- Email: [email protected]
Comparing smart metered, residential power demand with standard load profiles
Sustainable Energy, Grids and Networks 20 (2019) 100248
Contents lists available at ScienceDirect
Sustainable Energy, Grids and Networks journal homepage: www.elsevier.com/locate/segan
Comparing smart metered, residential power demand with standard load profiles ∗
Christoph Stegner a , , Oliver Glaß a , Thomas Beikircher b a b
ZAE Bayern Energy Storage, Unterkotzauer Weg 25, 95028 Hof, Germany ZAE Bayern Energy Storage, Walther-Meißner-Straße 6, 85748 Garching, Germany
article
info
Article history: Received 25 April 2019 Received in revised form 2 August 2019 Accepted 30 August 2019 Available online 3 September 2019 Keywords: Electric load profiles Residential Smart meter Standard load profiles Temporal resolution
a b s t r a c t Despite their age, residential standard load profiles (SLPs) are a widely used tool to represent the electric power demand of a household. However, the prospect of a future power system relying mainly on renewable and often intermittent, distributed energy resources (DER) is pushing SLPs to their limit. Determining self consumption rates and the potential of demand response through smart home applications or simulating distribution grids, especially the low voltage (LV) level—all require a realistic replication of residential load patterns. However, data of high temporal resolution for individual households is rare. Therefore, several smart meters were installed at participants’ homes within a research project and the measurements are analyzed. For the first time, complete load profiles for a whole year in a temporal resolution of 15 s are used to derive key characteristics. For example, the level of fluctuation is described by different quantiles of the instantaneous power. It is found that the 99% quantile exceeds mean power values by 5 – 10 times, but pooling of households reduces this factor strongly. Other findings, for example that one third to half of the energy is consumed at low power levels (< 0.75 kW) require bigger samples for validation, whereas the degree of fluctuation within the gained load profiles is considered representative. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Despite their development in the late 1990s [1], SLPs remain state of the art for approximating residential electric consumption and fulfill their purpose, when used to forecast aggregated power demand of several hundred consumers. SLPs are time series of electric power demand averaged over 15 min, which is a very common time interval in the German electric energy system. On the spot market, a quarter hour is the shortest block traded and utilities use the 15 min means of the power demand to determine peak power at the point of common coupling (PCC) for commercial and industrial consumers. However, 15 min is too long to include the dynamic use of many electric appliances, especially in the residential area, which take place at a time scale of 1 min and below. In the past, research projects were conducted in the distribution grid to gain data of a higher temporal resolution than 15 min. The distribution grid includes the LV level, where normally no continuous measurement takes place. In most cases, monitoring by the distribution system operator (DSO) ends at the coupling point between high and medium voltage, whereas ∗ Corresponding author. E-mail address: [email protected] (C. Stegner). https://doi.org/10.1016/j.segan.2019.100248 2352-4677/© 2019 Elsevier Ltd. All rights reserved.
further measurement usually is only conducted with mobile measuring equipment if problems occur. The research project Netz der Zukunft (grid of the future) included measurement in the distribution grid at transformer stations and selected PCCs providing 10 min mean values [2]. In [3], highly resolved voltage measurement at the transformer station and end of the LV grid are described, but without further defining the temporal resolution. Another extensive measuring campaign was analyzed in [4], including residential PCCs with a 1 min resolution and even 15 s current measurements, but without recording of the respective voltages. In the research project Smart Grid Solar of ZAE Bayern power demand and generation was measured via smart meter [5] focusing on two different distribution grids, which are characterized by a high presence of rooftop photovoltaic (PV) plants. For instance, one of the LV subnets studied in that project has an annual generation to consumption ratio of roughly 3 : 1 [6]. Part of such PV generation is being consumed on site and its quantification has been subject of various research projects. The temporal resolution of power profiles largely influences the accuracy of calculated self consumption rates, as stated in [7]. Similar simulations in [8] are based on high resolution data of 1 min values, but restrain to synthetic load profiles. Measured load profiles in 1 min resolution were used in [9] but are only available for a few days. The same time interval was available for data analyzed in [10] that used smart meters to study distribution
2
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
of power and voltages and found unbalanced phases to be an issue. [11] states, that with growing simulation intervals, the over estimation of the self consumption ratio becomes more significant. Additionally, the resulting error for different temporal resolutions is provided. On one hand, a suitable measuring infrastructure for households or DER has to follow the principles of scalability and subsidiarity to match the decentral architecture of distribution grids. Standards developed for higher voltage levels like IEC 61850 are powerful but also feature a high bandwidth consumption as explained in [12], who proposes intermediary units for data processing. On the other hand, applications that only rely on local measurements like voltage control through load management as tested in [13] exist but require knowledge about the characteristics of residential power demand. One long term goal of electrical metering campaigns is to incorporate the results into energy demand models. In fact, highly resolved data of several hundreds of consumers is necessary to derive resilient behavioral patterns, which exceeds the scope of our study. [14] for example analyzed more than 66 million daily load profiles of 220.000 residential consumers to create a load shape dictionary with profiles that can be scaled to a desired energy consumption. Their hourly time-resolution supports energy-based demand response strategies, which could be exploited by utilities for example. However, [15] makes a strong argument for social practices being the central driver that defines energy demand and criticizes forecasts basing on historical load patterns and scaling them due to trends like economic growth or an improvement in energy efficiency. [16] undertook first steps to combine social practice theory and energy demand models out of a social perspective. A related approach from technical side is the bottom-up, appliance based model of [17]. It consists of activity profiles derived from social surveys and a library of appliances with individual power characteristics. [18] confirms results from literature that recommend a temporal resolution of no longer than one minute to identify patterns of such appliances. 2. Materials and methods Together with two DSOs a smart meter rollout was conducted at the homes of several participants of a research project. From the measurements, two different classes of data are available and validated against each other before similarities to and deviations from SLPs are studied by means of a power analysis. 2.1. Smart meter One of the requirements in the project was that new meters were calibrated and approved for billing as they would replace existing Ferraris meter. The selection of the model (LZQJ-XC by EMH) was left to the two DSOs involved and their decision was also based on their experience with the manufacturer and compatibility of the meters with their data acquisition. The smart meters provide data of two different qualities: First, instantaneous current (Ii ), voltage (Ui ) and phase difference (ϕi ) are measured for all three phases (i). Note that instantaneous refers to the root mean square (RMS) values for I and U. This data type will be called instantaneous values class (IVC). Some literature refers to this kind of data as real time values but we restrain from that term, as in our understanding real time always implies that data is transmitted or processed within defined time constraints. Second, the smart meters aggregate current and voltage values for every phase over an adjustable time period and yield the respective minimum, maximum and mean values. This second class will be referred to as aggregated values class (AVC). Generally, the smart meters can provide a large variety of parameters, exceeding
Table 1 Parameters provided (all parameters are time series and should be denoted with an additional index for the time interval but we restrain from this for readability reasons). Measured parameters
Derived parameters
Measuring interval
P, S
15 sa
Savg
1 min
Instantaneous value class U i , Ii , ϕ i Aggregated value class Umin,i , Uavg,i , Umax,i , Iavg,i , Imax,i a
Normal setup only 1 min, but is not used in our analysis.
Ii , Ui and ϕi . The process of selecting parameters and setting intervals is called parameterization and must be performed via the optical interface, which requires an adaptor and proprietary software. The parameters chosen for the project are summarized in Table 1 together with the apparent and active powers (S and P) that are defined as S=
3 ∑
(Ui · Ii ) ,
i=1
Savg =
3 ∑ (
Uavg,i · Iavg,i ,
)
(1)
(Ui · Ii · cos ϕi ) .
(2)
i=1
P =
3 ∑ i=1
2.2. Measuring setup and temporal resolution During design of measuring equipment, the aim was to reach a temporal resolution as high as possible. The smart meters used, allow a wide range of measuring intervals, from hours down to a few seconds. Tests however revealed that too short intervals overstrain the smart meter in processing or transmitting the data, which will be explained in more details in the following paragraphs. The chosen measuring interval therefore had to be a compromise between high resolution and acceptable data loss. . At the same time, one of the two involved DSOs had specific requests consisting in the use of ready-made data transmission components because of his existing infrastructure. In consequence, two different setups were realized. The normal setup uses the smart meter mentioned above plus a supplemental mobile-network communication module of the same manufacturer EMH. For the AVC the aggregation interval was set to the shortest option possible (1 min). The smart meter itself has a limited RAM storage capacity and starts overwriting older data when full. The amount of data stored depends on the number of data channels and the temporal resolution, which was also set to 1 min for the IVC to assure the internal RAM is sufficiently large to buffer data over several hours. A second, enhanced setup could be realized where additional single-board computer (Raspberry Pi) were accepted by the DSO. Micro-Computers like these are affordable, have a low powerconsumption, can easily be programmed as they use standard operation systems like Linux and they proved to work stable over several years. The device connects with up to four smart meters via serial interface. Furthermore, it formats measured data to appropriate numeric classes which highly reduces traffic. A 32 GB SD card allows for a buffering, which is more reliable than the internal RAM of the smart meter, and also serves as a local backup storage. The data is finally encrypted and transferred to a central database by means of a GSM-module. The enhanced setup decreases dependency on mobile network availability, hence the
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
measuring time interval for the IVC could be improved to 15 s. Theoretically, even shorter measuring intervals can be chosen but test runs resulted in exponentially growing data gaps with higher frequency—also affecting the AVC data. It is assumed that the CPU performance of the smart meter is not sufficient for the aggregating tasks, when continually serving too many IVC measure requests at the same time. Results within this paper are based exclusively on data from the enhanced setup. 2.3. Evaluation of instantaneous parameters In hindsight, the parameterization of the smart meters, which means the selection of the values to be measured, was based on some assumptions that later proofed to be restricting for certain analysis. Average, active power values were not included in the AVC measurements because respective IVC data was deemed to be sufficient—although active power is a very relevant parameter, also for this study. The decision was especially regrettable because it could not be easily corrected after roll-out due to limited accessibility of the smart meters. Therefore, the following evaluation compares IVC and AVC data and quantifies the uncertainty when using instantaneous values instead of means. Measurements from the IVC provide only a snapshot of the electric quantities. However, it is important how close the mean of four U (or I) values from the IVC for a certain minute to the correspondent Uavg (or Iavg ) from the AVC value is. It defines for example, if using IVC data as time series in simulation leads to errors, when the simulation interprets the values as constant over one simulation interval. During evaluation and in order to identify congruence between the mean of four IVC and the AVC value, a filter is first applied to the IVC data. It sorts out all the samples where per phase and minute less than four values were recorded. Additionally, minutes without AVC values are discarded. Next, mean values per minute for voltage (U¯ avg,i ) and current (I¯avg,i ) are calculated and compared to their AVC counterparts. As phase difference is not available in the AVC, a respective analysis for the active power has not been undertaken. Common statistical criteria for comparison of synthetic and measured values are correlation and regression coefficients (r 2 and b). [19] introduced further criteria based on mean squared deviation. These were refined later by [20] to include numeric factors indicating to which degree the deviation is caused by translation (SB), rotation (NU) and scatter (LC ). Both, r 2 and b, as well as SB, NU and LC will be used for comparison. As stated above, active powers could not be validated, but apparent power values exist in both data classes. To also include a comparison in terms of energy, an additional analysis of these apparent powers is conducted. For both value classes (v) the total apparent energy (AE v ) is calculated by AEv =
Nv ∑ (
Sv,n · ∆tv,n ,
)
(3)
n=1
where v is the value class, N is the number of available values in v and ∆t the length of the measuring interval n in v, which is 15 s for IVC and 1 min for AVC. N must cover the same periods in both classes. Eventually, the relative error (∆AE) is determined by
∆AE = (AEIVC − AEAVC ) /AEAVC .
