HVDC primary protection schemes can be classified into two major categories: double-ended schemes (also called pilot, unit, or communication-based schemes) and single-ended schemes (also called non-pilot, non-unit, or communication-less schemes). The former group utilizes communication channels to exchange measurement data or signals between boundary relays at both ends of each transmission line or cable segment based on which trip or no-trip decisions will be made. On the contrary, for single-ended schemes, only local measurements are required and there is no need for far-end data.

Double-ended schemes are inherently selective, even for severe fault conditions such as high-resistance faults, since protection zones are formed between the boundary relays without the need for DC limiting reactors [66]. However, their slow operation, due to communication delays, is a major shortcoming that impedes their applicability as fast primary protection schemes; yet they can be effectively utilized as backup schemes. Hence, fast communication channels with adequate bandwidth, such as those provided by optical-fiber cables, have to be employed to limit this delay, increase the reliability of these channels, and enhance their immunity against noise such that unit protection schemes can be safely utilized for primary protection [67]. Furthermore, synchronization between the exchanged data should be carefully considered to avoid malfunctioning during normal operation or external faults.

As compared to double-ended protection schemes, single-ended schemes are more economical (no need for communication channels) and faster (no communication delays) [68]. However, their level of selectivity is deteriorated particularly in the event of high-resistance faults [69]. Therefore, DC reactors, installed at both ends of each segment, are necessary to divide the entire grid into individual protection zones such that internal and external faults can be reliably discriminated. Moreover, precise and noise-free local measurements are necessary to guarantee the secure operation of such schemes.

Backup protection schemes are not required to be as fast as primary protection schemes. Therefore, double-ended schemes can be employed to provide selective and reliable backup protection. Backup protection is essential to ensure power system protection in case of primary protection failure (due to relay or breaker failure). Several proposed single-ended primary protection schemes have been augmented with double-ended backup criteria based on, e.g., the rate of change of voltage (ROCOV) at line terminals [70,71], the polarities of current variation at line terminals [72], and the boundary reactor voltage [73].

Other backup protection schemes have been proposed in the literature. For example, the algorithm introduced in [74] provides rapid backup protection to detect both local and remote breaker failures based on double-ended voltage and current measurements. In [75], a single-ended backup protection algorithm is proposed that discriminates between relay and breaker failures employing classifiers that are trained based on the K-Nearest Neighbor (KNN) approach using voltage and current measurements of the local breaker during the interruption process. In [76], a double-ended backup scheme is proposed based on detecting the direction of the reactive energy flow at both ends of the line, which is extracted by Hilbert-Huang Transform (HHT), in order to discriminate between internal and external faults. The pilot backup protection algorithm investigated in [77] is based on extracting the frequency characteristics of the DC filter output current by Discrete Fourier Transform (DFT) to estimate the specific frequency current values that are utilized to distinguish between internal and external faults. Finally, Ref. [78] proposes a unit backup protection scheme based on Wavelet Packet Energy Entropy (WPEE) of the transient fault currents at line terminals to provide reliable and selective backup detection of high-resistance pole-to-ground faults.

Comparing the aforementioned backup schemes, the single-ended scheme proposed in [75] has the minimum cost since it does not require communication channels, yet remote relay and breaker failures are not considered. In terms of speed, the proposed schemes in [74,75,78] have the minimum delay between the detection instant of the primary protection failure and the backup protection operation since primary protection failure is detected as early as possible by tracking the voltage and current variations during the primary breaker operation such that uncleared faults are rapidly detected. The proposed scheme in [77] has the lowest speed with an operating time up to 145 ms.

Similar to AC differential protection schemes, DC differential schemes employ operating and restraining signals that are calculated based on the difference between and the average of boundary measurements, respectively. For instance, the principle of operation of current differential schemes is such that during normal operation or external faults, since measured currents at both ends of the protection zone have the same direction and approximately the same magnitudes, the differential current approaches zero. On the contrary, in the case of internal faults, the differential current will reach larger values. Therefore, by comparing the differential current with a non-zero threshold, to compensate for stray capacitive currents and other measurement errors, a reliable and selective fault indicator is achieved [81]. For example, current measurement information is exchanged between the two ends of the protection zone in the differential scheme introduced in [81], where the positive and negative pole currents at both ends of each segment are denoised using Discrete Wavelet Transform (DWT). Then, their extracted energy contents are employed to form the operating and restraining signals of the proposed criterion. The ratios between the operating and restraining signals of each line are utilized to discriminate between internal and external faults and identify the faulty pole. The large data window (1000 samples) is required in this algorithm, which is continuously processed, and the heavy wavelet computations significantly delay the fault detection process.

