# Short-term CO2 emissions forecasting based on decomposition approaches and
its impact on electricity market scheduling

Neeraj Bokde  Bo Tranberg  Gorm Bruun Andresen<EMAIL_ADDRESS>Department of
Engineering - Renewable Energy and Thermodynamics, Aarhus University, 8000,
Denmark  Ento Labs ApS, Inge Lehmanns Gade 10, 6, 8000, Aarhus C, Denmark

###### Abstract

The world is facing major challenges related to global warming and emissions
of greenhouse gases is a major causing factor. In 2017, energy industries
accounted for 46% of all CO2 emissions globally, which shows a large potential
for reduction. This paper proposes a novel short-term CO2 emissions forecast
to enable intelligent scheduling of flexible electricity consumption to
minimize the resulting CO2 emissions. Two proposed time series decomposition
methods are developed for short-term forecasting of the CO2 emissions of
electricity. These are in turn bench-marked against a set of state-of-the-art
models. The result is a new forecasting method with a 48-hour horizon targeted
the day-ahead electricity market. Forecasting benchmarks for France show that
the new method has a mean absolute percentage error that is 25% lower than the
best performing state-of-the-art model. Further, application of the forecast
for scheduling flexible electricity consumption is studied for five European
countries. Scheduling a flexible block of 4 hours of electricity consumption
in a 24 hour interval can on average reduce the resulting CO2 emissions by 25%
in France, 17% in Germany, 69% in Norway, 20% in Denmark, and just 3% in
Poland when compared to consuming at random intervals during the day.

###### keywords:

forecasting , CO2 emission , demand flexibility

††journal: Applied Energy

##  1 Introduction

The modern human society is facing many challenges related to global warming
and emissions of greenhouse gases into the atmosphere is a major factor
responsible for it [1, 2].

According to a report by the European Commission, in 2017 China was
responsible for 29% of total CO2 emission and surpassed other economies
including the USA, Europe, and India which contributed 14%, 10%, and 7%,
respectively [3]. Further, this report revealed that the global annual CO2
emissions and global per capita emissions have climbed to 37 billion metric
tons and 4.9 metric tons in the year 2014, respectively. In the same year,
energy industries accounted for 46% of all CO2 emissions globally [4]. This
shows a large potential for reduction.

In 2009, most countries have shown their intentions to reduce CO2 emission at
the Copenhagen Global Climate Conference (also known as the 2009 United
Nations Climate Change Conference) [5]. During this conference, the European
Union and the USA committed to lowering the CO2 emission by 20 to 30% and 4%
of the level in 1990, respectively. Whereas, by 2020, the developing
economies, China and India targeted reducing the CO2 emissions per GDP by
around 40% and 25% of the level in 2005 by 2020, respectively. Furthermore,
most countries as a united globe have set the targets for upcoming decades to
reduce greenhouse gases significantly [6]. In addition to this, the Paris
agreement (famously named as 20/20/20) set to reduce CO2 emissions by 20%,
increase the renewable energy share by 20%, and increase energy efficiency by
20% for the whole World [7]. The country-wise profiles related to CO2
emissions and climate change are discussed in detail by the CarbonBrief team
[8].

During recent years, most countries targeted specific CO2 emissions to meet
global warming challenges. This leads to lots of research contributions on the
trends of CO2 emissions to assist energy planning policies. Although, there
are numerous techniques proposed by research teams throughout the World. Ye
et. al. [9] roughly categorized these techniques into two forms, namely,
target decomposition and policy evaluation. Target decomposition is a simple
and easy technique, which decomposes the targeted goals of CO2 emissions into
sub-divisions. These sub-divisions can be based on various criteria based on
different departments or provinces [10, 11]. However, these studies quantify
the potential of a specific policy. Whereas, in policy evaluation techniques,
policies to reduce CO2 emissions are evaluated under present scenarios. These
techniques include statistical, econometric and computer simulation approaches
to forecast CO2 emissions.

Forecasting CO2 intensity and related CO2 emissions is important today and
will become urgent in the future to recommend effective CO2 emissions
reduction policies to the policymakers. Furthermore, it may aid the system in
integrating renewable energy. Most countries are now under tremendous pressure
to limit reduce their CO2 emissions. Hence, it is of great importance to
explore and analyze the responsible factors for CO2 emissions. Accurate
forecasting models enable such analyses.

Throughout Europe, there are multiple bidding areas in many countries in the
day-ahead electricity market. For each bidding area, the transmission capacity
availabilities vary and this may congest the power flow between neighboring
bidding areas. Such congestion leads to differences in the price between
bidding areas. Among the energy markets in Europe are Nord Pool covering
Scandinavian countries [12], and EPEX SPOT covering North-West Europe [13].

The purpose of electricity markets is price formation to establish equilibrium
between supply and demand. This is done on an hourly level in the day-ahead
market for electricity. The day-ahead market clears at noon and provides an
hourly price for the 24 hours of the following day based on matching bids and
offers received from producers and consumers. When bidding, one needs to
specify the amount of energy in MWh for an hour to be bought (consumed) or
sold (produced) at a certain price level (Eur/MWh) for the next day.

Consider the time framework as shown in Figure 1 for further understanding of
the electricity market bidding. So far, such time frameworks have been used to
plan the market price forecast in the day-ahead energy market. In Figure 1,
the day ($D+1$), i.e. tomorrow, is the forecasting period of interest and for
this auction, the consumer needs to bid before 12.00 AM today, i.e. day $D$.
In addition, considering some buffer periods and time to place bids in the
market, it will be better for the consumer to be ready with such a forecast
analysis at 09:00 - 10.00 AM on the day $D$. Hence, this day ahead electricity
market needs 12-36 hours, hourly resolved forecasts.

Figure 1: Time framework to forecast for the day-ahead energy market.

Normally, consumers schedule the time slots with reference to electricity
prices and it is based on the electricity prices forecasts. The motivation is
to reduce the overall cost of consumed electricity for the desired scheduled
period [14].

In recent years many countries, public buildings, public infrastructures, and
institutes started to take initiatives to understand the sources and the
nature of the energy they are consuming. Such entities want to keep track of
their CO2 emissions. In relation to energy consumption, this means focusing on
greener energy with lower CO2 intensity. In the case of bidding in the day-
ahead market, the consumer could schedule not just after the forecasted price,
but also accordingly to forecasted CO2 intensity as a primary or secondary
objective. However, this can only be achieved if appropriate forecasts of the
CO2 is available. With this motivation in mind, this study investigates new,
appropriate models for electricity bidding-friendly multi-step hours CO2
emissions forecasts.

From a system perspective, forecasts like the one proposed in this study are
important for the scheduling of flexible electricity consumption to have an
effect on the increasing integration of renewable energy resources in the
electricity system. Flexible consumers must be able to place bids in the day-
ahead market to provide timely signals for the market participants e.g., to
adjust production plans accordingly.

