Optimal Design and Operation of Wind Turbines in Radial Distribution Power Grids for Power Loss Minimization

Abstract

This research proposes a strategy to minimize the active power loss in the standard IEEE 85-node radial distribution power grid by optimizing the placement of wind turbines in the grid. The osprey optimization algorithm (OOA) and walrus optimization algorithm (WOA) are implemented to solve the problem. The two algorithms are validated in three study cases of placing two wind turbines (WTs) in the system for power loss reduction. Mainly, in Case 1, WTs can only produce active power, while in Case 2 and Case 3, WTs can supply both active and reactive power to the grid with different ranges of power factors. In Case 4, the best-applied methods between the two are reapplied to reach the minimum value of the total energy loss within one year. Notably, this case focuses on minimizing the total power loss for each hour in a day under load demand variations and dynamic power supply from WTs. On top of that, this case uses two different sets of actual wind power data acquired from the Global Wind Atlas for the two positions inherited from the previous case. Moreover, the utilization of wind power is also evaluated in the two scenarios: (1) wind power from WTs is fully used for all values of load demand, (2) and wind power from WTs is optimized for each load demand value. The results in the first three cases indicate that the WOA achieves better minimum, mean, and maximum power losses for the two cases than the OOA over fifty trial runs. Moreover, the WOA obtains an excellent loss reduction compared to the Base case without WTs. The loss of the base system is 224.3 kW, but that of Case 1, Case 2, and Case 3 is 115.6, 30.6 kW, and 0.097 kW. The placement of wind turbines in Case 1, Case 2, and Case 3 reached a loss reduction of 48.5%, 84.3%, and 99.96% compared to the Base case. The optimal placement of WTs in the selected distribution power grid has shown huge advantages in reducing active power loss, especially in Case 3. For the last study case, the energy loss in a year is calculated by WSO after reaching hourly power loss, the energy loss in a month, and the season. The results in this case also indicate that the optimization of wind power, as mentioned in Scenario 2, results in a better total energy loss value in a year than in Scenario 1. The total energy loss in Scenario 2 is reduced by approximately 95.98% compared to Scenario 1. So, WOA is an effective algorithm for optimizing the placement and determining the power output of wind turbines in distribution power grids to minimize the total energy loss in years.

1. Introduction

The radial distribution power grid (RDPG) is one of the crucial elements of the whole power system. In general, RDPG is in charge of conveying the power at medium voltage to receiving ends or loads. However, the power loss in the RDPG is always higher than the similar value in the transmission power network [1]. In addition, the large amount of power loss will negatively affect the whole RDPG efficiency and the voltage profile at load nodes [2]. Thus, minimizing power loss in the RDPG is acknowledged as the first priority in RDPG design and operation [3].

Many solutions have been proposed to minimize the power loss in RDPGs due to their essential role, including placing shunt capacitors (SCs) [4,5,6], distributed generators (DG) [7,8,9], and network reconfiguration [10,11,12]. These solutions will provide particular benefits due to their engineering characteristics. However, these solutions are generally combined to achieve the highest degree of efficiency in practice. For instance, the authors in [13] have combined reconfiguration and placing photovoltaic systems to reach the optimal power loss value in the IEEE 33-node and IEEE 69-node RDPGs. Next, the study [14] proposed a strategy for reducing power loss in a 24-node RDPG by optimizing the placements of both SC and DG placements. In [15,16], the placements of both SCs and DGs are not only for active power loss reduction but also aim to achieve other targets, such as minimizing the voltage stability index or optimizing the investment costs.

Currently, integrating clean energy sources in power system operations, such as wind and solar energy, is highly concerning. Therefore, the placement of such clean energy sources to boost the efficiency of RDPGs is also strongly encouraged [17,18,19]. These studies highly focus on placing wind turbines (WTs) and photovoltaic generators (PVGs) to reach the optimal values of different objective functions, and power loss reduction is one of them. Although the benefit of placing WTs and PVGs in the RDPGs is not deniable, the presence of such things has also caused some challenges in operating and controlling the RDPGs in general. The challenges mainly come from the intermittent and uncertainties of clean energies. In these circumstances, the model predictive control (MPC) [20,21] is considered to be an affordable solution to mitigate the adverse effects caused by the nature of clean energies while integrated into any RPDG.

Placing SCs, DGs, WTs, or PVG in RDPGs to reach the optimal value of different objective functions and satisfy the related constraints is a highly complex problem, especially in large-scale RDPGs. In general, backward and forward sweep (BS/FS) are primarily used to calculate the power flow in RDPGs. However, the optimal sizes and locations of such SCs, DGs, WTs, or PVG are mainly determined and evaluated by meta-heuristic algorithms. Particularly, the authors in [22] applied the modified slime mold algorithm (MSMA) to determine the optimal sizes and positions of photovoltaic generators and shunt capacitors (SCs) in three different RDPGs with 33, 69 and 85 nodes, for power loss reductions. In addition, the results achieved by MSMA are compared to other meta-heuristic algorithms to validate the real effectiveness of the proposed algorithm, including the Equilibrium Optimizer (EO) and the original version of the slime mold algorithm (SMA). Next, the study [23] employed ant lion optimization (ALO) to find out the best sizes and positions of distributed generators (DGs), to place various configurations of RDPGs from 15 to 85 nodes. Additionally, the study focused on discussing and analyzing the effect of DGs on the grid in several aspects, such as short circuit level, load loss variation, reliability, and voltage profile improvement. In [24], a modified version of particle swarm optimization (PSO) called adaptive particle swarm optimization (APSO) was used to optimize the allocation of DGs-based renewable energy for reaching the minimum value of a multi-objective function. In [25], the moth swarm algorithm (MSA) was executed to achieve the maximum penetration level of both PGs and SCs and reduce the reliance on conventional generating sources. The results obtained by MSA were then compared to two others and indicated the high capability of the applied method. In [26], the Coot optimization algorithm (COOA) and five other meta-heuristic algorithms, including the Archimedes optimization algorithm (AOA), the transient search optimization algorithm (TSOA), the crystal structure algorithm (CrSA), the war strategy optimization algorithm (WSA), and the average and subtraction-based optimizer (ASBO), were executed to optimize the sizes and location of PGs to IEEE 33-node RDPG and 69-node RDPG. The authors have conducted various scenarios of placing PGs on the grid for active power loss reduction. The results pointed out that COOA completely outperforms others and is recognized as the most effective search method. The study [27] applied the harmony search algorithm (HSA) to solve the network reconfiguration problem with the main objective of reaching the minimum value of active power loss and improving the voltage profile in IEEE 33- and IEEE 69-node RDPG. Then, the authors in [28] applied a new algorithm called the pathfinder algorithm (FPA) and successfully determined the best placements of DGs to reconfigure the 18-bus RDPG to reach the best value of energy loss. In [29], both wind and solar energy were considered to be placed in the RDPG to solve the optimal reconfiguration problem using the matrix moth–flame algorithm (MMFA). Improving stability and reliability was also the primary focus of the study. In [30,31,32], the crow search algorithm (CrOA), the improved human learning optimization algorithm (IHLOA), and the improved equilibrium optimization algorithm (IEOA) were also employed to optimize the allocation of the renewable energy systems to different RDPG. However, the most striking feature of these studies is considering the uncertainties of renewable-based DGs, which makes the considered problem even more complicated.

