Plane Thermoelastic Waves in Infinite Half-Space Caused FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 34, No 4, December 2021, pp. 569-588 https://doi.org/10.2298/FUEE2104569B © 2021 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper CUCKOO SEARCH ALGORITHM TO SOLVE THE PROBLEM OF ECONOMIC EMISSION DISPATCH WITH THE INCORPORATION OF FACTS DEVICES UNDER THE VALVE-POINT LOADING EFFECT Larouci Benyekhlef 1*, Sitayeb Abdelkader2, Boudjella Houari1, Ayad Ahmed Nour El Islam1 1Department of Electrical Engineering, Faculty of Applied Sciences, University Kasdi Merbah Ouargla, Ouargla, Algeria, 2Applied Research Unit on Renewable Energies “URAER Ghardaia”, Ghardaïa, Algeria Abstract. The essential objective of optimal power flow is to find a stable operating point which minimizes the cost of the production generators and its losses, and keeps the power system acceptable in terms of limits on the active and reactive powers of the generators. In this paper, we propose the nature-inspired Cuckoo search algorithm (CSA) to solve economic/emission dispatch problems with the incorporation of FACTS devices under the valve-point loading effect (VPE). The proposed method is applied on different test systems cases to minimize the fuel cost and total emissions and to see the influence of the integration of FACTS devices. The obtained results confirm the efficiency and the robustness of the Cuckoo search algorithm compared to other optimization techniques published recently in the literature. In addition, the simulation results show the advantages of the proposed algorithm for optimizing the production fuel cost, total emissions and total losses in all transmission lines. Key words: Combined economic emission dispatch, OPF, Cuckoo search algorithm, VPE, FACTS devices. 1. INTRODUCTION The production of electrical power is marked by several orientations as limiting the environmental impact of the generating and use of energy, increasing the energy efficiency of systems and developing low-cost production and minimizing gas emissions toxic in the atmosphere under the valve-point effect [1]. Received April 3, 2021; received in revised form August 14, 2021 Corresponding author: Larouci Benyekhlef Department of Electrical Engineering, Faculty of Applied Sciences, University Kasdi Merbah Ouargla, Street Ghardaia, 30000, Ouargla, Algeria E-mail: larouci.benyekhlef@univ-ouargla.dz 570 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM The impact of power plants on the environment has changed the way power grids are managed [2]. However, recent awareness of the toxic effects of gases emitted by fossil fuel power plants and the new stringent environmental laws imposed on power producers have led to the incorporation of environmental considerations into the methods that govern the production of electricity [3] so, the emissions and fuel cost must be considered simultaneously to provide the true measure of optimum production [4]. Currently, with the new energy market deregulation system [5], there is increased interest in FACTS (Flexible Alternative Current Transmission Systems) for the operation and control of power systems [6], this is due to the new load constraints and new contingencies. The installation of FACTS has become essential to increase the transmission capacity of the power system, reduce losses, and improve the safety and the controllability of an electrical network [7]. These FACTS devices are capable of changing network parameters quickly and efficiently to achieve better system performance [8]. The mathematical formulations of all the above tasks to be performed by power producers are therefore becoming more and more complex [9]. This growing complexity has led many researchers to turn to nature-inspired algorithms to