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The Zonal and Seasonal CO2 Marginal Emissions Factors for the Italian Power Market

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Abstract

This paper estimates the seasonal and zonal \({\mathrm{CO}}_{2}\) marginal emissions factors (MEFs) from electricity production in the Italian electricity system. The inclusion of the zonal configuration of the Italian wholesale power market leads to a complete measurement of marginal emission factors which takes into account the heterogeneous distribution of RES power plants, their penetration rate and their variability within the zonal power generation mix. This article relies on a flexible econometric approach that includes the fractional cointegration methodology to incorporate the typical features of long-memory processes into the estimation of MEFs. We find high variability in annual MEFs estimated at the zonal level. Sardinia reports the highest MEF (0.7189 \({\mathrm{tCO}}_{2}\)/MWh), followed by the Center South (0.7022 \({\mathrm{tCO}}_{2}\)/MWh), the Center North (0.4236 \({\mathrm{tCO}}_{2}\)/MWh), the North (0.2018 \({\mathrm{tCO}}_{2}\)/MWh) and Sicily (0.146 \({\mathrm{tCO}}_{2}\)/MWh). The seasonal analysis also shows a large variability of MEFs in each zone across time. The heterogeneity of results leads us to recommend that policymakers consider the zonal configuration of the power market and the large seasonal variability related to carbon emissions and electricity generation when designing incentives for renewable energy sources expansion and for achieving emission reduction targets.

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Notes

  1. In a subsequent paper, Hawkes (2014) further addresses the issue by distinguishing between the short-run MEFs, which rely on the assumption of a given structure of the power supply and the long-run MEFs, which include changes in the power supply structure.

  2. The GB power market is based on half-hourly settlement periods.

  3. For instance, this approach might be useful when studying the impact of Photo Voltaic (PV) generation on power markets as it is possible to consider data at midday (the hour of the day with the highest solar irradiation) and compare it with data from night hours. Other hours are considered (such as hour 11 and 18) when the analysis is focused on the consequences of ramping up and down of RES, which is observed in the so called duck-curve phenomenon (see Lazar 2016).

  4. We follow the characterization provided by the Italian TSO, Terna, with the identification of six physical zones (North, Center North, Center South, South, Sicily and Sardinia).

  5. In this analysis, the cross-zonal estimation of MEF is not included in order to keep the model as simple as possible.

  6. Note that we are considering the MEF of production, not the MEF of consumption. This means that the emissions from a plant are attributed to the zone where the plant is located, regardless of whether the energy produced by that plant is used within that zone or exported to another zone. Therefore, when the marginal technology is the import, the emissions in that zone are set to zero (since are included in the exporting one). However, we are not able to calculate the emissions of the plants located outside Italy and therefore the calculations do not include emissions from international imports (through interconnectors). For a detailed description on data construction, please refer to Beltrami et al. (2021).

  7. All unit root tests have been applied under the assumption of a constant deterministic component, with the exception of the ZA test, where a constant and a trend have been included.

  8. Seasonality is one of the most important stylised facts studied on electricity demand and prices (Weron 2006). Regular fluctuations are observed at different time scales depending on the sample frequency of the time series. When hourly time series are collected, a three-scale seasonality can be defined: daily, weekly and yearly seasonality. Daily seasonality is due to different levels of electricity demand/price during different hours of the day (peak and off-peak hours). Weekly seasonality is connected to the demand of electricity by business and industrial companies which is lower during week-end. Yearly seasonality is mainly induced by weather conditions causing an increase of demand/price when heating (winter) and cooling (summer) systems are intensively used. In this paper, low-scale seasonality (daily and weekly) has been removed in order to emphasise the effect of yearly seasonality which has been deeply studied in the quarterly analysis (see “Appendix”).

  9. We deal with a two-dimensional vector of variables \(X_{t}\) = (\({X_{1,t}};{X_{2,t}}\)) = (\({E_{t}};{G_{t}}\)), with \(t=1,\ldots ,T\). Although we omit the subscript z, the model applies individually to each zone z of the Italian market.

