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Electric Power Systems Research 132 (2016) 78–93
Contents lists available at ScienceDirect
Electric Power Systems Research
j o ur nal ho me page: www.elsev ier .com/ lo cate /epsr
esponse modeling of small-scale energy consumers for effectiveemand response applications
. Chrysopoulosa,b,∗, C. Dioua,b, A.L. Symeonidisa,b, P.A. Mitkasa,b
ECE Department, Aristotle University of Thessaloniki, Thessaloniki, GreeceInformation Technologies Institute, CERTH, Thessaloniki, Greece
r t i c l e i n f o
rticle history:eceived 11 September 2014eceived in revised form 5 May 2015ccepted 24 October 2015vailable online 11 December 2015
eywords:mart Gridmall-scale consumer modelsesponse modelingesponse simulationemand response applications
a b s t r a c t
The Smart Grid paradigm can be economically and socially sustainable by engaging potential consumersthrough understanding, trust and clear tangible benefits. Interested consumers may assume a more activerole in the energy market by claiming new energy products/services on offer and changing their con-sumption behavior. To this end, suppliers, aggregators and Distribution System Operators can providemonetary incentives for customer behavioral change through demand response programs, which are vari-able pricing schemes aiming at consumption shifting and/or reduction. However, forecasting the effectof such programs on power demand requires accurate models that can efficiently describe and predictchanges in consumer activities as a response to pricing alterations. Current work proposes such a detailedbottom-up response modeling methodology, as a first step towards understanding and formulating con-sumer response. We build upon previous work on small-scale consumer activity modeling and providea novel approach for describing and predicting consumer response at the level of individual activities.
The proposed models are used to predict shifting of demand as a result of modified pricing policies andthey incorporate consumer preferences and comfort through sensitivity factors. Experiments indicatethe effectiveness of the proposed method on real-life data collected from two different pilot sites: 32apartments of a multi-residential building in Sweden, as well as 11 shops in a large commercial centerin Italy.© 2015 Elsevier B.V. All rights reserved.
. Introduction
Due to the gradual restructuring and deregulation of Energyarkets, all the participating entities (utilities, energy suppliers,istribution System Operators (DSOs), etc.) have to attune theirhilosophy and their operation model to the changing market
andscape. In addition, the new upcoming Smart Grid paradigmecessitates a perfect balance between supply and demand in realime [1].
Even so, the economical and social sustainability of Smart Gridslso requires the active involvement of electricity consumers: they
ave to recognize the added value of new market system technolo-ies and be willing to change their consumption behavior wheneeded. For example, consumers could reduce or shift their demand∗ Corresponding author at: ECE Department, Aristotle University of Thessaloniki,hessaloniki, Greece. Tel.: +30 2310996349; fax: +30 2310996398.
E-mail addresses: [email protected] (A. Chrysopoulos), [email protected]. Diou), [email protected] (A.L. Symeonidis), [email protected]. Mitkas).
ttp://dx.doi.org/10.1016/j.epsr.2015.10.026378-7796/© 2015 Elsevier B.V. All rights reserved.
over time in response to electricity prices. Additionally, they canchoose among a wider range of providers (energy retailers, aggre-gators, etc.) and power options (e.g. green electricity and powerquality premiums).
In the past, energy stakeholders have made little effort to attractthe interest of small-scale consumers, even though the residen-tial sector accounts for a significant segment of the overall energyconsumption worldwide [2]. Thus, all consumers under contractwith a certain energy supplier or aggregator are provided with thesame prices, services and communication policies, without takinginto account potential groups of consumers with similar needs orbehavior. For example, a consumer may not be able to shift his/herconsumption according to price signals and benefit from DemandResponse (DR), if the proposed program is not taking into consider-ation his/her consumption behavioral patterns.
Modeling and shaping demand assumes the ability to predictsmall-scale consumer response due to pricing policy changes.
This is a complex task, since it involves several factors suchas consumers’ comfort, environmental awareness and sensitivityto monetary incentives. Nevertheless, the gains of successfullymodeling response behavior in an activity- and comfort-based
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A. Chrysopoulos et al. / Electric Pow
ontext would be substantial, since small changes in individualonsumers’ behavior can have a major impact on the aggregateower demand. Furthermore, correct consumer segmentationased on these attributes contribute to an open and competitiveetail market, as it implies: (i) more tailored electricity serviceso meet consumers’ needs, with a higher rate of acceptancef new products and services, and (ii) the possibility to targetnergy-savvy consumers as early adopters of new technologies.
Lately, consumer response behavior has been heavily studiednd analyzed, in an attempt to better understand and predict thempact of various DR programs to energy markets and power sys-ems in general. To this end, different approaches of response
odeling were presented recently [3–10]. The research that is mostlosely related to the context of this work was presented in [11].usta et al. proposed a simple mathematical response model to cal-ulate the optimal pricing rates for electricity, assuming “default”ustomers under different scenarios. Five different mathematicalunctions for the consumer response were defined: linear, hyper-olic, potential, logarithmic and exponential. Their target was toimulate the hourly changes in consumer response according tohe load level, the price of electricity, and the elasticity at everyour.
To this direction, our paper introduces an innovative responseodeling approach for small-scale consumers, based on pre-
ious work done by the authors on activity modeling [12].ppliance-level consumption measurements are used to buildetailed stochastic activity and appliance models that aggregate tomall-scale consumer models. Next, various response models areormulated and applied on the extracted activity models in ordero discover useful patterns or information for the consumer behav-or (at activity level), taking into consideration consumer comfortnd monetary sensitivity. The implemented response models mayorrespond to predefined, parametric response patterns, or may beomputed directly from consumption measurements.
It should be mentioned that the proposed method was exten-ively evaluated on real measurement data collected from two DRilot cases implemented in the context of CASSANDRA project1, one
n a multi-residential building and a second one in a large commer-ial center. Results indicate that the proposed modeling approach:i) enables the implementation of a large variety of response typesithout introducing too much complexity, and (ii) leads to accurate
esponse prediction at installation level.The main contributions of the presented work therefore are:
The introduction of a set of data-driven response models thatcan be used to evaluate the reaction of consumers to pricingsignals. These models are built on the basis of results of sev-eral DR pilot cases [13], that show how consumption patternschange by altering pricing policies and providing feedback. Thesemodels rely solely on electricity measurements, contrary to moststate of the art response modeling approaches, that use statis-tics/demographic data or require additional input.