(4)
Note that, apart from the apparent energies in (3) and (4), the term energy is used always in the sense of active energy corresponding to active power.
3
2.4. Data selection and completion with synthetic values The analysis in the following sections is based on the P values from the IVC. For this purpose, the data of 17 smart meters for the entire year 2015 is processed. To generate complete time series, an algorithm of four steps is applied: First, longer gaps of several days or weeks are identified and filled up with data from the year 2014 or 2016. Second, gaps consisting of one missing time step are filled by linear interpolation between preceding and following value. Third, time steps in longer gaps are filled with the mean of the two values that have been gathered exactly one week before and after. If no values can be found, the distance is increased to two, three weeks and so on, until at least two values exist. The fourth step completes recurrent 5–10 min gaps on Monday early mornings, which are caused by weekly reboots of the singleboard computers. These reboots had to be introduced to avoid desynchronization of the local timer. During this time of the day demand is normally negligible and gaps are filled with respective values from the following Tuesday. 2.5. Standard load profiles SLPs are available for several types of power customers. The so called H0 profile stands for the aggregated active power demand at a residential PCC and consists of nine different day profiles, one for each combination of a season class (interim, summer or winter) and day-of-the-week class (workday, Saturday or Sunday). In the analyzed year 2015, Christmas and New Year’s Eve fell on a Thursday but are treated as Saturdays. National and Bavarian holidays are taken into account and treated as Sundays. To account for the fact, that daily demand varies not stepwise over the seasons but rather gradually, dependent for example on ambient temperatures, an additional daily weighting factor is used for scaling. Both parts of the H0 SLP, the profiles for the different day classes as well as the daily weighting factor, constitute statistical mean values. Consequently, the actual load profile of a household for one day can differ significantly because of deviant consumer behavior or other circumstances, like the climate being untypical. Despite this lack of relevance for single households and a relatively low temporal resolution of 15 min, SLPs are often used in simulations, especially when no measuring data is available. 2.6. Power analysis and comparison with SLP For each meter the completed P time series is analyzed. For comparison with the respective SLP, it is necessary, that the integral over both time series, which is the annual energy demand, is the same. Therefore, the SLP is normalized accordingly in each case. The following sections describe the four steps of the final power analysis. Prior to the power analysis, the data is categorized into day classes, as defined in the SLP, for separate analysis within each step. 2.6.1. Individual load profiles In a first step, typical load profiles similar to SLPs are generated from the yearly data of each meter. This abstraction requires temporal averaging. Consequently, mean active power P is calculated as P d,h =
Xd,h ∑
Pd,h,n /Xd,h ,
(5)
n=1
where d indicates the day class, h indicates the hour of the day and X is the number of time steps that belong to the combination of d and h. Though kW is the SI unit of power, power is here labeled by kWh h−1 to underline the difference between averaged P and instantaneous P.
4
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
2.6.2. Frequency distribution SLPs strongly underestimate the range in which the power fluctuates. However, knowing exactly which powers occur and how much energy is retrieved at these levels, is essentially when designing smart home applications. Therefore, the frequency distribution of P is analyzed in the second step. More precisely, the data is categorized into power classes of a 0.25 kW. Then, the mean daily energy demand per power class (EDP) is calculated by Yd,p
EDPd,p =
∑(
Pd,p,n · ∆td,p,n /Dd ,
)
(6)
n=1
where p indicates the power class, Y is the number of time steps that belong to the combination d and p, and D is the number of days within d. Since IVC data is considered, ∆t is always 15 s. EDP corresponds to the frequency of P weighted by its magnitude, when assumed that all ∆t have the same length. Since this is the case, a bar chart of EDP is the same as a power weighted histogram of P. 2.6.3. Bandwidth analysis The extrema of the power demand are of importance, for example when dimensioning safety devices like fuses. In the third step, different quantiles and the means are calculated, as well as the extrema determined to give an impression of the fluctuation. Therefore, the P values are aggregated within 15 min intervals. The daily courses of these values are then plotted together with the accordingly scaled SLP. 2.6.4. Energy analysis The fourth part of the power analysis examines, whether the distribution of the consumption across the single day classes differs from the distribution within SLPs. Similar to EDP, the mean daily energy demand (ED) is calculated by EDd =
Zd ∑ (
Pd,n · ∆td,n /Dd ,
)
(7)
Table 2 Number of days per class. Winter Interim Summer
Workday
Saturday
Sunday
96 69 85
20 14 18
24 19 20
less than 1%, for details, see Table A.1. All but one meter have a ∆AE of less than 2%. The single exception (E_load10) reaches an AE IVC that is ca. 10% lower than AE AVC . One explanation is, that Ey for E_load10 is among the lowest recorded. Nonetheless, it is considered appropriate to consider the error as negligible and to use P as a representative average for the 15 s measuring interval, when determining energy demand. 4. Completion of power profiles A complete load profile for non-leap years in 15 s intervals consists of 2,102,400 values. Within the considered year 2015, data losses in the IVC amount to 5.2%. Longer, missing periods, which are treated in the first completion step, occurred at meter E_load07 over nearly 13 weeks as well as for E_load12, E_load13 and E_load14 with approximately six weeks failure each. Replacing longer gaps should be done with caution, because it dissects the temporal correlation of a time series. In case of the mentioned meters however, the missing data occurred at the beginning or at the end of 2015. Replacing these parts basically shifts the observation period to for example 2014-10-06 until 2015-10-05. The considered time span still covers a continuous year but, as a result, some replaced days will be categorized into an inadequate class. However, this is accepted for consistency reasons. The effect of the four completion steps is summarized in Table A.1. The values after step one, which leave unexpected malfunctioning of the single-board computers out of consideration, give an impression of the actual data loss to be expected when relying on mobile network in German rural areas.
n=1
where Z is the number of time steps that belong to day class d. Expressed as relative share (ER) of the annual energy demand (Ey ) Eq. (7) changes to ERd =
Zd ∑ (
Pd,n · ∆td,n /Ey .
)
(8)
n=1
3. Measuring data validation As mentioned above, only complete minutes are validated in the IVC vs. AVC comparison. The completeness for each meter is listed in Table A.1 together with the results of the statistical parameters. The r 2 and b values indicate a high consistency. When comparing SB, NU and LC, which add up to the mean squared deviation, LC always contributes the biggest part. As expected, instantaneous values scatter around the mean. The other two aspects have a weaker effect on the deviation, while rotation prevails for current and translation for voltage. Reconsidering SB and NU, one should keep in mind that voltages revolve around 230 V and currents range from zero to about 30 A. There are no negative voltage RMS values in AC metering because the phase angle determines the direction of the current or power flow. Such different value ranges reduce the distinctness between rotation and translation. An underlying deviation when using IVC data would be especially harmful, if it leads to erroneous simulated energy demand. Evaluating ∆AE reveals that for 12 out of 17 m, the error is
5. Results and discussion The days of the considered year 2015 are classified according to SLPs [1]. Table 2 summarizes the resulting number of days per class. 5.1. Power analysis Two of the 17 measured load profiles were discarded (E_load12 and E_load13), because measurements revealed that the respective households were not inhabited at all or for the most part of the year. 5.1.1. Individual load profiles Two exemplary individual load profiles (E_load11) and E_load16) are plotted in Figs. 1 and 2. For comparison, the graphs include the accordingly scaled course of the SLPs as black lines. Furthermore, the bars in the plot are subdivided into differently colored areas. Each area indicates at which P levels the respective amount of energy was consumed. Because of space restrictions, only winter workdays and Sundays, which have the highest number of days, are presented here. Figures of all nine day classes can be found in the supplemental material. The two meters are chosen as examples because the normalized root mean squared errors (NRMSE), indicating the deviation of P from the SLP, are the highest (E_load11) and the lowest (E_load16) respectively. Put simply, these two profiles represent the worst and the best fit
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
Fig. 1. Individual load profile compared to accordingly normalized SLP (black line) for worst fit (E_load11).
5
Fig. 3. Weighted power histogram for best fit (E_load16).
