Analysis of Optimal HVDC Back-to-Back Placement Based on Composite System Reliability

Abstract

HVDC is a promising interconnection solution for connecting asynchronous systems and ensuring power control. In Indonesia, a remote industrial system in Sumatra is experiencing load growth and has the option to draw power from the Sumatra system. However, due to frequency differences, the use of HVDC is crucial. The Generation Expansion Planning has proposed six converters but not their interconnection points. This study will determine the most reliable interconnection locations. The chosen converters are modular multilevel converters (MMCs) with high modularity. The converter reliability modeling considers voltage levels, the number of modules, and redundancy strategies. This modeling is then implemented at the power system level to obtain the best placement at the available high-voltage (HV) substation options. Determining the best placement is based on the optimal reliability index. The optimal placement also includes the option to convert from HV to medium-voltage (MV) interconnection. MV interconnection offers higher flexibility but tends to be more expensive. The availability for HV converters is 99.69%, while for MV converters, it is slightly higher, at 99.81%. Additionally, converting from HV to MV reduces the SAIFI (system average interruption frequency index) from 0.2668 to 0.2284 occurrences per year, lowering the interruption cost from 7.804 million USD to 5.737 million USD per year. The sensitivity of interruption, investment, and maintenance costs shows that converting at least one HV converter to MV remains economical. In this case study, the optimal converter placement includes Area VI–2, recommended for conversion from HV to a more distributed MV configuration, improving reliability and economic efficiency.

1. Introduction

The transformation toward a cleaner electrical system requires the more extensive use of new technologies. The increasing utilization of variable renewable energy (VRE) such as solar and wind is one of the key indicators of this transformation. Additionally, the idea of interconnecting separate electrical systems has emerged as an option. Such interconnections can enhance system reliability and expand VRE penetration [1,2,3]. High-voltage direct current (HVDC) technology is crucial to realizing these interconnections.

HVDC transmission offers several advantages over HVAC transmission, such as lower losses, higher transfer capacity without stability constraints, and the ability to connect asynchronous systems [4]. More advanced HVDC schemes can also provide power control like conventional generators. The voltage source converter (VSC), a part of the HVDC technology, enables the control of active and reactive power due to the fully controllable IGBT switches. This allows HVDC with VSC technology to have droop control and virtual inertia, transferring power and enhancing system stability [5,6]. Recent control strategies utilizing nonlinear observers have further improved VSC-based HVDC systems by enhancing robustness against uncertainties and ensuring stable voltage regulation, even under fluctuating grid conditions [7,8]. One increasingly adopted converter technology is the VSC modular multilevel converter (MMC). VSC MMC operates by converting voltage into multiple levels to achieve efficient power conversion. MMC is gaining popularity due to its modularity and disturbance resilience [9].

HVDC is based on power electronics (PE), which poses challenges in terms of reliability [10,11,12,13]. The large number of HVDC components raises concerns about component reliability, which can affect overall system reliability. Therefore, it is necessary to model the reliability of PE-based HVDC integrated with the overall power system reliability. Sufficient HVDC modeling will provide particular analysis regarding its impact on the power system.

An industrial area in Indonesia requires an additional power supply to meet the increasing load each year. This industrial system is in Sumatra but operates remotely, separate from the national system, due to different operating frequencies. On the other hand, the Sumatra system has a significant reserve and could be an option to supply power to this industrial system. HVDC back-to-back will help connect both systems and provide adequate power to the industrial system. The generation expansion planning for this industrial system has specified the number and capacity of HVDCs that need to be interconnected with the system. However, the optimal location selection has not been conducted.

This research analyzes the best interconnection point for the HVDC in the industrial system based on reliability analysis. This research models the detailed reliability of VSC MMC. The converter modeling considers voltage levels, the number of modules, and redundancy strategies. Combining the HVDC reliability model and the system reliability assessment will provide the optimal location for the HVDC. The selection of interconnection points will be not only for the location point but also the voltage level, whether medium voltage (MV) or high voltage (HV). Interconnection at MV offers higher installation flexibility than HV. Interconnection at MV also implies HVDC closer to the load, which means greater reliability. However, the network connection cost for MV tends to be higher than for HV for each MW of transmitted power. A comparison with costs will also yield the best configuration.

This paper analyzes reliability modeling and optimal placement of the converters, considering technical and economic aspects. This paper is structured as follows: Section 2 provides the study literature regarding HVDC reliability modeling, reliability-based optimal placement, and HVDC economic calculations. Section 3 offers a detailed explanation of HVDC reliability modeling and an overview of power system reliability. Section 4 provides the methodology and overview of the test system, including the location options for HVDC placement. Section 5 presents the test results and analysis of the best modeling and placement of the converters in the test system. Finally, Section 6 provides the conclusions of this paper.

2. Literature Review

MMC technology is currently one of the technologies experiencing growth in HVDC applications due to its increased efficiency and system reliability. HVDC with VSC technology offers high flexibility and effectively manages power between two asynchronous systems, thereby enhancing system stability and reliability [4,14]. With the MMC topology, scalability and fault tolerance are also achieved, which are essential for connecting two AC systems [15,16,17].

In addition to HVDC, MVDC technology also has prospects for interconnection. MVDC systems utilizing MMC have been adopted in industries and on train tracks due to their ability to manage power distribution; ensure stability in complex environments; and provide flexibility, scalability, and fault tolerance [18]. Moreover, MVDC based on MMC has also begun to be applied to the interconnection of renewable energy sources and between systems [19,20]. This capability of MVDC is essential in industry systems, where maintaining a stable power supply is crucial, as its ability to control power flows and manage reactive power ensures the reliable operation of interconnected grids [21,22].

Although many studies suggest that HVDC or MVDC can provide stability support to the system, there are still reliability risks. This technology is based on power electronics, and as it advances, the system will gradually shift to power electronic-based power systems (PEPSs). The reliability challenges in PEPSs require an in-depth study to ensure the stability and robustness of future power systems [23,24]. As this transition occurs, it becomes increasingly important to evaluate the reliability of PEPSs comprehensively.

Several studies have already evaluated the reliability of PEPSs. Reliability modeling for PEPSs is divided into three levels: the component level, subsystem or converter level, and system level [10,11,12,13]. These three levels are interconnected, forming a hierarchy that influences the overall reliability of the power system. Several analyses can be carried out at each level. At the component level, the physics of failure-based stress–strength analysis (SSA) is used to predict wear-out failure [11]. At the subsystem level, mission profile modeling of the converter is carried out to analyze wear-out in predicting component lifespan [10]. At the system level, machine learning is utilized for regression to connect converter reliability with system reliability [13].

