Reliability assessment method of wind power DC collection system based on MLFTA-SMC | Scientific Reports

Scientific Reports volume 14, Article number: 25341 (2024) Cite this article

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Wind power DC collection system, as a crucial component of wind farms, plays a vital role in ensuring the safe and stable operation of the entire wind farm. This paper proposes a reliability assessment method for wind power DC collection systems based on MLFTA-SMC. Firstly, it analyzes the topology and key equipment of wind power DC collection systems. Secondly, based on the topology of different wind power DC collection systems, it constructs multi-level fault tree models to calculate the comprehensive importance of different events, thus providing data support for subsequent reliability assessment. Then, it utilizes the MLFTA-SMC method to assess and analyze the reliability of different wind power DC collection system topologies. Finally, taking a 100 MW wind farm in Northwest China as an example, the proposed reliability assessment method is verified through simulation. The results indicate that this method exhibits good effectiveness and superiority.

Wind power, as a commercially viable renewable energy generation method, plays a crucial role in implementing energy development strategies, alleviating energy supply pressures, and adjusting power structures1. According to data, as of the end of 2022, the cumulative installed capacity of wind power nationwide had grown to 395.6 GW. In this context, it is of great significance to study the reliability of wind farms, especially the collection system that connects wind turbines and step-up converter stations2, in order to continuously improve wind power generation efficiency and reliability, ensure equipment safety, and promote the sustainable development of the wind power industry. As an important component of wind farms, the collection system has numerous electrical devices, and its economic cost accounts for about 75% of the wind farm. Once a fault occurs in the collection system, it will cause a significant loss of electricity for the entire wind farm, thereby affecting economic benefits. Therefore, the reliability of the collection system has important implications and significance for the reliable operation of the entire wind farm3. Currently, collection systems are mainly classified into AC collection and DC collection4. However, despite the long-term development and application of AC collection technology, which is characterized by high maturity, wide adaptability, and low maintenance costs, it still faces significant drawbacks such as high transmission losses, harmonic resonance, and reactive power transmission issues. To alleviate these issues, wind power DC collection systems have emerged as a new technological approach. Not only do they have lower losses and higher efficiency, but they also effectively address problems like harmonic resonance and reactive power transmission associated with AC collection. Consequently, wind power DC collection systems have gradually attracted widespread attention.

Currently, there are mainly two methods for assessing the reliability of collection systems: the Analytic Method5,6 and the Monte Carlo method7,8. The Monte Carlo method can be further categorized into Sequential Monte Carlo (SMC) and Non-Sequential Monte Carlo (NSMC). Among them, the Analytic Method is widely used in the evaluation of power system reliability due to its clear physical concepts and high model accuracy. The reliability of the wind farm collection system was evaluated using the Fault State Enumeration method in references9,10. This method focuses only on the occurrence of system failures and does not consider the impact of the internal component structure and logical connections between components on reliability assessment. Based on this, reference11 analyzes the structure of DC/DC converters in the wind farm collection system and evaluates their reliability using the Reliability Block Diagram method from a component-level perspective. Although this method can fully consider the logical connections within devices or equipment, it cannot assess the impact of the fault scope resulting from wind turbine faults under series connection when evaluating the topology structure of series-parallel DC collection systems. To address this issue, references12,13 extensively evaluate the reliability of the collection system using the Fault Tree Analysis method. This approach presents the fault tree of the collection system in a graphical format, allowing for an intuitive and clear depiction of complex fault paths and logical relationships between events. It offers a high level of accuracy in constructing mathematical models. However, when assessing the reliability of systems with a large number of components and complex structures, this method can encounter difficulties in constructing mathematical models and significantly reduce computational efficiency. Therefore, the Monte Carlo method has gained widespread popularity. Leveraging its advantage of being independent of sampling size and system scale, this method simplifies calculations when assessing the reliability of systems with numerous components and complex structures. Based on the construction of fault probability models for wind turbines outlined in references14,15,16, the Non-Sequential Monte Carlo method is utilized to evaluate the reliability of the collection system. While this method presents significant advantages in determining the reliability of the collection system, it fails to consider the impact of temporal sequences on the assessment results. Consequently, it cannot provide operation decision-makers with comprehensive and accurate information to better understand the system’s performance and maintenance requirements. To address this limitation, the sequential Monte Carlo method, leveraging its advantage of fully considering temporal correlations and accurately simulating the system’s fault and recovery processes, is widely employed in power system reliability assessment. However, according to the evaluation principle of the Monte Carlo method, when this method is employed, the given simulation time range is often extensive, resulting in a large number of component states being simulated. This leads to a significant decrease in computational efficiency as a considerable amount of time is required to sequentially assess the states of the aforementioned simulated components. Therefore, reducing the number of component states that need to be evaluated is crucial for improving the efficiency of the Sequential Monte Carlo method.

