An electric-gas integrated energy system cascading failure prediction method and system

Abstract

The application discloses an electric-gas comprehensive energy system cascade fault prediction method, and relates to the field of comprehensive energy system simulation control. The method comprises the following steps: firstly, an electric-gas comprehensive energy system cascade fault model is established, which comprises power system primary frequency modulation dynamics, natural gas fault propagation dynamics, coupling element dynamics and a fault model. Then, based on Newton interpolation and backward difference principles, an electric-gas cascade fault analysis model based on a numerical differential discrete formula is derived and established. Secondly, aiming at the high-dimension, nonlinearity and rigidity characteristics of the model, a variable order and variable step length calculation strategy is proposed to optimize the solving process, and a matrix updating and decomposition strategy based on the quasi-Newton method is adopted to reduce the operation cost. Finally, a key event positioning technology based on a backward difference vector is used to accurately lock the cascade generator tripping fault time. The application further discloses an electric-gas comprehensive energy system cascade fault prediction system, and the application can efficiently and accurately predict the cascade fault evolution process.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system simulation and control technology, and in particular to a method and system for predicting cascaded faults in an integrated electric-gas energy system. Background Technology

[0002] Integrated electric-gas (E-Gas) energy systems are a key approach to improving energy efficiency and absorbing renewable energy. However, the coupled operation of these two systems also introduces the risk of cross-system propagation of faults from a single system, posing a serious challenge to the safe operation of E-Gas integrated energy systems. There is an urgent need to accurately calculate, through simulation, the precise timing of faults such as natural gas system leaks and ice blockages propagating to the power system and triggering cascading disconnection events of synchronous generator units, providing early warning information so that operators can issue timely instructions based on fault warnings, thereby preventing the escalation of faults and the occurrence of cascading failures. However, the cascading fault model of an E-Gas integrated energy system constitutes a set of differential-algebraic equations with high-dimensional, nonlinear, and rigid characteristics, making it difficult to solve. Traditional methods based on characteristic lines / finite difference / Rosenbrock suffer from computational efficiency bottlenecks, making it difficult to achieve accurate and efficient prediction of cross-system cascading faults in electrical energy systems. Summary of the Invention

[0003] The technical problem this invention aims to solve is to overcome the shortcomings of existing technologies and provide a method and system for predicting cascade faults in integrated electric-gas energy systems. This involves establishing a cascade fault model for the integrated electric-gas energy system, including the dynamics of primary frequency regulation in the power system, the dynamics of natural gas fault propagation, the dynamics of coupling components, and the fault model. Based on Newton interpolation and backward difference principles, an electrical cascade fault analysis model based on numerical differential discretization formulas is derived and established. To address the high-dimensional, nonlinear, and rigid characteristics of the model, a variable-order, variable-step-size calculation strategy is proposed to optimize the solution process, and a matrix update and decomposition strategy based on the quasi-Newton method is adopted to reduce computational overhead. Furthermore, a key event location technology based on backward difference vectors is used to accurately pinpoint the timing of cascade tripping faults. This invention can efficiently and accurately predict the evolution of cascade faults, providing a valuable reference for system safety defense and control.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] A method for predicting cascaded faults in an integrated electric-gas energy system, according to the present invention, includes:

[0006] Step S1: Collect the operating parameters of the integrated electric-gas energy system. The operating parameters include the topology of the electric and gas systems, gas source output, generator parameters, primary frequency controller parameters, gas turbine parameters, line parameters, pipeline parameters, load data, and ambient temperature information.

[0007] Step S2: Based on the operating parameters of the integrated electric-gas energy system collected in Step S1, construct a cascaded fault model of the integrated electric-gas energy system in the form of differential-algebraic equations. The cascaded fault model of the integrated electric-gas energy system includes a power system model, a natural gas system model, and an electrical coupling element model. The power system model includes a power system electromechanical transient model, which includes a power network model, a synchronous machine model, and a dynamic model of the primary frequency regulation link. The natural gas system model includes a natural gas pipeline transport equation model, a natural gas flow node coupling model, and a model describing the leakage process. The electrical coupling element model includes an electric gas generator model and a gas turbine model.

[0008] Configure fault locations in advance;

[0009] Step S3: Solve the cascade fault model of the integrated electric-gas energy system constructed in step S2 using the numerical differential formula method to obtain the trajectories of the pressure of each natural gas node, the flow rate of natural gas pipeline, the power of the power bus, the power bus voltage, and the frequency variables of the power system.

