Trade-Offs in Modelling Accuracy and Complexity of DC Circuit Breakers: A Comparative Aggregated Approach

Abstract

The growing interest in high-voltage direct current (HVDC) technology and multi-terminal HVDCs (MTDCs) has motivated the evaluation of DC circuit breakers (DCCBs) for increased operational flexibility. While modeling DCCBs remains essential, their complex structures and modeling techniques require careful consideration. In this context, trade-offs in modeling accuracy and complexity of DCCBs are of paramount importance, and hence, benchmarking-based modeling methodology for hybrid and non-hybrid DCCBs is performed in this study. To this end, the performance of different aggregated DCCB technologies, namely hybrid DCCBs, simple DCCBs, and voltage-source DCCBs, is benchmarked for MTDC applications, with the full representation of hybrid DCCBs taken as the baseline for comparison. First, it is shown that the aggregated hybrid DCCB provides an accurate representation of the full hybrid DCCB’s performance. This is followed by an analysis of the parameters for the simple DCCB and voltage-source DCCB (VSCB) that enable their performance to closely match that of the aggregated hybrid DCCB. Finally, the impact of aggregated DCCB models on voltage transients within a test system is analyzed, demonstrating the effectiveness of aggregated modeling across different DCCB technologies. Simulation-based analyses are conducted in PSCAD/EMTDC to compare the performance of different aggregated DCCB models.

1. Introduction

The concept of circuit breakers (CBs) for direct current (DC) applications has evolved significantly over the years. Initially, CBs were primarily designed for alternating current (AC) systems, as AC technology was more prevalent. However, with the increasing adoption of high-voltage direct current (HVDC) technology for long-distance power transmission and renewable energy integration, the need for effective DC circuit protection became apparent. Unlike AC circuit breakers (ACCBs), DC circuit breakers (DCCBs) must handle high short-circuit currents without zero-crossing, and they must operate within a very short time, making them more inherently complex [1,2]. There are three primary categories of DCCBs based on their interrupting principles: mechanical, power electronics (solid-state), and hybrid designs, with each exhibiting distinct advantages and disadvantages. Mechanical DCCBs are characterized by high breaking capacity, cost-effectiveness, and simple design. They interrupt short-circuit currents by generating a zero-crossing through an LC circuit operating in parallel with the primary electromechanical switch. However, they are limited by relatively slow response time, large size, and issues related to arc. Power electronics DCCBs, on the other hand, utilize semiconductor devices to achieve fast and reliable fault interruption. Their advantages include ultra-fast response, compact size, and the absence of mechanical components. Nevertheless, they suffer from higher conduction losses, increased thermal management demands, and higher implementation costs. To overcome the limitations of purely mechanical or power electronic designs, hybrid DCCBs have been developed. These devices combine the low-loss conduction of mechanical switches with the fast fault interruption capabilities of solid-state components, making them particularly suitable for modern multi-terminal DC (MTDC) systems. Despite these advantages, hybrid DCCBs entail complex control, coordination system design, and higher costs, which may affect their practicality for certain applications [2,3,4,5]. Recently, numerous different DCCB topologies have been introduced in various research studies. Reference [6] introduces a new mechanical DCCB topology that integrates a fully controlled converter with a semi-controlled full bridge to produce a counter-current of progressively increasing amplitude. The proposed topology is cost-effective, with a simple structure and control. A prototype of the DCCB, designed according to the proposed topology, is currently under development. Reference [7] proposes a hybrid breaker design that combines a coupled inductor with a bridge-type circuit to achieve efficient fault current interruption in HVDC grids. The presented DCCB can handle high current stresses while maintaining relatively low cost and compact structure. The design supports bidirectional current flow, making it suitable for MTDC systems where power reversibility is essential. In [8], a dual-H-bridge-integrated multiport DCCB is presented to isolate bus faults in HVDC grids efficiently. By integrating dual H-bridge modules with a multiport structure, the breaker achieves fast fault interruption while reducing stress on semiconductor devices. The topology supports bidirectional current flow and enables flexible fault isolation across multiple HVDC lines, which is particularly valuable for offshore wind and MTDC systems. This configuration closely resembles the conducting branch of DCCB, which incorporates a load commutation switch (LCS) in series with an ultra-fast disconnector (UFD). Its primary difference is that, in the dual-H-bridge-integrated multiport DCCB, the LCSs are built from unidirectional series-connected insulated-gate bipolar transistors (IGBTs), while the H-bridge arrangement is implemented using diodes.

