Measuring aggregate electricity savings from the diffusion of more efficient lighting technologies

Abstract

Increasing concerns about sustainability and energy conservation, coupled with the proliferation of incentives in the EU to achieve energy savings, suggest that significant improvements in energy efficiency should be realized. A policy measure that should have a direct impact on energy savings is the replacement of incandescent and halogen light bulbs by more efficient lighting technologies, which was implemented in 2009. Due to the lack of detailed data, it is not feasible to measure the effect of energy-efficient improvements on electricity consumption at the aggregate level using a bottom-up approach. To overcome this limitation, this paper analyzes hourly electricity demand in a very specific period of the day: the transition from day to night. In this short period, it is plausible that lighting is the main driver of changes in electricity demand, thus making it possible to estimate the increase in electricity consumption when lights are switched on and to analyze the effects of higher energy efficiency in lighting, if any. The results of the analysis for Spain show that during the periods 2009–2011 and 2015–2016, an estimated energy savings of 251 GWh can be attributed to a reduction in the magnitude of the lighting effect, which accounts for 20.3% of the observed decrease in electricity consumption during these two periods.

Introduction: measuring energy efficiency improvements at macrolevel

In spite of the importance of energy efficiency gains and energy conservation in the fight against global warming, their estimation is not so straightforward. The conventional definition of efficiency (Patterson 1996; Herring 2006) is simple and intuitive. Efficiency gains occur when the same amount of services or output is obtained using less energy. However, the way energy services, output, and energy inputs are measured pose methodological issues that make it difficult to detect efficiency gains, as has been discussed in Berndt (1978), Herring (2006), Proskuryakova and Kovalev (2015), Patterson (1996), Li and Tao (2017), and Lowry (2016), among others.

In a controlled experiment, it is possible to measure energy savings, if any, after the installation of more efficient lighting. In a macrosetting, such as when a country needs to know if energy efficiency gains have taken place after subsidizing the purchase of compact fluorescent lamps, the issue becomes much more complex. First, as Ayala et al. (2021) pointed out for the case of Spain, energy intensity is not the most significant attribute for deciding whether to purchase energy-related goods, and therefore, incentives do not have to be fully effective. For instance, studies in single or small numbers of buildings have found that energy savings are difficult to determine even after investing in more efficient appliances Lowry 2016.

Ideally, widespread energy efficiency gains should reduce the energy intensity ratio Berndt 1978, but that reduction is of unforeseeable magnitude. Firstly, energy intensity is affected by the technical feasibility of substitution among energy sources and among production inputs. Secondly, it depends on the weight of energy costs in total production costs, and finally, it also depends on the price elasticity of output. If a firm’s production costs and output prices fall as a consequence of energy efficiency gains, more output demand could also lead to additional increases in energy consumption.

Moreover, in the case of households, if lower energy costs derived from energy efficiency gains increase the disposable household income, part of this increase could be spent on more equipment or on increasing the usage time of electrical appliances, thus increasing the observed energy consumption. These factors are behind the well-known rebound effect, which distorts the impact of adopting more energy-efficient technologies on consumption as studied extensively by Greening et al. (2000) and Saunders and Tsao (2012).

Another approach to estimate efficiency gains with a more microeconomic focus, as in the case of Giacone and Mancó (2012) and Siap et al. (2019), tries to overcome the abovementioned limitations. Using highly disaggregated information, Giacone and Mancó (2012) detailed all the tasks and energy uses in a given productive process. This rich set of information allows quantifying the relationship between the level of activity and energy consumption, distinguishing which part of the energy consumption is a fixed cost or a variable cost. Siap et al. (2019) estimated the energy savings obtained from using more efficient luminaries by computing total energy use from the energy consumption per luminaire and the total number of luminaires installed in the federal sector in the USA. The database used by the authors provided all the information needed to calculate energy use, including lamps per luminaire, lamp power, and luminaire power, among other factors. Although both studies are very appealing, they would be unviable in other cases due to the huge amount of information needed which, as typically occurs in Spain, is not readily available. Even when there are no data restrictions, Lowry (2016) underlined some difficulties with reported energy-saving claims for popular lighting control methods, such as reporting energy savings compared to the lights being used throughout the working day, which overestimate the energy savings potential. As Sunikka-Blank and Galvin (2012) indicated, agents’ behavior is a major determinant of the energy consumed, and overestimation of potential energy savings, or pre-bound effect, can occur if differences in behavior are not taken into account.

In this paper, we analyze the measurement of efficiency gains, if any, by observing changes in the shape of hourly aggregated electricity demand. In particular, we are interested in efficiency gains in electricity consumption for lighting. Instead of following a bottom-up approach based on the observed past behavior of agents, such as the method proposed by Zhang et al. 2021 to evaluate the impact of population ageing on future energy consumption or by Babrowski et al. 2014 to model the potential of electric vehicles to shift the load curve, we propose to directly measure the observed change in the shape of the hourly electricity demand. Due to our interest in energy efficiency gains in lighting, the analysis focuses on the evaluation of changes in electricity consumption during a very short period: the hours corresponding to the transition between day and night. In this short period, it is reasonable to assume that the lighting effect is the main driver of electricity demand.

Using the proposed method, we aim to estimate the effect on aggregate electricity consumption of regulatory changes in the EU to promote greater energy efficiency, mainly the EU Eco-Design (2005/32/EC) and Energy Labeling (92/75/EEC) framework directives.

