**1. Introduction**

In the last two decades, considerable progress has been made in the development of voltage source converter-based high-voltage direct current (VSC-HVDC) transmission systems. It is regarded as a promising solution for controlling real and reactive power and reducing losses. Among the different design topologies of VSCs, the modular multilevel converter (MMC) has many advantages, such as modular design, good scalability, low switching frequency, and few harmonic injections [1–3]. It serves as an effective solution for the large capacity and long-distance transmission systems which connect large-scale renewable energy resource centers in western China with the load centers on the eastern coast of China. At the same time, it improves the flexibility and reliability of the power grid operations [4,5]. Comparing with the traditional line-commuted converters (LCCs), VSC-based converters introduce completely different fault characteristics [6]. Especially, for a MMC-based HVDC system, fast and reliable protection is required to eliminate huge fault currents and discriminate transient disturbances. As a result, the protection methods of the traditional HVDC cannot be applied to MMC-HVDC systems. It is necessary to study the fault characteristics of the MMC and propose a protection method for the MMC-based transmission lines.

In traditional LCC-based HVDC transmission systems, the fault current is fully controllable, so line protection does not need to be very fast [7,8]. In the symmetrical monopole MMC-HVDC system, when a pole-to-pole fault (PPF) occurs, the bridge arm sub-module (SM) has a discharge circuit, which causes the fault current usually to climb to tens of times the rated current in a few milliseconds [9,10], and the AC power will feed to the fault point through the freewheeling diode. That is, the fault current is uncontrollable. Therefore, it is necessary to detect and isolate DC faults as fast as possible, such as in 3 ms [11,12]. In addition, when a pole-to-ground fault (PGF) occurs, the bridge arm SM has no discharge circuit. It will only cause small current fluctuations during the transient

period, which cannot easily be detected. Furthermore, the transient characteristics caused by lightning faults and lightning disturbances are also slight fluctuations in the current. Their characteristics are very similar and need to be effectively distinguished.

In existing LCC-based HVDC projects, the time of traveling wave protection is about 10 ms, and the action time of differential under-voltage protection is about 20 ms [13–16]. Compared with traditional HVDC, when a PPF occurs in MMC-HVDC, the fault current rises rapidly, which requires higher protection speed and sampling frequency. In this case, the reliability and sensitivity of traveling wave protection and differential under-voltage protection will be reduced. In addition, in terms of the transient recognition of lightning strikes, traditional LCC-based HVDC protection methods mainly distinguish between lightning and faults from the perspective of frequency domain spectrum characteristics or time domain waveform characteristics. However, under short time window scenarios, the resolutions in the frequency domain and discriminations in the time domain waveform are both reduced. Therefore, the protection method of the traditional LCC-based HVDC system does not work for the MMC-HVDC system. New requirements are put forward for the identification of interference from lightning strikes and noise. Compared with the traditional LCC-based HVDC system, the protection method of the MMC-HVDC system needs to consider the reliability of protection and the accuracy of lightning identification at extremely fast speeds.

In recent years, research on the protection of MMC-HVDC transmission lines mainly includes protection methods based on sudden changes of voltage or current protection [17,18], pilot protection [19–21], and traveling wave protection and its improvement methods [22–24]. Among them, the sudden change in voltage or current protection is based on the protection principle of single-ended electrical information. It has extremely fast action speed and is also sensitive. The pilot protection improves the reliability of the protection through the comparison and processing of double-ended information. Traveling wave protection uses corresponding mathematical methods to extract and analyze the high-frequency characteristics of transient traveling waves, such as amplitude, polarity, duration, etc., which has an extremely fast speed for fault detection. However, existing studies still have the following shortcomings: firstly, some protection methods do not consider the impact of lightning disturbances; secondly, some protection methods adopt double-ended information, which might not meet the requirements of the MMC-HVDC system for primary protection speed; finally, some protection methods need to be strengthened in terms of tolerance to ground resistor and anti-interference ability. In general, the protection method of MMC-HVDC is not ye<sup>t</sup> mature and needs further study. Therefore, this article pays more attention to how to improve the reliability of protection and the ability to identify lightning strikes and interference when the protection satisfies high-speed mobility.

In MMC-HVDC systems, different faults have different transient characteristics and different time–frequency distributions. Some faults have similar time domain waveforms, but their frequency domain distributions are different. Therefore, it is possible to propose a protection method based on the difference in time–frequency distribution. The existing signal analysis tools include Fourier transform, Hilbert–Huang transform, S transform, etc. They are the mainstream methods in the field of power system relay protection. However, the amplitude and ratio are usually used as the classification criteria, and consider fewer influencing factors. When considering the influence of factors such as noise and lightning, its setting calculation is complicated, and there are many simplified and equivalent treatments. Its stability and reliability need to be improved. Wavelet transform, a time–frequency analysis method, has the characteristics of multi-resolution analysis, and a strong ability to represent information [13,25,26]. Entropy is a tool to measure the disorder degree of the whole system [27–29]. Wavelet entropy is a combination of wavelet transform and information entropy. It can not only achieve the purpose of information fusion but also analyze the mutation signal more effectively [30,31]. It has been gradually applied in image processing, stock market forecasting, biology, machinery, power systems, and

other fields, with good achievements [32,33]. It has advantages in characterizing system distribution characteristics and degree of disorder.

In this paper, wavelet entropy is used to represent the characteristics of different fault transient characteristics, which can not only meet the requirements of the MMC-HVDC system for protection speed, but also has a good ability to distinguish lightning strikes. The main contributions of the paper are the following:


The content of this paper from Sections 2–6 is as follows: Section 2 analyzes the MMC-HVDC two-terminal transmission model in detail and introduces the fundamentals of the MMC-HVDC system and characteristics of the different faults. Section 3 explains the definition of wavelet entropy and the principles of wavelet entropy in describing spectrum features. Section 4 proposes the methods of transmission line protection. Section 5 shows the simulation results and verifies the effectiveness of the protection method based on wavelet entropy. Section 6 offers conclusions and discussions.

#### **2. Fault Characteristics of MMC-HVDC Transmission Lines**
