Chapter Four

Methodology  

4.1. Introduction 

The globe has also seen a change from its current design of concentrated generation to a potential rise in DG share. Integration of distributed generators dependent on EHO can be observed to minimize dependency on the reduction of fossil fuel supplies, improve electricity security, and provide an environmentally sustainable solution to the rising demand for energy. Different aspects, including the design of DG technologies, the effect of DGs on the operational properties of PS, and economic aspects must be taken into account in preparing PS integrating DGs. [72].

The optimal technique for DG units’ installation will be calculated based on an algorithm to measure the optimal positions in the current chapter. Moreover, the decreasing percentage of power loss would be determined.

This analysis is for the case study (IEEE-30 Bus) for both minimal and optimal loads and is utilized for many chosen network locations.

 

Figure 4.1: The 30 bus radial distribution system.

4.2. Optimization of Herding Elephants

Elephant herding optimizations (EHO) is an artificial search function for optimization issues suggested by Wang at the end of 2015 [73] for intelligence based on swarm intelligence meta-heuristics. The algorithm derives from the simulation of natural elephants’ herding behavior in nature. It is necessary, to sum up the herding actions as following.

• The swarms of elephants comprise a variety of sub-groups named clans, comprising a group of calves and female elephants. [74], as demonstrated in Figure. 4.2.
• Every clan should be under the guidance of a matriarch (leadership) (adult female elephant) [74]Figure 4.2.
• Male calves, which every maturity, as demonstrated in Figure 4.3, abandon the clan they belong.

 

Figure 4.2. Elephant Clan.

 

Figure 4.3. Separation of Adult Elephant Males.

EHO models the herding behaviors of elephants in two operations:

1. Updates of Clan (Updating the actual roles of the matriarchs and elephants in every clan)
2. Separation (In the next quest process, this increases demographic diversity.).

 

 

1. Updates Clan:

The females of elephants for every clan reside under the matriarch’s guidance (the oldest female), and the location of other clan elephants is affected by the roles of the matriarch in a way that the location of j elephant is changed in the ci clan utilizing Eq. (4.1) [73].

(4.1)

Where X_ci,j denotes an old position, whereas the X_{new, ci,j} denotes a newly updated j elephant position in ci clan, α denotes a scale operator ∈ [0, 1] for determining the effects of matriarch ci on X_ci,j [73]. Xbest, ci denotes the matriarch of ci clan [74], and finally, r is a type of stochastic distribution ∈ [0, 1] that can improve the diversity of elephant populations in the next search phase [75].

In Eq. (1), the matriarch elephant X_{best, ci} in clan ci, is not affected. X_{best, ci} can be updated by Eq. (4.2).

(4.2)

Where X_{center, ci} denotes the center of the ci clan, generates from the obtained information by the ci clan elephants, and β is the operator that determines the influences of the X_{center, ci} on X_{new, ci,j} and it ∈ [0, 1]. X_{center, ci} for the dth dimension can be found by Eq. (4.3).

(4.3)

Where d_th is a dimension between 1 and total number of dimensions (1 ≤ d ≤ D). n_ci represent the population number in ci clan. X_ci,j,d represents the dth of elephant X_ci,j, X_center,ci representing the center of ci clan [74].The clan update operation is demonstrated in Algorithm [73,76].

Algorithm 1: Clan Updating Operation [73,76].

Begin

For (Ci = 1 ∶ nClan)

For (j = 1 ∶ nci)

Updates (X_{ci, j}) & find (X_{new, ci, j}) Eq. (4.1).

If (X_{ci, j} = X_{best, ci})

Updates (X_{ci. j}) & find (X_{new. ci, j}) Eq. (4.2)

End

End

End

1. b) Separation:

In each elephant clan, the elephant’s male leaves the party after entering adult age to live alone. This separating mechanism is named separating operator in optimization problems. The adult male elephant with one of the worst efficiency divides utilizing Eq (4.4) at every generation in the EHO system.[73,74].