The introduced response models are detailed enough to esti-mate response behavior for each individual consumption activity.This enables the application of targeted (personalized) pricingschemes, aiming at specific peak shifting or energy reductiontargets.
The evaluation of the proposed models in two real-world
pilot cases: one consisting of apartments in a multi-residentialbuilding and a second one consisting of businesses in a largecommercial center (mall).1 http://cassandra-fp7.eu.
stems Research 132 (2016) 78–93 79
The rest of the paper is organized as follows. Section 2introduces our approach for response modeling, including the the-oretical background and the proposed methodology. In Section 3,a set of ad-hoc response models based on the proposed theoreticalformulation, as well as a set of models based on response data mea-surements are defined and implemented. Section 4 presents theexperimental evaluation of the proposed approach, while Section5 summarizes work performed, probes on directions for furtherresearch, and concludes the paper.
2. Consumer response modeling
Response modeling aims to indicate whether a consumer willrespond to a specific incentive or not, as well as how. As discussedin authors’ previous work [12], consumer consumption behaviorcan be described by a set of consumer activity models
Aa = {a, fN(n), fs(t), fd(t)} (1)
where a is an activity that may involve a set of one or more appli-ances a, the start time probability distribution fs(t) (assuming theactivity takes place), the probability distribution of the activityduration, fd, and the probability distribution of the number of timesthe activity takes place during a day, fN(n). In [12] a detailed com-putational approach was presented that leads to the estimation ofthe distributions fs, fd and fN from measurement data (i.e., train-ing of the activity models), along with an estimate of the expectedpower consumption Pa(t) of the activity during the day.
In this work, we study ways to modify the consumer activ-ity models in order to simulate consumer response to pricingincentives. Thus, the objective of the proposed models can be sum-marized as follows:
Objective: Given a set of activity models trained using data collectedunder certain (baseline) pricing conditions, our goal isto estimate the set of updated activity models that bestdescribes the consumer activities, when pricing conditionschange.
The following subsection provides an overview of the key factorsaffecting consumer response, as they were identified through anal-ysis of previous research projects and DR pilots [13], while latersubsections formulate these concepts into an applied responsemodeling methodology.
2.1. Factors affecting consumer response
Consumer response depends on changes in energy prices, how-ever it also strongly depends on the sensitivity of the consumer tomonetary incentives.
2.1.1. PricingMoney is probably the most significant factor for behavioral
change in electrical energy consumption. For response modeling,we assume a pricing scheme price(t) that varies depending on thetime of day t. Alterations in behavior are motivated by changing thebaseline pricing scheme pricebase(t) (i.e., the existing pricing schemeused when modeling the base load, which is commonly a fixed costpricing policy) to a new pricing scheme pricenew(t). In our case, con-
sumer response is estimated with the help of two (pricing) ratios:price ratio and daily energy cost ratio.Price ratio r(t) is used to control activity shifting, namely the starttime of the activities as a response to the price change. It is defined
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mula shows that when the overall energy daily cost for an activityincreases, consumers may choose to respond by reducing (and notjust shifting) their consumption, while in case the energy ratio is
0 A. Chrysopoulos et al. / Electric Pow
s the ratio of the new (DR) and the baseline pricing scheme forach minute of the day:
(t) = pricenew(t)pricebase(t)
(2)
his metric captures the fluctuations in energy pricing at each pointn time. An example is given in Fig. 1.
The calculation of the daily energy cost is achieved via the energyatio Er(a). This ratio is defined as the daily cost of energy consumedy an activity a with the new pricing scheme divided by the dailyost of energy consumed by the same activity with the baselinericing scheme:
r(a) =∑1440
t=1 Pa(t) · pricenew(t)∑1440t=1 Pa(t) · pricebase(t)
(3)
here Pa(t) is the average (expected) power consumption of activ-ty a at time t. The energy ratio affects the number of times anctivity is executed during a day. Notice that contrary to r(t), Er(a)epends on the activity a. The reason behind this is that activitiesre performed at different times throughout the day (i.e., have dif-erent Pa(t)), and therefore a variable pricing scheme affects eachctivity differently.
.1.2. Sensitivity factorIn order for behavioral change to occur, the consumers must be
ware, but also sensitive towards price alterations. The sensitivityactor is a set of real values in the [0, 1] range that provides an indi-ation on a consumer’s interest in money or comfort (for realizingach activity at a certain period of the day). This factor affects con-umer behavior change probability for an activity a after a change inrice and/or available information has occurred. In our approach,e define two different types of sensitivity factors: sensitivity to
ime shifting st(a, t) and sensitivity to energy reduction se(a).Sensitivity to time shifting st(a, t) indicates the consumers’ shif-
ing capability from time period t to another period of the day forctivity a, in case it is suggested by the new pricing scheme. Thisction may lead to cost reduction, but it may also affect consumers’onvenience. On the other hand, sensitivity to energy reductione(a) describes the consumers’ willingness to increase or reducehe overall daily consumption, by changing the number of timeserforming an activity or using an appliance. It should be notedhat we are assuming independence between the aforementionedensitivity factors, since they are affecting different aspects of theonsumers’ behavior.
The following subsections piece together activity models, priceodifications and consumer sensitivity into the proposed con-
umer response modeling methodology, which is focused on timehifting and daily activity frequency response modeling.
.2. Time shifting response modeling
Time shifting models describe the changes in fs(t) as a resultf changing the applied pricing scheme. The degree of change isssumed to depend upon the price ratio r(t) (Eq. (2)) and consumer’sensitivity to time shifting st(a, t) described in previous subsections.lso, consumers have specific time shifting preferences for theirctivities, categorized in the following types:
Proximity preference: Consumers prefer to carry out their activ-ities as close to the previously preferred time as possible (while atthe same time avoiding the increased cost). Usually, they performtheir activities right before or after a price increase.
