Introduction

Worldwide power consumption is anticipated to intensify at a rate of 1.6 percent each year1. Power distribution networks (PDNs) have always had to adjust according to the power demand variation. This results in more power losses and voltage drops in PDN. Higher power losses and voltage deviations indirectly affect the economic operation of power networks. Therefore, for a safer, more secure and economical operation of PDN, it is important to decrease the amount of power losses (PL) and limit the bus voltage deviation (VD) within the recommended level. Distributed generation (DG) deployment is an effective solution to minimize PL and VD in PDN. Predominantly, DG uses the solar radiation and wind energy as alternative sources to generate electricity locally. Moreover, DG placement has attracted the researchers more due to their inherent ability to reduce power losses, minimize voltage deviation and enhance stability. In addition, DGs can serve as a backup generation during power outages to ensure reliability. However, DG positioning (site and size) in the PDN is critical to obtain the optimized results. Erroneous allocation of DGs can lead to several undesirable results including more voltage dip, higher power losses, higher capital and operating costs, higher fault currents, etc. Therefore, DG location and size should be effectively optimized in the PDN to avoid undesirable results.

Typically, DG is categorized into conventional and non-conventional types based on the nature of primary resource used for the power generation. The conventional DGs use fossil fuels including combustion turbines, fuel cells and combustion engines. The non-conventional DGs use renewable energy resources including solar, wind, and geothermal for power generation. The type of DG selection depends on technical, economic and ecological factors. Usually, non-conventional energy DGs are preferred owing to their inherent availability and zero carbon emission characteristics.

Optimization plays a crucial role in wide areas for improving the performance, efficiency and effective resource utilization2,3. The researchers have applied several optimization techniques in the past to optimize DGs in the RDS. An analytical4 and iterative5 methodologies were proposed for optimizing DG capacity and position to curtail the net PL of a radial distribution system (RDS). Metaheuristic algorithms such as genetic algorithm (GA) and particle swarm optimization (PSO) algorithms were applied in6 to optimally deploy the solar photovoltaic (PV) system and wind turbine (WT) in IEEE 33-bus RDS to cut down the total real PL and enhance the voltage profile (VP). The grey wolf optimization (GWO) technique was implemented to optimize the site and rating of a DG to decrease the line PL of RDS7. The proposed GWO technique optimized the different types of DGs in the various IEEE RDSs with 16, 30, 57 and 118 no. of buses. The appropriate sites and sizes for different renewable DGs were computed using a modified Aquila optimizer (MAO) algorithm to minimize RPL and enhance the voltage profiles of RDS8. The effectiveness of the MAO method was examined on the standard 33-bus IEEE radial PDN. An optimization technique using an improved wild horse optimization (IWHO) algorithm was proposed and executed in9 to optimize DG in the different IEEE RDSs including 33, 69 and 119 no. of buses. The proposed technique optimized the site and size for DG with real power loss (RPL) minimization as an objective. A rider optimization algorithm (ROA) applied10 for appropriate computation of optimal sites and sizes for various renewable energy DG systems including PV, WT and biomass. The suggested ROA methodology optimized the DG to cut down the RPL of RDS. A novel technique using a shark optimization algorithm (SOA) was proposed in11 to optimize the DG to cut down the total RPL and enrich the VP and voltage stability (VS) of RDS. An optimization approach was proposed using an enhanced symbiotic organisms search (SOS) algorithm in12 to optimally incorporate the DGs of different power factors. The enhanced SOS algorithm optimized the DGs in different IEEE RDSs with 33, 69 and 118-buses to reduce RPL, improve VP and enhance VS. A single and multiple objectives DG placement problems were solved using a chaotic sine cosine algorithm (CSCA)13. The CSCA approach was implemented to optimize the sites and sizes for multiple DG units in the 33-bus and 69-bus standard IEEE RDSs. A water cycle algorithm (WCA) was applied14 to optimize multiple DGs to cut down RPL, operating cost and carbon emission. An optimization technique using GWO algorithm was introduced15 to allocate type-I and II DGs in RDS. An optimization method using metaheuristic algorithms such as a backtracking search optimization algorithm (BSOA)16 and ant lion optimizer (ALO)17 algorithm was proposed to allocate DG in the different RDSs. A modified PSO (MPSO) algorithm was developed and executed18 to optimize the site and size for DG to curtail the RPL in RDS. The best position and size for DG were computed using an enhanced coyote optimization algorithm (ECOA)19, GA20, PSO and differential evolution (DE) algorithms21.