In this article, two time series decomposition methods are compared for short-
term forecasting of the CO2 emissions of electricity. First, the CO2
intensities are obtained using the power flow tracing technique presented in
[15] and combined with country-specific average CO2 intensity per generation
technology as proposed in [16]. Second, these intensity time series are
decomposed into three components with two approaches. Finally, three different
forecasting models are employed to predict all components, and these predicted
magnitudes are combined to obtain the final forecasted values for a given CO2
intensity series. The performance of both decomposition approaches is then
compared with several state-of-the-art forecasting methods. The CO2 intensity
series exhibit non-stationary and nonlinear patterns, which are forecasted
effectively and precisely with the multi-scale integrated prediction methods.

Related studies in the literature focus on long-term forecasts of CO2
emissions. For electricity consumers to be able to provide flexible demand to
the system they need more accurate short-term forecasts as the novel methods
we are proposing in this study. Though these new methods are short-term
forecasts, they predict values that are 36 to 48 hours ahead in time in a
single step, which is a novel approach for this application. Consequently,
this paper contributes to the literature as follows:

  * 1.

The models to forecast the short-term CO2 intensity time-series for 36–48
hours ahead values, which are necessary for electricity market bidding.

  * 2.

Discussing the impact of forecasted CO2 emissions on the electricity market
schedule.

  * 3.

Enabling flexible electricity consumption scheduling to minimize CO2
emissions.

The remainder of this article is organized as follows: Section 2 discusses the
motivation behind 48 steps ahead forecasting of CO2 intensity and its effects
on electricity markets. Section 3 provides a precise review of various models
employed for CO2 intensity forecasting. The proposed methodology along with
two decomposition strategies are discussed in Section 4. Further, the
performance evaluation of the proposed methods is studied on sample standard
data sets in Section 5. In Section 6, a case study is discussed which
evaluates the performance of the proposed methods for short-term multi-step
CO2 intensity data set forecasting. Section 7 presents a case study on
potential CO2 emissions reductions resulting from scheduling flexible
electricity consumption. Finally, the conclusions of the paper are summarized
in Section 8. All abbreviations and variables used throughout the paper are
listed in Table 1.

Table 1: Nomenclature.

Abbreviations Variables ARIMA AutoRegressive Integrated Moving Average $x(t)$
a time series CO2 Carbon Dioxide $C_{i}(t)$ $i^{th}$ IMF DK Denmark $r_{m}(t)$
the final residual DPSF Differenced Pattern Sequence-based $e_{L}(t)$ Lower
envelope Forecasting method $e_{H}(t)$ Upper envelope EEMD Ensemble Empirical
Mode Decomposition $a(t)$ Average of lower EMD Empirical Mode Decomposition
and upper evelopes ENTSO-E European Network of Transmission $M$ Ensemble
numbers System Operators for Electricity $e$ Amplitude of the EPEX SPOT
European Power Exchange white noise series FFNN Feedforward Neural Network
$e^{{}^{\prime}}$ Final standard GDP Gross Domestic Product deviation of error
HVAC Heating, Ventilation, and $\mathrm{X_{i}}$ Observed data Air Conditioning
$\mathrm{\hat{X}_{i}}$ Forecasted data IMF Intrinsic Mode Functions
$\mathrm{N}$ Number of time steps IPT Integrated Powertrain for forecast
evaluation kWh Kilo-Watt Hour LSSVM Least-squares support-vector machine LSTM
Long-Short-Term Memory MAE Mean Absolute Error MAPE Mean Absolute Percentage
Error max. LE Maximum Lyapunov Exponent MWh Mega-Watt Hour NWP Numerical
Weather Prediction PSF Pattern Sequence-based Forecasting method RMSE Root
Mean Square Error SOPR Second-Order Polynomial Regression SVM Support Vector
Machine

##  2 Method

###  2.1 Review of CO2 emissions forecasts

Long-term CO2 emissions forecasting enables policymakers and planners to
estimate and reduce the future carbon footprint. However, the short-term CO2
emissions forecasting is critical to understand how much CO2 will be emitted
so that e.g., producers and consumers of electricity can schedule their
production and consumption to minimize their resulting emissions.

Globally, long-term CO2 emissions have been an attractive topic for research
and discussion, but there are very few articles discussing short-term
forecasting. Finenko et. al. [17] is one of the initial articles which
analyzed the hourly patterns of CO2 emissions for electricity generation and
stated that most CO2 emissions reduction can be achieved during day time with
a case study of Singapore. Mason et. al. [18] proposed a case study in
Ireland, which successfully forecasts short-term CO2 emissions using
evolutionary neural networks. There are few case studies [19, 20, 21] which
predicted air pollutants and ozone concentrations for short time horizons,
which were closely related to carbon footprints. Similarly, a light-use-
efficiency model based on numerical weather prediction (NWP) method is
proposed for short-term forecasting of CO2 fluxes in Europe [22].

For the first time, grid CO2 intensity in support of heating, ventilation, and
air-conditioning (HVAC) load is forecasted for the day ahead horizon by [23].
This study foresees the opportune time of the day for carbon saving based on
CO2 intensity forecasts and accordingly shutdown of the HVAC plant.

In contrast to the CO2 emissions time series used for long-term forecasting,
the one used for short-term forecasting is of higher complexity. For short-
term forecasting, the data set used has an hourly resolution, hence it
exhibits rapidly changing patterns. This highly chaotic time series is
challenging to forecast with the standard set of forecasting methods. As
discussed in the literature review, the models used for long-term CO2
emissions forecasting were mainly focused on understanding and estimating the
trends of the time series. However, in time series used for short-term
forecasting, there are many components apart from trends, which need to be
considered. Generally, a series can be segmented into three parts; these are
the seasonal, trend and random components. The seasonal component shows the
patterns in the series that repeat with a fixed period, whereas the trend
component shows the tendency of a series to increase or decrease over a long
period of time, which is a smoother, general and long-term tendency. Finally,
the random component is purely irregular in nature. It does not represent any
pattern and hence is an uncontrollable and unpredictable part of the series.
Minimizing the share of the random component, the time series becomes more
informative and non-chaotic in nature. Since all these components individually
have different patterns, it is not adequate to handle them jointly with a
single forecasting model as it is important to analyze the behavior of each
component individually.

In the present study, the time series is decomposed into the seasonal, trend
and random component series with two different approaches, and these
components are further forecasted with different models. Eventually, forecasts
of CO2 intensity are achieved and a comparison of the mentioned decomposition
approaches is done.

###  2.2 Decomposition with first approach

The first approach is a basic and well-known methodology, which first derives
the trend, seasonal and noise components one by one with various statistical
steps. The first step is to detect the trend in the time series using the
centered moving average method. In this step, a moving window with the length
of the seasonal period of the time series is used. The seasonality of a time
series is either observed by a seasonal period of the time series (daily,
weekly, monthly, or yearly) or estimated using the Fourier transform method.
Then, this moving window is replaced with the average of the window and the
trend series is obtained. The second step is detrending the time series by
removing the trend series obtained in the first step from the original time
series. The detrended series appears to be seasonal but infected with a noise
component. Now, to determine the actual seasonality component, the average
seasonality needs to be calculated. It is obtained in the third step by adding
seasonality of the detrended series together and dividing it by the
seasonality period. In the final step, the random noise component is extracted
by subtracting seasonal and trend components from the original time series.
The block-diagram of this approach is as shown in Figure 2(a).

(a) Decomposition with moving averages.