By fully acknowledging the practical benefit of placing the wind turbines in the distribution power system, this research also provides a strategy to reduce the overall active power loss in the IEEE 85-bus distribution power system. In execution, two novel meta-heuristic algorithms, including the osprey optimization algorithm (OOA) [33] and the walrus optimization algorithm (WOA) [34], are applied to optimize the size and location of the wind turbines in the given grid. Both the OOA and WOA are nature-inspired optimization algorithms. These algorithms are formed by simulating the living practices of animals in nature. Specifically, OOA is built based on the hunting behaviors of the osprey with two phases, including the identification and the movement phases. At the same time, WOA is proposed based on the simulations of the walrus behaviors in nature, where each behavior will be executed in a particular phase, including feeding, migrating, escaping, and fighting against enemies. The selection of OOA and WOA for solving the given problem is as follows:

• The OOA and WOA are modern meta-heuristic algorithms newly proposed in 2023.
• The two algorithms have proven their superior capabilities while dealing with different optimization problems, including theory and real-world optimization problems. Particularly, OOA and WOA have been tested with CEC 2011 and CEC 2017 test suits. For each optimization problem of the test suits, COA and WOA always prove they are more effective than the previous methods. The detailed comparison between OOA and WOA to other previous methods can be found separately in [33,34]. Therefore, comparing the two novel methods while solving a particular engineering problem will offer valuable evaluations in finding a new, highly effective search method.
• There is no previous research applying these algorithms and assessing their real performance in different case studies while solving the considered problems.

The main contributions and the key findings of the research can be summarized as follows:

• This research is the first to implement OOA and WOA to solve the considered problem based on their proven capabilities, which are clearly demonstrated in the various previous tests. Based on the previous demonstrations, the two algorithms are applied to optimize the placement of WT in RDPG for power loss reduction.
• Determine the best search method for the considered problem using detailed comparison, including the including the lowest power loss value (LST. Loss), the average power loss value (AVER. Loss), the highest power loss value (HST. Loss) and the standard deviation (STD).
• Indicate and evaluate the positive effects of placing wind turbines on the grid with different study cases using various graphs and calculations.
• Consider real one-year data of wind speed and power in a given location in the world. In addition, the real specification of the wind turbines from General Electric, one of the prestigious wind turbine producers on the world, are utilized while solving the considered problem in Case 4 to improve the practicality of the whole research.
• Optimize wind turbines’ operation to minimize total energy loss in one year for the two scenarios in Case 4: (1) wind turbines are optimized their power factor only, (2) wind turbines are optimized both their power supply and power factors. Through results and comparisons, Case 2 is acknowledged to be the best implementation for reaching the lowest value of the energy loss within a year.
• This research is also considered to be another performance test for OOA and WOA with three cases. After the first three cases, the best-applied algorithm between the two cases will be reapplied to the given problem with a larger search space featured by the actual wind power data within 24 h, as cited by Global Wind Atlas. Based on these real data, the value of the objective function for a month, a quarter, and a year will be determined, respectively.

In addition to the introduction, the rest of the research is organized as follows: Section 2 specifies the problem description with particular objective functions and the related constraints, Section 3 will shortly introduce the two novel meta-heuristic methods, Section 4 presents the obtained results in two study cases, and finally, Section 5 will reveal the key conclusions of the whole research.

2. Problem Description

2.1. The Main Objective Function

The objective function of the study is to minimize the overall active power loss (OAPL) in the considered RDPG. The value of OAPL is determined by using the expression below:

$$Minimize OAPL=3\sum _{i=1}^{N_{DL}}{I_{WTs, i}^2.RDL}_i$$

(1)

2.2. The Related Constraints

In addition to the objective function, there are important constraints, which must be strictly respected while solving the problem. The detail and the expression of these constraints will be presented as follows:

The power balance constraint: This constraint is mainly about the balance of the active and reactive power between the generating side and the consuming side (load). That means that the total active and reactive power generated by all sources at the generating side must equal the amount demanded by the loads and the loss caused by the transmission process. The mathematical expression of this constraint is given as follows:

$$P_{S1}+\sum _{w=1}^{N_{WTG}}{P}_w^{WT}=\sum _{j=2}^{N_{LD}}{P}_j^{LD}+OAPL$$

(2)

$$Q_{S1}+\sum _{w=1}^{N_{WTG}}{Q}_w^{WT}=\sum _{m=2}^{N_{LD}}{Q}_j^{LD}+OQPL$$

(3)

and the overall reactive power loss (OQPL) in Equation (3) is calculated as follows:

$$OQPL=3\sum _{i=1}^{ N_{DL}}{I_{WTGs, i}^{2}XDL}_i$$

(4)

Operating current constraints: This constraint is about the current-withstand capability of the distribution lines. The expression of the constraints is given as follows:

$$I_{WTG,i}\le I_{DL,i}^{Hst};i=1, \dots , N_{DL}$$

(5)

Operational voltage boundaries: This is also a crucial constraint that directly affects the operational status and the economic benefit of all loads connected with the grid. Unlike the current boundary, the operational voltage boundaries are specified within the lowest and the highest limits; any abnormal voltage value, such as under voltage or over voltage, will cause damage and unsafe conditions for the end users. The constraint is given below:

$$U^{Lst}\le U_n\le U^{Hst};n=1, \dots ,No$$

(6)

The working boundaries of wind turbines: These constraints are about the three important limits of wind turbines while placed in the grid, including active and reactive power generation and power factor limits; these constraints must be strictly imposed to satisfy all of the safety and engineering standards. On top of that, any violation of these constraints will not be accepted as a legal solution found by the optimization tool. The mathematical expressions of the three constraints are presented as follows:

$$P_{WT}^{Lst}\le P_w^{WT}\le P_{WT}^{Hst} with w=1, \dots , N_{WT}$$

(7)

$$Q_{WT}^{Lst}\le Q_w^{WT}\le Q_{WT}^{Hst} with w=1, \dots , N_{WT}$$

(8)

$${PF}_{WT}^{Lst}\le {PF}_w^{WT}\le {PF}_{WT}^{Hst} with w=1, \dots ,N_{WT}$$

(9)

