Detecting changes in price-sensitivity of household electricity consumption : The impact of the global energy crisis on implicit demand response behavior of Finnish detached households

The energy transition combined with the ongoing global energy crisis and soaring inflation has pushed household electricity prices to all-time high levels. The year 2022 was especially rough for customers due to significant electricity price increases, leading to, for instance, a fall in the European consumer confidence index to a new all-time low. When dealing with very high electricity prices, the only things household can do to reduce their utility bills is to reduce consumption, invest in self-generation, or change to a time-based electricity contract and shift consumption to cheaper times. In this study, we present a methodology for analysis of changes in customer electricity use behavior and price-sensitivity based on smart electricity meter data, correlation analysis and the k-means clustering algorithm. Electricity meter data is further used to cluster customers into different primary heating type groups to analyze whether there exist behavioral change differences between these groups. As a case study we utilize these methods to investigate the impact of the global energy crisis and rapidly risen electricity prices of 2022 on the price-sensitivity of Finnish detached house electricity use. Based on our results, almost a third of the analyzed households had a statistically significant increase in implicit demand response behavior from January to December of 2022. The largest shares of households with a statistically significant increase in price-sensitivity were in night-time water heating, oil, and ground-source heating groups.


Introduction
The global energy landscape is undergoing a significant transformation, driven by the urgent need to mitigate climate change and transition towards sustainable and renewable energy sources.This energy transition is accompanied by numerous challenges, including increasingly volatile electricity prices and difficulties in power grid balancing [1].Additionally, the global energy crisis that began in the aftermath of the COVID-19 pandemic and was escalated due to the invasion of Ukraine has pushed electricity and natural gas prices to record highs and induced considerable uncertainties to the market [2][3][4].The impact of the energy crisis combined with soaring inflation and rising prices and interest rates went so far in 2022 that the European consumer confidence fell to a new low [5].Based on the European consumer payment report [5], over one third of European consumers expected that they will not have enough money to pay their utility bills due to increasing energy prices of 2022.
In addition to lowering their electricity consumption, or generating their own electricity, the only way for consumers to minimize their electricity bill is by changing to a time-based electricity tariff and shifting their consumption from expensive to cheaper times.Time-based electricity contracts cover Time-Of-Use (TOU), Critical Peak Pricing (CPP) and Real-Time Pricing (RTP) tariffs [6].Of these, Real-Time Pricing, also known as dynamic pricing, reflects actual electricity market prices, which are inherently tied to variable production costs and are generally made available either day-ahead or closer to the actual time of use [6].Due to more frequent and market-based price changes, RTP contracts with prices known well in advance (e.g., day-ahead) offer the best possibilities for customers to affect their electricity bill by shifting their electricity consumption from one time to another.Adoption of RTP contracts with time-varying rates can thus increase the price-sensitivity of electricity use and further decrease the overall system peak demand.This price-sensitivity, where customers shift their electricity consumption to hours of cheap electricity, is also called implicit, or, time-based demand response (DR) [7,8].Financially motivated shift of consumption through real-time pricing is a cornerstone of demand flexibility, enabling consumers to actively save in their electricity bills by adjusting their electricity usage in response to price signals.Typically, consumers utilize demand flexibility by adjusting the usage times of time-shiftable home appliances such as washing machines, dishwashers, and dryers, as well as by optimizing the charging times of electric vehicles (EVs) [9][10][11].Overall, it can be stated that time-based electricity contracts and especially RTP contracts enable household implicit demand response.
However, RTP electricity contracts are not available for households in every country.In 2019, time-varying RTP contracts were available to households only in eight European countries: Finland, Estonia, Sweden, Spain, Netherlands, Denmark, UK, and Norway [12].These dynamic RTP contracts are however gradually spreading to other countries.Based on the European Commission, dynamic electricity contracts empower consumers to change their electricity use behavior and can in many cases significantly reduce household electricity bills [12].Customers that employ or have access to a dynamic RTP electricity contract are the best possible customer groups to analyze when assessing the impact of the global energy crisis on electricity use behavior, as they can influence their electricity bill not only by lowering their consumption but also by changing the time of their electricity use.Due to surging electricity prices of 2022, there was a significant shift towards dynamic exchangepriced electricity contracts especially among households in Finland [13].Finland belongs to the Nord Pool electricity market and has hourly priced spot electricity available to consumers through a day-ahead market.These hourly day-ahead electricity prices, effectively representing RTP for Finnish household consumers, are disclosed on the previous day around 2 pm and can be attained through various websites and applications, such as from [14][15][16].For these reasons, we use Finland as a case example for the methodology presented in this study.
