Hedging the temperature dependence of electricity demand in the
Dutch Electricity market with weather derivatives
Thesis
Master of Science in Business Administration Specialisation: Finance
University of Groningen Faculty of Economics and Business
Abstract
This paper uses a GARCH (1,1) model to test the existence of a V-shaped relation between electricity demand and air temperature in hourly data. The temperature for which electricity demand is assumed to be minimal is set at 16 ⁰C. The V-shaped relation is found during the period 2006-2011. Yearly estimations show that the increase in demand due to hot temperatures is not observed in every year. Insignificant coefficients are found during years in which the average summer temperature was close to the base temperature. An assessment of dynamic effects proves that increased demand due to heating needs is more persistent than demand increases due to cooling needs. A robustness check on the base temperature confirms that 16 degrees Celsius is the temperature at which electricity demand is at its minimum in The Netherlands. Furthermore a model is developed to assess the exposure of an electricity retailer to temperature fluctuations. The model is built on the assumption that market participants hedge their price exposures in the forward market. The model is tested with a constructed estimate for the cost function of an electricity distributing firm. Due to the restrictive assumptions underlying this variable, the results should be interpreted with caution. It is shown that temperature derivatives might be able to mitigate quantity risks in the electricity market, although the performance with this model is rather poor. Further research in which the model is tested with real company data is needed.
JEL classification
G11, L94
Keywords
1. Introduction
Around the millennium change, electricity markets in Europe and the United States have undergone a major transition. Before, electricity markets were considered a public responsibility. Energy supply and distribution was taken care of by regulated utilities who enjoyed regional monopolies. In Europe the transition started due to the acceptance of European Directive 96/92/EG1 at the end of 1996, in which the joint regulations for internal electricity markets are laid out. The Dutch electricity sector found itself starting the transition towards a competitive market environment in 1998 when the “Elektriciteitswet 1998”2 was accepted by the parliament.
Since the transition towards a market based electricity market, market participants have become increasingly aware of the market risks to which their business is exposed. The most apparent risk for most market parties is price risk. After the liberalization of various electricity markets, we have seen some extreme price spikes in wholesale markets, for example during the summer of 1998, when wholesale prices reached $7000 per MWh in the Midwest of the U.S., while the average price was in the range of $30 to $60 during that period. In the Netherlands prices spiked regularly in the year 2006, reaching levels of up to €900 per MWh, which is approximately 1750% above average. The occurrence of these price spikes has in some cases led to the bankruptcy of companies who were exposed to price fluctuations, emphasizing the need for proper hedging strategies for the market participants.
If we compare the volatility of electricity prices with the volatility in prices of other tradable commodities, it should be noted that volatility levels in electricity prices usually exceed those of other commodities. The reason for this is mainly the non-storability of electricity. Although it is technically possible to store electricity in for example large batteries, it is economically infeasible to do so. This basically means that the demanded amount of electricity has to be produced
simultaneously. Within the technological boundaries of the production portfolio, market participants need to balance supply and demand at every moment. This feature, combined with the rather inelastic price elasticity of electricity has led to situations in which the production side of the market reached its boundaries and as a consequence prices spiked.
Popular tools to hedge price exposure are futures and forward contracts. By means of these contracts, firms can fix the price for which they are selling/buying electricity for some
moment/period in the future. While this leads to price certainty for the firms involved in the futures
1
The directive can be found at:
http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:1997:027:0020:0029:EN:PDF
or forward contracts for the specified amount of electricity, it does not provide adequate insurance against quantitative risks. Take for example an electricity retailer, who buys electricity in the wholesale market, to sell it in the retail market for a fixed price per MWh. If the retailer wishes to hedge price risk, he will buy electricity forward in the wholesale market. However, the retailer cannot know on beforehand whether the consumption will be equal to the amount of electricity he bought in the forward contract. Typically, when demand exceeds expectations, the retailer needs to purchase additional electricity in the spot or intraday market. Since the unexpected additional demand has to be produced within the technical limitations of the production technologies, the more flexible and more expensive power plants will be used to serve the additional demand. This logically leads to higher prices in the wholesale market. In the case of a negative demand shock, the retailer needs to sell its surplus of electricity which was bought forward on the wholesale market, leading to lower wholesale prices. When the wholesale prices drop below the price for which the electricity was bought in the forward market, the sale of the surpluses causes a loss for the retailer. Thus in the presence of a demand shock, the retailer faces quantitative risk which is positively correlated with the additional price risk.
The question at hand is: What drives electricity demand and how can the various market participants hedge against demand shocks. Electricity demand is considered to be affected by a large number of variables. Among others, temperature plays an important role in determining the quantity of electricity demanded. During hot periods people tend to use air-conditioning or ventilation systems, whereas during cold periods people might use electric heaters. Especially during hot periods the market risks increase rapidly, since a higher temperature of cooling water lowers the capacity of the production portfolio simultaneously with the increased demand. Since temperature plays an
important role in both the production and consumption side of the market, it is of interest for market participants to hedge against these temperature risks. Since every distinct part of the electricity supply chain has a different temperature dependence of their cash flows, it is chosen to focus on the retailers, who buy their electricity in the wholesale market and sell it under fixed contracts in the retail market, for the hedging part of this paper.
hedging scheme based on heating degree day and cooling degree day3 options, to evaluate whether it can mitigate the temperature risks faced by electricity retailers.
Both questions will be evaluated by means of regression analysis. In the presence of ARCH effects, a GARCH (1,1) model is used in both cases. The model which is used to evaluate the effect of
temperature fluctuations on Dutch electricity demand is a modification of the model used in Hekkenberg et al. (2009). Whereas the model used by Hekkenber et al. (2009) was very basic and minimalistic, the model in this paper incorporates various additional variables which have an impact on electricity demand. The model used for determining the optimal temperature hedge for the retailing firm relates daily temperatures with the assumed cash flows of the retailing firm. More details of the models can be found in the methodology section of this paper. This paper focusses on the period 2006-2011, for which hourly data is used in the electricity demand model and daily data is used in the hedge optimization model. The exact description of the data used in the models can be found in chapter 5. In the results we observe the expected V-shaped relation between electricity demand and temperature. However, the increased demand due to high temperatures is not found to be consistent for every year in the sample. The effectiveness of a temperature hedge for a retailing firm is evaluated on the basis of various performance indicators. In this paper the standard deviation, Dollar offset method and variability reduction method are used.
We will commence with a description of several interesting aspects of the electricity market that are of relevance for this research in chapter 2. In chapter 3 a literature review is presented. Chapter 4 will describe the methodology used in this paper. In chapter 5 the data for this empirical study is discussed. Chapter 6 presents the results and a conclusion is given in chapter 7.
