Unified optimization model for energy management in sustainable smart power systems

Abstract

Peak power consumption is one of the most critical issues for power system operation and sustainability. To overcome this issue, the available energy resources may be utilized in an efficient way. Demand‐side management (DSM) may be used for the efficient utilization of the available resources to reduce the peak power consumption by rescheduling the shiftable appliances. Apart from this, a number of other objectives are also achieved by DSM. In the literature, DSM is used to reduce the electricity cost, curtail peak hour's demand, diminish peak‐to‐average power ratio, and minimize the distribution losses. To the best knowledge of the authors, none of the research articles has considered all the mentioned objectives in a single model. To fill this research gap, we propose a unified DSM model where we focus to get the abovementioned objectives of DSM in a single framework. This unified DSM framework also gives liberty to the power system administration for the operation of the system with exchange policies of government and the company itself. While getting the abovementioned objectives, our proposed unified model can take care of a number of DSM features including importance of heterogeneous load, load shedding, human interaction factor, peak clipping, valley filling, load shifting, appliances priorities, and consumer preferences.

Full text

SPECIAL ISSUE PAPER
Unified optimization model for energy management in
sustainable smart power systems
Sadiq Ahmad
1
| Muhammad Naeem
1,2
| Ayaz Ahmad
1
Department of Electrical & Computer
Engineering, COMSATS University
Islamabad, Wah Campus, Wah Cantt.,
Pakistan
2
Department of Electrical & Computer
Engineering, Ryerson University, Toronto,
Canada
Correspondence
Ayaz Ahmad, Department of Electrical &
Computer Engineering, COMSATS
University Islamabad, Wah Campus,
Islamabad, Pakistan.
Email: ayaz.ahmad@ciitwah.edu.pk, ayaz.
uet@gmail.com
Summary
Peak power consumption is one of the most critical issues for power system
operation and sustainability. To overcome this issue, the available energy
resources may be utilized in an efficient way. Demand‐side management
(DSM) may be used for the efficient utilization of the available resources to
reduce the peak power consumption by rescheduling the shiftable appliances.
Apart from this, a number of other objectives are also achieved by DSM.
In the literature, DSM is used to reduce the electricity cost, curtail peak
hour's demand, diminish peak‐to‐average power ratio, and minimize the distri-
bution losses. To the best knowledge of the authors, none of the research arti-
cles has considered all the mentioned objectives in a single model. To fill this
research gap, we propose a unified DSM model where we focus to get the
abovementioned objectives of DSM in a single framework. This unified DSM
framework also gives liberty to the power system administration for the opera-
tion of the system with exchange policies of government and the company
itself. While getting the abovementioned objectives, our proposed unified
model can take care of a number of DSM features including importance of
heterogeneous load, load shedding, human interaction factor, peak clipping,
valley filling, load shifting, appliances priorities, and consumer preferences.
KEYWORDS
consumer comfort level, peak‐to‐average power ratio, smart grid, unified demand‐side management
1|INTRODUCTION
In power system, consumers' electricity demand is one of the crucial and most important parameters. The first challenge
for any energy supplier is to satisfy consumers' peak electricity demand efficiently, keeping the peak‐to‐average power
ratio minimum at all‐time horizons. Intermittent weather condition and rapidly changing lifestyle due to technological
advancement force the consumers to use more electricity.
1,2
Fulfilling the increasing demand of each consumer is a
challenging task for generation companies due to certain limitations including generation cost and unavailability of
other resources. The generation companies cannot increase their generation capacity continuously. Therefore, they
are focusing on developing and implementing various algorithms, where they can manage the consumers' increasing
LIST OF SYMBOLS AND ABBREVIATIONS: DSM, Demand side management; DR, Demand response; PAPR, Peak to average power ratio; HIF,
Human interaction factor; LS, Load shedding; CPs, Consumer preferences; WM, Washing machine; DW, Dish washer Dy Dryer; EV, Electric vehicle;
GHG, Greenhouse gas emission; TOU, Time of use
Received: 2 September 2018 Revised: 30 May 2019 Accepted: 23 June 2019
DOI: 10.1002/2050-7038.12144
Int Trans Electr Energ Syst. 2019;e12144.
https://doi.org/10.1002/2050-7038.12144
© 2019 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/etep 1of18