Decision-making power over household energy consumption varies based on both the type of the building and form of ownership, with detached households wielding significantly more control in this regard compared for instance to tenants of housing cooperatives [17].Detached households have the largest possibilities to affect their electricity usage, heating type, energy efficiency etc. as they are not bound by choices and opinions of others.For instance, electric vehicle charging is a good example of a novel load that is easier and more lucrative to control for residents of detached households than residents of apartment buildings.Detached households can install their own charging points, change to a day-ahead RTP electricity contract and shift EV charging to cheap electricity hours, participate in explicit demand response schemes or utilize the EV as an household electricity storage, all of which can incur substantial cost savings directly to the resident [8,[18][19][20].Such high decision-making power and cost saving opportunities of detached households makes them an ideal target group for analyzing the impact of the global energy crisis on consumer electricity usage behavior.
It should however be noted that high decision-making power and high savings opportunities are not enough for behavioral change; consumers must also first be aware of dynamic electricity tariffs, must comprehend their features and understand how their behavior influences their electricity bill [21].In Sweden, a survey-based study found that only about 3.8-8.5 % of respondents had enough understanding of electricity pricing and time-based electricity tariffs to be fully able to change their behavior based on electricity price signals central to RTP electricity contracts and implicit demand response [21].The authors found that detached household residents were more likely than apartment residents to be able to meet the suggested preconditions for informed implicit demand response behavior [21].
In this study we analyze the impact of the energy crisis and rapidly increased electricity prices on the price-sensitivity of detached household consumers.This price-sensitivity is examined through a novel method combining correlation and cluster analysis and is based on automatic meter reading (AMR) electricity usage data and hourly spotmarket electricity price data.
Several previous studies have analyzed customer electricity use behavior or clustered consumers based on AMR data.AMR data has been used for instance in customer classification and load profiling for use in distribution network analysis and planning [22,23], in classification of new residential electricity customers [24,25] and in detection of load pattern changes [26].More recently, AMR data has also been used to assess the impact of the COVID-19 pandemic on household electricity use patterns [27,28] and to analyze the relationship between demographics and residential electricity consumption behavior [29].Overall, utilization of AMR data is a highly practical way to assess the social and behavioral side of electricity consumption and is becoming a more prominent area of study in tandem with the increasing deployment of smart meters.
With regards to the global energy crisis, the authors of [30] analyzed how Norwegian residential consumers changed their electricity usage behavior in the early energy crisis of winter 2021/2022 based on AMR data and a survey.They conducted a comparison between the "winter period," defined as November 2021 to March 2022, and the "reference period," defined as June 2019 to July 2021.Specifically, they examined the hourly demand during the winter period and compared it with the demand across all hours of the reference period.The authors found substantial reductions in average hourly demand compared to the reference period but on average no increase in intraday price-sensitivity [30].Surprisingly, households reduced their electricity consumption less during peak price hours compared to off-peak, implying the exact opposite of implicit demand response [30].
In addition to the presented novel methodology, we aim to uncover if the energy crisis and the skyrocketing electricity prices of 2022 had an impact on the price-sensitivity behavior of household electricity use based on AMR data from nearly 400 Finnish detached households.Daily correlations are calculated based on hourly household loads and electricity prices and utilized as monthly averages in clustering to identify customer groups that have heightened their sensitivity to hourly electricity prices in 2022.The analysis is further deepened by clustering the households by their primary heating type, enabling an examination of possibly differing price-sensitivity behaviors among various heating source users.The considered household primary heating types are introduced in Section 3.3.Overall, the presented methodology for analysis of how the behavior of households with different primary heating types is influenced by financial incentives of day-ahead RTP contracts can help decision-makers in efforts to incorporate more demand response into the grid.To our knowledge, no prior study has presented or utilized such methodology and analyzed the impact of rapidly risen electricity prices and the energy crisis on customer electricity use behavior this way.

