CHAPTER 5 EMISSION AND ECONOMIC DISPATCH PROBLEMS

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1 108 CHAPTER 5 EMISSION AND ECONOMIC DISPATCH PROBLEMS 5.1 INTRODUCTION The operation and planning of a power system is characterized by having to maintain a high degree of economy and reliability. Among the options available to the power system engineers to operate the generation system, the most significant is the economic dispatch. Traditionally electric power plants are operated on the basis of least fuel cost strategies and only a little attention is paid on the pollution produced by these plants. The generation of electricity from the fossil fuel releases several contaminants such as sulfur oxides, nitrogen oxides and carbon dioxide into the atmosphere. But on decreasing the pollution by suitably changing the generation allocation, the cost of generation increases deviating from the economic dispatch. The passage of the Clean Air Act Amendments of 1990 and its acceptance by all the nations has forced the utilities to modify their operating strategies to meet the rigorous environmental standards set by this legislation (Baskar et al 2002). Thus the modern operational strategies of the generating plants now include reduction of pollution level up to a safe limit set by environmental regulating authority, in addition to minimum fuel cost strategy and transmission security objective. The characteristics of emission of various pollutants are different and are usually highly non-linear. This increases the complexity of the economic and emission dispatch problems. Recently there

2 109 is an upsurge in the use of evolutionary algorithms such as genetic algorithms, evolutionary programming and bacteria foraging strategy. The BFA is a powerful and general global optimization method which does not require the strict continuity of classical search techniques; instead it allows nonlinearity and discontinuities to appear in the solution space. This chapter presents the application of proposed bacteria foraging optimization algorithm for the test case that has been solved for (i) (ii) Economic dispatch without considering emission constraints Emission dispatch (iii) Combined economic and emission dispatch (CEED) (iv) Emission constrained economic dispatch (ECED) The example problem of IEEE 30 bus system with 6 generating units has been taken for the study and using MATLAB 7.3 the proposed algorithm is implemented. The solution obtained by the proposed method is compared with the conventional method, real coded GA, hybrid GA and PSO methods taken from the source. 5.2 OBJECTIVE FUNCTION The Economic Load Dispatch (ELD) is minimization of total fuel cost without considering the emission limitations. The ED is minimization of total emission without considering the economic aspects. The emission is taken in to the formulation of economic dispatch by several ways. One approach called CEED is to minimize both the operating fuel cost and emission cost, since the economic dispatch deals with only minimizing the system fuel cost violating the emission constraints and emission dispatch deals with minimizing only the emission of NO x and SO x with the violation of

3 110 economic constraints. To achieve both these objectives in a single dispatch, the combined economic and emission dispatch technique is used (Sudhakaran et al 2007). Another approach called ECED is considering emission as an inequality constraint. Combined Economic and Emission Dispatch formulated as The combined economic and emission dispatch problem can be Minimize f (FC, EC) (5.1) Subject to P D +P L P i = 0 (5.2) P min P i P max (5.3) Here, FC is the total fuel cost and if the input-output characteristic of the i th generator is represented by a function Fi ( Pi ) in Rs/hr, then FC is given by FC = F i (P i ) (5.4) Similarly, if E i (P i ) denotes the emission released from i th generator, then the total emission released EC in Kg / hr is given by EC = E i (P i ) (5.5) by equation P D is the power demand; and P L is the transmission loss and is given P L = P m B mn P n (5.6)

4 111 where B mn is the coefficients of transmission loss formula. Now, by introducing a price penalty factor (h), the above said multi-objective function is converted into a single objective optimization problem as follows, Minimize F = FC + h EC Rs / hr (5.7) Subject to the power balance constraint of equations, h is the price penalty factor which blends the emission cost with the fuel cost. After introducing the price penalty factor, the total operating cost is the sum of fuel cost and the implied cost of emission. This factor avoids the use of two classes of dispatching and the need to switch over between them. A practical way of determining the value of h is discussed below. Assuming that the system is operating with a load of P D MW and it is necessary to find price penalty factor at this load (Scott and Marinho 1979). 1. The average fuel cost of each generator is evaluated at its maximum output, F i (P i max ) / P imax Rs / MW (5.8) 2. The average emission release of each generator is evaluated at its maximum output, E i (P imax ) / P imax Kg / MW (5.9) 3. The average cost of each generator is divided by its average emission release, i F i (Pi ) E (P ) i i 4. i = (F i (P i max ) / P imax ) / (E i (P imax ) / P imax ) (5.10)