solve these problems [10]. These algorithms are those developed by imitating natural phenomena and biological models [11-12]. They offer robust and competitive solutions. The objectif of this article is to propose a nature-inspired algorithm known as Cuckoo search algorithm (CSA) [10], in order to provide the optimal solution to the optimal power flow problems. The proposed technique is applied on IEEE 30-bus system considering valve-point effect (VPE) with and without installing two FACTS devices (Static Var Compensator (SVC) and Statcom), to reach the lowest values of fuel cost, installation cost of FACTS devices, and to reduce toxic gas emissions. The statistical results are as compared with other algorithms existing in the recent literature. The rest of this article is structured as follows: the definition and mathematically formulation of the OPF problem are offered in section 2, while section 3 addresses a brief description of the CSA. The simulation results are carefully studied and analyzed in section 4. Finally, conclusion and future suggestions are given in section 5. 2. OPTIMAL POWER FLOW The optimal power flow (OPF) was conceived as an extension of the conventional economic and emission dispatch [13-14]. The OPF problem is large-scale non-convex optimization problem, which may also have uncertain variables. In general, the OPF problem seeks to optimize the steady state performance of a power system in terms of an objective function while satisfying several equality and inequality constraints [15]. In contrast, OPF aims to optimize an objective function by finding optimal free variables while keeping the network constraints in their acceptable limits [16]. 2.1. Mathematical model of economic dispatch The cost of each generating unit is typically represented by fuel cost. Generator curves are generally represented as quadratic convex curves of second order function [17-18]. The total fuel cost function is formulated as follows: Cuckoo Search Algorithm to Solve The Problem of Economic Emission Dispatch with FACTS 571 igiigiigii cPbPaPF ++= 2 )( (1) The coefficients ai, bi and ci are numerically known. The optimal functioning of a set of thermal production units can be seen by the model:  = =      gN i gigi PPCMinimize 1 i1 )(F (2) Where: Ng is the total number of generators on the system under the constraints of equality and inequality type. 2.1.1. Constraints a. Equality constraint These constraints are represented by nonlinear power flow equations [20]. The sum of the active and reactive generated powers in the network must be equal to the sum of the active and reactive powers consumed with transmission losses, this constraint is given by [21]: 0 1 )cos( = = −−−− Ng j ijjiijYjViVPP digi  (3) 0 1 )sin( = = −−−− Ng j ijjiijYjViVQQ digi  (4) b. Inequality constraints These constraints represent the operating limits of the power system (Generator voltages, real and reactive power, transmission lines, transformers, FACTS, etc.) [22-23]. maxmin gigigi PPP  (5) maxmin gigigi QQQ  (6) maxmin kikiki VVV  (7) maxmin FACTSFACTSFACTS SSS  (8) maxmin svcsvcsvc QQQ  (9) 2.2. Mathematical model of economic dispatch with valve-point loading Effect In some large generators, their cost functions are also non-linear, due to the effect of valve-point loading (VPE) [24]. This effect will increase several local minimum points in the cost function and make the problem more difficult. The fuel cost function with the effect of the valve-point loading can be expressed as follows [25]: 572 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM ))(sin()( min, 2 gigiiiigiigiigii PPfecPbPaPF −+++= (10) Where Pgi is the real power generation of unit i in (MW), ei, and fi are cost coefficients of ith generator due to VPE. Chiang in [26-28], presented a realistic economic dispatching problem by simultaneously considering the fuels cost and the effect of the valve-point loading to make the economical dispatching solution more precise. 