Optimal Coordinated Planning of Distributed Generations and HVDC Links for Economic and Environmental Performance Improvement

1. Introduction

The increasing demand of electrical power systems due to urbanization and expansion of the cities, industrial growth, leads the recent researches to investigate how to meet the demand ,according to the IEA (The International Energy Agency) world energy outlook, during the next 20 years, there is expected to be a roughly 50% increase in the electricity demand [1], another challenge of the power systems is large distance between generation and distribution systems, this challenge also need to reconfigure and integrate the tradition power systems with techniques that can enhance the power grids [2].

The importance of this topic comes from combining two main techniques (SCs and HVDC) to enhance the overall performance of power system and reduce the cost with different load levels.

To emphasize the importance of this article and explain the contribution and research gap we investigated the other studies in the same area, for example in [3], integrate HVDC-LCC/VSC grids using optimization algorithm called Power Flow of the University of Padova (PFPD) to estimate power flow on Italian grid. In [4], Fitness-Distance Balance based Teaching-Learning-Based Artificial Bee Colony algorithm (FDB-TLABC) is demonstrated in a power network that incorporates stochastic Renewable Energy Sources (RESs).Voltage Source Converter-Multi Terminal DC (VSC-MTDC) systems proposed novel grid concept called Power Router (PR) for AC/DC hybrid power systems, it use IEEE-9 bus system added DC-line to reduce converter losses [5]. In [6] a deeply study is represented about Flexible AC Transmission Systems (FACTS) devices to demonstrate how the modern FACTS technology helps the transition of transmission networks to ‘’smart’’.

Many research focused last few years about how using optimization algorithm to enhance the power grid in terms cost, loss, emission..etc. For example in [7] Using a Symbiotic Organisms Search (SOS) algorithm, it focused on a solution to the security-constrained AC–DC OPF integrated with wind, solar sources using IEEE -30 and IEEE 57 bus test systems and comparing the (SOS) algorithm with others such as (ABC), Imperialist Competitive (ICA), Moth Swarm Algorithms (MSA), Shuffled Frog-Leaping(SFL), Genetic Algorithm (GA), and Particle Swarm Optimization Algorithms (PSO).In [8] examined the interaction between LCC-HVDC systems and the surrounding AC grid, their findings indicated that while SCs can assist in steady-state scenarios, but all these studies they did not deeply investigate under fluctuating load conditions. In [9] a complete picture of the existing literature based on the optimal placement and sizing of Static Synchronous Compensator (STATCOMs) as a reactive compensators represented, which is more complex system and expensive, these techniques don’t meet the research objectives in term of cost and emission.

In this article, two main technique are used HVDC and SCs, these two main techniques are integrated using BSA algorithm to optimize the (OPF) issues. The advantages of HVDC link are; cost effective in long distance power transmission, improved grid stability, ability to integrate renewable energy sources [10]. on another hand HVDC is expensive especially if the link is not long distance, there must be a balancing in the decision of choosing HVDC.

LCC and VSC represent two forms of HVDC systems employed for long-distance power transmission or connecting asynchronous AC systems [11], the LLC approached proposed in this research for cost effective factor while VSCs require large capacitors integrated within the converter valves to support their operations [12].

SCs is used in this article to get many advantages, its improving power factor, regulating voltage [13,14]. Shunt capacitors act in our case as a supplying reactive power source, which reduces the reactive power flow through transmission and distribution lines integrated with HVDC. Many articles are discussed the importance of using shunt capacitors in radial distribution systems in terms of sizing and locations with and without using optimization algorithms [15,16,17,18]. Other articles studied the impact of shunt capacitors on smart distribution grid, it was found that Capacitors bank mitigate the reactive power imbalance caused due to varying load [20].

The contributions of this study represent the integration of these components (HVDC,SCs) within OPF framework, also this study represents a comprehensive performance assessment across three loading scenarios (light, nominal, and heavy), which has not been thoroughly investigated in existing studies, joint minimization of generation costs, on the other hand this study considers the emission levels and voltage deviations. All these scenarios are implemented using BSA algorithm(detailed in the next section)for this category of hybrid AC/DC OPF problems. Although the IEEE 30-bus system is a medium-scale network rather than a long-distance transmission grid, it is extensively utilized in academic research for validating new methodologies.

