Swedish electricity
Erik Sjöström
Master thesis, 30 hp
Master programme of Energy engineering, 300 hp
Department of applied physics and electronics Autumn 2020 / Spring 2021
The Swedish electricity market was historically based on predictable and controllable power plants. The introduction variable renewable energy (VRE) sources in the market have led to less predictability and larger short-term variations in the generation profiles.
These effects are compounded as the market share of VRE sources are increasing, and in Sweden’s case as the nuclear power plants are being phased out. Different metrics of value are calculated to shed light on the economic potential of new power sources. A not yet commonly used metric is the value factor of a technology, which represents the net increase or net decrease in revenue due to if the generation coincides with a high or low spot price of electricity. The thesis seeks to calculate the value factors and analyse their place within the northern European electricity market.
In order to calculate the value factors and analysing them, the acquisition of datasets for varying market variables was required. The three sources of these datasets was for this thesis the ENTSO-E Transparency Platform, Nord Pool and Svenska kraftnät. These sources combined could supply datasets for market variables dating back to 2015 for Sweden and each country with an international connection with Sweden. This limits the scope of this analysis to 2015 - 2019 for Sweden and six other countries.
The value factors were calculated for each Swedish electric price region divided into five categorical technologies, wind-, solar-, hydro-, nuclear- and heat power. The results from this only gave concrete results for two technologies. Wind power are shown to generally have a value factor below one and hydro power in the two northern regions have a value factor above one. This indicates that the market is saturated for wind power while in demand for hydro power from northern Sweden. Every other pair of technology and region vary as to not indicate whether the market is in demand of it or not.
Analysing the association of variables was accomplished using a correlation study. Vari- ables that consistently have a critical correlation factor, either linear or monotonic, are identified as associated variables. Out of these pairs of associated variables, the ones with a shared trend in either correlation or normalized regression with the trend of the appro- priate value factor are identified as associated with the same value factor. This resulted in several associated variables for each value factor. Neither of these associations can by this methodology be identified as having a causal relation, it only displays correlations which could be incidental.
Sveriges elektricitetsmarknad var länge huvudsakligen baserad på förutsägbara och kon- trollerbara energikällor. Introduktionen av vind- och solkraft i marknaden har lett till att systemet har blivit mindre förutsägbart med större korttidsvariationer i generationsmixen.
Dessa effekter på elmarknaden blir större i takt med att de variabla energikällorna tar upp en större del av marknaden, vilket i Sveriges fall stärks av att kärnkraften är i en process av att avvecklas i Sverige. För att evaluera den ekonomiska potentialen för generationstekniker så har ett antal olika värden etablerats. Ett värde som hittills är relativt oanvänt är Värdefaktorn (eng. Value factor) för en genrationsteknik. Värdefak- torn representerar hur mycket generationstekniken går i vinst på grund av korrelationen mellan dess genereringsprofil och hur elpriset varierar. Målet med denna rapport är att beräkna Värdefaktorerna för Sverige och analysera hur de påverkas av variabler i den nordeuropeiska energimarknaden.
För att beräkna Värdefaktorerna krävdes det att dataset för olika marknadsvariabler samlades in. Tre källor av data användes i den här rapporten, ENTSO-E Transparency Platform, Nord Pool och Svenska kraftnät. De källorna kunde användas för att samla variabler tillbaka till 2015 för Sverige och de länder som delar en internationell länk med Sverige. Detta begränsar analysen till 2015 - 2019 för Sverige och sex andra länder.
Värdefaktorerna beräknades för varje av de fyra svenska elpris-regionerna uppdelat i fem olika generationstekniker, vind-, sol-, vatten-, kärn-, och värmekraft. Resultaten från detta gav bara konkreta resultat för två av teknikerna. Vindkraft visade sig generell värden under ett medan vattenkraft i de två norra elpris-regionerna hade värden över ett.
Detta visar att elmarknaden är mättad för vindkraft och har efterfrågan för vattenkraft från norra Sverige. Alla andra kombinationer av region och teknik varierar och är inte lägliga att dra några slutsatser om.
För att analysera vilka variabler som möjligen har en inverkan på varandra så utfördes en korrelationsstudie. Par av variabler som konsekvent gav signifikanta korrelationsfaktorer, antingen linjära eller monotona, identifierades som associerade. De av dessa associerade variabler med en korrelation eller normaliserad regression som delar trend med dess respektive Värdefaktor anses vara associerade med Värdefaktorn. Detta resulterade med ett antal variabler som ses vara associerade för varje Värdefaktor. Genom metoden som har använts så kan ingen av dessa associeringar identifieras som att ha en inverkan på Värdefaktorerna, de visar bara korrelationer vilka kan vara sammanträffande.
This thesis was conducted in cooperation with Johan Lindahl at Becquerel Sweden AB.
As it was performed during 2020 and 2021, the global Covid pandemic have made com- munications difficult. I’m thankful to Johan and my supervisor Jan-Åke Olofsson for keeping in touch with the help and assistance needed to complete the thesis.
I would also like to thank my friends and fellow students for making my time at Umeå University as hospitable as it has been. Most of all Enar J. for all the support and encouragement needed to keep me working toward my masters degree.
1 Introduction 1
1.1 Background . . . 1
1.2 Purpose . . . 1
1.3 Limitations . . . 1
2 The value factor 2 3 Theory 3 3.1 Electricity market . . . 3
3.2 Value factor . . . 3
3.2.1 Formal definition . . . 3
3.2.2 Specific definition . . . 4
3.3 Economics . . . 5
3.4 Statistics . . . 5
3.4.1 Correlation . . . 5
3.4.2 Confidence estimation . . . 6
4 Methodology 7 4.1 Included variables . . . 7
4.2 Available datasets . . . 8
4.3 Statistics . . . 9
4.4 Identifying correlations . . . 9
4.5 Comparing correlated datasets . . . 10
5 Results 12 5.1 Value factors . . . 12
5.2 Correlations . . . 13
5.3 Trends . . . 15
5.3.1 Wind power . . . 16
5.3.2 Solar power . . . 18
5.3.3 Hydro power . . . 20
5.3.4 Heat power . . . 21
5.3.5 Compiled trends . . . 22
6 Discussion 23 6.1 Value factors . . . 23
6.2 Identified correlated variables . . . 27
6.2.1 Generation and revenue . . . 27
6.2.2 International export . . . 28
7 Conclusion 30
A Example of correlation I
1 Introduction
Hydro- and nuclear power have been the backbone for the Swedish electric power market since the domestic nuclear plants were activated in the 1970s. These sources are highly robust and have effectively covered most of Sweden’s baseload and intermittent load [1].