Time frames preference: Consumers prefer to carry out an activ-ity during specific time periods of the day. If they choose to shifttheir activities as a result of change in pricing, they perform theiractivities during a set of preferred time frames of the day.
stems Research 132 (2016) 78–93
According to the proposed model, proximity preference ismodeled by a value st(a, t) that is high around the increased pricewindow W, while it is lower (or zero) during the rest of the day.Similarly, time frames preference is modeled by providing high sen-sitivity values at the preferred day periods and zero sensitivityvalues at the rest of the day.
Thus, the updated start time distribution for activity a afterapplying a new pricing scheme is given by:
f′sa
(t) = fsa (t) · (1 + shift(st(a, t), r(t))) (4)
The shifting function shift(st(a, t), r(t)) models the dependence of theconsumer behavioral change to the different factors of responsebehavior (time shifting sensitivity and price ratio) given some lim-itations: (i) there must be limits to the shifting capabilities, namelythere should be a lower and an upper threshold that would notallow unrealistic shifting, and (ii) in case no change in pricing hasoccurred, no load shifting should take place.
There are several mathematical functions that could be used asshifting functions, for example sigmoid functions, piecewise linearfunctions, parabolic functions, etc. In this work, a piecewise linearfunction was selected as our shifting function, since (i) it can be eas-ily parameterized and (ii) it provides the flexibility needed for themodels (e.g. different level of sensitivity for penalties and rewards,thresholds for large values, etc.). In addition, the piecewise linearfunction performed well in the response modeling experiments forboth datasets examined in this paper.
Generally, these functions are defined by equation:
shift(st(a, t), r(t)) =
⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩
c2 · st(a, t) r(t) < c1
c2
c1 − 1· (r(t) − 1) · st(a, t) c1 ≤ r(t) < 1
c4
c3 − 1· (r(t) − 1) · st(a, t) 1 ≤ r(t) < c3
c4 · st(a, t) r(t) > c3
(5)
where c1, c3 /= 1. Due to unavailability of detailed response data,we pre-selected certain values for the four constant parameters ofthe piecewise function which turned out to fit well for the problemat hand. Fig. 2 illustrates the piecewise linear function selected forour modeling approach.
After estimating the resulting values for each minute of the day,f′s(t) is normalized2:
f̂sa(t) = f′sa
(t)∑1440t=1 f′
sa(t)
(6)
2.3. Daily activity frequency response modeling
In addition to activity time shifting, consumers may respond byreducing or increasing the number of times they perform some oftheir activities. To model this behavior we assume that consumersmodify the probability density function fNa (n) of the daily times ofan activity a by:
�p(a) = (Er(a) − 1) · se(a) (7)
where Er(a) is daily energy ratio of activity a given by Eq. (3) andse(a) is the sensitivity to energy reduction. In essence, this for-
2 Technically, fs(t) describes the probability of the activity start time occurringduring the day, assuming the activity occurs exactly once. Then, multiple occur-rences are handled independently, through fN(n).
A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93 81
emes
da
2
tt
f
W
f
Fig. 1. Example of (a) ToU pricing sch
ecreased, they may start using the appliances participating in anctivity more often.
.3.1. Reducing end-useIn order to compute the change in case Er(a) > 1, we first identify
he maximum number of times (nmax) activity a is executed duringhe day, such that:
Na (n) = 0, ∀n ∈ N : n > nmax (8)
e then set
′Na
(n) ={
fNa (n) − �p(a) if n = nmax
fNa (n) · (1 + P�p(a)) elsewhere(9)
and (b) their resulting pricing ratio.
where P is given in each case by:
P =
⎧⎪⎪⎨⎪⎪⎩
1 − fNa (nmax) if nmax is affected
1 − fNa (nmax) − fNa (nmax −1) if nmax and nmax −1 are affected
......
(10)
2.3.2. Increasing end-useIn order to compute the change in case Er(a) < 1, we slightly
change the equations that were defined for the reduction, as weset:
f ′Na
(n) ={
fNa (n) − �p(a) if n = 0
fNa (n) · (1 + P�p(a)) elsewhere(11)
82 A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93
erime
w
P
3
emppih
3
stcsi
3
s
Ht
sipiP(prr
Fig. 2. The piecewise linear function used in all our exp
here P is given in each case by:
=
⎧⎪⎪⎨⎪⎪⎩
1 − fNa (0) if n = 0 is affected
1 − fNa (0) − fN(1) if n = 0 and n = 1 are affected
......
(12)
. Implemented response models
This section focuses on the implementation of response mod-ls that simulate real-life consumer behavior when motivated byonetary incentives. In the first subsection, a set of general pur-
ose response models based on response analysis of real-life DRrograms is defined, while in the second part we present a set of
mproved response models, fine tuned by using consumer responseistorical data.
.1. Generic response models
Even though the price ratio r is an important factor for the con-umers’ response behavior, the time shifting sensitivity factor st ishe one that fully describes the shifting capabilities of the activitiesonsumption. Based on results presented by real pilot cases fromeveral DR pilots [13], three different types of response models arentroduced in the following sections.
.1.1. Price-based responseIn this case the sensitivity factor is a constant number:
t(a, t) = c, t ∈ {0, 1440} (13)
ence, the shifting factor (as described in Eq. (5)), depends only onhe price incentives offered to the consumer.
This response model can describe consumers that are highlyensitive to monetary incentives, trying to reduce consumptionn critical peak hours by shifting it to more cost efficient dayeriods. This scenario is becoming more plausible given the
ncreased penetration of smart appliances in modern households.rice aware electrical appliances are able to shift their operation
automatically or by manual programming) to alternative timeeriods according to the pricing policy. This type of shifting canesult in valley fills, in case of monetary rewards (r(t) < 1), or peakeduction, in case of price penalties (r(t) > 1), without changingnts. Parameters are set as: c1 = 0, c2 = 10, c3 = 3, c4 = −5.
the appliance end-use drastically during the rest of the day. Anexample of a price sensitive response can be found in Fig. 3(a).
