Power grid black-start path optimization method and system

Abstract

The invention discloses a power grid black-start path optimization method and system, and belongs to the technical field of power system recovery control, and the method comprises the steps: obtaining power prediction data based on the inherent uncertainty of the output power of a new energy station; constructing a black-start path optimization model according to the power prediction data; according to the power grid black-start path optimization method and system, a traditional A star algorithm is improved by introducing the weight coefficient, the path smoothing strategy and other strategies, and a black-start path optimization strategy with higher applicability is provided for a novel power system after new energy is accessed. The stability of the power grid in the black-start recovery process is ensured, and the problem that a traditional black-start path optimization algorithm cannot fully consider new energy output characteristics is solved.

Description

Technical Field

[0001] This invention belongs to the field of power system recovery control technology, specifically relating to a method and system for optimizing black start paths in power grids. Background Technology

[0002] With the introduction of the "dual carbon" target, the large-scale integration of new energy sources has become a key characteristic of energy transition, while also posing new challenges to the stability and reliability of the power system. When a severe grid fault leads to a complete blackout, black-start path optimization technology conducts a comprehensive analysis of the grid, identifies critical nodes and lines, and formulates the optimal path by rationally allocating startup resources, thereby improving the grid recovery speed and reducing risks during the recovery process. However, current black-start path optimization does not fully consider the output characteristics of new energy sources, which to some extent limits its universality in practical applications. Due to the significant intermittency and uncertainty of new energy sources, traditional black-start paths may no longer be applicable after a large-scale power outage.

[0003] Currently, to obtain the optimal path during black start, mathematical models are used to characterize the complex constraints and objective functions of the black start process. Mainstream path optimization algorithms such as the RRT algorithm, A* algorithm, and Dijkstra's algorithm are employed to solve the problem, aiming to find the optimal balance between recovery time, cost, and system stability. Decision analysis is then used to support the decision-making process of operators, thereby improving the practicality and effectiveness of black start path optimization algorithms. However, all of the aforementioned path optimization algorithms have shortcomings, specifically: the RRT algorithm, due to its randomness, suffers from low search efficiency and excessively long search time in high-dimensional spaces, making it difficult to meet real-time requirements; while the A* algorithm has strong search directionality, its performance depends on the design of the heuristic function, making it difficult to accurately estimate path planning in complex environments, resulting in reduced search efficiency and poor adaptability in dynamic environments; the Dijkstra algorithm has high time complexity, making it unsuitable for path planning in large-scale systems, and it cannot effectively select the path when multiple identical shortest paths exist. Therefore, a new black start path optimization method and system for power grids is needed to address these existing problems. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for optimizing black start paths in power grids, so as to solve the problem that black start cannot be correctly optimized after new energy sources are added to the power grid.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for optimizing black start paths in power grids, comprising the following steps:

[0006] The inherent uncertainty of the output power of new energy power plants was analyzed, and a BP neural network was used to model the uncertainty, which enabled accurate prediction of the ultra-short-term output power of the power plants. The prediction results provided key dynamic data input for subsequent optimization models.

[0007] Based on the power prediction data provided in the above steps, the objective function is to minimize the transmission line restoration time. Simultaneously, actual operational constraints such as line commissioning status and generator start-up power are comprehensively considered, thus constructing a clear mathematical framework for solving the optimal restoration path.

[0008] By introducing weighting coefficients to balance the recovery speed and system stability of the traditional A* algorithm, and by adopting a path smoothing strategy to enhance the engineering practicality of the recovery path, the improved A* algorithm is used to solve the optimization model, thereby obtaining the optimal recovery path for black start of the power grid with renewable energy.

[0009] Preferably, wind turbine output is typically determined by wind speed, and the Weibull model can accurately simulate the distribution characteristics of wind speed. Furthermore, its shape and scale parameters have clear physical meanings; the shape parameter reflects the concentration of wind speed distribution, while the scale parameter represents the average level of wind speed, making it highly interpretable when describing wind speed distribution.

[0010] Considering that the relationship between the output power of a wind turbine and the actual wind speed is usually nonlinear, when the wind speed reaches the cut-in wind speed, the turbine begins to convert wind energy into electrical energy. At this time, the output power will show an approximately linear increasing trend with the increase of wind speed until the output power of the turbine reaches the rated value. If the wind speed continues to rise, the output power of the turbine remains constant. A piecewise function is used to approximate its output characteristics.

[0011] A backpropagation (BP) neural network trained on actual wind speed data can effectively fit the shape and scale parameters of the Weibull distribution at different time periods, thereby obtaining a parameter fitting curve that changes over time. Combined with a piecewise function, it can predict the power output under different wind speed conditions.

[0012] Preferably, based on the uncertainty of the output power of new energy power plants, the power prediction data obtained includes:

[0013] The wind speed model is established as shown in the following equation:

[0014]

[0015] In the formula: f v (v) represents the wind speed model, v represents the actual wind speed; s represents the scale parameter; k represents the shape parameter;

[0016] The unit output characteristics are described using a piecewise function, as shown in the following equation:

[0017]

[0018] In the formula: P out Indicates the unit output characteristics, v in Indicates the cut-in wind speed; v out Indicates the cut-out wind speed; v r Indicates the rated wind speed; P r Indicates the rated power.

