Integrated Scheme of Protection and Fault Localization for All-DC Collection Network in Offshore Wind Farm

Abstract

With the development of offshore wind power towards the deep and distant sea, the DC collection and DC transmission (all-DC) wind farm demonstrates distinct advantages, including the absence of the Ferranti effect and elimination of multi-level voltage conversion requirements. For the protection of the all-DC collection network in offshore wind farms, this paper first analyzes the zero-mode current relationship at line outlets of the collection network and wind turbine outlets during single-pole-to-ground (SPG) faults. Analysis reveals that (1) zero-mode current polarities are opposite between fault and non-fault lines, and (2) zero-mode current polarities are opposite between the upstream and downstream of the fault point. Based on these characteristics, a polarity comparison-based protection and fault localization scheme is proposed. The method implements waveform peak–valley detection through mathematical morphology algorithms, with detection results quantified by similarity algorithms to achieve fault section localization. An all-DC offshore wind farm simulation is built in PSCAD/EMTDC. A variety of simulations under different operating conditions are delivered, demonstrating the validity and effectiveness of the proposed protection and fault localization scheme. The method accurately distinguishes the SPG fault on lines and buses while remaining unaffected by fault resistance.

1. Introduction

In recent years, in order to cope with the energy crisis and climate change, clean energy represented by wind and solar has developed rapidly, which has become an effective way to build a low-carbon economy and society [1]. Among renewable energy technologies, despite potential yet manageable impacts on avian migration corridors and marine fauna habitats [2], offshore wind power exhibits the most favorable lifecycle greenhouse gas emission profile when implemented with strategic planning and mitigation deployment [3]. Therefore, its large-scale development and grid integration will play a pivotal role in constructing next-generation power systems and advancing toward carbon neutrality [4].

Compared to onshore and near-offshore wind power, far-offshore wind energy exhibits superior wind resources, including higher wind speeds and more favorable wind frequency distributions, demonstrating significant potential for future development [5]. Furthermore, continuous advancements in wind turbine rated power and rotor diameter have substantially enhanced offshore wind energy harvesting capabilities, while simultaneously driving an urgent demand for large-scale far-offshore wind farm deployment [6].

In terms of wind power collection (or harvesting) and transmission topology [7,8], the existing offshore wind power systems primarily adopt three configurations: the AC collection and AC transmission scheme, AC collection and DC transmission scheme, and DC collection and DC transmission (all-DC) scheme. Due to the serious Ferranti effect and large reactive power loss, the traditional AC collection and AC transmission scheme is incapable of long-distance, high-capacity power transmission. Consequently, it cannot serve as a viable solution for delivering offshore wind power from remote locations [9]. The second way is the mainstream scheme in the current project. However, it has disadvantages, such as large volume and weight, high cost, Ferranti rise in collection cables, etc., which limits its transmission efficiency [10]. If the topology of offshore wind power adopts the third way, it can not only solve the problem of long-distance submarine cable’s Ferranti effect [11] but also avoid the problems of grid control and multi-level voltage conversion required by AC collection, so it is an ideal solution for offshore wind power collection and transmission.

To date, all-DC schemes lack engineering implementation, positioning their fault protection as exploratory research. However, topological parallels exist between DC collection networks and DC distribution networks, which have had extensive fault detection studies [12,13] in recent years that inform all-DC wind farm protection strategies. However, in the DC distribution network, the high-frequency current boundary is generally formed by series current-limiting inductors at both ends of the line. Based on the characteristic that these inductors exhibit high impedance to high-frequency signals while maintaining low impedance to DC and low-frequency components, high-frequency transients generated by faults are effectively confined within the faulty line segment, which creates extremely favorable conditions for single-ending protection [14], while in far-offshore all-DC wind farms, it is not easy to install current-limiting inductors with large volume and high weight, which results in high-frequency components being observed throughout the entire collection network of all-DC wind farms after fault occurrence. Therefore, this type of protection principle cannot be directly adapted to offshore all-DC wind farms.

