Electric Power Systems Research: Sciencedirect
Electric Power Systems Research: Sciencedirect
Electric Power Systems Research: Sciencedirect
a
Department of Electrical Engineering, Techno India University, Salt Lake, West Bengal, India
b
Department of Electrical Engineering, Kalyani Government Engineering College, Kalyani, West Bengal, India
c
Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India
Keywords: Different types of optimization techniques are being applied in hydrothermal scheduling (HTS) problem for
Cumulative density function optimizing fuel cost, emission and combined cost emission. Usage of fossil fuel for thermal power generation
Short-term hydrothermal scheduling increases global warming and environment pollution. In this work, environment friendly, clean energy such as
Sine cosine algorithm wind energy, has been integrated with the HTS problem to overcome the effect of thermal pollution and to
Weibull probability density function
reduce generation cost. A novel sine cosine algorithm (SCA) has been implemented to minimize generation cost
Wind energy
and fuel emission. The different control parameters of the SCA have been properly utilized to balance the ex-
ploration and the exploitation phases leading to find out near global optimal solution. To study its performance
and efficiency, SCA has been applied to solve different cases (i.e., economic load scheduling, economic emission
scheduling, combined economic emission scheduling) of HTS and hydrothermal wind scheduling (HTWS) pro-
blems. Furthermore, optimal power flow (OPF) based HTWS is studied for a standard 9-bus system. Results
offered by some newly surfaced algorithms (like teaching learning-based optimization, gravitational search al-
gorithm, real-coded genetic algorithm etc.) have been compared with those offered by the SCA to establish its
effectiveness. Utility of wind energy in scheduling problem has been proposed in this work.
1. Introduction [4,5]. Recently, different criteria of market design is studied and ana-
lysed to achieve maximum profit [6].
In the recent year, major attention has given to efficient renewable Daily scheduled demand is mostly fulfilled by hydrothermal power
energy sources (RESs) such as wind and hydropower for protecting the generation (HTPG). Presently, wind power has been introduced to co-
crisis of conventional energy and global warming of the environment. ordinate with HTPG for satisfying power demand for scheduled periods.
Wind energy draws attention in power generation sector, which helps Coordination of wind with hydrothermal is very effective and profitable
to reduce power generation cost and pollutant emission from fossil for power generation. It is also effective for minimization of emitted
fuels. Most renewable resources for power generation in the world are NOx, SOx, CO, etc. from fossil fuel, by which global warming will be
wind power. Wind, the most appealing RES, has become the subject of controlled. So, clean energies (like wind, hydro, etc.) have a major
widespread concern over the last few decades. Main causes of global contribution to keep emission-free or pollution-free environment.
warming are the emission of NOx, SOx, CO, etc. These are produced Application of soft computing techniques on hydrothermal sche-
from fossil-fuelled generating plants. Power generated from winds duling (HTS) problem is very useful for getting optimal cost and
farms, under various emission reduction schemes across the world, are emission. Literature survey shows that different types of optimization
being utilized in the power sector. In some countries, production of techniques have been applied in HTS domain for presenting minimum
power generation from the wind farms has been started on large scale. emission and cost of fossil fuel for power generation. Over the past
Australian government proposed Carbon Pollution Reduction Scheme years, HTS problems have been solved using various mathematical
[1] by producing a large amount of power from the wind farm. Gen- optimization techniques. Such classical optimization techniques have
eration companies of Hong Kong and China have already proposed their some drawbacks such as they require longer time to yield optimal re-
respective plan of construction of wind farms [2,3]. Wind energy is used sults. Recently, many meta-heuristic algorithms, (for example, differ-
as a locally distributed energy resource for satisfying local load demand ential evolution (DE), evolutionary programming (EP) etc.) are applied
⁎
Corresponding author.
E-mail addresses: koustav2009@gmail.com, koustav.17dp000235@ee.iitism.ac.in (K. Dasgupta).
https://doi.org/10.1016/j.epsr.2019.106018
Received 21 January 2019; Received in revised form 12 July 2019; Accepted 27 August 2019
Available online 14 September 2019
0378-7796/ © 2019 Elsevier B.V. All rights reserved.
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Nomenclature min
VHYn max
, VHYn Minimum and maximum water storage volume of the
nth hydro reservoir, respectively
i, j Phase angle of bus i and j, respectively PWGi, QWGi Real and reactive power generation of the wind gen-
THk , THk , THk , THk , THk Emission coefficients of the kth erator, respectively
thermal unit PDh Load demand at time h
aTHk , bTHk , cTHk , dTHk , eTHk Fuel cost curve coefficients of the kth min
PHYn ,PHYn
max
Minimum and maximum power generation limits for the
thermal unit nth hydro unit, respectively
CH 1n , CH 2n , CH 3n , CH 4n , CH 5n , CH 6n Power generation coefficients PLh Transmission loss at time h
of the nth hydro unit
min
PTHk , PTHk
max
Minimum and maximum power generation limits for the
D ln Water transport delay from the lth reservoir to the nth kth thermal unit, respectively
reservoir PTHkh Power generation of the kth thermal unit at time h
Edir , Z , T Direct cost of wind power Power generation of the nth hydro unit at time h
EOVE, Z , T Overestimated cost of wind power
min
QTG i
, QTGmax
i
Minimum and maximum generation of reactive power
EUNE, Z , T Underestimated cost of wind power of the ith thermal generator, respectively
FC (PTH ) Total fuel cost of the thermal units
min
QHYn , QHYnmax
Minimum and maximum water discharge rate for the
Gij, Bij Conductance and susceptance, respectively, of the (i, j)th nth hydro reservoir, respectively
bus
min
QWG i
max
, QWG i
Minimum and maximum generation of reactive
h, H Number of time intervals i.e., scheduling period power of the ith wind turbine, respectively
IHYnh Inflow rate of the nth reservoir at time m QCmin
i
, QCmax
i
Minimum and maximum reactive power injection to
NT Number of thermal generating units the system by the ith shunt compensator, respectively
NH Number of hydro generating units
QHYnh Water discharge rate of the nth hydro reservoir at time h
PD , QD Real and reactive demand, respectively Run Number of upstream hydro generating plants directly
PTGi, QTGi Real and reactive power generation of the thermal gen- above the nth hydro reservoir
erator, respectively
SHYnh Spillage discharge rate of the nth reservoir at time h
Sh , Sf Shape and scale factor
T Number of interval of scheduled wind power generation
Timin , Timax Higher and lower range of tap setting of transmission SLmax
i
Maximum value of apparent power flow in the ith trans-
mission line
line of the ith transformer, in order
Vel Current wind speed
VHYnh Water storage volume of the nth hydro reservoir at the
Velin , Velout Cut-in and cut-out velocity, in order
beginning of time m
Velr Rated wind velocity
VGmin , VGmax Minimum and maximum voltage, respectively, the
i i
ith generator bus w Wind power
li
Vmin li
, Vmax Minimum and maximum limits of generator voltages of WR Rated wind power of turbine
the ith load bus, respectively z Number of wind power generating units
instead of classical optimization techniques. Different heuristic and wherein pre-mature convergence behaviour of PSO has been overcome
meta-heuristic optimizations have been applied for solving different by this new variant of PSO. Feasibility and effectiveness of this PSO
types of optimization problem. Nazari-Heris et al. [7,8] proposed a variant were explored by solving HTS problem. Consideration of valve-
comprehensive review on heuristic optimization techniques from the point effects and transmission losses in HTS problem make it more
perspective of economic and environmental optimal combined heat and complicated one. Wang et al. (see [18]) have implemented real-coded
power dispatch. Application of different stochastic methods in different quantum-inspired evolutionary algorithm with Cauchy mutation by
areas of power system has been studied in different literatures. utilizing clonal operator and Cauchy mutation.