[0019] Preferably, the goal of the black start process is to quickly, safely, and stably rebuild the entire power system after a failure or disaster, ensuring the continuity and reliability of power supply. Therefore, this invention constructs an optimization model with the maximum total power generation of the system as the objective function, as shown in the following formula;

[0020]

[0021] In the formula, max E sys Represents the objective function; E sys E represents the total power generation of all generating units. ggen E represents the power generation of unit g; gcrank Ω represents the power consumption of unit g; G This represents the set of all unit nodes;

[0022] The objective function is transformed as shown in the following equation.

[0023]

[0024]

[0025] In the formula, P g This indicates the rated power of unit g; Indicates the recovery time of unit g; This indicates the time required for the startup phase of unit g; T represents the time required for the ramp-up phase of unit g; C represents the system recovery time. g This indicates the starting power of unit g;

[0026] Combining the objective function in the system recovery process, we can obtain:

[0027]

[0028] in:

[0029]

[0030] The objective function is transformed as follows:

[0031]

[0032] Preferably, the constraints of the black-start path optimization model are as follows:

[0033] Power transmission line restoration time constraints;

[0034] The unit's recovery time shall not be less than the sum of the start time of the recovery path IM and the time required for recharging, as shown in the following formula.

[0035]

[0036] In the formula, Indicates the recovery time of non-black start unit m; T represents the initial charging time of the recovery path of unit m; im Indicates the expected shortest recovery time; b im Ω is a 0-1 variable indicating whether a path is selected as a recovery path; bus This is the set of all non-machine nodes;

[0037] Recovery time constraints for each node in the recovery path: Based on the connection relationship between the node and the power generation unit, nodes are divided into two main categories: unit nodes and non-unit nodes. Their recovery time constraints are shown in the following formula.

[0038]

[0039] In the formula, Indicates the recovery time of non-black start unit m; Indicates the recovery time of non-unit node k; d mk M1 represents a 0-1 variable that indicates the relationship between non-black start unit m and non-unit node k; M2 represents a sufficiently large set of numbers in the Big M algorithm, whose size can invalidate the corresponding constraints when the 0-1 variable takes certain values.

[0040] Cold and hot start time constraints: The linearization method for the maximum hot start time constraint and the minimum cold start time constraint is shown in the following equation:

[0041]

[0042] In the formula, The constraint represents the maximum hot start time. The constraint represents the minimum cold start time. and M1 represents a 0-1 variable indicating whether the unit meets the maximum hot start time limit or the minimum cold start time limit; M2 represents a sufficiently large set of numbers in the Big M algorithm.

[0043] Serial recovery constraint: The recovery times for establishing connection paths among non-black-start units are staggered, as shown in the following formula.

[0044]

[0045] In the formula, This indicates the initial charging time of the recovery path for non-black start unit m; Indicates the recovery time of non-black start unit m; This indicates the initial charging time of the recovery path for non-black start units; Indicates the recovery time of non-black start unit g; and M3 is a 0-1 variable representing the relationship between the recovery times of g and m in a non-black start unit; M3 represents a sufficiently large set of numbers in the Big M algorithm.

[0046] Frequency constraints: For a recovered system, the permissible transient frequency fluctuation range is as follows:

[0047]

[0048] In the formula, Δf lim Indicates the upper limit of transient frequency fluctuation; C m This indicates the starting power of the non-black start unit m; This represents the set of generating units currently in operation; df g This represents the transient frequency response coefficient of unit g;

[0049] Incorporating the transient frequency response into the black start path optimization model, the model is simplified as follows:

[0050]

[0051] In the formula, A 0-1 variable indicating whether unit m is in the startup phase; and This is a 0-1 variable representing whether unit g is in a ramp-up state or a rated output state when unit m starts up;

[0052] New energy power constraint: the power output range of new energy power generation units;

[0053] The limit on the rate of change of new energy power is shown in the following formula.

[0054]

[0055] In the formula, Let represent the actual power at time t-1, and Δt represent the time interval between adjacent times. This represents the predicted power of the new energy source at time t; Indicates actual power; ΔP t Indicates the maximum allowable prediction error; ΔP r Indicates the maximum permissible rate of power change; ΔP zThis represents the total cumulative error allowed within time T.

[0056] Preferably, the A* algorithm is a heuristic search algorithm widely used in path planning and graph traversal. It expands on the node with the smallest heuristic value first until the shortest path is found. The heuristic value of the A* algorithm reflects the expected cost from the current node to the target node, and consists of the actual cost g(n) of the starting point and the estimated cost h(n) of the target point, as shown in the following formula.

[0057] f(n) = h(n) + g(n)

[0058] In the formula, f(n) represents the heuristic evaluation value, and the output value is the shortest path.

[0059] Preferably, a weight coefficient w is introduced into the A* algorithm to dynamically adjust the ratio of actual cost to estimated cost. When the value of w increases, the algorithm will tend to consider heuristic information h(n) more when selecting paths, which is more efficient in the search process but will reduce the accuracy of the obtained optimal path. Conversely, when the value of w decreases, the algorithm will consider the actual path cost g(n) more and increase the possibility of obtaining the globally optimal path, but at the same time, it will also increase the number of nodes to be calculated and the search time. Therefore, it is necessary to determine an appropriate weight coefficient to balance the search efficiency and optimization performance of the algorithm.