In summary, this paper proposes a reliability assessment method for wind turbine DC collection systems based on Multi-Level Fault Tree Analysis-Sequential Monte Carlo (MLFTA-SMC). This method allows for an improved accuracy in constructing mathematical models for wind turbine DC collection systems while effectively evaluating the reliability of complex and large-scale grid-connected wind turbine DC collection systems. The effectiveness of the proposed method is validated using a 100 MW wind turbine DC collection system, providing a new approach to reliability assessment methods for wind turbine DC collection systems.

The main contributions of this article are as follows:

Taking into full consideration the characteristics of the topology structure of wind turbine DC collection systems, a multi-level fault tree method is proposed to enhance the modeling accuracy and improve computational efficiency.

Taking into account the importance of structure, probability, and criticality, we propose a comprehensive importance index to measure the impact of basic/intermediate events on the occurrence of top events. This, in turn, aids in guiding the formulation of maintenance optimization schemes for weak links.

A MLFTA-SMC method is proposed, which utilizes the comprehensive importance index to transform higher-order fault events into lower-order fault events. This approach effectively reduces the number of component states that need to be evaluated, thereby improving the evaluation efficiency of sequential Monte Carlo methods.

The remaining part of this article is organized as follows. Section 2 introduces the reliability models of wind turbine DC collection system topology structure and key equipment. Section 3 presents the multilevel fault tree method. Section 4 constructs sequential Monte Carlo method. Section 5 describes the reliability assessment of wind farm DC collection system. Numerical case studies are presented in Sect. 6, and the conclusion is provided in Sect. 7.

Parallel topology structure

The parallel topology structure, as shown in Fig. 1, is a configuration where the low-voltage DC output from the DC output wind turbine units is boosted by DC/DC converters. The energy is then concentrated onto the collection line through parallel connections. Multiple parallel branches are used to transmit the energy to the collecting bus, which is ultimately delivered to the converter station or the power grid. In case of a fault in a wind turbine unit or the collection line within a parallel cluster, the hybrid DC circuit breaker immediately disconnects it to ensure the normal operation of the remaining parallel clusters.

Parallel topology.

Series-parallel topology structure

The series-parallel topology structure, as illustrated in Fig. 2, refers to a configuration where the low-voltage DC output from multiple DC output wind turbine units is boosted by DC/DC converters first, then further elevated in series. The energy is then collected onto the bus through multiple parallel branches before being delivered to the converter station or the power grid. When a fault occurs in a wind turbine unit within a series-parallel cluster and reaches a specified threshold, the hybrid DC circuit breaker immediately disconnects the affected series-parallel cluster to ensure the normal operation of the remaining series-parallel clusters.

Series-parallel topology.

As mentioned earlier, in the wind turbine DC collection system, the DC output wind turbine units, DC/DC converters, and hybrid DC circuit breakers are crucial equipment to ensure the safe and reliable operation of the system. Therefore, it is necessary to conduct research on the reliability of these key devices, in order to provide important data support for the subsequent reliability assessment of the DC collection system.

As the functional main body of the wind turbine DC collection system, the DC output wind turbine units are essentially obtained by converting the AC wind turbine17,18. Considering the future technological trends and the advantages of full-power converter-based direct-drive AC wind turbines, such as high efficiency, low operating and maintenance costs, most of the current research on DC output wind turbine units focuses on full-power converter-based direct-drive AC wind turbines. The topology structure is shown in Fig. 319.

Structure of DC output wind turbine.

From Fig. 3, it can be seen that the DC output wind turbine is mainly composed of a permanent magnet direct-drive wind generator and an AC/DC converter. The reliability block diagram of the DC output wind turbine unit can be constructed using the reliability block diagram method, as shown in Fig. 4.

Reliability diagram of direct output wind turbines.

According to the aforementioned reliability block diagram, the reliability model of the DC output wind turbine unit is as follows:

In the formula, λg represents the failure rate of the DC output wind turbine unit. µg represents the repair rate of the DC output wind turbine unit. λWTG represents the failure rate of the wind turbine generator. λAC/DC represents the failure rate of the AC/DC converter. TMTTR, WTG represents the average repair time of the wind turbine generator. TMTTR, AC/DC represents the average repair time of the AC/DC converter.

DC/DC converters are the core equipment of wind power DC collection systems20. For this system, high efficiency, high power, high reliability topology, voltage stabilization control, and modular balanced control are the basic technical requirements of DC/DC converters. Therefore, the topology structure of DC/DC converters21 adopted in this paper is based on the Boost Full Bridge Isolated Converter (BFBIC) module, using a hybrid two-stage modular integration technology of Input Parallel Output Series (IPOS) and Input Parallel Output Parallel (IPOP) to increase power transmission, thereby meeting the requirements of DC voltage level and DC/DC converter capacity. The topology structure of the DC/DC converter based on BFBIC is shown in Fig. 5.

Topological structure of DC/DC converter.

In this section, the reliability model of the DC/DC converter is constructed using the reliability block diagram method, as shown in Fig. 6.

Reliability block diagram of DC/DC converter.

From Fig. 6, it can be seen that in the fourth module, the BFBIC module, all components are connected in series. If any component fails, the entire BFBIC module cannot function properly. The reliability model of the fourth module, the BFBIC module, is as follows.