Mohan et al. [9] have proposed decomposition approach and linear Self-organizing hierarchical PSO technique with time-varying ac-
programming (LP) method to solve HTS problem and they have es- celeration coefficients (SOHPSO-TVAC) was considered for HTS pro-
tablished convergence ability of the algorithm by getting optimal cost. blem by Mandal and Chakraborty (refer [19]), instead of PSO for
Wong [10] has presented simulated annealing (SA) technique, genetic avoiding its premature convergence. In [20], Roy has analysed HTS
algorithm (GA) and a hybrid of SA-GA technique for getting minimum problem with the help of teaching learning based optimization (TLBO)
fuel cost of HTS problem. Sinha et al. [11] have proposed Gaussian and where different nonlinearities like valve-point loading, prohibited op-
Cauchy mutations in EP techniques (known as fast EP) for solving HTS erating zone were considered. In this work, different practical diffi-
problem. The authors of this work have established the capability of EP culties (like cascading nature of hydro reservoirs, water transport delay,
towards finding very nearly global solutions of the objective function etc.) were considered in HTS for presenting more complicated HTS
within some reasonable time. Mandal and Chakraborty [12] have problem. Quasi-oppositional based TLBO (QOTLBO) was applied by
considered two test systems of HTS problem [13] and these were solved Roy et al. in [21] to solve different practical difficulties of HTS problem.
using DE method. Mandal et al. [14] have considered four hydro units Selvakumar has proposed civilized swarm optimization in [22] by
and thee thermal units for solving HTS problem using particle swarm modifying the PSO technique using food-searching strategy. This
optimization (PSO) and proposed its effectiveness by comparing the modified technique was applied to solve different cases of HTS pro-
results with those obtained while using EP and SA technique. Hota et al. blems. Culture belief based multi-objective hybrid DE algorithm was
[15] have proposed improved PSO (IPSO) in HTS problem to present considered by Zhang et al. [23] for solving different cases (like cost,
optimal fuel cost of the considered problem and established promising emission) of HTS problem. The authors of [23] have established that
convergence behaviour and convergence speed. Solution time of IPSO this algorithm is more effective to optimize fuel, emission and other
was found to be better than EP and DE in Ref. [15]. Swain et al. [16] cases of HTS problem in comparison to other techniques. Real-coded
have considered different generating constraints and clonal selection chemical reaction optimization (RCCRO) was implemented in short and
algorithm was applied for getting optimal fuel cost. Effectiveness of this large test systems of HTS problem by Bhattacharjee et al. in [24] where
algorithm was presented by comparing with gradient search, SA, EP, they have presented effectiveness of RCCRO by comparing the results
etc. Improved self-adaptive PSO was proposed by Wang et al. in [17] with different other techniques like PSO, DE, modified DE etc. Nguyen
2
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
et al. [25] considered a short-term fixed-head HTS problem and solved based on two phases which are the exploration phase and the ex-
the same using cuckoo search algorithm (CSA) for getting optimal fuel ploitation phase. These two phases are maintained by sine and cosine
cost. Norouzi et al. [26] have presented effectiveness of the CSA method functions. SCA creates multiple initial random candidate solutions and
by considering different controllable parameters and solved the HTS requires them to fluctuate outwards or towards the best solution using a
problem. Real-coded genetic algorithm (RCGA) helps to determine mathematical model based on sine and cosine functions. Several
better quality convergence results of the objective function. Artificial random and adaptive variables are also integrated to this algorithm to
fish-swarm algorithm (AFSA) is another important optimization tech- emphasize the exploration and the exploitation of the search space in
nique, based on the working behaviour of fish. Fang et al. [27] pro- different milestones of optimization. These two phases of SCA are able
posed the combined form of RCGA and AFSA. The authors of Ref. [27] to find out the near global optimal solution of the objective function.
implemented the same in HTS problem where different operating SCA overcomes different types of problems which are discussed in the
constraints were considered. Short-term economic/environmental HTS literature. SCA is tested in Ref. [48] on mathematical benchmark
was considered by Tian et al. [28] to solve fuel cost, emission and functions to analyse its exploration, exploitation, local optima avoid-
combined fuel-emission using an improved non-dominated sorting ance and convergence behaviour. It overcomes premature convergence
gravitational search algorithm (GSA) (NSGSA) with chaotic mutation behaviour of the multi-objective problems. The results of test functions
(NSGSA-CM). Yuan et al. [29] have proposed enhanced GSA for solving and performance metrics prove that the SCA algorithm is able to ex-
the dynamic nonlinear constrained optimization problem i.e., the daily plore different regions of the search space, avoid local optima, converge
economic dispatching of HTS. Mixed-integer linear programming towards the global optimum and exploit promising regions of the search
(MILP) method was considered by Ahmadi et al. [30] for getting op- space during optimization effectively. Recently, SCA has been used to
timal fuel cost and emission of different cases of HTS problem. Gau- solve different real life problem like, multi-objective engineering design
thamkumar et al. [31] have considered disruption operator in GSA for problems [49], parameter optimization [50], wind speed forecasting
increasing its exploration and exploitation abilities and the modified [51] etc.
technique was named as disruption based GSA (DGSA). It was applied In this work, wind energy is considered with the HTS problem and,
to HTS problem for establishing its better convergence accuracy. Krill thus, a new model of hydrothermal wind scheduling (HTWS) is formed.
herd algorithm was implemented by Roy and Pradhan for solving the This new model consists of RESs which produces clean energy. It re-
HTS problem (refer [32]). Nguyen and Vo [33] have tested effective- duces global warming, environmental pollution. Generation cost and
ness of modified CSA (MCSA) over CSA by producing optimal cost of emission will be reduced as compared to the traditional HTS model.
different test systems of HTS problem. Glotić and Zamuda [34] have Power flow constraints are separately considered, instead of traditional
solved different cases of HTS problem using parallel self-adaptive DE power balance constraints, to solve HTS and HTWS problem. An IEEE 9-
(PSADE) technique. Dubey et al. [35] have considered wind power with bus test system is considered to validate the proposed HTS and HTWS
HTS problem and applied ant lion optimization algorithm on the con- models. The SCA (a recently published novel optimization technique) is
sidered problem to determine optimal fuel. Gil and Araya [36] have considered in this paper to solve different cases of traditional power
established effectiveness and good convergence properties of paralle- balance constraints based HTS, HTWS problems and power flow con-
lized stochastic MILP algorithm by solving HTS problem and showing straints based problems such as economic load scheduling (ELS), eco-
optimal cost with minimum simulation time. Nguyen and Vo [37] have nomic emission scheduling (EES) and CEES. It reduces total generation
considered combined economic emission scheduling (CEES) case of HTS cost and emission of pollutant gases. Performance comparison with
problem and solved the considered case using cuckoo bird inspired existing algorithms in terms of solution optimality, consistency and
algorithm (CBIA). Nazari-Heris et al. [38] have considered valve-point computational time requirement is presented for ELS, EES and CEES
effect, transmission losses in HTS problem and solved the problem to problems. Obtained results, yielded by the proposed SCA technique (in
get optimal fuel cost by improved Mühlenbein mutation based real- terms of total cost and emission), are compared to those obtained by
coded GA. Narang [39] have considered different generating con- other methods available in the recent state-of-the-art literature in-
straints, like ramp rate limit, valve-point loading effect, prohibited zone cluding self-organizing hierarchical PSO technique with time-varying
etc. in HTS problem and solved it using improved predator influenced acceleration coefficients (SOHPSO-TVAC) [19], TLBO [20,21],
civilized swarm optimization technique. Nguyen and Vo [40] have QOTLBO [21], RCCRO [24], RCGA [27], NSGSA-CM [28], non-domi-
determined optimal fuel cost and emission of HTS problem using MCSA. nated sorting PSO (NSPSO) with chaotic mutation (NSPSO-CM) [28],
Zhang et al. [41] have introduced power flow constraints in HTS pro- NSGSA [28], NSPSO [28], MILP [30], GSA [31], DGSA [31], PSADE
blem and presented a small-population based parallel DE algorithm for [34] and CBIA [37] etc.
getting optimal fuel cost of the problem. An improved harmony search The remaining section of the paper is as follows. Power generation
algorithm was proposed to minimize generation cost of thermal power from wind source is described in Section 2. Generation cost of wind
plant by Nazari-Heris et al. in Ref. [42], where the authors have con- power is analysed in Section 3. Proposed SCA is reviewed in Section 4.
sidered valve-point effect in the cost function. Hoseynpour et al. [43] Application of SCA for HTS is furnished in Section 5. In Section 6, re-
considered different linear and nonlinear constraints of HTS problem sults of the considered test cases are presented and analysed. Finally,
and solved the same using dynamic nonlinear programming. Valinejad conclusion of the present work has been drawn in Section 7.
et al. [44] presented DC power flow model while considering wind
power and adopting MILP for optimizing nodal or zonal market price of
2. Wind power generation
electricity. Nazari-Heris et al. [45] considered ε-constraint method for
minimizing cost and emission of the micro grid dispatch problem.