The placement constraints for wind turbines in the grid: The constraint means that the placement of WTs in the grid is considered to be legal while their positions are from node two onward in the grid, as described by the equation below:

$$2\le {Po}_w^{WT}\le No$$

(10)

3. The Applied Algorithms

3.1. The Osprey Optimization Algorithm

As described above, the update process for new solutions of OOA will be executed in two phases, including the identification phase and the movement phase, to complete the whole process [33]. The mathematical model of each phase is briefly described as follows:

The identification phase: In this phase, the osprey will consider selecting a new and favorable position for hunting potential prey. The new position corresponds to a new solution in the optimization problem. The new position is determined by:

$$O_n^{new, p1}=O_n+{\delta }_1\left(O_{RD}-{\delta }_2{O}_n\right), with n=1, \dots , N_{ps}$$

(11)

The movement phase: In the phase, the osprey moves the prey to protect its food from other enemies. This action also updates the new position and new solutions to the problem are also found as a result. The update is applied as follows:

$$O_n^{new, p2}=O_n+\frac{{LB}_n+{\delta }_1\left({UB}_n-{LB}_n\right)}{CI}, with n=1, \dots , N_{ps}$$

(12)

3.2. The Walrus Optimization Algorithm

As mentioned earlier, the update process of the WOA for new solutions will be executed through three phases [34], and the mathematical expression of each behavior will be described one by one as follows:

The feeding phase: The feeding phase of the walrus group is controlled by the strongest individual and the strongest one has a large contribution in finding a new position as shown in the following equation:

$$W_n^{new, fp}=W_n+rnd\left(SW-\tau W_n\right), with n=1, \dots , N_{ps}$$

(13)

The migration phase: In this phase, the whole population will move to other positions for better living conditions. The mathematical model of this phase is given below:

$$W_n^{new, mp}=\left\{\begin{array}{c}{W}_n+rnd\left(W_{SE}-\tau W_n\right),{Fit}_{W_{SE}}<{Fit}_{W_n}\\ W_n+rnd\left(W_n-W_{SE}\right),else\end{array}\right.$$

(14)

The escaping and fighting phase: This phase is about the change in position while the walrus must escape or fight against their enemies in nature. The formulation of this phase is described by the following equation:

$$W_n^{new, efp}=W_n+\left[{LB}_n^{\ast }+\left({UB}_n^{\ast }-rnd{LB}_n^{\ast }\right)\right]$$

(15)

with

$${LB}_n^{\ast }=\frac{{LB}_n}{CI}; and {UB}_n^{\ast }=\frac{{UB}_n}{CI}$$

(16)

3.3. The Framework of Applying Meta-Heuristic Algorithms for Solving Optimization Problems

As presented in Section 3.1 and Section 3.2, it is easy to recognize that the main difference between the two applied algorithms, OOA and WOA, is their update mechanism for the new solutions. However, while these algorithms are applied to solve a given optimziation problem such the considerd problem in this study, both OOA and WOA share the same structure, which consists of certain steps as follows:

-

Step 1: Set up the initial control parameters, including the population size (Nps) and maximum number of iterations (MI).

-

Step 2: Randomly generate a set of populations based on the lowest and the highest limits characterized by the given optimization problem.

-

Step 3: Set the current iteration (CI) by 0.

-

Step 4: Calculate the fitness value for each individual of the population.

-

Step 5: Update the new solutions using the update mechanism featured by each applied algorithm. For instance, OOA updates the new solutions by using Equations (11) and (12), while WOA applies Equations (13)–(15) to complete its update process.

-

Step 6: All of the new solutions will be checked for their violations of the boundaries characterized by the given problem.

-

Step 7: Calculate the new fitness value for each individual in the population and determine the best solution.

-

Step 8: Check the terminated condition by evaluating the value of CI compared to MI as follows: If CI is slower than MI, increase CI by one and then return to Step 5; otherwise, stop the searching process and report the optimal solution.

4. Results and Discussions

In this section, the OOA and WOA are implemented to find the optimal locations and sizes of the wind turbines in the IEEE 85-node RDPG for active power loss reduction. All of the related data for the considered distribution network are cited by [22]. Originally, active and reactive power demand by all loads connected to the grid was 2570.28 kW and 2622.08 kvar. In addition, the original active and reactive power loss of the grid are 224.32 kW and 141.00 kvar. The single-line illustration of the grid is depicted in Figure 1. The placement of WTs in the IEEE 85-node RDPG is implemented in two cases as follows:

• Case 1: Placing two WTs. The WTs generate active power only. Suppose that the active power supplied by WTs varies from 0 to 3000 kW.
• Case 2: Placing two WTs. The two WTs can generate both active and reactive power. The active power generation capacity is the same as Case 1. In addition, the power factor is constricted within the range from 0.85 to 0.95 lead as evaluated in [35,36]. In practice, the particular value of power factors of WTs is decided by the operator and the grid’s specific operational condition [37].
• Case 3: Placing two WTs. The two WTs can generate both active and reactive power. The active power generation capacity is the same as Case 2; however, the range of power factor for WTs are extended from 0.95 lag to 0.95 lead as conducted in [38,39].
• Case 4: Evaluating the load demand variation and power supplied from WTs within 24 h in two scenarios:

  -

  Scenario 1: WTs’ power factor is only optimized.

  -

  Scenario 2: WTs’ active power and power factor are simultaneously optimized.

The results obtained by the two algorithms will be discussed and compared based on different criteria. For a fair comparison, the initial control parameters of the applied algorithms, population size (N_ps), and the highest iteration (HI), are equally set to 20 and 50 for Case 1, and 30 and 50 for Case 2, Case 3, and Case 4. In addition, each algorithm is operated for 50 trial runs to find the best solution.

Suppose that the considered RDPG IEEE-85 bus is located in the plain. Besides that, except for the bus one, the remaining busses of the network are supposed to satisfy all of the engineering conditions for placing WTs, including the availability of space, short-circuit ratings of existing switchgear, circuit capacity, the feasibility of connection, and environmental effects. On top of that, the availability of wind power on the buses having WTs is also fulfilled.

The whole study is conducted on a personal computer with the following basic specifications: 2.6 GHz of CPU and 8 GB of RAM.

4.1. The Results Obtained by the Two Algorithms in Case 1

Figure 2 shows the results obtained by OOA and WOA after 50 trial runs. In the figure, OOA shows a high fluctuation among the trial runs, with few optimal runs. On the contrary, WOA offers a lower fluctuation with more optimal values among 50 trial runs.