The Energy Efficiency Directive (European Comission. Directive 2012) aimed to reinforce the European legislative framework to promote energy efficiency by establishing a set of binding measures to help the EU reach its target of a 20% reduction in primary energy consumption by 2020. Article 7 of the Energy Efficiency Directive set a mandatory requirement for Member States to achieve 1.5% energy savings (of final energy sales) each year beginning in 2014. In 2018, as part of the Clean energy for all Europeans package, the amending Directive on Energy Efficiency (European Commission Directive (EU) 2018) updated the policy framework to 2030 and beyond, establishing an energy efficiency target of at least 32.5% for 2030. To reach this target, the EU countries will have to achieve new energy savings of 0.8% each year of final energy consumption for the 2021–2030 period.

Lighting products, among other products, are subject to EU energy labeling and eco-design requirements. According to these directives, lighting products come with energy labels and information printed on the product. Under regulation (EU) No 874/2012, the rating system ranges from A++ (the most efficient) to E (the least efficient). From September 1, 2021, the scale employed ranges from A (most efficient) to G (least efficient) according to the Regulation on energy labeling for light sources (EU) 2019/2015. Eco-design requirements¹ are mandatory for all standard bulbs, fluorescent lamps, and spotlights sold in the EU setting energy efficiency requirements and other factors such as bulb lifetime and warm-up time.

Given that the energy consumption of lighting in buildings is estimated to account for 20–40% of total building energy consumption (Jenkins and Newborough 2007) and approximately 14–20% of total energy consumption is used for Montoya et al. (2017) and De Almeida et al. (2014), it is clear that the potential savings from lighting efficiency are significant. According to Bertoldi et al. (2012), in 2011, LED lighting began to penetrate the market for replacement lamps, although their market price was still very high in 2011. In the case of compact fluorescent lamps (CFL), 426 million CFLs were sold in Europe in 2006, but 1747 million incandescent lamps were sold in the EU-27 in the same period. A more recent report from Zissis et al. (2021) pointed that global LED use has increased substantially in recent years, rising to nearly half of global lighting sales in 2019.

Although Eco-design and energy labeling regulation set minimum energy efficiency standards and other requirements such as bulb lifetime and warm-up time, in practical terms, they incentivized the replacement of old filament and halogen bulbs by more efficient lighting technologies (LED bulbs, CFLs, etc.). The substitution was scheduled in successive stages, beginning in September 2009 and presumably ending in September 2018 when halogen bulbs would no longer be sold. ²

The advantages of this substitution are clear. Table 1 (2006 data) shows the energy efficiency indicators of some representative lighting technologies reported near the beginning of the period analyzed in this paper. An updated review of the energy efficiency of lighting can be found in Zissis et al. (2021). As showed, LED bulbs tend to last longer and have a higher efficacy (total quantity of visible light per energy consumed, lumen/W) than their halogen equivalent. The lower energy used in LED bulbs and CFLs, as well as their decreasing price, should incentive the use of these new lighting technologies instead of incandescent bulbs, which could lead to clear energy savings in lighting.

Table 1 Comparison of different lighting technologies

According to the European Commission estimations, replacing standard bulbs with more efficient lighting technologies could achieve electricity savings of 50% and higher in lighting.³ Electricity consumption of household lighting in Europe (Bertoldi et al. 2012) was estimated to be around 84 TWh in 2007. Since then, consumption decreased by around 5%, resulting in an estimated electricity consumption of around 79.8 TWh in 2009. In that period (2008–2010), the number of CFLs sold in Europe increased by 45% over incandescent light bulbs. For Spain, Palacios-Garcia et al. (2015) estimated that average residential consumption could be reduced by 40% by replacing 50% of the current lamps with LED technology. However, despite the potential energy savings from these measures given the relevance of electricity consumption for lighting,⁴ few attempts have been made to verify if the expected savings have materialized in aggregated terms.

To partly fill this gap, this paper estimates electricity savings due to the progressive adoption of energy-efficient lighting technologies by analyzing changes in the shape of the aggregate hourly electricity demand. The use of hourly data has key advantages in our analysis. As electricity is employed to provide services like thermal comfort and lighting, hourly electricity consumption will reflect the short-term variation in the drivers of these services. For example, as reported in Palacios-Garcia et al. (2015) and Moral-Carcedo and Pérez-García (2019), the daily profiles of residential lighting consumption in Spain show two peak demand periods: one corresponding to mornings starting at 6:00 a.m. (before sunrise) and the other corresponding to nights (around sunset) ranging from 5:00 p.m. to 6:00 p.m. in January and to 9:00 p.m. in July. By analyzing variations in the response of electricity demand through “natural experiments” (i.e., sunrise and sunset when the main driver of electricity demand is lighting), it is possible to estimate the increase in consumption when lights are switched on, or the lighting effect. If energy savings are achieved due to improvements in the energy efficiency of lighting technology, the estimated lighting effect should be partially damped as the new and more efficient technology substitutes the old and less efficient one. As the substitution process is not immediate, this “switch-on” effect should be observed over several years in order to reveal the efficiency gains, after controlling for other long-term electricity drivers (the population, the business cycle, etc.). The period 2009–2016, a transitory period before the ban on selling incandescent bulbs and halogen lamps came into effect, is also important to highlight efficiency gains, as consumers have clear incentives to adopt more efficient technologies.⁵

In the following section, a descriptive analysis of the lighting effect in short-term electricity demand is reported. In Section 3, the estimation procedure and the estimated electricity-saving gains are presented. Finally, Section 4 concludes.

Lighting effect in electricity consumption

As previous studies such as Mestekemper et al. (2013), Moral-Carcedo and Pérez-García (2019), Wang and Bielicki (2018), and Mirasgedis et al. (2007) have highlighted, there are notable differences between the long- and short-term behavior of electricity demand. The typical long-term factors affecting electricity consumption are demographic factors, business cycles, substitution between energy sources, the adoption of more efficient technologies, and the mechanization of production processes. For example, changes in population, and changes in consumption habits have a clear impact in a long-term electricity demand as pointed for example in Zhang et al. (2021) where the impact of population aging on future energy consumption is analyzed or in Babrowski et al. (2014) where the potential of electric vehicles to shift the load curve is analyzed. In the short term, the variables affecting electricity demand are weekday effects, variations in temperature, or time-of-day demand (i.e., opening hours), as described in Taylor (2010) and Mestekemper et al. (2013).