(4.4)

Where ���_{������������������,} denotes the worst male elephant in the ci clan [12]. ���_{���������} & ���_{���������Â} denotes the Lower & Upper bounds of elephant’s positions. r is a type of stochastic and uniform distribution ∈ [0, 1] [73,74,77].The separating operation is demonstrated in Algorithm 2 [77].

Algorithm 2: Separating Operator [78]

Begin

For (������ = 1 ������ ���������������)

Exchange worst elephants individual in ������ Eq. (4).

End

End

Based on the Elephants herding optimizations operations modeled on algorithms I and II, The EHO can be developed as demonstrated in Algorithm 3 [73].

Algorithm 3: Elephant Herding Optimization [73]

Begin

Stp. I: Set counter of generations ��� = 1. in the search space, randomly initialize the set of an individual elephant with uniform a distribution; set the kept elephants number (������������), and the ������������������, scale operators( ��� & ���), clan number (nClan) and the number of elephants for ���������ℎ clan ���.������.

Stp.II: Evaluating every elephant individual depending on their fitness

Stp.III: while ��� < ������������������

Arrange all the elephants, depending on their fitness.

Save ������������ the elephant individuals.

Implements the clan updating by (Algorithm 1).

Implements are separating by (Algorithm 2).

Evaluating the elephant populations depending on the new updated positions. Replace the worst elephant individuals with the ������������ saved ones.

Step IV: Update the generation counter, ��� = ��� + 1.

Step V: Output. Optimal solution.

End

 

 

 

4.3. Applying PSO

4.3.1. PSO Procedure

The PSO-based approach for solving the OPDG issue to minimize the loss takes the following steps:

Stp.1: Inserting line and bus data and bus voltage limits.

Stp.2: Calculating the loss utilizing distribution load flow depending on the backward-forward sweep.

Stp.3: generating a primary population (array) of particles randomly with random velocities and positions on dimensions in the solution space. Set the iteration counter k=0.

Stp.4: For every particle, if the bus voltage is within limits, determine the total loss in formula (3.1). Alternatively, else that particle is infeasible.

Stp.5: For every particle, compared its objective magnitude with the individual optimal. If the objective magnitude is lower than Pbest, set this magnitude as the current P_best, and record the corresponding particle position.

Stp.6: Select the particle associated with the minimum individual optimum Pbest of all particles, and set the magnitude of this Pbest as the current overall optimum Gbest.

Stp.7: Updates particle velocity and position using (3.11) and (3.12) respectively.

Stp.8: If the iteration number reaches the maximum limit, going to Step 9. Otherwise, set iteration index k=k+1, and return to Stp.4.

Stp.9: Printing out the optimal solution to the target issue. The optimum location involves the optimal size and locations of DG or multi-DGs, and the corresponding fitness magnitude representing the minimum total real power loss.

 

Figure (4.4) PSO-OPDG computational procedure

 

4.4. Fundamental GA Algorithm

The fundamental GA algorithm steps as following [79]:

Stp.1: Generating h_pop chromosomes randomly population.

Stp.2: Estimate the fitness f (y) and the functional objective y (x) of every population chromosome x.

Stp.3: Selecting chromosome pairs as parents from the community, giving preference to selecting the right exercise parents in the pool’s matting.

Stp.4: Parents were crossed with a crossover chance depending on the pool’s matting and appropriately producing the offspring.

Stp.5: The crossed offspring were modified with a likelihood of mutation in which the ultimate source of the offspring varies significantly.

Stp.6: Considering the mutant descendants as a new group and utilizing them during the next millennium.

Stp.7: If the solution achieves the end condition, after that, pause and displaying the ideal solution.

Stp.8: Return to step 2 (Stp., 2).

The GA procedure standard is in a flowchart that is demonstrated in Figure 4.5.

 

Figure 4.5. Fundamental GA algorithms Flow-chart [80].

