The Impact of Wind Power Production on Electricity Price Volatility

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The Impact of Wind Power Production on

Electricity Price Volatility

A Time-Series Analysis

Alexander Wirdemo

Civilekonom 2017

Luleå tekniska universitet

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MASTER’S THESIS

The Impact of Wind Power Production

on Electricity Price Volatility

A Time-Series Analysis

Alexander Wirdemo

2017

Economics

Luleå University of Technology

2017-07-05

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Abstract

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Sammanfattning

Denna studie undersöker hur ökad vindkraftsproduktion (i MWh) i Sverige har påverkat elprisvolatiliteten i den nordiska grossistmarknaden Nord Pool. Vindkraftens betydelse samt tillväxten i vindkraftsproduktionen har uppstått i ljuset av de låga marginalkostnaderna för produktion och att det är en förnybar elkraftkälla med låga koldioxidutsläpp. Tidigare studier har funnit att medan ökad vindkraftsproduktion i allmänhet sänker det genomsnittliga grossistpriset på el tenderar prisvolatiliteten att öka på grund av vindkraftsproduktionens intermittenta karaktär. Genom att använda dagliga pris- och vindkraftsdata från den nordiska elmarknaden Nord Pool under perioden 2015-2017 används en GARCH-modell för att undersöka hur vindkraften påverkar prisvolatiliteten. Resultaten visar att elprisvolatiliteten ökar på lång sikt när vindkraftsproduktionen ökar. Skälen bakom detta kan hittas i bristande flexibilitet hos baskraftens produktion. Den svenska elmarknaden kännetecknas dock av en relativt hög grad av flexibilitet på grund av förekomsten av vattenkraftsreservoarer.

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Acknowledgements

I would like to thank my supervisor Professor Patrik Söderholm for many important insights in how to drive the work forward. Also a big thank you to Assistant professor Kristina Ek and fellow economics students, who have provided me with valuable feedback during our seminars. Finally, a special thank you to Professor Robert Lundmark for all the helpful hints in how to make the GARCH model work!

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This section will introduce the current electricity consumption situation, the challenges with price volatility and the purpose of the study. The section begins with a short introduction, followed by the problems related to price volatility of wind power. The section ends with a statement of the purpose, method, context and disposition of the report.

During the last decades, the world has experienced unsurpassed economic growth. Future global economic growth rates are expected to be between 1.0% and 2.8% annually during the 21st century, this based on projected growth in technology, factor productivity, output elasticity, as well as the input of labor and capital (Leimbach et al., 2017). The growth rate is expected to be higher in the developing countries and is on average expected to grow by 4.1% annually during the 21st century (Leimbach et al., 2017). As the living standard of people around the world increases, so does the demand for electricity. Panel studies have shown that there appears to exist a long-term causality between increases in income and consumption of electricity (Lee, 2005). There are however several challenges with future electricity consumption.

The challenges with future electricity consumption can be found both on the demand and the supply side. The perhaps most challenging issue with electricity is that it cannot be economically stored; hence supply must always meet demand (Bergman, 2016). Increased demand for electricity is a consequence of increased population growth, industrial activity and technological advancements (Dincer, 1999). However, to meet the expected demand in the coming two decades it would require installing as much electricity power generation capacity as was installed in the entire 20th_century

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cumulative R&D expenditure can be described in an S-curve, where increments in performance are slow in the beginning, then raising rapidly to eventually become flat or even negative (Schilling & Esmundo, 2009). In the case of fossil fuels, it has been reasoned that they reached their maturity stage by the 1990s, and performance in terms of kWh/$ has slowed, despite more investments in R&D, thus making the performance more influenced by price volatility (Schilling & Esmundo, 2009).

To cope with the problems and challenges of future electricity consumption, increased use of wind power is considered an important milestone. The advantages of renewable electricity sources, such as wind and solar power, are that they are abundant, inexhaustible, widely available and can be used with zero or near zero emissions (Asif & Muneer, 2007). Renewable electricity, which has historically only compiled a small proportion of total electricity supply, could according to Asif & Muneer (2007) possibly make up to 50% of total global electricity supply by the mid-21st century due to fossil fuel exhaustion and environmental concerns such as global warming. Asif & Muneer (2007) further point out that some renewable electricity sources work at optimum levels at certain latitudes: while solar power is most efficient in countries close to the equator, wind power is more efficient in countries far from the equator. Therefore, in the Nordic region, wind power is of particular interest. Wind power turbines have, according to Saidur et al. (2010), the potential to create economic growth and job opportunities, as well as improving security and protecting consumers from supply shortages.

1.1. Problem discussion

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2016). From a demand perspective, wind power is generated only in the correct weather-conditions (Ketterer, 2014). This implies limitations in matching electricity demand, which could make the price more volatile if wind power dependency is high (Ketterer, 2014). From a supply perspective, the electricity supplied by wind power adds excess supply, which reduces the electricity wholesale price (Ketterer, 2014). The electricity price rises again as the wind power feed-in stops, and this phenomenon of reduced electricity price in when wind power is feeding into the system is often referred to as the merit-order effect (Ketterer, 2014). However, this implies that during days without wind power, electricity prices rise again due to the loss of supply, increasing interday price volatility (Ketterer, 2014). It is also argued that this effect is more prominent in trading regions that generate a higher proportion of wind power relative to other regions (Woo et al., 2011).

These effects have several implications for policy and consumption. To deal with the demand problem, electricity markets would have to compensate the lack of wind with back-up systems such as coal-fired power and/or demand-side management to ensure supply of electricity and avoid peaks in prices (Mauritzen, 2010). To handle the supply problem, the electricity supply built up by these systems could also potentially harm the economic feasibility of wind power (Mauritzen, 2010). To fully understand these implications, more research about the sensitivity of the electricity market is to these changes was suggested by Mauritzen (2010). This has resulted in the purpose of this study.

1.2. Purpose

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1.3. The Case of Wind Power in the Nordic Electricity Market

The Nordic electricity market is structured into four parts: Generation, Transmission, Distribution and Retailing (EUFORIS, 2017). The players on the wholesale exchange market are producers, electricity suppliers and industrial companies with a high electricity intensity (Bergman, 2016). In most cases, there are few players in the Generation and Transmission parts, while the Distribution and Retailing parts have a larger number of players (EUFORIS, 2017). Due to market de-regulation, Generation and Retiling have opened up for competition, while Transmission and Distribution are considered natural monopolies and subject to regulation such as price regulations to not risk market efficiency (EUFORIS, 2017).

Regarding market structure, the electricity wholesale market works as follows. Electricity is purchased by actors in the Transmission part from power companies in the Generation part on a day-ahead basis from the Nord Pool exchange (Bergman, 2016). To ensure that electricity is provided in balance, any actor on the market who causes imbalance will compensate by paying the cost of restoring balance, reducing the incentives to drive up prices by offering a smaller supply (Bergman, 2016). Furthermore, research has shown that the actors on the electricity market have limited possibilities to exercise market power (Bergman, 2016). Although customers do not have perfect information, there are barriers to entry and exit, there are few companies serving few customers, the homogeneity of the product and the mechanisms of pricing mentioned above makes the market structure demonstrate characteristics of perfect competition. Throughout the report, perfect competition will be assumed.