In power systems, the application of model aggregation techniques is crucial for enhancing computational efficiency. By consolidating multiple detailed models into a single, simplified representation, these techniques significantly reduce complexity and time required for simulation and analysis. This is particularly important for large-scale power systems, where modeling every component in detail can be computationally prohibitive. Aggregation not only speeds up calculations but also helps preserve the accuracy of system behavior predictions, making it an essential practice for effective power system management and optimization [9,10,11]. Various types of aggregation approaches have been investigated in the existing literature. Reference [12] introduced an aggregated model for wind farm (WF) to analyze dynamic modeling. These WFs consist of both fixed and variable speed wind generators. The aggregated models were validated through faults and transients’ simulations. The aggregation method in [13] presented an improved WF aggregation model for stability analysis in the large-scale power systems. In [10], an aggregated controller model is developed using a numerical approach. The study demonstrates that transient and small-signal stability analyses yield consistent simulation results in the time domain. Reference [14] analyzed a large number of variable-frequency drives (VFDs) to model aggregated load behavior in power systems, introducing a generic positive sequence model to facilitate dynamic studies of numerous VFDs. Reference [15] focuses on developing a comprehensive model to simulate the impact of electric vehicle (EV) charging on large-scale power systems. The approach uses data-driven techniques to estimate aggregated load profiles for different EV charging scenarios. With advancements in HVDC systems—particularly in DCCB equipment—the control and modeling of DCCBs have become increasingly complex. Nonetheless, we have identified a lack of research on the development and analysis of different aggregated models of DCCBs in MTDC systems. The protection systems of HVDC systems have a significant influence on the operational effectiveness of DCCBs. In particular, the fault detection methodology employed in an HVDC network plays a direct and critical role in determining DCCB performance [16,17]. HVDC protection schemes are generally classified into pilot and non-pilot systems. Pilot protection methods, such as current differential and traveling-wave-based schemes, rely on high-speed communication between terminals to achieve selective and accurate fault detection. However, their dependence on communication links limits their suitability as primary protection in HVDC systems. In contrast, non-pilot methods operate solely on locally measured quantities and, being generally simpler in design, can in some cases provide faster fault detection under specific operating conditions, making them stronger candidates for primary protection in HVDC systems [18,19]. Among non-pilot protection systems, the rate-of-change-of-voltage (ROCOV) method is distinguished by its high speed, simplicity, and robustness, even under worst-case conditions. Furthermore, ROCOV detection does not require extensive training datasets or complex signal processing algorithms involving large data windows and filtering, thereby enhancing its practicality and reliability [18,20].

This paper compares the performance of various aggregated DCCB models for MTDC systems and identifies suitable parameters for evaluating each control strategy. The control strategies associated with each aggregated model are examined in detail, and the corresponding protection schemes for fault detection are also presented and discussed.

The paper is organized as follows: Section 2 presents an in-depth analysis of the performance of aggregated DCCBs according to their technology—hybrid, simple, and voltage-source DCCBs. Simulation results and a case study are provided in Section 3. Finally, Section 4 concludes the paper.

2. System Architecture for Aggregated DCCBs

This section outlines the performance of various aggregated DCCBs for MTDC systems. Initially, the performance of hybrid DCCBs under different control schemes and aggregation levels is discussed. Figure 1 shows the general block diagram used to evaluate the performance of the DCCB in relation to controller and protection systems. The controller plays a significant role in influencing DCCB performance, and different controller designs can have varying impacts on the breaker’s behavior. Additionally, fault detection time is a critical factor; faster protection systems can issue a trip command to the DCCB more quickly, preventing excessive fault current escalation. Furthermore, the modeling approach of the DCCB is essential for accurately interrupting the faulty section and ensuring reliable system operation. Therefore, this paper examines various types of DCCB modeling, along with different controller and protection system configurations, to compare the performance across multiple simulation models.