5 i is arranged in ascending order 6. The maximum capacity of each unit, (P max ) is added one at a time, starting from the smallest unit until P max P D (5.11) 7. At this stage, associated with the last unit in the process is the price penalty factor h, Rs/kg for the given load demand P D. Emission Constrained Economic Dispatch The main objective of this problem is to determine the most economical loading of the generators, such that, the load demand can be met and the operation constraints of the generators are satisfied. In addition, the total emissions need to satisfy the allowable emission limit. In ECED, FC is to be minimized subject to the power balance constraint equation, the generation limit constraint and the emission limit constraint equation E i (P i ) E lt (5.12) Where E lt is the total emission limit over the horizon. Constraint Satisfaction Technique In order to make all the members of the population as feasible solution, the constraint satisfaction technique is introduced. To satisfy the equality constraint of Equation (5.2), a loading of any one of the units is selected as the dependent loading P d and its present value is replaced by the value calculated according to the following equation, P d = P D + P L P i (5.13)

6 113 where i= 1 to n; i d Where P D can be calculated directly from the above equation with the known power demand P D and the known values of remaining loading of the generators. Therefore, the dispatch solution will always satisfy the power balance constraint provided that P d also satisfies the operation limit constraint as given in Equation (5.3). An infeasible solution is omitted and above procedure is repeated until P d satisfies its operation limit. Because P L also depends on P d, an expression for P L can be substituted in terms of P 1, P 2,.,P d,..,p n and B mn coefficients. After substituting it in the Equation (5.13), separate the independent and dependent generator terms to obtain a quadratic equation for P d. Solving the quadratic equation for P d, the power balance equality condition is exactly satisfied (Heydt and Grady 1983; Irrisari et al 1998 ). 5.3 ALGORITHMIC STEPS OF PROPOSED ALGORITHM follows: The step-by-step algorithm for the proposed method is explained as 1. Specify the maximum and minimum limits of generation power of each generating unit, maximum number of iterations to be performed and fuel cost coefficient of each unit. 2. Initialize randomly the individuals of the population of bacteria according to the limit of each unit including individual dimensions and searching points. These initial individuals must be feasible candidate solutions that satisfy the practical operation constraints. 3. To each bacterium of the population the dependent unit output P d will be calculated from the power balance equation and

7 114 B-coefficient loss formula is employed to calculate the transmission loss P L. 4. Calculate the evaluation value of each population P g using the i evaluation Equations (5.6) and (5.7). 5. Calculate the price penalty factor using the Equation (5.9). 6. Compute the new evaluation function using the Equation (5.8). 7. Complete the selection process among the candidate solutions. 8. Do the operators of BFA among the selected population of bacteria. 9. If the number of iterations reaches the maximum then go to step 11, otherwise go to step The best among the individual after the maximum number of iterations reached is the optimal generation power of each unit. 11. Stop 5.4 EXAMPLE PROBLEM AND SIMULATION RESULTS In order to compare the validity and usefulness of the proposed BFA method, IEEE 30 bus system with 6 generators has been taken (Bansal 2005). The example problem is solved by the proposed algorithm for Economic load dispatch, Emission dispatch, Combined economic and emission dispatch and Emission constrained economic dispatch. A reasonable B mn loss coefficients matrix of power system network was employed to draw the transmission line loss and satisfy the transmission capacity constraints.

8 115 Example Problem: IEEE-30 Bus system with 6 generators Fuel Cost Equations, Rs/h F1 = P P F2 = P P F3 = P P F4 = P P F5 = P P F6 = P P NOx Emission Equations, kg/h E1 = P P E2 = P P E3 = P P E4 = P P E5 = P P E6 = P P Generator Capacity Limits Generator P max, MW P min, MW

9 116 Loss formula coefficient (B mn ) Matrix B mn = The parameter selection for the proposed algorithm is shown below. Parameter Selection No.of iterations 50 No.of bacteria 20 No.of chemotactic steps 5 No.of reproduction 2 No.of swim 4 Probability of elimination and dispersal events 0.35 d attract , attract - 3e -6, h repellent , repellent - 15e -5 With the system load of 700 MW, the example problem is solved for economic load dispatch and emission dispatch by the proposed BFA method and the results are compared with the conventional method, real coded GA and hybrid GA and PSO method directly taken from reference Tables 5.1 and 5.2 respectively.

