Microsoft Word - 2-2904_s_ETASR_V9_N5_pp4586-4590 Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4586-4590 4586 www.etasr.com Torchani et al.: Dynamic Economic/Environmental Dispatch Problem Considering Prohibited … Dynamic Economic/Environmental Dispatch Problem Considering Prohibited Operating Zones Ahmed Torchani College of Engineering, University of Hail, Hail, Saudi Arabia and University of Tunis, ENSIT, LISIER Laboratory, Tunisia tochahm@yahoo.fr Attia Boudjemline College of Engineering, University of Hail, Hail, Saudi Arabia a_boudjemline@hotmail.com Hatem Gasmi College of Engineering, University of Hail, Hail, Saudi Arabia and University of Tunis El-Manar, ENIT, Tunisia gasmi_hatem@yahoo.fr Yassine Bouazzi College of Engineering, University of Hail Hail, Saudi Arabia and University of Tunis El Manar, ENIT, Photovoltaic and Semiconductor Materials Laboratory, Tunis, Tunisia yassine.bouazzi@gmail.com Tawfik Guesmi College of Engineering, University of Hail, Hail, Saudi Arabia and University of Sfax, ENIS, Tunisia tawfiq.guesmi@gmail.com Abstract—Along with economic dispatch, emission dispatch has become a key problem under market conditions. Thus, the combination of the above problems in one problem called economic emission dispatch (EED) problem became inevitable. However, due to the dynamic nature of today’s network loads, it is required to schedule the thermal unit outputs in real-time according to the variation of power demands during a certain time period. Within this context, this paper presents an elitist technique, the second version of the non-dominated sorting genetic algorithm (NSAGII) for solving the dynamic economic emission dispatch (DEED) problem. Several equality and inequality constraints, such as valve point loading effects, ramp rate limits and prohibited operating zones (POZ), are taken into account. Therefore, the DEED problem is considered as a non- convex optimization problem with multiple local minima with higher-order non-linearities and discontinuities. A fuzzy-based membership function value assignment method is suggested to provide the best compromise solution from the Pareto front. The effectiveness of the proposed approach is verified on the standard power system with ten thermal units. Keywords-dynamic environmental/economic dispatch; prohibited operating zones; multi-objective optimization; non- dominated sorting genetic algorithm I. INTRODUCTION In electric power systems, improvement of operation and planning has become more important under the current market conditions and several tools have been developed in this context [1, 2]. Economic load dispatch (ED) is one of them. It aims to schedule the outputs of the committed generating units so as to minimize the total fuel cost under specific system equality and inequality constraints. This objective can no longer be considered alone due to severe environmental standards imposed by legislations. In this respect, the Clean Air Act Amendments have been applied in the USA to reduce pollution and atmospheric emissions such as sulfur oxides, SOX, and nitrogen oxides, NOX, caused by fossil-fueled thermal units [3, 4]. Hence, improvements in dispatching electric power must consider both monetary profits and reduced emissions of gaseous pollution. Thus, we are facing a bi-objective minimization problem, which has been frequently known as the static environmental/economic dispatch (SEED) problem. SEED can only handle a single loading condition at a particular time instant [3-8]. Due to the large variation of the load demand and dynamic nature of the power systems in recent years, it is mandatory to schedule the generator outputs in real time according to the variation of power demands over a certain time period. There are several formulations of this problem, known as the dynamic environmental/economic dispatch (DEED) problem [9-12]. Generally, DEED is a dynamic optimization problem having the same objectives as SEED over a time period subdivided into smaller time intervals with respect to the constraints imposed on system operation by generator ramp-rate limits. Time period and time intervals can be one day and one hour, respectively. Therefore, the operational decision at an hour may affect the operational decision at a later hour. Authors in [11-16] summarize several techniques for solving dispatch problems. Conventional methods, such as dynamic programming, nonlinear programming, network flow method, and interior point method [16] have been criticized as they are iterative, sensitive to initial solution and converge