# Comparable investigation on TLBO algorithm for power system optimization

Comparable investigation on TLBO algorithm for power system optimization

D.S.N.M. RaoNiranjan Kumar

Department of Electrical and Electronics Engineering, Vignan’s Foundation for Science, Technology, and Research, Vadlamudi, Guntur 522213, Andhra Pradesh, India

Department of Electrical and Electronics Engineering, National Institute of Technology Jamshedpur, Jharkhand 831014, India

Corresponding Author Email:
2015rsee003@nitjsr.ac.in
Page:
559-571
|
DOI:
https://doi.org/10.3166/EJEE.20.559-571
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Accepted:
|
Published:
31 December 2018
| Citation

OPEN ACCESS

Abstract:

This paper discusses about ELD Problem is modeled by non-convex functions. These are problem are not solvable using a convex optimization technique. So there is a need for using a heuristic method. Among such methods Teaching and Learning Based Optimization (TLBO) is a newly known algorithm and showed promising results. This paper utilized this algorithm to provide load dispatch solutions. Comparisons of this solution with other standard algorithms like Particle Swarm Optimization (PSO), Differential Evolution (DE) and Harmony Search Algorithm (HSA). This projected algorithm is implemented to resolve the ELD problem for 6 unit and 10 unit test systems along with the other algorithms. This comparison investigation explored various merits of TLBO with respect to PSO, DE, and HSA in the field economic load dispatch.

Keywords:

valve point loading effects, non-convex, T & L based optimization, PSO, DE, HSA, economic dispatch

1. Introduction

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.

Economic load dispatch means minimizing the fuel cost, balanced Real power, and satisfying real power demand. The ELD problem is shown below (Thanushkodi and Selvakumar, 2007).

$FC({{P}_{i}})=\sum\limits_{i=1}^{N}{{{F}_{i}}}({{P}_{i}})$  (1)

Here, FC(Pi) = overall fuel cost,

N = Total number of thermal generating unit,

Pi = Power generation of

thermal generating unit

The fuel cost is quadratic function so it is,

${{F}_{i}}({{P}_{i}})={{a}_{i}}P_{gi}^{2}+{{b}_{i}}{{P}_{gi}}+{{c}_{i}}$    (2)

Subjected to  $\sum\limits_{i=1}^{n}{{{P}_{i}}={{P}_{D}}+{{P}_{L}}}$   (3)

${{P}_{i,\min }}\le {{P}_{i}}\le {{P}_{i,\max }}$  (4)

Here ai,bi,ci are fuel cost coefficients of the ith thermal generating unit,

Pi = Total true power generation of ith unit

PL = overall transmission line loss,

Pi,min = The minimum generation limit of unit i and

Pi,max = The maximum generation limits of unit i.

Here the combination of quadratic and sinusoidal functions of fuel cost to represent the valve-point loading effects. It follows as (Noman and Iba, 2008; Coelho and Mariani, 2009; Zou et al., 2016; Rao et al., 2011)

${{F}_{i}}({{P}_{i}})={{a}_{i}}+{{b}_{i}}{{P}_{i}}+{{c}_{i}}P_{i}^{2}+\left| {{e}_{i}}*\sin ({{f}_{i}}*(P_{i}^{\min }-{{P}_{i}})) \right|$  (5)

Here ei and fi are coefficient of the generating units reflecting valve-point loading effects.

The transmission line losses are written as

${{P}_{L}}=\sum\limits_{i=1}^{n}{\sum\limits_{j=1}^{n}{{{P}_{i}}{{B}_{ij}}{{P}_{j}}+\sum\limits_{i=1}^{n}{{{P}_{i}}{{B}_{0i}}+{{B}_{00}}}}}$    (6)

Here Bij, B0i and B00 are transmission line loss coefficients.

3. T & L based optimization algorithm

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 Mi= Mean

Ti = Teacher at any iteration i.

Ti Makes the mean Mito move towards its own knowledge level, therefore Ti

chosen as Mnew. Hence the best learner is treated as teacher. The variance of the current mean result of every subject and the matching result of the teacher for every subject is given by,

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

Where TF= 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)

4. Comparison of T&L based optimization algorithm with other algorithms

## 1.png

Figure 1. Flow Chart of T & L based optimization algorithm

There are several algorithms like PSO, HSA, ABC, GA. The 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.

5. Simulation results & discussion

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

 Number of units Global generations in MW PSO HSA DE TLBO 1 400.6115 399.4068 500 500 2 199.5996 200 149.9957 151.4009 3 232.1225 232.0630 230.3581 300 4 124.7998 125.2627 125.8899 87.7215 5 199.5996 200 149.9629 149.4573 6 120 120 120 88.4572 Min.cost ($/h) 15616.7991 15624.4473 15615.6937 15611.6988 Power loss (MW) 13.7331 13.5483 13.2068 14.0371 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.

