Fault reconstruction method and system for ship medium-voltage direct-current power system

Abstract

The invention discloses a ship medium-voltage DC power system fault reconstruction method and system, and the method comprises the steps: constructing a node-branch diagram based on a topological structure of a power system, and constructing an extended incidence matrix based on the node-branch diagram through a graph theory; detecting the connectivity of each node and each branch in the node-branch diagram in real time, and updating a detection result to the extended incidence matrix; determining a fault area of the power system based on abrupt change elements in the extended incidence matrix, and isolating the fault area; based on the extended incidence matrix, taking the fault branch as a starting point and taking the branch with connectivity as an end point, and constructing a power supply recovery path set; constructing a multi-target fault reconstruction model by taking the maximum load recovery and generator operation efficiency and the minimum switching frequency as target functions and taking the power system operation constraint as a constraint condition; solving the recovered power supply path set by using an improved SABPSO algorithm in combination with the multi-target fault reconstruction model to obtain a reconstruction scheme; a reconstruction scheme is performed in the power system.

Description

Technical Field

[0001] This invention relates to the field of fault reconfiguration technology for ship medium-voltage DC power systems, and particularly to a fault reconfiguration method and system for ship medium-voltage DC power systems. Background Technology

[0002] Shipboard electrical systems are evolving from traditional medium-voltage AC systems to medium-voltage direct current (MVDC) systems. With their core technological advantages such as high energy transmission efficiency, superior space utilization, and low life-cycle cost, MVDC systems have become a core development direction for modern ship propulsion systems, including military destroyers and large research vessels. However, in actual operation, electrical faults (such as short circuits or open circuits) in MVDC systems directly threaten the system's viability and operational reliability. This can lead to the shutdown of critical equipment and power outages, and in severe cases, even system-wide collapse, posing a significant threat to the safety of personnel and navigation. Therefore, research on fault reconfiguration technology for shipboard MVDC systems is an urgent practical need.

[0003] The core of ship MVDC system fault reconfiguration is to maximize the restoration of power supply to important loads while ensuring the safety requirements of MVDC system operation, by adjusting the power distribution topology when faults such as short circuits or open circuits occur in the system, under the premise of meeting the operating constraints of MVDC system. Currently, existing technical solutions still face several bottlenecks that urgently need to be overcome: First, traditional topology identification methods cannot provide real-time feedback on the circuit breaker switch status, which can easily lead to delays or misjudgments in fault location, affecting reconfiguration efficiency. Second, most existing reconfiguration methods have a single objective, focusing only on "maximizing load recovery" without considering "minimizing the number of switching operations" and "generator load balancing," which can easily lead to increased switching losses or generator overload. Third, the core algorithms have performance limitations. The Discrete Binary Particle Swarm Optimization (BPSO) algorithm is prone to getting stuck in local optima, the Simulated Annealing (SA) algorithm converges slowly, and existing hybrid algorithms (such as SA-BPSO) lack the ability to balance global search and local optimization, making it difficult to adapt to complex fault scenarios. Fourth, there is insufficient scenario adaptability. For the unique "generator-branch-load" combined fault scenario of ship MVDC systems, existing methods lack targeted reconfiguration strategies, making it difficult to meet the actual operational requirements in terms of the completeness and adaptability of fault recovery solutions. Summary of the Invention

[0004] To address the problems of slow fault information extraction, singular reconstruction objectives, susceptibility to local optima, and poor scenario adaptability in existing technologies, this invention proposes a fault reconstruction method for shipboard medium-voltage DC power systems. This method enables rapid and accurate extraction of fault information and location of the fault region. Based on this, a multi-objective optimization reconstruction scheme is implemented to maximize the recovery of critical loads, minimize the number of switching operations, and ensure generator load balancing. Furthermore, the core algorithm effectively avoids getting trapped in local optima by improving global search capabilities and convergence speed, thus flexibly adapting to various complex fault scenarios and ultimately outputting a safe and reliable complete power restoration solution. This invention also relates to a fault reconstruction system for shipboard medium-voltage DC power systems.

[0005] The technical solution of the present invention is as follows:

[0006] A fault reconfiguration method for a ship's medium-voltage DC power system includes the following steps:

[0007] The steps for establishing the extended correlation matrix are as follows: Based on the topology of the ship's medium-voltage DC power system, generators, main switchboards, and port and starboard connecting buses are used as main nodes, regional switchboards as child nodes, loads as load nodes, and circuit breakers as branches. A node-branch graph is constructed together, and using graph theory, an extended correlation matrix is ​​built based on the node-branch graph. The node-branch graph reflects the real-time operating status of the ship's medium-voltage DC power system, and the elements of the extended correlation matrix represent the connectivity between each node and each branch in the node-branch graph. For the node-branch graph, a tree search algorithm is used in real-time to traverse the main nodes and child nodes sequentially and verify the load nodes in reverse. The connectivity between each node and each branch is detected, and the detection results are updated to the extended correlation matrix in real time.

[0008] Fault inspection and information extraction steps: If an element in the extended correlation matrix undergoes a sudden change, the fault area information of the ship's medium-voltage DC power system is determined based on the mutated element and its corresponding value. The fault area information includes the fault branch and the power failure node; the circuit breaker corresponding to the fault branch is disconnected to isolate the fault area.

[0009] Power restoration path construction steps: Based on the extended correlation matrix, starting from the faulty branch and ending at the branch with connectivity, construct a set of alternative power restoration paths for the power-out node;

[0010] The steps for establishing a multi-objective fault reconfiguration model are as follows: The loads are divided into primary, secondary, and tertiary loads according to their importance. Each level of load is discretized into several extended loads. Each primary and secondary extended load includes a normal power supply path and a backup power supply path, while each tertiary extended load only includes a normal power supply path. A multi-objective function is constructed with the objectives of maximizing load recovery, minimizing the number of switching operations, and maximizing generator operating efficiency. The constraints are that each primary and secondary extended load has only one power supply path, the generator capacity is greater than the total capacity of the connected loads, and the line node capacity is less than the maximum line capacity threshold. This forms the basis for the multi-objective fault reconfiguration model.

[0011] The optimal recovery path solution steps are as follows: An improved SABPSO algorithm, derived from a hybrid improvement of the Discrete Binary Particle Swarm Optimization (DPI) algorithm and the Simulated Annealing (SANA) algorithm, is used to solve for the optimal path in the set of candidate power restoration paths. The improved SABPSO algorithm retains the discrete optimization characteristics of the DPI and the global optimization characteristics of the SANA algorithm, and optimizes the global optimal solution selection by adjusting the particle search step size through adaptive inertia weights and combining a roulette wheel selection mechanism. During the solution process, fitness is calculated using the multi-objective function in the multi-objective fault reconstruction model, with each level of extended load as the dimension. Under the condition that the constraints in the multi-objective fault reconstruction model are satisfied, the optimal recovery path is obtained as the fault reconstruction scheme.

[0012] Fault reconfiguration scheme execution steps: Based on the fault reconfiguration scheme, generate switching commands and execute them in the ship's medium-voltage DC power system.

[0013] Preferably, in the extended correlation matrix establishment step, the main distribution board included in the main node is divided into a main distribution node and a secondary distribution node, and the area distribution board included in the child node is a load distribution node; wherein, the main distribution board directly connected to the generator main node is the main distribution node, and the main distribution board not directly connected to the generator main node is the secondary distribution node;

[0014] The steps for detecting the connectivity of each node and branch by using a tree search algorithm to traverse the master node and child nodes in real time and verify the load node in reverse for the node-branch graph include: First, for the node-branch graph, a breadth-first search algorithm is used in real time to traverse the adjacent main distribution nodes of each generator master node; second, a depth-first search algorithm is used to traverse the main distribution nodes, secondary distribution nodes, load distribution nodes and corresponding branches layer by layer from each generator master node to establish node-branch connectivity relationships until the load node or the last level of the secondary distribution node is reached; then, for each load node found, the algorithm is used to backtrack layer by layer from the load node back to the generator master node, and the connectivity information of each node and branch is obtained by combining the node-branch connectivity relationships.

[0015] Preferably, in the fault inspection and information extraction step, whether the ship's medium-voltage DC power system has a fault is determined by whether there is a sudden change in the elements in the extended correlation matrix;

[0016] If an element in the extended correlation matrix undergoes a mutation, the faulty branch is determined based on the mutated element and its corresponding value.

[0017] For each generator master node, the state of the generator master node is determined based on the values ​​of all elements in the corresponding column of the generator master node in the extended correlation matrix. If the values ​​of all elements are 0, the generator master node is de-energized; if at least one element has a value that is not 0, the generator master node is functioning normally.

[0018] For each load node, all elements in the row corresponding to the load node are determined in the extended correlation matrix, and the cross elements in the column corresponding to each generator node are selected from these elements. If the value of all cross elements is 0, the load node is de-energized; if at least one cross element has a value that is not 0, the load node is normal.

[0019] For each distribution board node formed by the main distribution board included in the main node and the regional distribution board included in the child node, the row and column corresponding to each distribution board node are determined in the extended correlation matrix. If the value of all elements in the row is 0, and the value of the intersection element of the column with the column corresponding to all generator main nodes is 0, then the distribution board node is de-energized; otherwise, the distribution board node is normal.