At present, there are two primary methodologies that address DC line protection in the collector network of all-DC wind farms: traveling wave-based and fault transient quantity-based approaches. Traveling wave protection utilizes the properties of voltage/current waves generated by abrupt fault-induced voltage changes, including wavefront polarity, arrival time differences, and spectral characteristics [15], to achieve fault detection, protection, and localization. However, its implementation in the collection network of all-DC wind farms is limited by challenges in noise suppression and high-cost wave sensors. Furthermore, the absence of high-frequency boundaries consequently leads to this method demonstrating significantly reduced efficacy in the collection network of all-DC wind farms, compared to the application in DC distribution network. Conversely, fault transient quantity-based methods utilize post-fault transient voltage/current magnitudes, polarities, and change rates for protection. Ref. [16] proposed a fault line selection method based on transient current change rates in positive/negative poles, which employs instantaneous measurements captured at fault detection to select fault line, thereby achieving rapid response times. However, it carries a potential risk of failure to operate under high-impedance fault condition. Ref. [17] introduced an adaptive Spearman correlation coefficient-based method utilizing line-mode currents, with low clock synchronization requirements for information interactions. However, the Spearman correlation coefficient method fails to capture non-monotonic associations (e.g., waveforms exhibiting peaks or valleys). Consequently, its application imposes specific requirements on sampling frequency and time window selection in data analysis. Ref. [18] developed a dual-terminal Kendall’s correlation coefficient-based method utilizing positive/negative pole currents, which employs the current gradient rather than voltage threshold violations as the initiation criterion, thereby reducing the requirements for measurement devices. However, it exhibits heightened susceptibility to noise disturbance. Furthermore, while these accurately identify fault lines and distinguish line/bus faults, they lack exploration in fault section localization or distance ranging.

To support the operation and maintenance of all-DC wind farms and bridge the critical gap in ground fault section location for such systems, a protection and fault localization scheme for collection network is proposed in this article. After the occurrence of the SPG fault, the fault detection is realized through the change in the bus zero-mode voltage, and then the fault line is selected by collecting the zero-mode current at the outlet of the collection line and using the mathematical morphology algorithm to detect the peak–valley of waveform, and in the same way, the zero-mode current at the outlet of the wind turbine on the fault line is collected, and then the fault section is located. Comparative analysis with the method in ref. [18] demonstrates that the proposed scheme achieves enhanced reliability under high-impedance fault conditions and noise disturbance, albeit with a marginal compromise in response speed and communication cost, which offers superior practical engineering value, as quantitatively detailed in Section 4.5.

Research Gap and Contributions

In order to clarify the existing challenges and our work explicitly, the research gap and contributions are separately summarized as follows.

Research gaps in protection and fault localization for all-DC collection networks in offshore wind farms:

• Limitation of noise suppression and high-cost wave sensors of traveling wave-based approaches to be applied in all-DC collection networks;
• Absence of high-frequency boundaries leading to reduced performance of traveling-wave-based approaches to be applied in all-DC collection networks;
• Limited performance in the high-impedance fault condition of fault transient quantity-based approaches to be applied in all-DC collection networks;
• Limited performance in the noise interference condition of fault transient quantity-based approaches to be applied in all-DC collection networks.

Contributions of the proposed solutions in this paper:

• Fast fault detection utilizing the change in the bus zero-mode voltage;
• Precise fault line utilizing the zero-mode current at the outlet of the collection line;
• Enhanced reliability under high-impedance fault conditions;
• Robustness to noise interference.

The rest of the article is organized as follows. In Section 2, the topology and fault analysis of typical all-DC wind farms is introduced, and an integrated protection and fault localization scheme is presented in Section 3. A simulation verification and comparative analysis of the proposed protection and fault location scheme for the collection network of all-DC wind farms by PSCAD/EMTDC is presented in Section 4. Finally, Section 5 concludes this article.

2. Fault Analysis of All-DC Wind Farm

2.1. Topology of Typical All-DC Wind Farm

The existing offshore wind power systems are shown in Figure 1: As shown in Figure 1c, the all-DC wind farm features complex topology and constitutes a DC system with high-density power electronics devices. Consequently, compared to the AC collection and AC transmission scheme in Figure 1a and the AC collection and DC transmission scheme in Figure 1b, it exhibits low-inertia characteristics that enable extremely rapid DC fault propagation, accompanied by swift-rising high-magnitude fault currents capable of severe infrastructure damage [19]. Within this topology, multiple wind turbines are connected to the same collection line at intervals (the single capacity of permanent magnet direct-driven wind turbines is generally 10 MW or more [20]), multiple collection lines are connected to the same DC bus, and the offshore distance is long, so it is difficult to maintain the submarine cables. Adopting the protection and maintenance strategy of prolonged de-energization awaiting repairs, common in the first two topologies, for all-DC wind farms would result in significant economic losses, particularly in large-scale offshore applications. Therefore, it is urgent to study and solve the problem of protection and fault localization of offshore all-DC wind farms.

The topology of the typical all-DC wind farm for far-offshore wind power transmission is illustrated in Figure 2 [21].

As shown in Figure 2, the system topology of the far-offshore all-DC wind farm comprises three primary components: the collection network, offshore converter platform, and onshore converter platform. The collection network consists of eight radial feeder lines, each integrating five 10 MW DC wind turbines interconnected by 1 km submarine cables (approximately four times the rotor diameter [22]), with each feeder connected to the collection bus through submarine cables of varying lengths. For the DC wind turbines, the turbine-side AC/DC converter delivers an output voltage of 6.6 kV, which is subsequently boosted to ±33 kV by a medium-voltage DC/DC converter housed in the nacelle for connection to the DC collection lines; this conversion stage employs an IPOS-configured SAB converter [23]. Current measurement devices are installed at both the outlet of each collector line and each wind turbine. The offshore converter platform utilizes a FTF-MMC [24] to elevate the voltage to ±200 kV for high-voltage transmission, while the onshore platform employs a MMC to interface with the 500 kV AC transmission network.

