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A New Approach Computation for Determining Committed Power Outputs of Economic Power System Operation using HSABC Considering Space Areas

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An economic power system operation (EPSO) can be expressed by a total operating cost. Technically, this payment is presented by individual cost of generating units based on a schedule of committed power outputs (CPOs) to meet a total load demand. Presently, a minimum operating cost is performed by considering an economic dispatch and an emission dispatch, which are composed into a combined economic and emission dispatch (CEED) problem. This paper introduces a newest artificial intelligent computation, harvest season artificial bee colony (HSABC) algorithm, for determining CPOs based on a minimum total cost of CEED using IEEE-62 bus system. Simulation results show that HSABC has short time computations and fast convergences. Space areas give different implications on HSABC’s performances.
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  PE-13-119 PSE-13-135 1 / 6 Conference of Joint Technical Meeting of Power System Technology of IEEJ, Kyushu Institute of Technology, Kitakyushu, Japan, September 11-13, 2013  A New Approach Computation for Determining Committed Power Outputs of Economic Power System Operation using HSABC Considering Space Areas  A.N. Afandi, (Kumamoto University & State University of Malang) Hajime Miyauchi, (Kumamoto University)  An economic power system operation (EPSO) can be expressed by a total operating cost. Technically, this payment is presented by individual cost of generating units based on a schedule of committed power outputs (CPOs) to meet a total load demand. Presently, a minimum operating cost is performed by considering an economic dispatch and an emission dispatch, which are composed into a combined economic and emission dispatch (CEED) problem. This paper introduces a newest artificial intelligent computation, harvest season artificial bee colony (HSABC) algorithm, for determining CPOs based on a minimum total cost of CEED using IEEE-62 bus system. Simulation results show that HSABC has short time computations and fast convergences. Space areas give different implications on HSABC’s performances. Keywords: Artificial bee colony, economic dispatch, emission, combined economic and emission dispatch 1.   Introduction   Recently, an economic power system operation (EPSO) considers a global warming caused by pollutant emissions in the air from thermal power plants. These pollutants are released from combustions of fossil fuels in various types like CO, CO 2 , SO x  and NO x(1)-(4) . Presently, the EPSO becomes complex with considering pollutant discharges as an emission dispatch (EmD) under operational limitations. Practically, an EPSO is managed using economical cost strategies for providing electric energy from generator sites to supply load demand areas. These strategies are used to decide the minimum total cost of EPSO to meet a total load demand at a certain time. In particular, a minimum total cost is obtained by minimizing a total fuel cost of generating units troughout an economic dispatch (ED) problem and reducing pollutant emissions in the EmD problem. By involving an EmD, the ED problem is transformed into a combined economic and emission dispatch (CEED) problem for determining a committed power outputs (CPOs) of generating units during operations (5) . Many methods have been introduced to solve CEED problems using traditional and evolutionary methods (3), (6)-(15) . Evolutionary methods have been composed to attempts the natural phenomenons for creating various algorithms. These methods are frequent used to compute CEED problems because of traditional methods suffer for large systems and multidimension spaces. For a couple of years, the most popular evolutionary method is genetic algorithm and this algorithm is inspired by a phenomenon of natural evolution (16) . Recently, the newest evolutionary method is artificial bee colony (ABC) algorithm. This method was proposed in 2005, based on foraging behavior of honeybees in nature (17) . The latest generation of ABC is harvest season artificial bee colony (HSABC) algorithm intoduced in this paper for determining the CPOs of EPSO. The HSABC is applied to a CEED problem for the power system model of IEEE. 2. Harvest Season Artificial Bee Colony   The HSABC is inspired by a harvest season situation in nature for providing flowers. In the HSABC, multiple food sources (MFS) express many flowers located randomly at certain positions in the harvest season area (18), (19).  