1. Short-term resource scheduling of a renewable energy
based micro grid
Maziar Izadbakhsh a, *
, Majid Gandomkar a
, Alireza Rezvani a
, Abdollah Ahmadi b
a
Department of Electrical Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran
b
Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Fars, Iran
a r t i c l e i n f o
Article history:
Received 15 June 2014
Accepted 16 October 2014
Available online
Keywords:
Micro-gird
Renewable energy resources
Multi-objective mathematical programming
Short term environmental/economical
scheduling
Normal boundary intersection method
a b s t r a c t
In recent years due to the decreasing fossil fuel reserves and the increasing social stress, complex power
networks have no other choices except to seek for alternative energy sources to eliminate the envi-
ronmental issues caused by the traditional power systems. Thus, the scheduling of energy sources in a
complex Micro-Grid (MG) comprising Micro Turbine (MT), Photo Voltaic (PV), Fuel Cell (FC), battery units
and Wind Turbine (WT) has been investigated in this paper. Furthermore, a multi-objective framework is
presented to simultaneously handle the two objective functions including minimization of total opera-
tion cost and minimization of emission. In this regard, Normal Boundary intersection (NBI) technique is
employed to solve the proposed multi-objective problem and generate the Pareto set. Besides, a fuzzy
satisfying method is used for decision making process. Afterward, the results obtained from the pre-
sented method are compared to the ones derived from other methods. Finally, it is verified that the
proposed solution method results in better solutions for operation cost, emission and the execution time.
© 2014 Elsevier Ltd. All rights reserved.
1. Introduction
The electricity companies tend towards using the Distributed
Energy Resources (DERs) close to the load, because of many eco-
nomic/environmental and technical issues [1]. Many types of po-
wer sources can be categorized as DERs like diesel engines, battery
units, Photo Voltaic (PV), Fuel cell (FC), Wind Turbine (WT) and
Micro Turbine (MT) [1e4]. A concept recently introduced to power
systems is Micro-Grid (MG) that includes a low-voltage distribution
system with DERs, storage devices and controllable loads operating
in grid-connected or stand-alone modes taken into account as a
controlled entity [4].
So far, many research works have been dedicated to the control
and operation of the MGs. Various solution methods are proposed
in Refs. [1,4] for economic scheduling of MG. Over the recent years,
the conventional economic dispatch has been replaced by eco-
nomic/environmental dispatch [7e19], since it cannot satisfy the
requirements for optimal operation of MGs after the Clean Air Act
Amendments was passed in 1990 to take into account the emis-
sion concerns [5,6]. Ref. [7] proposes a Genetic Algorithm (GA)-
based approach in order to solve the sizing optimization problem
comprising multiple objectives as lifecycle cost minimization,
maximization of Renewable Energy Sources (RESs) penetration as
well as pollutant emission minimization. A comprehensive model
is presented in Ref. [8] for MG operating in stand-alone mode
while a multi-cross learning-based chaotic differential evolution
algorithm is used to solve the economic/environmental optimi-
zation problem. Ref. [9] employs a stochastic bidding strategy for
an MG participating in joint day-ahead energy and spinning
reserve markets considering the uncertainty of load and renew-
able DERs' power output. Ref. [10] uses a performance metric
taking into account the electricity price, emission and service
quality that each one is given a weighting factor. It is noted that
this performance metric is applied to MGs operating in stand-
alone, grid-tied and networked modes. The optimal operation of
WTs and other DERs operating in an interconnected MG is done in
Ref. [11] through an expert energy management system. The main
aim beyond using the presented approach was to determine the
optimal set points of DERs and storage devices in order to
concurrently minimize the total operation cost and the net
emission. Ref. [12] utilizes an intelligent energy management
system for optimal operation of an MG that is based on Combined
Heat and Power (CHP) generation over a 24-h horizon to simul-
taneously minimize the total operation cost and the net emission.
Artificial intelligence techniques along with linear-programming-
based multi-objective framework are used in Ref. [13] to present a
* Corresponding author. P.O. Box 79681-15356, Iran. Tel.: þ98 917 168 8909.
E-mail address: maziar.izadbakhsh.saveh@gmail.com (M. Izadbakhsh).
Contents lists available at ScienceDirect
Renewable Energy
journal homepage: www.elsevier.com/locate/renene
http://dx.doi.org/10.1016/j.renene.2014.10.043
0960-1481/© 2014 Elsevier Ltd. All rights reserved.
Renewable Energy 75 (2015) 598e606

2. generalized formulation for intelligent energy management of an
MG. Ref. [14] determines the optimal operation of an MG which is
on the basis of CHP generation. This MG includes energy storage
system, three types of thermal units and demand response pro-
grams. A stochastic multi-objective framework is proposed in
Ref. [15] using teaching-learning based optimization to obtain the
Pareto optimal solutions. Ref. [16] implements the MG planning in
a primary distribution system through a two-stage multi-objec-
tive model. In the first stage, the loss sensitivity factors are used to
specify the optimal region for the MG while the second stage
determines the optimal locations and the size of a number of DERs
in MG employing Non-dominated Sorting Genetic algorithm II
(NSGA-II). The optimal generation scheduling is done in Ref. [17]
using a Fuzzy Self-Adaptive Particle Swarm Optimization
(FSAPSO), while the objective functions are cost and emission
minimization. Ref. [18] presents an expert multi-objective adap-
tive modified particle swarm optimization algorithm for eco-
nomic/environmental operation of a typical MG including back-up
MT, FC and battery hybrid power source.