10 117 Table 5.1 Economic load dispatch results for a power demand P D =700 MW Method Conventional method Real Coded GA Hybrid GA PSO Method Fuel Cost Rs / hr Emission Kg / hr Losses P L (MW) Proposed BFA Table 5.2 Emission dispatch results for a power demand P D =700 MW Method Conventional Method Real Coded GA Hybrid GA PSO Method Fuel Cost Rs / hr Emission Kg / hr Losses P L (MW) Proposed BFA The CEED solution for the power demand of 900MW and 500MW has been done for the example problem. The price penalty factor for the above power demands are calculated as Rs/Kg and Rs/Kg

11 118 respectively. The fuel cost, emission, power losses and total cost for the above power demands are compared with other methods like conventional method, real coded GA, hybrid GA and PSO method and are shown in Tables 5.3 and 5.4. From the comparison of results it is proved that the proposed method is capable of finding the global optimal or near global optimal solution. The ECED solution for the example problem is solved for the power demand of 1100 MW with a predefined emission limit of 1060 Kg/hr. The solution obtained by the proposed BFA algorithm is shown in Table 5.4. The fuel cost, emission and total cost obtained by the proposed algorithm for the above demand is compared with the conventional method and PSO method. From the comparison, the ability of the proposed algorithm for the solution of nonlinear problems is proved. Table 5.3a Combined economic and emission dispatch results (a) For Power Demand (P D )= 900 MW; Price Penalty factor (h) = Rs/kg Method Conventional Method Real Coded GA Hybrid GA PSO Method Fuel Cost Rs / hr Emission Kg / hr Losses P L (MW) Total Cost Kg / hr Proposed BFA

12 119 Table 5.3b Combined economic and emission dispatch results (b) For Power Demand (P D ) = 500 MW; Price Penalty factor (h) = Rs/kg Method Conventional Method Real Coded GA Hybrid GA PSO Method Fuel Cost Rs / hr Emission Kg / hr Losses P L (MW) Total Cost Kg / hr Proposed BFA Table 5.4 Emission constrained economic dispatch results for power demand = 1100MW E lt Kg/hr Method Conventional Method PSO Method Fuel Cost Rs/hr Emission Kg/hr Losses P L (MW) Proposed BFA The convergence characteristics of the proposed bacteria foraging algorithm for the power demand of 500MW for the CEED solution of the example problem is shown in Figure 5.1. The reliability characteristics of the proposed algorithm for the above demand is shown in Figure 5.2 for 50 runs.

13 120 From the Figures 5.1 and 5.2 shown below, the ability of the proposed algorithm and the reliability of the algorithm for the solution of nonlinear problems are proved. The base case power flow results of Newton-Raphson method for the IEEE 30 bus system has been presented in APPENDIX 1. The power flow result for the actual generation of MW has been calculated in APPENDIX 2. The coding in MATLAB 7.3 has been developed for the implementation of the proposed algorithm and the execution of the MATLAB 7.3 programs are done in INTEL Pentium Core 2 duo processor with 2.6 GHz and a RAM of 1GHz. Figure 5.1 Convergence characteristics of the proposed algorithm for CEED solution (P D =500MW)

14 x Number of runs Figure 5.2 Reliability characteristics of the proposed algorithm (P D =500 MW) 5.5 CONCLUSION In this chapter, the BFA method was successfully employed to solve the economic dispatch, emission dispatch, combined economic and emission dispatch and emission constrained economic dispatch problems with all the constraints. The results by the proposed BFA algorithm was compared with other methods like conventional method, real coded GA, hybrid GA and PSO methods. In Table 5.1, a total fuel cost of 36,922 Rs/Hr for a power demand of 700 MW was obtained for the ELD solution by the proposed method which is less than the other methods addressed in literature. As shown in Table 5.2, the emission dispatch by proposed method resulted in total emission of Kg/Hr for a power demand of 700 MW which is less as compared with other methods. The CEED solution obtained by proposed method for the power demands of 900 MW and 500 MW were compared with other methods

15 122 which showed that the proposed method reduces both fuel cost and emission. The ECED solution obtained by the proposed method exactly satisfies the emission limitation which resulted in a total fuel cost of Rs/Hr. From the solution obtained, it has been demonstrated that the proposed algorithm can give high quality solution and stable convergence characteristics. Many nonlinear characteristics of the generators can be handled efficiently by the proposed algorithm. Figure 5.1 shows the convergence characteristics of the proposed algorithm for the six units system. Figure 5.2 shows the reliability of the proposed algorithm for different runs of the program, which shows that irrespective of the run of the program the proposed algorithm is capable of obtaining a same result for the example problem. From the comparison of results, it is proved that the algorithm has the ability of identifying global or near global optimum solution and also has the capability to handle the equality and inequality constraints.