Scheduling Smart Loads in Modern Buildings

based on Metaheuristic Optimization

Mohammed Hijjo and Georg Frey

Chair of Automation and Energy Systems, Saarland University, 66123 Saarbrücken, Germany

Keywords: Load Scheduling, Smart Loads, Metaheuristic Optimization.

Abstract: Load scheduling is one of the most promising trends in smart grids. It enables renewable energy to be

efficiently utilized and accommodated in the smart buildings. In this work, we propose a comprehensive

scheduling approach of a group of non-preemptive loads in a ‘greedy’ manner in order to reduce the deficit

between the aggregate scheduled load and the available low-cost generation and therefore, the levelized cost

of energy (LCoE) can be minimized. In order to reduce the massive searching space and attain a good

schedule within a reasonable time, an efficient metaheuristic optimization framework is proposed and

implemented based on genetic algorithms. An illustrative example is used to carry out this work using

artificially created loads representing different facilities inside a building complex.

1 INTRODUCTION

Recently developed technologies in smart grid

sector, including smart loads and smart metering,

have enabled a highly efficient prediction and

identification of the electricity consumption of a

facility in a smart building. Besides, the numerous

adoption of renewable energy sources (RES) to

replace fossil fuel generation, both together, provide

the opportunity to maximize the efficiency of the

system by good coordination of the existing power

assets and loads in order to reduce the net gap

between the demand and the low-cost energy offered

by RES generation and the utility grid in the off-

peak times.

Until recently, various approaches have been

proposed and applied to coordinate the generation

sources in order to meet the varying demand while

keeping the electricity cost at optimal levels (Zhu,

2009). However, due to ever increasing demand and

motivated by the affordable prices of the renewable-

energy based systems, a growing desire exists to

control or optimize the demand growth in order to

facilitate the integration of RES into domestic and

industrial sectors.

Yet, the fluctuating nature and intermittency of

the RES are the still forming a barrier against

entirely relying on them as a main power provider or

even increasing their penetration level in generation

side. In spite of that, this obstacle can be overcome

by using a proper energy storage to stabilize the

operation and compensate the shortage (Pickard et

al., 2012). This solution is not always affordable,

especially in standalone and remote systems, or in

buildings subject to severe power outages, where the

fluctuating supply cannot be matched by a greater

energy storage on all occasions. Otherwise, this will

simply add cost and complexity to the system.

A potential alternative solution will be

influencing the load demand, totally or partially, in

order to lower the need for larger energy reserve. A

proper scheduling of some shiftable loads can

improve the reliability of power delivery for

customers during (macro)grid blackouts or

emergency islanded operation. Once the system is

integrated with some smart loads, that can be

scheduled in advance, an efficient algorithm could

be developed to reallocate these loads in another

time, in which, the total energy cost can be

minimized and the utilization of RES can be

maximized as well.

The need for some controllability over load is not

only to assist in accommodating more RES into

different power systems around the world, but also

there is an important and persistent need to develop

and apply such a solution in countries which have

weak power systems or suffer from continuously

interruption of the utility grid. Especially in

developing countries, a large number of buildings

Hijjo, M. and Frey, G.

Scheduling Smart Loads in Modern Buildings based on Metaheuristic Optimization.

DOI: 10.5220/0006846201190126

In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2018) - Volume 1, pages 119-126

ISBN: 978-989-758-321-6

119

including healthcare facilities, schools and small

businesses are suffering from a serious lack of a

continuous and stable power supply. This issue has

forced the decision makers and the engineers to

develop some urgent solutions to meet the ever

increasing demand, usually depending on diesel

generators, which are costly and environmentally

unfriendly too. The reason behind not using such

logical approach previously, is the need for efficient

load forecasting techniques that can predict the

upcoming load accurately.

1.1 Related Works

A huge work has been done in the context of load

scheduling. A heuristic algorithm to schedule a

group of smart appliances in a smart building subject

to a real-time pricing has been proposed by (Lee et

al., 2013). Another work has been conducted on a

smart building environment but using a set of

household appliances that allow for a limited

interruption time (Caprino et al., 2015). A heuristic-

based load shifting optimization approach has been

proposed by (Logenthiran et al., 2012), where three

adjacent power networks have been chosen to carry

out the study.