(b) Decomposition with EEMD method.

Figure 2: Block diagram of the (a) moving averages and (b) EEMD method based
decomposition approaches.

###  2.3 Decomposition with second approach

Furthermore, the second approach is based on a decomposition methodology. This
ensemble empirical mode decomposition (EEMD) method is used to decompose the
time series into a number of sub-series. It is a modification of the EMD
method, which is an empirical and effective decomposition method with a less
complex procedure. EMD is efficient at handling non-linear and non-stationary
time series. The methodology was introduced by [24] and since then, it has
become increasingly popular in the research field of forecasting, and
substantially enhancing prediction process [25]. With the methodology, the
time series is decomposed into numerous intrinsic mode functions (IMF) and one
residual. The process is termed as the EMD sifting process and can be
expressed linearly as:

$x(t)=\sum_{i=1}^{m}C_{i}(t)+r_{m}(t)\ $ (1)

where, $m$ is the number of IMFs, $C_{i}(t)$ is the $i$th IMF at the time $t$,
and $r_{m}(t)$ is the final residual of the time series $x(t)$. All $C_{i}(t)$
have zero means and are nearly orthogonal to each other [26].

In the processes, firstly all local minima and maxima values of $x(t)$ are
identified. Then the cubic spline interpolation is used to obtain the lower
envelope $e_{L}(t)$ and upper envelop $e_{H}(t)$ for the minima and maxima
values. The average value of $a(t)$ of the lower and upper envelope is
calculated as:

$a(t)=\frac{(e_{L}(t)+e_{H}(t))}{2}.$ (2)

The first component $d(t)$ is given by:

$d(t)=x(t)-a(t).$ (3)

After the above step, if $d(t)$ meets the IMF properties, then it is
considered as the first IMF. Otherwise, $x(t)$ is replaced by $d(t)$, and the
above process is repeated. In case of the residual function $r(t)$, when it
becomes monotonic or only extreme values are present from which no more IMF is
achieved, the process is terminated [27]. The IMF should satisfy the following
two condition:

  * 1.

The number of extrema and zero crossings of the data set must either be equal
or differ at most by one.

  * 2.

At any point, the mean value defined by $e_{L}(t)$ and $e_{H}(t)$ should be
zero.

The EEMD method is an adaptive approach developed from EMD. It was proposed by
[28]. The methodology has an improvement over EMD, as it adds finite white
noise to the original data, to overcome the problem of mode mixing that exists
with EMD. In the mode mixing problem, the data may not decompose properly and
hence a similar scale series are found to exist in different IMFs [26], which
results in loss of physical meaning in them. To decompose the time series by
EEMD the following steps have been adopted [28]: Random white noise having
zero mean and given standard deviation $e$ has to be added to the available
time series $x(t)$.

This time series is decomposed into various IMFs and one residual component.
The above procedure is repeated with different white noise series each time.
The mean of corresponding IMFs of the decomposition is obtained as the final
results. The addition of all the IMFs will not be the same at the end [29].
The effect of white noise can be minimized based on the following equation
[28] and [30].

$e^{{}^{\prime}}=\frac{e}{\sqrt{M}},$ (4)

where $M$ is the ensemble numbers, $e$ is the amplitude of the added white
noise series, and $e^{{}^{\prime}}$ is the final standard deviation of error.
Many researchers have supported the use of EEMD for the decomposition of time
series and it has been implemented successfully in various fields [31].

The case studies in [32] and [33] applied EEMD to time series of carbon and
crude oil prices and decomposed them into three IMF components: high
frequency, low frequency, and trend as shown in Figure 2(b). These components
seem equivalent, but an alternative to the seasonality, noise, and trend
components, respectively. A fine-to-coarse reconstruction algorithm [33] is
used to separate the IMFs into high- and low-frequency components, whereas the
residual is the trend component. In this procedure, the mean of the algorithm
is traced and when it departs significantly from zero for the ‘$n$’th IMF, the
partial reconstruction using IMF1-IMF($n-1$) represents the high-frequency
component. Whereas IMF$n$ to the last IMF comprises the low-frequency
component. The detailed analysis is further discussed in the following
sections for the proposed case study.

###  2.4 Significance of decomposition in forecast

The significance of decomposition methods in a forecasting model can be
explained with human experience and observations. Consider an example of
weather in a particular region. If one observed extreme cold in December and
excessive rainfall in August every year, this suggests that next year, there
will be another colder December as well as sufficient rain in August.
Similarly, the decomposed seasonal component captures the seasonal patterns
which repeat after a specific time interval and a forecasting model can easily
observe and estimate the future within such seasonal or high-frequency
component series.

Again, though it is expected, extreme cold in December sometimes is delayed or
the extreme cold peak is not occurring in a particular year. Besides,
sometimes, unexpected rainfall is observed in the winter season. All these
unexpected observations are nothing but the random activities based on various
natural or unnatural processes of the Earth. The random or low-frequency
components obtained with the discussed decomposition approaches represent this
random behavior of the time series.

Further, climate change is another example. Earlier studies [34, 35] confirms
significant increase in temperature during decades as shown in Figure 3. The
broad sense of temperature change in the century represented a trend line.
Again, these trend series can help a forecasting model to estimate such long-
term behavior present in the time series. Both discussed decomposition
approaches generate trend components with different strategies.

Figure 3: A trend showing annual average temperature for years 1977–2016
(Source: [35])

In this way, a proper strategy to forecast each of the series (seasonal,
trend, and random components) individually with distinct suitable models may
better reproduce the respective patterns in the forecasted series. Eventually,
a more accurate forecast can be achieved.

###  2.5 Selection of forecasting models

After decomposing the time series with both approaches, as shown in Figure 4,
the decomposed component forecasting method is selected for each. The
forecasted values are then aggregated to produce the final forecast results
for the original time series as described in Figure 5. The first and second
decomposition-based forecasting methods are shown in Figure 5 (a) and (b),
respectively.

Figure 4: Decomposed components with both approaches. Figure 5: Block diagram
of the proposed forecasting methods.

Now, the selection of the forecasting models for each component is a crucial
process. A cross-validation approach is adopted to decide the most suitable
forecasting model for each decomposed component obtained in the discussed
decomposition methods. The data set used for this purpose is from the West
Denmark price area (DK-1), which is the same as discussed in detail in
subsequent Section 6. Ten continuous patches of time series with the length of
1200 samples are selected randomly with the Monte-Carlo strategy and
decomposed into three components with both approaches as discussed in earlier
sections. These components are forecasted for the next 48 values with ARIMA,
FFNN, PSF, and DPSF models. Throughout the article, the comparisons of
accuracies of forecasting models are executed with three error metrics; RMSE,
MAE, and MAPE, which are given as:

$\mathrm{RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left|X_{i}-\hat{X}_{i}\right|^{2}}}$
(5)

$\mathrm{MAE=\frac{1}{N}\sum_{i=1}^{N}\left|X_{i}-\hat{X}_{i}\right|}$ (6)

$\mathrm{MAPE=\frac{1}{N}\sum_{i=1}^{N}\frac{\left|X_{i}-\hat{X}_{i}\right|}{X_{i}}\times
100\%}$ (7)

where $\mathrm{X_{i}}$ and $\mathrm{\hat{X}_{i}}$ are the observed and
forecasted data at time $\mathrm{t}$, respectively. $\mathrm{N}$ is the number
of time steps for forecast evaluation.