Wind power generation [52] depends upon wind velocity due to
Zhang et al. [46] proposed HTS problem while integrating wind and
variable character of the wind speed. Wind power uncertainty con-
photovoltaic power and obtained optimal fuel and emission cost using
straints are considered for power generation from wind source. Ex-
gradient decent based multi-objective cultural DE. Patwal et al. [47]
pression of Weibull probability density function (pdf) for wind speed is
have considered RESs like solar power generation in pumped storage
expressed in (1).
hydrothermal system for reducing fuel cost of the thermal power gen-
eration. The authors of Ref. [47] have determined optimal fuel cost of Sh 1 Sh
Sh Vel Vel
the problem using time-varying acceleration coefficient PSO with mu- pdf (Vel; Sh; Sf ) = exp
Sf Sf Sf
tation strategies.
Recently, Mirjalili proposed a new population-based algorithm i.e., where Vel > 0, Sh > 0 and Sf > 0 (1)
sine cosine algorithm (SCA) [48] in 2016. This technique is, mainly,
3
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Cumulative density function (cdf) may be expressed in (2) de- Velin, Z S hZ Velout , Z ShZ
EUNE , Z , T = CUNE, Z × (wr , Z wZ ,T )[exp( ( ) ) exp( ( ) )]
pending on pdf of wind speed. Sf Z Sf Z
wr , Z Velin, Z Vel Vel
Sh +( + w Z , T)[exp( ( r , Z ) ShZ) exp( ( 1 ) ShZ )]
Vel vr , Z vin, Z Sf Z Sf Z
(2)
cdf (Vel; Sh; Sf ) = 1 exp Sf
wr , Z Sf Z 1 Vel1 S hZ 1 Velr , Z ShZ
+ { [1 + ( ) ] [1 + ( ) ]}
Velr , Z Velin, Z ShZ Sf Z ShZ S f Z
Generation of wind power (w) depends on wind velocity Vel . The
relation between wind velocity and power is represented by a linear (8)
model, as shown in (3). It is necessary to purchase the power from the wind farm operator to
fulfil the demand. This cost (i.e., the direct cost of wind power) is re-
0 (Vel < Velin or Vel Velout ) presented by (9)
(Vel Velin ) WR
w= (Velin Vel < Velr ) Edir , Z , T = gZ × wZ , T (9)
Velr Velin
WR (Velr Vel < Velout ) (3) where direct cost coefficient of the Zth wind generators is represented
by gZ .
Probability of wind power is considered as 0 and WR . It may be The wind cost function is considered in objective function for sol-
calculated using (4) and (5), respectively, ving HTWS problem. Wind cost function depends on three factors.
Direct wind cost component is the first factor. The second factor de-
Pw (w = 0) = cdf (Velin) + (1 cdf (Velout )) pends upon the wind uncertainty. Wind power is an uncertain resource
Velin
Sh
Velout
Sh which will be available more than scheduled wind power at the Tth
=1 exp + exp interval or less than scheduled wind power at the Tth interval. Excess
Sf Sf
(4) wind power is not utilized for the case of excess generation of wind
power. Penalty cost is considered for excess generation of wind power
Pw (w = WR ) = cdf (Velout ) + (1 cdf (Velr )) from the scheduled wind power. Sometimes, deficiency of wind power
Sh Sh
is observed when generated wind power is less than the scheduled wind
= exp
Velr
+ exp
Velout power. Deficiency of scheduled wind power is made up by the thermal
Sf Sf
(5) reservoir. The third factor is the reservoir cost function which is con-
sidered for deficiency of scheduled wind power. Three factors are
where cdf of the random variable (w ) is represented by integrating (4) considered for the cost of wind power of the Tth time interval. Eqs
and (5) and the same is given in (6). (7)–(9) are considered for the formulation of the cost function of the
wind power. The cost function of wind power generation is shown in
0 (w < 0) (10)
hw T NW
(1 + ) Velin
Sh hvin WR ETot _ wind = (EOVE , Z , t + EUNE , Z , t + Edir , Z , t )
fw (w ) =
[ ]Sh 1 (0 w < WR ) t=1 Z=1 (10)
WR Sf Sf
(1 + hw ) Velin
WR where the number of wind generators are shown by NW .
×exp { [ ]}
Sf
4
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Water storage (VHYnh ) and discharge capacity of the reservoir (QHYnh ) VGmin
i
VGi VGmax
i
i = 1, 2, 3, ....NG (30)
must be within respective minimum and maximum capacity, as laid
down, in order, in (21) and (22). VLmin VLi VLmax i = 1, 2, 3, ....NL (31)
i i
min max
VHYn VHYnh VHYn
Timin Ti Timax i = 1, 2, 3, ....NT (32)
n = 1, 2, …, NH and h = 1, 2, …, H (21)
5
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Table 2
Water discharge rates and thermal schedule obtained by SCA technique pertaining to ELS.
Hour Water discharge of reservoir Thermal power (MW)
3 3 3 3
Qh1 (m ) Qh2 (m ) Qh3 (m ) Qh4 (m ) Ps1 Ps2 Ps3
Fig. 1. Graphical characteristics of water storage volume vs. time period pertaining to ELS.
Table 3
Comparison of results obtained by the proposed SCA pertaining to ELS.
Methods EES
Minimum fuel cost ($) Average fuel cost ($) Maximum fuel cost ($) Simulation time (s) Number of trail runs
4. SCA problem). Mirjalili proposed SCA algorithm in Ref. [48] and success-
fully implemented the same to solve non-smooth objective function
A novel SCA is proposed in the present article for solving the con- based optimization problems.
sidered power system optimization problem (i.e., HTS and HTWS Like other population-based algorithms, the SCA is consisting of two
6
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Table 4
Water discharge rates, thermal and wind schedule obtained by SCA technique pertaining to ELS.
Hour Water discharge of reservoir Thermal power (MW) Wind power (MW)
Qh1(m3) Qh2 (m3) Qh3 (m3) Qh4 (m3) Ps1 Ps2 Ps3 Pw1 Pw2
phases i.e., the exploration phase and the exploitation phase. Two SCiI + z1 × sin(z2 ) × |z 3 PoiI SCiI | , z 4 < 0.5
equations (namely, sine and cosine functions) have been considered to SCiI =
SCiI + z1 × cos(z2 ) × |z 3 PoiI SCiI | , z 4 0.5 (37)
emphasize the two phases involved in the algorithm. These two equa-
tions are expressed as follow:
where z 4 is a random number in [0,1].
This algorithm is termed as SCA for the presence of both the com-
SCiI + 1 = SCiI + z1 × sin(z2) × |z 3 PoiI SCiI | (35)
ponents (i.e., sine and cosine), as represented in (37). Existence of the
sine and the cosine components in the algorithm is mentioned in [48].
SCiI + 1 = SCiI + z1 × cos(z2) × |z 3 PoiI SCiI | (36) The exploration and the exploitation are required to be balanced to find
the promising regions of the search space which may, eventually,
where SCiI is considered for denoting the position of the current solu- guarantee to converge to the global optimum. Eq. (38) is considered to
tion. Current position and dimension of the solution are considered by i change the range of sine and cosine in (35) and (36) for balancing the
and I , respectively. Here, z1, z2, z 3 are the random numbers in [0,1]. phase of exploration and exploitation. In order to balance exploration
PoiI is the position of the dimension point in the ith dimension and the and exploitation, the range of sine and cosine in (35) and (36) are
sign indicates the absolute values. Application of the sine component changed using (38)
is shown in (35) while the same for the cosine component is illustrated
in (36). z1 = k i
k
These two equations are combined and may be expressed by (37) I (38)
7
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Fig. 3. Graphical characteristics of water storage volume vs. time period pertaining to ELS (HTWS).
Table 5
Comparison of results obtained by the proposed SCA pertaining to ELS.