In this formula, λBFBIC and µBFBIC respectively represent the failure rate and repair rate of the fourth module, the BFBIC module. λCin, λIGBT1, λT, λIGBT2, λCout represent the failure rates of the primary side capacitor, IGBT1 module, transformer, IGBT2 module, and secondary side capacitor, respectively. TCinMTTR, TIGBT1MTTR, TTMTTR, TIGBT2MTTR, TCoutMTTR represent the mean time to repair of the primary side capacitor, IGBT1 module, transformer, IGBT2 module, and secondary side capacitor, respectively. F is the quantity of primary side capacitors. U is the quantity of IGBT1 modules. Q is the quantity of transformers. V is the quantity of IGBT2 modules. Z is the quantity of secondary side capacitors.

In the third module, the IPOS module, multiple BFBIC modules are connected in a series-parallel configuration. If any of the BFBIC modules fail, it will result in the entire IPOS module becoming non-functional. The reliability model of the IPOS module is shown below.

In this formula, λIPOS and µIPOS respectively represent the failure rate and repair rate of the IPOS module. TBFBICMTTR represents the mean time to repair of the BFBIC module. θ represents the quantity of BFBIC modules.

In the second module, the IPOP module, multiple IPOS modules are connected in parallel to achieve high-power applications of the DC/DC converter. The standby probability model is as follows.

In this formula, λIPOP and µIPOP respectively represent the failure rate and repair rate of the IPOP module. TIPOSMTTR represents the mean time to repair of the IPOS module. \(\varpi\) represents the quantity of IPOS modules.

In the first module, the DC/DC converter, the hardware main circuit system and the software control system are in a series logic relationship. If either system fails, the entire DC/DC converter cannot operate properly. Since the reliability of the DC/DC converter primarily depends on the hardware main circuit and its connections, and the reliability of its control system is difficult to quantify, this paper ignores the impact of the software control system on the equipment’s reliability when evaluating the reliability of the DC/DC converter. Only the influence of the hardware main circuit on the reliability of the DC/DC converter is considered. The reliability model is shown below.

In the formula, λDC/DC and µDC/DC respectively represent the failure rate and repair rate of the first module, the DC/DC converter. TIPOPMTTR represents the mean time to repair of the IPOS module. β represents the quantity of IPOP modules.

The fault types in the wind power DC collection system are diverse, the system structure is complex, fault identification and location are difficult, and DC circuit breakers are difficult to act quickly in the first time. Therefore, in practical applications, DC circuit breakers should have strong breaking ability, surge current carrying capacity, etc. Due to the advantages of compact devices, low losses, fast breaking speed, and high breaking capacity, hybrid DC circuit breakers22,23 are suitable for wind power DC collection systems with diverse fault types and complex system structures. Its topology is shown in Fig. 7.

Topology structure of hybrid DC circuit breaker.

The reliability model constructed using the reliability block diagram method is shown in Fig. 8.

Reliability diagram of hybrid DC circuit breaker.

As can be seen from the reliability block diagram of the aforementioned hybrid DC circuit breaker, its reliability model is shown below.

In the formula, λDCCB represents the failure rate of the hybrid DC circuit breaker. µDCCB represents the repair rate of the hybrid DC circuit breaker. λRLC represents the failure rate of the current-limiting reactor. λFD represents the failure rate of the mechanical switch. λADB represents the failure rate of the auxiliary switch. λTB represents the failure rate of the transfer branch IGBT module. λMOV represents the failure rate of the surge protective device; TRLCMTTR represents the mean time to repair of the current-limiting reactor. TFDMTTR represents the mean time to repair of the mechanical switch. TADBMTTR represents the mean time to repair of the auxiliary switch. TTBMTTR represents the mean time to repair of the transfer branch IGBT module. TMOVMTTR represents the mean time to repair of the surge protective device.

Based on the aforementioned topology of the wind power DC collection system and the construction of reliability models for key equipment, this section will use the multilevel fault tree method to establish fault tree models for different top events, laying the foundation for improving the computational efficiency of the Sequential Monte Carlo method in subsequent sections.

Fault Tree Analysis (FTA)24,25 is a graphical deductive method that starts from system failures, analyzes events in reverse chronological order according to causal relationships, and ultimately identifies the causes of failures. The mathematical expression of fault trees typically uses structure functions under the assumption of mutual independence between basic events and that system elements or components have only two states: normal and failure.

Assuming a fault tree is composed of n basic events, the structure function of an event is defined as X=(x1, x2, …, xn), where xi represents the state variable of the i-th basic event, and Ф represents the state variable of the top event. Based on the assumption conditions, the basic events xi and the top event Ф are only in two states, 0 and 1, defined as follows:

The state Ф of the top event in the fault tree entirely depends on the states of each basic event xi. This function, Ф=Ф(X)=Ф(x1, x2, …, xn), is called the structure function of the fault tree. The structure function primarily combines basic events through logic gates to describe the system’s failure states. A simple fault tree model is shown in Fig. 9, with event symbols, logic gates, and mathematical expressions detailed in Table 1.