Motivation

The above literature discussion presented the application of different metaheuristic algorithms to solve DG placement problems in radial distribution power networks. However, several algorithms have been reported for poor convergence and inaccuracy results in the context of finding the best solution for a complex DG placement problem. GA fails to discover the optimal solution to a complex optimization problem and ends up prematurely converging in a local optima solution. Likewise, the GWO algorithm prematurely converges to a local optima solution in the early stages of the optimization process due to its inaccuracy. Similarly, BSOA and ALO algorithms have suffered from slow convergence and local optimal stagnation problems. Thus, in the hope of finding the best solution (optimal) at a better convergence rate, a new technique using Osprey optimizer algorithm (OOA) is introduced in this study to optimize DG in the RDS. The OOA is developed inspiring the intelligence of Osprey’s hunting strategy. The OOA possess a balanced exploration and exploitation feature that makes it to achieve global optimal solution22. The literature22 also reported that application of OOA has produced superior solutions to 22 real-world optimization problems. This motivates the researchers of this work to implement OOA for solving the optimal DG placement and sizing problem.

Contribution

The contributions of the proposed optimization study are listed below.

  • An optimization methodology using a novel osprey optimization algorithm (OOA) is implemented to optimize the appropriate site and capacity of two different types of DG units.

  • Versatility of the OOA technique is examined on the small IEEE 33-bus RDS and a large 118-bus RDS for single and multiple DG optimizations.

  • Viability of the proposed approach is investigated on a real-time 54-bus Malaysian RDS.

  • Efficacy of the OOA is evaluated by relating its simulation results with different optimization algorithms cited in the literature.

The remaining parts of the proposed study are presented in different sections. Section “Motivation” details about problem formation including objective function framework, constraints and DG modelling. Section “Contribution” describes the mathematical framework of OOA. Section “Problem formation” summarizes the optimized simulation outcome of OOA for DG placement in different RDSs. Section “Constraints” concludes the summary of the research outcomes and future work.

Problem formation

Consider a RDS with buses ‘i’ and ‘i + 1’ (Fig. 1) interconnected via a distribution line with resistance ‘Ri’ and reactance ‘Xi’.

Fig. 1
Fig. 1The alternative text for this image may have been generated using AI.
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Two bus RDS.

The RPL along the distribution line is computed using (1).

$$RPL = R_{i} *\left( {\frac{{P_{i}^{2} + Q_{i}^{2} }}{{\left| {V_{i} } \right|^{2} }}} \right)$$
(1)

For a RDS with ‘n’ buses, the total RPL can be computed using (2).

$$RPL_{T} = \sum\limits_{i = 1}^{n - 1} {R_{i} *\left( {\frac{{P_{i}^{2} + Q_{i}^{2} }}{{\left| {V_{i} } \right|^{2} }}} \right)}$$
(2)

where, P is a real power demand, PL is a real power flow, Q is a reactive power demand, QL is a reactive power flow and Vi is a bus voltage.

The proposed OOA technique optimizes the suitable site and size of DG for an objective of minimizing the net RPL of RDS. So, the mathematical expression of the proposed objective function (F) is given in (3).

$$F = \min \left( {\frac{{RPL_{T(DG)} }}{{RPL_{T(no DG)} }}} \right)$$
(3)

where, RPLT(DG) is a total RPL after the DG integration and RPLT(no DG) is the total power loss before the DG allocation.

Constraints

The appropriate location and size for DG is optimized with reference to several constraints including thermal limit, real and reactive power injection limits, power balance constraint and voltage constraint.

Thermal constraint

The branch current of RDS must be restricted below the rated limit as given (4).

$$I_{i} \le I_{i}^{\max }$$
(4)

DG active power (PDG) injection constraint

The capacity of real power injection by DG should not exceed substation capacity23.

$$P_{DG}^{\min } \le P_{DG} \le P_{DG}^{\max }$$
(5)

DG reactive power (QDG) injection constraint

The capacity of reactive power injection by DG should not exceed substation capacity23.

$$Q_{DG}^{\min } \le Q_{DG} \le Q_{DG}^{\max }$$
(6)

Power balance constraint

The incoming power of DN must be sum of power demand and DG capacity24.

$$P_{swing} + P_{DG} = \sum\limits_{i = 1}^{n} {P_{i} } + \sum\limits_{k = 1}^{N} {P_{loss,k} }$$
(7)
$$Q_{swing} + Q_{DG} = \sum\limits_{i = 1}^{n} {Q_{i} } + \sum\limits_{k = 1}^{N} {Q_{loss,k} }$$
(8)

Bus voltage constraint

The bus voltages must be kept with a specific limit as expressed in (9) for ensuring safe and stable operation24.

$$V_{\min } \le V_{i} \le V_{\max }$$
(9)

where, ‘Ii’ is the branch current; PDG and QDG are the DG’s optimal real and reactive power rating, respectively; PDGmin and QDGmin are the DG’s minimum real and reactive rating, respectively, PDGmax and QDGmax are the DG’s maximum real and reactive power rating, respectively; Vmin and Vmax are the recommended minimum (0.95 p.u.) and maximum (1.05 p.u.) bus voltages, respectively; ‘N’ refers to the total number of branches.