The intraday cyclical nature of activity during regular business hours (i.e., working time, opening hours, school schedules, and leisure time) can shape the electricity demand profile both during the day and between days. Moreover, the intraday cycle of business activity determines how temperature and solar day duration affect electricity consumption, as shown in Moral-Carcedo and Pérez-García (2019). The Earth’s annual cycle causes sunset and sunrise times to vary during the year. As pointed out in Moral-Carcedo and Pérez-García (2017), when there is a day/night transition (sunset) throughout the year, an abnormal but smooth increase in electricity consumption can be observed, which could be attributed to the switch-on effect of lights. Do et al. (2016) also found an inverse relation between consumption and hours of daylight in the case of Germany. Daylight savings time is another interesting case that reveals the relationship between electricity consumption in lighting and daylight. For instance, Momani and Yatim (2009) showed that the implementation of daylight savings time in Jordan strongly affected lighting activities in residential buildings by reducing operating hours by 173 h.

From a macropoint of view, as sunrise/sunset does not take place simultaneously in all regions in Spain, the increase in electricity consumption driven by the switching on of lights does not behave like a “jump” process, but as a smooth transition. In Spain (Table 2), Barcelona and Vigo are the most populated cities on the east-west axis. In these two cities, the sun sets with a difference of about 50 min. That difference is slightly higher between Barcelona and Huelva, which are located on the south-west axis. To deal with these differences in sunset times, we will consider Madrid as the reference point to compute sunset and sunrise times. Madrid is one of the most populated regions of Spain (6.7 million inhabitants) and also generates 19.3% of Spanish GDP. The city of Madrid is located near the geographic center of peninsular Spain, and the difference in sunset times between these three cities and Madrid is less than 30 min (see Table 2).

Table 2 Sunrise and sunset times (official time) in distant cities in peninsular Spain and in Madrid

This lighting effect is asymmetric, and no decrease in electricity consumption is observed after sunrise. Such behavior is due to the fact that the sunrise coincides with the start of business activity on a typical working day, whereas part of the night period after sunset can overlap with normal business activity. When the nights are longer, as occurs during the winter in the northern hemisphere, part of the night period coincides with the normal working/activity time, and the lighting effect is more intense. In summer, when the sun sets between 9:00 p.m. and 10:00 p.m. and business activity is low, the lighting effect at sunset is less evident.

Figure 1 shows a direct examination of the shape of the electricity demand in two European countries: Peninsular Spain and Germany,⁶ which will help to clarify why the day/night transition period was chosen. The figure displays the hourly electricity demand on a working day for both countries in three different months (February, May, and July) for the period 2014–2015, as well as sunrise and sunset times to indicate whether the data were observed at night (i.e., the blue shaded area). The data on hourly electricity demand (mean instantaneous load observed in a given hour measured in MWh⁷) used in this work comes from the European Network of Transmission System Operators for Electricity (ENTSO-E) website (https://www.entsoe.eu/).

Fig. 1

Hourly electricity demand (MWh) and day/night (blue shaded) in February (left), May (center), and July (right). Working days only (2014–2015). a Spain. b Germany. Source: Electricity data from ENTSO-E. Night period variable is constructed from sunset and sunrise times in Madrid and Berlin, which are obtained from the NOAA National Oceanic & Atmospheric Administration (NOAA) calculator

On a working day in winter,⁸ the electricity demand in both countries exhibits a double hump. The first hump occurs between 10:00 a.m. and 1:00 p.m. The second hump occurs between 7:00 p.m. and 9:00 p.m. in Spain, and between 6:00 p.m. and 7:00 p.m. in Germany. In summer, only one hump is observed with a peak at 1:00 p.m. in Spain and at 10:00–11:00 a.m. in Germany. In both the winter and summer seasons, electricity demand is low from midnight to 6:00 a.m., which is when business and household activity has ceased. The differences between the summer and winter are due to fluctuations in temperature, but other variables are also involved, such as daytime. Although both variables are related since changes in thermal amplitude are caused by the seasonal cycle, they act as a distinct driver of electricity consumption. Extreme temperatures drive electricity consumption through heating (February) and cooling demand (July), but daytime drives electricity consumption due to lighting demand.

The shape of the hourly demand curves in Fig. 1 indicates the impact of the day/night transition on electricity consumption. This effect is clearly visible when the day/night transition occurs during business opening hours, as in the month of February, while in July, it is practically negligible because this transition occurs when commercial and business activity has ceased.

It is important to note that the lighting demand and the temperature effect have a different impact on electricity consumption. The temperature graphs (Fig. 2) show how the seasonal cycle affects the hourly temperature profile. Due to the thermal inertia of the atmosphere, there is no “jump” in temperature during the transition from day to night; therefore, the hump in electricity demand in the evening could hardly be attributed to the temperature effect. However, the effect of temperature on electricity demand is clear. When temperatures move around the comfort value (20 °C), the demand barely responds to temperature variations, whereas in extreme cases, the response is stronger, thus increasing electricity consumption.

