1. Introduction
With the development of new energy generation technologies, direct-current (DC) distribution networks based on voltage source converters (VSCs) have become important components of new power systems [
1,
2,
3]. However, owing to the low impedance characteristics of a DC distribution network based on VSCs, the fault current has a fast change rate and high amplitude when a short circuit or a grounding fault occurs, and there is no natural zero crossing in a DC distribution network [
4]. Without timely protection measures, the power electronic equipment in a DC system can be easily damaged, and the reliable operation of the DC distribution network can be affected [
5,
6]. Therefore, a fast and reliable DC fault protection method is essential to the safe operation of a DC distribution network.
For DC distribution network line protection, fault current differential [
7] and fault voltage differential [
8] protection schemes were proposed. The use of fault current or voltage information in these schemes improves the protection speed. However, in multiterminal DC distribution network structures, the protection accuracy is easily affected. A DC fault protection method based on a zero-mode fault current initial traveling wave was proposed [
9] that has the characteristics of high resistance to fault resistance and noise interference. However, its practicality in engineering is limited by an excessively high sampling rate. In other research [
10], a new protection scheme was proposed that uses the first and second derivatives of the fault current as the protection criteria for DC faults. The accuracy of this scheme is easily affected by fault resistance. Zhou et al. [
11] identified and determined faults based on the differences in voltage and direction characteristics of DC current-limiting reactors between faulty lines and nonfaulty lines, and their approach necessitates no communication and entails low hardware requirements. However, it exhibits low reliability and sensitivity when the transition resistance is high. Zhang et al. [
12] detected faulty lines using the zero-crossing feature of current. Li et al. [
13] proposed a full current direction longitudinal protection method. Nonetheless, it proves challenging to meet rapidity requirements when the transition resistance is significant. The authors of [
14] utilized the traveling waves of two rectilinear positive-sequence voltages of a current-limiting inductor for fault location and protection. However, the setting value of this protection method is susceptible to the influence of system harmonics. Jia et al. [
15] proposed a line protection method for a flexible DC distribution system based on the cosine similarity principle of the fault transient current. A DC fault protection scheme based on the fault current change rate of a current-limiting reactor was developed [
16] to achieve fast fault identification. However, its protection threshold is easily affected by the fault resistance. Current-limiting reactors were installed at both ends of the DC distribution network line. This limited the peak value of the fault current. Moreover, it possessed strong boundary characteristics that made it possible to use relevant electrical quantities to identify the fault area accurately. Considering that cosine similarity is less affected by amplitude and has a high evaluation accuracy [
17], it can be used for power system fault protection. Based on this, a fault protection method for a DC distribution network based on the cosine similarity of the transient current of the current-limiting reactor is proposed, which has great significance for the safe operation of DC distribution networks.
In this study, a method for identifying faults based on cosine similarity is proposed, the fault characteristics of the current-limiting reactor currents at both ends of the DC line under typical faults are discussed, the principle of cosine similarity is introduced, and a new protection scheme is proposed on this basis. The main contributions of this paper are summarized as follows:
(1) Based on the transient current characteristics of DC systems during internal or external faults, and combined with the principle of cosine similarity, a fault identification method satisfying the requirements of speed and selectivity of DC systems is proposed. Through simulation verification, it is shown that this method exhibits good anti-interference capabilities and has certain engineering application prospects.
(2) A comprehensive fault protection scheme is designed. Firstly, a five-point criterion is used to determine whether a fault has occurred. If a fault is detected, the protection is activated. Then, the cosine similarity value of the DC line current is utilized to determine whether the fault occurs internally or externally. If it occurs externally, the protection remains inactive; if it occurs internally, the fault location is determined based on the ratio of positive and negative pole voltages. This new protection scheme enables rapid and accurate fault location determination.
The remainder of this article is organized as follows. In
Section 2, the basic topology of a DC distribution network is introduced. The internal/external fault characteristics of DC distribution networks are analyzed. In
Section 3, a fault protection criterion for DC distribution networks based on the current cosine similarity of the current-limiting reactors is proposed. The simulation results for DC distribution network fault protection based on the proposed method are presented in
Section 4. Finally, the most important conclusions are summarized in
Section 5.