Methods Minimum fuel cost ($) Average fuel cost ($) Maximum fuel cost ($) Simulation time (s)
where the current iteration and the maximum number of iterations are, Furthermore, it may be stated while referring Figs. 6 and 7 of Ref. [46]
represented, respectively, by i and I , k is a constant, z1, z2, z 3 and z 4 that the SCA algorithm explores the search space when the ranges of the
are the main four parameters of the algorithm. Two phases (i.e., the sine and the cosine functions are, in sequence, in (1, 2] and [−2,−1].
exploration and the exploitation) are controlled by the prime parameter
of SCA (i.e. z1). This model has a circular search pattern (as illustrated in 5. Hydro-thermal-wind scheduling using SCA
Ref. [48]). The best solution or the desired destination point is in the
centre of a circle and the search agent is positioned around it. The HTWS has been solved using SCA. Detailed steps of SCA for the
parameter z1 indicates the movement in between the solution and the HTWS problem is described below.
destination regions or outside it. It may be noted that z1 is used to
balance the exploration and the exploitations steps. The parameter z2
indicates how far the movement should be outwards or towards the
• Consider total number of generating limits and other constraints of
the hydro and the thermal generating plants.
destination. The random number z2 lies between 0 and 2 . The effect of
desalination (in defining the distance) is emphasized (Z3 > 1) or
• The water discharge rates of all the committed hydro plants are
randomly set within water discharge limit for (T-1) hours using (39).
deemphasized (Z3 < 1) by giving random weights using the parameter
T MIN MIN MAX
z 3 for the destination. Finally, the parameter z 4 equitably changes be- QHYI = QHYI + rand × (QHYI QHYI )
tween the sine and the cosine components, as presented in (37). I = 1, 2, 3....., NH ; T = 1, 2, 3, ..., H (39)
8
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Table 6
Water discharge rates and thermal schedule obtained by SCA technique pertaining to EES.
Hour Water discharge of reservoir Thermal power (MW)
3 3 3 3
Qh1(m ) Qh2(m ) Qh3(m ) Qh4(m ) Ps1 Ps2 Ps3
T 1 T T
24 I FINAL J J J
QHYI = VHYI VHYI QHYI SHYI + IHYI
Table 7 J =1 J =1 J =1
Comparison of results obtained by the proposed SCA pertaining to EES. UI T
J DKI J DKI
Methods Cost ($) Emission Computational Number of + (QHYK + SHYK ) I = 1, 2, ....., NH
(lb/day) time (s) trail runs K =1 J =1 (40)
Limitation value of water discharge is considered for checking the
SCA [Proposed] 46730.20 15849.43 12.45 15
CBIA [37] – 16,303 96 50 last hour discharge. The complete solution set is abandoned, if any
PSADE [34] 49717 16495.62 26.25 – violation of constraint occurs for water discharge. Above procedure
SOHPSO-TVAC 44432 16803.00 112.56 50 is continued until the constraints are satisfied. The volume of the
[19]
reservoir of all the hydro generators is computed using (23). Water
reservoir volume is checked by considering water volume con-
straints. The population set will be discarded and reinitialized, if any
reservoir volume is not satisfied by inequality constraints. After that,
Water discharges all the hydro generators, for the last hiatus, are
power generation of all the hydro plants (for 24 h with the one-hour
determined by (40) where initial, last volume of the reservoir, dis-
interval) is calculated using (18).After that, the maximum part of
charge of previous hours, water spillage and inflow of 24 h are
remaining demand power is generated by committed thermal and
considered.
wind power generating plants, except slack generator using (41) and
(6), respectively. The slack generator of thermal and wind power
Fig. 5. Graphical characteristics of water storage volume vs. time period pertaining to EES.
9
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Table 8
Water discharge rates, thermal and wind schedule obtained by SCA technique pertaining to EES.
Hour Water discharge of reservoir Thermal power (MW) Wind power (MW)
generating plants generate remaining part of demand power. If violated, then go to Step 4, otherwise go to the next step.
generated power violates the nonlinear generating limit constraints, • The updated position of the particles of the HTWS problem is
then discard that population set and that set is reinitialized using checked whether water discharge rate and thermal power genera-
(41). tion, in sequence, satisfy (22) and (19) or not. If any value is higher
T MIN MIN MAX
than the maximum limit, then that value is set to the maximum
PHI = PHI + rand × (PHI PHI )
limit. Similarly, if any value is lower than the minimum limit, then
I = 1, 2, 3....., NT ; T = 1, 2, 3, ..., H (41) that value is replaced by its minimum limit.
• The water discharge rate of the last interval of all the hydro plants
• The fitness of an initial set of thermal power is evaluated using fit- are evaluated using (40) and the thermal power of the last gen-
erating unit is evaluated. The discharge rate of the last interval of all
ness function (described in (13)).
• Parameters of SCA (z1, z2, z 3 and z 4 ) are initialized. the hydro plant and the thermal power generation of the last unit
• In this step, the boundary condition is checked. If the limit is criterion [53] is satisfied. The maximum number of
consecutive iterations is considered as k = 20. When
10
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Fig. 7. Graphical characteristics of water storage volume vs. time period pertaining to EES (HTWS).
Table 9 power generating units with the same number of hydro and thermal
Comparison of results obtained by the proposed SCA pertaining to EES. generating units of HTS problem. Optimal values of three cases (i.e. ELS,
Methods EES
EES and CEES) of HTS and HTWS problems have been obtained by the
SCA. Different values of k for the SCA algorithm have been chosen for
Cost ($) Emission Computational time(S) determining near global optimal value. Sensitivity of the parameter (k)
(lb/day) for the SCA algorithm has been tabulated in Table 1. Near global op-
SCA with wind 77742.76 8258.24 14.30
timal solution is obtained when the value of k is considered as 2. The
CPLEX(software) with 79821.76 9899.62 114.71 effectiveness of wind plant on the HTS problem has been presented in
wind this work by showing the difference of the results for the two cases (i.e.,
SCA without wind 46730.20 15849.43 12.45 without wind and with wind) of HTS problem. Different linear, non-
linear constraints have been considered for HTS and HTWS problems.
The generating constraints of HTS and HTWS problem are taken from
abs ( fitness at kth iteration - fitness at(K-1)th iteartion
fitness at kth iteration ) 10 6 is achieved, the stop- Refs. [14,52]. Transmission loss is neglected for simplicity. The best
ping criterion of SCA is made. result is presented in this paper out of 15 independent trial runs. The
programming part of the proposed work has been completed using
6. Result analysis MATLAB.
Different cases of HTS and HTWS have been solved using a novel 6.1. Study and result analysis of ELS
algorithm, i.e. SCA. Here, the nonconventional energy sources (i.e.,
wind power generating plant) perform a vital role with the hydro and In this case study, the fuel cost of HTS problem has been minimized
the thermal power plants in fulfilling power demand. Fuel cost and using SCA. Wind power generation cost is also considered with thermal
emissions (like NO2, SO2, CO, etc.) are reduced by considering wind power generation cost for producing the optimum cost of HTWS pro-
power plants with hydro and thermal plants. Four hydro and three blem using SCA technique. Generating constraints are considered from
thermal power generating units are involved in the considered problem. Refs. [14,52] for both the problems. Valve-point effect is considered in
The considered problem has been modified by introducing two wind the objective function for both the problems. Here, transmission losses
11
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Table 10
Water discharge rates, thermal schedule obtained by SCA technique pertaining to CEES.
Hour Water discharge of reservoir Thermal power (MW)
3 3 3 3
Qh1(m ) Qh2(m ) Qh3(m ) Qh4(m ) Ps1 Ps2 Ps3
Fig. 9. Graphical characteristics of water storage volume vs. time period pertaining to CEES.
12
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Table 12
Water discharge rates, thermal and wind schedule obtained by SCA technique pertaining to CEES.
Hour Water discharge of reservoir Thermal power (MW) Wind power (MW)
3 3 3 3
Qh1 (m ) Qh2 (m ) Qh3 (m ) Qh4 (m ) Ps1 Ps2 Ps3 Pw1 Pw2
Fig. 10. Graphical characteristics of water storage volume vs. time period pertaining to CEES (HTWS).
Table 13
Comparison of results obtained by the proposed SCA pertaining to CEES.
Methods Cost ($) Emission (lb/day) Computational time (s)
schedule, as obtained from SCA, are included in Table 4. Graphical HTWS problems shows that fuel cost of HTWS is better than HTS pro-
characteristic of water storage volume versus hour, as obtained using blem.
SCA, is shown in Fig. 3. Optimal generation cost of 37999.28 $ for
HTWS problem, as obtained by using SCA, is expressed in Table 5.
6.2. Study and result analysis of EES
Computational time of the SCA for the solution of the HTWS problem is
14.50 s. CPLEX software is also considered to solve the ELS case of
Emission minimization of fuel is considered as the main objective
HTWS problem. Optimal generation cost (i.e. 39460.59 $), as obtained
function (see (14)) for HTS and HTWS problems using SCA. Hourly
by CPLEX software, is illustrated in Table 5. Convergence behaviour of
plant discharges and thermal schedule of HTS problem, as obtained by
generation cost for HTWS problem, as obtained by using SCA, is pre-
SCA, are illustrated in Table 6. Optimal emission of 15849.43 lb/day for
sented in Fig. 4. Comparison of proposed optimal costs of HTS and
HTS problem, as proposed by SCA technique, is shown in Table 7.