In Figure 2, the results obtained by WOA and OOA after 50 trial runs have been shown. The higher fluctuations between trial runs mean that OOA is less stable than WOA while dealing with the considered problem. The presence of the fluctuations given by the COA and WOA is necessary for judging the stability of these methods. Stability is one of the most crucial factors to acknowledge a powerful meta-heuristic algorithm, besides its capability of determining the best optimal solution to the particular optimization problem.

Figure 3 describes the best convergence curves of the OOA and WOA among 50 trial runs. In the figure, WOA is better than OOA by reaching the optimal power loss value after about 20 iterations, while OOA cannot offer the same capability even after the last iteration is reached.

Figure 4 offers more details about the real performance of the two algorithms in terms of different criteria, including the lowest power loss value (LST. Loss), the average power loss value (AVER. Loss), the highest power loss value (HST. Loss) and the standard deviation (STD). For the first criterion, WOA reaches a 155.5636 kW LST. Loss value, while that of OOA is 155.5637 kW. The difference between the WOA and OOA on this criterion is not much. However, while considering the last three criteria, the effectiveness and superiority of the WOA over the OOA started to become clear. Specifically, the WOA not only reaches better values of Aver. Loss and HST. Loss, but also proves itself to be the stable search method with a much better value of STD. For instance, the particular values of these criteria resulting from WOA are 115.6932 kW, 116.5983 kW, and 0.2205, while those of OOA are 117.1884 kW, 122.5941 kW, and 1.7227. By converting to percentage, the superiority of WOA over OOA on the last three criteria is 1.28%, 5.12%, and 87.20%.

The voltage profile of the systems with and without the presence of WTs is shown in Figure 5. Clearly, the voltage values at all nodes are substantially improved compared to the original configuration, where WTs were not placed. Additionally, the superiority of the WOA over the OOA in voltage improvement is minor. The WOA can reach better voltage for nodes 9–15, 44–56, 78, and 80–85. Nevertheless, the OOA can reach better voltage for nodes 57–77 and 79. The two algorithms have approximately the same voltage at other remaining nodes, such as nodes 16–43. The improvement in voltage profile achieved after placing WTs to the grid by applying COA and WOA is described in Figure 5, and their capacity is reported in

Table 1. The location and power output of WTs, determined by the two applied algorithms.

Method	WT1 Location—P (kW)	WT2 Location—P (kW)
OOA	32; 928	59; 1077
WOA	9; 1592	33; 670

. The WOA placed a WT with a high power of 1592 kW at node 9. Meanwhile, nodes that received electricity from node 9 are 10–15, 78, 80–85. So, WOA reached better voltage for these nodes. The OOA placed one WT with a high power of 1077 kW at node 59. Nodes that can receive electricity from node 59 are 57, 58, 60–77, and 79. So, OOA reached better voltage than WOA for these nodes. About the second WT, the OOA placed a WT at Node 32 with 928 kW, and the WOA placed a WT at Node 33 with 670 kW. The loads at nodes 34–36 and 40–54 can receive the power from nodes 32 and 33. So, WOA can reach a better voltage for these nodes.

Lastly, the optimal locations and power outputs of the two WTs in the grid found by the OOA and WOA are displayed in Table 1. It is easy to recognize that the total power outputs of WTs found by the OOA are smaller than those of the WOA.

The difference in the LST. Loss found by the OOA and WOA comes from the initial purpose of conducting this paper. Besides reaching the minimum value of active power loss in the grid, the two algorithms are also executed to investigate their performance. As presented in Figure 4, the difference between the LST. Loss values achieved by the OOA and WOA are only 0.0001 kW, which is very small and can be ignored. However, reaching a global solution is one of the most important considerations while applying any meta-heuristic algorithm to solve an optimization problem. In this regard, only the WOA offers this ability while the OOA is trapped in the local optima. Moreover, while taking a look at the remaining criteria, the differences are noticeable.

The difference in the positions of WTs found by the OOA and WOA, as presented in Table 1, can be explained as follows: the total power output of WTs found by the OOA is only 2005 kW while that of the WOA is up to 2262 kW. Clearly, the WOA can offer a large capacity of WTs connected to the grid. Due to the large capacity of WTs resulting from the WOA, finding the same positions for placing the two WTs and achieving a similar value of LST. Loss, as found by the OOA, is impossible. In terms of the voltage profile after placing WTs in the grid shown in Figure 5, the difference between the OOA and WOA is not really noticeable. However, when compared to the Base case where WTs are not connected, the node voltage profile improvement is unneglectable.

4.2. The Results Obtained by the Two Algorithms in Case 2

In this subsection, the number of WTs placed in the IEEE-85 is the same as the first case, which is 2 WTs. However, the WTs, in this case, offer the capability of generating both active and reactive power. Note that, in this case, the scale of the considered problem has been increased due to the addition of more variables needed for achieving the optimal solution. Specifically, the set of optimal solutions, in this case, consists of six variables instead of only four in Case 1.

Figure 6 shows the fitness values resulting from the two applied algorithms after 50 trial runs. In the figure, WOA provides a better search capability while reaching more optimal fitness values than OOA. Moreover, the fluctuation of the results among trial runs is substantially lower than OOA.

The best convergences among 50 trial runs of the two applied algorithms are presented in Figure 7. While the WOA only requires around 20 iterations to reach the optimal power loss value, the OOA cannot achieve the same result in the best trial runs.

The comparison between the two applied algorithms in different criteria, including LST. Loss, Aver. Loss, HST. Loss, and STD is presented in Figure 8. In the figure, the LST. Loss achieved by the WOA is 30.64586 kW which is lower than that of OOA 0.083 kW, corresponding to 0.27%. Similar to Case 1, the difference in the first criterion between the two applied algorithms is not that much, but the remaining criteria start to show clear differences on performance and stability. For instance, the values of Aver. Loss and HST. Loss obtained by WOA are all significantly lower than those resulting from the OOA. The better percentages of the WOA over OOA on the two criteria are 20.14% for the Aver. Loss and 25.15% for the HST. Loss. Lastly, the evaluation of the STD criterion also indicates that the WOA still provides outstanding stability over the OOA by 65.73%, regardless of the increase in the complexity degree in this case.

Figure 9 describes the voltage profile of the whole system in Case 2 under two circumstances: a Base case without WTs and two other cases with WTs. It is easy to observe that the placement of the WTs has brought a noticeable improvement in voltage magnitude at all nodes in the whole network compared to the original configuration. However, the superiority of WOA over OOA in this circumstance is a little. For instance, the WOA can only result in better voltage magnitudes over the OOA at nodes 5, 6, and 14–16, whereas the voltage improvement at other nodes is slightly lower than the OOA. The following terms can explain this phenomenon: (1) The main objective function considered is to reduce the power loss, not to improve the voltage profile; (2) Although both the OOA and WOA result in the same optimal positions of WT, the sizes of WTs found by the OOA and WOA are slightly different. By observing

Table 2. The optimal location, active and reactive power, determined by the two algorithms in Case 2.

