Fuzzy Logic Controlled Based Ant-Lion Optimization Hybridization for Economic Power Dispatch

Many conventional and latest methods had been used for solving the economic power dispatch issues by considering various objective functions. Different conventional techniques like lambda iterative technique, gradient-based technique, Bundle technique [19], non-linear method [20], mixed integer liner programming method [21], Newton-based method [22] etc., were present in literature for solving this economic power dispatch problem. But these existing methods have some disadvantages and failed to solve economic power dispatch issue. Along with these some population based meta-heuristic methods in literature have proved themselves effective performance. Such as Tabu search [23], Genetic Algorithm [24], Ant-Colony Optimization [25], Particle Swarm Optimization [26], Gravitational Search Algorithm with Fire-Fly [27] etc. These methods also always not guarantee in finding optimal outcome. These heuristic methods are also having their disadvantages slow rate of convergence around global solution, time consuming is high, not easy to tune control parameters, difficult in produce effective memory system, trapping into local optima. ALO technique imitates the catching behaviour of ant lions in general. The updating process is done with the elitism phase of ALO. The proposed hybrid technique improves the ability of global search of objective function which provides the better opportunity to increase the solution space. This also provides the global solution for EPD problem. The effectiveness of proposed technique was evaluated with IEEE-30 sus system with six generators in the system. The outcomes obtained by this proposed method compared with conventional ALO and ALO-PSO methods.

New genetic method based on arithmetic crossover was presented to improve the ELD solution quality. In this research arithmetic crossover, elitism both defines a linear combination of two chromosomes and to produce possible operating consecutive sets mutation used in the GA [28].

The solution for ELD problem was presented with line flow constraints the genetic algorithm application. The major advantage of this GA is that it used only the pay of information; hence it is nature independent of search space like smoothness and convexity [29].

An approach using fuzzy decision tree was presented for ELD problem. In this research an improvement has done in DT approach by fuzzy logic addition to load and unit limits. With this there is an improvement in the convergence rate. The cost of generation obtained is also less than the traditional formulation [30].

One hybrid algorithm was presented to solve the ELD problem is the genetic algorithm with fuzzy logic controller with multi-shunt flexible AC transmission systems, which continuously adjust parameters of mutation and crossover [31].

One new formulation was presented for economic dispatch to solve economic load dispatch problem. By reducing the variable numbers and by removing constraints of equality and inequality the new formulation has done. This transformed the constrained non-linear programming into unconstrained one. This new unconstrained formulation objective function is reduced by Hooke-Jeeves’ approach [32].

An effective optimization approach was presented to solve ELD problem based on genetic algorithm with continuous and non-smooth cost function by considering various constraints. The presented algorithm effectiveness finds out on various systems with system losses of thermal power plant [33].

Four evolutionary algorithms study was presented for ELD problem solvation, they are particle swarm optimization, genetic algorithm, ant-colony optimization and bacteria foraging optimization. This research is carried on IEEE-30 test system [34].

In this research, the one hybridization method is presented to solve the EPD issue. To analyse the generating unit’s outputs from the committed generating units, the objective function is defined for IEEE-30 mesh configuration network. By using this new hybrid technique, minimization of cost function by economically dispatch the power to meet the required load and also minimization of system total losses. For this, the test system bus data, line data, committed generating unit’s capacities, minimum and maximum generation capacities, are considered as the input for this new proposed hybrid approach. The total working procedure this new proposed hybrid approach for EPD is demonstrated in Figure 1.

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Figure 1. New hybrid technique flow chart

4.1 Fuzzy logic controller using Mamdani

For this new hybrid approach using Fuzzy Logic controller for inference the system using Mamdani type. The Loss sensitivity Factor (LSF) and the node voltages are considered as the input to the FLC and the fitness evaluation is considered as the output of the FLC.

Triangle membership functions are considered to construct the membership function plots.

Figure 2 shows that the node voltage triangle membership function plot and the low, medium and high are considered as membership function and this is ranging from 0 - 1.

Figure 3 shows that the LSF triangle membership function plot and the low, medium and high are considered as membership function and this is ranging from 0.9 - 1.1.

Figure 4 shows that the fitness triangle membership function plot and the low, medium and high are considered as membership function and this is ranging from 0 - 1.

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Figure 2. Membership function plot for p.u. Nodal Voltage

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Figure 3. Membership function plot for Loss Sensitivity

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Figure 4. Membership function for fitness

Table 1 represents the rule base for fitness.

Table 1. Decision matrix for determining fitness rule base

The ALO for training dataset

The ALO approach is used for optimal training dataset is briefly described by following section.

The random placements of the ant’s and ant-Lion’s

The random location of the ant’s and Ant-Lion’s are represented in M_ant-lion, M_ant [35].