2.3. Mathematical model of environmental dispatch The total emission can be expressed as [29]: igiigiigii PPPE  ++= 2 )( (11) Where: The coefficients γi, βi and αi are NOX emission coefficients numerically known [30]. 2.4. Mathematical model of Combined Economic Emission Dispatch Problem The study of economic-environmental dispatch consists of the simultaneous minimization of the two functions given by equations (1) and (11). We therefore transform the bi-objective optimization problem into a single-objective optimization problem, by introducing a price penalty factor [31]. This factor is defined as the ratio between the maximum cost and the maximum emissions of each generator [32]: Ng,………2,1,=i; Kg $ )( )( m ax m ax         = gi gi p PE PC F (12) The steps to determine the price penalty factor specific for a given load are: Determine the ratio of the maximum cost and the maximum emissions for each generator. Rank the values of these factors in ascending order. The sum of the maximum powers of each generator starting with the power of the plant with the lowest factor up to:  =  gN i DPP 1 m ax gi At this point, FP tied to the last unit in the process and the price penalty factor for the given load. After determining this factor, we can represent the Economic-Environmental Dispatch function by the following equation [33-34]: 2 2 1 1 ( ) ( ) ( ) g gN N gi i gi i gi i p i gi i gi i i i P a P b P c F P P = =  = + + +  +  +   (13) Equation (14) can be rewritten as follows [35]: 2 1 ( ) ( ) gN gi i gi i gi i i P C P b P A =  = + + (14) Cuckoo Search Algorithm to Solve The Problem of Economic Emission Dispatch with FACTS 573 With: . , . , .i i p i i i p i i i p iA a F B b F C c F= +  = +  = +  (15) The minimization of this function is done by taking into account the type of the equality and inequality constraints. 2.5. OPF with cost function model of SVC devices The cost of SVC device, was developed by the manufacturer Siemens. The cost function of the SVC in ($/KVar) is as follows [36]: 127.380.3051-0.00031 2 += SVCSVCsvc SSC (16) Where: SSVC is reactive power of SVC in MVar. The formulation of the optimal choice problem of SVC locations can be expressed as follows [37-38]: ( )fCPCCMin giTotal 21 +     = (17) 0),( 1 =gfE (18) 0)(,0)( 21  gBfB (19) CTotal: the total objective function comprising the SVC investment cost and the cost of production. Fi (Pgi) : the generator cost function given by equation (1). C1 (f): the investment cost function of SVC given by the equations (16) and (17). E1: represents the power flow equations. B1, B2: are the inequality constraints of the SVC and the optimal power flow, respectively. f, Pgi : represent the variables parameters of the SVC and the powers supplied by the alternators. The fuel cost is expressed in ($/hour) while the investment costs of FACTS are expressed in ($). These must be expressed in $/hour. Normally FACTS are designed to be in service for several years [39]. However, they are only used for a portion of their lifetimes for power flow control. In this research, three years are used to estimate the average cost of FACTS, i.e. the depreciation (from a financial view point) of FACTS is estimated at three years [40]: ( ) 38760 )( 1  = fc fC ($/Hour) (20) Where: C(f) is the investment cost of SVC. The SVC device, is composed of a capacitor, which is the VAR generator, and a TCR (Thyristor Controlled Reactor), which behaves as a variable VAR absorbing load (depending on the firing angle of the Thyristor valve) [41]. Thus, the SVC can inject or absorb a variable amount of reactive power to the power system, adapting the compensation to the load conditions at each instant (see Fig.1) [42]. 