2.2. Fault Characterization of All-DC Wind Farms

In an all-DC wind power collection network, for line protection systems, the operational strategy mandates protective tripping during internal faults while ensuring security against maloperation for external faults; specifically in collection line protection contexts, internal faults are defined as those occurring on the protected line itself, whereas external faults encompass faults at wind turbines, transmission networks, or other collection lines. This paper focuses on collection line faults, which occur on the collection lines or the bus. Collection line faults primarily consist of SPG faults and pole-to-pole short-circuit faults, with the former exhibiting significantly higher occurrence probability. Consequently, engineering protection designs predominantly focus on mitigating SPG faults.

In the collection network of all-DC wind farms, after the occurrence of a SPG fault on the collection line, an oscillated fault current with a high frequency will be generated, which may activate the overcurrent protection of the converter. The blocked converters often take days to troubleshoot, which seriously affects the safe and reliable operation of offshore wind power systems [25]. Therefore, it is of great significance to design a rapid fault handling method by using the fault characteristics during the fault transient process.

The zero-mode equivalent circuit for the collection network of the all-DC wind farm in Figure 1 after the occurrence of a SPG fault is shown in Figure 3. Each collection line containing five wind turbines is equivalent to six cascaded π equivalent lines; for example, R_10,1, L_10,1, and C_10,1 are, respectively, the equivalent resistance, inductance, and ground capacitance of the convergence line from the bus to the first wind turbine of Line 1. The fault resistance, the virtual power supply, and the line-mode equivalent network of the system in the equivalent circuit are equivalent to a two-port network, and the equivalent power supply and equivalent impedance are u_eq and z_eq, respectively. In addition, i₀₁–i₀₈ is the zero-mode current at the outlet of the line, i_f is the fault point current, i_0,up and i_0,down are the zero-mode current injected into the fault point upstream and downstream of the fault point by the fault line, respectively, and u₀ and u_0f are the bus zero-mode voltage and the fault point voltage, respectively. The switch S represents the fault point state; when the switch S is disconnected, the system operates normally, and when the switch S is disconnected, the SPG fault occurs.

According to Figure 3, it can be seen that for the zero-mode current at the outlet of each line, there is the following relationship based on Kirchhoff’s Current Law:

$$i_{10}={\displaystyle \sum _{\mathrm{n}=2}^8{i}_{n0}}$$

(1)

For the zero-mode current upstream of the fault point and downstream of the fault point, there is the following relationship at the fault point:

$$i_{\mathrm{f}}=i_{0,\mathrm{up}}+i_{0,\mathrm{down}}$$

(2)

Therefore, the zero-mode current at the outlet of the fault line is the sum of the zero-mode current at the outlet of the non-fault lines, and the zero-mode currents upstream and downstream of the fault point converge at the fault point and flow into the two-port network equivalent to the fault point and the line-mode equivalent network.

3. Integrated Scheme of Protection and Fault Localization in All-DC Collection Network

3.1. Fault Principle

According to the fault characteristic analysis, the basic principle of the protection and fault localization method of all-DC offshore wind farms can be given; that is, the zero-mode current at the outlet of the fault line is opposite to the zero-mode current at the outlet of the non-fault line, and the polarity of the zero-mode current upstream of the fault point and downstream of the fault point on the fault line is also opposite.

3.2. Implementation Method

The integrated scheme of protection and fault localization proposed in this paper is achieved by comparing the polarity of the transient zero-mode current at the line outlet and the wind turbine outlet, and the polarity comparison can be achieved by the peak-valley detection of the waveform.

The following describes the peak–valley detection of waveforms by mathematical morphology. Mathematical morphology is a signal and image processing tool based on set theory and integral geometry, which has been applied in some fields of electrical power systems in recent years. For instance, ref. [26] utilizes mathematical morphology combined with h-maxima transformation to extract regional maxima of waveforms for DC fault detection. Ref. [27] proposes a power quality disturbance detection and classification method by constructing a morphological gradient operator integrated with Walsh theory. Ref. [28] proposes a mathematical morphology-based method to eliminate decaying DC components in transient current signals, thus enhancing the measurement accuracy of the current transformer and the operation performance of the protection system. Since signals such as voltage and current are one-dimensional, grayscale morphology is commonly used in power systems [29].

The basic principle of mathematical morphology is to select the appropriate structural elements to move in the input signal to be processed, and through the interaction between the structural elements and the input signal, the required features are extracted within the neighborhood of each sampling point in the signal. For the case where the input signal is a sinusoidal signal, a planar structure with all elements set to zero is generally selected [30].