[0060] To better meet the path planning requirements during black start, the shortest path is defined as:

[0061] f(n) = (1-w)g(n) + wh(n)

[0062]

[0063] In the formula: w is the weight coefficient; l is the Euclidean distance from the current key node to the target point; L is the Euclidean distance from the initial node to the target point; a is the vector from the initial node to the target node; b is the vector from the current node to the target node; θ is the angle between vectors a and b.

[0064] Preferably, the A* algorithm is improved using a piecewise cubic Hermite interpolating polynomial (PCHIP) to reduce the risk of power grid collapse. The core principle of PCHIP interpolation is to utilize the local linearity and curvature information of data points to ensure the monotonicity and smoothness of the interpolation curve. Within each data interval, PCHIP interpolation constructs a cubic polynomial to fit the data points, ensuring that the polynomial's values ​​and first derivatives at the interval endpoints match the data points. n The cubic Hermite interpolation function f on ] k(x) is defined as follows:

[0065]

[0066] In the formula: x k y represents the ordered nodes within the interval; k For ordered node x k The corresponding function value; d k Let x be the first derivative of the interpolation function at the endpoints of the interval. k Represents ordered nodes within an interval; y k Represents an ordered node x k The corresponding function value; d k f represents the first derivative of the interpolation function at the endpoints of the interval. k (x) represents the cubic interpolation polynomial expression used to fit the curve within this interval, y k-1 x represents the coefficient of the linear term in the interpolation polynomial. k-1 d represents the coefficient of the quadratic term in the interpolation polynomial. k-1 This represents the coefficient of the cubic term in the interpolation polynomial.

[0067] Preferably, for each node, the actual recovery time cost from the initial state to the current state is calculated, and the heuristic recovery time cost from the current state to the target state is estimated, typically based on constraints such as the line's operational status and startup power. During the search process, the A* algorithm maintains a priority queue (i.e., an open set), sorted according to the value of the evaluation function, and prioritizes expanding the node with the smallest evaluation value. For each node, the algorithm checks whether its adjacent nodes satisfy constraints such as startup power. If they do, the recovery time cost of these adjacent nodes is calculated, and they are added to the open set. At the same time, the algorithm also needs to handle the constraints of the line's operational status to ensure that the power grid's operating rules are not violated during the recovery process.

[0068] When expanding a node, the A* algorithm updates the information of its neighboring nodes. If the path from the current node to the neighboring node has a lower recovery time cost, the parent node and cost of the neighboring node are updated. This continues until the target state is found, i.e., the state where all necessary paths are restored. Finally, the algorithm outputs the optimal recovery plan from the initial state to the target state.

[0069] The present invention also provides a power grid black start path optimization system, comprising:

[0070] The power prediction module is used to obtain power prediction data based on the inherent uncertainty of the output power of new energy power plants;

[0071] The black-start path optimization model construction module is used to construct a black-start path optimization model based on the power prediction data.

[0072] The module is used to solve the black-start path optimization model based on weighting coefficients and path smoothing strategies, and obtain the optimal recovery path for black-start of the power grid including new energy sources.

[0073] The technical effects and advantages of this invention are as follows: This black-start path optimization method and system for power grids improves the traditional A-Star algorithm by introducing strategies such as weighting coefficients and path smoothing. It proposes a more applicable black-start path optimization strategy for new power systems after the integration of new energy sources, ensuring the stability of the power grid during the black-start recovery process. It overcomes the problem that traditional black-start path optimization algorithms fail to fully consider the output characteristics of new energy sources. Compared with traditional black-start path optimization strategies, the black-start path optimization strategy for power grids with new energy sources proposed in this application, based on the improved A-Star algorithm, fully considers the uncertainty of the output power of new energy sources. It uses a BP neural network to perform ultra-short-term power prediction to support path decision-making, and combines weighting coefficients and path smoothing strategies to improve the A-Star algorithm. While ensuring the stable operation of the system, it improves the search efficiency of black-start paths and the practicality of recovery schemes. Attached Figure Description

[0074] Figure 1 This is a flowchart illustrating the steps of the black start path optimization strategy for power grids with new energy sources based on the improved A* algorithm of the present invention.

[0075] Figure 2 This is a schematic diagram of the ultra-short-term forecasting process in an embodiment of the present invention;

[0076] Figure 3 This is a schematic diagram illustrating the implementation process of the improved A* algorithm in an embodiment of the present invention;

[0077] Figure 4 This is a schematic diagram of the black start path optimization process based on the improved A* algorithm in an embodiment of the present invention;

[0078] Figure 5 This is a wiring diagram of the IEEE 39 system for new energy sources in an embodiment of the present invention;

[0079] Figure 6 This is a schematic diagram of the ultra-short-term power prediction curve in an embodiment of the present invention;

[0080] Figure 7 This is a schematic diagram comparing the available active power of different optimization schemes in the embodiments of the present invention;

[0081] Figure 8 This is a schematic diagram of the active power difference curves for different recovery schemes in this embodiment of the invention. Detailed Implementation

[0082] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0083] This invention provides, for example Figure 1 , Figure 4 The above describes a black-start path optimization method for power grids.

[0084] Specifically, the steps include the following:

[0085] Step 1: Analyze the inherent uncertainty of the output power of new energy power plants, and use a BP neural network to model the uncertainty, so as to realize the accurate prediction of the ultra-short-term output power of the power plants. The prediction results provide key dynamic data input for subsequent optimization models.