Fig. 4. Weighted power histogram for E_load01. Fig. 2. Individual load profile compared to accordingly normalized SLP (black line) for best fit (E_load16).
to SLPs. Again, further examples are available in the supporting information. Some typical features of SLPs are recognizable in Fig. 2. Both, the rough shape of the daily course and the lunch peaks on Sundays appear. Also, the range from baseload to highest mean values is similar, although this must be understood in the context that the aggregation time intervals are different, namely 1 h for P and 15 min for SLP. On the other hand, Fig. 1 is representative also for the other meters in proofing that consumer behavior is highly distinctive. 5.1.2. Frequency distribution Fig. 3 shows the weighted histogram of the best fit (E_load16). Similar to the previous plots (Figs. 1 and 2), the bars are colored, this time according to the temporal occurrence. One conclusion, which can be drawn from these frequency distributions, is that roughly one third to half of the energy is consumed at low power levels below 0.75 kW. This rule of thumb is also confirmed by analysis of the other meters, as shown in additional figures in the supporting information. Another peculiar phenomenon can be observed in the frequency distributions of several meters. Consider the Sunday panel in Fig. 3: Equidistant energy peaks occur as recurrent patterns. A more extreme example is Fig. 4, which shows the same analysis for E_load01.
Three indications exist towards the source of this phenomenon: First, the distance between peaks is nearly constant in the range 2.2–2.4 kW. Second, the effect is most prominent on Sundays, and third, occurring mostly from 10 to 12 a.m. Another helpful hint is that in Germany for cooking primarily electric stoves are used. Most likely, it is the use of the electric hotplates and oven heating that shapes the distribution peaks. These devices operate in a pulsed and not continuous power mode, which explains the equidistant peaks. Additionally, the temporal occurrences before lunchtime and higher number of peaks on Sundays, when more complex meals require several heating devices, are strong arguments for the electric stove. The phenomenon described is an excellent example for why a higher temporal resolution is essential and why also instantaneous measurements are indispensable. The same power profile, measured in mean values over longer periods, like 15 min in SLPs, would smooth out the equidistant frequency peaks into a continuous shape. 5.1.3. Bandwidth analysis The extremal fluctuations of P become visible in Fig. 5. Considering the curve labeled as max, the characteristics of the IVC must be kept in mind: One P value is calculated from instantaneous measurements every 15 s. Higher values of P might have been reached within a time interval, but were not recorded as they occurred between two measurements. For the reason given above,
6
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
Fig. 5. Bandwidth of instantaneous power values compared to accordingly normalized SLP (black line) for best fit (E_load16).
it is more appropriate to consider the 99% quantile than the max curve. These values are 5–10 times higher than the means. Note also that the mean curve in the bandwidth plots corresponds to the P values of the individual load profiles, but with a higher temporal resolution of 15 min. In contrast, 1 h was chosen for P in Figs. 1 and 2 because the spiky course of the 15 min means would have resulted in an unclear bar chart. The fluctuation will however diminish with a higher sample size when additional years of data are available. 5.1.4. Energy analysis The results from the energy distribution analysis are summarized in Fig. 6. Therein, the black error bars indicate the deviation from a respectively scaled SLP. Since the sample size of 15 households is small, no conclusions regarding the validity of the day classes can be drawn. Furthermore, in the data of some meters, winter deviates positively from SLP, while deviation is negative for other meters. Again, the low number of households and the observation of a single year allow no detailed conclusions. 5.1.5. Aggregation of meters In a final analysis, the power data of the 15 non-discarded meters are aggregated to one common load profile to examine the effect of pooling households. For the 15 m, the annual energy demand is 48,251 kWh resulting in a mean load of 5.5081 kW. Again, the four plots are generated: the common load profile (Fig. 7), the power histogram with power class intervals increased to 1 kW (Fig. 8), the bandwidth analysis (Fig. 9) and the energy distribution (Fig. 10). Please see supplemental material for the other day classes. The NRMSE of the common load profile compared to the SLP reduces to 58.6 (from 67.2 and 142.5 for best and worst fit), which is visible in the closer fit in Fig. 7, especially on Sundays. However, the base load in night time and early morning is generally higher than in the SLP, a deviation that was also observed in measuring data by [17] when compared to a UK SLP. The energy peaks in the power histogram (Fig. 8) disappear and the shape becomes more that of a Weibull or Gamma distribution. Furthermore, the base load is always higher than 1 kW and energy demand at power levels below 2 kW is negligible. The 99% quantiles in Fig. 9 are reduced to approximately the double of the mean values, compared to the factor 5–10 for individual profiles. The demand of energy in winter is slightly lower than for SLP, see Fig. 10, in summer the situation is vice versa. As mentioned before, conclusions based on one year and
Fig. 6. Mean daily energy demand (a and c) and share of annual energy demand (b and d) per day class for E_load11 (a and b) and E_load16 (c and d); black error bars indicate deviation from SLP.
Fig. 7. Common load profile of aggregated meters compared to accordingly normalized SLP (black line).
15 households contain valuable information, but for generalization should be rechecked in the future with larger, statistically relevant samples. 6. Conclusion and outlook The data of an exemplary smart meter roll-out was analyzed to gain a deeper understanding of residential electric consumption beyond the information provided by SLPs. The preliminary questions addressed include: how to design smart metering setups, if the use of instantaneous measurements is acceptable or if it
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
7
resolution of 15 s. Four steps are included in the analysis, each focusing on different characteristics of the gathered power profiles. When data is aggregated according to SLPs, which includes a classification into different day types, the individual load profiles obtained deviate strongly from the SLPs. In contrast, pooling a medium number of 15 households already reaches a high consistency with SLPs. Also, different quantiles of instantaneous power are analyzed and the 99% quantile is found to exceed mean power values by 5 – 10 times. When pooling 15 households, this factor reduces to roughly 2. Despite high peak values, it is low powers below 0.75 kW that contribute to relevant parts of the consumption on single house level, accounting for one third to the half of the energy demand. Fig. 8. Weighted power histogram for aggregated meters.
Some of the findings, like the ratio of 99% quantile to mean values or the effect of pooling households, probably have a general validity. Furthermore, they underline the need for a high temporal resolution when measuring residential loads. As [18] concludes, important information in form of power peaks is lost when aggregation intervals increase to several minutes and the authors rightfully state that logging intervals should not exceed 1 min to identify load patterns. Such patterns are often linked to habits or practices of inhabitants. The usage of electric stoves in Germany, as identified in this study, is a good example: it is driven by demands that have a certain temporal. Model-wise it could be predicted with activity profiles and calibration factors as realized in [17] or with the stock and flow concept used in social practice theory [16]. In any case and no matter what the
Fig. 9. Bandwidth of instantaneous power values compared to accordingly normalized SLP (black line) for aggregated meters.
approach, the identification of single appliances requires high resolution data. Residential energy demand is characterized by a certain amount of base load and sharp peaks, often at discrete power levels, caused by switching on and off appliances. Smooth SLPs or other models, which scale load profiles, and therefore power values, to map given energy consumption in detail, contradict this character. Bottom-up models that in- or decrease energy consumption by altering the frequency of appliance usage seem more suitable. The concept of rather altering the frequency instead of power levels has also a higher potential to realistically contribute to solutions that enable distribution grids to host more renewable energies. SLPs might be useful for addressing energy based challenges in the energy system, like which portfolio of power plants is necessary to supply a group of consumers. But the
Fig. 10. Mean daily energy demand (a) and share of annual energy demand (b) per day class for the aggregated meters; black error bars indicate deviation from SLP.
operation and planning of LV grids is based on power calculations, where worst case estimation often leads to restrictions or costly over-dimensioning. Finally, whether the predominant frequency of low power val-
leads to errors especially when calculating energies, and how to deal with measure gaps. The principal part however, is the power analysis and comparison with SLPs, based for the first time on complete time series over one year from 17 different smart meters in a temporal
ues applies to every household, remains subject to further studies. The analysis presented is a first glimpse into highly resolved residential load patterns and should be compared to upcoming results of bigger sample sizes in the future.
