Approach of economic‐emission load dispatch using Ant Lion Optimizer

To solve the problem of the economic emission load dispatch (EELD) is necessary minimize the total cost of fuel consumption and carbon emission. In this study is applied the ant lion optimizer (ALO) to this problem. The cost function and emission function with their respective restrictions are being using. To present the results this proposal is applied in IEEE 30 bus system that consists of six thermal units. The results for this case study with the application of ant lion with all generators on with demand being met, the total fuel cost is 48915.36652 ($/h). The results this method can be compared with another metaheuristic algorithms and helps the plant operators in the decision making of preventive maintenance.


I. INTRODUCTION
The Thermal Power Plant (TPP) operation is dependent upon incineration of fossil fuel which generates sulfur dioxide (SO2), carbon dioxide (CO2) and nitrogen oxides (NOx) which create atmospheric pollution. Reduce the emission level and total cost of generation and at the same time accomplishing the demand for electricity from the power plant is is the goal of economic emission load dispatch (EELD). To solve the EELD problem is necessary minimize the total cost of fuel consumption and

II. MATERIAL AND METHODS
To solve a problem of EELD, two important objectives in an electrical power system must be considered; they are: environmental, and economy impacts (Basu, 2014).

Economic Load Dispatch
where ai, bi and ci are the fuel cost coefficients of the ith unit generating, N the number of generators and Pi the active power of each generator. Fig. 1 illustrates the fuel cost curve without valve-point effects and emissions.

Economic Emission Dispatch
Emissions can be represented by a function, that links emissions with power generated by each unit. The emission function in kg/h, which normally represents the emission of SO2 and NOx, is a function of the power output of the generator, and it can be expressed as follows (Swain, Sarkar, Meher, & Chanda, 2017): Where di, ei and fi are the emission coefficients of the ith unit generating, N the number of generators and Pi the active power of each generator, from the TPP.

Economical load dispatch constrains
where Pi is the output power of each i generator, P D is the load demand and P L are transmission losses, in other words, the total power generation has to meet the total demand P D and the actual power losses in transmission lines P L (Dewangan, Jain, & Huddar, 2015).
The calculation of power losses P L involves the solution of the load flow problem, which has equality constraints in the active and reactive power on each bar as follows (Nwulu & Xia, 2015): A simplification is applied to model the transmission losses, setting them as a function of the generator output through Kron's loss coefficient derivatives of the Kron formula for losses (Huang et al., 2018).
where Bij, B0i and B00 are the energy loss coefficients in the transmission network and n is the number of generators. A reasonable accuracy can be obtained when the actual operating conditions are close to the base case, where the B coefficients were obtained (Gitizadeh & Ghavidel, 2014).

Production Capacity Constraint
The power capacity total generated from each generator is restricted by the lower limit and by the upper limit, so the constrain is (De et al., 2018): (6) where Pi is the output power of the i generator, Pmin.i, is the minimal power of the i generator and Pmax.i, the maximal power of the i generator.

Fuel Delivery Constraint
At each time interval, the amount of fuel supplied to all units must be less than or equal to the fuel supplied by the seller, i.e. the fuel delivered to each unit in each interval should be within its lower limit Fmin,i and its upper limit Fmax,i so that (Qu et al., 2018): where Fi,m is the fuel supplied to the engine i at the interval m, Fi,min is the minimum amount of fuel supplied to i generator and Fmax,i is the maximum amount of fuel supplied to i generator.

Optimization problem
The multi-objective optimization problem is defined as follow:

Ant lion optimization
The Ant Lion Optimizer (ALO) is a algorithm ins pired by nature (Mirjalili, 2015). The ALO algorithm mimics interaction between antlions and ants in the trap. To model such interactions, ants are required to move over the search space, and antlions are allowed to hunt them and become fitter using traps. Since ants move stochastically in nature when searching for food, a random walk is chosen for modelling ants' movement as follows [28]: where cumsum calculates the cumulative sum, n is the maximum number of iteration, t shows the step of random walk (iteration in this study), and r(t) is a stochastic function defined as follows (Trivedi, Jangir, & Parmar, 2016): where t shows the step of random walk (iteration in this study) and rand is a random number generated with uniform distribution in the interval of [0, 1].
To keep the random walk in the boundaries of the search space and prevent the ants from overshooting, the random walks should be normalized using the following equatio n (Yao & Wang, 2017): where is the minimum of i-th variable at t-th iteration, indicates the maximum of i-th variable at t-th iteration, is the minimum of random walk of i-th variable, and is the maximum of random walk in i-th variable. To simulate the trapping of ants the mathematical expression of the trapping of the ants to the ant lion's pits is given by following equations (Trivedi et  where, = the random walk nearby the ant lion chose by means of the roulette wheel at t th iteration, = the random walk nearby the elite at t th iteration, = the location of i th ant at t th iteration.

ALO applied to EELD
Initialize random walks on ants using Eq (10) and save generation scheduling of generating units as ant position using Eq (20) described below: where is the matrix for saving the position of each ant, , shows the value of the jth variable (dimension) of ith ant, n is the number of ants, and d is the number of variables.

International Journal of Advanced Engineering Research and Science (IJAERS)
[ Vol -5, Issue-7, July-2018]  https://dx.doi.org/10.22161/ijaers.5.7.26  ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com For evaluating each ant (i.e., generating units), the following objective functions described in Eq. (1) and Eq (2) are utilized during optimization and following matrix stores the fitness value of all ants: where is the matrix for saving the fitness of each ant, , shows the value of jth dimension of ith ant, n is the number of ants, and f is the objective function.
Save the optimal cost and generation scheduling using Eqs. (22) and (23)  This solution comprises the number of generations of the system that will be optimized, which results in minimization of cost and emissions described in Eq (8) by fulfilling all constraints described in Eq (3), Eq (6) and Eq (7). Equation (8) are applied in the performance evaluation of the EELD until the optimum cost and emission is achieved. For inequality constraints, similar to any other techniques, when the solutions obtained for any iteration are out of boundaries, ALO chooses the boundaries values, while for equality constraint, when it is violated, the penalty factor of 1000 is implemented and embedded in the cost function as per Eq. (8). The algorithm will continue until the maximum iteration is met, and the optimum results are obtained.  The data of IEEE 30 bus test system to apply in ALO optimizer is presented in table 1, table 2 and table 3.    The graphics with pareto front of costs versus emissions and the using all generators is presented in fig. 4. Source: Authors.

III. SIMULATION TESTS AND RESUTS
The graphics with power, emission and cost are presented in figure 5, 6 and 7 respectively.