[0086] Step 2: Based on the power prediction data provided in Step 1, the objective function is to minimize the transmission line recovery time. Taking into account actual operational constraints such as line commissioning status and unit starting power, a clear mathematical framework is constructed to solve for the optimal recovery path.

[0087] Step 3: By introducing weighting coefficients to balance the recovery speed and system stability of the traditional A-Star algorithm, and by adopting a path smoothing strategy to enhance the engineering practicality of the recovery path, the improved A-Star algorithm is used to solve the optimization model, thereby obtaining the optimal recovery path for black start of the power grid with new energy sources.

[0088] In this embodiment of the invention, step 1 is specifically performed as follows:

[0089] Wind turbine output is typically determined by wind speed, and the Weibull model can accurately simulate the distribution characteristics of wind speed. Furthermore, its shape and scale parameters have clear physical meanings; the shape parameter reflects the concentration of wind speed distribution, while the scale parameter represents the average level of wind speed, making it highly interpretable in describing wind speed distribution. In addition, the Weibull model is highly adaptable, effectively handling seasonal and periodic variations in wind speed data and fitting wind speed data from different regions and time periods well. Therefore, this invention uses the Weibull distribution to establish a wind speed model, as shown in the following equation:

[0090]

[0091] In the formula: v is the actual wind speed; s is the scale parameter; k is the shape parameter;

[0092] Considering the output power P of the wind turbine outThe relationship between the wind speed and the actual wind speed v is usually non-linear. When the wind speed reaches the cut-in wind speed, the unit begins to convert wind energy into electrical energy. At this time, the output power will increase approximately linearly with the increase of wind speed until the unit's output power reaches the rated value. If the wind speed continues to increase, the unit's output power remains constant. A piecewise function is used to approximate its output characteristics, as shown in the following formula:

[0093]

[0094] In the formula: P out Indicates the unit output characteristics, v in For the cut-in wind speed; v out To cut off the wind speed; v r Rated wind speed; P r Rated power;

[0095] A backpropagation (BP) neural network trained on actual wind speed data can effectively fit the shape and scale parameters of the Weibull distribution over different time periods, thus obtaining a parameter fitting curve that varies with time. Combined with a piecewise function, this curve predicts the power output under different wind speed conditions. The specific implementation steps are as follows: Figure 2 As shown.

[0096] Step 2 of the method of the present invention is as follows:

[0097] The goal of the black start process is to quickly, safely, and stably rebuild the entire power system after a fault or disaster, ensuring the continuity and reliability of power supply. Therefore, this invention constructs an optimization model with the maximization of the total power generation of the system as the objective function, as shown in the following equation.

[0098]

[0099] In the formula, max E sys Represents the objective function; E sys E represents the total power generation of all generating units. ggen E represents the power generation of unit g; gcrank The power consumption of unit g; Ω G This is the set of all unit nodes;

[0100] To establish a black-start path optimization model based on mixed-integer linear programming, the objective function needs to be transformed as shown in the following equation.

[0101]

[0102] In the formula, P g The rated power of unit g; The recovery time for unit g; This refers to the time required for the startup phase of unit g. T is the time required for the ramp-up phase of unit g; C is the system recovery time; g Let g be the starting power of unit g;

[0103] Combining the objective function in the system recovery process, we can obtain:

[0104]

[0105] in:

[0106]

[0107] Since equation (7) does not contain variables, the objective function can be transformed as follows, that is, the objective function can be transformed by performing an equivalent transformation:

[0108]

[0109] The constraints are as follows:

[0110] (1) Transmission line restoration time constraint:

[0111] If a non-black-start unit m experiences a fault and needs to regain starting power, a recovery path must be established with the already recovered area. Therefore, when formulating a recovery plan, it must be ensured that the unit's recovery time is not less than the sum of the start time of the recovery path im and the time required for recharging, as shown in the following formula.

[0112]

[0113] In the formula, The recovery time for non-black start unit m; T is the initial charging time for the recovery path of unit m; im b is the expected shortest recovery time; im Ω is a 0-1 variable indicating whether a path is selected as the recovery path; bus This is the set of all non-machine nodes;

[0114] (2) Recovery time constraints for each node in the recovery path:

[0115] During power system restoration, to reduce system complexity and more effectively plan and implement restoration strategies, different types of nodes are classified and managed. Based on their connection relationship with generation units, nodes are divided into two main categories: generator nodes and non-generator nodes. Their restoration time constraints are shown in the following formula.

[0116]

[0117] In the formula, The recovery time for non-black start unit m; d represents the recovery time of non-unit node k; mk M1 is a 0-1 variable representing the relationship between non-black start unit m and non-unit node k; M1 is a sufficiently large set of numbers in the Big M algorithm, whose size can invalidate the corresponding constraints when the 0-1 variable takes certain values.