3.1.2. Comfort-based responseThis response type assumes the consumer attempts to mini-
mize the impact on comfort, by minimizing shifting of the applianceoperation time. As an example, consider that most consumers canstall their activities for 10–15 min, whereas the suggestion of a 2 hdelay for some types of activities would probably not be accepted. Incase of a penalty incentive near the peak index, a percentage of theexpected power consumption proportional to the price variationis shifted right before and after the peak window for a temporaldistance of W, with an inclining effect over distance before peaktimes and a declining effect over distance after peak times. In casethere are additional reward incentives for valley filling, the residualexpected power can be transferred to the closest valley (in termsof time).
The sensitivity factor for this type of response, given a penaltyincentive in the peak price time frame t ∈ {Tstart, Tend}, is estimatedby the following equation:
st(a, t) =
⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩
N(Tstart − dmean, 2 ∗ W) 0 < t < Tstart − dmean
0 Tstart − dmean ≤ t < Tstart
c Tstart ≤ t ≤ Tend
N(Tend, 2 ∗ W) t > Tend
(14)
where N(�, �) symbolizes a Gaussian distribution with mean valueof � and standard deviation of �, dmean is the mean duration ofthe activity under examination, W is the aforementioned shiftingwindow and c is a large constant value.
Depending on the pricing policy applied in the DR program, theshifting may be realized only to earlier times of the day (Fig. 3(b)),only to later times of day (Fig. 3(c)) or on both sides of the peakpricing period (Fig. 3(d)).
3.1.3. Routine-based responseIn this response type case scenario, consumers respond to
penalty incentives by shifting their activities to the next preferreddaytime intervals for this activity. For a consumer that is usu-ally carrying out an activity twice a day (once at noon and oncein the evening), penalizing excessive power consumption at noon
A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93 83
Fig. 3. Example of the generalized response models implemented in this work for a window of W = 30 min. In this example, a critical peak pricing policy is applied aroundthe time index of the center of the large peak (minutes 775–825).
84 A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93
F ty fromt l mod
wtp
t
s
3
hvasea
tited
s
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s
F
f
ig. 4. This is an example of the procedure followed in order to compute sensitivihe response periods with the respective pricing schemes, resulting to the analytica
ould often move the activity during the evening. Thus, this shif-ing behavior is overcharging the smaller peaks of the expectedower consumption (Fig. 3(e)).
To simulate this behavior, the sensitivity factor is set equal tohe start time distribution for activity a multiplied by a factor c:
t(a, t) = c · fsa (t), t ∈ {0, 1440} (15)
.2. Computing the sensitivity factor from measurements
The Smart Grid paradigm and smart metering equipment, thatave started being widely used in the recent years, have pro-ided the opportunity to energy-oriented companies to designnd deliver new services aiming to raise consumption awareness,uch as real-time consumption/production monitoring, energy coststimation, information on installations’ most energy consumingppliances and so on.
In case this type of data is available, there is no need to usehe predefined response models presented in Section 2.2, since its possible to accurately estimate the sensitivity of the installationenants through measurements. The equation that can be used tostimate the time shifting sensitivity for an activity a can be derivedirectly through Eq. (5) and is given by:
(a, t) = f ′sa
(t) − fsa (t)
fsa (t) · shift′(r(t)), fsa (t) /= 0 (16)
here t ∈ {0, 1440} is the minute of the day, fsa (t) is the start timeistribution of the activity during the baseline period, f ′
sa(t) is the
tart time distribution of the activity during the demand responseeriod and shift′(r(t)) is given by:
hift′(r(t)) =
⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩
c2 r(t) < c1
c2
c1 − 1· (r(t) − 1) c1 ≤ r(t) < 1
c4
c3 − 1· (r(t) − 1) 1 ≤ r(t) < c3
(17)
c4 r(t) > c3
ig. 4 illustrates an example.Summarizing, the computation of sensitivity factors directly
rom consumption measurements enables the creation of precise
data. The inputs are the start time probability functions during the baseline andel of time shifting sensitivity.
and “personalized” consumer response models. A set of experi-ments based on this mathematical formulation is presented as aproof of concept in Section 4.1.3.
4. Experimental results
This section discusses the experiments performed usingconsumption measurements from various installations that partic-ipated in real-life DR programs. Results illustrate the effectivenessof the proposed small-scale consumer response modeling approachand indicate how precise modeling of the response to monetaryincentives can lead to successful decision making, peak powerreduction and grid stability.
Raw measurement data were obtained from the EU fundedresearch project CASSANDRA. CASSANDRA focused on modelingenergy market stakeholders and increasing the market power ofsmall-scale consumers through consumer coalitions (ConsumerSocial Networks – CSNs). The available data were collected fromthe two pilot case scenarios that were carried out as part of theproject evaluation.
Two groups of experiments were performed: (i) ResidentialDataset Experiments and (ii) Commercial Dataset Experiments. Forthe assessment of our methodology, three different evaluationtests were realized: (a) activity modeling evaluation to indicatethe accuracy of the individual small-scale consumer activity mod-els extracted from installation consumption measurements (asdescribed in authors’ previous work [12]), (b) response modelingevaluation, to examine how well the proposed generic modelspredict consumer response and (c) simulation of response modelscomputed from measurements (only for the residential dataset), tomeasure the effectiveness of the data-driven modeling approachpresented in Section 3.2. Fig. 5 depicts the methodology thatwas followed. Details for each set of experiments is discussednext.
It should be mentioned that direct comparison with other meth-ods presented in the bibliography was not possible due to several
reasons: (i) the datasets used in each case are not publicly avail-able, (ii) the goals and evaluation metrics are different, and (iii)other methods require more input data than the electricity con-sumption measurements used by our approach (occupancy data,
A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93 85
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7
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ent
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ent
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6
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artm
ent
34
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6
1.51
2.96
2.84
0.02
ig. 5. This figure illustrates the procedure followed during the experiments forach installation.
emographics, utility statistical data, etc.). Thus, it was impossibleo implement/replicate these approaches for the datasets that werevailable for the evaluation of the present work.
