Cuckoo Search based Long-term Emission Constrained Generation Scheduling for Thermal- Wind Hybrid System

Transcription

1 Cuckoo Search based Long-term Emission Constrained Generation Scheduling for Thermal- Wind Hybrid System Biswa Ranjan Kuanr, Niladri Chakraborty Department of Power Engineering Jadavpur University Kolkata, India Abstract In this work a cuckoo search based solution technique is proposed for long term emission constrained generation scheduling of a thermal-wind hybrid power system. While formulating the objective function running cost and maintenance cost of thermal unit is taken into consideration while for wind generating unit only maintenance cost is considered. Above formulated objective function is subjected to various constraints such as real power balance constraint, generation capacity limit constraint and reserve constraint. In this work a weight factor based approach is adopted to convert the multi-objective emission constrained generation scheduling problem to a single objective optimization problem. Proposed solution technique is applied to a test system comprising of 10 thermal generating units and 2 wind farms. A detailed analysis of the result established the superior computational capability of the cuckoo search algorithm in comparison to several other standard meta-heuristics. Keywords cuckoo searh; generation scheduling; hybrid system; multi-objective optimization. I. INTRODUCTION With growth in population and rapid industrialization electrical energy demand is getting sky-rocketed. Meeting such a vast energy demand only from fossil fuel fired power plant is not prudent as fossil fuel storage of earth is rapidly depleting and it s burning causes degradation in air quality and damage to the eco-system. In last few decades there has been substantial improvement in wind power technology and solar photovoltaic technology. Hence, now a day s energy producers prefer to produce energy from renewable sources instead of fossil fuel. But due to intermittent nature of wind and solar radiation meeting a load demand fully (if feasible) from renewable sources are not advisable. However, reliability of the energy supply can be increased by integrating production from these renewable energy sources to conventional thermal grid. In this way they will also complement thermal energy production. This type of systems where electrical energy is produced from both fossil fuel as well as renewable sources is termed as hybrid power systems. Emission constrained generation scheduling problem is one of the most primitive optimization problems [1] in power system whose primary objective is to minimize both operating cost as well as emission by proper allocation of load to different available generating units while satisfying all system constraints. Talaq et al. [2] in their work presented a brief review of modeling of thermal emissions, mathematical modeling of the problem and various dispatch strategies for emission constrained generation scheduling problem. Various solution techniques have been proposed to obtain optimum solution to complex generation scheduling problem. In a research work a liner programming based optimization technique was implemented [3] which was able to optimize a single objective at a time. But it fails to obtain the global optimum and gives no idea pertaining to trade-off between fuel cost and emission. Another group of researchers converted the multi objective generation scheduling problem to a single objective optimization problem by weighted sum approach [4]. By varying the weight factor a trade-off between cost and emission is attainable. ε-constant method, in which objective with highest priority is optimized while other objectives are considered as constraints and restricted within an permissible limit of ε are implemented elsewhere [5]. Various other metaheuristics which are successfully implemented to solve complex generation scheduling problem includes Nondominated Sorting Genetic Algorithm (NSGA) [6], Niched Pareto Genetic Algorithm (NPGA) [7], Strength Pareto Evolutionary Algorithm (SPEA) [8], Multi-Objective Particle Swarm Optimization (MOPSO) [9], Modified Bacterial Foraging Algorithm (MBFA) [10], Differential Evolution (DE) [11] and Cultural Algorithm (CA) [12]. In the world of optimization nature based meta-heuristics are very popular. Cuckoo search is one such technique which is based on the concept of brood parasitism of cuckoo species [13]. In nature, cuckoo lays eggs on nest of other birds and depends on them to bring up its offspring. The chances of survival of cuckoo gene are increased by this parasitic behavior as there is no need to expend energy on rearing offspring. Instead, it tries to breed more and increase its population. However, in case the host bird recognizes the cuckoo eggs it either throws the eggs or leave the nest. This behavior of cuckoo species is mathematically exploited in cuckoo search algorithm to find the global optimum of complex optimization problems /14/$ IEEE