In addition to component-level analyses, several studies have also modeled the reliability of HVDC with MMC technology, such as determining the mean time to failure (MTTF) [25] and calculating availability [26]. For instance, ref. [26] investigates the availability of HVDC systems across various topologies, considering the converter and other critical components such as transformers, reactors, AC filters, and capacitors that construct the HVDC unit. Furthermore, ref. [27] explores the impact of module redundancy on improving MMC reliability for medium-voltage applications, emphasizing how different redundancy strategies can result in varying reliability models. Additionally, ref. [28] also analyzes the reliability of MMC systems with different submodule topologies such as half bridge and full bridge. These detailed studies on converter reliability contribute to a deeper understanding of how system design choices affect overall reliability.

In addition to detailed converter component reliability modeling, selecting the interconnection points is crucial for enhancing system reliability. Some papers, such as [29,30,31,32,33], have conducted reliability optimization-based placement of components. Most of these placements focus on distributed generation like PV and wind turbines, optimizing reliability indices, and sometimes combining with loss or cost optimization. For instance, ref. [29] discusses HVDC placement considering wind turbine generators (WTGs) in the system, optimizing positions for the best reliability. However, the HVDC reliability model used in this paper is still relatively simple.

Economic analyses for HVDC have also been conducted by several studies, such as those in [34,35,36,37]. Reference [34] utilized particle swarm optimization and error function to obtain VSC HVDC investment parameters. Reference [35] optimized HVDC in a case study in China considering life cycle cost (LCC), which includes investment, operation and maintenance, outage, and salvage costs. Reference [36] conducted an economic evaluation of VSC in Turkey using LCC analysis and sensitivity to the discount rate. Another case example for HVDC analysis was carried out in Pakistan considering discounted cash flow [37].

Many papers have analyzed HVDC from both reliability and economic perspectives. However, detailed HVDC modeling, especially MMC VSC associated with the power system level, is still rare. Papers evaluating the impact of HVDC on the system have focused on power adequacy without considering the transmission system. Additionally, considerations for converter interconnection voltage levels have not been found in other papers. This research will provide a composite system reliability evaluation including detailed VSC MMC reliability modeling. The modeling is differentiated for HV and MV applications. From this evaluation, the best interconnection points in the system can be determined.

In addition to technical evaluation, an economic analysis is conducted to ensure the most optimal solution. Other papers have performed sensitivity analysis on investment cost components or discount rates. This paper performs a sensitive analysis of interruption costs. Reliability evaluation provides annual interruption costs based on interruption cost input relative to duration. This result illustrates the quantitative impact of lost load on investment decisions.

3. Converter Reliability

3.1. VSC MMC Back-to-Back Topology

Figure 1 shows the complete topology of a monopolar back-to-back HVDC. In this topology, there is no DC transmission line, and the two converters between the sending and receiving grid are connected by a DC link related to the function of this HVDC to convert the frequency from 50 Hz to 60 Hz. Each side of the converter is connected to the transformer and reactor. The reactor enables the full active and reactive control of the converters.

The converter utilizes the modular multilevel converter (MMC) as shown in Figure 2. A cascaded submodule (SM) is connected in each arm, which can produce multilevel voltages to mimic the sinusoidal wave. With a total of six arms, each arm is responsible for the full operation of a three-phase MMC.

3.2. Submodule Reliability

There are diverse topologies for the submodule; the simplest is the half-bridge. Other topologies may have great advantages during the operation; for example, the full-bridge topology has better DC short-circuit withstand [38,39]. A half-bridge submodule would be enough for the use of a frequency converter. The half-bridge submodule presents greater modularity due to the number of components and cost. Although a half-bridge is preferred for this analysis, the reliability analysis can also be adjusted to other chosen topologies.

Figure 3 illustrates the connection for a half-bridge submodule, which includes two sets of IGBTs, a capacitor, a thyristor, a vacuum contactor, and a control for each switch. Each component is crucial to the operation of the submodule (SM), allowing the reliability of the SM to be modeled as a series system, where the failure rate of the half-bridge SM is the sum of the failure rates of all its components. The failure rate data for the complete half-bridge SM in

Table 1. Submodule reliability data.

Component	FIT (Failures/109 h)
Module IGBT	180 (2)
IGBT module gate unit	150 (2)
SM capacitor	300
SM capacitor voltage sensor	150
Bypass thyristor	20
Bypass thyristor gate unit	100
Vacuum contactor	100
Vacuum contactor control	100
Total	1430

are obtained from the thesis in [27], providing a theoretical basis for reliability modeling. However, this approach does not account for the nonlinear behavior of the conversion system components, but focuses instead on the failure rates and the criticality of each component to the system’s overall success or availability. Although the impact of specific environmental and load conditions was not directly modeled, the failure rate data used reflect typical operating scenarios. The resulting FIT of a half-bridge submodule is 1430 failures/10⁹ h, equivalent to 0.0125 failures/year.

3.3. Arm Reliability

The failure rates, number of submodules, and redundancy strategy determine the arm’s reliability. The number of SMs can be determined from various aspects such as the configuration used for the SM (half-bridge, full-bridge, NPC, etc.), DC voltage level, capacity, and harmonic limits. For example, the number of modules in MV applications will be fewer than in HV applications due to the more lenient total harmonic distortion (THD) limits in MV compared with HV [40]. Increasing the number of modules will improve the power quality on the AC side but increase control complexity.

Equation (1) gives the number of SMs for the half-bridge [27]. The choice of IGBT class will affect the number of submodules. The designated DC voltage also needs to be fully considered.

$$N={\displaystyle \frac{1}{f_{us}}}{\displaystyle \frac{V_{dc}}{V_{svc}}}$$

(1)

where $f_{us}$ is the utilization factor of IGBT, $V_{dc}$ is the DC link voltage, and $V_{svc}$ is the IGBT voltage class.

In addition to the number of SMs, the redundancy strategy also influences the arm reliability. There are two basic redundancy strategies: active and passive. The active redundancy strategy allows the backup SM to operate with other SMs. With a suitable control scheme, it can distribute the voltage stress equally. The active redundant strategy is advisable for the medium voltage application [41]. The reliability of the scheme follows the k-out-of-N reliability model, with N as the total number of SMs and k as the minimum number of SMs to operate the arm.