.1. Residential dataset
The first pilot case took place at a multi-residential building inulea, Sweden [14]. This building consisted of 32 apartments and0 common areas. Measurements of active and reactive power, atne-minute intervals were collected from those installations fromanuary 2013 to February 2014, split in three time periods:
Baseline period (January 2013–May 2013): the pricing policy wasfixed and the tenants followed their normal consumption behav-ior.
Feedback period (June 2013–October 2013): the same pricingpolicy was retained, but the tenants were informed of theirconsumption behavior, as well as of the other tenants’ overallconsumption, at the end of each month.
Demand response period (November 2013–February 2014): mon-etary incentives, equivalent to a new pricing scheme, wereprovided to the tenants. This new scheme included some peakpricing periods, encouraging tenants to respond by shiftingand/or reducing their consumption.
.1.1. Residential dataset activity model experimentsThe first stage of model evaluation is the comparison between
imulated and actual baseline power consumption, in order toake sure that we have appropriately estimated baseline small-
cale consumer models to apply the proposed response models.o this end, a set of small-scale consumer models, one for eachpartment under examination, was extracted by applying the activ-ty modeling methodology (presented in authors’ previous work12]) on the available baseline measurements. It should be notedhat the common areas of the residential building were omit-ed from the experimental procedure, since their consumptionatterns diverged significantly from the “small-scale” consumers’atterns that this paper studies.
In order to evaluate the precision of our end-use models for each
nstallation four different metrics were employed. All the metricsresented below can be easily calculated from the measurementsime series provided for analysis: Table
1Th
e
acti
vit
Inst
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ti
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artm
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tme
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par
tme
Ap
artm
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par
tme
86 A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93
e res
•
•
•
•
m
Fig. 6. Example of a simulated apartment (Apartment 1) from th
Root mean square error (RMSE)
RMSE =√∑n
i=1(�i − pi)2
n(18)
where n is the number of time series samples, �i is the observedvalue of energy consumption for each time step i and pi is therespective predicted value.Symmetric mean absolute percentage error (SMAPE)
SMAPE = 1n
n∑t=1
|At − Ft |At + Ft
100% (19)
where At is the expected power extracted from the real mea-surements for a 15-min window centered around t minute of theday and Ft is the simulated power for the same time window.Given the tolerance levels of the transmission and distributionsegments of the power grid, a 10–15% SMAPE is consideredacceptable. Furthermore, the goal of the proposed framework isnot focused on consumption or activity forecasting but on con-sumer activity and response modeling for demand response orconsumption analysis applications.Mean daily energy error (MDEE)
MDEE =n∑
i=1
|�i − pi|�i
100% (20)
where n, �i and pi are defined as in the RMSE metric.Jensen–Shannon distance (JSD)
JSD(P||Q ) =√
12
DKL(P||M) + 12
DKL(Q ||M) (21)
where M = 12 (P + Q ) and DKL(P||M) is given by the
Kullback–Leibler divergence equation:
DKL(P||Q ) =∑
i
ln(
P(i)Q (i)
)P(i) (22)
In this work, JSD is used mainly for comparison of prediction accu-racy between the predefined response models and the models
that are computed from measurement data (Section 4.1.3).For the first pilot dataset, the baseline consumption of the apart-ents was analyzed and an automated disaggregation process was
idential pilot, compared with its actual baseline measurements.
used, which was introduced in [15]. This way, we were able toextract the individual appliances’ consumption specifications andtheir switching events, enabling us to build our activity models.Table 1 presents the results from the residential pilot apartmentsfor the activity model experiments. In addition to the similar-ity metrics defined above, the Real and the Simulated Mean DailyEnergy Consumption (RMDE and SMDE, respectively) measures areincluded in the table, showing how well the models approximatedreality. The results that show significantly good fitting with the realdata are presented in bold.
Given the complexity of the consumer models, one may easilynotice that most of the apartments were modeled pretty accurately,meaning small energy and percentage errors. The average SMAPEvalue for all apartments in this set of experiments was 8.52%, whilethe respective standard deviation was 2.78%. There are some rarecases where the complexity of the appliances within an installationincreased SMAPE (up to 13%), nevertheless within acceptable errorlimits for the proposed consumer modeling context. Furthermore,the MDEE values were also low (∼7.61± 5 %). In Fig. 6 illustrates thesimulation results of an example installation in fine time granular-ity (1 min period). The figure show that the proposed model providevery accurate peak time index forecasting and closely follow thetrends of the real average power.
4.1.2. Residential dataset response model evaluationThe second set of evaluation tests assessed the response models
generated by employing the methodology presented in Section 2.In order to evaluate the different response model types, the variousshifting operations outlined of Sections 2.2 and 2.3 were applied tothe bottom-up models of the small-scale consumers created forthe first set of experiments. The assessment of the models wasperformed by comparing the real measurements from the demandresponse period with the simulated response models, after apply-ing the same monetary incentives as the real pilots (rewards andpenalties). Thus, for the realization of these experiments, two dif-ferent pricing schemes were defined:
1 A baseline pricing scheme, pbase(t), with fixed price/kW h all daylong.
2 A critical peak pricing scheme, pnew(t), where the peak periods ofthe day have increased price, while the rest have slightly reduced
er Systems Research 132 (2016) 78–93 87
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A. Chrysopoulos et al. / Electric Pow
prices, in order to incentivize shifting away from on-peak to off-peak periods.
Fig. 7 provides an overview of the pricing schemes utilized in theaseline and the DR period of the residential pilot. It is importanto mention that (both pilot cases) DR programs under examina-ion were implemented through pricing schemes with increasednergy cost. This way the participants of the DR program werencouraged to reduce their overall consumption (mostly at the peakricing periods, but on the other hours of the day as well) in ordero maintain a low billing cost.
In the residential pilot case, given the 1 year difference betweenhe baseline and the DR period, some of the apartments becamenvalid for our model evaluation purposes. More specifically:
Some tenants were absent during the baseline period.Some the tenants changed their apartments’ electrical equip-ment.In certain apartments the consumption patterns changed signifi-cantly, indicating a change of tenant or a major change in behaviorfor reasons unknown to us.
n order to draw meaningful conclusions during the evaluation pro-edure of the response models, these apartments were excludedrom the response modeling evaluation experiments (since theesponse models for these apartments were considered obsoleteor the DR period).