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differences are noticeable if the composition of electricity supply is different across the regions (Woo et al., 2011), which is the case in Sweden who is more heavily dependent on hydropower in the northern region SE1 and more dependent on wind power in the southern region SE4. Although the bidding areas are integrated, they can at times work as singular markets, and how wind power affects price volatility in each of each of these bidding areas is of interest in this study.

Figure 1: Nord Pool bidding areas Source: nordpoolspot.com

Currently, Nord Pool runs two markets: the spot exchange market and the futures market (Christie & Wangensteen, 1998). Nord Pool operates on a day-ahead basis, where bids are provided for every hour the following day, thus establishing an equilibrium price (Mauritzen, 2010). For market bids made after the day-ahead Nord Pool market has closed, players can turn to the daily electricity market Elbas, and the operations are taken care of by the Swedish Transmission System Operator Svenska kraftnät (Bergman, 2016).

1.4. Method

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𝑦_! = 𝜇 + 𝜙_!𝑦_!!! ! !!! + 𝜃_!𝑤_!!! ! !!! + 𝜖_! (1) ℎ_! = 𝜔 + 𝛼_!𝜖_!!!! ! !!! + 𝛽_!ℎ_!!! ! !!! + 𝛾_!𝑤_!!! (2) ! !!!

The mean equation (1) explains how past price levels 𝑦_!!! and the chosen parameter 𝑤_!!! affect the long-term price level and the variance equation (2) explains how past price shocks ℎ_!!! and current price shocks 𝜖_!!!! as well as the chosen parameter 𝑤_!!! affect the price level (see further section 5). The GARCH model was used because it gives an understanding of the effects on wholesale price and price volatility over a long time span (Ketterer, 2014). Nord Pool wholesale price data in Sweden and each of the four bidding areas SE1, SE2, SE3 and SE4, adjusted for outliers and seasonal variation, will be used as response variables, and wind power production, total electricity production, and wind penetration in each of the four bidding areas will be used as independent variables.

1.5. Outline

The rest of the report is structured as follows. In section 2, theoretical considerations regarding supply, demand, and equilibrium in the electricity market will be presented. In section 3, a literature review will be presented with the key findings from earlier studies investigating the relationship between wind power and electricity price volatility. Section 4 will describe the data used in the study and how it was refined. Section 5 will explain the method used to reduce seasonal influences and an explanation of the GARCH method. Section 6 will present the empirical results of the analysis and some test for stability. In Section 7, the results will be discussed and compared with previous studies. In the concluding section 8, the general conclusions of the study will be drawn along with suggestions for future research.

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14 CHAPTER 2 THEORETICAL CONSIDERATIONS

This section will explain the most important theoretical considerations needed for the study. The section begins with an explanation of the factors affecting electricity supply, followed by an explanation of the forces of electricity demand. The section concludes with an explanation of how equilibrium in the electricity market is created in the short and long term.

2.1. Supply of electricity

There are several factors that influence the supply of electricity. According to Bird et al. (2005), the increase in the price of substitute electricity sources such as natural gas in combination with government and tax policy has made renewable electricity such as wind power more competitive. More precisely, renewable portfolio standards (RPS)1_,

system benefit funds2_{, integrated resource planning (IRP)}3_{and property & sales tax}

abatements are found to be effective policy-related factors driving the supply of renewable electricity such as wind power (Bird et al., 2005). According to Weron et al. (2004), fluctuation of fuel prices such as oil and gas influences the supply of electricity offered, as well as plant outages caused by maintenance, transmission constraints or breakdowns. In the case of Swedish electricity production, the most relevant factors affecting supply are available nuclear power and the price of coal (Brännlund et al., 2012). In the Nord Pool market, it should also be noted that Sweden and Norway share a common certificate system, which affects the supply of electricity.

1_{RPS – Renewable Portfolio Standards, a policy that requires every electricity supplier to devote at}

least a specific share of their portfolio to renewable electricity (Bird et al., 2005).

2_{System benefit funds – a policy that imposes electricity customers to pay a surcharge, which is placed}

into a fund to support the supply of renewable electricity (Bird et al., 2005).

3_{IRP – Integrated Resource Planning, a planning process that aims to forecast electricity demand and}

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Two important factors affecting the supply elasticity are the mix of installed capacity and the degree of integration with other electricity markets (Nicolosi, 2010). If the mix of installed capacity is dominated by base power plants, this causes inflexibility because output changes will affect the lifetime of the heat- and pressure-sensitive parts (Nicolosi, 2010). Furthermore, the plants have high installation costs and low variable costs, and must hence be run throughout the year with few changes in output to cover the investment costs. The second factor is market interconnectedness; misalignment can cause inefficiencies (Nicolosi, 2010).

The supply curve of electricity can be explained as follows. The base power forms the first blocks of electricity, with low marginal costs (Pöyry, 2010). In Sweden, the base load is made up of nuclear and hydropower (Weron et al., 2004). When demand is higher and the base supply is insufficient, higher marginal cost electricity sources such as oil and gas are used (Weron et al., 2004). This can be illustrated in Figure 2, where price (in €/MWh) is on the vertical axis, electricity demanded and produced (in MWh) is on the horizontal axis, and the curves represent the supply of electricity.

Figure 2: Supply of electricity (in MWh) and electricity wholesale price (in €/MWh) Source: Weron et al. (2010)

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2.2. Demand for electricity

There are a number of factors affecting the demand for electricity, and demand is derived from several sources. According to Lijesen (2007), production processes is an important factor, and its demand for electricity can be derived from the characteristics of the processes, such as the time of day, season and technology and economic growth. Berndes et al. (2003) also find economic growth as an important factor in electricity demand, but also pinpoint population growth as an important demand factor. In the case of the Swedish electricity market, another important factor affecting demand is temperature, since low temperature increases the demand for heating and hence electricity and vice versa (Brännlund et al., 2012).

The demand for electricity can also be described as inelastic in the short run. Electricity is considered a necessity with few easily obtainable substitutes, which makes demand more inelastic (Pöyry, 2010). One of the factors affecting the flexibility of the electricity market is the amount of must-run generation, which is the autonomous demand for electricity independent of electricity load (Nicolosi, 2010). The residual demand remaining after subtracting the must-run generation is according to Nicolosi (2010) inflexible and demands a flexible supply system. Furthermore, since consumers do not have access to real-time information about the electricity price or the ability to act on such information, consumer demand in the short run is inelastic (Bergman, 2016).

From a market demand curve perspective, this can be illustrated as follows. Depending on the availability of intermittent power (wind and solar power), this makes shifts in residual demand an important determinant of equilibrium price. In Figure 3, this is illustrated with RE_L and P_L being demand and price, respectively when production of intermittent power is low and REH and PH are demand and price, respectively when

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slope if the demand curve is also steep, which reflects the inelasticity of demand discussed before.

