Three powerful nature-inspired algorithms to optimize power flow in Algeria's Adrar power system

Energy 116 (2016) 1117e1130

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Three powerful nature-inspired algorithms to optimize power flow in Algeria's Adrar power system Saida Makhloufi a, b, *, Abdelouahab Mekhaldi a, Madjid Teguar a a b

Laboratoire de Recherche en Electrotechnique, Ecole Nationale Polytechnique, 10 Avenue Hassen Badi, B.P. 182, El-Harrach, 16200, Algiers, Algeria Centre de D
eveloppement des Energies Renouvelables, BP. 62, Route de l'ObservatoireBouzareah, 16340, Algiers, Algeria

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 March 2015 Received in revised form 15 June 2016 Accepted 19 October 2016

This paper is intended to solve the optimal power flow (OPF) dispatch in the presence of wind power generation (WPG) in the Adrar power system. Towards this aim, the performances of three powerful meta-heuristic algorithms-namely, the cuckoo search algorithm (CSA), firefly algorithm (FFA), and flower pollination algorithm (FPA) are investigated. The proposed algorithms are applied to best capture the active power produced with the minimum value of a multi-objective function. This latter includes: the fuel cost, the NOx emissions, and the imbalance cost of the WPGs. Furthermore, considering the uncertainties governing wind resources, the maximum wind power output is estimated using the wind speed carrying maximum energy. It was found that all algorithms perform well in providing accurate solutions. Interestingly, the convergence is reached in the first 135 iterations. A remarkable outcome of the present work is that CSA outperforms FPA and FFA. CSA has proved itself to be a great tool to optimize Adrar's power flow system in term of iterations and computational time. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Optimal power flow Cuckoo search Firefly Flower pollination Wind speed carrying maximum energy

1. Introduction Due to the uncertainties related to wind speed prediction, the integration of wind power generation (WPG) into the grid on a large scale is not always considered as the best investment. Unlike traditional forms of electricity generation, energy from wind power sources is intermittent by nature; this brings new challenges for both planners and operators of power systems. WPG cannot be predicted and is, therefore, non-dispatchable, whereas power from traditional generations is instantly dispatchable. In the absence of careful planning, capacity reserves may decrease and threaten power system reliability. A review on the reliability assessment of WPG has been presented in Ref. [1]. Ref. [2] proposes a model to study the impacts of intermittent renewable-energy sources on electrical systems. The impact of WPG is particularly significant for a small isolated power system that requires knowledge of the constraints and the corrective measures to preserve system reliability. In this context, and in order to achieve an increased capacity

* Corresponding author. Laboratoire de Recherche en Electrotechnique, Ecole Nationale Polytechnique, 10 Avenue Hassen Badi, B.P. 182, El-Harrach 16200, Algiers, Algeria. E-mail addresses: s.makhloufi@cder.dz (S. Makhloufi), abdelouahab.mekhaldi@ g.enp.edu.dz (A. Mekhaldi), [email protected] (M. Teguar). http://dx.doi.org/10.1016/j.energy.2016.10.064 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

utilization of WPG, the planners and operators of power systems must establish, in advance, the volume of energy generated from both conventional and renewable sources, by optimizing power flow problems. Optimal power flow (OPF) problems could be challenging to be solved by means of conventional methods. Momoh et al. presented a review of literature on OPF application using nonlinear and quadratic programming [3]. The same authors [4] offered an additional review on OPF treated by Newton-based, linear programming and interior point methods. Due to a large number of constraints and the nonlinear, non-convex optimization problem, these methods often cannot guarantee obtaining the global minima. Moreover, their performance depends on the initial points and sometimes requires large computation times. In this respect and in order to overcome the limitations of the conventional methods, several meta-heuristic algorithms have been applied successfully in recent times. The robustness of such algorithms overcomes the deficiencies of the traditional methods and allows finding the global optimum with shorter computation times. Moreover, due to their simple mathematical models, these methods are easy to apply and among the most efficiently used approaches. Other advantages and disadvantages of the metaheuristic algorithms are carefully examined by Sorensen [5]. The literature shows that several researches have been proposed to deal

1118

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

with OPF and economic dispatch (ED) and carry out emission reduction in the power system-integrated WPG. A novel evolutionary algorithm for dynamic ED with emission reduction and WPGs has been proposed by Liao [6]. Shi et al. [7] proposed a risklimiting OPF with high penetration of WPG. In doing so, the researchers only took the wind power fluctuation into account and did not consider the imbalance cost of the WPG, associated with the uncertainty of wind resources. Panda and Tripathy [8] employed a modified bacteria foraging algorithm for OPF, considering the cost origins from wind power variability and the reactive power capability of DFIG (doubly fed induction generator). Hetzer et al. [9] developed a model including the overestimation and underestimation of available wind power in the ED. The same model is used by Jabr and Pal [10] to solve OPF problem including reactive power model of WPG. Since none of the meta-heuristic algorithms proposed in previous studies is able to provide the best solution for multi-objective optimization problems, new algorithms have been developed and are being improved. Xing and Gao [11] offered a meaningful comparison analysis and synthesis of existing research on applications of the meta-heuristic algorithms. Cuckoo search algorithm (CSA) [12], the firefly algorithm (FFA) [13], and the flower pollination algorithm (FPA) [14] are considered among the more recently presented approaches that have proven their ability and efficiency in solving all kinds of science, engineering, and industrial problems. Such algorithms hold considerable promise and are still undergoing improvement. Liang et al. [15] developed an enhanced FFA to optimize both active and reactive power dispatches while considering load and WPG uncertainties. Younes et al. [16] combined the FFA with a modified genetic algorithm and implemented this to minimize the fuel cost and emissions simultaneously. Basu [17] recommended the CSA approach to tackle convex and nonconvex ED with WPG. In Ref. [18], the CSA has been successfully applied to reduce power loss, enhance voltage profile, and minimize thermal generators cost of distribution network reconfiguration. A high quality solution of short-term hydrothermal scheduling problem, given in Ref. [19], has been achieved by a modified CSA. In Ref. [20], the FPA was implemented to solve a combined economic and emission dispatch problem. Since CSA, FFA, and FPA improve their solutions using random decisions, the required number of iterations for reaching an optimal solution mainly determines the overall computational efforts and the performance of such algorithm. A better algorithm should obtain the optimal solution in a reasonable iterations number with less running time. It is worth noting that in previous Refs. [15e20], performance and computational efficiency are demonstrated considering the standard test power systems. These works did not study a real power system in which finding better solutions, within a practically acceptable timescale, is important for choosing a powerful algorithm. Moreover, for a real power system with several variables, the best solution under several constraints cannot be easily obtained using meta-heuristic algorithms, which are basically iterative approaches, with fewer iterations number. Consequently, the time to achieve a suitable number of iterations is important. In fact, despite the cost of the wind power is very low comparing to the thermal power generation (TPG) one; the uncontrollable nature of wind power introduces an additional managing intermittency cost. The minimization of this cost requires modelling the wind variability. For an isolated power system, which not contain a dispatching centre, the operators must have the power generation schedule in advance; this gives a good vision for an economically and safely future operation. At the same time, due to the intermittent nature and uncertainty of the wind resource, considering the rated power of the wind turbine as its upper bound is not