Table 2 shows averaged RMSE and MAE values for forecasted 48 values of the
time series for seasonal, trend, and random components with the first
decomposition approach.

Table 2: Averaged error values for forecasted 48 values of time series for
decomposed components with moving averages with Monte-Carlo strategy for
Danish dataset (* indicates best performing method. Both RMSE and MAE are
values of CO2 intensity in gCO2eq/kWh).

Models Original time series Seasonal component Trend component Random
component RMSE MAE RMSE MAE RMSE MAE RMSE MAE ARIMA 44.90 41.92 10.81 09.29
02.79* 02.37* 17.90* 14.70* FFNN 60.09 55.74 00.03* 00.02* 15.38 14.16 29.38
26.77 PSF 43.92 36.09 01.21 00.59 04.78 03.91 21.45 18.52 DPSF 31.88* 28.46*
09.61 08.66 03.55 03.09 19.92 17.74 Mean 293.1 7.90 82.31 10.88

From this table, it concludes that the seasonal component is efficiently
predicted with the FFNN model and the other two components with distinct ARIMA
models. Similarly, Table 3 shows error values for forecasted 48 values with
the second decomposition approach. For all cases, different ARIMA models have
fitted accurately and achieved the best forecasting results. In both tables (2
and 3), the last row represents the mean of corresponding time series
components.

Table 3: Averaged error values for forecasted 48 values of time series for
decomposed components with EEMD method with Monte-Carlo strategy for Danish
dataset (* indicates best performing method. Both RMSE and MAE are values of
CO2 intensity in gCO2eq/kWh).

Models Original time series High-frequency component Low-frequency component
Trend component RMSE MAE RMSE MAE RMSE MAE RMSE MAE ARIMA 44.90 41.92 12.10*
09.07* 01.63* 01.44* 0.005* 0.003* FFNN 60.09 55.74 13.17 10.08 22.22 19.04
01.99 01.81 PSF 43.92 36.09 15.59 11.32 26.28 25.93 06.33 06.32 DPSF 31.88*
28.46* 23.01 20.80 07.93 06.39 00.05 00.04 Mean 293.1 23.11 27.06 10.03

##  3 Performance evaluation of the proposed methods

In this section, the performance and robustness of both decomposition
approaches are checked on time series forecasting methods with various
distinct trends and seasonality. Then the forecasted results are compared with
state-of-the-art methods.

Similar to many other chaotic and intermittent time series found in nature
such as wind energy, the CO2 intensity time series seems to fail at achieving
outstanding forecasting performance. These time series are usually infected
with unusual and different patterns of trends and seasonality components.
Hence, it becomes necessary to choose a method, which can handle trends and
seasonality patterns individually to achieve more accurate predictions for
such data.

Before the CO2 intensity data set, the performance of proposed methods based
on two mentioned decomposition methods is evaluated for some standard time-
series data sets, which are available under a public license. The data sets,
used here, are listed in Table 4 and Figure 6. Additionally, the statistical
characteristics of the respective time series are provided in Table 5. This
table provides the basic statistical details of time series that includes
minimum (Min.) and maximum (Max.) values, Median, Mean, 1st and 3rd Quartiles.

Table 4: Details of time series used for validation (Source: [29]).

Time Series Description AirPassangers Time series for monthly totals of
international airline passengers for 11 years nottem Time series for average
air temperature at Nottingham Castle in degree Fahrenheit for 20 years.
sunspots Time series for monthly mean relative sunspot numbers for more than
two centuries. a10 Total monthly scripts for pharmaceutical products falling
under ATC code A10. It is collected by the Australian Health Insurance
Commission. ausbeer Total quarterly beer production in Australia (in
megalitres) reported for more than 50 years. cafe Total quarterly expenditure
on cafes, restaurants and takeaway food services in Australia collected for
around 30 years. debitcards Retail debit card usage in Iceland (million ISK).
elecequip Manufacture of electrical equipment: computer, electronic and
optical products. euretail Quarterly retail trade index in the Euro area in 17
countries, from 1996 to 2011. h02 Total monthly scripts for pharmaceutical
products falling under ATC code H02, as recorded by the Australian Health
Insurance Commission. usconsumptions Percentage changes in quarterly personal
consumption expenditure and personal disposable income for the US, 1970 to
2010. usmelec Electricity net generation measured in billions of kilowatt
hours (kWh).

Table 5: Statistical characteristics of time series used for validation (Source: [29]). Time Series | Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max.
---|---|---|---|---|---|---
AirPassengers | 104.0 | 180.0 | 265.5 | 280.3 | 360.5 | 622.0
sunspots | 0.00 | 15.70 | 42.00 | 51.27 | 74.92 | 253.80
nottem | 31.30 | 41.55 | 47.35 | 49.04 | 57.00 | 66.50
a10 | 2.815 | 5.844 | 9.319 | 10.694 | 14.290 | 29.665
ausbeer | 213.0 | 378.5 | 423.0 | 415.0 | 465.5 | 599.0
cafe | 1012 | 2190 | 3389 | 3716 | 5193 | 8426
debitcards | 7204 | 11330 | 16183 | 15514 | 18514 | 26675
elecequip | 62.47 | 86.17 | 94.03 | 95.71 | 103.95 | 128.75
euretail | 89.13 | 94.56 | 96.55 | 96.35 | 99.43 | 102.10
h02 | 0.3362 | 0.5889 | 0.7471 | 0.7682 | 0.9376 | 1.2572
usconsumptions | -2.2966 | 0.4050 | 0.8005 | 0.7553 | 1.1141 | 2.3171
usmelec | 139.6 | 192.6 | 252.5 | 254.1 | 307.0 | 421.8
Figure 6: Time series patterns (Source: [29]).

These time-series data sets were used for performance evaluation of a
forecasting model in [29]. The selection of these time series is crucial
because special precautions were taken to consider various kinds of
seasonality, trend components as well as a variety of periodic and chaotic
data sets, which are further discussed in [29]. The amount of chaos in the
time series data sets is quantified in terms of the maximum Lyapunov exponent
(max. LE) values. The max. LE value of the ‘sunspots’ time series is 0.6009,
which makes it a highly chaotic series, whereas, the ‘nottem’ time series is
highly periodic with max. LE value of 0.0065. For all of these time series,
the last 48 values are taken away for validation purpose, whereas the leftover
initial part of the time-series is used for training of the forecasting
methods. Then the proposed methods are compared with ARIMA, DPSF, FFNN, and
PSF methods. The R package ‘forecast’ [36] is used for ARIMA and FFNN; and
‘PSF’ [37, 38] is used for PSF methods.

Table 6 shows a comparison of the proposed decomposition methods in terms of
RMSE values with other methods in the study of a 48-hour forecast. It is
observed that the proposed methods achieved better results for almost all
time-series. Further, the accuracy of the proposed methods is backed by
Friedman’s non-parametric test with the distribution of predicted
observations. This test is generally used to find differences in treatments
within multiple outcomes. Non-parametric means the test does not assume that
data belongs to a particular distribution. In this test, the null hypothesis
assumes that data comes from a particular distribution. The null hypothesis of
this test states that samples in two or more groups are drawn from the same
mean value populations. Further, the null hypothesis is rejected when the
level of significance is below 0.05.