[0010] Step S4: Based on the trajectories of natural gas node pressure, natural gas pipeline flow, power bus power, power bus voltage, and power system frequency obtained in Step S3, calculate the time of occurrence, duration, and severity index of the cascade fault.

[0011] As a further optimization of the cascade fault prediction method for the integrated electric-gas energy system described in this invention, pre-configuring the fault location refers to setting parameters such as the location of the fault and the diameter of the pipeline leakage hole.

[0012] As a further optimization of the cascade fault prediction method for the integrated electric-gas energy system described in this invention, the cascade fault model of the integrated electric-gas energy system constructed in step S2 is specifically as follows:

[0013] ;

[0014] in, Represents the singular mass matrix, This represents the derivative of the variable to be solved. The variables to be solved in the cascade fault model of the integrated electric-gas energy system include natural gas node pressure, natural gas pipeline flow rate, power bus power, power bus voltage, and power system frequency. This represents the variable to be solved at time 0; This represents the value of the variable to be solved at time 0; This indicates the dynamic evolution time of cascaded faults in an integrated electric-gas energy system. Indicates the total duration of cascaded failures in an integrated electric-gas energy system; Differential-algebraic equation models representing power systems, natural gas systems, and coupling elements; This indicates the set parameters for the location of the fault and the diameter of the leaking hole in the pipeline.

[0015] As a further optimization of the cascade fault prediction method for the integrated electric-gas energy system described in this invention, step S3 employs the numerical differential formula method to solve the cascade fault model of the integrated electric-gas energy system constructed in step S2, including:

[0016] S31. Set the calculation step size The total time interval of cascading failures in the integrated electric-gas energy system The time series is obtained by dividing the data evenly.

[0017] ;

[0018] in, The moment when the cascading failure occurs. For the first cascading failure process There are n time points, where n ranges from 0 to M, and M represents the last time point. The distance between adjacent time points is... ;

[0019] S32. For the nth time node from the 0th time node to the Nth time node, the cascade fault model of the integrated electric-gas energy system is discretized successively using the numerical differential formula to obtain the discrete model of the cascade fault of the integrated electric-gas energy system:

[0020] ;

[0021] in, This represents the variable to be solved in the discrete model of the cascaded fault of the integrated electric-gas energy system at the nth time point. Indicates the damping coefficient; , The precision order of the cascade fault prediction method for the integrated electric-gas energy system is represented, and j represents the index variable of the summation formula; This represents the variable to be solved in the system at the (n+1)th time point; ; express backward difference operator of order, express Order difference factor, Let represent the variable to be solved at the (n+1)th time point in the system. The guess value, express Order difference factor, The results of the differential-algebraic equation model output of the power system, natural gas system and coupling elements at the (n+1)th time node; This represents the (n+1)th time node. This represents the nth time node;

[0022] S33. Solve the discrete model of cascaded faults in the integrated electric-gas energy system; details are as follows:

[0023] Step S33-0: Transform formula (2) using the Newton-Raphson iteration scheme to obtain:

[0024] ;

[0025] Here, i represents the iteration number, and the initial value of i is set to 0. express The first moment The result of the second iteration This represents the iteration matrix of the cascading fault model. Indicates to The i-th correction vector, This represents the output of the differential-algebraic equation model of the power system, natural gas system, and coupling elements at the (n+1)th time node. A guess value, This represents the weighted sum of the difference vectors;

[0026] ;

[0027] The Jacobian matrix has the following format:

[0028] ;

[0029] Representing dimensions and The same identity matrix, express exist Point about The partial derivatives;

[0030] Step S33-1: Solve equation (3) to obtain ;

[0031] Step S33-2: For Update and get

[0032] ;

[0033] in, This represents the (n+1)th time node. The result of the (i+1)th iteration;

[0034] Step S33-3: Increment the iteration number, i.e., the value of i, by 1;

[0035] Step S33-4: Calculation ,in, Represents the infinite norm, This indicates a pre-defined error limit; if If so, proceed to step S34; otherwise, return to step S33-1.

[0036] S34. Calculation of a discrete model for cascaded faults in an integrated electric-gas energy system. Moment Order truncation error ;

[0037] ;

[0038] in, The vector to be determined The k+1 order backward difference operator, ;

[0039] Update the calculation step size.