  10. A generic stochastic process \(y_t\) is both stationary and invertible if all roots of AR and MA polynomials lie outside the unit circle and \(|d|<0.5\). The process is nonstationary for \(|d|\ge 0.5\), as it possesses infinite variance; see Granger and Joyeux (1980).

  11. The model built under this constraint is called “baby model”. This restriction avoids the identification issues which are well described by Carlini and Santucci de Magistris (2019). As a matter of fact, when the number of lags k is unknown, the FCVAR model is not globally identified and this results in a multiplicity of not-identified sub-models for any possible combination of the parameters d and b.

  12. A conditional approach for the maximum likelihood estimation simplifies the computational procedure by reducing the numerical problem to least squares. Therefore, it is more convenient than the unconditional approach, which is computationally complex (see Johansen and Nielsen 2012).

  13. The main functions of the Matlab code, which has been adapted to our case, have been provided by Carlini and Santucci De Magistris, who are kindly acknowledged by the authors.

  14. To obtain the simulated p values of our cointegration rank test automatically, we made use of a separately installed program to be uploaded in Matlab, called fdpval. This is the C++ implementation of a Fortran program used to obtain simulated p values from MacKinnon and Nielsen (2014), who simulated numerical cumulative distribution functions (CDFs) as functions of \(b_{0}\).

  15. This has to be read sequentially. Starting from \(rank=0\), we firstly test the hypothesis that the rank of the matrix is null against the alternative that the rank is equal to p. If this null hypothesis is rejected, then the second step is carried out by testing if \(rank=1\) against the alternative that is equal to p, and so on.

  16. We here use the same notation as in Nielsen and Popiel Ksawery (2018).

  17. This test was applied by Jones et al. (2014) to check the validity of including additional exogenous regressors in the main equation.

  18. The long-run exogeneity tests verify the magnitude of short-term adjustments of each variable to shocks in the long-run equilibrium relationship.

  19. It should be noted that we consider only data accruing from the day-ahead market. Day-ahead schedules are adjusted in the balancing market. It is therefore possible that the marginal plant in the day-ahead market differs from the one which is actually dispatched in real time and consequently also the MEF would differ. However, note that the real-time emissions cannot be calculated on the basis of available information. On the one hand, the real time dispatching is selected by TSO, which operates on the basis of real-time intra-zonal congestions which are not reported. On the other hand, in the case of Italy only data of overall aggregated quantity accepted in the balancing market for both reserve margin and zonal congestion resolution is released, without further disaggregating the two components. Therefore, a disaggregated analysis by type of plant dispatched in real-time cannot be performed.

  20. Year 2020 has been excluded due to the structural variations brought about by the pandemic.

  21. Data for the virtual production zones, the limited production poles and the interconnectors are not shown in Table 4.

  22. The definition of Non-Relevant RES (NRRES) depends on the specific Italian encoding of plants and RES subsidy rules. Small-scale renewables, i.e. renewable energy plants smaller than 10 MW (mostly connected at distribution level), receive subsidies by means of a purpose-built public company, called GSE (Gestore Servizi Energetici, in Italian—Energy System Manager). The individual supply of NRRES is collected by the GSE, aggregated and placed on the market at zero price. This category includes various small-scale RES plants. Depending on the zone, the majority of these plants are either small PV or run-of-the-river hydro. However, there are also other types, such as small-scale wind, or small old co-generation plants (even not renewables). Further disaggregation is not possible and therefore they are classified as a single category within the RES group.

  23. From now on, we will focus only on the seasonally-adjusted time series, i.e. the stochastic component of the observed time series.

  24. In Beltrami et al. (2020) the British and Italian electricity markets are compared. Microdata are available for both markets, but the time frequency is different in terms of the sample frequency of collected data: half-hourly in Great Britain and hourly in Italy. In this paper, we focused on hourly Italian data. The main empirical features of generation and emission data are not affected by the different time frequency. Thus, multi-scale seasonality and fractional integration are observed both using hourly Italian and half-hourly British data.