 

4.5. Basic Optimization of GA for the allocation of DG

The primary goal of optimization is to recognize the scale and position of the delivery mechanism applied to a collection of DGs. A genetic algorithm achieves optimization of the problem in this distribution system preparation to define an inexpensive and stable network with better technological characteristics, including lesser energy loss, improved node voltage profile, and improved branch current/thermal limit proportion. Thus optimizing DG power (PDG) decreases the burden of excessive demand for active and reactive power from power transmission.

A GA has recently been addressed as an iterative process that starts primarily with a randomly created original solution. For the primary population, there were many various encoding techniques based on the issue to be optimized. For every population chromosome, objective role and health are computed. A collection of chromosomes is chosen by the allocation operators for the matting pool, depending on the measured health population functions [81].

In such a manner that the chromosome participates in the pool’s matting, the selection operator chooses the chromosome to have greater overall health than that of the original sample, thus retaining the same population number in the matting pool. To produce new offerings, a crossover and mutation operator were added to the chosen chromosome. As the iteration advance, this procedure is repeated iteratively; in most situations, the system seeks the change in solutions (for example, offspring provide greater fitness than parents), an optimum solution is achieved. The summary mentioned above describes in depth a basic algorithm genetic for the allocation of the DG issue as follows [81]:

4.5.1. The System of Coding 

The GA structure’s performance would lie in the scheme of encoding. Two separate approaches could be used in genetic algorithm coding:1) binary coding system and (2) actual number coding systems. In the optimization method analysis, the functional coding scheme is chosen and implemented in both radial distribution systems [82].

Almost all radial distribution systems have one possible node in this analysis. Moreover, all other nodes become nodes of the load. Thus, except for possible nodes, DG may be integrated into every load node accessible on the network. It is indeed applicable to the integration of capacitor banks. However, in OLTC, it may be inserted in any branch or between two neighboring network nodes [83].

Thus the position for DG and capacitor banks could be selected randomly from any node excluding the future node in functional chromosome encoding, and for OLTC, it could be randomly selected from any branch accessible in the network. For optimal production, versatility is provided for position selection and size/settings for capacitor banks, OLTC, and DG [84].

4.5.2. Algorithm for the allocation of DG

Reducing loss’s general structure and the Genetic Estimation for the allocated DGs issue is addressed in the previous heading. Underneath, several measures were suggested to resolve the issue of the allocated DG  as shown in the following steps (Stp.) [85]:

Stp.1: Interpret the data of line and bus of the distributions’ networks (for example, branch resistance, actual and reactive capacity for every load node) and define DG specifications.

Stp.2: Running the distribution load network flow and saving all voltage node and all network current branch intensities and overall power losses.

Stp.3: Setting GEN=0

Stp.4: Create the original population randomly. Suppose the chromosomes reflect the completely random tap number magnitudes, tap locations, select settings, number of DGs, DG location, and active power magnitude of DG, etc.

Stp.5: Decoding the initial population and change the load and bus details (for example, DG ratings and click settings) depending on their respective locations in the network matrixes.

Stp.6: Running the network distribution of the load flow with the reorganized data system. As well as determine total losses in power for every population.

Stp.7: Evaluating the functional goal and the magnitude of fitness for every and every chromosome.

Stp.8: Conducting the saving and elitism for the population.

Stp.9: GEN=GEN+1

Stp.10: Using the Roulette Wheel Collection technique to shape the matting pool from the original solution.

Stp.11: Conducting cross on every matting chromosome pair to build one offspring from the pair of chromosomes for every parent;

Stp.12: Conducting change on the offspring generated by the operational crossover.

Stp.13: Decoding the offspring set and identify the DG size and location for every chromosome.

Stp.14: evaluating the objective purpose and delegate health to every offspring, running the flow of foal to every offspring.

Stp.15: Conduct elitism and pick the strongest h_pop chromosome from the present populace and heirs. Change the existing population with the strongest population chosen and utilize it for the next millennium.

Stp.16: Return to step 9 until the converges solution.

Stp.17: STOPPED

The standard optimization procedure for the allocation of the DG issue is demonstrated in the flowchart, as demonstrated in Figure 4.6.

 

Figure 4.6. The allocation of DG flowchart of fundamental algorithm genetic [86]