Another load scheduling algorithm based on

game theory has been proposed by (Mohsenian-Rad

et al., 2010). The main objective was to optimize the

energy costs by reducing the aggregate peak-to-

average ratio of the total energy demand, while

respecting the privacy of the customers.

Considering the previously listed literature

review and the other ongoing work in this domain;

e.g. (Habib et al., 2016), (Manic et al. 2016), and

(O'Brien el al., 2016), it has been realized that the

number of studies that have discussed the problem

of scheduling dynamic non-preemptive loads from

the perspective of smart grids and smart buildings

are very few. Two reasons maybe behind that, which

are: the complexity of solving such a load

scheduling problem, which is agreed upon to be a

NP-hard problem (Baruah et al., 2004), and the

difficulties involved in modelling such continuously-

operating loads with a non-fixed power

consumption.

1.2 Scope of Work

This work takes care of the load scheduling in smart

building as an important function of the tertiary level

in controlling future microgrids. Thus, the scope of

this work does not include the voltage stability or

power quality at the point of common coupling

(PCC). However, it tackles the uppermost control

level, which has the longest discrete time steps; e.g.

ranging from intra-hours to intra-days. To this end,

this work offers a proactive scheduling plan for the

smart loads which announce their desired operation

pattern or the associated consumption profiles in

advance; e.g. a day ahead. In other words, the

proposed algorithm will attempt to reallocate the

aggregated loads to closely follow the low-price

available power; e.g. from utility grid or local RES

generation. The load profiles are known in

advanced, but they should be reallocated in better

time span in order to minimize the total energy cost.

Furthermore, the proposed approach will be

conducted on a deterministic system, where all load

profiles and RES generation as well as the off-peak

hours of the utility grid are known in advance. This

assumption provides the ‘best case’ scenario for a

stochastic system where the generation/demand

profiles are not precisely known ahead of time. Later

on the solution will be extended to include tackle the

uncertainty of the load as well as the RES

generation. Detailed description will be presented in

the following sections.

2 PROBLEM FORMULATION

Suppose that a part of a building complex consists of

several smart loads that declare their consumption

for the next day on the day ahead. These smart

loads, under this definition, can be called notified,

where the corresponding load profiles are known in

advance within a narrow margin of error. The load

profile per each is defined over T time slots

representing the schedule period (here is one day). A

time slot is chosen in consistence with the data rate

of the connected devices and the smart metering

system, which is usually taken as 10, 15, 30 or 60

minutes.

A non-empty set S consists of N smart shiftable

loads is assumed, =



ℓ∶ℓ∈ℕ



, where ℕ is the

set of the natural numbers, e.g. positive integers

greater zero. Each single load ℓ has a deterministic

load profile 

ℓ

(



)

announced in advance in

accordance with the planned operation of the next

day.

The total unscheduled load profile of these

shiftable loads can be mathematically formulated as

given below in Equ. 1



(



)

=

ℓ



ℓ

(



)

1≤≤

(1)

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

120

2.1 Smart Shiftable Load

A smart load can be a single appliance or a cluster of

devices operate in a particular way to perform a

certain function in one of the facilities inside the

whole system. The corresponding load profile of

each load is predetermined, as it is smart, and the

preferred operation time is predefined too. However,

as illustrated in Figure 1, the activation time must be

commanded by the system operator (active mode).

Active mode

(Unscheduled)

Sleeping mode

Deadline

Earliest

Starting-time-

Power Consumption

Daytime

(e)

(d)

(L)

(A)

(B)

Figure 1: Example load profile of a smart shiftable load.

Several examples can be given for such smart

loads in different sectors, for instance, washing

machines and dryers in residential sector can be

considered as smart loads. Heating, ventilation, and

air conditioning (HVAC) systems are a good

example for smart loads in the commercial and

industrial sector, and they have been used as a load

service for large scale of buildings (Lu, 2012). In the

healthcare facilities, different loads and plants can

be good candidates for performing load scheduling,

such as: laundry, sterilization unit, and waste

disposal unit. All of these facilities, generally, can be

considered as ‘stand-alone’ plants or loads and their

load profile can be efficiently forecasted depending

on the different operation circumstances.

Ideally, a shiftable load ℓ is modelled by a

quadruple: (e

ℓ

, d

ℓ

, L

ℓ

, A

ℓ

), where e

ℓ

, d

ℓ

, L

ℓ

, and A

ℓ

are the earliest possible starting time, the deadline,

the duration of the active mode, and the load level

during the active mode respectively.