2 Though applications of cuckoo search in solving complex optimization problems are many, its application to solve complex generation scheduling problem in hybrid systems is hard to find. In this work, a cuckoo search based solution technique is proposed to find generation scheduling of a hybrid system comprising of 10 thermal units and 2 wind firms. The scheduling period is of 1 year with monthly interval for generation change. For formulating the objective function both running and maintenance cost of thermal generating unit is taken into consideration while for wind only maintenance cost is considered. Constraints of this generation scheduling problem include real power balance constraint, generation capacity limit constraint and spinning reserve constraint. A comparative study of the obtained result with other standard techniques proves the superior computational efficiency of cuckoo search algorithm. II. ENERGY FROM WIND Output power developed by a wind turbine can be obtained from the wind-power curve of the unit provided by the manufacturer. Mathematically wind power generated by wind turbine can be modeled as [14]: = 0, 0 < (+ + ), < (1), < 0, > Where is the output power developed by wind turbine in MW, is the rated power of the turbine in MW,,, are actual, cut-in,cut-out and rated wind speed in m/sec. Constant A, B and C can be calculated as follows [14]. = ( ) ( + ) 4 (2) = 4( ( ) + ) (3 + ) (3) = ( ) 2 4 (4) III. PROBLEM FORMULATION Emission constrained generation scheduling problem is categorized as a multi-objective optimization problem as it has two contrasting objective that needs to be minimized simultaneously while satisfying several system constraints. Mathematical modeling of both objectives along with system constraints of emission constrained generation scheduling are detailed below. A. Minimization of Cost Fuel cost of a thermal generating unit with valve point effect can be expressed as:,, = +, +, + sin,, (5) Where, and, denote the fuel cost and power generated by i th thermal unit in time interval t;,,,, are the fuel cost coefficients of i th thermal generating unit, is the number of hours in each time interval and, is the lower generation capacity limit of i th thermal generating unit. Operation and maintenance cost of thermal generation units can be classified into variable operation maintenance cost and fixed operation maintenance cost. Variable operation and maintenance cost varies with the scheduled power output and reserve power of the unit whereas fixed operation and maintenance cost depends on maximum generation capacity of the unit. Variable operation and maintenance cost of a thermal generating unit in time interval t can be modeled as [15]:, Where, =, +, (6),, and denote variable operation and maintenance cost, power generated and spinning reserve of i th thermal unit in time interval t and, is the operating maintenance variable cost of i th thermal unit. Similarly fixed operation and maintenance cost can be expressed as [15]:, =,, Where, denotes fixed operation and maintenance cost of i th thermal unit in time interval t;, represents maximum generation capacity of i th thermal unit and, is the operating maintenance fixed cost of i th thermal unit. Though wind farm has no fuel cost, but it has operation and maintenance expenses. The fixed part of operation and maintenance cost in case of wind generation is negligible [15]. In this work only variable part of operation and maintenance cost is taken into account and given as [15]:, (7) =,, (8) Where, is variable operation and maintenance cost of j th wind turbine in time interval t;, is the power developed by j th wind turbine in time interval t and, is variable operation and maintenance cost of j th wind turbine. After formulation of mathematical model of cost associated with each type of generating unit objective function that has to be minimized can be given as: =, () +, () +, () +, () (9) Where represents total generating cost; denote total number of thermal and wind generating unit; (), () represents the status of i th thermal generating unit