Method	WT1 Location—P (kW)—Q (kvar)	WT2 Location—P (kW)—Q (kvar)
OOA	60; 1236.0772; 765.0668	32; 1085.5547; 672.2055
WOA	32; 1085.727; 672.8732	60; 1200.4984; 744.0021

, the active and reactive power found by the OOA for the WT at node 60 is noticeably larger than the similar values resulting from the WOA. Mainly, the OOA found 1236.0772 kW and 765.0688 kvar for the WT placed at node 60, while those of WOA are 1200.4984 kW and 744.0021 kvar, respectively. Due to these higher values, the OOA brings a better voltage improvement at many nodes thanks to the larger reactive power injected into the grid over the WOA, but the improvement is tiny.

4.3. The Results Obtained by the Two Algorithms in Case 3

In this subsection, the implementation of placing WTs in the considered RDPG remains the same as in Case 2. However, the range of power factors for WTs is primarily extended. Notably, the range of power factors varies between 0.95 lag and 0.95 lead. As a result, the scale of the considered problem has also vastly increased. The execution of this case is aimed at the following purposes: (1) continuously test the actual performance of the two applied methods while dealing with the larger scale of the considered problem; (2) and improve the practicality of the research while applying the full range of power factors for operating wind turbines, as implemented in practice.

Figure 10 describes the results obtained by the OOA and WOA after 50 trial runs in Case 3. Throughout 50 trial runs, WOA is the only method reaching optimal values multiple times, while OOA cannot provide the same capabilities. However, the fluctuation of the power loss value achieved by the WOA is larger than that of the OOA, in this case. This phenomenon results from the increase in search space, as mentioned earlier.

The best convergence curves achieved by the OOA and WOA are illustrated in Figure 11. The observation from the figure points out that the WOA only utilized over 30 iterations to reach the best power loss value, while the OOA could not even reach the best run at the last iteration. Clearly, the WOA still offers a surprising performance in Case 3 regardless of the substantial extension in the search space of the considered problem.

Similar to the first two cases, the detailed comparison between the OOA and WOA in Case 3 is clearly displayed in Figure 12. It is very easy to see that the WOA results in better power loss values than the OOA in terms of LST. Loss and Aver. Loss. In particular, the WOA reached 0.097 kW for LST. Loss and 16.994 kW for Aver. Loss, while the similar values obtained by the OOA are 1.665 kW and 23.354 kW by converting to percentage, the WOA is better than OOA 94.2% at LST. Loss and 27.23% at Aver. Loss. However, the evaluation of Max. Loss and STD have indicated the opposite. For instance, the Max. Loss and STD achieved by the OOA are 35.670 kW and 9.02, while those of the WOA are 47.785 kW for Max. Loss and up to 12.236 for STD. By using percentages, the OOA is better than WOA 33.97% for Max. Loss and 35.68% at STD, in this case.

The voltage magnitude at all buses of the considered RDPG resulting from OOA and WOA in Case 3 is displayed in Figure 13. Firstly, the voltage magnitude at all buses in RDPG are substantially improved in the first two cases in the previous section compared to the base case where WTs are not connected. Secondly, the voltage magnitude at buses achieved by the WOA is vividly enhanced compared to the OOA, especially from bus 24 to the end.

The optimal location, active, and reactive power supplied by WTs results from the two applied methods are given in

Table 3. The optimal location, active and reactive power, determined by the two algorithms in Case 3.

Method	WT1 Location—P (kW)—Q (kvar)	WT2 Location—P (kW)—Q (kvar)
OOA	50; 2336.179; −12,417.083	59; 2212.905; −1335.138
WOA	13; 445.827; −4212.145	60; 390.508; −88,362.216

. In the table, the negative value of reactive power means that WTs consume reactive power from the grid to reach the main objective function’s best value power loss values. The observation in Table 3 indicates that the optimal locations for placing WTs in this case are completely different from each other. For instance, the optimal locations found by WOA are at bus 13 and 60, respectively, while those of OOA are 50 and 59, respectively. In addition, the amount of active power supplied to the grid of WTs found by the two applied methods is also distinct. In particular, the active power resulting from the OOA is 2236.179 kW for WT1 and 2212.905 kW for WT2, while those found by the WOA are 445.827 kW for WT1 and only 390.508 kW for WT2. In terms of reactive power, the results achieved by both the OOA and WOA indicate that it is better to reach the best value of power loss if WTs consume reactive power from the grid. According to the data from Table 3, WTs found by WOA consume more reactive power than those of OOA. On top of that, the larger reactive power consumed by WTs led to a better enhancement of the voltage magnitude of buses, which can be observed in Figure 13.

The position of WTs in Table 3 is investigated in Case 3, where WTs are operated with a broader range of power factors, which is −0.95 to 0.95. The power loss values obtained by the two applied methods are presented in Table 3. In the table, the active power loss values given by OOA and WOA are 0.097 and 1.665 kW, respectively. The difference in power loss values between the two applied methods is only 1.568 kW, which is very small from a practical point of view. However, while considering both data from Figure 12 and Table 3, several terms can be found as follows:

-

The total active power supplied of WTs found by the WOA is only 836.335 kW, while the similarity of the OOA is up to 4449.084 kW, but the WOA results in a lower power loss value. Due to the low capacity of WTs connected to the grid, finding the same nodes for the two WTs in the grid, like the OOA, is infeasible.

-

The lower the active power output, the less capital cost is required to place WTs in the grid. If the WOA is employed in practice, the economic benefit for investors will be more optimized.

-

The WT’s positions found by the WOA consumed more reactive power from the grid than the OOA, but the voltage improvement at many nodes is slightly better than OOA. Although the difference is not much and can be ignored, the WOA has one more time shown its higher effectiveness than the OOA. Moreover, both the OOA and WOA offer a considerable enhancement of voltage profile when compared to the Base case, where WTs are not connected to the grid.

Figure 14 provides a brief graphical comparison of placing WTs in the IEEE 85-node RDPG in Cases 1, 2, and 3. As mentioned earlier, WTs can only supply active power to the grid in Case 1, while WTs in Case 2 and Case 3 offer the capability to supply active and reactive power to the grid. At first glance, both the OOA and WOA result in better power losses in Case 2 and Case 3 compared to Case 1. For instance, the power losses found by the OOA and WOA are 115.5637 kW and 115.5636 kW in Case 1, and 30.7289 kW and 30.6548 kW in Case 2. In Case 3, the power loss values found by the OOA and WOA are 1.665 kW and 0.097 kW. The improvement is massive compared to both Case 2 and Case 1. The results found by the WOA reduce the power loss by 63.4% in Case 1, 90.3% in Case 2, and 99.96% in Case 3 compared to the original configuration of RPDG. Moreover, the results indicate that the placement of wind turbines can reduce power losses significantly, and the placement of wind turbines with active and reactive generations can reduce the most significant power loss for radial distribution power systems.