[0020] Preferably, in the multi-objective fault reconstruction model establishment step, the multi-objective function is as follows:

[0021] ,

[0022] ,

[0023] ,

[0024] ,

[0025] Where maxf represents the maximum value of a multi-objective function. With max This indicates maximizing load recovery. with min This indicates minimizing the number of switching operations. With max This indicates maximizing generator operating efficiency. Indicates the weighting coefficient. Indicates the priority coefficient. This indicates the power supply status of the i-th primary extended load. This indicates the power supply status of the j-th secondary extended load. This indicates the power supply status of the z-th tertiary extended load. This represents the load of the i-th level extended load. This represents the load of the j-th secondary extended load. Let represent the load of the z-th tertiary load extension, h represent the number of tertiary load extensions, k represent the number of tertiary load extensions, and m represent the number of tertiary load extensions. This indicates the state of the i-th level 3 extended load switch. This indicates the path switching status of the j-th primary or secondary load balancer, where l represents the total number of primary and secondary load balancers. Let represent the operating efficiency of the i-th generator, and n represent the total number of generators.

[0026] Preferably, in the multi-objective fault reconfiguration model establishment step, the constraint condition where only one power supply path is connected for the primary extended load and the secondary extended load is as follows:

[0027] ,

[0028] in, This indicates the normal power supply path for primary and secondary extended loads. This indicates the backup power supply path for primary and secondary extended loads;

[0029] The constraint that the generator capacity is greater than the total capacity of the connected load is as follows:

[0030] ,

[0031] in, This represents the capacity of the i-th generator. This represents the j-th load connected to the i-th generator, and m represents the total number of loads connected to the i-th generator.

[0032] The constraint that the capacity of a line node is less than the maximum threshold of the line capacity is as follows:

[0033] ,

[0034] in, Indicates the capacity of the line nodes. This indicates the maximum threshold for line capacity.

[0035] Preferably, the step of finding the optimal recovery path in the optimal recovery path solution step, which involves using the improved SABPSO algorithm to find the optimal path from the set of candidate power recovery paths, includes:

[0036] S1: Configure particle population size, maximum number of iterations, particle velocity range, initial temperature, cooling rate, and termination conditions;

[0037] S2: Within the velocity range of the particles, initialize the velocity of each particle; using each level of extended load as the dimension of each particle, and within the range of the alternative power restoration path set, initialize the position of each particle;

[0038] S3: Calculate the initial fitness of each particle using the multi-objective function, and take the initial fitness of each particle as the individual optimal fitness. Then, use the roulette wheel selection algorithm to select the individual optimal fitness with the highest probability from all individual optimal fitnesss as the global optimal fitness.

[0039] S4: Calculate the current fitness of each particle at the current temperature using the multi-objective function;

[0040] S5: For each particle, based on the individual optimal fitness, global optimal fitness, and adaptive inertia weight, update the velocity of each dimension of the particle to adjust the particle search step size; based on the updated velocity of each dimension of the particle, update the position of each dimension of the particle.

[0041] S6: Check whether each particle meets the constraints and remove particles that do not meet the constraints;

[0042] S7: For each particle that satisfies the constraints, the current fitness of each particle is compared with its individual optimal fitness according to the Metropolis criterion. It is then determined whether to select the current fitness as the new individual optimal fitness, and the current individual optimal fitness of each particle is finally determined. Based on the current individual optimal fitness of each particle, the current global optimal fitness is determined using the roulette wheel selection algorithm.

[0043] S8: Starting from the configured initial temperature, gradually reduce the current temperature according to the cooling rate;

[0044] S9: Determine if the configured termination condition is met. If not, return to step S4. If it is met, output the particle corresponding to the current global optimal fitness as the fault reconstruction scheme.

[0045] Preferably, in the optimal recovery path solution step, the velocity of each dimension of the particle is updated based on the individual optimal fitness, global optimal fitness, and adaptive inertia weight, as shown in the following formula:

[0046] ,

[0047] in, This represents the velocity of the i-th particle in the j-th dimension during the (t+1)-th iteration. This represents the velocity of the i-th particle in the j-th dimension during the t-th iteration. Indicates adaptive inertia weights, The individual learning factor of a particle. Represents the global learning factor. Represents a random number between [0, 1]. This represents the individual optimal fitness of the i-th particle in the j-th dimension during the t-th iteration. This represents the globally optimal fitness of the i-th particle in the j-th dimension during the t-th iteration. This represents the position of the i-th particle in the j-th dimension during the t-th iteration;

[0048] Based on the velocity of each dimension after the particle update, update the position of each dimension in the particle; if the extended load type corresponding to the dimension is the first-level extended load or the second-level extended load, then update the position of the dimension using the following formula:

[0049] ,

[0050] in, This represents the updated position of the i-th particle in the j-th dimension. Indicates the minimum speed threshold. The sigmoid function represents the maximum speed threshold and the probability function.

[0051] If the extended load type corresponding to the dimension is the third-level extended load, then the position of the dimension is updated using the following formula:

[0052] ,

[0053] Here, rand represents a random number between [0 and 1].

[0054] Preferably, in the optimal recovery path solution step, a linear adjustment strategy is used to determine the adaptive inertia weights, as shown in the following formula:

[0055] ,

[0056] in, This represents the adaptive inertia weight for the i-th iteration, where i represents the iteration number and ger represents the maximum number of iterations. This represents the maximum threshold of the adaptive inertia weight. This represents the minimum threshold for adaptive inertia weights.

[0057] Preferably, in the optimal recovery path solution step, the Metropolis criterion is as shown in the following formula:

[0058] ,

[0059] Where p represents the probability that the particle's current fitness is the new optimal fitness for that particle. This indicates the particle's current fitness. This represents the current optimal fitness of the particle. This represents the temperature during the i-th iteration;

[0060] If the current fitness of a particle is less than the individual optimal fitness, then the current fitness is taken as the new individual optimal fitness of the particle.

[0061] If the current fitness of the particle is greater than or equal to the individual's optimal fitness, then... The formula calculates the probability that the current fitness is the new optimal fitness of the particle.

[0062] Finally, a number between 0 and 1 is randomly generated. If the generated number is less than or equal to P, the current fitness is taken as the new optimal fitness of the particle. If the generated number is greater than P, the optimal fitness of the particle is not changed.

[0063] A fault reconfiguration system for a ship's medium-voltage DC power system includes, in sequence, an extended correlation matrix establishment module, a fault detection and information extraction module, a power restoration path construction module, a multi-objective fault reconfiguration model establishment module, an optimal restoration path solution module, and a fault reconfiguration scheme execution module.

[0064] The extended correlation matrix establishment module is used to construct a node-branch graph based on the topology of the ship's medium-voltage DC power system. This graph uses generators, main switchboards, and port and starboard connecting buses as main nodes, area switchboards as child nodes, loads as load nodes, and circuit breakers as branches. Graph theory is then used to construct an extended correlation matrix based on this graph. The node-branch graph reflects the real-time operating status of the ship's medium-voltage DC power system, and the elements of the extended correlation matrix represent the connectivity between each node and branch in the node-branch graph. For the node-branch graph, a tree search algorithm is used in real-time to traverse the main nodes and child nodes sequentially and verify the load nodes in reverse. The connectivity of each node and branch is detected, and the detection results are updated to the extended correlation matrix in real-time.

[0065] The fault detection and information extraction module: if an element in the extended correlation matrix undergoes a sudden change, it determines the fault area information of the ship's medium-voltage DC power system based on the mutated element and its corresponding value. The fault area information includes the fault branch and the power failure node; it disconnects the circuit breaker corresponding to the fault branch to isolate the fault area.

[0066] The power restoration path construction module: Based on the extended correlation matrix, starting from the faulty branch and ending at the branch with connectivity, constructs a set of alternative power restoration paths for the power-loss node;

[0067] The multi-objective fault reconfiguration model building module is used to divide the loads into primary loads, secondary loads, and tertiary loads according to their importance, and to discretize each level of load into several extended loads. Each primary and secondary extended load includes a normal power supply path and a backup power supply path, while each tertiary extended load only includes a normal power supply path. The multi-objective fault reconfiguration model is constructed with the following constraints: maximizing load recovery, minimizing the number of switching operations, and maximizing generator operating efficiency as the multi-objective functions, and with the constraint that each primary and secondary extended load has only one power supply path, the generator capacity is greater than the total capacity of the connected loads, and the line node capacity is less than the maximum line capacity threshold.

[0068] The optimal recovery path solution module is used to solve for the optimal path of the candidate power restoration path set using an improved SABPSO algorithm, which is a hybrid improvement of the discrete binary particle swarm optimization algorithm and the simulated annealing algorithm. The improved SABPSO algorithm retains the discrete optimization characteristics of the discrete binary particle swarm optimization algorithm and the global optimization characteristics of the simulated annealing algorithm, and optimizes the global optimal solution selection by adjusting the particle search step size through adaptive inertia weight and combining the roulette wheel selection mechanism. During the solution process, the fitness is calculated with the multi-objective function in the multi-objective fault reconstruction model as the dimension, and the optimal recovery path is obtained as the fault reconstruction scheme under the condition that the constraints in the multi-objective fault reconstruction model are met.

[0069] The fault reconfiguration scheme execution module is used to generate switching commands based on the fault reconfiguration scheme and execute them in the ship's medium-voltage DC power system.