13
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Table 14
Optimal solution of OPF based HTS problem of 9-bus system using SCA pertaining to ELS.
Hour Water discharge of reservoir Generation (p.u.) Generators’ bus voltage (p.u.) Tap changing transformer (p.u.) Reactive power (p.u.)
3 3
Qh1(m ) Qh2(m ) Ph1 Ph2 Ps1 V1 V2 V3 Tc1 Tc2 Qc1 Qc2
1 67020 110130 0.6708 0.7501 1.7550 1.0241 1.0397 1.0460 0.9319 1.0321 0.0396 0.0035
2 77990 131150 0.7508 0.7840 1.7682 1.0780 1.0406 1.0885 0.9541 0.9985 0.0277 0.0384
3 50400 115730 0.5419 0.7649 1.6997 1.0852 0.9314 0.9140 0.9042 0.9364 0.0104 0.0406
4 125770 149680 0.9587 0.8696 0.9267 1.0986 1.0167 1.0652 0.9529 1.0942 0.0216 0.0009
5 54190 66470 0.5664 0.5593 1.7531 1.0785 0.9163 0.9343 0.9154 0.9243 0.0097 0.0150
6 73710 149750 0.7157 0.9464 1.7525 1.0749 0.9983 0.9160 0.9590 0.9365 0.0358 0.0118
7 53380 141380 0.5638 0.9111 2.5808 1.0750 0.9147 1.0122 1.0751 1.0041 0.0235 0.0213
8 83130 146610 0.7860 0.9204 2.5880 1.0384 1.0795 1.0848 0.9326 1.0509 0.0380 0.0050
9 90210 149650 0.8304 0.9151 2.8934 1.0385 1.0658 1.0716 0.9007 1.0398 0.0091 0.0041
10 50930 123740 0.5530 0.8799 3.3417 0.9084 0.9132 1.0783 1.0917 1.0920 0.0283 0.0302
11 58270 85720 0.6240 0.7557 3.4055 0.9536 0.9040 1.0907 1.0422 1.0183 0.0360 0.0168
12 50000 149500 0.5512 0.9951 3.4019 0.9948 1.0031 0.9565 1.0106 0.9791 0.0208 0.0368
13 50640 142100 0.5566 0.9765 3.3904 0.9029 0.9113 1.0738 1.0993 1.0929 0.0312 0.0330
14 84410 143740 0.8357 0.9782 2.5774 1.0796 0.9462 0.9887 0.9201 1.0388 0.0162 0.0373
15 71750 150000 0.7409 0.9859 2.5786 1.0643 1.0211 0.9678 1.0493 0.9560 0.0003 0.0123
16 102730 145760 0.9507 0.9882 2.5772 0.9661 1.0682 0.9496 0.9012 1.0136 0.0412 0.0053
17 92710 149540 0.8916 0.9915 2.5816 1.0980 1.0654 1.0251 0.9757 1.0434 0.0389 0.0282
18 50000 150000 0.5427 1.0000 3.4047 0.9026 1.0598 0.9289 1.0967 1.0848 0.0311 0.0084
19 115560 136740 1.0120 0.9831 2.5804 1.0821 1.0672 0.9130 1.0887 1.0719 0.0096 0.0063
20 91040 149780 0.8787 1.0031 2.5792 1.0674 1.0632 1.0734 0.9227 0.9998 0.0058 0.0362
21 137400 150000 1.0648 1.0346 1.7596 0.9988 1.0633 1.0943 0.9032 0.9685 0.0386 0.0031
22 85180 150000 0.8345 1.0509 1.7595 1.0302 1.0985 1.0749 0.9405 0.9628 0.0426 0.0252
23 83240 150000 0.8223 1.0836 1.7535 1.0939 0.9224 0.9013 0.9280 0.9073 0.0012 0.0460
24 50330 149260 0.5535 1.0891 1.7522 1.0295 1.0231 1.0599 1.0165 0.9132 0.0005 0.0025
Cost($) 18268.57
Emission (lb/Hr.) 11710.00
Computational time (s) 18.63
Table 15
Optimal solution of OPF based HTS problem of 9-bus system using SCA pertaining to EES.
Hour Water discharge of reservoir Generation(p.u.) Generators’ bus voltage(p.u.) Tap changing transformer (p.u.) Reactive power(p.u.)
1 66120 110530 0.6642 0.7515 1.7587 1.0299 1.0926 1.0843 0.9467 0.9767 0.0429 0.0056
2 77520 129520 0.7480 0.7805 1.7919 1.0707 0.9307 0.9472 1.0215 0.9078 0.0247 0.0053
3 50480 116210 0.5428 0.7666 1.6493 0.9694 1.0387 1.0203 0.9319 0.9354 0.0237 0.0410
4 124430 150000 0.9564 0.8694 0.9396 0.9925 1.0004 1.0465 1.0391 1.0918 0.0338 0.0470
5 54130 66590 0.5664 0.5596 1.7184 1.0375 0.9008 0.9480 0.9828 1.0204 0.0268 0.0102
6 74920 149410 0.7244 0.9445 1.7253 0.9403 1.0600 1.0232 0.9282 1.0146 0.0459 0.0194
7 53580 140880 0.5657 0.9089 2.5751 1.0328 0.9586 0.9544 1.0001 0.9695 0.0151 0.0401
8 83310 148240 0.7874 0.9223 2.5868 1.0830 1.0533 0.9936 0.9532 1.0726 0.0488 0.0099
9 90580 149330 0.8327 0.9135 2.8978 0.9814 1.0366 1.0842 0.9101 0.9229 0.0133 0.0336
10 51730 125630 0.5602 0.8843 3.1647 1.0491 1.0792 1.0480 0.9231 1.0780 0.0038 0.0482
11 58600 86340 0.6268 0.7577 3.3071 1.0428 1.0762 1.0934 0.9089 0.9823 0.0177 0.0028
12 50000 150000 0.5512 0.9942 3.3658 1.0848 1.0435 1.0522 0.9489 1.0160 0.0481 0.0323
13 51090 141680 0.5610 0.9741 3.1960 1.0672 1.0708 1.0666 0.9168 0.9865 0.0370 0.0328
14 83590 144730 0.8300 0.9785 2.5681 1.0569 1.0843 1.0900 0.9284 1.0515 0.0254 0.0450
15 72360 149360 0.7459 0.9833 2.5666 0.9898 1.0282 1.0360 0.9039 1.0207 0.0355 0.0151
16 103860 145370 0.9567 0.9858 2.5775 0.9541 1.0059 0.9717 0.9492 0.9511 0.0457 0.0345
17 92510 149350 0.8903 0.9901 2.5849 1.0449 1.0088 1.0972 0.9167 0.9583 0.0463 0.0224
18 50350 150000 0.5464 0.9995 3.2244 1.0939 1.0978 1.0888 0.9051 1.0061 0.0166 0.0316
19 115870 135170 1.0131 0.9790 2.5640 1.0058 1.0224 1.0330 0.9388 1.0438 0.0140 0.0163
20 90870 150000 0.8775 1.0040 2.5840 0.9841 1.0737 1.0567 0.9114 0.9905 0.0132 0.0316
21 135100 149830 1.0595 1.0349 1.7792 0.9439 1.0350 0.9951 1.0033 0.9019 0.0443 0.0107
22 85830 149920 0.8388 1.0513 1.7658 1.0539 0.9759 0.9400 0.9557 1.0615 0.0051 0.0029
23 83020 149380 0.8208 1.0819 1.7083 0.9843 0.9511 1.0606 0.9933 1.0001 0.0207 0.0160
24 50130 149360 0.5517 1.0893 1.7525 1.0509 0.9848 1.0858 0.9742 0.9809 0.0087 0.0265
Cost($) 18550
Emission (lb/Hr.) 10905
Computational time (s) 20.74
Water storage volume of reservoir versus time is expressed graphically to be less than the compared techniques. Wind power generation is
in Fig. 5. Convergence mobility of emission versus iteration is shown in considered in the same problem for fulfilling demand power and re-
Fig. 6. Obtained optimal emission of HTS problem using SCA is com- ducing emission. Wind power reduces not only fuel cost but also the
pared with the latest optimization techniques for the same problem. emission of fuel. Application of wind plant in power generation reduces
Proposed result is compared with SOHPSO-TVAC [19], PSADE [34] and the need of thermal power generation for satisfying load demand. So,
CBIA [37]. Computational time (i.e. 12.45 s) of SCA technique is found the necessity of fuel for thermal power generation is reduced. SCA is
14
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
Table 16
Comparison of statistical results of OPF based HTS problem of 9-bus system.