8
Table A.1 Detailed results for the different smart meters. Validation of IVC against AVC values
ID
Complete minutes in %
r 2a
E_load01
97.713
0.99048 0.99894
0.99137 0.99897
2.6705e−05 2.7243e−05
2.3575e−04 6.3316e−06
2.9904e−02 6.3954e−03
E_load02
90.968
0.98786 0.99908
0.98790 0.99911
1.8912e−05 2.7807e−05
2.4961e−04 2.0819e−06
E_load03
99.974
0.98806 0.99905
0.98813 0.99907
1.8611e−05 2.7298e−05
E_load04
95.916
0.98185 0.99920
0.99234 0.99922
E_load05
95.961
0.99079 0.99922
E_load06
97.537
0.99005 0.99911
E_load07
83.074
E_load08
ba
Completeness of P time series/% SBa
NU a
LC a
∆AE in %
As measured
After step 1
After step 2
0.602
99.708
99.708
99.722
2.0445e−02 2.4264e−03
0.624
97.188
97.188
1.4584e−04 4.4155e−06
1.2210e−02 4.8328e−03
0.767
99.977
2.2993e−05 2.7635e−05
1.5449e−05 1.1456e−06
4.7886e−03 1.4989e−03
−1.694
0.99676 0.99921
1.9921e−06 2.5689e−05
4.2939e−06 1.3354e−06
3.7795e−03 1.6659e−03
0.98981 0.99916
2.8118e−05 2.7657e−05
5.1400e−05 3.0801e−06
4.8771e−03 3.8784e−03
0.98013 0.99886
0.98019 0.99893
1.5584e−05 2.8628e−05
1.1277e−03 7.8535e−06
99.571
0.98386 0.99911
0.98540 0.99916
4.1501e−06 2.7695e−05
E_load09
97.777
0.98940 0.99901
0.98979 0.99908
E_load10
98.248
0.98982 0.99916
E_load11
98.245
E_load12b
Completed load profiles After step 4
Ey in
99.993
100.000
4532.8
74.0
97.521
99.993
100.000
3664.6
68.4
99.977
99.978
99.993
100.000
2807.9
72.5
96.534
96.534
96.831
99.993
100.000
1427.3
76.4
−0.428
99.970
99.970
99.975
99.993
100.000
1251.6
90.0
1.042
99.775
99.775
99.776
99.994
100.000
2531.3
129.5
5.6006e−02 7.8419e−03
0.238
75.958
98.847
98.855
100.000
8532.1
71.2
2.6977e−04 5.9563e−06
2.0168e−02 7.4917e−03
−0.585
99.847
99.847
99.848
99.993
100.000
1863.0
86.2
2.0789e−05 2.7425e−05
1.1526e−04 5.4796e−06
1.1612e−02 6.3767e−03
0.601
96.796
96.796
96.799
99.992
100.000
3745.0
87.3
0.99673 0.99917
1.7861e−04 2.6610e−05
4.3106e−06 2.7389e−06
4.1319e−03 3.3026e−03
−10.314
99.865
99.865
99.867
99.996
100.000
619.5
85.3
0.99259 0.99919
0.99789 0.99919
3.4391e−07 2.7204e−05
2.8448e−06 2.5831e−06
4.7475e−03 3.1889e−03
−0.098
99.856
99.856
99.857
99.991
100.000
2486.2
142.5
96.201
0.98806 0.99915
0.99092 0.99919
8.6873e−07 2.7852e−05
4.8105e−05 2.5880e−06
6.9207e−03 3.3201e−03
0.395
82.066
93.957
94.362
99.992
100.000
966.1
97.3
E_load13b
96.193
0.99988 0.99925
1.01396 0.99924
4.4803e−05 2.7686e−05
5.6287e−05 2.3010e−06
3.4923e−05 2.9785e−03
−1.890
82.045
93.934
94.315
99.982
100.000
76.8
188.7
E_load14
96.224
0.98839 0.99917
0.98921 0.99919
2.0707e−05 2.7578e−05
1.7177e−04 2.5797e−06
1.6964e−02 3.2667e−03
0.498
82.058
93.948
94.346
99.988
100.000
4254.6
119.1
E_load15
96.954
0.98360 0.99914
0.98354 0.99917
2.5798e−05 2.7718e−05
3.1989e−04 3.3315e−06
1.9039e−02 4.1336e−03
1.073
99.880
99.880
99.884
99.982
100.000
2309.7
70.3
E_load16
96.967
0.98998 0.99914
0.99001 0.99917
2.1793e−05 2.7180e−05
1.2272e−04 3.3085e−06
1.2199e−02 4.1257e−03
0.638
99.845
99.845
99.850
99.976
100.000
3537.1
67.2
E_load17
95.544
0.99177 0.99910
0.99216 0.99910
2.1804e−05 2.7224e−05
8.5760e−05 1.7438e−06
1.1394e−02 1.9530e−03
0.521
99.812
99.812
99.821
99.989
100.000
4688.5
91.4
a 1st value refers to current, 2nd to voltage. b Meters discarded from the power analysis.
After step 3
100.00
kWh y−1
NRMSE vs. SLPs
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
Smart meter
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
9
Appendix A
7. Symbols used 7.1. Symbols
A.1. Detailed results AE b D E ED EDP
kVAh – – kWh kWh d−1 kWh d−1
ER
%
I LC NU P P
A – – kW kWh h−1
r2 S SB t U
– kVA – hh:mm V
apparent energy Regression coefficient Number of days per class Energy demand Mean daily energy demand Mean daily energy demand per power class Relative share of the annual energy demand RMS current Lack of correlation or scatter factor Nonunity slope or rotation factor Instantaneous active power Mean power or mean energy demand per time Correlation coefficient Apparent power Squared bias or translation factor Time RMS voltage
7.2. Greek letters
∆
ϕ
◦
Length (in case of time interval) or relative error (in case of AE) Phase difference
7.3. Sub- and superscripts d i p v y
Indicates Indicates Indicates Indicates Annual
day class phase power class value class
7.4. Abbreviations AVC DER DSO H0 IVC LV NRMSE PCC PV RMS SLP
Aggregated values class Distributed energy resources Distribution system operator Name of the residential SLP Instantaneous values class Low voltage Normalized root mean squared error Point of common coupling Photovoltaic Root mean square Standard load profile
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The research project Smart Grid Solar was co-financed by the European Union through the European Regional Development Fund and by the Free State of Bavaria.
Appendix B. Supplementary data Supplementary material related to this article can be found online at https://doi.org/10.1016/j.segan.2019.100248. References [1] B. Schieferdecker, C. Funfgeld, H. Meier, T. Adam, Repräsentative VDEW-Lastprofile, Frankfurt (Main), 1999, https://www.bdew.de/media/ documents/1999_Repraesentative-VDEW-Lastprofile.pdf. [2] R. Pardatscher, R. Witzmann, G. Wirth, G. Becker, M. Garhamer, J. Brantl, Analyse von Lastgangzählerdaten aus dem Projekt ‘‘Netz der Zukunft", in: VDE-Kongress 2012, 2012. https://www.vde-verlag.de/proceedings-de/ 453446103.html. [3] R. Köberle, M. Fiedeldey, B. Brennauer, E.-P. Meyer, M. Metzger, A. Szabo, J. Bamberger, S. Krengel, T. Wippenbeck, Messungen und analysen für aktive verteilnetze mit hohem anteil regenerativer energien und elektromobilität, in: ETG-Fachbericht-Internationaler ETG-Kongress 2012, Stuttgart, 2012. http://www.vde-verlag.de/proceedings-en/453446151.html. [4] J.D. Rhodes, C.R. Upshaw, C.B. Harris, C.M. Meehan, D.A. Walling, P.A. Navrátil, A.L. Beck, K. Nagasawa, R.L. Fares, W.J. Cole, H. Kumar, R.D. Duncan, C.L. Holcomb, T.F. Edgar, A. Kwasinski, M.E. Webber, Experimental and data collection methods for a large-scale smart grid deployment: Methods and first results, Energy 65 (2014) 462–471, http://dx.doi.org/ 10.1016/j.energy.2013.11.004. [5] C. Stegner, J. Bogenrieder, S. Auer, P. Luchscheider, R. German, C. Brabec, Wirtschaftlichkeitsbetrachtung von Haushaltsspeichern und realdatengestützte Untersuchung des elektrischen Eigenverbrauchs von PV-Strom, in: D. Schulz (Ed.), Nachhaltige Energieversorgung und Integration von Speichern, Springer Fachmedien Wiesbaden, 2015, pp. 34–41, http://dx.doi.org/10.1007/978-3-658-10958-5_6. [6] C. Stegner, M. Dalsass, P. Luchscheider, C.J. Brabec, Monitoring and assessment of PV generation based on a combination of smart metering and thermographic measurement, Sol. Energy 163 (2018) 16–24, http: //dx.doi.org/10.1016/j.solener.2018.01.070. [7] G. Notton, M. Muselli, P. Poggi, A. Louche, Autonomous photovoltaic systems: Influences of some parameters on the sizing: Simulation timestep, input and output power profile, Renew. Energy 7 (1996) 353–369, http: //dx.doi.org/10.1016/0960-1481(96)00017-1. [8] J. Moshövel, K.-P. Kairies, D. Magnor, M. Leuthold, M. Bost, S. Gährs, E. Szczechowicz, M. Cramer, D.U. Sauer, Analysis of the maximal possible grid relief from PV-peak-power impacts by using storage systems for increased self-consumption, Appl. Energy 137 (2015) 567–575, http://dx.doi.org/10. 1016/j.apenergy.2014.07.021. [9] S. Cao, K. Sirén, Impact of simulation time-resolution on the matching of PV production and household electric demand, Appl. Energy 128 (2014) 192–208, http://dx.doi.org/10.1016/j.apenergy.2014.04.075. [10] A. Barbato, A. Dedè, D. Della Giustina, G. Massa, A. Angioni, G. Lipari, F. Ponci, S. Repo, Lessons learnt from real-time monitoring of the low voltage distribution network, Sustain. Energy Grids Netw. 15 (2018) 76–85, http://dx.doi.org/10.1016/j.segan.2017.05.002. [11] C. Stegner, J. Bogenrieder, P. Luchscheider, C.J. Brabec, First year of smart metering with a high time resolution—realistic self-sufficiency rates for households with solar batteries, Energy Procedia 99 (2016) 360–369, http: //dx.doi.org/10.1016/j.egypro.2016.10.126. [12] S. Lu, S. Repo, D.D. Giustina, F.A. Figuerola, A. Löf, M. Pikkarainen, Realtime low voltage network monitoring—ICT architecture and field test experience, IEEE Trans. Smart Grid. 6 (2015) 2002–2012, http://dx.doi.org/ 10.1109/TSG.2014.2371853. [13] F. Hoornaert, R. D’hulst, P. Vingerhoets, K. Vanthournout, J. Driesen, LV distribution network voltage control mechanism: Analysis of large-scale field-test, Sustain. Energy Grids Netw. 6 (2016) 7–13, http://dx.doi.org/10. 1016/j.segan.2015.11.008. [14] J. Kwac, J. Flora, R. Rajagopal, Household energy consumption segmentation using hourly data, IEEE Trans. Smart Grid. 5 (2014) 420–430, http://dx.doi. org/10.1109/TSG.2013.2278477. [15] E. Shove, G. Walker, What is energy for? Social practice and energy demand, Theory Cult. Soc. 31 (2014) 41–58, http://dx.doi.org/10.1177/ 0263276414536746. [16] S.L. Higginson, E. McKenna, M. Thomson, Can practice make perfect (models)? Incorporating social practice theory into quantitative energy demand models, in: Behave Energy Conference, 2014.
10
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
[17] I. Richardson, M. Thomson, D. Infield, C. Clifford, Domestic electricity use: A high-resolution energy demand model, Energy Build. 42 (2010) 1878–1887. [18] A. Wright, S. Firth, The nature of domestic electricity-loads and effects of time averaging on statistics and on-site generation calculations, Appl. Energy 84 (2007) 389–403, http://dx.doi.org/10.1016/j.apenergy.2006.09. 008.
[19] K. Kobayashi, M.U. Salam, Comparing simulated and measured values using mean squared deviation and its components, Agron. J. 92 (2000) 345–352, http://dx.doi.org/10.1007/s100870050043. [20] H.G. Gauch, J.T.G. Hwang, G.W. Fick, Model evaluation by comparison of model-based predictions and measured values, Agron. J. 95 (2003) 1442–1446, http://dx.doi.org/10.2134/agronj2003.1442.