Fault tree model.

As mentioned earlier, the essence of the fault tree construction process is to investigate the logical relationships between system failures and the factors that lead to these failures. This is achieved by representing these relationships using event symbols and logic gate symbols in a tree diagram. However, when constructing a fault tree for a wind power DC collection system, the large number of components and the complex structure can make it difficult to build a mathematical model of the system, leading to a significant decrease in computational efficiency. In this context, this section proposes the Multi-level Fault Tree Method, which not only simplifies the fault tree model of the wind power DC collection system layer by layer but also provides data support for improving the computational efficiency of subsequent SMC methods.

The multi-level of a fault tree refers to the decomposition and combination of fault events into multiple hierarchical structures within the fault tree analysis method. Each level consists of a top event and a set of intermediate events or basic events that cause other faults, as well as logical gate combinations that lead to the occurrence of the top event. These levels can be connected together to form a complete fault tree.

This section divides the multi-level structure of the fault tree into the following levels:

Level 1 Fault Tree: This level includes the top event of Level 1, the basic events that directly cause the top event, and the intermediate events that cause other faults.

Level 2 Fault Tree: This level includes the top event of Level 2, the basic events that directly cause the top event, and the intermediate events that cause other faults.

Higher-level Fault Trees: This level includes the top event corresponding to higher levels, the basic events that directly cause the top event, and the intermediate events that cause other faults.

Based on the above, taking the fault tree model in Fig. 9 as an example, this section divides it into a multi-level fault tree model, as shown in Fig. 10.

Multi-level fault tree model.

The fault propagation principle of the multi-level fault tree model refers to the process in fault tree analysis where fault events are transmitted and propagated from one level to another through combinations of logical gates. The mathematical description of this process, using Fig. 10 as an example, is as follows.

The third level fault tree

The second level fault tree

The first level fault tree

Considering the existence of different basic/intermediate events in different levels of fault trees, these events are not equally important in the system. For example, some basic/intermediate events may cause system failure once they occur, while others may not. Therefore, this section proposes a comprehensive importance model, which takes into account structural importance, probability importance, and critical importance26, to measure the impact of basic/intermediate events on the occurrence of the top event. This enables the identification of weak links and the development of improvement designs and maintenance optimization plans.

Structural importance refers to the significance of each basic/intermediate event in the fault tree structure, determined by the position of the basic/intermediate event in the fault tree. It is independent of the failure probability of the basic/intermediate event itself. The mathematical expression for different logical gates is as follows:

In the formula, \({I_{{\text{AND}}}}\left( {{x_i}} \right)\) represents the structural importance of basic/intermediate event xi under an AND gate. \({I_{{\text{OR}}}}\left( {{x_i}} \right)\) represents the structural importance of basic/intermediate event xi under an OR gate. \({I_{{\text{VOT}}}}\left( {{x_i}} \right)\) represents the structural importance of basic/intermediate event xi under a voting gate. \({m_i}\) represents the number of basic events xi in the minimal cut set E. H represents the number of minimal cut sets. p represents the number of combinations for the voting gate.

Probability importance is the degree to which a change in the probability of occurrence of a basic/intermediate event xi (corresponding to the unreliability of the unit) causes a change in the occurrence rate of the top event (system unreliability), expressed mathematically as:

In the formula, \(\Delta {g_{{\text{AND}}{x_i}}}\left( t \right)\) represents the probability importance of the basic/intermediate event xi under an AND gate. \(\Delta {g_{{\text{OR}}{x_i}}}\left( t \right)\) represents the probability importance of the basic/intermediate event xi under an OR gate. \(\Delta {g_{{\text{VOT}}{x_i}}}\left( t \right)\) represents the probability importance of the basic/intermediate event xi under a voting gate. \({F_{{x_i}}}\left( t \right)\) represents the occurrence probability of the basic/intermediate event xi. \({F_{{x_{i+1}}}}\left( t \right)\) represents the occurrence probability of the basic event xi+1. \({F_s}\left( t \right)\) represents the occurrence probability of the top event.

Critical importance refers to the degree of change in the occurrence probability of the top event caused by the probability change of the basic/intermediate event xi. Its mathematical expression is:

In the formula, \(I_{{{\text{AND}}{x_i}}}^{{{\text{CR}}}}\left( t \right)\) represents the critical importance of the basic/intermediate event xi. \(I_{{{\text{OR}}{x_i}}}^{{{\text{CR}}}}\left( t \right)\) represents the critical importance of the basic/intermediate event xi. \(I_{{{\text{VOT}}{x_i}}}^{{{\text{CR}}}}\left( t \right)\) represents the critical importance of the basic/intermediate event xi.

