Modelling carbon emissions in electric systems

Energy Conversion and Management 80 (2014) 573–581

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Modelling carbon emissions in electric systems E.T. Lau a, Q. Yang a, A.B. Forbes b, P. Wright b, V.N. Livina b,⇑ a b

Brunel University, Kingston Lane, Uxbridge, Middlesex UB8 3PH, UK National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, UK

a r t i c l e

i n f o

Article history: Received 27 August 2013 Accepted 24 January 2014 Available online 25 February 2014 Keywords: Energy system modelling Ensemble Kalman Filter Carbon emissions

a b s t r a c t We model energy consumption of network electricity and compute Carbon emissions (CE) based on obtained energy data. We review various models of electricity consumption and propose an adaptive seasonal model based on the Hyperbolic tangent function (HTF). We incorporate HTF to define seasonal and daily trends of electricity demand. We then build a stochastic model that combines the trends and white noise component and the resulting simulations are estimated using Ensemble Kalman Filter (EnKF), which provides ensemble simulations of groups of electricity consumers; similarly, we estimate carbon emissions from electricity generators. Three case studies of electricity generation and consumption are modelled: Brunel University photovoltaic generation data, Elexon national electricity generation data (various fuel types) and Irish smart grid data, with ensemble estimations by EnKF and computation of carbon emissions. We show the flexibility of HTF-based functions for modelling realistic cycles of energy consumption, the efficiency of EnKF in ensemble estimation of energy consumption and generation, and report the obtained estimates of the carbon emissions in the considered case studies. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Following the European Union legislations on CE (the so-called ‘‘20-20-20 target’’, which requires, in particular, 20% reduction of CE by 2020 [1]), the United Kingdom has committed to reducing CE by at least 15% across national industries. CE are reported in grams equivalent of carbon dioxide (gCO2eq) and can be measured directly, using on-site tools, or indirectly, using carbon factors derived by Life Cycle Assessment techniques [2]. The reduction of CE in energy generation at power plants and in households has gained much attention in order to meet the national need for sustainability. The UK Government has targeted several low carbon energy plans: to ensure the transition together with the Europen Union (EU) as a low carbon economy, and development of the new Carbon Capture and Storage technology (CCS) and in power plants before the year 2030 with investment worth £110 billion in generation, transmission and distribution of electrical power [3]. The large amount of investment by the UK government indicates that there is a serious concern about the carbon footprint of the energy industry throughout the generation and distribution of electrical power. A good balance between

⇑ Corresponding author. Tel.: +44 20 8943 6092; fax: +44 20 8614 0482. E-mail addresses: [email protected] (E.T. Lau), [email protected] (Q. Yang), [email protected] (A.B. Forbes), [email protected] (P. Wright), [email protected] (V.N. Livina). http://dx.doi.org/10.1016/j.enconman.2014.01.045 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.

traditional and renewable electricity is important in keeping the financial costs down and for environmental benefits. Studying dynamical changes of electricity consumption is therefore important in reducing of the total CE. It is therefore necessary to study both profiles of electricity usage based on different types of consumers and electricity generation patterns for the purpose of reducing CE and energy losses.

1.1. Modelling background overview Numerous models have been proposed for the description of electricity data. Shang [4] used the univariate time series forecasting method and regression techniques in predicting very shortterm (in minutes) electricity demands. This method avoided seasonality considerations (daily, weekly and yearly). Dordonnat et al. [5] presented a model for hourly electricity forecasting based on stochastically time-varying processes with various parametric trends (including seasons, short-term dynamics, weather regression effects and non-linear function for heating effects) using Fourier series for the daily cycle base function. However, Dordonnat et al. [5] reported that multiple unknown parameters were introduced if the variance matrices in the regression model became very large and consequently various assumptions and restrictions were required. Brossat [6] stressed the sophistication, efficiency and high specifications of Fourier series, except for the difficulties in fitting many parameters into the

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Nomenclature ANNs ANOVA AR ARIMA ARMA CE EnKF