The passive or standby strategy would not operate in normal conditions. Rather, it operates when the normal SM goes to failure. This strategy would be suitable for high-voltage applications due to the reduction in unnecessary switching losses [41]. The standby conditions will lower the stress voltage in the SM components, hence lowering the failure rates. According to [42], the failure rate of a standby SM can be multiplied by α of 0.01.

$${\lambda }_{stby}=\alpha {\lambda }_{SM}$$

(2)

Figure 4 shows the reliability modeling for each strategy. The reliability modeling of active and standby strategies requires the Markov process modeling.

3.4. MMC Reliability

The reliability of the MMC is the combination of the reliability of the six arms. One failure of an arm will fail the whole MMC. Hence, the reliability of the MMC is a series of six-arm reliability:

$$R_{\mathrm{M}\mathrm{M}\mathrm{C}}\left(t\right)=\prod _{i=1}^6{R}_{\mathrm{a}\mathrm{r}\mathrm{m},\mathrm{i}}\left(t\right)$$

(3)

The resulting reliability function of the MMC describes the reliability over time. The expected time to fail (TTF) can be obtained by integrating the reliability function. Associating the TTF and MTTR data will result in the MMC’s availability and unavailability. Along with the reliability data of the complete HVDC component, the whole reliability of the unit will be obtained. The calculated converter’s availability and failure rate will become input in calculating the reliability of the power system level.

$$\mathrm{T}\mathrm{T}\mathrm{F}={\int }_0^{\infty }{R}_{\mathrm{M}\mathrm{M}\mathrm{C}}\left(t\right)dt$$

(4)

3.5. Reliability-Based Optimum Placement

The reliability of power systems can be categorized into three hierarchies, as shown in Figure 5. The first hierarchy focuses only on generation adequacy to supply the load. The second hierarchy considers the generation and the system line connection and is called the composite system. This hierarchy considers the transmission system’s topology and various contingency combinations. The third hierarchy dives deeper into the distribution network.

The system reliability index describes the whole power system’s reliability. The indices are SAIFI (system average interruption frequency index), SAIDI (system average interruption duration index), ENS (energy not supplied), and EIC (expected interruption cost). These indices are integral to assessing the system’s performance.

The reliability assessment function from DIgSILENT PowerFactory 2021 contributes to this evaluation by generating contingency cases based on selected settings (N-1 or N-2). The tool adjusts the load flow to ensure no overloaded components. This feature optimizes load shedding at each load point to prevent a complete disconnection of the load points. The total load shedding in each contingency case constructs the load point indices, the key performance indicators at each load point. The load point indices are average customer interruption frequency (ACIF), average customer interruption time (ACIT), load point energy not supplied (LPENS), and load point interruption cost (LPIC). The formula for the load-point indices is presented in [43] as follows.

$$\mathrm{A}\mathrm{C}\mathrm{I}\mathrm{F}=\sum _{k}F{r}_k·fra{c}_{i,k}$$

(5)

$$\mathrm{A}\mathrm{C}\mathrm{I}\mathrm{T}=\sum _{k}8760·{Pr}_k·fra{c}_{i,k}$$

(6)

$$\mathrm{L}\mathrm{P}\mathrm{E}\mathrm{N}{\mathrm{S}}_i=\mathrm{L}\mathrm{P}\mathrm{I}{\mathrm{T}}_i·\left(P{d}_i+P{s}_i\right)$$

(7)

$$\mathrm{L}\mathrm{P}\mathrm{E}\mathrm{N}{\mathrm{S}}_i=\mathrm{L}\mathrm{P}\mathrm{I}{\mathrm{T}}_i·\left(P{d}_i+P{s}_i\right)$$

(8)

where $i$ is the load point index and k is the contingency index. The aggregate of the load point indices across all load points results in the system indices.

$$\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}={\displaystyle \frac{\sum \mathrm{A}\mathrm{C}\mathrm{I}{\mathrm{F}}_i·C_i}{\sum C_i}}$$

(9)

$$\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}={\displaystyle \frac{\sum \mathrm{A}\mathrm{C}\mathrm{I}{\mathrm{T}}_i·C_i}{\sum C_i}}$$

(10)

$$\mathrm{E}\mathrm{N}\mathrm{S}=\sum \mathrm{L}\mathrm{P}\mathrm{E}\mathrm{N}{\mathrm{S}}_i$$

(11)

$$\mathrm{E}\mathrm{I}\mathrm{C}=\sum \mathrm{L}\mathrm{P}\mathrm{I}{\mathrm{C}}_i$$

(12)

The converter’s placement relates to the transmission connection to the interconnection point. Different choices of interconnection points will result in various impacts on reliability. Therefore, optimal placement can be determined through system reliability calculations. Hierarchy level II is adequate for determining the best substation for interconnection. The optimal placements prioritize the smallest reliability index, indicating the most reliable system condition.

The objective function to achieve optimal reliability combines the four existing indices. A normalization value for each index allows an operation to determine the optimal value. Each system index is normalized to the highest value among all the values in the tested scenarios. The total of each normalized index is compared to find the minimum value. The minimum value represents the scenario with the best reliability.

$$Min\left({\displaystyle \frac{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}{\mathrm{I}}_i}{{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}+{\displaystyle \frac{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{D}{\mathrm{I}}_i}{{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}+{\displaystyle \frac{{\mathrm{E}\mathrm{N}\mathrm{S}}_i}{{\mathrm{E}\mathrm{N}\mathrm{S}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}+{\displaystyle \frac{{\mathrm{E}\mathrm{I}\mathrm{C}}_i}{{\mathrm{E}\mathrm{I}\mathrm{C}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}\right)$$

(13)

4. Methodology

4.1. Test System

The test system referenced is based on the electrical system of the oil and gas industry in Sumatra. The industry system is divided into several areas, as depicted in Figure 6. The whole system can be separated into two subsystems by the central busbar, the northern and southern subsystems. Areas I–IV are in the north subsystem and the rest are in the south. The industry system has a relatively constant load for 24 h of operation. Three generator units supply the electrical load: Gen 1, Gen 2, and Gen 3. Gen 1 in the north has the highest capacity, with a total value of 300 MW.