But as electricity from variable renewable energy (VRE) sources increases, the system is becoming less robust and importantly less predictable. Their market share will also increase as the domestic nuclear reactors are in the process of being decommissioned. This does not mean that the change is negative since it also means that less non-renewable energy sources are being used. It does mean that the generation arrangement and price calculations must be made more flexible since the VRE cannot be planned on a short timescale.
1.1 Background
With the goal of demystifying the future of the Swedish electricity market, the non-profit company Energiforsk are conducting a project named “El från nya anläggningar” (Eng.
“Electricity from new plants”). The aim of the project is to calculate and present the economic potential of commercially available techniques in Sweden, with the main interest being the levelized cost of electricity (LCOE). LCOE is a widely used tool for comparing the costs of different power plants or generating technologies. The calculation of the LCOE is based on the equivalence of the present value of the sum of discounted revenues and the present value of the sum of discounted costs. Another way of looking at LCOE is that it expresses the average electricity tariff needed for recover the costs of building and operating a power plant during an assumed financial lifetime. The averaging is done over large timescales which makes sense for predictable baseloads since it does not fluctuate significantly on a short timescale. But since VRE sources fluctuate on such a scale, other factors that are not as easily presented as a levelized cost will also be calculated.
1.2 Purpose
The aim of this thesis is to calculate and analyse the value factors of the energy sources in Sweden. The analysis seeks to answer which of the variables in the northern European electricity market influence the value factors within the Swedish electricity market. This will be accomplished by developing a methodology which can be used to compare any variables in the market.
1.3 Limitations
The analysis will only consider Sweden and the six countries that has a direct connection.
The availability of datasets from these countries limits the historical data from 2015 to 2019. The economics of different technologies are only considered using the value factor and should not interpreted as an overall economic viability.
2 The value factor
The levelized cost of electricity (LCOE) is one of the most common metrics for evaluating the capital cost of generating electricity [2]. Although, since LCOE is based on typical costs and generation of a technology, it does not accurately describe the weather and geographical variability that are big factors for variable renewable energy (VRE) sources [3, 4]. For the World Energy Outlook 2018 a new metric, value-adjusted LCOE (VALCOE) was presented. VALCOE is based on the average LCOE by technology with three added metrics of value; energy, capacity and flexibility [5]. Each of these values are added to the LCOE in order to give a better representation of the actual cost of electricity, this is important for VRE sources as it takes into account the generation profiles and the alignment with energy demand [5, 6]. One of these metrics is the Energy value which represents the average wholesale price of the electricity from a specific energy source or unit during a year. This introduces the importance of correlation between hourly prices and hourly generation into the model. While this metric does give a better understanding of what the actual cost of electricity is, its value is not that informative without the other values that give the entire VALCOE. This is unfortunate since it could be of interest to compare such a factor between technologies and regions. Fortunately, a unitless factor commonly denoted as the Value factor (VF) describes the same correlations in a easily comparable form. The VF uses the spot price of electricity on the market instead of the wholesale price but is otherwise highly similar to the Energy value but normalized such as to describe if an energy source has a net positive or net negative correlation between price and generation [4]. As such the stable generation of baseload generation would be expected to have a neutral VF while balancing power would be expected to have a positive VF. VF has previously been used to analyse the economic potential of VRE sources and the effect that their increasing market penetration has on their market value [3, 4, 7, 8, 9].
3 Theory
The VF is a single dimensionless number that describes the ratio between the yearly revenue calculated on two different levels of detail in time. Typically, the sum of hourly revenue, and the revenue using the means over an entire year. This makes comparing different power sources easy, but it also makes it easy to draw to wide conclusions from such a simple factor. To alleviate the analysis and readability of the results the notation will be expanded and given careful explanation.
3.1 Electricity market
The electricity within Sweden and its directly connected countries are traded on the spot market offered by Nord Pool. Within this market actors from all 15 participating countries settle how much electricity each will generate, import, export and so on. From this a day-ahead price is calculated for each price region, and to compensate for unpredictability in the generation and consumption, intraday prices are traded up until the hour of generation1. The structure of price regions differs from country to country. Sweden, Norway and Denmark have divided their countries into separate geographical price regions.
Finland, Latvia and Poland have the entirety of their countries in a single price region.
Germany shares their single price region with Luxembourg2 .
3.2 Value factor
The definition of VF is typically presented in a formal definition. This will be expanded into a more descriptive, specific definition.
3.2.1 Formal definition
Defining the VF will be done with the formal definition presented by Hirth [4]. Principally it is the relation between the average spot price, ¯pt, from a technology t and the average spot price ¯p.
V Ft= p¯t
¯
p (1)
Using the matrix notation presented by Hirth these are calculated using vectors of equal length representing the spot price, p, the generation of the technology, gt, and a vector of ones, t. Note the difference in t and t.
¯
pt= (p0gt)
(gt0t) (2)
¯
p = (p0t)
(t0t) (3)
1Some regions also trade in shorter time periods.
2Before October 2018 Austria was also part of the same price region.
The length of the vector is the same as the amount of timesteps used for the calculated time period, typically the number of hours in a year. Hirth defines ¯pt as a vector of factors that when summed, results in the full load hours of the technology. This involves dividing the generation with the rated power of that technology over the entire time period. Since this division would apply to both the numerator and denominator it does not algebraically change the equation, the choice between the actual generation and the factors is not important. The actual generation was in this definition chosen as it easily applied in the methodology. In another article Hirth also simplifies the definition in this manner and also presents it without the vector notation3 [10]. This definition serves well in outlining the general form of the VF. But as is, it does not specify in what regions the spot price or generation is representing.
3.2.2 Specific definition
Using the formal definition of VF works well if only one single region is considered, which could work well for countries with a single price region. For the Swedish regions it could be misunderstood if the generation is defined on a national level or considered within the same region as the price. Therefore, explanatory subscripts are added to the variables to make it immediately comprehensible. With added price region, P R, and generation region, GR, the formulas become:
V FP R,GRt = p¯tP R,GR
¯
pP R (4)
¯
ptP R,GR = (pP R0gtGR)
(gGRt 0t) (5)
¯
pP R = (pP R0t)
(t0t) (6)
This makes it possible to calculate some nonsensical VFs such as if the price region were chosen as Poland while the generation is chosen for one of the Norwegian price regions.
But it makes it clear to compare the difference between the generation region being the whole of Sweden or just one of the regions for the same price region. The factor is only natively interesting when both P R and GR are the same region, R, in which case it can simply be denoted V FRt. This should be considered as the ordinary definition of the VF and unless otherwise stated any VF presented should be assumed to be of this form. Only this form will be used in this thesis, but the VF with different regions could possibly be used to speculate on how a generation profile from one region would interact with another one’s price profile.
3This form of the equation could be easier to comprehend. In this case t is a step in time and t∗is the technology.
