1. Introduction
HVDC transmission technology exhibits remarkable advantages, including its vast transmission capacity [
1,
2]. It proves particularly beneficial for long-distance power grid transmission [
3]. However, one notable drawback of HVDC transmission is its significant consumption of reactive power, often amounting to approximately half of the transmitted active power [
4]. This issue is commonly addressed through the utilization of filters and power compensators [
5]. A typical fault that may occur in HVDC transmission systems is commutation failure [
6]. When such a failure arises, it causes substantial fluctuations in the system’s voltage and reactive power. Consequently, it can result in DC locking faults and pose a threat to the stability of the power grid [
7]. In particular, in multi-send HVDC systems, commutation failure-induced power fluctuations between multi-send HVDC transmissions may intensify the occurrence of overvoltage and other faults [
8]. A study analyzing the transient overvoltage of a bipolar system is conducted in [
9], and the behavior of equipment under different overvoltage conditions is examined in [
10].
There are various forms of faults in DC transmission systems, with commutation failure and DC locking being prominent issues leading to overvoltage problems. Commutation failure results in a sharp drop in DC power, and if it occurs repeatedly, it can lead to DC locking. Such occurrences have a substantial impact on the AC grid [
11]. Following a commutation failure fault, the control link within the DC system increases the trigger angle to delay the current rise, which causes a rapid increase in reactive power absorption by the system. Consequently, the voltage at the rectifier side experiences a significant decline [
12]. Furthermore, due to the presence of a low-voltage current limiting link, the DC current diminishes rapidly, resulting in a substantial reduction in the reactive power absorbed by the rectifier system [
13]. Consequently, the reactive power compensation capacitor in the rectifier system generates a considerable amount of residual reactive power, leading to overvoltage at the rectifier bus [
14]. Moreover, in the event of a DC blocking fault, the active power consumed by the DC system rapidly drops to zero, and the resulting residual reactive power significantly elevates the AC voltage at the rectifier end [
15,
16]. The AC voltage gradually decreases once the reactive power compensation capacitor is disconnected [
17,
18].
According to [
19], overvoltage resulting from commutation failure and DC blocking faults is primarily influenced by the system’s short-circuit capacity and residual reactive power. Another ref. [
20] describes how the level of overvoltage is closely associated with factors such as the short-circuit capacity and the timing of the safety control cutter action. Improper coordination can likely lead to a secondary increase in voltage. Moreover, ref. [
21] categorizes the voltage dynamic process into two phases and asserts that converter fault overvoltage is affected by the system’s short-circuit ratio. Furthermore, the high/low-voltage ride-through characteristics of wind turbines also impact the magnitude of converter fault overvoltage. Generally, when wind farms are closer to the converter bus, the transfer of reactive power from the wind farm to the faulty AC bus becomes easier. Addressing this, another ref. [
22] explores the mechanism behind overvoltage caused by commutation failure and DC blocking, as well as the influence of wind turbine LVRT characteristics. It reveals that commutation failure induces a low-voltage state in turbines located in the vicinity, consequently exacerbating the overvoltage problem. Conversely, ref. [
23] examines the mechanism of high-voltage off-grid wind turbines and the role of thermal turbines in supporting voltage.
Hence, these factors necessitate consideration when evaluating the grid-connected capacity of wind power [
24]. Particularly, when integrating a large-scale wind power system into the delivery side, fault overvoltage characteristics emerge from the interaction between the transient properties of the DC system and the LVRT characteristics of the wind farm [
25]. Therefore, a comprehensive examination of the LVRT characteristics of wind power clusters is essential for a better understanding of the fault overvoltage issue in the DC system. Such comprehensive analysis facilitates an enhanced comprehension of the fault overvoltage problem [
26]. In the case of multi-send HVDC systems, the causes of commutation failure in the system become more intricate due to the presence of multiple rectifier stations in the region and electrical coupling among multiple DCs [
27]. Additionally, the causes of failure exhibit greater diversity owing to the existence of various potential causal factors [
28]. Currently, the literature concerning converter failure in multi-send HVDC systems does not adequately reflect the impact of the multi-send structure on the converter failure-induced overvoltage problem [
29,
30,
31]. Furthermore, the mechanism underlying the overvoltage problem induced by converter failure in a multi-send structure remains undisclosed, with the related literature and data being outdated [
32,
33], and some research findings not being updated in real-time. Consequently, it becomes imperative to propose an overvoltage assessment methodology for a multi-send HVDC system incorporating wind turbines, aiming to provide a clear direction for future research endeavors.
Regarding the rectifier side of the HVDC transmission system connected to wind power, the dynamics of wind power’s reactive power also influence overvoltage. However, ref. [
34] takes into account the active and reactive power dynamics of wind turbines and proposes an iterative calculation method for obtaining transient overvoltage. Nonetheless, this approach is time-consuming and fails to consider the impact of LVRT characteristics of wind turbines on overvoltage. Ref. [
35] establishes a detailed analytical model for transient reactive voltage during multi-mode switching of wind turbines. Nevertheless, the modeling method is overly complex, impeding quick analysis of the overvoltage level. Both low- and high-penetration characteristics of the disturbed wind turbine generators (WTGs) can exacerbate overvoltage in the delivery system [
36]. When examining the specific role of WTGs, ref. [
34] considers the turbine’s impact on grid operation as a reduction in short-circuit capacity. Furthermore, another study [
36] investigates the scenario of wind power in the near zone on the rectifier side, considering near-zone LVRT following commutation failure in the HVDC system. In this analysis, the surplus reactive power of the turbine’s reactive power compensation capacitor during the fault is introduced. The mechanism of system overvoltage generation at the sending end after converter failure is analyzed in a different study, which clarifies the influence of the turbine’s LVRT reactive power characteristics on overvoltage. Additionally, through simulation, ref. [
22] examines the mode of operation of low-penetration power characteristics and concludes that the wind farm produces additional reactive power delivery to the converter bus during LVRT, exacerbating the voltage issue. The analysis conducted thus far fails to account for the impact of the machine-end voltage on the wind farm’s active power after the disturbance.
