Volatility of electricity price in Denmark and Sweden

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Energy Procedia 158 Energy Procedia 00(2019) (2017)4331–4337 000–000 www.elsevier.com/locate/procedia

10th th

International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10 International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China

Volatility of electricity price in Denmark and Sweden Volatility electricity price in Denmark and The 15thof International Symposium on District Heating and Sweden Cooling

Shuaili Donga,b , Hailong Li*bb, Fredrik Wallinbb, Ander Avelinbb, a,b Shuaili Dong , Hailong Li* Fredrikthe Wallin , Ander Avelin , Assessing the feasibility of ,using heat demand-outdoor Qi Zhang†aa , Zhixin Yucc temperature function for long-term district heat demand forecast , Zhixin Yu Qi aZhang†

a China University of Petroleum, China a China University of Petroleum, China Future Energy, Mälardalens högskola, a,b,c a a b Sweden c c c Mälardalens högskola, Sweden of Stavanger Department ofbFuture EnergyEnergy, and Petroleum Engineering, University c Department of Energy and Petroleum Engineering, University of Stavanger a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract

I. Andrić

b

*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre

Under the pressure of global environmental climate change, all countries in the world are developing renewable energy such as Under the pressure globaland environmental all countries the world renewable energy such as hydropower, wind of energy, solar energyclimate As a change, result, the electricityinprice variesare in developing different patterns depending on the hydropower, wind energy, and solar energy As a result, the electricity price varies in different patterns depending on the penetration of renewable energy. In this paper, a non-parametric model is employed to analyze the historical data of electricity Abstract penetration of renewable energy. a non-parametric model is of employed to analyze the price historical of Nord electricity spot price from Danish price areasInofthis the paper, Nord Pool (with high percentage wind power), Swedish areasdata of the Pool spot price from Danish of price areas of theand Nord Pool (with (with high percentage of wind power), Swedish price areas of the Nord Pool (with high percentage hydropower) PJM market little renewable energy penetrated). The objective is to deeply District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the (with high percentage of hydropower) and PJM market (with little renewable energy penetrated). The objective is to deeply understand the influence of renewable energies on electricity price volatility. It is found that electricity prices are more stable in greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat understand the influence of renewable energies onand electricity price volatility. It is found prices are could more stable in Swedish price as hydropower a more stable energy source. The electricity price in electricity PJM market is also comparatively sales. Due toareas the changed climateisconditions building renovation policies, heatthat demand in the future decrease, Swedishonly pricemore areasvolatile as hydropower is a more stable energy source. The electricity priceresources. in PJM market is alsoprice comparatively stable, than Swedish market, as fossil fuels are dominant energy For Danish areas, the prolonging the investment return period. stable, only moreofvolatile than Swedish market, as fossil fuels areheat energy resources. Danish areas, the volatility ofscope electricity prices isisclearly affected by wind power, which isdominant a demand highly intermittent energyFor resource. The main this paper to assess the feasibility of using the – outdoor temperature functionprice for heat demand volatility of electricity prices is clearly affected by wind power, which is a highly intermittent energy resource. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Copyright ©that 2018 Elsevier Ltd. All rights reserved. buildings vary in both construction period (low, medium, high) and three district © 2019 The Authors. Published by Elsevier Ltd. and typology. Three weather scenarios th International Conference on Applied Copyright © 2018 Elsevier Ltd. Allresponsibility rights reserved. Selection and peer-review under of the scientific committee of thethe10error, renovation scenarios were developed (shallow, intermediate, deep). To estimate obtained heat demand values were This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) th International Conference on Applied Selection and peer-review responsibility of the scientific committee of the 10 Energy (ICAE2018). compared with results fromunder a dynamic heat demand model, and validated byConference the authors. Peer-review under responsibility of the scientific committee ofpreviously ICAE2018developed – The 10th International on Applied Energy. Energy (ICAE2018). The results showed that when only weather change is considered, the margin of error could be acceptable for some applications Keywords: of elecctricity price,lower electricity renewable considered). energy, electricity market after introducing renovation (the errorvolatility in annual demand was than spot 20%price, for penetration all weatherofscenarios However, Keywords: volatility of elecctricity price, electricity spot price, penetration of renewable energy, electricity market scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. * Corresponding author. Hailong Li, Tel.: +4621103159. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Corresponding Hailong Li, Tel.: +4621103159. E-mail address:author. [email protected] Cooling. address:author. [email protected] * E-mail Corresponding Qi Zhang, Tel.: +8689739186 * Corresponding Qi Zhang, Tel.: +8689739186 E-mail address:author. [email protected] Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]