Artificial Neural Networks Analysis of Variance Autoregressive Autoregressive Integrated Moving Average Autoregressive Moving Average Carbon emissions Ensemble Kalman Filter

model. According to McLoughlin et al. [7], the use of Fourier series in the electrical load is applicable when electricity demand is stable, but the performance is relatively poor in response to sudden changes in demands. Autoregressive Integrated Moving Average (ARIMA) models have been extensively used in forecasting due to the need for fewer assumptions to be made. Jia et al. [8] reported that ARIMA is more flexible in application and more accurate in prediction compared with the Autoregressive (AR), Moving Average (MA), and Autoregressive Moving Average (ARMA) models. ARIMA models are often associated with seasonality for better prediction of future demands. The stochastic modelling of monthly inflows into a reservoir system using an ARIMA model based on 25 years of data by Mohan and Vedula [9] showed that ARIMA models were applicable in long-term forecasting. Based on quantitative analysis using an ARIMA model, Jia et al. [8] concluded that they were effective in simulation and prediction of ecological footprints. A comparison of ARIMA forecasting and heuristic modelling by Wang et al. [10] showed that ARIMA models are more accurate than heuristic models. However, the benefits of ARIMA models are contested by the findings of Sumer et al. [11], who employed ARIMA, Seasonal Autoregressive Integrated Moving Average (SARIMA) and regression models with seasonal latent variables in forecasting electricity demand and the results indicated both ARIMA and SARIMA models were unsuccessful in forecasting these data. Mecˇiarová [12] also challenged the possible difficulties in the interpretation of results based on ARIMA models. In forecasting aggregated diffusion models, ARIMA models tended to provide inaccurate results for longterm predictions [13]. Meanwhile, a large number of Artificial Neural Networks (ANNs) have been proposed to handle seasonal variations, but with several potential drawbacks. The simulation study in Zhang and Qi [14] has demonstrated that ANNs are unable to model seasonal trends accurately unless the raw data is pre-processed (deseasonalising and detrending) along with an adequate neural forecaster. Hippert et al. [15] highlighted the two main features of ANNs: (a) forecast ANNs might be over-parameterized with a large number of components (neurons) resulting in (at least) hundreds of parameters to be estimated in a small data set; and (b) the results generated using ANNs were not always adequate and realistic. In electric power systems, ANNs can be classified as a ‘black box approach’, where the coefficients of variables do not represent temporal and magnitude components of the electrical load profile [7,16]. Other ANNs issues raised by Maier and Dandy [17] were: (i) possible lack of appropriate model inputs; (ii) availability of data and pre-processing data in the backpropagation algorithms; and (iii) inadequate process of choosing the stopping criteria and optimising the system. These factors could affect accuracies of seasonal trends. On the other hand, several recent studies, particularly in the energy field, showed the use of ANNs to provide accurate results. The statistical test completed by Schellong [18] showed that using the backpropagation technique with ‘‘momentum term’’ and ‘‘flat spot elimination’’ as a learning rule, together with measured consumption in the previous week, forecast results would be more

HTF MA NIR PV SARIMA SME

Hyperbolic tangent function Moving Average Near Infrared Spectroscopy Photovoltaic Seasonal Autoregressive Integrated Moving Average Small-medium Enterprise