applicable in the practical power systems. Therefore, the first contribution of this paper is to develop a powerful approach to OPF dispatching applied to a real power system using the FFA, the CSA, and the FPA. This work is intended for implementation in an existing power system in the region of Adrar, located in south-western of Algeria. The main purpose of OPF is to establish the volume of active power generated by the production units, with the minimum value of a multi-objective function involving the fuel cost, the NOx emission, and the cost caused by the uncertainties of the wind resources. The wind power cost is based on the calculation of the overestimation and underestimation costs of available wind energy, using the Weibull distribution function of wind speed and the wind turbine power curve. The second contribution consists in the proposition to use the wind speed carrying maximum energy for computing the maximum power output of WPG at the Adrar's site. Such formulation has never been proposed in the field of OPF problems so far. The rest of this paper is organized as follows. Section 2 presents the mathematical model expressing the typical OPF in the presence of WPG and NOx emission. Section 3 describes the concept of the employed CSA, FFA, and FPA for solving OPF problem. Section 4 performs the efficiency of the solutions obtained by these algorithms and demonstrates their merit considering their computational time and iterations taken to converge as criteria. Finally, Section 5 concludes the paper. 2. OPF formulation with WPG 2.1. Multi-objective function Nowadays, OPF is becoming an important and powerful tool for ensuring better operation and planning of a modern power system. The main purpose of OPF is to establish the volume of active power generated by the production units. This is achieved by minimizing the total operating costs, while facing various equality and inequality constraints [21]. In recent years, with rising interest in environmental issues and large-scale integration of renewable energies, it has become more necessary than ever before to consider them in the OPF. Helpful guides on theoretical and application of OPF considering renewable energies [22] and environmental issues [23] can be found. In this context, a multi-objective (fitness) function that sums up the operating costs of the TPGs and WPGs, and NOx emission targets to formulate an OPF problem is expressed as:

fitness ¼

TPG X i¼1

ðCf þ EmÞi þ

WPG X

  Cost PWPG j

(1)

j¼1

P With: TPG i¼1 ðCf þ EmÞi ¼ ∁i where (Cf þ Em)i: the sum of the fuel cost and the NOx emission of the ith TPG; PWG : the power generj ated by the jth WPG. 2.1.1. Cost of TPG The first term of Eq. (1) represents the total cost of the fuel and the NOx emission, approximated by two quadratic functions of PGi:

∁i ¼ u1

TPG  X i¼1

TPG    X 2 2 ai þ bi PGi þ ci PGi þ u2 h di PGi þ ei PGi þ f i i¼1

(2) where ai, bi, and ci:the constants of the ith TPG fuel cost; di, ei, and fi: the NOx emission coefficients; u1 and u2: the weighting factors; h: the price penalty factor.

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

According to Ref. [24], the price penalty factor hi is given by:

  Cf i PGi;max P   Gi;max hi ¼ Emi PGi;max P Gi;max

(3)

where kp$j: the penalty cost function of not using all available power from the jth wind farm; fW(Pw): the probability density function (PDF) of wind energy output. Similarly, the cost function to cover the under-generation of energy by the jth wind farm and for calling the reserves lr$w$j is given by Ref. [10]:

(4)

  lr$w$j Pwj  Pwj$av ¼ kr$j

The average cost of TPG and NOx emission is given by:

    ai þ bi PGi;max þ ci P2Gi;max Cf i PGi;max ¼ PGi;max PGi;max     2 di PGi; Emi PGi; max max þ ei PGi; max þ f i ¼ PGi; max PGi; max

(5)

1 Sort hi in ascending order. PTPG 2 Calculate the i¼1 PGi; max from the lowest value of PGi to the highest one until:

PGi;max  PD

Pw Z r$j

  Pw  Pwj f w ðPwÞdPw

(9)

0

Considering the total power load (PD) of the power system, the price penalty factor h is calculated following these steps:

TPG X

1119

(6)

i¼1

3 When Eq. (6) is fulfilled, the price penalty factor h corresponds to hi of the ithTPG of the last unit.

where kr$j is the required reserve cost function, relating to uncertainty of wind power. This is effectively a penalty associated with the overestimation of the available wind power. The wind speed distribution function is described by Ref. [25]:

f v ðvÞ ¼

k vk1 c c

  k  e

vc

(10)

where v: the wind speed; k: the shape factor; c: the scale parameter. Matlab is used to compute the values of k and c. The Weibull PDF is given by Ref. [26]:

 k

Zv FV ðvÞ ¼

f V ðtÞdt ¼ 1  e



v c

(11)

0

2.1.2. Cost of WPG Since the nature of wind speed is stochastic, the output power of the WPG may be different from that scheduled. Here, two situations can be occurred: overestimation or underestimation of the wind power. Therefore, the cost of WPG is calculated considering the overestimation and underestimation of the available wind resources, based on the Weibull distribution function of the wind speed [9], represented by the second term of Eq. (1). The total cost function of wind energy generation is given by: WG X

 X    X  ¼ Cost PWPG lp$w$j Pwj:av  Pwj þ lr$w$j Pwj j

j¼1

 Pwj$av

 (7)

where Pwj and Pw$j$av: respectively the scheduled power output and the actual available power output of the jth wind farm; lp.w.j: the cost associated with wind power shortage (overestimation) of the jth wind farm; lr.w.j:the cost associated with wind power surplus (underestimation), depending on how much surplus the actual available wind power is and the probability of surplus occurrence. lr.w.j is not a real cost; rather, it is a penalty term for not exploiting the available wind resource. In this case, a fast re-dispatch of conventional generations is usually adopted or calling the reserves is instantly required. l p$w$j depends on the amount of the power deficit and the probability of the occurrence of a deficit for a given scheduled power, mathematically expressed as [10]:





Pw Z r$j

lp$w$j Pwj$av  Pwj ¼ kp:j Pwj

  Pw  Pwj f w ðPwÞ

(8)

Using the power curve of the wind turbine generators (WTG), a simplified linear progressive function is used to express the relationship between the wind power output and the wind speed [27]:

8 > > > > > > > < > > > > > > > :

0

v < vcutin

ðV  Vcutin Þ P ðVrated  Vcutin Þ R

vcutin  v < vrated

PR

vrated  v < vcutoff

0

(12)

v  vcutoff

where Vcut-in and Vcut-off: respectively the wind speeds at which the wind turbines start producing energy and the second at which the turbines are disconnected; Vrated: the wind speed corresponding to the rated power production of the wind turbine. The wind energy conversion system (WECS) power output is a mixed random variable, which is continuous between values of zero and the rated power, and is discrete at values of zero and the rated power output. For a linear transformation, wind power random variable (Pw) is given by Ref. [9]:

PW ¼ TðVÞ ¼ aV þ b

(13)

and

  dT1 ðwÞ f W ðPW Þ ¼ f V T1 ðwÞ dw

!

¼ fV

  w  b 1 a a

(14)

where T: a transformation, in general; V: the wind speed random variable; w:a realization of the wind power random variable; v:a realization of the wind speed random variable. The Weibull PDF power output random variable of the WECS in the continuous range becomes:

S. Makhloufi et al. / Energy 116 (2016) 1117e1130



klvcutin ð1 þ rlÞvcutin k1 f w ðwÞ ¼ c c

! ð1 þ rlÞvcutin k exp  c

  Sij   Smax (15)

In our case, WPGs do not consume or deliver reactive power. 2.3. Maximum wind power output

vcutin Þ where r ¼ PwPw and l ¼ ðvratedvcutin rated For the Weibull function, the discrete portions of the WECS power output random variable will take the following expressions:

1 for the probability of event Pw ¼ 0

 k

v Prated fPw ¼ 0g ¼ 1  exp  cutin c

! vcutoff k þ exp  c

(16)

In the practical power systems, when we prepare to solve the OPF problem, the bound limits of the conventional power generations (Pupper and Plower) are well-known in advance and are not significantly affected by weather conditions. Conversely, WPG is highly sensitive to variations in the wind resources; hence, setting the limits for short- or mid-term forecasting of a power system cannot be considered as criteria. In order to estimate the maximal wind power output, the Weibull distribution given by Eq (10) is used to extract the value of the corresponding wind speed carrying maximum energy. This latter is given by Ref. [25]:

vop ¼ c 

2 for the probability of event Pw ¼ PR

 k

v Prated fPw ¼ Pwrated g ¼ exp  rated c

! vcutoff k þ exp  c

(24)

ij

(17)

1 kþ2 k k =

1120

(25)

Consequently, the wind speed carrying maximum energy is substituted into Eq (12) to calculate the upper bound power output of the wind farm. 3. Implementation of CSA, FFA, and FPA on the OPF 3.1. CSA description

2.2. Power system security and operational limits The equality constraints of the OPF problem represent the active and the reactive power balance equations, which are typically the load flow equations, expressed as:

Pi 

N X jVi Vk Yik jcosðqik  di þ dk Þ ¼ 0

(18)

k¼1

Qi þ

BN X jVi Vk Yik jsinðqik  di þ dk Þ ¼ 0

(19)

k¼1

where Pi and Qi: the real and the reactive powers injected at bus i; N: the number of bus in the power system; Yik: the element admittance matrix from the bus i to the bus k; qik: the angle of the element of the admittance matrix Yik;Vi and Vk: respectively the voltage magnitude of buses i and k, and their corresponding voltage angles are di and dk. The inequality constraints represent the operating and physical limits of each component in the power system. They include active and reactive power limits (including the slack generation), the capacity limits of lines and transformers, and the limits of all voltage buses:

PG$i$min  PG$i  PG$i$max

(20)

Q G$i$min  Q G$i  Q G$i$max

(21)

0  Pw$i  Pw$i$max

(22)

 Vi  Vmax Vmin i i

(23)