3. Principle of Breakage Protection
3.1. Principle of Cosine Similarity
Cosine similarity is the extension and application of the cosine concept of the angle between two vectors in analytical geometry. It is used in multivariate space and emphasizes the differences in the directions of the independent variables. Moreover, it is not influenced by the amplitude and provides a high accuracy. When there are two discrete signals with independent change laws in space, the cosine similarity [
15] can be expressed as follows:
This shows that, in the case of internal faults, the change directions of ∆ip1 and ∆ip2, as well as ∆in1 and ∆in2, are consistent. Therefore, the cosine angle between ∆ip1 and ∆ip2, as well as between ∆in1 and ∆in2, is less than 90°. At this time, cos (∆ip1, ∆ip2) > 0 and cos (∆in1, ∆in2) > 0 are satisfied. When an external fault occurs, the change directions of ∆ip1 and ∆ip2, as well as ∆in1 and ∆in2, are opposite. Therefore, the cosine angle between ∆ip1 and ∆ip2, as well as between ∆in1 and ∆in2, is greater than 90°. In addition, cos (∆ip1, ∆ip2) < 0 and cos (∆in1, ∆in2) < 0 are satisfied. Combining the cosine similarity method with the transient current of the current-limiting reactors can accurately distinguish the similarities and differences in fault characteristics when an internal or an external fault occurs. This is helpful for improving the protection accuracy.
3.2. Fault Detection Criterion
To avoid frequent start-ups of protection, it is necessary to set a fault detection criterion. In this study, the voltage change rate of the current-limiting reactors was used to set the fault detection criterion. The fault detection criterion is expressed as follows:
where
Kset is the maximum value of the rate of voltage change in the positive and negative current-limiting reactors, d
uP/d
t and d
uN/d
t are the voltage change rates of the current-limiting reactors for the positive and negative lines, respectively, and ∆
1 is the protection starting threshold. When the maximum value of the voltage change rate of the current-limiting reactors of the positive and negative lines is greater than ∆
1, the protection starts.
In engineering, this difference is often used to calculate the voltage change rate in current-limiting reactors. However, there are some problems with this method, such as poor accuracy and the ease of disturbance caused by noise. Therefore, a five-point numerical differentiation algorithm for the first derivative was used to calculate the voltage change rate in current-limiting reactors [
21]. The calculation formulae are as follows:
where ∆
t is the sampling time interval,
up1–
up5 are the data of five consecutive voltage sampling points for the positive current-limiting reactors, and
un1–
un5 are the data of five consecutive voltage sampling points for the negative current-limiting reactors.
3.3. Broken Pole Selection and Fault Identification
The fault identification criteria are based on the cosine similarity of the current-limiting reactors. The equations are as follows:
According to Equation (8), and in combination with the characteristics of the internal faults and external faults, the cosine values of the current angle between the current-limiting reactors at both ends of the line are 1 and −1, respectively. Hence, the cosine values 1 and −1 of the current angle are used to build the protection criterion. However, in practical engineering applications, factors such as fault resistance, measurement errors, and communication delays may affect the accuracy of the protection criterion. Hence, considering the above factors, the identification conditions for the internal and external faults are as follows:
When a line fault of the flexible DC power system occurs, the cosine similarity value is calculated according to Equation (8) and satisfies Equation (9), which can be judged as an internal fault, and vice versa for an external fault.
In this study, the absolute ratio HL of the average voltage of the current-limiting reactor of the positive and negative pole lines was used to determine the fault pole. The time window was set to 0.2 ms. The broken pole selection criteria are defined as follows:
where
n is the total number of sampling points in the 0.2 ms time window,
uL+(
h) and
uL−(
h) represent the sampled voltage values of the positive and negative current-limiting reactors, respectively, and
HL is the absolute ratio of the average voltages of the positive and negative current-limiting reactors. When an internal single line-to-ground fault occurs, the voltage ratio of the fault pole to the nonfault current-limiting reactor is approximately the coupling coefficient between the bipolar lines (maximum of 0.6) [
17]. When an internal line-to-line short-circuit fault occurs, the voltage ratio of the two current-limiting reactors is approximately 1. To distinguish between different types of faults,
hset = 0.6 is set. The broken pole selection criteria for the DC line are as follows:
When Equation (11) is satisfied, the fault is determined as a line-to-line short-circuit fault. If Equation (12) is satisfied, the fault is determined to be a positive grounding fault. Similarly, if Equation (13) is satisfied, it is a negative grounding fault.
3.4. Breakage Protection Flow Chart
A flowchart of the proposed fault protection method is presented in
Figure 7. Protection is initiated when the sampled data satisfy the fault detection criterion in Equation (6). After the protection device is started, the current in the current-limiting reactor is calculated to determine whether Equation (9) is satisfied according to the current cosine similarity. Hence, internal and external faults can be identified. A continuous judgment calculation is performed three times to avoid protection misoperation. If the protection criterion is satisfied three consecutive times, the internal faults of the DC line are determined. Finally, the types and locations of DC faults are determined using Equations (11)–(13).