Contents lists available at ScienceDirect
Sustainable Energy, Grids and Networks journal homepage: www.elsevier.com/locate/segan
Comparing smart metered, residential power demand with standard load profiles ∗
Christoph Stegner a , , Oliver Glaß a , Thomas Beikircher b a b
ZAE Bayern Energy Storage, Unterkotzauer Weg 25, 95028 Hof, Germany ZAE Bayern Energy Storage, Walther-Meißner-Straße 6, 85748 Garching, Germany
article
info
Article history: Received 25 April 2019 Received in revised form 2 August 2019 Accepted 30 August 2019 Available online 3 September 2019 Keywords: Electric load profiles Residential Smart meter Standard load profiles Temporal resolution
a b s t r a c t Despite their age, residential standard load profiles (SLPs) are a widely used tool to represent the electric power demand of a household. However, the prospect of a future power system relying mainly on renewable and often intermittent, distributed energy resources (DER) is pushing SLPs to their limit. Determining self consumption rates and the potential of demand response through smart home applications or simulating distribution grids, especially the low voltage (LV) level—all require a realistic replication of residential load patterns. However, data of high temporal resolution for individual households is rare. Therefore, several smart meters were installed at participants’ homes within a research project and the measurements are analyzed. For the first time, complete load profiles for a whole year in a temporal resolution of 15 s are used to derive key characteristics. For example, the level of fluctuation is described by different quantiles of the instantaneous power. It is found that the 99% quantile exceeds mean power values by 5 – 10 times, but pooling of households reduces this factor strongly. Other findings, for example that one third to half of the energy is consumed at low power levels (< 0.75 kW) require bigger samples for validation, whereas the degree of fluctuation within the gained load profiles is considered representative. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Despite their development in the late 1990s [1], SLPs remain state of the art for approximating residential electric consumption and fulfill their purpose, when used to forecast aggregated power demand of several hundred consumers. SLPs are time series of electric power demand averaged over 15 min, which is a very common time interval in the German electric energy system. On the spot market, a quarter hour is the shortest block traded and utilities use the 15 min means of the power demand to determine peak power at the point of common coupling (PCC) for commercial and industrial consumers. However, 15 min is too long to include the dynamic use of many electric appliances, especially in the residential area, which take place at a time scale of 1 min and below. In the past, research projects were conducted in the distribution grid to gain data of a higher temporal resolution than 15 min. The distribution grid includes the LV level, where normally no continuous measurement takes place. In most cases, monitoring by the distribution system operator (DSO) ends at the coupling point between high and medium voltage, whereas ∗ Corresponding author. E-mail address: [email protected] (C. Stegner). https://doi.org/10.1016/j.segan.2019.100248 2352-4677/© 2019 Elsevier Ltd. All rights reserved.
further measurement usually is only conducted with mobile measuring equipment if problems occur. The research project Netz der Zukunft (grid of the future) included measurement in the distribution grid at transformer stations and selected PCCs providing 10 min mean values [2]. In [3], highly resolved voltage measurement at the transformer station and end of the LV grid are described, but without further defining the temporal resolution. Another extensive measuring campaign was analyzed in [4], including residential PCCs with a 1 min resolution and even 15 s current measurements, but without recording of the respective voltages. In the research project Smart Grid Solar of ZAE Bayern power demand and generation was measured via smart meter [5] focusing on two different distribution grids, which are characterized by a high presence of rooftop photovoltaic (PV) plants. For instance, one of the LV subnets studied in that project has an annual generation to consumption ratio of roughly 3 : 1 [6]. Part of such PV generation is being consumed on site and its quantification has been subject of various research projects. The temporal resolution of power profiles largely influences the accuracy of calculated self consumption rates, as stated in [7]. Similar simulations in [8] are based on high resolution data of 1 min values, but restrain to synthetic load profiles. Measured load profiles in 1 min resolution were used in [9] but are only available for a few days. The same time interval was available for data analyzed in [10] that used smart meters to study distribution
2
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
of power and voltages and found unbalanced phases to be an issue. [11] states, that with growing simulation intervals, the over estimation of the self consumption ratio becomes more significant. Additionally, the resulting error for different temporal resolutions is provided. On one hand, a suitable measuring infrastructure for households or DER has to follow the principles of scalability and subsidiarity to match the decentral architecture of distribution grids. Standards developed for higher voltage levels like IEC 61850 are powerful but also feature a high bandwidth consumption as explained in [12], who proposes intermediary units for data processing. On the other hand, applications that only rely on local measurements like voltage control through load management as tested in [13] exist but require knowledge about the characteristics of residential power demand. One long term goal of electrical metering campaigns is to incorporate the results into energy demand models. In fact, highly resolved data of several hundreds of consumers is necessary to derive resilient behavioral patterns, which exceeds the scope of our study. [14] for example analyzed more than 66 million daily load profiles of 220.000 residential consumers to create a load shape dictionary with profiles that can be scaled to a desired energy consumption. Their hourly time-resolution supports energy-based demand response strategies, which could be exploited by utilities for example. However, [15] makes a strong argument for social practices being the central driver that defines energy demand and criticizes forecasts basing on historical load patterns and scaling them due to trends like economic growth or an improvement in energy efficiency. [16] undertook first steps to combine social practice theory and energy demand models out of a social perspective. A related approach from technical side is the bottom-up, appliance based model of [17]. It consists of activity profiles derived from social surveys and a library of appliances with individual power characteristics. [18] confirms results from literature that recommend a temporal resolution of no longer than one minute to identify patterns of such appliances. 2. Materials and methods Together with two DSOs a smart meter rollout was conducted at the homes of several participants of a research project. From the measurements, two different classes of data are available and validated against each other before similarities to and deviations from SLPs are studied by means of a power analysis. 2.1. Smart meter One of the requirements in the project was that new meters were calibrated and approved for billing as they would replace existing Ferraris meter. The selection of the model (LZQJ-XC by EMH) was left to the two DSOs involved and their decision was also based on their experience with the manufacturer and compatibility of the meters with their data acquisition. The smart meters provide data of two different qualities: First, instantaneous current (Ii ), voltage (Ui ) and phase difference (ϕi ) are measured for all three phases (i). Note that instantaneous refers to the root mean square (RMS) values for I and U. This data type will be called instantaneous values class (IVC). Some literature refers to this kind of data as real time values but we restrain from that term, as in our understanding real time always implies that data is transmitted or processed within defined time constraints. Second, the smart meters aggregate current and voltage values for every phase over an adjustable time period and yield the respective minimum, maximum and mean values. This second class will be referred to as aggregated values class (AVC). Generally, the smart meters can provide a large variety of parameters, exceeding
Table 1 Parameters provided (all parameters are time series and should be denoted with an additional index for the time interval but we restrain from this for readability reasons). Measured parameters
Derived parameters
Measuring interval
P, S
15 sa
Savg
1 min
Instantaneous value class U i , Ii , ϕ i Aggregated value class Umin,i , Uavg,i , Umax,i , Iavg,i , Imax,i a
Normal setup only 1 min, but is not used in our analysis.
Ii , Ui and ϕi . The process of selecting parameters and setting intervals is called parameterization and must be performed via the optical interface, which requires an adaptor and proprietary software. The parameters chosen for the project are summarized in Table 1 together with the apparent and active powers (S and P) that are defined as S=
3 ∑
(Ui · Ii ) ,
i=1
Savg =
3 ∑ (
Uavg,i · Iavg,i ,
)
(1)
(Ui · Ii · cos ϕi ) .
(2)
i=1
P =
3 ∑ i=1
2.2. Measuring setup and temporal resolution During design of measuring equipment, the aim was to reach a temporal resolution as high as possible. The smart meters used, allow a wide range of measuring intervals, from hours down to a few seconds. Tests however revealed that too short intervals overstrain the smart meter in processing or transmitting the data, which will be explained in more details in the following paragraphs. The chosen measuring interval therefore had to be a compromise between high resolution and acceptable data loss. . At the same time, one of the two involved DSOs had specific requests consisting in the use of ready-made data transmission components because of his existing infrastructure. In consequence, two different setups were realized. The normal setup uses the smart meter mentioned above plus a supplemental mobile-network communication module of the same manufacturer EMH. For the AVC the aggregation interval was set to the shortest option possible (1 min). The smart meter itself has a limited RAM storage capacity and starts overwriting older data when full. The amount of data stored depends on the number of data channels and the temporal resolution, which was also set to 1 min for the IVC to assure the internal RAM is sufficiently large to buffer data over several hours. A second, enhanced setup could be realized where additional single-board computer (Raspberry Pi) were accepted by the DSO. Micro-Computers like these are affordable, have a low powerconsumption, can easily be programmed as they use standard operation systems like Linux and they proved to work stable over several years. The device connects with up to four smart meters via serial interface. Furthermore, it formats measured data to appropriate numeric classes which highly reduces traffic. A 32 GB SD card allows for a buffering, which is more reliable than the internal RAM of the smart meter, and also serves as a local backup storage. The data is finally encrypted and transferred to a central database by means of a GSM-module. The enhanced setup decreases dependency on mobile network availability, hence the
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
measuring time interval for the IVC could be improved to 15 s. Theoretically, even shorter measuring intervals can be chosen but test runs resulted in exponentially growing data gaps with higher frequency—also affecting the AVC data. It is assumed that the CPU performance of the smart meter is not sufficient for the aggregating tasks, when continually serving too many IVC measure requests at the same time. Results within this paper are based exclusively on data from the enhanced setup. 2.3. Evaluation of instantaneous parameters In hindsight, the parameterization of the smart meters, which means the selection of the values to be measured, was based on some assumptions that later proofed to be restricting for certain analysis. Average, active power values were not included in the AVC measurements because respective IVC data was deemed to be sufficient—although active power is a very relevant parameter, also for this study. The decision was especially regrettable because it could not be easily corrected after roll-out due to limited accessibility of the smart meters. Therefore, the following evaluation compares IVC and AVC data and quantifies the uncertainty when using instantaneous values instead of means. Measurements from the IVC provide only a snapshot of the electric quantities. However, it is important how close the mean of four U (or I) values from the IVC for a certain minute to the correspondent Uavg (or Iavg ) from the AVC value is. It defines for example, if using IVC data as time series in simulation leads to errors, when the simulation interprets the values as constant over one simulation interval. During evaluation and in order to identify congruence between the mean of four IVC and the AVC value, a filter is first applied to the IVC data. It sorts out all the samples where per phase and minute less than four values were recorded. Additionally, minutes without AVC values are discarded. Next, mean values per minute for voltage (U¯ avg,i ) and current (I¯avg,i ) are calculated and compared to their AVC counterparts. As phase difference is not available in the AVC, a respective analysis for the active power has not been undertaken. Common statistical criteria for comparison of synthetic and measured values are correlation and regression coefficients (r 2 and b). [19] introduced further criteria based on mean squared deviation. These were refined later by [20] to include numeric factors indicating to which degree the deviation is caused by translation (SB), rotation (NU) and scatter (LC ). Both, r 2 and b, as well as SB, NU and LC will be used for comparison. As stated above, active powers could not be validated, but apparent power values exist in both data classes. To also include a comparison in terms of energy, an additional analysis of these apparent powers is conducted. For both value classes (v) the total apparent energy (AE v ) is calculated by AEv =
Nv ∑ (
Sv,n · ∆tv,n ,
)
(3)
n=1
where v is the value class, N is the number of available values in v and ∆t the length of the measuring interval n in v, which is 15 s for IVC and 1 min for AVC. N must cover the same periods in both classes. Eventually, the relative error (∆AE) is determined by
∆AE = (AEIVC − AEAVC ) /AEAVC .