[0040] ;

[0041] in, Indicates the updated step size. express The One portion, Indicates the relative error limit. As a safety factor, Indicates to From 1 to Take the maximum value among them. For the variables to be solved The k+1th order local truncation error at time n+1 One component;

[0042] After updating the step size, Update using backward differences of each order to obtain

[0043] ;

[0044] in, , Indicates the step size transformation coefficient. Represents the original difference transformation matrix. Represents the step size transformation coefficients The difference transformation matrix under, Indicates the new step size. Indicates step size The vector formed by the backward differences of each order, Indicates a new step size The vector formed by the backward differences of each order;

[0045] ;

[0046] in, This represents the element in the p-th row and r-th column of the original difference transformation matrix U. express The element in the p-th row and r-th column of the difference transformation matrix;

[0047] Indicates step size The vector formed by the backward differences of each order;

[0048] ;

[0049] in, The vector to be determined The q-order backward difference operator;

[0050] Indicates a new step size The vector formed by the backward differences of each order;

[0051] ;

[0052] Indicates a new step size Defined q-order backward difference operator;

[0053] Update step S32: The accuracy order of the cascade fault prediction method for the integrated electric-gas energy system is calculated separately.

[0054] ;

[0055] ;

[0056] in, express The step size corresponding to the order scheme, express The step size corresponding to the order scheme, The discrete model of cascaded faults in the integrated electric-gas energy system is shown in Moment The i-th component of the truncation error. The discrete model of cascaded faults in the integrated electric-gas energy system is shown in Moment The i-th component of the truncation error. This is the l-th component of the absolute error limit;

[0057] like Then the accuracy order of the cascade fault prediction method for the integrated electric-gas energy system is reduced by 1, i.e., k = k - 1. Then, the accuracy order of the cascade fault prediction method for the integrated electric-gas energy system is increased by 1, i.e., k=k+1.

[0058] As a further optimization scheme for the cascade fault prediction method of the integrated electric-gas energy system described in this invention, When performing the calculation, a quasi-Newton method is used, that is, if and only if The number of iterations exceeds the set maximum number of iterations. At that time, Update and decompose.

[0059] As a further optimization of the cascade fault prediction method for an integrated electric-gas energy system described in this invention, step S4 includes:

[0060] S41. Construct the following dense output formula for the time interval. Locate the internal fault;

[0061] ;

[0062] in, Indicates taking the first element of the matrix. Column elements, Indicates time interval The point that does not belong to any point in the time series of step S31 The variable to be solved at time t The value, Indicates step size The difference transformation matrix is ​​given by the fault equation. This indicates the occurrence of a fault event such as the natural gas pressure dropping to a threshold. This represents the difference between the gas turbine inlet pressure at time t and the natural gas pressure threshold that causes the fault to occur.

[0063] S42. Test the expression within every two adjacent time nodes. Is it less than 0? If the expression Then, according to equation (15), a binary search is used to locate the time when the fault occurred. ; express The difference between the gas turbine inlet pressure at any given moment and the natural gas pressure threshold that would cause a fault to occur; express The difference between the gas turbine inlet pressure at any given moment and the natural gas pressure threshold that would cause a fault to occur;

[0064] S43, Positioning Time Interval The moment of the first failure within The second fault occurred at the time The third failure occurred at that time. Until the nth failure occurs The interval between the occurrence times of each fault is calculated as the fault duration.

[0065] The pressure of each natural gas node, the flow rate of the natural gas pipeline, the power bus power, the power bus voltage, and the power system frequency obtained in step S3 are input into the emergency dispatch model for cascading faults of the integrated electric-gas energy system. The load shedding amount of each node in the natural gas system and the power system is solved, and the severity index of the cascading fault is obtained based on the load shedding amount of each node in the natural gas system and the power system.

[0066] ;

[0067] in, Indicates the first The load shedding amount of each node, This represents the total load of the v-th node. This is an indicator of the severity of cascading failures.

[0068] A cascaded fault prediction system for an integrated electric-gas energy system, comprising:

[0069] The data acquisition module is used to collect the operating parameters of the integrated electric-gas energy system. The operating parameters include the topology of the electric and gas systems, gas source output, generator parameters, primary frequency controller parameters, gas turbine parameters, line parameters, pipeline parameters, load data, and ambient temperature information.

[0070] The model building module is used to construct a cascade fault model of the integrated electric-gas energy system in the form of differential-algebraic equations based on the collected operating parameters of the integrated electric-gas energy system. The cascade fault model of the integrated electric-gas energy system includes a power system model, a natural gas system model, and electrical coupling element models. The power system model includes a power system electromechanical transient model, which includes a power network model, a synchronous machine model, and a dynamic model of the primary frequency regulation link. The natural gas system model includes a natural gas pipeline transport equation model, a natural gas flow node coupling model, and a model describing the leakage process. The electrical coupling element models include an electric gas generator model and a gas turbine model.