The cuckoo search algorithm (CSA) is inspired by the natural behaviour of a species of bird named the ‘cuckoo’. Cuckoo birds lay their eggs in the nests of other birds. Some species such as the ‘Ani’ and ‘Guira’ cuckoos lay their eggs randomly in collective nests; they may even remove or displace other eggs to increase the hatching probability of their eggs. However, if the host bird discovers that the eggs are not its own, it will either throw these alien eggs away or simply abandon its nest to build a new nest elsewhere. Yang and Deb [12] proposed a novel and evolutionary CSA, named after the bird species. Furthermore, in order to make the CSA more efficient in exploring the search space, the algorithm is
vy flight’ probability density enhanced by the so-called ‘Le distribution. The CSA approach is a tool for optimizing the objective function. The number of nests is the size of the cuckoo population, while the egg represents a solution. Applied to the context of formulating our algorithm and describing the approach of the cuckoo bird in spotting the nest and the right place for its eggs, a balanced combination of a local random walk with a permutation and the global explorative random walk are used. This will be controlled by a switching parameter linked to the similarity between the possible and the existing egg (solution). Consequently, the presence of more similar eggs will make them more likely to survive and be part of the next generation. Based on the above rules, the basic steps of the CSA are summarized by the pseudo code in Fig. 1. The mathematical expression [12] of the CSA combines a local random walk and a global explorative random walk, where ‘pa’ is the switching parameter. The local random walk is given by:

  xtþ1 ¼ xti þ fs5Hðpa  εÞ5 xtj  xtk i

(26)

where xtj and xtk : two different solutions chosen by random permutation; H(u): a Heaviside function; ε: a random number drawn from a uniform distribution; s: the step size.
vy flight concept, the global explorative random Using the Le

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

Objective function f (x), x = (x1 ,…, xd ) Generate the initial population of ‘n’ host nests xi (i= 1, 2…, n) While (tFj), Replace j by the new solution; end if A fraction (pa) of worse nests are abandoned and new ones are built; Keep the best solutions (or nests with quality solutions); Rank the solutions and find the current best End while Print the results End

1121

where a is the step size related to the scale of application of the
vy distribution, which is: Le

Levyðs; lÞ ¼

lGðlÞsinðpl=2Þ 1 ; ðs[s0[0Þ p s1þl

(28)


vy flight method, a fast algorithm In order to implement the Le
vy distribution. called Mantegna's algorithm approximates the Le According to Ref. [12], this algorithm follows three steps: Step 1: calculate

s¼

u

(29)

1

jvjb

Step 2: calculate the parameters m and g using normal distributions:

    u ¼ N 0; s2u ; v ¼ N 0; s2u

(30)

Step 3: calculate the variance r using Eq (31), with 1  b  2.

Fig. 1. Pseudo code of CSA.

G(z) is the gamma function.

su ¼



8 91b pb < Gð1 þ bÞsin 2 = :G½ð1 þ bÞ=22bðb1Þ=2 ;

; sv ¼ 1

(31)

3.2. FFA description The firefly algorithm (FFA) is a nature-inspired optimization algorithm developed by Xin-She Yang [28]. The FFA is based on flashing patterns that simulate the behaviour of fireflies when searching for food or interacting with co-members of their community. In the FFA, the quality of the solution is valued by the magnitude of the firefly's brightness, which is associated with the fitness function of the problem of interest. In essence, the FFA is mainly built using the following rules [28]:

Fig. 2. Pseudo code of FFA.

walk becomes:

xtþ1 ¼ xti þ f5Levyðs; lÞ i

(27)

1 All fireflies are unisex and, therefore, are attracted to each other irrespective of their sex. 2 The attractiveness between the fireflies is proportional to the magnitude of their brightness, thus decreasing with the growing distance between them. As a consequence, for any two

Fig. 3. Pseudo code of FPA.

1122

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

flashing fireflies, the less bright one will move towards the brighter one. The light intensity of a firefly is derived from the fitness function. 3 If a firefly fails to spot a brighter one, it will randomly move in the search space losing brightness, as expressed by the fitness function. Following these three rules, the basic steps of the FFA are

summarized by the pseudo-code illustrated in Fig. 2. In the FFA, as the distance between the two fireflies increases, the relative brightness perceived by a given firefly varies according to [28]:

 





bij rij ¼ b0  exp grm ij ; m  1

(32)

where bij: the attractiveness of firefly i relative to firefly j; b0: the

Fig. 4. Flow diagram representing the solution search methodology for CSA.

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

initial attractiveness at a distance of rij ¼ 0; g: the absorption coefficient of light in the environment, used to express light intensity (brightness decline rate); rij: the distance between the ith and jth fireflies and, given by the Euclidian distance, is defined as follows:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u d  2 X u Xi;k  Xj;k rij ¼ Xi  Xj ¼ t

1123

where Xi and Xj are the positions of the i and j fireflies in the search space, and d is the search space dimension of the problem of interest. The movement of firefly i towards a brighter one j, required updating the position Xj. This is expressed as follows:

(33)

k¼1

  Xi ¼ xi;1 ; xi;2 ; …; xi;k ; …; xi;d i h Xj ¼ xj;1 ; xj;2 ; …; xj;k ; …; xj;d

  1 Xj ¼ Xj þ b0  expðgrm Þ  Xi  Xj þ f rand  2

(34)

where a is the randomization parameter in the range of [0, 1] and ‘rand’ is a random number generator, uniformly distributed in the same range.

Fig. 5. Flow diagram representing the solution search methodology for FFA.