[0070] The beneficial effects of this invention are as follows:

[0071] This invention provides a fault reconfiguration method for a ship's medium-voltage DC power system. To achieve better optimization results when solving the fault reconfiguration problem of a ship's medium-voltage DC power system, the BPSO and SA algorithms are combined, integrating the advantages of both algorithms while improving their limitations. This enhances the reliability and efficiency of the ship's power system under complex fault scenarios. Therefore, it can also be called a fault reconfiguration method for a ship's medium-voltage DC power system based on an improved particle swarm optimization algorithm, or a fault reconfiguration method for a ship's medium-voltage DC power system based on an improved SABPSO algorithm. This method abstracts the topology of the ship's medium-voltage DC power system into a node-branch graph and constructs an extended correlation matrix, accurately quantifying the connectivity relationships between generators, loads, switchboards, and circuit breakers. This system provides an intuitive mathematical description of the system's operating status. Simultaneously, by combining the real-time detection and matrix update mechanism of the tree search algorithm, it provides real-time feedback on the status of equipment such as circuit breakers, enabling accurate and rapid fault information location and extraction. Relying on the element mutation characteristics of the extended association matrix, it can quickly pinpoint faulty branches and power-loss nodes, locating the fault area within 0.01 seconds. This solves the problem of low efficiency in traditional fault location methods that rely on "point-by-point investigation," significantly shortening fault identification time and improving accuracy by 30% compared to traditional adjacency matrix methods. By promptly disconnecting the circuit breaker corresponding to the faulty branch, the fault area is effectively isolated, preventing the fault from spreading to the normal power supply section, reducing the impact of the fault on the overall system stability, and clearly defining the power loss range, thus facilitating subsequent power restoration. The precise construction of power paths provides a clear basis, ensuring the targeted and safe handling of faults. Based on the updated extended correlation matrix, branches with connectivity are selected to construct a set of alternative power restoration paths. This eliminates invalid paths without connectivity while ensuring the comprehensiveness of alternative paths, avoiding the risk of recovery failure due to a single path failure. Simultaneously, the formation of the alternative set narrows the search range of subsequent algorithms, improving the efficiency of optimal path finding and providing sufficient feasible solutions for multi-objective optimization, ensuring the flexibility and reliability of the reconstruction scheme. By discretizing the load into extended loads of different levels according to importance and configuring dual power supply paths for important loads, this ensures that when the ship's medium-voltage DC power system cannot meet the full power requirements of the load... When calculating the load power, discretization is chosen to enable partial power supply, achieving power balance among loads and ensuring the power supply priority of core loads. The construction of the multi-objective function takes into account the maximum load recovery rate, minimum switching loss, and maximum generator efficiency, which is more in line with actual needs. It balances power supply reliability and losses in the ship's medium-voltage DC power system while avoiding reconfiguration defects caused by a single objective. The primary and secondary extended loads have only one power supply path, avoiding the risk of unnecessary manual intervention after a fault. Two capacity constraints, namely, the generator capacity being greater than the total capacity of the connected loads and the line node capacity being less than the maximum line capacity threshold, ensure that the load recovery process does not lead to potential risks such as generator and branch overload.The improved SABPSO algorithm, using extended load levels as dimensions and combining multi-objective function calculations for fitness, retains the fast convergence characteristics of the particle swarm optimization algorithm while escaping local optima through simulated annealing, ensuring the global optimality of the solution. The optimal recovery path obtained by the algorithm is transformed into directly executable switching commands, achieving seamless integration between "algorithm optimization results and actual engineering operation," efficiently completing fault recovery of the ship's medium-voltage DC power system. This invention establishes an extended correlation matrix, performs fault inspection and information extraction, constructs a power restoration path, establishes a multi-objective fault reconstruction model, solves for the optimal recovery path, and executes the fault reconstruction scheme. It combines the extended correlation matrix and tree search algorithm to achieve dynamic topology updates and rapid fault location. The improved SABPSO algorithm, combined with a multi-objective model, solves for the optimal recovery path (and fault reconstruction scheme), taking into account load recovery, switching losses, and generator efficiency. It can quickly isolate faults, efficiently and accurately restore power to the lost-power area, and output complete reconstruction schemes for generator-side, power supply branches, sudden load failures, and combined faults. The recovery rate of important loads is ≥95%, and non-important loads are reasonably unloaded, meeting the needs of complex ship operating conditions.

[0072] This invention clarifies the power supply relationships between different levels of distribution nodes by subdividing the distribution board nodes into main distribution nodes, secondary distribution nodes, and load distribution nodes, making the hierarchical logic of the topology clearer and providing accurate traversal anchors for tree search. The combined search method of Breadth-First Search (BFS) traversing the main distribution nodes and Depth-First Search (DFS) delving into the secondary distribution nodes and load distribution nodes and their corresponding branches, and the reverse tracing of load nodes, allows for rapid coverage of the power supply backbone through BFS and in-depth penetration into secondary distribution nodes and end load distribution nodes through DFS. Reverse verification ensures the accuracy of connectivity information, enabling rapid topology identification and real-time feedback of circuit breaker status. This effectively avoids omissions or misjudgments in topology detection, making the connectivity information of the extended association matrix more accurate and reliable, and providing high-quality topology data support for subsequent fault location and path construction.

[0073] This invention uses the mutation of extended correlation matrix elements as a fault trigger signal, enabling rapid fault detection and avoiding the lag of traditional fault detection. Simultaneously, it customizes differentiated matrix element judgment rules for different power supply logics of generators, loads, and distribution boards—generators are judged by all zeros in their corresponding columns, loads by all zeros in their intersections with generators, and distribution boards by all zeros in their intersections with generator columns. This not only aligns with the functional attributes of each node but also transforms state judgment into a simple quantitative verification of matrix elements, eliminating the need for complex topology traversal. This significantly improves the accuracy and efficiency of fault branch and power failure node judgment, providing a fast and reliable decision-making basis for subsequent fault isolation and power restoration.

[0074] This invention significantly improves optimization efficiency by precisely configuring the core parameters of the algorithm and initializing particle positions to constrain the range of alternative power restoration paths. This avoids invalid searches from the outset. The application of the roulette wheel selection algorithm effectively maintains population diversity and suppresses premature convergence. Adaptive inertial weights and velocity / position update mechanisms balance global exploration and local optimization capabilities. The constraint verification stage removes invalid particles in real time, ensuring all candidate solutions are compliant. The Metropolis criterion supports accepting inferior solutions with a certain probability, helping the algorithm escape local optima. Combined with a gradual cooling strategy, it balances the breadth of optimization with later convergence stability. The overall process is progressive and optimized in a closed loop, retaining the rapid convergence characteristics of the improved SABPSO algorithm while ensuring the global excellence and compliance of the optimal path. It can efficiently output fault reconstruction solutions that meet multiple objectives and adapt to the real-time and reliability requirements of ship MVDC system fault recovery. The introduction of adaptive inertial weights to balance global / local search, simulated annealing to escape local optima, and roulette wheel selection to optimize fitness selection significantly improves algorithm performance. The algorithm achieves a 100% probability of finding the optimal solution, with an average search time of 0.05s. This represents a significant improvement over the BPSO algorithm (average search time 0.22s) and the SA algorithm (average search time 0.34s), by 77% and 85% respectively.

[0075] This invention's velocity update formula integrates adaptive inertia weights with individual and global learning factors. This maintains particle search inertia while guiding particles to iterate towards their own and the population's optimal direction, effectively balancing global exploration and local optimization capabilities and avoiding premature convergence. Position updates are designed differently based on load type. For first- and second-level extended loads, the sigmoid function maps velocity to probability, adapting to the selection logic of dual-power supply paths. For third-level extended loads, random numbers are used to adapt to single-path characteristics, accurately matching the power supply requirements of different loads. Minimum / maximum velocity thresholds further standardize the update range, ensuring compliant and efficient position adjustments. The overall formula logic aligns with the characteristics of extended loads and the algorithm's optimization needs, significantly improving the accuracy and rationality of particle updates and helping the improved SABPSO algorithm converge quickly to the global optimum.

[0076] This invention introduces adaptive inertia weights, which dynamically balance the global search and local optimization capabilities of the algorithm through a linear decreasing design from the maximum weight threshold (e.g., 0.9) to the minimum weight threshold (e.g., 0.4) during the iteration process. In the early stages of iteration, the weights are larger, driving particles to extensively traverse alternative recovery paths, quickly locking in the potential range of the optimal solution and avoiding overlooking effective solutions. In the later stages of iteration, the weights decrease, guiding particles to focus on the discovered high-quality regions for refined optimization, improving the accuracy of the solution.

[0077] The Metropolis criterion of this invention, when the current fitness of a particle is less than the individual optimal fitness, sets the current fitness as the new individual optimal fitness for that particle; when the current fitness of a particle is greater than or equal to the individual optimal fitness, a probability acceptance mechanism is introduced based on the current temperature. Through differentiated logic of directly accepting excellent solutions and accepting inferior solutions with probability, this ensures that particles can quickly iterate towards a better fitness, guaranteeing optimization efficiency, while also allowing the acceptance of inferior solutions with a certain probability, effectively breaking the local optimum trap and improving the algorithm's global optimization capability. The effectiveness of the probability acceptance mechanism is ensured by comparing a randomly generated number (0-1) with the probability P to determine whether to update, achieving global optimality of the optimization result.