Comprehensive importance refers to the contribution of the basic/intermediate event xi to the occurrence of the top event, taking into account the structural importance, probability importance, and critical importance. Its mathematical expression is:

In the formula, CI represents the comprehensive importance of the basic/intermediate event xi. α, β, and γ represent the weights for the structural importance, probability importance, and critical importance, respectively. Operators can adjust these weights based on their own priorities. In this case, all weights are set to 1/3 in this document.

With the development of DC collection technology, the issue of computational complexity is bound to become the biggest obstacle in the reliability assessment of wind farm DC collection systems. Although the aforementioned fault tree analysis method can use rigorous mathematical models and effective algorithms for system reliability calculations, it has high accuracy. However, the computational complexity increases exponentially with the number of components, resulting in a sharp contradiction between calculation accuracy and time. Therefore, Monte Carlo simulation method, with its advantage of convergence speed independent of system size, determines its applicability in solving multidimensional problems. In order to formulate reasonable maintenance strategies and decisions for subsequent wind farm DC collection systems, this section adopts the SMC method for reliability assessment.

The basic principle of SMC method27,28 is to first simulate the random process of the system’s temporal operation, forming a random sequence of system states over a certain time span, and then analyze the system state and calculate reliability indicators. For the DC collection system of wind power, the calculation process is as follows:

Specify the initial state of all components in the wind power DC collection system, typically assuming that all components are initially in operating condition.

Treat internal components as two-state units that continuously switch between operating and fault conditions. The working time t1 and repair time t2 are used to describe the duration of each component in different states. It is generally assumed that both the working and repair times follow exponential distributions. Through sampling, the temporal state distributions of each component can be obtained as follows:

In the formula, λ and µ represent the failure rate and repair rate of the component, respectively. γ is a random number that follows a uniform distribution in the range [0,1].

Repeat step 2 over the studied time span (a large number of sampled years) and record the sampled duration of each state for all components. This will yield the temporal state transition process for each component within the given time span. Combine the state transition processes of all components to establish the system’s temporal state transition cycle, as shown in Fig. 11.

System timing state transition loop process.

Perform a system analysis for each different system state to calculate reliability metrics. During the evaluation process, assume that the output of the units and the load power remain constant for each hourly period throughout the year. Reliability metrics can be statistically calculated using the following formula.

Let x represent any reliability indicator, with the number of simulations denoted as Nn. If xδ denotes the reliability indicator obtained from sampling in the δ year for the wind farm collection system, then the sample mean is calculated as follows29:

Although the Monte Carlo simulation method is widely favored for its simplicity and efficiency in assessing the reliability of systems with numerous components and complex structures, the random sampling of component sequences in Monte Carlo simulations leads to a noticeable increase in the time required for evaluating each system state as the system size grows. Consequently, the computational efficiency of this method significantly decreases. To address this issue, this section proposes a reliability assessment method for wind farm DC collection systems based on MLFTA-SMC. This method aims to enhance simulation convergence speed while reducing the time required for each state assessment.

By combining the MLFTA method to establish fault tree models for different top events and utilizing SMC method, a reliability assessment model for wind farm DC collection systems is developed. The specific steps are as follows:

Step 1: Input the failure rates, repair rates, and topological structure of components such as wind turbines and cables in the wind farm DC collection system.

Step 2: Construct fault tree models for different top events using the MLFTA method and calculate the integrated importance of different basic events within the same level of fault trees.

Step 3: Use the SMC method to sample the duration of states for each component in the aforementioned wind farm DC collection system.

Step 4: Rank the different components based on the integrated importance from the MLFTA method and downgrade each system state according to the ranking results.

Step 5: Calculate the reliability indicators for the wind farm DC collection system.

Step 6: Determine if the specified evaluation period NR for the reliability assessment of the wind farm DC collection system has been reached. If yes, output the reliability indicators. If not, return to Step 3.

In conclusion, the reliability assessment process for the wind farm DC collection system can be summarized as shown in Fig. 12.

Reliability assessment model of wind power DC collection system based on MLFTA-SMC.

Considering that the wind farm DC collection system is a unit of the power generation side, greater attention should be paid to its operational status, equipment reliability, and power supply capability. Therefore, this section formulates corresponding reliability indicators to quantitatively describe the reliability of the system, in order to provide some reference value for the formulation of maintenance plans, and thus improve the overall reliability level of the wind farm DC collection system.

Energy Availability (EA).

In the formula, TTE represents the rated energy that the wind farm DC collection system can deliver within the statistical time period. Pm represents the rated power of the wind farm DC collection system during the statistical time period. PH represents the number of hours in the statistical period.

Expected Value of Power Loss (EVPL).

In the formula, Y represents the set of system outage states within the given time range. Cy represents the power loss during the statistical time period. Dy represents the duration of state y during the statistical time period.

Loss of Load Probability (LOLP).

In the formula, LOLPWF, LOLPDCDCF, LOLPCLF, LOLPDCCBF, and LOLPCBF respectively represent the probability of power output blockage caused by wind turbine generator failure, DC/DC converter failure, collector line failure, hybrid DC circuit breaker failure, and collector bus failure. Tall represents the given time range. s represents the set of cut-off states within the given time range. ti, WF, ti, DCDCF, ti, CLF, ti, DCCBF, and ti, CBF respectively represent the duration of the cut-off state caused by the failure of wind turbine generator with DC output, DC/DC converter, collector line, hybrid DC circuit breaker, and collector bus.