3
Cooling degree day options pay an amount of money for every degree by which the average daily
2. Electricity market
This chapter will give a brief description of the Dutch electricity market and highlight several relevant aspects with respect to the research performed in this paper.
2.1. General characteristics
The electricity market is a competitive market in which the interaction between supply and demand determines the outcome in terms of price and quantity. Electricity, however, is a rather specific good. Unlike most other goods, the production and consumption occur simultaneously. Basically this means that when an electric device is turned on, additional electricity needs to be generated at the same moment in time in order to address the increased demand. This characteristic of the electricity market is caused by the fact that large quantities of electricity cannot be stored in an, from a
business perspective, profitable way and the instantaneous nature of electricity transportation. Since electricity was invented, its role in our everyday life has ever increased in importance. Nowadays one can argue that a reliable supply of electricity is a matter of national economic importance. To guarantee the stability of electricity supply within a competitive market, a special regulatory framework is put in place. It should be noted that the supply of electricity to the consumers is a competitive market, while the transportation of the good is carried out by various firms enjoying regional monopolies. Within the Dutch market for electricity we can distinguish various different types of firms. First of all the consumers contract their needs at an electricity supplier. Some of these retail suppliers are electricity producers as well, others focus purely on intermediating between the wholesale and retail market. The electricity is transported through the transmission network. The lower level networks are operated by various regional network operators. The high voltage network is operated by the transmission system operator (TSO) Tennet. Tennet is furthermore responsible for balancing the national network. It achieves this balance by constantly quoting imbalance prices. In cases of electricity shortage, the imbalance prices rise. In this way producers can profit from firing up additional capacity or large scale consumers can save money by decreasing their electricity demand. These imbalances are billed to the so-called
while the suppliers are jointly responsible for the stability of the network. The role and
responsibilities of the PV and Tennet are the key to ensuring the network stability within a market based framework.
Another interesting aspect of electricity markets is the price elasticity of demand. Since a large share of electricity consumers are on fixed contracts, the incentive to cut down consumption when prices increase is limited to a group of large scale consumers. These industrials purchase their electricity directly in the wholesale market and are thus exposed to price fluctuations in for example the Amsterdam Power Exchange (APX) spot market. All in all this leads to the situation where the demand for electricity is said to be rather inelastic. Therefore, the balancing of supply and demand through price movements does not perform as good as in certain other markets where the price elasticity of demand is at higher levels. The group of industrials who are exposed to wholesale price levels do make sure that electricity demand is not totally inelastic. It has been reported4 that during price spikes some firms would decrease their electricity consumption and resell the electricity in the market as this was more profitable than using the electricity for the core operations of the firm.
2.2 Technologies
At the supply side of the market we observe a variety of electricity generating technologies. In Figure 1 we can see that in the Netherlands the largest share of electricity is supplied by gas fired power plants. The endowment of the country with natural gas makes gas plants
relatively favorable. Apart from gas plants we see a vast share of coal power and smaller shares of nuclear and renewable energy. The
technologies vary in their cost functions and technical characteristics. Focusing on the technical differences, it should be noted that gas plants are relatively more flexible in terms of firing up and
4
In the magazine Forum distributed by VNO NCW in the article: “Ook grote afnemers kunnen inspelen op prijsschommelingen: De bijzondere spelregels van de stroombeurs”
shutting down then coal plants5. Wind energy, in contrast, is somewhat harder to adjust. The typical aspect of wind energy is that its level of production is dependent on the wind strength, which means that one can never forecast the amount of wind produced electricity with certainty. The amount of wind energy supplied in the market is adjustable by the option for the wind farm owner to shut down operations. Since his input is available for free, the wind farm owner will want to avoid shutting down operations and will always6 supply the produced electricity to the market. The intermittent
nature of wind energy needs to be balanced by the other available technologies in the market. With respect to the weather dependence of the production technologies, wind is not the only factor influencing electricity supply. Cooling water temperatures play an important role in determining the capacity of thermal power plants. Especially during prolonged warm periods significant decreases in capacity can be observed.
With a different cost function for every power plant, there exists a merit order which ranks the plants from low marginal costs to higher. The place of a specific plant in this merit order determines
whether or not a plant is operating at a specific point in time, depending on the level of demand and the technological boundaries regarding the flexibility of its dispatch. The merit order changes over time. As input prices fluctuate, plants may shift from the left to the right in the merit order. On the basis of present market prices and technologies, we usually see wind and solar power at the left side of the merit order. This has to do with the freely available inputs and thus exceptionally low marginal costs. The next in line on average are nuclear, coal and gas powered plants respectively, with the marginal costs of gas power plants being the highest on average. Figure 2 gives an overview of the cost structure of the various available technologies. The purple segment of the cost line gives a rough estimation of the marginal costs faced by the plants using that technology. The ordering of the technologies in Figure 2 is opposite to the ranking of them in the merit order, with the exception of coal & biomass. It should be noted that even though wind energy does not have any variable costs, the high fixed costs lead to a situation in which wind energy is not yet competitive with gas and coal power.
5
In a letter to the Ministry of Economic Affairs the ECN stresses the relative start up and turn down times for coal plants are larger than those of gas plants. The relative inflexibility of coal plants could lead to supply exceeding demand or vice versa under certain conditions.
6
This is only true in case of positive electricity prices. In Germany negative electricity prices have been
Figure 2, overview of generation costs of different technologies including fixed and external costs. CCGT stands for combined cycle gas turbine, CHP means combined heat and power, CCS is carbon capture and storage and EPR stands for European pressurized reactor.
Source CE Delft: “Nuclear energy: The difference between costs and prices, page 9.
Figure 3, the average marginal cost curve for The Netherlands for the years 2006-2009. The curves are based on modeled marginal costs for Dutch power plants.
Source: “Monitor groothandelsmarkten gas en elektriciteit 2010” by the energiekamer of the NMa, page 64.
2.3 Trading
Apart from the responsibility of the PV to balance supply and demand for electricity within their portfolio at every point in time, electricity trading is not very different from regular commodity trading. The parties involved in the wholesale market have various options available to purchase or sell electricity. One option is to trade electricity in the over the counter (OTC) market. Here it is possible to tailor electricity deals to specific demands. Another option is to trade electricity on a power exchange, on which standardized products are traded. In The Netherlands the power exchange is operated by the company APX ENDEX. At this exchange long term and short term markets are available. The long term market is called the ENDEX, here trades with delivery dates ranging from 4 weeks up to years in the future are conducted. The APX (short for Amsterdam Power Exchange) market is there to serve the demand for short term trading. At the APX market, deals are being made for delivery during a specific hour the next day. APX ENDEX also offers an intraday market which can be used to adjust for last minute imbalances in the portfolio in order to avoid additional imbalance costs billed by the TSO.