In this work, an advanced version of this model

is introduced, in which, the load can have multiple

modes of operation that feature the individual

functionalities associated with each smart load.

Thus, the resulting model will be modelled as a

quintuple. Specifically, the added element B

ℓ

represents a nother mode of operation, e.g., sleeping

mode, in which, the load consumes a much less

power than usual to be ready for the normal

operation upon request. Furthermore, the stochastic

nature of the each individual load is modelled using

some statistical properties added to each mode of

operation.

Three exemplary loads are defined in Table 1

and illustrated as shown in Figure 2, showing

different timings and power consumptions as well as

highlighting two modes of operation with their

means and standard deviations.

Table 1: Three exemplary shiftable smart loads.

Load

Tuples (units)

ℓ

(time)

ℓ

(time)

ℓ

(time)

ℓ

(,)

(power)

ℓ

(,)

(power)

ℓ

2 12 6 (135, 8) (15, 5)

ℓ

4 11 3 (220, 5) (20, 10)

ℓ

7 15 5 (60, 10) (0, 0)

Figure 2: Illustrative profiles of three smart loads.

Obviously, the presented loads here have two

modes of operation. However, the sleeping mode of

the third load is adjust to zero.

Here, the proposed algorithm is dedicated to

provide the operator with the optimal execution time

of each of these loads in order to minimize the LCoE

and maximize the net utilization of the local RES

generation. To this end, the permissible operation

interval 

ℓ

of each load ℓ should be declared in

advance, in which, the active mode period must be

accomplished. See Equ. (2):



ℓ

=[

ℓ

,

ℓ

]

(2)

Under this definition, the latest activation time 

ℓ

is given by Equ. (3):



ℓ

=

ℓ

−

ℓ

(3)

Thus, a mapping function should be defined in

order to shift the load in accordance with the

aforementioned parameters. A typical mapping

function  may bring the selected load

time-slots

forward or backward, as defined in Equ. (4):



ℓ



→



ℓ

=(

ℓ

)=

ℓ

[−



ℓ

]

(4)

Scheduling Smart Loads in Modern Buildings based on Metaheuristic Optimization

121

As the proposed algorithm is offline and deals

with a notified system, the value of the shifting

index can be positive or negative. However, in real-

time systems, in order to fulfill the causal

consistency condition, the shifting index

associated

with a scheduling operator κ is chosen to be positive

integer.

2.2 Low-Price Power Signal

The low-price power signal has an important role in

solving this problem, where it must be tracked as

closely as possible. In isolated systems, which is

powered solely by renewables, this signal results

from the RES-power alone. On the other side, in

grid-connected systems, it can result from both; the

renewable generation and the incentive off-peak

periods of the utility grid, where the power price is

negligible, as compared with peaking times. In

modern power systems, this signal can be notified in

advanced as an incentive for customers to schedule a

part of their consumption accordingly.

In this work, it is assumed that the utility grid

adopts a two-level power price, in which, the off-

peak times follow a lower fixed price c

and the

counterpart peaking times follow a higher price c

given in Equ. (5):





(



)

=





,∈[



,



]





,ℎ

(5)

The low-price signal Υ() is represented by the

total sum of the solar generated power from the

installed array over the building and the utility grid

capacity during off-peak, ∈[



,



], see Figure 5.

The target is therefore to accumulate the greatest

possible amount of these loads in these time spans

without overriding the capacity limit of the main

power feeder.

2.3 Optimization Algorithm

In order to find the optimal scheduling operator κ

associated with each smart load in the system, we

chose here to penalize the absolute-value norm of

the error between the low-price power signal and the

aggregate scheduled load profiles as formulated in

Equ. (6):



(



)

=

(



)

−

ℓ

[−



ℓ

]



ℓ



(6)

Where Υ

(



)

is the low-price power signal and

ℓ

[−



ℓ

] is the shifted version of the smart load ℓ

corresponding to the scheduling operator κ. The

general overview of the proposed offline load

scheduling scheme is shown in Figure 3.

Figure 3: General overview of the proposed load

scheduling system.