into local optimum solution. To overcome these difficulties, more recent works centered around artificial intelligence (AI), such as genetic algorithm [17], Tabu search [18], particle swarm optimization [19-20], simulated annealing [12], differential evolution [13] and bacterial Corresponding author: Ahmed Torchani Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4586-4590 4587 www.etasr.com Torchani et al.: Dynamic Economic/Environmental Dispatch Problem Considering Prohibited … foraging [14]. These techniques proved to have a clear edge over traditional methods in solving DEED problems without any or less restrictions on the shape of the objective functions curves where multiple Pareto-optimal solutions can be obtained in a single run. Most of the past studies have only focused on the SEED problem except for a few where the multi-objective DEED problem is considered [14]. In [14], prohibited operating zones, ramp rate limit constraints and valve point loading effects (VPLE) have been considered. Therefore, the DEED becomes highly nonlinear and with discontinuous and non-convex cost functions. Within this context, this paper presents an elitist multi- objective approach for solving the DEED problem including POZ, valve point loading effects, and ramp rate limit constraints. This proposed method, called second version of the non-dominated sorting genetic algorithm (NSAGII), incorporates a crowding distance comparison at the end of each iteration in order to facilitate the convergence of the optimization algorithm to the real Pareto optimal front. In general terms, the contribution of this study is to show that the NSGA approach used frequently for solving continuous problems can be efficient for non-smooth and non-convex DEED problems if a non-domination sorting technique is incorporated in the optimization algorithm. In addition, the ramp rate limit constraints have been considered during transition from the last hour of a day to the first hour of the next. A fuzzy set theory [5] is used to extract the best compromise solution from the Pareto optimal front for the decision makers. The proposed approach was tested on a ten- unit test system incorporating all above constraints. This approach showed a very competitive performance when compared with the original NSGA algorithm. II. PROBLEM FORMULATION The DEED problem is considered as a multi-objective problem (MOP). It aims to minimize simultaneously the total fuel cost and total emission of thermal units over a certain period of time subdivided into smaller time intervals. Several equality and inequality constraints are considered in the problem formulation. Considering a power system with N generators, the total fuel cost function TC in ($/h) including VPLE and emission in (ton/h) are, respectively described by (1) and (2) [20]: ( ) ( ) 2 min sin 1 1 T N t t t C a b P c P d e P PT i i i i ii i i i t i    = + + + −∑ ∑     = =   (1) ( ) ( ) 2 2 10 exp 1 1 T N t t t E P P PT i i i i ii i i t i α β γ η λ   −  = + + +∑ ∑   = =    (2) where, t iP is real power output of the i-th unit at time t. T is the number of hours. ia , ib , ic , id and ie are the cost coefficients of the i-th unit. iα , iβ , iγ , iη and iλ are the emission coefficients of the i-th unit. Objective functions CT and ET are optimized subject to the constraints described below. A. Generation Limits min max , 1,..., t P P P i Ni i i≤ ≤ = (3) B. Power Balance Constraints Total demand power t DP and total losses t LP must be covered at each interval of time t. 0, 1,..., 1 N t t t P P P t T i D L i − − = =∑ = (4) In this study, total losses are expressed as follows [20]: 1 1 1 N N N t t t t P P B P B P B L i ij j oi i oo i j i = + +∑ ∑ ∑ = = = (5) where ijB , oiB , ooB are called B coefficients. C. Ramp Rate Limits 1t t down P P R i i i − − ≤ (6) 1 upt t P P R i i i −− ≤ (7) where down iR and up iR are the down and up rate limits of the i- th unit, respectively. D. Constraints Due to Prohibited Operating Zones min 1 1 , 2,..., max t P P Pii i kt t k P P P P k zi ii i i z tiP P P i ii  ≤ ≤   − ∈ ≤ ≤ =   ≤ ≤ (8) where iz is the number of prohibited operating zones for the i- th unit, and k iP and k iP are upper and lower bounds of the prohibited zone number k. III. IMPLEMENTATION OF THE PROPOSED METHOD Multi-objective evolutionary algorithms using non- dominated sorting and sharing, such as NSGA and NPGA, have been criticized for the absence of elitism. Therefore, the second version of NSGA, called NSGAII [21] is utilized in this study for solving the DEED problem. In this approach, the sharing