Fig. 2

Hourly temperature (°C) and day/night period. 2014–2015 in February (left), May (center), and July (right). Working days only. Spain. Germany. Source. Temperature from Spain measured in Adolfo Suarez-Barajas Airport, Madrid. (Source Rp5.ru) Temperature for Germany from Open Power System Data https://doi.org/10.25832/weather_data/2019-04-09

A more in-depth analysis of the characteristics of electricity demand in Spain during the hours close to sunrise and sunset times is shown in Fig. 3. In the figure, the hourly demand by month is shown in two subperiods: 5:00 a.m. to 11:00 a.m. (sunrise) and 5:00 p.m. to 11.00 p.m. (sunset). By representing the data in this way, it is possible to observe how the shape of electricity demands around sunrise and sunset changes throughout the year. The first conclusion that can be drawn is that the shape of the electricity demand during the sunrise period does not change substantially. In an almost systematic way, demand jumps sharply at around 7:00 a.m. and with a greater intensity in the winter. This is consistent not only with the higher demand due to lighting, but also to the higher demand driven by extreme temperatures. Conversely, at sunset, there are clear differences in the shape of the electricity demand. Throughout the first half of the year, the peak demand in the evening gradually disappears and later reappears in October until the end of the year. The duration and the timing of the peak demand in the evening vary consistently with the “legal” sunset time (daylight savings time is implemented in Spain). This behavior, and the asymmetric response at sunset and sunrise times, depends on “when” sunset time occurs, as business and commercial activity interacts with the lighting effect.

Fig. 3

Electricity demand (MWh) asymmetries at sunrise and sunset. Hourly electricity demand in Spain by month between 5.00 and 11.00h, and between 17.00 and 23.00h. 2013–2015. a Sunrise. b Sunset. Note: The red lines are the kernel fit line for the electricity demand in each month. Source: Electricity data from ENTSO-E

Modeling electricity demand: short-term drivers vs. long-term drivers

Previous discussions have shown that all the main drivers of short-term electricity consumption have to be taken into account simultaneously bearing in mind the asymmetry in their effects depending on the level of business activity. As explained, the duration and intensity of the lighting effect depend nonlinearly on the sunset time. As economic activity decreases during the night period, the lighting effect is only transitory and will quickly fall when business activity has ceased. When sunset time occurs after typical business opening times, as in the summer season in Spain, the lighting effect is negligible.

To capture this behavior in the lighting effect, and taking into account other variables affecting electricity demand, the hourly demand at observation t, denoted by E_t , is characterized as follows:

$$ {E}_t=f\left({O}_t,{A}_t,{T}_t,{L}_t\right) $$

(1)

where A_t is an index variable that denotes the active or rest/inactive state of economic activity. As mentioned, if the sunset takes place when there is no daily economic activity (e.g., in summer), the lighting effect on electricity demand will be lower. In winter, however, that effect will be clearly be significant as sunset takes place when economic activity is still high. The lighting effect, L_t, should be disentangled from the effect of temperature variations, T_t, but considering that daily economic activity also affects the temperature effect on the electricity demand. For example, it should be expected that the electricity consumption in a mall will not be so sensitive to outdoor temperatures during closing times as during opening times. The interaction between T_t, L_t, and the activity effect A_t implies that temperature and lighting effects will have a different impact on electricity demand if economic activity is in either an active or a rest state. We will employ the notation (T_t + L_t| A_t) to denote that the effect of temperatures and the lighting effect is conditional on the state of economic activity.

We denote as T_t the electricity consumption that depends on the outdoor temperature recorded at time t, L_t is the consumption linked to lighting, and O_t is the consumption due to other variables (e.g., the business cycle, population, commercial surface, technology). In short periods (i.e., less than 3 years), it is assumed that the effect of the other variables O_t is nearly constant. The effect of these variables is to shift the electricity response (T_t + L_t| A_t), which will be captured by the intercept terms in the regression model described in what follows.

We will assume that daily economic activity will depend on the hour of the day to capture opening and closing times, and on the type of weekday (working and non-working day). Considering the society as a whole, daily activities are usually stable,⁹ since the commercial activity is scheduled around set opening/closing hours and the daily activity on working days is routine due to social norms and cultural customs. Specifically, we will assume A_t = g₁(h, W_d), where h¹⁰ represents the hour of the day (h=0,1,2,..23) and W_d is the type of day when E_t is observed (typically d = {working day, weekend, or public holiday}. For simplicity sake, only working days will be considered in the analysis. The outcome of the function A_t = g₁(h, W_d) is similar to the probability of being in a hidden active state of economic activity. If A_t = 0, economic activity is in the rest state, while A_t = 1 indicates that economic activity is in an active state. To mimic the usual hump shape of daily economic activity (e.g., businesses closed 12:00–6:00 a.m., open 7:00 a.m.–8:00 p.m., and then closed; see Fig. 4), it will be assumed that g₁(h, W_d) is a smooth hump function. In more concise terms, it is assumed to behave as a quadratic logistic function with a double threshold (LSTR2) of parameters γ_d, τ₁, τ₂ according to the following expression:

$$ {g}_1\left(h,{W}_d\right)={f}_1\left(h,{W}_d,{\gamma}_d,{\tau}_{1,d},{\tau}_{2,d}\right)=\frac{1}{1+\exp \left[-{\gamma}_d\left(h-{\tau}_{1,d}\right)\left(h-{\tau}_{2,d}\right)\right]} $$

(2)

Fig. 4

Quadratic logistic function with a double threshold (γ_d =  − 0.008, τ₁ = 8 , τ₂ = 23 )

where parameters τ_{1. d} and τ_{2, d} are the threshold hours when economic activity starts and ends, respectively, and γ_d is a parameter that modulates the speed of transition between rest and active states. This function captures the effect of the transition from some activities to others on the aggregate hourly electricity demand throughout the day. This includes variations in commercial consumption (opening-closing hours, public transport, industrial facilities, schools, etc.) and in residential consumption (school/work time and time at home), but also variations in public lighting in roads and streets. In fact, we are modeling the variations in the intensity of electricity usage of these activities throughout the day irrespective of their exact contribution, as we are only interested in analyzing aggregate consumption. Changes in the daily economic activity pattern due to changes in working hours for example will affect the estimated parameters τ_{1. d} and τ_{2, d} , but, in our estimations, see Table 5 in the Annex, we do not find any evidence about changes in these parameters.

