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Efﬁcient Customer Selection for Sustainable

Demand Response in Smart Grids

Vasileios Zois†, Marc Frincu‡, Charalampos Chelmis‡, Muhammad Rizwan Saeed‡, Viktor Prasanna‡

University of Southern California

Email: {vzois,frincu,chelmis,saeedm,prasanna}@usc.edu

Department of Computer Science†, Department of Electrical Engineering‡

Abstract—Regulating the power consumption to avoid peaks

in demand is a known method. Demand Response is used as

tool by utility providers to minimize costs and avoid network

overload during peaks in demand. Although it has been used

extensively there is a shortage of solutions dealing with real-time

scheduling of DR events. Past attempts focus on minimizing the

load demand while not dealing with the uncertainty induced by

customer intervention which hinder sustainability of the reduced

load. In this paper we describe a smart selection algorithm that

solves the problem of scheduling DR events in a broad spectrum

of customers observed in common Smart Grid Infrastructures.

We deal both with the problem of real-time operation and

sustainability of the reduced load while factoring customer

comfort levels. Real Data were used from the USC campus micro

grid in our experiments. On the overall achievable reduction

the results produced a maximum average approximation error

≈0.7%. Sustainability of the targeted load was achieved with

maximum average error of less than 3%. It is also shown that

our solution fulﬁls the requirements for Dynamic Demand

Response providing a solution in a reasonable amount of time.

Keywords: smart grid, scheduling, optimization, sustainability,

demand response, selection algorithm, real time, change making,

customer comfort

I. INTRODUCTION

As demand for power increases so does the complexity

involving safe and reliable [20] energy distribution. Recent

innovations in power grids have provided smart tools, to help

utility providers monitor and predict [3] [4] power demand.

All together an automated power distribution network was

created on top of the old power grid infrastructure, now

know as a smart grid [13] cyberphysical system. It consists of

different components [20] addressing reliability, load manage-

ment and security. Smart meters [6], capable of bi-directional

communication, are a vital part of the smart grid. They are

used for real time monitoring of power consumption helping

utility providers predict future demand. Fulﬁlling the necessary

energy requirements is based on these predictions. However

installing additional power generation capability to meet peak

demands sometimes is neither feasible nor sufﬁcient. Demand

Response(DR) [2] is a well known method employed by

energy providers to control demand. It is used to ﬁnd the

equilibrium between energy production and demand through

load control.

Energy providers use different paradigms in their attempt

to control customer load including: direct control [10], price

incentives [19] as well as voluntary participation. Although

these techniques have been broadly used in practice they

still are unable to produce good results while dealing with

uncertainty induced by the customer behaviour. Real-time

techniques need to be employed to cope with unexpected peak-

demands or situations where adaptation during a DR event is

needed(dynamic DR) to sustain a consistent power reduction

under a deﬁned safe threshold. A DR event is deﬁned as

a schedule consisting of customers and their corresponding

strategies for a speciﬁc period of the day. It is initiated by

energy providers to achieve a combined load reduction from

the participating customers.

A DR event is said to be sustainable if it achieves consistent

load reduction for the scheduled time frame. A consistent load

reduction is considered to be a reduction of the typical power

consumption under a speciﬁed threshold. This threshold is usu-

ally deﬁned by the utility providers. The goal can be to ensure

reliability in power distribution, protect the equipment on the

grid or simply maximize proﬁt. Sustainable load reduction is

a hard problem. Customers employed on top of the power grid

are inherently unpredictable. This uncertainty hinders attempts

on achieving sustainability. Customer comfort [23] is deﬁned

as the ability of users in the power grid to decide independently

about the time and way to consume power. Each one has a

different footprint characterized by their behaviour and dif-

ferent reactions to exogenous events(e.g rise in temperature).

When scheduling a DR event all of this has to be taken into

consideration. It is imperative to deal with uncertainty [9],

instead of relying too much on predictable loads in order to

sustain a consistent reduction. Hence it is important also to

quickly(dynamic DR) react and adapt to changes induced by

uncertainty from the behaviour of individual customers. If the

above points are to be considered then sophisticated scheduling

algorithm is needed. This algorithm should produce a selection

of customers to participate in a DR event aiming to minimize

uncertainty while maximizing comfort. These two notions are

complementary since a comfortable customer is more likely

to comply with a DR event. This paper addresses the above

gap by introducing an algorithm that ﬁts the aforementioned

properties.

The contribution of this paper can be summarized in the

following points:

•The proposed algorithm deals with customers as indivis-

ible entities. Detailed description of the consumption of

individual devices is not needed. We just focus on the

consumption patterns initiated by different DR strategies.

•Dealing with customer comfort is not included as an extra

variable. We argue that large deviation in power reduction

throughout a DR event represent customer discomfort. A

selection of unique strategies deﬁne different levels of

intrusiveness.

