Analysis of Local Measurement-Based Algorithms for Fault Detection in a Multi-Terminal HVDC Grid

: One of the most important challenges of developing multi-terminal (MT) high voltage direct current (HVDC) grids is the system performance under fault conditions. It must be highlighted that the operating time of the protection system needs to be shorter than a few milliseconds. Due to this restrictive requirement of speed, local measurement based algorithms are mostly used as primary protection since they present an appropriate operation speed. This paper focuses on the analysis of local measurement based algorithms, speciﬁcally overcurrent, undervoltage, rate-of-change-of-current, and rate-of-change-of-voltage algorithms. A review of these fault detection algorithms is presented. Furthermore, these algorithms are applied to a multi-terminal grid, where the inﬂuence of fault location and fault resistance is assessed. Then, their performances are compared in terms of detection speed and maximum current interrupted by the HVDC circuit breakers. This analysis aims to enhance the protection systems by facilitating the selection of the most suitable algorithm for primary or backup protection systems. In addition, two new fault type identiﬁcation algorithms based on the rate-of-change-of-voltage and rate-of-change-of-current are proposed and analyzed. The paper ﬁnally includes a comparison between the previously reviewed local measurement based algorithms found in the literature and the simulation results of the present work.


Introduction
High-voltage direct current (HVDC) technology has earned relevance in power systems. Its characteristics make it a promising solution for long distance power transmissions [1]. Some of those characteristics, compared with AC systems, are: • Lower power losses transporting the same amount of power [1][2][3][4]. • Lesser number of electrical conductors (two poles in DC, three phases in AC) [1,5].
However, there are some unsolved technical challenges limiting the development of multi-terminal HVDC (MTDC) grids. During fault conditions, DC current reaches very high values and voltage • As a backup system to enhance the performance of the main protection system [53].

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In high impedance fault conditions where the requirements of speed are not so important [54].

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In cases of short transmission distances [51].
Likewise, fast HVDC CB are needed. They must operate in a range of a few milliseconds and their current interruption capability must be high [55]. In addition, to interrupt the current they have to produce a current zero because the DC current does not cross zero 'naturally' as in AC systems. Furthermore, they have to be able to dissipate the energy stored in the system during fault conditions [56].
Fault clearing strategies are key on how faults affect the system. There are non-selective, partially-selective, or full-selective strategies [19,57].
• Non-selective strategy: the entire system is shut down after fault detection; this strategy is usually based on AC CBs. • Full-selective strategy: only the faulty part of the system is disconnected, usually accomplished with HVDC CBs. • Partially-selective strategy: it is a combination of the previous strategies. The system is divided in several protection zones. When a fault occurs inside one of these zones, that zone, including the healthy parts, is shut down and afterwards the faulty part is isolated, usually by fast disconnectors. After fault isolation, the healthy parts of the affected zone are re-energized.
So, the adopted fault clearing strategy determines the impact of a fault condition on the system and which type of components of the protection system are selected; including breaker devices and protection algorithms.
The main focus of the present paper is set on protection systems for HVDC grids. Specifically, local measurement based algorithms are studied in Section 2, due to their capability of meeting the requirement of speed. Overcurrent, undervoltage, rate-of-change-of-voltage and rate-of-change-of-current algorithms are applied to a multi-terminal VSC based system. The application of the protection algorithms under study is analyzed for similar scenarios against different fault types, fault resistances, and fault locations. Then, the performance of the algorithms is discussed and compared in Section 3. This way, their advantages and disadvantages are highlighted in order to estimate their applicability. Besides, two new fault type identification algorithms are proposed. In addition, a comparison between the discussed protection algorithms on this paper and some of the most representative algorithms in the literature is included. Finally, the conclusions of the work presented in the paper are detailed in Section 4.