In [82], fault-tolerant inductor-capacitor-inductor (LCL) VSCs, which can greatly limit fault currents for extended periods, are employed along with mechanical DCCBs such that a low-speed, yet highly-reliable and highly-selective protection system is realized based on a current differential protection criterion. However, the large operating time of the proposed algorithm (30–60 ms) may adversely impact the stability, security, and supply continuity of the overall transmission network. A similar scheme is proposed in [83] but with full-bridge MMCs exploiting their distinctive fault-handling capabilities such that slower and more cost-effective mechanical DCCBs with smaller ratings can be utilized. However, the enhanced control of these converters can substitute the need for DCCBs; thus, achieving improved speed at a much lower cost.

A fast differential algorithm has been recently proposed in [84] which realizes a compromise between selectivity and speed. Transmission lines are modeled by the approximated Bergeron model based on which the 1-mode components of the measured currents at boundary relays are rapidly computed. Then, their differential component is utilized to detect internal fault events. Although the Bergeron line model strengthens the immunity of the proposed scheme against malfunctioning during system disturbances and external faults, its precision needs further investigation considering the line distributed capacitances. A similar approach was proposed in [85], but applied only to point-to-point configurations. The backward traveling wave-based differential algorithm proposed in [86] utilizes Marti’s frequency-dependent line model to exploit the implicit fault-transient high-frequency components. It can precisely detect and discriminate various DC faults, including faults that involve the metallic return path in asymmetric bipolar configurations, without using computationally intensive signal processing approaches. A voltage differential protection criterion is proposed in [87] based on the calculated differential-mode components considering the impact of the line frequency-dependent parameters. The improved algorithm does not require data synchronization for its effective operation since it can detect out-of-synchronization events and then resynchronize the mismatched information.

In summary, the common ground of the above differential protection schemes is that accurate, synchronized, and denoised current or voltage measurements have to be exchanged through an efficient communication medium to guarantee their reliable operation. In addition, the speed of the proposed algorithms does not necessarily comply with the stringent speed requirements recently imposed for multi-terminal HVDC grids [63].

Compared to differential schemes, directional algorithms result in faster double-ended protection schemes that require communication channels with limited capacity. They vary based on the exchanged pilot signals, e.g., the directions of fault current measurements, the polarities of reactor voltages, and the signs of traveling waves transient energies. This section discusses various types of the proposed directional protection schemes.

Digital signals that represent the direction of fault currents at the remote terminal can be utilized as pilot signals alongside local measurements for selective fault detection. Similar to AC systems, the developed scheme may be a tripping scheme (where the local tripping command will be initiated only if a fault confirmation signal is received from the remote end) or a blocking scheme (where the local tripping command will be initiated if a blocking signal from the remote end is not received). A tripping scheme is proposed in [88] based on exchanging the sign of fault current directions. It is concluded that an internal fault is detected if the two terminal currents have the same sign, whereas opposite signs indicate an external fault. In [89], orientations of the transient fault currents at line ends are determined by the Wavelet Transform Modulus Maximum (WTMM) technique; then, they are communicated and compared with each other based on which internal and external faults are identified. However, the required large sampling frequency of 100 kHz increases the computational burden of this algorithm.

Although DC boundary reactors are not required with double-ended schemes for grid segmentation, they may be utilized as current limiters to reduce the sharp rise of the fault current. In [90], the polarities of the boundary reactor voltages at both line ends are exchanged and compared to decide whether the detected fault is internal (positive polarities) or external (opposite polarities). In addition, the faulty pole is identified by integrating the reactor voltage over a data window to eliminate the coupling effect between the faulty and healthy poles. Likewise, transient properties of boundary reactor voltages are extracted by Wavelet transform in [91] based on which a pilot discrimination criterion is proposed.

During DC faults, traveling waves are initiated at the fault point, then propagate in both directions along the faulted segment until reaching the boundary terminals where one part of these waves is refracted into the healthy part of the grid and the other part is reflected into the faulted segment, and so forth [92]. Traveling wave-based algorithms are widely used to design unit and non-unit protection schemes. The permissive scheme designed in [79] classifies forward and reverse faults via calculating the energy content ratio of the fault incident backward wave over the reflected forward wave at boundary relays. Then, a permissive (or blocking) signal is sent to the other end to initiate (or prevent) the tripping signal of local DCCBs in case of forward (or reverse) faults.