Background
The average household electricity prices in EU reached all-timehighs in 2022 based on Eurostat's records [3].Evolution of EU household consumer electricity prices from 2010 to the end of 2022 are presented in Fig. 1 based on Eurostat statistics [31].The impact of the global energy crisis can clearly be seen from the figure as the electricity prices start to skyrocket after the first half of 2021, reaching 26.5 c/kWh in the fall of 2022.Compared with the second half of 2021, the highest increase to fall of 2022 was recorded in Romania where the household electricity price increased by over 112 %, with the average increase in the EU being over 22 % [3,31].These increases are far more substantial than for instance in the US, where the average residential retail electricity price increased only by 11 % from 2021 to 2022, and only by 2.5 % if adjusted for inflation [32].
In the last quarter of 2022, the average household electricity prices in Finland also rose to a new all-time high.According to Statistics Finland, the average overall electricity price for Finnish households considering all different tariffs was 20-34c/kWh in the last quarter of 2022, an increase of 23-26 % from the previous quarter, and an increase of 41-49 % when compared with the last quarter of 2021 [33].The rapidly risen average overall electricity price, covering all electricity tariffs, for a typical detached household from Finland is presented in Fig. 2.
In this study we analyze the price-sensitivity of household electricity use based on inter-daily hourly correlations.The correlations are calculated between the hourly electricity usage and the hourly electricity spot-market prices.The daily and monthly averages, medians, and minimums/maximums of the Finnish hourly day-ahead spot-market (RTP) electricity prices in 2022 are presented in Fig. 3a & b.It should be noted that differing from Fig. 2 these day-ahead spot-market prices do not include taxes, charges, marginals, or transmission fees.One important observation is that whereas the average hourly spot-prices were highest in August and declined afterwards, the average overall household electricity prices (Fig. 2) continued to increase substantially in the following months.
In the fall of 2022 Finnish electricity companies initiated significant raises in old ongoing contract prices or terminated them all together.For instance, Fortum terminated old cheap ongoing electricity contract types in the fall of 2022, leading to over 200 % price increases to the consumers [34].These enormous price hikes combined with a vast media coverage about the energy crisis and the need for electricity conservation led to extensive shift towards spot-priced electricity contracts in the last half of 2022 [35][36][37][38].Based on Finnish Energy Authority, the share of hourly spot-priced contracts of all consumer electricity contracts grew from 9 % at the end of 2021 to 13.7 % at the end of 2022 [13].This trend continued in 2023, with 17 % of Finnish households having an hourly day-ahead RTP contract in June [35,36].In this study we analyze if these trends affected the pricesensitivity of electricity use in detached households.
It should be noted that in day-ahead electricity markets, where electricity prices result from matching demand and supply, prices typically peak during conventional high-demand hours such as late afternoons and early evenings [39,40].That is, consumers without marketbased RTP contracts have no economic incentive to alter their consumption to respond to hourly changes in electricity price [41,42].Consequently, increased price-sensitivity should be mainly evident among those with RTP contracts, as their electricity bills are directly influenced by the changes in hourly market prices.As Finland is a single electricity market bidding area, hourly day-ahead RTP market prices for all consumers are identical.
As Finland is part of the Nord Pool electricity market and is interconnected to Swedish and Estonian power grids, the results of our Finland case example can also be seen to indicate the situation of Nordic and Baltic countries.Due to the shared electricity market, similar hourly RTP pricing and grid interconnections, the electricity prices between Finland and Sweden differ only when the interconnections are congested and cannot transmit electricity according to market demand, in this electricity price difference between Finland and Sweden rose to a Fig. 1.Bi-annual electricity prices in the EU for household consumers with annual consumption 5,000 kWh -14,999 kWh, all taxes and levies included.new high [4].The power system of Finland was also interconnected to Russia with around 10 % of total electricity consumption of Finland imported from Russia [43].This interconnection was however disconnected in May of 2022 in the aftermath of the invasion of Ukraine [44].The reductions in supply of Russian natural gas drove energy prices even higher across Europe and the Nordic countries [1].Overall, the sanctions on Russia and other consequences of the invasion of Ukraine have had a major impact on the Finnish energy sector and are one of the key reasons for all-time-high electricity prices of 2022.These special circumstances make Finland an especially interesting case country when assessing the impacts of the energy crisis on household electricity use behavior.

Data normalization
Weather influences household energy use in many ways.Of different weather factors, outdoor temperature has the largest impact on household electricity demand [22,23].This is why many previous studies [23,26,[45][46][47] utilizing AMR measurements temperature normalize the data to remove the impact of temperature variation on loads.However, there also exists highly-cited studies that do not temperature normalize AMR data and only normalize the data with respect to customer maximum loads [24,25,48].Load normalization is a common practice as annual energies of different customers can differ significantly [22].In this study we will first temperature normalize the data and then conduct load normalization for each customer separately by dividing each hourly load by the load vector's average load similarly as in [23].
Temperature normalization of the AMR measurement data was conducted similarly as in [22,23,26,47].That is, we utilize temperature dependence parameters, α, calculated via linear regression analysis for every two-month period of the year, as found to be the best compromise between sensitivity and yearly temperature dynamics modeling capability in [23].These temperature dependence parameters α i x are defined for each household, x, and for each two-month period of the year, i, separately via linear regression as presented in [22,47]: Here the regressand vector E i x denotes the difference between daily electricity consumption and average daily electricity consumption on a similar day.The regressor T i x denotes the vector of differences between daily average effective temperatures and average effective temperatures of similar days.Similar day is defined as the same weekday in the same month as in [22], and effective temperatures as the average outdoor temperature of the 24 h preceding each hour as in [23].Effective temperatures are calculated based on the previous 24 h period to account for the delay in temperature dependency of household electricity use [22,49] After the temperature dependence parameters are calculated, the AMR measurements are normalized to long-term (30 years) average temperatures.The temperature normalization for a load of household x at hour t is performed with equation (2) similarly as in [26].