Analysis of Local Measurement Based Algorithms
In this section, local measurement based fault detection algorithms are analyzed. These methods use directly the DC current and voltage magnitudes or some variables mathematically derived from them, i.e., their derivatives. The local measurement based algorithms using directly the signal magnitudes are overcurrent and undervoltage algorithms. Besides, the derivative based algorithms under study for the present paper are the rate-of-change-of-current and the rate-of-change-of-voltage. Their characteristics and performances in a multi-terminal (MT) grid are described in the following subsections. The system used for this analysis is presented in Figure 1. It is a four-terminal half-bridge modular multilevel converter (MMC) based grid with a symmetrical monopole configuration. It is modelled in PSCAD and available in [29]. The converters are interconnected through five cables, their lengths are showed in Table 1. Two of the MMCs are connected to offshore wind power plants, the other two to onshore AC grids. Converters 1, 2, and 3 have a rated capacity of 900 MVA, whilst converter 4 presents a rated power of 1200 MVA.  A full-selective strategy is adopted in this grid. HVDC hybrid CBs and inductive reactors are located in series at both ends of all cables. The operating time of the CBs is assumed to be 2 ms. The value of the inductors is selected depending on the characteristics of the grid and the protection algorithm. In the study case, a value of 150 mH has been selected for the analysis of the OC and UV algorithms and a value of 100 mH has been chosen for the ROCOC and ROCOV algorithms for selectivity purposes. This component is very important when using local measurement based algorithms since it improves its selectivity. Inductors demarcate the borders of protection zones by damping external signals. In addition, they limit the rate-of-rise-of-current allowing the use of HVDC CBs with lower current interruption capability.
Furthermore, the performance of a local algorithm is dependent on the threshold used to discriminate between external and internal faults and normal operating conditions. The value of the threshold is characteristic of the grid conditions and must be selected through simulations. Selectivity and sensitivity of the protection algorithm are affected by the selected threshold. Higher threshold values increase the selectivity and decrease the sensitivity. Thus, a trade-off value between these two requirements must be considered.
In the following subsections, the performances of these algorithms are analyzed for different fault conditions. Different pole-to-pole (PtP) and pole-to-ground (PtG) faults are considered. Only positive PtG faults have been considered since it is assumed that the algorithms will show the same behavior for negative PtG faults. Different fault conditions are simulated, varying the location and resistance of the faults.  A full-selective strategy is adopted in this grid. HVDC hybrid CBs and inductive reactors are located in series at both ends of all cables. The operating time of the CBs is assumed to be 2 ms. The value of the inductors is selected depending on the characteristics of the grid and the protection algorithm. In the study case, a value of 150 mH has been selected for the analysis of the OC and UV algorithms and a value of 100 mH has been chosen for the ROCOC and ROCOV algorithms for selectivity purposes. This component is very important when using local measurement based algorithms since it improves its selectivity. Inductors demarcate the borders of protection zones by damping external signals. In addition, they limit the rate-of-rise-of-current allowing the use of HVDC CBs with lower current interruption capability.

Overcurrent Algorithm
Furthermore, the performance of a local algorithm is dependent on the threshold used to discriminate between external and internal faults and normal operating conditions. The value of the threshold is characteristic of the grid conditions and must be selected through simulations. Selectivity and sensitivity of the protection algorithm are affected by the selected threshold. Higher threshold values increase the selectivity and decrease the sensitivity. Thus, a trade-off value between these two requirements must be considered.
In the following subsections, the performances of these algorithms are analyzed for different fault conditions. Different pole-to-pole (PtP) and pole-to-ground (PtG) faults are considered. Only positive PtG faults have been considered since it is assumed that the algorithms will show the same behavior for negative PtG faults. Different fault conditions are simulated, varying the location and resistance of the faults.