[0078] This invention also relates to a fault reconstruction system for a ship medium-voltage DC power system. This system corresponds to the aforementioned fault reconstruction method for ship medium-voltage DC power systems and can be understood as a system that implements the aforementioned fault reconstruction method for ship medium-voltage DC power systems. It includes an extended correlation matrix establishment module, a fault inspection and information extraction module, a power restoration path construction module, a multi-objective fault reconstruction model establishment module, an optimal recovery path solution module, and a fault reconstruction scheme execution module. These modules work collaboratively to achieve efficient and accurate implementation of fault reconstruction in the ship's MVDC system: A dynamic topology awareness foundation is constructed using an extended correlation matrix combined with a tree search algorithm to capture the connectivity of nodes and branches in real time, providing accurate data support for fault handling; faulty branches and power-loss nodes are quickly located and isolated using matrix element mutations to prevent fault propagation; a set of alternative power restoration paths is constructed based on effective topology information to narrow the search range; load grading and extended design, multi-objective functions, and constraints are used to balance core load priority, switching losses, and system safety; the improved SABPSO algorithm is then used to efficiently solve for the optimal path, and finally, power restoration is achieved through precise switching commands. The system not only relies on core technologies (extended correlation matrix and improved SABPSO algorithm) to ensure the real-time performance and optimization accuracy of fault handling, but also ensures the reliability and compliance of the reconstruction scheme through multi-objective function and constraint design, significantly improving the efficiency and stability of power supply restoration after system failure and effectively guaranteeing the core power needs of ships. Attached Figure Description

[0079] Figure 1 This is a schematic diagram of the fault reconfiguration method for shipboard medium-voltage DC power systems according to the present invention.

[0080] Figure 2 This is a flowchart of the fault reconfiguration method for a shipboard medium-voltage DC power system according to the present invention.

[0081] Figure 3 This is a topology diagram of a medium-voltage DC power system for ships.

[0082] Figure 4 This is a schematic diagram of a node-branch in this invention.

[0083] Figure 5 This is a schematic diagram of the improved SABPSO algorithm of the present invention.

[0084] Figure 6a This is an example diagram illustrating the evolution process of fitness values ​​in Example 1 of the present invention.

[0085] Figure 6b This is an example diagram of the globally optimal switching state in Example 1 of the present invention.

[0086] Figure 6c This is an example diagram of DC bus voltage variation for Example 1 of the present invention.

[0087] Figure 6d This is an example diagram illustrating the load-side current variation in Example 1 of the present invention.

[0088] Figure 7a This is an example diagram illustrating the evolution process of fitness values ​​in Example 2 of the present invention.

[0089] Figure 7b This is an example diagram of the globally optimal switching state in Example 2 of the present invention.

[0090] Figure 7c This is an example diagram illustrating the DC bus voltage variation in Example 2 of the present invention.

[0091] Figure 7d This is an example diagram illustrating the load-side current variation in Example 2 of the present invention.

[0092] Figure 8a This is an example diagram illustrating the evolution process of fitness values ​​in Example 3 of the present invention.

[0093] Figure 8b This is an example diagram of the globally optimal switching state in Example 3 of the present invention.

[0094] Figure 8c This is an example diagram of DC bus voltage variation in Example 3 of the present invention.

[0095] Figure 8d This is an example diagram illustrating the load-side current variation in Example 3 of the present invention.

[0096] Figure 9a This is an example diagram illustrating the evolution process of fitness values ​​in Example 4 of the present invention.

[0097] Figure 9b This is an example diagram of the globally optimal switching state in Example 4 of the present invention.

[0098] Figure 9c This is an example diagram illustrating the DC bus voltage variation in Example 4 of the present invention.

[0099] Figure 9d This is an example diagram illustrating the load-side current variation in Example 4 of the present invention.

[0100] Figure 10 This is a structural block diagram of the shipboard medium-voltage DC power system fault reconfiguration system of the present invention. Detailed Implementation

[0101] The present invention will now be described with reference to the accompanying drawings.

[0102] This invention discloses a fault reconfiguration method for a ship's medium-voltage DC power system, which is used to quickly complete the entire fault reconfiguration process, including topology identification, fault detection, fault location, fault isolation, and fault recovery, when a fault occurs in the ship's MVDC system (its principle block diagram is shown below). Figure 1 (As shown). Among them, fault location relies on the extended correlation matrix, and fault recovery adopts the improved SABPSO algorithm, which solves the problems of "slow location and low recovery scheme quality" in the traditional process.

[0103] like Figure 2 As shown, the method specifically includes the following steps:

[0104] I. Steps for establishing an extended association matrix (corresponding to...) Figure 1 The topology identification steps are as follows: Based on the topology of the ship's medium-voltage DC power system, generators, loads, and switchboards are used as nodes (specifically, generators, main switchboards, and port and starboard connecting buses are the main nodes, regional switchboards are the child nodes, and loads are the load nodes), and circuit breakers are used as branches. Nodes are connected through corresponding branches to jointly construct a node-branch graph. Using graph theory, an extended correlation matrix is ​​constructed based on the node-branch graph. The node-branch graph reflects the real-time operating status of the ship's medium-voltage DC power system, and the elements of the extended correlation matrix represent the connectivity between each node and each branch in the node-branch graph. For the node-branch graph, a tree search algorithm is used in real-time to traverse the main nodes and child nodes sequentially and verify the load nodes in reverse. The connectivity between each node and each branch is detected, and the detection results are updated to the extended correlation matrix in real time.

[0105] like Figure 3The diagram illustrates a shipboard MVDC system topology (also known as a shipboard medium-voltage DC ring power system topology). In this diagram, the ship's generators and loads are connected to the ring distribution network via power electronic conversion modules and circuit breakers. The generators distribute power to different area boards / distribution boards via the main switchboard. Loads can be directly connected to the main switchboard or powered by the distribution boards. Two power supply paths are provided for critical loads. The switching state of the circuit breakers can alter the power system topology, enabling rapid isolation and reconfiguration in case of faults in the shipboard medium-voltage DC power system.

[0106] In the diagram, solid lines represent closed circuit breakers, and dashed lines represent open circuit breakers. The power supply and loads of the ring-shaped ship's MVDC power system are interconnected, forming a closed loop, making power transmission in the system more stable and reliable. Each ring bus connects a main generator and an auxiliary generator, with the inner layer featuring radial power distribution. Therefore, under normal operating conditions, at least one of the tie switches on the port and starboard busbars Bus16 and Bus17 must be open. To more easily illustrate the components and structural changes of the ship's MVDC system, the symbols and meanings of each structure are shown in Table 1.

[0107] Table 1

[0108]

[0109] The node-branch graph constructed in this embodiment of the invention is as follows: Figure 4 As shown, it includes nodes (where G1-G4 are generator master nodes or simply generator nodes, L1-L7 are load nodes, and the others are distribution board nodes) and branches (B1-B33). The distribution board nodes include main distribution nodes, secondary distribution nodes, and load distribution nodes. Among them, the main distribution board directly connected to the generator master node is the main distribution node, the main distribution board not directly connected to the generator master node is the secondary distribution node, and the area load distribution board is the load distribution node.

[0110] Based on graph theory, this invention establishes an extended correlation matrix M to more accurately describe the topology of a ship MVDC system (hereinafter referred to as the power system) with multiple generators, as shown below:

[0111]

[0112] Where i represents the total number of power stations, and j represents the total number of jumper branches. For the correlation between generators, This refers to the connection between the power station and the jumper branch (i.e., the connectivity between the node and the branch).

[0113] For elements in matrix M If node i and branch j are not connected, then Assign a value of 0; if node i is connected to branch j, and the current flows from node i to branch j, then Assign a value of 1; if node i is connected to branch j, and the current flows from branch j to node i, then The value is assigned to -1.

[0114] After matrix M is generated, a tree search algorithm is used in real time to traverse the main nodes and child nodes sequentially and verify the load nodes in reverse. The connectivity of each node and branch is detected. The specific steps include: In the node-branch graph, firstly, a breadth-first search (BFS) algorithm is used in real time to traverse the adjacent main distribution nodes of each generator node; secondly, a depth-first search (DFS) algorithm is used to traverse the main distribution nodes, secondary distribution nodes, load distribution nodes and corresponding branches layer by layer from each generator node to establish the node-branch connectivity relationship, and finally find the load node or the last level of the secondary distribution node; finally, for each load node found, the algorithm is used to backtrack layer by layer from the load node to the generator node, and the connectivity information of each node and each branch is obtained by combining the node-branch connectivity relationship.

[0115] II. Fault Inspection and Information Extraction Steps (corresponding to) Figure 1 (Fault inspection, fault location, and fault isolation steps in the process): If an element in the extended correlation matrix undergoes a sudden change, the fault area information of the ship's medium-voltage DC power system is determined based on the mutated element and its corresponding value. The fault area information includes the fault branch and the power failure node. The circuit breaker corresponding to the fault branch is disconnected to isolate the fault area.

[0116] This invention determines whether the ship's medium-voltage DC power system has malfunctioned by checking whether the elements in the extended correlation matrix undergo abrupt changes.

[0117] If an element in the extended correlation matrix undergoes a mutation, the faulty branch is determined based on the mutated element and its corresponding value.

[0118] For each generator node, the state of the generator node is determined based on the values ​​of all elements in the corresponding column of the generator node in the extended correlation matrix. If all elements are 0, the generator node is de-energized; if at least one element is not 0, the generator node is functioning normally.

[0119] For each load node, all elements in the row corresponding to the load node are determined in the extended correlation matrix, and the cross elements in the column corresponding to each generator node are selected from these elements. If the value of all cross elements is 0, the load node is de-energized; if at least one cross element has a value that is not 0, the load node is normal.

[0120] For each distribution board node, the row and column corresponding to each distribution board node are determined in the extended correlation matrix. If the value of all elements in the row is 0, and the value of the intersection element with the column corresponding to all generator nodes is 0, then the distribution board node is de-energized; otherwise, the distribution board node is normal.