Figure 3: Market equilibrium when intermittent electricity supply is high and low Source: Bergman (2016)

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Figure 4: Demand for electricity (in MWh) and wholesale price of electricity (in €/MWh) during Day, Night and Peak

Source: Pöyry (2010)

From Figure 4, it can be concluded that demand during peak hours results in a higher equilibrium price compared to the average daily demand, and demand during low demand hours results in a lower equilibrium price.

2.3. Short and long term dynamics in the electricity market

From a short-term electricity market perspective, the electricity market is exposed to supply shocks caused by intermittent power such as wind power. As mentioned previously, wind power cannot be controlled, which makes supply difficult to predict (Bergman, 2016). However, since the marginal costs of wind power and other intermittent power sources are low, these electricity kinds provide the base of the supply curve (Bergman, 2016). The residual demand, which is the demand not covered by intermittent electricity, must therefore be covered by conventional power such as nuclear power (Bergman, 2016).

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the flexibility of conventional power is limited, this will have effects on price volatility. During the summer season, when wind and solar intermittent power are supplied in large amounts to the electricity market, and flexibility is limited in conventional power, the excess supply will create a downward pressure on prices (Bergman, 2016). The opposite happens when the supply of intermittent power is low; the electricity price has to be high in order to give incentives to conventional power suppliers to supply more electricity (Bergman, 2016). If forecasting abilities are bad, this will have an effect of market institutions; if forecasts are difficult, more trading will occur on the daily market Elbas, while if they are good, trading will take place on the spot market (Bergman, 2016).

From a short-term market equilibrium perspective, this can be explained as follows. When wind power enters the supply curve, the near zero marginal cost causes a short-term shift in the supply curve to the right, because other sources of electricity have higher marginal costs (Pöyry, 2010). The situation is explained in Figure 5 below, where price (in €/MWh) is on the vertical axis, electricity demanded and produced (in MWh) is on the horizontal axis, the curves represent the supply of electricity without wind power, with wind power, and low, normal and peak demand.

Figure 5: Demand, supply and supply shift of electricity (in MWh) and wholesale electricity price (in €/MWh)

Source: Pöyry (2010)

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In a long-term perspective, electricity markets have different ways of re-establishing old equilibrium. As mentioned previously, the base power plants are unlikely to change their output in order to maintain the lifetime of the parts (Nicolosi, 2010). However, hydro power has more flexibility in terms of output deployment and can adjust output to both meet peak demand and reduce excess supply (Weron et al., 2004). This flexibility reduces electricity price volatility in the long run.

From a long-term market equilibrium perspective, this can be explained as follows. In an electricity market with a high degree of flexibility, the market is better equipped to re-balance the excess supply. The reduction of hydro power output causes the supply curve to shift left in the long term and forming the equilibrium levels before the supply shocks. In an electricity market with a lower degree of flexibility, the market is not well-equipped to deal with the supply shocks caused by wind power. This causes the supply curve to shift long term to the left, but much slower, or in the extreme case not at all. This will potentially drive the high margin power sources out of the market. These two long-term scenarios are illustrated in Figure 6 below, which shows electricity in MWh on the vertical axis and marginal cost (in SEK) on the horizontal axis, a fast supply shift on the left and a permanent supply shock to the right.

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From Figure 6, it can be concluded that if supply flexibility allows, the effects from supply shocks caused by wind power can be reverted back to old equilibrium levels. This mean-reverting effect is an important aspect to consider when analyzing electricity markets (Ketterer, 2014). In the other case, when supply is not flexible enough, the effects of supply shocks are longer lasting or even permanent. It can also be noted that demand is more elastic in the long run.

To conclude this section, the effect when periods of high wind power cause a lower electricity price is known as the merit-order effect. The electricity market’s ability to revert the supply shocks also depends on the flexibility of supply. Although this conceptual clarification of supply and demand indicates that prices will be lower but more volatile with more wind power in the system, a deep-dive into the results from previous studies in the area is needed and is the topic of the next section.

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CHAPTER 3 LITERATURE REVIEW

This section will give a literature review on the topic. The section begins with a general summary, followed by a discussion about previous studies about wind power and its effect on electricity price volatility and contemporary findings. The section concludes with a summary of key findings. For the literature review, the database Google Scholar has been used. The dominating keywords have been: wind power, electricity price, and volatility.

Table 1: Summary of previous studies

Author Objective Method Results

Couture & Gagnon (2010)

To determine the effect on Trade-in-tariff-policy on energy prices

Review of Trade in tariff-systems

Increased use of renewable energy will decrease volatility caused by fossil fuels

Doherty (2006)

To allocate wind power in a portfolio of energy to diversify away the impact of fossil fuel volatility

MV-portfolio theory Wind power can potentially diversify away part of the volatility from fossil fuels in countries heavily dependent on fossil fuels, such as Ireland

Milstein & Tishler (2011)

To understand the outcome of a Cournot-duopoly with conventional and renewable energy.

Theoretical and computer simulation

Both market prices and price volatility increased

Clò et al. (2015)

To understand the effect of wind and solar power on wholesale electricity price in Italy

OLS The merit-order effect is present in the Italian market and has increased price volatility

Tveten et al. (2013)

To understand the effects of solar power in the German market

OLS The merit-order effect is present in the German market Cludius et

al. (2014)

To study the combined effects of wind and solar power in Germany

OLS The merit-order effect is present, and increasing due to capacity expansions

Würzburg et al. (2013)

Review paper Literature review The merit-order effect is stronger in small markets compared to bigger markets

Mauritzen (2010)

To understand the impact of wind power on price volatility

Econometric models Intraday volatility decreased due to lower marginal costs; long-run volatility increased due to weather changes Ketterer

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To understand how wind power affects pricing of energy

GARCH econometric model

Average price of electricity decreased, but volatility increased

Rintamäki et al. (2017)

Compare the effect of wind power in Germany and Denmark

SARMA time series analysis

Wind power causes intraday price volatility to increase in Germany, while it decreases in Denmark

Pereira & Rodriguez (2015)

To understand how wind power affects price volatility in Portugal

ARX-ERGARCH econometric models

Increased wind penetration reduces electricity price and increases price volatility

Woo et al. (2011)

To understand how wind power affects pricing of energy in Texas

Econometric models Price of energy decreased, but volatility increased

Traber & Kemfert (2011)

To understand how wind power affects energy supply and incentives to invest in renewable energy

Computer simulation using predicted costs

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3.1. Renewable energy and electricity price volatility

From a policy perspective, Couture & Gagnon (2010) are of the opinion that increased use of renewable electricity will decrease volatility caused by fossil fuels, based on the different policy alternatives available. Doherty (2006) is of a similar opinion, and found in a portfolio study of electricity source allocation in Ireland that wind power will be an important contribution in future electricity portfolios, and will diversify away part of the volatility of electricity price from the heavily oil-dependent island. In a theoretical paper, Milstein & Tishler (2011) studied the outcome of a Cournot-duopoly where one firm provided conventional electricity from a combined cycle gas turbine (CCGT) with low capacity cost and high variable cost, and the other firm provided renewable electricity from photovoltaic cells (PV) with high capacity costs and zero variable cost. The method used was numerical, infinitely repeated simulation, where the two firms decided electricity production based on solar conditions (Milstein & Tishler, 2011). Due to the supply uncertainty, Milstein & Tishler (2011) found that market prices and price volatility increased.