[0071] Configure fault locations in advance;

[0072] The fault prediction module is used to solve the cascade fault model of the electric-gas integrated energy system using the numerical differential formula method, and obtain the trajectories of the pressure of each natural gas node, the flow rate of natural gas pipeline, the power bus power, the power bus voltage, and the frequency variables of the power system.

[0073] The fault information output module is used to calculate the time of occurrence, duration, and severity index of cascade faults based on the trajectories of natural gas node pressure, natural gas pipeline flow, power bus power, power bus voltage, and power system frequency obtained in step S3.

[0074] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0075] Compared with existing technologies, this invention discloses a method and system for predicting cascade faults in an integrated electric-gas energy system based on numerical differential formulas. Compared with existing technologies, it has achieved significant and verifiable beneficial effects in terms of computational efficiency and prediction accuracy.

[0076] In terms of computational efficiency, this invention shortens the total computation time steps for fault prediction by constructing an innovative numerical differential formula and adjusting the order and step size. It also reduces the overhead of matrix updates and decomposition through a quasi-Newton method. Therefore, this invention can significantly reduce the time and computational resources required for fault prediction.

[0077] In terms of prediction accuracy, this invention proposes a dense output format based on high-order backward numerical differentiation to achieve precise location of the fault occurrence time, thereby providing accurate information for fault early warning and control. Attached Figure Description

[0078] Figure 1 This is a schematic diagram of a typical integrated electric-gas energy system structure for which the method of this invention is applied;

[0079] Figure 2This is a flowchart of the steps of the present invention, which is a method for predicting cascaded faults in an integrated electric-gas energy system based on numerical differential formulas.

[0080] Figure 3 This is a description of cascaded fault events and their order of occurrence in the test examples of this invention. Detailed Implementation

[0081] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0082] Example

[0083] This embodiment is applied to an integrated electric-gas energy system, the structure of which is as follows: Figure 1 As shown, the system consists of a 9-node power system and an 11-node natural gas network. The power system comprises three generating units, and the natural gas system comprises two gas sources. Two gas turbine units and an electric gas generator operate as coupling devices between the power system and the natural gas system.

[0084] A method for predicting cascaded faults in an integrated electric-gas energy system based on numerical differential formulas, such as... Figure 2 As shown, it includes the following steps:

[0085] S1. Data Acquisition: Obtain the operating parameters of the integrated electric-gas energy system. The operating parameters include the topology of the electric and gas systems, gas source output, generator parameters, primary frequency controller parameters, gas turbine parameters, line parameters, pipeline parameters, load data, and ambient temperature information.

[0086] S2. Model Construction: Based on the data collected in step S1, construct a cascaded fault model of the integrated electric-gas energy system with differential algebraic equations. The electric system model includes an electromechanical transient model of the electric system containing the primary frequency regulation process; the natural gas system model includes a natural gas pipeline transport equation model, a natural gas flow node coupling model, and models describing the evolution of leakage and ice blockage; the electrical coupling component models include an electric gas generator model and a gas turbine model. Set the fault location and detailed fault parameters.

[0087] The cascaded fault model of the integrated electric-gas energy system is as follows:

[0088]

[0089] in, Represents the singular mass matrix; This represents the natural gas node pressure, natural gas pipeline flow rate, power bus power, power bus voltage, and power system frequency variables to be solved in the system. These represent the derivatives of the variables to be solved; This represents the initial values ​​of these variables to be solved; This represents the value of the variable to be solved at time 0; Indicates the system's dynamic evolution time; Indicates the total simulation time; Differential-algebraic equation models representing power systems, natural gas systems, and coupling elements; It indicates the location of the fault and detailed fault parameters.

[0090] S3. Fault Prediction: The cascade fault prediction model constructed in step S2 is solved using a numerical differential formula method to obtain the trajectories of natural gas node pressure, natural gas pipeline flow, power bus power, power bus voltage, and power system frequency variables.

[0091] The fault prediction method includes the following steps:

[0092] S31. Initialization: Set the calculation step size The simulation time interval Uniform division yields time series.

[0093]

[0094] The distance between adjacent time nodes is Time nodes The corresponding variables to be solved are: .