So far, there are many research works devoted to the operation
of MGs using Meta heuristic optimization algorithms to deal with
multi-objective economic/environmental operation of MGs. Meta
heuristic approaches are usually employed to solve multi-objective
problems like economic/environmental operation of MGs, as they
have a population-based search capability, simplicity and conver-
gence speed [19]. It is worth noting that the papers previously cited
have employed the weighted sum method to transform the original
multi-objective problem into a single-objective optimization
problem, then they use Meta heuristic approaches to solve them.
The weighted sum method is widely used for economic/environ-
mental management problems rather than other optimization
methods [20]. In this regard, this paper proposes a multi-objective
framework for the problem of short-term economic/environmental
scheduling of an MG employing Normal Boundary Intersection
(NBI) technique. However, there are two main controversial issues
with the weighted sum method as follows:
1. In the case of non-convex Pareto set, the Pareto points on the
concave sections of the trade-off surface will be failed to be
obtained.
2. For an even spread of the weights, generally the optimal solu-
tions in the criterion space are not evenly distributed [20].
In this regard, NBI technique is an efficient method for numer-
ical computation of fairly distributed points on the Pareto optimal
front in multi-objective optimization problems [20].
A comprehensive literature survey on the stochastic modeling
and optimization tools for an MG can be found in Ref. [21].
This paper proposes a multi-objective framework for the prob-
lem of short-term economic/environmental scheduling of an MG
using Normal Boundary Intersection (NBI) method. The main con-
tributions of this paper can be summarized as follows:
1. Presenting a bi-objective framework for short-term scheduling
of an MG considering cost and emission objective functions.
2. Employing NBI technique to solve the proposed multi-objective
framework.
3. Using a fuzzy satisfying method for the decision making process.
4. Obtaining superior solutions using the presented method in
comparison with recently employed methods.
The remainder of this paper is organized as follows: Section 2
presents the problem formulation. The description of NBI method
is included in Section 3. Section 4 proposes the simulation results
with detailed discussion. Finally, some relevant conclusions are
drawn in Section 5.
Nomenclature
Indices
b battery index
f fuel cell index
i emission index
g grid index
m micro turbine index
p photo voltaic index
t time index
w wind turbine index
Sets
BA battery units
ET Emission group consists of CO2, SO2 and NOx
FC fuel cell units
MT micro turbine units
PV photo voltaic units
WT wind turbine units
T time study horizon
Constants and parameters
b weighting factor in NBI method
B(*,t) bid at hour t
Ei(*,t) emission coefficient of ith emission type (CO2, SO2 and
NOx) of unit at hour t
PMax(*,t) maximum power output at hour t
PMin(*,t) minimum power output at hour t
PFMax(*,t)maximum forecasted power output at hour t
PFMin(*,t) minimum forecasted power output at hour t
Load(t) load at hour t
SUC* start-up cost
SDC* shut-down cost
Variables
F payoff table
mr
i value of the ith membership function in the rth Pareto
optimal solution
mr
total membership function of the rth Pareto optimal
solution
U feasible region
D Objective function of NBI method
f U
, f N
, f SN
Utopia and nadir point and pseudo nadir point,
respectively
F1 first objective function (cost minimization)
F2 second objective function (emission minimization)
Fr
i value of the ith objective function in the rth Pareto
optimal solution
bn denote the unit normal to the CHIM simplex towards
the origin
P(*,t) power generation at hour t
V(*,t) binary variable which is equal to one if unit is online at
hour t
x*
i vector of decision variables which optimizes the
objective function fi
wi weighting factor of the ith objective function in fuzzy
decision making
M. Izadbakhsh et al. / Renewable Energy 75 (2015) 598e606 599

3. 2. Mixed integer nonlinear programming (MINLP)
formulation for MG
The following expression indicates the two objective functions
of the proposed model for MG:
Multi À objective functions ¼
&
F1 Cost minimization
F2 Emission minimization
(1)
where the objective functions are denoted by F1 and F2 and rep-
resented in details as below:
2.1. Cost and emission minimization
The first objective function of the proposed multi-objective
model is total operation cost stated as follows:
Note that F1 is stated in Vct (Euro cent) or $ and includes the fuel
costs of Distributed Generations (DGs), start-up and shut-down
costs as well as the costs due to power exchange between the
MG and the utility grid (macro-grid, LV network). For example, the
first item indicates the operation cost of MT, while P(m,t) is the
power output of the mth MT at hour t. B(m,t) indicates the bid of the
mth MT at hour t while the start-up and shut-down costs of the mth
MT unit are denoted by SUCm and SDCm, respectively. Besides,
V(m,t) is a binary variable showing the status of the mth MT and it is
equal to 1 if the mth MT is online at hour t. Accordingly, rows 2e5
represent the operation cost of FC, PV, WT and battery units.
Moreover, P(g,t) in the last row is the active power that is bought/
sold from/to the utility grid at hour t. Finally, the bid of utility grid at
hour t is denoted by B(g,t) [17,18].
The second objective of the proposed multi-objective model
relates to the emission intended to be minimized as follows:
where Ei() includes three significant pollutants as Carbon Dioxide
(CO2), Sulfur Dioxide (SO2) and Nitrogen oxides (NOx). In addition,
F2 is stated in terms of kg MW hÀ1
and it is comprised of emission
generation by MT, FC, PV and battery units, respectively. Finally, the
emission generated because of power transactions with the utility
grid is indicated by the last term of Eq. (3) [17,18].
2.2. Constraints
The Power balance constraint is taken into consideration as one
of the most important constraints in MG scheduling guaranteeing
that the power generated by DG units satisfies the total load de-
mand of the grid.
X
m2MT
Pðm; tÞ þ
X
f 2FC
Pðf ; tÞ þ
X
p2PV
Pðp; tÞ
þ
X
w2WT
Pðw; tÞþ
X
b2BA
Pðb; tÞ þ Pðg; tÞ ¼ LoadðtÞ (4)
The transmission losses are negligible, as a small 3-feeder LV
radial system is used [17,18].