[0121] When a fault occurs (such as) Figure 4 (If G2 fails), the fault area can be located within 0.01s by changing the element mutation of matrix M (the corresponding elements of branches B15, B16, and B32 become 0), obtaining the faulty branches (B15, B16, and B32) and the power-off nodes (G2 and L6). Then, BK30 is disconnected to isolate the fault, avoiding the delay of the traditional method of "point-by-point detection".

[0122] III. Steps for constructing a restored power supply path (corresponding to) Figure 1 (Fault recovery steps in the process): Based on the extended correlation matrix, starting from the faulty branch and ending at a branch with connectivity, construct a set of alternative power restoration paths for the power-loss node.

[0123] In this embodiment of the invention, after locating the faulty branch and the power-loss node, a recovery path is constructed based on the extended correlation matrix, starting from the faulty branch and searching for branches with current signals (i.e., connectivity) as the endpoints. When constructing the recovery path, matrix M is used as the basis. Branches marked 0 at the time of fault location (branches without connectivity) are not considered as recovery paths until a branch with a status signal of 1 (connectivity) is found. Finally, the paths with a status signal of 1 are integrated as a set of candidate power restoration paths.

[0124] IV. Steps for establishing a multi-objective fault reconstruction model (corresponding to) Figure 1(Fault recovery steps in the model): To more reasonably meet the power balance of important loads and restore the power supply demand of important loads as much as possible when a fault occurs, the loads are divided into primary loads, secondary loads, and tertiary loads according to their importance. Each level of load is discretized into several extended loads. For example, the primary load is discretized into 4 primary extended loads, the secondary load into 2 secondary extended loads, and the tertiary load into 1 tertiary extended load. Each primary and secondary extended load includes a normal power supply path and a backup power supply path, and each tertiary extended load includes only a normal power supply path. The model uses maximizing load recovery, minimizing the number of switching operations, and maximizing generator operating efficiency as multi-objective functions, and uses the constraints that each primary and secondary extended load has only one power supply path, the generator capacity is greater than the total capacity of the connected loads, and the line node capacity is less than the maximum line capacity threshold as constraints to construct a multi-objective fault reconstruction model.

[0125] Power system fault reconfiguration is an optimization problem under fault conditions, which is essentially a nonlinear multi-objective and multi-constraint optimization problem. Therefore, a multi-objective fault reconfiguration model is constructed using multi-objective functions and constraints.

[0126] The multi-objective function is shown below:

[0127] ,

[0128] ,

[0129] ,

[0130] ,

[0131] Where maxf represents the maximum value of a multi-objective function. With max This indicates maximizing load recovery. with min This indicates minimizing the number of switching operations. With max This indicates maximizing generator operating efficiency. These represent their respective weighting coefficients, and , Indicates the priority coefficient, preferably, , , , This indicates the power supply status of the i-th primary extended load. This indicates the power supply status of the j-th secondary extended load. This indicates the power supply status of the z-th tertiary extended load. This represents the load of the i-th level extended load. This represents the load of the j-th secondary extended load. Let represent the load of the z-th tertiary load extension, h represent the number of tertiary load extensions, k represent the number of tertiary load extensions, and m represent the number of tertiary load extensions. This indicates the state of the i-th level 3 extended load switch. closure, disconnect, This indicates the path switching status of the j-th primary or secondary extended load balancer. This is the normal power supply path. For backup power supply paths, 'l' represents the total number of primary and secondary extended loads. Let represent the operating efficiency of the i-th generator, and n represent the total number of generators.

[0132] The constraint that only one power supply path is available for both the primary and secondary extended loads is as follows:

[0133] ,

[0134] in, This indicates the normal power supply path for primary and secondary extended loads. This indicates the backup power supply path for primary and secondary extended loads;

[0135] The constraint that the generator capacity is greater than the total capacity of the connected load is as follows:

[0136] ,

[0137] in, This represents the capacity of the i-th generator. This represents the j-th load connected to the i-th generator, and m represents the total number of loads connected to the i-th generator.

[0138] The constraint that the capacity of a line node is less than the maximum threshold of the line capacity is as follows:

[0139] ,

[0140] in, Indicates the capacity of the line nodes. This indicates the maximum threshold for line capacity.

[0141] The multi-objective fault reconfiguration model constructed based on the above-mentioned multi-objective functions and constraints can avoid the problem of "heavy load recovery and light loss balancing" in traditional models, ensuring that the reconfigured system is both reliable and economical.

[0142] V. Steps for finding the optimal recovery path (corresponding to) Figure 1 The fault recovery steps in the model are as follows: An improved SABPSO algorithm, derived from a hybrid improvement of the Discrete Binary Particle Swarm Optimization (DBPSO) algorithm and the Simulated Annealing (SAX) algorithm, is used to find the optimal path for the set of candidate power restoration paths. This improved SABPSO algorithm retains the discrete optimization characteristics of the DBPSO algorithm and the global optimization characteristics of the SAX algorithm, and optimizes the global optimal solution selection by adjusting the particle search step size through adaptive inertia weights and combining a roulette wheel selection mechanism. During the solution process, fitness is calculated using the multi-objective function in the multi-objective fault reconstruction model, with each level of extended load as the dimension. Under the condition that the constraints in the multi-objective fault reconstruction model are satisfied, the optimal recovery path is obtained as the fault reconstruction scheme.

[0143] like Figure 5 As shown, the process of finding the optimal path for the set of candidate power restoration paths using the improved SABPSO algorithm includes "algorithm initialization, fitness calculation, roulette wheel selection for global optimum, adaptive inertia weight update, particle velocity / position update, simulated annealing, and termination judgment". The core improvements (adaptive inertia weight, simulated annealing, and roulette wheel selection) are all integrated into the process, solving the problems of traditional BPSO being prone to local optima and SA having slow convergence. The specific steps are as follows:

[0144] S1: Configure the particle population size N (e.g., N=100), maximum number of iterations (e.g., 50 times), particle velocity range (e.g., [-4,4]), initial temperature, cooling rate, and termination condition;

[0145] S2: Within the velocity range of the particles, initialize the velocity of each particle; using each level of extended load as the dimension D (D=14) of each particle, and within the set of alternative power restoration paths, initialize the position of each particle; in this embodiment of the invention, the initial position of each dimension of the particles is discretized according to the type of load, and the position value of the particles is divided into three types: 0 indicates load power failure, 1 indicates normal path power supply, and 2 indicates backup path power supply. The discretization formula for the position value of important loads (primary load, secondary load) is as follows:

[0146] ,

[0147] in, Represents the j-th dimension of the i-th particle;

[0148] The discretization formula for the location value corresponding to non-critical loads (level 3 loads) is shown below:

[0149] ,

[0150] S3: Calculate the first fitness (i.e., initial fitness) of each particle using the multi-objective function, and take the first fitness of each particle as the individual optimal fitness. Then, use the roulette wheel selection algorithm to select the individual optimal fitness with the highest probability from all individual optimal fitnesss as the global optimal fitness.

[0151] The calculation formula for the roulette wheel selection algorithm is as follows:

[0152]

[0153] in, This represents the probability that the optimal fitness of the individual corresponding to the i-th particle in the j-th iteration is selected. This represents the optimal fitness of the individual corresponding to the i-th particle in the j-th iteration. It represents the sum of the individual optimal fitness of all particles in the j-th iteration;

[0154] S4: Calculate the second fitness (i.e., current fitness) of each particle at the current temperature using the multi-objective function.

[0155] S5: For each particle, based on its individual optimal fitness, global optimal fitness, and adaptive inertia weight, update the velocity in each dimension of the particle to adjust the particle search step size, as shown in the following formula:

[0156] ,

[0157] in, This represents the velocity of the i-th particle in the j-th dimension during the (t+1)-th iteration. This represents the velocity of the i-th particle in the j-th dimension during the t-th iteration. Indicates adaptive inertia weights, The individual learning factor of a particle. Represents the global learning factor. Represents a random number between [0, 1]. This represents the individual optimal fitness of the i-th particle in the j-th dimension during the t-th iteration. This represents the globally optimal fitness of the i-th particle in the j-th dimension during the t-th iteration. This represents the position of the i-th particle in the j-th dimension during the t-th iteration;

[0158] Based on the velocity of each dimension of the particle after the update, update the position of each dimension in the particle; if the extended load type corresponding to the dimension is the first-level extended load or the second-level extended load, then update the position of the dimension using the following formula:

[0159] ,

[0160] in, This represents the updated position of the i-th particle in the j-th dimension. Indicates the minimum speed threshold. The sigmoid function represents the maximum speed threshold and the probability function.

[0161] If the extended load type corresponding to the dimension is the third-level extended load, then the position of the dimension is updated using the following formula:

[0162] ,

[0163] Where rand represents a random number between [0 and 1];

[0164] This invention employs a linear adjustment strategy to determine the adaptive inertia weights, as shown in the following formula:

[0165] ,

[0166] in, This represents the adaptive inertia weight for the i-th iteration, where i represents the iteration number and ger represents the maximum number of iterations. This represents the maximum threshold of the adaptive inertia weight. This represents the minimum threshold for adaptive inertia weights;

[0167] S6: Check whether each particle meets the constraints and remove particles that do not meet the constraints;

[0168] S7: For each particle that satisfies the constraints, the second fitness corresponding to each particle is compared with the individual optimal fitness according to the Metropolis criterion. It is determined whether to select the second fitness as the new individual optimal fitness, and finally the current individual optimal fitness of each particle is determined. Based on the current individual optimal fitness of each particle, the current global optimal fitness is determined using the roulette wheel selection algorithm.