1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility the scientific Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.788

Shuaili Dong et al. / Energy Procedia 158 (2019) 4331–4337 Author name / Energy Procedia 00 (2018) 000–000

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1. Introduction Facing climate change and much more rigorous carbon emission requirements, all countries in the world focus on the development of renewable energy, such as hydropower, wind power, and solar energy. The increasing penetration of intermittent renewable energy can clearly influence the volatility of electricity price, which is a measure of the dispersion or fluctuation in electricity prices observed over a time period. The volatility of electricity price is dependent on a large number of factors such as fuel prices, availability in generating units, hydro or wind generation, and network congestions [1]. Knowledge of electricity price volatility is of vital importance to each market player as it can influence all the decisions made in electricity market [1]. To understand how different factors influence the volatility of electricity is complex [2]. There are plenty of literature about measuring or forecasting electricity price volatility. The most common method is based on tradition time series parametric models that are usually used in financial market to find relationships between certain factors and the price volatility. Another common method to measure the electricity volatility is the non-parametric jumpdiffusion (or jump test) model developed by Knittel et al. [3], Chan et al [4], and Ullrich [5]. Usually, electricity prices show obvious daily, weekly and seasonal patterns. Moreover, electricity prices are usually higher either in winter or in summer when the system peaks are mainly related to heating or cooling demands, respectively. There have been some studies about Australian market, American PJM market and Canadian market. However, the Nord Pool has its own unique characters. For example, the Nordic countries have longer winters and relatively colder summers, which leads to different demand side patterns. Another important feature is the high adoption of renewable energy in electricity generation process, which could have a big influence on the variation of electricity price. In order to understand the characteristics of electricity price volatility of Nordic countries and understand the impacts of energy mix, this work studied the electricity price in the Swedish (with high percent hydro-power) and the Danish (with high percent wind-power) price areas of the Nord Pool and PJM market (with little renewable energy, for contrast). 2. Methodology High volatility of the electricity market price does not mean that the market is unstable. A regular, but high price volatility can also mean it is a stability of a certain market, which then also could be managed by various stakeholders of that particular market. To avoid risks or identify business opportunities, stakeholders usually pay more attention to the extremes, upwards and downwards of electricity price, i.e. jumps, which may have great impact on their decisions. To estimate volatility, the non-parametric model is used, which decomposes the total variation of price into jump and non-jump components: the realized volatility (RV), which is defined as the sum of squared high-frequency returns, and the realized bi-power variation (BV), which is defined as the sum of the product of adjacent absolute intraday returns. RV estimates the total variation, including both jump and non-jump components; while BV provides a consistent estimate of the continuous non-jump volatility, even in the presence of discontinuous jumps. The difference between the realized volatility and the bi-power variation provides a consistent estimator of the discontinuous jump component of the variation (JV). The estimated continuous volatility (CV) of total variation is defined as the difference between RV and estimated JV. 2.1. Realized volatility The realized volatility ( RVt ) for each day

t is calculated as the sum of the squared intraday price differences:

M

RVt = ∑ rt 2,j j =1

where rt , j is defined as the prices change between two adjacent prices. if pt , j is denoted as the spot electricity price in day t , time j , the price difference is calculated as:

(1)



Shuaili Dong et al. / Energy Procedia 158 (2019) 4331–4337 Author name / Energy Procedia 00 (2018) 000–000

1,..., M , t = 1,..., T rt , j = pt , j − pt , j −1 , j =

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(2)

The strong daily, weekly and seasonal patterns of electricity price variation should also be considered into the calculation of price differences. Following Knittel et al.’s work, the patterns are investigated parametrically using an ARMAX (1, 0) model. The procedure is as follow: The price process is governed by an Ohrnstein-Uhlenbeck model:

dpt , j = k (θ − pt , j )dt + σ db(t )

(3)

where b(t ) is a standard Wiener process; θ is drift and k is the rate of spot price reverting to mean. Prices changes are not mean-equal because of electricity prices patterns. Assume that the spot price reverts to the mean µ at a rate of k>0:

= µ (t , j ) k (θ (t , j ) − p(t , j ))

(4)

where p (t , j ) = pt , j , θ (t , j ) = α1 I (t ∈ Peak ) + α 2 I (t ∈ Off − peak ) + α 3 I (t ∈ Weekend ) + α 4 I (t ∈ Jan.) + α 5 I (t ∈ Feb.) + α 6 I (t ∈ Mar.) + α 7 I (t ∈ Apr.) +α 8 I (t ∈ May ) + α 9 I (t ∈ Jun.) + α10 I (t ∈ Jul.) + α11 I (t ∈ Aug .) + α12 I (t ∈ Spet.) + α13 I (t ∈ Oct.) + α14 I (t ∈ Nov.)