If the unit is on, the power generated by each unit in each period
of scheduling is limited to its lower and upper bounds. Constraints
(5e9) show the power output limit of MT, FC, PV, WT and battery
units. Moreover, the power transaction of MG with the utility grid is
limited which is indicated in constraint (10).
PMinðm; tÞ*Vðm; tÞ Pðm; tÞ PMaxðm; tÞ*Vðm; tÞ (5)
PMinðf ; tÞ*Vðf ; tÞ Pðf ; tÞ PMaxðf ; tÞ*Vðf ; tÞ (6)
PFMinðp; tÞ*Vðp; tÞ Pðp; tÞ PFMaxðp; tÞ*Vðp; tÞ (7)
PFMinðw; tÞ*Vðw; tÞ Pðw; tÞ PFMaxðw; tÞ*Vðw; tÞ (8)
PMinðb; tÞ*Vðb; tÞ Pðb; tÞ PMaxðb; tÞ*Vðb; tÞ (9)
PMinðg; tÞ Pðg; tÞ PMaxðg; tÞ (10)
F1 ¼
X
t2T
8
>>>>>>>>>>>>>>>>>>><
>>>>>>>>>>>>>>>>>>>:
P
m2MT
Pðm; tÞ*Bðm; tÞ þ SUCm*Vðm; tÞ*½1 À Vðm; t À 1ÞŠ þ SDCm*Vðm; t À 1Þ*½1 À Vðm; tÞŠþ
P
f 2FC
Pðf ; tÞ*Bðf ; tÞ þ SUCf *Vðf ; tÞ*½1 À Vðf ; t À 1ÞŠ þ SDCf *Vðf ; t À 1Þ*½1 À Vðf ; tÞŠþ
P
p2PV
P
À
p; t
Á
*B
À
p; t
Á
þ SUCp*V
À
p; t
Á
*½1 À Vðp; t À 1ÞŠ þ SDCp*Vðp; t À 1Þ*½1 À Vðp; tÞŠþ
P
w2WT
Pðw; tÞ*Bðw; tÞ þ SUCw*Vðw; tÞ*½1 À Vðw; t À 1ÞŠ þ SDCw*Vðw; t À 1Þ*½1 À Vðw; tÞŠþ
P
b2BA
Pðb; tÞ*Bðb; tÞ þ SUCb*Vðb; tÞ*½1 À Vðb; t À 1ÞŠ þ SDCb*Vðb; t À 1Þ*½1 À Vðb; tÞŠþ
Pðg; tÞ*Bðg; tÞ
9
>>>>>>>>>>>>>>>>>>>=
>>>>>>>>>>>>>>>>>>>;
(2)
F2 ¼
X
t2T
X
i2ET
8
><
>:
P
m2MT
Pðm; tÞ*Eiðm; tÞ þ
X
f 2FC
Pðf ; tÞ*Eiðf ; tÞ þ
X
p2PV
Pðp; tÞ*Eiðp; tÞþ
P
b2BA
Pðb; tÞ*Eiðb; tÞ þ Pðg; tÞ*Eiðg; tÞ
9
>=
>;
(3)
M. Izadbakhsh et al. / Renewable Energy 75 (2015) 598e606600

4. 3. Multi-objective mathematical optimization and solution
methodology
3.1. Multi-objective optimization principles
The goal beyond implementing multi-objective optimization
(also called multi-performance, multi-criterion or vector optimi-
zation) is to concurrently minimize or maximize several objective
functions. The purpose of multi-objective problem in the mathe-
matical programming framework is to optimize various objective
functions. As a result, there is no longer a single optimal solution
and a set of non-dominated set of solutions exist instead [22e27].
The following mathematical expression demonstrates a typical
optimization problem:
min FðxÞ ¼ ðf1ðxÞ; …; fmðxÞÞT
s: t : fx2RjgðxÞ 0; hðxÞ ¼ 0g
(11)
3.2. Normal-boundary intersection (NBI) method
The first step in NBI [26,27] method is to construct the payoff
table F. Usually, the individual minima of the objective functions
are calculated to form the payoff table for an arbitrary problem
including m objective functions. Afterward, with the solution
optimizing the objective function fi(x), the minimum value of fi(x)
derived from the solution x*
i is denoted by f *
i ðx*
i Þ. The calculated
values of other objective functions are indicated by
f1ðx*
i Þ; …; fiÀ1ðx*
i Þ; fiþ1ðx*
i Þ; …; fmðx*
i Þ. The following expression
demonstrates the ith column of the payoff table (anchor points):
Â
f1
À
x*
i
Á
; …; fiÀ1
À
x*
i
Á
; fiþ1
À
x*
i
Á
; …; fm
À
x*
i
ÁÃT
(12)
where,
x*
i ¼ arg minfi
s: t : fx2RjgðxÞ 0; hðxÞ ¼ 0g
(13)
Using the same procedure, the remaining columns of the payoff
table are calculated:
f ¼
0
B
B
B
B
B
B
B
B
B
B
@
f *
1
À
x*
1
Á
::: f1
À
x*
i
Á
::: f1
*
m
« 1 «
fi
À
x*
1
Á
::: f *
i
À
x*
i
Á
::: fi
*
m
« 1 «
fm
À
x*
1
Á
fm
À
x*
i
Á
f *
m
À
x*
m
Á
1
C
C
C
C
C
C
C
C
C
C
A
(14)
NBI technique is an efficient method proposed for numerical
computation of fairly distributed points on the Pareto optimal front
in multi-objective optimization problems [26]. To the best of the
authors; knowledge, there is no published paper using the NBI
technique to deal with the problem of short-term economic/envi-
ronmental scheduling of an MG. This technique has many advan-
tages compared to many methods used to solve multi-objective
problems. But, there is a vital issue regarding the NBI technique that
should be investigated. The rage of objective function within the
efficient set is not ensured to be optimized. Hence, this paper
employs lexicographic optimization to encounter this demerit [24].