1124

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

3.3. FPA description Flowering plants are fascinating by nature, not only because of their beautiful colour and their enjoyable scent, but also because of their prodigious reproduction strategy. In a natural environment, pollination occurs within the same flower and/or by transferring pollen containing male cells to another flower, carried by insects (bees, butterflies, moths or flies) or wind. The pollination by insects is called biotic pollination and abiotic when it takes other transport agents such as wind. Most flowering plants follow the first pollination mode. Glover [29] offered a useful background on flowers evolution. Pollination can occur in two ways. Self-pollination involves fertilization by the pollen of the same flower or a different flower of the same plant. Cross-pollination occurs by the pollen of a flower of a different plant.

In the past two decades, pollination ecologists have observed that the honeybee is an excellent pollinator. When honeybees gather flower nectar, the flower spores stick on their legs. Thereafter, they carry the spores often over long distances to land them on another flower species. In this manner, the pollination of flowering plants visited by honeybees permits maximizing the reproduction of the same flower species. With their limited memory and minimum cost of learning, honeybees ascertain in advance the availability of nectar in the explored area. Thus, honeybees work to minimize their effort and cost to access nectar resources. Since, honeybees can fly over long distances (large exploration landscape), the pollination process of the flowering plants can be considered as global pollination. The most likely scenario is that the honeybees will fly randomly while looking for nectar. Bees switch from one field to another almost arbitrarily, while assessing the potential of the resources. The behaviour of the honeybees can be

Fig. 6. Flow diagram representing the solution search methodology for FPA.

S. Makhloufi et al. / Energy 116 (2016) 1117e1130


vy flight search patterns. As a result, flower pollinahandled by Le tion is a process that enables the optimum reproduction of plants in terms of numbers and quality. This can be considered as a plant species optimization process. Yang introduced this concept and built an algorithm with the same name [14]. Taking into account the key phases described above, the main steps of implementing FPA can be summarized as follows [30]: 1 Biotic cross-pollination can be considered as a process of global
vy flight pollination and pollen-carrying pollinators adopt a Le motion pattern. 2 Local pollination is best described by abiotic pollination-and self-pollination.

1125

3 Pollinators such as honeybees can develop flower constancy [31], which is a reproduction probability that is proportional to the similarity of two given flowers. 4 The interaction between local and global pollination is driven by a switch probability pa 2 [0, 1], slightly biased in local pollination due to physical proximity. The basic steps of the FPA are summarized within the pseudocode given by Fig. 3. In Rule 1, flower pollen and spores are transported by pollinators over long distances. This concept, combined with flower constancy (Rule 3), allows expressing both as:

Fig. 7. Single line diagram of Adrar power system.

Table 1 Output of the iterations with the best solutions reached. Run

Case 1 1 2 3 4 5 Average Case 2 1 2 3 4 5 Average

Convergence iterations taken

Computational time for convergence (s)

Total computational time (s)

Multi-objective function

CSA

FPA

FFA

CSA

FPA

FFA

CSA

FPA

FFA

CSA

FPA

FFA

227 201 145 181 205 192

1741 1445 1293 609 635 1145

632 852 685 682 732 717

450.9 392.4 288.3 371.2 409.5 382

831.1 712.9 618.1 290.7 301.9 551

361.4 478.6 395.3 396.6 447.1 416

3889.2 3841.0 3941.7 4051.7 3873.7 3919

952.9 979.6 948.8 944.5 874.8 940

1140.8 1129.6 1150.3 1175.2 1179.8 1155

8668.6 8668.6 8668.6 8668.6 8668.6 8668.6

8668.6 8668.6 8668.6 8668.6 8668.6 8668.6

8668.6 8668.6 8668.6 8668.6 8668.6 8668.6

135 135 185 200 150 161

722 1665 693 748 1433 1052

732 805 821 707 644 749

144.1 144.8 196.4 197.9 158.7 168.4

357.2 736.3 338.6 365.2 705.4 500.5

447.1 519.4 505.1 427.9 394.9 458.9

2141.8 2092.4 2023.3 1968.7 2055.6 2056.4

986.9 887.1 975.5 985.0 984.4 963.8

1239.6 1250.9 1221.1 1214.1 1238.9 1232.9

8548.6 8548.6 8548.6 8548.6 8548.6 8548.6

8548.6 8548.6 8548.6 8548.6 8548.6 8548.6

8548.6 8548.6 8548.6 8548.6 8548.6 8548.6

1126

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

260

(a)

  xtþ1 ¼ xti þ ε xtj  xtk i xtj

NOx (kg/hr)

where xti : the pollen i of solution vector xi at iteration t; g*: the best solution selected among all solutions at the iteration t; g: a scaling
vyfactor to control the step size; L(l): the parameter of the Le flight-based step size, given by Eq (28). Similarly to the CSA, the Mantegna's algorithm is used to express
vy distribution. the Le For local pollination, both Rules 2 and 3 are written as:

Case 1 CSA FFA FPA

250 245 240 235 0

265

(36)

500

1000 Iteration

(b)

1500

2000

Case 2

260

and xtk

where are pollen from different flowers of the same plant species. This essentially mimics flower constancy in a limited neighbourhood. Mathematically, if xtj and xtk originate from the same species or are selected from the same population of flowers, this equates a local random walk with ε extracted from a uniform distribution in the range [0, 1]. In principle, flower pollination can occur both locally and globally. However, in reality, adjacent flower patches or flowers in the close neighbourhood are prompted to be pollinated by local flower pollen than distant ones. In order to mimic this feature, a switch probability pa (Rule 4) can be effectively used to shift between common global pollination and intensive local one.

(a)

255

(35)

NOx (kg/hr)

xtþ1 i

  ¼ xti þ gLðlÞ g  xti

CSA FFA FPA

255 250 245 240 235 0

500

1000 Iteration

1500

2000

Fig. 9. Convergence curve of the NOx emission value for CSA, FFA and FPA. (a) case 1, (b) case 2.