The main idea is that to maximize the

autocorrelation between the low-price signal and the

aggregate load subject to the permissible activation

time of each load. It is important here to distinguish

between this problem and other classical constraint-

based scheduling problems (Wall, 1996), where the

tasks, i.e. the loads, are constant and require a

certain share of the resource. However, the dynamic

nature of the loads here makes it even harder to

solve the problem without using relaxation

techniques to eliminate the effect of the fluctuating

demand. As presented in Figure 3, the proposed

scheduling approach targets to reallocate the

different loads to minimize the difference between

announced low-price power profile and the

aggregate scheduled loads, so as to increase the

benefit from the available low-price power as much

as possible. The existing scheduling problem is a

complicated optimization problem, which is NP-

hard (Baruah et al., 2004). Therefore, finding an

optimal schedule for a huge set of schedulable loads

is very complicated problem and thus, the exact

solution might be hard to find without enumerating

all possible schedules and then evaluating them.

To elaborate on this issue, if we have a set of 

loads with at least  possible positions for each load

to start the active operation, the complexity of the

searching space will be 



. Obviously, the

complexity of the problem is exponentially

increasing with the number of loads and/or the

possible schedules of each load. In order to cut down

the computation time, the developed optimization

approach applies the Genetic Algorithms to handle

this problem (Mitchell, 1996).

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

122

The genetic-based approach belongs to the

bigger class of evolutionary algorithms (EA), which

is one of the metaheuristic stochastic optimization

techniques that can provide a solution to an

optimization problem with less computational effort

than iterative ones. Compared to conventional

algorithms, metaheuristics sample a set of solutions

which is too large to be completely sampled. Thus,

by searching over a large set of feasible solutions,

metaheuristics can often find good solutions with

less computational effort than optimization

algorithms, iterative methods, or simple heuristics

(Blum et al., 2003).

A group of initial schedules are randomly

generated at the beginning. Some of the feasible

schedules are selected and then merged as a one

schedule by the crossover and mutation operations,

and then the schedule set is evolved by replacing a

schedule in the old set by the newly generated

schedule. This process is repeated until the schedule

set converges (Lee et al., 2013).

An abstract pseudo-code of the applied GAs is

given below in Figure 4.

1.Inputs

Load profiles, Possible schedules , Off-peak

periods, PV generation.

2.Initialization:

randomly seeded schedules.

3.Cost function evaluation (Equ. 6)

4.Selection:

Select the best candidate solution among the

present generation before step in the next

generation.

5.Crossover and mutation:

The new possible candidate solution is

generated from the parents which survived.

6.Evaluate the cost control function

again (STEP 4)

7.Termination:

After exceeding the time budget or generation

limit or satisfying the minimum criteria.

8.Output:

The values correspond to the best/final

solution.

Figure 4: Pseudo-code of the GA-optimization algorithm.

3 NUMERICAL EXAMPLE

A preliminary simulation is conducted using a

clinical facility building incorporating a group of six

shiftable loads. The low-price power signal is

generated from the aggregation of the off-peak

period from the utility grid in Gaza-city and the

onsite solar generation. Other essential loads are

assigned to be supplied using the conventional

generation as they need a continuous and stable

supply without any interruption. The building is

mainly supplied from the utility grid, which has a

feeder capacity of 18 kW. In spite of the low-price

power, the grid is interrupting on a daily basis,

which makes relying solely on it impossible.

Therefore, the building was fitted recently with a

20kW

solar array to assist the legacy standby diesel

generator.

The used diesel generator has a capacity of 20

kW and its associated fuel cost is modelled by fitting

the manufacturer data (Diesel Service, 1981). The

grid price is considered c

= 0.16 $/kWh during off-

peak hours and the price associated with diesel

operation under the rated load is c

= 0.56 $/kWh.

Half of the grid capacity is reserved for essential

loads and the second half is assigned for the

shiftable loads.

The off-peak signal and the available PV

generation over a four-days are shown below in

figure 5.

Figure 5: Sample 4-days off-peak and PV generation.

The system is modeled using MATLAB and the

optimization algorithm is conducted using the

provided optimization toolbox.

The optimization window is considered here as a

single day and then the optimization process should

be repeated in accordance with the new timing

Powe

Scheduling Smart Loads in Modern Buildings based on Metaheuristic Optimization

123

constraints for the day after. The convergence of the

optimization process for one sample day is depicted

in figure 6, where the searching process is converged

after about 100 generation, and then the

improvement rate is almost negligible. The resulting

value here (approx. 820) represents the penalized

absolute-value norm of the error between the low-

price power signal and the aggregate scheduled load

profiles as formulated in Equ. (6).

