Fully Native DPL-Based Conductor Sizing Optimization for Distribution Networks in DIgSILENT PowerFactory

Abstract

This paper presents a fully native optimization framework, implemented within DIgSILENT PowerFactory, which is aimed at solving the optimal conductor sizing problem (OCSP) in electrical distribution systems under realistic operating conditions. Our methodology integrates a tabu search algorithm (TSA) directly with the three-phase power flow routines and database objects available in the DigSILENT programming language (DPL), thereby eliminating the need for external data exchange and synchronization between independent optimization and network simulation environments. Our framework considers balanced and unbalanced operating conditions while incorporating peak demand, multilevel demand, and hourly demand load profiles. The optimization process minimizes annual investment and operating costs while satisfying voltage regulation and conductor ampacity constraints. The methodology was validated using a 27-bus benchmark system and the IEEE 33- and 123-bus distribution systems under different operating scenarios. The numerical results indicate that chronological demand scenarios significantly influence conductor allocation decisions and annual operating costs. Compared to the conventional peak demand load profile, the multilevel and hourly load profiles produced lower annual costs by distributing conductor sizing decisions across multiple operating states instead of considering worst-case loading conditions. Additionally, the unbalanced scenarios increased the operating losses and modified the conductor selection patterns due to unequal phase loading and current asymmetries. The proposed TSA-DPL implementation maintained stable convergence behavior and low statistical dispersion under all the evaluated benchmark systems and operating conditions. Even for the IEEE 123-bus feeder under unbalanced hourly operating conditions, the standard deviation remained below 0.70% of the average annual cost, confirming the robustness and repeatability of the methodology. Although the detailed three-phase chronological simulations increased the computational requirements, the proposed implementation demonstrated computational applicability to the evaluated benchmark systems. Overall, the proposed TSA-DPL framework constitutes a robust native implementation for realistic conductor sizing studies in modern three-phase distribution systems.

1. Introduction

1.1. General Context

Electrical distribution systems are undergoing significant operational and structural transformations, driven by the increasing penetration of distributed energy resources (DERs), the continuous growth in electrical demand, and the need to improve the efficiency, reliability, and operational flexibility of modern power networks [1,2]. Under these conditions, distribution planning studies have become increasingly important to ensure a secure, reliable, and economically efficient operation [3,4]. Among the various planning problems associated with distribution networks, the optimal conductor sizing problem (OCSP) constitutes one of the most relevant optimization tasks, given its direct influence on investment costs, active power losses, voltage regulation, conductor loading, and long-term operational performance [5,6].

Studies addressing the OCSP seek to determine the most suitable conductor type for each feeder section while satisfying the operational constraints of the distribution network and minimizing the overall economic costs associated with conductor installation and network operation [7]. Since conductor sizing directly affects feeder impedance characteristics, branch loading conditions, voltage regulation, and network losses, the resulting allocation has a substantial impact on both the electrical and economic performances of distribution systems. Consequently, the OCSP has been widely studied for several decades, using different mathematical formulations and optimization methodologies [5,8,9].

1.2. Motivation

Despite the significant progress made in recent OCSP research, several important limitations remain in the existing literature. First, many studies still rely on simplified balanced network representations that neglect the phase asymmetries commonly observed in modern distribution systems. Second, numerous optimization methodologies have been implemented through external co-simulation frameworks based on MATLAB, GAMS, Python, Julia, or similar computational environments [10,11,12,13]. Under these approaches, the optimization algorithm and the electrical simulation model operate in separate computational platforms, requiring data exchange and synchronization between independent software environments during the iterative optimization process. Furthermore, the dependence on external communication layers may increase implementation complexity and introduce additional software integration requirements for distribution planning studies under realistic operating conditions [3,14].

Although several studies have explored automation capabilities within DIgSILENT PowerFactory (DPF), most of them have focused on applications such as probabilistic power flow analysis [15], phasor measurement unit placement [16], metaheuristic implementation [17], and multi-period power flow analysis [18]. These works demonstrated the capabilities of the DIgSILENT Program Language (DPL) for implementing automation and optimization procedures directly within industrial-grade power system simulation environments.

However, limited research has addressed the development of a fully native OCSP framework within DIgSILENT PowerFactory while simultaneously preserving detailed three-phase electrical modeling, unbalanced operating conditions, and chronological demand scenarios, as well as enabling the computational evaluation of benchmark distribution systems directly within the native simulation environment [3,12].

1.3. Literature Review

Early OCSP studies have mainly focused on balanced radial distribution systems using simplified mathematical representations and heuristic optimization approaches. Classical works such as [8] established the foundational formulation of the conductor selection problem in radial feeders and highlighted the tradeoff between conductor investment costs and operating losses. Subsequently, several metaheuristic approaches were proposed to improve the exploration of the discrete search space associated with conductor allocation problems. Among these methodologies, harmony-search-based approaches [19] and tabu search implementations [20] demonstrated the suitability of metaheuristic optimization techniques for solving nonlinear conductor sizing problems with discrete decision variables. In addition, studies based on evolutionary and population-based optimization approaches further confirmed the applicability of metaheuristic frameworks to large-scale combinatorial conductor sizing problems [21,22].

Alongside metaheuristic methodologies, exact optimization formulations based on mixed-integer programming techniques have also been proposed for solving the OCSP. Mixed-integer linear programming (MILP) and mixed-integer nonlinear programming (MINLP) approaches were introduced in [5] and [23] in order to obtain mathematically rigorous conductor sizing solutions under constrained operating conditions. More recently, exact optimization frameworks have evolved towards advanced multi-objective formulations capable of integrating DERs, annualized operating costs, and integrated feeder planning strategies [5,6]. Although these methodologies provide high-quality solutions and rigorous mathematical representations, the applicability of exact formulations to large-scale practical distribution systems remains challenging due to the nonlinear, nonconvex, and combinatorial characteristics of the OCSP, particularly under detailed three-phase operating conditions [3,10,11].

Recent research trends have progressively shifted toward the analysis of unbalanced three-phase distribution networks and time-varying operating conditions, seeking to provide more realistic conductor sizing methodologies. In practical electrical distribution systems, unequal phase loading conditions, asymmetrical feeder configurations, and temporal demand variability affect branch currents, voltage profiles, and active power losses. Consequently, simplified balanced representations may not adequately capture the actual operating behavior of modern distribution systems [10,11].

Several recent studies have addressed the OCSP while considering three-phase asymmetric conditions and time-dependent demand scenarios. In [24], the influence of time-varying load conditions on conductor sizing decisions was analyzed, demonstrating the importance of incorporating temporal operating scenarios into the optimization framework. More recently, metaheuristic methodologies based on the generalized normal distribution optimization algorithm (GNDO) [10], the gradient-based metaheuristic optimizer (MGbMO) [11], the Newton metaheuristic algorithm (NMA) [12], and the discrete vortex search algorithm (DVSA) [13] have been proposed for solving the OCSP in three-phase unbalanced distribution systems. These studies have shown that explicitly representing phase asymmetry and temporal demand variability leads to more realistic conductor allocation strategies and improved long-term economic assessments. Recent studies have also incorporated renewable generation, battery energy storage systems, and multi-period operational analyses into the conductor sizing framework [18].

The accurate representation of unbalanced operating conditions also requires efficient three-phase power flow methodologies capable of preserving detailed network characteristics while maintaining acceptable computational performance during iterative optimization procedures [25]. In this context, advanced three-phase power flow formulations such as the derivative-free triangle-based approach have been developed to improve the computational efficiency of optimization frameworks that involve repeated power flow evaluations under asymmetric operating conditions [26]. These developments have facilitated the implementation of more realistic optimization methodologies for active distribution systems while improving the computational performance of repeated three-phase power flow evaluations under asymmetric operating conditions [10,12,13].