The BSA is a population-based meta-heuristic that is well known for its strong global exploration ability. However, its application to OPF problems in hybrid AC/DC networks, which include LCC-HVDC links and multiple SCs under varying loading conditions, has received limited attention in the literature.

The key novelties and contributions of this study are summarized as follows:

• Development of a unified AC/DC OPF formulation for hybrid power systems that integrates LCC-HVDC links and multiple shunt capacitor banks.
• A complete performance assessment, across three loading scenarios—nominal and heavy—has not been fully explored in previous studies. There is a need to jointly minimize generation costs while taking into account emission levels and voltage deviations.
• Joint minimization of generation costs with consideration of emission levels and voltage deviations involves finding the balance between running power plants efficiently and keeping environmental impact low.
• Implementation of BSA for this category of hybrid AC/DC OPF problems, demonstrating its effectiveness and robustness.
• Benchmark comparison with the ABC algorithm to illustrate improvements in convergence behavior and solution reliability.

This work presents OPF strategy for hybrid AC/DC systems that incorporate LCC-HVDC link and multiple SCs. The BSA is employed to minimize generation costs while simultaneously evaluating the system’s performance in terms of emission levels and voltage deviations under various load conditions, including light, nominal, and heavy demand scenarios. While previous studies have investigated the BSA, LCC-HVDC systems, and SCs in isolation, the novelty of this research lies in the integration of these components within OPF framework. This allows for a comprehensive assessment of their combined effects on system performance across different load conditions.

The proposed approach is further validated by comparing the results of the proposed approach, with those obtained using the ABC.This comparison demonstrates the effectiveness of the BSA in enhancing both the quality of the solutions and the stability of the system.

In summary, this research helps the field by giving an OPF strategy that uses the strengths of BSA, LCC-HVDC and SCs, leading to improve operational efficiency and environmental performance in hybrid AC/DC power systems.

2. Problem Formulation

It is important to note that the fitness function of the optimization algorithms in-corporate only the OPF objective function. The emission and voltage deviation indices are subsequently calculated as performance metrics based on the resulting OPF solution and are not directly optimized.

Figure 1 illustrates the equivalent circuit of HVDC system, all the circuit parameters are deeply described in [20,21,22] where

V_dr is Rectifier DC voltage , V_di is Inverter DC voltage , V_r and V_i are the AC bus voltages , α_r and α_i are the ignition angles of the rectifier and inverter and three resistances r'''_cr, r''_ci,, r''_d .

The equations related to the operation of a converter’s rectifier are provided below, offering a clear and rigorous mathematical foundation for the study [22]:

V_dor =kV_rt_r ,(${\displaystyle \raisebox{1ex}{$\mathrm{k}=3\sqrt{2}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{ᴨ}$}\right.}$) (1)

$${\mathrm{V}}_{\mathrm{dr}}={\mathrm{V}}_{\mathrm{dor}}\cos {\mathsf{\alpha }}_{\mathrm{r}}-{\displaystyle \frac{3{\mathrm{X}}_{\mathrm{cr}}}{\mathrm{ᴨ}}}{\mathrm{I}}_{\mathrm{d}}$$

(2)

The reactive power on the rectifier side is calculated as follows:

Q_dr = |P_dr tanɸ_r| (3)

The phase angle between the alternating current and voltage can be calculated using the following equation:

$${\mathrm{ɸ}}_{\mathrm{r}}={\cos }^{-1}\left({\displaystyle \frac{{\mathrm{V}}_{\mathrm{dr}}}{{\mathrm{V}}_{\mathrm{dor}}}}\right)$$

(4)

2.1. Generation Cost

The generation cost is a frequent objective function in optimizing power generation and distribution systems. The objective of generation cost is expressed mathematically by the following equation:

$$\mathrm{Cos}t={\displaystyle \sum _{i=1}^{\mathit{Ngn}}\left(a_i{P}_{\mathit{gi}}^2+b_i{P}_{\mathit{gi}}+c_i\right)}$$

(5)

2.2. Emission

Considering emissions as an objective function in electric power system optimization attempts to reduce the negative environmental effects of electricity generation as in the following equation

$$\mathrm{Emission}=\left(\mathrm{NOx}+\mathrm{SO}2+\mathrm{CO}2\right){\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{Ngn}}}{\mathrm{P}}_{\mathrm{gi}}$$

(6)

The emission factors for grid power are NOx=5.06 lb/MWh, SO2=11.6 lb/MWh and CO2=2031 lb/MWh [23].