electricity demand indirectly.
3,4
Consumers' electricity demand can be managed in two ways, ie, using demand response
(DR) schemes,
5-7
and demand‐side management (DSM).
8,9
DR is further classified into two groups, ie, direct control
direct control of consumers' load and reshaping of consumers demand curve through dynamic pricing.
10
In DR, the
control of electricity management is at the supplier's end where the supplier proposes a scheme for energy consumption
and the consumers respond to the proposed scheme. On the other hand, in DSM, the consumers manage their energy
consumption by devising DSM schemes and implementing it at the consumers' side.
11-13
DSM plays an important role in energy consumption. It can adjust the consumers' electricity demand within the con-
sumer's premises according to the tariff provided by the electric utility, which helps the supplier to manage the peak
hours load and make the power system stable.
14,15
DSMs are typically employed at the consumers' end to fulfill the elec-
tricity demand without the installation of additional power plants.
13,16
DSM reduces the gap between peak demand and
generated available electrical energy during peak hours. Increased energy consumption in peak hours can generate
severe surges which adversely affect the grid station that in turn destabilize the power system.
17
Therefore, by reducing
the demand in peak hours, the overall energy consumption in the peak hours will be reduced.
18
This reduction in
demand is done by reshaping the demanded curve through shifting the flexible load from peak to off‐peak hours, which
in turn plays a vital role in power system stability, reliability, and efficiency.
19-23
DSM can reduce the electricity price for
consumers as well as the generation cost and the overall expenditures incurring in transmitting high power during peak
hours to the end users.
16
Consumers participation is the key to successful DSM, ie, the more consumers participate in a
given DSM, the more successful the scheme would be considered. Various schemes in the form of incentives can be used
to inspire the consumers to participate in a given DSM, eg, lower electricity price and extra energy supply..
24,25
In the literature, various DSM objectives are documented, which include peak‐to‐average power ratio reduction,
26
consumers' electricity bill minimization,
27-29
transmission and distribution losses minimization,
30
maximization of con-
sumers' welfare, and economic efficiency of residential energy consumption.
31
The minimization of overall cost (gener-
ation, operation, and maintenance cost), flattening of the demand profile of consumers,
32,33
,
34,35
and minimization of
consumers' discomfort level
30
are the other objectives of DSM. All the above objectives are summarized in Table 1. This
table shows that different authors focused to get a set of different objectives. From this table, we can conclude that none
of the previous works considered all the objectives in a single DSM scheme. Therefore, to fill this research gap, we
propose a unified mathematical model to get most of the given objectives of DSM in a single framework. The words
“performance metrics”and “DSM objectives”are used interchangeably throughout this paper.
1.1 |Motivation
In the literature, various objective‐oriented DSM schemes are documented. In each DSM scheme, a different perspective
in term of performance metrics has been evaluated. The performance metrics associated to DSM are used to improve the
consumers' utility as well as the supplier's utility. In order to get multiple DSM performance metrics and to improve the
consumers'/supplier's utility, various DSM schemes need to be executed in parallel. For example, if we want to reduce
the consumer's electricity bill, peak demand, distribution losses, peak‐to‐average power ratio, etc, then, we need to
implement various DSM schemes in parallel, because in the literature, for every objective attainment, there is a dedi-
cated DSM scheme. This parallel operation of multiple DSM schemes not only costs more but their operation becomes
more complex when we extend our objectives domain. Therefore, a low complexity and a unified energy management
solution is the ultimate need where various performance metrics can be achieved which would help to improve the
consumers'/supplier's utility. In order to fill this research gap, we proposed a framework, where we provide a complete
taxonomy of DSM performance metrics and how these performance metrics can be attained in single DSM using a
unified approach. Though we could not attain all the performances metrics associated to DSM, but still we understand
that devising a unified DSM model can attain various performance metrics in efficient way. In the proposed framework,
we incorporate the importance of heterogeneous load, CPs, load priorities, load profile, human interaction factor
(HIF), and load shedding (LS). Moreover, the impact of all these factors on a given DSM model is also elaborated in
the given framework.
1.2 |Contributions
The contributions of this paper, are encapsulated as follows:
2of18 AHMAD ET AL.

