A power system frequency constraint reliability evaluation method and system based on state similarity and convex hull approximation

Abstract

The application discloses a power system frequency constraint reliability evaluation method and system based on state similarity and convex hull approximation. The method derives an analytical expression of the frequency minimum point constraint based on the swing equation and converts it into a mixed integer second-order cone form, uses a progressive vertex search method to construct a convex hull approximation in the primary frequency reserve space, converts the non-convex frequency minimum point constraint into a linear inequality constraint set and embeds it into a direct current optimal power flow model. On this basis, the linear programming optimality condition is used to determine the state similarity of different power generation and load scenarios, and the optimal base multiplexing is used to replace the repeated calling of the solver by matrix operation, so that the optimal solution of each state is efficiently obtained and the reliability index is calculated. The application eliminates the non-convexity of the frequency constraint without sacrificing the constraint accuracy, and significantly reduces the calculation amount of large-scale state enumeration through the state similarity method, and is suitable for the frequency constraint reliability evaluation of a low-inertia power system.

Description

Technical Field

[0001] This invention relates to the field of power system reliability assessment technology, and in particular to a power system frequency-constrained reliability assessment method and system based on state similarity and convex hull approximation. Background Technology

[0002] With the large-scale grid connection of renewable energy, the proportion of conventional synchronous generators in the power system is gradually decreasing, the system's rotational inertia is continuously declining, and frequency security issues are becoming increasingly prominent. Traditional power system reliability assessment methods are usually based on steady-state operating constraints and optimal power flow models, calculating reliability indices by minimizing load shedding. However, under low-inertia operating conditions, these methods do not consider the impact of dynamic frequency constraints on dispatch decisions, causing the allocation requirements of primary frequency regulation reserve capacity to be ignored, and the assessment results are often overly optimistic. Although some studies have attempted to incorporate frequency security into the reliability assessment framework, they are mostly limited to ex-post verification of frequency indices or only consider frequency stability under specific scenarios, failing to explicitly impose frequency constraints in the optimal power flow model. The analytical modeling of the minimum frequency constraint itself involves conditional logic judgments, which, after transformation, form a mixed-integer second-order cone programming problem. Its non-convexity increases the difficulty of solving the problem and also restricts the application of frequency constraints in large-scale reliability assessments.

[0003] Meanwhile, reliability assessment based on state enumeration faces a severe bottleneck in computational efficiency. Taking an annual assessment as an example, considering hourly resolution of power generation and load scenarios and multi-order fault combinations in the network topology, the system state space can reach tens of millions of units, corresponding to an equivalent number of optimal power flow problems requiring solutions. Existing acceleration methods either rely on dimensionality reduction and scenario clustering to compress the state space, or use machine learning models to approximate the optimal power flow solution. The former may miss critical states, while the latter cannot guarantee the feasibility and optimality of the solution. Although post-optimization analysis methods can accelerate the convergence process of a single solution, they do not reduce the total number of problems to be solved. Therefore, how to effectively reduce the computational load of frequency-constrained reliability assessment while ensuring accuracy is a critical problem that urgently needs to be solved. Summary of the Invention

[0004] To address the problems in existing technologies where power system reliability assessments fail to effectively incorporate frequency constraints, leading to overly optimistic assessment results, and where the computational efficiency of large-scale state enumeration after the introduction of frequency constraints is insufficient to meet engineering requirements, this invention provides a power system frequency-constrained reliability assessment method and system based on state similarity and convex hull approximation.