In order to assess the results of the response models, their simi-arity with the actual response measurements was estimated. Apartrom the metrics used in the previous subsection (RMSE, SMAPE,
DEE, JSD), three more metrics were used for the comparison withhe real response measurements from the installations:
Peak reduction: This metric shows the load reduction over thepeak periods of the day as a percentage.
�peak =∑
iEbaseline(i) −∑
iEresponse(i)∑iEbaseline(i)
100% (23)
where i ∈ {0, 1440} the subset of the minutes of the day withinthe critical peak pricing period, Ebaseline is the mean daily energyvector for the baseline measurements and Eresponse is the meandaily energy vector for the demand response measurements. Pos-itive values imply that there was a reduction in consumption,while negative values signify an increase in consumption duringthe same period.Off-peak reduction: This metric specifies the load percentagereduction over the off-peak periods of the day. It is definedaccordingly:
�off −peak =∑
iEbaseline(i) − ∑iEresponse(i)∑
iEbaseline(i)100% (24)
where this time i ∈ {0, 1440} the subset of the minutes of the dayoutside the critical peak pricing period.Overall reduction: This metric shows the overall daily reduction:
�overall =∑1440
i=1 Ebaseline(i) −∑1440
i=1 Eresponse(i)∑1440i=1 Ebaseline(i)
100% (25)
Table 2 presents the results from individual residential apart-ents comparison between real and simulated response. The first
ection of the table shows the results from the real measurementsnalysis, representing the reduction or shifting by the pilot caseonsumers as they were actually estimated from the available mea-urements. The second part of the table shows the attributes of the Ta
ble
2Pr
edefi
ned
re
Inst
alla
tion
Ap
artm
ent
Ap
artm
ent
Ap
artm
ent
Ap
artm
ent
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ent
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artm
ent
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artm
ent
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artm
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ent
Ap
artm
ent
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artm
ent
Ap
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ent
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ent
88 A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93
Fig. 7. The TOU pricing schemes for the residential pilot case.
Apartm
sm(EMmrccnb
aalostpdcfmo
Fig. 8. Example of a simulated response from the residential pilot (
hifting model that best fit the actual response period measure-ents, namely the type of response model used (as defined in Section
3.1)), the Time Shifting Sensitivity factor (TSS) in [0, 1] and thenergy Ratio Sensitivity factor (ERS) with three different levels (Low,edium, High). The third part of the table shows the similarityetrics (RMSE, SMAPE, MDEE, JSD) comparing real and simulated
esponse, while the forth part presents the reduction metrics inomparison with the real baseline measurements, trying to followlosely the actual response reduction. The results that show sig-ificantly good fitting with the real response data are presented inold.
From the results presented, it is obvious that some tenants werectively trying to reduce their overall consumption as expected (e.g.partments 4, 14, 29). These consumers were successfully simu-ated by models that have medium or high ERS. At the same time,ther tenants preferred time shifting from reducing their daily con-umption (for example apartments 2, 7, 8). In some of those cases,he large consumption shifting from the on-peak periods to the off-eak ones in combination with a small increase in the consumptionuring off-peak periods resulted in an increase in the overall daily
onsumption. These tenants were simulated mostly by a low ERSactor and a medium or large TSS factor. Finally, there was one apart-ent that the tenants did not reduce the consumption at any periodf the day (apartment 20), which was simulated best from a model
ent 2), compared with the actual response period measurements.
with no response, as it should have. It should be noted that the bestfitted exported response models were based on comfort or routine,meaning that the tenants of the households were susceptible tochange their behavior, but without having to change their habits orto decrease their comfort significantly. Fig. 8 shows the comparisonchart between the real and the simulated response of an apartment.
In summary, the results from the residential pilot apartmentsshow that SMAPE stayed in low levels (10.97± 5.14 %), as well asMDEE (3.66± 3.94 %). This means that we succeeded in portray-ing the actual installation response with the generalized modelsintroduced in Section 3.1. From all apartments analyzed, onlytwo apartments had SMAPE over 20%, leading to deduce that, inthis case, our response models were not able to follow the actualresponse trends accurately.
4.1.3. Response model simulations computed from measurementsThis final set of evaluation tests for the residential pilot case
aims at evaluating the proposed approach for computing the sen-sitivity factor from DR measurements, as described in Section 3.2.Unfortunately, the small duration of the DR period of the pilot case
did not allow a full training/test set evaluation cycle. Instead, werestricted ourselves to presenting a proof of concept by estimatingthe sensitivity factor using the entire DR period and then showinghow the newly computed response models fit the data.
A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93 89
Table 3Result of the response models with computed sensitivity factor for residential pilot apartments.
Installation Real response reduction Simulated response
�peak (%) �off−peak (%) �overall (%) Similarity Reduction
RMSE (kW h) SMAPE (%) MDEE (%) JSD �on−peak (%) �off−peak (%) �overall (%)
Apartment 2 9.88 −6.40 −3.90 1.16 5.94 0.22 0.065 8.97 −6.60 −4.21Apartment 4 21.51 13.31 14.68 1.24 5.46 1.15 0.06 18.89 14.89 15.56Apartment 7 7.29 −12.00 −8.48 1.58 6.54 7.82 0.06 9.05 −2.01 0.00Apartment 8 30.83 −13.39 −6.12 0.80 4.29 0.49 0.05 18.65 −11.15 −6.61Apartment 10 4.96 1.55 2.05 1.50 9.70 2.17 0.08 5.78 −1.04 −0.03Apartment 11 28.49 −4.88 0.32 0.80 6.76 5.42 0.06 31.91 1.30 6.07Apartment 14 25.00 24.59 24.65 2.57 4.83 1.25 0.05 26.19 23.47 23.86Apartment 20 −6.09 −6.47 −6.42 1.38 6.06 6.00 0.05 −0.00 0.01 0.01Apartment 22 42.67 −0.49 6.52 1.54 8.29 2.24 0.08 36.60 3.19 8.62Apartment 23 3.98 −0.96 −0.27 1.05 12.53 0.59 0.09 4.65 −1.69 −0.81Apartment 26 25.02 3.74 6.92 2.58 9.63 2.67 0.10 13.60 2.83 4.44Apartment 29 22.73 17.83 18.56 0.89 5.12 4.00 0.05 28.34 20.65 21.75Apartment 33 4.14 −13.54 −11.71 1.40 8.83 10.09 0.08 −0.00 −0.00 −0.00Apartment 34 8.26 −2.9 −1.51 1.17 2.16 1.58 0.02 8.49 −1.22 0.04
F gain)
m
oscTnwi
ictamfiItiriiTsp
shops from the commercial center were assessed. This time, theinstallation models were created manually using the CASSANDRA
ig. 9. Example of a simulated response from the residential pilot (Apartment 2 aeasurements.