Methods Cost Emission Combined economic emission
Minimum fuel cost Average fuel cost Maximum fuel cost Minimum emission Average emission Maximum emission Cost ($) Emission (lb/h)
($) ($) ($) (lb/h) (lb/h) (lb/h)
Table 17
Optimal solution of OPF based HTWS problem of 9-bus system using SCA pertaining to ELS.
Hour Water discharge of reservoir Generation(p.u.) Generators’ bus voltage(p.u.) Tap changing transformer (p.u.) Reactive power(p.u.)
3 3
Qh1(m ) Qh2(m ) Ph1 Ph2 Ps1 Pw V1 V2 V3 V4 Tc1 Tc2 Qc1 Qc2
1 0.6708 1.1105 0.6712 0.7532 1.0431 0.7219 1.0065 1.0566 0.9542 0.9499 1.0871 0.9300 0.0112 0.0285
2 0.7774 1.2907 0.7492 0.7791 1.1799 0.6019 0.9950 0.9613 0.9441 1.0131 0.9730 0.9980 0.0427 0.0467
3 0.5026 1.1480 0.5407 0.7630 0.8121 0.8505 1.0705 0.9203 1.0650 0.9575 1.0055 0.9206 0.0107 0.0151
4 1.2529 1.5000 0.9579 0.8713 0.1948 0.7359 0.9717 1.0223 1.0782 1.0708 1.0093 1.0278 0.0014 0.0492
5 0.5373 0.6660 0.5627 0.5609 1.0287 0.6979 1.0412 0.9962 0.9690 1.0313 0.9686 0.9040 0.0105 0.0275
6 0.7468 1.4874 0.7224 0.9457 0.9615 0.7780 1.0609 1.0678 1.0172 0.9975 1.0911 1.0996 0.0260 0.0340
7 0.5357 1.4294 0.5654 0.9145 1.6795 0.8983 1.0040 1.0329 0.9305 0.9051 1.0342 1.0037 0.0121 0.0219
8 0.8417 1.4827 0.7922 0.9231 1.7366 0.8596 1.0327 0.9101 1.0839 1.0383 0.9114 1.0909 0.0193 0.0491
9 0.8979 1.4996 0.8279 0.9149 2.6709 0.2441 1.0795 1.0124 0.9718 1.0096 0.9635 0.9069 0.0246 0.0280
10 0.5119 1.2475 0.5553 0.8828 2.5772 0.6170 1.0022 0.9792 0.9297 0.9276 0.9709 1.0691 0.0294 0.0315
11 0.5783 0.8568 0.6201 0.7549 2.7828 0.5442 1.0417 1.0443 0.9825 0.9371 0.9048 0.9812 0.0433 0.0437
12 0.5000 1.4942 0.5512 0.9943 2.6670 0.7256 1.0464 0.9272 0.9423 1.0625 1.0078 0.9339 0.0351 0.0176
13 0.5093 1.4078 0.5594 0.9732 2.4183 0.8018 1.0660 0.9266 1.0734 1.0204 0.9911 1.0109 0.0177 0.0308
14 0.8403 1.4361 0.8331 0.9779 1.8546 0.7257 1.0376 1.0755 0.9667 1.0737 0.9952 1.0646 0.0447 0.0040
15 0.7178 1.5000 0.7412 0.9861 1.8069 0.7693 1.0794 0.9677 1.0815 0.9126 0.9867 1.0614 0.0016 0.0217
16 1.0399 1.4689 0.9574 0.9900 1.6872 0.8897 1.0299 0.9757 1.0463 1.0840 1.0464 0.9896 0.0253 0.0036
17 0.9119 1.5000 0.8819 0.9915 1.7965 0.8247 1.0024 1.0844 0.9031 1.0918 1.0314 1.0539 0.0119 0.0132
18 0.5000 1.4964 0.5427 0.9992 2.5468 0.7301 0.9014 0.9846 0.9050 1.0375 0.9366 0.9024 0.0014 0.0051
19 1.1612 1.3625 1.0143 0.9812 1.8260 0.7588 0.9207 0.9641 1.0460 0.9732 1.0020 0.9553 0.0289 0.0234
20 0.9151 1.4981 0.8816 1.0026 1.9632 0.6580 0.9210 0.9880 0.9984 1.0458 0.9862 1.0862 0.0242 0.0182
21 1.3724 1.4955 1.0642 1.0337 1.0753 0.7026 1.0211 0.9459 0.9140 1.0034 0.9307 1.0678 0.0049 0.0031
22 0.8485 1.5000 0.8323 1.0511 0.9961 0.7819 1.0148 0.9215 0.9221 0.9032 0.9851 0.9601 0.0136 0.0328
23 0.8290 1.5000 0.8200 1.0837 1.0177 0.6895 1.0031 0.9958 1.0748 1.0626 0.9906 1.0480 0.0192 0.0132
24 0.5015 1.4913 0.5515 1.0889 1.7398 0.0175 1.0197 0.9669 0.9586 1.0364 1.0086 1.0297 0.0107 0.0246
Cost($) 14840.00
Emission (lb/Hr.) 4851.80
Computational time (s) 25
Table 18
Comparison of statistical results of OPF based HTWS problem of 9-bus system.
Methods Cost Emission Combined economic emission
Minimum fuel Average fuel Maximum fuel Minimum emission Average emission Maximum emission Cost ($) Emission (lb/h)
cost ($) cost ($) cost ($) (lb/h) (lb/h) (lb/h)
SCA(with wind) 14840.60 14843.73 14845.51 3711.00 3712.65 3715.56 15766.45 3958.95
SCA(without wind) 18268.57 18271.23 18275.38 10905.74 10907.50 10910.93 18308.79 10996.45
applied in the objective function of emission of fuel for HTWS problem optimal generation schedule.
to produce optimal emission of fuel. Hourly plant discharges, thermal
and wind schedule, as obtained by the SCA pertaining to HTWS pro-
6.3. Study and result analysis of CEES
blem, are given in Table 8. Hourly water storage volume versus time is
shown graphically in Fig. 7. Proposed optimal emission of 8258.24 lb/
In this case study, fuel costs and emissions are given attention for
day, as obtained by using SCA for HTWS problem, is shown in Table 9.
getting optimal combined fuel cost-emission of HTS and HTWS problem
The SCA based convergence characteristic of emission is shown in
using SCA. Water discharge rates, thermal schedule obtained by SCA
Fig. 8. Computational time of SCA (i.e., 14.30 s) for the current study is
technique of the considered problem (i.e., HTS) are shown in Table 10.
less than the other compared techniques (see Table 9). This case is also
Water storage volume versus time is presented graphically in Fig. 9. In
solved using CPLEX software for getting global optimal emission of
Table 11, optimal combined generation cost-emission schedule (i.e.,
HTWS problem. Optimal emission (i.e. 9899.62 lb/day), as obtained by
42957.30$ as fuel cost and 16319.850295 lb/day as emission) is
CPLEX software, is illustrated in Table 9. The proposed result (i.e.,
shown. Proposed results of HTS problem is compared with resent op-
optimal emission obtained by SCA for HTWS problem) is compared
timization techniques like NSGSA-CM [28], NSPSO-CM [28], NSGSA
with the same for HTS problem. Proposed results for the considered
[28], NSPSO [28], CBIA [37] and SOHPSO-TVAC [19]. Obtained results
case of HTWS problem are better than that of HTS problem. These re-
of optimal combined fuel-emission are also compared with MILP [30]
sults reveal that the proposed method is very effective in reaching
and PSADE [34]. Comparison of cost and emission of the combined
15
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
cost-emission result obtained by SCA and MILP [30] shows the SCA the said algorithm are compared with serial DE [41] to establish its
offers better result than MILP [30]. SCA reduces the fuel cost of CEES effectiveness. Proper utilization of wind energy in power generation is
problem from MILP by 544.596$. The presented result shows that the shown by comparing the results of OPF based HTWS problem with the
SCA has helped to reduce the emission of 1661.549705 lb/day from results of OPF based HTS problem (see Table 18).