574 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM L C TCR  C() L() Fig. 1 Static VAR compensator configuration. 2.5.1. OPF with model and mathematical analysis of STATCOM A static synchronous compensator (STATCOM), also known as a static synchronous condenser [43] is a regulating device used on alternating current electricity transmission networks. It is based on a power electronics voltage-source converter and can act as either a source or sink of reactive AC power to an electricity network. If connected to a source of power it can also provide active AC power. It is inherently modular and electable. STATCOM is modelled as a controllable voltage source (Ep) in series with impedance [43]. The real part of this impedance represents the copper losses of the coupling transformer and converter, while the imaginary part of this impedance represents the leakage reactance of the coupling transformer. STATCOM absorbs requisite amount of reactive power from the grid to keep the bus voltage within reasonable range for all power system loading. Fig. 2 shows the circuit model of a STATCOM connected to the ith bus of a power system. Fig. 2 Schematic static model of STATCOM https://en.wikipedia.org/wiki/Static_synchronous_compensator#cite_note-IEEE_Conference_Publication_2017-2-2 https://en.wikipedia.org/wiki/Alternating_current https://en.wikipedia.org/wiki/Power_electronics https://en.wikipedia.org/wiki/AC_power https://en.wikipedia.org/wiki/AC_power Cuckoo Search Algorithm to Solve The Problem of Economic Emission Dispatch with FACTS 575 The injected active and reactive power flow equation of the ith bus are given below: 2 cos( ) cos( ) 1 p p k k k p k p p n P G V V E Y V V Y i j ij i j ij j = −  −  −  +  −  −  = (21) 2 sin( ) sin( ) 1 p p k k p p k p p n Q B V V E Y V V Y i j ij i j ij j = − −  −  −  +  −  −  = (22) The implementation of STATCOM in transmission system introduces two state variables (|Ep| and δp); however, |Vk | is known for STATCOM connected bus. 3. CUCKOO SEARCH ALGORITHMS The Cuckoo Search Algorithm (CSA) is one of the newer nature-inspired metaheuristic algorithms developed by Xin-She Yang and Suash Deb in 2009 [10], [44]. CSA is a population-based search method that is used as a tool for optimization to solve complex, nonlinear and non-convex optimization problems. The algorithm of CSA uses three idealized rules [45]: (a) Each cuckoo lays an egg Place them in time and randomly chosen nest. (b) The best nest with high quality eggs is passed on to the next generation. (c) The number of available host nests is fixed and a host bird can discover an exotic egg with a conversation of pa ϶ [0, 1]. In this case, the host bird can either drop the egg or leave the nest to build a brand new nest in a new location. The CS method's key steps can be described as [46-47]: 1. Select the value of the CSA parameter, which is the number of nests (eggs) (n), step size parameter (β), probability of discovering (pa), and maximum number of iterations to end the cycle. 2. Randomly generate an initial population of n host nests   ( )nix i ,....,2,1, = . Each nest represents a possible solution to an optimization problem using objective functions ( )xf and decision variables    T mi xxxx ,...,, 21 = . 3. Use Levy Flights to get a cuckoo randomly and evaluate its fitness i F .   . 1 += + ii xx (23) Where λ is a random walk based on Levy flight (1 < λ ≤ 3). 4. Randomly choose a nest among n (say j) and evaluate its fitness Fj. If Fj < Fi, replace j with the new solution. 