Table 6: Comparison of proposed methods in terms of RMSE values (* indicates
best performing method).

Time Series ARIMA FFNN PSF DPSF Method 1 Method 2 AirPassengers 113.72 78.72
97.80 83.09 42.19* 65.31 sunspots 103.07 32.24 52.29 42.51* 47.03 59.34 nottem
2.52 2.46 2.13 2.18 2.01* 2.87 a10 4.88 4.20 6.66 4.65 2.83* 3.18 ausbeer
33.23 33.19 76.85 85.95 30.18* 31.12 cafe 1208.62 2534.18 2888.15 1208.62
1195.02 380.44* debitcards 2638.13 3353.65 3060.86 6664.44 1029.00* 3069.27
elecequip 27.76 15.80 15.57 32.27 20.79 10.82* euretail 06.17 04.52 12.39
08.32 03.13* 05.29 h02 0.22 0.17* 0.08 0.18 0.17* 0.18 usconsumptions 0.98
0.96* 1.15 1.10 0.99 0.99 usmelec 38.33 15.12* 50.22 34.17 21.71 34.27

The p-values for all-time series for Friedman’s test for the proposed methods
are shown in Table 7. In all cases, the null hypothesis is rejected with
p-values lower than 0.05. This concludes that the proposed methods have
achieved statistically significant outcomes.

Table 7: p-values of Friedman’s test for proposed methods. Time Series | Method 1 | Method 2
---|---|---
AirPassengers | 1.749e-04 | 2.871e-12
sunspots | 7.764e-09 | 4.262e-12
nottem | 2.400e-03 | 1.222e-12
a10 | 1.490e-05 | 1.902e-12
ausbeer | 2.141e-10 | 3.551e-12
cafe | 7.764e-09 | 1.401e-03
debitcards | 4.331e-03 | 4.262e-12
elecequip | 7.764e-09 | 4.002e-12
euretail | 3.147e-11 | 4.139e-08
h02 | 4.139e-08 | 1.974e-12
usconsumptions | 1.400e-03 | 3.892e-03
usmelec | 5.312e-05 | 4.262e-12

##  4 CO2 intensity forecast. A case study

In this section, the performance of the proposed methods is examined for
short-term CO2 intensity forecasting with the consideration of two
decomposition approaches. As discussed in earlier sections, these methods are
based on two decomposition approaches which decompose a time series into three
distinct components. The comparison of these methods is applied for CO2
intensity forecasting for 48 hours ahead with recursive and Dirrec strategies
of predictions. In a recursive approach, the first value is predicted with a
prediction model and then appended to the data set. The same model is then
used to predict the next value. In the Dirrec approach, the first value is
predicted with a model and appended to the data set. A new model is then
fitted and used to predict the next value and so on. As the Dirrec approach is
a more time-consuming technique, it will be interesting to understand its
effect on forecasting accuracy.

###  4.1 Data

The data set used in this study is provided by the ENSTO-E Transparency
platform [39]. Transmission system operators of each price area report data
for production mix, demand, import and export flows, and prices to this
platform on daily intervals with hourly resolution. A visualization of this
data is provided by the electricityMap [40]. This data for 2017 was the
foundation for [16], where a real-time carbon accounting method was proposed
for the European electricity markets. This method was based on power flow
tracing techniques and introduced a new consumption-based accounting method
that represents the underlying physics of the electricity system physics in
contrast to the state-of-the-art input-output carbon accounting models [41,
42, 43].

In this case study, data is used from the ENSTO-E Transparency platform for
2018 and 2019. The data set includes electricity generation per technology and
electricity demand per price area, as well as power flows between
interconnected areas. The flow tracing is used to map power flows between
importing and exporting countries as described in [15]. Country-specific
average CO2 emission intensity per generation technology is applied to the
flow tracing results to calculate the hourly CO2 intensity of electricity
consumption for each price area following the method proposed in [16]. It
refer to this as the consumption intensity. Based on the local generation mix,
the CO2 intensity of electricity generation for each price area is referred to
as the production intensity.

Figure 7 shows the countries and their inter-connectors (indicating import and
export of power flow) for a specific hour considered in the present study. The
width of inter-connectors indicates the proportions of the power flow within
the countries. And the color allotted to each country represents the
consumption-based CO2 intensity for the specific country within the given
color palette. The color sheds vary from green to red color indicating low to
high CO2 intensities for the specific hour.

Figure 7: The countries with carbon consumption intensities (shown in
different color ranges) and their inter-connectors (indicating import and
export of power flow) for a specific hour.

In Figure 8, the average hourly production and consumption intensity are
compared for each country as a function of the share of non-fossil generation
in the country’s generation mix. A clear pattern of decreasing intensity is
seen with an increasing share of non-fossil generation. With few exceptions,
the consumption intensity is higher than the production intensity for high
shares of non-fossil generation. This is an indication of the imported
electricity having a higher intensity than the local generation on average.
The pattern reverses for low shares of non-fossil generation.

Figure 8: For each country, the compared average hourly production (blue) and
consumption (orange) intensity as a function of the share of non-fossil
generation in the country’s generation mix.

For the detailed demonstration, CO2 intensity data from 25-05-2019 to
10-07-2019 (i.e. 1248 hours = 52 days) for France is selected randomly for
analysis as illustrated in Figure 9. This time series is divided into two
parts, i.e., training data which contains data of initial 1200 sampling (1200
hours = 50 days) and validation data as the last 48 samplings (48 hours = 2
days). Further, Table 8 shows the statistical characteristics of the training
data set.

Figure 9: CO2 intensity time series data set from France for 1248 hours (52 days). Table 8: Statistical characteristics of CO2 intensity time series data set from France. Location | Mean | Median | Minimum | Maximum | Standard Deviation
---|---|---|---|---|---
France | 74.16 | 78.93 | 16.35 | 136.89 | 27.01

###  4.2 Model selection

Forecast result accuracy is primarily dependent on the proper selection of
models. In this section, the model selection of the proposed methods and
state-of-the-art methods are discussed. These state-of-the-art methods are
modeled for the original time series as follows. ARIMA models are consist of
three parameters, $p$ (number of auto-regressive terms), $d$ (number of
nonseasonal differences needed for stationarity) and $q$ (number of lagged
forecast errors in the prediction equation); for the given time series these
values are 2, 1 and 1, respectively. For PSF models, the optimum window ($W$)
and cluster size ($K$) parameters are derived with the R package PSF [38] and
for given time series, these values are 4 and 3, respectively. Similarly, for
the DPSF model, these values are 5 and 3, respectively. For the FFNN model,
two parameters ($p$ lagged inputs and $k$ nodes in the single hidden layer)
are calculated and for a given time series, these values are 26 and 14,
respectively.