When forming the payoff table, it should be guaranteed that the
solutions obtained from the individual optimization of the objec-
tive functions are all Pareto efficient solutions. In the case of
another optima, the optimal solution derived is no longer a certain
efficient solution. In this regard, the lexicographic optimization is
utilized in this paper to construct the payoff table which includes
only efficient solutions [24]. The basic principle of lexicographic
optimization is to optimize the first objective function when a se-
ries of objective function exists. In general, the lexicographic opti-
mization of a series of objective functions is to optimize the first
objective function and then among the possible alternative optima
optimize for the second objective function and etc. The procedure
of lexicographic optimization can be described as follows:
The first step is to optimize the first objective function resulting
in min f1 ¼ z*
1. After that, the next objective function is taken and
optimized while constrained to f1 ¼ z*
1. Therefore, the optimal so-
lution intended to be found is min f2 ¼ z*
2 subject to f1 ¼ z*
1. Af-
terward, the third objective function is optimized while
considering the constraints f1 ¼ z*
1 and f2 ¼ z*
2 to keep in mind the
optimal solution derived, previously, etc. up until the first row of
the payoff table F in (14) is produced. With the same process, the
other rows of the payoff table are completed. For instance, when
forming the second row of the payoff table, the second objective
function is optimized, i.e. min f2 ¼ z*
2. Then, the first of the third
objective function is optimized while keeping in mind the
constraint f2 ¼ z*
2 and etc. It is noted that all solution obtained from
the lexicographic optimization are all non-dominated or efficient
solutions [24].
In the payoff table, the obtained values for the objective function
fi(x) are included in the ith row. These values specify the maximum
and the minimum of this objective function. Note that these are
significant reference points used to normalize the objective space.
However, it seems necessary to introduce few concepts. In this
regard, the first concept relates to a specific point, usually located
outside the feasible region corresponding to all objectives that
concurrently take their best possible values. This point is named
“Utopia point” [24,27], indicated by fU
as below:
f U
¼
Â
f1
À
x*
1
Á
; …; fi
À
x*
i
Á
; …; fm
À
x*
i
ÁÃT
(15)
The second concept is Nadir point [24,27] relating to a point in
the design space, wherein all objectives have simultaneously their
worst possible values. This point can be mathematically stated as:
f N
¼
h
f N
1 ; …; f N
i ; …; f N
m
iT
(16)
where,
f N
i ¼ maxfiðxÞ
s: t : fx2RjgðxÞ 0; hðxÞ ¼ 0g
(17)
Another possible way to represent the Nadir point is as follows:
f N
i ¼ max
È
fi
À
x*
1
Á
; …; fi
À
x*
i
Á
; …; fm
À
x*
m
ÁÉ
(18)
It is noted that the point demonstrated in (16) represents the
next concept known as Pseudo Nadir Point having a close concept to
Nadir point, when Eq. (18) is employed to definefN
. This point is
located in the design space with the worst design objective values
of the anchor points.
In the case of different magnitudes or physical meanings of the
objective functions indicated in (11), it is necessary to first
normalize the objectives to derive a set of Pareto solutions well
representing the Pareto frontier. For this end, Utopia and pseudo
Nadir points can be used to compute the normalized value of
objective functions denoted byfi(x) [26,27].
f ðxÞ ¼
fiðxÞ À f U
i
f N
i
À f U
i
; i ¼ 1; …; m (19)
M. Izadbakhsh et al. / Renewable Energy 75 (2015) 598e606 601

5. Using the normalization (19), the initial range of objective
functions falls within the interval [0e1] and the multi-objective
optimization problem is solved in a non-dimensional, unit-less
criterion space. The normalized payoff table is formed utilizing
these values. The normalized payoff table is represented by F
which its elements are derived from normalized values of (19).
The set of points in R, that are convex combinations of each row
of the payoff table, is referred to as the Convex Hull of Individual
Minima (CHIM) that any point P(b1,…,bm) in the normalized space
on this line can be stated as:
Pðb1; :::; bmÞ ¼
(
fb; b2R;
Xm
i¼1
bi ¼ 1;bi ! 0
)
(20)
If the unit normal to the CHIM towards the origin is denoted by
bn, the set of points on that normal is represented by fb þ Dbn; D2R.
The initial optimization problem shown in (11) is converted into a
set of parameterized single-objective optimization problems with
the objective to maximize the distance between the Utopia line and
the Pareto surface. Thus, the intersection point of the normal and
the boundary of the feasible space closest to the origin gives the
global solution of the following sub-problem (NBIb):
Maximize D
s: t : fb þ Dbn ¼ F
À
x
Á
where : fx2RjgðxÞ 0; hðxÞ ¼ 0g
(21)
A point-wise approximation of the Pareto front can be obtained
by solving (21) for different values of bi. The flowchart of the pre-
sented multi-objective solution method is depicted in Fig.1, while n
denotes the number of optimal Pareto solutions.
4. Case study and simulation results
Two different cases are used in this paper to implement the
proposed method in order to show the efficiency and the effec-
tiveness of the lexicographic optimization and augmented-
weighted epsilon-constraint method. The system employed to
solve the presented problem is a laptop computer with 2.4 GHz
Pentium IV CPU and 3 GB RAM while SBB solver under GAMS [28],
has been used. The next section presents the results obtained
through solving the proposed problem with two case studies.