PSADE [34]. The computation time of SCA is found to be 13.16 s (refer
Table 11). Effectiveness of wind plant for power generation along with 7. Conclusion
the hydro and the thermal plants is shown by obtaining the optimal
combined fuel-emission cost of the proposed problem (i.e., HTWS using The basic purpose of this paper is to present and demonstrate the
the SCA). Hourly water discharges, thermal and wind schedule, as ob- effectiveness and robustness of the proposed SCA for solving different
tained by using the SCA, are given in Table 12. Hourly water storage cases of both HTS and HTWS problems of power systems. This paper
volume versus time is presented graphically in Fig. 10. Optimal com- proposes the nonconventional energy source (such as wind energy)
bined cost-emission (i.e., 38877.1685$ as fuel cost and with HTS problem. The stochastic behaviour of wind speed is modelled
10897.626856 lb/day as emission), as obtained by using the SCA) is by Weibull distribution. The significant outcomes of the present work
shown in Table 13. Computational time of SCA for the solution of the are outlined in the following aspects:
problem is 14.30 s. CPLEX software is introduced to solve the CEES case
of HTWS problem. Optimal emission (i.e., 39820.6654$ as fuel cost and (a) The wind energy (being environment friendly and clean in nature)
11284.7366 lb/day as emission), as obtained by CPLEX software, is il- has been integrated with the traditional HTS problem to overcome
lustrated in Table 13. Proposed optimal combined fuel-emission ob- the impact of thermal pollution and to reduce generation cost.
tained by SCA is compared with the result of HTS problem. Obtained (b) A recently surfaced SCA has been properly realized to minimize
results help to infer that the considered case of HTWS problem offer generation cost and fuel emission.
better convergence ability than the other techniques. (c) Control parameters of the SCA have been properly activated to
balance the exploration and the exploitation phases leading to ob-
6.4. Result analysis of OPF based HTS and HTWS problem tain near global optimal solution.
(d) The proposed SCA has been effectively employed to solve different
In order to consider the AC power flow power flow constraint, IEEE ELS, EES and CEES problems of HTS and HTWS.
9-bus test system has been considered for solution of OPF based HTS (e) The SCA based obtained results are compared with those offered by
and HTWS problems. Here, two hydro units and one thermal unit have a range of well-established algorithms (like, SOHPSO-TVAC, TLBO,
been taken for hydro thermal generation. Moreover one wind power QOTLBO, RCCRO, RCGA etc) to project the optimizing efficacy of
generation unit has been considered with hydro-thermal generation for the proposed SCA for this power system optimization application.
hydro-thermal-wind generation. This test system consists of nine buses, (f) Effectiveness of wind energy for OPF based HTS scheduling pro-
nine branches, two reactive power compensators, two transformers and blem has been anticipated in this work.
three generators for the problem of HTS (i.e. two hydro and one thermal
unit) and four generators for the problem of HTWS (i.e. two hydro, one Conflict of interests
thermal and one wind power generating unit). Bus data, line data and
fuel cost coefficients of generators are taken from Ref. [54]. The p.u. The authors declare that they have no known competing financial
value of load buses and generator buses are considered within interests or personal relationships that could have appeared to influ-
0.9–1.1 p.u. Range of reactive power injection is 0–0.05 p.u. The per- ence the work reported in this paper.
missible ranges of transformer taps are taken from 0.9 p.u. to 1.1 p.u.
In this work, both single objective function (i.e. fuel cost and References
emission minimization) and multi-objective function (i.e. combined fuel
cost and emission minimization) are considered to solve the OPF based [1] Australian Energy Market Operator (AEMO) website, http://www.aemo.com.au.
HTS and HTWS problems. SCA algorithm has been applied to determine (Accessed 14 February 2018).
[2] Hong Kong Electric website, http://hec.com.hk. (Accessed 14 February 2018).
near global optimal solution of fuel, emission and combined fuel- [3] China Light and Power Group website, http://www.clp.com.hk. (Accessed 14
emission function. Optimal solution of generation cost of OPF based February 2018).
HTS problem of 9-bus system using SCA is shown in Table 14. The [4] M. Javadi, M. Marzband, M.F. Akorede, R. Godina, A.S. Al-Sumaiti, E. Pouresmaeil,
A centralized smart decision-making hierarchical interactive architecture for mul-
optimal generation cost of 18268.57 $/day, as obtained by using SCA tiple home microgrids in retail electricity market, Energy 11 (2018) 3144.
for HTS problem, is shown in Table 14. The simulation results of [5] M. Marzband, F. Azarinejadian, M. Savaghebi, E. Pouresmaeil, J.M. Guerrero,
emission of OPF based HTS problem using SCA is illustrated in G. Lightbody, Smart transactive energy framework in grid-connected multiple home
microgrids under independent and coalition operations, Renew. Energy 126 (2018)
Table 15. Emission of 10905 lb/day for OPF based HTS problem is
95–106.
achieved by SCA technique. Detailed results of combined cost-emission [6] J. Valinejad, T. Barforoshi, M. Marzband, E. Pouresmaeil, R. Godina, J.P.S. Catalão,
of OPF based HTS problem is not given in the manuscript for space Investment incentives in competitive electricity markets, Appl. Sci. 8 (10) (2018)
1978.
limitation. Optimal cost and emission of 18308.79 $/day and
[7] M. Nazari-Heris, B. Mohammadi-Ivatloo, G.B. Gharehpetian, Short-term scheduling
10996.45 lb/day for multi-objective optimization as achieved by SCA, of hydro-based power plants considering application of heuristic algorithms: a
are shown in Table 16. Comparison of statistical results of cost, emis- comprehensive review, Renew. Sustain. Energy Rev. 74 (2017) 116–129.
sion and combined cost-emission of OPF based HTS problem of 9-bus [8] M. Nazari-Heris, B. Mohammadi-Ivatloo, G.B. Gharehpetian, A comprehensive re-
view of heuristic optimization algorithms for optimal combined heat and power
system are also listed in Table 16. Effectiveness of wind plant for power dispatch from economic and environmental perspectives, Renew. Sust. Energy Rev.
generation along with the hydro and the thermal plants is examined by 81 (2018) 2128–2143.
solving OPF based HTWS problem. It is observed from Table 17 that [9] M.R. Mohan, K. Kuppusamy, A.M. Khan, Optimal short-term hydrothermal sche-
duling using decomposition approach and linear programming method, Int. J.
optimal generation cost of 14840.00 $ is achieved by the proposed Electr. Power Energy Syst. 14 (1) (1992) 39–44.
approach. Detailed results of emission and combined cost-emission are [10] S.Y.W. Wong, Hybrid simulated annealing/genetic algorithm approach to short-
not shown in the manuscript for space limitation. The optimal emission term hydro-thermal scheduling with multiple thermal plants, Int. J. Electr. Power
Energy Syst. 23 (7) (2001) 565–575.
of 3711.00 lb/day achieved, as obtained by SCA, is shown Table 18. [11] N. Sinha, R. Chakrabarti, P.K. Chattopadhyay, Fast evolutionary programming
The optimal cost and emission of 15766.45 $/day, 3958.95 lb/day for techniques for short-term hydrothermal scheduling, Electr. Power Syst. Res. 66 (2)
combined cost-emission objective, as obtained by SCA, are shown in (2003) 97–103.
[12] K.K. Mandal, N. Chakraborty, Differential evolution technique-based short-term
Table 18. To judge the superiority of the proposed SCA approach, ob- economic generation scheduling of hydrothermal systems, Electr. Power Syst. Res.
tained results of different cases, i.e. ELS, EES, CEES, OPF based HTS by
16
K. Dasgupta, et al. Electric Power Systems Research 178 (2020) 106018
78 (11) (2008) 1972–1979. [34] A. Glotić, A. Zamuda, Short-term combined economic and emission hydrothermal
[13] G.L. Decker, A.D. Brooks, Valve point loading of turbines, Electr. Eng. 77 (6) (1958) optimization by surrogate differential evolution, Appl. Energy 141 (2015) 2–56.
481–484. [35] H.M. Dubey, M. Pandit, B.K. Panigrahi, Ant lion optimization for short-term wind
[14] K.K. Mandal, M. Basu, N. Chakraborty, Particle swarm optimization technique integrated hydrothermal power generation scheduling, Int. J. Electr. Power Energy
based short-term hydrothermal scheduling, Appl. Soft Comput. 8 (4) (2008) Syst. 83 (2016) 158–174.
1392–1399. [36] E. Gil, J. Araya, Short-term hydrothermal generation scheduling using a parallelized
[15] P.K. Hota, A.K. Barisal, R. Chakrabarti, An improved PSO technique for short-term stochastic mixed-integer linear programming algorithm, Energy Procedia 87 (2016)
optimal hydrothermal scheduling, Electr. Power Syst. Res. 79 (7) (2009) 77–84.
