministic component (f(t)), fully predictable captures the electricity price behavior such as deterministic trend and seasonality.
2. Stochastic component (S t ) - a diffusion stochastic process which follows a stationary mean reversing process.
lnP t = f(t) + S t
Day ahead model price – Stochastic component
Captures the movement of prices outside the deterministic behavior. d S t = αS t dt + σdZ where
α
is the speed with which the price revert to the long time mean α >0.
dZ it’s the increment of the standard Brownian motion Z t . the long time mean, deviation from zero
μ,
was included in the deterministic component the mean reversing process is model from a To estimate the stochastic process using discreet information it’s needed to formulate the model in a discreet way. S t = (1 α) S t-1 +εt where t takes values from 0 to N, the error term is normal random variable with mean 0 and variance σ2.
Day ahead model price – Deterministic component
captures the predictable and regulates behavior – include: long term mean
μ
(the level at which the price tend on long term) variation of mean for weekend for every month f(t) = μ + β*D t 12 +
M i
2
it
where rest D t is 1 for weekend day and legal holiday and 0 in the M it is 1 for all the day of month i and 0 in rest
Data analysis – Base load index
Maximum price 77.91 euro/MWh OPCOM 177.85 euro/MWh EXAA 34.35 euro/MWh Gielda Minimum price 5.71 euro/MWh OPCOM 13.60 euro/MWh EXAA 21.05 euro/MWh Gielda
Data analysis – Base load index
negative skewness show that the probability to have on OPCOM and Gielda extreme low prices is bigger than the normal distribution probability positive skewness indicate that probability to have extreme high prices at EXAA is bigger that the normal distribution probability
Results – base load index
Toward the model proposed by Lucia and Schwartz I split the dummy variable sets for weekend in two dummy variables, one sets for Sunday (D 1 ) and one sets for Saturday (D 2 ) I excluded the dummies set for months, because on analyzed series the coefficients for months weren’t significant lnP(t) = μ * α + β 1 *(D 1 (t) + (α-1)*D 1 (t-1)) + +β 2 *(D 2 (t) + (α-1)*D 2 (t-1)) – α*lnP(t-1)+ε t
Results – base load index - OPCOM
C(4) coefficient of dummy sets for Saturday is insignificant - which price tend (the long term mean) is not different from the week day C(3) coefficient of the dummy sets for Sunday is significant, and the minus shows that the long term mean for Sunday is smaller than that for the week day. C(2) coefficient is the long term mean at which converge the price log, its value is 3.72, which means 41.43 euro/MWh C(1) is the speed with which the price, after taking a extreme value, return to the long time mean
Results – base load index - EXAA
Both dummy coefficients are significant and with minus, which shows that the prices in weekend are smaller than in week day long term mean is 3.89 which mean 48.88 euro/MWh, lower with 0.51 for Sunday and with 0.25 for Saturday
Results – base load index - Gielda
Coefficient of dummy variable sets for Saturday is not significant long time mean is 29.85 euro/MWh, and for Sunday 28.39
euro/MWh.
Results – base load index
Autocorrelation of residual term
for the three exchanges estimations the value of Durbin Watson test is near to 2, this means that the first level autocorrelation is not present applying Ljung-Box test/Q correlogram is obvious that it’s present a 7th lag autocorrelation - can be explain by the seasonal character of electricity prices, the prices for day
t
aren’t correlated with the prices from day
t-1
, but with the prices from day
t
a week before.
White
heteroskedasticity test
- for all series the value of F statistics is higher that its critical value computed through =@qchisq(.95,5) → residual are heteroskedastics.
Results – base load index
For analyzing the influence of the cold season on electricity prices I included another dummy variable (D 3 ) sets with value 1 for all day in period October – March and 0 in rest lnP(t) = μ * α + β 1 *(D 1 (t) + (α-1)*D 1 (t 1)) + β 2 *(D 2 (t) + +(α-1)*D 2 (t 1)) + β 3 *(D 3 (t) + (α-1)*D 3 (t-1)) – α*lnP(t-1) + ε t Only for Romania in the cold season the electricity prices are higher than in the warm one. For Polish and Austrian markets the coefficient for the dummy variable sets for cold season isn’t significant.
In Romania for cold season the long term mean is 45.43
euro/MWh.
Results – base load index
Re-estimating equation
•New estimation base on significant term and introduction of an autoregressive term for 7 th lag lnP(t) = μ * α + β 1 * (D 1 (t) + (α-1) * D 1 (t-1)) + β 2 * (D 2 (t) + +(α-1) * D 2 (t-1)) + β 3 *(D 3 (t) + (α-1)*D 3 (t-1)) – α * lnP(t -1) + + * lnP(t-7) + ε t * With blue are common terms for all exchanges
Results – base load index – OPCOM
All coefficients are significant: long time mean is 35.83 euro/MWh, for the cold season is 45.31 euro/MWh and for Sunday is 25.02 euro/MWh. Ljung-Box test (correlogram of residual -21 lags) - autocorrelation is not present for any lag heterokedasticity the F statistic value of White test is F = 8.71, below to it’s critical value → the residual series is homoskedastic.
Results – base load index – EXAA
model use is GARCH (1,1) with distributed residual
t
Student’s.
series all significant coefficients are long term mean is 50.35
euro/MWh, for Saturday is 40.83
euro/MWh and Sunday is 31.48 euro/MWh for Ljung-Box test (correlogram of residual) - autocorrelation is not present
Data analysis – Peak load index
Big difference between base load and peak load index The biggest – EXAA, where the mean price for the analyze period is 59.45 euro/MWh for peak hour and 47.71 euro/MWh for base load, this means a difference above
11 euro/MWh
.