[0169] The Metropolis criteria are shown in the following formula:

[0170] ,

[0171] Where p represents the probability that the particle's second fitness is the particle's new optimal fitness. This represents the second fitness of the particle. This represents the current optimal fitness of the particle. This represents the temperature during the i-th iteration;

[0172] If the second fitness corresponding to a particle is less than the individual optimal fitness, then the second fitness is taken as the new individual optimal fitness of the particle.

[0173] If the second fitness corresponding to the particle is greater than or equal to the individual's optimal fitness, then... The formula calculates the probability that the second fitness is the new optimal fitness of the particle.

[0174] Finally, a number between 0 and 1 is randomly generated. If the generated number is less than or equal to P, the second fitness is taken as the new individual optimal fitness of the particle; if the generated number is greater than P, the individual optimal fitness of the particle is not changed.

[0175] S8: Starting from the configured initial temperature, gradually reduce the current temperature according to the cooling rate;

[0176] S9: Determine if the configured termination condition is met. If not, return to step S4. If it is met, output the particle corresponding to the current global optimal fitness as the fault reconstruction scheme.

[0177] VI. Execution Steps of Fault Reconfiguration Plan (corresponding to) Figure 1 (Fault recovery steps in the process): Based on the fault reconstruction scheme, generate switching commands and execute them in the ship's medium-voltage DC power system.

[0178] For example, Example 1: Auxiliary generator G2 fails, and branches B15, B16, and B32 are disconnected.

[0179] Circuit breaker BK30 disconnected, isolating the fault area; this branch cannot participate in the reconfiguration. The improved SABPSO algorithm was run 50 times, and the results are as follows: Figure 6a As shown, the optimal particle fitness value was found in the second iteration; Figure 6b The optimal particle's decoded state is the final output of the algorithm. The optimal switch state is X = [1111111111111101]. This indicates that the 13th extended load's switch is closed, the switching frequency is 1, and the algorithm's average search time is 0.0211s. When the fault occurs, the circuit breaker BK30 is promptly disconnected. Load L6 (the 13th extended load), being a level 3 load, has no backup power supply path and is directly de-energized, without affecting other normal power supply branches.

[0180] Changes in bus voltage and load current of the ship's MVDC system during fault reconfiguration, such as Figure 6c and Figure 6dAs shown in the diagram, before the fault occurred, the entire power system was operating stably, with no changes in DC bus voltage or load current. The fault occurred at 1.01 seconds, with the current suddenly increasing to 406.6A and the DC bus voltage plummeting to 4931V. After disconnecting the circuit breaker in the fault area, the voltage quickly recovered, reaching 5060V within 0.2 seconds. Then, under the regulation of the excitation device, it returned to near its rated value (rated voltage 5000V) and fluctuated around it. At this time, the load current also gradually recovered to around 400A, matching the rated load demand, verifying the algorithm's speed and stability in generator-side fault scenarios. This ensures the reconfiguration scheme is feasible and that the system remains stable after recovery, avoiding the problem of "feasible scheme but unstable in practice."

[0181] For example, Example 2: A fault occurs on the BUS1 side branch of the main engine G1 in the power system, and branches B12, B23, and B24 are disconnected.

[0182] The left tie bus BUS16 disconnects, and the right tie bus BUS17 closes. Power is restored to the de-energized load through the right tie bus. Circuit breaker BK24, which is involved in the reconfiguration, closes to provide a power path for the de-energized load. The improved SABPSO algorithm is run 50 times, and the results are as follows: Figure 7a and Figure 7b As shown. Figure 7a This reflects the convergence of the algorithm. As can be seen from the figure, the global optimal fitness value was reached in the earliest second iteration. The algorithm converges quickly and does not get trapped in local optima. Figure 7b This represents the globally optimal particle switch encoding state, and the optimal switch state for fault recovery is... It can be seen that the switches of the 1st, 2nd, 3rd, 4th, 10th, and 11th extended loads change, with a minimum number of switching operations of 6 and an average search time of 0.0198s. Therefore, the optimal power restoration path selection for the load is as follows: after L1 loses power, the backup power path is activated, and the extended load sequence is... If L5 fails to power, a backup path is activated; if the L4 load (a third-level load) does not have a backup path, it will be directly powered off.

[0183] from Figure 7c and Figure 7d As can be seen, when the fault occurred, the voltage dropped rapidly to 4941.2V. After the circuit breaker at the fault point was disconnected and the fault area was isolated, the voltage suddenly increased to 5065.3V. After 0.02s, it stabilized again at around 5000V. At this time, as the power supply was restored, the load side dropped to 395.73A and then began to rise. After the fault was cleared, it gradually stabilized.

[0184] During actual navigation, ships inevitably experience load failures due to complex and variable operating conditions. Different load failures require different coping strategies. Therefore, it is extremely important to conduct failure simulation experiments using important loads and non-important loads as examples.

[0185] For example, in Example 3: a circuit breaker fault occurs between BUS2 and BUS12, and the extended load sequence number corresponding to the push load L1 is... A sudden malfunction occurred during normal operation.

[0186] System parameters are set as follows: Ship MVDC system, DC bus voltage 5kV, G1 / G3 main generator (36MW), G2 / G4 auxiliary generator (4MW), primary load L1 / L2 (20MW), secondary load L5 (4MW), tertiary load L3 / L4 / L6 / L7 (2MW).

[0187] The specific initialization parameter settings in the improved SABPSO algorithm are shown in Table 2:

[0188] Table 2

[0189]

[0190] To more effectively balance the power of the propulsion motor (main load) and restore the power supply to the main load as much as possible in the event of a fault, the decomposed load information is shown in Table 3:

[0191] Table 3

[0192]

[0193] The extended correlation matrix detects that when the branch connectivity between BUS2 and BUS12 becomes 0 (a circuit breaker fault occurs between BUS2 and BUS12), and load L1 also fails, the BFS+DFS search algorithm confirms the fault area. BK26 disconnects to isolate the fault, causing a power outage in the tertiary load L4. The primary load L1 activates its backup power supply path to ensure that critical loads quickly regain normal power and maintain the stability of the power system. The fault reconstruction algorithm yields the following results: Figure 8a and Figure 8b . Figure 8a As can be seen, the optimal fitness value is reached in the 4th iteration, which is 97% faster than the traditional BPSO algorithm (which requires 70 or more iterations); Figure 8bThe optimal switching state output by the algorithm is X=[11211111101111]. This shows that the switching of the 3rd and 10th extended loads changes, the minimum number of switching operations is 2, and the average search time is 0.0208s. Compared to the SA algorithm (which requires at least 3 switching operations), this reduces switching actions by 67%, thus reducing equipment losses. When circuit breakers BK5 and BK26 open, loads L1 and L4 lose power and disconnect. At this time, the extended load sequence of the primary load... The backup power supply path is activated, but the level 3 load L4, which does not have a backup power supply path, loses power directly.

[0194] When a sudden failure occurs while the power supply to loads L1 and L4 is normal, the changes in the bus voltage and the current at the drive load end of the power system are as follows: Figure 8c and Figure 8d The DC bus voltage of the medium-voltage power system dropped to 4974.2V, and the current at the primary load terminal dropped to 3000A. After the circuit breaker at the fault point was disconnected, the backup power supply path of the primary load was started through fault reconfiguration to restore power supply. At this time, the voltage and current began to rise back to near their rated values. Figure 8c and Figure 8d It can be seen that the recovery time of DC bus voltage and load current after the fault is ≤0.2s, which is far below the fault recovery threshold (0.5s) of the ship's MVDC system, and meets the real-time requirements.

[0195] Overall, the target optimization effect is good. The recovery rate of level 1 / 2 load is 100%, and the recovery rate of level 3 load is 75% (only L4 unloading); the number of switching operations is only 1; the generator output power is balanced, and the efficiency is ≥90%; the fault location is 0.01s + algorithm solution is 0.0208s + execution verification is 0.2s, and the total time is ≤0.23s, which meets the real-time requirements.

[0196] For example, in Example 4: Auxiliary generator G2 fails, load L5 on the main generator G3 side suddenly fails while supplying power normally, and branch B26 and branch B33 fail at the same time (combined fault situation).

[0197] When load L6, powered by the auxiliary generator, loses power, circuit breaker BK30 trips to protect the normal power supply to other areas. When branch B26 and branch B33 fail, circuit breakers BK26 and BK33 trip, causing loads L4 and L7, which are directly connected to them, to lose power. Figure 9a This is the process of fitness value change. As can be seen from the figure, the optimal fitness value is reached in the second iteration, indicating that the algorithm converges quickly. Figure 9bThe optimal switching state output by the algorithm can be represented as X=[11111111101200], with 4 switching actions and an average search time of 0.0442s. When generator G2 fails, circuit breaker BK2 opens, causing non-critical load L6 powered by G2 to lose power. Since non-critical loads do not have backup power supply paths, circuit breaker BK30 cannot participate in the reconfiguration recovery after opening. When branches B26 and B33 experience circuit breaker failures, circuit breakers BK26 and BK33 open, causing non-critical loads L4 and L7 to lose power directly due to the lack of backup power supply paths. When critical load L5 experiences a sudden failure, the backup power supply path is activated.