2.3. Voltage Deviation Index

This study employs the voltage deviation for each bus is computed as ${{(\mathrm{v}}_{\mathrm{i}}-1)}^2$and the VDI, calculated using Equation (7) from reference [24].

VDI = ${\displaystyle {\sum }_{\mathrm{i}}^{\mathrm{N}}}{{(\mathrm{v}}_{\mathrm{i}}-1)}^2$ (7)

2.4. Equality and Inequality Constraints

Optimization problems require the satisfaction of specific requirements and constraints, which include both equality and inequality conditions. At each bus the equality constraints make sure that active power and reactive power are balanced. This is explained in detail in the reference. [25,26].

2.5. Fitness Function

The fitness function in (31) is then described using the augmented objective function, as detailed in reference [21].

Fitness = objective + error (8)

where ∆x is the difference between the state variable and its limit, ki is the penalty factor, and ke is the number of state variables (30 variables in our case ) expressed mathematically below:

$$\mathrm{ke}=\left[{\mathrm{p}}_{\mathrm{gref}},{\mathrm{q}}_{\mathrm{g}1},...,{\mathrm{q}}_{\mathrm{gNg}},{\mathrm{v}}_{\mathrm{L}1},...,{\mathrm{v}}_{\mathrm{L}{\mathrm{N}}_{\mathrm{l}}}{\mathrm{t}}_{\mathrm{r}},{\mathrm{t}}_{\mathrm{i}},{\mathsf{\alpha }}_{\mathrm{r}},{\mathsf{\alpha }}_{\mathrm{i}},{\mathrm{v}}_{\mathrm{dr}},{\mathrm{v}}_{\mathrm{di}}\right]$$

(9)

3. Backtracking Search Algorithm

This study introduces the Backtracking Search Optimization Algorithm (BSA), an evolutionary algorithm (EA) designed to address numerical optimization problems [27]. EAs are renowned stochastic search methods that handle nonlinear, non-differentiable, and complex numerical optimization challenges [28,29,30].

The proposed algorithm’s five-step process is illustrated in Figure 2.

Although only ABC results are presented for comparison in this study, previous work [22] has already demonstrated a broader comparative evaluation involving GA, BSA, ABC, and other algorithms under identical test conditions, confirming the validity of the chosen benchmark. To ensure a fair comparison, all algorithms were evaluated using a fixed population size of 50 and a maximum of 200 iterations. The control parameters for the BSA were selected based on commonly reported values in the literature and subsequently refined through preliminary trial runs to achieve stable convergence performance. These parameter settings were consistently applied across all test cases under all loading conditions. The termination condition was met when either the maximum number of iterations was reached or the objective function exhibited no further improvement.

4. Simulation Results

This study utilizes the IEEE 30-bus system as the test model. The network includes two generators located at buses 1 and 2, along with four synchronous condensers positioned at buses 5, 8, 11, and 13. The system also contains 28 load buses, supplying a total demand of 283.4 MW of active power and 126.2 MVAr of reactive power. In addition, the grid consists of 41 transmission lines and four transformers. Comprehensive bus and line specifications for this test system are provided in Reference [31].

Load conditions are classified based on the load factor as follows:

Light Load: 80% of the nominal load.

Nominal Load: 100% of the rated load.

Heavy Load: 120% of the nominal load.

Three distinct scenarios are analyzed under varying load conditions to determine the optimal cost.

Case 1: The baseline system operating under light, nominal, and heavy load power flow conditions.

Case 2: The system with an HVDC link installed between buses 2 and 16, analyzed under light, nominal, and heavy load conditions.

Case 3: The system incorporating an HVDC link between buses 2 and 16 together with three SCs, evaluated under light, nominal, and heavy load conditions.

The constraints for the DC connection parameters and variables in Cases 2 and 3 are identical to those employed in the previous case, as detailed in reference [32].