V F = TPT t=1gtt∗pt
PT
t=1gtt∗PT t=1pt
3.3 Economics
As the VF is the ratio between sum of hourly revenue and yearly mean revenue, a value larger than one would mean that the generation profile for the technology within the region has a net positive correlation with the spot price. And by the same reasoning a value below one would mean a net negative correlation. A positive correlation means that the price of electricity from that technology is higher than the average. But according to the economic price theory, most easily represented by the Marshallian supply-and-demand curve, the high price shows that there is a higher demand on the market for electricity that coincides with the generation profile of that technology [11]. Therefore, increasing the installed capacity of that technology could by meeting the demand, decrease the price of electricity as well as alleviate the electric system in times of lacking generation.
3.4 Statistics
Analyzing the VF requires statistical methods to determine the importance of different aspects. Determining how different variables affect the VF is not feasibly possible to calculate. Instead, correlations can be calculated to give insight to what variables might be of importance. To further validate the calculated values, it is important to determine some level of confidence. Calculating the confidence from the datasets alone will not be possible since there is only one data set per year, region and variable. This makes the use of a method of resampling necessary.
3.4.1 Correlation
A very common measurement of correlation is the Product-moment correlation4 (PMC), r [12]. PMC is a statistic that is used to determine the linearity of the relation of two paired datasets. The calculation is done using the standard deviation of each data, σX/Y, and the covariance between them, σXY,
r = σXY
σXσY . (7)
This gives a value between −1 and 1 that each correspond to an exact negative or positive linear correlation. Principally the correlation between the datasets decreases as the value gets closer to 0, but as it only describes a linear correlation a low PMC does not disqualify the sets from being non-linearly correlated.
To further interpret the PMC the rank correlation for the datasets can also be cal- culated. Unlike PMC, rank correlation is a measurement on how monotonic the two datasets are. In the case that the rank correlation is significant while the PMC is not, a nonlinear correlation could be present. There are two principal statistics for rank correlation, the Spearman rank correlation (SRC), ρ, and the Kendall rank correlation (KRC), τ. Both SRC and KRC also have values between −1 and 1 that correspond to a
4Commonly denoted PCC.
negative or positive correlation without giving any information to the relation between the datasets . SRC is calculated using the rank-distance, di, between each paired datapoints in the two datasets and the number of datapoints in each dataset, n [13].
ρ = 1 − 6Pn i=1di
n(n2− 1) (8)
KRC is calculated using the number of concordant pairs, nc, and the number of discordant pairs, nd, that can be found between the datasets [14].
τ = nc− nd
n 2
(9)
KRC generally results in lower values of monotonic correlation than SRC, but KRC generally show less error in large datasets and should be given more weight within analysis [15].
3.4.2 Confidence estimation
Calculating the correlation coefficients in this manner reveals no value of confidence.
When datasets cannot be reproduced due to there only being one dataset available for each variable a resampling method can be used. Bootstrap is a wide term that is used to define several different methods that are all based on the core method of doing a large set of resampling to acquire an estimate of the distribution of the calculated value. In order to estimate a level of confidence for VF and correlation coefficients a non-parametric bootstrap method will be implemented [16]. Using a non-parametric no assumption or prior analysis of the distribution of the individual datasets is made, but instead the resamples are created by randomly drawing data from the original datasets with replacement to create artificial datasets. Since the datasets are time series and therefore coupled the method will have to use a pairwise algorithm. A large amount of these artificial datasets are created and are statistically treated as if they are reproduced measurements of the original dataset. With the new set of datasets, regular ANOVA methods of statistical analysis is possible. Among these are the ability to calculate confidence intervals using the now calculatable standard deviation.
4 Methodology
A large part of the practical application of the methodology in this thesis is implementing it into a program that can easily recreate the statistics. The coding of this program will not be explained in any detail and the methodology will be left broadly applicable.
Specific problems that occurred and had to be circumvented will be explained as to explain any discrepancies in the results.
4.1 Included variables
As the analysis is interested in the European electricity market, what variables the Trans- mission System Operators (TSOs) and the power market Nord Pool presents is of greatest interest. As the TSOs in the different countries present widely different variables, trying to find which variables are comparable would be difficult. Luckily, this problem has been alleviated by the establishment of the European Network of Transmission System Opera- tors for Electricity (ENTSO-E), who has the technical cooperation between the European TSOs as one of their objectives. As a part of this they have developed the ENTSO-E Transparency Platform that present data from the TSOs in a somewhat cohesive state [17]. Here data for electricity generation, consumption and spot sprice can be found.
An article by Hirth et.al. reviewed the quality and availability of the datasets within the platform and found that the data consistently deviate from the same datasets from other sources [18]. This might lead to some faults in the results and makes it increasingly important to preface all results with this bias. As the goal is to analyse the Swedish value factors, the data for generation of electricity in Sweden will be gathered from the Swedish TSO Svenska kraftnät (SVK) to keep it as detailed as possible [19]. As the electricity market in northern Europe, Nord Pool presents a lot of data concerning the spot sprice and the exchange of electricity between regions [20]. They also have data for generation, consumption, this overlap of data between Nord Pool and ENTSO-E likely mean that they share the data between them. In total 9 different types of market variables were chosen to be included in the analysis, see tab. 1.
Generation profiles was gathered for each entire country and combined into 5 distinct technologies, hydro-, wind-, solar-, nuclear- and heat power. Heat power is used as a term for any remaining power source, be it gas turbines, geothermal or combustion based.
Unfortunately, this does not differentiate electricity from certain fossil and renewable sources, which could have added an environmental aspect to the value factor of heat power. But as SVK mainly present their data within these categories, and as this thesis is applied on the Swedish electricity market it is conformed to SVKs categorisation. Due to the importance of separating the generation profiles into each region to be able to calculate VFs, profiles for Sweden are gathered for each region from SVK. This leaves Denmark and Norway as the only countries that has their generation profiles combined for their regions. In addition, the share that each technology has for the total generation could be of interest, so percentage-based generation profiles were also created.
Table 1 – Market variables that are included in this analysis.
Variable Sweden Neighbouring countries Unit Generation Each region Each country MWh Consumption Each region Each region MWh
Spot price Each region Each region EUR/MWh
Import Each region - MWh
Export Each region - MWh
Generation% Each region Each country MWh/MWh
Imp. Gen.% Each region - MWh
Exp. Gen.% Each region - MWh
Revenue Each region - EUR
Both consumption and spot price data were gathered for each region. The spot prices are limited to the Day-ahead prices since no comprehendible intraday prices could be found.
As revenue is what is being compared with VF, it will be important to include it as a variable in the analysis. The revenue can easily be calculated from the generation profiles and spot price.