4.1. Case 1
This case is the same as the one used in Refs. [11,18,29e31]. This
test system includes three plants and six thermal generating units,
while the only pollutant emission taken into consideration is NOx
and CO2 and SO2 are ignored. The main purpose beyond solving the
problem is to obtain the best dispatch with the least cost and
emission [11,18,29e31]. Furthermore, this case takes into account
the transmission loss in the model. The Appendix section includes
the needed data for this case.
The total real power demand of this test system is 900 MW. NBI
technique is used to solve the proposed multi-objective framework
and obtain the Pareto optimal solutions while the two objective
functions are cost minimization (F1) and emission minimization
(F2). The resulted payoff table for this case is represented as below:
F1 ¼
47329:041 863:272
50265:302 701:456
As it can be observed from this payoff table, when the cost
function is only taken into consideration, it is improved to
47329.041 ($) while the emission is equal to 863.272 (kg). On the
other hand, when the problem is solved only with the second
objective function (emission propagation), the emission would be
701.456 (kg), but in this case the cost deteriorates to reach
50265.302 ($). The number of variables and constraints for this case
are 12 and 8, respectively. Besides, the solution time to form the
payoff table using CONOPT is 0.502 (Sec).
The obtained Pareto optimal solutions using NBI method are
represented in Fig. 2. As it can be seen, the two objectives of the
proposed framework have competing behaviors. It is worth noting
that each Pareto solution includes 13 variables and 9 equations
while all solutions are feasible [24,27]. The solution time of Pareto
Fig. 1. NBI flowchart.
650
700
750
800
850
900
47000 47500 48000 48500 49000 49500 50000 50500
Emission(kg)
Cost ($)
Fig. 2. Pareto solutions for case 1.
M. Izadbakhsh et al. / Renewable Energy 75 (2015) 598e606602

6. solutions varies from 0.082 (Sec) to 0.197 (Sec) while this solution
time is exceptional.
The decision making process is done using a fuzzy decision
making method as Ref. [5]. The next step after obtaining the Pareto
set is to select the most compromise solution, according to the
specific application of the problem and the decision maker's pref-
erences. In this regard, a linear membership function is introduced
to each objective function. For the objective function intended to be
minimized, the following membership function is defined:
mr
i ¼
8
:
1 f r
i f min
i
f max
i À f r
i
f max
i À f min
i
f min
i f r
i f max
i
0 f r
i ! f max
i
(22)
Accordingly, the following membership function is defined for
the objective functions set to be maximized:
mr
i ¼
8
:
0 f r
i f min
i
f r
i À f min
i
f max
i À f min
i
f min
i f r
i f max
i
1 f r
i ! f max
i
(23)
where f min
i and f max
i indicate the range of objective functionfi, ob-
tained from the payoff table. In addition,f r
i is the value of the ith
objective function in the rth Pareto optimal solution andmr
i is its
corresponding membership function. It is worth to mention thatmr
i
specifies the nicety of the solution resulted for the ith objective
function in the rth Pareto optimal solution. Also, the total mem-
bership function (mr
) is defined for the rth Pareto optimal solution
based on its individual membership functions as Eq. (24).
mr
¼
Pm
i¼1 wimr
i
Pm
i¼1 wi
(24)
where wi is the weighting factor of the ith objective function and m
is the number of objective functions. According to the significance
of the objective functions, the decision maker chooses the
weighting factors. It is noted that the Pareto optimal solution with
the highest value of total membership is the most compromise
solution. The values of cost, emission and total membership are
shown in Fig. 3 while the same weighting factors are assigned to
each objective function.
According to Fig. 3, the best optimal solution is Pareto optimal
solution 10, since it has the highest total membership value (0.760).
The total membership function is defined for each Pareto solution
to specify its optimality degree. The Pareto solution 10 is associated
with a cost equal to 48034.915 ($) that is close to its ideal value, i.e.
47329.041 ($). Moreover, the emission of Pareto optimal solution 10
is equal to 740.356 (kg). The solution time of Pareto solution 10 is
0.095 (Sec) and total loss is 39.087 (MW). It is worth mentioning
that the membership value of cost and emission in Pareto solution
10 is 0.760 and 0.759, respectively. Fig. 4 represents the Pareto
solution 10 in details.
However, different combination of weighting factors can be
selected by the decision maker. For instance, if the decision maker
seeks the lower cost, the weighting factor assigned to the cost
function would be higher and the weighting factor of the emission
would be lower. Thus, a Pareto front with lower cost and higher
emission will be found. If the weighting factors of the cost and
emission are 3 and 1, respectively, the Pareto solution 15 is selected
as the most compromise solution, since it is associated with the
highest total membership value as 0.819. In this Pareto solution, the
membership value of the cost is 0.944 while the emission mem-
bership is 0.444. Fig. 5 represents the Pareto solution 15 in details.
Furthermore, this figure includes the detailed results obtained from
other methods.
Table 1 shows the total cost, net emission and CPU time related
to Pareto solution 15 and other methods. The results reported in
Table 1 show the superiority of the presented technique over others
used in Refs. [11,18,29e31] in the case of quantity. For example, the
result obtained from the proposed method is comprised of cost as
Fig. 3. Variation of total membership, cost and emission functions versus Pareto-
optimal solutions for case 1.
0
50
100
150
200
250
300
1 2 3 4 5 6
Powergeneration(MW)
Generator number
Fig. 4. Details of best Pareto solution for equal weighting factor and case 1.