5. Abandon a fraction of the worst nests behind and create new ones. This is done depending on the probability parameter (pa). First, check whether each nest maintains its current position (equation (24)). The matrix R stores the values 0 and 1 so that each of them can be assigned to any component of the ith nest. 0 means that the current position is kept and 1 means that the current position is updated.      ⎯⎯ parandif parandif Ri 0 1 (24) 576 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM The new nest is carried out by Eq. 25: ( ) iii t i t i permpermRrxx 21 1 −+= + (25) Where: r is a random number from 0 to 1. Perm1 and Perm2 are two row permutations of the corresponding nests. R defines a probability matrix. Fig. 3 A simplified flowchart of the CSA 6. Rank solutions and find the current best one. 7. Repeat steps 3-6 until completion criteria is satisfied, which are usually considered the maximum number of iterations. A simplified flowchart of the CS algorithm is demonstrated in Fig. 3 [48]: Cuckoo Search Algorithm to Solve The Problem of Economic Emission Dispatch with FACTS 577 4. NUMERICAL RESULTS AND DISCUSSION In this work, four cases of OPF problem are studied; the proposed algorithm is applied on standard IEEE 30-bus system considering VPE in presence of two FACTS devices, SVC and Statcom, in order to solve the optimal power flow and solving the combined economic emission dispatch problem. The single-line diagram of which is illustrated by the Fig. 4. All the cases studies are executed in MATLAB 2017 under windows 8.1 on Intel Core(TM) i5-3110 CPU 2.40 GHz, with 4 GB RAM. Table 1 and Table 2 groups the values of the coefficients of the cost an emission functions of the 06 generators, and the limit powers Pmax and Pmin. The cost functions of generators 1 and 2 are obtained based on the ripple curve; this curve contains a higher order of non-linearity and discontinuity due to the valve-point effect. The cost coefficients of these units are given in Table 1. The parameters of the Cuckoo search algorithm are: ▪ Maximum number of iterations (Kmax) is 100. ▪ The rate of discovery of eggs (pa) / solutions is 0.25. ▪ The number of nests is 70. 30 29 28 27 25 26 8 24 23 22 15 18 19 20 21 6 10 9 14 16 17 12 11 3 1 2 4 13 7 5 Fig. 4 IEEE 30 bus system structure 578 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM Table 1 Cost coefficients of generators for IEEE 30-bus system Bus Pmin (MW) Pmax (MW) ci ($/h) bi ($/MWh) ai ($/MW²h) di ($/MWh) ei ($/MW²h) 1 50 200 150 2 0.0016 50 0.0630 2 20 80 25 2.5 0.0100 40 0.0980 5 15 50 0 1.00 0.0625 / / 8 10 35 0 3.25 0.00834 / / 11 10 30 0 3.00 0.025 / / 13 12 40 0 3.00 0.025 / / The coefficients of the gas emission function are shown in Table 2. Table 2 Emission coefficients of generators for IEEE 30-bus system Node γi ($/h) βi ($/MWh) αi ($/MW²h) 1 22.983 -1.1000 0.0126 2 25.313 -0.1000 0.0200 5 25.505 -0.0100 0.0270 8 24.900 -0.0050 0.0291 11 24.700 -0.0040 0.0290 13 25.300 -0.0055 0.0271 4.1. Case 1: Optimal Power Flow (OPF) An optimal power flow program with the valve-point loading effect based on the Newton-Raphson method, to determine the voltages at the different bus, the generated powers and the transmission losses. The results obtained for case1 are shown in Table 3. Table 3 Optimal Power Flow Results Bus V Angle Injection Generation Load No p.u Deg MW Mvar MW Mvar MW Mvar 1 1.06 0 200.00 -7.157 200 -7.157 0 0 2 1.043 -4.141 -1.7 26.044 20 38.744 21.7 12.7 5 1.01 -10.6513 -73.418 7.276 20.782 26.276 94.2 19 8 1.01 -7.9854 -6.254 -15.163 23.746 14.837 30 30 11 1.082 -8.0311 15.419 15.324 15.419 15.324 0 0 13 1.071 -9.66 13.613 8.157 13.613 8.157 0 0 Total 10.266 -6.720 293.566 119.48 283.400 126.20 Comparisons of our results with those obtained by other methods are grouped in Tables 4. The results show that the CS-OPF algorithm gives a better result compared to other methods reported in the literature. The total cost found by