[0095] S32. Model Discretization: For time n from time 0 to time M, the cascaded fault model is discretized successively using the numerical differentiation formula, resulting in the following model:

[0096]

[0097] in, Indicates the damping coefficient; ; express The value of the variable to be solved at time t; ; express backward difference operator.

[0098] S33. Solving the discrete model: For scheme (2), a Newton-Raphson iterative scheme is used to solve it, and the model is obtained as follows:

[0099]

[0100] in, express The first moment The result of the next iteration;

[0101]

[0102] The Jacobian matrix has the following format:

[0103]

[0104] Representing dimensions and The same identity matrix, express exist Point about The partial derivatives of .

[0105] In the The calculation is performed using a quasi-Newton method. That is, if and only if The number of iterations exceeds the set maximum number of iterations. When, for the formula (5) shown Update and decompose.

[0106] Calculated using equation (3) Afterwards, Update and get

[0107]

[0108] Repeat the above process until... ,in, Represents the infinite norm, This indicates the given error limit.

[0109] S34, Step Size, Order Update: Calculation Formula (2) Moment Order truncation error

[0110]

[0111] in, , Calculated from S33.

[0112] Update the calculation step size.

[0113]

[0114] in, Indicates the updated step size. express The One portion, Indicates the relative error limit. As a safety factor, Indicates taking pairs From 1 to Take the maximum value among them.

[0115] After updating the step size, Update using backward differences of each order to obtain

[0116]

[0117] in, , and They represent Transformation matrix of order,

[0118]

[0119] Indicates step size The vector formed by the backward differences of each order

[0120]

[0121] Indicates step size The vector formed by the backward differences of each order

[0122]

[0123] Indicates step size The defined backward difference.

[0124] The optimal order was calculated, and the results were obtained separately.

[0125]

[0126]

[0127] in, express The step size corresponding to the order scheme, express The step size corresponding to the order scheme, Formula (2) means that... Moment First-order truncation error, Formula (2) means that... Moment Truncation error.

[0128] like Then the order is reduced by 1, if Then the order is increased by 1.

[0129] S4. Fault Information Output: Based on the output results of step S3, calculate indicators such as the time of occurrence, duration, and severity of cascade faults.

[0130] S41. Dense Output Formula Construction: Construct the following dense output formula for the time interval. Locating internal faults

[0131]

[0132] in, Indicates time interval any inner The variable to be solved at time t The value of . Let the fault equation be... This indicates the occurrence of a fault event such as the natural gas pressure dropping to a threshold.

[0133] S42. Fault occurrence time search: Check within each time step. Is it less than 0? If so... Then, according to equation (15), a binary search is used to accurately locate the time of the fault occurrence. .

[0134] S43. Fault Information Calculation: Location Time Interval All fault moments within , , , The interval between the occurrence times of each fault is calculated as the fault duration. The load shedding at each node of the natural gas and power systems is statistically analyzed to obtain a fault severity index.

[0135]

[0136] in, Represents a node Shear load, Represents a node Total load.

[0137] S5. Information Dissemination: The fault information generated in step S4 is disseminated to the integrated electric-gas energy system control center to execute the corresponding control and fault recovery strategies.

[0138] Test case

[0139] The integrated energy system in this embodiment is as follows: Figure 1 As shown, the system consists of a 9-node power system and an 11-node natural gas network. The power system comprises three generating units, and the natural gas system comprises two gas sources. Two gas turbine units and an electric gas generator operate as coupling devices between the power system and the natural gas system. The natural gas pipeline is 51 kilometers long and 0.5 meters in diameter. A leakage fault with a diameter of 0.3 meters is set between natural gas nodes 2 and 3. The fault occurrence time is set at 300 seconds, and the total simulation time is 15 hours. The sequence of fault occurrence in the system is as follows: Figure 3 As shown, where, Indicates the time when the fault occurred. , , These represent the times when P2G devices are saturated, GT1 switches off, and GT0 switches off, respectively.

[0140] To verify the advantages of the method of this invention over traditional fault prediction methods, the invention was tested in a comprehensive energy system test case comprising a 9-node power system and an 11-node natural gas network. The method characteristics used for comparison are shown in Table 1 below:

[0141] Table 1. Introduction to Comparison Methods

[0142]

[0143] In the table, the baseline method, M1, and M2 are traditional methods, while M3 and M4 are the methods proposed in this invention. M3 is used to verify the acceleration effect of the quasi-Newton method proposed in this invention. For M3 and M4, parameters are set... , ,right When, set ,right When, set ,right When, set .