[0005] This invention provides a power system frequency-constrained reliability assessment method based on state similarity and convex hull approximation, comprising the following steps:

[0006] A dynamic frequency model of the system after disturbance is established based on the swing equation. The primary frequency regulation response process of conventional generator sets and renewable energy is linearized, and the analytical expression of frequency deviation is derived. Based on the condition that the derivative of frequency deviation with respect to time is zero, the time interval of the frequency minimum point is determined, and a piecewise frequency minimum point constraint is established. This constraint is then transformed into a mixed-integer second-order cone form. An asymptotic vertex search method is used to approximate the feasible region of the mixed-integer second-order cone form of the frequency minimum point constraint within the primary frequency regulation reserve space using a convex hull approximation. The boundary vertices of the convex hull are obtained by iteratively solving an optimization problem with the search direction as the objective. The convex hull is gradually expanded until the convergence accuracy requirement is met. The minimum frequency constraint is transformed into a set of linear inequality constraints. The linearized minimum frequency constraint and quasi-steady-state frequency constraint are embedded into the DC optimal power flow model to construct a frequency-constrained optimal power flow model with the goal of minimizing load shedding. This model is then transformed into a standard linear programming form. Based on the optimality conditions of linear programming, the state similarity of the optimal power flow problem corresponding to different generation and load scenarios is determined. By reusing the obtained optimal basis and verifying the feasibility of the basic feasible solution under the new state, matrix operations are used to replace repeated calls to the solver, efficiently obtaining the optimal load shedding amount for each state. Based on the load shedding amount and its probability of occurrence for each system state, reliability indicators such as the expected power shortage are calculated.

[0007] As a preferred embodiment of the present invention, the analytical expression for the frequency deviation is:

[0008]

[0009] in, For system inertia parameters, For the rated frequency, and These are the primary frequency regulation reserve capacities for conventional generating units and renewable energy units, respectively. and These are the corresponding first-order frequency modulation response times. and These are the corresponding response dead time, This refers to the imbalance of active power. This indicates a positive operation; the lowest frequency point occurs in one of the following three time intervals: the renewable energy response phase only, the phase where conventional generators and renewable energy respond simultaneously, and the phase where conventional generators respond only. The constraint on the lowest frequency point in each interval has a second-order cone structure.

[0010] As a preferred embodiment of the present invention, the asymptotic vertex search method includes: an initialization phase, in which a mixed-integer second-order cone optimization problem is solved along the positive and negative coordinate axes of the first-order frequency-modulated spare variable to obtain four initial vertices and construct an initial convex hull; an iterative expansion phase, in which a mixed-integer second-order cone optimization problem is solved for each face of the current convex hull with the outward normal vector of that face as the search direction to obtain new boundary vertices and update the convex hull; and a convergence determination phase, in which the expansion degree of the convex hull is evaluated based on the normalized distance from the new vertex to the corresponding face, and the iteration is terminated when the maximum expansion distance does not exceed a preset convergence threshold.

[0011] As a preferred embodiment of the present invention, in the convergence determination stage, the metric for the degree of convex hull expansion is defined as follows:

[0012]

[0013] in, For the first The set of faces of the convex hull at the next iteration. For noodles The outer normal vector, The corresponding intercept, For the surface The new vertex is obtained by searching the direction of the outer normal vector; when The iteration terminates at time. The preset convergence tolerance; the minimum frequency constraint after convex hull approximation is expressed as: ,in The normal vector matrix, The intercept vector, This is a vector of standby variables for primary frequency regulation.

[0014] As a preferred technical solution of the present invention, the frequency-constrained optimal power flow model includes node power balance constraints, upper and lower bound constraints on load shedding, constraints on the output and reserve capacity of conventional generator sets, constraints on the output and reserve capacity of renewable energy sources, constraints on line transmission capacity, constraints on the lowest frequency point, and constraints on quasi-steady-state frequency. The quasi-steady-state frequency constraint requires that the sum of the primary frequency regulation reserve capacity of conventional generator sets and renewable energy sources is not less than the active power imbalance.

[0015] As a preferred embodiment of the present invention, the step of determining and reusing the optimal basis based on state similarity includes: transforming the frequency-constrained optimal power flow model into a standard linear programming form. , For a given set of power generation and load scenarios under a given topological state, select one scenario and solve a linear programming problem to obtain the optimal basis matrix. Assemble the right-hand vectors of all scenes in the scene set into a matrix, and calculate... The product of the matrix and the current scenario is used to filter out scenarios where all components of the product are non-negative, and these scenarios are considered to have state similarity to the current scenario. For scenarios with state similarity, their optimal solutions are directly calculated using the optimal basis. and objective function value There is no need to call the solver again; remove the solved scenarios from the set, and repeat the above process for the remaining scenarios until all scenarios have been solved.