To decrease communication delays and traveling wave attenuations in case of long cables, Reference [93] proposes a protection algorithm that utilizes multiple intelligent sensors located at cable joints and along the entire cable length. The proposed algorithm is based on a directional comparison criterion where a trip signal is initiated if two consecutive sensors detect a forward fault. Moreover, proactive (or two-stage) DCCBs [54], which discard the initial trip signal if the fault is not confirmed before the breaker opens, are employed to further reduce the total fault detection and clearing time. Therefore, the algorithm speed and security are greatly improved. However, the main deficiency of this scheme is the increased cost of the additional sensors.

Another pilot scheme is proposed in [94] based on comparing the orientations of transient energies (TEs) computed from the initial fault voltage traveling waves at both cable ends. The proposed algorithm effectively discriminates between internal (both TEs are negative) and external (one or two TEs are positive) faults. It also identifies the faulty pole based on the ratio between the computed TEs of positive and negative poles of the faulted segment. In addition, it estimates the fault location based on detecting the initial voltage surge arrival instants at both cable terminals, which are extracted by Stationary Wavelet Transform (SWT). However, the reliable performance of the proposed scheme requires substantial sampling frequency (1 MHz), which increases the computational burden. A similar algorithm based on TE is proposed in [95], where the propagation of current traveling waves and voltage measurements at boundary relays are used to estimate the TE values such that forward and backward faults are distinguished and the faulty pole is rapidly identified. In [96], the transient fault current increments in addition to their polarities at both line ends are evaluated and employed to discriminate between internal (opposite polarities) and external (same polarities) faults and precisely estimate the fault distance.

In [97,98], the phase-mode transformation is applied to bipolar DC cables resulting in six decomposed current and voltage components based on which multiple protection criteria are obtained. In [97], the high-frequency contents of the sixth mode current components are extracted employing the S-transform (which combines the advantages of Fourier and wavelet transforms). The proposed detection criterion is based on detecting the abrupt changes in the extracted high-frequency contents, while the fault discrimination criterion depends on comparing their polarities at cable ends. Finally, the extracted zero-frequency components are utilized to avoid malfunctioning in case of disturbances. Likewise, the proposed scheme in [98] utilizes the phase-mode transformation decoupling approach, applied to the forward and backward initial fault current traveling waves at cable ends, to calculate the fifth and sixth mode current components. Then, SWT is employed to estimate their amplitudes and polarities in order to be adopted in the fault discrimination and faulty-pole selection criteria.

In such schemes, converters’ harmonic currents at line terminals are extracted and analyzed to identify internal and external faults. In [99], first carrier frequency harmonic (FCFH) currents are extracted by DFT at cable ends. Based on their magnitudes during a certain window length, the protection units at both terminals detect internal faults and distinguish them from external faults. The proposed algorithm was only applied to point-to-point configurations and did not consider high-resistance faults. A similar, yet improved scheme is proposed in [100] based on FCFH currents extracted by HHT, which has several advantages over Fourier and wavelet transforms in terms of instantaneous frequency detection precision in the time domain. Furthermore, compared with the previous scheme, the algorithm was evaluated in a multi-terminal grid rather than a simple point-to-point configuration; besides, a larger range of fault resistances was tested. It is worth mentioning that harmonic-based schemes require high computation capacity and they are easily affected by noise and disturbances. Therefore, their sensitivity and selectivity may be endangered under particular fault scenarios.

Recently, new mathematical approaches, which require lower computation capacity compared with conventional methods, are exploited to design fast and effective DC protection schemes. Morphological gradient theory is employed in [101] to develop the Multi-resolution Morphological Gradient (MMG) algorithm, which efficiently extracts the desired waveform information even during the loss of communication. In [101], MMG, which eliminates the errors resulting from data-synchronization mismatches, is applied to the line-mode voltage traveling waves. The proposed scheme discriminates between internal and external faults by estimating the correlation coefficient between the MMGs of line-mode voltage traveling waves at line terminals (the forward wave at one end and the backward wave at the other end). Finally, faulty pole identification is achieved based on calculating the ratio of MMG for the positive pole over that of the negative pole of the faulted segment. However, the operating time of this algorithm (5 ms) needs to be reduced to comply with the recent DC protection system speed requirements.