•Sustainable reduction throughout the DR event was our

initial goal. We achieve that by analysing in a coarse

grained manner the potential reduction(ﬁxed intervals) of

each customer.

•The complexity of the algorithm conﬁrms the efﬁciency

claim. We achieve polynomial complexity in the number

of customers. Our experimental results show a linear

and polynomial increase in the relative execution time

consistent with the complexity analysis.

We start by describing in section II the related work. Next

we continue by formulating our problem in section III. An

analytical description for the algorithm developed is provided

in IV. We conclude with the analysis of the conducted exper-

iments in section V.

II. RE LATE D WOR K

Some of the earliest work focused on directly controlling

device schedules to minimize power consumption. In [11]

[10] dynamic programming was employed to minimize the

controllable load. In [21] linear programming in combination

with customer grouping was used based on a proﬁt based

approach to minimize load consumption.

A recent trend on the ﬁeld of load manipulation is fac-

toring customer comfort. Arguments in favour of it are the

uncertainty induced by users who may override the system and

cause peaks in demand. Different approaches emerged based

on modelling consumption of speciﬁc devices according to

their usage patterns. In [23] particle swarm optimization was

used to control demand by focusing on water heaters which

accounted for 30% of the overall load. The same technique was

employed in [12] and [18]. The former focused on the special

case of Plug-in Hybrid Electronic Vehicles (PHEVs). The latter

examined residential cases where a schedule was provided

based on the optimal time to operate domestic appliances.

In [17] load manipulation was studied conforming to con-

straints induced by dynamic pricing policies. An heuristic

approach was proposed providing a solution to the scheduling

problem in O(AT N 2log T N )time. Other approaches include

a game theoretic analysis on the minimization of load demand.

This was addressed in [9] using a residential environment

with real-time pricing as the case of study. Also in [19] a

similar technique was employed by relying on smart pricing

as an incentive to achieve the necessary load reduction. These

approaches relay on distributed calculation to provide a real

time solution to the scheduling of power reduction to different

customers. Our solution also considers the need for real time

execution.

Other proposed solutions with similar goals include [22].

There a multi-objective optimization problem was formulated

adhering to speciﬁc constraints. Those are induced by the

need to minimize consumption and maximize utility. Moreover

evolutionary algorithm was used to solve the constrained

problem. In [16] an ofﬁce environment was the use case. Power

consumption was minimized based on dynamic pricing and

production of electricity from renewable energy sources. The

ultimate goal was to leave productivity unaffected. Finally in

[30], a ﬁne grained description of a smart home is used to

schedule usage of individual appliances in respect to residen-

tial needs.

It is important at this point to note that many of the research

done so far deals with residential cases [14] [19]. Also many

approaches focus on speciﬁc devices [15] [18] [25] [8] [7].

This scenario is unrealistic for energy providers as they cannot

sustain information for all the different appliances and their

consumption patterns. A similar problem statement to ours

has been made in [24]. There the authors study the case of a

feeder failure in the distribution network. They made a mixed-

integer programming formulation of the scheduling problem

and proposed three approximate methods to solve it. Contrary

to ours their work assumes customer compliance during the

DR event. Also it deals with distributing a portion of the load

demand on other transformers. We deal only with ﬁnding a

schedule of customers to reduce the load demand.

Our solution considers the abstract notion of a customer

associated with available strategies. These strategies are the

different plans available by utility providers. Each one deﬁnes

a speciﬁc level of intrusiveness. Comfort is implied by the

overall achievable reduction and the observed inconsistencies

of the reduced load across the whole event. A dynamic pricing

policy associated with each strategy can be used as incentive

for participation in curtailment. Similar incentives have been

assumed in [5]. We avoided a device based analysis since it

is heavily dependent on their individual characteristics. It is

a realistic scenario since in many cases utility providers do

not have access to this kind of information. Our goal was to

capture the overall customer behaviour during a DR event and

use it as reference to schedule future ones.

III. PROB LE M DEFI NI TI ON

We formulate the problem as follows: We are given a set

of ncustomers. Each one is associated with mavailable

strategies. As we mentioned before each strategy represents

an individual plan provided by an energy provider. The

strategy provides some possible incentives in exchange for

voluntary participation in a DR event. Achievable reduction is

strongly related to the incentives provided. For each customer-

strategy combination there exists a curtailment vector <

r1, r2, ..., rk>. Each value rk∈ R is calculated at ﬁxed

time intervals. It represents the curtailment level which is the

difference between the predicted baseline consumption and the

predicted consumption during a DR event. A positive num-

ber indicates a successful power reduction while a negative

number indicates an increase in consumption. The baseline is

based on the observed consumption of the customer during

normal operation. The accuracy of the values indicating the

level of curtailment, depends on the predictions of the methods

used. Discussing in more detail the different kind of prediction

methods is out of the scope of this paper.

