Multi Objective Adaptive Tumbling Bacterial Foraging in VAR Solutions for Sustainable Power System Operation

E. E. Hassan, T. K. A. Rahman, Z. Zakaria, N. Bahaman, M. H. Jifri 1,5 Faculty of Electrical Engineering, Universiti Teknikal Malaysia Melaka (UTeM) 2 School of Science and Technology, Asia eUniversity, Wisma Subang Jaya, Selangor Malaysia 3 Faculty of Electrical Engineering, Universiti Teknologi Mara, Shah Alam, Selangor, Malaysia 4 Faculty of Information and Communication Technology, University Teknikal Malaysia Melaka (UTeM)


INTRODUCTION
In modern development, Reactive Power Planning becomes one of the most vital study areas in power system [1]. Thus, they found that reactive power support is critical and vital to sustain voltage and regulate power factor in electric power systems. In recent years, numerous blackouts in the world have been occurred, such as 2003 North American caused by poor planning and managing of reactive power in US power system [2]. As a consequence, several objectives functions are suggested from researchers in this field in order adequate Reactive Power Planning (RPP). As referred to [3], their approach was first dealt with an objective to minimize the real power losses hence reducing operational cost while improving the voltage profile. Other considerations are minimizing deviation of given voltage profile, Voltage Stability Margin (VSM) improvement and also combinations of different single objective functions to form multi-objective functions. Reactive power planning is one of the most challenging problem for efficient and source operation of an interconnected power network [4]. RPP can also be combined with Optimal Power Flow (OPF) in which cost minimization has become one of the considerations in the optimization. The cost reductions obtained through both OPF were compared with the total system costs during Base Case.
The principle of SCRPP is to optimize the power system control variables so as to achieve the optimal objective function value or fitness value, while at the same time satisfying the nonlinear operational constraints. The equality constraint is developed from the nodal power balance equation whereas the edge of all control or state variables representing the inequality limitations. The merging of optimality and security contribute to the complexity of SCRPP problem since it is necessary to treat all components simultaneously. The control variables considered are voltage variation, capacitor or reactor switching, transformer tap changing, active power of generator, FACTs and STATCOMs switching [5] to facilitate the requirement of SCRPP.
Throughout years, numerous conventional techniques offered solutions to RPP or VAR sources planning problem included LP [6], NLP, MINLP and Non Linear Interior Point Method (NIPM) [7]. However, it frequently resulted in local optima rather than giving a solution of global optima. It also caused divergence in solution when trying to optimize two objective functions simultaneously. Consequently, new advanced optimization methods were introduced which exhibit some artificial intelligence behaviors such as Simulated Annealing (SA), Evolutionary Algorithms (EA), Genetic Algorithm (GA) and Tabu Search (TS) [8]- [11]. These techniques offered global optimal solutions, however, at the expense of computational time [12]. Therefore, recent researches are inspired to merge conventional methods and advanced optimization techniques for better and faster optimization approaches.
This study introduced a new Adaptive Tumbling Bacterial Foraging Optimization (ATBFO) algorithm which is an improvement to the basic Bacterial Foraging Optimization (BFO) algorithm. The proposed technique was implemented for RPP multi-objective functions. Several identified objective functions were generalized into single objective function via the weighted sum method then known as the multi-objectives function. For that reason, the ATBFO for multi-objectives function is named as the multiobjective Adaptive Tumbling Bacterial Foraging algorithm (MOATBFO). Finally, the performances of the newly developed technique MOATBFO were compared with that provided by the multi objective Meta-EP method. The smallest total system losses and larger maximum loading point that the system can withstand are declared as the best solutions.

MULTI OBJECTIVE SECURED REACTIVE POWER PLANNING
The multi-objective SCRPP or named as MOSCRPP aimed to maximize the MLP and minimize the total system losses simultaneously. Both objective functions are combined to be one objective function using the weighted sum method and applied to the new MOATBFO technique.

Maximizing MLP objective function
Load margin analysis has known to be one of the significant parameters for voltage stability studies. In maximum load ability limit evaluation, the load was increased until the occurrence voltage collapse, that when the system begins to lose its equilibrium as in Figure 1. Graphically, the load margin is portrayed by the range between λ0 or the loading for base case and λmax, or identified as the maximum loading position [13]. During the assessment, the weakest or critical bus among the network and maximum load that it can sustain can also be determined. The load margin is determined by an increment of load at 0.05 or 5% repeatedly from the overall load. In the approach, minimum voltage, Vmin has been set at 0.85V as the cutoff point for the voltage limit and the system is assumed to operate in stress situation when reaching this value [14]. The flowchart as in Figure 2 is presented the calculation of objective function MLP.