To characterize the effect of temperature on electricity demand, and following Moral-Carcedo and Vicens-Otero (2005), Sailor and Pavlova (2003), Mirasgedis et al. (2007), and Wang and Bielicki (2018), among others, a nonlinear relationship for the temperature effect, T_t ∣ A_t = g₂(C_t| A_t) will be assumed, where C_t is the temperature in °C at observation t. This nonlinear effect comes from the observed increase in electricity demand both when the temperature decreases on cold days (heating demand) and when the temperature increases on hot days (cooling demand). The “true” nonlinear relationship between temperature and electricity consumption, g₂(C_t| A_t), will be approached using a polynomial approximation; more precisely, a 3-degree polynomial in temperature C_t.

It will be assumed that the lighting effect is linear and given by L_t ∣ A_t = g₃(S_t| A_t), where S_t is a binary variable that takes the value of 1 if it belongs to the night period (sunset time-sunrise time), and 0 otherwise.

As O_t is near constant in short periods, Eq. 1 can be rewritten as follows:

$$ {E}_t\mid {A}_t=\left({T}_t+{L}_t|{A}_t\right) $$

(3)

where Pr[A_t = 1] = f₁(h, W_d, γ_d, τ_{1, d}, τ_{2, d}) is the probability of being in the active state in period t. We can denote the expected value of electricity demand in period t as follows:

$$ {\displaystyle \begin{array}{c}{E}_t=\sum \limits_{i=1,0}\Pr \left({A}_t=i\right)\left({T}_t+{L}_t|\ {A}_t=i\right)\\ {}={f}_1\left(h,{W}_d,{\gamma}_d,{\tau}_{1,d},{\tau}_{2,d}\right)\left[{\delta}_o+{\delta}_1{C}_t+{\delta}_2{C}_t^2+{\delta}_3{C}_t^3+{\delta}_4{S}_t\right]\\ {}\left[{\delta}_o+{\delta}_1{C}_t+{\delta}_2{C}_t^2+{\delta}_3{C}_t^3+{\delta}_4{S}_t\right]+\left[1-{f}_1\left(h,{W}_d,{\gamma}_d,{\tau}_{1,d},{\tau}_{2,d}\right)\right]\left[\delta {\prime}_o+\delta {\prime}_1{C}_t+\delta {\prime}_2{C}_t^2+\delta {\prime}_3{C}_t^3+\delta {\prime}_4{S}_t\right]\end{array}} $$

(4)

Or simply, with β′_i = δ_i − δ′_i .

$$ {E}_t=\left[\delta {\prime}_o+\delta {\prime}_1{C}_t+\delta {\prime}_2{C}_t^2+\delta {\prime}_3{C}_t^3+\delta {\prime}_4{S}_t\right]+\left[\beta {\prime}_o+\beta {\prime}_1{C}_t+\beta {\prime}_2{C}_t^2+\beta {\prime}_3{C}_t^3+\beta {\prime}_4{S}_t\right]{f}_1\left(h,{W}_d,{\gamma}_d,{\tau}_{1,d},{\tau}_{2,d}\right) $$

(5)

The coefficients β′_i, δ′_i in Eq. 5 can be easily estimated by standard methods (OLS) if f₁(h, W_d, γ_d, τ_{1, d}, τ_{2, d}) was given, as the resulting model is linear.¹¹ The iterative procedure used to estimate f₁(h, W_d, γ_d, τ_{1, d}, τ_{2, d}) is described in the Appendix. The analysis is restricted to type d = working days.

For simplicity sake, and based on the stability of the estimated coefficients between subsamples,¹² the same coefficient values (γ_d =  − 0.008, τ₁ = 8 , τ₂ = 23) will be used in the estimation of the lighting effect for the complete period 2006–2016. Once f₁(h, W_d, γ_d, τ_{1, d}, τ_{2, d}) has been determined, Eq. 5 will be estimated. While the daily activity cycle is estimated using the 24-h data in each subsample, the estimation of the lighting effect will only take into account the hourly time span [5:00–11:00 p.m.] containing the sunset time, which is the same time span employed in Fig. 3b.

From Eq. 5, electricity consumption in the active state, that is, when f₁(h, W_d, γ_d, τ₁, τ₂) = 1, is characterized by the following:

$$ {E}_t\mid {A}_t=1=\left[{\delta}_o+{\delta}_1{C}_t+{\delta}_2{C}_t^2+{\delta}_3{C}_t^3+{\delta}_4{S}_t\right]=\left[\left(\beta {\prime}_o+{\delta}_o^{\prime}\right)+\left(\beta {\prime}_1+\delta {\prime}_1\right){C}_t+\left(\beta {\prime}_2+{\delta}_2^{\prime}\right){C}_t^2+\left(\beta {\prime}_3+{\delta}_3^{\prime}\right){C}_t^3+\left(\beta {\prime}_4+{\delta}_4^{\prime}\right){S}_t\right]. $$

(6)

When daily economic activity is in rest state, the estimated model will be as follows:

$$ {E}_t\mid {A}_t=0=\left[\delta {\prime}_o+\delta {\prime}_1{C}_t+\delta {\prime}_2{C}_t^2+\delta {\prime}_3{C}_t^3+\delta {\prime}_4{S}_t\right]. $$

(7)

To disentangle the efficiency gains in lighting due to the adoption of more efficient lighting technologies, we will now focus on variations in the coefficients associated with the lighting effect in Eq. 6. Lighting efficiency gains can be observed by comparing electricity consumption under similar levels of lighting provision.¹³ However, this assumption can only be maintained over short periods of between 1 and 3 years or during periods of economic stagnation when investment in new buildings is low. For this reason, the model in Eq. 5 is estimated in non-overlapping sampling periods of 2–3 years.