Loss of Load Expectation (LOLE).

In the formula, LOLEWF, LOLEDCDCF, LOLECLF, LOLEDCCBF, and LOLECBF respectively represent the expected time of power output blockage caused by wind turbine generator failure, DC/DC converter failure, collector line failure, hybrid DC circuit breaker failure, and collector bus failure. s represents the set of cut-off states within the given time range. ti, WF, ti, DCDCF, ti, CLF, ti, DCCBF, and ti, CBF respectively represent the duration of the cut-off state caused by the failure of wind turbine generator with DC output, DC/DC converter, collector line, hybrid DC circuit breaker, and collector bus.

Expected Energy Not Served (EENS).

In the formula, EENSWF, EENSDCDCF, EENSCLF, EENSDCCBF, and EENSCBF respectively represent the expected blocked power caused by wind turbine generator failure, DC/DC converter failure, collector line failure, hybrid DC circuit breaker failure, and collector bus failure. Ci,WF, Ci,DCDCF, Ci,CLF, Ci,DCCBF, and Ci,CBF respectively represent the amount of cuts caused by the failure of wind turbine generator with DC output, DC/DC converter, collector line, hybrid DC circuit breaker, and collector bus. Fi,WF, Fi,DCDCF, Fi,CLF, Fi,DCCBF, and Fi,CBF respectively represent the frequency of cuts caused by the failure of wind turbine generator with DC output, DC/DC converter, collector line, hybrid DC circuit breaker, and collector bus. ti,WF, ti,DCDCF, ti,CLF, ti,DCCBF, and ti,CBF respectively represent the duration of cuts caused by the failure of wind turbine generator with DC output, DC/DC converter, collector line, hybrid DC circuit breaker, and collector bus.

In this paper, a wind power collector system with a total installed capacity of 100 MW is taken as an example. The structural parameters of the system are shown in Table 2. The reliability data of the main components of the wind power DC collector system are referenced from30,31,32, as shown in Tables 3 and 4.

To verify the efficiency of the MLFTA-SMC reliability assessment method, we take the parallel DC collector system topology as an example and compare MLFTA-SMC (Scheme 1), Scheme 2, and Scheme 3. In Scheme 2, the SMC method is used to assess the reliability of the DC collector system. Scheme 3 involves using the reliability block diagram method to equivalently represent the DC collector system as a power generation system, followed by reliability assessment using the SMC method. With a simulation count of 100, the comparative results are shown in Tables 5 and 6.

According to Table 5, it can be observed that compared to the evaluation system states of Scheme 2, Scheme 1 using the reliability assessment method reduces the evaluation system states by 3890 and 3912, respectively. This clearly demonstrates that Scheme 1 (the method proposed in this paper) decomposes the fault tree into multiple levels, breaking down complex fault tree problems into smaller and more manageable sub-problems. Through the integration of importance measures, higher-order fault events are transformed into lower-order fault events. This approach not only reduces the complexity of the fault tree but also decreases the number of evaluation system states, thereby improving evaluation efficiency.

According to Table 6, it is evident that the reliability indicators obtained using the methods proposed in Scheme 3 for calculating the reliability of the two topological structures are significantly better than the reliability indicators obtained using the methods in Scheme 1. The reason behind this can be attributed to the simplification of the wind farm DC collection system into an equivalent power source in Scheme 1. Typically, it is assumed that each component has an independent and identical failure rate, and failures are mutually independent. This assumption overlooks the complexity present in actual systems, such as interdependencies among components, shared resources, communication networks, etc. In reality, in wind farm DC collection systems, there exist complex topological structures and interactions among various components like individual DC output wind turbines, DC/DC converters, hybrid DC circuit breakers, collection lines, etc. Failures in one component may affect and propagate to others. Compared to this, reliability indicators calculated considering the topological structure would be more accurate as this method fully considers the interdependencies and propagation effects among components. By establishing the topological structure model of the system, factors like inter-component dependencies can be analyzed more accurately, leading to a more precise assessment of system reliability. This approach provides more accurate reliability indicators, aiding engineers and decision-makers in better understanding the reliability level of wind farm DC collection systems and implementing corresponding improvement and optimization measures.

Parallel topology.

Using a multi-level fault tree method to hierarchically reduce the order of the parallel collection system’s topological structure, as shown in Fig. 13.

Multi-level fault tree model of parallel collector system topology structure.

Based on the aforementioned multi-level fault tree model, the integrated importance of different basic/intermediate events in the parallel collection system’s topological structure can be obtained, as shown in Table 7.