Overcurrent Algorithm
The magnitude of the DC current in the links is measured and compared with a threshold. A fault is detected inside its protection zone if the current exceeds the threshold as in (1); where i DC is the current magnitude and Octh is the selected overcurrent threshold. The relay sends a tripping signal to its respective HVDC CB in order to clear the fault. 150 mH inductors are used to confine the protection zones and a threshold of 3 kA is used to ensure fault discrimination between internal and external faults.
i DC > OC th (1) The performance of the OC algorithm is analyzed varying the fault type, location and resistance.  Table 2. Fault locations are related to bus 1, meaning that a 0 km fault location is a fault located close to this bus and a 200 km fault location is a fault located at the end of the cable, close to bus 3. Relay 13 is located at the beginning of the cable (bus 1) and relay 31 at the end (bus 3). For PtP faults, relay 13 needs between 1.260 and 2.165 ms since fault inception to detect a fault, meanwhile relay 31 is slower and needs between 2.185 and 2.915 ms. Likewise, for PtG faults, the relays need between 1.460 and 2.280 ms, and 3.020 and 4.125 ms, respectively. Relay 31 is slower detecting faults since the current direction at this end of the link is reversed when a fault occurs, as it is shown in Figure 2, so the current magnitude needs more time to cross the positive OC threshold.
In both fault type cases, CB 13 has to interrupt higher values of current than CB 31, the highest being 6.500 kA for PtP fault and 5.712 kA for PtG fault versus the 6.081 kA and 4.123 kA interrupted by CB 31. For PtP faults, relay 13 needs between 1.260 and 2.165 ms since fault inception to detect a fault, meanwhile relay 31 is slower and needs between 2.185 and 2.915 ms. Likewise, for PtG faults, the relays need between 1.460 and 2.280 ms, and 3.020 and 4.125 ms, respectively. Relay 31 is slower detecting faults since the current direction at this end of the link is reversed when a fault occurs, as it is shown in Figure 2, so the current magnitude needs more time to cross the positive OC threshold.

Fault Resistance
In this section, different PtP and PtG faults are simulated varying the fault resistance. The fault is located close to bus 1, in link 13. Fault inception is at 0.41 s. Figure 2 shows how the current wave is affected by the fault resistance. Higher fault resistance values reduce fault currents, making them lower than the algorithm threshold. This algorithm can detect high impedance PtP faults up to 200 Ω but it is limited to 20 Ω PtG faults. Then, PtG faults are more critical since their maximum values are not as high as those of the PtP faults.

Undervoltage Algorithm
In this case, the DC voltage magnitude is measured and directly compared with a threshold as in (2); where v DC is the voltage magnitude and UVth is the selected undervoltage threshold. A fault is detected when three consecutive samples of the DC voltage drop below the threshold value. A sampling frequency of 10 kHz is used. As in the OC algorithm, 150 mH inductors are used. The fault discrimination threshold is 32 kV (0.1 p.u.). v DC < UV th (2)

Fault Location
The same 0.01 Ω PtP and PtG faults described in sub Section 2.1.1. are simulated to analyze the performance of the UV algorithm. The results of this analysis are summarized in Table 3.
Conversely to the OC algorithm case where the detection time depends on the pre-fault current direction, in the UV algorithm case, both relays need between 0.205 and 1.375 ms to detect the fault since fault inception, independently of the fault type. Similarly to the case of the OC algorithm, CB 13 interrupts higher values of current than CB 31. The maximum currents in PtP faults are higher than in PtG faults.  faults and 5 Ω in PtG faults. In this case, the UV algorithm sensitivity to high impedance faults is worse than the OC algorithm sensitivity.

ROCOC Algorithm
DC current derivative is calculated in (3) and its value is compared with a threshold. Similarly to the overcurrent method, when the ROCOC value exceeds the threshold as in (4), a fault is detected and a tripping signal is sent to the CB in order to clear the fault. In (3) and (4), ROCOC is the calculated current derivative, I1 is the current magnitude at time t1, I2 is the current magnitude at time t2, being t2 greater than t1, and ROCOVth is the selected ROCOV threshold.