(5)

where I () denotes the indicator function. For example,

1, t ∈ [6 : 00a.m.,10 : 00 p.m.] I (t ∈ Peak ) =  otherwise 0,

(6)

Extending Eq. (4) with Eq. (5), and then integrating Eq. (4) yields:

pt , j = α t , j + β1 pt , j −1 + ε t , j

(7)

where = α t,j θ (t , j )(1 − e − k ), β1 = e − k , and ε t , j is the error term. Eq. (7) is an ARMAX (1, 0) model with fourteen exogenous variables. Estimation on the parameters of this ARMAX (1, 0) model can deduce α in Eq. (5) and k in Eq. (4) and then µt , j can be calculated. In Eq (5), the mean price of weekdays in December is set as a benchmark. Parameter α1 gives the average price in the weekday’s peak time of December in each specific year. And α 2 gives the mean price of weekday’s off-peak time of December. The negative values of α mean that the mean electricity price in certain month, certain day and certain time is lower than benchmark. * Then modified price difference rt= rt , j − µt , j is used in calculation of RVt , BVt and TQt in Eq. (1), Eq. (8) and ,j Eq. (10) respectively 2.2. Bi-power variation Realized bi-power variation ( BVt ) of day

BVt = µ1−2 (

M M ) ∑ | rt*, j || rt*, j − (i +1) | M − (1 + i ) j =+ 1 ( i +1)

t is calculated as (8)

Shuaili Dong et al. /Procedia Energy Procedia 158 (2019) 4331–4337 Author name / Energy 00 (2018) 000–000

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2

where µ1 ≡

π

and

i determine the lag length in the multiplication of returns. According to Ullrich (2012)’s

work, the number of jumps will increase with the increase of i , most jumps can be detected when i = 6 . As only extreme jumps which may cause damage to electricity system are focused on, i = 1 is applied in our analysis. 2.3. Jump detection test A test statistic ( Z t ) is employed to identify the presence of a jump on day t :

( RVt − BVt ) / RVt

Zt = M

( µ1−4 + 2 µ1−2 − 5) max(1,

where TQt = ( 4

7 6

TQt ) BVt 2

4 4 4 M M2 )( µ 4−3 ) ∑ | rt*, j | 3 | rt*, j − (i +1) | 3 | rt*, j − 2(i +1) | 3 M − 2(1 + i ) 3 j = 1+ 2(1+ i )

(9)

(10)

1 2

µ 4 ≡ 2 3 Γ( )Γ( ) −1 ≈ 0.8308609 , i also determines the lag length and the same as calculation of BV, 3

where i = 1 . The Z t test statistic is calculated for each day t , and a jump is identified if Z t exceeds the critical value Φ1−α of the standard normal distribution. For a chosen level of significance α, usually α=0.01, the day t jump component of volatility is identified by

JVt = I{Zt >Φ1−α } ( RVt − BVt )

(11)

RVt measures the total volatility of sample data, while JVt describes the jump component of realized volatility, the differences between RVt and JVt estimate the continuous component of day t of the total volatility as: CV = RVt − JVt t

(12)

2.4. Intensity of the jumps After a jump on day t is identified through the above procedure the jump intensity ( λJ ) is calculated as the number of days with significant jumps divided by the total sample period. For example, if there are 5 days with jumps in January 2001 in a certain market, then,

= λJ 5 / 31 ≈ 0.1613 3. Data and results 3.1. Sample data Hourly wholesale electricity spot prices data from three price areas in the Nordic power market and the PJM market are analysed in this study. Denmark is divided into two price areas-- DK1 for western Demark and DK2 for eastern Demark. The data covers the period January 1st 2013 through December 31st 2017. Denmark's wind power generation has grown rapidly. Around year 2000, wind farms established by large enterprises started large-scale production [6]. Nowadays, wind-power provides more than 40% of Danish electricity.