In this experimental set, we were trying to improve the resultsf the previous response experiments set. The new results are pre-ented in Table 3, using the same metrics as above so that theyan be easily compared with the ones from the previous approach.o help the reader with the comparison and outline the effective-ess of the analytical approach, the similarity metrics results thatere improved in comparison with the previous set are presented
n bold.It can be seen that, in all cases, the analytical approach resulted
n better SMAPE and JSD, from slightly better up to 300% in someases. Overall, the results are better than the ones provided fromhe predefined models of the previous set (SMAPE: 6.86± 2.58 %nd MDEE: 3.26± 2.90 %, respectively). This means that the newodels follow more closely the actual response of consumers in
ne time granularity, leading to more realistic and flexible models.t should be mentioned that in some cases the absolute error onhe reductions (peak, off-peak and overall) was ameliorated, butn all cases it stayed within acceptable limits, meaning that theesults are reliable and useful. Fig. 9 illustrates an example of themproved response models with the use of the analytical approach,
n comparison with the generic approach of the previous section.he same apartment used in the previous experiment was selectedo that an immediate comparison between the two approaches isossible.with the custom sensitivity modeling, compared with the actual response period
4.2. Commercial dataset
The second pilot took place at a commercial center near Milan,Italy [16]. This mall contains many shops, a swimming pool andlarge common areas. In this case, 11 businesses of various types(i.e., gym, jewelry, beauty shop, etc.) actively participated in theDR program of the pilot. Their measurements of active and reactivepower, at one-minute intervals were collected using the BuildingManagement System of the commercial center.
This pilot was also separated in three periods with the samecharacteristics as the ones in the previous pilot: (i) baseline period(September 2012–January 2013), (ii) feedback period (September2013–January 2014) and (iii) demand response period (February2014).
4.2.1. Commercial dataset activity model experimentsFor the first stage of the second pilot case evaluation, the small-
scale consumer models simulating the consumption behavior of the
platform,3 which serves as a friendly and comprehensive GUI for
3 http://www.cassandra-fp7.eu/page/cassandra software platform.
90 A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93
Table 4The activity model simulation results for each shop participating in the commercial center pilot.
Installation RMDE (kW h) SMDE (kW h) RMSE (kW h) SMAPE (%) MDEE (%) JSD
Shop 1 114.13 114.82 15.05 5.04 0.60 0.03Shop 2 101.61 101.2 4.50 0.97 0.40 0.01Shop 3 33.37 33.27 1.44 6.56 0.30 0.03Shop 4 376.10 376.38 25.16 3.73 0.07 0.03Shop 5 87.66 87.42 5.68 4.53 0.27 0.02Shop 6 33.57 33.37 10.46 16.39 0.36 0.13Shop 7 100.32 99.12 6.21 5.90 1.19 0.03Shop 8 57.87 57.63 2.64 8.60 0.40 0.02Shop 9 11.81 12.02 1.97 6.56 1.76 0.06Shop 10 52.42 51.89 4.89 5.94 1.00 0.04Shop 11 843.83 845.65 76.22 2.15 0.21 0.02
merci
bseBcour
mwHppSrfae
4
scpkiu
Fig. 10. Example of a simulated shop (Shop 9) from the com
uilding analytical activity and appliance models. The participatinghopkeepers administered the specifications of the shops’ electricalquipment, as well as their daily schedule of appliances end-use.ased on the information provided, detailed activity models werereated, matching closely the mean daily energy consumption asbserved from the baseline measurements of the shops. The metricssed for evaluation were the same as the ones presented for theesidential pilot dataset.
Table 4 presents the results from the shops in the mall. Oneay easily notice that the shops that have a tight, regular scheduleere very accurately portrayed by the extracted activity models.owever, there were also some individual shops with more com-lex schedule or specialized electrical equipment which led to lessrecise models (e.g. shop 6, which is a Laundry Service, exhibitsMAPE of ∼16%). Overall, the results are within acceptable errorange (SMAPE: 6.03± 3.85 % and MDEE: 0.59± 0.48 %, respectively)or the activity modeling context of the work. Fig. 10 compares thectual and estimated power consumption for a representative shopxample.
.2.2. Commercial dataset response model evaluationBefore citing the results, it is important to present the pricing
chemes utilized in the baseline and the DR period of the commer-ial pilot (Fig. 11). This DR program also uses an increased energy
rice (i.e., Energy Ratio Er > 1 for most activities), so that the shop-eepers are encouraged to reduce their overall consumption, if thiss permitted by operational restrictions. The metrics used for eval-ation were the same as with the residential pilot dataset.al center, compared with the actual baseline measurements.
Moving on to the results, Table 5 shows that the extracted shopresponse models generated very accurate results as well. SMAPEvalues were estimated at ∼9.83± 5.00 % and MDEE was also at thesame low levels as before (0.59± 0.48 %), meaning that we can accu-rately portray the actual installation response in this pilot as well.Fig. 12 shows the comparison chart between the real and the sim-ulated response of a selected shop.
As far as the general response behavior of the shops isconcerned, there were some shops that could not reducetheir consumption at all due to operational limitations, whileother shops reduced their consumption significantly, showinggreat response/reduction potential. For commercial installations,routine-based and price-based responses were more common,since the monetary incentives and the tight time schedule playeda more important role in shop managers’ consumption patterns.This fact was successfully identified by the extracted models. As inthe previous pilot, certain shops with specialized appliances andmachinery (pool, gym, etc.) were not as accurately portrayed (hav-ing SMAPE slightly over 10%).