ROCOC
∆I ∆t ROCOC ROCOC (4) The ROCOC values are calculated every 0.1 ms (sampling frequency of 10 kHz). To enable fault discrimination, a threshold of 3000 kA/s and 100 mH inductors are selected.

ROCOC Algorithm
DC current derivative is calculated in (3) and its value is compared with a threshold. Similarly to the overcurrent method, when the ROCOC value exceeds the threshold as in (4), a fault is detected and a tripping signal is sent to the CB in order to clear the fault. In (3) and (4), ROCOC is the calculated current derivative, I 1 is the current magnitude at time t 1 , I 2 is the current magnitude at time t 2 , being t 2 greater than t 1 , and ROCOV th is the selected ROCOV threshold.

Fault Location
Again, different 0.01 Ω PtP and PtG fault conditions are simulated varying their location through link 13 to analyze the performance of the ROCOC algorithm.
As it can be seen in Table 4, both relays need between 0.095 and 1.250 ms to detect a fault since fault inception independently of its type. CB 13 interrupts a maximum current of 6.373 kA for PtP faults and 5.848 kA for PtG faults versus the 4.803 kA and 3.532 kA interrupted by CB 31.

Fault Resistance
As in the two previous cases, the fault is located in link 13, close to bus 1. Both PtP and PtG faults with different fault resistances are simulated. Fault inception is at 0.41 s. The value of the calculated ROCOC for different fault conditions at both ends of the link is shown in Figure 4.

Fault Resistance
As in the two previous cases, the fault is located in link 13, close to bus 1. Both PtP and PtG faults with different fault resistances are simulated. Fault inception is at 0.41 s. The value of the calculated ROCOC for different fault conditions at both ends of the link is shown in Figure 4. The sensitivity of the ROCOC algorithm to fault impedance is not high enough. It is limited to 2 Ω PtG faults and 5 Ω PtP faults. This incapability of detecting higher impedance faults is due to the selected threshold. Therefore, a threshold lower than 3000 kA/s should be selected for high impedance faults. Nevertheless, this solution is not recommended since the algorithm selectivity would be affected and external faults might be interpreted as internal faults.

Fault Type Identification
A new fault type identification algorithm is proposed in this paper using the characteristics of the rate-of-change-of-current during fault conditions. When an internal fault occurs, regardless of the fault type, the sign of the first peak of the ROCOC is always positive for the positive pole and negative The sensitivity of the ROCOC algorithm to fault impedance is not high enough. It is limited to 2 Ω PtG faults and 5 Ω PtP faults. This incapability of detecting higher impedance faults is due to the selected threshold. Therefore, a threshold lower than 3000 kA/s should be selected for high impedance faults. Nevertheless, this solution is not recommended since the algorithm selectivity would be affected and external faults might be interpreted as internal faults.

Fault Type Identification
A new fault type identification algorithm is proposed in this paper using the characteristics of the rate-of-change-of-current during fault conditions. When an internal fault occurs, regardless of the fault type, the sign of the first peak of the ROCOC is always positive for the positive pole and negative for the negative pole. This criterion is not satisfied during external faults.
To discriminate between PtP and PtG faults additional criteria are proposed: • PtP fault: the ROCOC of both poles exceeds their respective thresholds, as in (5).
• Positive PtG fault: only the positive pole ROCOC exceeds its threshold, as in (6).
• Negative PtG fault: only the negative pole ROCOC exceeds its threshold, as in (7).
In (5)-(7), ROCOCp is the current derivative in the positive pole, ROCOCn is the current derivative in the negative pole and ROCOCth is the selected ROCOC threshold.
All simulated fault type cases are correctly identified within 1.3 ms since fault inception, as it can be seen in Table 5. Both PtP and PtG faults are identified almost immediately after fault detection, between 5 and 10 µs later.