First, the performance of simple and voltage-source DCCBs, along with their controllers, is described and compared in this section. Subsequently, the protection model is also explained within the modeling framework.

2.1. Hybrid DCCB

The hybrid DCCB has emerged as a solution that combines mechanical and power electronics technologies, offering a balance between speed, reliability, and efficiency. Hybrid DCCBs achieve both low on-state losses and fast fault-clearing capability, addressing the limitations of purely mechanical or fully solid-state designs. However, several issues still remain regarding hybrid DCCBs such as higher cost and complex control and coordination [16,21]. Different hybrid DCCB controllers are presented in this study. ABB and Alstom have conducted tests on hybrid DCCB devices capable of interrupting currents up to 16 kA with an operating time of just 2 ms [22]. Device ratings have progressed significantly—from the initial 80 kV/9 kA laboratory prototypes to full-scale 535 kV/25 kA units. These advanced breakers have now been successfully deployed in multi-terminal HVDC (MTDC) projects, including Nan’ao, Zhoushan, and Zhangbei in China [23].

2.1.1. Operation of the Hybrid DCCB

Figure 2 illustrates the hybrid model of DCCBs for MTDC systems [24,25]. Hybrid DCCBs consist of load and main CB branches connected in parallel. To reduce the short-circuit current, a DC reactor (DCR) is connected in series with the DCCBs.

The main CB branch consists of multiple main breakers (MBs), each comprising series-connected IGBTs (SIs). In actual hybrid DCCBs, several MBs are connected in series. Surge arresters are placed in parallel with each MB. Furthermore, the residual current breaker (RCB) is responsible for interrupting any remaining current—typically minimal and composed solely of leakage current—after the main fault current has been diverted and absorbed. Figure 3 shows the aggregated model of the hybrid DCCB, represented by one MB and one SI. In the aggregate hybrid DCCB model, only one MB and one SI are included, which simplifies the modeling process and enhances simulation performance.

2.1.2. Control of the Hybrid DCCB

The hybrid DCCB requires a sophisticated control system to operate different switches and triggers within an extremely short time frame. The performance of DCCBs can be around 3 to 5 ms when combining the control and switching actions. This rapid coordination is essential to detect faults, initiate commutation and safely divert current into the energy absorption path before damage occurs. In multi-terminal HVDC networks, the control system must also communicate with other breakers to ensure selective and reliable fault isolation. Two control systems are presented for the hybrid DCCB model in this study. Control mode 1 consists of several time delays for switching (t_h) and pulse switching (t_p1), as shown in Figure 4. The fault detection time is taken into account as t_d.

Figure 5 shows control strategy 2 for the hybrid DCCB model, which is based on logical functions. This model incorporates a time delay (t_h) as well as AND and XOR gates. Both control logics can be applied to the hybrid DCCB model. Control mode 1 includes additional time delays for fine-tuned timing control, making it suitable for different types of hybrid DCCBs with varying time performance requirements. Conversely, control mode 2 is designed for conditional control and adaptive responses, particularly in scenarios where fault types vary or complex interactions occur. The parameters for control modes 1 and 2 of the aggregated hybrid DCCB are detailed in Appendix A.

On the other hand, the hybrid control structure mainly comprises the control of RCB control, UFD control, and LCS in the auxiliary DC breaker control and the main DC breaker control. The objective is determined as to operate in an effectively coordinated manner. In this context, the control structure is formed in three stages. In the first stage, the fault detection logic sends a signal to the control components to disconnect the faulted line. In the second stage, logic gates are utilized to determine when to activate the fast disconnector and the main DC breaker. The load and main branch CBs are activated at this stage. In the third stage, the operation of the main DC breaker based on the synchronization status is decided. Additionally, a comparator block can be incorporated to coordinate the final signal at this stage. It can be seen that the control structure is constituted by using logic gates, time delay blocks, and comparators. In the control structure, it is significant to determine the sequence of operation. In this manner, the breakers are activated in a proper manner. The control structure is illustrated in Figure 6.