2.4 Hedging
we investigate for example the market risks of an electricity retailer, who delivers electricity to consumers at a fixed price and buys electricity in the wholesale market, we observe that the retailer is exposed to both price and quantity risk. To hedge against price risks, the retailer usually purchases the expected amount of electricity through a forward contract. If the quantity demanded by its customers exceeds the amount which was bought under the forward contract, the retailer is exposed to price risk for the additional amount. If, on the other hand, expectations were too high, and
consumers consume less than expected, the retailer will have to sell the surplus on the spot market. Under the assumption that all market parties experience the same deviations from expected demand, prices in the spot market will increase when demand exceeds expectations and prices will decrease when demand is less than expected. Both these scenarios are unfavorable for the retailer. In the first case he has to buy additional electricity at high prices, whereas in the second case he has to sell the surplus at a low price, most likely lower than the initial purchase price. Thus after
purchasing electricity forward, the retailer is still susceptible of quantity and price risks.
As stated in Oum et al. (2005), electricity markets are incomplete markets7 in general, since not every risk factor can be hedged by market traded instruments. In particular, the quantity risk described above is not traded in the market. This means market participants are limited to derivatives which partially hedge a certain exposure. Since the demand for electricity generally shows a strong correlation with temperatures, weather derivatives are often used to hedge against the risks described above.
3. Literature review
When reviewing the literature regarding the topic of this paper, we can broadly divide the papers in two groups: papers regarding the temperature dependence of electricity demand and papers investigating methods to hedge quantitative risks in the electricity and other markets.
3.1 Electricity demand and temperature
The relationship between electricity demand and air temperature has frequently been studied for various regions in the world. In Hekkenberg et al. (2009) we find a regression analysis for the Dutch electricity market. With a rather simple and straightforward approach it is suggested that the coefficient determining the relation between demand and temperature has shifted from negative to positive during the summer months in the period 1970 – 2007. This basically means that during the
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beginning of that period, electricity demand used to decline during hot days. Around 1990, the first positive coefficients during summer months are observed, indicating increased electricity
consumption during high temperature periods.
As mentioned above, the methodology used by Hekkenberg et al. (2009) is rather simplistic. A large number of separate regressions are conducted for every month in the dataset. The dependent variable is daily electricity consumption and the explanatory variable is the average daily
temperature. Since the amount of electricity consumption during weekends and national holidays is significantly lower than during working days, the authors have decided to drop these observations from the sample. This leads to a loss of one third of the observations in the sample, meaning that the estimations are made based on an average of 20 data points per regression. Furthermore it should be noted that no other variables are included that could have an impact on electricity consumption. The authors admit that this simple setup is bound to be subject to significant amounts of noise in the results. It is argued that it is not the aim of the paper to estimate the exact relation between
temperature and electricity demand, the main goal is to assess whether the increased use of cooling devices has led to a shift in temperature dependence in The Netherlands. The results of the study do signal increased electricity usage during warm periods during recent years.
Lee and Chiu (2011) use a panel smooth transition regression (PSTR) model to estimate the determinants of demand for electricity in 24 OECD countries. The model, with electricity
consumption as dependent variable and electricity price, real GDP per capita and temperature as dependent variables is estimated with yearly data. In the results, a U-shaped relationship with temperature is found with the threshold value at approximately 15 ⁰C. Furthermore, they find evidence for increasing demand elasticity with respect to temperature during the timeframe under investigation, suggesting the importance of temperature on electricity demand is increasing. This is consistent with the results found by Hekkenberg et al. (2009) for The Netherlands. Another
interesting finding of Lee and Chiu (2011) is that the elasticity of demand varies significantly from region to region, indicating the effect of cultures and climates with respect to electricity demand. Although Lee and Chiu (2011) demonstrates the importance of non-linear estimation when analyzing the dependence of electricity demand on temperatures, it can be doubted whether the methodology used in the paper captures the non-linear relation in the proper way. The PSTR model allows
for data points with temperatures above and below this threshold value. Lee and Chiu (2011) determine which variable to use as threshold variable by testing which variable shows the strongest non-linearity. A model with income as threshold variable is found to be optimal, but the models with the other variables as threshold variable are regressed as well. It should however be noted that with income or price selected as threshold variable, the model is not capable of capturing the V-shaped8 temperature dependence. Resulting in for example a negative temperature elasticity in the optimal model for Spain, a country for which positive elasticity at higher temperatures is found by, among others, Pardo et al. (2002) and Cancelo et al. (2007).
Bessec and Fouquau (2008) uses the same PSTR model with a dataset containing monthly data of 15 European countries. Temperature is used as the threshold variable. The threshold value is located at 16 degrees Celsius for their entire sample, meaning that electricity demand is at its minimum at 16 degrees. Furthermore separate regressions are done for a group of South European countries and for a group of countries located in the Northern part of Europe. They find that the non-linear relation between temperature and electricity demand is more pronounced in the warmer countries. Furthermore, Bessec and Fouqaua also find an increasing temperature elasticity of demand during the sample period. They argue that the elasticity has increased over the years due to the increased penetration of air-conditioning systems and the technological advancements making the equipment cheaper. An interesting aspect of this study is the way in which the influences of other factors than temperature are eliminated from the demand for electricity series. Three different filters are tested, a third degree polynomial trend function with a term for monthly manufacturing is considered to be the best filter. The filtered demand, which is given by the residuals of the filter function, is then used as input in the PSTR model. This methodology is somewhat different compared to Lee and Chiu (2011), who directly include the additional variables in the PSTR model. Another difference between the two studies is the assumption by Bessec and Fouquau (2008) regarding the price elasticity of demand. Since no price variable is included in the model it is assumed to be zero. This assumption might lead to an underestimation of the temperature elasticity.
In the papers discussed above, the frequency of the data used varies from daily to yearly data. It is interesting to see that with every different frequency the non-linear relation between temperature and electricity demand is found. Though results obtained with higher frequency data do establish the link with more precision. For example yearly analysis does not provide a clear insight in the exact timing of the demand increases. The higher demand witnessed during years with on average higher temperatures could as well be caused by some external factor during the cooler periods of that year.
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With respect to higher frequency data, Peirson and Henley (1994) emphasizes the dynamic nature of the relation between temperature and electricity load9. Various dynamic models are tested and evaluated. It is concluded that forms of autoregressive specification give a good explanation of present load.