[0118] (3) Cold and hot start-up time limit constraints:

[0119] Cold start and warm start are two key stages for restarting a generating unit. Cold start typically refers to the process of restarting the unit after a complete shutdown, while warm start refers to the process of restarting the unit after a short shutdown. Because the two start-up methods have different time limits, it is difficult to simultaneously implement them in existing optimization studies. Therefore, to solve this problem, this invention provides a linearization method that can simultaneously achieve the maximum warm start time limit constraint and the minimum cold start time limit constraint, as shown in the following equation:

[0120]

[0121] In the formula, The constraint represents the maximum hot start time. The constraint represents the minimum cold start time. and M1 is a 0-1 variable representing whether the unit meets the maximum hot start time limit or the minimum cold start time limit; M2 represents a sufficiently large set of numbers in the Big M algorithm;

[0122] (4) Serial recovery constraint:

[0123] Parallel recovery strategies accelerate the overall system recovery speed by processing multiple transmission lines simultaneously. However, due to the capacitive effect of the lines, capacitive reactive power is generated at both ends. If compensation or adjustment is not made in time, voltage fluctuations will occur during the black start process. Therefore, this invention staggers the recovery times for establishing connection paths among non-black start units. The recovery time of each unit is calculated only after the previous unit has successfully started and is running stably. The serial recovery constraint constructed in this way can ensure the voltage stability of the system and reduce the impact on other equipment, as shown in the following formula.

[0124]

[0125] In the formula, The initial charging time for the recovery path of non-black start unit m; The recovery time for non-black start unit m; The initial charging time for the recovery path of the non-black start unit g; This refers to the recovery time of non-black start unit g; and M3 is a 0-1 variable representing the relationship between the recovery times of g and m in a non-black start unit; M3 represents a sufficiently large set of numbers in the Big M algorithm.

[0126] (5) Frequency constraint:

[0127] System frequency is a crucial indicator of power system operating status. Frequency fluctuations exceeding safe limits can damage equipment and disrupt the normal operation of black-start processes. Therefore, this invention introduces transient frequency response constraints to limit the starting power of non-black-start units, mitigating the impact of unit startup on system frequency. For a restored system, the permissible transient frequency fluctuation range is as follows:

[0128]

[0129] In the formula, Δf lim This represents the upper limit of transient frequency fluctuation, set to 0.5Hz; C m This indicates the starting power of the non-black start unit m; This represents the set of generating units currently in operation; df g This represents the transient frequency response coefficient of unit g;

[0130] In order to incorporate the transient frequency response into the black start path optimization model, it needs to be simplified:

[0131]

[0132] In the formula, A 0-1 variable indicating whether unit m is in the startup phase; and This is a 0-1 variable representing whether unit g is in a ramp-up state or a rated output state when unit m starts up;

[0133] (6) Power constraints of new energy sources:

[0134] To better utilize renewable energy resources and ensure the stability and security of grid recovery, this invention incorporates renewable energy power limitation constraints to achieve effective control and optimization of renewable energy power generation units during grid black start-up. These constraints are mainly reflected in the following two aspects: first, the power output range of the renewable energy power generation units, ensuring that renewable energy power plants can adjust their output power according to grid demand during grid recovery; second, a limit on the rate of change of renewable energy power, to prevent rapid fluctuations in renewable energy power from affecting grid stability, as shown in the following formula.

[0135]

[0136] In the formula, Let represent the actual power at time t-1, and Δt represent the time interval between adjacent times. Let be the predicted power of the new energy source at time t; This represents the actual power; ΔP t The maximum allowable prediction error; ΔP r The maximum allowable rate of power change; ΔP z This represents the total cumulative error allowed within time T.

[0137] In this embodiment of the invention, step 3 is specifically performed as follows:

[0138] The A* algorithm is a heuristic search algorithm widely used in path planning and graph traversal. It expands on the node with the smallest heuristic value first until the shortest path is found. The heuristic value of the A* algorithm reflects the expected cost from the current node to the target node, and consists of the actual cost g(n) of the starting point and the estimated cost h(n) of the target node, as shown in the following formula.

[0139] f(n)=h(n)+g(n) Formula (16)

[0140] The algorithm's iterative process involves updating and maintaining two lists: an open list that stores nodes to be checked, and a closed list that records nodes that have already been checked. The specific implementation steps are as follows:

[0141] Step 31: Initialize the open list and the closed list, put the starting node into the open list, and assign it an initial heuristic evaluation value f(n);

[0142] Step 32: In each iteration, the A* algorithm selects the node with the smallest evaluation value from the open list as the current node. The current node is then expanded to generate all possible child nodes, and the g(n), h(n), and f(n) function values ​​are calculated for each child node.

[0143] Step 33: Check if each child node is already in the closed list. If it is, ignore the child node; otherwise, add it to the open list. At the same time, if the child node is already in the open list and the new g(n) value is less than the previous value, update its f(n) value and parent node information.

[0144] Step 34: Repeat the above iterative process until the target node is found or the open list is empty. Output the obtained optimal path by backtracking the parent node.

[0145] To further improve the search efficiency of the A* algorithm and adapt it to specific problems, this invention introduces weighting coefficients and path smoothing strategies to improve the traditional algorithm. The improved A* algorithm guides the search through a heuristic evaluation function to find the path that minimizes the objective function. Optimizations have been made to the search strategy and path evaluation. The algorithm flow is as follows: Figure 3 As shown.

[0146] The traditional A* algorithm evaluation function is a simple sum of the actual cost and the heuristic cost. However, in the power grid restoration problem, different types of costs may have different priorities. By assigning weight coefficients to different costs, the evaluation function of the A* algorithm can be optimized, allowing for more flexible control over the algorithm's search preferences.