2.2. Simple DCCB

The simple model of the DCCB captures the essential fault-clearing behavior—interruption of current and energy absorption by the surge arrester—without modeling every internal component.

2.2.1. Operation of the Simple DCCB

Typically, the simplified model of the DCCB is used for VSC-HVDC simulation studies and could be used to represent mechanical DCCBs. This model includes a CB with surge arresters connected in parallel. Figure 7 shows the basic model of the aggregated DCCB with a DCR.

2.2.2. Control of the Simple DCCB

The control system of this simple DCCB is straightforward, requiring only basic fault detection signals to operate. Upon fault detection, a trip signal is sent to the DCCB, which then opens the faulted line. The protective level of the surge arrester can be optimized for the operation of a simple DCCB, in comparison to the aggregated hybrid DCCB. This study considers the impact of surge arrester rating sensitivity on DCCB performance.

2.3. Voltage-Source DCCB (VSCB)

The VSCB is represented as another simplified DCCB in the HVDC systems. This model is simple for fast and reliable fault interruption in HVDC systems. This approach is interesting in simulations because it is simpler to model than a full hybrid DCCB, yet it still captures the essential behavior of using a voltage source to control fault current flow.

2.3.1. Operation of the VSCB

A VSCB is a specialized type of CB designed to rapidly and effectively interrupt fault currents in HVDC systems. The basic operation of this type of DCCB is straightforward and depends on the voltage source relative to the system’s nominal voltage. In this case, the voltage source is activated after fault detection. When the voltage levels on both sides are nearly identical, current does not flow due to the lack of potential difference. However, the voltage level of the source may need to be tuned to ensure proper operation under varying conditions. This DCCB consists of a controlled voltage source in series with a switch, as illustrated in Figure 8.

2.3.2. Control of the VSCB

When a fault occurs, the voltage source is activated by protection and control systems. By setting its output voltage appropriately, it can oppose or counteract the fault current, effectively limiting or forcing it to zero so the breaker can open safely. This requires detecting the fault and activating the control system, as well as selecting voltage reference values that are sufficiently high to suppress the fault current, yet carefully limited to avoid causing overvoltage in other parts of the system

Figure 9 presents the control model of the VSCB, highlighting key parameters such as nominal voltage (Vn), k-factor (k), and the fault detection system. The performance of this DCCB depends significantly on the voltage level defined by the k-factor. By adjusting the k-factor, the voltage level varies, enabling evaluation of the DCCB’s behavior under different operating conditions. The generated voltage is regulated in response to the terminal voltage after fault detection time. During normal operation, the source voltage is zero and remains inactive. After fault detection, a voltage is generated between the system’s terminals, reducing short-circuit current and allowing the CB to isolate the faulted section.

In this study, the k-factor is used to enhance VSCB operation and to compare it with hybrid and simple aggregated DCCBs.

2.4. Protection System

Fault detection time is one of the most critical factors influencing the effective operation of a DCCB in an MTDC network. DC fault currents escalate extremely rapidly—often reaching hazardous levels within just a few milliseconds. As a result, even minor delays in fault detection can significantly affect breaker performance, increase stress on system components and compromise overall network stability.

In this study, the ROCOV protection method identifies faults by monitoring the rate of change of DC voltage over time. Sudden, steep drops or rises in voltage are indicative of abnormal conditions. This approach offers a fast, simple, and localized detection mechanism capable of triggering HVDC protection devices—such as DCCBs—within milliseconds. Since it relies on straightforward threshold-based logic, the dv/dt protection scheme is highly reliable and operates independently of communication links, making it well suited for primary non-pilot protection. Equation (1) presents the mathematical formulation of the ROCOV protection method:

$$ROCOV={\displaystyle \frac{∆V}{∆t}}={\displaystyle \frac{V_2-V_1}{t_2-t_1}}$$

(1)

where V₁ and V₂ are voltage magnitudes measured at times t₁ and t₂, respectively, with t₂ > t₁.