There are two basic operators in mathematical morphology [31]: dilation ($\oplus$) and erosion ($\ominus$), which are defined as follows: assuming that the input signal is f(n) and the structural element is g(m), the dilation and erosion operators are

$$\begin{array}{r}{f}_{\mathrm{dil}}(n)=f(n)\oplus g(m)=\max \{f(n-m)+g(m)\}\\ (n-m)\in D_f,m\in D_g\end{array}$$

(3)

$$\begin{array}{r}{f}_{\mathrm{ero}}(n)=f(n)\ominus g(m)=\min \{f(n+m)-g(m)\}\\ (n+m)\in D_f,m\in D_g\end{array}$$

(4)

where D_f and D_g are the definition domains of the input signal and structural element, respectively.

Dilation and erosion operators can, respectively, expand and suppress the input signal, and they are irreversible operations. By combinations of dilation and erosion, the opening ($\circ$) and closing ($•$) operators [32] can be obtained as follows:

$$f_{\mathrm{open}}(n)=f(n)\circ g(m)=[f(n)\ominus g(m)]\oplus g(m)$$

(5)

$$f_{\mathrm{close}}(n)=f(n)•g(m)=[f(n)\oplus g(m)]\ominus g(m)$$

(6)

The opening operator smooths the sharp corners that are convex to the outside in the waveform, which can flatten the peaks; the closing operator smooths the sharp corners that are concave to the inside, which can fill in the valleys. Based on this, peak–valley detection of waveforms [33] can be realized as follows:

$$f_{\mathrm{H}}(n)=2f(n)-[f(n)\circ g(m)]-[f(n)•g(m)]$$

(7)

f_H(n) can simultaneously detect the peaks and valleys of waveforms; therefore, it achieves enhanced computational efficiency and improves waveform information utilization.

In addition, considering that there is a certain amount of noise interference in the collected waveform, the method can utilize the morphology-mean filter [34] to preprocess the current waveform before peak-valley detection, that is,

$$f_{\mathrm{MMF}}(n)={\displaystyle \frac{1}{2}}\cdot \{f(n)•[f(n)\circ g(m)]+f(n)\circ [f(n)•g(m)]\}$$

(8)

The following is an example of the role of mathematical morphology in filtering and peak–valley detection. In the sinusoidal current waveform, noise with a SNR of 30 dB is superimposed. The waveform after filtering and peak–valley detection by mathematical morphology is shown in Figure 4.

As shown in Figure 4, the current waveform with added noise contains significant spikes, which would be mistakenly identified as peaks or valleys if peak–valley detection was performed directly. After filtering by mathematical morphology, the current waveform becomes smoother. The filtered waveform maintains monotonicity on both sides of the peak or valley moment, allowing the peak–valley detection algorithm to effectively identify the peaks and valleys. The detection current exhibits abrupt changes near the peak or valley moment while remaining zero at other times.

To further quantify the abrupt changes in the detection current, an integration operation can be performed on it. For a given abrupt change, if the integral result is positive, the detection current exhibits a convex shape, corresponding to a peak in the original current waveform. Conversely, if the integral result is negative, the detected current shows a concave shape, corresponding to a valley in the original current waveform.

To further quantify and compare the differences in the detection currents among different lines or wind turbine outlets on fault lines, a similarity analysis can be performed on the detection currents. Taking the cosine similarity algorithm as an example, cosine similarity is an algorithm used to measure the directional similarity between two vectors [35]. Its core idea is to evaluate the similarity by calculating the cosine of the angle between the vectors [36], expressed as

$$\mathrm{cosine-sim}\left(A,B\right)={\displaystyle \frac{A\cdot B}{‖A‖\cdot ‖B‖}}={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{A}_i{B}_i}}{\sqrt{{\displaystyle \sum _{i=1}^n{A}_i^2}}\cdot \sqrt{{\displaystyle \sum _{i=1}^n{B}_i^2}}}}$$

(9)

where A = (A₁, A₂, …, A_n) and B = (B₁, B₂, …, B_n) represent two vectors, which may directly utilize time-series numerical values or extracted features (e.g., Fourier coefficients, statistical characteristics, and peak–valley detection results). The cosine similarity (cosine-sim) ranges within [−1, 1], where

• cosine-sim(A,B) = 1 indicates identical vector directions (maximum similarity);
• cosine-sim(A,B) = 0 indicates orthogonal vectors (no similarity);
• cosine-sim(A,B) = −1 indicates diametrically opposite directions (minimum similarity).