Import and export data was gathered for Sweden only. This includes both connec- tions between specific regions and between countries. There is no separation between the import and export within the datasets so they have to be divided into two. To analyse what technologies are being used in neighbouring countries in cases of import or export, variables are created by multiplying import and export by the percentage-based generation profiles of the originating region.
4.2 Available datasets
As there is an overlap of data a scheme for where what data would preferably be taken from had to be established. Due to the level of detail that ENTSO-E presents in their generation data they were chosen as the preferred source for all generation data except for Sweden as previously mentioned. Data for consumption, spot sprice and exchange are chosen to preferably be taken from Nord Pool as it is more accessible through their service.
As the ENTSO-E Transparency Platform was established in January of 2015, this was cho- sen as the start point of what timespan of the entire analysis. But seemingly not all TSOs started their cooperation on the same date, this might introduce discrepancies in the results based in ENTSO-E data from 2015. But as all countries at most lack data for a couple of the first weeks of the year it will be neglected in this analysis. For future analysis 2016 could be set as the first year instead, as at that point additional years will have been added.
In some cases datasets from Nord Pool were not available, but in these cases, they could be gathered from ENTSO-E instead. One of these cases were the spot price of
Poland. These are problematic since between March 2017 and November 2019 the price in the region was presented in Polish złotys instead of euros. This makes the 2017 and 2019 datasets of this variable highly unreliable. An implementation of currency conversion was tried, but as the European Central Bank did not have continuous data for the conversion rates, the datasets will be left as is. As the spot sprice in Poland is not of any specific interest no specific analysis of these datasets will be performed.
Due to the nature of the analysis being the comparison of data on an hourly basis, it is very important to ensure that all datasets are correctly aligned. The results from two datasets with a one-hour discrepancy would be false and would not necessarily give an approximation of the correct result. Therefore, all datasets had to be stated within the same time zone. Although most countries considered are the within the CET zone, UTC +0 was chosen. The reason CET was not chosen is that it still applies summertime which makes the data impractical with repeating and missing hours. UTC +0 was chosen instead of UTC +1 since both ENTSO-E and SVK have made their data available in this format. This left all datasets from Nord Pool to be corrected. This was accomplished by shifting the data over the one or two hour discrepancy within each year. Shifting the data for each year separately removed the last hour of each year of data within all these datasets, since the last hour in UTC +0 would appear as the first hour in CET. The loss of one hour was considered an acceptable loss.
The solar power datasets that SVK presents for the Swedish power region seemingly has some error. For regions SE3 and SE4 the generation never reaches 0, even during nights. Although the magnitude is low during the nights, so these errors will be kept within the data. The reason for this error has been stipulated that it might be the self-consumption by inverters [21]. It could also be a result of either some discharge from connected batteries or mislabeled electricity from wind/solar-hybrid parks. But as the reasons cannot be determined, the fault could possibly imply larger errors in the datasets.
4.3 Statistics
All variables gathered resulted in around 220 datasets per year. This large number of datasets made it necessary to condense the data into lists of datasets that might have an interesting correlation.
4.4 Identifying correlations
If all datasets that would have an influence over another, would either have a significant linear or monotonic correlation factor creates a powerful method of ruling out pairs of datasets. It necessitates that a value of significance is stated, and likely misses and removes any pair with a strong non-monotonic correlation if such a pair would exist.
Defining what value for a correlation factor is significant is something that has to be made on a case to case basis. As the electricity market is very fluctuating it would be unlikely to find any datasets that shared a very strong correlation. The significance was
chosen as “moderate”, which in different fields and sources are defined differently but implies a value between 0.3 and 0.7 [22]. What value in this range was specifically chosen had to be evaluated as a point where it resulted in a manageable amount of data while still including enough pairs to compare between. In fig. 1 examples of correlation can be seen. For this analysis, a value of 0.4 have been chosen as the critical value. Also, assuming that any pair of datasets that do not only share an incidental correlation would have a significant correlation for each year, the results can be reduced further. Since the connection between Sweden and Lithuania was not put into use until 2016 this will exclude Lithuanian import and export from this methodology since correlations for 2015 can not be calculated. The methodology will be repeated for the span 2016 – 2019, but only data related to this connection will be presented or discussed.
In order to ensure that each correlation factor properly represents the datasets, the non-parametric pair-wise bootstrap was implemented. Using 250 resamples of the same size as the datasets an estimate of the probability distribution was calculated. Using this estimate a value that could with 95% confidence be stated as being the lower bound of the correlation factor is calculated and hence used instead of a non-bootstrapped value.
Lastly these lists of correlated datasets were identified as either linear or monotonic.
As linearity implies monotonicity, separating them is not trivial. It is also notable that it is preferable to identify as many correlations as linear as possible, as it eases the process of analysis. As a start they are separated as linear if they have an r larger than the critical value and monotonic if they have an r less than the critical value while either ρ or τ is larger. To compliment this with the cases where the monotonic correlation are much stronger, the linear cases that has a τ with a value of at least 0.2 larger than r are counted as monotonic. Only KRC is used for this rule as it gives a steeper condition to not be linear. This results in one rule for linearity and three rules for monotonicity.
linear : r > 0.4, r + 0.2 > τ (10)
monotonic :
r < 0.4, ρ > 0.4 r < 0.4, τ > 0.4 r > 0.4, r + 0.2 < τ
(11)
4.5 Comparing correlated datasets
As the purpose is to determine which variables that might have an influence over the VFs, identifying which datasets have a recurring correlation is only the first step. As a strong correlation could still represent an association between the variables with a low magnitude. Thus a method for establishing the magnitudes of the associations had to be implemented.
In the cases of linear correlation, the magnitude for each year can easily be calcu- lated as the derivation of a linear regression between the datasets. As the requirement for
linearity is only chosen as “moderate” these regressions will likely not accurately represent the nuances in the datasets but will give a rough estimate of magnitude, se fig. 1. These associative values have varying units between variables and ranges within the same main variable. Therefore, the regressions between one main variable and its linearly correlated variables will be complimented with the regressions where all variables are normalized by division of their mean. These will all be unitless, while retaining the variation of the variables around their mean. These values will be easier to compare in cases such as the solar power in Germany compared to Norway as it considers that Germany trivially has larger variation as it has more installed power capacity and therefore a larger mean. To identify variables that show a strong possibility to have an association with the VFs, they will be compared with the main variables that are known to associate with the VFs5. This will be accomplished by comparing the fluctuations in the correlation- and regression values with the fluctuations with the corresponding VF to the main variable. If they share the fluctuations of the VF it will be noted as a shared trend and if they have the inverse fluctuation, they are noted as a negative shared trend. To determine if the correlations with larger coefficient- or regression values are more likely to share a trend with VFs they will be analysed in more detail. For each main variable the correlated variables with the largest average correlation factor and largest average normalized regressions will be identified and compared with their respective VF. This will show if there is a trend between the VF and any of these correlation factors and regressions. To identify both the impact that the variables might have on whether the VF is above or below 1 and the relative fluctuations of the VF, both the VF and the VF normalized by its average over all years will be compared. The correlation factors and regressions will also be normalized by their respective average for all years to make them on the same scale as VF. Additionally all identified trends will be listed without any values. Since monotonic correlations do not necessarily represent any specific relation between variables they cannot simply be regressed. This fact limits the comparison of these cases to only looking at the correlation factors.