3.2 Hedging quantitative risks in the electricity market
Regarding risk management in the energy sector by using electricity derivatives, Deng and Oren (2006) gives a formidable overview of the available derivatives and their applications. It is also mentioned that derivatives explicitly constructed to hedge against quantitative risks are usually unavailable in the marketplace. To overcome the absence of these types of derivatives, the application of weather derivatives is suggested, as load usually fluctuates with temperatures. Another strategy is proposed by Oum et al. (2005). The authors suggest optimizing a utility function for the load serving entity (LSE). Two different utility functions considered by the authors are a constant absolute risk aversion utility function and a mean-variance approach, in which utility increases with mean profits and decreases in variance. It is mathematically proven that the payoffs associated with the maximization of the utility functions can be produced by a set of standard electricity derivatives10. While the theoretical proof is solid for the proposed strategy, some
assumptions make its performance in practice questionable, for example the assumption that the LSE can borrow an unlimited amount of money in order to get the hedging portfolio in place. In order to come to conclusions about the efficiency of the proposed approach, the method should be
empirically tested.
In order to hedge quantitative risks in the electricity market, one first needs to construct a function that is able to forecast the load for some moment in the future. Soares and Medeiros (2008) develop a two stage forecasting model which is tested in an area in the South-East of Brazil. In the first stage, an OLS regression is used to remove seasonality and other deterministic trends from the demand series. In the second stage, a linear autoregressive model is used on the residuals of the first step. The developed model proves to be an improvement over the benchmark model, which is a seasonal integrated autoregressive moving average model. The decision of the authors not to include weather variables in the model should be noted. Their main argument is that the weather differences within the region of investigation are too large to include a sensible weather variable.
Pardo et al. (2002) uses an autoregressive model which also corrects for the dynamic relationship between temperature and electricity load, which is tested in the Spanish market. The model proves
9
The amount of electricity consumed is often referred to as electricity load.
to contain high predictive power. An interesting finding is the difference between the dynamics of temperature and electricity demand on cold and hot days. On heating degree days (HDD) a lag of 4 days still shows up significant in the test results, whereas during a cooling degree day (CDD) only one lag proves to be significant. HDD and CDD are thought to provide a good estimate for the amount of energy that is needed for either heating or cooling purposes. The HDD and CDD variable indicate the number of degrees below or above a base temperature respectively. The base temperature can be seen as the point at which energy demand is at its minimum. The above finding indicates that the effect of low outside temperatures on electricity demand is more persistent. The separate inclusion of a CDD and HDD variable allow the relation between cold days and electricity demand to be different from the influence of hot days on electricity demand. The higher coefficient for HDD, which is highly significant, proves this separation of temperature effects into variables for hot and cold days is beneficial in analyzing the factors influencing electricity load. In the light of mitigating temperature risks with HDD and CDD options, it is convenient to construct the forecast model with separate variables for HDD and CDD.
A theoretical application of weather derivatives serving as risk management tools in the electricity market is shown in Mount (2002). In a conceptual and highly simplified electricity market, the possibility of constructing a mutual beneficial forward contract for a generating company with a distributing company is explored. Risk averse utility functions are introduced for both companies. On the basis of peak price probabilities and its correlation with high temperature days, the forward is constructed in such a way, that the distributing company always pays a fixed price for its electricity, with a mark-up during a hot day. Structuring a forward deal in this fashion leads to perfect
correlation of high prices with hot days. A collar strategy with CDD options is proposed to perfectly hedge the risks involved in the realized number of hot days. In the end the proposed strategy results in utility increases for both companies and zero volatility in earnings. Although the concept of the electricity market used in this paper is highly simplified compared to the real world, the
computations and conclusions do prove that, when the construction of the forward contract is aimed at strengthening the relation between hot days and price movements, temperature derivatives can be valuable risk management tools. A very fundamental point of criticism to the framework proposed is the lack of demand uncertainty. Quantities are always known, and only fluctuate between the hot and cold day regimes. In practice it is exactly this uncertainty for which weather derivatives are considered a valuable hedging tool.
briefly touch upon the subject by proposing a weather derivative hedging strategy suitable for the electricity market. The proposition is an extension of the main subject of the paper; the spatial risk premia of European cumulative average temperature (CAT) futures. The performance of the
proposed hedging scheme is not addressed in the paper, making it impossible to draw conclusions on whether this hedging scheme is feasible for the industry.
Further insights in the performance of weather derivatives as hedging instruments can be found in studies focusing on the gas or agriculture market. Fleege et al. (2004), Vedenov and Barnett (2004) and Chen et al. (2006) assess the performance of weather derivatives in agricultural businesses. Fleege et al. (2004) analyzes yield/profit functions of raisins, nectarines and almonds in California to test the performance of CDD options to hedge the farmers his profits. It is concluded that the hedge proves to be most valuable in cases where a natural hedge11 is less pronounced. Simple long-put,
long-call and long-straddle option strategies prove to be effective in increasing expected firm profits. Chen et al. (2006) finds hypothetical weather derivatives with payouts based on temperature to be effective means of reducing variance in profits for dairy farmers in the US. Vedenov and Barnett (2004) constructs optimal weather derivatives based on econometric analysis for different soybeans, corn and cotton producing districts in the US. They find that hedging performance varies significantly over crops and regions. The major difference between testing the application of weather derivatives in agriculture and energy markets is the lack of feasible storage possibilities for electricity, and the dependence of agricultural supply on weather factors, whereas in energy markets the weather effects are more pronounced at the demand side of the market. In a study of the application of weather derivatives in the US natural gas market, Leggio and Lien (2002) finds the use of a
combination of price and temperature derivatives to be optimal in reducing the chance of high gas bills for the consumers. The reduction of high gas bills for consumers is beneficial for gas utility companies, as this reduces dissatisfaction of consumers with high gas bills. In this market the consumers are directly influenced by the price movements in the wholesale market, leading to the situation where it is desirable when the gas utility company hedges its price and weather exposures, so that stable prices for the end consumers are ensured. Tests on the effectiveness of the proposed hedging strategies are conducted both in and out of sample; both results signal the potential benefit of hedging with weather derivatives.
All in all, the effectiveness of temperature derivatives has been proven for industries other than electricity. In addition to this, the link between electricity consumption and temperature, which is well documented in the literature discussed above, hints at possibilities for successful
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implementation of temperature hedging schemes in the electricity sector. Although the discussed papers do not directly address the application of weather derivatives in the electricity market, numerous useful insights can be obtained from them. For example the methodology used by Pardo et al. (2002), which treats hot and cold days as separate variables, is a useful insight to keep in mind when developing the methodology for this paper. Furthermore, the methodology used in
Hekkenberg et al. (2009) gives good guidance in how to test for a relationship between electricity demand and temperature using a relatively simple model.