[0016] This invention also provides a power system frequency constraint reliability assessment system based on state similarity and convex hull approximation, comprising: a frequency constraint modeling module, used to establish a dynamic model of the system frequency after disturbance based on the swing equation, derive the analytical expression of the frequency minimum point constraint, and transform it into a mixed integer second-order cone form; a convex hull approximation module, used to perform convex hull approximation on the feasible region of the frequency minimum point constraint in the primary frequency regulation reserve space using an asymptotic vertex search method, transforming the frequency minimum point constraint into a set of linear inequality constraints; an optimal power flow construction module, used to embed the linearized frequency constraint into the DC optimal power flow model, construct the frequency constraint optimal power flow model, and transform it into a standard linear programming form; a state similarity solution module, used to efficiently obtain the optimal load shedding amount under each system state based on the optimality conditions of linear programming through optimal basis reuse and matrix operations; and a reliability index calculation module, used to calculate the expected power shortage amount based on the load shedding amount and its probability of occurrence under each state.

[0017] As a preferred embodiment of the present invention, in the convex hull approximation module, the convergence of the asymptotic vertex search method is guaranteed by the property that the projection of the minimum frequency point constraint onto the primary frequency modulation reserve space is a convex set. This convexity is determined by the linear structure of the minimum frequency point constraint with respect to the primary frequency modulation reserve variable.

[0018] As a preferred embodiment of the present invention, the state similarity determination condition in the state similarity solution module is: the change in the right-hand vector corresponding to the new power generation and load scenario. ,verify Whether it is valid, among which Given the known optimal basis matrix, if this condition holds, the new scenario shares the same optimal basis as the known scenario.

[0019] As a preferred embodiment of the present invention, the formula for calculating the expected power shortage in the reliability index calculation module is as follows: ,in For system status index, The set of all enumerated states. For state The total load shedding amount obtained from the optimal power flow solution under lower frequency constraints. Let be the probability of this state occurring. To assess the duration of the evaluation period.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] This invention transforms the frequency minimum point constraint in the form of a mixed-integer second-order cone into an equivalent set of linear inequality constraints through an asymptotic vertex search method. This allows the frequency constraints to be embedded into the optimal power flow model in the form of a convex polyhedron, eliminating the solution difficulties caused by non-convexity without sacrificing constraint accuracy, and achieving efficient integration of frequency safety constraints in reliability assessment. The proposed state similarity-based solution method utilizes the optimality condition of linear programming to transform the optimal power flow problem under large-scale power generation and load scenarios into matrix operations, avoiding repeated calls to the solver. This significantly reduces the computational load while maintaining an accurate solution, making large-scale state enumeration reliability assessment considering frequency constraints computationally feasible. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the system frequency response process after disturbance in an embodiment of the present invention;

[0023] Figure 2 This is a schematic diagram of the convex hull construction process of the asymptotic vertex search method in an embodiment of the present invention;

[0024] Figure 3 This is an overall flowchart of the frequency-constrained reliability assessment method based on state similarity in this embodiment of the invention;

[0025] Figure 4 This is a schematic diagram of the improved standard test system structure in an embodiment of the present invention.

[0026] The figures in the diagram are labeled as follows: 1. Conventional generator set; 2. Renewable energy generation unit; 3. Load node; 4. Transmission line; 5. Busbar. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] This invention provides a power system frequency-constrained reliability assessment method based on state similarity and convex hull approximation. The core idea is to transform the non-convex expression of the minimum frequency constraint after disturbance into a linear constraint through convex hull approximation, and utilize the optimal basis structure similarity between different generation and load scenarios to replace a large number of repetitive optimization solutions with matrix operations, thereby significantly improving computational efficiency while ensuring assessment accuracy. Figure 3 As shown, the overall process of this method includes five main steps: frequency constraint modeling, convex hull approximation, construction of frequency constraint optimal power flow model, efficient solution based on state similarity, and calculation of reliability index.