the CSA small compared with those found by the methods GA, PSO, FPSO and GA-MGA which are of the order of 923.07$/h, 928.56 $/h, 923.72$/h, 923.54$/h and 922.77 $/h respectively. The cost ranges from 0.1-0.71% in relation to the values obtained by the CS OPF algorithm. Cuckoo Search Algorithm to Solve The Problem of Economic Emission Dispatch with FACTS 579 Table 4 Optimal output power for IEEE 30-bus system with different algorithms Variable CS OPF GA [49] MGA [49] PSO [49] FPSO [49] GA-MGA [49] Pg1 (MW) 200.00 199.34 199.66 199.78 199.78 199.73 Pg2 (MW) 20.00 20.03 20.14 20.24 20.00 20.00 Pg3 (MW) 20.78 23.13 18.70 21.60 25.42 18.49 Pg4 (MW) 23.74 22.78 17.18 19.91 22.43 24.29 Pg5 (MW) 15.41 13.97 10.31 14.22 13.37 16.74 Pg6(MW) 13.61 14.56 27.77 18.13 12.94 14.57 PG Total (MW) 293.56 293.81 293.76 293.88 293.94 293.82 Fuel cost ($/hr) 921.88 923.07 928.56 923.72 923.54 922.77 Losses (MW) 10.26 10.41 10.360 10.480 10.55 10.42 The value of the active losses found by CSA is of the order of 10,266 MW; it is smaller compared to those obtained by of GA, PSO, FPSO and GA-MGA techniques. Figures 5, 6, 7 and 8 respectively, illustrates the variations of fuel cost, transmission losses, the generated powers and the values of the nodal voltages respectively. These graphs clearly indicate that CSA converges rapidly to the optimal solution. Fig. 5 Convergence of fuel cost Fig. 6 Optimal values of the powers generated. Fig. 7 Variation of active losses Fig. 8 Nodal voltage values 580 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM 4.2. Case 2: Economic / environmental dispatch (with variable losses) To demonstrate the effectiveness of the proposed approach, the combined economic environmental dispatch with the optimal power flow applied by introducing the price penalty factor is resolved. The transmission losses are variable depending on the generated power. The price penalty factors of each generator, are valued at 2.000, 1.9888, 2.2296, 2.0534, 2.2198 and 2.3378 ($/ton) respectively. The optimal values of generated power, transmission losses, fuel cost, NOx emission and a comparison of our results with those obtained using the HSABC algorithm (Harvest Season Artificial Bee Colony) are given by the table 5. For the case of economic dispatch (OPF), the value of the production cost is reduced to the minimum (921.88 $/h) and its value is better than that of economic / environmental dispatch (959.94 $/h) and environmental dispatch (1071.64 $/h). For the case of environmental dispatch, the value of total emission is very low (295.92 Kg/h) compared to the combined economic environmental dispatch (336.98 Kg/h) and economic dispatch (457.43 Kg/h). According to table 5, it is clear that the gas emissions found by our algorithm (295.92 Kg/h) are lower compared to those found by the HSABC technique which are estimated at 309.84 (Kg/h). The total emission, are minimized by 13.92 (Kg/h). Characteristics convergence of fuel cost, NOx emissions and total cost are depicted in Figures 9, 10, and 11 respectively. The graphs clearly indicate that CSA converges rapidly to the optimal solution. Table 5 Economic-environmental dispatch with variable losses Variable Economic dispatch Combined economic emission dispatch Environmental dispatch CS OPF CS HSABC [50] CS Pg1 (MW) 200.00 149.46 126.07 114.99 Pg2 (MW) 20.00 51.41 49.74 49.07 Pg3 (MW) 20.78 18.37 28.40 37.08 Pg4 (MW) 23.75 31.29 31.80 28.11 Pg5 (MW) 15.42 25.33 26.63 29.69 Pg6 (MW) 13.61 14.99 27.17 30.41 Total PG (MW) 293.56 290.85 289.81 289.36 Cost ($/hr) 921.88 959.95 1048.68 1071.64 Emission ($/hr) 457.43 336.98 309.84 295.92 Total Cost ($/hr) / 1655.53 / / losses (MW) 10.26 7.783 6.41 5.40 Fig. 9 Production cost Fig. 10 NOx emissions Cuckoo Search Algorithm to Solve The Problem of Economic