5Spot price, generation and revenue.
(a) (b)
Figure 1 – Examples of different correlation coefficients, and how unprecise the linear regressions are. a). r = 0.3. b) r = 0.5.
5 Results
Analysing all data acquired by applying the methodology as defined in previous section would be an extensive and laborious process. Therefore, the results and further discussion will limit its focus on price region SE4 while occasionally presenting results of other regions which presented some especially interesting results. The results from this will be used as a proof of concept for the methodology.
5.1 Value factors
As the VFs are the core of this analysis, they are presented for all 4 Swedish regions, see tab. 2. No confidence interval is presented for these values. A two-sided 95% confidence interval were created using the same bootstrap method as for the correlation factors.
None of the values showed a deviation as it pertains to being larger or smaller than 1, this gives further reliance for the values. It is notable that 2018 have the maximum peak for solar power in all regions, and the minimum peaks for both hydro- and heat power in all regions.
Table 2 – Value factors for the Swedish electric regions for the period 2015 - 2019. Nuclear power only appears in SE3 since every active reactor is in that region.
Region Year Solar power Hydro power Wind power Heat power Nuclear p.
2015 0.924 1.068 1.019 1.132 -
2016 1.045 1.050 0.972 0.990 -
2017 1.039 1.059 0.977 0.995 -
2018 1.094 1.044 0.975 0.979 -
SE1
2019 0.947 1.084 0.965 1.043 -
2015 0.913 1.015 0.992 1.146 -
2016 1.058 1.029 0.961 1.010 -
2017 1.040 1.044 0.956 1.012 -
2018 1.071 1.006 0.954 0.989 -
SE2
2019 0.955 1.037 0.969 1.038 -
2015 0.915 1.028 0.976 1,147 1.025
2016 1.051 0.997 0.977 1,058 0.989
2017 1.042 1.047 0.948 1,014 0.991
2018 1.061 0.966 0.950 0,991 0.990
SE3
2019 0.946 1.012 0.967 1,091 1.005
2015 0.967 1.098 0.934 1.156 -
2016 1.041 0.924 0.956 1.002 -
2017 1.021 1.034 0.930 1.018 -
2018 1.070 0.915 0.935 0.976 -
SE4
2019 0.953 1.032 0.958 1.067 -
5.2 Correlations
Since the VFs are calculated using the variables generation, spot price and revenue, these variables will be of main interest and called main variables. In tab. 3 the summarized cor- relations for spot price and generation in SE4 are presented. All correlations are identified as linear except for the heat generation of SE4, which has monotonic correlations with Lithuanian heat generationm, Swedish solar generation share and solar export to Denmark.
Revenue is not presented as it shares most correlations with their corresponding generation.
Table 3 – Summarised consistent correlations for the spot price and generations in SE4.
Specifications for correlations are; (-): negative, (v): monotonic, (x): deviation between negative and positive. Unless otherwise stated the correlation is positive and linear.
· All other spot prices besides in PL
· Consumption within DE, LT and PL
· Heat power generation within DE and PL
· Hydro power revenue in SE1 and SE2
· Heat power revenue in SE4 Spot price
· Nuclear power revenue within SE
· Consumption within DK, FI, NO and SE
· Total generation within DK and FI
· Heat power generation within SE2 and SE3 Generation hydro power
· It’s own revenue
· Heat power export to DK
· Wind power generation within DE, DK, LT, PL and SE3
· Heat power generation share within DK(-), PL(-) and SE4(-)
· Hydro power generation share within SE4(-) Generation wind power
· It’s own revenue
· Solar power export to DK(-v)
· Consumption within DK2, FI, NO and SE
· Heat power generation within DK, FI, LT(xv) and SE
· Hydro power generation within NO
· Nuclear generation within SE
· Solar power generation share within SE(-v) Generation heat power
· It’s own revenue
· Solar power export to DE, DK and PL
· Solar power generation within DK, FI and SE
· Solar power import from DK Generation solar power
· It’s own revenue
To widen the analysis the international import and export of electricity is also correlated as main variables. These are divided by technology and country, and also limited by the connections in SE4. SE4 has international connections with Denmark, Germany, Lithuania and Poland, this results in 32 variables. Only the export of wind- and solar power, and import of heat power will be presented, see tab. 4. These are chosen since they could give insight on the fossil fuel-based electricity Sweden imports as well as how our export of power from VRE sources fit into the wider market. It is notable that the import of heat power correlates with very few variables of which none are domestic variables for Sweden. As with the correlations for spot price, generation and revenue in SE4, most non-linear cases are identified between solar- and heat power.
Table 4 – Summarised consistent correlations for the export of VRE and import of heat power in SE4. Specifications for correlations are; (-): negative, (v): monotonic, (x):
deviation between negative and positive. Unless otherwise stated the correlation is positive and linear.
· Total import from DE
Germany · The import from DE of every other technology Denmark · Total import from DK
Lithuania · Total import from LT
· Total import from PL Import Heat power
Poland · Hydro power import from PL
· Total export to DE
Germany · Wind power generation share in SE4
· Total export to DK
Denmark · Wind power generation share in SE4 Lithuania · Total export to LT
Export wind power
Poland · Total export to PL
· Solar power export to DK and PL
· Solar power generation in SE Germany
· Solar power revenue in SE
· Solar power export to DE and PL
· Solar power generation in DE, PL, LT and SE
· Heat power generation in SE4(-v)
· Heat power generation share in SE2(-v) Denmark
· Solar power revenue in SE
· Total export to LT
· Solar power export to DK and PL
· Solar power generation in DE, DK, LT and SE Lithuania
· Solar power revenue in SE
· Total export to PL(v)
· Solar power export to DE and DK
· Heat power export to PL(v)
· Solar power generation in DE, DK, LT and SE
· Solar power import from DK Export solar power
Poland
· Solar power revenue in SE
5.3 Trends
For the trend analysis, firstly the 3 largest correlation factors and the 3 largest regressions for each variable will be investigated as to determine if the size of these values coincides with a shared trend with the VF. Additionally, every shared trend will be listed. Since the correlations for one variable in different regions of the same country often are very similar, no such duplicates will be displayed, instead the region with the highest value will be chosen. In cases where only 3 or fewer correlated variables exist, all will be presented.