DG modelling

The following subsection presents the mathematical modelling of type I and type III DG.

Type-I DG

In this work, the solar PV system is modelled as a type I DG. Type-I DG generates real power only. The output power of a solar PV system is expressed in (10)25.

$$P_{{}} = \left\{ {\begin{array}{*{20}c} {P_{r} \times \left( {\frac{G}{{G_{r} }}} \right),} & {0 \le G \le G_{r} } \\ {P_{r,} } & {G_{r} \le G} \\ \end{array} } \right\}$$
(10)

where Pr is the rated real power, ‘G’ is the incident solar irradiance at the optimal site and ‘Gr’ is the rated solar irradiance received on the earth’s surface. The reactive power injection of a solar PV system is neglected in the modelling.

Type-III DG

Type-III DG can generate both as real and reactive powers. The wind turbine (WT) system is modelled as the Type-III DG in this study. Equations (10) and (11) expresses the real (P) and reactive (Q) power output of a WT system, respectively25.

$$P = \left\{ {\begin{array}{*{20}c} {0,} \\ {P_{r} \times \left( {\frac{{v - v_{cin} }}{{v_{r} - v_{cin} }}} \right),} \\ {P_{r} ,} \\ \end{array} \begin{array}{*{20}c} {0 \le v \le v_{cin} } \\ {v_{cin} \le v \le v_{r} } \\ {v_{r} \le v \le v_{cout} } \\ \end{array} } \right\}$$
(11)

and

$$Q = P_{{}} \times \tan (\cos^{ - 1} (p.f.{}_{DG}))$$
(12)

where Pr is the rated real power output of a WT system and vr and v is the rated and actual wind speed (WS) at the optimal site. vcin and vcout are the cut-in and cut-out WS. The type I and III DG sizes are optimized in kW and kVA rating, respectively.

Power flow

The power flow (PF) execution is an important process in an electrical power network to determine the power losses and voltage profiles under different operating conditions. The application of PF methods using Gauss–Seidel (GS) and Newton–Raphson (NR) algorithms in RDS becomes ineffective because of its unique radial structure. Moreover, GS and NR algorithms converge slowly for RDS due to the high number of load buses. Therefore, researchers recommend a backward/forward sweep (BFS) algorithm for an accurate and faster PF solution11. BFS computes the line flows, power losses and bus voltages of RDS in two phases.

Phase 1: backward sweep

The line current is calculated in this phase. The computation is begins from far end branch and ends at head bus.

Phase 2: forward sweep

The bus voltages are computed in this phase of the algorithm. Contrast to previous phase, the calculation begins from initial bus of the RDS and carried forward to far end bus. Flowchart for BFS algorithm is presented in Fig. 2.

Fig. 2
Fig. 2The alternative text for this image may have been generated using AI.
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Flowchart for BFS power flow assessment technique.

Osprey optimizer algorithm: a solution technique

The osprey optimizer algorithm (OOA) is a metaheuristic algorithm developed inspiring the hunting behavior of an osprey. The osprey is a piscivorous bird and is also called a fish hawk and sea hawk. A typical osprey weighs between 0.9 and 2.1 kg with a length and wingspan ranging from 50 to 66 cm and 127 to 180 cm, respectively. Almost 99% of the osprey’s food diet is fish26. Normally, osprey can hunt a fish weighing from 150 to 300 g and 25 to 35 cm in length. Nevertheless, it has the strength to catch 2 kg of fish. The osprey possesses excellent eye vision and can identify a fish under the water reservoir while hovering at 10–40 m altitude over the water surface. Once the osprey spots a fish, it catches the fish by dipping its feet and diving under the water27. Then it takes the prey to an adjacent rock and starts eating it28.

The hunting characteristic of an osprey is modelled in the osprey optimizer algorithm to solve diversified engineering problems. The following sub-sections present the mathematical modelling of OOA.

Mathematical modelling

This subsection elaborates on the mathematical background of OOA in three stages starting with initialization followed by exploration and exploitation phases.