## 2.png

Figure 2. Convergence characteristics of 6 unit system

Table 2. Minimum cost obtained for 25 runs

 Number of runs Minimum cost in $/h PSO HSA DE TLBO 1 15616.8546 15688.4303 15635.2652 15681.9111 2 15616.8756 15677.7093 15660.2286 15611.6988 3 15758.1765 15750.0689 15646.7544 15680.6254 4 15782.4748 15647.0857 15645.1185 15621.5284 5 15616.8511 15657.9900 15631.8830 15624.2276 6 15625.1855 15726.5923 15615.6937 15621.4526 7 15738.7735 15739.6564 15632.6176 15659.3512 8 15743.2094 15647.9531 15636.6707 15650.3453 9 15626.6348 15655.4437 15626.5942 15650.3141 10 15665.8478 15688.3176 15673.4684 15621.5109 11 15627.0714 15703.6266 15641.7270 15622.5178 12 15616.7991 15759.3145 15665.2332 15621.6119 13 15691.2273 15624.4473 15652.6820 15622.4532 14 15626.6205 15656.2226 15665.7099 15622.1312 15 15616.9367 15695.9180 15679.2265 15621.6684 16 15623.5040 15715.6528 15638.6161 15621.6008 17 15625.1855 15740.7103 15648.2682 15621.5467 18 15626.5741 15688.7322 15670.0528 15621.3824 19 15626.7418 15750.1998 15629.4167 15620.9401 20 15626.7085 15769.2848 15643.9360 15621.6385 21 15618.0267 15725.9458 15626.4920 15622.2550 22 15647.0017 15834.2254 15639.1709 15622.9964 23 15619.6076 15751.9471 15635.1169 15621.7541 24 15623.5005 15744.5482 15633.0052 15622.5070 25 15624.3020 15694.8515 15637.5919 15621.6983 Min. cost ($/h) 15616.7991 15624.4473 15615.6937 15611.6988 Max. cost ($/h) 15782.4748 15834.2254 15679.2265 15681.9111 Avg. cost ($/h) 15649.2276 15709.3950 15644.4216 15630.0667

## 3.png

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

 Number of units Global generation in MW PSO HSA DE TLBO 1 55 50.8495 55 55 2 80 75.8420 78.7733 80 3 107.3388 115.8420 99.3983 106.9392 4 100.3117 94.02348 107.1068 100.5765 5 81.4700 109.7019 89.0972 81.5012 6 82.9208 95.2030 81.4078 83.0217 7 300 295.8420 296.1400 300 8 340 335.8420 340 340 9 470 465.8420 470 470 10 470 446.8475 470 470 Min.cost ($/h) 111497.6596 111907.4666 111537.6219 111497.6301 Power loss (MW) 87.0414 85.8360 86.9237 87.0387 ## 4.png 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

 Number of runs Minimum cost in $/h PSO HSA DE TLBO 1 111641.4441 111959.2697 111569.1983 111500.9854 2 111525.8322 112694.2246 111673.5325 111505.7236 3 111497.6763 111947.6861 111695.2852 111497.6765 4 111521.5108 112047.7053 111567.3306 111521.7364 5 111525.8275 112302.8949 111742.5223 111525.7565 6 111525.6877 112206.2944 111743.0718 111521.5768 7 111525.7571 112052.4801 111670.3818 111502.6754 8 111525.7976 112071.9085 111705.6591 111505.8768 9 111525.8834 111947.8623 111751.1809 111497.6301 10 111497.7631 111987.3196 111648.195 111497.6764 11 111497.6695 111919.8793 111645.2498 111497.6765 12 111497.7148 112337.6419 111601.2568 111497.6987 13 111497.6784 112250.1165 111689.5033 111497.6877 14 111525.7557 112185.1190 111663.6215 111500.6301 15 111497.8285 112235.6711 111679.4047 111504.6375 16 111497.7403 112094.2826 111654.574 111525.6384 17 111525.6996 112026.1773 111629.5029 111518.6311 18 111525.7043 112125.7557 111537.6219 111499.6343 19 111525.5897 112010.5037 111706.3123 111497.6301 20 111525.8344 112131.3220 111714.4087 111497.6301 21 111525.7345 112421.2877 111551.2658 111497.6301 22 111525.7724 112461.9869 111675.4585 111499.6383 23 111497.6596 112385.1277 111707.5187 111499.6376 24 111525.71 112111.6850 111608.6125 111497.6301 25 111497.7123 111907.4666 111652.1783 111497.6301 Min cost($/h) 111497.6596 111907.4666 111537.6219 111497.6301 Max. cost($/h) 111641.4441 112694.2246 111751.1809 111525.7565 Avg.cost($/h) 111520.1193 112152.8667 111659.3138 111504.2789

## 5.png

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

6. Conclusion

Hence form the above results we can conclude that 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 extreme points and inefficient mechanism to analyzing the constraints. The proposed T&L based optimization on 6 unit test system, 10 unit test system compared with PSO, DE, HSA. Finally TL based optimization technique gives the Effective high quality solution for Economic load dispatch problem.

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