[0147] Based on the above analysis, a weight coefficient w is introduced into the A* algorithm to dynamically adjust the ratio of actual cost to estimated cost. When the value of w increases, the algorithm will tend to consider heuristic information h(n) more when selecting paths, which is more efficient in the search process but will reduce the accuracy of the obtained optimal path. Conversely, when the value of w decreases, the algorithm will consider the actual path cost g(n) more and increase the possibility of obtaining the globally optimal path, but at the same time it will increase the number of nodes to be calculated and the search time. Therefore, it is necessary to determine an appropriate weight coefficient to balance the search efficiency and optimization performance of the algorithm.

[0148] To better meet the path planning requirements during black start, the shortest path is defined as:

[0149] f(n)=(1-w)g(n)+wh(n) Formula (17)

[0150]

[0151] In the formula: w is the weight coefficient; l is the Euclidean distance from the current key node to the target point; L is the Euclidean distance from the initial node to the target point; a is the vector from the initial node to the target node; b is the vector from the current node to the target node; θ is the angle between vectors a and b.

[0152] During black start, the initial path obtained by the A* algorithm often consists of a series of turning points, which may lead to transient instability in the system during recovery and trigger the action of protection devices. Therefore, the A* algorithm is improved by using the piecewise cubic Hermite interpolating polynomial (PCHIP) to reduce the risk of power grid collapse.

[0153] The core principle of PCHIP interpolation lies in utilizing the local linearity and curvature information of data points to ensure the monotonicity and smoothness of the interpolation curve. Within each data interval, PCHIP interpolation constructs a cubic polynomial to fit the data points, ensuring that the values ​​and first derivatives of the polynomial at the interval endpoints match the data points. This makes the transition paths obtained by the A* algorithm smoother, within the interval [x0, x...]. n The cubic Hermite interpolation function f on ] k (x) is defined as follows:

[0154]

[0155] In the formula: x k y represents the ordered nodes within the interval; k For ordered node x k The corresponding function value; d k f is the first derivative of the interpolation function at the endpoints of the interval. k (x) represents the cubic interpolation polynomial expression used to fit the curve within this interval, y k-1 x represents the coefficient of the linear term in the interpolation polynomial. k-1 d represents the coefficient of the quadratic term in the interpolation polynomial. k-1 This represents the coefficient of the cubic term in the interpolation polynomial.

[0156] Based on the preliminary recovery path obtained from the black start, the path points are set as point set M. The coefficients of the above polynomial are determined by solving the linear equation. Hermite interpolation is applied to consider the coordinate sequence of data points. An appropriate number of interpolation points are selected between the start and end points to generate a smooth path that considers both the key points of the route and has continuous derivatives.

[0157] The black start path optimization process proposed in this invention is as follows: Figure 3 As shown, when A* algorithm processes the black-start recovery optimization model with transmission line recovery time as the objective function, it first abstracts the problem into a graph search problem, where nodes represent the various components in the power grid and their states, and edges represent the connection relationships between components; the objective function is to minimize the recovery time of the transmission line, while also considering constraints such as line commissioning status and startup power.

[0158] For each node, calculate the actual recovery time cost from the initial state to the current state, and estimate the heuristic recovery time cost from the current state to the target state. This calculation is usually based on constraints such as the line's operational status and startup power. The heuristic function needs to satisfy the consistency condition to ensure that the optimal path found is indeed the shortest recovery time path.

[0159] During the search process, the A* algorithm maintains a priority queue, or open set, sorted according to the value of the evaluation function, and prioritizes expanding the node with the smallest evaluation value. For each node, the algorithm checks whether its adjacent nodes meet constraints such as startup power. If they do, the algorithm calculates the recovery time cost of these adjacent nodes and adds them to the open set. Simultaneously, the algorithm also needs to handle constraints related to the line's operational status to ensure that the power grid's operating rules are not violated during the recovery process.

[0160] When expanding a node, the A* algorithm updates the information of its neighboring nodes. If a path from the current node to a neighboring node has a lower recovery time cost, the parent node and cost of the neighboring node are updated. This continues until the target state is found, i.e., the state where all necessary paths are restored. Finally, the algorithm outputs the optimal recovery plan from the initial state to the target state.

[0161] To verify the effectiveness of this invention, the following example illustrates the advancement of the proposed black start path optimization strategy for power grids with new energy sources based on the improved A-Star algorithm.

[0162] Using the IEEE 10-machine 39-node system as a simulation model, the proposed black-start path optimization model incorporating new energy units is verified. The topology of this system is as follows: Figure 5 As shown, the system consists of 10 generator sets, 46 transmission lines, 12 transformers, and 19 load nodes. Nodes 1, 2…39 in the diagram represent the node numbers of the power grid. The specific simulation settings and parameters are as follows: the generator set number is consistent with its node number; the generator start-up and bus restoration times are synchronized; generator set 30 is a black-start power source with a transient frequency response coefficient of 0.1683, while the other generator sets are non-black-start types, with a transient frequency response coefficient of 0.105 for all thermal power units. Detailed parameters are shown in Appendix Table 1. Wind farms are connected at nodes 36 and 37, each with an installed capacity of 400MW and equipped with 1.5MW DFIG wind turbines. Specific parameters are shown in Table 2. Furthermore, the restoration time for all transmission lines is set to 4 minutes. Throughout the simulation, all generator sets will strictly follow the output curves for power generation.