8800

Total fuel cost (US$/hr)

8750

(a)

Case 1 CSA FFA FPA

8700 8650 8600 8550 8500 8450 0

500

1000 Iteration

8750

Total fuel cost (US$/hr)

2000

Case 2 CSA FFA FPA

(b) 8700 8650 8600 8550 8500 8450 0 Fig. 8. Convergence curve of the fitness function value for CSA, FFA and FPA. (a) case 1, (b) case 2.

1500

500

1000 Iteration

1500

2000

Fig. 10. Convergence curve of the fuel cost value for CSA, FFA and FPA. (a) case 1, (b) case 2.

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

3.4. Flowchart of CSA, FFA and FPA for OPF This section provides the detailed flowcharts of the proposed approaches for solving OPF. The flowcharts illustrated in Fig. 4, Fig. 5, and Fig. 6 include the rules and equations with their implementation in Matlab. 4. Simulation results and discussion Adrar's power system, located in the southwest of Algeria, is designed to fulfil the local demand for energy, with a total peak load of 291.2 MW. It consists in five TPG plants with a capacity of 425.6 MW and three wind farms with a capacity of 30 MW. The choice of turbine has been set for Gamesa G52-850 kW machines. The wind farms feed the 30 kV/220 kV substations of Adrar, Kaberten, and Timimoun. This system is not connected to the Algerian power network. The single-line diagram of the power system is illustrated in Fig. 7. The work on the OPF requires a clear identification of system load (demand) and all available power generation sources over the study period. In this paper, the year's highest peak load (291.2 MW), reached in July 2015, and a power factor of cos(r) ¼ 0.85 were used. The present work aims to apply the three algorithms (FFA, FPA, and CSA) to optimize the power flow in the Adrar power system, as described earlier. In this context, the three algorithms targeting to minimize the end value of the multi-objective function are tested. To assess the quality of the different solutions obtained for each component of the multi-objective function (fuel cost, NOx emissions, and wind power cost), the number of iterations required to converge and the best value obtained for the multi-objective function are used as the main criteria. The simulations are run with the three algorithms using the same initial starting value, obtained from 10different randomly selected populations. Because of the randomness factor included in all three algorithms, their stability and robustness cannot be evaluated in a single trial. Thus, the same five randomly selected run trials for each algorithm are used. The number of iterations has been set to 2,000, and the algorithms have been run using the following parameters:

1127

order to get representative statistical results, the average of the independent trials is also recorded. It transpires that the best solution (value of the multi-objective function) is obtained throughout the five different runs. This reveals that all three algorithms perform well with high stability and robustness in finding the global solution for OPF. The results reveal how the CSA, with a minimum computational time, has remarkably reached the best solution. It took 144.1 s to run 135 iterations (C2) and 288.3 s for 145 iterations (C1). Undeniably, the CSA outperforms both the FFA and the FPA in the majority of the cases and runs. The minimum values reached for the multi-objective function over the five runs by all three algorithms and for both cases, are illustrated in Figs. 8e12. Thesefigures illustrate the best solution for the fitness function, NOx emission, fuel cost, computational time, and effective active power of Adrar's wind farm. A common feature, revealed in Fig. 8, is the abrupt drop of the solutions obtained for the multi-objective function, over the first iterations (up to 100) and then a steady decrease thereof. It is worth noting that same behaviour of the fitness function is observed for its components (fuel cost and NOx emission), as shown in Fig. 9 and Fig. 10. This reflects the processing durations for each iteration to reach stable values of the solutions, thus enabling the algorithms to extensively explore a large search space [32]. After about 250 iterations, the solution values stabilize and all algorithms converge to the same solution. Looking at Fig. 11 and Table 1, though the CSA requires more time to run one iteration (2 s), compared to the FFA and the FPA,

 CSA: pa ¼ 0.25, a ¼ 1and b ¼ 3/2.  FFA: a ¼ 0.25and b ¼ 0.2 and g ¼ 1.  FPA: l ¼ 1.5, g ¼ 0.1 and pa ¼ 0.8. The contribution of WPG and TPG to reduce the fuel cost as well as NOx emission depends on the fixed values of penalty coefficients w1 and w2. Results have been obtained for two sets of penalty coefficients:  Case 1 (C1): w1 ¼ 0.5 and w2 ¼ 0.5.  Case 2 (C2): w1 ¼ 0.8 and w2 ¼ 0.2. Meanwhile, based on the wind speed data collected over 10 years and the Weibull distribution function, the scale and shape parameters of the Adrar site for July arek ¼ 1.5 and c ¼ 2.72. The wind turbine characteristics of Gamesa G52 are: Prated ¼ 850 kW, Vrated ¼ 13 m/s, Vcut-in ¼ 4 m/s, and Vcut-off ¼ 24 m/ s. Using Eq (12) and Eq (25), the estimated wind speed carrying maximum energy and the corresponding maximum wind power output of a wind farm are respectively 11.36 m/s and 6.3 MW. The penalty and the reserve factors are set to kp$j ¼ 0.03 $/MWh and kr$j ¼ 0.03 $/MWh. Table 1 summarizes the best OPF solution reached for the multiobjective function, number of iterations, and computational time taken for convergence as well as the total computational time. In

Fig. 11. Computational time as a function of the number of iterations for CSA, FFA and FPA. (a) case 1, (b) case 2.