3.2. The merit-order effect

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wind and solar power in Germany. The method used was also OLS, with electricity spot price as the response variable and wind power, solar power and load as the explanatory variables (Cludius et al., 2014). Cludius et al. (2014) found that the merit order effect is not only present but also increasing over time due to capacity expansion.

Wind power and its’ impact on the merit-order effect differs between electricity markets. In a review of past theoretical and empirical studies, Würzburg et al. (2013) found wind power crowds out technologies with higher marginal costs through the merit-order effect, but the effect is different across markets. In the review, Würzburg et al. (2013) converted the data from previous studies into homogeneous units (€/MWh per each added GWh in wind power) to compare the impact across markets. The results showed that the merit-order effect was the smallest in large markets such as the Nordic and German markets (ranging from -0,24 to -2,83), while smaller market such as Ireland and the Netherlands had much greater impact (ranging from -6,17 to -9,9) from the merit-order effect (Würzburg et al., 2013).

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left and during peak hours to the right, and demanded quantity of electricity on the horizontal axis.

Figure 7: Supply shifts during base and peak load times Source: Mauritzen (2010)

Figure 7 shows that the merit-order effect is present in the Danish case, and that wind power affects price volatility in the short run, in line with the theoretical outline presented by Nicolosi (2010) and Pöyry (2010). Mauritzen (2010) also found long-term price volatility, and the reasons behind this can be explained by changes in weather (e.g. prolonged periods of wind-still weather reduces supply).

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In a comparative study between the electricity markets of Denmark and Germany, Rintamäki et al. (2017) found that wind power and similar zero marginal cost technologies cause German intraday electricity price volatility to increase, while it decreases in Denmark. These findings are similar to those of Mauritzen (2010), and to further explain the differences, Rintamäki et al. (2017) pinpoint the access to flexible generation capacity and differing wind power generation pattern as the main contributing reasons behind the differences. More specifically, wind power generation occurs more at off-peak hours in Germany and Denmark has better access to hydropower reservoirs from the other Nordic countries compared to Germany, hence the differences (Rintamäki et al., 2017). The model used to obtain these results was a seasonally adjusted autoregressive moving average (SARMA) function, with data sets of daily electricity prices, wind penetration and wind power (Rintamäki et al., 2017), which methodologically differs from earlier studies such as Ketterer (2014). The SARMA method was chosen because it utilizes weekly demand patterns and past price data to forecast short-term price data (Rintamäki et al., 2017).

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Portuguese and Spanish markets, was suggested as an area of further studies (Pereira & Rodriguez, 2015).

In an empirical study of wind power and its effects on electricity prices in Texas, Woo, et al. (2011) used 15-min price data from four regions in Texas and a seven lag function to study the variance of price data. Woo et al. (2011) found that while wind power decreased price levels, it also increased price volatility. Their findings are also in contrast to the portfolio study by Doherty (2006). Furthermore, Woo et al. (2011) proposed that the changes in price volatility depend on the load of wind power; zones who had a higher proportion of wind power relative to other zones experienced more price reductions yet higher price volatility, similar to the findings of Mauritzen (2010). To cope with the challenges or more volatile electricity prices, Woo et al. (2011) suggest that policy makers should use financial instruments to handle the risks associated with increased price volatility. Similarly, Traber & Kemfert (2011) found that the market price of electricity decreased as wind electricity supply increased, but also pinpoint that the reduction in electricity price also reduced incentives to invest in other electricity sources such as natural gas-fired thermal units.

3.3. Key findings

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merit-order effect (Cludius, 2014; Mauritzen, 2010). From these themes, key findings were developed and can be found in Table 2. As proposed by Woo et al. (2011), bidding areas that generate more wind power experience a lower electricity price yet higher volatility relative to other regions. However, similar studies in how wind power generated in smaller bidding areas of the Nordic electricity exchange and how it affects the electricity price and price volatility in each of these regions are missing. Therefore, this study will hopefully position itself as a contribution in this regard and is needed to deepen the understanding on the effects of wind power on price volatility. After these concluding remarks on the literature overview, a closer examination of necessary data to do the analysis is needed and is the topic of the next section.

Table 2: Key findings

Average daily electricity wholesale price Short-term price volatility Long-term price volatility Increases

Milstein & Tishler (2011) Clò et al. (2015) Würzburg et al. (2013) Ketterer (2014) Cludius (2014) Mauritzen (2010) Decreases Clò et al. (2015) Tveten et al. (2015) Würzburg et al. (2013) Mauritzen (2010) Ketterer (2014)

Pereira & Rodriguez (2015) Traber & Kemfert (2011) Woo et al. (2011)

Tveten et al. (2015) Mauritzen (2010)

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CHAPTER 4

DATA SOURCES AND DESCRIPTION

This section will explain the data necessary for the study and how it was collected. The section begins with a description of what data is needed and how it was collected. Then follows an explanation of the initial data collected and how it was refined. The section concludes with an explanation of what further econometric refinement is needed before the analysis.

4.1 Data description

The data used for this study are provided by Nord Pool (http://www.Nord

Poolspot.com/historical-market-data/, 2017-03-09). The data used were price daily

elspot prices, daily power production in Sweden and in the different areas SE1, SE2, SE3 and SE4 and wind power production in these areas (also per day). The time period of interest is 24.01.2015-24.01.2017, due to available data with enough detail, giving a total of 732 observations. Although the regions are integrated, the regional data was used to test if there are regional differences in price volatility, as proposed by Woo et al. (2011).

The result from the data collection of daily prices 2015-2017 (measured in SEK/MWh) and wind power produced to Nord Pool can be summarized in figures 8-17 below. The figures indicate price series with some distinct outliers, causing skewness in the model.

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In Figure 8, the daily electricity prices in Sweden during the time period 24.01.2015-24.01.2017 is shown (top part), with prices in SEK on the vertical axis and time on the horizontal axis. In Figure 8, the daily wind power production in Sweden during the same time period is also shown (bottom part), with wind power production measured in MWh on the vertical axis and time on the horizontal axis.

Figure 8: Daily electricity prices (in SEK) (top) and daily wind power production (in MWh) (bottom) in Sweden 24.01.2015-24.01.2017

Source: Nord Pool

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In Figure 9, total daily power load (in MWh) (top) and wind penetration (total load/wind power production, in %) (bottom) during the time period is shown for Sweden.

Figure 9: Total daily power load (MWh) and wind penetration (%) for Sweden 24.01.2015-24.01.2017

Source: Nord Pool

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In Figure 10, the daily electricity prices in Sweden during the time period 24.01.2015-24.01.2017 is shown (top), with prices in SEK on the vertical axis and time on the horizontal axis. In Figure 10, the daily wind power production in Sweden during the same time period is shown (bottom), with wind power production measured in MWh on the vertical axis and time on the horizontal axis.