[0144] The location results of each simulation event are shown in Table 2 below:

[0145] Table 2 Comparison of Simulation Event Localization Results

[0146]

[0147] For the timing of saturation events in electro-gas conversion equipment Method M3 achieved the highest accuracy, followed closely by M4 and M2. The positioning errors of these methods were all within 2 seconds. In stark contrast, M1 exhibited a huge error exceeding 100 seconds, which would inevitably lead to incorrect predictions of equipment state transitions. Regarding the GT1's switching timing... A similar trend can be observed; compared to the baseline method, both M3 and M4 can pinpoint the event time with high accuracy. However, M1 and M2 show significant deviations, exceeding 200 seconds from the actual event time. Regarding the final event where GT0 was removed... M3 and M4 successfully simulated the cascade shearing process of the gas turbine and obtained similar timing results. Conversely, M1 diverged at this stage and failed to yield valid simulation results; M2 was affected by... The calculation bias leads to a large error in the prediction of fault results.

[0148] The computational overhead of the above methods is shown in Table 3 below:

[0149] Table 3 Comparison of Simulation Calculation Costs

[0150]

[0151] The proposed M4 method is clearly the most computationally efficient, being more than 193 times faster than M1 and more than 7 times faster than M2. This significant performance gap can be explained as follows. The inefficiency of M1 is mainly attributed to its alternating solution strategy, which requires expensive alternating iterative loops between the power system and the natural gas system subsystems. Furthermore, as a fixed-step solver, it requires an extremely large total number of time steps. Simultaneous variable-step solvers (M2-M4) are inherently more efficient because they require far fewer time steps. Although M2 has a higher time order, it performs conservatively in the highly dynamic post-leakage stage where variable fluctuations are significant. M3 and M4 are more flexible, allowing for larger step sizes in this stage, thus validating the importance of variable-step capability for improving computational performance. Besides the number of time steps, computational cost is also primarily affected by matrix operations. In the current simulation scenario, the Jacobian matrix becomes highly complex, with a dimension of 10243 and containing over 100,000 non-zero elements. On average, evaluating the Jacobian matrix takes 1.8 milliseconds, and performing its LU decomposition takes 3.2 milliseconds. As shown in Table 3, the quasi-Newton strategy in M4 significantly reduces these operations. The lower computational performance of M2 is also attributed to these requirements: it needs to perform accurate Jacobian matrix evaluation and decomposition at every step, and each step also requires an additional six linear solutions.

[0152] The comparative results of this test case fully demonstrate that the present invention constructs an electrical cascade fault analysis model based on numerical differential discretization formulas. Addressing the high-dimensional, nonlinear, and rigid characteristics of the model, it proposes a variable-order, variable-step-size calculation strategy to optimize the solution process. Furthermore, it employs a matrix update and decomposition strategy based on the quasi-Newton method to reduce computational overhead. Utilizing a key event localization technique based on backward difference vectors, it can quickly and accurately pinpoint the fault moment of the cascade switch, thus verifying the significant advantages and practicality of the present invention.

[0153] In the description of this specification, the references to terms such as "an embodiment," "example," and "specific example" indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. It should be noted that the above description merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting cascaded faults in an integrated electric-gas energy system, characterized in that, include: Step S1: Collect the operating parameters of the integrated electric-gas energy system. The operating parameters include the topology of the electric and gas systems, gas source output, generator parameters, primary frequency controller parameters, gas turbine parameters, line parameters, pipeline parameters, load data, and ambient temperature information. Step S2: Based on the operating parameters of the integrated electric-gas energy system collected in Step S1, construct a cascaded fault model of the integrated electric-gas energy system in the form of differential-algebraic equations. The cascaded fault model of the integrated electric-gas energy system includes a power system model, a natural gas system model, and an electrical coupling element model. The power system model includes a power system electromechanical transient model, which includes a power network model, a synchronous machine model, and a dynamic model of the primary frequency regulation link. The natural gas system model includes a natural gas pipeline transport equation model, a natural gas flow node coupling model, and a model describing the leakage process. The electrical coupling element model includes an electric gas generator model and a gas turbine model. Configure fault locations in advance; Step S3: Solve the cascade fault model of the integrated electric-gas energy system constructed in step S2 using the numerical differential formula method to obtain the trajectories of the pressure of each natural gas node, the flow rate of natural gas pipeline, the power of the power bus, the power bus voltage, and the frequency variables of the power system. Step S4: Based on the trajectories of natural gas node pressure, natural gas pipeline flow, power bus power, power bus voltage, and power system frequency obtained in Step S3, calculate the time of occurrence, duration, and severity index of the cascade fault.