Figure 6: Convergence of the proposed GA-Scheduling.

The activation times of five sample loads are

expressed in figure 7, showing the original operation

and the proposed activation during the first day.

Figure 7: Scheduling results of three sample loads.

Figure 8 shows the final results over a four-days

simulation window. It presents the aggregated low-

price power (green), i.e. which has to be tracked as

well as the total loads before performing the

scheduling (dotted red) and finally, the total loads

after performing the scheduling (blue).

Figure 8: Scheduling results over four-days simulation.

Figure 9 illustrates the instantaneous energy cost

before (red) and after (blue) performing the

proposed scheduling algorithm.

Figure 9: Instantaneous end-price of energy.

Some performance indices and end results are

calculated and concluded in Table 2, presenting the

net utilization factor of the solar power and LCoE as

well.

Table 2: Performance indices.

Performance index

Before

scheduling

After

scheduling

Total PV

production (kWh)

323.48

Aggregate Shiftable

Loads (kWh)

388.63

Net PV usage

(kWh)

146.54 180.38

Total supply cost

($)

117.6 82.13

PV Utilization

Factor (%)

45.3 55.76

LCoE ($/kW) 0.30 0.21

4 DISCUSSION

Unlike other works, such as (Habib et al., 2016), and

(Leithon et al., 2017), where preemptive loads have

been used to reshape the aggregate load, e.g. that is

they can be supplied with interruptions, the proposed

work here aims at reallocating each shiftable load to

another time interval instead of reshaping them so

0 50 100 150

Generatio

820

860

900

940

Penalty value

Best: 821.459 Mean: 825.27

Best penalty value

Mean penalty value

0120

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

124

that the resulting consumed energy after scheduling

is similar to their unscheduled counterpart. The

reason behind that is to avoid the so-called “rebound

effect”, because simply switching the loads ON and

OFF will not lead to the same desired performance if

they work continuously as usual. In such cases,

energy is naturally not saved and expectedly another

peak will be generated (Palensky et al., 2011).

Additionally, it is important here to highlight the

difference between the addressed model in this work

and other classical models (Ali et al., 2012) that use

4-tuples only expressing the timing constraints and a

constant power demand over a single mode of

operation, which makes the problem somehow

similar to constraint-based problems (Wall, 1996).

Unlikely, the presented model here expresses the

fluctuating nature of the load that can have multiple

operation modes with some variability on the power

consumption.

Another practical aspect is the scheduling

window, which is taken here as a single day and then

the algorithm is repeated for the next day using the

new data. In this regards, one load cannot be

requested more than once within the same window.

Otherwise, two or more identical loads with

different activation constraints should be used in

order not to allow any overlapping of the operation

of same load in that facility.

Formerly, the developed scheduling algorithms

were adopting some scheduling policies used in real-

time processing such as Earliest Deadline First

(EDF) and Least Laxity First (LLF) which assign the

tasks, e.g. loads, according to their deadlines or the

slack times (Subramanian et al., 2012). However, in

renewable energy systems with versatile loads, such

algorithms still need an accurate forecasting tools

and systems to handle the fluctuating nature of the

RES and the dynamic price of the grid.

Therefore, the matter of prioritizing loads should

consider both: timings of the loads and their

consumption level at each time slot. Obviously, the

dominants loads will be those with higher

consumption and less timing flexibility than others,

which will diminish the effect of other shiftable

loads but with lower consumption.

5 CONCLUSION AND OUTLOOK

An easy-to-implement load scheduling approach

based on the notified nature of the system was

proposed. Besides, a straightforward model for

smart shiftable loads was introduced in this work.

The proposed approach has adopted the GAs to cut-

down the searching space and find the optimal

schedule within a reasonable time budget.

There are three important topics that have not

been explored in this paper, and will be the subject

of our future publications:

(a) Reduction the capacity of the conventional

generation, e.g. diesel generator. The

economic basis for this issue should be

clearly justified through synthetic examples

and much more comprehensive simulations

using real data.

(b) The incorporated energy management

scheme, which will highlight the power

routing between all system components,

including the static and the essential loads

which cannot be shifted in time.

using shorter time window instead of

performing the algorithm once per day.

Thus, the improvement rate can be further

increased according to the recent

measurements of the RES generation and the

loads as well.