Let Rbe the targeted overall reduction throughout the

whole DR event. Our goal is to ﬁnd a subset of the available

customers which should accumulatively curtail R

tper interval,

where tis the number of intervals in a speciﬁc DR event.

Each customer must conform to a single strategy from the

available ones through the whole DR time frame. Based

on the above deﬁnition, our problem is deﬁned as ﬁnding

a set Aof customer-strategy combinations that collectively

achieves R

treduction per interval. This is described more

formally in (1) where ri,k is the reduction achieved by the

i-th customer-strategy combination ∈Aat the k-th interval

from the curtailment vector.

|A|

X

i=1

ri,k =R

t(1)

Our problem can also be expressed as Integer Linear Pro-

gramming [28] Problem(ILP). It is known that ILP is N P-

hard [28]. This means that for a small number of customers

the solution is achievable in reasonable time but it is not the

same case for a large number of customers. We can also

deal with it as a knapsack problem [29]. However dynamic

programming does not ﬁt well to our deﬁnition of the problem.

A real time solution independent of the targeted reduction is

needed. Moreover it important to use the minimum number of

participating customers. Also we are dealing with real numbers

for weights and we need to solve an 0-1 knapsack problem. In

the next section we present our approximative solution which

is based on the change making [27] problem.

IV. PROPOSED ALGORITHM

In this section we focus on describing the developed algo-

rithm. At the beginning we discuss the motivation behind our

choice to implement an approximative solution. An overview

of the major steps which constitute the algorithm is presented.

Finally we focus in discussing further some parts which

affect the accuracy, sustainability and the complexity of our

approach. In the previous section we made a strong case in

favour of sustainability. Also we emphasized the need for a

dynamic demand response scheduling to deal with uncertainty.

These are two of the strongest points which impelled us to

provide an approximative solution. Real Time scheduling of

DR events is important. As it was mentioned before solutions

provided by formulation of our problem as a 0-1 knapsack

or as an ILP are feasible but not efﬁcient. Moreover we

need a way to incorporate in the selection procedure the

uncertainty induced by the customers. This can be realized

when considering the control of an AC unit during a warm

summer day. The discomfort induced can force a customer to

override the DR event causing unpredictable peaks in demand.

Finally we can see that eliminating discomfort provides us

with predictable load reduction. This makes it easier to sustain

a stable reduction throughout the event time frame. In the

next section the proposed solution is described in more detail

following the properties deﬁned above.

A. Notation

Before we begin describing the algorithm in detail we need

to deﬁne some common notation used:

U:set of representatives of the n customers.

uj:j-th estimate from set U.

xi:Number of customers in i-th bin.

˜

C:set of coins

˜ci:i-th coin from US domination.

C:set of bin values.

ci:i-th bin value from C, ci= ˜ci·v

v:unit value used to deﬁne the bins ranges.

M:reduction per interval.

˜

M:Amount to be payed using change making.

Bi:i-th building in a bin.

Bij :j-th strategy of i-th customer.

rk:reduction value of k-th interval.

BN :set of bin ranges.

B. Algorithm Description

Our procedure involves formulating the solution based on

the change making problem. The initial step is to distribute the

customers into bins. Each bin has a speciﬁc range determined

by a quantity we call unit value(v). The upper value of each

bin is deﬁned as the bin value. Customers are distributed into

speciﬁc bins according to an estimated reduction value. We

refer to this value with the term representative of a customer.

min

∀ci∈C,∀Bi∈(ci−1,ci]X

rk∈Bij

(ci−rk)2(2)

After distribution we conform each customer to a speciﬁc

strategy. We decide on this by choosing the strategy which

minimizes the accumulated error produced by the difference

between the bin value and the reduction per interval values(2).

This is done for all available strategies to each customer.

The last step is to greedily iterate over the bins and select

the customer-strategy combinations to pay for the needed

reduction. The algorithm for change making is used at this

point to index the necessary bins.

We describe here more formally the above procedure. Con-

sider that we need a reduction of MKWh per interval across

a DR event of size k(M=R

k). Assuming a known unit

value we get ˜

M=M

vas the amount needed to be paid in

order for the necessary reduction to be achieved. By using

the change making approach we get (3). Starting from the

biggest coin which is equal or less than ˜

Mwe use zero or

more coins of value ˜cito pay for the amount ˜

M. The set

of coins ˜

C={1,2,5,10,25,50,100}is based on the US

denominations which always gives an optimal solution using

the minimum number of coins. If we multiply (3) by vwhich

is the unit value we get (4). This way we can construct seven

bins using the values from ˜

Cmultiplied by v. If we do this we

get the bin ranges in (5). Every customer with reduction per

interval in the ranges deﬁned by the boundaries of the i-th bin

from (5) belongs in that bin. The estimate for the reduction is

the customer’s representative. A pseudo code describing the

ChangeMakingScheduler(buildings, M )

Data: List of building-strategy reduction vectors,

Reduction needed

Result: List of building-strategy

representatives =buildings.representatives();

u=calc unit value(representatives);

for i←1to c.size do

c[i] = ˜c[i]∗u

end

˜

M=M/u;

bins =distribute(˜c, building s);

for i←1to buckets.size do

sort(bins[i])

end

for i←c.size to 1do

j= 0

while M−˜c[i]≥0do

while c[j]−bins[i].building[j].reduction ≥

0and j≤bins[i].length do

result.add(bins[i].building[j])

c[j] = c[j]−bins.building[j].reduction

j=j+ 1

end

˜

M=˜

M−c[i]

end

end

Algorithm 1: Change Making Scheduler

major steps of our change making scheduler is presented in

Algorithm 1.