This space area (SA) is explored by bees to search food sources. To exploit a large number of food sources, bees can fly randomly during foraging for foods and move from a selected current food source to another positions (16), (19), (20) . In the HSABC, MFS are consisted of the first food source (FFS) and other food sources (OFSs). Each position of OFSs is directed by a harvest operator (ho) from the FFS (18), (19). Mathematically, HSABC algorithm is introduced as following expressions:            , ………………... (1)             , ………………………………….. (2)  2 / 6 Conference of Joint Technical Meeting of Power System Technology of IEEJ, Kyushu Institute of Technology, Kitakyushu, Japan, September 11-13, 2013                 , … .....(3)                , …………………………….. (4)         . ………………………………………………. (5) Here, x ij  is a current food, i is the i th  solution of the food source, j  {1,2,3,…,D}, D is the number of variables of the problem, x minj  is a minimum limit of x ij , x maxj  is a maximum limit of x ij , v ij  is the food position, x kj  is a random neighborof x ij , k  {1,2,3,…,SN}, SN is the number of solutions, Ø i,j  is a random number within [-1,1], H iho  is the harvest season food position, ho  {2,3,…,FT},  FT is the total number of flowers for harvest season, x fj  is a random harvest neighborof x kj , f  {1,2,3,…,SN}, R  j  is a randomly chosen real number within [0,1], MR is the modified rate of probability food, F i  is an objective function of the i th  solution of the food, fit i  is the fitness value of the i th  solution and p i  is a probability of the i th quality of food. The HSABC has three agents for exploring the SA, those are employed bees, onlooker bees and scout bees. Each agent has different taks and it is colaborated to obtain the best food as the optimal solution. An employed bee is defined to search a neighbor food source in the SA. Each food source chosen represents a possible solution to the problem. An onlooker bee is subjected to select the best food for the optimal solution. This bee chooses a food source based on the probability value each nectar quality. A scout bee is used to explore food sources for replacing abandoned values.  A set of MFS is prepared for providing candidate foods in the SA for every foraging cycle. A foraging for the foods of HSABC is preceded by searching the FSS and it will be accompanied by OFSs located randomly at different positions in the SA. A set initial population is generated as candidate solutions and it is created randomly by considering objective constraints. For each solution, it is corresponded to the number of parameter to be optimized, which is populated using equation (1). The nectar quality is evaluated using equation (4) and the probability of each food source is determined using equation (5). Each position of candidate food is searched using equation (2) for the FSS and it is followed by OFSs using equation (3). 3. Economic Power System Operation   Technically, the EPSO is presented by a minimum total operating cost. This payment is optimized using a CEED problem considered operational constraints for determining the CPOs of generating units (7), (12), (15), (21), (22) . Basically, the CEED problem of the EPSO considers a total cost of ED as shown in (7) with a fuel cost of each generating unit is given in (6). Pollutant emissions are also included in the CEED (15), (22), (23) .   