4.4. The Results Obtained by WOA in Case 4

In this section, the WOA is reapplied to reach the optimal power loss value of the IEEE-85 with the evaluation of load demand variation and power supplied from WTs within 24 h in two scenarios, as mentioned earlier. According to [40], load demand varies within 24 h in a day, by specific load factors corresponding to four quarters of a year. The load factors are cited and displayed in

Table A1. The load factors corresponding to each month of a year.

Hour	January	February	March	April	May	June	July	August	September	October	November	December
1	0.48	0.48	0.40	0.40	0.40	0.64	0.64	0.64	0.37	0.37	0.37	0.48
2	0.45	0.45	0.39	0.39	0.39	0.60	0.60	0.60	0.37	0.37	0.37	0.45
3	0.43	0.43	0.38	0.38	0.38	0.58	0.58	0.58	0.35	0.35	0.35	0.43
4	0.42	0.42	0.37	0.37	0.37	0.56	0.56	0.56	0.34	0.34	0.34	0.42
5	0.42	0.42	0.37	0.37	0.37	0.56	0.56	0.56	0.35	0.35	0.35	0.42
6	0.43	0.43	0.41	0.41	0.41	0.58	0.58	0.58	0.38	0.38	0.38	0.43
7	0.53	0.53	0.45	0.45	0.45	0.64	0.64	0.64	0.42	0.42	0.42	0.53
8	0.61	0.61	0.54	0.54	0.54	0.76	0.76	0.76	0.50	0.50	0.50	0.61
9	0.67	0.67	0.60	0.60	0.60	0.87	0.87	0.87	0.56	0.56	0.56	0.67
10	0.68	0.68	0.62	0.62	0.62	0.95	0.95	0.95	0.58	0.58	0.58	0.68
11	0.68	0.68	0.63	0.63	0.63	0.99	0.99	0.99	0.59	0.59	0.59	0.68
12	0.67	0.67	0.62	0.62	0.62	1.00	1.00	1.00	0.58	0.58	0.58	0.67
13	0.67	0.67	0.59	0.59	0.59	0.99	0.99	0.99	0.55	0.55	0.55	0.67
14	0.67	0.67	0.58	0.58	0.58	1.00	1.00	1.00	0.54	0.54	0.54	0.67
15	0.66	0.66	0.57	0.57	0.57	1.00	1.00	1.00	0.53	0.53	0.53	0.66
16	0.67	0.67	0.55	0.55	0.55	0.97	0.97	0.97	0.52	0.52	0.52	0.67
17	0.70	0.70	0.57	0.57	0.57	0.96	0.96	0.96	0.53	0.53	0.53	0.70
18	0.71	0.71	0.58	0.58	0.58	0.96	0.96	0.96	0.54	0.54	0.54	0.71
19	0.71	0.71	0.60	0.60	0.60	0.93	0.93	0.93	0.57	0.57	0.57	0.71
20	0.68	0.68	0.62	0.62	0.62	0.92	0.92	0.92	0.58	0.58	0.58	0.68
21	0.65	0.65	0.60	0.60	0.60	0.92	0.92	0.92	0.57	0.57	0.57	0.65
22	0.59	0.59	0.57	0.57	0.57	0.93	0.93	0.93	0.53	0.53	0.53	0.59
23	0.52	0.52	0.50	0.50	0.50	0.87	0.87	0.87	0.47	0.47	0.47	0.52
24	0.45	0.45	0.44	0.44	0.44	0.72	0.72	0.72	0.41	0.41	0.41	0.45

in the Appendix A. By using these load factors, the particular load demand at each hour in a day of a month on the considered grid is calculated. Note that the optimized positions of WTs are taken from Case 2; these positions are already determined in the previous section. The selected WTs are the three-megawatt platforms of General Electric manufacturers [41]. All of the basic specifications of the selected WTs are listed in

Table A2. The basic specifications of wind turbine model used in the research.

Specification	Value
Rated power	3200 kW
Rotor diameter	137 m
Swept area	14,742 m2
Specific area	4.61 m2/kW
Number of blades	3
Power control	Pitch

in Appendix A. In addition to that, the two WTs are supposed to be placed at two different coordinates: the first WT is placed at Ninh Hai District, Ninh Thuan province, Vietnam, with the exact coordinate 11.697626° N 109.15947° E, and the average wind speed is 8.5 m/s; the second WT is placed at Loi Hai, Thuan Bac District, Ninh Thuan province, Vietnam, with the exact coordinate 11.771915° N 109.073639° E, and the average wind speed is 7.37 m/s. Additionally, all of the related data about the wind indexes of the two WTs for twelve months within a year are collected from the Global Wind Atlas (GAS) [42], and these data are described in

Table A3. The wind speed index at the first location where the first WT is placed.

Hour	January	February	March	April	May	June	July	August	September	October	November	December
1	1.74	1.3	1.02	0.67	0.62	0.76	0.83	0.71	0.61	0.84	1.42	1.81
2	1.73	1.3	1.02	0.66	0.63	0.75	0.8	0.7	0.62	0.82	1.42	1.82
3	1.73	1.3	1.02	0.65	0.63	0.75	0.79	0.69	0.61	0.8	1.42	1.83
4	1.72	1.29	1.02	0.65	0.64	0.74	0.79	0.68	0.63	0.79	1.42	1.82
5	1.74	1.29	1.02	0.63	0.63	0.72	0.77	0.67	0.6	0.8	1.42	1.82
6	1.71	1.28	1.02	0.62	0.62	0.71	0.75	0.65	0.57	0.8	1.41	1.81
7	1.71	1.28	1.02	0.61	0.59	0.67	0.72	0.62	0.55	0.81	1.42	1.81
8	1.68	1.33	0.98	0.63	0.48	0.63	0.56	0.52	0.45	0.72	1.71	1.74
9	1.64	1.27	0.94	0.6	0.47	0.59	0.54	0.51	0.44	0.7	1.38	1.71
10	1.63	1.24	0.93	0.6	0.48	0.61	0.58	0.55	0.48	0.7	1.33	1.67
11	1.63	1.24	0.94	0.64	0.54	0.67	0.65	0.61	0.56	0.73	1.32	1.66
12	1.63	1.25	0.95	0.98	0.62	0.74	0.72	0.68	0.65	0.77	1.33	1.67
13	1.61	1.25	0.95	0.69	0.66	0.81	0.77	0.75	0.7	0.8	1.32	1.66
14	1.6	1.24	0.94	0.69	0.67	0.84	0.81	0.79	0.73	0.82	1.31	1.64
15	1.61	1.23	0.93	0.68	0.67	0.85	0.84	0.8	0.75	0.83	1.31	1.63
16	1.64	1.22	0.93	0.66	0.66	0.85	0.84	0.8	0.76	0.83	1.31	1.64
17	1.68	1.23	0.93	0.65	0.65	0.85	0.84	0.8	0.74	0.84	1.34	1.67
18	1.7	1.26	0.95	0.65	0.63	0.82	0.83	0.79	0.72	0.85	1.38	1.71
19	1.72	1.28	0.97	0.66	0.63	0.81	0.83	0.77	0.7	0.86	1.41	1.74
20	1.72	1.29	0.98	0.67	0.63	0.83	0.84	0.77	0.7	0.86	1.44	1.74
21	1.73	1.3	1	0.69	0.63	0.85	0.85	0.77	0.69	0.87	1.44	1.75
22	1.74	1.3	1.01	0.69	0.62	0.84	0.85	0.76	0.68	0.84	1.44	1.77
23	1.74	1.31	1.03	0.68	0.62	0.81.	0.85	0.74	0.65	0.86	1.43	1.79
24	1.74	1.31	1.03	0.68	0.61	0.78	0.86	0.73	0.62	0.85	1.42	1.8