function approach is replaced with a crowded comparison. Initially, an offspring population Qt is created from the parent population Pt at the t-th generation. Then, a combined population Rt is formed: R P Q t t t = ∪ (9) Rt is sorted into different no-domination levels Fj. So, we can write: 1 rR F jt j  =  =   ∪ (10) Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4586-4590 4588 www.etasr.com Torchani et al.: Dynamic Economic/Environmental Dispatch Problem Considering Prohibited … where, r is the number of fronts. To offer a higher precision with reduced CPU time, this algorithm has been implemented using real-coded genetic algorithm in [5, 19]. IV. RESULTS AND SIMULATION The effectiveness of the proposed optimization algorithm for solving the DEED problem is assessed on the 10-unit system. All system data are taken from [14, 20]. The B-loss coefficients are given below. 0.49 0.14 0.15 0.15 0.16 0.17 0.17 0.18 0.19 0.20 0.14 0.45 0.16 0.16 0.17 0.15 0.15 0.16 0.18 0.18 0.15 0.16 0.39 0.10 0.12 0.12 0.14 0.14 0.16 0.16 0.15 0.16 0.10 0.40 0.14 0.10 0.11 0.12 0.14 0.15 0.16 0.17 0.12 0.14 0.35 0.11 0.13 0.13 0.4 10B −= 15 0.16 0.17 0.15 0.12 0.10 0.11 0.36 0.12 0.12 0.14 0.15 0.17 0.15 0.14 0.11 0.13 0.12 0.38 0.16 0.16 0.18 0.18 0.16 0.14 0.12 0.13 0.12 0.16 0.40 0.15 0.16 0.19 0.18 0.16 0.14 0.15 0.14 0.16 0.15 0.42 0.19 0.20 0.18 0.16 0.15 0.16 0.15 0.18 0.16 0.19 0.44                                  (11) The NSGAII algorithm is implemented in MATLAB R2009a on a 64-bit operating system on a PC with an Intel i3- 2370M CPU at 2.40GHz. The best compromise solution is generated from the Pareto front using a fuzzy based membership function value assignment method [5]. The NSGAII parameters to find the best Pareto set for the SEED problem have been chosen by trial and error and they were used for the DEED problem. In this study, the maximum number of generations and the population size were both chosen to be 200. • Test case 1: The SEED problem for the ten-unit system with PD=1036MW was considered in this case. Optimal outputs of thermal units for best cost, best emission and best compromise solution have been computed using the proposed optimization algorithm. Results have been compared with those obtained using NSGA. • Test case 2: The DEED for the test system over a 24-hour time horizon was solved under all previous constraints. POZ limits in MW shown in Table I are taken from [22]. Therefore the problem will be more complicated with discontinuities. The hourly variation of the load is depicted in Figure 1. TABLE I. UNIT OPERATING LIMITS IN MW Unit min iP max iP down iR up i R Prohibited zone 1 150 470 80 80 [150 165], [448 453] 2 135 470 80 80 [90 110], [240 250] 3 73 340 80 80 - 4 60 300 50 50 - 5 73 243 50 50 - 6 57 160 50 50 - 7 20 130 30 30 - 8 47 120 30 30 [20 30], [40 45] 9 20 80 30 30 - 10 10 55 30 30 [12 17], [35 45] A. SEED Problem: Test Case 1 For the validation of the proposed algorithm, a comparison with the first version of NSGA is suggested in this case. From Figure 1, it is clear that NSGAII provides the best results and it has better diversity characteristics of non-dominated solutions. From Table II, the minimum fuel cost and emission provided by NSGAII are $61,775.44 and 3,785.47lb respectively. Moreover, the highest value of the fuel cost is found for minimum emission and the highest value of the emission corresponds to the minimum fuel cost since they are conflicting objective functions. Fig. 1. Hourly load variation Fig. 2. Pareto solutions with NSGAII and NSGA (case 1) B. DEED Problem Considering All Constraints: Test Case 2 In this case, the generation output of unit at each hour has been adjusted considering POZ. Consequently, discontinuities are introduced in cost and emission curves corresponding to the POZ. The hourly evolution of the optimum generations using the proposed algorithm for minimum cost is shown in Figure 3. It is clear that the outputs of all units are maximum at hour 12 which corresponds to the maximum load (2150MW). In this sub-section, optimum solution for minimum emission is not displayed due to the space limitation. Table III shows the compromise solution extracted from the Pareto solutions. It is clear that the proposed scheduling of generations satisfies all previous constraints. Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4586-4590 4589 www.etasr.com Torchani et al.: Dynamic Economic/Environmental Dispatch Problem Considering Prohibited … Fig. 3. Hourly evolution of the optimum solution for minimum cost V. CONCLUSION The DEED problem is one of the most crucial issues to be solved in the power system field. It has a great importance in reducing emission of harmful gases and saving energy. In this study, the DEED problem has been formulated as a bi- objective optimization problem with nonlinear constraints including VPLE, ramp rate limits and prohibited operating zones. The second version of the non-dominated sorting genetic algorithm (NSGAII) has been suggested for solving the DEED problem for 24-hour dispatch intervals. To demonstrate the effectiveness of the proposed approach, the standard power system with ten thermal units was used. Various cases with different levels of complexity and discontinuity have been considered. The results of the proposed approach are significantly improved when compared with NSGA. In addition, this approach has the capacity to optimize any number of objective functions simultaneously and generate the Pareto front in a single run. Therefore, other objectives can be included in the main problem such as voltage drop and real power losses. TABLE II. OPTIMUM SOLUTIONS FOR CASE 1 Minimum fuel cost Minimum emission Best compromise solution Method NSAGII NSGA NSGAII NSGA NSGAII NSGA P1 165.657 165.304 165.465 165.277 165.092 165.400 P2 135.000 135.000 136.471 138.754 135.000 135.073 P3 73.0000 73.0000 85.943 89.8068 78.3817 73.0000 P4 60.0000 60.0000 87.8645 88.9776 85.9374 77.8433 P5 221.551 224.103 135.325 124.263 123.237 131.320 P6 120.835 118.647 126.733 126.764 128.576 124.444 P7 130.000 130.000 91.4739 97.8403 129.019 130.000 P8 120.000 120.000 91.9147 89.3054 84.4827 120.000 P9 20.0000 20.0000 79.6906 79.8941 79.5035 51.7425 P10 10.0000 10.0000 55 55.0000 46.6442 47.0783 Cost ($/h) 61775.4 61802.6 63914.4 63905.5 62974.5 62486.2 Emission (lb/h) 4781.79 4800.55 3785.47 3785.51 3880.30 3998.43 ACKNOWLEDGMENT The present work was undertaken within the research project (No: 160803), funded by the Deanship of Scientific Research, at the University of Hail, which is gratefully acknowledged. TABLE III. BEST COMPROMISE SOLUTION OF DEED FOR TEST CASE 2 Hour P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 1 165.0185 136.1190 73.0000 88.1843 125.1063 121.1142 130.0000 119.4657 52.5923 45.2700 2 165.1026 135.1579 81.5542 108.405 173.2150 122.5238 100.0000 120.0000 80.0000 46.7179 3 165.0594 135.7696 130.6567 127.3521 183.7788 159.8147 129.6961 120.0000 80.0000 54.5710 4 165.5635 182.8389 164.0515 160.2915 225.3338 159.3824 130.0000 119.8330 79.8469 54.9029 5 165.4107 202.1567 185.8223 182.477 240.2090 159.8194 129.8451 119.7818 79.8544 54.6686 6 205.1453 218.9835 245.006 228.7587 243.0000 160.0000 121.126 120.0000 80.0000 55.0000 7 200.0936 220.9863 294.5041 278.7587 243.0000 160.0000 106.1606 120.0000 77.1945 55.0000 8 232.4056 297.4300 259.7886 263.0712 243.0000 157.1222 127.8133 120.0000 80.0000 55.0000 9 295.7609 309.5763 339.7886 263.2257 241.7996 160.0000 130.0000 120.0000 80.0000 55.0000 10 317.6374 355.8988 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 11 358.3159 412.7551 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 74.8769 55.0000 12 379.7618 434.7244 339.9887 299.9990 242.9959 160.0000 129.9935 119.9976 80.0000 54.9757 13 346.8023 381.7131 340.0000 299.9520 242.9962 159.9909 130.0000 119.977 79.9899 55.0000 14 302.4077 308.1888 300.5633 295.9688 243.0000 160.0000 130.0000 119.9821 80.0000 55.0000 15 228.2163 264.2944 285.2806 270.8877 243.0000 159.4424 129.6214 119.887 79.9751 54.5439 16 165.3236 222.6713 209.3282 239.4035 243.0000 159.4886 129.903 120.0000 54.6538 54.5022 17 165.1747 216.9418 186.1643 189.4035 242.8615 159.9508 129.8344 119.8230 55.0000 55.0000 18 226.6097 223.5607 229.9497 234.5908 242.8186 160.0000 130.0000 119.9758 55.0000 54.7545 19 239.3959 299.4056 276.9271 258.0446 242.9016 159.8063 129.7669 119.8321 54.7896 54.8522 20 276.0364 342.8300 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 21 302.8172 308.8301 298.5865 298.2182 242.3453 159.9713 129.7167 119.7893 80.0000 54.8529 22 224.9485 228.8301 218.5865 258.7530 209.6452 160.0000 130.0000 120.0000 80.0000 46.5327 23 165.4124 149.0684 141.616 209.7076 166.2512 157.8307 128.9253 119.6998 79.8154 45.7563 24 165.5672 135.0000 73.0000 138.1843 175.1063 145.5599 123.5542 120.0000 80.0000 53.6633 Total cost ($) 2526555.7207 Total emission (lb) 302900.8703 Total losses (MW) 1301.8534 Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4586-4590 4590 www.etasr.com Torchani et al.: Dynamic Economic/Environmental Dispatch Problem Considering Prohibited … REFERENCES [1] F. 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