2. The method for predicting cascaded faults in an integrated electric-gas energy system according to claim 1, characterized in that, Pre-configuring fault locations refers to setting parameters such as the location of the fault and the diameter of the leaking hole in the pipeline.

3. The method for predicting cascaded faults in an integrated electric-gas energy system according to claim 2, characterized in that, The cascading fault model of the integrated electric-gas energy system constructed in step S2 is as follows: ； in, Represents the singular mass matrix, This represents the derivative of the variable to be solved. The variables to be solved in the cascade fault model of the integrated electric-gas energy system include natural gas node pressure, natural gas pipeline flow rate, power bus power, power bus voltage, and power system frequency. This represents the variable to be solved at time 0; This represents the value of the variable to be solved at time 0; This indicates the dynamic evolution time of cascaded faults in an integrated electric-gas energy system. Indicates the total duration of cascaded failures in an integrated electric-gas energy system; Differential-algebraic equation models representing power systems, natural gas systems, and coupling elements; This indicates the set parameters for the location of the fault and the diameter of the leaking hole in the pipeline.

4. The method for predicting cascaded faults in an integrated electric-gas energy system according to claim 3, characterized in that, Step S3 uses the numerical differential formula method to solve the cascading fault model of the integrated electric-gas energy system constructed in step S2, including: S31. Set the calculation step size The total time interval of cascading failures in the integrated electric-gas energy system The time series is obtained by uniformly dividing the data. ； in, The moment when the cascading failure occurs. For the first cascading failure process There are n time points, where n ranges from 0 to M, and M represents the last time point. The distance between adjacent time points is... ; S32. For the nth time node from the 0th time node to the Nth time node, the cascade fault model of the integrated electric-gas energy system is discretized successively using the numerical differential formula to obtain the discrete model of the cascade fault of the integrated electric-gas energy system: ； in, This represents the variable to be solved in the discrete model of the cascaded fault of the integrated electric-gas energy system at the nth time point. Indicates the damping coefficient; , The precision order of the cascade fault prediction method for the integrated electric-gas energy system is represented, and j represents the index variable of the summation formula; This represents the variable to be solved in the system at the (n+1)th time point; ; express backward difference operator of order, express Order difference factor, Let n represent the (n+1)th time node, and the variable to be solved at the (n+1)th time node in the system. The guess value, express Order difference factor, The results of the differential-algebraic equation model output of the power system, natural gas system and coupling elements at the (n+1)th time node; This represents the (n+1)th time node. This represents the nth time point; S33. Solve the discrete model of cascaded faults in the integrated electric-gas energy system; details are as follows: Step S33-0: Transform formula (2) using the Newton-Raphson iteration scheme to obtain: ； Here, i represents the iteration number, and the initial value of i is set to 0. express The first moment The result of the second iteration This represents the iteration matrix of the cascading fault model. Indicates to The i-th correction vector, This represents the output of the differential-algebraic equation model of the power system, natural gas system, and coupling elements at the (n+1)th time node. A guess value, This represents the weighted sum of the difference vectors; ； The Jacobian matrix has the following format: ； Representing dimensions and The same identity matrix, express exist Point about The partial derivatives; Step S33-1: Solve equation (3) to obtain ; Step S33-2: For Update and get ； in, This represents the (n+1)th time node. The result of the (i+1)th iteration; Step S33-3: Increment the iteration number, i.e., the value of i, by 1; Step S33-4: Calculation ,in, Represents the infinite norm, This indicates a pre-defined error limit; if If the result is positive, proceed to step S34; otherwise, return to step S33-1. S34. Calculation of a discrete model for cascaded faults in an integrated electric-gas energy system. Moment Order truncation error ; ； in, The vector to be determined The k+1 order backward difference operator, ; Update the calculation step size. ； in, Indicates the updated step size. express The One portion, Indicates the relative error limit. As a safety factor, Indicates to From 1 to Take the maximum value among them. For the variables to be solved The k+1th order local truncation error at time n+1 One component; After updating the step size, Update using backward differences of each order to obtain ； in, , Indicates the step size transformation coefficient. Represents the original difference transformation matrix. Represents the step size transformation coefficients The difference transformation matrix under, Indicates the new step size. Indicates step size The vector formed by the backward differences of each order, Indicates a new step size The vector formed by the backward differences of each order; ； in, This represents the element in the p-th row and r-th column of the original difference transformation matrix U. express The element in the p-th row and r-th column of the difference transformation matrix; Indicates step size The vector formed by the backward differences of each order; ； in, The vector to be determined The q-order backward difference operator; Indicates a new step size The vector formed by the backward differences of each order; ； Indicates a new step size Defined q-order backward difference operator; Update step S32: The accuracy order of the cascade fault prediction method for the integrated electric-gas energy system is calculated separately. ； ； in, express The step size corresponding to the order scheme, express The step size corresponding to the order scheme, The discrete model of cascaded faults in the integrated electric-gas energy system is shown in Moment The i-th component of the truncation error. The discrete model of cascaded faults in the integrated electric-gas energy system is shown in Moment The i-th component of the truncation error. This is the l-th component of the absolute error limit; like Then the accuracy order of the cascade fault prediction method for the integrated electric-gas energy system is reduced by 1, i.e., k = k - 1. Then, the accuracy order of the cascade fault prediction method for the integrated electric-gas energy system is increased by 1, i.e., k=k+1.