P t
x,norm = Where:

P t
x,norm is the temperature normalized load of household x at hour t, P t x is the measured load at hour t, T d avg is the daily average effective temperature, T m avg is the long-term average monthly outdoor temperature, α i x is the temperature dependency parameter of the two-month period i.
After temperature normalization we conduct load normalization similarly as in [23], that is by dividing each customer-specific hourly load by the load vector's average load.The normalization process will result in a load vector for each customer with mean value of one.

Correlation and cluster analysis
In this study we analyze the price-sensitivity of household electricity use based on hourly Pearson correlation coefficients.As a starting point, we calculate for each household x daily correlation coefficients r x,d between hourly electricity usage and hourly electricity spot-market prices for each day d.Lower correlation coefficient implies higher pricesensitivity of electricity use, that is, higher hourly consumption during hours with low electricity price.We employ these daily correlation coefficients to evaluate the potential growth in intraday implicit demand response behavior of households.Implicit DR involves, for instance, shifting the usage of home appliances by some hours, from expensive hours to cheaper ones.Household loads are generally more conveniently shifted within a single day (intraday) rather than between different days (interday).This is largely due to behavioral patterns, human needs, comforts, and freedom [11].Based on, for instance [11], consumers are typically willing to shift household appliance use by a maximum of 10 h, but the duration for willingness to shift can be even shorter depending on the specific appliance.
It should be noted that inelastic (non-price-sensitive) consumption patterns typically lead to high positive daily correlation between electricity use and hourly prices due to electricity market pricing based on supply-demand dynamics.That is, higher and positive correlation between electricity use and electricity price is typical when electricity use is not influenced by the hourly electricity prices.For instance, the overall electricity consumption of Finland in 2022 [50], can be calculated to have had an average daily correlation of over 0.73, indicating high consumption during hours with high electricity prices.In addition to the daily correlation coefficients, we considered utilization of 33-hour periods from 15:00 to 23:59 of the following day (from when market prices are available, to the end of published price period) to account for intra-day price-sensitivity.This method will however result in overlaps (as each timeframe would include hours from the timeframe of another day), that would complicate accurate analysis and estimation of changes in price-sensitivity, and lead to unreliable results due to double accounting of possible load shifts.That is, daily coefficients were deemed more reliable in estimation of changes in household price-sensitivity.
For the clustering we utilized the widely used k-means clustering algorithm, which is particularly useful when the objective is to distinguish clusters that have similar data points from those that have significantly different data points.The optimal number of clusters was determined based on the elbow method, which helps identify the point where the improvement in sum of squared errors (SSE) starts to level off as the number of clusters increases [51].By visually inspecting the plot of SSE values against the number of clusters, the "elbow" point was identified as the optimal number of clusters for the given data.As simple clustering based on daily correlation coefficients r x,d cannot cluster the households based on change of price-sensitivity during the year 2022, we explored different approaches on how to best catch and cluster the possible increase of price-sensitivity towards the end of the year.During our iterative process we experimented with clustering based on daily correlations across daily, weekly, and monthly timeframes.However due to limitations of the clustering method, these approaches utilizing data of the whole year were not effective in distinctly separating households with increasing price-sensitivity.Ultimately, we determined that clustering based on the difference between the monthly averaged household daily correlation coefficients of December and January was most effective in identifying households that became more pricesensitive towards the year's end.January and December are ideal reference months for assessing changes in household price sensitivity from the beginning of the year while considering the impact of the significant rise in electricity prices during the fall of 2022.The utilization of January and December as reference months is further supported by their typically similar load profiles and temperatures; in 2022, the difference in the standardized heating degree days in the case region was just 7, and the difference in average temperatures was a minimal 0.2 • C [52].To account for potential load variations due to changes in outdoor temperature, we temperature normalized the AMR data as discussed in section 3.1.
To quantify the change in price-sensitivity of a household x during the year we utilize the monthly averaged daily price-sensitivity correlation coefficients of January and December, r x,Jan , r x,Dec , correspondingly.If r x,Jan -r x,Dec > 0, it indicates that the customer has become more price-sensitive, and <0 indicates the opposite.In other words, a reduction between monthly correlations implies that the household tends to consume less electricity during high-priced hours (or more during lowpriced hours) in the end of the year compared to its beginning, signifying increased price-sensitivity and implicit DR behavior.Due to the central limit theorem, the average correlation coefficients (and their differences) can be considered as Gaussian distributed stochastic variables.This allows us to determine for each household if the change is statistically significant at given confidence level [53].In this study we utilize the standard 95 % confidence level and conduct hypothesis testing using the Z-test.

