Optimal load dispatch solution of power system using enhanced harmony search algorithm

Operation of power system network at low price is the most precious factor and this can be achieved effectively by distributing the true power demand from available source of generation properly. Running of the system with effective economic point view termed as ED problems. The ED Problem have association to solve 2-dissimmer obstacles (Wood & Wollenberg, 1996). Here the pre dispatch obstacle is the first one that is how to meet the requirement of the load by selecting the available unit out of other units optimally for required time and online ED is second obstacle that means to decrease the generation cost how to select the one unit from parallel running units for minute to minute requirements. The effective work of ED problem is by satisfying the load demand requirement produce the real power with low price. So the production cost always depending on the load demand at particular time (Rad & Amjady, 2010).

Due to large interconnection of electrical power system, the power demand is huge and that will continuous hike in the cost of energy, so we must diminishes the operating cost of plant by minimizing the fuel consumption for a particular load. ED is one of the aspects of Optimal Power Flow (OPF) has to decrease overall input generating costs of generating units, objective function and total generation must maintain load demand and transmission line losses, equality constraints (Walters & Sheble, 1993). Traditionally ED is solved by Lagrangian approaches, Lambda-iteration approach, Newton methods, linear programming and quadratic programming and Gradient approaches (Mahor et al., 2009). For higher test systems above mentioned approaches solve the ED problem with lower efficiency.

The generation cost of the power system can be minimized with proper economic load dispatch only. To make economic dispatch as a convex issue, generating units cost function taken in quartic form this can be solved using general existed methods. By one of the conventional method we can solve the ED without considering the transmission losses (Xia & Elaiw, 2010). Another traditional approach solved ED problem by bearing in mind network transmission losses (Li & Wang, 2013), and those approaches are unable to give the exact results due to approximation power balance equations. Hence for improved solution those can be united with an iterative to obtain precise result for convex problem.

ED problem cracking approaches can be divided into three assemblies. The first assembly comprises the approaches applied to ED problems in their unique versions. Rare samples are tabu search algorithm (TS) (Boonseng et al., 2012), particle swarm optimization (PSO), differential evolution (DE) (Iba & Noman, 2008). The approaches of the second assembly are the modified kinds of the first assembly including modified tabu search (MTS) (Li et al., 2002), improved PSO (IPSO) (Joong-Rin et al., 2010), shuffled differential evolution (SDE) (Vaisakh & Srinivasa, 2013). Final assembly comprises of the mixture approaches as the grouping of approaches from the earlier groups mentioned above.

In this work, we recommend an advanced approach for cracking the ED problem by means of an Enhanced harmony search (EHS) algorithm. An ED problem constructed on a 13-unit test system (Chattopadhyay et al., 2003) through incremental fuel cost function captivating into account the valve-point loading effects is employed to validate the presentation of the EHS. The valve-point loading effects familiarize various minima in the solution space. Numerical outcomes gained with the projected EHS approach were compared with classical HS technique and other optimization outcomes stated in literature.

Geem et al. (2001) suggested an effective harmony search meets-heuristic algorithm that was impressed by music process for a perfect state of harmony. Optimization technique and music in harmony both are similar and musician’s improvisations are similar to local and global quest optimization methods. Harmony Search (HS) algorithm never asks about initial values and uses a stochastic random quest instead of gradient quest that is based on Harmony Memory Considering Rate (HMCR) and the Pitch Adjusting Rate (PAR).

HS algorithm, musical performances requires an effective state of harmony find from aesthetic estimation, as the optimization algorithms requires a perfect state find from objective function value. It has been effectively applied to different optimization problems in computation and engineering sectors.

The Optimization procedure of the HS algorithm has 1-5 steps, as bellow (Javadi et al., 2012).

Step1. Frame the optimization problem, objective function with constraints and initialize the HS parameters.

Step 2. Harmony Memory (HM) is initialized.

Step 3.  New Harmony from the HM is improved.

Step 4. Modernize the memory of harmony.

Step 5. Continue the loop of steps 3 and 4 until the total iterations are completed, stopping criterion.

3.1. Enhanced harmony search (EHS) algorithm

HS is effective one to give the best performance with in minimum time, but facing problems to local quest for data applications. To enhance the effectiveness of HS algorithm and knock out the defects lie with feasible values of Harmony Memory Considering Rate (HMCR) and the Pitch Adjusting Rate (PAR). Fesanghary et al. (2007) introduced an effective HS algorithm that uses variable PAR and Band Width (BW) in improvisation step and also introduced different in harmony search, termed as global apex harmony search and main data is dumped from swarm to obtain the effective results from HS. The EHS adopted in this work have similar steps like conventional HS without step 3, and in this PAR has been dynamically changed show bellow.

$PAR=PA{{R}_{\min }}+\frac{PA{{R}_{\max }}-PA{{R}_{\min }}}{NI}*gn$   (4)

where, PAR, Pitch Adjusting Rate for generation

$bw=b{{w}_{\max }}{{e}^{\left( \frac{\ln \left( \frac{b{{w}_{\min }}}{b{{w}_{\max }}} \right)}{NI}*gn \right)}}$ (5)

where,

$b w$ is the generation bandwidth,

$b w _ { \min }$ is the min. bandwidth and $b w _ { \max }$ is the max. bandwidth

3.2. Application of harmony search algorithm to ED problem

After the initial development of HS algorithm in 2001, HS algorithm applications have been expanded in a huge range of obstacles. The scientific range is so broad, that one can conclude that Harmony Search Algorithm has generally accepted as a robust optimization technique (Coelhos & Mariani, 2009).

Step1. Initialize parameters.

Step2. Initialize the harmony memory.

Step3. Improvise a new harmony

Step4. Adaptive selection

Step5. Update harmony memory

Step6. Stopping criterion

3.3. Application of enhanced harmony search algorithm to ED problem

Although HSA has better capability in identifying the search space in sensible time it is not capable in finding local optimums in case of numerical issues. The drawbacks like fixed values of HMCR and fewer PAR values with large band widths may reduce the performance. Hence increase in iteration number may happen to find optimal solution. So 4 and 5 equations are utilized to change BW and PAR values.