5. The method for predicting cascaded faults in an integrated electric-gas energy system according to claim 3, characterized in that, right When performing the calculation, a quasi-Newton method is used, that is, if and only if The number of iterations exceeds the set maximum number of iterations. At that time, Update and decompose.

6. The method for predicting cascaded faults in an integrated electric-gas energy system according to claim 3, characterized in that, Step S4 includes: S41. Construct the following dense output formula for the time interval. Locate the internal fault; ； in, Indicates taking the first element of the matrix. Column elements, Indicates time interval The point that does not belong to any point in the time series of step S31 The variable to be solved at time t The value, Indicates step size The difference transformation matrix is ​​given by the fault equation. This indicates the occurrence of a fault event such as the natural gas pressure dropping to a threshold. This represents the difference between the gas turbine inlet pressure at time t and the natural gas pressure threshold that causes the fault to occur. S42. Test the expression within every two adjacent time nodes. Is it less than 0? If the expression Then, according to equation (15), a binary search is used to locate the time when the fault occurred. ; express The difference between the gas turbine inlet pressure at any given moment and the natural gas pressure threshold that would cause a fault to occur; express The difference between the gas turbine inlet pressure at any given moment and the natural gas pressure threshold that would cause a fault to occur; S43, Positioning Time Interval The moment of the first failure within The second fault occurred at the time The third failure occurred at that time. Until the nth failure occurs The interval between the occurrence times of each fault is calculated as the fault duration. The pressure of each natural gas node, the flow rate of the natural gas pipeline, the power bus power, the power bus voltage, and the power system frequency obtained in step S3 are input into the emergency dispatch model for cascading faults of the integrated electric-gas energy system. The load shedding amount of each node in the natural gas system and the power system is solved, and the severity index of the cascading fault is obtained based on the load shedding amount of each node in the natural gas system and the power system. ； in, Indicates the first The load shedding amount of each node, This represents the total load of the v-th node. This is an indicator of the severity of cascading failures.

7. A cascaded fault prediction system for an integrated electric-gas energy system, characterized in that, include: The data acquisition module is used to collect the operating parameters of the integrated electric-gas energy system. The operating parameters include the topology of the electric and gas systems, gas source output, generator parameters, primary frequency controller parameters, gas turbine parameters, line parameters, pipeline parameters, load data, and ambient temperature information. The model building module is used to construct a cascade fault model of the integrated electric-gas energy system in the form of differential-algebraic equations based on the collected operating parameters of the integrated electric-gas energy system. The cascade fault model of the integrated electric-gas energy system includes a power system model, a natural gas system model, and electrical coupling element models. The power system model includes a power system electromechanical transient model, which includes a power network model, a synchronous machine model, and a dynamic model of the primary frequency regulation link. The natural gas system model includes a natural gas pipeline transport equation model, a natural gas flow node coupling model, and a model describing the leakage process. The electrical coupling element models include an electric gas generator model and a gas turbine model. Configure fault locations in advance; The fault prediction module is used to solve the cascade fault model of the electric-gas integrated energy system using the numerical differential formula method, and obtain the trajectories of the pressure of each natural gas node, the flow rate of natural gas pipeline, the power bus power, the power bus voltage, and the frequency variables of the power system. The fault information output module is used to calculate the time of occurrence, duration, and severity index of cascade faults based on the trajectories of natural gas node pressure, natural gas pipeline flow, power bus power, power bus voltage, and power system frequency obtained in step S3.

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