and

Table A4. The wind speed index at the first location where the second WT is placed.

Hour	January	February	March	April	May	June	July	August	September	October	November	December
1	1.52	1.17	0.9	0.63	0.52	0.66	0.58	0.55	0.49	0.67	1.23	1.53
2	1.52	1.17	0.92	0.64	0.52	0.66	0.58	0.55	0.52	0.68	1.25	1.54
3	1.57	1.22	0.95	0.67	0.55	0.68	0.62	0.57	0.57	0.74	1.31	1.6
4	1.62	1.26	1	0.7	0.59	0.71	0.66	0.6	0.61	0.78	1.36	1.65
5	1.67	1.33	1.05	0.75	0.64	0.77	0.7	0.65	0.65	0.81	1.42	1.69
6	1.72	1.36	1.08	0.79	0.7	0.84	0.77	0.73	0.7	0.87	1.46	1.74
7	1.73	1.39	1.09	0.82	0.77	0.92	0.85	0.81	0.75	0.93	1.48	1.76
8	1.73	1.38	1.1	0.84	0.85	0.98	0.89	0.85	0.79	0.96	1.48	1.76
9	1.72	1.36	1.11	0.86	0.85	1.03	0.91	0.88	0.82	0.98	1.47	1.75
10	1.7	1.34	1.12	0.88	0.87	1.06	0.95	0.93	0.85	1	1.45	1.73
11	1.65	1.3	1.11	0.88	0.89	1.03	0.98	0.95	0.87	0.99	1.43	1.68
12	1.58	1.25	1.07	0.85	0.88	0.98	0.97	0.91	0.84	0.94	1.39	1.61
13	1.53	1.2	1.02	0.81	0.82	0.93	0.93	0.86	0.78	0.87	1.35	1.57
14	1.51	1.17	1	0.77	0.76	0.9	0.91	0.8	0.73	0.85	1.31	1.54
15	1.5	1.18	0.98	0.75	0.72	0.85	0.88	0.76	0.67	0.82	1.28	1.53
16	1.51	1.16	0.98	0.72	0.69	0.8	0.87	0.74	0.64	0.78	1.26	1.54
17	1.51	1.16	0.97	0.7	0.67	0.78	0.84	0.72	0.62	0.75	1.25	1.55
18	1.51	1.15	0.96	0.68	0.65	0.76	0.81	0.69	0.63	0.74	1.26	1.55
19	1.51	1.15	0.96	0.66	0.65	0.75	0.8	0.71	0.63	0.74	1.26	1.55
20	1.5	1.14	0.95	0.65	0.65	0.75	0.8	0.71	0.61	0.72	1.26	1.55
21	1.49	1.13	0.94	0.64	0.66	0.73	0.8	0.7	0.61	0.72	1.25	1.55
22	1.49	1.13	0.93	0.63	0.65	0.72	0.77	0.68	0.6	0.73	1.25	1.54
23	1.48	1.13	0.93	0.6	0.61	0.7	0.74	0.66	0.58	0.72	1.26	1.54
24	1.48	1.13	0.92	0.58	0.57	0.66	0.71	0.63	0.54	0.71	1.27	1.54

, respectively, of the Appendix A. By using the data collected from GAS, the power supplied by the WTs within 24 h of an average day in twelve months is fully determined.

Figure 15 describes the power loss of 24 h in a day of the twelve months obtained in Scenario 1. In the figure, the months with the lowest and the highest power loss values belong to September and November, respectively. Note that the two WTs are only optimized for their power factors, while the power supplied by these WTs is fully injected into the grid.

Figure 16 illustrates the power loss of 24 h in a day of twelve months obtained by the WOA in Scenario 2. In the figure, November and August are the two months with the lowest and highest power loss values within 24 h. Note that the WTs are optimized for both their power supply to the grid and their power factors in this scenario. Moreover, the power loss values within 24 h of each month achieved in Scenario 2 are substantially decreased compared to the similar ones achieved in Scenario 1 that has been presented above.

By multiplying the power loss at each hour of a day with the number of days corresponding to each month, the energy loss value of each month is determined. Figure 17 shows the comparison of the power loss values of twelve months in three cases: (1) Base system without WTs, (2) Scenario 1, (3) and Scenario 2. It is easy to realize that the energy loss values of the twelve months resulting from Scenario 2 are noticeably lower than those from the Base system and Scenario 1 from January to June and from October to December. From July to September, the differences in the energy loss values given by Scenario 2 are still very large compared to the Base. However, compared to Scenario 1 in these months, the differences in the energy loss values achieved by Scenario 2 are not that much, and even a bit lower in September.

Figure 18 summarizes the total energy loss of the three cases in the year as described earlier. The implementation of Scenario 2 results in the best energy loss values compared to others. Specifically, the energy loss values obtained in Scenario 2 are only 223,090.53 kW, while the similar values obtained in Scenario 1 are 5,554,596.56 kW and up to 7,376,664.27 kW in the Base case. By converting into percentages, the results achieved by Scenarios 2 are 95.98% better than Scenarios 1. Having said that, the optimization of both the power supplied from WTs and their power factors has resulted in a huge improvement in energy loss values compared to the implementation of Scenario 1.