accurate. A comparative study by Jebaraj et al. [19] demonstrated tha ANNs provided better results in forecasting coal consumptions. The recent approach with the combination of ANNs and regression model based Analysis of Variance (ANOVA) showed accurate forecast of annual electricity consumption [20]. Still, there is a need for a model that would be able to reproduce realistic behaviour of electricity data, as well as being computationally light, requiring a reasonably small number of parameters and providing adequate flexibility in fitting diverse types of data profiles. To this end, the HTF can be applied in fitting the model of seasonal trends. It is one of the most common sigmoid transfer functions in forecasting trajectories of dynamical systems in many fields. Earlier, HTF was applied in forecasting energy related demands in ANNs [21–24]. The HTF in multi-layer perceptron did not work well in the calibration model based on gasoline Near Infrared Spectroscopy (NIR) performed by Balabin et al. [25]. Schellong [18] also recommended the use of HTF along with logistics and limited sine function in training neurons in ANNs for adequate forecasting of the heat and power demand in Germany. In order to build an electricity data model, a valid seasonal trend of the power consumption is needed for further state-estimations of CE. In this paper, HTF is chosen as the base in stochastic modelling of seasonal trends in power consumptions due to its need for fewer parameters and high flexibility in fitting the distribution curves. Since we are interested in building a basic stochastic model for various consumption profiles, HTF is implemented without the application of ANNs. Methods in modelling the seasonal trends using HTF will be explained in detail in the following sections. 1.2. Electric system structure In Fig. 1, we show a schematic representation of the electricity network that includes generation, transmission, distribution and consumption of electricity. Generation and consumption of electricity require different approaches in modelling and different carbon factors for estimation of CE. In the electrical industry, it is crucial to model electricity consumption in order to be able to organise energy generation, because electricity has very low storage capacity due to the current technologies. Once the electricity consumption is known, CE can be calculated with the up-to-date carbon footprints provided, for the UK energy industry, in the two post notes of the Parliamentary of Science and Technology [26,27] and Carbon Trust [28]. Calculation of the national carbon footprints in the UK is performed by the company Ricardo-AEA [29], with quality assurance performed by DEFRA and DECC and published by DEFRA in annual reports. The latest data are available in the form of Microsoft Excel spreadsheets on the website [30], where statistics are currently stored for the years 2002–2013 inclusive. The carbon factors for the year 2013 are valid until 31/05/2014, after which date they will be revised. The electricity network is changeable, with consumers and generators connecting and disconnecting from the grid depending on

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Fig. 1. Schematic of electric network. Note that electricity consumption and generation use different carbon factors for estimation of CE.

conditions and demand. This means that the modelling approach requires adequate flexibility in terms of the network nodes. This is also important for taking into account the rising number of renewable generators that modify the structure of the network and the energy flow. This paper proposes a novel approach in modelling electricity consumption and estimation of CE using HTF and EnKF. Section 2 provides details of the stochastic model and explains the use of EnKF in estimation of CE. Section 3 discusses the simulations of the power consumptions of four different types of consumers: working family, pensioner, standard office working hours and one-shift industrial factory (operating from morning to late afternoon). Section 4 presents case studies of energy generation and consumption using real data sets provided by Brunel University, the Elexon national database and the Irish Smart Grid pilot project. The energy data plots of the case studies are further compared with the model results. Section 5 provides a discussion and Section 6 concludes and comments on future work. 2. Methodology 2.1. Stochastic modelling of electricity consumption The generated electrical data (alternating current) oscillates continuously as a sine wave with frequency f ¼ 50 Hz, whereas the consumed electricity data (energy) are recorded at longer time scale and sampled discretely, as the amount of power per time unit (W h). According to the specification of smart meters, the metering data are recorded every 30 min — it has still been decided at which time interval these data will be stored by the energy providers in industrial databases. As electricity consumption changes with time and has various influencing factors (in particular weather-related change of consumers’ behaviour), the generated time series of the electricity data should have diurnal, DðtÞ, and annual, AðaÞ, periodicities. The state representation of the consumed electricity signal can be generally expressed in terms of hypothetical periodic functions as follows:

    t t þD þ e; xðtÞ ¼ A T1 T2

ð1Þ

where x is the true state of electricity consumption at time t; AðtÞ is the annual cycle function; DðtÞ is the diurnal cycle function; T 1 is the annual periodicity, 365 days; T 2 is the diurnal periodicity, 24 h; t is the time variable sampled at hourly rate; e is the signal noise. In the electrical grid, the signal noise may be a combination of the following sources: (i) thermal noise; (ii) harmonic generation noise; (iii) transient noise; and (iv) frequency deviation. We assume that the stochastic component e includes all of these noises combined. Two types of periodicities, AðtÞ and DðtÞ, are adopted to describe trends of the energy consumption. Trend AðtÞ is modelled deterministically based on four seasons, when the level of electricity consumption generally changes because of heating, air conditioning, holiday periods, and other factors [5,31]. Using an asymmetric HTF-based function, the seasonal trend AðtÞ can be expressed as:

AðtÞ ¼ C 1 þ

 K  X t  ak  T 1 ðk  1Þ ; tanh L k¼1

ð2Þ

where C 1 is the y-axis adjustment constant; T 1 ¼ 365 days; ak is time parameter (can be in seconds, minutes or hours); L represents the width and the slope of the HTF; k is the time index of the number of data subsets to be modelled by a single HTF function — those are later ‘‘stitched’’ together by using appropriate parameters to obtain a smooth curve, see Fig. 2. DðtÞ similarly models the trend of the electricity consumptions during the period of every 24 h. DðtÞ profiles are constructed based on four categories of electricity consumers: (i) working family; (ii) pensioner; (iii) daytime office; and (iv) one-day- shift industrial. The analytical expression of DðtÞ is similar to AðtÞ in using asymmetric HTFs:

DðtÞ ¼ C 1 þ

K  X k¼1

C 2 ðkÞ  tanh

 t  a  T 2 ðk  1Þ ; L

ð3Þ

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where H is the measurement model, and the Kalman gain is as follows:

Energy consumed (kWh)

3

K¼

2.5 1st

2nd

3rd

4th

5th

P H HP HT þ R 

ð7Þ

;

R is the measurement covariance error. Finally, the posteriori covariance update Pþ is computed in the following way:

2

Pþ ¼

1.5

Apost ATpost ; N1

ð8Þ

where 1

Dec12 Jan

Feb

Mar

Apr

May

Jun

July

Aug

Sep

Apost ¼ X þ  X þ ¼ X þ ðI  1N Þ;

Oct Nov13

Time (month) Fig. 2. Annual cycle plot of electricity consumption based on different seasons: 1st = winter; 2nd = mid to end of winter season; 3rd = spring; 4th = summer; 5th = autumn.

where T 2 ¼ 24 hours; C 1 is the y-axis adjustment; a is the particular time interval (can be in seconds, minutes and hours); L is the width of the HTF; k is the index of the data subset, C 2 is the adjustment constant of a particular HTF term (if necessary; otherwise C 2 ¼ 1). Together Eqs. (2) and (3) form regular trends in the dynamic model of the electricity network, as defined in Eq. (1). 2.2. EnKF for modelling electrical data We use an EnKF to update the state estimations of the dynamic model, for the purposes of short-range forecasting of energy data. The implementation of EnKF is based on the Monte-Carlo approach using ensemble realizations of a model and state updates that are acquired through the combinations of model predictions and new measurements [32]. The updated state estimates (posterior) are represented by ensembles of a model propagation with Kalman update. EnKF is widely used in high-dimensional systems, thereby extending the limitation of the standard Kalman Filter, by replacing the evolving covariance matrix of the probability density function with its ensemble estimate. Eq. (1) simulates the true state value xðtÞ of the dynamical model with the assumption of random process Gaussian noise Q with zero mean and covariance W. The measured state estimates yðtÞ are obtained with Gaussian noise R with zero mean and covariance V, i.e. values R and Q are assumed to be drawn from Gaussian distributions with R  Nð0; VÞ and Q  Nð0; WÞ. The formulation of the EnKF can be found in Evensen [33]; Jensen [34]; Chen et al. [35]; Nævdal et al. [32]. Here we follow Evensen [33] and Jensen [34], with only key equations outlined. The EnKF comprises two main steps, the prediction and filter step. Values xðtÞ are generated based on Eq. (1) and measured concurrently. The output measurements are denoted as yðtÞ. We denote the ensemble of N members as matrix X, and the a priori error covariance ensemble P is computed as follows:

P ¼

Aprior ATprior ; N1

ð4Þ

where

Aprior ¼ X  X ¼ XðI  1N Þ;

ð5Þ

X is the matrix of ensemble true state, 1N is the matrix where each element is equal to 1=N. In the next, filtering step, the Kalman gain K is computed and the new state ensemble estimates X þ is updated in Eq. (6):

X þ ¼ X þ KðY  HXÞ;

ð6Þ

ð9Þ

X þ are posteriori state ensemble estimates. During the simulation process, X þ based on EnKF is compared with X and Y and the X þ should converge towards X. A summary of the EnKF algorithm is presented in Table 1. 2.3. Carbon factors and emissions of energy consumption and generation The carbon factors are reported in grams (or kilograms) of carbon dioxide CO2 equivalent per unit of energy. Since generated energy is given in kWh and carbon factors in gCO2eq/kWh, the CE can be estimated as CO2 equivalents for a given time period:

CO2 emission ¼

S X N X C n Pn ðsÞDtðsÞ:

ð10Þ

s¼1 n¼1

where C n is the carbon factors; Pn ðsÞ is the power generated (W) at time step s = 1, . . . , S; DtðsÞ is time step s = 1, . . . , S; N is the number of samples. The average carbon factor for the grid electricity consumption is 524.6 gCO2eq/kWh as reported [28]. The carbon factors of the plants that generate energy are adopted as stated in [26,27]; these are listed in Table 2. We apply EnKF accordingly in this case study. 3. Artificial data of electricity consumption This section discusses the calculation of CE based on AðtÞ and DðtÞ cycles of electricity consumption in a hypothetical network. Profiles based on four categories of consumers (working family, pensioner, daytime office and one-shift day industrial) are calculated. A large number of samples are required to constitute an ensemble in order to represent the system state. We consider an ensemble of 100 members (65 working families, 20 pensioners, 10 daytime offices, and 5 one-shift day industrial factories). The analytical expression of AðtÞ and DðtÞ based on Eqs. (1)–(3) are used to simulate the electricity consumptions, which are then estimated by EnKF.

Table 1 EnKF algorithm. Predict step Q; R X ¼AþDþW yk ¼ Hk þ V k P ¼

Compute Compute Compute Compute

Aprior ATprior N1

input noises true state (1) measurement state a priori covariance ensemble

Filter step 1

K k ¼ P  Hk ðHk P  HTk þ RÞ X þ ¼ X þ KðY  HXÞ

Compute Kalman gain Compute a posteriori state ensemble

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Types of energy

Carbon factors

Fuel code

Oil Coal Gas Nuclear Wind Hydro

700 990 488 26 96 13

OIL COAL CCGT NUCLEAR WIND NPSHYD

CE (gCO2eq)

Table 2 Carbon factors (gCO2eq/kWh) for power plants.

12000 11000 10000 9000 8000 7000 6000 5000 4000 3000 2000

working family pensioner office industrial

0

1

2

3

4

5

6

7

Time (day)

3.1. Annual cycle

Fig. 4. Weekly carbon emissions of four types of consumers.

3.2. Diurnal cycle

7

x 10

7

working family pensioner office industrial

6

CE (gCO2eq)

Fig. 2 shows a representative plot of the seasonal trend AðtÞ. Based on Fig. 2, the five stages that reflect the following changes of consumption: (1) winter heating; (2) decrease of heating before the end of winter period; (3) gradual decrease of heating as spring season approaches; (4) small rise in summer due to air conditioning and then a gap (minimum amount of consumed energy from early to mid September) due to the summer holiday breaks; and (5) increase amount of energy use in the following autumn season.

5 4 3 2 1

Trend DðtÞ for (1) is modelled according to typical electricity consumption patterns of different consumers with respect to day time. DðtÞ plots for the four types of consumers are shown in Fig. 3. We assume that a working family electricity consumption drops during work hours, whereas a pensioner would use heating longer hours; we model daytime office and one-shift day industrial consumption assuming shifts and heating demands but not 24/7 constant regime. When an enterprise runs continuous shifts (operating day and night), their daily energy consumption is more or less constant, and there is no need to model its daily profile (there is still need to model seasonal variability). This is why we do not consider this case for diurnal profile modelling. 3.3. Carbon emissions A weekly plot of CE based on the four types of consumers can be found in Fig. 4. Fig. 5 illustrates the cumulative function of CE corresponding to each type of electricity consumer. These simple plots are useful in dynamical estimation of CE at any moment of the simulations. The one-shift day industrial factory has the highest CE, followed by daytime office, pensioner and lastly the working family. Due to the randomised nature of the simulations, the final values of cumulative summation are uncertain.

0

0

2

4

6

8

10

12

Time (month) Fig. 5. Cumulative carbon emissions of four types of electricity consumers.

the true system state X and the output measurements Y. The synthesized plots of X; Y, and X þ are shown in Fig. 6. Fig. 6 shows that X þ converges towards X. 4. Case studies 4.1. Photovoltaic energy generation at Brunel University This case study implements a dynamic model for calculation of CE based on the Photovoltaic (PV) electrical data generation obtained at Brunel University (dataset period 01/01/2012–31/12/ 2012). The PV data were recorded at 5-min intervals. In this case the base function AðtÞ from the PV data replaces the seasonal trend of the first dynamical model. The DðtÞ function is not implemented. An ensemble of five samples is considered as an example. Overall, the PV data represents the real data that is to be estimated by EnKF.