˜

M=

7

X

1

ci·xi,xi∈N(3)

M=

7

X

1

ci·v·xi,xi∈N(4)

BN ={(0, v],(v, 2v],(2v, 5v], . . . (50v , 100v]}(5)

The most crucial step of the mapping described above is

selecting a suitable unit value. A unit value is suitable if we

can ﬁnd at least one customer-strategy combination in each

bin which achieves the bin value per interval. An inaccurate

decision at this point will limit the true potential reduction

of a customer. Although we can have another case which is

omitting a customer-strategy by placing it in a bigger bin.

Since customer-strategies are sorted in each bin before the

bins are indexed, choices which deviate much from the bin

value are not chosen. These limitations will always provide

us with a suboptimal solution that does not achieve the target

set. This affects both sustainability and the overall achievable

reduction through the whole DR event. Much of this paper is

devoted in inventing sophisticated procedures for choosing the

unit value. In the next subsection we describe them in detail.

C. Unit Value

Finding a suitable unit value must be a compromise between

accuracy and speed. From the equality ˜

M=M

vdescribed

before we only know M. So we must ﬁnd a way to assume an

approximate value for one of the variables in the right hand

side. We start by assuming that v=Mand built the bins

accordingly. This technique is deﬁned as the greedy approach.

All the customers under consideration will be limited in the

ﬁrst bin since bins of larger value will overshoot our target

and won’t be considered in the ﬁnal solution. Although simple

and efﬁcient this technique does not achieve the best accuracy.

This is because iterating greedily through the bins, provides

us with a solution containing customer-strategy combinations

of the highest reduction level less than M. It may be the

case that there is a selection of intermediate customer-strategy

combinations that are able to achieve the targeted reduction.

For that reason we need a solution adaptable to the speciﬁc

reduction patterns of each customer during a DR event.

Taking into account customer behavioural patterns we as-

sumed that there must be a suitable unit value from the set of

representatives for each customer. In this case we developed

three procedures to select from this set a suitable value. Our

solution begins by examining each individual representative

separately. This is done by using it as potential unit value to

built the bin ranges. Then assuming those bin range an error

measure is employed to decide which representative to select.

This error measure estimates the effect of our choice to the

ﬁnal solution. It selects as the unit value the representative that

minimizes this corresponding error measure.

The ﬁrst technique which we call Minimum Goal Ac-

cumulated Bin Error(MGABE), focuses on minimizing two

quantities (6) connected to the choice of the unit value. The

ﬁrst quantity is the accumulated error produced by the absolute

difference of the bin value from the reduction level estimated

by the representatives of that bin. The second quantity is

the absolute difference between the target reduction Mand

the sum of the bin values produced and being used from

the solution provided by the change making algorithm. This

approach is expected to produce relative good results in the

subject of sustainability since it considers minimizing the error

from the bin values. However i will have a hard time matching

the overall reduction needed since it focuses on two targets

independently. It will be argued from the experiments that

minimizing the latter quantity does not produce better results.

However we can see that the maximum error produced from

that quantity will not exceed 0.5 due to rounding of M

v.

min

uj∈UX

ci∈C

(ci−( max

ci−1≤uk≤ci

uk)) + min

uj∈U(M−X

ci∈CM

(ci))

(6)

A simpler technique is to consider only minimizing the

quantity connected with the bin values. The second technique

we developed, which is known as Minimum Accumulated

Average Bin Error(MAABE) does exactly that. It considers the

average reduction of the representatives that belong in each bin

and tries to minimize their difference from the bin value. Again

this is done for all the representatives from U. We describe this

minimization problem by deﬁning equation (7). We expect to

get better results here in respect to the overall reduction since

we don’t have the independent quantities of (6). Also in the

matter of sustainability since we are dealing with reduction

per interval we will manage to acquire a solution achieving a

sustainable reduction.

min

uj∈UX

vi∈v

(ci−(1

xi

·X

vi−1≤uk≤vi

(uk))) (7)

Both of the described techniques consider all bins when

calculating the overall error. It would be more advantageous

to focus only on bins that are going to be used in the end result.