Figure 10: Daily electricity prices (in SEK) (top) and daily wind power production (in MWh) (bottom) in SE1 24.01.2015-24.01.2017

Source: Nord Pool

From Figure 10, it can be noticed that prices have ranged from as low as around 50 SEK per MWh up to levels of over 800 SEK. There are also two periods of distinct spikes noticeable, one in January 2016 and one in July 2016. From Figure 10, it can be noticed that daily wind power production has ranged from 0 to over 10 000 MWh. In

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Figure 11, total daily power load (in MWh) (top) and wind penetration (total load/wind power production, in %) (bottom) is shown for SE1 during the same time period.

Figure 11: Total daily power load (MWh) and wind penetration (%) for SE1 24.01.2015-24.01.2017

Source: Nord Pool

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In Figure 12, the daily electricity prices in region SE2 during the time period 24.01.2015-24.01.2017 is shown (top), with prices in SEK on the vertical axis and time on the horizontal axis. In Figure 12, the daily wind power production in the same region and time period is also shown (bottom), with wind power production measured in MWh on the vertical axis and time on the horizontal axis.

Figure 12: Daily electricity prices (in SEK) (a) and daily wind power production (in MWh) in SE2 24.01.2015-24.01.2017

Source: Nord Pool

From Figure 12, it can be noticed that prices have ranged from as low as around 50 SEK up to levels of over 800 SEK. There are also two periods of distinct spikes noticeable, one in January 2016 and one in July 2016. From Figure 12, it can be noticed that daily wind power production has ranged from 0 to over 40 000 MWh.

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In Figure 13, total daily power load (in MWh) is shown on top and wind penetration (total load/wind power production, in %) is shown on the bottom.

Figure 13: Total daily power load (MWh) and wind penetration (%)for SE2 24.01.2015-24.01.2017

Source: Nord Pool

From Figure 13, it can be noted that total load fluctuates between 40000 up to 180000 MWh and wind penetration fluctuates between 0-50 % in the region. It can also be noticed that wind penetration seems to be increasing over time in both in terms of mean and fluctuation.

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In Figure 14, the daily electricity prices in region SE3 during the time period 24.01.2015-24.01.2017 is shown (top), with prices in SEK on the vertical axis and time on the horizontal axis. In Figure 14, the daily wind power production in the same region and time period is also shown (bottom), with wind power production measured in MWh on the vertical axis and time on the horizontal axis.

Figure 14: Daily electricity prices (in SEK) (top) and daily wind power production (in MWh) (bottom) in SE3 24.01.2015-24.01.2017

Source: Nord Pool

From Figure 14, it can be noticed that prices have ranged from as low as around 50 SEK up to levels of over 800 SEK. There are also two periods of distinct spikes noticeable, one in January 2016 and one in July 2016. From Figure 14, it can be noticed that daily wind power production has ranged from 0 to over 40 000 MWh.

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In Figure 15, total daily power load (in MWh) (top) and wind penetration (total load/wind power production, in %) (bottom) is shown.

Figure 15: Total power load (MWh) and wind penetration (%) in SE3 24.01.2015-24.01.2017 Source: Nord Pool

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In Figure 16, the daily electricity prices in region SE4 during the time period 24.01.2015-24.01.2017 is shown (top), with prices in SEK on the vertical axis and time on the horizontal axis. In Figure 16, the daily wind power production in the same region and time period is shown (bottom), with wind power production measured in MWh on the vertical axis and time on the horizontal axis.

Figure 16: Daily electricity prices (in SEK) (a) and daily wind power production (in MWh) in SE4 24.01.2015-24.01.2017

Source: Nord Pool

From Figure 16, it can be noticed that prices have ranged from as low as around 50 SEK up to levels of over 800 SEK. There are also two periods of distinct spikes noticeable, one in January 2016 and one in July 2016. From Figure 16, it can also be noticed that daily wind power production has ranged from 0 to over 30 000 MWh.

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In Figure 17, total daily power load (in MWh) (top) and wind penetration (total load/wind power production, in %) (bottom) is shown.

Figure 17: Total daily power load (MWh) and wind penetration (%) in SE4 24.01.2015-24.01.2017

Source: Nord Pool

From Figure 17, it can be noted that total load shows some seasonal patterns with a peak in winter season around 40 000-50 000 MWh and a decline in summer season around 10 000 MWh. Wind penetration also demonstrates some seasonal variation with a peak in late summer season where wind penetration reaches 70-80% and a decline in winter where wind penetration is around 10% in the region. It can also be noticed that wind penetration rises when total load reduces.

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4.2. Reliability and validity

The validity of the data concerns if the findings help in achieving the research purpose (Saunders, 2009). To give valid results, the data used have been introduced stepwise to compare the explanatory power.

Reliability concerns if the data collection method will consistently yield the same results (Saunders, 2009). In terms of reliability, all data used are secondary from a reliable source (Nord Pool) and can easily be obtained. The influence of participant of observer bias is insignificant. To sustain the reliability of the data, round-off actions have been saved until the last step. It is also important to not allow certain observations to influence the result. These spikes can be either normal or abnormal, where normal spikes are caused by seasonal effects and revert back to mean while abnormal spikes reach an unusually high price before reverting back, respectively (Gianfreda, 2010). In the Nord Pool market, regulation of maximum allowable price limits these spikes, which could otherwise be even higher. These abnormal outliers have been dealt with to improve the validity of the results.

4.3. Removing outliers

From observing the price charts, some spikes can be noticed. These spikes represent outliers, which cause kurtosis4_{and their impact should be reduced without removing}

any observation (Bierbrauer et al., 2007). This can be achieved by using a threshold value three times the standard deviation from the mean (Gianfreda, 2010). To improve the model, outliers were therefore detected as follows. The mean value and standard deviation from the entire data set were calculated, and prices above or below three standard deviations of the entire data set were identified, in line with previous studies (Ketterer, 2014; Gianfreda, 2010). In this case, 8 outliers were detected. These values were replaced with a value equal to three standard deviations from the mean. The new data sets are illustrated in the figures below. In Figure 18, the new data set adjusted for outliers can be found.

4_{Kurtosis – a statistical characteristic, where positive kurtosis indicated heavy tails and peakedness}

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Figure 18: Daily electricity prices in Sweden (adjusted for outliers) 24.01.2015-24.01.2017

Source: Nord Pool

From the figure, it can be noticed that the pattern smoothers a bit to reduce the impact of outliers. Figure 19 shows the daily electricity prices for region SE1, with prices on the vertical axis and time on the horizontal axis.

Figure 19: Daily electricity prices in SE1 (adjusted for outliers) 24.01.2015-24.01.2017

Source: Nord Pool

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Figure 20: Price data for region SE2 (adjusted for outliers) 24.01.2015-24.01.2017

Source: Nord Pool

In Figure 20, the same pattern as noted previously in Figure 19 can be noted, but the spikes have been cut around 500 SEK. In Figure 21, the adjusted daily electricity prices for region SE3 is shown, with prices in SEK on the vertical axis and time on the horizontal axis.