  25. The final model is a regression with AR(F)IMA errors. See Equation (4) and (5) of Beltrami et al. (2020).

  26. The preliminary unit root and stationarity tests by quarter and by zone are presented in “Appendix”.

  27. Although for Q1 in the Center North the ADF test does not reject the null of unit root, the other unit root tests reject the null. Hence, in this case, there is not sufficient evidence to use the variable in first differences and the variable is kept in levels.

  28. With the same argument of the case of Q1 for Center North, the rejection of the null hypothesis of the ADF test for Q4 does not give sufficient evidence to use first differences. Hence, emissions in Q4 for Sardinia are kept in levels.

  29. We also tried to estimate the AEF by removing the generation from RES, thus obtaining a “conventional” measure of the AEF. “Conventional” AEF in the Center South is 0.7106 \({\mathrm{tCO}}_{2}\)/MWh, thus revealing an almost perfect correspondence with the result of the MEF in Table 2.

  30. Intuitively, the simple aggregation of data of the 6 physical zones would create an hypothetical Italian macrozone, which is clearly not the case for a zonal power market that is constrained by a given transmission capacity and results in market splitting situations more than 50% of the times.

Abbreviations

ACF:

Autocorrelation function

AEF:

Average emission factor

FCVAR:

Fractional cointegration vector auto regressive

LR:

Likelihood ratio

MEF:

Marginal emission factor

MISO:

Midcontinent independent system operator

NRRES:

Non relevant renewable energy sources

OLS:

Ordinary least squares

PACF:

Partial autocorrelation function

PV:

Photo voltaic

RES:

Renewable energy sources

TSO:

Transmission system operator

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Acknowledgements

We wish to thank two anonymous reviewers and the guest editor for their helpful comments that have contributed to improve the overall quality of the paper. Filippo Beltrami gratefully acknowledges Paolo Santucci de Magistris and Federico Carlini from Luiss University for their overall econometric support and the implementation of the original Matlab code for the FCVAR estimation. Monica Giulietti gratefully acknowledges funding from UKERC (Grant FF3/3). Luigi Grossi acknowledges the financial support from the Italian Ministry of Education and University (MIUR: Ministero dell’Istruzione, dell’Università e della Ricerca), Award Code FFABR 2017. We wish to thank the participants to the seminar given in April 2020 at the University of Padua, Department of Economics DSEA. We would like to thank participants to the Energy Policy Research Group seminar, at the University of Cambridge for their useful comments and suggestions. We are grateful to the participants of the online IX International Academic Symposium: Energy transition and opportunities for global economic recovery organised by the IEB of Barcelona in February 2021. The usual disclaimer applies.

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Appendix

Appendix

1.1 Descriptive Statistics

See Table 4.

Table 4 Zonal configuration of the Italian power market: yearly load, yearly calculated emissions, accepted generation by RES type and Average Emission Factors (AEF)

1.2 Seasonal Adjustment

See Figs. 3 and 4.

Fig. 3
figure 3

Unadjusted and adjusted versions of carbon emissions data in January 2018—Zone Center North

Fig. 4
figure 4

Unadjusted and adjusted versions of generation data in January 2018—Zone Center North

1.3 Zone North

See Figs. 5 and 6 and Tables 5 and 6.

Fig. 5
figure 5

Zone North, ACF (a) and PACF (b) for seasonally adjusted emissions

Fig. 6
figure 6

Zone North, ACF (a) and PACF (b) for seasonally adjusted generation

Table 5 Unit root and stationarity tests for North for the seasonally adjusted emissions (\(E_t\)) and generation (\(G_t\)) time series. Sample period: quarters (I, II, III, IV) of 2018
Table 6 Summary findings for the zone North—FCVAR results