ROCOV Algorithm
DC voltage derivative is calculated in (8). An internal fault is detected when its value drops below a certain threshold as in (9). In (8) and (9), ROCOV is the calculated voltage derivative, V 1 is the voltage magnitude at time t 1 , V 2 is the voltage magnitude at time t 2 , being t 2 greater than t 1 , and ROCOV th is the selected ROCOV threshold.
ROCOV < ROCOV th (9) The sampling frequency of the measurements is 10 kHz. A threshold of −0.2 MV/ms and 100 mH inductors are selected for fault discrimination purposes. This algorithm is very fast since the rate-of-change-of-voltage presents very high values due to the extremely sharp and almost instantaneous voltage drop during fault conditions.

Fault Location
In this subsection, the influence of the fault location on the ROCOV performance is analyzed. Several 0.01 Ω PtP and PtG faults at different locations in link 13 are simulated. The analysis of the ROCOV algorithm performance is summarized in Table 6. Independently of the fault type, both relays need between 0.005 ms and 1.100 ms since fault inception to detect the faults. Once again, CB 13 interrupts higher values of current than CB 31 and these currents are higher in PtP fault conditions than in PtG fault conditions (6.167 kA and 5.590 kA versus 4.591 kA and 3.280 kA).

Fault Resistance
The performance of the ROCOV algorithm against higher fault impedance values is tested simulating different PtP and PtG faults. Fault point is located in link 13, close to bus 1.
Even when the value of the DC voltage is severely affected by the fault resistance (as analyzed in Section 3.2.), the voltage drop remains sharp and almost instantaneous, as it is shown in Figure 5. Due to this, very high values of ROCOV appear and the faults can still be detected as it is shown in Figure 6. ROCOV algorithm shows great performance detecting high impedance faults. It can detect faults with resistances as high as 750 Ω in the case of PtP faults and as high as 400 Ω in the case of PtG faults.  The performance of the ROCOV algorithm against higher fault impedance values is tested simulating different PtP and PtG faults. Fault point is located in link 13, close to bus 1.
Even when the value of the DC voltage is severely affected by the fault resistance (as analyzed in Section 3.2.2.), the voltage drop remains sharp and almost instantaneous, as it is shown in Figure  5. Due to this, very high values of ROCOV appear and the faults can still be detected as it is shown in Figure 6. ROCOV algorithm shows great performance detecting high impedance faults. It can detect faults with resistances as high as 750 Ω in the case of PtP faults and as high as 400 Ω in the case of PtG faults.

Fault Type Identification
Similarly to the analysis done for the ROCOC algorithm, using the characteristics of the rate of change of voltage during fault conditions, a new fault type identification algorithm is proposed in the paper. The following criteria are proposed to discriminate between pole-to-pole (PtP) and poleto-ground (PtG) faults:  PtP fault: the ROCOV of both poles exceeds their respective thresholds, as in (10). All simulated fault type cases are correctly identified within 1.2 ms since fault inception, as it can be seen in Table 7. In this case, the time difference between fault detection and type identification is between 5 and 10 μs.

Fault Type Identification
Similarly to the analysis done for the ROCOC algorithm, using the characteristics of the rate of change of voltage during fault conditions, a new fault type identification algorithm is proposed in the paper. The following criteria are proposed to discriminate between pole-to-pole (PtP) and pole-to-ground (PtG) faults:

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PtP fault: the ROCOV of both poles exceeds their respective thresholds, as in (10).
• Positive PtG fault: only the positive pole ROCOV exceeds its threshold, as in (11).
• Negative PtG fault: only the negative pole ROCOV exceeds its threshold, as in (12).
In (10)- (12), ROCOVp is the voltage derivative in the positive pole, ROCOVn is the voltage derivative in the negative pole and ROCOVth is the ROCOV threshold.
All simulated fault type cases are correctly identified within 1.2 ms since fault inception, as it can be seen in Table 7. In this case, the time difference between fault detection and type identification is between 5 and 10 µs.