Each pollutant discharge of generating unit is formed in (8) and the minimized function of EmD is given in (9) for a total pollutan emission. Currently, a minimizing total fuel cost and a reducing total pollutant emission become an important thing in the EPSO. An objective function of CEED is composed using ED and EmD problems with including penalty and compromised factors. Each penalty factor is performed in (10) to shows the rate coefficient of each generating unit at its maximum output for the given load (7), (12) . A compromised factor shows the contribution of ED and EmD in CEED’s computations (19) . The CEED problem is expressed in (11) and this single objective function is constrained using equations (12)  –   (19). In general, the dispatching problem is formulated by using mathematical functions as follows: F i (P i ) =c i +b i P i  +a i P i2  , ………………………………… . … (6) ED minimize                 …………. (7)                    , ……………………………… (8) EmD minimize                     ……….. (9)                 , ………………………………………. (10) CEED minimize      , … . …….. (11)       , ………………………………………... (12)                      … (13)                     ..(14)               , ………  (15)        , ………………………………………. (16)       , ………………………………………. (17)          ……………………………………… (18)     , ………………………………………………. (19) where F i is a fuel cost of the i th  generating unit ($/h), P i  is a output power of the i th  generating unit, a i , b i , c i  are fuel cost coefficients of the i th  generating unit, E i is an emission of the i th  generating unit (kg/h), F tc  is a total fuel cost,  i ,  i ,  i are emission coefficients of the i th  generating unit, E t  is a total emission of generating units (kg/h), E tc  is a total emission cost ($/h), h i  is each penalty factor of the i th  generating unit,   is the CEED ($/h), w is the compromised factor, h is the penalty factor selected from ascending of h i , ng is the number of generators, P imin  is a minimum output power of the i th      3 / 6 Conference of Joint Technical Meeting of Power System Technology of IEEJ, Kyushu Institute of Technology, Kitakyushu, Japan, September 11-13, 2013 generating unit, P imax  is a maximum output power of the i th  generating unit, P D  is the total demand, P L  is the total transmission loss, P p  and P q  are power injections at bus p and q, P Gp  and Q Gp  are active and reactice power injections at bus p from generator, P Dp  and Q Dp  are load demands at bus p, V p  and V q  are voltages at bus p and q, Q imax  and Q imin are maximum and minimum reactive powers of the i th  generating unit, V pmax  and V pmin are maximum and minimum voltages at bus p, S pq  is a total power transfer between bus p and q, S pqmax  is a limit of power transfer between bus p and q. 4. Sample System and HSABC’s Procedures   In these works, IEEE-62 bus system is adopted as a sample model of power system. This system is shown in Figure 1 cosisted 62 buses, 89 lines and 32 load buses. This figure also shows locations of generating units and load positions in the power system. Load data, fuel cost coefficients, power limits and emission coefficients are listed in Table 2, Table 3 and Table 4, respectively. B ee’s parameter are listed in Table 1. Fig. 1. One-line diagram of IEEE-62 bus system Table 1 . Bee’s parameters for running test   No Parameters quantity 1 Colony size 100 2 Food source 50 3 Foraging cycle 100 Fig. 2. Flow chart of HSABC’s application  Table 2. Fuel cost and emission coefficients of generators   Bus Gen a, x10 -3   ($/MWh 2 ) b ($/MWh) c  (kg/MWh 2 )  (kg/MWh)   1 G1 7.00 6.80 95 0.0180 -1.8100 24.300 2 G2 5.50 4.00 30 0.0330 -2.5000 27.023 5 G3 5.50 4.00 45 0.0330 -2.5000 27.023 9 G4 2.50 0.85 10 0.0136 -1.3000 22.070 14 G5 6.00 4.60 20 0.0180 -1.8100 24.300 17 G6 5.50 4.00 90 0.0330 -2.5000 27.023 23 G7 6.50 4.70 42 0.0126 -1.3600 23.040 25 G8 7.50 5.00 46 0.0360 -3.0000 29.030 32 G9 8.50 6.00 55 0.0400 -3.2000 27.050 33 G10 2.00 0.50 58 0.0136 -1.3000 22.070 34 G11 4.50 1.60 65 0.0139 -1.2500 23.010 37 G12 2.50 0.85 78 0.0121 -1.2700 21.090 49 G13 5.00 1.80 75 0.0180 -1.8100 24.300 50 G14 4.50 1.60 85 0.0140 -1.2000 23.060 51 G15 6.50 4.70 80 0.0360 -3.0000 29.000 52 G16 4.50 1.40 90 0.0139 -1.2500 23.010 54 G17 2.50 0.85 10 0.0136 -1.3000 22.070 57 G18 4.50 1.60 25 0.0180 -1.8100 24.300 58 G19 8.00 5.50 90 0.0400 -3.000 27.010 Table 3. Power limits of generators Bus Gen P min (MW) P max (MW) Q max (MVar) Q min (MVar) 1 G1 50 300 0 450 2 G2 50 450 