This system will undergo load increases and be interconnected with the Sumatra grid. Due to frequency differences, HVDC back-to-back with VSC MMC topology will be utilized. Based on generation expansion planning (GEP), there are six converters with 75 MVA capacity and a power factor of 0.8 that will be interconnected. From field studies, there are seven options for the interconnection location for the 115 kV voltage terminals (Figure 7). The option locations for 115 kV interconnection are the central substation (central), Area I (north), Area II–1 (north), Area II–2 (north), Area V (south), Area VI–1 (south), and Area VI–2 (south). The combination of tie-in points for all six converters is based on the seven options provided.

These 115 kV converters also have the option to be converted into interconnections at a 13.8 kV distribution voltage. Unlike the 115 kV terminals, the alternatives at 13.8 kV voltage are more flexible. Installation at 13.8 kV can also be performed more quickly due to the smaller capacity requirements and land usage. The selection of 13.8 kV terminals is further explained in the following section.

4.2. Converter Placement Strategy

There are four major steps to determine the optimal placement of the converter in the test system. The detailed flowchart is shown in Figure 7. The summary of this flowchart is as follows.

• HVDC reliability modeling, focusing on the HV and MV converter’s reliability model based on the design parameter. The calculation is completed with the help of MATLAB, especially in modeling the Markov process.
• HV converter placement, determining the best placement for the high-voltage substation based on the reliability index. The combination reliability calculations is conducted using the DIgSILENT PowerFactory 2021 software. The best placement of this step becomes the baseline for determining the combination of MV converter in the next step.
• MV converter deployment, determining the number of HV converters converted to MV converter. The terminal for MV interconnection can be freely determined because of the flexibility of the MV system. The selection of the MV terminal is based on the highest dV/dP. This method will ensure the terminal selection has a greater impact.
• Economic analysis, determining the number of HV and MV converters in the system considering the cost. This includes the investment, interruption, and maintenance costs. The variation in the cost component may result in different HV and MV converter combinations.

5. Results and Discussion

5.1. HVDC Reliability Modeling

The MMC specification for the HV and MV applications is shown in

Table 2. MMC reliability data.

Parameter	Unit	HV 115 kV	MV 13.8 kV
$V_{svc}$	kV	6.5	3.3
$f_{us}$	%	55	51
$V_{dc}$	kV	160	24
N	unit	45	14
NR	unit	4	2
NT	unit	49	16
TTF	h	39,832	56,802
MTTR	h	19	19

. The DC voltage level for the HV application refers to HVDC in Nanao, China, with a value of 160 VDC [44]. The AC grid used in Nanao is near the same level as in the test system. As for the MV application, this research uses a formula from [45], $V_{dc,MV}\approx 1.5\times V_{LL}$. The number of redundancy modules for each converter is approximately 10% of the total minimum module to operate one arm.

Table 3. Converter reliability data.

Component	HV			MV
	$\mathit{\lambda }$ (f/ Year)	$\mathit{r}$ (h)	U (h/ Year)	$\mathit{\lambda }$ (f/ Year)	$\mathit{r}$ (h)	U (h/ Year)
MMCS	0.2199	24.0	5.278	0.1542	24.0	3.701
BreakerS	0.0475	51.1	2.427	0.0235	14.8	0.348
TransformerS	0.0500	48.0	2.400	0.0184	60.0	1.104
ReactorS	0.1399	24.0	3.359	0.1400	24.0	3.360
Cap DC Link	0.0015	10.0	0.015	0.0015	10.0	0.015
MMCR	0.2199	24.0	5.278	0.1542	24.0	3.701
BreakerR	0.0475	51.1	2.427	0.0235	14.8	0.348
TransformerR	0.0500	48.0	2.400	0.0184	60.0	1.104
ReactorR	0.1399	24.0	3.359	0.1400	24.0	3.360
Total	0.9162	29.37	26.91	0.6738	25.27	17.03

gives the failure rate, MTTR, and unavailability data for the components of the converters in HV and MV applications. The component follows the topology in Figure 1. The MTTR of both converters in the HV and MV applications refer to reference [46]. The references for other components in the system—switch breaker, transformer, reactor, and DC link—are used in different sources for each application. The converter in the HV applications utilizes data from [26], and for the MV application, uses the IEEE Std. 493–2007 [47].The resulting unavailability of the converter in HV applications is almost two times the converter in MV per hour per year. However, the resulting availability for both HV and MV are 99.69% and 99.81%, respectively. From a unit perspective, each will exhibit unique reliability characteristics; however, when considered within the broader context of a power system, their reliability is nearly identical. The subsequent section illustrates the impact of reliability modeling for both applications.

5.2. Optimum Location 115 kV

After the reliability modeling of the HVDC, we then proceed to the placement of the HVDC. The system has seven options for the 115 kV terminals’ converter interconnections. These seven locations were selected based on land availability and the availability of bays at the substations. Based on the generation expansion planning (GEP) conducted for the industrial system under study, there will be six converters, each with a capacity of 75 MVA and a power factor of 0.8. These six converters will be optimally placed within the system.

Three assumptions are used in this reliability-based placement process:

• Each tie-in location option in the industrial system will accommodate only one converter. This ensures that the converters are more dispersed, enhancing system reliability more evenly. Due to this assumption, seven placement scenario combinations will be used for the 115 kV voltage.
• In this placement process, the capacity of each converter will be made following the capacity recommended by the GEP, so there will be no capacity optimization for each location in this study.
• Optimal placement will be based on the load value for the year 2025, which is 550 MW. In 2025, according to the GEP, all converters will be integrated into the system. Since the converters will be operational that year, optimal placement must be achievable from the initial installation. Optimal placement for this year can be considered representative, as the load changes in each area will tend to occur concurrently.

These assumptions evaluate the optimal placement at the 115 kV HV terminals. The seven scenarios based on this assumption are Scen_Area-I_OFF, Scen_Area-II.1_OFF, Scen_Area-II.2_OFF, Scen_Central_OFF, Scen_Area-V_OFF, Scen_Area-VI.1_OFF, and Scen_Area-VI.2_OFF. Each scenario name means the option location that does not have a converter interconnected. For example, Scen_Area I_OFF means no converter placed in Area I.

The placement process will be conducted using two methods. The first method is reliability-based placement, which is proposed in this study. Here, reliability calculations assume a constant load due to minimal fluctuations. These calculations are static and probabilistic, without considering transient conditions, and optimal converter placement is determined by analyzing different configurations. The second method is placement using the brute force technique. The brute force technique utilizes load flow and stability studies to determine the best placement. Historical large disturbances in the industrial system are used for the stability study. The second method serves as a verification of the placement results provided by the reliability-based placement method.