That is because we want to focus on minimizing less goals to

get a better result. It is important to consider a good heuristic

in order to get a real estimate on the bins used. Our approach

was to estimate ˜

Msince we already have a potential v. Using

this information we can decide on which bins are being used

in the end result. Then we select vfrom the representatives

to minimize the accumulated error induced by these bins.

This technique Minimum Coin Error(MCE), is similar to (6)

although we only deal with choosing the representative that

minimizes the accumulative bin error. Also another difference

is that we consider ˜

Mand not M. We describe MCE using

(8). It is expected our results to be strongly dependent to the

estimate we have for the bins being used.

min

uj∈UX

ci∈C

(ci−( max

ci−1≤uk≤ci

uk)) (8)

The presented methods focused on searching the unit value

from the representative set. The major drawback in this is that

it assumes a suitable unit value is present in that set. It is

clear that there might be cases where that is not true. This

is the reason behind the development of our last technique

which is called Unit Data Trend(UDT). Our reasoning behind

this method is that we need to try and ﬁt the patterns in the

dataset to the constructed builds. Only this way we can achieve

sustainability which will also ensure achieving the overall load

reduction. We focus on using as bin values the initial values

of the coins from the change making problem. Then we state

that a unit value is needed to ﬁt the dataset and provide

corresponding bin ranges. We initially distribute the buildings

into the corresponding bins. Based on this distribution we

calculate the weighted average(9) which serves as a unit value.

The weight is the number of customers in a bin and the value

is the max reduction from the representatives in that bin. We

expect to get good results in respect to sustainability as we

try to match the patterns existing in our dataset. The overall

achievable reduction might not be achieved since sustainability

might produce reduction close to the needed one but less or

more than that.

v=P7

i=1 (xi·max∀uj∈U,ci−1<uj≤ciuj)

P7

i=1 xi

(9)

D. Representatives

The previous section made the role of the representatives

clear. They are used as estimates for the achievable reduction

of each customer. Based on them we created heuristic methods

to calculate a suitable unit value. Also we use them to decide

on how buildings are divided into bins. It is clear that their

role is important and affects the robustness of the scheduling

algorithm. Making a wrong estimate will give an unsuitable

unit value which in turn limits the potential reduction of each

customer. This is because we conform each customer to the

only strategy that provides the lowest deviation from the bin

value (2). Realizing this we decided to test different ways

of calculating representatives. Our choices we are motivating

by the need to show estimates that produce good results

as well as bad ones. It was our to goal to give a clear

understanding on the importance of these selections to the end

result. Moreover we focused on ﬁnding simple and efﬁcient

solutions which should not add much to the overall complexity.

We present brieﬂy the three methods used and get into a

detailed discussion of their affect in the experiments section.

The ﬁrst method(MAX) calculated the maximum value from

all intervals of all possible strategies for a customer. The

second method(AVG) calculated the average reduction from all

intervals of each available strategy for a customer. Finally the

third methomd (MAVG) used as a representative the maximum

average reduction from each individual strategy available to

a customer. In general we expect to get the worst results

by AVG since large deviations between strategies is going

to provide an inaccurate estimation. It is important to note

that the representatives affect strategies which are heavily

based on them. Those are all the strategies which use them

to calculate an approximate unit value. Between the other two

methods (MAX and MAVG) we expect better results from the

former. This is connected to the bin values which constraint

the selection of strategies. MAVG uses an averaging estimation

for the whole interval giving a bad estimation in cases where

large deviations in the reduction exist. So our safest choice will

be MAX since it is not so restricted on the max bin values

constructed.

E. Complexity

For the complexity part we can divide the algorithm into

two sections. We ﬁrst have the section where some common

steps are executed (e.g distribution of customers into bins,

representative calculation e.t.c). This section is common for

all methods and provides a standard complexity. In the second

section we deal with the individual methods used to calculate

the unit value. There the complexity differs among each

method.

In general our algorithm consists of some common steps

independent from the technique used to calculate the unit

value. These include calculating the representatives, distribut-

ing the customers into bins and conforming them to a speciﬁc

strategy, sorting the customer-strategy combinations in each

bin according to their corresponding error.Finally we iterate

greedily over the bin and produce the indices used to select

which customers are going to participate in the DR event. The

size of the input is deﬁned as n·m·kwhere nis the number of

customers mis the number of available strategies and kis the

number of intervals in the DR event. In practice we have 3-10

strategies to consider and at most 96 intervals of 15 minute

granularity, exist in a day. These choices were made during

our experiments and present a realistic scenario. We conclude

that the size of the input is linear in the number of customers.

The common steps we described before have a complexity of

O(n),O(n),O(n log n)and O(n)respectively considering

an input size of ncustomers. So in conclusion the overall

complexity is O(n log n)for the ﬁrst part.