Minimizing total system losses objective Function
The objective function for total loss minimization is given by equation (1).
where, Qi and Qj are reactive power at sending and receiving buses respectively, is generated reactive power of bus i, are voltage magnitude at sending and receiving buses respectively. , is total active power loss over the network, is load bus, is voltage controlled bus and is reference (slack) bus.

The weighted sum method
The approach that used to formulate two or more objective functions and represents into one general mathematical formula as described in equation (2).
k is numbers of objective function, αi is weighting factor for i th objective function and fni is normalised value for i th objective function.

METHODOLOGY 3.1. Bacterial Foraging Optimization Algorithm
Bacterial Foraging Optimization (BFO) algorithm is motivated through the foraging activities of the Escherichia coli (E.coli) bacteria. The details on the biological aspects, regarding to their hunting strategies, considered their motile behavior for decision-making mechanism, is explained in [15]. Several process of E. coli foraging that are present in our intestines are called chemotaxis, swarming, reproduction and elimination and dispersal [16].

New Adaptive Tumbling Bacterial Foraging Optimization Algorithm
Using the E.coli foraging strategy as in BFO, the global searching space is improved by modifying the tumbling approach by adapting the mutation technique applied in Meta-EP into tumbling expression implemented in basic BFO thus represented by new equation (3)  , where ∆( )= random vector for each bacterium, ∆ ( )= transpose of random vector for each bacterium. Then, mutate the new position of by using given by equation (3).
normally distributed one dimensional random number with mean 0 and 1.
(0,1) Indicates the random number will be new for each value of j.

New MOATBFO algorithm for the multi-objective function for SCRPP optimization solution
A new MOATBFO algorithm was developed with multi-objective function in solving the SCRPP problems in power system. The multi-objective functions would minimize the total system losses and maximize the MLP at the same time. The related objective functions were combined and formulated into a single objective function via the weighted sum method as in equation (2)

RESULT AND DISCUSSION 4.1. Result for multi-objective of SCRPP
Initially, the increase in the MLP before and after the implementation of multi objective SCRPP on the critical bus during Case 1 and overall load busses in Case 2 are discussed here. Firstly, the comparison between pre-SCRPP with post-SCRPP is analyzed through the two identified points called as Point A and B respectively as in Figure 4 for both unstressed and stressed condition. As referred to the graph, Point A indicates the MLP before the implementation of SCRPP. On the other hand, Point B indicates the MLP after the implementation of SCRPP. The difference between Point A and Point B is identified as MLP enhancement. The voltage profile and total system losses were also recorded for different RPP technique with different objective function.  This section details on study of multi-objective function, MOSCRPP. The findings concluded that the best suitable optimization solution performed by RPP+TTCS+CP technique that have been simplified Table 1 below, during Case 1 (load increment at critical bus). Overall, MOSCRPP shows that the enhancement in voltage profile. On the other hand, MOSCRPP approach resulted in the lowest total losses minimization. While, the following Table 2 shows the results of MOSCRPP for Case 2 (load increment at all load busses) under unstressed and stressed conditions.

Comparison among others optimization techniques
The solutions for multi-objective solutions from MOATBFO were also compared with that obtained from MOBFO and MOMeta-EP in order to identify the best solutions for MOSCRPP as simplified in Table 3. In Table 4, the performance of each optimization technique is ranked and value 1 is given to the best result, while value 3 is given to the worst. The least total aggregate indicates the best performance overall. Results in Table 4 shows that MOATBFO always resulted in the best overall performance. This conclusion is summarized in Table 5. Therefore, the outstanding optimization computational tool is recorded by the new MOATBFO, followed by MOMeta-EP and finally the original MOBFO algorithm. As a conclusion, the MOATBFO technique provided the best results in solving multi-objective SCRPP problem or MOSCRPP.

CONCLUSION
Mainly the multi objective SCRPP aiming to maximize the MLP so that the number of voltage collapse events could be reduced. Hence, the study conducted for P, Q and P & Q load increases, while two cases MLP at the critical bus (case 1) and MLP for all load buses simultaneously (case 2) were analyzed. Several significant objective functions were developed and implemented in the MOATBFO optimization technique in order to overcome the problems in solving the SCRPP problems. Individual objective functions namely, total losses minimization and MLP improvement were combined to form the multi-objective function using the weighted sum method. Besides, all identified RPP approaches were studied and it was found that optimizing RPD, CP and TTCS simultaneously obtained the best results. Thus, MOATBFO was utilized in MOSCRPP in order to optimize the RPD, CP and TTCS simultaneously so that the optimal results would be provided. The performance of MOATBFO was compared with that of MOBFO and MOMeta-EP. Throughout the analysis, the MOATBFO shows the best achievement in terms of MLP improvement, minimum voltage improvement as well in total losses minimization.