The import of heat power and the spot price will not be included as they do not pair with any specific VF. What is being searched for is cases where a pair of variables continually is above average when VF is above average and below average when VF is below average, or the opposite.
5.3.1 Wind power
Wind has 6 main variables to analyse, the generation, revenue and export variables. For each of these values the relative correlation- and regression values is analysed. As the VF for wind in SE4 is always below 1 these values can only be compared with the relative change in VF. In fig. 2 these relative values are displayed as well as the actual VF, for brevity the export variables that do not include any trends are not shown. 3 values are shown to share the trend of the relative VF for all years, the relative regression of wind revenue and Danish wind power share and both the relative correlation and relative regression of wind export to Lithuania and the total export to Lithuania. The trend for export to Lithuania are inverse to the relative VF which implies that a relatively low regression increases the VF. Various values share the trend except for a single year.
(a) (b)
(c) (d)
(e) (f )
Figure 2 – Trends for VF, relative VF(*) and either the correlation or regression between a main variable and other variables. a) Correlation trends for wind power generation SE4.
b) Regression trends for wind power generation SE4. c) Correlation trends for wind power
5.3.2 Solar power
Solar includes the same number of main variables as wind. As the VF from wind power fluctuate above and below 1, trends can be found between either the actual VF or the relative VF. Fig. 3 shows the values, for brevity the export variables that do not include any trends are not shown. Neither generation nor revenue share any trends but the relative correlation of solar export to Lithuania and solar export to Poland, as well as the relative regression between solar export to Lithuania and the solar generation for both Germany and SE4.
(a) (b)
(c) (d)
(e) (f )
Figure 3 – Trends for VF, relative VF(*) and either the correlation or regression between a main variable and other variables. a) Correlation trends for solar power generation SE4.
b) Regression trends for solar power generation SE4. c) Correlation trends for solar power
5.3.3 Hydro power
Since any export of hydro power is not considered main variables it only has 2 main variables, see fig. 4. Since the average VF of hydro is very close to 1 there is no difference between it and the relative VF. 2 trends are identified, the relative regression between the generation of hydro power and both the consumption of SE1 and NO3.
(a) (b)
(c) (d)
Figure 4 – Trends for VF, relative VF(*) and either the correlation or regression between a main variable and other variables. a) Correlation trends for hydro power generation SE4. b) Regression trends for hydro power generation SE4. c) Correlation trends for hydro power revenue SE4. d) Regression trends for hydro power revenue SE4.
5.3.4 Heat power
Heat power share the same amount of main variables as hydro power. Again the VF fluctuate above and below 1, trends can be therefore be found between either the actual VF or the relative VF. Within these variables no trends matching either of the VFs are found, see fig. 5.
(a) (b)
(c) (d)
Figure 5 – Trends for VF, relative VF(*) and either the correlation or regression between a main variable and other variables. a) Correlation trends for heat power generation SE4.
b) Regression trends for heat power generation SE4. c) Correlation trends for heat power revenue SE4. d) Regression trends for heat power revenue SE4.
5.3.5 Compiled trends
Using the largest values as in previous sections gave 8 cases of trends shared with the relative VF. Looking through every case of correlation gave 32 cases, see tab. 5.
An example is that the revenue of hydro power has a negative shared trend with the consumption in Germany, when using the relative regression values.
Table 5 – Summarized variables that show a shared trend with their respective VF. (-): a negative trend.
Tech. Main variable Relative correlation Relative regression
Gen. · Gen. share wind power PL · Gen. share wind power DK
Rev. - -
Exp. DE - -
Exp. DK - -
Exp. PL - · Exp. PL
Wind
Exp. LT · Exp. LT (-) · Exp. LT (-)
Gen. · Con. SE2 and SE3 (-) -
Heat Rev. - · Gen. hydro power SE4
· Con. DK2 (-)
· Con. NO1, NO3 and NO4 (-)
Gen. -
· Con. SE1 and SE4 (-)
· Con. DK1 and DK2 (-)
· Con. DE (-)
· Con. LT (-)
· Con. PL (-) Hydro
Rev. · Con. DK2
· Gen. hydro power SE4
Gen. - · Gen. share solar power LT
Rev. · Gen. share solar power DK -
· Gen. share solar power SE3 (-)
Exp. DE · Rev. solar power SE2 (-) -
Exp. DK - -
· Solar power exp. PL · Solar power exp. PL
· Solar power exp. DK2 (-) · Solar power exp. DK2 (-)
· Gen. solar power DE
· Gen. share solar power DK Exp. LT
· Gen. solar power SE2 and SE4 Solar
Exp. PL - -
6 Discussion
The correlations and trends presented in the results will in this section be discussed.
6.1 Value factors
As the VFs of energy technologies has not been established as a common measurement of interest in the energy market there are very few previously calculated values for Sweden.
Two sources have been identified. Firstly Hirth presented the VFs for wind power for the period 2007 – 2010 [4]. This data is not only over a very different period but also calculated on the Swedish electricity market before the creation of the different electrical price regions. Therefore, it cannot be used for validation of the VFs presented in this report, but it can be used to estimate the change in VF over the span of around 10 years.
Hirth presents his conclusion that VRE sources, in this case wind power, has a decreasing VF relating to its market share. A VF in the range 0.5 – 0.8 is expected at a market share of 30%, in tab. 6 the VFs and market shares for the entirety of Sweden are shown.
Comparing the average VFs and market shares, MS, confirms the relationship of a lowering VF for an increasing MS. This phenomena is dramatically called the “self-cannibalization effect” which occurs due to market depression, due to the abundance of cheap electricity in hours of high VRE output [10]. The exact values can neither be confirmed or denied since the MS have not reached 30% for Sweden yet, but values are decreasing as the MS is increasing. The value of the wind power could also be kept more stable due to the large market share of hydro power in Sweden. Since hydro power can easily be used to compensate for fluctuations in the wind power generation, the Swedish energy market might be more ideal for wind power compared to other countries that are more dependent upon heat power [9]. Looking at the VFs in SE4 shows even lower values, while wind is the majority of the MS. These values are not in line with what Hirth’s conclusion expected, this is likely due to the low self-reliance that SE4 has on its own generation. In the span of 2015 - 2019 SE4 only produced between 25% - 31% of its own consumption per year. This likely negates the “self-cannibalization effect” since the region has such high demand that the market is barely suppressed by its own generation.