Cosine distance criterion is another recent approach proposed in [102]. This criterion is based on comparing the orientations of the reference internal fault voltages and currents with the corresponding orientations of the actual superimposed fault quantities via calculating the cosine distance function. Protection algorithms based on the Hausdorff Distance (HD) approach are proposed in [66,103]. The HD between two nonempty sets can be mathematically defined as the maximum distance of a set to the nearest point in the other set. The proposed methods in [66,103] provide major advantages in terms of noise-tolerance capability and elimination of the compulsory data synchronization requirement. The fundamental principle proposed in both algorithms is based on evaluating the degree of similarity, via HD theory, between the initial fault voltage backward and forward traveling waves at line terminals (the forward wave at one terminal and the backward wave at the other terminal) to detect and discriminate between internal and external faults. Moreover, the faulty pole is identified in [103] based on the ratio of the transient energy of the positive pole over its counterpart of the negative pole. However, due to the relatively low speed of this scheme, it can be employed for backup protection rather than primary protection.

Double-ended schemes are mostly slow due to the inevitable communication delays, which become longer as the transmission line or cable length increases. Furthermore, various errors in the exchanged data may occur due to noise and loss of synchronization. Consequently, unit schemes are practically recommended to provide reliable backup protection. Non-unit protection algorithms, which depend merely on local measurements, are required to provide fast primary protection. The main challenge that hinders the design of single-ended schemes is achieving high selectivity, especially in the case of remote faults with large resistances. Furthermore, to guarantee high accuracy, a large sampling frequency is commonly required, which increases the algorithm’s computational burden. Additionally, attenuation of traveling waves associated with long transmission lines should be carefully considered to avoid the maloperation of the designed algorithms [104]. Various approaches and methodologies have been proposed to design selective, sensitive, and reliable non-unit protection schemes that will be reviewed in this section.

One of the earliest approaches that has been adopted to design non-unit protection schemes is based on the continuous computation of the ROCOV values based on local voltage measurements. Since DC faults are accompanied by a rapid voltage decline, the ROCOV value can be exploited to detect fault events. However, these schemes require large sampling frequencies to accurately calculate the ROCOV value. Additionally, their selectivity is endangered in case of high-resistance faults. For instance, the proposed scheme in [105] depends on the local line-side reactor voltage measurements to estimate the ROCOV value that is compared to a pre-adjusted threshold for DC fault detection and localization. A comparable scheme is proposed in [106], which is equipped with an additional overcurrent criterion to increase the fault resistance coverage.

The authors of [70,71] have further improved the selectivity, reliability, and fault resistance coverage of the ROCOV scheme by proposing an extra directional feature based on the ratio of ROCOV values measured at both sides of the boundary reactors. In addition, the proposed scheme is augmented with a directional comparison ROCOV-based criterion to selectively detect high-resistance faults. This directional criterion has been further improved in bipolar grids with a metallic return path via inserting small reactors at the return conductor ends in [71]. In [107], a double-stage scheme is proposed. In the first stage, fault is detected based on undervoltage criterion, while the second stage is the discrimination stage based on an undervoltage and voltage derivative criterion to discriminate between internal and external forward faults as well as a current derivative criterion to identify forward faults from reverse faults. Furthermore, the concept of applying a reduced grid model to accurately determine the algorithm thresholds is introduced.

Analogous to voltage derivative-based schemes, current derivative-based schemes have been proposed, in which the instantaneous increase of fault current and the rate of change of current (ROCOC) are utilized to detect fault events. The ROCOC can be integrated with other criterion to develop selective algorithms and improve the algorithm reliability and immunity against maloperations. In [108], five ROCOC indices are calculated based on which various faults are detected (including faults that involve the metallic return conductor in asymmetric bipolar configurations) and the faulty pole is identified as well. Another ROCOC-based scheme is proposed in [109], which provides both primary and backup protection for multi-terminal HVDC grids. In [109], a statistical Bayesian classifier is adopted to select the necessary thresholds and establish a proper time-coordination between primary and backup relays.