1. In the proposed model, we provide a unified DSM framework, in which a number of performance metrics are
jointly considered in a single DSM model.
2. The proposed framework considers various factors and parameters that influence efficiency of DSM, eg, load
profile, LS, heterogeneous load, peak clipping, valley filling, human interaction, appliances priority, and CPs.
3. A multi‐objective optimization problem is formulated for the unified DSM framework to minimize the electricity
cost, greenhouse gases emission cost, perform peak clipping, and minimize the peak‐to‐average power ratio.
4. The proposed framework also considers the consumers demand curve distribution which affects the power system
stability. From power stability, we mean that the overall energy demand does not exceed a safe limit. To cope with
this situation, we use peak clipping in the proposed unified framework to flatten the electricity demand curve and
uniformly redistribute the overall power demand.
5. The multi‐objective problem is converted into a single objective problem.
6. Extensive simulations are performed to highlight and present the effectiveness of the proposed framework.
7. Integer linear programming solver is used for the solution of the given problem.
TABLE 1 Literature survey of DSM objectives
Reference PAPR
Electricity
Bill
Transmission
and Distribution
Losses
Consumers' Welfare
and Economic
Efficiency
Generation
Cost
Voltage
Fluctuation
Minimization
of Consumers'
Discomfort Level
Ye et al
36
xx
Zhu et al
37
x
Zhao et al
30
xx x
Ferreira et al
38
xx x
Deilami et al
39
xx
Maharjan et al
31
xx
Tran et al
32
xxxx
Ma et al
27
xx
Chanda and De
40
xx
Taylor et al
41
xx
Gudi et al
42
x
Nguyen et al
43
xx
Barbato et al
44
xx
Deng et al
45
xx
Acharya et al
14
x
Roh and Lee
46
xx
Fadlullah et al
47
xx
Ye et al
36
xx
Di Silvestre et al
48
xx
Adika and Wang
49
x
Hassan et al
50
x
Nunna et al
51
x
Muralitharan et al
52
xx
Ma et al
53
xx
Yu and Hong
33
x
Shi et al
54
x
Yaqub et al
28
x
Our proposed model x x x x x x
Abbreviation: DSM, demand‐side management.
AHMAD ET AL.3of18

1.3 |Paper organization
The rest of the paper is organized as follows. The mathematical model of the given unified DSM scheme is discussed in
Section 2. Simulation results are discussed in Section 3. Section 4 concludes the paper.
2|MATHEMATIC FORMULATION OF THE PROPOSED FRAMEWORK
In our proposed framework, we considered a residential compound with a number of houses. There are different types
of loads in each house (shiftable, seasonal, and base load). The residential compound is provided with the electricity
pricing tariff, CO
2
emission penalty tariff, availability of electricity supply, duration of LS, and daily maximum demand.
Some household appliances require human existence for the operation, eg, washing machine (WM) , iron, and dish
washer (DW). Therefore, the existence of a human as an operator for the given appliance is also assumed. We have
to schedule the home appliances of the residential compound in a unified way to jointly get the minimum electricity
cost, low Peak to average power ratio (PAPR), less greenhouse gas emission (GHG), and flattened demanded load curve
to stabilize the power system of the compound. Moreover, in achieving the aforementioned objectives, certain con-
straints need to be met. These constraints include consideration of consumers' preferences, peak clipping, appliances
priorities, and consumers satisfaction level. The notations used in the modeling of the above framework are given in
Table 2.
Let Kbe the total number of consumers in the residential compound with Ntypes of load in each home. Each load
type consists of A
n
set of appliances with energy profile of Ek;t
n;a. The LS and HIF is represented by L
t
and Ht;k
n;a.The sched-
uling time are divided into Ttime slots. The appliance operation duration and starting time are given as tk
n;aand tsk
n;a.
Another factor that needs to be considered while designing an efficient unified DSM scheme is consumer's willingness
and preferences. Therefore, to cater for the CPs, we introduce another input vector, ie, λt;k
n;a. The LS, HIF, and CPs are
shown in Figure 1.
Prior to modeling and applying the given unified DSM model, certain parameters need to be defined. These param-
eters include the total time duration for which the proposed unified DSM framework would work, pricing tariff used in
the proposed framework, and the power profile of each appliance. The proposed framework is assumed to do DSM
during “h”hours and employ time of use (TOU) tariff. Each hour is divided into a number of time slots. The duration
of a time slot in minutes is represented by Γ
i
. The number of slots in one hour can be calculated as follows:
Γh¼60=Γi:(1)
The total number of time slots, T, is equal to the multiplication of the number of slots per hour with the total number
of hours, ie, T=hΓ
i
. Let t∈{1,2⋯T} represent a time slot. Similarly, the HIF vector for each appliance of each type of
load for the kth consumer during the hhours is also transformed into Tper slot values as represented by
Ht;k
n;a¼H1;k
n;a;H2;k
n;a;H3;k
n;a;⋯HT;k
n;a
no
∀k;a∈An:(2)
The LS factor is also transformed into Tper slot values, as given by
Lt¼L1;L2;L3;⋯LT

∀k;a∈An:(3)
Similarly, the consumer willingness to operate certain appliance in terms of CP is also represented as Tper slot
values, as given by
λt;k
n;a¼λ1;k
n;a;λ2;k
n;a;λ3;k
n;a;⋯λT;k
n;a
no
∀k;a∈An:(4)
In our proposed model, we have multiple types of household appliances having different power profiles. The energy
profile Et;k
n;a¼E1;k
n;a;E2;k
n;a;E3;k
n;a;⋯ET;k
n;a
no
where a∈A
n
,Et;k
n;ais the energy consumption of the ath appliance of the nth type
in the tth time slot for the kth consumer. If the per hour power consumption of appliance aof the type nfor the kth
consumer per hour is Pk
n;a, then the energy consumption for tth time slot of appliance ais represented by
4of18 AHMAD ET AL.