True value Measured EnKF

3.4. EnKF for modelling electricity data

Energy consumed (kWh)

25 20 15 10

Energy consumed (kWh)

7

The EnKF algorithm described in (4)–(9) is used to obtain the new state estimates X þ . Values X þ are also used in comparing

6

5

5 0

working family

0

5

pensioner

10

office

15

industrial

20

0 25

20

40

60

80

100

120

Time (hrs)

Time (hrs) Fig. 3. Diurnal energy consumptions.

Fig. 6. Five-day forecast of energy consumption of the working family. Note two peaks of energy demand each day.

E.T. Lau et al. / Energy Conversion and Management 80 (2014) 573–581

The PV data in the year 2012 is shown in the top panel of Fig. 7, sample No. 3 (out of five obtained samples that have similar patterns). It is assumed that a high level of measurement noise was encountered — the uncertainty was reduced by using EnKF and the trend of PV production was made clear. It can be seen that PV generated a large amount of energy during summer, where the maximum amount of solar radiation is absorbed, as expected. It is necessary to stress, however, that this findings occured during the particular case study. In general, the efficiency of PVs may be different, depending on climate conditions. A weekly plot of PV generation is shown in the bottom panel of Fig. 7. A total of seven diurnal trends are visible, and they are very close to those given by the DðtÞ implemented with an HTF function. HTF function may be applied in this case to generate the PV data, providing good energy forecasts. A carbon factor of 116 gCO2eq/kWh representing the carbon factor for solar energy is used in calculating CE [26,27]. The total CE for the PV generation is approximately 1.36  107 gCO2eq in the year 2012, as displayed in Fig. 8.

4.2. UK national aggregated data of electricity generation The UK national data of electricity generation is provided by the National Grid subsidiary Elexon, which aggregates data according to fuel types of the power stations. This allows one to estimate the nationwide CE generated by clusters of power stations using the same fuel to produce electricity: coal, gas, nuclear sources, renewables, etc. A total of four years data (from 01/01/ 2008–30/09/2012) are considered in estimating CE, with data recorded every 5 min. Table 3 shows the CE for each type of energy source.

Energy generated (kWh)

10

8

6

4

x 10

12 10 8 6 4 2 0

0

50

100

150

200

250

300

350

400

Time (days) Fig. 8. Accumulated plot of CE for the year 2012, sample No 3.

Table 3 CE calculated for the Elexon datasets. Types of energy

CE, gCO2eq

Sample size

COAL

6:002  1012

482,562

CCGT

3:547  1012

482,562

NUCLEAR

9:053  1010

482,562

WIND

3:443  1010

482,560

OIL

1:091  1010

HYDRO

2:271  109

24,921 482,383

The results of quarterly data corresponding to the particular energy source are given in Fig. 9. Due to the low availability of energy data obtained from the oil and open cycle gas turbine plants, the HTF is difficult to apply to those energy plants, although most of the energy plots obtained can be fitted with HTF. Periodic cycle trends in the coal, combined cycle gas turbine, nuclear and hydro plants demonstrate oscillations that can be best fitted with HTF. In contrast, the increasing trend of wind energy generation suggested that an exponential function better fits the distribution of wind plant than HTF. Fig. 9 represents the data in semi-logarithmic plots for convenient comparison of different fuel types of power stations: their production differs by orders of magnitude. One can see that the main part of electric energy in the UK is produced by gas and coal plants, which also generate most of the CE. The low CE of nuclear energy plants are calculated without taking into account the background emissions (like construction of concrete installations) but as those directly emitted from this type of fuel.

2

0

4.3. Irish SmartGrid pilot project 0

100

200

300

Time (days)

Energy generated (kWh)

6

14

CE (gCO2eq)

578

True Measured EnKF 1

0.5

0

1

2

3

4

Time (days) Fig. 7. Top panel: PV generation at Brunel University year 2012, installation unit No 3. Bottom panel: weekly PV generation at Brunel University year 2012, installation unit No 3.