The cosine similarity algorithm demonstrates directional sensitivity to vector polarity and computational efficiency, rendering it particularly suitable for fault line selection and fault section localization based on polarity difference. In the collection network, the fault line exhibits minimal current similarity with other lines, accompanied by opposing cosine similarity polarity. On the fault line, the detection currents at wind turbine outlets upstream of the fault point exhibit high similarity with consistent cosine similarity polarity, while those downstream demonstrate significantly reduced similarity with inverted polarity. Therefore, after obtaining the peak–valley detection currents of the zero-mode current at the line outlets, taking the detection currents of the Line 1 outlet as a reference, the cosine similarity of the Line 1 outlet with other line outlets is calculated, and the line with the lowest similarity and negative polarity is selected as the fault line. After obtaining the peak–valley detection currents of the zero-mode current at the wind turbine outlets on the fault line, taking the detection currents of fault line outlet as a reference, the cosine similarity of fault line outlet with other wind turbine outlets is calculated. When the similarity is negative for the first time, the line between the outlet of the previous and the present wind turbine is selected as the fault section.

For the collection network of an all-DC offshore wind farms, during a low-impedance SPG fault on the line, the zero-mode electrical quantity manifests as a decaying sinusoidal signal with a dominant resonant frequency around 1000 Hz. Therefore, the time window can be set to 0.5 ms, within which the detected current waveform can exhibit at least one complete peak or valley. During a SPF fault on the bus, due to altered electromagnetic wave propagation impedance, the dominant resonant frequency is higher, so a time window with a length of 0.5 ms can also ensure that at least one complete peak or valley is detected.

3.3. Initiation Criterion

The protection and fault localization scheme is started by using the bus zero-mode voltage u₀. During the normal operation of the DC offshore wind farm, the positive and negative voltages of the collection line are equal and opposite in the opposite direction, and the bus zero mode voltage is 0. When a SPG fault occurs, the voltage amplitude of the grounding electrode rapidly drops to 0, and the voltage amplitude of the non-fault pole rises to twice the original due to coupling, and the bus zero-mode voltage is no longer 0. Therefore, when the bus zero-mode voltage is detected to exceed 0.1 times the rated interpole voltage, the SPG fault is judged to have occurred, and the SPG fault protection and localization are carried out. Therefore, the initiation criterion can be expressed as

$$\left|u_0\right|\ge u_{0,\mathrm{set}}=0.1\times \left(u_{\mathrm{p}}-u_{\mathrm{n}}\right)$$

(10)

where u_p and u_n are, respectively, the rated voltage of positive and negative pole. u_0,set is the threshold of the initiation criterion. In the system used in this paper, the interpole voltage is rated at 66 kV, so the threshold is 6.6 kV.

3.4. Workflow

According to the analysis and design of the above protection and fault localization scheme of all-DC wind farms, the integrated scheme of protection and fault localization processes is as follows:

• Continuously detect the bus zero-mode voltage u₀; when the voltage between the rated poles is more than 0.1 times the rated interpole voltage, it is judged that an SPG fault occurs, and the polarity of the fault is judged according to the magnitude of the positive bus voltage and the negative bus voltage.
• Collect the transient zero-mode current i_n0 (n = 1, 2, …, 8) at the outlet of each line and use the mathematical morphology algorithm to detect the peak and valley of the waveform; select a time window and analyze the similarity of the detection current, taking the detection current of Line 1 as a reference.

• Fault line selection criteria. If the similarity polarity of Line x is opposite to that of Line 1, the line is judged as a fault line, and enter step 3. If the similarity polarities of all lines are the same, it is judged as a bus grounding fault; if the similarity polarities of other lines are opposite to that of Line 1, Line 1 is judged as a fault line.

3.

Collect the transient zero-mode current i_{x0_i} (i = 1, 2, …, 5) at the outlet of each wind turbine on the fault line and the transient zero-mode current i_{x0_0} at the outlet of fault line, use the mathematical morphology algorithm to detect the peak-to-valley waveform, and select a time window to analyze the similarity of the detection current, taking the detection current of the outlet of the fault line as a reference.

• Fault section localization criteria. When the similarity polarity at the outlet of the wind turbine x_i outlet is opposite to that of the outlet of the fault line, and the similarity polarity at the outlet of the wind turbine x_i−1 outlet is identical to that of the outlet of fault line, it is determined that the section from the wind turbine x_i−1 outlet to the wind turbine x_i outlet is the fault section, which is recorded as x_i−1x_i. If I = 1, the fault section is the collection line of the fault line.

The workflow diagram of the fault localization method is shown in Figure 5.

4. Simulation Verification

4.1. The Structure and Setup of Simulation

Based on PSCAD/EMTDC, a model of an all-DC offshore wind farm is built as shown in Figure 6, in which a total of eight collection lines are set up in the collection network, and the distance from the bus to the first turbine outlet on the collection line varies from 2 km to 10 km, as shown in

Table 1. The length of the collection lines.