0
50
100
150
200
250
300
350
1 2 3 4 5 6
Powergeneration(MW)
Generator number
Ref. [11] Ref. [18] Ref. [29] Ref. [30] Ref. [31] Proposed method
Fig. 5. Results obtained from different methods for case 1.
M. Izadbakhsh et al. / Renewable Energy 75 (2015) 598e606 603

7. 47492.740 ($), which is less than the ones reported in
Refs. [11,18,29e31] by 56.22 (47548.96e47492.740 ¼ 56.22), 56.23,
311.81, 316.29, and 57.13 ($), respectively. The emission associated
with this Pareto solution is 791.785 (kg) which is less than those
resulted in Refs. [11,18,29e31] by 31.965, 31.965, 52.035, 52.145,
and 31.975 (kg), respectively. The results derived in this case study
would be an evidence of the efficiency of the presented approach.
4.2. Case 2
The second test system comprises MT, FC, PV, WT and battery
and the goal is finding the best unit commitment schedule and the
economic/environmental dispatch of the units. It is worth noting
that the considered planning horizon is 24-h period on the hourly
basis. Besides, this case study takes into consideration all three
types of pollutants, i.e. CO2, SO2 and NOx [17,18].
All DG sources are considered to operate in unity power factor
without absorbing or generating reactive power. Moreover, the MG
is connected to the utility grid via a power exchange link consid-
ered for power transactions over the scheduling period based on
the decisions made by the MG Central controller (MGCC). The Ap-
pendix section includes the required data.
The resulted payoff table (F2) for this case is represented as
follows:
F2 ¼
177:550 552:672
1269:48 108:105
0
100
200
300
400
500
600
0 200 400 600 800 1000 1200 1400
Emission(kg)
Cost (€ct)
Fig. 6. Pareto solutions for case 2.
-40
-20
0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Power(kW)
Time (h)
MT FC PV WT Battery Utility
Fig. 7. Results obtained for Pareto solution 11 for case 2.
-40
-20
0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Power(kW)
Time (h)
MT FC PV WT Battery Utility
Fig. 8. Results obtained for Pareto solution 15 for case 2.
-40
-20
0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Power(kW)
Time (h)
MT FC PV WT Battery Utility
Fig. 9. Results obtained for Pareto solution 19 for case 2.
-40
-20
0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Power(kW)
Time (h)
MT FC PV WT Battery Utility
Fig. 10. Results obtained from the Ref.[17].
Table 1
Results obtained from different methods for case 1.
Optimization method Ref. [11] Ref. [18] Ref. [29] Ref. [30] Ref. [31] Proposed
Total cost ($/h) 47,548.96 47,548.97 47,804.55 47,809.03 47,549.87 47,492.740
Net emission (kg/h) 823.35 823.35 843.42 843.53 823.36 791.385
CPU time (s) 14.36 12.54 0.195 0.814 12.03 0.082
M. Izadbakhsh et al. / Renewable Energy 75 (2015) 598e606604

8. As it can be observed from this payoff table (F2), if the cost
function is only considered, it can be improved to 177.55 (Vct)
while the emission in this case is 552.672 (kg). On the other hand,
when the emission is the only objective function considered, it can
be reduced to 108.105 (kg) while the cost in this case rises to
1269.48 (Vct). The Pareto optimal solutions obtained from the
proposed method are represented in Fig. 6. This figure well dem-
onstrates the competing nature of these two objective functions. It
is noticed that using RESs like WT and PV results in pollution
reduction due its zero-emission nature, but leads to higher cost as
the bid by such units are high. This means that using such units are
not economical and must be limited from the economic viewpoint.
It is worth to mention that each Pareto solution consists of 267
variables and 364 equations while all solutions are feasible [24,27].
The presented solution technique results in a set of feasible and
well-distributed Pareto optimal solutions that makes the decision
maker able to employ a proper power dispatch strategy on the basis
of economic and environmental requirements. The solution time of
Pareto solutions varies from 18.362 (Sec) to 23.368 (Sec) while this
solution time is exceptional.
This paper employs fuzzy decision maker to determine the most
preferred solution among all Pareto solutions [5]. In fuzzy decision
making procedure, a linear membership function is defined for
each objective function to specify their nicety. For example, if the
decision maker assigns equal weights to both objective functions,
Pareto optimal solution 11 will be selected as the most compromise
solution among all due to its highest total membership value ob-
tained as 0.706. The cost membership of this Pareto solution is
0.756 and the emission membership is 0.656. On the other hand, if
the decision maker wants to more minimize the cost rather than
the emission, for example the weighting factors for cost and
emission are 2 and 1, respectively. Under such conditions, the total
membership will be 0.765 while Pareto solution 15 will be selected
as the most compromise solution. The cost membership of Pareto
solution 15 is equal to 0.932 while the emission membership is
0.432. Fig. 7 and Fig. 8 include the detailed information on Pareto
optimal solutions 11 and 15, respectively.
As it can be seen in Fig. 8 for Pareto solution 15, during the hours
1 to 9, the major part of the system load is supplied by the utility
grid through the Point of Common Connection (PCC), because
during this period, the bids of the utility grid are lower than other
generating units. Between hours 10 to 16, DG sources generate
more based on their bids and emission, as the system load in-
creases. The MG exports energy to the utility grid during these
hours to get more revenue and lower the net emission. Over the
other hours of scheduling, the energy is imported from the utility
grid due to its decreasing price. The results obtained for Pareto
solution 11 has the same trend as Pareto solution 15 with a little
difference in the power generation by MT and PV which is more
compared to Pareto solution 15. For example, WT generates during
hours 17e20 and 22e23 and PV generates power in hour 12 in the
Pareto solution 11 while in the same time, the power generated by
WT and PV are zero in Pareto solution 15.