5.2.1. Reliability-Based Placement

The optimal reliability-based placement is performed by evaluating the system’s reliability for each combination placement scenario. The reliability indices SAIFI, SAIDI, ENS, and EIC are assessed for each scenario. The evaluation results for the seven placement scenarios are provided as follows.

The best placement determination can be made by identifying the scenario with the lowest system indices.

Table 4. Reliability evaluation of HV converter placement.

No	Scenario	SAIFI (1/Ca)	SAIDI (h/Ca)	ENS (MWh/a)	EIC (MUSD/a)	Obj Fun
1	Scen_Area I_OFF	0.2900	2.446	1140	8.968	2.838
2	Scen_Area II.1_OFF	0.2908	2.447	1141	8.976	2.841
3	Scen_Area II.2_OFF	0.2686	2.264	990	7.812	2.555
4	Scen_Area V_OFF	0.2903	2.447	1140	8.972	2.839
5	Scen_Area VI.1_OFF	0.3679	3.160	1881	13.247	3.988
6	Scen_Area VI.2_OFF	0.3682	3.168	1898	13.247	4.000
7	Scen_Central_OFF	0.2902	2.449	1143	8.972	2.841

shows that the placement with the minimum index is Scen_Area II.2_OFF. This scenario has the smallest values of objective function compared with the other placement scenarios. This best placement scenario suggests connecting two converters to the 115 kV northern terminal and distributing four converters across terminals in the southern region. The best placement scenario based on these reliability indices is depicted in Figure 8.

5.2.2. Brute Force Method

The second method is to verify the results of the reliability index-based placement. Two evaluations are used to determine the best placement with this method: power flow evaluation and stability evaluation. The power flow evaluation is conducted to observe the impact of placement on system voltage levels and loading.

The system stability evaluation is performed with three major disturbances in the system. This stability assessment ensures the system’s security during disturbances. The three disturbances tested in Figure 9 are as follows:

• Disconnection of all lines from the northern subsystem to the southern subsystem.
• Tripping of all units of Gen 1 simultaneously. This trip will cause generators with a total capacity of 300 MW to disconnect from the system.
• A short circuit on the 230 kV line connecting the Gen 1 terminal to the central substation followed by a trip after 120 ms.

These major disturbances can trigger the activation of defense schemes, such as under-frequency relay (UFR), which can result in load shedding in the system. The impact of load shedding caused by each scenario combination will also be considered in the optimal placement of this second method. The results of the power flow and stability evaluations are provided as follows.

Load Flow Analysis

The recapitulation of the power flow evaluation for each placement scenario combination is provided in

Table 5. Load flow evaluation of HV converter placement.

Scenario	Minimum Voltage pu	Maximum Voltage pu	Maximum Loading %
Scen_Area I_OFF	0.949	1.019	70.8
Scen_Area II.1_OFF	0.958	1.021	70.8
Scen_Area II.2_OFF	0.956	1.021	70.8
Scen_Area V_OFF	0.949	1.007	70.8
Scen_Area VI.1_OFF	0.948	1.010	74.6
Scen_Area VI.2_OFF	0.900	1.009	126.2
Scen_Central_OFF	0.953	1.007	70.8

. The table summarizes the lowest and highest voltages of each substation in the test system. Additionally, it summarizes the highest loading lines for the entire system.

The system voltage remains within the safe range of 0.9–1.05 pu, per network regulations, for each placement scenario. Among the seven placement scenarios, it can be observed that the Scen_Area VI.2_OFF has the lowest voltage. This scenario lacks a converter in Area VI–2, indicating that a converter in Area VI–2 is crucial for providing MVAR support to maintain voltage. When considering the line loading parameters, the Scen_Area VI.2_OFF has lines with loading exceeding 100%. This also indicates that a converter in Area VI–2 can prevent the need for new lines. The converter in Area VI–2 is crucial based on the load flow analysis.

From the voltage analysis, it can also be noted that Scen_Area II.1_OFF and Scen_Area II.2_OFF tend to have higher voltages compared with other areas. In these two scenarios, there are only two converters in the north. The loading analysis shows that scenarios other than the Scen_Area VI.2_OFF have line loadings that tend to be safe.

This power flow analysis alone is not sufficient to determine the best placement. The results of the power flow analysis will be associated with the stability evaluation results.

Stability Analysis

The stability evaluation recapitulation for each disturbance scenario for each placement scenario is shown in

Table 6. Stability evaluation of HV converter placement.

Scenario	Disturbance	Frequency (Hz)		Load Shedding (MW)
		Nadir	Steady
Scen_Area I_OFF	Separation North–South	59.03	59.34	68.78
	Tripping Gen I	58.84	59.10	91.20
	Tripping Line 230 kV	59.62	59.99	-
Scen_Area II.1_OFF	Separation North–South	59.03	59.34	68.78
	Tripping Gen I	58.86	59.11	91.20
	Tripping Line 230 kV	59.61	59.99	-
Scen_Area II.2_OFF	Separation North–South	58.78	59.01	86.16
	Tripping Gen I	58.86	59.11	91.2
	Tripping Line 230 kV	59.58	59.99	-
Scen_Area V_OFF	Separation North–South	59.02	59.34	68.78
	Tripping Gen I	58.85	59.10	91.2
	Tripping Line 230 kV	59.62	59.99	-
Scen_Area VI.1_OFF	Separation North–South	58.75	59.00	86.16
	Tripping Gen I	58.84	59.10	91.2
	Tripping Line 230 kV	59.64	59.99	-
Scen_Area VI.2_OFF	Separation North–South	58.74	59.00	86.16
	Tripping Gen I	58.85	59.10	91.2
	Tripping Line 230 kV	59.73	59.99	-
Scen_Central_OFF	Separation North–South	58.73	58.98	86.16
	Tripping Gen I	58.85	59.09	91.2
	Tripping Line 230 kV	59.76	59.99	-

. These results summarize the frequency (including the nadir, or lowest frequency, and the steady-state frequency after the disturbance) and the load shedding that occurs due to the activation of the under-frequency relay (UFR).

For the first disturbance, involving the disconnection of the northern and southern systems, there are differences in frequency response and load shedding. Scen_Area I_OFF, Scen_Area II.1_OFF, and Scen_Area II.2_OFF exhibit lower load shedding than the other four scenarios. The commonality among these three scenarios is that four converters are placed in the south. This indicates that converters in the south are more crucial for maintaining stability. Thus, each of the four converter locations in the south will have its converter interconnection.