Table 6 – VFs for wind power as presented by Hirth (2007 - 2010) and those calculated in this report [4]. Market shares for all of Sweden are calculated using values presented by Energimyndigheten, while the ones for SE4 are calculated using the variables gathered from SVK [1]
MS Average MS MS SE4*
Year Sweden (%) Year Sweden SE4 (%) (%)
2007 1.03 0.99 2015 0.98 0.93 10.26 56.34
2008 0.97 1.37 2016 0.97 0.96 10.16 56.97
2009 1.01 1.87 2017 0.95 0.93 10.98 62.56
2010 1.01 2.41 2018 0.95 0.94 10.42 61.86
2019 0.97 0.96 - 62.63
The second source of Swedish VFs is a bachelor thesis whose results have been presented in a report on Swedish solar power by the International Energy Agency (IEA) [23, 24]. This thesis calculated the VFs for all Swedish regions for the period 2014 - 2019. Unfortunately, a misconception of the VFs definition leads to a faulty result that cannot be compared to.
Thus, ultimately the VFs presented in this report cannot be confirmed.
Analysing the VFs as presented shows that only a few pairs of technology and regions has a consistent positive or negative VF. Wind power has a value below one in all cases except one region for one year. This indicates that as is, the energy market is saturated for wind power. On the other hand, hydro power in regions SE1 and SE2 are consistently values above one. Meaning that the market is in demand of hydro power in these regions.
As hydro power is the main balancing power in Sweden the VFs would be expected to tend toward positive. Every other pair show varying values which does not lend them to be interpreted in such easy manner. Heat power in SE2, SE3 and SE4 have values above one for every year besides 2018. But with a sample length of only 5 years, it is difficult to disregard it, in the same manner as hydro power it would be expected to tend to a positive value. Nuclear power would as baseload be expected be neutral around one, which might explain why it varies between positive and negative, but again it is hard to draw a conclusion with only 5 years of data. All these variations reveal the main weakness of VF as a metric of value, it unpredictably changes from year to year depending on any number of variables. Likely, any single-value metric that is based on datasets of this size will have this weakness. This thesis will as stated identify which variables in the northern electricity market that might affect the VFs, but this of course does not include every possible variable of interest. It is a metric that rarely can be stated as a stably positive or negative, and unlikely to be able to statable as a fixed number. Theoretically, if they were calculated over many years, they could be stated with some interval of confidence. But as the energy market is ever changing with new sources being introduced and old sources being phased out, the comparability of years only a decade apart might be very low. It might be better used for short term observations. Instead using VF as a tool to identify a notable variation in the short term for an energy source and then looking for variables that coincide with that specific variation. With an estimate of how much an unpredicted change of the vari- able could have on the revenue of the energy source. This might be a more appropriate use.
The fact that 2018 had peak values for three of the four technologies was intriguing and was chosen to be looked closer at. Looking at the association between every tech- nology’s VFs and respective correlation between spot price and generation, shows that they always share trend. In fig. 6 these trends can be seen for solar- and heat power in SE4. Note that unlike the figures in the previous section these are not normalized by the average for all years as the correlation and VF are always positive and negative at the same years. Since the correlation is centred around 0 while the VF is centred around 1, the correlations have been added by 1. This does not necessarily scale the factors correctly but shows the shared trend around the centre value. The requirement of a critical value is here discarded as the VF is known to be dependent on both the variables. Looking in the
(a) (b)
Figure 6 – Linear correlation between spot price and generation, and their respective VF a) Heat power. b) Solar power.
table for variables that trended with heat power the consumption in SE2 and SE3 share a negative trend with generation and the hydro power generation a positive trend with revenue. Both the consumption in SE3 and the hydro power generation also peak in 2018, consumption a maximum peak and generation a minimum peak as would be expected by their respective negative and positive shared trend. The consumption of SE2 does not share this peak, which makes this variable less likely to be associated with the VF of heat power in SE4. In the same manner the solar power VF shares its peak with the Lithuanian solar generation share but not with the Danish generation share. This identification does neither confirm that a direct association exist nor that a correlation does not exist, but gives some credibility to the ability the methodology has to identify potential associations.
To further analyse the peaks of 2018 the VF could be divided into a more granular scale.
Dividing the VFs into quarterly values could feasibly be accomplished in two ways, either the VF for the internal period could be calculated by changing the entire time span when calculating the VFs or by only changing the time span of the actual revenue while leaving the average revenue as the entire year. The second approach results in separate values that add up to the VF for the entire year, see fig 7.
Analysing with this granularity shows during which period these peaks appear. As for the 2018 peaks they can be identified as prominent in Q3 - Q4 for hydro power, Q1 for heat power and solar at Q3. Notably both wind- and heat power also has a maximal peak value during Q3. The peak in Q1 for heat power coincides as before with the consumption in SE3 but not any of the other two variables. This could indicate that since the analysis up to this point only considers the entire year, the results cannot be applied on specific internal time periods. As for the peaks during Q3, it is known that the very dry and warm summer of 2018 led to a diminished hydro power generation [25, 26]. These variables
(a) (b)
(c) (d)
Figure 7 – VFs divided into different quarters of the year. Only 2018 is given an individual line-style as it is the one being analysed. a) Wind power. b) Heat power. c) Hydro power.
d) Solar power.
Figure 8 – The average hourly generation of hydro power and average hourly spot price during the third quarter for SE4.
unfortunately are not included in this analysis, but the effects can be seen in fig. 8. The limited amount of hydro power spiked the spot price in the region and therefore increased the VFs for every other technology.
6.2 Identified correlated variables
The variables identified were either of the known to related to VF, generation and revenue, or from the chosen export data.
6.2.1 Generation and revenue
Using the methodology of shared trends 20 pairs of variables out of around a possible 1800 pairs for the generations and revenues of SE4 were identified. Unfortunately, both wind- and solar power only had correlated variables that could have been assumed to be correlated. Both have the generation share of the same technology in two other countries.
As the technologies are highly dependant on meteorological parameters such as wind speed and cloud coverage they would be expected to correlate with the same technologies in adjacent regions. The fact that variables are all in other countries could imply that fluctuations for these VFs are more associated with the energy market in other countries than the other Swedish regions. For hydro power the consumption in most regions is identified. This is logical as hydro power is the primary balancing power within Sweden, this means that an increase in consumption is typically met by an increase in hydro power generation. Most of the consumptions are identified using the relative regression, they are unpredictably identified negative unlike the expected positive that the relative correlation
gave. The fact that the relative regression identified so many expected variables gives credence to the use of this metric in this manner. But that the trends are identified as negative, in the case of consumption in DK2 even as the correlation gives a positive trend, implies a misinterpretation of what should be considered negative.
6.2.2 International export
As the export of energy from a technology is not known to associate with its corresponding VF, the trends from the export of wind- and solar power cannot be considered more likely to be associated with the VF. But as the trade of electricity between regions are an integral part of the energy market their trends can still be compared to the VFs to identify any coinciding variables. These exports mostly resulted in trends with other export data, but also 4 export variables lacked trends all together. This likely stems from a bias that was introduced when separating the import and export data. For example, in the hours of export the dataset for import could either be set as zero or without value.