Initialization

OOA is a typical population-based metaheuristic algorithm that adopts randomness for finding the optimal solutions to a numerous problems. All the ospreys contribute a solution to problem variables according to their location. Hence, the candidate solution for the problem is modelled as a vector. The populations in OOA are represented as a matrix as (13). The initial position for an osprey is randomized by (14).

$$X = \left[ {\begin{array}{*{20}c} {X_{1} } \\ \vdots \\ {X_{i} } \\ \vdots \\ {X_{N} } \\ \end{array} } \right]_{N \times m} = \left[ {\begin{array}{*{20}c} {x_{1,1} } & \ldots & {x_{1,j} } & \cdots & {x_{1,m} } \\ \vdots & \ddots & \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \\ {x_{i,1} } & \cdots & {x_{i,j} } & \cdots & {x_{i,m} } \\ \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots & \ddots & \vdots \\ {x_{N,1} } & \cdots & {x_{N,j} } & \cdots & {x_{N,m} } \\ \end{array} } \right]_{N \times m}$$
(13)
$$x_{i,j} = Lb_{j} + r_{i,j} \bullet \left( {Ub_{j} - Lb_{j} } \right),\begin{array}{*{20}c} {where} & {i = 1,2, \ldots ,N} & {j = 1,2, \ldots ,m} \\ \end{array}$$
(14)

where X is a matrix that refers to the locations of osprey, Xi denotes a candidate solution (osprey), xi,j is a problem variable, ri,j is a random variable between 0 and 1, N and m refers to the number of ospreys and problem variables, respectively, Lbj and Ubj relates to a lower and upper limit of problem variable, respectively.

All ospreys contribute to a candidate solution for the intended objective function (OF). Hence, the fitness values for the OF are expressed as a vector (F) as (15).

$$F = \left[ {\begin{array}{*{20}c} {F_{1} } \\ \vdots \\ {F_{i} } \\ \vdots \\ {F_{N} } \\ \end{array} } \right]_{N \times 1} = \left[ {\begin{array}{*{20}c} {F(X_{1} )} \\ \vdots \\ {F(X_{i} )} \\ \vdots \\ {F(X_{N} )} \\ \end{array} } \right]_{N \times 1}$$
(15)

where Fi is the fitness value of an osprey.

The quality of the candidate solution for an optimization problem is assessed based on the fitness values of OF. The fittest osprey is considered the best (elite) candidate solution. The osprey’s location is updated in each iteration; hence, the elite solution should also be updated after each iteration.

Exploration

Ospreys possess clear eyesight where they can easily locate and hunt the prey (fish) under the water. This is the first phase in the OOA where the population size is updated. The position of an osprey is updated after it attacks the fish. This phase increases the exploration characteristics of OOA and helps to evade the local optima stagnation problem.

For every osprey in the search space, the positions of other ospreys that have better fitness value for the OF are characterized as fishes. Equation (16) expresses the set of fish locations (FPi) for every osprey in the search space.

$$FP_{i} = \left\{ {\left. {X_{k} } \right|k \in \left\{ {1,2, \ldots ,N} \right\} \wedge F_{k} < F_{i} } \right\} \cup \left\{ {X_{best} } \right\}$$
(16)

where Xbest refers to the best candidate solution (elite).

The osprey randomly picks a fish out of these sets and attacks it. Hence, the location of the osprey is updated with its movement toward the fish as given in (17). If the osprey at the updated location has a better fitness value, then replace the previous location of an osprey using (18).

$$x_{i,j}^{P1} = x_{i,j} + r_{i,j} \bullet \left( {SF_{i,j} - I_{i,j} \bullet x_{i,j} } \right)$$
(17a)
$$x_{i,j}^{P1} = \left\{ {\begin{array}{*{20}c} {x_{i,j}^{P1} } \\ {Lb_{j} } \\ {Ub_{j} } \\ \end{array} } \right.\begin{array}{*{20}c} , \\ , \\ , \\ \end{array} \begin{array}{*{20}c} {Lb_{j} \le x_{i,j}^{P1} \le Ub_{j} ;} \\ {x_{i,j}^{P1} < Lb_{j} ;} \\ {x_{i,j}^{P1} > Ub_{j} ;} \\ \end{array}$$
(17b)
$$X_{i} = \left\{ {\begin{array}{*{20}c} {X_{i}^{P1} } \\ {X_{i} } \\ \end{array} } \right.\begin{array}{*{20}c} , \\ , \\ \end{array} \begin{array}{*{20}c} {F_{i}^{P1} < F_{i} ;} \\ {else,} \\ \end{array}$$
(18)

where, XiP1 and xi,jP1 refer to the new location of an osprey (first phase) and its jth dimension, respectively; FiP1 denotes to a fitness value for the objective function, SFi and SFi,j refer to the randomly picked fish for an osprey in its jth dimension and Ii,j is a random number between {1,2}.

Exploitation

The osprey carries the hunted prey (fish) to an appropriate location to eat. This phase is simulated in the exploitation process of OOA. The process of osprey carrying the fish to a suitable location causes a change in its location in the search space. This accelerates the exploitation process of OOA and helps to converge at a faster rate.