4. Methodology
With the obtained insights from the literature discussed above, this chapter will develop two models to answer the research questions of this paper. First we have to develop a model which is capable of capturing the fluctuations in energy demand. Second a model which can forecast the optimal purchase of weather derivatives for a retailer will be constructed. In order to evaluate the relation between electricity demand and temperature with as much precision as possible, it is chosen to work with hourly data. After the relationship between temperature and demand has been established by the model, we will continue with testing a simple hedging strategy based on CDD and HDD options during the summer and winter months for an electricity distributing firm. It is chosen to focus on winter and summer months, because in these periods the demand for heating and cooling peaks and the exposure of the electricity sector to temperatures is at its peak as well. Since CDD and HDD options have a daily character, we have to construct a model estimating the dependence of firm profits on weather variables with daily data. Furthermore the multi-market trading character of electricity needs to be incorporated in this model. On the basis of this model it will be tested whether CDD options are a good tool to reduce the variance in firm profits. This chapter will describe the considerations and choices made during the construction of these two models in detail.
4.1 Hourly Electricity demand model
high frequency data. If the presence of ARCH effects is detected, the model is easily converted into a GARCH (1,1) model.
When identifying the factors responsible for the movements in electricity demand, the first thing one should notice are the repeating patterns in the observations. Seasonal, day of the week and daily patterns are observed in the data. Figure 4 gives a plot of the observations for system load12, which is generally assumed to be a good approximation13 of national electricity demand in The Netherlands.
Figure 4, plot of the hourly system load. On the left seasonal patterns are clearly visible. In a more detailed view on the right, daily and intraday patterns can be observed during the period 1-14 January 2008.
Before considering any other variables to include in the model, we have to propose variables to control for the patterns in consumption. Dummy variables for every hour of the day, day of the week and quarter of the year will be used to achieve this. It should be noted that some of the dummy variables will also capture part of the temperature dependence of electricity demand. The
temperature is also subject to daily and seasonal patterns. It is therefore expected that part of the temperature dependence of electricity demand will be captured in the dummy variables. Comparison with the literature and the fact that seasonal and intraday fluctuation in electricity demand are also caused by other influences has led to the decision to include these dummies in the model. Besides the patterns which are now corrected for, there are some more special days and periods in the sample during which demand is notably different from a normal working day. Therefore national
12
The data is taken from the publicly available system load information published by Tennet on its website www.tennet.org
13
System load differs from national electricity demand it includes only the load measured on the high voltage network. Small scale electricity production on lower level networks is not included in the figure.
6,000 8,000 10,000 12,000 14,000 16,000 18,000
celebration days are also assigned with a special dummy variable. Furthermore a significant drop in demand is observed during the Christmas holiday, making it necessary to create dummies for this holiday as well. During the summer holidays, no drop in the demand data is observed. This could possibly be due to the spreading of the holidays over different geographical regions, or the offsetting effect of extra demand due to heating needs and decreased demand caused by the holidays. Since this means we will not be able to capture the effects of decreased productivity with summer holiday dummies, it is chosen not to include these in the model. To avoid the dummy variable trap, always one of the hourly, daily and quarterly dummy variables is left out of the model. This means the coefficients of the dummy variables will indicate the difference from the variable that has been left out. After creating the dummies, a preliminary regression with only the dummy variables as
explanatory variables is done. The residuals of this regression are checked for presence of additional patterns which are not attributable to stationary variables. A clear time trend is witnessed. There are multiple possibilities to capture this time trend in the model. It is chosen to adopt the approach used in Pardo et al. (2002), where the time trend is removed by including a time variable in the regression equation.
Before diving into the relation between temperature and demand, we first need to consider a basic textbook economics effect. Although electricity demand is known to be price inelastic, this does not mean demand is totally price inelastic. The inclusion of a variable for price into the model could therefore be considered an improvement to the model. However, only one of the papers discussed in the previous chapter uses a price variable in their model, suggesting the effect of prices on electricity demand is considered to be insignificant by the majority of the authors. It is decided to stick with the majority and not to include a price variable in the model.
Since the OLS type of models are not capable of endogenously determining the minimum point of the U shaped relation between temperature and electricity demand, we have to impose the value on the model. According to Bessec and Fouqaua (2008) the minimum lies at approximately 16 degrees Celsius for their complete sample of countries. Other studies have found different values, for example Lee and Chiu (2011) find the minimum demand at approximately 15 degrees Celsius.
electricity demand dynamics determine the coefficients of the intraday lagged variables. Information on how persistent responses are to temperature fluctuations are on an intraday basis are therefore difficult to capture with intraday lagged variables. Day to day dynamics are considered by including lags of up to 4 days as is suggested by Pardo et al. (2002). Which lags to include in the model is determined by an iterative process in which the Akaike information criterion (AIC) is minimized. A preliminary regression run indicated the presence of ARCH effects in the residuals, indicating a GARCH model is more suitable for the estimation at hand. We finally arrive at Equation 1, which is a GARCH (1,1) model:
(Equation 1)
With the conditional variance equation:
(Equation 2)
To improve readability, the dummy variables are not written down separately. For instance in
fact denotes a series of 23 separate dummy variables. ED is short for electricity demand, CDD and HDD denote the number of degrees by which the average temperature is above and below 16 degrees Celsius respectively for the hour t. The conditional variance equation is standard for a GARCH (1,1) model.
The model will be estimated for the period may 2006 to September 2011. As a robustness check the model will be tested for every separate year in the sample. Furthermore the robustness of the base temperature will be tested by evaluating the fit of the model with base temperatures ranging from 14 to 18 degrees Celsius.
4.2 Daily weather dependence model for a distributing firm
The model linking the daily profits of an electricity distributing firm to the air temperature in order to evaluate potential hedging strategies is less straight forward, since for competitive reasons no electricity distributing company is willing to share information on daily earnings or profits. This lack of data forces us to create data for a hypothetical company. The hypothetical electricity distributing company we will be investigating buys its electricity in the wholesale market and sells it to
are interested in the quantitative risks this company faces, we do not have to consider the share of electricity bought forward in our model. We should however, assume that this amount of electricity bought forward is based on demand forecasts. Since it is not possible to obtain a reliable weather forecast with a long time horizon, we assume the forecast is based on average values. The
fluctuations in the company its costs arise when weather variables deviate from their average values, causing weather induced demand shifts.