Shuaili Dong et al. / Energy Procedia 158 (2019) 4331–4337 Author name / Energy Procedia 00 (2018) 000–000

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For Sweden, hydropower has been the cornerstone of power supply. The Swedish electricity is provided almost 40% by hydro power, another 40% by nuclear power, about 10% by wind and another 10% by others like CHP cogeneration. The PJM market is dominated by fossil fuel based electricity generation together with nuclear power plants, with little renewable energy penetration. 3.2. Results The realized volatility (RV) is calculated in daily frequency and partitioned into continuous variation components (CV) and jump components (JV). Table 1 shows the descriptive statistics of the RV, CV and JV of each market for each year. “Mean” is the mean value, while STDE refers to the standard deviation, and the coefficient of variation (COV, defined as the quotient of the standard deviation divided by the mean) indicates the dispersion on unit mean. JV/RV ratio is calculated by the sum of JV divided by the sum of RV, which shows the influence of jumps on the total variation. The volatility estimators (RV, CV and JV) are used in standard deviation form. Table 1. The distribution of the realized volatility, continuous volatility and jumps of each market 2013

2014

2015

2016

2017

RV Mean

STDE

COV

Mean

STDE

COV

Mean

STDE

COV

DK1

33.66

163.9

4.87

18.85

12.12

0.64

20.13

13.57

0.67

DK2

24.44

16.01

0.65

18.48

12.41

0.67

21.47

16.23

0.76

SE

14.39

10.93

0.76

10.03

7.44

0.74

9.67

8.42

0.87

PJM

22.78

20.83

0.91

44.67

74.67

1.67

29.62

26.07

0.88

Mean

STDE

COV

Mean

STDE

COV

14.13

10.19

0.72

19.74

12.9

0.65

19.55

25.34

1.3

21.02

13.4

0.64

15.43

22.46

1.46

12.52

10.27

0.82

20.41

9.69

0.47

18.56

12.49

0.67

CV Mean

STDE

COV

Mean

STDE

COV

Mean

STDE

COV

Mean

STDE

COV

Mean

STDE

COV

DK1

30.58

115.99

3.79

18.04

11.89

0.66

18.7

12.79

0.68

13.46

9.76

0.73

18.31

11.95

0.65

DK2

23.63

15.43

0.65

17.71

12

0.68

19.96

15.58

0.78

18.96

22.77

1.2

19.89

12.29

0.62

SE

14.16

10.68

0.75

9.55

7.07

0.74

9.15

8.08

0.88

14.98

19.38

1.29

12.07

9.31

0.77

PJM

22.15

20.81

0.94

41.5

65.98

1.59

28.47

24.76

0.87

19.53

9.67

0.5

17.73

12.2

0.69

Mean

STDE

COV

Mean

STDE

COV

Mean

STDE

COV

Mean

STDE

COV

Mean

STDE

COV

DK1

7.37

116.41

15.8

1.91

5.66

2.97

3.27

8.08

2.47

1.46

5

3.43

3.06

8.31

2.72

DK2

1.77

7.35

4.15

1.75

5.89

3.36

3.45

8.47

2.45

1.46

12.01

8.22

2.33

8.32

3.58

SE

0.42

3.46

8.24

1.09

3.71

3.4

1.2

3.75

3.13

1.13

11.9

10.53

1.08

5.37

4.97

PJM

1.46

5.16

3.53

7.39

37.97

5.14

2.68

11.24

4.19

2.01

5.63

2.79

1.88

5.8

3.08

JV

JV/RV DK1

0.0431

0.0837

0.1206

0.0754

0.1154

DK2

0.0579

0.0674

0.1153

0.0407

0.0817

SE

0.0189

0.0847

0.0904

0.0279

0.0569

PJM

0.062

0.0828

0.079

0.0931

0.0806

Taking Danish east area (DK2) in year 2013 and year 2015 as examples, CV measures the continuous volatility of electricity price. The mean of CV in year 2013 (23.63) is larger than that in year 2015 (19.96), which means the average of continuous volatility in year 2013 is bigger than in year 2015. However, the standard deviation of CV in year 2013 (15.43) is less than that in year 2015 (15.58), which means that the change of volatility in year 2013 is less than in year 2015. Hence COV can be used to determine the continuous volatility that a higher COV means a larger volatility. As the COV of CV in year 2013 (0.65) is small than that in year 2015 (0.78), the continuous volatility is larger in year 2015. The COV of RV shows the same order of magnitude compared with CV’s while the