Emission Dispatch with FACTS 581 Fig. 11 Total cost 4.3. Case 3: OPF with the presence of SVC To solving OPF problem with SVC device, the investment cost of SVC is integred in the power system. We are increasing the load from 283.40 MW to 383.40 MW, adding 100 MW at bus 20. The candidate bus at the location of the SVC is the bus where the voltage drop is important, so we have chosen bus 20 to install the SVC. The parameters of the SVC are grouped in table 6: Table 6 SVC Parameters’ Qsvcmax (MVar) Qsvcmin (MVar) c ($/kVar) b ($/kVar²) a ($/kVar3) 100 -100 188.22 -0.2691 0.0003 The power flow in power system without and with installation of SVC, are reported in Tables 7 and 8 respectively. From Table 7, the voltage level at bus 20 (without SVC) is considered the lowest (0.8939 p.u) the voltage drop, it is lower than the minimum allowable value (10.61% < 5 %). Table 7 Optimal Power Flow without SVC (Pload = 383.9 MW) Bus V Angle Injection Generation Load No p.u deg MW MVar MW MVar MW MVar 1 1.06 0.00 199.78 2.31 199.98 2.31 0.00 0.00 2 1.043 -3.70 58.30 28.59 80.00 41.29 21.70 12.70 5 1.01 -10.89 -65.72 12.69 28.48 31.69 94.20 19.00 8 1 -9.46 4.38 1.23 34.38 31.23 30.00 30.00 11 1.062 -11.28 27.02 23.71 27.02 23.71 0.00 0.00 13 1.071 -12.52 39.10 23.96 39.10 23.96 0.00 0.00 20 0.8939 -28.42 -102.20 -0.70 0.00 0.00 102.20 0.70 Total 25.36 51.29 408.76 177.49 383.40 126.20 The results obtained with CSA considering SVC device, are reported in Table 8. 582 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM Table 8 Optimal Power Flow with SVC. Bus V Angle Injection Generation Load No p.u deg MW MVar MW MVar MW MVar 1 1.06 0 200.00 -0.884 200.00 -0.884 0 0 2 1.043 -3.692 58.251 19.767 79.951 32.467 21.7 12.7 5 1.01 -10.75 -64.28 7.724 29.916 26.724 94.2 19 8 1.01 -9.591 4.966 4.719 34.966 34.719 30 30 11 1.082 -11.07 30 24.123 30 24.123 0 0 13 1.071 -13.28 32.222 14.397 32.222 14.397 0 0 20 0.95 -28.34 -102.2 16.908 0 17.608 102.2 0.7 Total 23.692 46.254 407.09 172.45 383.4 126.2 According to Table 8, it is remarkable that SVC device at bus 20 will be more effective in the bus with the greatest voltage drop. The installation of SVC significantly reduces the fuel cost, transmission losses and improve the level of voltages from 0.8939 to 0.95 p.u. Table 9 Optimal results with and without SVC. Variable CS with SVC CS without SVC Pg1(MW) 200.00 199.98 Pg2(MW) 79.95 80 Pg5(MW) 29.91 28.48 Pg8(MW) 34.96 34.38 Pg11(MW) 30 27.02 Pg13(MW) 32.22 39.10 V1 (pu) 1.06 1.06 V2 (pu) 1.043 1.043 V5 (pu) 1.01 1.01 V8 (pu) 1.01 1 V11 (pu) 1.082 1.062 V13 (pu) 1.071 1.071 V20 (pu) 0.95 0.8939 Total PG (MW) 407.09 408.96 Losses (MW) 23.69 25.36 Qsvc (MVar) 2.696 / Cost SVC $/KVar 187.49 / Cost ($/hr) 1372.23 1375.49 From Table 9, the total cost (1372.23$/h) obtained by our algorithm with the location of SVC at bus 20 is lower compared to without SVC (1375.49$/h). The cost is minimized by 3.2581$/h. The transmission losses in this case are minimal (23.691 MW) compared to without installing SVC device (25.36 MW). They are reduced by 1.66 MW. Cuckoo Search Algorithm to Solve The Problem of Economic Emission Dispatch with FACTS 583 Fig. 12 Production cost Fig. 13 Variation of active losses Fig. 14 Optimal values of the generated powers Fig. 15 Voltage profile We also deduce that the Cuckoo search algorithm quickly converges to the optimal solution. 4.4. Case 4: OPF with the presence of STATCOM In the third application, we are interested in the resolution of the optimal power flow with the integration of STATCOM in the power system. We increase the load demand from 283.40 MW to 383.40 MW. To maintain all the voltages at acceptable values, the candidate bus for the STATCOM location is the bus where the voltage drop is important; we have chosen the bus n°20 to install STATCOM. The voltage source value is considered 1.00 p.u. An optimal power flow program based on the Newton-Raphson method [51, 52] determines the voltages (magnitude and angle) at the different bus, the generated powers and the transmission losses. The OPF results obtained with installation of STATCOM are cited in tables 10 and 11 respectively. 