As summarized in

Table 1. Comparison of representative OCSP approaches and representative native DPL applications related to distribution system optimization.

Reference	Method	Optimization Implementation	System Representation	Network Model	Year	Topic	Main Contribution
Representative OCSP studies
[8]	Heuristic	Standalone	Balanced Peak demand	Custom mathematical model	2002	OCSP	Classical formulation of the OCSP considering investment cost and energy losses.
[5]	MILP	GAMS	Balanced Peak demand	Custom mathematical model	2013	OCSP	Exact optimization model for conductor sizing.
[13]	DVSA	MATLAB	$3\varphi$ Unbalanced Hourly demand	Custom three-phase mathematical model	2021	OCSP	Three-phase conductor sizing considering hourly operating conditions.
[12]	NMA	MATLAB	$3\varphi$ Unbalanced Hourly demand	Custom mathematical model	2022	OCSP	Metaheuristic optimization for unbalanced distribution systems.
[11]	MGbMO	MATLAB	$3\varphi$ Unbalanced Hourly demand	Custom three-phase mathematical model	2023	OCSP	Gradient-based metaheuristic for three-phase conductor sizing.
[6]	Robust Optimization	MATLAB	Balanced Demand uncertainty	Custom mathematical model	2025	OCSP	Robust conductor sizing considering uncertain demand conditions.
Representative native DPL applications
[15]	Analytical	Native DPL	Three-phase	Native DIgSILENT model	2018	Power Flow	Automation of probabilistic power flow analysis.
[16]	Optimization	Native DPL	Transmission	Native DIgSILENT model	2018	PMU Placement	Native optimization framework for PMU allocation.
This work	Tabu Search	Native DPL	Balanced 3 $\mathit{\varphi }$ Unbalanced Peak, multilevel and hourly demand	Native DIgSILENT PowerFactory object model	2026	OCSP	First native DPL implementation of the OCSP, integrating the optimization process with the built-in three-phase power flow solver within DIgSILENT PowerFactory

, previous OCSP studies have primarily focused on improving optimization algorithms and mathematical formulations while relying on custom mathematical network models implemented in external computational environments, such as MATLAB, Python, or GAMS.

Although these approaches have demonstrated satisfactory performance in technical and economic aspects, the optimization algorithm and the electrical network model generally operate outside specialized power system simulation environments. Meanwhile, several studies have showed the capabilities of the DPL for automation and optimization tasks. However, these applications have addressed problems other than the OCSP. In contrast, the proposed framework constitutes the first native DPL implementation of the OCSP within DIgSILENT PowerFactory, directly integrating the optimization process with the built-in three-phase power flow solver, thereby avoiding external data exchange between separate optimization and network simulation platforms. Consequently, the main contribution of this work lies in the implementation of a unified, reproducible, and fully integrated optimization framework that supports balanced and unbalanced distribution systems under peak, multilevel, and hourly demand representations, rather than in proposing a new optimization algorithm.

Recent research has explored emerging directions for distribution system planning based on machine learning techniques and multi-objective optimization. Reinforcement learning and deep learning approaches have been investigated to support planning and operational decision making by enhancing decision support and automation capabilities [27,28]. Likewise, multi-objective planning frameworks have incorporated environmental criteria (e.g., carbon emissions reduction) together with traditional economic and technical objectives [29,30]. Although these approaches represent promising research directions, this work focuses on the development of a fully native optimization framework for the OCSP within DIgSILENT PowerFactory. The proposed implementation provides a flexible foundation that can be extended to incorporate advanced optimization paradigms in future developments.

1.4. Contributions and Scope

Motivated by the above-presented research gaps, this paper presents a fully native DPL framework implemented within DIgSILENT PowerFactory for solving the OCSP under realistic operating conditions. The proposed methodology integrates a tabu search algorithm (TSA) with the three-phase power flow routines and network database objects available within the simulation environment [22]. The framework preserves detailed representations of balanced and unbalanced three-phase systems while evaluating peak, multilevel, and hourly demand scenarios.

The proposed methodology was validated using a 27-bus benchmark and the IEEE 33- and 123-bus feeders to assess its economic performance and convergence under different operating conditions [10,11,13,24].

The main scientific contributions, supported by the obtained quantitative results, are summarized as follows:

• A fully native TSA-DPL framework for the OCSP implemented within DIgSILENT PowerFactory, integrating the optimization algorithm and the native three-phase power flow solver in a unified environment while avoiding external data exchange between separate optimization and network simulation platforms.
• A comprehensive evaluation of conductor sizing under peak demand, multilevel, and hourly demand representations, showing that the multilevel and hourly formulations produced reductions in the total annual planning costs of up to approximately 35% with respect to the conventional peak demand formulation while satisfying voltage regulation and conductor loading constraints.
• A quantitative assessment of balanced and unbalanced operating conditions, showing that phase asymmetry modified the optimal conductor sizing, increased the annual operating costs, and mainly affected medium-capacity conductor selections, while the primary feeder reinforcements remained comparatively stable.
• Validation of the proposed native implementation on the 27-, 33-, and IEEE 123-bus benchmark systems, where independent executions exhibited low solution dispersion. For the IEEE 123-bus feeder, the standard deviation remained below 0.7% of the average annual cost under all evaluated demand scenarios, demonstrating low solution dispersion and repeatable optimization results across the evaluated benchmark systems.
• Public release of the developed implementation, benchmark systems, and source code is conducted to facilitate transparency, reproducibility, and future research based on the proposed native DPL framework [31].

1.5. Document Structure

The remainder of this paper is organized as follows: Section 2 presents the mathematical formulation of the OCSP, the adopted operational constraints, the adopted load profiles, and the proposed TSA-based optimization framework implemented in the DPL. Section 3 describes the evaluated distribution systems, the conductor catalog, the simulation scenarios, and the performance metrics. Section 4 presents and discusses the optimization results obtained under the balanced and unbalanced operating conditions while considering different demand scenarios. Finally, Section 5 summarizes the main conclusions of this work and outlines potential directions for future research.

2. Methodology

This section presents the proposed TSA-DPL framework for solving the OCSP in distribution networks. The OCSP is formulated as an MINLP model that minimizes the costs associated with conductor investment and operating losses [13].

The proposed implementation integrates the TSA with the native power flow routines available in the DPL, enabling a direct evaluation of conductor configurations and operational constraints without external co-simulation procedures. Figure 1 summarizes the proposed workflow.

2.1. Mathematical Formulation of the OCSP

The objective function considers a one-year operating horizon and minimizes both conductor investments and annual energy loss costs [11,13]. This planning horizon was selected to maintain consistency with the benchmark methodologies available in the literature. Consequently, it enables a fair and meaningful comparison of the obtained results.

$$\begin{array}{c}\hfill Minimize{C}_{total}=(C_{loss}+C_{inv})\end{array}$$

(1)

$$\begin{array}{c}\hfill C_{loss}=C_{kWh}\sum _{h\in {\Omega }_h}\sum _{p\in {\Omega }_p}\sum _{c\in {\Omega }_c}\sum _{ij\in {\Omega }_{ij}}{R}_{km}^c{L}_{ij}{\left|I_{ij,h,p}^c\right|}^2{\lambda }_{ij}^c{\Delta }_h\end{array}$$

(2)

$$\begin{array}{c}\hfill C_{inv}=\sum _{c\in {\Omega }_c}\sum _{ij\in {\Omega }_{ij}}{C}_{km}^c{L}_{ij}{\lambda }_{ij}^c\end{array}$$

(3)

Here, $C_{loss}$ is the variable associated with the energy loss costs; $C_{inv}$ represents the investment costs; $C_{kWh}$ denotes the average energy cost coefficient; the indices h, p, c, $ij$, and k denote the load levels, phases, conductor types, network sections, and system nodes, respectively; $R_{km}^c$ is the per-kilometer resistance of a specific conductor type; $L_{ij}$ is the length of the network section, $ij$; $I_{ij,h,p}^c$ denotes the rms value of the electric current; ${\lambda }_{ij}^c$ is the binary variable that defines whether a type-c gauge should be installed (${\lambda }_{ij}^c$ = 1) or not (${\lambda }_{ij}^c$ = 0) in the network section that connects nodes i and j; ${\Delta }_h$ denotes the hours of load level h; $C_{km}^c$ is the cost of a type-c conductor per kilometer; and ${\Omega }_h$, ${\Omega }_p$, ${\Omega }_{ij}$, ${\Omega }_c$, and ${\Omega }_k$ represent the set that defines the load levels considered in the planning horizon, the set of system phases, the set of system lines, the set of conductors considered, and the set of network nodes.