Figure 21: Daily electricity prices in SE3 (adjusted for outliers)

Source: Nord Pool

In Figure 21, the spikes noted earlier have been cut off around 500 SEK. In Figure 22, the adjusted daily electricity prices for region SE4 is shown, with electricity price in SEK on the vertical axis and time on the horizontal axis.

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Figure 22: Daily electricity prices in SE4 (adjusted for outliers)

Source: Nord Pool

In Figure 22, it is noticeable that the previous spikes have been cut off and are now of equal amplitude at about 500 SEK. Now that the data series have been set up, an explanation of the method used to get results and how the data will be used in the model is needed and is the topic of the next section.

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44

CHAPTER 5 METHODOLOGY

This section will describe the method needed to fulfil the purpose of the study. The section begins with an explanation of the GARCH model and its’ variables. The section then explains the tests that will be performed to analyse the results.

5.1. Seasonal variation

Seasonal variation, which means effects on the price depending on the season, needed to be addressed before the analysis. Put in other words, to finalize the data the effects from changes in demand depending on the day of week and month needed to be taken into account (Ketterer, 2014). Mathematically, the data can be described as 𝑝_! = 𝑦_!+ 𝑠_!, where 𝑝_! is the electricity price, 𝑦_! a stochastic part and 𝑠_! a seasonal component. The seasonal component 𝑠_! can be further divided into a constant parameter 𝑐 , a weekday part 𝜉_!𝑑_! and a monthly part 𝜈_!𝑚_!, where 𝜉_! and 𝜈_! are parameters and 𝑑_! and 𝑚_! are weekday dummy variables. 𝑖 ranges from 1-7 and 𝑗 ranges from 1-12. Put together, the seasonal variation component can be described as Equation (3): 𝑠_!= 𝑐 + 𝜉_!𝑑_! + 𝜈_!𝑚_! 𝑠_!− 𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 𝑐, 𝜉_!, 𝜈_!− 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠 𝑑! − 𝑤𝑒𝑒𝑘𝑑𝑎𝑦 𝑑𝑢𝑚𝑚𝑦 𝑚!− 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑑𝑢𝑚𝑚𝑦 !" !!! ! !!! (3)

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5.2. GARCH-model

To investigate how volatility changes over time, the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model was used. The reason for why the GARCH model was used is because it has the advantages of determining the effects of price volatility both in the short and long run, as well as effects of the mean price in one single run (Ketterer, 2014). Similar to other methods such as ARMAX (Mauritzen, 2010) and SARMA (Rintamäki et al., 2017), the GARCH model also relies on autoregressive terms (Ketterer, 2014), which makes it equally suitable for studying seasonal effects. In contrast to studies using OLS (Clò et al., 2015; Tveten et al., 2013; Cludius et al., 2014), the GARCH model is more dynamic and better captures the impact of past shocks compared to OLS. GARCH also has the advantages of being simpler to run compared to hybrid variants such as ARX-EGARCH (Pereira & Rodriguez, 2015), hence the GARCH model was chosen for this study.

The GARCH model is used to determine interrelationships in time series where volatility might change according to a pattern. The GARCH model can be written as:

𝑦_! = 𝜇 + 𝜙_!𝑦_!!! ! !!! + 𝜃_!𝑤_!!! ! !!! + 𝜖_! (4) ℎ_! = 𝜔 + 𝛼_!𝜖_!!!! ! !!! + 𝛽_!ℎ_!!! ! !!! + 𝛾_!𝑤_!!! (5) ! !!!

In equations (4) and (5) above, ℎ! represents the variance equation (in SEK) and 𝑦!

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In the conditional variance equation, 𝜔 represents the value of the variance will tend towards in the long run (Ketterer, 2014). The coefficients 𝛼 represents how the value is affected by current shocks, and the value 𝛽 represents the persistent effect of past shocks, hence the inclusion of the term ℎ!!! (Ketterer, 2014). 𝛾! is the wind power

production parameter and 𝑤_!!! is the natural logarithm of wind power production. The error term 𝜖_!!!! is ℎ!𝑧!!, where 𝑧! is independently normally distributed, N(0,1).

Stable and efficient electricity markets are characterized by occasional spikes in price, which then revert back to a mean value due to the forces of supply and demand (Ketterer, 2014). To test the stability of the Swedish market, measured in the conditional variance equation, the parameters 𝛼 and 𝛽 were investigated (Ketterer, 2014). If 𝛼_! + 𝛽_! < 1 and 𝛼_!, 𝛽_! > 0, i.e. both are positive and their sum is greater than one, the model is mean reverting, and the effects of shocks, both current and past, only have a temporary effect on the conditional variance ℎ_! (Ketterer, 2014).

The variables were introduced stepwise. First, a data series with only price and variance was calculated.

𝑦_! = 𝜇 + 𝜙_!𝑦_!!! ! !!! + 𝜖_! (6) ℎ! = 𝜔 + 𝛼!𝜖!!!! ! !!! + 𝛽!ℎ!!! (7) ! !!!

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Finally, wind penetration 𝑝 (wind power/total load) was introduced. 𝑦!= 𝜇 + 𝜙!𝑦!!! ! !!! + 𝜃!𝑤!!! ! !!! + 𝜓!𝑙!!!+ ! !!! 𝜉!𝑝!!! + ! !!! 𝜖! (10) ℎ_! = 𝜔 + 𝛼_!𝜖_!!!! ! !!! + 𝛽_!ℎ_!!! ! !!! + 𝛾_!𝑤_!!!+ 𝜓_!𝑙_!!! + ! !!! 𝜉_!𝑝_!!! ! !!! (11) ! !!!

In line with previous studies, the aim of the time series analysis was to investigate the role of wind power and its effects on price volatility. To test the results, significance tests on a 10% significance level was performed.

5.3. Econometric issues

The model was run through the software LIMDEP by Econometric Software, Inc. There was only one econometric issue that caused concern, and that was the warning of non-positive Sigma in the iteration. This occurs because of the model fit. Since it only occurred 5 times in the entire data set, the effect on the model result was deemed to be insignificant. After this outline of the method used, it is now time to examine the results of the time series analysis, which is the topic of the next section.

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48 CHAPTER 6 RESULTS

This section will present the results of the regression and time series analysis. The section begins with the results from the regression made to reduce the seasonal effects of the data. Then follows the results from the time series analysis in three separate subsections, each with additional explanatory variables.

6.1. Seasonal variation

The results from the OLS regression to reduce seasonal variation can be found in Table 3 below. Table 3 shows results for the entire Swedish market (SE) and regions SE1, SE2, SE3, and SE4, with coefficients for the dummy variables and p-values, respectively.