Discussion
In this section, the performance of the different algorithms is compared regarding fault detection time, maximum interrupted current, and fault identification time. Figure 7 summarizes the data from the tables presented in previous sections. It can be extracted that, in terms of fault detection speed, OC is the slowest algorithm, being the ROCOV algorithm the fastest one followed by the ROCOC and UV algorithms. The margin between the latter three algorithms is relatively small (in the range of 100 µs). Moreover, the fault detection time is proportional to the fault distance to the relay for all algorithms but the OC one. In that case, the current direction reversal affects the detection time. In this section, the performance of the different algorithms is compared regarding fault detection time, maximum interrupted current, and fault identification time. Figure 7 summarizes the data from the tables presented in previous sections. It can be extracted that, in terms of fault detection speed, OC is the slowest algorithm, being the ROCOV algorithm the fastest one followed by the ROCOC and UV algorithms. The margin between the latter three algorithms is relatively small (in the range of 100 μs). Moreover, the fault detection time is proportional to the fault distance to the relay for all algorithms but the OC one. In that case, the current direction reversal affects the detection time.

Maximum Interrupted Current
In accordance with the results of the simulations presented in previous tables, circuit breakers need to interrupt the highest values of current when the OC algorithm is used. The lowest values are presented when the UV algorithm is used. Nevertheless, this fact is influenced by the inductor, as different values have been selected. This way, the ROCOV and ROCOC algorithms are using 100 mH inductors instead of the 150 mH ones used in the cases of the OC and UV algorithms. The current is not as damped so their CBs have to deal with higher values of current in some cases even though they are faster detecting faults, as Figure 8 shows.

Maximum Interrupted Current
In accordance with the results of the simulations presented in previous tables, circuit breakers need to interrupt the highest values of current when the OC algorithm is used. The lowest values are presented when the UV algorithm is used. Nevertheless, this fact is influenced by the inductor, as different values have been selected. This way, the ROCOV and ROCOC algorithms are using 100 mH inductors instead of the 150 mH ones used in the cases of the OC and UV algorithms. The current is not as damped so their CBs have to deal with higher values of current in some cases even though they are faster detecting faults, as Figure 8 shows.

Fault Identification Time
As it can be seen from the results presented in Tables 5 and 7, both ROCOC and ROCOV based algorithms present a fault type identification time between 5 and 10 μs after fault detection.
Given that both fault type identification algorithms start after a fault is detected, their response time is limited by the detection time. Then, since the ROCOV fault detection algorithm is faster than the ROCOC one, its fault identification algorithm is also faster, as it can be seen in Figure 9. The faster operation of the ROCOV based algorithm is due to the sharp voltage drop during fault conditions; the ROCOV increases almost instantaneously to a very high value. Meanwhile, the current rises fast but not as sharply as the voltage drop. In addition, since the detection time depends on the fault distance, the faulty type identification time is also dependent on the fault distance. The operation time of the fault type identification algorithms, as well as the operation time of the fault detection algorithm, increases linearly with the fault distance, as it can be seen in Figure 9, since the faultinduced travelling wave has to cover the distance between the fault point and the location of the relay.

Fault Identification Time
As it can be seen from the results presented in Tables 5 and 7, both ROCOC and ROCOV based algorithms present a fault type identification time between 5 and 10 µs after fault detection.
Given that both fault type identification algorithms start after a fault is detected, their response time is limited by the detection time. Then, since the ROCOV fault detection algorithm is faster than the ROCOC one, its fault identification algorithm is also faster, as it can be seen in Figure 9. The faster operation of the ROCOV based algorithm is due to the sharp voltage drop during fault conditions; the ROCOV increases almost instantaneously to a very high value. Meanwhile, the current rises fast but not as sharply as the voltage drop. In addition, since the detection time depends on the fault distance, the faulty type identification time is also dependent on the fault distance. The operation time of the fault type identification algorithms, as well as the operation time of the fault detection algorithm, increases linearly with the fault distance, as it can be seen in Figure 9, since the fault-induced travelling wave has to cover the distance between the fault point and the location of the relay.
but not as sharply as the voltage drop. In addition, since the detection time depends on the fault distance, the faulty type identification time is also dependent on the fault distance. The operation time of the fault type identification algorithms, as well as the operation time of the fault detection algorithm, increases linearly with the fault distance, as it can be seen in Figure 9, since the faultinduced travelling wave has to cover the distance between the fault point and the location of the relay.