[0029] I. Frequency Constraint Modeling

[0030] After an active power disturbance occurs in a power system, the dynamic behavior of the system frequency can be described by the swing equation. For example... Figure 1 As shown, let the system inertia parameter be... The rated frequency is The frequency deviation is The primary frequency regulation response power provided by conventional generator sets and renewable energy sources are respectively and The active power imbalance is The system frequency dynamic equation is then:

[0031]

[0032] To facilitate analytical derivation, the primary frequency regulation response processes of conventional generator sets and renewable energy sources are linearized. Let... and These are the primary frequency regulation reserve capacities for conventional generating units and renewable energy units, respectively. and This corresponds to the first frequency modulation response time. and To respond to the dead time, the linearized expression for the primary frequency modulation response power is:

[0033]

[0034]

[0035] The above expression reflects the piecewise characteristics of the primary frequency regulation response: before the dead time, the unit has not yet responded; thereafter, the primary frequency regulation power increases linearly with time until it reaches the upper limit of reserve capacity and then remains constant. This embodiment assumes that the parameters satisfy... The relationship is that renewable energy responds faster than conventional generator sets.

[0036] Substituting the linearized first-order frequency modulation response expression into the swing equation, and integrating, we can obtain the analytical expression for the frequency deviation:

[0037]

[0038] in This represents the positive operation, i.e. .

[0039] The lowest frequency point corresponds to the moment when the frequency deviation's derivative with respect to time is zero. Since the frequency deviation expression is a piecewise function, the lowest frequency point may occur in three different time intervals. The first case is... In this scenario, only renewable energy sources begin to provide a primary frequency regulation response while conventional generators have not yet started operating; the second scenario is... In this case, both conventional generators and renewable energy sources provide a frequency regulation response; the third scenario is... At this point, all primary frequency regulation reserves of renewable energy have been released, and only conventional generating units continue to respond. For these three time intervals, the minimum frequency point constraint... The specific expressions are as follows:

[0040] when hour:

[0041]

[0042] when hour:

[0043]

[0044] when hour:

[0045]

[0046] in The maximum allowable frequency deviation is a positive value. The above three conditions constitute conditional logic constraints, where the right-hand side of each condition has a quadratic form structure, and the left-hand side is a linear term. According to the processing method for conditional logic constraints, binary variables can be introduced. The minimum frequency constraint described above is transformed into a mixed integer second-order cone form, and its feasible region is denoted as . ,in This is a vector of standby variables for primary frequency regulation.

[0047] In addition, to ensure that the primary frequency regulation reserve capacity can compensate for the active power imbalance after it is fully released, a quasi-steady-state frequency constraint must be applied:

[0048]

[0049] II. Asymptotic Vertex Search Method

[0050] like Figure 2 As shown, the frequency minimum point constraint in the form of a mixed integer second-order cone. Due to binary variables The introduction of this constraint results in the loss of convexity, and directly embedding it into the optimal power flow model leads to a large-scale mixed-integer programming problem, which is difficult to solve efficiently within the computational framework of reliability assessment. To address this issue, this invention employs an asymptotic vertex search method to approximate the feasible region of the constraint within the primary frequency modulation spare space using a convex hull approximation. The basic idea is to start from an initial convex hull contained within the original feasible region and iteratively expand the convex hull by searching the boundary vertices of the feasible region until the approximation accuracy reaches the preset requirement.

[0051] The specific implementation steps of the asymptotic vertex search method are as follows.

[0052] During the initialization phase, set the iteration counter. Given the system inertia Active power imbalance Primary frequency modulation response time and and dead zone time and Parameters, etc. The search direction is determined separately. for , , and Solve the following mixed-integer second-order cone optimization problem in each direction:

[0053]

[0054] After solving, four initial vertices are obtained, corresponding to... and The maximum and minimum values ​​of the vertices. Construct the initial convex hull based on these four vertices. .