REFERENCES

Zhu, J., 2009. Optimization of Power System Operation,

Wiley publishing, Institute of Electrical and

Electronics Engineers

Pickard, W., Abbott, D., 2012. Addressing the

intermittency challenge: Massive energy storage in a

sustainable future, Proceedings of the IEEE, vol. 100,

no. 2.

Lee, E., B., Hyokyung, 2013. Electricity Usage

Scheduling in Smart Building Environments Using

Smart Devices, The Scientific World Journal

Caprino, D., Vedova, M., Facchinetti, T., 2015. Applying

limited-preemptive scheduling to peak load reduction

in smart buildings, IEEE 20

Conference on Emerging

Technologies & Factory Automation (ETFA),

Luxembourg

Logenthiran, T., Srinivasan, D., Shun, T., 2012. Demand

Side Management in Smart Grid Using Heuristic

Optimization, IEEE Transactions on Smart Grid, vol.

3, no. 3, pp. 1244-1252

Palensky, P., Dietrich, D., 2011. Demand side

management: demand response, intelligent energy

systems, and smart loads,” IEEE Transactions on

Industrial Informatics, vol. 7, no. 3, pp. 381–388

Habib, A. et al., 2016. Model predictive load scheduling

using solar power forecasting, American Control

Conference (ACC), Boston, MA.

Manic, M. et al., 2016. Building Energy Management

Systems: The Age of Intelligent and Adaptive

Buildings, IEEE Industrial Electronics Magazine, vol.

10, no. 1, pp. 25-39

Scheduling Smart Loads in Modern Buildings based on Metaheuristic Optimization

125

O'Brien, G., Rajagopal, R., 2016. Scheduling Non-

Preemptive Deferrable Loads, IEEE Transactions on

Power Systems, vol. 31, no. 2, pp. 835-845

Baruah, S., Goossens, J., 2004. Scheduling real-time tasks:

Algorithms and Complexity, in Handbook of

Scheduling: Algorithms, Models and Performance

Analysis, J.Y-T. Leung, Ed. Boca Raton, FL: CRC

Press,

Lu, N., 2012. An Evaluation of the HVAC Load Potential

for Providing Load Balancing Service, IEEE Trans-

actions on Smart Grid, vol. 3, no. 3, pp. 1263-1270

Wall, M., 1996. A Genetic Algorithm for Resource-

Constrained Scheduling, Massachusetts Institute of

Technology

Mohsenian-Rad, A., Wong, V., Jatskevich, J., Schober, R.,

Leon-Garcia, A., 2010. Autonomous demand-side

management based on game-theoretic energy

consumption scheduling for the future smart grid.

IEEE Transactions on Smart Grid, vol. 1, no. 3, pp.

320–331.

Goldberg, D., 1989. Genetic Algorithms in Search,

Optimization & Machine Learning, Addison-Wesley.

Conn, A. et al., 1997. A Globally Convergent Augmented

Lagrangian Barrier Algorithm for Optimization with

General Inequality Constraints and Simple Bounds,

Mathematics of Computation, vol. 66, no. 217, pp

261–288.

Mitchell, M. 1996. An Introduction to Genetic Algorithms.

MIT press Cambridge, MA, USA.

Blum, C., Roli, A., 2003. Metaheuristics in combinatorial

optimization: Overview and conceptual comparison.

35 (3). ACM Computing Surveys: 268–308.

Deep, K., Singh, K., Kansal, M.L., Mohan, C., 2009. A

real coded genetic algorithm for solving integer and

mixed integer optimization problems. Applied

Mathematics and Computation, 212(2), pp. 505–518.

Diesel Service, 1981. Diesel Fuel Consumption [online]

Available at: http://www.dieselserviceandsupply.com

[Accessed Feb. 2018].

Leithon, J., Sun, S., Lim, T. J., 2017. Demand Response

and Renewable Energy Management using

Continuous-Time Optimization, IEEE Transactions on

Sustainable Energy, Volume PP, Issue 99.

Subramanian, A., Garcia, M., Domínguez-García, A.,

Callaway, D., Poolla K., Varaiya, P., 2012. Real-time

scheduling of deferrable electric loads, American

Control Conference (ACC), Montreal, pp. 3643-3650.

Ali, S. Q., Maqbool, S. D., Ahamed T. P. I., Malik, N. H.,

2012. Pursuit Algorithm for optimized load

scheduling, IEEE International Power Engineering and

Optimization Conference, Malaysia, Melaka, pp. 193-

198.

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