The second disturbance is the tripping of all units of Gen I, with a total capacity of 300 MW. The frequency drop will activate UFR in the north and south up to stage 5, equivalent to a load shedding of 91.2 MW. The frequency nadir and the amount of load shedding due to UFR are generally similar for each placement combination. A more detailed look shows that the frequency nadir varies for each scenario, but only by up to 0.02 Hz.

For the disturbance scenario involving a short circuit followed by a trip after 120 ms on the 230 kV line, the response is quite safe for each placement scenario. No load shedding occurs after this disturbance in any placement scenario.

This comprehensive analysis from both the power flow and stability evaluations suggests that the optimal placement of converters should prioritize the four southern locations, with additional consideration given to the placement of converters in the north based on specific system requirements and performance under disturbance conditions.

Optimal Placement Based on Load-Flow and Stability Analysis

From the stability evaluation results, it can be concluded that four converters will be placed in the south. The other two converters will be placed in the north. Therefore, the best placement options are between Scen_Area I_OFF, Scen_Area II.1_OFF, and Scen_Area II.2_OFF. Based on the power flow results, the Scen_Area II.1_OFF has the highest minimum voltage compared with the other scenarios. This indicates better MVAR support at that placement position. Thus, based on this method, the most optimal placement is the Scen_Area II.1_OFF.

5.2.3. Comparison Reliability Method and Brute Force Method

The results provided by the reliability-based method and the brute force method yield different scenarios for optimal placement. The difference in the two optimal scenario recommendations lies in the converter located in Area II. In the power flow evaluation of the second method, the converter in Area II–2 is preferred because it has a slightly higher minimum voltage than the converter in Area II–1. However, in the system reliability evaluation, the placement in these two locations shows a significant difference in indices.

The reliability-based method’s solution is better for the optimal solution. This is because this scenario remains quite relevant to the results of the second method. As previously mentioned, the voltage difference that arises is not too significant. Therefore, it can be said that the reliability-based optimal placement method is verified.

The reliability evaluation is the association of contingency analysis and failure rate data. The reliability assessment simultaneously evaluates power flow and failure modes in the system. The consistency of these results indicates that reliability-based optimal placement can be used in other cases or as a complement to other studies to ensure the best placement results.

There are several advantages to reliability-based placement. The first advantage is that the evaluation performed is simpler because it seeks only the system reliability indices. The brute force method requires two evaluations: load flow and dynamic simulation. Additionally, based on the previous results, conclusions for the best placement can be drawn only from the analysis of both evaluations.

The second advantage is related to the first. The reliability assessment provides easily quantifiable indices. From the reliability evaluation results of all scenarios, the comparison of indices can be easily seen. The scenario with the minimum index is the optimal placement scenario. The second method requires analytical skills to observe the distribution of voltage or loading and the system’s response to disturbances. These parameters can be quantified but are more difficult than directly using reliability indices.

This reliability-based placement method has some important notes. The failure rate data for each piece of equipment are crucial, so it is essential to obtain credible data built from the system’s historical data. In this study, the failure rate from IEEE standards is used. Nevertheless, with this failure rate data, a good picture of reliability-based optimal placement has been obtained.

5.3. Optimum Placement HV and MV

The placement results from the 115 kV terminals will be the basis for determining the placement at 13.8 kV. Among the six predetermined locations, there is one that cannot convert to 13.8 kV: the central substation. Therefore, there are 32 placement combinations for the 5 remaining locations. The optimum configuration decision between HV and MV will still use the 550 MW load.

The conversion from the HV converter to the MV converter follows the previously described methodology. Specifically, one HV converter unit rated at 75 MVA will be replaced by four MV converter units, each rated at 19 MVA, and installed at 13.8 kV terminals within the same area. The selected MV terminals have the highest dV/dP sensitivity in the HV converter interconnection area. By choosing terminals or busbars with the highest dV/dP sensitivity, we can identify the most critical locations for component placement. This approach ensures enhanced voltage and improved performance of the power system by strategically placing distributed generation at these sensitive nodes [48,49,50,51].

Table 7. dV/dP Area II.

Terminal	Area	dV/dP (pu/ MW)
Area II_13.8 kV_#2	Area II	0.00272
Area II_13.8 kV_#1	Area II	0.00204
Area II_13.8 kV_#3	Area II	0.00188
Area II_13.8 kV_#4	Area II	0.00122
Area II_13.8 kV_#5	Area II	0.00102

provides an example of dV/dP values in Area II. From this table, it can be determined that the MV converters in Area II will be sequentially installed at the terminals Area II_13.8 kV_#2, Area II_13.8 kV_#1, Area II_13.8 kV_#3, and Area II_13.8 kV_#4. If fewer 13.8 kV terminals are in an area, the next MV converters will be installed at the same 13.8 kV terminal with the highest dV/dP.

The reliability calculation methodology remains the same as the optimal placement selection at HV.

Table 8. Reliability results for HV and MV combination.

No	Scenario Code	MV Converter	SAIFI (occ/yr)	SAIDI (h/yr)	ENS (MWh/yr)	EIC (MUSD/yr)	Obj Fun
1	0101010101	0	0.2668	2.248	971.7	7.804	4.00
2	0101100101	4	0.2665	2.241	966.3	7.762	3.99
3	1001010101	4	0.2642	2.235	960.5	7.693	3.96
4	0110010101	4	0.2652	2.232	957.8	7.714	3.96
5	0101011001	4	0.2340	1.936	696.7	6.110	3.24
6	0101010110	4	0.2329	1.922	690.5	6.079	3.22
7	1001100101	8	0.2642	2.229	955.5	7.655	3.95
8	0110100101	8	0.2651	2.225	952.4	7.672	3.95
9	1010010101	8	0.2629	2.219	947.2	7.607	3.92
10	0101101001	8	0.2340	1.929	691.9	6.067	3.22
11	0101011010	8	0.2326	1.922	688.5	5.985	3.20
12	1001011001	8	0.2316	1.923	685.7	5.996	3.20
13	0101100110	8	0.2329	1.916	685.3	6.037	3.20
14	0110011001	8	0.2326	1.919	682.4	6.016	3.20
15	1001010110	8	0.2305	1.910	680.0	5.965	3.18
16	0110010110	8	0.2315	1.906	676.9	5.986	3.18
17	1010100101	12	0.2627	2.212	941.8	7.564	3.91
18	0101101010	12	0.2324	1.915	683.3	5.942	3.19
19	1001101001	12	0.2315	1.916	681.0	5.958	3.18
20	0110101001	12	0.2325	1.912	677.5	5.973	3.18
21	1001011010	12	0.2298	1.909	677.0	5.862	3.16
22	1001100110	12	0.2304	1.903	674.6	5.928	3.16
23	0110011010	12	0.2310	1.905	673.8	5.892	3.16
24	1010011001	12	0.2301	1.907	672.0	5.907	3.16
25	0110100110	12	0.2314	1.899	671.5	5.944	3.16
26	1010010110	12	0.2290	1.894	666.3	5.877	3.14
27	1001101010	16	0.2297	1.903	671.9	5.832	3.15
28	0110101010	16	0.2307	1.898	668.0	5.848	3.15
29	1010101001	16	0.2298	1.900	666.6	5.863	3.14
30	1010011010	16	0.2284	1.893	662.7	5.781	3.12
31	1010100110	16	0.2288	1.887	660.5	5.833	3.12
32	1010101010	20	0.2284	1.886	657.5	5.737	3.11