[0198] from Figure 9c and Figure 9d As can be seen, when the fault occurred, the medium-voltage DC bus voltage dropped rapidly to 4955V, and the load current rose to 404.7A. After the circuit breaker at the fault point was disconnected, the power system was reconfigured. At this time, the bus voltage surged to 5070V, and the load current gradually decreased from 404.7A at the time of the fault to 395.6A. When the power supply was restored, the voltage and current gradually stabilized.

[0199] As can be seen from the above exemplary calculations, the present invention can output complete and differentiated reconfiguration solutions for generator-side faults (isolate the faulty generator and provide power through the backup path), power supply branch faults (switch the tie bus and restore the power-loss load), sudden load faults and combined faults (prioritize unloading non-critical loads and ensure power supply to critical loads), and has strong scenario adaptability.

[0200] Based on the same inventive concept, one or more embodiments of this specification also provide a fault reconfiguration system for a ship medium-voltage DC power system. Since the working principle of the fault reconfiguration system for a ship medium-voltage DC power system is the same as the aforementioned fault reconfiguration method for a ship medium-voltage DC power system, the implementation of the fault reconfiguration system for a ship medium-voltage DC power system can refer to the aforementioned implementation of the fault reconfiguration method for a ship medium-voltage DC power system, and the repeated parts will not be described again.

[0201] Figure 10 This is a block diagram illustrating the fault reconfiguration system structure of a shipborne medium-voltage DC power system provided in one or more embodiments of this specification. Figure 10 As shown, the system includes, in sequence, an extended correlation matrix establishment module 101, a fault detection and information extraction module 102, a power restoration path construction module 103, a multi-objective fault reconstruction model establishment module 104, an optimal recovery path solution module 105, and a fault reconstruction scheme execution module 106. Among them,

[0202] The extended correlation matrix establishment module 101 is used to construct a node-branch graph based on the topology of the ship's medium-voltage DC power system. This graph uses generators, main switchboards, and port and starboard connecting buses as main nodes, area switchboards as child nodes, loads as load nodes, and circuit breakers as branches. Using graph theory, an extended correlation matrix is ​​constructed based on this node-branch graph. The node-branch graph reflects the real-time operating status of the ship's medium-voltage DC power system, and the elements of the extended correlation matrix represent the connectivity between each node and branch in the node-branch graph. For the node-branch graph, a tree search algorithm is used in real-time to traverse the main nodes and child nodes sequentially and verify the load nodes in reverse. The connectivity of each node and branch is detected, and the detection results are updated to the extended correlation matrix in real-time.

[0203] The fault detection and information extraction module 102, if an element in the extended correlation matrix undergoes a sudden change, determines the fault area information of the ship's medium-voltage DC power system based on the mutated element and its corresponding value. The fault area information includes the fault branch and the power failure node; and disconnects the circuit breaker corresponding to the fault branch to isolate the fault area.

[0204] The power restoration path construction module 103, based on the extended correlation matrix, constructs a set of alternative power restoration paths for the power-loss node, starting from the faulty branch and ending at a branch with connectivity.

[0205] The multi-objective fault reconfiguration model building module 104 is used to divide the loads into primary loads, secondary loads, and tertiary loads according to their importance, and to discretize each level of load into several extended loads. For example, the primary load is discretized into 4 primary extended loads, the secondary load into 2 secondary extended loads, and the tertiary load into 1 tertiary extended load. Each primary and secondary extended load includes a normal power supply path and a backup power supply path, and each tertiary extended load includes only a normal power supply path. The multi-objective fault reconfiguration model is constructed with the following constraints: maximizing the load recovery degree, minimizing the number of switching operations, and maximizing the generator operating efficiency as the multi-objective functions, and the constraints being that each primary and secondary extended load has only one power supply path, the generator capacity is greater than the total capacity of the connected loads, and the line node capacity is less than the maximum line capacity threshold.

[0206] The optimal recovery path solution module 105 is used to solve for the optimal path of the candidate power restoration path set using the improved SABPSO algorithm, which is a hybrid improvement of the discrete binary particle swarm optimization algorithm and the simulated annealing algorithm. The improved SABPSO algorithm retains the discrete optimization characteristics of the discrete binary particle swarm optimization algorithm and the global optimization characteristics of the simulated annealing algorithm, and optimizes the global optimal solution selection by adjusting the particle search step size through adaptive inertia weight and combining the roulette wheel selection mechanism. During the solution process, the fitness is calculated with the multi-objective function in the multi-objective fault reconstruction model as the dimension of each level of extended load. Under the condition of satisfying the constraints in the multi-objective fault reconstruction model, the optimal recovery path is obtained as the fault reconstruction scheme.

[0207] The fault reconfiguration scheme execution module 106 is used to generate switching instructions based on the fault reconfiguration scheme and execute them in the ship's medium-voltage DC power system.

[0208] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail with reference to the accompanying drawings and embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention. In short, all technical solutions and improvements that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention patent.

Claims

1. A fault reconfiguration method for a ship's medium-voltage DC power system, characterized in that, Includes the following steps: The steps for establishing the extended correlation matrix are as follows: Based on the topology of the ship's medium-voltage DC power system, generators, main switchboards, and port and starboard connecting buses are used as main nodes, regional switchboards as child nodes, loads as load nodes, and circuit breakers as branches. A node-branch graph is constructed together, and using graph theory, an extended correlation matrix is ​​built based on the node-branch graph. The node-branch graph reflects the real-time operating status of the ship's medium-voltage DC power system, and the elements of the extended correlation matrix represent the connectivity between each node and each branch in the node-branch graph. For the node-branch graph, a tree search algorithm is used in real-time to traverse the main nodes and child nodes sequentially and verify the load nodes in reverse. The connectivity between each node and each branch is detected, and the detection results are updated to the extended correlation matrix in real time. Fault inspection and information extraction steps: If an element in the extended correlation matrix undergoes a sudden change, the fault area information of the ship's medium-voltage DC power system is determined based on the mutated element and its corresponding value. The fault area information includes fault branches and power-loss nodes. Disconnect the circuit breaker corresponding to the faulty branch to isolate the faulty area; Power restoration path construction steps: Based on the extended correlation matrix, starting from the faulty branch and ending at the branch with connectivity, construct a set of alternative power restoration paths for the power-out node; The steps for establishing a multi-objective fault reconfiguration model are as follows: The loads are divided into primary, secondary, and tertiary loads according to their importance. Each level of load is discretized into several extended loads. Each primary and secondary extended load includes a normal power supply path and a backup power supply path, while each tertiary extended load only includes a normal power supply path. A multi-objective function is constructed with the objectives of maximizing load recovery, minimizing the number of switching operations, and maximizing generator operating efficiency. The constraints are that each primary and secondary extended load has only one power supply path, the generator capacity is greater than the total capacity of the connected loads, and the line node capacity is less than the maximum line capacity threshold. This forms the basis for the multi-objective fault reconfiguration model. The optimal recovery path solution steps are as follows: An improved SABPSO algorithm, derived from a hybrid improvement of the Discrete Binary Particle Swarm Optimization (DPI) algorithm and the Simulated Annealing (SANA) algorithm, is used to solve for the optimal path in the set of candidate power restoration paths. The improved SABPSO algorithm retains the discrete optimization characteristics of the DPI and the global optimization characteristics of the SANA algorithm, and optimizes the global optimal solution selection by adjusting the particle search step size through adaptive inertia weights and combining a roulette wheel selection mechanism. During the solution process, fitness is calculated using the multi-objective function in the multi-objective fault reconstruction model, with each level of extended load as the dimension. Under the condition that the constraints in the multi-objective fault reconstruction model are satisfied, the optimal recovery path is obtained as the fault reconstruction scheme. Fault reconfiguration scheme execution steps: Based on the fault reconfiguration scheme, generate switching commands and execute them in the ship's medium-voltage DC power system.

2. The method according to claim 1, characterized in that, In the step of establishing the extended correlation matrix, the main distribution board included in the main node is divided into a main distribution node and a secondary distribution node, and the area distribution board included in the child node is a load distribution node; wherein, the main distribution board directly connected to the generator main node is the main distribution node, and the main distribution board not directly connected to the generator main node is the secondary distribution node. The steps for detecting the connectivity of each node and branch by using a tree search algorithm to traverse the master node and child nodes in real time and verify the load node in reverse for the node-branch graph include: First, for the node-branch graph, a breadth-first search algorithm is used in real time to traverse the adjacent main distribution nodes of each generator master node; second, a depth-first search algorithm is used to traverse the main distribution nodes, secondary distribution nodes, load distribution nodes and corresponding branches layer by layer from each generator master node to establish node-branch connectivity relationships until the load node or the last level of the secondary distribution node is reached; then, for each load node found, the algorithm is used to backtrack layer by layer from the load node back to the generator master node, and the connectivity information of each node and branch is obtained by combining the node-branch connectivity relationships.

3. The method according to claim 1, characterized in that, In the fault inspection and information extraction steps, whether the ship's medium-voltage DC power system has malfunctioned is determined by whether there is a sudden change in the elements of the extended correlation matrix. If an element in the extended correlation matrix undergoes a mutation, the faulty branch is determined based on the mutated element and its corresponding value. For each generator master node, the state of the generator master node is determined based on the values ​​of all elements in the corresponding column of the generator master node in the extended correlation matrix. If the values ​​of all elements are 0, the generator master node is de-energized; if at least one element has a value that is not 0, the generator master node is functioning normally. For each load node, all elements in the row corresponding to the load node are determined in the extended correlation matrix, and the cross elements in the column corresponding to each generator node are selected from these elements. If the value of all cross elements is 0, the load node is de-energized; if at least one cross element has a value that is not 0, the load node is normal. For each distribution board node formed by the main distribution board included in the main node and the regional distribution board included in the child node, the row and column corresponding to each distribution board node are determined in the extended correlation matrix. If the value of all elements in the row is 0, and the value of the intersection element of the column with the column corresponding to all generator main nodes is 0, then the distribution board node is de-energized; otherwise, the distribution board node is normal.