DC fault events are associated with a abrupt increase in the fault current and sudden dips in the voltage. Therefore, direct measurements of local voltages and currents can provide fault indicators and can be employed in the design of rapid fault detection algorithms. It is worth noting that reliable voltage and current measurement devices with a high bandwidth should be utilized in order to provide precise and noise-free measurements based on which correct decisions can be made by the proposed algorithms [110]. For instance, a transient-based protection scheme applicable to MMC-HVDC grids with unidirectional solid-state DCCBs is proposed in [111] based on three criteria, i.e., overcurrent, undervoltage, and ROCOC. In [21], the proposed criterion depends on transient voltage measurements at both sides of the terminal reactors. In [21], the ratio of the transient voltages (ROTV) at reactor ends is used to distinguish between internal and external faults. In [112], fault detection and identification (FDI) units are arranged at each bus to promptly detect faults, discriminate between bus and line faults, and selectively identify the faulted line or busbar based on local transient current measurements. A similar scheme is proposed in [113]. A general analytical criterion for threshold estimation is proposed in [104], which is capable of determining transient voltage-based algorithms’ thresholds in a systematic way and without requiring extensive simulations.

The non-unit differential criterion established in [114] depends on transient current measurements obtained from distributed fiber-optic current sensors along the protected lines in order to precisely identify the faulted segment. The proposed local differential criterion in [115] detects and discriminates between internal and external faults after computing the ratio between the transverse differential (cross difference) currents and the sum of the locally-measured fault currents of both positive and negative poles. Although the proposed scheme cannot be directly applied as a stand-alone primary protection algorithm, it can be utilized as either auxiliary primary protection or backup protection. In [116], the proposed criterion depends on cable sheath voltage measurement, which is typically zero during normal operation while having a non-zero value during the fault. Furthermore, in [116], the amplitude and polarity of the measured sheath voltage are utilized to identify the faulted segment and determine the faulty pole. In [117], the rate of change of the current-to-voltage ratio, i.e., conductance derivative of the local transient voltage and current measurements, is employed to detect fault events. The proposed scheme in [118] utilizes the transient fault voltage measurements to estimate the first peak time (FPT), which represents the time duration between the sudden voltage decline instant and when the first peak is detected in the filtered voltage waveform, based on which the protection criterion is established. In [119], the change in the average voltage of positive and negative poles is employed to selectively detect various fault events. However, the employed measurement data window length is large (5 ms).

In [120], the magnitudes and derivatives of the common-mode (CM) and differential-mode (DM) components of the local fault current are extracted based on modulus decomposition transformation. Then, the extracted values are projected on a protection phase plane, which is divided into fault regions according to the fault type. Consequently, internal faults can be detected and discriminated from external faults, and the faulted pole can be identified as well. The proposed scheme in [121] utilizes the local fault voltage and current measurements to estimate three independent fault indicators, i.e., pole-current variations, pole-to-earth voltage variations, and converter neutral current variations, based on which different faults can be detected. In [122,123], initial fault currents are analyzed and calculated by proposing a transient high-frequency equivalent model for the employed meshed grid. Next, a fault detection and discrimination criterion is proposed based on estimating the transient energy of the superimposed high-frequency components of the local current measurements [122]. In [123], the derived current expressions during the initial fault stage are used to detect and discriminate between internal and external faults.

As previously highlighted in Section 2.1, DC reactors are installed at both ends of the transmission line or cable segments in HVDC grids not only to limit the sharp increase of fault currents but also to divide the grid into separate protection zones. Various protection schemes based on boundary reactor measurements have been proposed in the literature. In [72], the estimated value of the limiting reactor power is utilized to detect and discriminate between internal and external faults. However, the proposed scheme is not reliable in detecting high-resistance faults. Therefore, an auxiliary pilot backup criterion is developed for such faults. In [73], the proposed criterion depends on voltage measurements across the boundary reactors to detect and discriminate various faults and identify the faulty pole. Depending on the rate of change of the reactor voltage measurements, the proposed scheme in [124] detects fault events. Besides, internal faults are discriminated from external faults depending on the voltage polarities and amplitudes of the reactors that are connected to the same bus. However, in [124], only pole-to-pole faults are tested without providing a faulty-pole identification criterion. In [125], the proposed algorithm detects DC faults by calculating the difference between the ratios of the root mean square values of transient voltages (DTVRs) at both sides of the boundary reactor. Moreover, the faulted pole is identified by calculating the instantaneous zero-sequence voltage (IZSV) at the converter AC-side. The concept of asymmetric pole inductors has been recently proposed in [126], where the value of the DC reactor installed at the positive pole is different from that of the negative pole. The difference between the inductor voltages of the two poles is utilized as the fault detection criterion. However, this scheme is incapable of detecting unsymmetrical DC faults, i.e., pole-to-ground faults.