At first, a new random location for each population is determined using (19) and it is assigned as a “suitable location to eat the prey (fish)”. The location of the osprey is updated as in (20) if the fitness value of the new location is better than the previous location.

$$x_{i,j}^{P2} = x_{i,j} + \frac{{Lb_{j} + r \bullet \left( {Ub_{j} - Lb_{j} } \right)}}{t},\begin{array}{*{20}c} {for} & {i = 1,2, \ldots ,N;j = 1,2, \ldots ,m;} \\ \end{array} t = 1,2, \ldots ,T.$$
(19a)
$$x_{i,j}^{P2} = \left\{ {\begin{array}{*{20}c} {x_{i,j}^{P2} } \\ {Lb_{j} } \\ {Ub_{j} } \\ \end{array} } \right.\begin{array}{*{20}c} , \\ , \\ , \\ \end{array} \begin{array}{*{20}c} {Lb_{j} \le x_{i,j}^{P2} \le Ub_{j} ;} \\ {x_{i,j}^{P2} < Lb_{j} ;} \\ {x_{i,j}^{P2} > Ub_{j} ;} \\ \end{array}$$
(19b)
$$X_{i} = \left\{ {\begin{array}{*{20}c} {X_{i}^{P2} } \\ {X_{i} } \\ \end{array} } \right.\begin{array}{*{20}c} , \\ , \\ \end{array} \begin{array}{*{20}c} {F_{i}^{P2} < F_{i} ;} \\ {else,} \\ \end{array}$$
(20)

where, XiP2 and xi,jP2 refer to the new location of osprey (second phase) and its jth dimension, respectively; FiP2 designates fitness value for the objective function; t and T refer to an iteration counter and a total number of iterations, respectively.

The various stages of OOA are illustrated as a flowchart in Fig. 3. Furthermore, the implementation of OOA for DG placement problem is described below.

Fig. 3
Fig. 3The alternative text for this image may have been generated using AI.
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Flowchart of OOA.

Step 1: Acquire RDS line and bus data.

Step 2: Run power flow and find TLP and bus voltages.

Step 3: Initialize OOA parameters and set operational constraints of RDS.

Step 4: Set population = 50 and Iteration count = 100

Step 5: Find the fitness value for the objective function (OF) without a DG accommodation.

Step 6: Randomize the population using (14) and find the fitness value for OF. Also, initialize it as a best solution.

Step 7: Use the exploitation and exploration phases of OOA to optimize the site and size of DG unit, respectively.

Step 8: Run the power flow and compute fitness value for the updated population. Replace the best solution if it is fitter.

Step 9: Otherwise, move to Step 7 and repeat.

Step 10: Print the candidate optimized solution, if the algorithm’s stopping criteria is reached. Otherwise, move to Step 6.

The OOA optimization technique solves the DG placement problem iteratively. The locations of ospreys are updated in the first iteration. The best candidate solution (elite) is updated based on the fitness value of the objective function. This process is repeated with the updated Ospreys locations until the maximum iteration is reached. The elite solution is considered the optimal solution for the problem.

Simulation outcome and discussion

This section presents and discusses the simulation outcome for different types of RDS with single and multiple numbers of DG accommodations. Simulation results were obtained using MATLAB (version R2020b) software. The OOA was executed for 50 trials to compute a best solution to a DG placement problem. Simulation studies were carried considering a constant power demand on the RDS and ignoring the uncertainties associated with Type-I DG (solar energy) and Type-III DG (wind energy). The control parameter of OOA is presented in Table 1.

Table 1 Control parameter and constraints.
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Test system I: IEEE 33-bus RDS

A simplified single-line model of a 33-bus RDS29 is presented in Fig. 4. The test system is built with 32 load buses and 32 distribution lines (branches). The test system delivers 3720 kW and 2300 kVAr of active power (AP) and reactive power, respectively. The substation operates at 12.66 kV.

Fig. 4
Fig. 4The alternative text for this image may have been generated using AI.
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IEEE 33-bus RDS: Single line diagram.

Simulation results before DG deployment

The power flow result of a 33-bus radial distribution test system without DG accommodation is presented in Table 2. Bus voltages are calculated in per unit (p.u) for a 12.66 kV base voltage. The PF study result in a cumulative RPL of 210.98 kW and a Vmin of 0.9038p.u. Figure 5 presents the VP and RPL of a 33-bus test system without DG deployment. 21 numbers of buses of the test system have recorded voltages below the minimum recommended level (Vmin).

Table 2 IEEE 33-bus RDS without DG: PF results (VP and power loss).
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Fig. 5
Fig. 5The alternative text for this image may have been generated using AI.
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VP (p.u) and RPL of IEEE 33-bus RDS before DG deployment.