Table 3: Coefficients and p-values for seasonal adjustments for SE, SE1, SE2, SE3 and SE4

SE SE1 SE2 SE3 SE4

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From Table 3, the results from the regression indicate that in Sweden as a whole, the constant, the weekdays Saturday and Sunday are negative and significant. This means that the electricity wholesale price is significantly lower during the week-ends. The regression also shows that all months except October are significant, meaning the season has an impact on the electricity price. The results from the different regions show that in region SE1 the constant, the weekdays Saturday and Sunday and every month except October demonstrate seasonal effects at a 10% significance level. The results also indicate that in region SE2 the constant, weekdays Saturday and Sunday and all months except October demonstrate seasonal variation. From Table 3, the results also indicate that in region SE3, the constant, the weekdays Saturday and Sunday and every month except October demonstrate seasonal variation at a 10% significance level. In region SE4, the constant, weekdays Saturday and Sunday and every month except October demonstrate seasonal variation at a 10% significance level. As the last step before running the data through the GARCH-model, the natural logarithm of the data was run. Some comparative statics from the data sets can be found in Table 4, which shows mean, median, max, min, standard deviation, skewness and kurtosis for the data set before and after adjusting for outliers and seasonal effects.

Table 4: Descriptive statistics for SE, SE1, SE2, SE3 and SE4 before and after seasonal adjustment

Series Mean Median Max Min Standard deviation Skewness Kurtosis

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Table 4 indicates that while the mean and median only demonstrate small changes, the data set is smothered after removing outliers and reducing seasonal variation, which can be seen in a smaller skewness and kurtosis.

6.2. Results from GARCH model with prices

In Table 5, results for the GARCH model derived from Equation (6) and (7) can be found, with the autoregressive parameters Φ₁-Φ₇ in the mean equation and ω, α and β in the variance equation for regions SE1, SE2, SE3, and SE4, respectively. P-values are within parenthesis.

Table 5: Results from GARCH model with prices

Mean

equation SE SE1 SE2 SE3 SE4

Constant 0,05550 (0,8749) 0,5151 (0,0001) 4,93613 (0,0000) 0,16858 (0,0000) 0,74015 (0,0000) Φ1 0,06452 (0,6881) 0,6228 (0,0000) -0,14394 (0,0000) 0,02652 (0,0000) -0,00397 (0,9367) Φ2 -0,09927 (0,1526) -0,476 (0,0000) -0,11961 (0,0000) -0,01546 (0,0008) -0,00288 (0,9554) Φ3 0,05216 (0,4403) 0,2506 (0,0000) -0,13608 (0,0000) -0,00597 (0,1467) -0,05111 (0,1736) Φ4 -0,02733 (0,5891) -0,078 (0,0145) -0,12753 (0,0000) 0,02661 (0,0000) 0,02709 (0,5014) Φ5 0,00415 (0,9460) -0,1784 (0,0000) -0,12806 (0,0000) -0,07225 (0,0000) -0,04993 (0,1813) Φ6 0,02990 (0,7538) 0,3045 (0,0000) -0,13876 (0,0000) 0,03155 (0,0000) 0,01786 (0,6650) Φ7 0,88947 (0,0000) 0,4597 (0,0000) 0,8765 (0,0000) 0,97835 (0,0000) 0,9259 (0,0000) Variance equation ω -0,01876 (0,9980) 0,0003 (0,3775) ,21809D_-05 (0,0000) ,17166D-₀₅ (0,0000) 0,00011 (0,0628) α 0,00031 (0,9943) 0,5671 (0,0000) -0,00177 (0,0000) ,28244D-₀₄ (0,2627) 0,2406 (0,0000) β 1,83619 (0,9681) 0,4788 (0,1165) 1,59577 (0,0000) 20,1277 (0,0000) 1,96833 (0,0029) Adj, R2 0,35718 0,2586 0,25906 0,27999 0,28306 Log likelihood -465,007 973,987 1032,75 1343,166 1119,51513

From Table 5, a few patterns emerge. In the mean equation, the weekly seasonal lag Φ7 is significant in Sweden and in all regions, which indicates a weekly seasonal

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6.3. Results from GARCH model with prices, log(wind) and log(load)

In Table 6, results for the GARCH model derived from Equation (8) and (9) can be found, with the autoregressive parameters Φ1- Φ7, log(wind) 𝑤 and log(load) 𝑙 in the

mean equation and ω, α, β, log(wind) 𝑤 and log(load) 𝑙 in the variance equation for Sweden and for regions SE1, SE2, SE3 and SE4, respectively. P-values are within parenthesis.

Table 6: Results from GARCH model with prices, log(wind) and log(load)

Mean

Constant -2,99489 (0,6844) 2,0848 (0,0000) 0,1998 (0,20738) 0,40699 (0,0590) 0,11865 (0,0003) Φ1 0,16883 (0,5313) 0,1309 (0,1419) 0,07586 (0,03418) -0,02217 (0,5624) 0,00027 (0,7833) Φ2 0,02490 (0,2754) -0,0111 (0,8293) -0,04439 (0,02778) -0,01139 (0,7657) 0,00797 (0,0010) Φ3 -0,00042 (0,7872) 0,1093 (0,1095) 0,03821 (0,03000) -0,03696 (0,3151) -0,03118 (0,0020) Φ4 0,04306 (0,0887) 0,0454 (0,7262) -0,03399 (0,02996) 0,073 (0,0307) 0,04845 (0,0000) Φ5 -0,33210 (0,2230) -0,3169 (0,0003) -0,01797 (0,02169) -0,06153 (0,0638) -0,02981 (0,0049) Φ6 0,15296 (0,2958) 0,0242 (0,6588) 0,01823 (0,02423) 0,00608 (0,8744) 0,04621 (0,0001) Φ7 0,06799 (0,0000) 0,1984 (0,0275) 0,95016 (0,03243) 0,96221 (0.0000) -0,02545 (0,0054) Log(wind) 0,00504 (0,0472) 0,01319 (0,7950) 0,0193 (0,88560) 0,02069 (0,8584) -0,01659 (0,8525) Log(load) 0,54824 (0,9872) 0,24587 (0,6574) 0,10367 (0,70070) 0,22685 (0,8110) 0,10763 (0,8251) Variance equation ω -0,00724 (0,9980) 0,0023 (0,0000) 0,0006 (0,00130) 0,0004 (0,0722) ,35284D-04 (0,0000) α 0,06782 (0,9943) 0,0066 (0,5987) 0,14746 (0,02850) 0,00011 (0,9181) ,85618D-04 (0,2728) β 0,67654 (0,9681) 0,9656 (0,0000) 0,94927 (0,17670) 1,59077 (0,0054) 9,93064 (0,0000) Log(wind) 0,02564 (0,8736) 0,0065 (0,0096) -0,00055 (0,00203) -0,00151 (0,4419) -0,01332 (0,1477) Log(load) 0,52002 (0,8017) 0,2105 (0,0000) -0,01012 (0,00985) 0,00804 (0,6712) 0,96846 (0,0000) Adj, R2 0,56744 0,4227 0,31024 0,35691 0,33486 Log likel. -2965,273 678,9187 1302,0714 1257,3291 1257,51

Results from the mean equation in SE indicate that that 𝜙! and 𝜙! are significant, as

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𝛼 (the impact of new shocks) is insignificant at this level. The sum of 𝛼 + 𝛽 = 0,9722 < 1, which indicates that the conditional variance is mean-reverting. In other words, effects from shocks are not permanent but temporary. All variables are positive.