In this case they were set without value, which leads to all these hours are lost when comparing to that specific dataset. The extreme case is the import from Poland in 2015 that only contains 212 hours of data, while Germany and Denmark has datasets that are closer to half the hours of the year. The majority of the datasets has more hours of export than import. However many hours are lost with this method, it increases the likelihood that some nuance is lost. Keeping these hours with a value of zero retains the nuances but introduces its own problems. It would place a large amount of data on the same value on the export axis, which would have non representative effects on the covariance and regression slope.
Leaving the values without value at least leaves the results representative of the hours with values. It is possible that keeping the import and export within the same dataset could give better results, although this would probably require some other form of pre-processing if a trend of specifically the import or export was to be analysed. It would have been interesting to find a correlation between the import of heat power, that assumedly would largely be fossil based, and domestic VRE as a further incentivisation to reduce emissions.
In fig. 9 the correlation between the import of heat power from Poland and the generation within SE4 are shown. Domestic heat power have a consistently positive correlation while solar power have a negative, although weakly correlated. If these were representative of the entire years it might have indicated that an increase in solar power would not have diminished our dependency on foreign heat power, but with the problems described it would be false to draw any conclusions based on these values. Further development of this analysis that solved this problem could create a method to easily estimate how each technology affects the self-reliance of a region.
Figure 9 – Correlations between the import of heat power from Poland and the generation of electricity within SE4.
7 Conclusion
The purpose of this thesis was to calculate the VFs of Swedish electricity generation divided into different technologies, identify variables in the northern European energy market that influence these VFs and develop a methodology that can be repeated for any variable.
Firstly, the VFs for 2015 - 2019 have been calculated and presented in this report.
A lack of previously published calculations removes the possibility of comparison and validation. The closest point of comparison was for wind power during the previous decade. The estimation of VFs compared to market share that was predicted using earlier values indicate that the VF should be decreasing with an increasing market share. This holds true for the VFs calculated in this thesis. This ultimately cannot validate the result and leaves them as only probably correct.
Secondly, variables that show consistent correlation with the spot sprice and gener- ation profiles of SE4 have been identified. Out of these variables, several was identified as sharing the trend behaviour of their respective VF.
Thirdly, the methodology is devised in such a way as to be easily repeatable for any set of variables. As discussed with the import and export datasets, non-consistent datasets can introduce biases in the analysis and should be evaluated using another method. This method also does not result in a numerical value on how variables and VFs associate with each other.
Recommendations for further work
The first step in any future work should be to remake all results using different sources and/or methods. The VFs cannot be approached with a different method without intrin- sically calculating a different metric. So only calculations based on other data sources, if such exists, could be made to verity their validity. Identification of which variables share an association with the VFs could also be verified with other sources, but more interestingly a proper multivariate analysis could be performed.
Further development of the metric should focus on defining a practical application of it. As discussed, it rarely results in a clear indicator of market demand or saturation.
One practical application could be indicator of short-term variation, such as discussed for 2018. This could possibly be developed into a tool for risk and effect analysis.
References
[1] Statens Energimyndighet. Energiläget 2020. Statens Energimyndighet, 2020.
[2] Chun Sing Lai and Malcolm D. McCulloch. Levelized cost of electricity for solar photovoltaic and electrical energy storage. Applied energy, 190:191–203, 2017.
[3] Manuel Eising, Hannes Hobbie, and Dominik Möst. Future wind and solar power market values in germany — evidence of spatial and technological dependencies?
Energy economics, 86:104638, 2020.
[4] Lion Hirth. The market value of variable renewables. Energy economics, 38:218–236, 2013.
[5] IEA. World energy outlook, 2018.
[6] IEA. World energy model, 2020.
[7] Mark Capellaro. Prediction of site specific wind energy value factors. Renewable energy, 87:430–436, 2016.
[8] Javier López Prol, Karl W. Steininger, and David Zilberman. The cannibalization effect of wind and solar in the california wholesale electricity market. Energy economics, 85:104552, 2020.
[9] Lion Hirth. The benefits of flexibility: The value of wind energy with hydropower.
Applied energy, 181:210–223, 2016.
[10] Lion Hirth and Simon Müller. System-friendly wind power. how advanced wind turbine design can increase the economic value of electricity generated through wind power. Energy economics, 56:51–63, 2016.
[11] E. Glen Weyl. Price theory. Journal of economic literature, 57(2):329–384, 2019.
[12] Jeremy Adler and Ingela Parmryd. Quantifying colocalization by correlation: The pearson correlation coefficient is superior to the mander’s overlap coefficient. Cytom- etry Part A, 77A(8):733–742, 2010.
[13] G.W. Corder and D.I. Foreman. Nonparametric Statistics: A Step-by-Step Approach.
Wiley, 2014.
[14] Maurice G Kendall. A new measure of rank correlation. Biometrika, 30(1/2):81–93, 1938.
[15] Weichao Xu, Yunhe Hou, Y. S. Hung, and Yuexian Zou. A comparative analysis of spearman’s rho and kendall’s tau in normal and contaminated normal models. Signal processing, 93(1):261–276, 2013.
[16] Roger W. Johnson. An introduction to the bootstrap. Teaching statistics, 23(2):49–54, 2001.
[17] ENTSO-E. Tranparency platform, 2020.
[18] Lion Hirth, Jonathan Mühlenpfordt, and Marisa Bulkeley. The entso-e transparency platform – a review of europe’s most ambitious electricity data platform. Applied energy, 225:1054–1067, 2018.
[19] Svenska kraftnät. Elstatistik, 2020.
[20] Nord Pool. Market data, 2020.
[21] D. Lingfors and J. Widén. Development and validation of a wide-area model of hourly aggregate solar power generation. Energy (Oxford), 102:559–566, 2016.
[22] Haldun Akoglu. User’s guide to correlation coefficients. Turkish Journal of Emergency Medicine, 18(3):91–93, 2018.
[23] Sara Särnblad, Nora Ekström, Katarina Vanky, and Agnes Bråve. The Value of Value Factors: Time-dependent Development of Value Factors on the Swedish Electricity Market. Thesis, 2020.
[24] Johan Lindahl et al. National survey report of pv power applications in sweden.
Technical report, IEA, 2019.
[25] C. Dellby. Så påverkades elproduktionen av den varma sommaren 2018. Energimyn- digheten, 2018.
[26] SMHI. Sommaren 2018 - extremt varm och solig. 2018.
A Example of correlation
(a) (b)
Figure A.1 – Examples of correlation matrices. In this case the average (a): PMC and (b): KRC, for Swedish generation over the span 2015 - 2019.