Figure 19 describes the total energy supplied from the main transformer to the grid in twelve months of a year. Except for May and August, the power supplied to the grid in the remaining months of both scenarios are all negative. This means that the power injected into the grid by WTs in the two scenarios is large enough to fulfill load demand and to fulfill even more than required. Hence, the extra power supplied from the main transformer is not needed.

Figure 20, Figure 21, Figure 22 and Figure 23 show the amount of energy supplied from the main transformer to the grid in the four quarters of the year. The observation of Figure 20 indicates that the energy supplied from the transformer to the grid in the first three months of the year are all negative, which means the total amount of energy supplied to load by WTs is greater than enough for both scenarios. However, things have changed when evaluating the next three months of the second quarter, as described in Figure 21. Specifically, there are many hours within a day of the three months that the energy supplied from the main transformer are greater than zero for two scenarios. This means that the amount of energy supplied by WTs is lower than the amount needed by load demand. Similar results are also described while analyzing the data shown in Figure 22. In the figure, it is easy to realize that the amount of energy supplied to the grid by the main transformer in July, August, and September is noticeably larger than that of the second quarter. Nevertheless, while observing the last three months of the year in the fourth quarter, presented in Figure 23, the shape of the graph is almost similar to what happened in the first quarter, where the energy supplied by WTs was greater than the load demand needed.

Figure 24, Figure 25, Figure 26 and Figure 27 show the total power supplied by WTs in one day of each month of the four quarters for two scenarios. While looking at Figure 24, the energy supplied by WTs in Scenario 1 in the first three months of the year is noticeably larger than that in Scenario 2. The reason for this phenomenon can be explained by looking at the main objective function considered in this research, which is to minimize power loss, not maximize penetration of wind power. Hence, the use of less energy supplied by WTs in Scenario 2 for reaching the best power loss values is a better implementation than what resulted in Scenario 1.

The power supplied by WTs in Scenario 1 and Scenario 2 in the second and third quarters is presented in Figure 25 and Figure 26, respectively. In these figures, although the power supplied by WTs in Scenario 2 is still less than in Scenario 1, the difference can be observed mostly from the 3rd hour to the 13th hour for the second quarter. For the third quarter, the difference between the mount power supplied by WTs in Scenario 1 and Scenario 2 can be observed clearly from the 1st hour to the 13th hour of July and from the 6th hour to the 14th hour of September.

Figure 28 shows the total power supplied by WTs obtained in the two scenarios. Clearly, for the main objective function of reaching the best energy loss value within a year, the use of less total energy supplied by WTs in Scenario 2 is better for reaching the desired value of the main objective function than in Scenario 1, where a lot more total energy from WTs is injected into the grid.

4.5. The Discussion on the Main Findings of the Research in Practical Reference

Based on the results and evaluation of the four cases regarding placing WTs on a grid with different settings, as implemented in Section 4.1, Section 4.2, Section 4.3 and Section 4.4, the paper is focused on the following terms:

• For the planning problems, the first priority of these problems is to determine the optimal sizes and positions of the wind turbines (WTs) placed in the grid so that the power loss value will be reduced, and other operational characteristics of the original grid will still be reserved. The presence of WTs must improve both economic and engineering benefits. Hence, the research has implemented different cases of placing WTs on the grid, as presented in the first three cases. Particularly, if WTs can only supply active power to the grid, the WTs should be placed at the positions and sizes found by the WOA, as shown in Table 1, to reach the best power loss value. However, this option results in a relatively high WT capacity, leading to a high capital cost for construction, operation, and maintenance. In addition, the lack of reactive power supply from WTs is considered to be a disadvantage of this option and leads to the limited enhancement of the voltage profile at some periods in the operation process. To partly remove the downsides of the first option, which was implemented in Case 1, Case 2 and Case 3 have been conducted. As a result, the power loss values in Case 2 and Case 3 are dramatically reduced, as shown in Figure 12 and Figure 18. Especially in Case 3, the total capacity of WTs resulted in this case is the lowest value compared to previous cases. Hence, Case 3 will be an affordable option to implement while considering both economic and engineering aspects.
• For operational problems, load demand and power supplied by WTs are not constant values. In fact, load demand and power supplied by WTs consistently change within a day based on the rate of use and the wind speed at a specific period. Therefore, Case 4 is conducted to evaluate the power loss values and the operational characteristics of the grid with load demand variation and dynamic power supplied from WTs in 24 h using the optimal position as determined by the previous cases.

In summary, the main findings of the entire research are that different cases and scenarios for solving the planning problems and operational problems while integrating WTs in the grid to optimize the benefits are proposed. Besides that, the research is only executed and reveals the conclusions in the radial distribution power grid, specifically IEEE-85. Research must be completed with other RDPG configurations, load demand, and wind data before coming to any conclusions.

5. Conclusions

In this research, two novel meta-heuristic algorithms, including osprey optimization and the walrus optimization algorithm, are successfully applied to optimize the size and locations of wind turbines in the IEEE-85 bus distribution power system for power loss minimization. The comparison of the results obtained by the two algorithms indicates that the WOA completely outperforms the OOA, especially in terms of reaching the best power loss value in the first three cases of the research. Besides always reaching the better values of active power loss (Lst. Loss) in those cases, the WOA is also more effective than COA in other criteria, such as Aver. Loss, Hst. Loss, and STD. Remarkably, the better percentages of WOA over COA in those criteria of Case 1 are 1.28%, 5.12%, and 87.20%; the percentages of Case 2 are 20.14%, 25.25%, and 65.73%. Lastly, in Case 3, the WOA is better than COA by 27.23% for Aver. Loss. Regrading Hst. Loss and STD, the results of WOA are not better than those of COA. Moreover, the WOA is also reapplied to reach the optimal power loss value in the case that both load demand variation and dynamic wind power supplied within 24 h are all evaluated. The results obtained by the WOA, in this case, indicate that for reaching the best power loss value, both supplied energy and power factors of WTs must be simultaneously optimized; otherwise, the use of maximum supplied energy with the optimized power factors of WTs will not return the positive results. Hence, WOA proves to be a highly effective search method to deal with the given problem, even in the scaled-up version of the initial problem. However, the research also has several downsides that need to be improved for better quality in the future:

• Other objective functions, such as minimizing the voltage deviation index (VDI), minimizing capital costs, etc., are not considered.
• Solar energy and the combination of both solar energy and wind power are not evaluated in this research.
• The whole research is still conducted on the IEEE-85 bus distribution network, not the real one in Vietnam.
• The availability of wind power in terms of installed site, short-circuit ratings of existing switchgear, circuit capacity, the feasibility of connection, and environmental effects on buses still need to be thoroughly investigated.
• The economic exchange for the case that power supplied from WTs is larger than load demand and flow back to the transmission network is not discussed.

By fully understanding these drawbacks, future research must resolve all problems mentioned above for better quality overall.