$M_{\text {ant }-\text {lion}}=\left(\begin{array}{cccc}A L_{1,1} & A L_{1,2} & \ldots & A L_{1, n} \\ A L_{2,1} & A L_{2,2} & \ldots & A L_{2, d} \\ \vdots & \vdots & \vdots & \vdots \\ A L_{n, 1} & A L_{n, 2} & \ldots & A L_{n, d}\end{array}\right)$

$M_{\text {ant }}=\left(\begin{array}{cccc}A_{1,1} & A_{1,2} & \ldots & A_{1, n} \\ A_{2,1} & A_{2,2} & \ldots & A_{2, d} \\ \vdots & \vdots & \vdots & \vdots \\ A_{n, 1} & A_{n, 2} & \ldots & A_{n, d}\end{array}\right)$       (4)

Fitness function of all ant-lion’s and ant’s has been given in the matrix M_OAL, M_OA [36] and function f is given as,

$M_{O A L}=\left(\begin{array}{c}f\left(\left[A L_{1,1}, A L_{1,2}, \ldots, A L_{1, n}\right]\right) \\ f\left(\left[A L_{2,1}, A L_{2,2}, \ldots, A L_{2, d}\right]\right) \\ \vdots \\ f\left(\left[A L_{n, 1}, A L_{n, 2}, \ldots, A L_{n, d}\right]\right)\end{array}\right)$       (5)

$M_{O A}=\left(\begin{array}{c}f\left(\left[A_{1,1}, A_{1,2}, \ldots, A_{1, n}\right]\right) \\ f\left(\left[A_{2,1}, A_{2,2}, \ldots, A_{2, d}\right]\right) \\ \vdots \\ f\left(\left[A_{n, 1}, A_{n, 2}, \ldots, A_{n, d}\right]\right)\end{array}\right)$       (6)

Ant’s Movement randomly

For search of pray total ants permitted to move randomly. The movement of ant’s is shown by (7),

$X(t)=\left[\begin{array}{l}0, \text { cumsum }\left(2 r\left(t_{1}\right)-1\right), \text { cumsum }\left(2 r\left(t_{2}\right)-1\right), \\ \ldots, \text { cumsum }\left(2 r\left(t_{n}\right)-1\right)\end{array}\right]$       (7)

where, cumsum represents the total sum, n represents total ants, t represents step random walk, and random generation represents with r(t), production of random number between [0,1] with uniform distribution,

$r(t)=\left\{\begin{array}{l}1 \text { if rand }>0.5 \\ 0 \text { if rand } \leq 0.5\end{array}\right.$      (8)

Updating the position of ant’s as,

$X_{i}^{t}=\frac{\left(X_{i}^{t}-p_{i}\right)\left(s_{i}-r_{i}^{t}\right)}{s_{i}^{t}-p_{i}}+r_{t}$      (9)

Here, q_i and p_i are max and min values of ant’s walk randomly, r^t_i and s^t_isignifies min and max m^th variable at t^thiteration.

Ants trapping

Random walk of ant’s is changed by traps, which are developed by ant lion’s given by:

$c_{m}^{t}=A n t-\operatorname{lion}_{n}^{t}+c^{t}$      (10)

$d_{m}^{t}=A n t-l i o n_{n}^{t}+d^{t}$       (11)

Trap construction

The ALO algorithm is for ant-lion’s selection by roulette wheel operator depends on ant-lion fitness.

Ants sliding into pits

Sliding of ant’s into traps characterized by,

$c^{t}=\frac{c^{t}}{I}$       (12)

$d^{t}=\frac{d^{t}}{I}$       (13)

Here, I = 10^{w t/s}, t is current iteration, S is the max iterations and w is a constant, and its value is given by,

$w=\left\{\begin{array}{ll}2 & \text { if } t>0.1 S \\ 3 & \text { if } t>0.5 S \\ 4 & \text { if } t>0.75 S \\ 5 & \text { if } t>0.9 S \\ 6 & \text { if } t>0.95 S\end{array}\right.$       (14)

Prey catching and pit reconstruction

To catch the new ants, now ant-lions update their current location,

$A n t-\operatorname{lion}_{n}^{t}=A n t_{m}^{t} \quad$ if $f\left(A n t_{m}^{t}\right)>f\left(A n t-\operatorname{lion}_{j}^{t}\right)$      (15)

Elitism

Every ant is estimated to associate with an ant-lion using roulette wheel as,

$A n t^{t}=\frac{R_{A}^{t}+R_{B}^{t}}{2}$      (16)

An efficient method is proposed in this research to solve an EPD problem in IEEE-30 bus system. Initially, NR method was considered for optimal load flow issues. In addition, the expressed optimal load flow problems have been fixed while satisfying system inequality and equality constraints. Proposed FLC hybrid technique was verified for its efficiency by initializing the iteration process with a decent principal value and reaches an absolute best value in a smaller number of iterations. Hence, it is decided that the final improvement in cost minimization, scheduling all committed generating units in an optimal way to minimize the total operating cost.