Similar to double-ended schemes, traveling wave propagation theory has been widely applied in the design of single-ended schemes. In such schemes, fault-induced traveling waves are detected and their high-frequency contents and arrival instants are extracted by utilizing various signal processing tools based on which DC faults are detected. However, the impacts of the superimposed noises and wave attenuations in case of long distances should be minimized to guarantee the reliable performance of these protection schemes. For example, DWT applied to local fault voltage traveling waves is exploited in [127] to identify the faulted segment. In [128], DWT is applied to local fault current measurements to design the protection criterion, where the fault discrimination is achieved by detecting the high-frequency components that exist during internal faults. In case of external faults, these components are attenuated due to the shunt capacitors installed at the grid tie buses and the stray capacitances at each bus. The proposed discrimination criterion employs the ratio of the high- to low-frequency transient energies to distinguish between internal and external faults. However, the proposed scheme lacks generalization since it is tested in a special grid structure that contains tie buses. In [129], DWT is applied to local voltage measurements to detect various faults where the faulted line is identified based on integrating the square of the transient voltage, i.e., transient energy. Moreover, the faulted pole is discriminated based on tracking the change of the positive and negative poles’ transient voltages. The proposed scheme in [130] locally extracts the distinctive frequency contents of the first incident traveling wave of the fault current utilizing DWT to distinguish between internal and external faults. In [131], DWT is used to extract the high-frequency components of the line-mode voltages and currents of the fault induced forward and backward traveling waves to discriminate between forward and reverse faults.

A multi-criteria wavelet-based scheme is proposed in [22], where the proposed algorithm utilizes two out of three criteria (voltage wavelet coefficients, current wavelet coefficients, and local voltage magnitude and derivative) to reliably detect various faults. Moreover, each criterion consists of a fault detection stage based on voltage and current measurements and a fault localization stage based on the comparison between the wavelet coefficients of each cable within the grid. The proposed scheme in [132] is based on extracting the dominant frequency component of the local current measurements using the multiple signal classification (MUSIC) approach. Furthermore, transient wave energy calculated by wavelet transform is utilized to discriminate between far-end internal and external faults, while WTMM is applied to identify the faulty pole. In [133], the proposed fault detection and discrimination criterion is based on the Synchrosqueezing Wavelet Transform (SWT) applied to the measured voltage signals across the boundary reactors.

Fourier transform is employed in [23] to extract the high-frequency components of the local current measurements, which have different features in the case of internal and external faults. In [134], the high-frequency content extraction is performed by Short Time Fourier Transform (STFT) applied to local fault current measurements to develop a frequency-domain-based relaying algorithm. Moreover, a time-domain-based detection criterion is proposed based on estimating the correlation degree between the DC link capacitor discharge current and the local fault current. Fast Fourier Transform (FFT) is employed in the protective scheme proposed in [135]. In [136], the orientations and the high-frequency content of the initial fault current traveling wave extracted by FFT are utilized to construct the fault detection and identification criteria. However, the proposed method requires a large sampling frequency and high computation capacity.

Recently, HHT has been used in several protection schemes due to its capability of extracting instantaneous features with a physical meaning in the time-domain [137]. For instance, in [138], the average frequency of the transient voltage signal is estimated by HHT and the marginal Hilbert spectrum (MHS). Then, the estimated value is compared with a predefined distance-frequency curve to assess the fault location. However, this scheme requires extensive calculations to find the distance-frequency curve for each segment within the grid. In addition, the selectivity of this scheme is examined only for low-resistance (1 Ω) faults. In [139], the instantaneous energy density, estimated by HHT, is selected as the fault detection criterion. However, the frequency band, within which the density level is estimated, depends on the operating point of the system. Moreover, the fault resistance coverage of this scheme is relatively small (50 Ω).