Unrestricted model:

$$\begin{aligned} \varDelta ^{\hat{d}}&\left(\begin{bmatrix}E_{t}\\ G_{t}\end{bmatrix}-\begin{bmatrix}1605.680\\ 5516.842\end{bmatrix}\right)=L_{\hat{d}}\begin{bmatrix}-0.44\\ -0.167\end{bmatrix}v_{t}+\sum _{i=1}^{4} \widehat{\varGamma _{i}}\varDelta ^{\hat{d}}L_{\hat{d}}^{i} (X_{t}-\hat{\mu })+\hat{\epsilon _{t}}\\ \hat{d}&=\underset{(0.011)}{0.206}, Q_{\hat{\epsilon }}(24) =\underset{(pv=0.000)}{2456.580}, log(\mathscr {L})=-128553.739 \end{aligned}$$

Long-term equilibrium relationship:

$$\begin{aligned} E_{t} = 502.31 + 0.2G_{t} + v_{t} \end{aligned}$$
(9)

Hypothesis tests:

 

\({\mathscr {H}}_{d}^{1}\)

\({\mathscr {H}}_{\beta }^{1}\)

\({\mathscr {H}}_{\alpha }^{1}\)

\({\mathscr {H}}_{\alpha }^{2}\)

df

1

1

1

1

LR

866.252

51.327

18.842

1.042

p value

0.000

0.000

0.000

0.307

Restricted model:

$$\begin{aligned} \varDelta ^{\hat{d}}&\left( \begin{bmatrix}E_{t}\\ G_{t}\end{bmatrix}-\begin{bmatrix}1583.383\\ 5485.098\end{bmatrix}\right) =L_{\hat{d}}\begin{bmatrix}-0.3973\\ 0.000\end{bmatrix}v_{t}+\sum _{i=1}^{4} \widehat{\varGamma _{i}}\varDelta ^{\hat{d}}L_{\hat{d}}^{i} (X_{t}-\hat{\mu })+\hat{\epsilon _{t}}\\ \hat{d}&=\underset{(0.004)}{0.203}, Q_{\hat{\epsilon }}(24) =\underset{(pv=0.000)}{2456.559}, log(\mathscr {L})=-128554.260 \end{aligned}$$

Long-term equilibrium relationship:

$$\begin{aligned} E_{t} = 476.49 + 0.2018G_{t} + v_{t} \end{aligned}$$
(10)

1.4 Zone Center North

See Figs. 7 and 8 and Tables 7 and 8

Fig. 7
figure 7

Zone Center North, ACF (a) and PACF (b) for seasonally adjusted emissions

Fig. 8
figure 8

Zone Center North, ACF (a) and PACF (b) for seasonally adjusted generation

Table 7 Unit root and stationarity tests for Center North for the seasonally adjusted emissions (\(E_t\)) and generation (\(G_t\)) time series
Table 8 Summary findings for the zone Center North—FCVAR results

Unrestricted model:

$$\begin{aligned} \varDelta ^{\hat{d}}&\left( \begin{bmatrix}E_{t}\\ G_{t}\end{bmatrix}-\begin{bmatrix}103.942\\ 1478.090\end{bmatrix}\right) =L_{\hat{d}}\begin{bmatrix}-0.092\\ 0.673\end{bmatrix}v_{t}+\sum _{i=1}^{4} \widehat{\varGamma _{i}}\varDelta ^{\hat{d}}L_{\hat{d}}^{i} (X_{t}-\hat{\mu })+\hat{\epsilon _{t}}\\ \hat{d}&=\underset{(0.01)}{0.231}, Q_{\hat{\epsilon }}(24) =\underset{(pv=0.000)}{1369.419}, log(\mathscr {L})=-98532.904 \end{aligned}$$

Long-term equilibrium relationship:

$$\begin{aligned} E_{t} = -488.77 + 0.401G_{t} + v_{t} \end{aligned}$$
(11)

Hypothesis tests:

 

\({\mathscr {H}}_{d}^{1}\)

\({\mathscr {H}}_{\beta }^{1}\)

\({\mathscr {H}}_{\alpha }^{1}\)