In the control of aggregated DCCB models, fault detection time is denoted by t_d. Depending on the specific detection method and its response characteristics, t_d may vary.

3. Simulation and Results

3.1. Case Study Network Description

Figure 10 presents an MTDC network used for the case study, modeled using PSCAD/EMTDC software, version 5. The MTDC network features four converters: converters 1 and 2 are connected to offshore wind farms (OWFs), while converters 3 and 4 interface with point-to-point AC grid systems. The case study employs four half-bridge (HB) modular multilevel converters (MMCs), utilizing data from the MMC topology and MTDC system presented in [26]. The transmission system comprises two 200 km lines (cable 1–3 and cable 1–4), two 100 km lines (cable 1–2 and cable 3–4), and one 150 km line (cable 2–4). The rated voltage is V_dcn = ±320 kV and DCR = 100 mH. In this study, the fault location is at the midpoint of cable 1–3. The research examines the impact of various aggregated DCCB types on the far busbar voltage, specifically focusing on the voltages of line 2 to 1 (V21), line 3 to 4 (V34), and line 1 to 4 (V41).

All faults are initiated at 0.7 s, and the threshold for the ROCOV protection system is set at 20% of the rated voltage. Figure 11 illustrates fault detection under various fault locations and impedance fault conditions in the case study. In Figure 11a, the fault occurs at the midpoint of the line, with a detection time of approximately 0.56 ms. The worst-case scenario, shown in Figure 11b, involves the longest transmission line combined with impedance fault. In this case, the fault is located at 97.5% of the line length, as the line is 200 km long and the fault occurs at 195 km with an impedance of 250 Ω, resulting in a detection time slightly exceeding 1 ms. Therefore, the fault detection time (t_d) is conservatively set to 2 ms in this study.

Figure 12 illustrates the impact of fault detection time on DCCB performance during short-circuit conditions. As shown, the short-circuit current reaches approximately 5.39 kA at 2 ms and increases to 7.85 kA after 5 ms. At 41 ms following the fault, the current surges to 20.56 kA. This figure highlights the critical role of fault detection speed—delays in detection lead to significantly higher short-circuit current levels, which can increase stress on the DCCBs and compromise system stability.

3.2. DCCBs Performance

This section provides a detailed analysis and comparison of the performance of aggregated DCCB models for each DCCB technology: simple, VSCB, and hybrid—within the context of the MTDC applications. Additionally, it explains the control strategies and best-suited parameter settings for each model.

3.2.1. Hybrid Aggregated DCCB Model

For the aggregated hybrid DCCB model, two different control strategies were proposed and introduced in Section 2. Figure 13 displays the operation of these control schemes, showing that their performance may be nearly identical during the operation of this DCCB type. In this case, the maximum short circuits for both controllers are around 7.15 kA and the fault current suppression time (FCST) cut-off is approximately 0.7056 s. To achieve optimal control mode operation, the delay parameter (th1) in control scheme 2 is tuned to ensure consistent performance.

Figure 14 illustrates the performance of the aggregated hybrid DCCB under two cases: case 1 (MB = SI = 1) and case 2 (MB = SI = 2). In this comparison, the impact of varying the multiple main breakers (MBs) and the inclusion of series-connected IGBTs (SIs) on hybrid DCCB performance is evaluated, as initially illustrated in Figure 2. The performance differences between hybrid DCCB models equipped with one or two MBs and SIs are presented. In case 2, the time between the operation of MB1 and MB2 is set to 0.5 ms. The maximum overshoot (MP) of the short-circuit current remains constant at approximately 7.15 kA at 0.7036 s for both cases. The FCST for the hybrid in case 1 and case 2 are recorded as 0.7054 s and 0.7056 s, respectively. The performance variation between the two models with differing numbers of MB and SI is approximately 0.2 ms in the FCST.