The optimization problem is subject to the operating constraints of the distribution network, including nodal voltage regulation limits, conductor ampacity restrictions, and the power flow equations governing the steady-state operation of the system.

2.2. Operational Constraints

The optimization problem is subject to power flow, voltage regulation, conductor ampacity, and conductor assignment constraints:

$$\begin{array}{cc}\hfill EQ=f(V_k,I_{ij},P_k^g,P_k^d,& Q_k^g,Q_k^d,P_{ij},Q_{ij})\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill V^{\min }\le V_{k,h,p}\le V^{\max },& \left\{\begin{array}{c}\forall k\in {\Omega }_k\\ \forall h\in {\Omega }_h\\ \forall p\in {\Omega }_p\end{array}\right\}\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill I_{ij,h,p}^c\le I_{\max }^c,& \left\{\begin{array}{c}\forall ij\in {\Omega }_{ij}\\ \forall h\in {\Omega }_h\\ \forall p\in {\Omega }_p\end{array}\right\}\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill \sum _{c\in {\Omega }_c}{\lambda }_{ij}^c=1,& \forall ij\in {\Omega }_{ij}\hfill \end{array}$$

(7)

where (4) represents the three-phase AC power flow model. This model is solved using the native power flow engine available in DIgSILENT PowerFactory. The software employs an enhanced non-decoupled Newton–Raphson algorithm for both balanced and unbalanced distribution networks, which provides the bus voltages, branch currents, and active and reactive power flows required for the evaluation of each candidate solution [32]. Equation (5) enforces voltage regulation limits between 0.95 and 1.05 p.u., (6) imposes conductor ampacity constraints, and (7) ensures a unique conductor assignment for each feeder section.

Additionally, the operational constraints related to voltage regulation and conductor ampacity are verified after every execution of the power flow. The constraint violations associated with the voltage regulation or conductor ampacity limits are incorporated into the evaluation function through additive penalty terms that account for both the number and the magnitude of the violations [33].

The penalized objective function can be expressed as follows:

$$\begin{array}{c}\hfill \min EF=C_{total}+f{p}_v+f{p}_L\end{array}$$

(8)

$$\begin{array}{c}\hfill f{p}_v=C_{total}\left[{\displaystyle \frac{NVLL}{TNN}}+{\displaystyle \frac{NVUL}{TNN}}+\sum _{p\in {\Omega }_p}\sum _{k\in {\Omega }_k}\left|V_{min}-V_{k,p}\right|{\delta }_{LL}+|V_{max}-V_{k,p}|{\delta }_{UL}\right]\end{array}$$

(9)

$$\begin{array}{c}\hfill f{p}_L=C_{total}\left[{\displaystyle \frac{NVL}{TNL}}+\sum _{p\in {\Omega }_p}\sum _{ij\in {\Omega }_{ij}}\left|{\displaystyle \frac{L{L}_{ij,p}-L{L}_{max}}{100}}\right|{\delta }_L\right]\end{array}$$

(10)

where $EF$ is the evaluation function; $f{p}_v$ is the voltage penalty factor; $f{p}_L$ is the loading penalty factor; $NVLL$ denotes the number of violations of the lower voltage limit; $NVUL$ is the number of violations of the upper voltage limit; $NVL$ represents the number of conductor loading violations; and $TNN$ and $TNL$ denote the total number of nodes and feeder sections, respectively. $L{L}_{ij,p}$ denotes the loading percentage of branch $ij$ on phase p, obtained from the native load–flow solution, whereas $L_{max}=100\%$ corresponds to the maximum admissible conductor loading adopted in this work. The binary variables ${\delta }_{LL}$ and ${\delta }_{UL}$ are equal to 1 when $V_{k,p}<V_{\min }$ and $V_{k,p}>V_{\max }$, respectively, and are 0 otherwise. Likewise, ${\delta }_L$ is equal to 1 when the conductor loading exceeds $L_{max}$ and is 0 otherwise.

The penalty terms combine two complementary measures of constraint violation. The first component represents the proportion of violated nodes or branches with respect to the total number of elements. The second component accounts for the magnitude of the voltage violations expressed in per-unit terms and the conductor loading violations expressed as normalized loading percentages with respect to the admissible loading limit ($L{L}_{\max }=100\%$). Consequently, both penalty components are dimensionless. Multiplying the resulting penalty factor by the equivalent annual cost preserves the monetary units of the evaluation function while proportionally increasing the objective value of infeasible solutions. Therefore, feasible solutions are ranked according to their economic performance, whereas infeasible solutions are penalized according to both the number and the severity of the constraint violations.

2.3. Load Profile Scenarios

Three load profile scenarios were considered to evaluate the impact of demand variability on conductor sizing and operating costs [10]:

• Peak demand profile (PDP);
• Multilevel load profile (MLP);
• Hourly load profile (HLP).

The peak demand profile evaluates the network under maximum loading conditions, the multilevel load profile considers three operating states over the planning horizon (100% loading for 1000 h, 60% loading for 6760 h, and 30% loading for 1000 h), and the hourly load profile evaluates the network using chronological hourly demand values, as presented in

Table 2. Hourly loading data [10].

Time (h)	Demand (pu)	Time (h)	Demand (pu)	Time (h)	Demand (pu)
1	0.684511335492475	9	0.706039245570585	17	0.874071251666984
2	0.644122690036197	10	0.787007048961707	18	1
3	0.613069156029720	11	0.839016955610593	19	0.983615926843208
4	0.599733282530006	12	0.852733854067441	20	0.936368832158506
5	0.588874071251667	13	0.870642027052772	21	0.887597637645266
6	0.598018670222900	14	0.834254143646409	22	0.809297008954087
7	0.626786054486569	15	0.816536483139646	23	0.745856353591160
8	0.651743189178891	16	0.819394170318156	24	0.733473042484283

.

For the multilevel and hourly profiles, the operating cost is computed from the accumulated energy losses, considering the duration of each loading level, ${\Delta }_h$, according to (2).

These three demand representations provide increasing levels of operational realism, enabling a systematic evaluation of the influence of temporal demand variability on conductor sizing decisions.

2.4. Tabu Search-Optimization Framework

TSA was adopted to solve the discrete OCSP due to its suitability for combinatorial optimization problems with discrete decision variables [34]. The iterative exploration of neighboring solutions allows the algorithm to efficiently navigate the discrete search space while incorporating engineering constraints directly into the candidate-generation process [35]. In particular, the neighborhood structure can be designed to preserve the radial network topology and enforce conductor sizing coherence along feeder sections, thereby reducing the generation of infeasible solutions and improving the efficiency of the search [36].

Each candidate solution is represented by

$$X=[c_1,c_2,\dots ,c_n]$$

(11)

where $c_k$ denotes the conductor type assigned to branch k and n is the total number of feeder sections.

The optimization process starts from an initial feasible solution, which is obtained by assigning the largest conductor type to all branches and subsequently reducing the conductor sizes according to the ampacity constraints. Neighboring solutions are generated by modifying the conductor assignments of selected feeder sections.