\({\mathscr {H}}_{\alpha }^{2}\)

df

1

1

1

1

LR

1068.479

36.906

1.353

15.016

p value

0.000

0.000

0.245

0.000

Restricted model:

$$\begin{aligned} \varDelta ^{\hat{d}}&\left( \begin{bmatrix}E_{t}\\ G_{t}\end{bmatrix}-\begin{bmatrix}119.326\\ 1531.562\end{bmatrix}\right) =L_{\hat{d}}\begin{bmatrix}0.000\\ 0.7022\end{bmatrix}v_{t}+\sum _{i=1}^{4} \widehat{\varGamma _{i}}\varDelta ^{\hat{d}}L_{\hat{d}}^{i} (X_{t}-\hat{\mu })+\hat{\epsilon _{t}}\\ \hat{d}&=\underset{(0.013)}{0.236}, Q_{\hat{\epsilon }}(24) =\underset{(pv=0.000)}{1367.562}, log(\mathscr {L})=-98540.412 \end{aligned}$$

Long-term equilibrium relationship:

$$\begin{aligned} E_{t} = -529.44 + 0.4236G_{t} + v_{t} \end{aligned}$$
(12)

1.5 Zone Center South

See Figs. 9 and 10 and Tables 9 and 10.

Fig. 9
figure 9

Zone Center South, ACF (a) and PACF (b) for seasonally adjusted emissions

Fig. 10
figure 10

Zone Center South, ACF (a) and PACF (b) for seasonally adjusted generation

Table 9 Unit root and stationarity tests for Center South for the seasonally adjusted emissions (\(E_t\)) and generation (\(G_t\)) time series
Table 10 Summary findings for the zone Center South

The rank test shows the absence of cointegrating relationships. Therefore, we estimate the MEF by following the methodology by Beltrami et al. (2020). Note that the s is the selected order of the autoregressive (AR) component of the process, while q is the selected order of the moving average (MA) component.

 

Hawkes

Hawkes FE

US-FE

ARIMA-FE

ARFIMA-FE

\(\hat{\beta }\)

0.6967821

0.6967676

0.6639039

0.7030515

0.7022071

SE \(\hat{\beta }\)

0.0042

0.0042

0.0038

 

0.0043

t value

165.4015

165.1048

172.4515

  

p value

0.00

0.00

0.00

  

AIC

111,349.2

111,349.2

124,338.7

110,723.2

85,861.78

BIC

111,370.5

111,631.4

124,565.2

110,970.9

86,123.66

s

   

1

1

q

   

3

3

\(\hat{d}\)

    

0.2823146

SE \(\hat{d}\)

    

0.04467662

Confidence interval of \(\hat{d}\)

    

[0.1947485; 0.3698808]

1.6 Zone Sicily

See Figs. 11 and 12 and Tables 11 and 12.

Fig. 11
figure 11

Zone Sicily, ACF (a) and PACF (b) for seasonally adjusted emissions

Fig. 12
figure 12

Zone Sicily, ACF (a) and PACF (b) for seasonally adjusted generation

Table 11 Unit root and stationarity tests for Sicily for the seasonally adjusted emissions (\(E_t\)) and generation (\(G_t\)) time series
Table 12 Summary findings for the zone Sicily—FCVAR results

Unrestricted model:

$$\begin{aligned} \varDelta ^{\hat{d}}&\left( \begin{bmatrix}E_{t}\\ G_{t}\end{bmatrix}-\begin{bmatrix}25.905\\ 774.52\end{bmatrix}\right) =L_{\hat{d}}\begin{bmatrix}-0.282\\ -0.256\end{bmatrix}v_{t}+ \sum _{i=1}^{4}\widehat{\varGamma _{i}} \varDelta ^{\hat{d}}L_{\hat{d}}^{i}(X_{t}- \hat{\mu })+\hat{\epsilon _{t}}\\ \hat{d}&=\underset{(0.011)}{0.289}, Q_{\hat{\epsilon }}(24) =\underset{(pv=0.000)}{1232.508}, log(\mathscr {L})=-95151.957 \end{aligned}$$