On Romanian market the difference isn’t so remarkable as for EXAA, but is for 5 euro/MWh, the mean for peak being 47.09 euro/MWh.
In Poland is notice the smallest difference between base load and peak load index, almost 2 euro/MWh.
Results – peak load index – OPCOM
Following the same model as for base load index the result are: •the long term mean for warm season is 38.22 euro/MWh and for the cold season is 51.62 euro/MWh computing Ljung – Box test → the residual series isn’t autocorelated White test → the residual series is homesckedastic.
Results – peak load index – EXAA
Using the model Garch (1,1) the final result are: •A long term mean is 59.21 euro/MWh, were Sunday is 31.48 euro/MWh and Saturday 44.65 euro/MWh. •Speed with which the price return to the long term mean is higher then for base load, but steel the smallest between the exchanges
Results – peak load index – Gielda
For peak load the coefficient for dummy sets for cold season is significant and goes to a 2.5% above the long tern tendency of the price.
Computing: Ljung-Box test → residual series isn’t autocorrelated.
White test → the residual series is homesckedastic.
Hourly spot Model: Romanian evidence
To capture the intra-day correlation of the hours I use a panel worksheet and I analyzed the correlogram of residual result from LS estimation using coefficient covariance method cross- section SUR (which permit cross section correlation between residuals ). lnP h (t) = f h (t) + S h (t) f h (t)= μ 0 + μ h + Σ β d *Dum d S h (t) = (1 α h ) * S h (t 1) + ε h (t) for seeing only the variation from the long time mean a restriction is impose α h = α 0
Hourly spot Model: Romanian evidence
computing ADF test for each series, comparing calculated value of
t
statistic with the critical value → series are stationary, and the key characteristic stationary series is that are mean reverting
Hourly spot Model: Romanian evidence
μ 0 is 3.51 meaning 33.60 euro/MWh, the speed with which price return to the mean α 0 (C2) is 0.41. coefficients of the dummy variables set for each day βd (C3-C8). Beside C(4) coefficient (the coefficient of dummy variable sets for Sunday) which shows that Sunday prices are lower, the rest of them has a positive value which show that in the other day prices tend to a value bigger than the mean level. Coefficients from C(9) to C(31) represent hourly deviation from the long time mean. μh takes value between -0,53, for hour 4 (3:00-4:00) to 0,41, for hour 21 (20:00-21:00). So the smallest price is for hour four, and the biggest one for hour nine.
I can notice also that for interval 1-7 the price tendency is below the mean and for hour 8 the coefficient is not significant.
In correlation matrix computed for residual series was pointed out the values bigger than 0.5 which shows a significant correlation. I can be observed that are some hourly blocks which are strongly correlated. The strongest correlation is between hour 11 and 12 with a value of 0.94.
Conclusion
capture the price behavior and the one of the factors which influences the price.
Long term mean Seasonality Weekly Monthly → not significant Seasonal (significant for Romania and only Peak load index for Poland )
Conclusion
In Austria, as a develop country, prices for weekend are significantly lower than for the working day, and we cannot see a difference between cold and warm season. The polish exchange according to its behavior I can say that is still in development phase. The volume traded on this exchange is smaller comparing with the one traded on other exchanges. The price on this exchange has a low volatility and is very small comparing with the other exchange.
Conclusion
Regarding the Romanian Power Market Operator through price deterministic component I capture the differences from the tendency of the price on long term for Sunday and Saturday and also for cold season. I can see that for Sunday the price tendency is below the long time mean, but not for Saturday. This means that Saturday is a working day in Romania. In the cold season the price tendency is higher the long term mean. The speed with which the price revert to the long time mean, captured by the stochastic part of the model much bigger that in Austria, the price return to its long time mean three time faster than in Austria.
Bibliography
Escribano, A., Pena, I. J. and Villaplana, P. (2002), „Modeling Electricity Prices: International Evidence” , Working Paper 02-27, Economisc Series 08, Universidad Carlos III Fezzi, C., (2007), „Econometric Models For Analysis of Electricity Markets”, Doctor of Philosophy Thesis, Alma Mater Studiorum Universita’ Di Bologna Green, W.H., (2003), „Econometric Analysis”, Prentice Hall Higgs, H. and Worthington, A. C. (2006) „Stochastic price modelling of high volatility, mean-reverting, spike-prone commodities: The Australian wholesale electricity market”, Working Papers Series, University of Wollongong Huisman, R. and Huurman, C. (2003), „Fat tails in Power Price”, Report Series Research in Management, Erasmus Research Institure of Management Huisman, R. and Mahieu, R. (2001), „Regime Jumps in Electricity Prices”, Report Series Research in Management, Erasmus Research Institure of Management Huuman, C. (2007), „Dealing with electricity prices”, ERIM Ph.D Series Research in Management, Erasmus Research Institure of Management Jong, C and Huisman, R. (2002), „Option Formulas for Mean Reverting Power Prices with Spikes”, Report Series Research in Management, Erasmus Research Institure of Management Lucia, J. and Schwartz, E. (2002), „Electricity and power derivatives: Evidence from the Nordic Power Exchange”, Review of Derivatives Research 5, pp. 5 - 50 *** Operatorul Pieţei de Energie Electrică din România. www.opcom.ro
*** Towarowa Gielda Energii, Polish Power Exchange. www.polpx.pl
*** Energy Exchange Austria. www.exaa.at
*** www.riskglossary.com
*** www.puc_rio.br