(4)
Note that, apart from the apparent energies in (3) and (4), the term energy is used always in the sense of active energy corresponding to active power.
3
2.4. Data selection and completion with synthetic values The analysis in the following sections is based on the P values from the IVC. For this purpose, the data of 17 smart meters for the entire year 2015 is processed. To generate complete time series, an algorithm of four steps is applied: First, longer gaps of several days or weeks are identified and filled up with data from the year 2014 or 2016. Second, gaps consisting of one missing time step are filled by linear interpolation between preceding and following value. Third, time steps in longer gaps are filled with the mean of the two values that have been gathered exactly one week before and after. If no values can be found, the distance is increased to two, three weeks and so on, until at least two values exist. The fourth step completes recurrent 5–10 min gaps on Monday early mornings, which are caused by weekly reboots of the singleboard computers. These reboots had to be introduced to avoid desynchronization of the local timer. During this time of the day demand is normally negligible and gaps are filled with respective values from the following Tuesday. 2.5. Standard load profiles SLPs are available for several types of power customers. The so called H0 profile stands for the aggregated active power demand at a residential PCC and consists of nine different day profiles, one for each combination of a season class (interim, summer or winter) and day-of-the-week class (workday, Saturday or Sunday). In the analyzed year 2015, Christmas and New Year’s Eve fell on a Thursday but are treated as Saturdays. National and Bavarian holidays are taken into account and treated as Sundays. To account for the fact, that daily demand varies not stepwise over the seasons but rather gradually, dependent for example on ambient temperatures, an additional daily weighting factor is used for scaling. Both parts of the H0 SLP, the profiles for the different day classes as well as the daily weighting factor, constitute statistical mean values. Consequently, the actual load profile of a household for one day can differ significantly because of deviant consumer behavior or other circumstances, like the climate being untypical. Despite this lack of relevance for single households and a relatively low temporal resolution of 15 min, SLPs are often used in simulations, especially when no measuring data is available. 2.6. Power analysis and comparison with SLP For each meter the completed P time series is analyzed. For comparison with the respective SLP, it is necessary, that the integral over both time series, which is the annual energy demand, is the same. Therefore, the SLP is normalized accordingly in each case. The following sections describe the four steps of the final power analysis. Prior to the power analysis, the data is categorized into day classes, as defined in the SLP, for separate analysis within each step. 2.6.1. Individual load profiles In a first step, typical load profiles similar to SLPs are generated from the yearly data of each meter. This abstraction requires temporal averaging. Consequently, mean active power P is calculated as P d,h =
Xd,h ∑
Pd,h,n /Xd,h ,
(5)
n=1
where d indicates the day class, h indicates the hour of the day and X is the number of time steps that belong to the combination of d and h. Though kW is the SI unit of power, power is here labeled by kWh h−1 to underline the difference between averaged P and instantaneous P.
4
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
2.6.2. Frequency distribution SLPs strongly underestimate the range in which the power fluctuates. However, knowing exactly which powers occur and how much energy is retrieved at these levels, is essentially when designing smart home applications. Therefore, the frequency distribution of P is analyzed in the second step. More precisely, the data is categorized into power classes of a 0.25 kW. Then, the mean daily energy demand per power class (EDP) is calculated by Yd,p
EDPd,p =
∑(
Pd,p,n · ∆td,p,n /Dd ,
)
(6)
n=1
where p indicates the power class, Y is the number of time steps that belong to the combination d and p, and D is the number of days within d. Since IVC data is considered, ∆t is always 15 s. EDP corresponds to the frequency of P weighted by its magnitude, when assumed that all ∆t have the same length. Since this is the case, a bar chart of EDP is the same as a power weighted histogram of P. 2.6.3. Bandwidth analysis The extrema of the power demand are of importance, for example when dimensioning safety devices like fuses. In the third step, different quantiles and the means are calculated, as well as the extrema determined to give an impression of the fluctuation. Therefore, the P values are aggregated within 15 min intervals. The daily courses of these values are then plotted together with the accordingly scaled SLP. 2.6.4. Energy analysis The fourth part of the power analysis examines, whether the distribution of the consumption across the single day classes differs from the distribution within SLPs. Similar to EDP, the mean daily energy demand (ED) is calculated by EDd =
Zd ∑ (
Pd,n · ∆td,n /Dd ,
)
(7)
Table 2 Number of days per class. Winter Interim Summer
Workday
Saturday
Sunday
96 69 85
20 14 18
24 19 20
less than 1%, for details, see Table A.1. All but one meter have a ∆AE of less than 2%. The single exception (E_load10) reaches an AE IVC that is ca. 10% lower than AE AVC . One explanation is, that Ey for E_load10 is among the lowest recorded. Nonetheless, it is considered appropriate to consider the error as negligible and to use P as a representative average for the 15 s measuring interval, when determining energy demand. 4. Completion of power profiles A complete load profile for non-leap years in 15 s intervals consists of 2,102,400 values. Within the considered year 2015, data losses in the IVC amount to 5.2%. Longer, missing periods, which are treated in the first completion step, occurred at meter E_load07 over nearly 13 weeks as well as for E_load12, E_load13 and E_load14 with approximately six weeks failure each. Replacing longer gaps should be done with caution, because it dissects the temporal correlation of a time series. In case of the mentioned meters however, the missing data occurred at the beginning or at the end of 2015. Replacing these parts basically shifts the observation period to for example 2014-10-06 until 2015-10-05. The considered time span still covers a continuous year but, as a result, some replaced days will be categorized into an inadequate class. However, this is accepted for consistency reasons. The effect of the four completion steps is summarized in Table A.1. The values after step one, which leave unexpected malfunctioning of the single-board computers out of consideration, give an impression of the actual data loss to be expected when relying on mobile network in German rural areas.
n=1
where Z is the number of time steps that belong to day class d. Expressed as relative share (ER) of the annual energy demand (Ey ) Eq. (7) changes to ERd =
Zd ∑ (
Pd,n · ∆td,n /Ey .
)
(8)
n=1
3. Measuring data validation As mentioned above, only complete minutes are validated in the IVC vs. AVC comparison. The completeness for each meter is listed in Table A.1 together with the results of the statistical parameters. The r 2 and b values indicate a high consistency. When comparing SB, NU and LC, which add up to the mean squared deviation, LC always contributes the biggest part. As expected, instantaneous values scatter around the mean. The other two aspects have a weaker effect on the deviation, while rotation prevails for current and translation for voltage. Reconsidering SB and NU, one should keep in mind that voltages revolve around 230 V and currents range from zero to about 30 A. There are no negative voltage RMS values in AC metering because the phase angle determines the direction of the current or power flow. Such different value ranges reduce the distinctness between rotation and translation. An underlying deviation when using IVC data would be especially harmful, if it leads to erroneous simulated energy demand. Evaluating ∆AE reveals that for 12 out of 17 m, the error is
5. Results and discussion The days of the considered year 2015 are classified according to SLPs [1]. Table 2 summarizes the resulting number of days per class. 5.1. Power analysis Two of the 17 measured load profiles were discarded (E_load12 and E_load13), because measurements revealed that the respective households were not inhabited at all or for the most part of the year. 5.1.1. Individual load profiles Two exemplary individual load profiles (E_load11) and E_load16) are plotted in Figs. 1 and 2. For comparison, the graphs include the accordingly scaled course of the SLPs as black lines. Furthermore, the bars in the plot are subdivided into differently colored areas. Each area indicates at which P levels the respective amount of energy was consumed. Because of space restrictions, only winter workdays and Sundays, which have the highest number of days, are presented here. Figures of all nine day classes can be found in the supplemental material. The two meters are chosen as examples because the normalized root mean squared errors (NRMSE), indicating the deviation of P from the SLP, are the highest (E_load11) and the lowest (E_load16) respectively. Put simply, these two profiles represent the worst and the best fit
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
Fig. 1. Individual load profile compared to accordingly normalized SLP (black line) for worst fit (E_load11).
5
Fig. 3. Weighted power histogram for best fit (E_load16).