For each candidate solution, the network’s operating conditions are evaluated through power flow simulations, and the objective function is computed as presented in Section 2.1. Constraint violations are handled using the penalty terms defined in (8)–(10).

Recently explored movements are stored in a tabu list during a predefined tabu tenure to avoid cycling. An aspiration criterion allows for tabu movements when they improve the best solution found.

The search process stops when the maximum number of iterations is reached or when no improvement in the objective function is obtained over a predefined number of consecutive iterations.

Algorithm 1 summarizes the proposed TSA-based implementation.

To reduce the dependence on a single search trajectory, the proposed implementation performs multiple independent tabu search restarts. Each restart begins from the same deterministic initial solution and executes a complete local tabu search. The best solution obtained among all restarts is retained as the final OCSP solution.

Algorithm 1: Proposed TSA-based OCSP implemented in the DPL

1: Import network data and conductor catalog       2: Define TSA parameters: tabu tenure, maximum iterations, and stopping criteria       3: Generate initial conductor configuration: Assign the largest conductor to all branches Execute power flow Assign each conductor using an ampacity criterion       4: Evaluate objective function and constraints       5: Store initial solution as the best solution       6: Initialize the tabu list       7: while  stopping criteria are not satisfied  do       8:      Generate neighboring solutions      for each candidate solution       9:           Modify conductor allocation     10:           Update network model in the DPL     11:           Execute three-phase power flow in DIgSILENT PowerFactory     12:           Retrieve voltages, currents, and losses     13:           Evaluate objective function     14:           Apply penalty terms to objective function      end     15:      Select best admissible neighboring solution     16:      Update tabu list     17:      if current solution improves best solution     18:           Update best solution      end end     19: Return the best conductor configuration and the minimum annual cost

2.5. Native TSA-DPL Implementation and Workflow

The proposed TSA-based OCSP framework was implemented entirely in the DPL within DPF. Our implementation directly couples the optimization algorithm with the native three-phase power flow routines, thereby avoiding external co-simulation procedures.

During each iteration, the conductor allocation is updated in the network model and the power flow is executed. The resulting voltages, branch currents, and active power losses are then retrieved to evaluate the objective function and operational constraints.

Figure 1 summarizes the general workflow of the proposed methodology.

The developed implementation, benchmark systems, and simulation scripts were made publicly available to facilitate reproducibility [31]. The repository includes the complete DPL implementation; the 27-, 33-, and 123-bus benchmark systems modeled in DIgSILENT PowerFactory; and the necessary files to reproduce the simulations presented herein. This public implementation facilitates results verification, comparative studies, and future extensions of the proposed optimization framework.

3. Test Systems and Simulation Scenarios

This section describes the operating scenarios, benchmark distribution systems, and TSA parameter configuration adopted to validate the proposed OCSP framework.

3.1. Balanced and Unbalanced Operating Conditions

The proposed OCSP framework was evaluated under balanced and unbalanced operating conditions [11]. The balanced operation assumed symmetrical three-phase loading and identical phase impedances throughout the feeder, while the unbalanced operation considered phase-dependent load distributions and unequal operating conditions [37].

For the unbalanced scenarios, the three-phase power flow solver available in DPF was used to evaluate phase voltages, branch currents, and active power losses. Voltage regulation and conductor ampacity constraints were verified independently for each phase, considering the most critical phase loading conditions of each feeder section [38].

3.2. Evaluated Distribution Systems

The proposed optimization framework was validated using three widely adopted benchmark distribution systems that are commonly employed in conductor sizing and distribution planning studies, namely a 27-bus benchmark system, a 33-bus feeder, and the IEEE 123-bus grid.

These test systems were selected to evaluate the applicability and computational performance of the proposed methodology across benchmark systems of different sizes and operating conditions. In particular, the 27-bus and 33-bus systems were used as reference cases for performance comparisons against literature-reported methodologies [10,11] while also allowing the assessment of the convergence behavior, solution quality, and statistical robustness of the proposed TSA-DPL implementation.

The 27-bus test system is a three-phase radial distribution network that operates with a phase-to-neutral voltage of 13.8 kV and a unity power factor at the substation node (see Figure 2). This feeder was initially reported by the authors of [12].

The second test system has 33 nodes and corresponds to a three-phase grid with a radial topology that operates with a phase-to-neutral voltage of 12.66 kV and a unity power factor at the substation node (see Figure 3). This test system was initially reported by the authors of [39].

The IEEE 123-bus feeder was also considered to evaluate the computational performance of the proposed optimization framework using a larger benchmark distribution system. This feeder exhibits higher network complexity due to its increased number of nodes, branches, loading conditions, and phase configurations, providing a representative benchmark for assessing the computational applicability of the proposed implementation under unbalanced operating conditions.

The IEEE 123-bus test system is a three-phase unbalanced radial distribution feeder operating at a nominal line-to-line voltage of 4.16 kV. It includes a realistic configuration with laterals, single- and three-phase branches, and distributed loads (see Figure 4). This test feeder was originally introduced in IEEE’s feeder documentation [40].

All network models were implemented directly within the DPF environment. Detailed information regarding network topology and load data is provided in Appendix A.1.1 of Appendix A.

Table 3. Main characteristics of the evaluated distribution systems.

System	Buses	Branches	Voltage Level	Operating Conditions
27-bus benchmark	27	26	13.8 kV	Balanced/Unbalanced
33-bus	33	32	12.66 kV	Balanced/Unbalanced
IEEE 123-bus	123	122	4.16 kV	Unbalanced

summarizes the main characteristics of the evaluated benchmark distribution systems.

3.3. Conductor Catalog and Electrical Parameters

The adopted conductor catalog includes different conductor sizes with varying electrical resistances, reactances, current-carrying capacities, and installation costs.

Table 4. Main characteristics of the evaluated benchmark distribution systems [11].

Gauge (c)	r ($\mathbf{\Omega }$/km)	x ($\mathbf{\Omega }$/km)	${\mathit{I}}^{\mathit{c},\mathit{max}}$ (A)	Cc (US$/km)
1	0.8763	0.4133	180	1986
2	0.6960	0.4133	200	2790
3	0.5518	0.4077	230	3815
4	0.4387	0.3983	270	5090
5	0.3480	0.3899	300	8067
6	0.2765	0.3610	340	12,673
7	0.0966	0.1201	600	23,419
8	0.0853	0.0950	720	30,070

summarizes the main electrical and economic parameters associated with the adopted conductor catalog [13].

3.4. Model Assumptions

The proposed OCSP framework was developed under the following assumptions, which define the scope of the planning problem and are consistently adopted for all evaluated benchmark systems:

• The distribution systems are operated under radial network configurations.
• The electrical loads are modeled as constant power demands.
• Each line section is assigned a single conductor type selected from the predefined conductor catalog.
• The bus voltage magnitudes are maintained within the allowable limits (0.95–1.05 p.u.).
• Conductor loading is limited to 100% of the rated current-carrying capacity.
• The planning horizon corresponds to one year, and conductor investment costs are included directly in the objective function.

3.5. Simulation Parameters and TSA Configuration

A fixed TSA parameter configuration was adopted for all test systems and operating scenarios. The adopted parameter values were established through preliminary numerical experiments during the development of the proposed framework. Several parameter combinations were evaluated to verify the convergence behavior and the quality of the obtained solutions. The final configuration was selected because it consistently produced stable convergence behavior and competitive solutions when compared to the benchmark results reported in the literature. To ensure a fair and consistent assessment, the same parameter configuration was maintained for all benchmark systems and operating scenarios. The stopping criteria were based on the maximum number of iterations and the maximum number of consecutive non-improving iterations. A tabu tenure parameter was also included to avoid cycling during neighborhood exploration.

Table 5. Simulation parameters adopted for the TSA implementation.