The intercept terms δ_o and δ′_o capture the effect on the electricity consumption of other variables, O_t, that are assumed to be constant in the 2–3-year estimation period, but are allowed to change between estimation periods. These intercept terms capture the effect of the business cycle, changes in population, commercial surface, or technology, among other long-term effects on electricity consumption.

Table 3 shows the results of the estimation of the model in Eq. 5 under two alternative specifications. The model is estimated using hourly data from 5:00 to 11:00 p.m. for weekdays in 2–3-year non-overlapping subsamples for the period 2006–2016. These specific hours have been selected because it is possible to assign the variations in electricity consumption to gains in efficiency linked to the lighting effect. In this period, the lighting demand is expected to be price inelastic because businesses are open, and electricity consumption cannot be postponed or anticipated in response to changes in electricity prices.¹⁴ In version 2 of the model, daily dummies are considered in order to capture approximation errors in the true response to temperature variations or to other variables with a daily variation that could affect electricity consumption, or specific day effects. These dummies are not included in version 1 of the specification.

Table 3 Estimation results and estimated ‘lighting’ effect between periods

By comparing the estimated coefficients of Eq. 5 in two non-overlapping samples, T and T*, the efficiency gains in electricity demand for lighting between T and T* can be computed when [(A_t = 1) ∩ (S_t = 1)] as follows:

$$ {\mathrm{E}}^T\mid \left({\mathrm{A}}_{\mathrm{t}}=1\cap {S}_t=1\right)-{\mathrm{E}}^{T\ast}\mid \left({\mathrm{A}}_{\mathrm{t}}=1\cap {S}_t=1\right)=\left[{\left(\beta {\prime}_4+{\delta}_4^{\prime}\right)}_T-{\left(\beta {\prime}_4+{\delta}_4^{\prime}\right)}_{T\ast}\right] $$

(8)

where${\left(\beta {\prime}_4+{\delta}_4^{\prime}\right)}_T$ are the estimated coefficients of the lighting effect in subsample T and ${\left(\beta {\prime}_4+{\delta}_4^{\prime}\right)}_{T\ast }$ are the coefficients estimated in subsample T*. It should be noted that in this case the efficiency gains correspond to a period where economic activity is in the active state, A_t = 1, and during the night period, S_t = 1, ceteris paribus, therefore assuming that the same temperature and other variables remain constant.

As discussed in the introduction, incentives to substitute incandescent and halogen light bulbs for more efficient lighting technologies began in 2009. In both versions of the model, the results in Table 3 clearly show a reduction in the coefficient assigned to the lighting effect after 2009–2011. This reduction is in clear contrast with the estimated increase in the lighting effect between 2008–2010 and 2009–2011 from 2331.4 to 2933.8 MWh. The coefficient reduction between the periods 2015–2016 and 2009–2011 was 12.5% in the first specification (see Fig. 5) and 10.5% in the second. As a key feature, the observed reduction in the lighting effect is not accompanied by a similar change in the temperature effect (see Fig. 6). In fact, a significant shift is observed in the electricity consumption response to temperatures estimated in the period 2015–2016, which is probably due to the cumulative effect of more frequent heat waves and higher temperatures recorded in 2015.

Fig. 5

Estimated lighting effect, $\beta {\prime}_4+{\delta}_4^{\prime }$, by subsamples (‘Active State’). MWh. Model version 1

Fig. 6

Estimated temperature effect, $\left(\beta {\prime}_1+\delta {\prime}_1\right){C}_t+\left(\beta {\prime}_2+{\delta}_2^{\prime}\right){C}_t^2+\left(\beta {\prime}_3+{\delta}_3^{\prime}\right){C}_t^3$, by subsamples (‘Active State’). MWh. Model version 1

One alternative way to visualize such savings is to compare the models (version 1) estimated from subsamples 2009–2011 and 2015–2016. In Fig. 7, the coefficients of both models are used to estimate the electricity demand in both periods and compare them with the actual electricity demand data.¹⁵ As the figure shows, each model fits the actual data well with the respective subsample used for their estimation. These figures clearly show how the demand response caused by the lighting effect has evolved over time. When comparing both estimates, we observe a reduction in the response of consumption to the lighting effect in recent years, which could give empirical support to the effectiveness of the EU labeling and energy efficiency policies on lighting appliances.

Fig. 7

Estimated demand response (model 1) to lighting effect in November. Comparison of estimated responses (predicted) and electricity demand in 2009–2011 (left) and 2015–2016 (right). MWh

As represented in Fig. 5, the day-night transition increased electricity demand by 2933.8 MWh in 2009–2011, whereas that lighting effect increased consumption by 2566.6 MWh in 2015–2016. Both values are just point estimates, that is, the variation observed in just 1 h, assuming that the economic activity state remains active. In order to quantify the savings in terms of electricity consumption (MWh), it is necessary to compute the estimated savings in the time slots analyzed (4:00–10:00 p.m.) for the whole year. Effective savings depend as much on the savings potential of the technology as on the effective period of time that such equipment is used (Lowry 2016). For instance, LED is clearly more efficient than incandescent bulbs, but the observed aggregate savings could be negligible if LED lighting is used only a fraction of the time. The proposed approach focuses on the analysis of a very specific time span around sunset on working days only, taking into account the state of economic activity. To estimate the annual savings when the lighting effect changes between period T and T*, we first compute the savings in hour t from Eq. 8 (repeated here for convenience):

$$ {\mathrm{E}}^T\mid \left({\mathrm{A}}_{\mathrm{t}}=1\cap {S}_t=1\right)-{\mathrm{E}}^{T\ast}\mid \left({\mathrm{A}}_{\mathrm{t}}=1\cap {S}_t=1\right)=\left[{\left(\beta {\prime}_4+{\delta}_4^{\prime}\right)}_T-{\left(\beta {\prime}_4+{\delta}_4^{\prime}\right)}_{T\ast}\right] $$