Simulation outcome after DG accommodation

Table 3 presents the simulation outcome for a 33-bus RDS after the DG’s accommodation. Figures 6 and 7 demonstrate the optimal solution obtained for Type I and III DG allocation in each trial of OOA. The potential bus for DG placement is discovered by referring to the fitness value of the objective function. The bus at which the DG placement gives a minimum fitness value is chosen as the optimal site. It is evident from Figs. 6 and 7 that DG placement at the 6th bus yields the least fitness value compared to all other combinations. The OOA gives the best solution for Type I and III DG in the 32nd and 27th runs of the simulation study.

Table 3 Simulation outcome (Best) for IEEE 33-bus RDS after DG deployment.
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Fig. 6
Fig. 6The alternative text for this image may have been generated using AI.
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Demonstration of optimal bus selection for single type I DG allocation in 33-bus RDS.

Fig. 7
Fig. 7The alternative text for this image may have been generated using AI.
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Demonstration of optimal bus selection for single type III DG allocation in 33-bus RDS.

The proposed OOA technique optimizes the Type I and III DG unit for a capacity of 2014.67 kW and 2436.12 kVA, respectively. The optimal deployment of DG significantly reduced the RPL of 33-bus RDS from 210.98 to 100.27 kW (for Type-I) and 59.16 kW (for Type-III). Figure 8 presents the RPL along the distribution lines of a 33-bus test system after the DG inclusion. The optimal deployment of DG curtailed the RPL and enhanced the VP of the test system. Figure 9a presents the VP of the 33-bus test system preceding and following the DG placement. The Vmin of the radial power network is improved from 0.9038 to 0.9621 p.u and 0.971 p.u following a Type I and III DG placement, respectively. It was obvious from the test result presented in Table 3 that the OOA-optimized DG deployment substantially reduced the RPL. Furthermore, a significant enhancement in VP is achieved with no buses registering a voltage below the minimum recommended value (0.95 p.u). Besides, the OOA took only 8 iterations for Type-I DG and 11 iterations for Type-III DG placement to converge. The convergence curve of OOA for Type I and III DG optimized 33-bus RDS is illustrated in Fig. 9b. It was evident from the convergence plot that the OOA algorithm never got stuck in the local optimal solution.

Fig. 8
Fig. 8The alternative text for this image may have been generated using AI.
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RPL of IEEE 33-bus RDS following the optimized DG allocation.

Fig. 9
Fig. 9The alternative text for this image may have been generated using AI.
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(a) VP of IEEE 33-bus RDS preceding and following DG deployment. (b) Convergence curve of OOA.

Comparative study

This subsection presents the comparative study between the simulation outcomes of OOA and other optimization algorithms. For the comparative analysis, the simulation outcomes of ROA10, SOA11, ALOA17, ECOA19, GA20, and SCA23 algorithms were compared with OOA. For a Type-I optimized DG placement, SOA11 reduced the total RPL of the test system to 102.8 kW with a DG capacity of 2600 kW. ALOA17 optimized DG allocation with a rating of 1542.67 kW, minimizing the RPL to 125.16 kW. Likewise, ROA10 and ECOA19 optimized Type-I DG integration with 2590.2 kW and 1000 kW ratings have reduced the RPL to 111.02 kW and 127.28 kW, respectively. Furthermore, GA20 and SCA13 have curtailed the RPL to 105.48 kW and 111.02 kW for an optimal DG capacity of 2580 kW and 2590.1 kW, respectively. It is observed from the above summary that SOA11, ALOA17, ROA10, ECOA19, GA20, and SCA23 algorithms have achieved 51.27, 40.67, 47.38, 39.67, 48.21, and 47.38% PL reduction after the optimized Type-I DG placement. However, the proposed OOA optimization approach has cut down the RPL of the test system to 100.27 kW through 2014.67 kW optimized DG allocation and achieved a 52.47% PL reduction. A graphical presentation of the simulation result (RPL) of different algorithms after the optimized Type-I DG accommodation is presented in Fig. 10.

Fig. 10
Fig. 10The alternative text for this image may have been generated using AI.
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RPL of 33-bus RDS for different algorithms after Type-I DG placement.