Except for the greedy technique, calculating the unit value

adds an extra computational cost. In MGABE and MCE,

there is an extra computational cost of O(n log n). This is

because we consider nrepresentatives at most and for each we

need to consider the one closer to the bin value. In MAABE

the extra cost is O(n2)because we calculate for each of

the nrepresentatives the average of the customers reduction

that belong in each bin. The ﬁnal method(UDT) calculates

the weighted average. Here we need to iterate over all the

representatives which adds O(n)additional complexity.

It can be argued that the devised algorithm fulﬁls the

requirement for an efﬁcient solution. In any case we need

at most polynomial time to provide a solution. It will be

shown in the experiments that the above complexities are

veriﬁed. Also it is noted that the bottleneck in the execution

is loading the data from the hard disk. Finally some common

operations like calculating the representatives can be executed

as a preprocessing step.

V. EXPERIMENTS & RESULTS

The experiments we conducted were designed to test the

accuracy of the algorithm in terms of the targeted reduction

and the sustainability of the reduced load. Also we measured

the number of buildings used in the solution to argue about

the level of intrusiveness of our solution. Finally we simulated

consecutive DR events and measured the collective execution

time for a solution to be provided.

The algorithm was implemented using Java and was exe-

cuted on Windows operating system. The experiments where

executed in single quad core CPU system(Intel Core i7

3632QM @ 2.20 GHz) with system memory(8,00 GB Dual-

Channel DDR3 @ 665 MHz).

A. Dataset Used & Experiment Categories

To test our implementation we used measurements from

meters in the USC campus micro grid. The dataset is populated

with values representing the average power reduction(KWh)

for a ﬁxed periods of time(15 minute granularity).In total 33

buildings participated in 380 DR tests by employing speciﬁc

reduction strategies or a combination of them.The time frame

of the DR events is from 1:00 - 5:00 PM. We chose this time

frame because it is the time of the day where peak demand

is observed. The available strategies for each building consist

of equipment groupings which are controlled directly during

a DR event. Measurements from past DR events conducted

on campus buildings were used as input to the ARIMA [26]

prediction model. We needed to predict the actual building

consumption during past DR events. Southern California Edi-

son(CASCE) [1] was used as the baseline to deﬁne the actual

consumption on a regular day for each building. As it was

mentioned before we measured the curtailment level by taking

the difference between the baseline and the predicted reduction

during a DR event. CASCE was used because we found from

previous work [3] that it gave the most accurate results in

terms of the predicted consumption during a normal day.

We consider two cases in our experiments: The ﬁrst case

includes all the buildings and strategies available in our

dataset. We do this to evaluate the accuracy of each technique

developed in terms of overall load reduction and sustainable

load during a DR event. Absolute Percentage error was used

as the metric for our evaluation. The second case randomly

selects buildings and strategies to be eliminated. Every build-

ing or strategy has a probability of 50 % to be selected. This

decision was made in order to simulate a harder instance of

the problem being solved. The results from these experiments

were used to evaluate the robustness of each technique. In

this case we run a thousand requests and used Mean Absolute

Percentage Error(MAPE) as the metric for the evaluation of

each individual technique.

The overall performance for the developed methods is

evaluated against two random selection approaches used as

baselines. The ﬁrst baseline is a uniform random selection

of buildings and their corresponding strategies. The second

baseline implements a probabilistic selection. It is based on

the distribution of buildings into bins of ﬁxed length according

to their reduction estimated by the representatives. Bins with

more buildings in them have greater probability to be selected.

The ranges of the bins are built in increments of 10 beginning

from 0. There were some buildings with negative reduction

but we ignored them for the baselines.

B. Overall Reduction

Achieving an optimal reduction is strongly related to the

method used for calculating the unit value. Since many of

the developed methods are based on the representatives it is

imperative to have a good initial estimate for them. As it was

stated a good estimate is the one that does not limit the po-

tential reduction of each customer. Limitation exists if the bin

value conforms a customer to a strategy with lower reduction

than the maximum achievable. Each individual technique was

tested against the different estimations we presented in section

IV. As it was expected when using AVG as the estimate on the

representatives we got the worst result(maximum average error

≈2.5%)(Fig.1). Although compared to MAX and MAVG

estimates (maximum average error ≈0.7% and ≈1.3%

respectively) AVG seems to produce the worst results, it still

outperforms the baseline we set by much. In general the

estimate that gives us the best result is MAX. This correlated

to the need we have not to bin limited by the bin value

when choosing a strategy. So if we build our bins using this

estimate we can always ﬁt the maximum reduction provided by

a speciﬁc strategy. In the case of MAVG we are more restricted

from the bin value in comparison to MAX. However we are

less restricted than in the case of AVG. So it was expected

to get results in between MAX and AVG.In (Fig.2)we chose

to present the results produced by the MAX estimate. This

decision was made because we get the best results out of it.

Fig. 1: Case 1 - Overall Targeted Reduction(AVG).