(9)

Intuitively, this amount is the reduction in the lighting effect between period T (2009–2010) and period T* (2015–2016). As the model is estimated with hourly data, the estimated savings only correspond to an hour t that belongs to time window ∣ A_t = 1 ∩ S_t = 1∣. In fact, when S_t is 0 (between sunrise and sunset), there are no computed savings.

Using Eq. 9, we then aggregate the computed savings in hour t for all t belonging to a given year y, taking into account that every observation t is weighted by the probability of economic activity being in the active state.

Denoting by S(T, T^∗) the estimated electricity savings between period T and T* in year y, it will be equal to the following:

$$ ES{\left(T,{T}^{\ast}\right)}_y=\sum \limits_{t\in y}\left[\left({\upbeta}_4^T+{\upbeta^{\prime}}_4^T\right)-\left({\upbeta}_4^{T\ast }+{\upbeta^{\prime}}_4^{T\ast}\right)\right]{S}_t{f}_1\left(h,{W}_d\right) $$

(10)

For the sake of comparison, electricity consumption during the same time span is also computed, that is, electricity consumption during the night on working days with economic activity in the active state on a yearly basis, given by the expression:

$$ {E}_y=\sum \limits_{t\in Y}{E}_t{S}_t{f}_1\left(h,{W}_d\right). $$

(11)

The annual values for electricity consumption and estimated savings are presented in Table 4 as mean values in each subperiod analyzed (2009–2011, 2012–2014, and 2015–2016). The reduction in the mean electricity consumption from 2009–2011 to 2015–2016 amounted to 6520 GWh, of which only 1237 GWh were reduced in the time window analyzed (working days, night, and active state). From the latter figure, an estimate of 251 GWh can be attributed to the reduction in the magnitude of the lighting effect. This value represents 20.3% of the total reduction. In mean terms, the reduction in electricity consumption from 2009–2011 to 2015–2016 due to lighting effect savings is 11% higher than in the period 2012–2014, thus denoting a higher penetration of the more efficient lighting technologies.

Table 4 Electricity consumption and lighting effect savings (GWh)

Conclusion

The demand for energy responds to several variables whose interaction generates interesting dynamics. In the case of electricity demand in Spain, the years following the deep crisis of 2008 have shown an atypical behavior in electricity consumption, mainly over the period 2015–2016. During that period, a moderation in the growth of electricity consumption was observed despite the fact that economic activity grew by over 3%, whereas both variables historically exhibited a correlation near one. This divergence seems to suggest the existence of significant energy efficiency gains consistent with the proliferation of EU incentives under the Europe 2020 Strategy.

One of the measures promoted by the EU is the replacement of light bulbs with more efficient lighting devices. Due to their advantages in terms of energy consumption and durability, a clear effect on electricity consumption should be seen. To the best of our knowledge, however, the impact of this measure has not been evaluated at the macrolevel.

The method proposed in this paper takes into account the main drivers of short-term electricity demand; specifically, the effect of economic activity, the effect of temperature variations, and the effect of lighting needs. Considering these three factors, we have studied a very specific period of the day—the transition from day to night—in order to disentangle the effect of lighting demand on electricity consumption.

Given the progressive adoption of more efficient lighting technologies, it can be expected that the electricity demand response during the transition from day to night has changed in recent years. The results of this analysis show that from 2009–2011 to 2015–2016, 20.3% of the observed reduction in electricity consumption during the transition from day to night responded to a reduction in the lighting effect on electricity consumption.

This finding leaves the question open about the relevance of savings in lighting during other hours of the day. This issue can be of interest in business activities where lights are always on during opening hours. The results presented here also show that other factors have influenced the reduction in electricity consumption during the time window analyzed. In 2015–2016, the electricity consumption (on working days, at night, in active state) fell by 2.0%, while total electricity demand increased by 0.8%. As electricity prices used to be higher in the 7:00–10:00 p.m. time period, a shift in consumption across time periods in response to price changes must have played a key role. However, this factor requires a more in-depth analysis, as hourly pricing was implemented fairly recently (2014). As a caveat to the findings, it is important to note that the proposed methodology and our results are limited by the lack of detailed data. To make the model tractable, some simplifications have also been imposed. For example, the long-term drivers of electricity demand (population, GDP, etc.) have not been explicitly included in the tested model, assuming they are constant over the 2–3-year estimation period, but changing between periods. Another simplification is to approximate the effect of temperature using a 3° temperature polynomial. It would be desirable to have detailed information on the demand for electricity by households and businesses to see how the lighting effect is distributed among different types of consumers. If each type of consumer behaves differently, the real savings may be underestimated. We acknowledge that the availability of more in-depth data about equipment and a breakdown of electricity consumption by agent type (commercial and residential) would make the results more conclusive.