0 500 5 G3 50 450 -50 500 9 G4 0 100 0 150 14 G5 50 300 -50 300 17 G6 50 450 -50 500 23 G7 50 200 -50 250 25 G8 50 500 -100 600 32 G9 0 600 -100 550 33 G10 0 100 0 150 34 G11 50 150 -50 200 37 G12 0 50 0 75 49 G13 50 300 -50 300 50 G14 0 150 -50 200 51 G15 0 500 -50 550 52 G16 50 150 -50 200 54 G17 0 100 0 150 57 G18 50 300 -50 400 58 G19 100 600 -100 600  4 / 6 Conference of Joint Technical Meeting of Power System Technology of IEEJ, Kyushu Institute of Technology, Kitakyushu, Japan, September 11-13, 2013 Table 4. Load demands of each bus Bus no MW MVar Bus no MW MVar 1 0.0 0.0 32 0.0 0.0 2 0.0 0.0 33 46.0 25.0 3 40.0 10.0 34 100 70.0 4 0.0 0.0 35 107 33.0 5 0.0 0.0 36 20.0 5.0 6 0.0 0.0 37 0.0 0.0 7 0.0 0.0 38 166 22.0 8 109 78.0 39 30.0 5.0 9 66.0 23.0 40 25.0 5.0 10 40.0 10.0 41 92.0 910 11 161 93.0 42 30.0 25.0 12 155 79.0 43 25.0 5.0 13 132 46.0 44 109 17.0 14 0.0 0.0 45 20.0 4.0 15 155 63.0 46 0.0 0.0 16 0.0 0.0 47 0.0 0.0 17 0.0 0.0 48 0.0 0.0 18 121 46.0 49 0.0 0.0 19 130 70.0 50 0.0 0.0 20 80.0 70.0 51 0.0 0.0 21 0.0 0.0 52 0.0 0.0 22 64.0 50.0 53 248 78.0 23 0.0 0.0 54 0.0 0.0 24 28.0 34.0 55 94.0 29.0 25 0.0 0.0 56 0.0 0.0 26 116 52.0 57 0.0 0.0 27 85.0 35.0 58 0.0 0.0 28 63.0 8.0 59 0.0 0.0 29 0.0 0.0 60 0.0 0.0 30 77.0 41.0 61 0.0 0.0 31 51.0 25.0 62 93.0 23.0 Main procedures of the HSABC application for determining the CPOs of EPSO are illustrated in Figure 2. This figure also describes sequencing computations for searching the optimal solution based on a total minimum cost of EPSO. HSABC’s procedures are consisted of three steps. The first step is   a formation of objective function for the CEED problem, which is used to compute a minimum total cost for every foraging cycle. The second step is an algorithm composition using employed bees, onlooker bees and scout bees to search the optimal solution. The third step is programming developments for three categories of subprograms in terms of data input program, CEED program and algorithm program. The data input program is consisted of a set data input of parameters, such as generating units, transmission lines, loads and constraints. The CEED program is created to compute an objective function under operational constraints and the number of CEED’s variable is associated with exploring limits of food source. The algorithm program is developed for searching the optimal solution of the CEED problem based on HSABC’s hierarchies. In these programs, three types of bee are collaborated to explore food sources in the SA and the programs are executed for choosing the best food as the optimal solution of CPOs using bee’s parameters as listed in Table 1. Specifically, the best food is selected by using a greedy process in every cycle. 5. Simulation Results   In this section, these simulations are addressed to determine the CPOs of EPSO considered operational constratints given in Section 3. The HSABC is run out using three food sources and the SA is demonstrated using four scenarios for 100%, 75%, 50% and 45% areas.  A set population of these simulations are initialed in Figure 3 for candidate foods considering power constraints of generating units. The population is created for 50 candidate solutions for G1 to G19 in every foraging cycle. Convergence speeds of HSABC for determining the optimal solutions are illustrated in Figure 4. These characteristics are performed using 45%, 50%, 75% and 100% of the SA. Obtained iterations and time consumptions are listed in Table 5. Fig. 3. Initial population Fig. 4. Convergence speeds of HSABC Table 5. Time consumptions of HSABC - 100 200 300 400 500 600 700 0 10 20 30 40 50    F  o  o   d  c  a  n   d   i   d  a   t  e  s   (   M   W   ) Populations G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12 G13 G14 G15 G16 G17 G18 G19 26,000 27,000 28,000 29,000 30,000 31,000 32,000 33,000 34,000    16   1   1   1   6   2   1   2   6   3   1   3   6   4   1   4   6   5   1   5   6   6   1   6   6   7   1   7   6   8   1   8   6   9   1   9   6   O  p   t   i  m  a   l  p  o   i  n   t   (   $   /   h  r   ) Iterations HSABC 45% Area HSABC 50% Area HSABC 75% Area HSABC 100% Area
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