Comparison with Other Methods
Finally, a comparison between different local measurement based algorithms found in the literature and the algorithms that have been analyzed on this paper is shown in Table 8. The type of configuration, converter and breaker device employed in each system are also listed. In addition, the size of the limiting inductor and the operation time of all protection systems are indicated. The operation time comprises the time needed for the algorithm to detect the fault and the operating time of the used breaker device. From the comparison, it can be extracted that the operation times of the proposed algorithms are similar to those algorithms found in the literature. In addition, it can be noted that the circuit breaker type most commonly used in the literature under analysis corresponds to hybrid HVDC CBs and the size of the limiting reactors is usually set around 100 mH.

Conclusions
In this paper, protection systems for multi-terminal VSC-HVDC systems have been addressed. The characteristics and classification of algorithms into local measurement based and communication based have been overviewed. Communication based algorithms offer great selectivity but they are relatively slow due to communication time delay, whilst local measurements based algorithms are very fast detecting faults but they lack selectivity. The most common types of local measurement based algorithms are overcurrent, undervoltage, rate-of-change-of-current and rate-of-change-of-voltage algorithms. Several application cases of these algorithms as found in the literature have been reviewed in the present work. The paper emphasizes the use of local measurement based algorithms and highlights the importance of the selected fault clearing strategy, as well as inductors and thresholds.
The paper considers four local measurement-based algorithms and applies them to a four-terminal symmetric monopole half-bridge MMC grid in order to analyze and compare their behavior with different fault types, fault locations, and fault resistances. The considered algorithms are overcurrent, undervoltage, rate-of-change-of-current, and rate-of-change-of-voltage. In addition, two new fault type identification algorithms based on the characteristics of the ROCOC and ROCOV have been proposed in the paper.
From the results presented in Section 3, it can be determined that voltage based algorithms are faster than current based ones. This can be attributed to the sharp voltage drop when a fault occurs inside the protection zone, whilst inductors limit the rate-of-rise-of-current. Likewise, those algorithms using derivatives rather than magnitudes are considerably faster detecting faults; especially if compared with the OC algorithm. Moreover, fault type identification is faster using the characteristics of ROCOV rather than ROCOC, given that fault detection based on ROCOV is faster. Under high impedance fault conditions, ROCOV algorithm shows the best performance in fault detection and discrimination, followed by the OC algorithm. Though the voltage drop is not very large, it is still sharp. Therefore, ROCOV values are still high and high impedance faults can be correctly detected ( Figure 5). ROCOV algorithm performance is barely affected by the fault resistance.
Furthermore, regarding OC algorithm, the CBs need to interrupt higher levels of current than using the UV, ROCOC, or ROCOV algorithm. Nevertheless, the derivative based algorithms have to deal with relatively higher levels of current in some cases, as they are using smaller inductors.
Also, it can be concluded that inductors are essential for the limitation of protection zones and the value of the threshold is very important to enable fault discrimination.
As a result of the work presented in this paper, the use of combined protection algorithms can be recommended, instead of using one single algorithm. This way, the performance of the protection system will be improved; and it will benefit from their combined characteristics and advantages. In addition, the combined action of several algorithms will provide backup in case of fault detection failure. However, correct threshold values and inductor sizes should be selected for this purpose.
Finally, a comparison of the main features of the reviewed OC, UV, ROCOV, and ROCOC algorithms found in the literature and the algorithms analyzed in this paper has been summarized in the present paper. The analysis shows that the algorithms analyzed in this paper present similar operation times to those algorithms reviewed in the literature.