Further, for the first proposed method, there are three models for three
components (i.e. seasonal, trend, and random components) and are shown in
Figure 10(a). For the seasonal component, FFNN is modeled with $p=28$ and
$k=14$. Whereas, trend and random components are forecasted with ARIMA models.
The corresponding parameters are $p=1$, $d=1$, $q=0$ and $p=3$, $d=0$, $q=1$,
respectively.

(a) Decomposition with the moving averages.

(b) Decomposition with EEMD method.

Figure 10: Decomposed components obtained with the (a) moving averages and (b)
EEMD method based decomposition approaches.

Similarly, in the second proposed method, the time series first decomposes
into the number of sub-series with EEMD, named as IMFs. For the given time
series, the 10 generated IMFs are shown in Figure 11. Then, with the help of
the fine-to-course reconstruction method, all IMFs are combined into three
components based on the mean values of IMFs shown in Figure 12. Then all three
components (i.e. low-frequency, high-frequency, and trend components) shown in
Figure 10(b) are forecasted with ARIMA models with parameters as shown in
Table 9.

Figure 11: Decomposition of CO2 intensity [gCO2eq/kWh] time series for France. Figure 12: The mean of the fine-to-coarse reconstruction algorithm as a function of index $K$. Table 9: Parameters for ARIMA models in Method 2. Components | Models | p | d | q
---|---|---|---|---
High-frequency | ARIMA | 2 | 0 | 3
Low-frequency | ARIMA | 1 | 0 | 0
Trend | ARIMA | 0 | 2 | 0

###  4.3 Results and discussion

This subsection discusses the forecasting results of both proposed methods on
the CO2 intensity time series data set from several European countries. Apart
from the comparison of both decomposition-based methods, other state-of-the-
art forecasting methods have been compared in the study to prove the
accuracies of both strategies. These models include ARIMA, FFNN, SVM, PSF, and
DPSF, which are among the best ones to perform on such chaotic and
intermittent data set used in this study. All these models are compared with
both recursive and Dirrec prediction approaches for 48 hours ahead forecasting
results for the French data set and are shown in Table 10. For both
approaches, the proposed models show better forecasting performance in terms
of RMSE, MAE, and MAPE with Method 1 outperforming Method 2. There are several
models to forecast one or two-step ahead values precisely.

Table 10: Comparison of proposed methods with state-of-the-art models for CO2 intensity data in France (* indicates the best performing method). Models | Recursive approach | Dirrec approach
---|---|---
RMSE | MAE | MAPE | RMSE | MAE | MAPE
ARIMA | 28.86 | 22.83 | 21.64 | 28.34 | 22.41 | 21.40
FFNN | 26.43 | 20.28 | 21.14 | 25.93 | 19.73 | 20.88
SVM | 62.96 | 50.50 | 59.20 | 58.11 | 43.90 | 55.05
PSF | 20.47 | 15.31 | 15.26 | 20.38 | 15.29 | 15.21
DPSF | 26.12 | 21.93 | 22.62 | 26.05 | 21.88 | 22.56
Method 1 | 15.57* | 11.99* | 11.47* | 15.53* | 11.80* | 11.46*
Method 2 | 18.28 | 14.58 | 15.98 | 18.16 | 14.43 | 15.91

Furthermore, all these models are examined for the same French data set for
different multi-step ahead forecasting. Figure 13 shows the error values
(RMSE) with distinct models for 1, 3, 6, 12, 24 and 48 hours ahead forecasts.
It can be seen that concerning the proposed methods, ARIMA, PSF, and DPSF
models are showing lower or comparable errors for shorter multi-step
forecasts, but it gets drastically higher for longer steps (48-step ahead)
ones. Whereas, for 48 hours ahead forecast, both proposed models have shown
higher accuracy, and especially Method 1.

Figure 13: Multi-step ahead error values (RMSE) with various models for
France.

Apart from this, the statistical significance of the proposed methods is
evaluated with Friedman’s test. The p-values of this test for the French data
set are 0.020 and 0.057 for the 48 hours ahead forecast for Method 1 and
Method 2, respectively. In both cases, the null hypothesis is rejected with
lower p-values and approves its statistical significance.

In such studies, the complexity of a methodology is considered as an important
metric apart from forecasting error comparison to evaluate the forecasting
performance. Usually, the complexity is estimated only with the size of the
data set, not other possible parameters such as the number of features, tuning
parameters, etc. In the present study, the time complexity of the proposed
methods is estimated with the GuessCompx tool [44]. This tool empirically
guesses the time and memory complexities of a methodology. It tests multiple,
increasing size random samples of the input data sets and attempts to fit
distinct complexity function $O(N)$, $O(N^{2})$, $O(logN)$, etc. Based on the
best fit, this tool estimates the full computational time for given data set
and it is discussed in detail in [45].

Table A.1 shows the time and memory complexities of individual decomposition
approaches and forecasting models for each decomposed component for both
proposed methods for the French data set. The overall complexities of both
methods are calculated by observing the complexities of each sub-step involved
in the methods. This individual complexity study is done since all sub-steps
(decomposition and forecasting models) are performed on different data series.

The overall complexity of the methods is finalized based on the most complex
process within each method. In Method 1, the seasonal component forecasting
with the FFNN model is the most complex step with quadratic ($O(N^{2})$)
nature in terms of time complexity. Hence, the overall time complexity of
Method 1 is quadratic ($O(N^{2})$). Similarly, the decomposition approach in
Method 2 appeared to be the most time consumption-based complex task, which is
Linearithmic $O(NlogN)$. Furthermore, the memory complexity is observed to be
the Logarithmic $O(logN)$ for both methods. Considering the same length of
time series, similar complexity observations are obtained for the other
countries.

An unbiased comparison study is performed with the Monte-Carlo strategy for
all countries’, in which 25 different patches of 1248 continuous samples are
selected randomly. For each patch, initial 1200 samples are used as training
data and the remaining 48 values are used for validation purposes. Finally,
the mean of error values for each patch is considered as the performance of
the methods compared in the study. This Monte-Carlo strategy is implemented
with the ForecastTB tool [46, 47], and it ensures the suitability of the
models for the given time series and rejects the possibility of favorable
results by chance.

Table 11: Comparison of proposed methods with state-of-the-art models in terms
of RMSE for CO2 emissions data for European countries (* indicates the best
performing method for the respective country).