The third case study represents the calculation of CE based on Irish smart grid data. The data were recorded every 30 min (in kWh). 541 days of data in total are included in estimating CE (dataset period 01/01/2009–25/06/2010). An ensemble of 72 samples (53 residents and 19 Small-medium Enterprise (SME)) are selected as an example. As earlier, the carbon factor for the grid electricity consumption is 524.6 gCO2eq/kWh [28]. The data of a resident and a SME are shown in Fig. 10. The electricity consumptions show periodical oscillation trends, and HTF can be applied to model these data. The electricity consumption trends are very close to the AðtÞ trend in the dynamic model. This means that the HTF function is a useful sigmoid function in generating smart grid data and predicting the usage of grid electricity in the short-term range. We also show cumulative CE for participating households and SMEs in the right panels of Fig. 10. Based on this figure, one can conclude that the amount of CE by SMEs are higher than for regular residents, with similar gradual dynamics.

579

1×10

1×10

4

CCGT

3

2008

CE (gCO2eq)

Power generated (kWh)

E.T. Lau et al. / Energy Conversion and Management 80 (2014) 573–581

2009

2010

2011

1×10

1×10

6

2008

2012

CCGT

4

2009

1×10

4

COAL

3

2008

CE (gCO2eq)

Power generated (kWh)

1×10

2009

2010

2010

2011

1×10

1×10

2012

2009

2010

HYDRO

2009

2010

2011

1×10

1×10

2009

2010

4

NUCLEAR

3

2008

2009

2010

2011

1×10

1×10

2009

4

OIL 3

2008

2009

2010

2011

1×10

1×10

4

2008

2012

2009

WIND

3

2008

2009

2010

2010

2011

2012

2011

2012

Time (year)

CE (gCO2eq)

Power generated (kWh)

1×10

4

2012

OIL

6

Time (year)

1×10

2010

Time (year)

CE (gCO2eq)

Power generated (kWh)

1×10

2011

4

2008

2012

NUCLEAR

6

Time (year)

1×10

2012

Time (year)

CE (gCO2eq)

Power generated (kWh)

1×10

2011

4

2008

2012

HYDRO

6

Time (year)

1×10

2012

Time (year)

3

2008

2011

COAL

4

2008

CE (gCO2eq)

Power generated (kWh)

1×10

4

2012

6

Time (year)

1×10

2011

Time (year)

Time (year)

2011

2012

1×10

1×10

WIND

6

4

2008

2009

Time (year)

2010

Time (year)

Fig. 9. Semi-logarithmic plot of CE for energy plant.

5. Discussion In this paper, we have proposed a novel approach in stochastic modelling of electricity consumption of various types of customers. Furthermore, we estimated carbon emissions from electricity generation in the UK energy market. Adaptive HTFs have demonstrated reliable results in reproducing dynamics of electricity data, and also provided some advantages, such as great flexibility and simplicity of modelling with a few parameters. A comparative study of simulated and real data is performed and it indicates that the HTF is a useful function in providing estimates, fitting and forecasting of electrical data. EnKF was successfully applied for estimations of electricity consumption and generation in short-range forecasts. Ensembles of multiple samples were simulated, and EnKF was further applied in three case studies in computing CE in electricity networks. Comparison of filtered and recorded data demonstrates good

agreement of time series. We have modelled electricity consumption with various customers profiles and calculated CE for the electricity data from Brunel University, Elexon data archive and Irish smart grid pilot project. The modelling results show that PV data exhibited a very similar seasonal trend with the artificial seasonal dynamic model, although the HTF does not work well in data without a pronounced seasonal trend, and adding seasonal/diurnal trends is essential in such cases. EnKF algorithms have proved successful in the estimation of energy consumptions and CE. The ability to model nonlinear behaviour with values converging towards observed data under the influences of various noises demonstrate the strength of EnKFs in the estimation of the true state of the energy system. CE have been successfully calculated for the artificial data and also for observed records in the three case studies. The obtained

E.T. Lau et al. / Energy Conversion and Management 80 (2014) 573–581

7 6

Resident

CE (gCO2eq)

Electric consumed (kWh)

580

5 4 3 2

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6

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Fig. 10. Electricity consumed by a resident and a SME.

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