Et;k
n;a¼Pk
n;a=Γh∀k;a∈An;t:(5)
In power profile calculation, it is mandatory to know the appliance power rating and its operation duration. To better
explain this concept, we take an example of four appliances, ie, WM, dryer (Dy), DW, and electric vehicle (EV). Let WM
operate for 30 minutes, Dy operates for 10 minutes, DW operates for 18 minutes, and EV operates for 60 minutes. The
operating time is then represented in the number of time slots. If the span of a time slot is 5 minutes, then, for WM, the
operating time will be six slots, for Dy, the operating time will be two slots, for DW, the operating time will be four slots,
while the operating time for EV will be 12 slots. In general, the operating time in number of slots for the ath appliance of
the nth type of the kth consumer is represented by tk
n;a.The mathematical model that conforms the operation of a given
appliance for ttime slots is
tk
n;a¼∑
T
t¼1
Xt;k
n;a∀k;a∈An;(6)
where Xk;t
n;ais the decision variable which decides to turn on the ath appliance of type nat the tth time slot for consumer
k. Another very important concept needed to be understood is the continuous operation of a specific appliance. For
TABLE 2 Nomenclature of the paper
C
t
Cost of electricity at time t
Ct
CO2Cost of GHG emission at time t
Given parameters and variables
T Total number of time slots
KTotal number of consumers
NTypes of load, eg, shiftable, seasonal, and base load
A
n
Set of appliances in the nth load type
ITotal group of appliances on the basis of priority, eg, washing machine and dryer are in one group
β
i
Appliances' sequence, eg, washing machine should be used before the dryer
L
t
Load shedding factor at the tth time slot
Hk;t
n;aHuman interaction factor for the kth consumer in the tth time slot for the ath appliance of the nth type load
λk;t
n;aConsumer preferences of the kth consumer to operate the ath appliance of type nat time t
Ek;t
n;aEnergy consumption of the ath appliance of the nth type of the kth consumer in time t
tk
n;aOperation time of the ath appliance of the nth type load of the kth consumer
tsk
n;aStarting time of the ath appliance of the nth type load of the kth consumer
h Number of hours
Γ
i
Slot interval
Γ
h
Total number of slots in an hour
α
1
∈[0,1] Weighted value for the selection of objective function to be minimized with continuous values between 0 and 1
α
2
∈{0,1} Binary indicator for load shedding
α
3
∈{0,1} Binary indicator for human interaction
α
4
∈{0,1} Binary indicator for peak clipping
α
5
∈{0,1} Binary indicator for continuous operation of a given appliance
α
6
∈{0,1} Binary indicator for consumer preference of a given appliance
γ
k,t
Peak clipping maximum limit for the kth consumer at time t
Decision variable
Xk;t
n;aDecision variable for selection of the ath appliance of the nth type of the kth consumer at time t
Abbreviation: GHG, greenhouse gas emission.
AHMAD ET AL.5of18

example, if the washing machine starts operating, then it would operate continuously till the allocated final time slot.
To ensure the continuous operation of a specific appliance continuously for the required time slot, we formulate the
following constraint:
∑
tsk
n;aþtk
n;a−1
t¼tsk
n;a
Xk;t
n;a⩾tk
n;a∀k;n;a∈An;(7)
where tsk
n;ais the starting time of the ath appliance of the type for the kth consumer. For the given unified DSM
model, the consumers' profile consists of different types of loads and some loads should be served/operated before
the others. For example, the Dy cannot be operated before the clothes are washed. Therefore, we group these types
of loads in different groups represented by β
i
wherei= {1,2,3⋯I}. The decision variable Xk;t
n;awould select only single
appliance from each group at each time slot, which is mathematically represented as follows:
∑
a∈βi
Xk;t
n;a⩽1∀k;n;t;i(8)
In the given problem, we have two objective functions, ie, electricity cost and GHG emission penalty cost. Cost is one
of the important objective function among DSM objectives. Once the electricity cost is minimized, then the PAPR is also
reduced, which results in flattening the consumers demand curve. In addition to it, the electricity cost reduction also
reduces the peak hours' demand, which in turn curtails the high current flow in distribution lines and reduces the
transmission/distribution losses.
The electricity cost can be calculated by multiplying the total energy consumed by all the consumers with the tariff
provided by the supplier. The consumers are provided with two types of tariffs, ie, energy tariff and CO
2
emission tariff.
Since there are two types of tariffs, the cost function for both the tariffs is calculated as given by
FIGURE 1 Residential compound architecture
6of18 AHMAD ET AL.