Household clustering based on primary heating source
In order to further investigate the differences in household pricesensitivity and to analyze if there exist some groups that have changed their behavior more than others, we further clustered the household AMR data based on primary heating type.The households belonging to these heating type groups were then analyzed and clustered similarly as described in section 3.2.
In this study, we utilized temperature normalized household AMR data to cluster the households based on temperature normalized primary heating type load curves.The household primary heating types considered are district heating (DH), ground source heating (GSH), oil heating, and heating types based on electricity; direct electric (DirEl), electric storage heaters (ElStor) and electric heating with night-time tap water heating (ElNight).These heating types cover the most common detached household primary heating sources.
The clustering of the households to different primary heating groups was done with k-means based on the most up-to-date Finnish detached household load curves available, developed in research contracted by the Helsinki distribution system operator, Helen Sähköverkko Oy [46,54].These load curves were generated based on AMR data of 2016-2018 from nearly all detached households in Helsinki and compiled to respond to the 2018 calendar year [54].The clustering process used to generate the load curves is similar to that described in detail in [23].These household load curves have been previously applied, for instance, in household electricity cost optimization with vehicle-to-home and vehicle-to-grid technology [18,19].

Case data description
The household AMR dataset used as a case example for the methodology of this study covers all detached households from municipality of Orivesi in central Finland.Orivesi is a detached household-centric municipality with around 9,000 residents located within commuting distance to the third largest city in Finland, Tampere.This municipality appropriately represents the share and heating source distribution of detached/semi-detached houses of Finnish semi-urban and rural municipalities based on Statistics Finland [55].In 2022, half of all Finnish detached/semi-detached houses were located in semi-urban or rural municipalities [55].
During data cleaning we removed clearly erroneous measurements, households with yearly consumption less than 2 MWh or more than 40 MWh, households with multiple long gaps, missing values or errors in the measurements, and the small number of households that transferred electricity back to the grid.Similarly to [22], we also omitted households with missing data intervals longer than five hours, which led to exclusion of over 70 % of the remaining households.This criterion constituted the single most significant exclusion factor in data cleaning and selection.Even if we had applied a criterion of missing data interval exceeding 24 h for exclusion, it would have resulted in the removal of approximately half of the households.This suggests potential issues in AMR data collection or extended maintenance interruptions.
The original timescale of the data was 5-min.After data cleaning and processing, the data was transformed to hourly scale to correspond to hourly electricity prices.In the end the dataset consisted of the hourly electricity usage data for nearly 400 detached households in 2022.The daily median electricity loads of the households clustered by primary heating source are presented in Fig. 4.Here the electricity-based heating types (DirEl, ElStor, ElNight) are combined into a single group to maintain customer privacy of ElStor cluster with only one household.
As can be seen from Fig. 4, there exists major peaks in daily electricity consumption especially in the winter season.These peaks generally coincide with sudden decreases in outdoor temperatures, implying they might result from electricity use for heating.The impact of outdoor temperatures on electricity consumption highlights the need for temperature normalization to accurately analyze and compare the price-sensitivity of electricity use.The temperature data used to temperature normalize the AMR data was downloaded from the open data portal of the Finnish Meteorological Institute [56], and the hourly electricity spot price data for the Finnish market zone in 2022 was downloaded from the ENTSO-E Transparency portal [57].