584 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM Table 10 Optimal Power Flow with STATCOM Bus V Angle Injection Generation Load No pu Degree MW MVar MW MVar MW MVar 1 1.06 0 180.245 -5.581 199.868 -5.581 0 0 2 1.043 -3.703 58.3 8.114 80 20.81 21.7 12.7 5 1.01 -10.93 -65.75 -0.161 25.44 18.84 94.2 19 8 1.02 -9.682 4.916 0.653 34.91 30.65 30 30 11 1.082 -11.04 29.97 16.64 29.97 16.64 0 0 13 1.081 -12.57 36.29 9.226 36.29 9.226 0 0 20 1 -27.97 -102.3 34.4 0 35.1 102.2 0.7 Total 23.33 42.5 406.5 168.7 383.4 126.2 The simulation results illustrate in table 10, show that the addition of STATCOM at bus 20 improve the voltage profile (from 0.8939 to 1.00 p.u) and the levels of other voltage buses. Table 11 Simulation results of optimal values Variable CS with SVC (bus N°20) CS with STATCOM CS without SVC Pg1(MW) 200.00 199.8688 199.98 Pg2(MW) 79.95 80.0000 80 Pg5(MW) 29.91 25.4363 28.48 Pg8(MW) 34.96 34.9129 34.38 Pg11(MW) 30 29.9736 27.02 Pg13(MW) 32.22 36.2903 39.10 V1 (pu) 1.06 1.06 1.06 V2 (pu) 1.043 1.043 1.043 V5 (pu) 1.01 1.01 1.01 V8 (pu) 1.01 1.02 1 V11 (pu) 1.082 1.082 1.062 V13 (pu) 1.071 1.081 1.071 V20 (pu) 0.95 1.000 0.8939 Total PG (MW) 407.09 406.4819 408.96 Losses (MW) 23.69 23.3280 25.36 Cost ($/hr) 1372.23 1363.83387 1375.49 Table 12 STATCOM Parameter result Vsh of STATCOM Thst of STATCOM Qsh of STATCOM Bus p.u deg p.u 20 1.00 -28.1606 -0.3505 We can see from the Table 11, that the obtained OPF results indicate that CSA with STATCOM give a better fuel cost (1363.83387 $/h) compared to case without STATCOM (1375.49069$/h), the cost is reduced by 11.65 $/h. The power losses have considerably decreased from 25.3580 MW to 23.3280 MW, they are minimized by 2.03 MW. Therefore, the OPF problem with STATCOM using the proposed algorithm Cuckoo Search Algorithm to Solve The Problem of Economic Emission Dispatch with FACTS 585 performing well represented a best solution. The fuel cost and the transmission losses are reduced and voltage magnitude are maintained at the specified value. The variations of fuel cost, transmission losses, optimal values of generated powers and nodal voltages values are illustrated in Figures 16, 17, 18 and 19 respectively. Fig. 16 Production cost Fig. 17 Variation of the powers generated. Fig. 18 Variation of active losses Fig. 19 Voltage profile We also deduce that the Cuckoo search algorithm quickly converges to the optimal solution. 5. CONCLUSIONS The main difficulty of such an optimization problem is linked to the presence of a conflict between the production cost function, the toxic gas emission function, the valve-point loading effect and the control function cost of the FACTS. It requires the transformation of this multi- objective problem into a single-objective optimization problem. To do this, we have changed the problem of optimizing economic-environmental dispatching into a single-objective optimization problem, by introducing a price penalty factor. 586 L. BENYEKHLEF, S. ABDELKADER, B. HOUARI, A. A. N. EL ISLAM The CSA tests were validated on the IEEE 30-bus system. The simulation results prove that the proposed technique present as a competing algorithm for the resolution of the mentioned problems. A comparison of obtained results with those recently published in the literature confirms the efficiency and robustness of the algorithm in finding precise solutions. 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