fcEk;t
n;a

¼Ek;t
n;a×Ct∀k;n;t;a∈An;(9)
fCO2Ek;t
n;a

¼Ek;t
n;a×Ct
CO2∀k;n;t;a∈An:(10)
The proposed model is a unified framework, in which a number of performance metrics can be achieved under var-
ious limitations imposed from both consumers' as well as from the supplier's end. Apart from the performance metrics,
the proposed unified model has the option of switching the associated constraints on and off. To select the desired out-
come as well as the associated constraints, we utilize certain selection parameter as shown in Table 3. The administrator
has the privileges to select the desired objective and constraints. The selection of objective and constraints depends upon
the geographical nature of the residential compound and the governmental policies. For example, in Europe, the objec-
tive of CO
2
emission minimization will be selected. Similarly, in countries with shortage of electricity, the LS factor will
be selected. One of the selection parameters is α
1
∈[0,1] used for the selection and priorities setting of job operation, ie,
cost minimization and GHG penalty minimization as shown in Equation (11). There are a number of household appli-
ances that must not be switched on/off frequently. For example, if a WM is turned on/off before its operating time
frame, it may reduce its life time and may affect its efficiency. This nature of the appliances is modeled as the continuity
constraint as given in Equation (7). To decide either to ensure the appliance continuous operation or not we use α
5
. Sim-
ilarly, for the CPs, peak clipping, HIF, and LS constraints, we used selection parameters α
6
,α
4
,α
3
, and α
2
, respectively.
The disconnection of power supply by the utility company due to maintenance or some other reasons is modeled as
LS constraint. Similarly, there are appliances that need human existence for the operation as discussed earlier, eg, an
iron needs human existence as an operator. To ensure consumer presence, the residential compound is provided with
HIF input vector. Another factor which may also be included in the modeling is consumers' preferences. Sometimes, the
cost of electricity may be too low, but due to some reasons, the consumer may not be willing to operate his/her
appliances. This behavior of consumers is named as CPs. The selection of decision variable should show that an appli-
ance is turned on or off on the basis of LS, HIF, and CP constraints along with the pricing tariff. We can summarize it
through the following equation:
Xk;t
n;a≔Xk;t
n;aλk;t
n;a

α6Hk;t
n;a

α3Lt
ðÞ
α2∀k;n;t;a∈An;(11)
TABLE 3 Various performance matrices selection variables α
i
∈{0,1} ∀i= 2,3,4,5,6
α
i
∈[0,1] α
i
α
i
α
i
α
i
α
i
Remarks
0 0 0 0 0 0 The cost of CO
2
is considered only.
0.5 1 0 0 0 0 Load shedding factor is involved and equal weightage is given to both electricity cost and CO
2
penalty cost.
0.5 1 1 0 0 0 Load shedding and human interaction factor are involved and equal weightage is given to both electricity cost
and CO
2
penalty cost.
0.5 1 1 1 0 0 Load shedding, human interaction factor, and peak clipping are considered. Equal weightage is given to both
electricity cost and CO
2
penalty cost.
0.5 1 1 1 1 0 Load shedding, human interaction factor, peak clipping, and appliances continuous operation are considered.
Moreover, equal weightage is given to both electricity cost and CO
2
penalty cost.
0.5 1 1 1 1 1 Load shedding, human interaction factor, peak clipping, appliances continuous operation, and consumer
preferences are considered. Moreover, equal weightage is given to both electricity cost and CO
2
penalty cost.
1 0 0 0 0 0 Only electricity cost is considered.
1 1 0 0 0 0 Electricity cost and load shedding factor are considered.
1 1 1 0 0 0 Electricity cost, load shedding factor and human interaction factor are considered.
1 1 1 1 0 0 Electricity cost, load shedding factor, human interaction factor, and peak clipping are considered.
1 1 1 1 1 0 Electricity cost, load shedding factor, human interaction factor, peak clipping, and appliances continuous
operation are considered.
1 1 1 1 1 1 Electricity cost, load shedding factor, human interaction factor, peak clipping, appliances continuous
operation, and consumer preferences are considered.
AHMAD ET AL.7of18

where α
2
,α
3
, and α
6
are the LS, HIF, and CP selection parameters. To make the proposed unified DSM model cost
effective and to ensure the power system's reliability, the total energy consumption of each consumer should not
exceed a given threshold. The threshold limit can be set by utility or consumer. Based on the meteorological data
and the generation unit type, the utility companies as well the consumers can predict the consumers' maximum
energy demand. In our proposed model, we do it through peak clipping constraint. That is, we set a threshold γ
k,t
at each time slot. The peak clipping constraint is given as
∑
N
n¼1
∑
a∈An
Xk;t
n;aEk;t
n;a⩽α4γk;t∀k;t;(12)
where α
4
is the selection parameter either to select the peak clipping option or not. The peak limit should be such
that γk;t⩾max P1
1;1;…Pk
n;a