3.2.2. Simple DCCB Model

Figure 15 illustrates the performance of the simple DCCB under various protective voltage levels or residual voltage, Varr of the surge arrester, alongside that of the aggregated hybrid DCCB. The surge arrester’s Varr is typically set at 1.5 Vn, but in this study, the effect of different Varr ratings (from 1.3 Vn to 1.6 Vn) is analyzed and compared against the aggregated hybrid DCCB. The maximum short-circuit current is approximately 7.15 kA at 0.7036 s. The FCSTs are 0.7056 s for the hybrid one and 0.7056 s, 0.7055 s, 0.70542 s, and 0.7053 s for Varr 1.3, 1.4, 1.5, and 1.6 Vn, respectively. Although the simple DCCB’s performance across all Varr levels considered is similar to that of the hybrid DCCB in terms of the FCST, its performance at Varr = 1.3 Vn more closely resembles that of the aggregated hybrid DCCB.

3.2.3. Voltage-Source DCCB (VSCB) Model

Figure 16 shows the performance of the VSCB for different values of the k-factor, compared to the aggregated hybrid DCCB. In this case, k-factors of 1.6 and 1.9 are modeled. Increasing the k-factor to 1.9 results in closer alignment between the VSCB’s performance and that of the hybrid DCCB. Moreover, reducing the k-factor from 1.9 to 1.6 increases the FCST of the VSCB model. However, variations in the k-factor values do not affect the short-circuit current overshoot or system’s transient voltage response. Each study should include a sensitivity analysis using a reasonable k-range. By confirming that the system outcomes remain appropriate across this range, one can validate that the selected k-factor is sufficiently robust for the study case. The maximum short-circuit current is about 7.15 kA at 0.7036 s. The FCSTs are 0.70652 s and 0.70636 s for k-factors of 1.6 and 1.9, respectively.

3.3. Comparison of Adjusted Aggregated Models

Figure 17 compares three different aggregated DCCB models with the optimal adjustment component: the aggregated hybrid model, the simple model (Varr = 1.3), and the voltage-source model (k = 1.9). As shown in the figure, none of the aggregated DCCB models’ operations affect the maximum overshoot of the short-circuit current; however, differences in FCSTs are marginal. The FCSTs of the aggregated hybrid, simple, and VSCB DCCBs are approximately 0.70562 s, 0.70568 s, and 0.70636 s, respectively. Relative to the hybrid DCCB model, the FCST differences are 60 µs for the simple model and 74 µs for the VSCB model. These results indicate that the aggregated hybrid and simple DCCBs demonstrate comparable performance in terms of both FCST and Mp. The FCST is used to analyze the stability of the system, while Mp represents the maximum short-circuit current after switching. The differences in FCST and Mp among the presented aggregated DCCBs are negligible. According to the figure, the maximum short-circuit currents are the same for all the presented DCCBs, since the fault detection time is identical (2 ms) and all faults are initiated at 0.7 s. Consequently, the initial response of the DCCBs is similar, which indicates that their performance during the fault detection stage can be considered equivalent. This suggests that, for studies focusing solely on the detection phase, any of the DCCBs can be applied interchangeably. In contrast, significant differences emerge during the interruption process, i.e., when the DCCBs begin to open. At this stage, the dynamic performance of each breaker diverges due to variations in interruption mechanisms, energy absorption strategies, and current-limiting capabilities. These distinctions are crucial for assessing the overall effectiveness, efficiency, and reliability of each DCCB design, particularly in the context of practical HVDC grid applications where operational stability and fault-clearing performance are paramount.