The Number of Line	Length (km)	The Number of Line	Length (km)
Line 1	2	Line 5	6
Line 2	5	Line 6	4
Line 3	7	Line 7	5
Line 4	10	Line 8	5

, while the distance between each wind turbine is 1 km. The cable line is implemented by the frequency-dependent cable model in PSCAD/EMTDC, with its parameter definitions specified in Figure 7.

The medium-voltage DC/DC converter within wind turbines employs a neutral-point grounding configuration via high-resistance termination (Rg = 10 kΩ) at the inter-pole capacitor, while the high-voltage DC/DC converter on the wind farm export side utilizes a pole-to-pole high-resistance clamping circuit (Rg = 10 kΩ) for grounding purposes.

Table 2. The main simulation parameters of all-DC offshore wind farm.

Main Simulation Parameters	Value	Main Simulation Parameters	Value
ULV (kV)	6.6	f2 (Hz)	200
UMV (kV)	±33	C1/C2 (μF)	100/470
UHV (kV)	±200	C3/C4 (μF)	200/300
N1	6	L (μH)	50
N2/N3	40/200	Ls (mH)	10
f1 (kHz)	10

U_LV, U_MV, and U_HV are, respectively, the output voltage of the wind turbine, DC collecting voltage, and DC transmission voltage. N₁ is the number of medium-voltage converter submodules. N₂ and N₃ are, respectively, the number of high-voltage converter submodules. f₁ and f₂ are, respectively, the frequency of the medium-voltage converter and high voltage converter. C₁ and C₂ are, respectively, the submodule capacitors on the input-parallel and output-series sides of the IPOS converter. C₃ and C₄ are, respectively, the submodule capacitors on the low-voltage and high-voltage sides of the FTF-MMC converter. L is the submodule inductor of IPOS converter. L_s is the arm inductor of the FTF-MMC converter.

shows the other main simulation parameter settings. In addition, a single wind turbine’s capacity is 10 MW, and the wind farm’s total capacity is 400 MW.

Table 3. The key parameters of the permanent magnet machine.

Main Simulation Parameters	Value	Main Simulation Parameters	Value
air density (kg/m3)	1.225	rated wind speed (m/s)	12
rotor radius (m)	125	nominal frequency (Hz)	15
cut-in wind speed (m/s)	3	rated voltage (kV)	0.69
cut-out wind speed (m/s)	25

shows the key parameters of the permanent magnet machine.

4.2. Simulation Case 1: Basic Verification of Integrated Scheme of Protection and Fault Localization

In the collection grid, six locations are selected to simulate metallic SPG faults occurring at 1.5 s, and the simulation frequency is 100 kHz with a sampling rate of 20 kHz. After fault occurrence, transient zero-mode currents within a 0.5 ms time window were collected to determine the fault line and section. The specific fault locations and corresponding protection/localization results for these six fault cases are presented in

Table 4. Simulation case 1: fault setting and localization result.

Fault Number	Fault Location Setting	Fault Localization Result
1	Line 4 (12.5 km)	Line 4 x3x4
2	Line 5 (8.5 km)	Line 5 x3x4
3	Line 3 (7.5 km)	Line 3 x1x2
4	Line 7 (8.5 km)	Line 7 x4x5
5	Line 2 (6.5 km)	Line 2 x2x3
6	Line 6 (6.5 km)	Line 6 x3x4

Fault location is defined as the length of the line from the fault point to the medium-voltage collection bus on the fault line, composed of two geometrically sequential segments: (1) fixed collection line segment in Table 1 and (2) variable subsea cable segment. For the distance (0–4 km) along the fault line from the first turbine outlet to the fault point, 4 km is the cumulative inter-turbine cable span.

.

Taking Fault 1 as an example, the bus zero-mode voltage waveform, the zero-mode current waveforms at the outlets of all collection lines, and the zero-mode current waveforms at the outlets of each wind turbine on the fault line are shown in Figure 8, respectively. In Figure 8, Line 4 is marked in detail as a fault line, and the other lines are non-fault lines; only the zero-mode current at the wind turbine outlet before and after the fault point and the zero-mode current at the fault line outlet are retained for the sake of simplification (the same applies hereinafter). The peak–valley detection results of the above zero-mode currents by the mathematical morphological method used in this paper are shown in Figure 8. The calculation results of the cosine similarity between the detection currents are presented in

Table 5. Simulation case 1: The calculation results of the cosine similarity.

Line	1	2	3	4			5	6	7	8
				x0	x3	x4
Cosine similarity	1.00	0.61	0.63	−0.61			0.97	0.98	0.61	0.61
				1.00	0.65	−0.33

In Table 5, the cosine similarity of Line 4 contains two rows: the up row represents the cosine similarity between the outlet of Line 1 and Line 4 during fault line selection, while the down row represents the cosine similarity among wind turbine x₃, the x₄ outlet, and the outlet of Line 4 during fault section localization. The same applies hereinafter.