Results
We computed the correlation between the electricity usage and price for all households separately for each day.Then we computed the monthly averaged correlation, shown by the dashed line in Fig. 5.We note that price-sensitivity is indicated by low correlation between hourly prices and loads.As detailed in Section 3.2, an increase in sensitivity to electricity prices is reflected by decrease in the month-bymonth correlation coefficients.The difference between the January and December averaged daily correlations was used for k-means clustering of the households into 4 clusters.Optimal number of clusters was decided based on the elbow method as described in Section 3.2, and as shown in Fig. 5.The monthly averaged correlations of these clusters are presented in Fig. 6.It should be noted that these clusters, resulting from   k-means clustering, do not inherently carry explanatory names; however, upon further analysis, Cluster 1 can be described as households exhibiting a major change towards higher price-sensitivity, Cluster 2 shows a moderate shift in the same direction, Cluster 3 remains quite stable with little change in price-sensitivity, while Cluster 4 indicates a counterintuitive trend with increased loads during hours of higher prices.The increase in correlation during summer months can be estimated to result mainly from lower overall electricity consumption due to longer daytime and warmer temperatures, from increased inconvenience, or reduced possibilities for load shifting as these months are typical summer vacation time.
From Fig. 6 it can be seen that there exist two clusters (clusters 1 & 2) that have considerably lower correlation between their hourly electricity usage and hourly price in the end of the year than in January.These clusters cover 34 % of all households.Cluster 1 customers that are significantly more price-sensitive in December than in January, contains around 6.1 % of the households.In this cluster the average correlation drops from almost 0.26 in January to less than − 0.11 in December.For clusters 3 and 4, there is no trend of increasing price-sensitivity, even to the extent that households of cluster 4 tend to use even more electricity during expensive hours at the end of year than in the first half of 2022.In addition to changes in price-sensitivity, the overall temperaturenormalized electricity consumption of the households was also influenced by the energy crisis.On average, the electricity consumption of households decreased by over 15 % from January to December 2022.
The shares of statistically significant changes in price-sensitivity for all households and for each household cluster are presented in Table 1.
Here the percentages of Stat.Sig.increase/decrease express the portions of the groups in which the change in price-sensitivity was statistically significant at a 95 % confidence level (p < 0.05).The increase/decrease groups express households that have small changes in their pricesensitivity, but where the change was not statistically significant.
Based on Table 1, there is statistically significant increase in the price-sensitivity of electricity use in almost one third of the detached households.Almost 70 % of the households exhibited increase in pricesensitivity from January to December if the households where the change was not statistically significant were included.In cluster 1, all households expressed a statistically significant increase in pricesensitivity, whereas majority of the households in cluster 2 also had a significant increase in implicit demand response habits.
To further showcase the change in customer behavior, we have plotted the average fraction of electricity usage during daily peak, offpeak and normal price hours for cluster 1 in January and December in Fig. 7.Here the peak price hours are defined, similarly as in [30], as hours with electricity price that is at least 10 % higher than the average spot price of the day, and off-peak hours as those with at least 10 % lower price than the average.All other hours of the day are considered normal price hours.For this cluster, there has been a 5.6 % decrease in electricity consumption during peak hours and a 6.9 % increase in consumption during off-peak.
If all households with statistically significant increase in the pricesensitivity were to be analyzed similarly as in Fig. 7, the behavioral change is lower with a 2.8 % decrease in electricity consumption during peak hours and a 2.2 % increase in consumption during off-peak.When a similar analysis is conducted on the whole dataset, only a small increase (0.4 %) is noted in consumption on off-peak with no change in consumption on peak hours, indicating no substantial increase in response to intraday electricity prices for the average detached household.
The price correlations of the 2022 case data clustered by primary heating source, as described in section 3.3., are presented in Fig. 8.The clustered data by heating type is further clustered as in Fig. 6 to separate possible households that have increased their price-sensitivity towards the end of the year.The average line in each plot considers the differing number of cluster members and represents monthly averaged daily load/price correlation of that heating type group.It should be noted, that in the electric storage heaters (El_Stor) cluster there exists only one household, and thus further clustering is impossible, and no generalizations should be made based on this heating type.From the figure it can be noted that there exists at least one cluster per all heating type groups (except in El_Stor) where the price-sensitivity increases substantially towards the end of year from the beginning of 2022.
Based on Fig. 8, the most stable customers regarding the pricesensitivity throughout the year seem to be somewhat surprisingly the direct electric heated detached households (DirEl).In this heating group, only one of the households (Cluster 1) became significantly more price-sensitive towards the end of the year, whereas the behavior of other households was quite consistent throughout the year.The Cluster 1 of district heated (DH) households shows the second largest clusterspecific increase in price-sensitivity, here the correlation factor decreased from a comparable high value of over 0.28 in January to less than − 0.12 in December, indicating also a statistically significant change (− 143 %) in customer electricity usage behavior.Based on the average correlation curves for the heating groups, the largest increase in price-sensitivity from January to December can be seen in the night-time water heating (El_Night) & ground-source heat pump (GSH) households.
When assessing the share of households where the increase in pricesensitivity was statistically significant at a 95 % confidence level (p < 0.05), the El_Night, Oil and GSH groups were most prominent.In each of these heating groups, around a third of households had a statistically significant increase in price-sensitivity from January to December.If also the households with non-statistically significant increase in pricesensitivity are considered, over 70 % of the households in El_Night and Oil groups exhibited some positive behavioral change in pricesensitivity.The shares of statistically significant changes in pricesensitivity for all different household heating type groups and for each cluster are presented in Table 2.