3 and j th wind farm at time interval t. Values of these status variables are set as 1 or 0 depending on whether corresponding unit is ON or OFF. T represents total number of equal time intervals in scheduling horizon. B. Minimization of Pollutants Emission The amount of pollutants such as CO 2, SO 2 emitted from a fossil fueled generating unit can be expressed as:,, = ( +, +, +, ) (10) Where,,,, are emission coefficients of th generating unit. Final objective function for minimization of emission can be given as: =, () (11) Where, and () represent the emission and status of i th thermal generating unit in time interval t. C. Combined Objective Function By adopting weighted sum approach a single objective function is formulated which can be mathematically stated as: = (1 )( ) + ( ) (12) Where weight factor w can be varied between 0 and 1. Value of price penalty factor (in $/lb) for each scheduling interval is calculated by adopting the procedure given in [11]. D. Constraints of the Problem Real power balance constraint: This is an equality constraint which is based on the fact that total real power generated by all the units must be capable of supplying total demand. This constraint can be mathematically stated as:, () +, () = + (13) For = 1,2,3.. Where and represent total power demand and transmission losses in time interval t. Generation capacity limits: Output power generated by each generating unit must lie within its generating limit. For thermal and wind generating unit this constraint can be mathematically represented as:,, + (), (14) = 1,2,3 ; = 1,2,3. 0, (), ; (15) = 1,2,3 ; = 1,2,3. Where all symbols have their usual meaning as stated previously in this paper. Reserve constraint: Amount of reserve requirement in a power system depends on the accuracy of fore casted load, predicted wind speed. Increase in penetration of wind energy in a power system results in more reserve requirement due to intermittent nature of wind energy. The total reserve requirement during a scheduling interval for the present test system is equal to sum of 5% of forecasted load demand and 10% of forecasted renewable energy generation [14]. Mathematically this can be stated as: () = +, () (16) Where LR is a factor that compensates fluctuation in load demand and PSR makes up for any mismatch between forecasted and actual renewable generation. IV. IMPLEMENTATION OF CUCKOO SEARCH ALGORITHM Cuckoo search that imitates the brood parasitism behavior of cuckoo species operates on 3 basic rules[13]. In an optimization problem each feasible solution represents a cuckoo egg. The 3 basic rules of the algorithm are given below. I. Each cuckoo can lay only one egg at a time and it dumps it in a randomly chosen nest. II. Nests those contain high quality eggs move forward to the next generation. III. Number of host nest is constant. Probability of a host bird discovering cuckoo eggs is Pa [0, 1]. Cuckoo search algorithm also implements Levy flight for search process which is more efficient than regular random walks or Brownian motion. Levy flight is characterized by variable step size punctuated by 90 degree turns. Detailed procedure for implementation of cuckoo search algorithm is described below. A. Initialization of parameter In this step algorithm parameter such as number of nests (n), step size parameter (α), discovering probability ( ) and maximum number of iteration are set. Generally number of nest is set between 5 to 10 times of number of decision variable of the optimization problem. Each cuckoo egg contains variables for output of conventional thermal generation unit, variables for reserve amount considered for thermal units and variables for output power of each wind farm. As there are 10 thermal units and 2 wind farms total number of decision variable is 22. Hence, number of nests is set at 150. Step size is set at 0.05 and discovering probability of cuckoo eggs is taken as B. Generation of initial eggs Initial cuckoo eggs are generated according to following equations., =, +,, 0 h (17)