presents the reliability calculation results using DIgSILENT, providing the system indices. This table contains data such as the scenario code indicating the placement combination (explained by Figure 10), the number of converters placed at the 115 kV and 13.8 kV voltage levels, and the composite system reliability indices, including SAIFI, SAIDI, ENS, and EIC. This table is collected according to the number of MV converters and sorted from the highest to the lowest objective function values.

From Table 8, it can be seen that the placement of all converters at 13.8 kV voltage will have the lowest objective function, and the placement of converters at 115 kV will have the highest objective function. This indicates that placing converters closer to the load improves reliability.

The results presented consider the reliability aspect only. The five best scenarios for each number of MV converters can be obtained from Table 8. A summary of the best scenarios is provided in

Table 9. Best scenario for each MV converter number.

Number Converter MV	Best Scenario	Transformed HV Converter
4	0101010110	Area VI–2
8	1001010110	Area VI–2, Area II
12	1010010110	Area VI–2, Area II, Area I
16	1010011010	Area VI–2, Area II, Area I, Area VI–1
20	1010101010	Area VI–2, Area II, Area I, Area VI–1, Area V

. The five best scenarios also provide HV converters that are transformed into MV converters. From this summary, the priority of HV converters that can be converted into MV converters can also be determined. This can be identified by observing the transformation sequence of HV converters from the scenario with the fewest total MV converters. The priority order from these five best scenarios is as follows.

• Area VI–2,
• Area II,
• Area I,
• Area VI–1,
• Area V.

5.4. Sensitivity of Converter Reliability

The previous analysis has shown the result by combining the HV and MV converters in the system. The reliability results follow the converter component data from Table 2 and Table 3. This section shows how impactful the number of redundancies in the converter is in the power system manner. Sensitivity analysis for HV and MV scenarios is summarized in

Table 10. Reliability results in redundancy variation HV converter.

Number of Redundant	Availability %	SAIFI 1/Ca	SAIDI h/Ca	ENS MWh/a	EIC MUSD/a
0	97.9720674	0.2867981	2.690699	1470.293	7.9250
1	99.3235648	0.2724755	2.355284	1093.104	7.8372
2	99.5596256	0.2699818	2.296692	1027.219	7.8212
3	99.6481343	0.2690475	2.274723	1002.516	7.8152
4	99.6928342	0.2685756	2.263627	990.040	7.8121

and

Table 11. Reliability results in redundancy variation MV converter.

Number of Redundant	Availability %	SAIFI 1/Ca	SAIDI h/Ca	ENS MWh/a	EIC MUSD/a
0	99.3148698	0.2282983	1.882080	650.572	5.8823
1	99.7321615	0.2283157	1.881906	650.507	5.7769
2	99.8056137	0.2283189	1.881869	650.493	5.7574
3	99.8333649	0.2283202	1.881854	650.487	5.7500
4	99.8474793	0.2283208	1.881847	650.484	5.7462

. The redundancy of both converters will be varied from 0 to 4.

The sensitivity results of the number of redundancies show that with a decrease in availability, the system reliability index will increase. The percentage change in the system reliability index for variations in the number of redundancies tends to be greater for HV converters than for MV converters. This is due to their larger capacity and fewer numbers, making a single HV converter failure more impactful. Redundancy consideration becomes important for HV converters.

The change in the system index does not significantly vary with changes in the number of redundancies for each converter application. Changes in the number of redundancies will have a more significant impact on the availability of HV converters. When no redundancy is provided, availability immediately drops below 99%. However, changing the redundancy number does not alter the optimal results of the HV and MV converter combination. Scenarios with the highest total MV converters will still have the best reliability.

5.5. Economic Analysis

In the previous analysis, the best configuration is the most MV converter scenario. However, this did not consider an economic analysis, which is crucial to ensure the most optimal techno-economic solution. For cost comparison, two parameters are examined: investment cost and outage cost. The investment cost is annualized with an assumed interest rate of 10% and combined with the annual outage cost.

Table 12. Cost Component.

Parameter	Unit	Value
Investment cost	kUSD/Converter HV	24,000
Total converter		6
Operation period	years	17
Interest rate	%	10

provides the investment parameters for each HV converter with a capacity of 75 MVA over a project duration of 17 years (2025–2041). The cost of MV converters tends to be higher compared with the investment cost of HV converters. The investment cost per MVA for MV converters is varied against the investment cost of HV converters. This investment ratio will determine the number of converters at HV and MV terminals. The simulations are for the five best scenarios for each number of MV converters.

Figure 11 provides a summary result of the cost comparison in several line graphs. When the cost of converters at MV and HV is the same or in a 1:1 ratio, the scenario with all five HV converters converted to MV will be more advantageous due to the lowest outage cost. As the cost ratio increases to 1.1–1.4 times, only one HV converter needs to be converted to MV, resulting in four MV converters. There is no need for conversion from HV to MV when the cost ratio rises to 1.5 times. The investment cost variation provides different optimal configurations for HV and MV converters.