For Type-III DG allocation, SOA11, ALOA14, GWO15, ROA10, HHO30, LSF-SA31, and WHO9 algorithms have reduced the total RPL of the test system to 65.14 kW, 71.75 kW, 81.43 kW, 67.83 kW, 69.44 kW, 67.81 kW, and 61.31 kW via an optimized capacity of 2550, 2238.8, 1000, 3144.6, 2952.95, 3098.2, and 3081.7 kVA, respectively. Furthermore, it is assessed that SOA11, ALOA14, GWO15, ROA10, HHO30, LSF-SA31, and WHO9 algorithms have achieved 69.12, 65.99, 61.40, 67.85, 67.08, 67.86, and 70.94% PL reduction for the optimized type III DG allocation. In the present study, OOA-optimized Type-III DG placement has minimized the total RPL to 59.16 kW and achieved a 71.95% PL reduction with a 2436.12 kVA DG rating. A graphical representation of the simulation test result (RPL) for different algorithms after the optimized Type-III DG placement is illustrated in Fig. 11. The comparative study discloses that the OOA-optimized DG allocation (Type I and III) has achieved better RPL reduction than the other algorithms. The comparative analysis also conveys the ability of OOA to provide a comprehensive solution for a DG placement problem. The summary of simulation outcomes for different algorithms to an optimized Type I and III DG placement is highlighted in Table 4.

Fig. 11
Fig. 11The alternative text for this image may have been generated using AI.
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RPL of 33-bus RDS for different algorithms after Type III DG placement.

Table 4 IEEE 33-bus RDS: Comparison of test outcomes.
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Test system II: IEEE 118-bus RDS

Validation of the proposed technique on the 33-bus RDS alone may not guarantee its superiority and adoptability. Hence, in this section, the robustness of the suggested OOA optimization technique is tested on the 118-bus RDS large distribution power system. This test system carries 22,709.71 kW active power demand (APD) and 17,041.07 kVAR reactive power demand (RPD). Seven units of DGs are optimally integrated into this test system to obtain significant power loss reduction.

Simulation findings without DG inclusion

BFS algorithm load flow execution on the test system without DG integration results in 1296.3 kW total AP losses and 0.6424 per unit minimum voltage. Bus voltages are expressed in per unit on a base voltage of 11 kV. Bus voltages of the 118-bus RDS before DG compensation are shown in Fig. 12. It was noticed that 45 out of 118 buses of the RDS have experienced a voltage magnitude fall below the recommended minimum voltage level (0.95 p.u.).

Fig. 12
Fig. 12The alternative text for this image may have been generated using AI.
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VP of IEEE 118-bus RDS without and with seven units of type I and III DG inclusions.

Simulation findings with DG inclusion

Simulation findings of the large 118-bus RDS without and with multiple Type I and III DGs are presented in Table 5. The results represent the best values obtained after 50 independent runs. Figure 12 presents the VP of IEEE 118-bus RDS with seven units of Type I and III DG inclusions. The convergence characteristic of OOA for optimizing multiple units of DGs is presented in Fig. 13.

Table 5 Simulated findings of IEEE 118-bus RDS with and without 7 units of DG inclusions.
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Fig. 13
Fig. 13The alternative text for this image may have been generated using AI.
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Convergence curve of OOA for multiple Type I and III DG unit optimizations.

Case I: type I DG units optimization

The proposed OOA technique takes 55 iterations and 67 s to optimize seven units of Type-I DG. OOA optimally allocates Type-I DG units at the buses 36, 69, 32, 75, 108, 49 and 97 in the 32nd run of the optimization study. Total RPL of the 118-bus test system is minimized from 1296.3 to 452.1 kW following the optimized disbursement of multiple DG units. Further, the optimized DG inclusion has also improved the magnitude of the bus voltages and maintains it within the recommended minimum and maximum values. After the optimized placement of Type-I DGs, the Vmin is improved from 0.6424 to 0.9802p.u.

Case II: type III DG units optimization

For multiple Type-III DG unit optimizations, OOA takes 61 iterations and 74 s of CPU time for optimal convergence. The buses 24, 109, 34, 85, 62, 111 and 53 are found to be the optimal locations for Type-III DG assimilation. The best solution is obtained in the 28th run of the simulation study. The total RPL is minimized to 98.56 kW and the minimum bus voltage is increased to 0.9971p.u following the Type-III DG allocations. The simulation findings witnessed better performance for Type-III DG than Type-I DG allocation.

Comparative study

The simulation findings of the OOA-optimized DG allocation are related to the popular optimization techniques such as I-DBEA32, IMOEHO33, QTLBO34, TLBO34, SA35, and LSFSA35. The simulation results of different optimization techniques for the multiple units of Type I and III DG placement are outlined in Tables 6 and 7, respectively. For an optimized multiple Type-I DG allocation, the RPL of the test system is reduced by 65.12%. Furthermore, it is witnessed that OOA gives a better percentage of RPL reduction than I-DBEA32, IMOEHO33, QTLBO34, TLBO34, and SA35. Additionally, better VP improvement is achieved with OOA than with other cited techniques. Likewise, for multiple Type-III DG units, the proposed OOA technique delivered better RPL reduction than I-DBEA32, IMOEHO33, and LSFSA35 techniques. Noticeably, superior results are obtained with Type-III DG allocation than with Type-I DG due to its reactive power for the distribution power system.