Table 1
Shares of statistically significant change in price-sensitivity for the household clusters.To further showcase the most dramatic change in customer behavior, we have plotted the average fractions of electricity usage during daily peak, off-peak and normal price hours for cluster 1 of direct electric heated households to Fig. 9.It should be noted that this cluster covers only one household, but the figure is presented to show how significant an increase in implicit demand response behavior can be.When comparing the hourly electricity consumption of this cluster in January and December, we notice a dramatic shift of loads to cheap electricity hours.In this cluster there has been an over 30 % decrease in electricity consumption during peak hours and an almost 38 % increase in consumption during off-peak, with overall consumption decreasing by 46 %.

Discussion and conclusions
This study introduced a novel method for analysis of changes in customer electricity use behavior and price-sensitivity based on smart electricity meter data.This method was further enhanced by clustering the households by their primary heating type to analyze whether there exist behavioral change differences between these groups.Overall, the presented methodology can help decision-makers in efforts to incorporate more demand response into the grid and help researchers to assess changes in consumer electricity use price-sensitivity.
As a case study to showcase the methodology, we investigated the impact of the global energy crisis and rapidly risen electricity prices of 2022 on the price-sensitivity of Finnish detached household electricity use.The analysis was based on smart meter electricity consumption data from nearly 400 detached households and on the hourly spot-market electricity price data of 2022.On average, the electricity consumption of these detached households decreased by over 15 % from January to December 2022.
Based on the case results, almost a third of the analyzed detached households had a statistically significant increase in the price-sensitivity of their electricity consumption.The largest average increase in pricesensitivity from January to December was in detached household groups with night-time water heating or ground-source heating.The largest shares of households with a statistically significant increase in price-sensitivity were in night-time water heating, oil and ground-source heating groups.These observations might be explainable by various factors, among which the adoption of RTP contracts stands as plausible rationale.In oil-heated houses, the total electricity consumption is typically low, and therefore even comparatively limited changes in consumption behavior could result to significant increase in pricesensitivity.RTP contracts are relatively common in night-time water heating households, as time-based electricity contracts are the only way to financially benefit from the scheduling of the water heating to nighttime, that is in these households the increase in price-sensitivity might be attributable to increase in shifting of various other loads without the need to change to an RTP contract.The increase of pricesensitivity of ground-source heated households could be attributable to scheduling possibilities of modern heat pumps and to possible uptake in RTP contracts.The groups with smallest share of members to increase their price-sensitivity statistically significantly were the direct electric and district heated households.The overall low price-sensitivity among electric heated households might result from the typically large share of fixed-price contracts among these types of households [58].However, the most drastic increase in price-sensitivity was noticed in cluster 1 of direct electric households.Whereas in January the household of this cluster used around 44 % of total electricity during peak hours, in December peak usage covered only less than 14 % of total consumption, with off-peak consumption covering over 75 %, indicating a major behavioral change.This dramatic increase in implicit demand response behavior can be viewed highly indicative of a change from a fixed-price electricity contract to a dynamic day-ahead RTP contract.
Contrasting from our results where a statistically significant shift towards more price-sensitive electricity use can be seen in almost a third of the households.The Norwegian households analyzed in [30] did not exhibit such increased demand response behavior.In [30], the authors analyzed the impact of the early energy crisis on Norwegian households in the winter 2021/2022 compared to pre-crisis time.Their results demonstrated that the crisis resulted in an average hourly energy savings of 11.4 % during November to March 2022.However, they observed that during peak price hours, electricity demand decreased less compared to off-peak, suggesting that on average the households did not react at all to intraday variation in hourly prices, rather than to the overall high price level of the analyzed winter period.The authors however found that households that often utilized digital platforms to check electricity prices and households that utilized electric vehicle smart charging showed some signs of increased price-sensitivity to hourly electricity prices not observed in other subgroups.It should be noted that the study [30] utilized AMR data which covered all types of residential households, not only detached houses, and that majority of households were direct electric heated with no analysis conducted on differing behavior of households with different primary heating types.In Norway, the vast majority of households are electric heated, with electricity covering over 81 % of total household energy consumption in 2022 [59].
The major differences between the behavior of the analyzed primary heating type groups might result from heating need.That is, the groups with heating based on something other than electricity might be able to shift a larger share of their daily electricity demand based on hourly electricity prices.In direct electric heated households, the heating during the winter months consumes significant amounts of electricity and it might be impossible or inconvenient to shift large shares of daily consumption to hours with cheaper electricity prices while maintaining comfortable indoor temperatures.However, installation of air-source heat pumps or utilization of other heating methods (e.g., wood stoves) can enable larger possibilities for electric load shifting.Based on Statistic Finland, heating covered over 57 % of total energy consumption of electric heated Finnish households in 2021 [60].
Another key aspect that can explain the behavioral differences between heating groups and individual households is the electricity contract type of the household.The record-breaking electricity cost hikes of 2022 affected only households with ongoing electricity contracts and those with fixed-term contracts that expired in 2022.That is, the households with long fixed-term contracts signed before the full-blown energy crisis enjoyed cheap fixed-price electricity even during the most expensive winter months of 2022.These customers shielded from the price hikes had no financial incentive to change their electricity use behavior.Fixed-term contacts have been the most popular retail electricity contract type in Finland since 2019, with 50 % share of all contracts at the end of 2022 [13].Differences in contract types and expiration dates of fixed-term contracts led to increased financial inequality between households, with some households enjoying cheap fixed-price electricity while others could have suffered ten-time increases in electricity bills [61,62].
The changes in increased price-sensitivity based on our results occurred mostly in the fall of 2022 when the hourly spot prices were highest and when overall electricity prices across all tariffs skyrocketed.This coincides also with the major media coverage about rapidly rising electricity prices [37,38,63].High electricity prices and news coverage about the need for electricity conservation led to decreased overall electricity consumption in the fall of 2022.According to transmission system operator Fingrid, the overall electricity usage in Finland during the fall and winter months of 2022 was considerably lower than in 2021