Let us assume that all firms at the demand side of the wholesale market operate as described above, meaning that the amount of electricity traded in the spot market is directly linked to deviations from average temperature values. Aside from temperature, however, wind is also a significant factor in this market. We assume that wind producers sell their electricity forward according to average wind forecasts and the difference between this value and the actual production is settled in the spot market. Besides the wind farm operators, who sell their surpluses or buy shortcomings in the spot market, it is assumed that there are two other groups of traders active in the wholesale market. One group of for example arbitrageurs and speculators, who are assumed to be responsible for a fixed cash amount traded every day, which is free to increase or decrease over time. In our model this amount is captured by a constant and a time trend. The rest of the quantity of electricity traded is assumed to be due to distributing companies balancing demand fluctuations. This means that, except for the wind induced fluctuations, the quantity of electricity traded on the spot market is determined by deviations of demand from average values. Only through these strict and perhaps unrealistic assumptions it is possible to come to an estimation for the costs of the hypothetical electricity distributing company. Variance in the cost function of the firm is brought about by the need to trade on the spot market. Since the amount of electricity traded by arbitrageurs and speculators is
captured in the regression model, we continue with a variable which equals the total amount of electricity traded at the spot market minus the amount of wind farm balancing during that day. After the average amount of wind energy sold forward is estimated, we can determine the amount of trading in the spot market due to wind energy trading. Deducting this from the total amount of electricity traded in the spot market gives us the amount of electricity traded by the other players in the market.
(Equation 3)
( )
In Equation 3, denotes the quantity traded by the distributing firm and the constant amount
traded by the arbitrageurs and speculators. is the amount of electricity traded in the spot
and realized quantity of wind energy. The absolute value is taken, since both lower than average and above average wind production will increase the amount of wind energy trading on the APX market. The quantity traded by the firm is not the only factor responsible for fluctuations in the firm its cash flows. It is assumed that all distributing firms in the spot market are affected in the same way by market fluctuations. These fluctuations are bound to have an impact on spot market prices. The total money amount of the volatile part of the cost function (VCF) in the cost function of the firms which are still included in the variable is equal to price times quantity traded.
(Equation 4)
In which VCF is the volatile part of the cost function of the firms included in and is the
price in the APX spot market. It should be stressed that the volatile part in the cost function is not the only variable cash flow determining the profits of our firm. Earnings are also affected by swings in demand. When demand is lower than expected, the distributing firm will sell less electricity, and therefore generate fewer earnings. In case demand spikes, earnings will increase, but the variable part of the cost function is likely to increase as well. It is however not possible to include the earnings dynamics in our variable. The inputs we have to construct this variable are limited to market price and traded quantity. The difficulty is that the traded quantity rises with both higher and lower than expected demand. It is therefore difficult to determine during which day the distributing firm has to buy additional electricity in the spot market and on which day it sells surpluses. A possibility would be to impose a relationship between temperature and earnings in the variable, by for example assuming that earnings increase when temperatures deviate further from the minimum demand temperature and increase when the temperature moves towards this value. However, this would artificially improve the performance of the temperature hedge. It is therefore decided to abstract from earnings, meaning the constructed variable will focus on the cost function of our distributing firm.
selling surpluses. The result from this shortcoming is that the real loss for the firm is overstated by the variable we constructed. The base temperature is the temperature for which the demand for electricity is found to be the lowest by our first model.
Now that we have constructed the variable part of the cost function for our hypothetical company, we can advance with the formulation of the empirical model in which we will assess the effect of temperature on this part of the firm its cash flow. We have to be cautious in how to implement the temperature dependence into the model. Basically the dependence of price times quantity depends on whether the firm needs to buy additional electricity, or needs to sell surplus electricity already bought in the forward market. Since the relationship of electricity demand and temperature is assumed to be V-shaped with the minimum point at 16 degrees, we have to verify whether the measured temperature is above or below 16 degrees Celsius. Then the variables will be grouped based on their deviation from the expected long term average value. By separating the variables for a negative and a positive deviation from the expected temperature and for temperatures above and below 16 degrees, the model is able to capture an asymmetric response to temperature movements. Furthermore the trading actions of wind farmers affect the profitability of our firm through their influence on the spot market price. A preliminary regression run indicated the presence of ARCH effects, so a GARCH(1,1) model is adopted. The model to be estimated is described by the following equation:
(Equation 5)
( ( ) )
With the conditional variance equation:
(Equation 6)
In which Positive and correspond to the deviations from the expected temperature. The term ( ( ) ) reflects the trading activities of wind farm operators. If wind farm
wind trading is expected to be limited to the price component of the VCF. For the temperature effect, both a linear and quadratic effect will be tested. Based on the value of the R-squared the appropriate relation will be incorporated in the model.
The coefficients , , and will indicate the dependence of the VCF on temperature
deviations. As stated above, the VCF values corresponding to situations with positive deviations for expected temperatures below the base temperature and negative deviations for expected
temperatures above the base temperature are overstated by the constructed VCF variable. However, for the sake of exposition of the model it is decided to continue calculating with the overstated values, as if they were the actual cash flow deviations. The reason for this is straightforward: The purpose of the model is to test the hedge effectiveness of temperature derivatives for the
distributing firm. And although the VCF values are not completely right in 2 of the 4 situations, it is assumed that the values used are proportionate to the actual losses of the distributing firm. Through this assumption we can still test the hedge performance of our model. The overstated VCF values will lead to higher values for the coefficients of and . Since the hedging strategy is based on the coefficients found in the regression model, the hedge effectiveness is not affected significantly. The way in which the arbitrageurs and speculators are included in the model needs some further explanation. By including a constant, the average value of the VCF is assumed to be due to these groups of traders. While this is far from ideal, it will also lead to negative expected coefficients for and . This does however not mean that the cost function decreases when temperatures deviate from the expected temperature in the way specified by the variables associated with these betas. The reason for the expected negative coefficients is that the VCF variable is expected to drop below the average in these situations. When the actual temperature is below the expected temperature for temperatures above the base temperature, it is likely to cause a drop in electricity demand. This drop is associated with increased trading on behalf of the distributing companies, as they need to sell their surpluses bought in the forward market. The increased supply in the spot market will have a negative effect on prices. The lower prices will cause a lower value of the VCF variable. In the situation where the actual temperature exceeds the expected temperature at temperatures above the base
temperature, both prices and quantities traded rise. Since arbitrageurs and speculators are included in the model with a constant, the swings in the VCF variable induced by temperature makes swings around this average. Therefore the expected coefficients for and are negative. This does not necessarily mean that costs decrease with deviations in these directions. It is merely the
In order to hedge a situation in which deviations from the expected temperature lead to losses for the firm, a strategy which compensates the firm when either positive or negative deviations occur is put in place. A temperature derivative strategy with the payoff of a usual long straddle option strategy is most suited to serve this purpose. A long straddle in the light of temperature derivatives consists of a HDD and a CDD option with the same base temperature, in this case the expected temperature. In case the average daily temperature exceeds the expected temperature, the CDD call option will deliver a payout to the company equal to the number of degrees by which the measured temperature exceeded the expected temperature times the amount of money which was specified in the option contract to be paid out per degree of increased average temperature. In case the actual temperature is below the expected temperature, the HDD option will generate income for the firm in the same way. The cost of this strategy is limited to the option premium. Figure 5 gives a graphical representation of the payoffs generated by the option strategy.