Table 6 Simulated findings comparison with 7 units of Type-I DG inclusions.
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Table 7 Simulated findings comparison with 7 units of Type-III DG inclusions.
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Test system III: 54-bus Malaysian RDS

The applicability of the OOA optimization technique is tested on a practical 54-bus Malaysian distribution power system besides IEEE benchmark RDSs. Malaysian RDS incorporates 54 buses and supplies a net real power of 4.595 MW and a reactive power of 2.298 MVAr at a substation voltage of 11 kV. The single-line model of the 54-bus Malaysian RDS is presented in Fig. 14. The PF execution for the test system results in 338.46 kW of real power losses and 0.9082 p.u of minimum voltage (@bus no. 22). Before the placement of a DG unit, the test system has an average bus voltage of 0.9383 p.u.

Fig. 14
Fig. 14The alternative text for this image may have been generated using AI.
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Malaysian 54-bus RDS.

The simulation results for the Malaysian 54-bus RDS after the allocation of the DG unit are presented in Table 8. The deviation in bus voltages of Malaysian 54-bus RDS after the optimized assignment of a DG is illustrated in Figs. 15a, 16b. The convergence plots of OOA for the DG-optimized 54-bus Malaysian RDS are presented in Figs. 15b, 16b.

Table 8 Simulation outcome for Malaysian 54-bus radial distribution power network.
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Fig. 15
Fig. 15The alternative text for this image may have been generated using AI.
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(a) Voltage profile variation after Type-I DG placement. (b) Convergence curve of OOA for Type-I DG allocation.

Fig. 16
Fig. 16The alternative text for this image may have been generated using AI.
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(a) Voltage profile variation after Type-III DG placement. (b) Convergence curve of OOA for Type-III DG allocation.

The potential bus for DG placement is discovered based on the fitness value of the objective function. Figures 17 and 18 exhibit the optimal solution obtained for Type I and III DG unit allocation in each trial of OOA execution. It is evident from Figs. 17 and 18 that optimization of DG (both Type I and III) at the 16th bus yields the least fitness value compared to all other combinations. For Type I and III DG optimization, OOA yields the best results in the 36th and 38th simulation runs.

Fig. 17
Fig. 17The alternative text for this image may have been generated using AI.
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Demonstration of optimal bus selection for single Type-I DG allocation in 54-bus Malaysian RDS.

Fig. 18
Fig. 18The alternative text for this image may have been generated using AI.
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Demonstration of Optimal bus selection for single Type-III DG allocation in in 54-bus Malaysian RDS.

The optimized Type-I DG placement minimizes the power losses of the test system from 338.46 to 92.87 kW and enhanced the Vmin from 0.9082 to 0.9615 p.u. Similarly, optimized Type-III DG deployment has cut down the power losses to 17.32 kW and increased the minimum bus voltage to 0.9708 p.u. The mean bus voltage of the test system has been increased to 0.9769 and 0.9819 p.u. following a Type I and III DG allocation, respectively. The optimized Type I and III DG employment significantly reduced the network line power losses by 72.56 and 94.88%, respectively. It was obvious from the test results presented in Table 8 that Type-III DG integration has given a superior result to Type-I DG placement. Type-III DG placement achieved this outcome because of its competence to inject reactive power besides a real power injection. However, the optimal size of Type-III DG is more than that of Type-I DG.

Conclusion

In this work, an optimization approach using the Osprey optimization algorithm (OOA) was successfully implemented to optimally allocate DG units in the different RDSs. The position and size of a Type-I (solar PV) and Type-III (WT) DG were optimized to minimize the total RPL of RDS. The performance of OOA has been realized on the 33-bus and 118-bus IEEE-testified RDSs and a real-time Malaysian 54-bus RDS. The optimized single Type I and III DG placement in the 33-bus RDS reduced the total RPL by 52.47 and 71.95%, respectively, with significant improvement in the bus voltage profiles. The optimized Type I and III DG deployment has enhanced the minimum bus voltage by 0.0569 and 0.0666 p.u., respectively. Likewise, optimized inclusion of multiple Type I and III DG units has reduced the RPL of the 118-bus RDS by 65.12 and 92.39%, respectively. A comparative study was made between the simulation findings of OOA and the popular algorithms. The comprehensive comparison outlined that the OOA-optimized DG deployment yielded better results than other algorithms. Furthermore, the versatility of the proposed simulation study was tested on a real-time Malaysian 54-bus RDS. The simulation outcomes signify the effectiveness and adaptability of OOA on a real-world DG placement problem.