4 , =, (18) =,, 0 h (19) Where, represents random number generated for i th thermal unit and j th wind farm and denotes the random number generated for allocating reserve to i th thermal unit in time interval t. C. Generate new cuckoo eggs by Levy flight New cuckoo eggs are produced with Levy flights which replaces eggs in other nests apart from the best one based on their quality. Formulation process of new cuckoo eggs can be given as[13]: () = () +.. () (). (20) Where () is the current position of the egg in i th nest, α is the step size parameter, is a random number from a standard () normal distribution and is the position of the best nest so far and is a random walk based on Levy flights. Best nest is found out by evaluating the objective function for all eggs. Step length for the random walk is drawn from a Levy distribution using Mantegna algorithm. Step length can be calculated by: = / (21) Where β is a parameter between [1,2] ; and are drawn from normal distribution as: ~(0, )~(0, ) (22) = ()... /, =1 (23) D. Allien egg discovery The alien eggs discovery is modeled by replacing a fraction of total number of eggs in nests by new random solutions. Generally eggs (solutions) those are replaced are of poor quality with lower fitness values. E. Termination Generation of new cuckoo eggs and alien egg discovery process are performed alternatively for a predefined number of iteration. In this work number of maximum iteration is set at 150. V. SIMULATION AND RESULT Proposed solution methodology is applied to a hybrid system consisting of 10 thermal units and 2 wind farms. Emission coefficients, cost coefficients and power generation limits of 10 thermal unit test system is taken from elsewhere [12, 14], hence are not repeated here. Each wind farm has 40 wind turbine generators each of capacity 2MW. For calculating available wind power cut-in speed, cut-out speed and rated speed are taken as 2.5m/sec, 25m/sec and 14m/sec respectively [14]. Monthly wind speed, wind power generation from wind farms and load demand for the test system is presented in [15]. Programs were developed in house in MATLAB 8.1 computational environment and executed in an Intel corei5 2.3 GHz processor with 4GB RAM PC. By varying the weight factor from 0 to 1, 50 different set of solutions are generated to the economic constrained generation scheduling. All these solutions are plotted as a pareto-optimal front in fig. 1. When the objective function is optimized by taking weight factor as zero only cost is minimized while only emission is minimized by taking weight factor as one. The best compromise solution out of the fifty solutions is determined by applying a fuzzified approach as stated in [7]. Monthly generation cost and corresponding emission for minimum of cost, minimum emission and best compromise solution are presented in Table I. TABLE I. MONTHLY COST AND EMISSION FOR MINIMIZATION OF COST, EMISSION AND BEST COMPROMISE SOLUTION Minimization of cost Minimization of emission Compromise solution Month Cost($) Emission (lb) Cost($) Emission (lb) Cost($) Emission (lb) January February March April May June July August September October November December Total Fig. 1. Pareto optimal font for thermal-wind test system by cuckoo search Monthly generation schedule and resolve allocation for above discussed three different scenarios are presented in Table II, Table III and Table IV respectively l

5 TABLE II. GENERATION SCHEDULING FOR MINIMIZATION OF LOSS IN MW Unit Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec (28.32) (48.44) (55.17) (49.91) (59.19) (66.06) (33.21) (29.70) (50.04) (51.56) (12.69) (17.88) (37.41) (39.67) (17.76) (35.51) (12.91) (16.62) (13.27) (60) 25 (60) (19.16) Total (MW) 1317 (67.86) 1125 (59.19) (66.06) 1350 (70.62) 1344 (69.37) 1200 (63.83) 1170 (61.35) (68.18) 1410 (73.27) 1500 (79.16) TABLE III. GENERATION SCHEDULING FOR MINIMIZATION OF EMISSION IN MW Unit Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec (3.65) (10.28) (57.33) (60.94) (32.32) (23.25) (57.51) (0.01) (10.77) (64.07) (0.01) (58.66) (36.10) (0.32) (0.61) (2.31) (0.04) (2.35) (63.55) (5.40) (3.14) (35.79) (2.37) (2.81) (0.07) (1.51) (28.98) (33.22) (7.11) (3.60) (0.38) (0.5) (15.62) (0.21) (10.32) (0.01) (0.1) (51.7) (48.42) (4.96) (41.84) (0.36) (1.91) (2.81) (0.19) (0.66) (0.17) (7.51) (0.73) (2.82) (1.07) (1.27) (3.01) (4.19) (2.35) (0.16) (2.12) (1.02) Total (MW) 1317 (67.86) 1125 (59.19) (66.06) 1350 (70.62) 1344 (69.37) 1200 (63.83) 1170 (61.35) (68.18) 1410 (73.27) 1500 (79.16) TABLE IV. GENERATION SCHEDULING FOR BEST COMPROMISE SOLUTION IN MW Unit Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec (0.06) (29.52) (37.27) (0.17) (3.74) (21.79) (1.80) (20.65) (16.02) (29.59) (14.48) (3.87) (6.24) (14.64) (60.09) (27.77) (10.91) (6.18) (16.84) (13.84) (10.06) (25.91) (25.52) (40.38) (1.93) (41.19) (32.20) (34.85) (29.47) (37.91) (0.05) (3.52) (39.35) (37.41) (0.82) (0.59) (4.40) (27.47) (36.39) (0.03) (0.40) (0.85) (0.02) (0.74) (1.48) (11.81) (9.26) (9.89) (4.00) (1.93) (3.41) 64.54(5.99) Total (MW) 1317 (67.86) 1125 (59.19) (66.06) 1350 (70.62) 1344 (69.37) 1200 (63.83) 1170 (61.35) (68.18) 1410 (73.27) 1500 (79.16)

6 From Table I it should be observed that while cost is minimized ( $) emission remains maximum ( lb) and when emission is minimized ( lb) cost becomes maximum ( $). The best solution provides a compromise between total cost and emission. For best solution total cost and emission stand at $ and l lb respectively. However, the best solution is suboptimal both in terms of emission and cost. In the pareto font presented in fig. 1 it is also evident that with gradual increase in weight factor cost gradually increase while emission decreases. This happens due to the conflicting nature of objectives. From a thorough analysis of Table II it can be inferred that thermal unit 1, 2, 3 and 4 are cost efficient units as they run on full load for cost minimization schedule. But unit 7, 8, 9 and 10 almost remain offline during the entire scheduling period primarily because of their high fuel cost. Similarly unit 7, 8, 9 and 10 are emission efficient as they run on full load for emission minimization schedule. It should also be noted that for all the three types of scheduling output from both wind farm remains maximum as they have no operating cost and no emission. A comparative study of the performance of cuckoo search with different meta-heuristics in case of cost minimization is presented in Table V. TABLE V. PERFORMANCE COMPARISON OF CUCKOO SEARCH WITH OTHER META-HEURISTICS Algorithm Cost ($) ( 10 8 ) Cuckoo search Imperialistic competitive algorithm [15] Particle swarm optimization [14] GAMS-OQNLP [14] GAMS-DICPOT [14] From Table V it is clear that generation scheduling provided by cuckoo search algorithm decreases the annal cost by a substantial amount. VI. CONCLUSION In this work a solution technique based on cuckoo search algorithm is proposed to obtain the emission constrained generation scheduling of a hybrid power system consisting of 10 thermal generating units and two wind farms for a scheduling period of 1 year with monthly interval for scheduling change. Objective function of the problem is formulated by taking fuel cost, maintenance cost and emission from thermal units and only maintenance cost from wind unit into consideration. Above objective function is optimized by cuckoo search algorithm subjected to constraints such as power balance constraints, generation limit constraints and spinning reserve constraints. A trade-off curve of total cost and emission is also generated by varying the weight factor. From a comparative study of the result it is observed that cuckoo search outperforms several other modern meta-heuristics such as imperialistic competitive algorithm and particle swarm optimization. ACKNOWLEDGMENT A part of this work was supported by Departmental Research Scheme (DRS) of University Grant Commission of Government of India awarded to the Department of Power Engineering, Jadavpur University, Kolkata. REFERENCES [1] M.R. Gent, J.Wm. Lamont, "Minimum-Emission Dispatch". IEEE Trans. On Power Apparatus and Systems, Vol. PAS-90, pp , November 1971 [2] J. Talaq, F. El-Hawary, M. El-Hawary, "A summary of Environmental/Economic Dispatch Algortihms". IEEE Trans. on Power Systems, Vol. 9, pp , August [3] A. Farag, S. Al-Baiyat, and T.C. Cheng, Economic load dispatch multi-objective optimization procedures using linear programming techniques. IEEE Trans on Power Systems, vol. 10, pp , May [4] J.S. Dhillon, S.C. Parti, D.P. Kothari, Stochastic economic emission load dispatch. Electric Power Systems Research, vol. 26, pp , April [5] R. Yokoyama, S.H. Bae, T. Morita, H. Sasaki, Multi-objective generation dispatch based on probability security criteria. 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