Parameter	Value
Number of Independent Searches	20
Max. local searches	250
Max. local non-improving	20
Tabu tenure	3
Neighborhood size	5
Voltage limits	0.95–1.05 p.u.
Loading limits	100

summarizes the adopted TSA parameters.

3.6. Performance Metrics

The proposed framework was evaluated using economic, electrical, and computational performance indicators, including:

• The total annual cost.
• The operating cost associated with energy losses.
• The conductor investment cost.
• The active power losses.
• The minimum nodal voltage magnitude.
• The maximum branch current loading.
• The computational execution time.
• The TSA’s convergence behavior.

4. Results and Discussion

This section presents the validation and performance assessment of the proposed native DPL-based optimization framework implemented in DPF.

The proposed framework was evaluated using the 27-bus benchmark feeder and the IEEE 33- and 123-bus distribution systems under balanced and unbalanced operating conditions while considering peak demand, multilevel, and hourly load profiles, as described in Section 2.3.

This analysis includes comparisons with literature benchmarks, economic evaluations, computational performance assessments, and validations under realistic three-phase operating conditions.

4.1. Validation Against Literature Benchmarks

The 27-bus benchmark distribution system and the IEEE 33-bus feeder were used to validate the proposed TSA-DPL framework against benchmark solutions reported for the GNDO [10], MGbMO [11], NMA [12], and DVSA [13]. The comparison considered the total annual cost together with its two components: conductor investment costs and operating loss costs.

For the benchmark methods (DVSA, GNDO, MGbMO, and NMA), the conductor configurations reported in the analyzed publications were reconstructed and evaluated using the proposed TSA-DPL framework. Thus, the benchmark algorithms were neither reimplemented nor retuned in this work. Instead, the published conductor allocation solutions were assessed using the same objective function, economic model, and native three-phase load–flow engine adopted throughout this study. This procedure ensured that all benchmark solutions were evaluated under identical conditions, allowing for a consistent and fair comparison of the resulting objective function values.

4.1.1. Comparison Under Balanced Operating Conditions

Table 6. Comparison of results under balanced operating conditions.

Demand Scenario	Method	Total Annual Cost	Loss Cost	Investment Cost
		(USD/Year)	(USD/Year)	(USD)
27-bus benchmark distribution system
Peak demand	DVSA	562,024.48	217,672.33	344,352.15
Peak demand	NMA	557,695.26	219,950.46	337,744.80
Peak demand	GNDO	550,709.31	230,941.23	319,768.08
Peak demand	MGbMO	550,709.31	230,941.23	319,768.08
Peak demand	Proposed TSA	550,668.37	227,075.29	323,593.08
Multilevel	DVSA	388,238.27	155,671.76	232,566.51
Multilevel	Proposed TSA	362,431.59	166,714.86	195,716.73
Hourly profile	DVSA	475,633.64	196,153.64	279,480.00
Hourly profile	Proposed TSA	439,566.05	215,767.21	223,798.83
33-bus distribution feeder
Peak demand	Proposed TSA	424,561.30	202,067.17	222,494.13
Multilevel	Proposed TSA	275,154.72	121,886.30	153,268.41
Hourly profile	Proposed TSA	333,865.49	150,927.45	182,938.04

summarizes the results obtained under balanced operating conditions for the peak demand, multilevel, and hourly load profiles.

For the 27-bus benchmark system under the peak demand scenario, the proposed TSA achieved the lowest total annual cost among the compared methodologies while maintaining competitive conductor investment costs and lower operating losses. Although GNDO and MGbMO obtained slightly lower investment costs, the TSA reduced the operating losses cost by approximately 1.67%, resulting in the lowest overall annual cost.

Under the multilevel and hourly demand profiles, the proposed TSA reduced the total annual cost by 6.65% and 7.58%, respectively, in comparison with the DVSA. These improvements were mainly associated with lower conductor investment costs, indicating that the proposed optimization framework selected more cost-effective conductor configurations while satisfying all operational constraints.

For the IEEE 33-bus feeder, all evaluated operating scenarios satisfied the voltage regulation and conductor ampacity constraints. Among the considered demand representations, the multilevel profile produced the lowest total annual cost, reducing the planning cost by 35.19% compared to the conventional peak demand formulation. This result highlights the influence of demand representation on conductor sizing decisions, since considering multiple operating states avoids oversizing conductors based solely on maximum loading conditions.

Since no benchmark solutions for the balanced IEEE 33-bus feeder were found in the available OCSP literature, the results reported herein may serve as reference values for future studies conducted under similar operating conditions.

The complete conductor allocation for all balanced operating scenarios is provided in Appendix A.2.

4.1.2. Comparison Under Unbalanced Operating Conditions

Table 7. Comparison of results under unbalanced operating conditions.

Demand Scenario	Method	Total Annual Cost	Loss Cost	Investment Cost
		(USD/Year)	(USD/Year)	(USD)
27-bus benchmark distribution system
Peak demand	DVSA	608,392.14	257,999.19	350,392.95
Peak demand	NMA	597,579.01	252,624.61	344,954.40
Peak demand	GNDO	589,482.45	257,654.37	331,828.08
Peak demand	MGbMO	589,482.45	257,654.37	331,828.08
Peak demand	Proposed TSA	589,482.45	257,654.37	331,828.08
Multilevel	DVSA	404,887.32	148,536.87	256,350.45
Multilevel	Proposed TSA	383,998.00	167,056.42	216,941.58
Hourly profile	DVSA	489,849.48	223,894.68	265,954.80
Hourly profile	Proposed TSA	467,507.06	230,779.73	236,727.33
33-bus distribution feeder
Peak demand	GNDO	902,809.84	88,162.69	814,647.15
Peak demand	Proposed TSA	438,637.18	215,216.94	223,420.23
Multilevel	GNDO	642,128.41	48,350.74	593,777.67
Multilevel	Proposed TSA	278,939.39	128,573.63	150,365.76
Hourly profile	GNDO	386,941.98	191,754.52	195,187.46
Hourly profile	Proposed TSA	343,332.93	169,377.33	173,955.61

summarizes the results obtained under unbalanced operating conditions.

For the 27-bus benchmark system under the peak demand scenario, the proposed TSA achieved the same total annual cost as GNDO and MGbMO while outperforming DVSA and NMA. These results confirm that the proposed implementation is capable of reproducing the best benchmark solutions reported in the literature under identical evaluation conditions.

Under the hourly demand profile, the proposed TSA reduced the total annual cost by 4.56% compared to the DVSA. This improvement was primarily associated with a 10.99% reduction in the conductor investment cost while maintaining comparable costs in terms of operating losses.

For the IEEE 33-bus feeder, the proposed TSA achieved the lowest annual costs under all the operating scenarios. Under the hourly demand profile, the total annual cost decreased by 11.27% compared to the GNDO solution, while the conductor investment and operating loss costs were reduced by 10.88% and 11.67%, respectively.

Compared to a balanced operation, the unbalanced scenarios generally produced higher operating losses and required larger conductor sizes in several feeder sections to satisfy voltage regulation and conductor ampacity constraints under asymmetric phase loading.

The complete conductor allocation for all unbalanced operating scenarios is provided in Appendix A.2.

4.2. Economic Impact of Operating Conditions and Load Profiles

This subsection analyzes the influence of demand representations and operating conditions on the economic performance of the OCSP for the 27-bus benchmark system and the IEEE 33-bus feeder.

4.2.1. Influence of Load Profiles

Figure 5 compares the total annual costs obtained under the peak demand, multilevel, and hourly demand profiles for balanced operating conditions.

The peak demand formulation yielded the highest total annual costs for both benchmark systems.

For the 27-bus benchmark system, the multilevel and hourly load profiles reduced the total annual cost by approximately 34.2% and 20.2% compared to the peak demand formulation. Similarly, for the 33-bus feeder, the multilevel and hourly formulations reduced the total annual cost by approximately 35.2% and 21.4%.