3.4. Voltage Transient During the Different DCCBs’ Performance

To investigate the performance of different aggregated DCCBs, we examined their impact on the measured voltage at remote busbars. Accordingly, the voltages of V21, V34, and V41 were analyzed in relation to the performance of the hybrid, simple, and VSCB models. Figure 18 illustrates the voltage transients during the operation of the different aggregated DCCBs. These transients differ due to the performance characteristics of each DCCB type. The voltage transients settle after the DCCB operation. Although the duration of transients among the DCCBs is similar, the aggregated hybrid DCCB exhibits larger oscillations in the branch connected to the OWFs. According to the result, the hybrid CB exhibits a higher initial transient response. This is primary due to increased switching from the load and main CB benches and also RCB, with the effect being most pronounced in V12 as shown in Figure 18a. In this scenario, the transmission line is connected between two OWFs. The maximum transient voltage is 857.67 kV at 0.70712 s, while the maximum voltages for the simple and VSCB cases are 854.822 kV at 0.70698 s and 828.807 kV at 0.76088 s, respectively. After the initial disturbances, the voltage transients stabilize around the same level, indicating that the long-term steady-state performance of the presented DCCBs is the same. The voltage transients and oscillations settle around 0.9 s. Figure 18b shows the voltage of V34 that is connected between two AC grids. In this case, the maximum voltages are 881.411 kV, 826.523 kV, and 828.341 kV for the hybrid, simple, and VSCB DCCS, respectively. The voltage measurements at V41 represents the interface between the OWFs and the main AC grid. The voltage of hybrid, simple, and VSCB DCCBs are 815.781 kV, 797.312 kV, and 767.056 kV, respectively. In the case of V41, the Mp of the hybrid aggregated model is approximately 1.02 and 1.07 times greater than those of the simple and voltage-source models, respectively. In all cases, the voltages settle around 0.84 s. The voltages of the simple and VSCB DCCBs are notably close. However, the hybrid DCCB’s higher initial transient suggests that while it may offer certain operational advantages, it also introduces additional stress on the system during switching events. This highlights the importance of carefully evaluating CB selection in OWFs integration with the presence of HVDC systems.

4. Discussion

The study presents the performance of different aggregated DCCB models in the context of the MTDC systems. The aggregated hybrid, simple, and voltage-source DCCB models, along with their control strategies, are compared. The objective of this comparison is to demonstrate how tuning model parameters enables different DCCB designs to achieve comparable performance. While the hybrid DCCB offers advanced technological features, its modeling is complex and particularly challenging when applied to large systems with multiple breakers. Therefore, this study introduces an aggregated DCCB approach, in which simpler models are tuned to replicate the hybrid DCCB’s behavior. Various aggregated topologies can mimic hybrid performance, depending on modeling requirements. The Mp is consistent across all DCCB types, indicating that each model is suitable for protection studies. However, the FCST varies across different models with the voltage-source DCCB exhibiting the longest FCST, which may influence system transient behavior. This study also analyzes the effect of each aggregated DCCB model on the voltage at the remote busbar. The hybrid DCCB exhibits more voltage transients in the line connecting two OWFs (V21), whereas the simple and voltage-source DCCBs show more transients in the line connecting the two AC grids (V34).

Table 1. Comparison of different aggregated DCCBs.

	Hybrid	Simple	VSCB
Complexity	+	-	-
Control strategy	+	-	-
Mp of the short-circuit current	+	+	+
FCST	+	+	++
Mp of the voltage	++	+	+
Protection study	+	+	+
Initial transient	++	+	+
Adjusting parameter	Switching and time delay	Surge arrester rating	k-factor

The symbol “++” indicates that a very high level of the characteristic., “+”: denotes a high level, and “-”: indicates a low or less pronounced level of the characteristic.

compares the different characteristics of the proposed aggregated DCCB models.

5. Conclusions

This paper presents the performance of aggregated DCCB models for three technologies employed in MTDC systems. Furthermore, the control system strategies for each model are thoroughly detailed, and the results show that both control schemes for the aggregated hybrid DCCB yield similar outcomes. The performance of aggregated hybrid, simple, and voltage-source DCCB models is compared based on current and voltage characteristics. Simulations indicate that while the maximum short-circuit current is consistent across the technologies, the FCST varies slightly. The simple DCCB and VSCB models avoid complex control implementation, and by adjusting Varr and k-factor separately, they can achieve performance comparable to the aggregated hybrid DCCB. The simulation results confirm the effectiveness of modeling various DCCB technologies as aggregated models. These aggregated models provide high accuracy across a range of applications, including protection, transient analysis, and stability studies, while reducing computation time and modeling complexity.