From Table 7, it can be seen that the integrated importance of basic/intermediate events under different top events in different hierarchical fault tree structures of the parallel collection system’s topology. Analyzing the data in Table 7 shows that: (1) Intermediate events are paths that lead to the occurrence of the top event by combining or logically operating basic events. Therefore, the integrated importance of intermediate events expresses the degree of “contribution” of the path to the system failure, which is the comprehensive importance of the path. Taking the top event in the second level fault tree as Parallel wind turbine cluster 1 fault M3, the integrated importance of intermediate events for fault M3 is ranked as Hybrid DC circuit breaker fault M8 > Complete turbine fault M7 > Feeder line fault M9. This indicates that the path of Hybrid DC circuit breaker fault M8 contributes the most to the Parallel wind turbine cluster 1 fault M3. Taking the top event in the first level fault tree as the Parallel type collection system topology fault MM, the integrated importance of intermediate events for fault MM is ranked as The wind turbines in all parallel clusters fault M2 > Collector bus fault M1. This indicates that the path of The wind turbines in all parallel clusters fault M2 contributes the most to the Parallel type collection system topology fault MM. (2) Basic events refer to specific fault events. By calculating the integrated importance of basic events, the impact of the basic event on the overall system reliability can be determined. Taking the top event in the third level fault tree as the Turbine 1 fault M19 as an example, the integrated importance ranking of basic events for the top event Turbine 1 fault M19 is DC/DC converter fault x20 > Wind turbine fault x19, indicating that the DC/DC converter fault has the greatest impact on the Turbine 1 fault M19. Taking the top event in the second level fault tree as the fault M3 of the parallel wind turbine cluster 1 as an example, the integrated importance ranking of basic events for the top event Parallel wind turbine cluster fault 1 M3 is Hybrid DC circuit breaker 1 fault x3 = Hybrid DC circuit breaker 2 fault x4 > Feeder line 1 fault x5 = Feeder line 2 fault x6 > Turbine 1 fault M19 = Turbine 2 fault M20 = Turbine 3 fault M21 = Turbine 4 fault M22 = Turbine 5 fault M23, indicating that the Hybrid DC circuit breaker fault has the greatest impact on the fault M3 of the parallel wind turbine cluster 1. Analyzing the top event in the first level fault tree as the Parallel type collection system topology fault MM, the integrated importance ranking of basic events for the top event Parallel type collection system topology fault MM is Collector bus 1 fault x1 = Collector bus 2 fault x2 > Parallel wind turbine cluster 1 fault M3 = Parallel wind turbine cluster 2 fault M4 = Parallel wind turbine cluster 3 fault M5 = Parallel wind turbine cluster 4 fault M6, indicating that the faults of collector bus have the greatest impact on the Parallel type collection system topology fault MM.

Series-parallel topology.

Using the multi-level fault tree method to hierarchically reduce the complexity of the series-parallel configuration of the collection system’s topology. Within each series-parallel wind turbine cluster, a maximum of 2 faulty wind turbine units is allowed, with the withstand voltage level of the wind turbines being 1.5 times33. The results are shown in Fig. 14.

Multi-level fault tree model of series-parallel collector system topology structure.

Based on the aforementioned multi-level fault tree model, the integrated importance of different events/intermediate events in the series-parallel configuration of the collection system’s topology can be obtained. The results are shown in Table 8.

The comprehensive importance of basic/intermediate events in different hierarchical fault trees of series-parallel wind farm collector system topology can be inferred from Table 8. Analysis of the data in Table 8 reveals the following: (1) Taking the Series-parallel wind turbine cluster 1 fault M3 as an example for analysis with the top event in the second layer fault tree, the intermediate event comprehensive importance ranking for Series-parallel wind turbine cluster 1 fault M3 is as follows: Hybrid DC circuit breaker fault M9 > Complete turbine fault M8 > feeder fault M10. This indicates that the path with Hybrid DC circuit breaker fault M9 contributes the most to Series-parallel wind turbine cluster 1 fault M3. Taking the top event in the first layer fault tree as the fault MM of parallel collector system topology for analysis, the intermediate event comprehensive importance ranking for series-parallel collector system topology structure fault MM is as follows: The wind turbines in all series-parallel wind turbine clusters fault M2 > Collector bus fault M1. This indicates that the path with The wind turbines in all series-parallel wind turbine clusters fault M2 contributes the most to series-parallel collector system topology structure fault MM. (2) Analyzing the top event Turbine 1 fault M23 in the third layer fault tree, the comprehensive importance ranking of basic events for the top event Turbine 1 fault M23 is as follows: DC/DC converter fault x24 > Wind turbine fault x23. This indicates that the impact of DC/DC converter fault x24 on Turbine 1 fault M23 is the greatest. Analyzing the top event Series-parallel wind turbine cluster 1 M3 in the second layer fault tree, the comprehensive importance ranking of basic events for the top event Series-parallel wind turbine cluster 1 M3 is as follows: Hybrid DC circuit breaker 1 fault x3 = Hybrid DC circuit breaker 2 fault x4 > feeder 1 fault x5 = feeder 2 fault x6 > Turbine 1 fault M23 = Turbine 2 fault M24 = Turbine 3 fault M25 = Turbine 4 fault M26. This indicates that the impact of hybrid DC circuit breaker fault is the greatest on fault M3 of series-parallel wind turbine cluster 1. Analyzing the top event series-parallel collector system topology structure fault MM in the first layer fault tree, the comprehensive importance ranking of basic events for the top event fault MM of parallel collector system topology is as follows: Collector bus 1 fault x1 = Collector bus 2 fault x2 > Series-parallel wind turbine cluster 1 fault M3 = Series-parallel wind turbine cluster 2 fault M4 = Series-parallel wind turbine cluster 3 fault M5 = Series-parallel wind turbine cluster 4 fault M6 = Series-parallel wind turbine cluster 5 fault M7. This indicates that the impact of collector bus faults is the greatest on fault in series-parallel collector system topology structure MM.