Country ARIMA FFNN SVM PSF DPSF Method 1 Method 2 Austria 52.42 50.93 51.66
57.20 51.82 35.49* 46.34 Belgium 191.75 200.17 298.35 223.17 321.50 195.17
181.22* Bulgaria 36.40 55.15 85.12 61.21 43.14 32.98 31.71* Switzerland 95.52
96.33 62.63 95.60 139.56 86.04* 95.00 Czech Republic 71.33 74.49 87.92 86.08
74.94 49.01* 63.91 Germany 102.72 85.70 106.71 83.40 77.96 42.18* 62.77
Denmark 30.74 40.65 84.52 42.49 46.11 31.09 28.09* Estonia 87.48 122.11 244.91
100.38 117.31 57.70* 64.45 Spain 132.35 134.81 126.32 147.66 226.93 131.89*
135.57 Finland 21.31 39.76 45.30 23.88 28.00 18.00 16.57* France 22.80 26.10
52.86 21.44 22.35 14.91* 20.49 UK 149.87 332.34 298.71 171.00 176.16 140.35
133.75* Greece 72.11 48.01 96.65 46.72 35.61 30.68* 43.69 Hungary 29.69 45.54
61.60 45.84 29.52 16.13* 26.50 Ireland 71.46 70.47 95.88 68.17 63.39 45.23*
67.66 Italy 120.33 120.51 152.04 85.24 80.58 48.66* 111.43 Lithuania 86.81
122.01 213.56 78.77 98.17 61.59* 76.44 Latvia 66.62 79.01 89.68 62.05 83.67
49.11* 56.59 Montenegro 166.84 170.73 234.48 132.44 161.84 97.44* 151.89 North
Macedonia 74.44 65.44 89.26 82.73 92.14 67.37 58.81* Netherlands 53.99 84.66
52.94 56.57 55.30 43.27* 44.11 Norway 59.36 81.32 167.89 69.09 57.32 37.70*
42.38 Poland 64.03 68.62 85.79 62.75 51.59 50.30* 52.09 Portugal 56.50 56.74
80.74 66.73 61.95 48.90* 53.75 Romania 37.06 43.55 47.62 51.20 43.31 33.02*
36.96 Serbia 57.00 42.77 96.06 71.87 85.83 44.44* 51.72 Sweden 67.97* 108.96
102.01 71.79 59.68 69.59 74.19 Slovenia 45.96 40.63 59.61 53.34 40.37 29.23*
31.55 Slovakia 34.92 36.84 60.47 43.46 42.73 27.90* 33.69

Based on Tables 10, 11, and A.1, the following points can be observed:

  * 1.

For the sample French data set, both proposed methods have performed better
than other models for 48 hours ahead CO2 intensity forecasting. The RMSE, MAE,
and MAPE of Method 1 are 15.57, 11.99, and 11.47 for the recursive approach;
and 15.53, 11.80, and 11.46 for Dirrec one. Whereas, in Method 2, for the
recursive approach, these errors are 18.28, 14.58, and 15.98; and for the
Dirrec approach are 18.16, 14.43, and 15.91, respectively. In terms of RMSE,
Method 1 has 14.82% and 14.48% improvement in forecasting in comparison to
Method 2 for recursive and Dirrec approaches.

The percentage of improvements with Method 1 as compared to all other methods
in the study are shown in Table 12 for both recursive and Dirrec approaches.

Table 12: Percentage improvements of Method 1 with state-of-the-art models for CO2 intensity data in France. Models | Recursive approach | Dirrec approach
---|---|---
RMSE | MAE | MAPE | RMSE | MAE | MAPE
ARIMA | 46.04 | 47.48 | 46.99 | 45.20 | 47.34 | 46.44
FFNN | 41.08 | 40.82 | 45.74 | 40.10 | 40.19 | 45.11
SVM | 75.52 | 76.23 | 80.62 | 73.23 | 73.12 | 79.18
PSF | 23.93 | 21.61 | 24.83 | 23.79 | 22.82 | 24.65
DPSF | 40.39 | 54.28 | 49.29 | 40.38 | 46.06 | 49.20
Method 2 | 14.82 | 17.69 | 28.22 | 14.48 | 18.22 | 27.96
  * 2.

Dirrec is found to be an expensive forecasting strategy in which the first
forecasted value is appended to the data set and a new model is fitted to
forecast the next value. It means, for 48 hours ahead forecast, the execution
time of the Dirrec model is nearly 48 times that of the recursive one. From
Tables 10 and 12, it can be seen that the error improvements with Dirrec
strategy are negligible as compared to the recursive one. Hence, the recursive
strategy comes out to be the better-suited forecasting strategy for short-term
multi-step CO2 intensity forecasting.

  * 3.

Based on Table 11, with the Monte-Carlo strategy, among 29 European countries,
Method 1 outperformed all methods for 22 countries, and for 6 countries,
Method 2 was the best performing method. The overall average percentage
improvements of Method 1 as compared to ARIMA and FFNN methods range from
-2.38% (for Sweden) to 58.93% (for Germany) and -3.97% (for Serbia) to 64.58%
(for Hungary), respectively in terms of RMSE collectively for all countries.
Similarly, the same improvements ranges with Method 2 are -9.15% (for Sweden)
to 39.41% (for Greece) and -20.92% (for Serbia) to 59.74% (for UK),
respectively. Here, the negative sign indicates that Method 1 or 2 performed
in a less efficient way than the methods in the comparison study. The country-
wise percentage improvements in RMSE for ARIMA and FFNN methods are shown in
Figures 14 and 15, respectively.

  * 4.

Method 1 achieved superior accuracy with the statistical significance at the
cost of computational complexity. Considering the computational complexity
(especially, the time complexity), Method 1 ($O(N^{2})$) observed more complex
than Method 2 ($O(NlogN)$).

Figure 14: Percentage improvements in RMSE with respect to ARIMA. Figure 15:
Percentage improvements in RMSE with respect to FFNN.

##  5 Impact on electricity market scheduling

The ultimate goal of the short-term CO2 intensity forecast is to enable the
scheduling of flexible demand in the electricity market to minimize the
resulting CO2 emissions. Figure 16 shows the realized CO2 emissions per kWh
electricity consumed (black) and corresponding forecasted values (red) with
Method 1 for France for consecutive 48 hours. The start point of the time
series (12.00 PM) is the point in time today (day $D$) at which the day-ahead
electricity market is cleared. Bids submitted to the day-ahead power exchange
before this time is targeted the whole of the next-coming day (24 hours of the
day $D+1$). This interval is marked in the grey between the dashed blue lines.

In this example, a flexible electricity consumer is willing to bid in specific
hours in day $D+1$ to minimize the associated CO2 emissions. Specifically,
electricity consumption is scheduled during the four hours with least
forecasted CO2 intensity. The dots on the red line denote the four minimum
values of the forecast within the 24-hour window. The horizontal line shows
the maximum CO2 emissions per kilowatt-hour electricity consumed value within
the scheduled hours with reference to the forecasted series. The dots on the
black line highlight the corresponding realized values. The mean intensity for
these four hours is 76.35 gCO2eq/kWh and 72.51 gCO2eq/kWh, respectively, for
the forecasted and realized values.

Similar examples of scheduling for Germany, Norway, Denmark, and Poland are
shown in Figure B.1. These countries have been selected based on their
location in Figure 8: Poland with a very low share of non-fossil generation,
France with a high share of nuclear, Norway with a high share of hydro,
Denmark with a high share of wind and Germany somewhere in between.

Figure 16: Example of scheduling 4 hours of flexible electricity consumption
one day in advance in France. The gray area shows the day-ahead interval. The
red and black lines show forecasted and realized values of the CO2 intensity,
respectively. The four hours minimum of the forecast is market with red dots.
The corresponding realized values are marked with black dots.

Figure 16 shows just a single example of scheduling four hours of electricity
consumption in France. In Figure 17, the emissions between scheduling and
consuming are compared at a random time during the 24-hour interval for an
entire year in France. Each bar shows results for different durations of
flexible consumption from one to 24 hours. The ratio between the bars is shown
as the red line. A ratio of one means there are no savings from scheduling
compared to consuming at a random time. This is the case when the flexible
consumption takes up all 24 hours of the window. The ratio decreases as the
duration of flexible consumption decreases. This is to be expected as a
shorter duration of consumption means more flexibility for scheduling during
the 24 windows.