In order to compare the effectiveness of the techniques

developed we plotted the Cumulative Distribution Function

(CDF) of the normalized error. In (Fig.3) we present the

result we got using the MAX estimate for the representatives.

Although we argued that against the greedy technique it seems

that we are getting better results in comparison to the other

approaches. This can be explained by the nature of the dataset.

In the campus there exist many buildings similar to each

other that have a low deviation on their achievable reduction.

Taking this into account we can realize that a greedy choice

of building-strategy combination will approximate the target

reduction accurately most of the time. However this is not the

case for reduction of higher value. There are a few buildings

with larger reduction that need to be included into the ﬁnal

solution. So the relative error increases for these values.

A clearer view of the robustness of each approach can be

realized in the second part of the experiments we conducted.

Fig. 2: Case 1 - Overall Targeted Reduction(MAX).

In general the results showed that MAABE is the technique

which provides the best accuracy and stability. This is because

we just focus only in minimizing one quantity when deciding

on the unit value to be selected. Also by using an averaging

method to estimate the achievable bin value, we can always get

the best result given a good representative estimate as it was

explained before. An average closer to the bin value always

considers the maximum potential reduction of the customers

in a bin. In MGABE the results produce the worst error from

the targeted reduction. Given the reasoning we just presented

this was expected. The independent minimization of the two

quantities is responsible for this performance. Selecting a

suitable unit value is based in the speciﬁc targeted reduction.

Nevertheless we consider all the bins for the accumulated error

which results in conﬂicting objectives. MCE was developed on

that reasoning and focused to minimize the accumulated error

on speciﬁc bins indexed by the change making algorithm.

As the results show, it produces lower approximation error

outperforming MGABE. It keeps up with MAABE but shows

less stability and eventually performs worst. The problem in

this case is that we consider each bin as having the necessary

number of buildings needed. This in practice is not the case

as sometimes the construction of bin ranges produce empty

ones. Finally we consider the solution provided by UDT. In

this case the results are follow a similar pattern to that of MCE.

This approach is strongly correlated with the data distribution.

A pitfall exists when the deviation between the reduction

provided by each one of the buildings is large. The unit value

selected ﬁts the buildings with a small reduction and restricts

the ones with a large reduction. This happens because the bin

values are small considering the unit value chosen. In our case

the deviation between the buildings is small that is why such

a case is not clearly visible. It will become more clear in the

next part of the experiments.

The second round of experiments aimed at testing the

robustness of each method. In (Fig.4) we present the results

we got using AVG for the calculation of representatives. The

results are consistent with our claims about the importance

of choosing a good estimate for the representatives. In this

case(AVG) none of the methods we developed can match the

Fig. 3: Case 1 - Accuracy of Unit Value Techniques(MAX).

performance of the greedy technique. In (Fig.5) we chose to

present the results for the case of MAX since they are similar

to that of MAVG although a little bit worst. We realize that

the results follow the same pattern as in the ﬁrst round of

the experiments. Our claim in favour of MAABE is supported

since it manages to match and outperform every other method.

The greedy approach ranks second along with MCE. Finally

we see that MGABE has an unstable performance in terms

of accuracy. It manages to follow at some cases the accuracy

of other methods but it is unpredictable for the most part.

Finally UDT manages to match the error produced by the

greedy approach as expected. A point we need to make is

that the overall error in this round of results has increased

signiﬁcantly. Since we discard randomly selected buildings

from the original set there might not be a solution that fulﬁls

our request. The error curve presented in Fig.5 is expected. In

campus there are many buildings of low reduction which can

be combined to achieve an overall low reduction. However to

achieve a bigger reduction we need to include buildings with

high reduction levels. Those are eliminated more easily from

the ﬁnal set since few of them exist.

Fig. 4: Case 2 - Overall Targeted Reduction(AVG).

C. Reduction Sustainability

A strong asset of the selection algorithm we developed

is achieving sustainability. We argue in favour of this by

Fig. 5: Case 2 - Overall Targeted Reduction(MAX).

presenting the results for the ﬁrst case of our experiments.

We focused on the highest overall reduction we could achieve

in our experiments(3000 KWh). We present the deviation

from the optimal reduction per interval using the absolute

percentage error as a metric. Our choice is based on the

collective number of buildings used in the DR event. The goal

behind this decision is to show how the behaviour of different

buildings hinders our ability to achieve sustainability.

It is important to point out that sustainability it is not

connected directly to achieving the overall load reduction

across a DR event. A large average deviation from the target

per interval might again provide the overall reduction we want

by establishing lower reduction in the beginning of the event

and higher close to the end.