.

As shown in Table 4 and Table 5 and Figure 8 and Figure 9, it is noted that after the occurrence of a SPG fault, the bus zero-mode voltage rises rapidly and exceeds the threshold at t = 1500.02 ms; meanwhile, the zero-mode current polarity of the fault line is opposite to that of other lines, and the polarity of the zero-mode current at the outlet of wind turbine before the fault point is the same as that at the outlet of the line, while the polarity of the zero-mode current at the outlet of the wind turbine after the fault point is opposite to the above two. The mathematical morphology algorithm demonstrates high sensitivity in detecting peaks and valleys of waveforms. The calculated cosine similarity results indicate distinct polarity differences among fault lines and non-fault lines, as well as between upstream and downstream sections of the fault point on the fault line. Therefore, the scheme proposed in this paper accurately realizes the selection of fault lines and the localization of fault sections. However, since only the zero-mode current measurement is set at the outlet of wind turbine, only the fault section can be located, and fault distance ranging cannot be realized.

4.3. Simulation Case 2: Applicability of Bus SPG Fault

In collection networks, the bus is selected to simulate metallic SPG faults occurring at 1.5 s, and other simulation settings are the same as those in simulation case 1. The bus SPG fault is named Fault 7.

The bus zero-mode voltage waveform is similar to that in simulation case 1 and also reaches the start-up threshold at t = 1500.02 ms, so it is omitted here. The zero-mode current waveforms at the outlets of all collection lines are shown in Figure 10. The peak–valley detection results of the above zero-mode currents by the mathematical morphological method used in this paper are shown in Figure 11. The calculation results of the cosine similarity between the detection currents are presented in

Table 6. Simulation case 2: calculation results of the cosine similarity.

Line	Cosine Similarity	Line	Cosine Similarity
1	1.00	5	0.57
2	0.49	6	0.15
3	0.48	7	0.49
4	0.78	8	0.49

.

As shown in Figure 10 and Figure 11 and Table 6, it is noted that after the occurrence of a SPG fault on the bus, the bus zero-mode voltage rises rapidly and exceeds the threshold, meanwhile the zero-mode current polarity is the same for all lines; this fault characteristic is different from that in simulation case 1. Therefore, the scheme in this paper can be used to correctly judge the SPG fault on the bus.

4.4. Simulation Case 3: Effect of Fault Resistance

In the collection network, the fault point is selected on Line 4, 13.5 km away from the bus, which is the same as that of Fault 1 in simulation case 1, and the SPG faults occur at 1.5 s, with fault resistance set to 0 (metallic), 10, and 50 Ω, respectively, and other simulation settings remaining the same as those in simulation case 1. The specific fault transition resistance and corresponding protection/localization results for these three fault cases are presented in

Table 7. Simulation case 3: fault setting and localization result.

Fault Number	Fault Resistance Setting	Fault Localization Result
1	0 (metallic)	Line 4 x3x4
8	10 Ω	Line 4 x3x4
9	50 Ω	Line 4 x3x4

.

Taking Fault 9 as an example, the bus zero-mode voltage waveform, the zero-mode current waveforms at the outlets of all collection lines, and the zero-mode current waveforms at the outlets of each wind turbine on the fault line are shown in Figure 12. The peak–valley detection results of the above zero-mode currents by the mathematical morphological method used in this paper are shown in Figure 13. The calculation results of the cosine similarity between the detection currents are presented in

Table 8. Simulation case 3: calculation results of the cosine similarity.

Line	1	2	3	4			5	6	7	8
				x0	x3	x4
Cosine similarity	1.00	0.05	0.47	−0.60			0.44	0.09	0.05	0.05
				1.00	0.38	−0.45

.

As shown in Table 7 and Table 8 and Figure 12 and Figure 13, it is noted that when a high-impedance SPG fault occurs in the system, the waveform characteristics of the fault electrical quantities differ significantly from those observed in simulation case 1 and simulation case 2. The bus zero-mode voltage after the fault exhibits a more gradual variation trend. Nevertheless, the proposed fault localization method initiates at t = 1500.17 ms; i.e., it still triggers before the zero-mode current of the line reaches its first peak. The zero-mode currents at the outlets of all lines and those at the wind turbine outlets on the fault line no longer exhibit decaying sinusoidal signals, and their amplitudes decrease. However, the polarity relationships remain unchanged. Consequently, the proposed scheme can still accurately identify the fault section.

4.5. Simulation Case 4: Effect of Noise Disturbance

In Fault 1 of simulation case 1, inherent harmonics induced by power electronic switching devices within the all-DC wind farm simulation model are evident in the waveforms of Figure 8. To simulate practical measurement interference and instrumentation errors, additive Gaussian white noise (SNR = 30 dB) is superimposed on these waveforms, yielding the noise-contaminated waveforms of the bus zero-mode voltage waveform, the zero-mode current waveforms at the outlets of all collection lines, and the zero-mode current waveforms at the outlets of each wind turbine on the fault line presented in Figure 14a.