Figure 17: Comparison of emissions between scheduling and consuming at a
random time during the 24-hour interval for an entire year in France. Each bar
shows results for different durations of flexible consumption. The ratio
between the bars is shown as the red line.

Figure 18 shows similar results for Germany, Norway, Denmark, and Poland.
Comparing the benefit of scheduling between the five countries, for a duration
of flexible consumption of four hours, observed on average 25 % emissions
reductions in France, 17 % in Germany, 69 % in Norway, 20 % in Denmark, and
just 3 % in Poland.

Figure 18: Comparison of emissions between scheduling and consuming at a
random time during the 24-hour interval for an entire year in four countries.
The bars show results for durations of flexible consumption of 4, 8 and 12
hours.

Furthermore, Figure 19 shows the variation in the ratio of forecasted
($V_{F}$) and realized ($V_{V}$) values for each of the 48 hours of the
forecast horizon with Monte-Carlo strategy with 50 iterations for France. This
figure represents the statistical relation between forecasted and realized
values in terms of box plots. The red dots are the mean values of these ratios
for the whole year. The dashed blue lines show the standard deviations from
the mean values throughout the year. The shaded regions in the figure show the
24 hours of the forecasts, which are to be used for the scheduling of flexible
consumption. It is observed that the forecast at initial and last 8 hours is
more consistent throughout the year, whereas, those in middle hours (day-time
hours) express higher variations. This outcome concludes that, though these
variations are not much significant (merely varies between 0.091 to 0.185)
throughout the year, the electricity market bidder could consider a bit higher
chances of deviation in the day time hour values. Similar results for Denmark,
Germany, Norway, and Poland are shown in Figure B.2.

Figure 19: Variation in the ratio of forecasted ($V_{F}$) and realized
($V_{V}$) values for each of the 48 hours of the forecast horizon. The red
dots in are the mean values of these ratios for the whole year. The dashed
blue lines show the standard deviations from the mean values throughout the
year. The shaded regions show the 24 hours of the forecasts, which are to be
used for the scheduling of flexible consumption.

##  6 Conclusions

Accurately forecasting the CO2 intensity plays a crucial role in the socio-
economic and environmental benefits derived from appropriate energy
management. It can affect the energy policies of a country to a certain
extent. Hence, more accurate methods to improve CO2 intensity forecasts become
sensible. A simple model without preprocessing of a chaotic time series
usually seems unachievable in most of the cases. Hence, the preprocessing of
the data set with suitable methodologies enhances the forecasting accuracy.
Preprocessing with decomposition methods helped many researchers in superior
forecasting outcomes.

In this study, the accuracies of two decomposition strategies are examined for
48 hours ahead of CO2 intensity data forecasting. The first decomposition
approach is a pure and simple statistical method that decomposes a time series
into seasonal, trend, and random series components. Similarly, the second
decomposition approach bases on the EEMD method again decomposes a time series
into three components, those are, high-frequency, low-frequency, and trend
series components. These decomposition approaches separate outs of distinct
meaningful patterns from the original time series and assists in achieving
forecast-friendly data series components. Summarizing the observation, it can
be concluded that the performance of meaningful decomposition approaches can
improve the multi-step short-term CO2 intensity forecast as discussed in the
paper. In this study, for CO2 intensity forecasting, the first decomposition-
based method (with time complexity $O(N^{2})$) has been found to outperform
the second method with time complexity $O(NlogN)$). For 23 of the 29 European
countries, the first decomposition method obtained the highest accuracy. The
result is a trade-off between forecast accuracy and computational complexity.
The memory complexity of both methods is the same, i.e., $O(logN)$. In this
case, the higher computing time is acceptable since the forecast is only
performed once per day for the day-ahead market.

After validating the correctness of Method 1 of the proposed forecasting
method, it was used to assess the impact scheduling of flexible electricity
consumption. The CO2 emissions from scheduling were studied for France,
Germany, Norway, Denmark, and Poland. It was found for all countries that
scheduling the consumption after the forecasted intensity compared with
consuming at a random time leads to reductions in emissions. Reductions
increase with decreasing duration of consumption because of the increased
flexibility of scheduling within the 24-hour window. In the case of a duration
of flexible consumption of four hours, it found emissions reductions ranging
from 3 % in Poland to 69 % in Norway.

In future work, forecasts with a longer horizon and finding the optimal trade-
off between CO2 emissions and electricity prices can be examined to propose a
meaningful strategy for scheduling flexible electricity consumption in the
day-ahead and future markets of electricity.

## Acknowledgments

This study was funded by Apple Inc. as part of the APPLAUSE bio-energy
collaboration with Aarhus University. Bo Tranberg acknowledges funding from
ELFORSK via project 351-054.

##  A Tables

Table A.1: Complexity study of the proposed methods. Complexity of Method 1
---
Complexity |  | Decomposition with
---
moving averages
| Seasonal component
---
forecast with FFNN
| Random component
---
forecast with ARIMA
| Trend component
---
forecast with ARIMA
Overall
Time |  | Constant
---
$O(1)$
| Quadratic
---
$O(N^{2})$
| Constant
---
$O(1)$
| Logarithmic
---
$O(logN)$
| Quadratic
---
$O(N^{2})$
Memory |  | Logarithmic
---
$O(logN)$
| Constant
---
$O(1)$
| Logarithmic
---
$O(logN)$
| Logarithmic
---
$O(logN)$
| Logarithmic
---
$O(logN)$
Complexity of Method 2
Complexity |  | Decomposition with
---
EEMD method
| High-freq. component
---
forecast with ARIMA
| Low-freq. component
---
forecast with ARIMA
| Trend component
---
forecast with ARIMA
Overall
Time |  | Linearithmic
---
$O(NlogN)$
| Constant
---
$O(1)$
| Constant
---
$O(1)$
| Constant
---
$O(1)$
| Linearithmic
---
$O(NlogN)$
Memory |  | Logarithmic
---
$O(logN)$
| Constant
---
$O(1)$
| Constant
---
$O(1)$
| Logarithmic
---
$O(logN)$
| Logarithmic
---
$O(logN)$

##  B Figures

(a) Germany

(b) Norway

(c) Denmark

(d) Poland

Figure B.1: Example of scheduling 4 hours of flexible electricity consumption
one day in advance in four different countries. The gray area shows the day-
ahead interval. The red and black lines show forecasted and realized values of
the CO2 intensity, respectively. The four hours minimum of the forecast is
market with red dots. The corresponding realized values are marked with black
dots.

(a) Germany

(b) Norway

(c) Denmark

(d) Poland

Figure B.2: Variation in the ratio of forecasted ($V_{F}$) and realized
($V_{V}$) values for each of the 48 hours of the forecast horizon. The red
dots in are the mean values of these ratios for the whole year. The dashed
blue lines show the standard deviations from the mean values throughout the
year. The shaded regions show the 24 hours of the forecasts, which are to be
used for the scheduling of flexible consumption.

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