Fig. 4. Weighted power histogram for E_load01. Fig. 2. Individual load profile compared to accordingly normalized SLP (black line) for best fit (E_load16).
to SLPs. Again, further examples are available in the supporting information. Some typical features of SLPs are recognizable in Fig. 2. Both, the rough shape of the daily course and the lunch peaks on Sundays appear. Also, the range from baseload to highest mean values is similar, although this must be understood in the context that the aggregation time intervals are different, namely 1 h for P and 15 min for SLP. On the other hand, Fig. 1 is representative also for the other meters in proofing that consumer behavior is highly distinctive. 5.1.2. Frequency distribution Fig. 3 shows the weighted histogram of the best fit (E_load16). Similar to the previous plots (Figs. 1 and 2), the bars are colored, this time according to the temporal occurrence. One conclusion, which can be drawn from these frequency distributions, is that roughly one third to half of the energy is consumed at low power levels below 0.75 kW. This rule of thumb is also confirmed by analysis of the other meters, as shown in additional figures in the supporting information. Another peculiar phenomenon can be observed in the frequency distributions of several meters. Consider the Sunday panel in Fig. 3: Equidistant energy peaks occur as recurrent patterns. A more extreme example is Fig. 4, which shows the same analysis for E_load01.
Three indications exist towards the source of this phenomenon: First, the distance between peaks is nearly constant in the range 2.2–2.4 kW. Second, the effect is most prominent on Sundays, and third, occurring mostly from 10 to 12 a.m. Another helpful hint is that in Germany for cooking primarily electric stoves are used. Most likely, it is the use of the electric hotplates and oven heating that shapes the distribution peaks. These devices operate in a pulsed and not continuous power mode, which explains the equidistant peaks. Additionally, the temporal occurrences before lunchtime and higher number of peaks on Sundays, when more complex meals require several heating devices, are strong arguments for the electric stove. The phenomenon described is an excellent example for why a higher temporal resolution is essential and why also instantaneous measurements are indispensable. The same power profile, measured in mean values over longer periods, like 15 min in SLPs, would smooth out the equidistant frequency peaks into a continuous shape. 5.1.3. Bandwidth analysis The extremal fluctuations of P become visible in Fig. 5. Considering the curve labeled as max, the characteristics of the IVC must be kept in mind: One P value is calculated from instantaneous measurements every 15 s. Higher values of P might have been reached within a time interval, but were not recorded as they occurred between two measurements. For the reason given above,
6
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
Fig. 5. Bandwidth of instantaneous power values compared to accordingly normalized SLP (black line) for best fit (E_load16).
it is more appropriate to consider the 99% quantile than the max curve. These values are 5–10 times higher than the means. Note also that the mean curve in the bandwidth plots corresponds to the P values of the individual load profiles, but with a higher temporal resolution of 15 min. In contrast, 1 h was chosen for P in Figs. 1 and 2 because the spiky course of the 15 min means would have resulted in an unclear bar chart. The fluctuation will however diminish with a higher sample size when additional years of data are available. 5.1.4. Energy analysis The results from the energy distribution analysis are summarized in Fig. 6. Therein, the black error bars indicate the deviation from a respectively scaled SLP. Since the sample size of 15 households is small, no conclusions regarding the validity of the day classes can be drawn. Furthermore, in the data of some meters, winter deviates positively from SLP, while deviation is negative for other meters. Again, the low number of households and the observation of a single year allow no detailed conclusions. 5.1.5. Aggregation of meters In a final analysis, the power data of the 15 non-discarded meters are aggregated to one common load profile to examine the effect of pooling households. For the 15 m, the annual energy demand is 48,251 kWh resulting in a mean load of 5.5081 kW. Again, the four plots are generated: the common load profile (Fig. 7), the power histogram with power class intervals increased to 1 kW (Fig. 8), the bandwidth analysis (Fig. 9) and the energy distribution (Fig. 10). Please see supplemental material for the other day classes. The NRMSE of the common load profile compared to the SLP reduces to 58.6 (from 67.2 and 142.5 for best and worst fit), which is visible in the closer fit in Fig. 7, especially on Sundays. However, the base load in night time and early morning is generally higher than in the SLP, a deviation that was also observed in measuring data by [17] when compared to a UK SLP. The energy peaks in the power histogram (Fig. 8) disappear and the shape becomes more that of a Weibull or Gamma distribution. Furthermore, the base load is always higher than 1 kW and energy demand at power levels below 2 kW is negligible. The 99% quantiles in Fig. 9 are reduced to approximately the double of the mean values, compared to the factor 5–10 for individual profiles. The demand of energy in winter is slightly lower than for SLP, see Fig. 10, in summer the situation is vice versa. As mentioned before, conclusions based on one year and
Fig. 6. Mean daily energy demand (a and c) and share of annual energy demand (b and d) per day class for E_load11 (a and b) and E_load16 (c and d); black error bars indicate deviation from SLP.
Fig. 7. Common load profile of aggregated meters compared to accordingly normalized SLP (black line).
15 households contain valuable information, but for generalization should be rechecked in the future with larger, statistically relevant samples. 6. Conclusion and outlook The data of an exemplary smart meter roll-out was analyzed to gain a deeper understanding of residential electric consumption beyond the information provided by SLPs. The preliminary questions addressed include: how to design smart metering setups, if the use of instantaneous measurements is acceptable or if it
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
7
resolution of 15 s. Four steps are included in the analysis, each focusing on different characteristics of the gathered power profiles. When data is aggregated according to SLPs, which includes a classification into different day types, the individual load profiles obtained deviate strongly from the SLPs. In contrast, pooling a medium number of 15 households already reaches a high consistency with SLPs. Also, different quantiles of instantaneous power are analyzed and the 99% quantile is found to exceed mean power values by 5 – 10 times. When pooling 15 households, this factor reduces to roughly 2. Despite high peak values, it is low powers below 0.75 kW that contribute to relevant parts of the consumption on single house level, accounting for one third to the half of the energy demand. Fig. 8. Weighted power histogram for aggregated meters.
Some of the findings, like the ratio of 99% quantile to mean values or the effect of pooling households, probably have a general validity. Furthermore, they underline the need for a high temporal resolution when measuring residential loads. As [18] concludes, important information in form of power peaks is lost when aggregation intervals increase to several minutes and the authors rightfully state that logging intervals should not exceed 1 min to identify load patterns. Such patterns are often linked to habits or practices of inhabitants. The usage of electric stoves in Germany, as identified in this study, is a good example: it is driven by demands that have a certain temporal. Model-wise it could be predicted with activity profiles and calibration factors as realized in [17] or with the stock and flow concept used in social practice theory [16]. In any case and no matter what the
Fig. 9. Bandwidth of instantaneous power values compared to accordingly normalized SLP (black line) for aggregated meters.
approach, the identification of single appliances requires high resolution data. Residential energy demand is characterized by a certain amount of base load and sharp peaks, often at discrete power levels, caused by switching on and off appliances. Smooth SLPs or other models, which scale load profiles, and therefore power values, to map given energy consumption in detail, contradict this character. Bottom-up models that in- or decrease energy consumption by altering the frequency of appliance usage seem more suitable. The concept of rather altering the frequency instead of power levels has also a higher potential to realistically contribute to solutions that enable distribution grids to host more renewable energies. SLPs might be useful for addressing energy based challenges in the energy system, like which portfolio of power plants is necessary to supply a group of consumers. But the
Fig. 10. Mean daily energy demand (a) and share of annual energy demand (b) per day class for the aggregated meters; black error bars indicate deviation from SLP.
operation and planning of LV grids is based on power calculations, where worst case estimation often leads to restrictions or costly over-dimensioning. Finally, whether the predominant frequency of low power val-
leads to errors especially when calculating energies, and how to deal with measure gaps. The principal part however, is the power analysis and comparison with SLPs, based for the first time on complete time series over one year from 17 different smart meters in a temporal
ues applies to every household, remains subject to further studies. The analysis presented is a first glimpse into highly resolved residential load patterns and should be compared to upcoming results of bigger sample sizes in the future.
8
Table A.1 Detailed results for the different smart meters. Validation of IVC against AVC values
ID
Complete minutes in %
r 2a
E_load01
97.713
0.99048 0.99894
0.99137 0.99897
2.6705e−05 2.7243e−05
2.3575e−04 6.3316e−06
2.9904e−02 6.3954e−03
E_load02
90.968
0.98786 0.99908
0.98790 0.99911
1.8912e−05 2.7807e−05
2.4961e−04 2.0819e−06
E_load03
99.974
0.98806 0.99905
0.98813 0.99907
1.8611e−05 2.7298e−05
E_load04
95.916
0.98185 0.99920
0.99234 0.99922
E_load05
95.961
0.99079 0.99922
E_load06
97.537
0.99005 0.99911
E_load07
83.074
E_load08
ba
Completeness of P time series/% SBa
NU a
LC a
∆AE in %
As measured
After step 1
After step 2
0.602
99.708
99.708
99.722
2.0445e−02 2.4264e−03
0.624
97.188
97.188
1.4584e−04 4.4155e−06
1.2210e−02 4.8328e−03
0.767
99.977
2.2993e−05 2.7635e−05
1.5449e−05 1.1456e−06
4.7886e−03 1.4989e−03
−1.694
0.99676 0.99921
1.9921e−06 2.5689e−05
4.2939e−06 1.3354e−06
3.7795e−03 1.6659e−03
0.98981 0.99916
2.8118e−05 2.7657e−05
5.1400e−05 3.0801e−06
4.8771e−03 3.8784e−03
0.98013 0.99886
0.98019 0.99893
1.5584e−05 2.8628e−05
1.1277e−03 7.8535e−06
99.571
0.98386 0.99911
0.98540 0.99916
4.1501e−06 2.7695e−05
E_load09
97.777
0.98940 0.99901
0.98979 0.99908
E_load10
98.248
0.98982 0.99916
E_load11
98.245
E_load12b
Completed load profiles After step 4
Ey in
99.993
100.000
4532.8
74.0
97.521
99.993
100.000
3664.6
68.4
99.977
99.978
99.993
100.000
2807.9
72.5
96.534
96.534
96.831
99.993
100.000
1427.3
76.4
−0.428
99.970
99.970
99.975
99.993
100.000
1251.6
90.0
1.042
99.775
99.775
99.776
99.994
100.000
2531.3
129.5
5.6006e−02 7.8419e−03
0.238
75.958
98.847
98.855
100.000
8532.1
71.2
2.6977e−04 5.9563e−06
2.0168e−02 7.4917e−03
−0.585
99.847
99.847
99.848
99.993
100.000
1863.0
86.2
2.0789e−05 2.7425e−05
1.1526e−04 5.4796e−06
1.1612e−02 6.3767e−03
0.601
96.796
96.796
96.799
99.992
100.000
3745.0
87.3
0.99673 0.99917
1.7861e−04 2.6610e−05
4.3106e−06 2.7389e−06
4.1319e−03 3.3026e−03
−10.314
99.865
99.865
99.867
99.996
100.000
619.5
85.3
0.99259 0.99919
0.99789 0.99919
3.4391e−07 2.7204e−05
2.8448e−06 2.5831e−06
4.7475e−03 3.1889e−03
−0.098
99.856
99.856
99.857
99.991
100.000
2486.2
142.5
96.201
0.98806 0.99915
0.99092 0.99919
8.6873e−07 2.7852e−05
4.8105e−05 2.5880e−06
6.9207e−03 3.3201e−03
0.395
82.066
93.957
94.362
99.992
100.000
966.1
97.3
E_load13b
96.193
0.99988 0.99925
1.01396 0.99924
4.4803e−05 2.7686e−05
5.6287e−05 2.3010e−06
3.4923e−05 2.9785e−03
−1.890
82.045
93.934
94.315
99.982
100.000
76.8
188.7
E_load14
96.224
0.98839 0.99917
0.98921 0.99919
2.0707e−05 2.7578e−05
1.7177e−04 2.5797e−06
1.6964e−02 3.2667e−03
0.498
82.058
93.948
94.346
99.988
100.000
4254.6
119.1
E_load15
96.954
0.98360 0.99914
0.98354 0.99917
2.5798e−05 2.7718e−05
3.1989e−04 3.3315e−06
1.9039e−02 4.1336e−03
1.073
99.880
99.880
99.884
99.982
100.000
2309.7
70.3
E_load16
96.967
0.98998 0.99914
0.99001 0.99917
2.1793e−05 2.7180e−05
1.2272e−04 3.3085e−06
1.2199e−02 4.1257e−03
0.638
99.845
99.845
99.850
99.976
100.000
3537.1
67.2
E_load17
95.544
0.99177 0.99910
0.99216 0.99910
2.1804e−05 2.7224e−05
8.5760e−05 1.7438e−06
1.1394e−02 1.9530e−03
0.521
99.812
99.812
99.821
99.989
100.000
4688.5
91.4
a 1st value refers to current, 2nd to voltage. b Meters discarded from the power analysis.