Among the evaluated demand scenarios, the multilevel formulation consistently produced the lowest total annual cost for both benchmark systems, while the hourly representation yielded intermediate results.

Compared to the peak demand formulation, the multilevel and hourly load profiles selected smaller conductor sizes for moderately loaded feeder sections while maintaining acceptable voltage profiles and satisfying conductor ampacity constraints.

4.2.2. Influence of an Unbalanced Operation

This subsection analyzes the influence of unbalanced operating conditions on the economic performance of the OCSP. Figure 6 compares the total annual costs obtained under balanced and unbalanced operating conditions for the evaluated demand scenarios.

Unbalanced operating conditions consistently produced higher total annual costs than their balanced counterparts for all benchmark systems and demand scenarios.

For the 27-bus benchmark system under the peak demand scenario, the unbalanced scenario increased the total annual cost by approximately 7.05% compared to the balanced case. Similarly, for the IEEE 33-bus feeder under the hourly demand profile, the total annual cost increased by approximately 2.84%.

Moreover, compared to the balanced operation, unbalanced conditions required larger conductor sizes in specific feeder sections to satisfy voltage regulation and conductor ampacity constraints under asymmetric phase loading. This behavior is mainly attributed to unequal current distribution among phases, which increases losses and produces more restrictive operating conditions in heavily loaded branches.

4.3. Computational Performance Assessment

This subsection assesses the computational performance of the proposed TSA-DPL framework under different network sizes, operating conditions, and load profile scenarios. The analysis focuses on the robustness of the optimization process, its convergence characteristics, and the computational effort required to solve the OCSP under increasingly realistic operating conditions.

4.3.1. Statistical Robustness Analysis

The robustness of the proposed TSA-DPL framework was evaluated through independent optimization runs performed with the TSA parameter configuration described in Section 3.5. Each run consisted of several independent tabu search restarts. All runs started from the same deterministic initial solution, which was constructed using the conductor current–capacity criterion described in Section 2.4. The stochastic component of the algorithm was introduced during the local search, where the pseudo-random routines embedded in the DPL environment were used to generate different neighborhood exploration trajectories.

Standard deviations equal to 0.000 indicate that all independent runs converged to the same best solution within the reported numerical precision.

Table 8. Statistical convergence analysis of the TSA-DPL framework under different operating conditions.

System	Operating	Load	Avg.	Min.	Max.	Min.	Max.	Best Cost	Worst Cost	Standard
	Condition	Profile	Iterations	Iterations	Iterations	Time (s)	Time (s)	(USD/Year)	(USD/Year)	Deviation
27-bus	Balanced	Peak Demand	51.7	49	55	23	27	550,668.371	550,668.371	0.000
27-bus	Balanced	Multilevel Demand	47.2	40	51	37	48	362,431.588	362,431.588	0.000
27-bus	Balanced	Hourly Demand	43.0	42	45	250	430	439,566.045	439,566.045	0.000
27-bus	Unbalanced	Peak Demand	57.3	53	67	32	41	589,482.447	589,482.447	0.000
27-bus	Unbalanced	Multilevel Demand	48.0	44	51	49	58	383,998.001	383,998.001	0.000
27-bus	Unbalanced	Hourly Demand	51.0	48	53	430	592	467,507.064	467,507.064	0.000
33-bus	Balanced	Peak Demand	56.5	28	60	22	43	424,561.302	450,815.602	10,543.750
33-bus	Balanced	Multilevel Demand	54.3	50	63	68	114	275,154.716	275,154.716	0.000
33-bus	Balanced	Hourly Demand	57.2	56	58	473	582	333,865.488	333,865.488	0.000
33-bus	Unbalanced	Peak Demand	58.2	52	67	39	84	438,637.176	438,637.176	0.000
33-bus	Unbalanced	Multilevel Demand	54.7	50	62	97	166	278,939.389	278,939.389	0.000
33-bus	Unbalanced	Hourly Demand	57.8	56	60	554	724	343,332.933	343,576.252	99.330
123-bus	Unbalanced	Peak Demand	206.2	191	229	377	461	252,799.946	255,566.643	1270.479
123-bus	Unbalanced	Multilevel Demand	188.8	174	203	776	1161	193,948.013	196,673.907	1224.373
123-bus	Unbalanced	Hourly Demand	137.0	109	180	3182	5199	214,194.516	216,037.114	661.163

summarizes the statistical results obtained for representative benchmark systems and operating conditions.

The 27- and 33-bus systems exhibited low dispersion levels, with most optimization runs converging to identical or nearly identical objective function values. For the 33-bus feeder under balanced peak demand conditions, the difference between the best and worst solutions remained below 6.08% of the average annual cost, corresponding to a standard deviation of USD 10, 543.75/year. Under the unbalanced hourly operation, the standard deviation decreased to USD $99.33$/year, representing approximately 0.03% of the average objective function value.

The IEEE 123-bus feeder exhibited the largest variability due to the increased combinatorial complexity associated with unbalanced operation and the evaluation of multiple load profiles. The hourly load profile required execution times ranging from 3182 s to 5199 s and exhibited greater variability in the number of convergence iterations. Nevertheless, the variability in the objective function remained low for all demand scenarios. The peak demand, multilevel, and hourly formulations produced standard deviations of USD 1270.48, USD 1224.37, and USD $661.16$/year, respectively, corresponding to approximately 0.50%, 0.63%, and 0.31% of the average annual cost.

Overall, the statistical analysis showed that the proposed TSA-DPL framework provides robust and repeatable solutions across different network sizes and operating conditions. Even for the largest benchmark system, the observed variability remained below 0.70% of the average annual cost, confirming the numerical stability and consistency of the proposed implementation.

4.3.2. Convergence Behavior

In addition, the convergence behavior was analyzed for the 27-bus benchmark, the IEEE 33-bus feeder, and the IEEE 123-bus feeder under unbalanced operating conditions while considering the hourly demand profile. Figure 7 presents normalized convergence trajectories for the evaluated benchmark systems.

The 27-bus benchmark exhibited rapid convergence during the initial iterations, followed by a stabilization stage. The IEEE 33-bus feeder showed a smoother convergence pattern with a more gradual refinement of the objective function, whereas the IEEE 123-bus feeder exhibited longer refinement and stagnation stages due to the larger search space associated with unbalanced three-phase modeling and chronological demand representation.

Despite the increased complexity of the IEEE 123-bus feeder, all benchmark systems exhibited stable convergence without abrupt oscillations or numerical instabilities. Most improvements in the objective function occurred during the early iterations, followed by smaller refinements around promising regions of the search space. The embedded tabu memory mechanism contributed to preserving solution diversity while reducing the likelihood of premature convergence.

4.3.3. Computation Time Analysis

Figure 8 compares the average computation times required by the proposed TSA-DPL framework for different benchmark systems, operating conditions, and demand scenarios. A logarithmic scale on the vertical axis was adopted to facilitate the visualization and comparison of execution times spanning several orders of magnitude. The execution times, in seconds, are reported in Table 8.

The computation time increased with feeder size, demand profile resolution, and network modeling complexity. The balanced peak demand scenario of the 27-bus benchmark required the lowest computational effort, whereas the IEEE 123-bus feeder exhibited the highest execution times under an unbalanced hourly operation, given the repeated three-phase load–flow evaluations performed across multiple operating states. This behavior is expected because larger benchmark systems contain a greater number of electrical elements to be processed during each power flow solution, while multilevel and hourly demand representations require the same candidate solution to be evaluated repeatedly under multiple operating states.

These results indicate that the computational burden of the proposed framework is primarily governed by the number of operating states considered in the planning model. Although hourly demand representations substantially increase the execution time, they provide a more realistic characterization of the operating conditions than conventional peak demand formulations. The reported execution times characterize the computational behavior of the proposed implementation for the evaluated benchmark systems. Despite this additional computational effort, the proposed native TSA-DPL implementation successfully solved all the evaluated benchmark systems, including the IEEE 123-bus feeder, demonstrating its computational applicability to the benchmark systems evaluated in this work.