4. The method according to claim 1, characterized in that, In the steps of establishing the multi-objective fault reconstruction model, the multi-objective function is as follows: ， ， ， ， Where maxf represents the maximum value of a multi-objective function. With max This indicates maximizing load recovery. with min This indicates minimizing the number of switching operations. With max This indicates maximizing generator operating efficiency. Indicates the weighting coefficient. Indicates the priority coefficient. This indicates the power supply status of the i-th primary extended load. This indicates the power supply status of the j-th secondary extended load. This indicates the power supply status of the z-th tertiary extended load. This represents the load of the i-th level extended load. This represents the load of the j-th secondary extended load. Let represent the load of the z-th tertiary load extension, h represent the number of tertiary load extensions, k represent the number of tertiary load extensions, and m represent the number of tertiary load extensions. This indicates the state of the i-th level 3 extended load switch. This indicates the path switching status of the j-th primary or secondary load balancer, where l represents the total number of primary and secondary load balancers. Let represent the operating efficiency of the i-th generator, and n represent the total number of generators.

5. The method according to claim 4, characterized in that, In the steps of establishing the multi-objective fault reconfiguration model, the constraint that only one power supply path is connected for the primary extended load and the secondary extended load is as follows: ， in, This indicates the normal power supply path for primary and secondary extended loads. This indicates the backup power supply path for primary and secondary extended loads; The constraint that the generator capacity is greater than the total capacity of the connected load is as follows: ， in, This represents the capacity of the i-th generator. This represents the j-th load connected to the i-th generator, and m represents the total number of loads connected to the i-th generator. The constraint that the capacity of a line node is less than the maximum threshold of the line capacity is as follows: ， in, Indicates the capacity of the line nodes. This indicates the maximum threshold for line capacity.

6. The method according to claim 1, characterized in that, The optimal recovery path solution step includes the following steps: using the improved SABPSO algorithm to solve for the optimal path in the set of candidate power recovery paths. S1: Configure particle population size, maximum number of iterations, particle velocity range, initial temperature, cooling rate, and termination conditions; S2: Within the velocity range of the particles, initialize the velocity of each particle; using each level of extended load as the dimension of each particle, and within the range of the alternative power restoration path set, initialize the position of each particle; S3: Calculate the initial fitness of each particle using the multi-objective function, and take the initial fitness of each particle as the individual optimal fitness. Then, use the roulette wheel selection algorithm to select the individual optimal fitness with the highest probability from all individual optimal fitnesss as the global optimal fitness. S4: Calculate the current fitness of each particle at the current temperature using the multi-objective function; S5: For each particle, based on the individual optimal fitness, global optimal fitness, and adaptive inertia weight, update the velocity of each dimension of the particle to adjust the particle search step size; based on the updated velocity of each dimension of the particle, update the position of each dimension of the particle. S6: Check whether each particle meets the constraints and remove particles that do not meet the constraints; S7: For each particle that satisfies the constraints, the current fitness of each particle is compared with its individual optimal fitness according to the Metropolis criterion. It is then determined whether to select the current fitness as the new individual optimal fitness, and the current individual optimal fitness of each particle is finally determined. Based on the current individual optimal fitness of each particle, the current global optimal fitness is determined using the roulette wheel selection algorithm. S8: Starting from the configured initial temperature, gradually reduce the current temperature according to the cooling rate; S9: Determine if the configured termination condition is met. If not, return to step S4. If it is met, output the particle corresponding to the current global optimal fitness as the fault reconstruction scheme.

7. The method according to claim 6, characterized in that, In the optimal recovery path solution step, the velocity of each dimension of the particle is updated based on the individual optimal fitness, global optimal fitness, and adaptive inertia weight, as shown in the following formula: ， in, This represents the velocity of the i-th particle in the j-th dimension during the (t+1)-th iteration. This represents the velocity of the i-th particle in the j-th dimension during the t-th iteration. Indicates adaptive inertia weights, The individual learning factor of a particle. Represents the global learning factor. Represents a random number between [0, 1]. This represents the individual optimal fitness of the i-th particle in the j-th dimension during the t-th iteration. This represents the globally optimal fitness of the i-th particle in the j-th dimension during the t-th iteration. This represents the position of the i-th particle in the j-th dimension during the t-th iteration; Based on the velocity of each dimension after the particle update, update the position of each dimension in the particle; if the extended load type corresponding to the dimension is the first-level extended load or the second-level extended load, then update the position of the dimension using the following formula: ， in, This represents the updated position of the i-th particle in the j-th dimension. Indicates the minimum speed threshold. The sigmoid function represents the maximum speed threshold and the probability function. If the extended load type corresponding to the dimension is the third-level extended load, then the position of the dimension is updated using the following formula: ， Here, rand represents a random number between [0 and 1].

8. The method according to claim 6, characterized in that, In the optimal recovery path solution step, a linear adjustment strategy is used to determine the adaptive inertia weights, as shown in the following formula: ， in, This represents the adaptive inertia weight for the i-th iteration, where i represents the iteration number and ger represents the maximum number of iterations. This represents the maximum threshold of the adaptive inertia weight. This represents the minimum threshold for adaptive inertia weights.

9. The method according to claim 6, characterized in that, In the optimal recovery path solution step, the Metropolis criterion is shown in the following formula: ， Where p represents the probability that the particle's current fitness is the new optimal fitness for that particle. This indicates the particle's current fitness. This represents the current optimal fitness of the particle. This represents the temperature during the i-th iteration; If the current fitness of a particle is less than the individual optimal fitness, then the current fitness is taken as the new individual optimal fitness of the particle. If the current fitness of the particle is greater than or equal to the individual's optimal fitness, then... The formula calculates the probability that the current fitness is the new optimal fitness of the particle. Finally, a number between 0 and 1 is randomly generated. If the generated number is less than or equal to P, the current fitness is taken as the new optimal fitness of the particle. If the generated number is greater than P, the optimal fitness of the particle is not changed.

10. A fault reconfiguration system for a ship's medium-voltage DC power system, characterized in that, It includes, in sequence, an extended correlation matrix establishment module, a fault detection and information extraction module, a power restoration path construction module, a multi-objective fault reconstruction model establishment module, an optimal recovery path solution module, and a fault reconstruction scheme execution module. The extended correlation matrix establishment module is used to construct a node-branch graph based on the topology of the ship's medium-voltage DC power system. This graph uses generators, main switchboards, and port and starboard connecting buses as main nodes, area switchboards as child nodes, loads as load nodes, and circuit breakers as branches. Graph theory is then used to construct an extended correlation matrix based on this graph. The node-branch graph reflects the real-time operating status of the ship's medium-voltage DC power system, and the elements of the extended correlation matrix represent the connectivity between each node and branch in the node-branch graph. For the node-branch graph, a tree search algorithm is used in real-time to traverse the main nodes and child nodes sequentially and verify the load nodes in reverse. The connectivity of each node and branch is detected, and the detection results are updated to the extended correlation matrix in real-time. The fault detection and information extraction module: if an element in the extended correlation matrix undergoes a sudden change, it determines the fault area information of the ship's medium-voltage DC power system based on the mutated element and its corresponding value. The fault area information includes the fault branch and the power failure node; it disconnects the circuit breaker corresponding to the fault branch to isolate the fault area. The power restoration path construction module: Based on the extended correlation matrix, starting from the faulty branch and ending at the branch with connectivity, constructs a set of alternative power restoration paths for the power-loss node; The multi-objective fault reconfiguration model building module is used to divide the loads into primary loads, secondary loads, and tertiary loads according to their importance, and to discretize each level of load into several extended loads. Each primary and secondary extended load includes a normal power supply path and a backup power supply path, while each tertiary extended load only includes a normal power supply path. The multi-objective fault reconfiguration model is constructed with the following constraints: maximizing load recovery, minimizing the number of switching operations, and maximizing generator operating efficiency as the multi-objective functions, and with the constraint that each primary and secondary extended load has only one power supply path, the generator capacity is greater than the total capacity of the connected loads, and the line node capacity is less than the maximum line capacity threshold. The optimal recovery path solution module is used to solve for the optimal path of the candidate power restoration path set using an improved SABPSO algorithm, which is a hybrid improvement of the discrete binary particle swarm optimization algorithm and the simulated annealing algorithm. The improved SABPSO algorithm retains the discrete optimization characteristics of the discrete binary particle swarm optimization algorithm and the global optimization characteristics of the simulated annealing algorithm, and optimizes the global optimal solution selection by adjusting the particle search step size through adaptive inertia weight and combining the roulette wheel selection mechanism. During the solution process, the fitness is calculated with the multi-objective function in the multi-objective fault reconstruction model as the dimension, and the optimal recovery path is obtained as the fault reconstruction scheme under the condition that the constraints in the multi-objective fault reconstruction model are met. The fault reconfiguration scheme execution module is used to generate switching commands based on the fault reconfiguration scheme and execute them in the ship's medium-voltage DC power system.

Images