After step 3
100.00
kWh y−1
NRMSE vs. SLPs
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
Smart meter
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
9
Appendix A
7. Symbols used 7.1. Symbols
A.1. Detailed results AE b D E ED EDP
kVAh – – kWh kWh d−1 kWh d−1
ER
%
I LC NU P P
A – – kW kWh h−1
r2 S SB t U
– kVA – hh:mm V
apparent energy Regression coefficient Number of days per class Energy demand Mean daily energy demand Mean daily energy demand per power class Relative share of the annual energy demand RMS current Lack of correlation or scatter factor Nonunity slope or rotation factor Instantaneous active power Mean power or mean energy demand per time Correlation coefficient Apparent power Squared bias or translation factor Time RMS voltage
7.2. Greek letters
∆
ϕ
◦
Length (in case of time interval) or relative error (in case of AE) Phase difference
7.3. Sub- and superscripts d i p v y
Indicates Indicates Indicates Indicates Annual
day class phase power class value class
7.4. Abbreviations AVC DER DSO H0 IVC LV NRMSE PCC PV RMS SLP
Aggregated values class Distributed energy resources Distribution system operator Name of the residential SLP Instantaneous values class Low voltage Normalized root mean squared error Point of common coupling Photovoltaic Root mean square Standard load profile
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The research project Smart Grid Solar was co-financed by the European Union through the European Regional Development Fund and by the Free State of Bavaria.
Appendix B. Supplementary data Supplementary material related to this article can be found online at https://doi.org/10.1016/j.segan.2019.100248. References [1] B. Schieferdecker, C. Funfgeld, H. Meier, T. Adam, Repräsentative VDEW-Lastprofile, Frankfurt (Main), 1999, https://www.bdew.de/media/ documents/1999_Repraesentative-VDEW-Lastprofile.pdf. [2] R. Pardatscher, R. Witzmann, G. Wirth, G. Becker, M. Garhamer, J. Brantl, Analyse von Lastgangzählerdaten aus dem Projekt ‘‘Netz der Zukunft", in: VDE-Kongress 2012, 2012. https://www.vde-verlag.de/proceedings-de/ 453446103.html. [3] R. Köberle, M. Fiedeldey, B. Brennauer, E.-P. Meyer, M. Metzger, A. Szabo, J. Bamberger, S. Krengel, T. Wippenbeck, Messungen und analysen für aktive verteilnetze mit hohem anteil regenerativer energien und elektromobilität, in: ETG-Fachbericht-Internationaler ETG-Kongress 2012, Stuttgart, 2012. http://www.vde-verlag.de/proceedings-en/453446151.html. [4] J.D. Rhodes, C.R. Upshaw, C.B. Harris, C.M. Meehan, D.A. Walling, P.A. Navrátil, A.L. Beck, K. Nagasawa, R.L. Fares, W.J. Cole, H. Kumar, R.D. Duncan, C.L. Holcomb, T.F. Edgar, A. Kwasinski, M.E. Webber, Experimental and data collection methods for a large-scale smart grid deployment: Methods and first results, Energy 65 (2014) 462–471, http://dx.doi.org/ 10.1016/j.energy.2013.11.004. [5] C. Stegner, J. Bogenrieder, S. Auer, P. Luchscheider, R. German, C. Brabec, Wirtschaftlichkeitsbetrachtung von Haushaltsspeichern und realdatengestützte Untersuchung des elektrischen Eigenverbrauchs von PV-Strom, in: D. Schulz (Ed.), Nachhaltige Energieversorgung und Integration von Speichern, Springer Fachmedien Wiesbaden, 2015, pp. 34–41, http://dx.doi.org/10.1007/978-3-658-10958-5_6. [6] C. Stegner, M. Dalsass, P. Luchscheider, C.J. Brabec, Monitoring and assessment of PV generation based on a combination of smart metering and thermographic measurement, Sol. Energy 163 (2018) 16–24, http: //dx.doi.org/10.1016/j.solener.2018.01.070. [7] G. Notton, M. Muselli, P. Poggi, A. Louche, Autonomous photovoltaic systems: Influences of some parameters on the sizing: Simulation timestep, input and output power profile, Renew. Energy 7 (1996) 353–369, http: //dx.doi.org/10.1016/0960-1481(96)00017-1. [8] J. Moshövel, K.-P. Kairies, D. Magnor, M. Leuthold, M. Bost, S. Gährs, E. Szczechowicz, M. Cramer, D.U. Sauer, Analysis of the maximal possible grid relief from PV-peak-power impacts by using storage systems for increased self-consumption, Appl. Energy 137 (2015) 567–575, http://dx.doi.org/10. 1016/j.apenergy.2014.07.021. [9] S. Cao, K. Sirén, Impact of simulation time-resolution on the matching of PV production and household electric demand, Appl. Energy 128 (2014) 192–208, http://dx.doi.org/10.1016/j.apenergy.2014.04.075. [10] A. Barbato, A. Dedè, D. Della Giustina, G. Massa, A. Angioni, G. Lipari, F. Ponci, S. Repo, Lessons learnt from real-time monitoring of the low voltage distribution network, Sustain. Energy Grids Netw. 15 (2018) 76–85, http://dx.doi.org/10.1016/j.segan.2017.05.002. [11] C. Stegner, J. Bogenrieder, P. Luchscheider, C.J. Brabec, First year of smart metering with a high time resolution—realistic self-sufficiency rates for households with solar batteries, Energy Procedia 99 (2016) 360–369, http: //dx.doi.org/10.1016/j.egypro.2016.10.126. [12] S. Lu, S. Repo, D.D. Giustina, F.A. Figuerola, A. Löf, M. Pikkarainen, Realtime low voltage network monitoring—ICT architecture and field test experience, IEEE Trans. Smart Grid. 6 (2015) 2002–2012, http://dx.doi.org/ 10.1109/TSG.2014.2371853. [13] F. Hoornaert, R. D’hulst, P. Vingerhoets, K. Vanthournout, J. Driesen, LV distribution network voltage control mechanism: Analysis of large-scale field-test, Sustain. Energy Grids Netw. 6 (2016) 7–13, http://dx.doi.org/10. 1016/j.segan.2015.11.008. [14] J. Kwac, J. Flora, R. Rajagopal, Household energy consumption segmentation using hourly data, IEEE Trans. Smart Grid. 5 (2014) 420–430, http://dx.doi. org/10.1109/TSG.2013.2278477. [15] E. Shove, G. Walker, What is energy for? Social practice and energy demand, Theory Cult. Soc. 31 (2014) 41–58, http://dx.doi.org/10.1177/ 0263276414536746. [16] S.L. Higginson, E. McKenna, M. Thomson, Can practice make perfect (models)? Incorporating social practice theory into quantitative energy demand models, in: Behave Energy Conference, 2014.
10
C. Stegner, O. Glaß and T. Beikircher / Sustainable Energy, Grids and Networks 20 (2019) 100248
[17] I. Richardson, M. Thomson, D. Infield, C. Clifford, Domestic electricity use: A high-resolution energy demand model, Energy Build. 42 (2010) 1878–1887. [18] A. Wright, S. Firth, The nature of domestic electricity-loads and effects of time averaging on statistics and on-site generation calculations, Appl. Energy 84 (2007) 389–403, http://dx.doi.org/10.1016/j.apenergy.2006.09. 008.
[19] K. Kobayashi, M.U. Salam, Comparing simulated and measured values using mean squared deviation and its components, Agron. J. 92 (2000) 345–352, http://dx.doi.org/10.1007/s100870050043. [20] H.G. Gauch, J.T.G. Hwang, G.W. Fick, Model evaluation by comparison of model-based predictions and measured values, Agron. J. 95 (2003) 1442–1446, http://dx.doi.org/10.2134/agronj2003.1442.