4.4. Computational Applicability Assessment Using the IEEE 123-Bus System

This subsection evaluates the computational applicability of the proposed TSA-DPL framework using the IEEE 123-bus distribution feeder under unbalanced operating conditions while considering peak demand, multilevel, and hourly load profiles. As the largest benchmark system evaluated in this work, the IEEE 123-bus feeder provides a representative test case for assessing the computational behavior and robustness of the proposed native optimization framework under unbalanced operation and multiple demand representations.

4.4.1. Optimization Performance Analysis

(a)

Comparative cost analysis:

Table 9. Best OCSP cost results for different load profiles in the unbalanced IEEE 123-bus system.

Load Profile	Total Cost	Investment Cost	Operational Cost
	(USD/Year)	(USD/Year)	(USD/Year)
Peak	252,799.946	156,724.253	96,075.694
Multilevel	193,948.013	154,951.071	38,996.942
Hourly	214,194.516	155,129.089	59,065.427

and Figure 9 summarize the optimal OCSP solutions obtained for the evaluated load profile scenarios.

The multilevel load profile yielded the lowest total annual cost, reaching USD 193,948.013/year, which represents reductions of 23.3% and 9.5% relative to the peak demand and hourly formulations, respectively. The cost of operating losses was also minimized under the multilevel representation, decreasing by 59.4% compared to the peak demand case and by 34.0% relative to the hourly formulation.

In contrast, the conductor investment costs remained nearly unchanged across the evaluated scenarios, with variations below 1.2%. Consequently, the differences in the total annual cost were primarily driven by changes in the cost of operating losses rather than by conductor investments, highlighting the importance of representing demand variability when solving the OCSP.

(b)

Cost evolution during local search:

Figure 10 illustrates the evolution of the total objective function together with the conductor investment and operating losses cost during a representative local search execution.

The total objective function decreased from approximately USD $1.204\times {10}^6$ to USD $2.147\times {10}^5$/year, corresponding to an overall reduction of 82.2%. During the same optimization process, the cost of operating losses decreased by 45.2%, whereas the conductor investment cost increased by 40.1%. This tradeoff reflects the replacement of low-cost conductors with larger conductor sizes that reduce electrical losses and improve the overall economic performance of the network.

During the initial iterations, the total objective function exceeded the sum of the conductor investment and the operating losses costs because of the penalty terms associated with voltage regulation and conductor ampacity violations. As the search progressed, these infeasible solutions were gradually eliminated, causing the penalty contribution to vanish and the objective function to converge towards feasible conductor allocation solutions. Consequently, the final objective value corresponds exclusively to the economic costs associated with a feasible network configuration.

4.4.2. Robustness of the Local Search Process

Six independent local search executions were carried out for the hourly load profile scenario under unbalanced operating conditions, in order to assess the robustness and repeatability of the proposed TSA-DPL framework.

Table 10. Summary of local search executions for the hourly load profile in the unbalanced IEEE 123-bus system.

Search	Iterations	Total Cost	Investment Cost	Loss Cost	Time (s)
1	162	214,194.516	155,129.089	59,065.427	4355
2	125	214,746.445	155,472.553	59,273.892	3376
3	116	216,037.114	156,241.678	59,795.437	3182
4	130	214,541.065	155,416.264	59,124.801	3626
5	180	214,652.923	155,537.163	59,115.760	5199
6	109	214,412.169	154,884.407	59,527.762	3240

summarizes the results obtained.

The total annual cost ranged from USD 214,194.516 to USD 216,037.114/year, corresponding to a maximum variation of only 0.86% among the six executions. Similarly, the costs of conductor investment and operating losses varied by only 0.88% and 1.23%.

The number of local search iterations ranged from 109 to 180, whereas the execution time varied between 3182 s and 5199 s, with an average computational time of approximately 3830 s.

Figure 11 illustrates the convergence trajectories obtained for the six executions.

All executions exhibited a monotonic reduction in the objective function and converged towards a narrow region of final solutions, despite starting from different initial search conditions. Most of the objective function reductions occurred during the early iterations, whereas the remaining iterations were devoted to progressively refining the conductor allocation around promising regions of the search space.

The small dispersion among the final objective function values confirms the robustness and repeatability of the proposed TSA-DPL framework for the evaluated IEEE 123-bus benchmark system under unbalanced operating conditions.

The simulation results show the proposed TSA-DPL framework consistently identifies high-quality solutions while maintaining stable convergence characteristics across independent optimization runs for the evaluated benchmark systems.

4.4.3. Conductor Allocation Characteristics

Figure 12 compares the conductor type distributions obtained for the evaluated load profiles in the IEEE 123-bus unbalanced distribution system.

Type-1 conductors dominated all optimal planning solutions, accounting for more than 80% of the selected feeder sections in every scenario. Specifically, branches 102, 103, and 101 were assigned to Type-1 conductors under the peak demand, multilevel, and hourly load profiles, respectively.

The most significant differences between the evaluated scenarios were observed in the intermediate-capacity conductors. Compared to the peak demand solution, the hourly load profile increased the number of Type-2 conductors from four to six branches, whereas the multilevel load profile increased the number of Type-3 conductors from four to six branches. These differences reflect the ability of time-varying demand representations to better match conductor capacities to the actual loading conditions, thereby avoiding unnecessary oversizing while observing the operational constraints.

In contrast, the allocation of high-capacity conductors (Types 7 and 8) remained virtually unchanged across all load profile scenarios, indicating that the heavily loaded sections of the feeder consistently required network reinforcement, regardless of the adopted demand representation. This behavior suggests that the selection of large conductors is primarily determined by the network topology and peak current requirements rather than by the temporal variation in the load profile.

The high similarity between the conductor allocations indicates that the proposed optimization framework consistently identifies a stable network reinforcement pattern, while only a limited number of feeder sections require conductor adjustments to accommodate different demand representations.

The complete conductor allocations obtained for all analyzed unbalanced operating scenarios are provided in Appendix A.2.

4.4.4. Electrical Performance Assessment

(a)

Voltage performance:

Figure 13 compares the minimum voltage profiles obtained for the evaluated load profiles in the IEEE 123-bus unbalanced distribution system.

As expected for radial distribution feeders, the voltage magnitude gradually decreased towards the terminal sections of the network under all evaluated scenarios. The peak demand formulation produced the lowest voltage magnitudes, whereas the multilevel load profile provided the best voltage regulation. The hourly representation exhibited an intermediate behavior.

All voltage magnitudes remained within the admissible operating range of 0.95–1.05 p.u., showing that the proposed TSA-DPL framework successfully satisfies the voltage regulation constraints under all the evaluated operating conditions. Although the terminal buses approached the lower voltage limit under the peak demand scenario, no voltage violations were observed.

(b)

Loss analysis:

Table 11. Comparison of power losses and energy costs under different load profiles.

Load Profile	Loss Cost	Days	Energy Cost	Loss Energy	Average Losses	Peak Loss
	[USD]	Days	[USD/kWh]	[kWh/Day]	[kW]	[kW]
Peak Demand	96,075.694	365	0.139	1893.677	78.903	78.903
Multilevel load profile	38,996.942	365	0.139	768.640	32.027	81.555
Hourly Load Profile	59,065.427	365	0.139	1164.195	48.508	80.576

summarizes the global loss indicators obtained for the evaluated loading conditions.

The peak demand formulation produced the highest daily energy losses, reaching 1893.68 kWh/day and an annual operating cost of USD 96,075.69. In contrast, the multilevel representation achieved the lowest daily energy losses ($768.64$ kWh/day), whereas the hourly formulation exhibited intermediate values (1164.19 kWh/day).