Long-term equilibrium relationship:

$$\begin{aligned} E_{t} = -87.17 + 0.146G_{t} + v_{t} \end{aligned}$$
(13)

Hypothesis tests:

 

\({\mathscr {H}}_{d}^{1}\)

\({\mathscr {H}}_{\beta }^{1}\)

\({\mathscr {H}}_{\alpha }^{1}\)

\({\mathscr {H}}_{\alpha }^{2}\)

df

1

1

1

1

LR

513.896

19.63

19.194

8.157

p value

0.000

0.000

0.000

0.004

The unrestricted model is the correct specification.

1.7 Zone Sardinia

See Figs. 13 and 14 and Tables 13 and 14.

Fig. 13
figure 13

Zone Sardinia, ACF (a) and PACF (b) for seasonally adjusted emissions

Fig. 14
figure 14

Zone Sardinia, ACF (a) and PACF (b) for seasonally adjusted generation

Table 13 Unit root and stationarity tests for Sardinia for the seasonally adjusted emissions (\(E_t\)) and generation (\(G_t\)) time series
Table 14 Summary findings for the zone Sardinia—FCVAR results

Unrestricted model:

$$\begin{aligned} \varDelta ^{\hat{d}}&\left( \begin{bmatrix}E_{t}\\ G_{t}\end{bmatrix}-\begin{bmatrix}513.503\\ 1438.099\end{bmatrix}\right) =L_{\hat{d}}\begin{bmatrix}0.003\\ 0.017\end{bmatrix}v_{t}+\sum _{i=1}^{3} \widehat{\varGamma _{i}}\varDelta ^{\hat{d}}L_{\hat{d}}^{i} (X_{t}-\hat{\mu })+\hat{\epsilon _{t}}\\ \hat{d}&=\underset{(0.024)}{0.64}, Q_{\hat{\epsilon }}(24) =\underset{(pv=0.000)}{784.022}, log(\mathscr {L})=-87991.149 \end{aligned}$$

Long-term equilibrium relationship:

$$\begin{aligned} E_{t} = 1540.30 + 0.714G_{t} + v_{t} \end{aligned}$$
(14)

Hypothesis tests:

 

\({\mathscr {H}}_{d}^{1}\)

\({\mathscr {H}}_{\beta }^{1}\)

\({\mathscr {H}}_{\alpha }^{1}\)

\({\mathscr {H}}_{\alpha }^{2}\)

df

1

1

1

1

LR

194.160

19.884

0.73

14.185

p value

0.000

0.000

0.393

0.000

Restricted model:

$$\begin{aligned} \varDelta ^{\hat{d}}&\left( \begin{bmatrix}E_{t}\\ G_{t}\end{bmatrix}-\begin{bmatrix}466.937\\ 1433.553\end{bmatrix}\right) =L_{\hat{d}}\begin{bmatrix}0.000\\ 0.0143\end{bmatrix}v_{t}+\sum _{i=1}^{3} \widehat{\varGamma _{i}}\varDelta ^{\hat{d}} L_{\hat{d}}^{i}(X_{t}-\hat{\mu })+\hat{\epsilon _{t}} \\ \hat{d}&=\underset{(0.024)}{0.609}, Q_{\hat{\epsilon }}(24) =\underset{(pv=0.000)}{795.844}, log(\mathscr {L})=-87998.242 \end{aligned}$$

Long-term equilibrium relationship:

$$\begin{aligned} E_{t} = -563.644 + 0.7189G_{t} + v_{t}. \end{aligned}$$
(15)

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Beltrami, F., Fontini, F., Giulietti, M. et al. The Zonal and Seasonal CO2 Marginal Emissions Factors for the Italian Power Market. Environ Resource Econ 83, 381–411 (2022). https://doi.org/10.1007/s10640-021-00567-9

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  • DOI: https://doi.org/10.1007/s10640-021-00567-9

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