The detailed data for Pareto solution 19 obtained from the
proposed method is included in Fig. 9 while Fig. 10 shows the
detailed data reported by Ref. [17] to show the effectiveness of the
presented solution method. However, comparing the obtained re-
sults with those reported in Ref. [18] is impossible, since the best
solution is not given in this paper. Total cost and total emission of
Pareto solution 19 are 185.150 (Vct) and 511.310 (kg), respectively.
While, total cost and total emission reported by Ref. [17] are
191.042 (Vct) and 721.076 (kg), respectively.
It is obvious that the results obtained from the proposed method
are superior compared to the ones reported in Ref. [17] in the case
of quantity, e.g. the cost derived using NBI method is less than
Ref. [17] by 5.8916 (191.0416e185.150 ¼ 5.8916) (Vct). Further-
more, the emission obtained from the proposed method is 511.310
(kg), which is considerably less than the one reported in Ref. [17].
This case study verifies the efficiency of the proposed method.
5. Conclusion
This paper used NBI method to solve the multi-operation
management problem of a typical MG with RESs. The presented
solution method resulted in a well-distributed set of Pareto optimal
solutions enabling the system operator to take the most desired
operation strategy considering the economic and environmental
considerations. Besides, a fuzzy decision making method has been
used to determine the best Pareto optimal solution. The obtained
results verify the efficiency of the proposed method while less time
is needed to solve the problem. Also, the presented method leads to
better solutions compared to other methods recently used. It is
found that high penetration of RESs in MGs will considerably in-
fluence the MG operation, esp. in the case of emission, while the
operation cost increases.
A. Appendix
A.1. Require data for case 1
The data of the fuel cost, emission and the limits on power
generation are reported in Table A1 [11,18,29,30] and Table A2
[11,18,29,30] includes the B loss coefficients.
A.2. Required data for case 2
Table A3 [17,18] represents the upper and the lower bounds of
DGs' power output, bid coefficients in cents of Euro per kilo-Watt
hour (Vct/kWh) and the emission coefficients of DGs in kg/MWh.
It is noted that an expert prediction model and neural networks
are used to estimate the maximum power outputs of WT and PV for
a day ahead, which is not in the scope of this paper and will be
presented in future works. In addition, Table A4 represents the data
of daily load in a typical MG and also the real-time market energy
prices for the scheduling period [17,18].
Table A1
Thermal unit's data for case 1.
Plant Unit Fuel cost coefficients Emission coefficients PMin PMax
ai bi ci di ei fi
1 G1 0.15274 38.53973 756.79886 0.00419 0.32767 13.85932 10 125
G2 0.10578 46.15916 451.32513 0.00419 0.32767 13.85932 10 150
G3 0.02803 40.39655 1049.32513 0.00683 À0.54551 40.2669 40 250
2 G4 0.03546 38.30553 1243.5311 0.00683 À0.54551 40.2669 35 210
G5 0.02111 36.32782 1658.5696 0.00461 À0.51116 42.89553 130 325
3 G6 0.01799 38.27041 1356.65920 0.00461 À0.51116 42.89553 125 315
M. Izadbakhsh et al. / Renewable Energy 75 (2015) 598e606 605

9. References
[1] Niknam T, Golestaneh F, Malekpour A. Probabilistic energy and operation
management of a microgrid containing wind/photovoltaic/fuel cell generation
and energy storage devices based on point estimate method and self-adaptive
gravitational search algorithm. Energy 2012;43:427e37.
[2] Benatiallah A, Kadi L, Dakyo B. Modeling and optimization of wind energy
systems. Jordan J Mech Ind Eng 2010;4(1):143e50.
[3] Kusiak A, Verma A, Wei X. Wind turbine frontier from SCADA. Wind Syst Mag
2012;3(9):36e9.
[4] Dali M, Belhadj J, Roboam X. Hybrid solar wind system with battery storage
operating in grid-connected and standalone mode: control and energy man-
agement e experimental investigation. Energy 2010;35(6):2587e95.
[5] Norouzi MR, Ahmadi A, Esmaeel Nezhad A, Ghaedi A. Mixed integer pro-
gramming of multi-objective security-constrained hydro/thermal unit
commitment. Renew Sust Energy Rev 2014;29:911e23.
[6] Ahmadi A, Aghaei J, Shayanfar HA, Rabiee A. Mixed integer programming of
multi-objective hydro-thermal self-scheduling. Appl Soft Comp 2012;12(8):
2137e46.
[7] Zhao B, Zhang X, Li P, Wang K, Xue M, Wang C. Optimal sizing, operating
strategy and operational experience of a stand-alone microgrid on Dong-
fushan Island. Appl Energy 2014;113:1656e66.
[8] Hemmati M, Amjady N, Ehsan M. System modeling and optimization for
islanded micro-grid using multi-cross learning-based chaotic differential
evolution algorithm. Int J Electr Power Energy Syst 2014;56:349e60.
[9] Shi L, Luo Y, Tu GY. Bidding strategy of microgrid with consideration of un-
certainty for participating in power market. Int J Electr Power Energy Syst
2014;59:1e13.
[10] Zhang L, Gari N, Hmurcik LV. Energy management in a microgrid with
distributed energy resources. Energy Convers Manage 2014;78:297e305.
[11] Motevasel M, Seifi AR. Expert energy management of a micro-grid considering
wind energy uncertainty. Energy Convers Manage 2014;83:58e72.
[12] Motevasel M, Seifi AR, Niknam T. Multi-objective energy management of CHP
(combined heat and power)-based micro-grid. Energy 2013;51:123e36.
[13] Chaouachi A, Kamel RM, Andoulsi R, Nagasaka K. Multiobjective intelligent
energy management for a microgrid. IEEE Trans Ind Elect 2013;60(4):
1688e99.