The BSA was evaluated under both light and heavy load scenarios to assess its effectiveness in minimizing generation costs and reducing emissions as demonstrated in Table 1.

4.1. Light Load Scenario

In Case 1, with a light load, the cost to generate electricity was $536.08 per hour, and emissions were 493.29 klb/MW. Adding the LCC-HVDC link in Case 2 cut the cost by 13.35% and slightly lowered emissions by 0.92%. Case 3, which used SCs with the LCC-HVDC, showed even better results: the generation cost dropped by 15.60%, and emissions decreased by 14.26% compared to Case 1. This suggests that while the LCC-HVDC link on its own offers good cost savings, using both LCC-HVDC and SCs together really boosts both economic and environmental performance when the load is light.

4.2. Heavy Load Scenario

When the load was heavy, Case 1 had a generation cost of $589.60 per hour and emissions of 785.54 klb/MW. In Case 2, implementing the LCC-HVDC link reduced costs by 10.18% and emissions by 3.32%. Case 3, which included SCs, further lowered the cost by 15.14% and emissions by 12.90% compared to the initial setup. These results show that combining LCC-HVDC with reactive support improves how well the system works, especially when demand is high, leading to better voltage stability and less environmental impact.

4.3. Nominal Load

Case 1:

Under nominal loading conditions, the IEEE 30-bus system is analyzed using a Newton-Raphson (NR) power flow optimization technique designed to minimize both generation costs and emissions. The results indicate a generation cost of $597.26 per hour, an emission level of 827.36 lb/MW, and VDI of 0.5953 as shown in Table 2.

Case 2:

The test system has been enhanced to include HVDC link connecting buses 2 and 16. The BSA is subsequently applied to the modified system to address the optimization problem within the network. The results for the HVDC link are illustrated in Figure 3. Table 2 presents the BSA results for both the AC and DC systems, along with a comparison to the ABC algorithm. The table indicates that both the BSA and ABC methods yield results within acceptable limits for their respective approaches. The simulation showed that the BSA method worked better than the ABC algorithm.

Figure 3. A two-terminal HVDC transmission link schematic illustration for Case 2.

Figure 3. A two-terminal HVDC transmission link schematic illustration for Case 2.

Case 3:

The test system has been further modified to incorporate an HVDC link connecting buses 2 and 16, along with three SCs. The optimization problem associated with this updated configuration is addressed using the BSA. Figure 4 illustrates the outcomes of the HVDC link. Table 4 presents the BSA results for both the AC and DC systems, alongside a comparison with the ABC method. The simulation results indicate that the BSA method performs better than the ABC algorithm.

The placement of SCs is determined through an optimization procedure that targets buses exhibiting suboptimal voltage performance or significant reactive power deficits, with the objective of maximizing improvements in the VDI.

5. Results Discussion

5.1. Voltage Profile

Figure 5 demonstrates a significant improvement in bus voltage profiles for Cases 2 and 3 compared to Case 1. The enhancement in voltage levels is evident in both cases. In Case 2, the integration of the HVDC link contributes to this improvement, while in Case 3, the combined application of SCs with the HVDC link further enhances the voltage profiles. Importantly, all voltage levels depicted in the figure remain within acceptable limits.

5.2. Voltage Deviation

Figure 6 illustrates the voltage deviation at each bus under nominal load conditions, utilizing the BSA. The voltage deviation has greatly reduced from Case 1 to Case 2 and Case 3. Additional reduction in deviation obtained in Case 3 over that in Case 2 due to the addition of SCs in the network.

5.3. Statistical Performance Analysis

A comprehensive comparison between the BSA and the ABC was conducted under nominal loading conditions as shown in Table 3. In Case 2, the BSA achieved a reduction of 0.0965% in generation costs and a 0.4150% reduction in emissions compared to the ABC. In Case 3, the improvements were more pronounced, with the BSA reducing costs by 0.3693% and emissions by 1.7200%. Conversely, the ABC underperformed in all scenarios, exhibiting relative declines of −0.0966% and −0.4168% in costs and emissions, respectively, for Case 2, and −0.3707% and −1.7501% for Case 3. Although the numerical margins are small, the consistent superiority of the BSA underscores its robustness, efficiency, and superior convergence behavior in solving OPF problems involving LCC-HVDC integration and SCs.