Table 2
Shares of statistically significant change in price-sensitivity for the heating type group clusters.[64].For instance, in December the overall consumption was 10 % lower than in 2021 [64].Based on our study, the electricity consumption of the analyzed detached households decreased by over 15 % from January to December 2022.Price hikes and media coverage about the energy crisis also led to an extensive shift towards spot-priced electricity contracts in the last half of 2022 [35,36].The share of Finnish households with a day-ahead exchange electricity (RTP) contract grew from 9 % at the end of 2021 to 13.7 % at the end of 2022 [13,35].
Multiple previous studies, such as [30,65,66], have suggested that easy access to real-time electricity price information increases the pricesensitivity and implicit DR behavior of households.In Finland there exists multiple free apps and websites that enable easy access to electricity price data for consumers, which might, for some part, explain the increased price-sensitivity of electricity use noted in our study.
The main limitation of the case study arises from the utilized dataset which only covered detached households from one Finnish municipality.This makes the generalization of the results to apply to the whole country difficult, nevertheless the findings align with reports of significant shifts towards dynamic RTP-contracts in the fall and winter of 2022.As Finland is part of the NordPool electricity market and has a power grid that is interconnected to Norway, Sweden and Estonia, these results can also be indicative of the situation in these countries.The behavioral change might have been even larger in the winter 2022/ 2023, for instance, in Norway where around 75 % of households had RTP contracts tied to spot prices in the first half of 2022 [67].
In future research it would be interesting to study the pricesensitivity of different household loads, for instance whether household appliance use is more price-sensitive than space heating in crisis conditions.Additionally, the methodology presented in this study could be utilized with data from different household types and countries to compare the differences in behavioral change during and also after the global energy crisis.The methodology could also be expanded through a comparison of different clustering algorithms and methods for identification of households exhibiting increases in price-sensitivity of electricity use behavior.In the future as sub-hourly scale and possibly intraday RTP contracts become available to consumers, it is also important to study how this change, and these new contract types, affect consumer behavior.
Overall, the energy crisis demonstrated how strongly households of different heating types are impacted and react to sudden changes in electricity prices, which is fundamental knowledge to successful energy transition and electrification.Based on the results of this study, there existed a significant trend of increased price-sensitivity and implicit demand response behavior in the electricity consumption of detached households due to the energy crisis.It can be estimated that the skyrocketing electricity prices led many households to shift to day-ahead hourly RTP electricity contracts as to minimize their electricity bills by shifting consumption to cheap electricity hours.This trend can be seen as an increase in price-sensitivity of household electricity use for around a third of detached households in the last quarters of 2022.
In general, it can be asserted that real-time priced electricity contracts, featuring time-varying rates tied to actual production costs, empower consumers to reduce their electricity expenses by adjusting their usage patterns, thus enhancing their energy-resilience.This implicit demand response behavior not only benefits the consumers, but also contributes to power grid stabilization and emission reduction.Ensuring the availability of these time-varying electricity rates across the globe is crucial for successful energy transition, facilitating demand response adoption, and providing consumers with additional means to react to sudden electricity price increases and fluctuations such as those experienced during the global energy crisis in 2022.

Fig. 3 .
Fig. 3. a & b.Daily and monthly averages and medians of the spot-market electricity prices in Finland in 2022.

Fig. 5 .
Fig. 5. Elbow method, sum of squared errors (SSE) and the number of clusters.

Fig. 7 .
Fig. 7. Comparison of the average fraction of electricity usage on peak, normal and off-peak electricity price hours in January and December (all households, Cluster 1).

Fig. 8 .
Fig. 8. Price correlations of household clusters with different primary heating sources.