[14] Aghaei J, Alizadeh MI. Multi-objective self-scheduling of CHP (combined heat
and power)-based microgrids considering demand response programs and
ESSs (energy storage systems). Energy 2013;55:1044e54.
[15] Niknam T, Abarghooee RA, Narimani MR. An efficient scenario-based sto-
chastic programming framework for multi-objective optimal micro-grid
operation. Appl Energy 2012;99:455e70.
[16] Buayai K, Ongsakul W, Mithulananthan N. Multi-objective micro-grid plan-
ning by NSGA-II in primary distribution system. Euro Trans Electr Power
2012;22:170e87.
[17] Moghaddam AA, Seifi A, Niknam T. Multi-operation management of a typical
micro-grids using Particle Swarm Optimization: a comparative study. Renew
Sust Energy Rev 2012;16:1268e81.
[18] Moghaddam AA, Seifi A, Niknam T, Pahlavani MRA. Multi-objective operation
management of a renewable MG (micro-grid) with back-up micro-turbine/
fuel cell/battery hybrid power source. Energy 2011;36:6490e507.
[19] Kusiak A, Wei X. A data-driven model for maximization of methane produc-
tion in a wastewater treatment plant. Water Sci Technol 2012;65(6):1116e22.
[20] Vahidinasab V, Jadid S. Normal boundary intersection method for suppliers'
strategic bidding in electricity markets: an environmental/economic
approach. Energy Convers Manage 2010;51(6):1111e9.
[21] Liang H, Zhuang W. Stochastic modeling and optimization in a microgrid: a
survey. Energies 2014;7:2027e50.
[22] Noruzi MR, Ahmadi A. Sharaf AM, Esmaeel Nezhad A. Short-term environ-
mental/economic hydrothermal scheduling. Electr Power Syst Res 2014;116:
117e27.
[23] Ahmadi A, Ahmadi MR. Comment on “Multi-objective optimization for com-
bined heat and power economic dispatch with power transmission loss and
emission reduction” Shi B, Yan LX, Wu W. Energy 2013;56:226e34. Energy
2014; 64: 1-2.
[24] Ahmadi A, Ahmadi MR, Esmaeel Nezhad A. Short term combined heat and
power economic/emission dispatch using lexicographic optimization and
augmented ε-constraint technique. Electr Power Comp Syst 2014;42(9):
945e58.
[25] Mavalizadeh H, Ahmadi A. Hybrid expansion planning considering security
and emission by augmented epsilon-constraint method. Electr Power Energy
Syst 2014;61:90e100.
[26] Das I, Dennis JE. Normal boundary intersection: a new method for generating
the Pareto surface in nonlinear multicriteria optimization problems. SIAM J.
Optim 1998;8:631e57.
[27] Charwand M, Ahmadi A, Heidari AR, Esmaeel-Nezhad A. Benders decompo-
sition and normal boundary intersection method for multiobjective decision
making framework for an electricity retailer in energy markets. IEEE Syst J
2014;99:1e10.
[28] Generalized algebraic modelling systems (GAMS). http://www.gams.com.
[29] Palanichamy C, Babu NS. Analytical solution for combined economic and
emissions dispatch. Electr Power Syst Res 2008;78(7):1129e39.
[30] Palanichamy C, Srikrishna K. Economic thermal power dispatch with emission
constraint. J Indian Inst Eng India 1991;72:11.
[31] Jiejin C, Xiaoqian M, Qiong L, Lixiang L, Haipeng P. A multi-objective chaotic
particle swarm optimization for environmental/economic dispatch. Energy
Convers Manage 2009;50(5):1318e25.
Table A2
B loss coefficients for case 1.
Bij ¼
2
6
6
4
0:000091 0:000031 0:000029
0:000031 0:000062 0:000028
0:000029 0:000028 0:000072
3
7
7
5
Table A3
DG unit's data for case 2.
Type PMin
(kW)
PMax
(kW)
Bid (Vct/
kWh)
SUC/SDC
(Vct)
CO2 (kg/
MWh)
SO2 (kg/
MWh)
NOx (kg/
MWh)
MT 6 30 0.457 0.96 720 0.0036 0.1
FC 3 30 0.294 1.65 460 0.003 0.0075
PV 0 25 2.584 0 0 0 0
WT 0 15 1.073 0 0 0 0
Bat À30 30 0.38 0 10 0.0002 0.001
Utility À30 30 Table A4 0 0 0 0
Table A4
Forecasted output of WT, PV, load and market price.
Hour Forecasting output (kW) Load (kW) Market price
(VCt/kWh)
PV WT
1 0 1.7855 52 0.23
2 0 1.7855 50 0.19
3 0 1.7855 50 0.14
4 0 1.7855 51 0.12
5 0 1.7855 56 0.12
6 0 0.9142 63 0.20
7 0 1.7855 70 0.23
8 0.1937 1.3017 75 0.38
9 3.754 1.7855 76 2.5
10 7.5279 3.0854 80 4.00
11 10.4412 8.7724 78 4.00
12 11.964 10.4133 74 4.00
13 23.8934 3.9228 72 1.5
14 21.0493 2.3766 72 4.00
15 7.8647 1.7855 76 2.00
16 4.2208 1.3017 80 1.95
17 0.5389 1.7855 85 0.6
18 0 1.7855 88 0.41
19 0 1.3017 90 0.35
20 0 1.7855 87 0.43
21 0 1.3017 78 1.17
22 0 1.3017 71 0.54
23 0 0.9142 65 0.3
24 0 0.6124 56 0.26
M. Izadbakhsh et al. / Renewable Energy 75 (2015) 598e606606