Figure 14b is shown as the waveforms in Figure 14a, processed through mathematical morphology filtering. The peak–valley detection results of the above zero-mode currents by the mathematical morphological method used in this paper are shown in Figure 15. The calculation results of the cosine similarity between the detection currents are presented in

Table 9. Simulation case 4: calculation results of the cosine similarity.

Line	1	2	3	4			5	6	7	8
				x0	x3	x4
Cosine similarity	1.00	0.93	0.92	−0.95			0.48	0.39	0.93	0.93
				1.00	0.92	−0.49

.

As shown in Figure 13 and Figure 14 and Table 9, it is noted that following mathematical morphology filtering, glitches, and fluctuations in the waveform of Figure 14a are effectively suppressed, demonstrating the efficacy of the filtering approach. Although the detected fault occurrence time is delayed by 0.05 ms compared to Fault 1 due to this filtering, it does not compromise the proposed fault protection and location scheme.

4.6. Simulation Case 5: Comparative Analysis of Fault Protection Performance

In simulation case 5, the fault line selection method proposed in this work is compared with the current-derivative-based method in ref. [18]. The applicability of both methods is evaluated by fault scenarios from simulation case 1, simulation case 4, and simulation case 5, with comparative results presented in

Table 10. Simulation case 5: comparison of fault protection performance.

Method	Operating Time	Fault Resistance	Noise Disturbance
This paper	1.50052 s	√	√
Ref. [18]	1.50002 s	×	√

The √/× represent whether the protection methods can function correctly in a certain fault case. For Fault 9 in simulation case 4, the di/dt measured at the outlet of Line 4 is 914.6 A/s for the positive pole and 379.3 A/s for the negative pole. Neither value exceeds the protection threshold setting, consequently causing the method in [18] to fail to trigger.

.

As shown in Table 10, it is noted that since both methods employ bus zero-mode voltage as the fault detection criterion, their response speeds are considered identical. However, the method in ref. [18] utilizes instantaneous data captured at the moment of fault detection to select fault lines, whereas the proposed method requires data acquisition over a time window. Consequently, for Fault 1 in simulation case 1, the method in [18] achieves a faster response time than the proposed method. For high-resistance SPG faults with long fault distances, the method in ref. [18] fails to reach the operation threshold, necessitating backup protection that significantly compromises its protective performance. The proposed method necessitates a corresponding filtering method to mitigate noise disturbance. As previously discussed, the filtering method results in smoother waveform transitions, which consequently extends the operating time to some extent. In contrast, the method in ref. [18] demonstrates negligible sensitivity to noise disturbances. However, both methods correctly identify fault lines under noise disturbance (SNR = 30 dB). In summary, although the proposed method exhibits a marginally longer operating time compared to ref. [18] due to the aforementioned factors, it maintains accurate fault identification while accommodating a wider range of fault scenarios. Consequently, it offers superior practical engineering value.

In summary, PSCAD/EMTDC simulation results demonstrate that the proposed integrated scheme of protection and fault localization can accurately select the fault line and precisely locate the fault section in the all-DC offshore wind farm collection network during SPG fault. Additionally, it is insensitive to fault resistance and noise disturbance.

5. Conclusions

This article proposes a SPG fault protection and localization scheme based on waveform peak–valley detection for all-DC collection networks in offshore wind farms, and the following conclusions are obtained:

(1)

When a SPG fault occurs in the collection network of all-DC wind farms, the zero-mode current polarity at the outlet of the fault line is opposite to that of the non-fault line, and the zero-mode current polarity upstream of the fault point and downstream of the fault point on the fault line is also opposite.

(2)

The mathematical morphology algorithm enables sensitive peak–valley detection in waveforms, while the similarity algorithm provides accurate quantification of the detection results. This combined approach facilitates protection and fault localization based on polarity difference.

(3)

The proposed integrated scheme utilizes differential polarity characteristics of fault currents in all-DC collection networks to accurately discriminate line faults and bus faults while maintaining high reliability against high-resistance SPG faults and noise disturbance, despite communication costs for collecting zero-mode currents from the collection network to the central unit.

(4)

PSCAD/EMTDC simulation results verify that the proposed integrated scheme withstands fault resistance of at least 50 Ω while initiating protection before the first peak of the zero-mode current of the line and accurately selecting a fault line/localizing fault section by post-fault data within 1 ms, with response times further reducible to approximately 0.5 ms for metallic SPG faults prevalent in submarine cables. A low-voltage physical experimental simulation platform is currently constructed for further validation of the proposed method.

Future research will focus on (1) characteristic analysis of bipolar short-circuit faults, and (2) research on precise fault distance ranging methodology.