Fig. 6: Case 1 - Deviation of Sustainable Load(MAX)

The average deviation from the optimal sustainable reduc-

tion was less than ≈3%. The results(Fig.6) showed that

we achieved the lowest deviation in the cases of MGABE,

MAABE and UDT. Higher deviation has been observed for

the case of the greedy method and MCE. The results are

related to the method used to calculate the unit value. Although

MGABE gives a high approximation error for the overall load

reduction it is among the best to achieve sustainability of the

load. Similar results are observed for MAABE and UDT. A

common property of these methods is that they are trying to

construct bin values that ﬁt the patterns in the dataset. At

this point our decision to present the results of an overall

reduction achievable by the largest number of buildings is

justiﬁed.In our attempt to provide a solution, we index all the

bins and choose at least one building from each one. Creating

a sustainable schedule requires us to minimize the error from

the bin values. The bin values are calculated based on the

unit value. So every approach that considers the existence of

curtailment vectors that ﬁt the reduction deﬁned by the bin

values can achieve the best sustainability. That is why the

MAABE, UDT and MGABE achieve the best results. Given

this statement one would expect to get the same results for

the case of MCE. However this is not veriﬁed by the results.

It is also not expected to be veriﬁed. MCE is set to minimize

the error considering only speciﬁc bins. Also those bins are

assumed to have the needed amount of buildings which is not

Fig. 7: Case 1 - Average Number of Building Selected.

the case. So MCE makes a wrong estimation that results in a

unit value that poorly ﬁts the dataset. In this way sustainability

of the curtailed load is hindered. Similar reasoning can be

applied for the greedy method, although in this case it is more

obvious since there is no consideration of customers reduction

patterns from the start.

D. Comfort Level

Since we used the change making approach to index the

bins we expect to get the minimum number of building-

strategy combinations to achieve the necessary reduction. In

(Fig. 7) we see that for different techniques of calculating the

representatives we used ≈15−34% of the campus buildings to

achieve the overall targeted reduction. The increase in building

selection when using AVG is caused by the choice of the

unit value. As it was noted before the unit value limits the

potential reduction of each building from the resulting bin

values. In that case the overall reduction is achievable through

selection of more buildings. It was stated that the comfort

levels are implied through the intrusiveness of each strategy.

This is induced into the potential sustainable reduction patterns

of each building associated with a speciﬁc strategy. It is the

goal of the algorithm to detect those patterns and discard the

ones that do not achieve a consistent reduction. In (Fig. 8) a

heat map was created including the buildings of the provided

solutions. Each building has an available strategy depicted with

different code in the second column. To construct the heat map

strategies of the same building were grouped together. Higher

and lower reduction per interval is depicted by different levels

of green and red respectively. Reduction level in the middle is

drawn with yellow and orange. It can be seen that our solution

selects buildings with consistent high reduction. We can asso-

ciate the curtailment vectors which produce inconsistent load

reduction to intrusive strategies. In that case we would have

consistent low reduction or inconsistent patterns with reduction

of high deviation among intervals. It is important to note that

the algorithm return the optimal selection of building-strategy

combinations in respect to the ones available.

Fig. 8: Case 1 - Heat Map of Building - Strategy.

E. Execution Time

Evaluation of the efﬁciency was done by using synthetic

data. A simulation of 1000 DR requests provided us with the

maximum average execution time. We present the results in

(Fig. 9). The number of customers ranged from 1000 to 32000

each one having 10 available strategies. The DR event time

frame was 4 hours (16 intervals). In our results we observed

an almost linear increase in the execution time for all methods

excepts in MAABE. There we got a polynomial increase in the

execution time. All results were expected and derive directly

from the complexity analysis in the subsection IV-E. It is

important to note that the bottleneck in the execution was the

calculation of the unit value. Since the algorithm inherently

does not have any data dependencies a distributed election

algorithm can be used to decide on the unit value.

VI. CONCLUSION & FUTURE

In this paper we focused on solving the problem of Dynamic

DR scheduling. Our goals where to achieve a sustainable

targeted reduction while factoring uncertainty induced by

customer discomfort. It was shown that our proposed solution

achieves a sustainable load reduction in respect to the targeted

one. It detects behavioural patterns implied in the reduc-

tion levels of customers associated with speciﬁc strategies.

The provided solution fulﬁls the dynamic requirements as

it provides a schedule in a reasonable amount of time in

respec to the number of customers. In our future work we

Fig. 9: Timings of Consecutive DR events.

will be focusing in two parts. Although the algorithm has a

low complexity it presents a bottleneck when retrieving the

customer information. It is imperative to provide a distributed

solution to overcome this pitfall. Moreover we need to deal

with uncertainty induced by changes in the customer behaviour

through multiple DR events. This again affects the dynamic

nature of the algorithm. It is important to factor on demand

update of dataset to be accurate in our scheduling.

VII. ACKNOWLEDGMENT

This material is based upon work supported by the United

States Department of Energy under Award Number number

DE-OE0000192, and the Los Angeles Department of Water

and Power (LA DWP). The views and opinions of authors

expressed herein do not necessarily state or reﬂect those of

the United States Government or any agency thereof, the LA

DWP, nor any of their employees.

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