∀k;n;a∈An. The proposed scheduling framework is summarized as follows:
1. Given values and parameters
•finite time horizon for usage of electricity
•time‐dependent price tariffs
•GHG penalty
•load profile
•LS factor
•peak clipping limit
•continuous operation time
•number of homes
•various types of load in every home
•set of appliances in each type
•HIFs for different appliances
•different appliances' priorities
•consumers' willingness
•Determine for total available time slots, T
•peak‐to‐average power ratio
•the consumer's electricity bill for the consumed energy
•the total cost of energy consumed
The values of selection variables used in the proposed model for the selection of different constraints are tabulated
in Table 3. To better understand Table 3, we show some random cases in Table 4. In this table, three different sce-
narios are given, ie, simplified DSM, moderate DSM, and unified DSM. In simplified DSM, all the constraints are off
(as all the selection parameters are assigned with zero values), and the objective function is to reduce the emission
cost. Moderate DSM represents the model where the objective function is still emission cost reduction, while the con-
straints selected are appliances priority constraint, and appliance continuous operation constraint. While in the uni-
fied DSM, the objective function is cost of electricity and all the associated constraints are selected by assigning one
to α
1
,α
2
,α
3
,α
4
,α
5
, and α
6
3|SIMULATIONS AND RESULTS
We conducted extensive simulation based on the flow chart shown in Figure 2 to show the effectiveness of the proposed
approach for minimizing the cost of electricity under various constraints in a unified fashion. The proposed approach in
the flow chart takes a number of inputs including
8of18 AHMAD ET AL.

min
Xk;t
n;a∈0;1fg
∀k;n;t;a
∑
K
k¼1
∑
N
n¼1
∑
a∈An
∑
T
t¼1
α1fcEk;t
n;a

|fflfflfflfflffl{zfflfflfflfflffl}
Electricity cost function
þ1−α1
ðÞfCO2Ek;t
n;a

|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
Emission cost function
0
B
B
@
1
C
C
A
zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{
Total CostXk;t
n;a
2
6
6
6
6
4
3
7
7
7
7
5
;(13)
min
Xk;t
n;a∈0;1
fg
∀k;n;t;a
∑
K
k¼1
∑
N
n¼1
∑
a∈An
∑
T
t¼1
α1fcEk;t
n;a

|fflfflfflfflffl{zfflfflfflfflffl}
Electricity cost function
þ1−α1
ðÞfCO2Ek;t
n;a

|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
Emission cost function
0
B
B
@
1
C
C
A
zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{
Total CostXk;t
n;a
2
6
6
6
6
4
3
7
7
7
7
5
:(14)
TABLE 4 Detail description of the selection parameters
α
1
α
2
α
3
α
4
α
5
α
6
Objective Function and Constraints Remarks
Simplified DSM min
Xk;t
n;a∈0;1
fg
∀k;n;t;a
∑
K
k¼1
∑
N
n¼1
∑
a∈An
∑
T
t¼1
fCO2Et
n;a

Xk;t
n;a
As the value of is α
1
zero; therefore, emission tariff is selected
000000C1: ∑
T
t¼1
Xk;t
n;a¼tn;a∀k;n;aAppliance operation for complete interval is ensured
C5: ∑
a∈βi
Xk;t
n;a⩽1∀k;n;i¼1;2:; ; ; ; I
fg
Appliance priority constraints is selected
Moderate DSM min
Xk;t
n;a∈0;1
fg
∀k;n;t;a
∑
K
k¼1
∑
N
n¼1
∑
a∈An
∑
T
t¼1
fCO2Et
n;a

Xk;t
n;a
As the value of is α
1
zero; therefore, emission tariff is selected
C1: ∑
T
t¼1
Xk;t
n;a¼tn;a∀k;n;aAppliance operation for complete interval is ensured
010101C3:Xk;t
n;a≔Xk;t
n;aλk;t
n;a

Lt
ðÞ ∀k;n;t;aAs α
2
and α
6
is one, so load shedding and consumer preferences
constraints are selected
C4: ∑
N
n¼1
∑
a∈A
Xk;t
n;aEt
n;a⩽γt
k∀k;tAs α
4
is one, so, peak clipping constraint is selected
C5: ∑
a∈βi
Xk;t
n;a⩽1∀k;n;i¼1;2:; ; ; ; Ifg
Appliance priority constraints is selected
min
Xk;t
n;a∈0;1fg
∀k;n;t;a
∑
K
k¼1
∑
N
n¼1
∑
a∈An
∑
T
t¼1
fcEt
n;a