5.6. Sensitivity of Interruption Cost

The interruption cost used in the previous analysis was based on IEEE standards for industrial loads. However, in the case of industrial systems in Indonesia, interruption costs may be different. Studies in [52,53] have calculated the value of lost load (VoLL) for the Java–Madura–Bali power system. The highest VoLL for industrial consumers was estimated at IDR 67,446.75 per kWh, equivalent to USD 4.12 per kWh.

A sensitivity analysis of interruption costs was conducted to assess its impact on decision-making regarding the placement of HV and MV converters. Sensitivity was analyzed at USD 5/kW, USD 10/kW, and USD 15/kW for one hour. These values were used as multipliers based on the IEEE Std. The interruption costs for each sensitivity value are shown in Figure 12.

5.6.1. Interruption Cost Sensitivity I

Figure 13 provides the cost comparison graph of USD 5 per kW interruption cost for one hour. It can be observed that the NPV decreases by approximately USD 50 million from the previous result. When the prices of HV and MV converters are at a 1:1 ratio, the scenario where all five HV converters are converted to MV is more advantageous, as it yields the lowest NPV. As the price ratio increases to 1.1, converting one HV converter to MV still results in the lowest NPV. However, at a ratio of 1.2, converting HV converters to MV converters becomes unprofitable.

5.6.2. Interruption Cost Sensitivity II

Figure 14 provides the cost comparison graph of USD 10 per kW interruption cost for one hour. When the prices of HV and MV converters are at a 1:1 ratio, the scenario where all five HV converters are converted to MV is more advantageous, as it yields the lowest NPV. As the price ratio increases to 1.1, converting one HV converter to MV still results in the lowest NPV. Converting the HV converter to the MV converter becomes uneconomical when the price ratio increases to 1.3.

5.6.3. Interruption Cost Sensitivity III

Figure 15 provides the cost comparison graph of USD 15 per kW interruption cost for one hour. The NPV decreases by approximately USD 20 million from the earlier result. When the prices of HV and MV converters are at a 1:1 ratio, the scenario where all five HV converters are converted to MV is more advantageous, as it yields the lowest NPV. As the price ratio ranges from 1.1 to 1.3, converting one HV converter to MV still results in the lowest NPV. However, at a ratio of 1.4, converting HV converters to MV converters becomes unprofitable.

5.6.4. Interruption Cost Sensitivity Analysis

This sensitivity analysis indicates that the valuation of interruption cost will influence decisions regarding the interconnection of converters in the tested industrial system. When interruption costs are considered low, converters are preferably placed at the HV terminals, primarily supplying power. When interruption costs critically impact industrial production, reliability considerations become crucial. Based on the sensitivity analysis, when the investment cost ratio between the HV and MV converters remains at 1:1.1, at least one HV converter can still be converted into an MV converter.

5.7. Maintenance Cost Considerations

The previous techno-economic analysis determined the optimal converter combination considering investment costs, interruption costs, and variations in the price ratio between HV and MV converters. Another cost component to consider is maintenance costs. Maintenance strategies can differ between HV and MV converters. Several studies have analyzed the impact of preventive and reliability-based maintenance on the performance of HVDC/MVDC [54,55,56]. These studies also show that different configurations or designs can influence maintenance strategies. As a result, maintenance strategies for HV and MV converters differ due to the number of components and redundancy schemes. This section solely assesses the effect of maintenance cost factors on the operational lifespan of HV and MV converters without evaluating how maintenance impacts the reliability performance of these converters.

Annual maintenance costs for each converter are estimated at 0.5% of the investment cost, based on reference [37]. The investment costs already accommodate the price ratio between HV and MV converters, resulting in higher maintenance costs for MV converters due to their larger number and distribution.

Maintenance intervals for HV and MV converters are different and are determined based on their reliability functions, modeled earlier. The reliability curves for HV and MV converters are depicted in Figure 16. For HV converters, a maintenance interval of every 2 years is chosen to ensure reliability above 0.95. Conversely, MV converters have a maintenance interval of every 3 years to maintain reliability above 0.90. A reliability threshold of 0.95 is chosen for HV converters, because their smaller number in the system means that the failure of one HV converter has a more significant impact than that for the MV converters. Therefore, the maintenance period will be shorter for HV converters than for MV converters. Figure 17 presents an economic analysis considering maintenance costs, with calculations based on interruption costs from the IEEE Std. 493–2007 [47].

The results indicate changes in outcomes when maintenance costs are considered. Previously, with a price ratio of HV to MV converters at 1:1.1, the number of HV converters to be converted changed from one to two. Additionally, at this ratio, converting one HV converter remains economical even at a ratio of 1:1.5. However, at a ratio of 1:1.6, converting HV converters becomes less attractive. These results can change according to different maintenance strategies between the HV and MV converters.

6. Conclusions

This research paper has discussed the reliability modeling of HVDC back-to-back systems using MMC technology, considering voltage levels, the number of modules, and redundancy strategies for both HV and MV applications. This modeling was then implemented to determine the best placement and combination of HV and MV converters based on the minimum system reliability index. An economic analysis was also conducted, considering investment, interruption, and maintenance costs. Price sensitivity analysis demonstrated the impact on the selection of converter combinations.

The availability of MV converters tends to be higher than HV because of fewer components. The resulting availability for HV converters is 99.69%, while for MV converters, it is slightly higher, at 99.81%. Converting HV converters to MV also offers better reliability, because they are closer to the load. The SAIFI for all HV converters is 0.2668 occurrences per year, with interruption costs of USD 7.804 million per year, while for MV converters, the SAIFI is 0.2284 occurrences per year, and the interruption costs are USD 5.737 million per year.

When economic components are considered, there is a change in the decision for the best combination of HV and MV converters. For an investment cost ratio between HV and MV converters of 1:1.1, converting one HV converter into four MV converters remains economical. This configuration yields a net present value (NPV) of USD 199.02 million. The optimal placement of converters is in Area VI–2, Area II, Area I, Area VI–1, Area V, and the central substation. It is recommended that the converter in Area VI–2 be converted from HV to a more distributed MV configuration for improved performance.

The research suggests that shifting from a high-voltage (HV) converter to a more distributed medium-voltage (MV) converter can boost the system’s reliability. Furthermore, an economic analysis can validate the most effective combination of HV and MV converters.

Further research could focus on optimizing the capacity at each interconnection location using appropriate algorithms. Additionally, incorporating the nonlinear behavior of HVDC system components and detailed modeling of HVDC systems with various topologies, including considerations for derating conditions and complex frequency variation scenarios, could be explored to enhance system reliability and stability.