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Shuaili Dong et al. / Energy Procedia 158 (2019) 4331–4337 Author name / Energy Procedia 00 (2018) 000–000

COV of JV in year 2013 (4.15) is much larger than that in year 2015 (2.45). JV/RV ratio in year 2013 (0.0579) is much smaller than that in year 2015 (0.1153), which means the jumps contribute less to the total variation in year 2013 than in year 2015, so the high COV of JV in year 2013 does not lead to the high COV of RV in the same year. The COVs in DK2 and Swedish area always show the same trend as these two markets are closely connected through power transmission lines. DK1 has the lowest COVs over the four years while it is still dominated by wind power. Usually, the COVs of RV and CV have the same trend. To a large extent, the different COV of CV for different years can be explained by the varying weather conditions. The COV of CV differences across pricing areas can be explained by their different sources of power. Area differences mainly relate to the limitations in transmission capacities, then the generation mix of individual pricing area becomes important. The Swedish area has large percent low-cost and stable hydro power, as a result, the volatility is relatively low. The volatility of Danish East area and Swedish area are in the same pattern. Whereas, the volatility of Danish west area is the lowest because of consistent low cost wind power supply. The PJM market has relatively high volatility because of both the higher volatility and price of fossil fuels. The appearance of a jump is determined by many factors, such as unexpected extreme weather, transmission congestion and unexpected large demand. The jumps accompanied with high electricity price may have great impact on the decision making process of all market players. Besides the magnitude of jumps given by estimator JV, the intensity of jumps is also an important estimator to market anticipants. Figure 2 plots the jump intensity of each market. The jump intensity ranges from 0.0247 (Swedish market, year 2010) to 0.1671 (Danish west market, year 2015). These estimates imply that electricity spot prices Fig. 2 the jump intensity of each market tend to jump approximately once every 40 days in Swedish area in year 2010, and once every 6 days in Danish West area in year 2015. Generally speaking, the Swedish area has the lowest jump intensity while the Danish areas has highest one. This can also be explained by their different electricity generation resources. The Swedish market relies heavily on hydro power. The volume of hydro power is relatively stable day by day. The Danish areas relies heavily on low-cost, high-intermittent wind power. The PJM market relies on fossil fuel, while the price of fossil fuel has high volatility. 4. Conclusions and discussion This paper use this non-parametric jump-diffusion approach to detect the patterns of electricity price volatility.. Results show that: •The penetration of renewable energy into electricity generation has had great influence on the electricity price volatility. Electricity prices are more stable in Swedish market as hydropower is low-cost and relatively stable by time of day. As PJM market is dominated by more expensive fossil fuels, the volatility of electricity price might be influenced by the volatility of fuel price. •The market with high percentage of wind power is not necessary to be more volatile than other markets with more stable energy generation mix. The volatility of Danish west market electricity prices keeps a low level as wind takes a large percentage of total generation sources. It is worth noting that this model can only capture the daily volatility of electricity price. On the one hand, the “stable” electricity price in Danish West market might be the result of the really high percentage of wind power generation, which can cover most of the total demand in Denmark in most time. On the other hand, this result might be influenced by the accuracy of the jump test model. As wind power generation changes second by second according to the weather conditions, the accuracy level of model would better to be improved to capture hourly



Shuaili Dong et al. / Energy Procedia 158 (2019) 4331–4337 Author name / Energy Procedia 00 (2018) 000–000

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jumps. To investigate the influence of renewable energy on electricity price and improve the model to capture more accurate volatility are two urgent tasks in the future study. References [1] Michele Benini, Mirko Marracci, Paolo Pelacchi, Member, IEEE, Andrea Venturini, “Day-ahead market price volatility analysis in deregulated electricity markets.” 2002 [2] Mika Goto, G. Andrew Karolyi, “Understanding Electricity Price Volatility Within and Across Markets” [3] Christopher R. Knittel, Michael R. Roberts, "An empirical examination of restructured electricity prices.” Energy Economics, vol. 27, pp. 791–817, 2005. [4] K. F. Chan, P. Gray, and B. van Campen, "A new approach to characterizing and forecasting electricity price volatility," International Journal of Forecasting, vol. 24, pp. 728-743, 2008 [5] Carl J. Ullrich" Realized volatility and price spikes in electricity markets: The importance of observation frequency." Energy Economics, vol. 34, pp. 1809–1818, 2012 [6] Danish Energy Agency, “Off-shore wind power development experience” 2013.