1128

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

which take half the time (0.5 s), saving about 75% in computational time, the CSA converges more rapidly during its first iterations. This suggests that the CSA has good convergence characteristics. Looking at the first 100 iterations of the effective wind power of Adrar's wind farm (Fig. 12), it is remarkable how the shape evolves

during the optimization process. This is due to the cost component of the WPG which is low compared to the TPG one. On the other hand, the figures show that the randomness factor, included in the CSA in Eq (25), the FFA in Eq (33), and the FPA in Eq (36), controls the variation of the wind farm's effective active power, which

6.5 6

Wind power output (MW)

Case 1 5.5

CSA FFA FPA

(a)

5 4.5 4 3.5 3 0

500

1000 Iteration

1500

2000

6.5

Wind power output (MW)

6 5.5

Case 2 CSA FPA FFA

(b)

5 4.5 4 3.5 3 2.5 2 0

500

1000 Iteration

1500

2000

Fig. 12. Convergence curve of the effective wind power of Adrar's wind farm for CSA, FFA and FPA. (a) case 1, (b) case 2.

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

decreases gradually and in small steps throughout the successive iterations, within the limits of the total wind power capacity (maximum power output of18.9 MW). Past the first 100 iterations, the proposed algorithms tend to converge towards steady solutions for the set value of wind power capacity, translating their high efficiency in OPF. From Fig. 12, it is visible that both the CSA and the FFA converged quickly to the optimal solutions, whereas the FPA is unable to converge before the 1000 iterations. Table 2 gives the initial fitness function, its variation (Fvar) calculated from the initial to the end iteration, and the mean convergence speed (VCmean). Table shows clearly that the CSA has the fastest running speed compared to FFA and FPA, independently from the initial position. As can be seen, despite the CSA begins with the biggest value of 9161 US$/hr or with the lowest of 8777 US$/hr, it reaches the convergence with the lowest VCmean of 0.125 US$/hrs, compared to FFA with 0.314 US$/hrs and FPA with 0.439 US$/hrs. It is also observed that the choice of the weight factors (w1 and w2) does not affect the speed convergence of CSA. The best OPF solutions are presented in Table 3, including the active power of both TPG units and wind farms, the total active power loss, and the cost component of the multi-objective function. The choice of the coefficientsw1 and w2, affects both scheduling TPG and minimizing total active power loss. For instance, in Case 2, the active power loss is less than in Case 1. It is also obvious from the results that the active power schedules suggested by the

Table 2 VCmean of CSA, FFA, and FPA.

Case 1 CSA FFA FPA Case 2 CSA FFA FPA a b

Fitness (iter ¼ 0) [US$/hr]

a

9161 9027 9083

492.4 358.4 414.4

0.1249 0.3142 0.4388

8777 8825 8858

228.4 276.4 309.4

0.1066 0.2231 0.3172

Fvar [US$/hr]

b

VCmean [US$/hrs]

1129

proposed algorithms are the same, allowing to consider them as resourceful and practical tools for OPF. 5. Conclusion This paper investigates the performances of the CSA, the FFA, and the FPA for solving the OPF issue of the Adrar power system in the presence of WPGs. The proposed algorithms are applied to minimize fuel costs, NOx emissions, and wind power costs simultaneously. Furthermore, the maximum wind power output is explicitly considered in the suggested model. The proposed algorithms successfully solved the OPF problem, whereby their applicability and computational efficiency are demonstrated. Several conclusions are made:  Independently of the initial population, the CSA is the fastest algorithm with a mean convergence speed of 0.125 US$/hrs compared to the FFA with 0.314 US$/hrs. The FFA is followed by the FPA with 0.4388US$/hrs. In addition, the CSA takes few iterations of all, about190, in converging to the optimal solutions of 8668.6 US$/hr and 8548.6 US$/hr.  The same cost convergence characteristic was obtained by the CSA in Ref. [17], where fast-dropping and a lower number of iterations are the main advantages.  Comparing the results obtained by the FFA with those of Ref. [16], the cost convergence characteristic of the standard FFA drops slowly and converges after 300 iterations; this is also observed in our work, where the FFA converges after 500 iterations.  The plotting volatility characteristic of each component of the multi-objective function should be considered to handle the OPF in an optimal manner.  Substituting the estimated maximum wind power output as an alternative of the rated power and setting it as an upper bound is required in a practical power system. Finally, the CSA enables efficiency in solving the OPF issue and is a powerful tool to deal with the conventional and WPG units. Hence, extend CSA to solve dynamic OPF of the Algerian power system with various renewable energy sources and even combine different objective functions can be applied efficiency.

Fvar ¼ fitness (iter ¼ 0)-finess (iter ¼ 2000). VCmean ¼ Fvar/(total_computational_time).

Table 3 Best solutions of the multi-objective function (C1 and C2). Plant

Case 1 w1 ¼ 0.5; w2 ¼ 0.5

Case 2 w1 ¼ 0.8; w2 ¼ 0.2

FFA

FPA

CSA

FFA

FPA

CSA

Run 1

Run 4

Run 3

Run 5

Run 3

Run 1

Active power (MW) Adrar Timimoune Z.E.Kounta In Salah Kabertane Total (MW) NOx (kg/hr) x 1 US$/kg Total fuel cost (US$/hr)

83.7 44.0 48.5 53.1 44.0 273.3 237.3 8471.7

83.7 44.0 48.5 53.1 44.0 273.3 237.3 8471.7

83.7 44.0 48.5 53.1 44.0 273.3 237.3 8471.7

81.3 41.9 49.1 58.4 42.4 237.1 237.7 8465.4

81.2 42.1 48.9 58.3 42.6 273.1 237.7 8465.6

81.3 41.9 49.1 58.4 42.4 273.1 237.7 8465.4

Adrar (WECS) Kabertane (WECS) Timimoune (WECS) Total (MW) Total active power losses (MW) Total wind cost (US$/hr) Multi-objective function (US$/hr)