1047–1053. [37] T.T. Nguyen, D.N. Vo, An efficient cuckoo bird inspired meta-heuristic algorithm for
[16] R.K. Swain, A.K. Barisal, P.K. Hota, R. Chakrabarti, Short-term hydrothermal short-term combined economic emission hydrothermal scheduling, Ain Shams Eng.
scheduling using clonal selection algorithm, Int. J. Electr. Power Energy Syst. 33 (3) J. 9 (4) (2018) 483–497.
(2011) 647–656. [38] M. Nazari-Heris, B. Mohammadi-Ivatloo, A. Haghrah, Optimal short-term genera-
[17] Y. Wang, J. Zhou, C. Zhou, Y. Wang, H. Qin, Y. Lu, An improved self-adaptive PSO tion scheduling of hydrothermal systems by implementation of real-coded genetic
technique for short-term hydrothermal scheduling, Expert Syst. Appl. 39 (3) (2012) algorithm based on improved Mühlenbein mutation, Energy 128 (2017) 77–85.
2288–2295. [39] N. Narang, Short-term hydrothermal generation scheduling using improved pre-
[18] Y. Wang, J. Zhou, L. Mo, S. Ouyang, Y. Zhang, A clonal real-coded quantum-in- dator influenced civilized swarm optimization technique, Appl. Soft Comput. 58
spired evolutionary algorithm with Cauchy mutation for short-term hydrothermal (2017) 207–224.
generation scheduling, Int. J. Electr. Power Energy Syst. 43 (1) (2012) 1228–1240. [40] T.T. Nguyen, D.N. Vo, Modified cuckoo search algorithm for multiobjective short-
[19] K.K. Mandal, N. Chakraborty, Daily combined economic emission scheduling of term hydrothermal scheduling, Swarm Evol. Comput. 37 (2017) 73–89.
hydrothermal systems with cascaded reservoirs using self-organizing hierarchical [41] J. Zhang, S. Lin, H. Liu, Y. Chen, M. Zhu, Y. Xu, A small-population based parallel
particle swarm optimization technique, Expert Syst. Appl. 39 (2012) 3438–3445. differential evolution algorithm for short-term hydrothermal scheduling problem
[20] P.K. Roy, Teaching learning based optimization for short-term hydrothermal considering power flow constraints, Energy 123 (2017) 538–554.
scheduling problem considering valve point effect and prohibited discharge con- [42] M. Nazari-Heris, A.F. Babaei, B. Mohammadi-Ivatloo, S. Asadi, Improved harmony
straint, Int. J. Electr. Power Energy Syst. 53 (2013) 10–19. search algorithm for the solution of non-linear non-convex short-term hydrothermal
[21] P.K. Roy, A. Sur, D.K. Pradhan, Optimal short-term hydro-thermal scheduling using scheduling, Energy 151 (2018) 226–237.
quasi-oppositional teaching learning based optimization, Eng. Appl. Artif. Intell. 26 [43] O. Hoseynpour, B. Mohammadi-ivatloo, M. Nazari-Heris, S. Asadi, Application of
(10) (2013) 2516–2524. dynamic non-linear programming technique to non-convex short-term hydro-
[22] A.I. Selvakumar, Civilized swarm optimization for multiobjective short-term hy- thermal scheduling problem, Energies 10 (9) (2017) 1440.
drothermal scheduling, Int. J. Electr. Power Energy Syst. 51 (2013) 178–189. [44] J. Valinejad, M. Marzband, M.F. Akorede, I.D. Elliott, Long-term decision on wind
[23] H. Zhang, J. Zhou, Y. Zhang, Y. Lu, Y. Wang, Culture belief based multi-objective investment with considering different load ranges of power plant for sustainable
hybrid differential evolutionary algorithm in short term hydrothermal scheduling, electricity energy market, Sustainability 10 (2018) 3811.
Energy Convers. Manage. 65 (2013) 173–184. [45] M. Nazari-Heris, S. Abapour, B. Mohammadi-Ivatloo, Optimal economic dispatch of
[24] K. Bhattacharjee, A. Bhattacharya, S. Halder nee Dey, Real coded chemical reaction FC-CHP based heat and power micro-grids, Appl. Therm. Eng. 114 (2017) 756–769.
based optimization for short-term hydrothermal scheduling, Appl. Soft Comput. 24 [46] H. Zhang, D. Yue, X. Xie, C. Dou, F. Sun, Gradient decent based multi-objective
(2014) 962–976. cultural differential evolution for short-term hydrothermal optimal scheduling of
[25] T.T. Nguyen, D.N. Vo, A.V. Truong, Cuckoo search algorithm for short-term hy- economic emission with integrating wind power and photovoltaic power, Energy
drothermal scheduling, Appl. Energy 132 (2014) 276–287. 122 (2017) 748–766.
[26] M.R. Norouzi, A. Ahmadi, A.M. Sharaf, A.E. Nezhad, Short-term environmental/ [47] R.S. Patwal, N. Narang, H. Garg, A novel TVAC-PSO based mutation strategies al-
economic hydrothermal scheduling, Electr. Power Syst. Res. 116 (2014) 117–127. gorithm for generation scheduling of pumped storage hydrothermal system in-
[27] N. Fang, J. Zhou, R. Zhang, Y. Liu, Y. Zhang, A hybrid of real coded genetic algo- corporating solar units, Energy 142 (2018) 822–837.
rithm and artificial fish swarm algorithm for short-term optimal hydrothermal [48] S. Mirjalili, SCA: a sine cosine algorithm for solving optimization problems, Knowl.
scheduling, Int. J. Electr. Power Energy Syst. 62 (2014) 617–629. Based Syst. 96 (2016) 120–133.
[28] H. Tian, X. Yuan, B. Ji, Z. Chen, Multi-objective optimization of short-term hy- [49] M.A. Tawhid, V. Savsani, Multi-objective sine-cosine algorithm (MO-SCA) for multi-
drothermal scheduling using non-dominated sorting gravitational search algorithm objective engineering design problems, Neural Comput. Appl. 31 (S-2) (2019)
with chaotic mutation, Energy Convers. Manage. 81 (2014) 504–519. 915–929.
[29] X. Yuan, B. Ji, Z. Chen, Z. Chen, A novel approach for economic dispatch of hy- [50] S. Li, H. Fang, X. Liu, Parameter optimization of support vector regression based on
drothermal system via gravitational search algorithm, Appl. Math. Comput. 247 sine cosine algorithm, Expert Syst. Appl. 91 (C) (2018) 63–77.
(2014) 535–546. [51] J. Wang, W. Yang, P. Du, T. Niu, A novel hybrid forecasting system of wind speed
[30] A. Ahmadi, A. Kaymanesh, P. Siano, M. Janghorbani, A.E. Nezhad, D. Sarno, based on a newly developed multi-objective sine cosine algorithm, Energy Convers.
Evaluating the effectiveness of normal boundary intersection method for short-term Manage. 163 (2018) 134–150.
environmental/economic hydrothermal self-scheduling, Electr. Power Syst. Res. [52] F. Yao, Z.Y. Dong, K. Meng, Z. Xu, H.H. Iu, K.P. Wong, Quantum-inspired particle
123 (2015) 192–204. swarm optimization for power system operations considering wind power un-
[31] N. Gouthamkumar, V. Sharma, R. Naresh, Disruption based gravitational search certainty and carbon tax in Australia, IEEE Trans. Ind. Inf. 8 (4) (2012) 880–888.
algorithm for short term hydrothermal scheduling, Expert Syst. Appl. 42 (20) [53] A.I. Selvakumar, K. Thanushkodi, A new particle swarm optimization solution to
(2015) 7000–7011. nonconvex economic dispatch problems, IEEE Trans. Power Syst. 22 (2007) 42–51.
[32] P.K. Roy, M. Pradhan, T. Paul, Krill herd algorithm applied to short-term hydro- [54] J. Zhang, S. Lin, X. Zeng, Q. Tang, Short-term optimal hydrothermal scheduling
thermal scheduling problem, Ain Shams Eng. J. 9 (1) (2018) 31–43. problem considering power flow constraint, IEEE Congress on Evolutionary
[33] T.T. Nguyen, D.N. Vo, Modified cuckoo search algorithm for short-term hydro- Computation (CEC) (2015).
thermal scheduling, Int. J. Electr. Power Energy Syst. 65 (2015) 271–281.
17