Figure 5, The payoff of the proposed option strategy with HDD and CDD options. The HDD option will pay whenever the observed temperature is below the expected temperature, the CDD option will deliver a cash flow when temperatures exceed the expected temperature E(T).
The payout of the HDD and CDD option in relation to the temperature index will be constructed according to the coefficients to . Only significant coefficients are considered for the hedging strategy. For example indicates the effect of one degree of positive deviation from the expected temperature for expected temperatures over 16 degrees on the VCF variable. The coefficient will determine how much the CDD contract will have to pay out per degree by which the actual temperature exceeds the expected temperature.
The option strategy is based on the estimation of the model over a certain period and its
the winter of 2010-2011. We will estimate the model over the years prior to the test period, the same three months one year back and the same three months during the last three years. The performance of the hedge will be evaluated in three ways. First, the standard deviation of the daily VCF after the hedge will be calculated. Then the dollar offset and variability reduction method will be used as proposed by Finnerty and Grant (2003). The different periods over which the model is estimated will be compared with each other and the no hedge alternative. Standard deviation will be calculated with Equation 7:
(Equation 7)
√∑ ∑
The dollar offset method is calculated as the percentage of change in the VCF variable which is offset by the cash flows from the options. Equation 8 shows how the dollar offset method is calculated.
(Equation 8) (∑ ∑ )
In Equation 8, corresponds to the amount of money which is paid out by the hedging strategy, equals the amount of change in the cash flow of the firm. The ideal hedge would result in a value of 1. The negative sign in front of Equation 8 is due to the different signs for and . Finnerty and Grant (2003) argue that an effective hedge reaches a value of at least 0.80 and below 1,25.
The variability reduction method evaluation variable is calculated by Equation 9. (Equation 9)
(∑ ∑
)
5. Data
5.1 Hourly electricity demand model
The data necessary for the empirical tests proposed above comes from different sources. For our first model we need data on electricity demand, temperatures and scarcity. The data for electricity demand is found on the website of the Dutch TSO Tennet. There is no exact measure available for demand, but the values for the amount of electricity being fed into the network is generally assumed to be a reliable estimate. Hekkenberg et al. (2009) also uses these values as an estimation for
electricity demand. Temperature data is retrieved from the KNMI. Hourly average temperatures from the weather station of De Bilt are used, as this is a central place in The Netherlands. The HDD and CDD variables are then constructed by calculating the negative and positive deviation from the 16 degrees Celsius point respectively. The dummy variables used in the model will not be discussed in this chapter, since their characteristics are straightforward. Plots of the described series are given in Figure 6 and the descriptive statistics are given in Table 1.
Figure 6,Overview of the time series used in the hourly electricity demand model. Units on the vertical axes in the two graphs on the right are degrees Celsius, the units on the vertical axes of the left graphs are MWh.
6,000 8,000 10,000 12,000 14,000 16,000 18,000
II III IV I II III IV I II III IV I II III IVI II III IV I II III 2006 2007 2008 2009 2010 2011 SYSTEMLOAD 0 4 8 12 16 20 24 28
II III IV I II III IV I II III IV I II III IVI II III IV I II III 2006 2007 2008 2009 2010 2011 HDD 0 5 10 15 20
II III IV I II III IV I II III IV I II III IVI II III IV I II III 2006 2007 2008 2009 2010 2011
Table 1, Descriptive statistics of the time series used in the hourly electricity demand model.
The variables are tested for a unit root by both the Augmented Dickey Fuller (ADF) and the Phillips-Perron (PP) test. The outcome of the test suggests there is no unit root present in any of the series at a 1% significance level, meaning we can proceed to use these variables with the proposed
methodology.
5.2 Daily weather dependence model
In the daily model we use quantity and price data of the APX market. These time series are obtained from the data management department at the company APX ENDEX. Furthermore values for wind power production are used in the model. In The Netherlands the production data of electricity companies is not freely available and due to the competitive sensitivity of this kind of data, it has not been easy to construct a wind power production estimate. Some producers in the wind energy sector have been willing to share their production data, allowing us to extrapolate this into an estimate for national wind energy production. To construct a meaningful estimate, it is important that the spatial dispersion of the sample observations is approximately comparable to the spatial dispersion of actual wind power production sites. It should be noted that the sample used consists of approximately 4% of the total wind power capacity in The Netherlands. Furthermore the sample is under populated with respect to the actual production sites in the Noord-Holland region. For the wind production sites in the sample the production per MW of capacity is calculated. This is then multiplied with the total amount of wind capacity in the Netherlands, which can be found on a monthly basis on the database website of the CBS14. The expected wind power production is calculated by assuming the probability of wind is equal during the year. Therefore the average value of wind production is the expected wind production for every day. Perhaps a seasonal correction or a monthly average would be appropriate, but the 6 years of data in our dataset are thought to be insufficient to derive a sensible long term monthly average for the wind power production. The data on temperature is retrieved from the KNMI website. Again the location of the temperature measurements is De Bilt. As a measure for daily temperature there is a wide variety of different types of averages and a
maximum and a minimum temperature available. It is chosen to work with maximum temperatures, as the largest part of temperature dependence is expected to happen during daytime, and is thus more affected by maximum temperature then average temperature. The expected temperatures are found on this website as well. They are the long term monthly maximum temperature for De Bilt. With this data on temperature the four different variables can be constructed can be constructed by using a double if function in excel. The variables will equal the absolute deviation from the expected value when the specific conditions15 are met, and zero otherwise. The plots of the variables used in the model are given in Figure 7 and the descriptive statistics in Table 2.
Figure 7, Graphical representation of the variables used in the daily model. In the top four graphs the vertical axes measure the deviation from the expected temperature in degrees Celsius. The denotations POS and NEG describe whether the deviation from the expected value is either positive or negative, U16 and A16 tell us whether the measured temperature is above or under 16 ⁰C. The VCF is the variable part of the cost function for our distributing firm and DWIND equals the deviation of wind power production from the expected amount.