In [140], a protection algorithm is proposed based on the zero- and line-mode components of the fault backward traveling waves extracted by Phase-Modal Transformation (PMT). Similarly, PMT is employed in [141], where internal faults are detected by using the line-mode components of the boundary reactor voltage and the faulty pole is identified based on the zero-mode components. In [142], likewise, a PMT-based algorithm is proposed, which uses two criteria to detect fault events: (1) the derivative of the line-mode forward traveling wave and (2) a directional criterion based on the surge arrival time difference (SATD) between the line-mode components of backward and forward traveling waves. In [143], depending on the local fault voltage and current measurements, a parametric model is developed, which extracts the transients of the fault voltage and current traveling waves to detect various fault events based on an the iterative maximum-likelihood (ML) approach.

Distance protection concept is adopted in [144,145]. In [144,145], the accurate frequency-dependent line model is employed. Based on the local voltage and current measurements, the fault distance is precisely estimated by solving a set of line differential equations. A similar approach is proposed in [146], where the lumped π-model of the line is utilized. The probe capacitors are inserted at the DC-side of each grid terminal in [147]; then, based on the estimated resonance frequency (by least-squares technique) between the added capacitors and grid inductances, internal and external faults are distinguished. Finally, in [148], a distance algorithm is proposed based on estimating the equivalent capacitance voltages (ECV) of half-bridge MMCs and tracing their polarity.

Various artificial neural network (ANN)-based protection schemes have been proposed, which benefit from intelligent fault detectors and classifiers. In [149], an ANN-based scheme depending on local fault current measurements is proposed. However, this scheme has a long operating time of 5 ms. The proposed scheme in [150] uses a feed-forward ANN to extract the energy involved in the current signal spectrum at two distinct frequency bands for fault detection. In [151], wavelet transform along with Principal Component Analysis (PCA) are applied to the local current measurements to extract distinctive features, which are utilized as inputs to a Genetic Fuzzy System (GFS) to discriminate between internal and external faults. Furthermore, in [152], an artificial intelligence-based discrimination criterion is proposed based on the fault induced initial traveling wave propagation features extracted by a convolutional neural network (CNN). It is worth mentioning that artificial intelligence-based schemes require high computation capacity, exhaustive simulations, and large data sets to train the algorithms.

Recently, various mathematical approaches have been used to design efficient single-ended protection algorithms. The authors of [153] have developed a non-unit protective scheme based on the Morphological Gradient (MG) theory. In [153], the MG theory is used to extract the amplitude and the arrival instant of the initial fault wavefront of the local voltage to detect fault events. In [154], this scheme is modified based on the multiplication of the estimated second-level MG values of the line-mode components of the fault voltage and current traveling waves. The proposed scheme in [155] depends on detecting the sudden changes of the transients associated with the local fault voltage and current traveling waves using the Median Absolute Deviation (MAD) statistical approach.

In [156,157], the Levenberg-Marquart (LM) curve fitting technique is applied to the zero-mode component of the first incident traveling wave of the measured fault current to extract the index coefficients, which are utilized to distinguish internal from external faults. A similar scheme is developed in [158], where the fault resistance and location are respectively estimated based on the magnitude and the distortion degree of the incident fault current traveling wave. Moreover, in [158], the effect of the fault resistance is eliminated by utilizing adaptive thresholds, which are adjusted based on the extracted fault information from a curve fitting criterion. Although the proposed scheme can reliably identify pole-to-ground faults with large fault resistances, it fails to detect pole-to-pole faults. Furthermore, it requires a large sampling frequency and a large computation capacity. Finally, a recent algorithm is proposed in [159] based on the statistical random matrix theory (RMT) applied to local current measurements. This algorithm detects faults with a large range of resistances.

Protection schemes are required to reliably detect bus faults and discriminate them from line faults. Bus faults will result in tripping not only the associated converter station but also all the connected lines. Therefore, bus protection algorithms must not maloperate in the case of line faults and other transients. The fundamental bus protection criterion is based on Kirchhoff’s Current Law (KCL), where the infeed current into the bus from the converter station must be equal to the summation of the outgoing currents in the connected lines. The current differential criterion based on KCL has been widely adopted in the literature [112,127]. Furthermore, a ROCOV-based criterion is proposed in [70,71] to detect bus faults. In [160], the cosine distance criterion is employed to design a non-differential bus protection algorithm based on the bus voltage and the direction of the superimposed fault currents of the lines connected to the protected bus.

There are three significant aspects that should be carefully considered while evaluating the performance of single-ended schemes. First, the fault resistance coverage of the proposed schemes should be large enough such that severe fault conditions can be detected. The maximum fault resistance coverage is 800Ω