6.3 6.3 6.3 18.9 1.0 0.1223 8668.6

6.3 6.3 6.3 18.9 1.0 0.1223 8668.6

6.3 6.3 6.3 18.9 1.0 0.1223 8668.6

6.3 6.3 6.3 18.9 0.8 0.1223 8548.6

6.3 6.3 6.3 18.9 0.8 0.1223 8548.6

6.3 6.3 6.3 18.9 0.8 0.1223 8548.6

1130

S. Makhloufi et al. / Energy 116 (2016) 1117e1130

Acknowledgment
rateur du The authors deeply appreciate the support of “Ope me Electrique” of Algeria for providing access to the Adrar Syste power system data. References [1] Wen J, Zheng Y, Donghan F. A review on reliability assessment for wind power. Renew Sustain Energy Rev 2009;13:2485e94. [2] Brouwer AS, Broek M, Seebregts Ad, Faaij A. Impacts of large-scale intermittent renewable energy sources on electricity systems, and how these can be modeled. Renew Sustain Energy Rev 2014;33:443e66. [3] Momoh JA, Adapa R, El-Hawary ME. A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches. IEEE Trans Power Syst 1999;14(1):96e104. [4] Momoh JA, El-Hawary ME, Adapa R. A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods. IEEE Trans Power Syst 1999;14(1):105e11. € rensen K. Metaheuristicsdthe metaphor exposed. Int Trans Oper Res [5] So 2015;22:3e18. [6] Liao G. A novel evolutionary algorithm for dynamic economic dispatch with energy saving and emission reduction in power system integrated wind power. Energy 2011;36(2):1018e29. [7] Shi L, Wang C, Yao L, Ni Y, Bazargan M. Optimal power flow solution incorporating wind power. IEEE Syst J 2012;6(2):233e41. [8] Panda A, Tripathy M. Optimal power flow solution of wind integrated power system using modified bacteria foraging algorithm. Electr Power Energy Syst 2014;54:306e14. [9] Hetzer J, Yu DC, Bhattarai K. An economic dispatch model incorporating wind power. IEEE Trans Energy Convers 2008;23(2):603e11. [10] Jabr RA, Pal BC. Intermittent wind generation in optimal power flow dispatching. IET Gener Transm Distrib 2009;3(1):66e74. [11] Xing B, Gao WJ. Innovative computational intelligence: a rough guide to 134 Clever Algorithms. Library 62. Switzerland: Springer International Publishing; 2014.
vy flights. In: Proc World Congr Nat Biol [12] Yang XS, Deb S. Cuckoo search via Le Inspired Comput; 2009. p. 210e4. [13] Yang XS. Cuckoo search and firefly algorithm: theory and applications. Studies in computational intelligence. Library 516. Switzerland: Springer International Publishing; 2014. [14] Yang XS. Flower pollination algorithm for global optimization. In: Unconventional computation and natural computation, Lecture notes in computer science, vol. 7445; 2012. p. 240e9.

[15] Liang R, Wang J, Chen Y, Tseng W. An enhanced firefly algorithm to multiobjective optimal active/reactive power dispatch with uncertainties consideration. Int J Electr Power 2015;64:1088e97. [16] Younes M, Khodja F, Kherfane RL. Multi-objective economic emission dispatch solution using hybrid FFA (firefly algorithm) and considering wind power penetration. Energy 2014;67:595e606. [17] Basu M, Chowdhury A. Cuckoo search algorithm for economic dispatch. Energy 2013;60:99e108. [18] Nguyen TT, Truong AV. Distribution network reconfiguration for power loss minimization and voltage profile improvement using cuckoo search algorithm. Int J Electr Power 2015;68:233e42. [19] Nguyen TT, Vo DN. Modified cuckoo search algorithm for short-term hydrothermal scheduling. Int J Electr Power 2015;65:271e81. [20] Abdelaziz AY, Ali ES, Abd Elazim SM. Combined economic and emission dispatch solution using Flower Pollination Algorithm. Int J Electr Power 2016;80:264e74. [21] Zhu J. Optimization of power system operation. second ed. Hoboken, NJ, USA: John Wiley & Sons, Inc; 2015. [22] Venkatesh P, Gnanadass R, Padhy NP. Comparison and application of evolutionary programming techniques to combined economic emission dispatch with line flow constraints. IEEE Trans Power Syst 2003;18(2):688e97. [23] Kulkarni PS, Kothari AG, Kothari DP. Combined economic and emission dispatch using improved back propagation neural network. Electr Mach Power Syst 2000;28(1):31e44. [24] Dozein MG, Ansari J, Kalantar M.Economic dispatch incorporating wind power plant using Particle Swarm Optimization. Second Iranian conference on ICREDG'12, pp. 178e182, 6-8 March 2012, Tehran. Iran. [25] Celik A. A statistical analysis of wind power density based on the Weibull and Rayleigh models at the southern region of Turkey. Renew Energy 2004;29(4): 593e604. [26] Carta JA, Ramirez P. Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions. Renew Energy 2007;32(3):518e31. [27] Roy S. Market constrained optimal planning for wind energy conversion systems over multiple installation sites. IEEE Trans Energy Convers 2002;17(1):124e9. [28] Yang X. Firefly algorithms for multimodal optimization. Lect Notes Comput Sci 2009;5792:169e78. [29] Glover BJ. Understanding flowers and flowering: an integrated approach. second ed. Oxford, UK: Oxford University Press; 2007. [30] Yang XS, Karamanoglu M, He X. Multi-objective flower algorithm for optimization. Procedia Comput 2013;18:861e8. [31] Waser NM. Flower constancy: definition, cause and measurement. Am Nat 1986;127(5):596e603. [32] Van den Bergh F, Engelbrecht AP. A study of particle swarm optimization particle trajectories. Inf Sci 2006;176(8):937e71.