There is a limited number of studies that analyze the impact of multiple DC coupling on converter fault overvoltage. In [
37], a calculation method is proposed for determining the converter bus overvoltage in a multi-send HVDC system based on the interaction factor of the sending voltages. However, the method yields a large error, as it fails to consider the reactive power flow during the fault. Therefore, it is necessary to conduct in-depth research on the effects of multiple DC coupling and turbine reactive power characteristics on converter fault overvoltage. Additionally, there is a need to develop quantitative assessment methods to evaluate overvoltage in turbine-connected multiple DC feeder systems after a converter fault. It is important to note that most existing studies primarily focus on analyzing the peak of the converter fault overvoltage and do not account for the voltage crossing integral safety constraint. Consequently, a more comprehensive evaluation of the system’s voltage safety level following a converter fault has not been adequately addressed.
Therefore, this paper builds upon the existing HVDC model and takes into account the mutual coupling between multiple DC transmissions. It conducts calculations and derives an analytical expression for the transient overvoltage of the multi-send HVDC system, while also analyzing the impact of overvoltage in such a system. The analysis demonstrates that the transient overvoltage of a multi-terminal HVDC system is influenced by factors such as the strength of the AC system, the electrical distance between two systems, and the DC power. Ultimately, the accuracy of the obtained formula is validated through a simulation model.
To quantitatively assess transient overvoltage in a multi-send HVDC system integrated with a wind farm, it is crucial to conduct a comprehensive investigation into the dynamic response of DC-DC coupling and the LVRT capability of the wind farm.
DC-DC coupling is of paramount importance within the framework of a multi-send HVDC system, as it, along with AC-DC coupling, significantly influences the transient characteristics of the power system, as well as ensuring the security and stability of the sending HVDC system. Understanding the interplay between these coupling mechanisms is vital for accurately assessing and analyzing the system’s behavior during fault events.
In the event that the voltage at the wind farm bus falls below a predetermined threshold value (typically around 0.9 p.u.) due to a fault in the nearby system, the wind farm engages in a low-voltage ride-through procedure. During this procedure, the current of the wind turbines is rapidly controlled to decrease within a specific range in order to prevent inverter over-current. To maintain the voltage within permissible limits, the wind farm adjusts its current proportionally to the magnitude of the voltage reduction. This control strategy ensures the safe and effective operation of the wind farm during low-voltage conditions.
Initially, the paper focuses on examining the analytical expression for transient overvoltage in a single-send HVDC system. Subsequently, it addresses the influence of DC-DC coupling and the LVRT capability of the wind farm, presenting a methodology for analyzing the disturbed transient voltage. The accuracy of this methodology is then verified through appropriate validation techniques. By exploring these key aspects, a comprehensive understanding of the transient overvoltage behavior in the integrated multi-send HVDC system with a wind farm can be achieved.
4. Conclusions
This paper introduces an analytical approach that aims to determine the transient peak value resulting from two types of faults: DC blocking (DCB) and commutation failure (CF). In a single-sending HVDC system, the transient overvoltage is primarily influenced by the short-circuit capacity and the surplus reactive power associated with DCB and CF faults. However, in a multi-sending HVDC system, it is crucial to consider the impact of DC-DC interaction on the transient voltage behavior.
When wind turbines are located in close proximity to the fault, the occurrence of DC blocking does not trigger a LVRT response in the turbines. This is because the converter station becomes the sole reactive source responsible for mitigating the transient overvoltage. On the other hand, commutation failure leads to multiple wind turbines entering LVRT. The LVRT characteristics of these wind turbines transform the wind farm into an additional reactive power source, acting in conjunction with the converter station. This collaboration between the two reactive power sources intensifies the transient overvoltage. In a single-send HVDC system, the overvoltage level is predominantly influenced by the short-circuit ratio. An increased short-circuit ratio leads to a reduction in the overvoltage level. Conversely, in a multi-send HVDC system, the overvoltage level is determined by the equivalent impedance of each individual system. In DC systems with turbines located in the vicinity of the DC zone, the overvoltage level at the converter bus is affected by the power characteristics of the turbines during LVRT.
To validate the proposed calculation method and accurately assess the severity of overvoltage, simulation results are provided. The results demonstrate the effectiveness of the proposed approach in accurately evaluating the extent of overvoltage and its implications.
The simplification employed in this paper for the AC system involves representing it as an electromotive force in series with an impedance. However, this analytical approach introduces certain inaccuracies. It is imperative to conduct additional research in the future to comprehensively examine the impact of various factors on the excitation characteristics of AC system generators. Furthermore, apart from investigating the influence of LVRT characteristics in wind turbines, this paper solely focuses on the effects of DC near-zone turbines. Therefore, it is crucial to extend the analysis to encompass the influence of wind farms operating as decentralized distribution systems on overvoltage.