Although the multilevel and hourly formulations exhibit slightly higher peak-power losses than the peak demand solution, this behavior is consistent with the adopted objective function. Unlike the peak demand formulation, which optimizes conductor selection for a single operating condition, the multilevel and hourly formulations minimize the total planning cost by simultaneously considering conductor investment and accumulated energy loss costs over multiple demand levels. Consequently, the optimization process intentionally selects slightly smaller conductor sizes in some feeder sections, accepting a slight increase in peak losses while reducing the overall annual cost.

Table 12. Lines with the highest power losses under different demand profiles.

Line	Peak (kW)	Multilevel (kW)	Hourly (kW)
Line 115	10.416	10.429	10.424
Line 13	9.521	9.539	9.538
Line 3	7.156	7.165	7.162
Line 10	6.513	6.521	6.518
Line 58	5.861	5.867	5.863
Line 7	4.704	4.710	4.708
Line 116	3.697	3.701	3.698
Line 55	2.836	2.839	2.837
Line 114	2.511	2.819	2.517
Line 67	2.238	2.518	2.238

presents the lines with the highest power losses.

A limited number of feeder sections concentrated a significant portion of the total network losses, with several branches remaining among the highest-loss lines under all evaluated scenarios. Some feeder sections optimized under the multilevel and hourly demand representations exhibited slightly higher peak losses than those obtained with the peak demand formulation, reflecting the economic tradeoff between the conductor investments and the accumulated energy loss costs considered during the optimization process.

(c)

Line loading analysis:

Table 13. Most heavily loaded distribution lines and conductor types under different load profiles.

Line	Peak		Multilevel		Hourly
	Loading (%)	Type	Loading (%)	Type	Loading (%)	Type
Line 115	97.291	Type 8	97.343	Type 8	97.322	Type 8
Line 3	94.672	Type 8	94.723	Type 8	94.702	Type 8
Line 7	93.358	Type 8	93.409	Type 8	93.388	Type 8
Line 10	86.757	Type 8	86.808	Type 8	86.788	Type 8
Line 13	83.097	Type 5	83.168	Type 5	83.161	Type 5
Line 116	62.562	Type 7	62.588	Type 7	62.566	Type 7
Line 52	59.383	Type 7	59.409	Type 7	59.388	Type 7
Line 114	56.483	Type 4	56.560	Type 4	56.553	Type 4
Line 53	56.200	Type 7	56.226	Type 7	56.205	Type 7
Line 67	55.867	Type 4	65.633	Type 3	55.869	Type 4
Line 73	52.336	Type 4	61.497	Type 3	52.338	Type 4
Line 41	42.173	Type 4	57.035	Type 2	49.588	Type 3

summarizes the most heavily loaded feeder sections under the evaluated operating scenarios.

Lines 115, 3, and 7 consistently exhibited the highest loading levels, operating above 93% of their rated ampacity under all evaluated demand scenarios. Lines 10 and 13 also remained among the most heavily loaded feeder sections, with loading levels between 83% and 87%.

The multilevel load profile produced localized increases in the loading of feeder sections 67, 73, and 41 because the optimization favored slightly smaller conductor sizes in these branches to reduce the overall annual planning cost.

Most of the heavily loaded feeder sections were assigned Type-8 conductors, confirming that the optimization consistently reinforced the network backbone with the largest available conductor sizes. In contrast, Type-4 and Type-5 conductors were mainly allocated to moderately loaded branches, where a better compromise between investment and operating costs could be achieved.

Overall, the electrical performance assessment confirms that the proposed TSA-DPL framework achieves significant economic savings while maintaining satisfactory voltage regulation, acceptable conductor loading levels, and low operating losses under all evaluated demand scenarios. These obtained results indicate that the obtained conductor allocations satisfy both the economic and technical objectives of the OCSP.

4.5. Discussion Regarding the Proposed Native DPL-Based Implementation

The proposed TSA-DPL framework integrates the optimization process and the three-phase electrical simulation model within the same DPF environment, allowing conductor allocation decisions to be evaluated directly through the native power flow solver while avoiding external co-simulation procedures.

The unbalanced operation increased the operating costs and altered the conductor allocation decisions, particularly under the hourly load profile and in heavily loaded feeder sections. The adopted load profiles also affected both economic performance and conductor selection. In general, the multilevel and hourly load profiles produced lower annual costs than the conventional peak demand load profile because conductor sizing was evaluated across multiple operating states rather than under a single set of worst-case loading conditions. The choice of load profile primarily affected medium-capacity conductor selections, whereas the primary feeder reinforcements remained comparatively stable across the evaluated operating scenarios.

From an electrical performance perspective, the obtained solutions maintained acceptable voltage profiles and thermal loading conditions under all the evaluated cases. The loss and loading analyses also identified a reduced set of feeder sections concentrating the highest electrical stress levels. Although the multilevel and hourly formulations accepted slightly higher peak losses in some branches, these solutions achieved lower annual operating costs by balancing conductor investment against accumulated energy loss costs over the planning horizon.

Independent executions converged to similar solutions with low dispersion under all evaluated operating conditions. The IEEE 123-bus benchmark exhibited less than 0.7% variation in the average annual cost, confirming the repeatability of the proposed implementation.

The unbalanced operation and chronological demand scenarios increased the computational effort because each optimization step required repeated three-phase power flow evaluations across multiple operating states, with the highest execution times observed for the IEEE 123-bus feeder. Although these modeling assumptions increased the execution time, they provided more realistic representations of feeder operating conditions during the optimization process.

5. Conclusions

This paper presented a fully native TSA-DPL optimization framework implemented within the DPF environment for solving the OCSP in electrical distribution systems. The proposed methodology directly integrates the optimization procedure with the three-phase power flow routines and database objects available in the simulation platform. Consequently, it eliminates the need for external co-simulation environments while avoiding data exchange and synchronization between independent optimization and simulation software environments.

The developed framework was validated using a benchmark 27-bus feeder and the IEEE 33- and 123-bus distribution systems under balanced and unbalanced operating conditions. Additionally, different demand scenarios, including peak demand, multilevel, and hourly load profiles, were evaluated to analyze the impact of chronological load variability on conductor sizing decisions, electrical performance, and economic planning results.

The comparative analyses confirmed that both the loading and operating conditions influence the economic and technical performances of OCSP solutions. In particular, multilevel and hourly demand profiles consistently yielded lower annual costs than conventional peak demand formulations because conductor sizing decisions were distributed across multiple operating states instead of being determined exclusively by worst-case loading conditions. The comparative analysis indicated that an unbalanced operation increases the operating losses, modifies conductor allocation patterns, and requires additional reinforcements in heavily loaded feeder sections due to unequal phase loading and current asymmetries.

From an electrical performance perspective, the proposed TSA-DPL implementation maintained detailed three-phase modeling capabilities throughout the optimization process. The phase-dependent voltage profiles obtained, the loading analyses, and the loss evaluations confirmed the importance of explicitly considering unbalanced operation and chronological demand variability in practical distribution planning studies. The conductor allocation analyses further demonstrated that demand representation primarily affects medium-capacity conductor selections, while the backbone structure of the distribution network remains comparatively stable across the evaluated demand scenarios.

The statistical and convergence analyses showed low solution dispersion under all evaluated operating conditions and network sizes. Independent executions converged to similar solutions despite the stochastic nature of the adopted metaheuristic. For the IEEE 123-bus benchmark, the variation in the average annual cost remained below 0.7%, confirming the repeatability of the proposed implementation.

Future work will extend the proposed native framework to incorporate high penetrations of DERs, energy storage systems, capacitor placement, network reconfiguration, reliability assessment, stochastic renewable generation models, and multi-objective optimization formulations by introducing additional decision variables and operational constraints within the same DPF environment.