Similarly, parameters 𝜙_! - 𝜙_! in SE2 in the mean equation are significant at a 10% significance level. The variance equation indicates that 𝜔, 𝛼, Log(wind) and Log(load) are all significant at a 10% level. The value 0,94927 of 𝛽 indicates the persisting impact of past shocks, while the value 0,14746 of 𝛼 indicates the impact of new shocks. The sum of 𝛼 + 𝛽 = 1,09673 > 1, which indicates that the conditional variance is not mean-reverting. In other words, effects from shocks are permanent. Log(wind) and Log(load) are negative, all other variables are positive. A glimpse at the results for region SE3 also provide some insights. The constant and parameter 𝜙_! in the mean equation are significant at the 10% significance level. In line with previous reasoning, the parameter indicates seasonal weekly variation. The sum of 𝛼 + 𝛽 = 1,59088 > 1, which indicates that the conditional variance is not mean-reverting. In other words, effects from shocks are permanent. 𝜔 and 𝛽 in the variance equation are significant at a 10% level. The value 1,59077 of indicates the impact of new shocks. Log(wind) is negative, yet insignificant, all other variables are positive.

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6.4. Results from the GARCH model with prices, log(wind), log(load) and wind penetration

In Table 7, results for the GARCH model derived from Equation (10) and (11) can be found, with the autoregressive parameters Φ₁- Φ₇, log(wind) 𝑤, log(load) 𝑙 and wind penetration 𝑝 in the mean equation and ω, α, β, log(wind) 𝑤, log(load) 𝑙 and wind penetration 𝑝 in the variance equation for Sweden and for regions SE1, SE2, SE3 and SE4, respectively. P-values are within parenthesis.

Table 7: Results from GARCH model with prices, log(wind), log(load) and wind penetration

Mean

Constant 0,08124 (0,6844) 1,192 (0,0000) 3,67998 (0,0000) 0,43407 (0,0000) 0,1373 (0,3770) Φ1 0,03387 (0,5313) 0,1199 (0,0900) -0,19587 (0,0000) -0,00833 (0,1330) -0,01594 (0,1680) Φ2 -0,07317 (0,2754) -0,0174 (0,2742) -0,03818 (0,1158) 0,00036 (0,9535) 0,00568 (0,6502) Φ3 0,01937 (0,7872) 0,0272 (0,1273) -0,1598 (0,0000) -0,03121 (0,0000) 0,06243 (0,0952) Φ4 0,05526 (0,0887) 0,05 (0,2272) -0,06575 (0,0044) -0,00061 (0,8827) 0,03337 (0,3890) Φ5 -0,04994 (0,2230) -0,1497 (0,0000) -0,00416 (0,8055) -0,00787 (0,0781) -0,01366 (0,7201) Φ6 0,04061 (0,2958) -0,0155 (0,6706) -0,16424 (0,0000) 0,00583 (0,1985) 0,00686 (0,8664) Φ7 0,92827 (0,0000) 0,0635 (0,0049) 1,00756 (0,0000) 1,00329 (0,0000) 0,02062 (0,6254) Log(wind) 0,01803 (0,0472) -0,0164 (0,7116) -0,00122 (0,9791) 0,01223 (0,8788) 0,05765 (0,6487) Log(load) 0,00032 (0,9872) 0,29228 (0,6648) 0,13154 (0,7305) 0,23543 (0,8107) 0,03923 (0,8893) Wind/load -0,33653 (0,0061) 0,6234 (0,7494) 0,22403 (0,8109) 0,16035 (0,8160) -0,2176 (0,7284) Variance equation ω 0,00019 (0,5596D_-04) 0,0041 (0,0000) 0,00029 (0,0000) ,87587D-05 (0,0003) 0,00083 (0,0023) α 0,10421 (0,06171₎ -0,0466 (0,0000) -0,0006 (0,0000) ,79054D-04 (0,2549) 0,018 (0,1653) β 1,68072 (0,82476₎ 0,7421 (0,0000) 1,29998 (0,0000) 10,0988 (0,0000) 1,6132 (0,0307) Log(wind) 0,02457 (0,8398) -0,0082 (0,2163) 0,01132 (0,0000) 0,0067 (0,0000) -0,04661 (0,0905) Log(load) 0,52116 (0,8050) 0,3513 (0,0000) -0,03741 (0,0000) -0,02247 (0,0000) 0,03208 (0,3814) Wind/load 0,01252 (0,9786) 0,3449 (0,0090) -0,15636 (0,0000) -0,15381 (0,0000) 0,95312 (0,0000) Adj, R2 0,56684 0,431 0,31299 0,35623 0,33892 Log likelihood 1321,709 655,656 926,23937 1411,5904 1215,364

The results from Table 7 indicate that in the mean equation for Sweden as a whole, 𝜙!and 𝜙! as well as the variables Log(wind) and Wind/load (wind penetration) are

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indicates the effect of current shocks and a 𝛽-value of 1,68072 indicates the effect of past shocks. The sum 𝛼 + 𝛽 = 1,78493 > 1, which means that the market in non-mean-reverting. In other words, effects from past shocks are permanent.

Results from the mean equation in region SE1 indicates that the constant, parameters 𝜙!, 𝜙!, and 𝜙! are significant at a 10% level. While the significance of 𝜙!and 𝜙! is of

little interest, the seventh lag term 𝜙! represents the weekly seasonal variation. Results

from the variance equation indicate that 𝜔, 𝛼, 𝛽, Log(load) and Wind/load are all significant at a 10% level. The value 0,7421 of 𝛽 indicates the persisting impact of past shocks, while the value -0,0466 of 𝛼 indicates the impact of new shocks. The sum of 𝛼 + 𝛽 = 0,6955 < 1 , which indicates that the conditional variance is mean-reverting. In other words, effects from shocks are not permanent but temporary. All variables except 𝛼 and the insignificant Log(wind) are positive.

Similarly, in the second region SE2, the constant and parameters 𝜙_!, 𝜙_!, 𝜙_!, 𝜙_! and 𝜙_! in the mean equation are significant at a 10% significance level. The variance equation indicates that 𝜔, 𝛼, 𝛽, Log(load) and Wind/load are all significant at a 10% level. The value 0,1,29998 of 𝛽 indicates the persisting impact of past shocks, while the value -0,0006 of 𝛼 indicates the impact of new shocks. The sum of 𝛼 + 𝛽 = 1,29938 > 1, which indicates that the conditional variance is not mean-reverting. In other words, effects from shocks are permanent. 𝛼, Log(load) and Wind/load are negative, all other variables are positive.

The Impact of Wind Power Production on Electricity Price Volatility

The Impact of Wind Power Production on

Electricity Price Volatility

A Time-Series Analysis

Alexander Wirdemo

MASTER’S THESIS

The Impact of Wind Power Production

on Electricity Price Volatility

A Time-Series Analysis

Alexander Wirdemo

2017

Economics

Luleå University of Technology

2017-07-05

Abstract

Sammanfattning

Acknowledgements

Table of Contents