[0163] Table 1 Simulation parameters of thermal power units

[0164]

[0165] Table 2 DFIG Parameters

[0166]

[0167]

[0168] A BP neural network trained based on actual wind speed data fits the shape and scale parameters of the Weibull distribution over different time periods. Combined with a piecewise function, it predicts wind power output under different wind speed conditions. Figure 6 As shown;

[0169] Depend on Figure 6The comparison curves show that the proposed prediction algorithm, through deep learning of a large amount of wind speed and power data, can accurately capture the nonlinear relationship between wind speed and wind power, thereby achieving high-precision prediction of wind power. The small deviation between the prediction results and the actual power indicates that the algorithm has good fitting ability and can effectively cope with the impact of wind speed changes on wind power output, providing a theoretical basis for subsequent path optimization strategies.

[0170] According to the solution process, there are 13 key nodes (2, 3, 4, 6, 10, 14, 16, 17, 19, 22, 23, 25, 26) and 57 candidate recovery paths in this scenario. The recovery paths of the non-black start units are shown in Table 3.

[0171] Table 3. Unit Recovery Sequence in Path Optimization Scheme

[0172]

[0173]

[0174] During a black start, the available active power of the system is a crucial factor affecting the system recovery process. In the initial recovery phase, sufficient starting power is needed to restore all generators and critical loads. In the middle recovery phase, the available active power needs to meet the continuously increasing load demand to ensure the continuity and stability of the recovery process. In the later recovery phase, when the available active power reaches the total load of the outage system, the black start recovery process is considered complete. Therefore, using available active power as the evaluation index for optimization schemes, the changes in available active power after path optimization using the RRT algorithm, the traditional A-Star algorithm, and the improved A-Star algorithm proposed in this paper are compared as follows: Figure 7 and Figure 8 As shown;

[0175] Depend on Figure 7 and Figure 8 The comparative curve analysis shows that the improved A-Star algorithm exhibits superior performance in the black start recovery process of a power grid containing new energy sources. While ensuring stable recovery, it significantly improves the available active power of the power grid. Specifically, compared with RRT and the traditional A-Star algorithm, the proposed algorithm increases the maximum available active power by 283MW and 178MW respectively during the recovery process. It can dynamically adjust the recovery path according to the actual output of new energy sources and the real-time status of the power grid, maximizing the available active power of the system during the black start process.

[0176] The present invention also provides a power grid black start path optimization system, comprising:

[0177] The power prediction module is used to obtain power prediction data based on the inherent uncertainty of the output power of new energy power plants;

[0178] The black-start path optimization model construction module is used to construct a black-start path optimization model based on the power prediction data.

[0179] The module is used to solve the black-start path optimization model based on weighting coefficients and path smoothing strategies, and obtain the optimal recovery path for black-start of the power grid including new energy sources.

[0180] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing black-start paths in a power grid, characterized in that: include: Based on the uncertainty of the output power of new energy power plants, power prediction data is obtained; Based on the power prediction data, a black start path optimization model is constructed; Based on weighting coefficients and path smoothing strategies, a black-start path optimization model is solved to obtain the optimal recovery path for black-start power grids containing new energy sources.

2. The power grid black start path optimization method according to claim 1, characterized in that: The power prediction data obtained based on the uncertainty of the output power of new energy power plants includes: The wind speed model is established as shown in the following equation: In the formula: f v (v) represents the wind speed model, v represents the actual wind speed; s represents the scale parameter; k represents the shape parameter; The unit output characteristics are described using a piecewise function, as shown in the following equation: In the formula: P out Indicates the output characteristics of the unit, v in Indicates the cut-in wind speed; v out Indicates the cut-out wind speed; v r Indicates the rated wind speed; P r This indicates the rated power.

3. The power grid black start path optimization method according to claim 1, characterized in that: The step of constructing a black start path optimization model based on the power prediction data includes: constructing a black start path optimization model with the maximum total power generation as the objective function, as shown in the following formula; In the formula, max E sys Represents the objective function; E sys E represents the total power generation of all generating units. ggen E represents the power generation of unit g; gcrank Ω represents the power consumption of unit g; G This represents the set of all unit nodes; The objective function is transformed as shown in the following equation. In the formula, P g This indicates the rated power of unit g; Indicates the recovery time of unit g; This indicates the time required for the startup phase of unit g; T represents the time required for the ramp-up phase of unit g; C represents the system recovery time. g This indicates the starting power of unit g; Combining the objective function in the system recovery process, we can obtain: in: The objective function is transformed as follows:

4. A method for optimizing black-start paths in a power grid according to claim 1 or 3, characterized in that: The constraints of the black-start path optimization model include: Power transmission line restoration time constraints; The unit's recovery time shall not be less than the sum of the start time of the recovery path IM and the time required for recharging, as shown in the following formula. In the formula, Indicates the recovery time of non-black start unit m; T represents the initial charging time of the recovery path of unit m; im Indicates the expected shortest recovery time; b im Ω is a 0-1 variable indicating whether a path is selected as a recovery path; bus This is the set of all non-machine nodes; Recovery time constraints for each node in the recovery path: Based on the connection relationship between the node and the power generation unit, nodes are divided into two main categories: unit nodes and non-unit nodes. Their recovery time constraints are shown in the following formula. In the formula, Indicates the recovery time of non-black start unit m; Indicates the recovery time of non-unit node k; d mk M1 represents a 0-1 variable that indicates the relationship between non-black start unit m and non-unit node k; M2 represents a sufficiently large set of numbers in the Big M algorithm, whose size can invalidate the corresponding constraints when the 0-1 variable takes certain values. Cold and hot start time constraints: The linearization method for the maximum hot start time constraint and the minimum cold start time constraint is shown in the following equation: In the formula, The constraint represents the maximum hot start time. The constraint representing the minimum cold start time. and M1 represents a 0-1 variable indicating whether the unit meets the maximum hot start time limit or the minimum cold start time limit; M2 represents a sufficiently large set of numbers in the Big M algorithm. Serial recovery constraint: The recovery time for establishing a connection path for each non-black-start unit is staggered, as shown in the following formula. In the formula, This indicates the initial charging time of the recovery path for non-black start unit m; Indicates the recovery time of non-black start unit m; This indicates the initial charging time of the recovery path for non-black start units; Indicates the recovery time of non-black start unit g; and M3 is a 0-1 variable representing the relationship between the recovery times of g and m in a non-black start unit; M3 represents a sufficiently large set of numbers in the Big M algorithm. Frequency constraints: For a recovered system, the permissible transient frequency fluctuation range is as follows: In the formula, Δf lim Indicates the upper limit of transient frequency fluctuation; C m This indicates the starting power of the non-black start unit m; This represents the set of generating units currently in operation; df g This represents the transient frequency response coefficient of unit g; Incorporating the transient frequency response into the black start path optimization model, the model is simplified as follows: In the formula, A 0-1 variable indicating whether unit m is in the startup phase; and This is a 0-1 variable representing whether unit g is in a ramp-up state or a rated output state when unit m starts up; New energy power constraint: the power output range of new energy power generation units; The limit on the rate of change of new energy power is shown in the following formula. In the formula, Let represent the actual power at time t-1, and Δt represent the time interval between adjacent times. This represents the predicted power of the new energy source at time t; Indicates actual power; ΔP t Indicates the maximum allowable prediction error; ΔP r Indicates the maximum permissible rate of power change; ΔP z This represents the total cumulative error allowed within time T.

5. The power grid black start path optimization method according to claim 1, characterized in that: The solution to the black-start path optimization model includes: expanding by prioritizing the node with the smallest heuristic value until the shortest path is found; Update and maintain the open list of nodes to be inspected and the closed list of nodes that have already been inspected.

6. The power grid black start path optimization method according to claim 5, characterized in that: The process of expanding by prioritizing the node with the smallest heuristic value until the shortest path is found consists of the actual cost g(n) of the starting point and the estimated cost h(n) of the target point, as shown in the following equation. f(n) = h(n) + g(n) In the formula, f(n) represents the heuristic evaluation value, and the output value is the shortest path.

7. The power grid black start path optimization method according to claim 5, characterized in that: The process of updating and maintaining the open list of nodes to be inspected and the closed list of nodes that have already been inspected includes: Initialize the open and closed lists, add the starting node to the open list, and assign it an initial heuristic evaluation value f(n); In each iteration, the node with the smallest evaluation value is selected from the open list as the current node. The current node is expanded to generate all possible child nodes, and the actual cost g(n), estimated cost h(n), and function value f(n) of each child node are calculated. Check if each child node is already in the closed list. If it is, ignore the child node; otherwise, add it to the open list. Also, if the child node is already in the open list and the new g(n) value is less than the previous value, update its f(n) value and parent node information. Repeat the above iterative process until the target node is found or the open list is empty, and output the obtained optimal path by backtracking the parent node.

8. The power grid black start path optimization method according to claim 1, characterized in that: The weighting coefficients and path smoothing strategy include defining the shortest path as: f(n) = (1-w)g(n) + wh(n) In the formula: w represents the weight coefficient; l represents the Euclidean distance from the current key node to the target point; L represents the Euclidean distance from the initial node to the target point; a represents the vector from the initial node to the target node; b represents the vector from the current node to the target node; θ represents the angle between vectors a and b.

9. The method for optimizing black-start paths in a power grid according to claim 5, characterized in that: The black-start path optimization model also includes: Within each data interval, PCHIP interpolation fits the data points by constructing a cubic polynomial, ensuring that the values ​​and first derivatives of the polynomial at the endpoints of the interval match the data points. n The cubic Hermite interpolation function f on ] k (x) is defined as follows: In the formula: x k Represents ordered nodes within an interval; y k Represents an ordered node x k The corresponding function value; d k f represents the first derivative of the interpolation function at the endpoints of the interval. k (x) represents the cubic interpolation polynomial expression used to fit the curve within this interval, y k-1 x represents the coefficient of the linear term in the interpolation polynomial. k-1 d represents the coefficient of the quadratic term in the interpolation polynomial. k-1 This represents the coefficient of the cubic term in the interpolation polynomial.

10. A power grid black start path optimization system, characterized in that: include: The power prediction module is used to obtain power prediction data based on the uncertainty of the output power of new energy power plants; The black-start path optimization model construction module is used to construct a black-start path optimization model based on the power prediction data. The acquisition module is used to solve the black start path optimization model based on weight coefficients and path smoothing strategies to obtain the optimal recovery path for black start of the power grid including new energy sources.

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