Xk;t
n;a
As the value of α
1
is 1, therefore, energy consumption tariff is
selected
C1: ∑
T
t¼1
Xk;t
n;a¼tn;a∀k;n;aAppliance operation for complete interval is ensured
Unified DSM
C2: ∑
tsk
n;aþtk
n;a−1
t¼tsk
n;a
Xk;t
n;a⩾tk
n;a∀k;n;a
As α
5
is one, so continuous operation constraints selected
111111C3:Xk;t
n;a≔Xk;t
n;aλk;t
n;a

Lt
ðÞ ∀k;n;t;aAs α
2
and α
6
is one, so load shedding and consumer preferences
constraints are selected
C4: ∑
N
n¼1
∑
a∈A
Xk;t
n;aEt
n;a⩽γt
k∀k;tAs α
4
is one; so, peak clipping constraint is selected
C5: ∑
a∈βi
Xk;t
n;a⩽1∀k;n;i¼1;2:; ; ; ; I
fg
Appliance priority constraints is selected
Abbreviation: DSM, demand‐side management.
AHMAD ET AL.9of18

Subject to C1: ∑
T
t¼1
Xk;t
n;a¼tk
a
zfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflffl{Operation time constraint;∀k;n;a;
C2: ∑
tsk
n;aþtk
n;a−1
t¼tsk
n;a
Xk;t
n;a⩾tk
aα5
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
Appliances time continuity constraint
;∀k;n;a;
C3: Xk;t
n;a¼Xk;t
n;aλk;t
n;a

α6Hk;t
n;a

α3Lt
ðÞ
α2
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
Consumer preferences;human interaction and load shedding factors consideration constraint
;∀k;n;a;t;
C4: ∑
N
n¼1
∑
a∈An
Xk;t
n;aEt
n;a⩽α4γk;t
Peak clipping constraint
;∀k;t;
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
C5: ∑
a∈βi
Xk;t
n;a⩽1
Appliances priorities constraint
;∀shiftable appliances;k;t;i¼1;2;3…I
fg
:
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
energy pricing tariff, CO2 emission tariff, number of consumers, type of loads, set of appliances, power profile of each
appliance, and the associated constraints. After collecting these inputs, the integer linear programming solver is used to
minimize the cost of electricity by scheduling the given set of appliances.
We present five cases, each for a different scenario. Case 1shows the results without any constraint. In Case 1, all the
indicators, ie, α
1
,α
2
,α
3
,α
4
,α
5
, and α
6
used for the selection of constraints are taken zero. The values of the given con-
straints after switching off all the selection indicators are shown in Figure 3. In this figure, the value of HIF, LS, and CP
is 1. The top two sub‐figures in Figure 3 show that the consumer is available throughout the 24 hours for the operation
FIGURE 2 Proposed flow chart
10 of 18 AHMAD ET AL.

of WM, Dy, DW, and EV. While the remaining two sub‐figures show that there is no LS and the consumers are ready to
operate their appliances according to the schedule given by the unified DSM.
The corresponding unified approach without constraints is shown in Figure 4. In this figure, we use the cumulative
constraints (CCs) concept, which is the combination of CP, HIF, and LS constraints. CC for (WM, Dy, DW) and for (EV)
is equal to one, which means that no constraints is added. Figure 4 shows that the unified DSM is based on the pricing
tariff and all the appliances are shifted to those time slots in which the price is less in order to minimize the cost func-
tion. In addition, the peak clipping constraint is also off. The summation of the power consumption of all the appliances
at each instance is shown in Figure 5. This figure shows that as we have not restricted the peak demand, its value
reaches to 4500 W.
In Case 2, the peak clipping constraint is imposed while the other constraints are still relaxed, ie, α
1
,α
2
,α
3
,α
5
, and α
6
= 0 and α
4
= 1. The appliances shift into position where price is low and the total power is not exceeding the threshold
limits as shown in Figures 6 and 7, respectively. In Figure 6, the position of appliances is changed, as we restrict the total
consumption not to exceed the given threshold. The cost is low from 0 to 380 minutes and then from 650 to 950 minutes,
but the accumulative demand is exceeding the peak limit. Therefore, one appliance is shifted to the time slot where the
cost is high. Similarly, from Figure 7, it is clear that the peak demand is now reduced to 2000 W. As the PAPR is directly
FIGURE 4 Demand‐side management (DSM) without any constraints
FIGURE 3 Demand‐side management
(DSM) constraints
AHMAD ET AL.11 of 18

FIGURE 5 Peak clipping with no demand‐side management (DSM)
FIGURE 6 Demand‐side management (DSM) with peak clipping
FIGURE 7 Peak clipping after applying demand‐side management (DSM) under no constraint
12 of 18 AHMAD ET AL.