To evaluate the robustness and reliability of the optimization algorithms, twenty independent runs were performed under the nominal operating condition of case3 as shown in Table 4. Since the objective is a minimization problem, lower objective function values indicate better performance. The statistical indicators considered include the best (minimum) value, mean value, and standard deviation (SD).

Table 4. Statistical Performance Comparison of BSA and ABC under Nominal load of Case 3.

Results	BSA	ABC	Results	BSA	ABC
1	476.5254	478.7324	13	475.9341	478.0198
2	476.0800	478.5896	14	476.2470	478.2372
3	476.0782	480.6411	15	476.3598	477.8618
4	476.1565	480.5134	16	477.0126	478.0143
5	476.1184	477.9729	17	475.8822	477.5305
6	475.9092	478.0013	18	476.2181	478.0284
7	476.1218	479.2297	19	476.2487	477.5563
8	476.5103	478.4744	20	476.2852	477.9715
9	476.5767	479.7465	Best Cost	475.7667	477.5305
10	476.5640	478.5453	Worst Cost	477.0126	480.6411
11	475.7667	477.6941	Mean Cost	476.2185	478.4850
12	475.7749	478.3415	SD	0.3054	0.9716

Table 4. Statistical Performance Comparison of BSA and ABC under Nominal load of Case 3.

Results	BSA	ABC	Results	BSA	ABC
1	476.5254	478.7324	13	475.9341	478.0198
2	476.0800	478.5896	14	476.2470	478.2372
3	476.0782	480.6411	15	476.3598	477.8618
4	476.1565	480.5134	16	477.0126	478.0143
5	476.1184	477.9729	17	475.8822	477.5305
6	475.9092	478.0013	18	476.2181	478.0284
7	476.1218	479.2297	19	476.2487	477.5563
8	476.5103	478.4744	20	476.2852	477.9715
9	476.5767	479.7465	Best Cost	475.7667	477.5305
10	476.5640	478.5453	Worst Cost	477.0126	480.6411
11	475.7667	477.6941	Mean Cost	476.2185	478.4850
12	475.7749	478.3415	SD	0.3054	0.9716

The statistical results indicate that BSA outperforms ABC under nominal operating conditions for Case3. BSA achieved the lowest objective value (475.7667) and a lower mean value (476.2185) compared to ABC (477.5305 and 478.3971, respectively). In addition, BSA exhibited a substantially smaller standard deviation (0.3054) than ABC (0.9716), demonstrating greater consistency and robustness across multiple runs. These results confirm the superior convergence quality and robustness of the BSA algorithm.

6. Conclusion

This study examines the integration of HVDC systems with SCs and advanced optimization algorithms to enhance overall power system performance HVDC technology is important for making power transmission more efficient, helping to connect renewable energy sources, and keeping the power grid stable.When combined with HVDC systems, SCs provide vital reactive power support and contribute to cost-effective operations. More recently optimization methods, like the BSA are seen as capable of tackling important problem like cost and emission reductions, load variation management and others. Though real-time control, high computation cost and adaptability under varying operating conditions still represent significant problems.

The BSA features a simpler structure and fewer control parameters compared to ABC and other algorithms. While the ABC algorithm may achieve convergence in fewer iterations, the BSA consistently delivers superior final solution quality, particularly regarding generation cost.

This article delineates the advancements made in the field while identifying significant gaps, particularly in the optimization of generation costs under variable load conditions. Future study focuses on building up hybrid and real time optimization approaches toward the integration and reactive power compensation of HVDC systems. If these challenges are solved, it will enable a movement of the power industry towards more reliable, sustainable, and economical power system that fulfills the requirement of this dynamic energy world.

Although the IEEE 30-bus system is a widely adopted benchmark for comparative studies, it does not capture all the complexities of real transmission networks, such as renewable intermittency, N-1 security constraints, and dynamic load behavior. Future work will extend the proposed framework to larger-scale systems (e.g., IEEE 118-bus and Polish 2383-bus networks) and incorporate stochastic renewable generation and contingency analysis.