4.3. Discussion
The activity model evaluation phase employed single instal-lation measurements in order to: (a) assess the effectiveness of
the proposed activity modeling approach in simulating small-scaleconsumers, (b) directly compare real and predicted energy con-sumption and, finally, (c) evaluate the accuracy of the activitymodels in fine temporal granularity.
A. Chrysopoulos et al. / Electric Power Systems Research 132 (2016) 78–93 91
Fig. 11. The TOU pricing schemes for the residential pilot case.
r pilot
liriav
astapt
icsvtcr
b
Fig. 12. Example of a simulated response from the commercial cente
Judging by the better performance of the second pilot’s instal-ations models, it seems that having an appliance specification list,n addition to the detailed schedule of the shops led to more accu-ate models that the ones provided by the disaggregation. Thus,n the first pilot we have less accurate models, as a result to thebundance of electrical appliances in each house and an arbitrary,arying schedule of the tenants living in.
As far as the response model evaluation is concerned, twospects were evaluated: (a) the time shifting capabilities of con-umption from the peak to the off-peak periods of the day, showinghe accuracy of the time shifting models and, (b) the impact of
non-neutral pricing scheme (i.e., one where the total electricityrice increases), where the consumers are incentivized to reducehe overall consumption throughout the day.
Summarizing, the error level of the response modeling exper-ments is more than adequate to characterize and/or grouponsumers and support the design of effective DR programs. Ithould be noted that in some cases the achieved SMAPE and JSDalues (which are more fine grained metrics) are even satisfac-ory for consumption prediction problems. Overall, the small-scale
onsumer models extracted from the measurements portray accu-ately the installations under examination.Another practical aspect of the proposed work was revealedy the fact that the DR period took place one year later than the
(Shop 9), compared with the actual response period measurements.
baseline period. Some of the installations of the residential datasethad undergone significant changes during this time (in terms ofoccupancy profile, consumer behavior or appliance equipment),which affected the validity of the response models for the DRperiod. In practice stakeholders can easily tackle this issue by (i)continuously collecting data to update their activity and responsemodels and (ii) by continuously evaluating, via the proposedsensitivity factor (Section 2.1.2), the sensitivity and responsebehavior of individual consumers.
The results of all the scenarios examined indicate that a signif-icant decompression in the peak area is feasible without havingto increase prices too much or heavily penalize consumers whochoose not to accept the end-use change. Additionally, one shouldmention that this set of experiments also reveals a significant bene-fit of the presented bottom-up modeling approach: having detailedsmall-scale models allows for sending different incentive schemesto each consumer (or groups of them), thus leading to finer con-trol of the power curve. This intuition should be further exploredin future work.
In conclusion, these simulations illustrate how the proposed
response model methodology, along with the proposed activitytraining mechanism, can be used to model and predict the con-sumer reactions for a range of DR scenarios involving a varietyof incentives/pricing schemes and different consumer responses,
92 A. Chrysopoulos et al. / Electric Power Sy
Tab
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3.57
stems Research 132 (2016) 78–93
providing effective decision support, both from the supplier andthe demand side. Examples of such decision support applica-tions of the proposed methodology are (i) aggregators, wishingto optimize their portfolio management, (ii) DSOs, wishing toeliminate high peaks in demand, (iii) municipalities, companies, ororganizations aiming at lowering the environmental impact andcost of electrical energy consumption, (iv) individual consumers,wishing to select their energy provider or optimally adapt theirconsumption to reduce household electricity costs. In addition,these experiments indicate that even though the demand of eachindividual small-scale consumer is very small in the contextof the distribution system, change in consumption behavior ofthe individual consumers can aggregate and have significantimpact.
5. Conclusion and future work
Current work presents detailed bottom-up response models forsimulating the consumption behavioral change of small-scale con-sumers under DR program policies. By providing measurementsfrom installation-level power consumption data, detailed activ-ity models are initially built, which can simulate the observedappliance end-use. Then, a set of response models that buildson these activity models is generated to predict changes in con-sumption due to the individuals’ change of behavior, simulatedvia monetary incentives and taking into account monetary sen-sitivity and comfort. Finally, in case the necessary input data areavailable, an analytical way to compute the sensitivity of the con-sumer is provided, allowing the response behavior to be modeledfor each consumer individually and with greater accuracy. Usingthe proposed approach, an Energy Provider or DSO can map theobserved power consumption to consumer activities and there-fore model and simulate a wide range of DR scenarios for loadshaping.
A number of experiments were carried out based on measure-ments that were collected from apartments of a residential buildingin Sweden and from shops in a commercial center in Italy as part ofthe CASSANDRA research project. The result of these experimentsillustrated the accuracy and applicability of our implemented activ-ity and response models. An interesting observation is that eventhough the proposed generic response models were able to sim-ulate with adequate accuracy the actual consumer response, theresult were significantly improved when available data enabledthe computation of the sensitivity parameter. This is quite impor-tant, since the emergence of Smart Grids allows Energy Providersto collect large amounts of detailed measurement data from theirconsumers.
Results presented in this paper are promising, however thereis room for future improvement. Activity models can also becomecontext-dependent, e.g. different models for working/non-workingdays, different seasons of the year, etc. It is also possibleto examine the use of a different type of shifting functions(sigmoid, parabolic) and have their parameters trained fromavailable data. Also, more factors may be introduced in the con-sumer sensitivity estimation such as environmental awarenessand social factors. Another aspect worth exploring is the pos-sibility of having dynamic pricing schemes that may changeover time, which would require an automated procedure thatwould retrain the models when the pricing policy changes.Finally, as more Smart Grid measurement data become avail-able, the models can be encapsulated to multi-agent systems
with several agents playing the role of the installation tenants inorder to experiment with different Demand Response incentivesapplied at varying community sizes (such as neighborhoods orcities).
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Technologies (ISGT Europe), IEEE, 2013, pp. 1–5.
A. Chrysopoulos et al. / Electric Pow
cknowledgements
This work was supported in part by the EU funded researchroject CASSANDRA (FP7-ICT-288429).
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