Appendix

Annex. Model estimation procedure

For estimation purposes, the model employed will be

$$ {E}_t=\left[\delta {\prime}_o+\delta {\prime}_1{C}_t+\delta {\prime}_2{C}_t^2+\delta {\prime}_3{C}_t^3+\delta {\prime}_4{S}_t\right]+\left[\beta {\prime}_o+\beta {\prime}_1{C}_t+\beta {\prime}_2{C}_t^2+\beta {\prime}_3{C}_t^3+\beta {\prime}_4{S}_t\right]{f}_1\left(h,{W}_d,{\gamma}_d,{\tau}_1,{\tau}_2\right)+{\varepsilon}_t $$

(12)

where ε_t captures the approximation errors to the unknown temperature and lighting effects. It is expected that this term exhibits some degree of correlation of order similar to the dominant periodicity (24 h) in the variables T_t, and L_t.

Model in Eq. 13 could be estimated directly by restricted nonlinear least squares (NLS). Hours have to be restricted to the [0,23] range, and hence parameters τ₁ and τ₂ have to satisfy the following constraints 0 ≤ τ₁ ≤ τ₂ ≤ 23. We propose an iterative restricted NLS procedure. Starting with an initial guess value for the smoothness coefficient ${\gamma}_d^0$, we compute the optimal threshold parameters that minimize the sum of squared residuals.

$$ {\tau}_1^0,{\tau}_2^0= argmin\left[{\sum}_{t=1}^T{u}_t{\left({\gamma}_d^0,{\tau}_1,{\tau}_2\right)}^2\right], $$

(13)

where ${u}_t\left({\gamma}_d^0,{\tau}_1,{\tau}_2\right)=\left({E}_t-{\hat{E}}_t\right)$ and,

$$ {\hat{E}}_t=\left[\delta {\prime}_o+\delta {\prime}_1{C}_t+\delta {\prime}_2{C}_t^2+\delta {\prime}_3{C}_t^3+\delta {\prime}_4{S}_t\right]+\left[\beta {\prime}_o+\beta {\prime}_1{C}_t+\beta {\prime}_2{C}_t^2+\beta {\prime}_3{C}_t^3+\beta {\prime}_4{S}_t\right]{f}_1\left(h,{W}_d,{\gamma}_d,{\tau}_1,{\tau}_2\right) $$

Optimal thresholds, ${\tau}_1^0={\tau}_1^0\left({\gamma}_d^0\right)$and ${\tau}_2^0={\tau}_2^0$(${\gamma}_d^0$) are restricted to lie in the intervals, τ₁ ∈ [4, 11], and τ₂ ∈ [τ₁, 23]. Given the value for ${\gamma}_d^0$ and the previously determined thresholds, ${\tau}_1^0$ and ${\tau}_2^0$, the sum of squared residuals (SSR) is given by

$$ \varphi \left({\gamma}_d^0,{\tau}_1^0,{\tau}_2^0\right)={\sum}_{t=1}^T{\left({E}_t-{f}_1\left(h,{W}_d,{\gamma}_d^0,{\tau}_1^0,{\tau}_2^0\right)\left({T}_t+{L}_t\right)\right)}^2. $$

(14)

The iterative procedure aims to minimize this SSR, and the outcome will be the optimal parameter value for γ_d that minimizes the SSR.

$$ {\gamma}_d^{\ast }= argmin\left[\varphi \left({\gamma}_d^0,{\tau}_1^0,{\tau}_2^0\right)\right]. $$

(15)

Then, given ${\gamma}_d^{\ast },$ the threshold parameters ${\tau}_1^{\ast }={\tau}_1^{\ast}\left({\gamma}_d^{\ast}\right)$ and ${\tau}_2^{\ast }={\tau}_2^{\ast }$(${\gamma}_d^{\ast }$) will also be optimal, and by construction lie in the rage [0,23].

Finally, to validate the coefficients obtained, a full NLS model is estimated using these coefficients as starting values. The estimated coefficients for the samples 2006–2008, 2009–2011, 2012–2014, and 2015–2016 are included in Table 5. The final estimation of this procedure allows to conclude that there are negligible differences in the estimated coefficients for f₁(h, W_d, γ_d, τ₁, τ₂) for the different subsamples. This outcome is in line with the structural character of the activity hours. In the absence of changes in labor regulations on working time, new laws on opening hours of business, etc., it can be expected that the activity profile along the day will remain the same.

Exploiting this stability and in order to avoid extra complexity, it will be assumed the following values for the coefficients in f₁(h, W_d, γ_d, τ₁, τ₂): γ_d =  − 0.008, τ₁ = 8 , τ₂ = 23 in all the subperiods analyzed. These values lie in the range of the estimated values in Table 5 so the errors due to this approximation are expected to be low.

Although their apparent complexity, the LSTR2 model has several advantages compared to a simple version using hour dummies (see Annex Fig. 8 for a comparison). First, they allow to capture the interaction between activity, and temperature and lighting effect. Including this interaction in the model with hourly dummies will increase notably the number of coefficients. Another advantage is the robustness of the specification employed facing the correlation between intraday temperatures and the economic activity cycle.

In Annex Fig. 9, actual electricity demand is presented jointly with the activity cycle estimated using the hourly dummies model. The data belonging to the subperiod 2009–2011 are grouped by month. In Spain, cold temperatures are observed in the period December–March, temperate temperatures in April, May, and October, and hot temperatures between June and September. The daily activity cycle estimated by the hourly dummies model mimics the electricity demand shape in summer months. In winter months, there are more clear differences. Taking into account that the estimated activity cycle and the intra daily temperatures cycle are near coincident¹⁶, the hourly dummies model will underestimate the temperature effect when temperatures are extreme.

Fig. 8

Estimated economic activity profile for Spain. LSTR2 model with γ_d =  − 0.008, τ₁ = 8 , τ₂ = 23 versus model with hourly dummies (subperiod 2009–2011)

Table 5 Nonlinear least squares (NLS) estimation result of Eq. 12. Working days only

Fig. 9

Activity cycle estimated with hourly dummies model and electricity demand. Breakdown by month. Subperiod 2009–2011