In this section, the MLFTA-SMC method was used to evaluate the reliability of parallel/series-parallel wind power DC collection systems, and the evaluation results are shown in Table 9.

According to Table 9, the reliability of the parallel topology structure is better than that of the series-parallel topology structure. The analysis reveals that in the parallel topology structure, the paths and components are independent of each other. Therefore, when a fault occurs, it only affects the specific path or component, while the other paths and components can still operate normally. This distributed fault characteristic allows the parallel topology structure to tolerate failures in individual paths or components, thereby improving the overall system’s reliability. In contrast, in the series-parallel topology structure, although the overvoltage limit of the DC/DC converter is considered, if the number of faulty turbines within any series-parallel wind turbine cluster exceeds or equals 2, the entire series-parallel wind turbine cluster will be paralyzed. Additionally, compared to the parallel topology structure, in this topology structure, each series-parallel wind turbine cluster consists of 4 DC output-type wind turbine units and DC/DC converters. While this mitigates the impact of a single series-parallel wind turbine cluster failure on the overall system reliability, the number of hybrid DC circuit breakers and Feeder lines within the parallel wind turbine cluster is higher than that in the parallel topology structure. This increases the probability of power output obstruction and the amount of obstructed power in the collection system when a failure occurs in these devices or components, resulting in lower reliability.

It is worth noting that in both of the above topology structures, the probability, expected value of power output obstruction time, and expected value of obstructed power output caused by collector bus failure are all 0. However, the collector bus is an important component of the wind power DC collection system, responsible for collecting the electrical energy from each wind turbine. When the collector bus fails, it may lead to the paralysis of the entire wind power DC collection system, severely affecting the system’s reliability. Therefore, although the reliability results caused by collector bus failure are 0, it is still necessary to take such failures seriously and implement appropriate preventive measures and emergency response measures to ensure the reliable operation of the wind power DC collection system.

This paper proposes a reliability assessment method for wind power DC collection system based on MLFTA-SMC. Based on the simulation results, the following conclusions can be drawn:

Compared to the method of evaluating the reliability of the DC collection system using SMC, the proposed MLFTA-SMC-based reliability assessment method in this paper reduces the number of evaluations by 3890 and 3912 times, respectively. This method effectively reduces the number of evaluated system states and improves evaluation efficiency.

Compared to the method of using reliability block diagram to treat the DC collection system as a power generation system and evaluating its reliability using SMC, the proposed MLFTA-SMC-based reliability assessment method in this paper takes into account the dependencies between components and other factors when evaluating the reliability of wind power DC collection systems. This enables a more accurate assessment of system reliability, helping decision-makers better understand the reliability level of wind power DC collection systems and take appropriate improvement and optimization measures.

The comprehensive importance index proposed in this paper fully considers structural importance, probability importance, and critical importance, measuring the impact of basic/intermediate events on the occurrence of top events. This helps identify weak links and improve design and maintenance optimization plans.

There are still some limitations in this study. The influence of economics on the reliability of wind power DC collection systems has not been considered. In future research, the reliability and economics of different topology structures of wind power DC collection systems should be comprehensively compared and analyzed.

The datasets used and/or analyzed during the current study are available from the first author upon reasonable request. (First author E-mail address: [email protected])

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This work was supported in part by Tianshan Talent Training Program (2022TSYCLJ0019), Excellent doctoral student innovation project at Xinjiang University (XJU2023BS057).

School of Electrical Engineering, Xinjiang University, Urumqi, 830000, China

Xueyan Bai, Yanfang Fan & Junjie Hou

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Xueyan Bai: Writing – original draft, Conceptualization, Formal analysis, Methodology, Software, Writing - review & editing. Yanfang Fan: Resources, Supervision, Writing - review & editing. Junjie Hou: Supervision, Writing - review & editing. All authors reviewed the manuscript.

Correspondence to Yanfang Fan.

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Bai, X., Fan, Y. & Hou, J. Reliability assessment method of wind power DC collection system based on MLFTA-SMC. Sci Rep 14, 25341 (2024). https://doi.org/10.1038/s41598-024-76570-z

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Received: 03 September 2024

Accepted: 15 October 2024

Published: 25 October 2024

DOI: https://doi.org/10.1038/s41598-024-76570-z

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