Comparable investigation on TLBO algorithm for power system optimization

As a Power Engineer scheduling the generators is very big Problem. Since from the past so many techniques are in practice for the economic load dispatch. Economic load dispatch means optimal allocation of loads to the generators so as to maintain power supply must be equal to load demand also to decrease the losses and fuel cost (Wood and Wollenberg, 1996). We are all know that power generation is highly costlier. In countries like India the major power generation is form thermal power plants only where the running cost is very high. The one of the best way to minimize the cost and losses of generating station is to Economic dispatch of loads (Amjady and Nasiri-Rad, 2010; Pothiya et al., 2011; Walters and Sheble, 1993). Researchers developed lot of methods for Economic load dispatch. In this work concentrates on an innovative optimization algorithm that is teaching and learning based optimization.

Electrical power plays vital role for any county development. For achieving proper load demand we should have the optimal power flow generation to reduce the cost of production and this can be achieved by economic load dispatch with proper integration of sources to the load centres. The principal goal of Economic Load Dispatch (ELD) is to build effective power flow path while compromising all constraints. The cost function of every alternator can be characterized with quadratic function and it can solve by minimization methods like Lambda iteration and gradient based methods in convention ELD problem (Mahor et al., 2009; Elaiw and Xia, 2010; Chakrabory et al., 2011).

Anciently we developed many methods to clear up the ELD problem like mathematical programming methods and these are more delicate for start and occasionally converge to local optimum solution or diverge altogether. Linear programming approaches are quick and effective however main bad thing is correlated with the piecewise linear cost. Nonlinear programming approaches have a struggle of convergence and algorithmic trouble. Newton based approaches cannot handle many number of equality constraints (Sharifzadeh and Amijady, 2010; Wang, 2013).

This paper explains TLBO algorithm to resolve ELD problem with valve point loading effect of thermal plants by taking transmission losses in to account. We proposed the effectiveness of T&L based Optimization on 6 unit test system and compared with PSO, DE, HSA. Finally T & L based optimization technique gives the high quality solution.

Teaching and Learning (T&L) inspired optimization process proposed by Rao et al. (2011) and Rao and Patel (2013) depends on Teacher and Learner Mechanism. The Teaching and Learning (T&L) based optimization is a meta-heuristic population based search algorithm like HSA, Ant Colony Optimization (ACO), PSO and Artificial Bee Colony (ABC). The Teaching and Learning (T&L) based optimization method is a simple mathematical model to resolve different optimization difficulties.

The projected work concentrates on a new optimization algorithm that is teaching and Learning (T&L) based optimization. Incorporated T&L based optimization algorithm is effective remedy for diminishing the flaws in traditional approach like provincial optimal trapping, inadequate effective to identify adjacent risky points and inefficient appliance to analyzing the constraints. According to our T&L based optimization algorithm a learner can gains knowledge in two ways: (i) by teacher and (ii) interacting with the neighbor learners. In this algorithm beginners are called as population. Design variable are called as subjects of the learners. The top beginner is treated as Teacher.

3.1. Teacher phase

Pupil gains information from the instructor ever and instructor should expand the mean outcome of class by his skills. The best learner is that once knowledge is equal to the teachers knowledge means teacher make to learners to reach his knowledge. But practically is not possible because all learners are not cleverer. This follows as (Kyruakides and Ciornei, 2012)

Let M_i= Mean

T_i = Teacher at any iteration i.

T_i Makes the mean M_ito move towards its own knowledge level, therefore T_i

$Difference=r*({{M}_{new}}-{{T}_{F}}{{M}_{i}})$  (7)

Where T_F= Teaching factor. It is given as follows:

${{T}_{F}}=round[1+rand*(0,1)*(2-1)]$ (8)

This difference modifies the existing solution according to the following expression

${{X}_{new,i}}={{X}_{old,i}}+difference$ (9)

3.2. Learner phase

The input for the beginner phase is the teacher in beginner phase learner gains knowledge learner gains knowledge by two ways: one is gaining knowledge form teacher and other is by sharing knowledge between learners interaction.

The learner phase is shows as follows. Randomly select two learners and   where i≠j

${{X}_{new,i}}={{X}_{old,i}}+r*({{X}_{i}}-{{X}_{j}})$ if $f({{X}_{i}})<f({{X}_{j}})$

${{X}_{new,i}}={{X}_{old,i}}+r*({{X}_{j}}-{{X}_{i}})$ if $f({{X}_{i}})>f({{X}_{j}})$  (10)

The Proposed T & L based Optimization algorithm was implemented for two cases case: 1 consisting 6-Baseload generation units preferring loading valve point loading effect and losses. The T & L based optimization algorithm was written using MATLAB 8.5 (R2018b) running on i5 processor, 2.56GHz, 8GB RAM, PC.

A. Case 1

This case contains 6-base load generation units considering loading valve point loading effect and losses. Generating units have to attain the load demand of 1263MW. To calculate the efficiency of the T & L based optimization method, 25 individual trails can made at 60-population with 200 iterations.

Table 1. Global generations for 6unit system per trail

The comparisons of cost and global are tabulated in Table 1 and Table 2. The global generations and the independent trails convergence characteristics are also plotted which are shown in fig. 2 and 3 respectively.

Table 1 clearly shows that for PSO the minimum cost attained was 15616.7991 \$/h, for HSA the minimum cost attained was 15624.4473 \$/h, for DE the minimum cost attained was 15615.6937\$/h, and for TLBO the minimum cost attained was 15611.6988. Hence the above results shows that, the minimum cost is attained for TLBO as compared with the other algorithms. The power loss attained for TLBO was 14.0371MW.

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Figure 2. Convergence characteristics of 6 unit system

Table 2. Minimum cost obtained for 25 runs

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Figure 3. Comparison characteristics of minimum cost Obtainedfor 25 runs

This case consists of ten thermal generation units considering loading valve point loading effect and losses. Generating units have to attain the load demand of 2000 MW. To calculate the efficiency of the T & L based optimization method, 25 individual trails can ready at 100-population with 200 iterations per trail.

The comparisons of cost and global are tabulated in Table 3 and Table 4. The global generations and the independent trails convergence characteristics are also plotted which are shown in fig 4 and 5 respectively.

B. Case 2

Table 3. Global generations for 10unit system

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Figure 4. Convergence characteristics of 10-unit system

Table 3 shows that for PSO the minimum cost attained was 111497.6596\$/h, for HSA the minimum cost attained was 111907.4666\$/h, for DE the minimum cost attained was 111537.6219\$/h, and for TLBO the minimum cost attained was 111497.630. Hence the above results shows that, the minimum cost is attained for TLBO as compared with the other algorithms. The power loss attained for TLBO was 87.0387MW.

Table 4. Minimum cost values for 25 runs

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Figure 5. Comparison features of minimum cost obtained for 25 runs