15
The conditions being an either positive or negative deviation from the expected value and the measured temperature above or below 16 ⁰C.
0 2 4 6 8 10
II III IV I II III IV I II III IV I II III IV I II III IV I II III 2006 2007 2008 2009 2010 2011 POSU16 0 4 8 12 16
II III IV I II III IV I II III IV I II III IV I II III IV I II III 2006 2007 2008 2009 2010 2011 POSA16 0 2 4 6 8 10 12 14
II III IV I II III IV I II III IV I II III IV I II III IV I II III 2006 2007 2008 2009 2010 2011 NEGU16 0 1 2 3 4 5 6 7
II III IV I II III IV I II III IV I II III IV I II III IV I II III 2006 2007 2008 2009 2010 2011 NEGA16 -10,000 0 10,000 20,000 30,000 40,000 50,000
II III IV I II III IV I II III IV I II III IV I II III IV I II III 2006 2007 2008 2009 2010 2011 DWIND 0 4,000,000 8,000,000 12,000,000 16,000,000 20,000,000
II III IV I II III IV I II III IV I II III IV I II III IV I II III 2006 2007 2008 2009 2010 2011
Table 2, Descriptive statistics of the variables used in the daily weather dependence model for a distributing firm. The four variables on the left indicate either positive (POS) or negative (NEG) deviation from expected temperatures with the measured temperature being either above (A16) or below (U16) 16 ⁰C. VCF is the volatile part of the cost function for our hypothetical firm and DWIND is the difference of wind production from its expected production amount.
The presence of a unit root is tested by conducting the ADF and PP test. All variables except for VCF show no reason to believe there is a unit root in the data at 1% significance. For the VCF variable, the null of a unit root is marginally rejected with the ADF test, but a strong rejection by the PP test convinces us to continue working with this variable. Since there are no other variables included in the model which hint at having a unit root, the risk for running a spurious regression is low.
6. Results
Before interpreting the results of our regression models it is important to check the validity of the regression results. One of the assumptions of the GARCH(1,1) specification is a normal distribution of the residuals. Both the models do not produce normally distributed residuals, fortunately we can correct for this by using the heteroscedasticity consistent covariance due to Bollerslev and Wooldridge.
6.1 Hourly electricity demand model
The hourly model is optimized by considering sensible lags for the HDD and CDD variables and simultaneously minimizing the AIC. Exponential relationship between the temperature variables and electricity demand have also been tested, but a linear relationship results in a better fit and a lower AIC. The iterative process has resulted in the configuration shown in Table 3. Please note that only the dynamics of the HDD and CDD variables are shown in Table 3, the rest of the output is presented in the Appendix. The dynamics in the CDD and HDD variables are interesting. The outcome suggests that the increased need for energy in case of low temperatures is relatively more persistent than the increased energy need caused by high temperatures. Although a part of the temperature
is caused by the increased temperature during that hour. At an average price of 50 Euro per MWh, the cash flow impact is equal to 12.000 Euro in this case.
Dependent
Variable: Elecricity Demand
Variable Coefficient Std. Error Significance
CDD(-24) 10.65 1.73 *** CDD 28.32 1.74 *** HDD(-24) 1.04 0.34 *** HDD(-48) 14.72 1.33 *** HDD(-72) 17.14 0.91 *** HDD 11.16 1.15 *** R-squared 0.85 Adjusted R-squared 0.85
, regression output for the hourly electricity demand model:
Table 3
Only the output for the HDD and CDD variables are shown, the rest of the output can be found in the appendix. Three stars means the coefficient is significant at the 1% level, no star means the coefficient is not significantly different from zero.
The explanatory power of the model is good, with an R-squared of 0,85. However, if we compare this with the alternative of not including lags, we discover that the increase in R-squared for the dynamic model is only marginal. For interpretational ease, it is therefore decided to perform a robustness check of the results without the lagged HDD and CDD variables. The outcomes of the regressions for every separate year are given in Table 4. The output for the additional variables is not shown, but available upon request.
Table 4, robustness check of the HDD and CDD coefficients in the hourly electricity demand model. Standard errors are given in parenthesis. Coefficients for the additional variables in the model are available upon request. Three stars means the coefficient is significant at the 1% level, no star means the coefficient is not significantly different from zero.
then by heating degree days over the whole data set. This is shown by the higher coefficient which is found for the CDD coefficient over the whole sample. Even though we find a positive and significant value for the CDD coefficient over the whole period, some yearly coefficients show insignificant values as well. If we compare the outcome of the CDD coefficients with a plot of the temperatures in Figure 8, we find that the insignificant and negative values for the CDD coefficients are found in years with relatively cool summers. Table 5 which shows an overview of the average summer temperatures confirms that the insignificant coefficients are indeed found in the coldest summers based on
average temperatures. In fact it makes sense that the coefficient becomes less significant when the average temperature moves towards the base temperature, as less data points above the base temperature are recorded. The summers of 2006 and 2010 on the other hand, which show major hot spikes, both show a very strong positive relation between hot days and electricity demand.
Figure 8, a plot of the hourly average temperature developments at De Bilt weather station in ⁰C.
Table 5, average temperature during the summer months June, July and August.
The coefficients for heating degree days are relatively more stable, but also show some fluctuations. The low coefficient for 2006 is assumed to be insignificant because the dataset starts at the 25th of April 2006, which means the winter of 2006 is not included in the data. All in all it should be concluded that the coefficients prove to be fairly stable over the years. Furthermore, the imposed base temperature of 16 degrees is verified in a second robustness check. Table 6 gives an overview of the values of R-squared for the different regressions. It can be seen that, although the differences are small, the R-squared reaches its maximum with a base temperature at 16 degrees. This means that
-20 -10 0 10 20 30 40
II III IV I II III IV I II III IV I II III IV I II III IV I II III
2006 2007 2008 2009 2010 2011
the presence of a positive relationship between temperatures either higher or lower than 16⁰C and electricity demand has been established by the model.
Table 6, R-squared of the hourly electricity demand model when using different base temperatures.
6.2 Weather dependence of the distributing firm
As described in the methodology section, the model for firm weather dependence will be estimated for three different periods: the entire period for which data is available excluding the last three months, all summers in the sample and the summer months of 2010. The output for these estimations is given in Table 7.
Table 7, output for the daily volatile cost function model for the distributing firm.
( ( ) )
The model is estimated over five different periods. Three stars means the coefficient is found to be significant at the 1% level, two stars is significant at the 5% level, 1 star at the 10% level. No star means the coefficient is not significantly different from zero.