FIGURE 8 Demand‐side management (DSM) with consumer preference (CP) and peak clipping constraints
FIGURE 9 Peak clipping after applying demand‐side management (DSM) under consumer preference (CP) constraint
FIGURE 10 Demand‐side management (DSM) with consumer preference, human interaction factor (HIF), and peak clipping constraints
AHMAD ET AL.13 of 18

dependent on the peak demand, the peak demand minimization will lead to reduced PAPR. Moreover, the peak
demand is also linked with the distribution losses.
That is, by reducing the peak demand, the distribution losses will also be reduced. The consumer's demand curve
flattening plays an important role in power system stability by equally dividing the energy demand among different time
slots. Some time fulfilling the peak demand make the power system overloaded. The peak clipping in Case 2, prevail
the power system stable by preventing it from overloading.
In Case 3, in addition to peak clipping constraint, the CP constraint is also considered. The appliances' positions after
applying the unified DSM under the given constraints are changed accordingly as shown in Figure 8. It shows that
although the pricing tariff is low between 200 and 300 minutes interval, but at that time, the consumer does not want
to operate the appliances. Thereafter, the unified DSM has to search other low cost intervals while not violating the CP
constraint, ie, 650 to 950 minutes. The peak clipping limit is still 2000 W, but the graph pattern is changed from the
previous one as the CP constraint is added as shown in Figure 9.
In Case 4, we added the HIF constraint to peak clipping and CP constraints. The unified DSM and peak clipping
based on HIF and CP constraints changed the position of different loads as visualized form Figures 10 and 11, respec-
tively. For operating WM, Dy, and DW, the consumer's presence is mandatory, while the appliances should be shifted to
FIGURE 11 Peak clipping after applying demand‐side management (DSM) under consumer preference and human interaction factor
(HIF) constraints
FIGURE 12 Demand‐side management
(DSM) constraints turned on
14 of 18 AHMAD ET AL.

the time frame where the cost is low and the value of CC is 1, as shown in Figure 10. The position of EV is also changed
according to the CC. Similarly, Figure 11 shows that the peak demand is still reduced to 2000 W, but the peak pattern is
changed according to the imposed constraints.
Case 5 demonstrates the proposed unified DSM by considering all the associated constraints, ie, LS, HIF, CP, and
peak clipping as shown in Figure 12. The results in Figure 13 depicts that the position of the shiftable appliances
changed to the time slots where cost is low and the value of CC is 1. Further, the unified DSM ensures that the value
of peak demand is not exceeding the set threshold, ie, 2000 W as shown in Figure 14.
4|CONCLUSION
We have designed a unified DSM framework that considers the CPs, appliances uninterrupted operation, HIF, LS, and
peak clipping while scheduling the consumers' shiftable load. We have modeled the given scenario as a linear optimi-
zation problem and then solved it via integer linear programming solver that efficiently shifts the consumers' shiftable
load under various constraints. The peak hours' demand has been curtailed, which in fact increases the system
FIGURE 13 Demand‐side management (DSM) with load shedding, consumer preference, human interaction factor (HIF), and peak
clipping constraints
FIGURE 14 Peak clipping after applying demand‐side management (DSM) under load shedding, consumer preference, and human
interaction factor (HIF) constraints
AHMAD ET AL.15 of 18

reliability and reduces the PAPR. The distribution losses which are directly dependent on the demanded current are also
reduced through peak clipping. Simulations show that our proposed framework increased the consumers' as well as the
electricity supplier's benefit. Moreover, the simulations show that large numbers of performance metrics are achieved
under the umbrella of a unified DSM, including electricity cost reduction, CO
2
emission minimization, PAPR reduction,
peak clipping, and distribution losses reduction. Furthermore, the redistribution of energy demand and flattening of
consumers' demand curve avoids the power system overloading. The future research should be focused on considering
the consumer privacy issues and the implementation complexity reduction of the proposed model.
ORCID
Sadiq Ahmad https://orcid.org/0000-0001-5202-0300
Muhammad Naeem https://orcid.org/0000-0001-9734-4608
Ayaz Ahmad https://orcid.org/0000-0002-2253-6004
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How to cite this article: Ahmad S, Naeem M, Ahmad A. Unified optimization model for energy management
in sustainable smart power systems. Int Trans Electr Energ Syst. 2019;e12144. https://doi.org/10.1002/2050‐
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