[0055] During the iterative expansion phase, the current convex hull... Each face Extract its outer normal vector and intercept ,by Solve the above mixed-integer second-order cone optimization problem in the search direction to obtain new boundary vertices. After traversing all faces, the newly obtained vertices are merged into the existing vertex set, and the updated convex hull is reconstructed. .

[0056] During the convergence determination phase, the normalized distance from the new vertex to the corresponding face is used as a measure of the extent of convex hull expansion:

[0057]

[0058] in For the first The set of faces of the convex hull during the next iteration. If the convex hull approximation is deemed to have reached sufficient accuracy, the iteration terminates; otherwise, it returns to the iteration expansion phase to continue execution.

[0059] After the asymptotic vertex search method converges, the original mixed-integer second-order cone frequency minimum point constraint is obtained. It is equivalently approximated by a set of linear inequality constraints:

[0060]

[0061] in The normal vector matrix, The intercept vector, Let be the number of faces of the convex polyhedron. This set of linear constraints is fully defined in the first-order frequency modulation spare variable space; binary variables have been naturally eliminated during the projection process.

[0062] The convergence of the asymptotic vertex search method can be guaranteed by analyzing the projection property of the minimum frequency constraint onto the first-order frequency tuning spare space. Define an auxiliary function. as well as The frequency deviation can then be written as ,in The minimum frequency constraint is equivalent to constraining all... All have Established, that is For all This constraint holds true. For a given set of infinite intersections of linear constraints, its feasible region is still a convex set. Therefore, the asymptotic vertex search method approximates a convex feasible region, and its convergence within a finite number of iterations can be guaranteed.

[0063] III. Frequency-Constrained Optimal Power Flow Model

[0064] After completing the convex hull approximation of the frequency constraints, the linearized minimum frequency constraint and the quasi-steady-state frequency constraint can be embedded into the DC optimal power flow model to construct the frequency-constrained optimal power flow model. The objective function of this model is to minimize the total system load shedding.

[0065]

[0066] The constraints include: node power balance constraints, meaning that the net power injected into the line at each node is equal to the generator output minus the load plus the load shedding; upper and lower bound constraints on load shedding, meaning the load shedding is not less than zero and does not exceed the load value of the node; constraints on conventional generator output and reserve capacity, requiring that the sum of the output of conventional generators and the primary frequency regulation reserve capacity does not exceed their maximum output limit; constraints on renewable energy output and reserve capacity, requiring that the sum of the output of renewable energy and the primary frequency regulation reserve capacity does not exceed their maximum available output, the upper limit of which is determined by the predicted value of renewable energy output; line transmission capacity constraints, limiting the transmission power on each line to not exceed its rated capacity; and minimum frequency point constraints. Quasi-steady-state frequency constraints .

[0067] The specific mathematical form of the above model is as follows:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] in Number the nodes. For a set of nodes, For nodes The load shearing variable, and They are nodes The output of conventional generator sets and renewable energy sources, and This corresponds to the primary frequency regulation reserve capacity. and Each is its maximum output limit. For nodes voltage phase angle, For the line Transmission capacity limit, This refers to the line reactance.

[0074] Since all constraints are linear, this frequency-constrained optimal power flow model can be directly transformed into a standard linear programming form:

[0075]

[0076] in The coefficient vector of the objective function. This is a vector of decision variables, which, in addition to the variables defined above, also includes slack variables introduced to transform inequality constraints into equality constraints. and These are the constraint coefficient matrix and the right-hand constant vector, respectively. For variables with non-zero lower bounds, they can be equivalently represented by the difference between two non-negative variables.

[0077] IV. Efficient Solution Method Based on State Similarity

[0078] In reliability assessment, a frequency-constrained optimal power flow problem needs to be solved for a large number of system states to obtain the load shedding amount for each state. The system states are jointly determined by the network topology and the generation load scenario, where the network topology corresponds to different orders of equipment failure combinations, and the generation load scenario reflects the time-series changes in renewable energy output and load during the assessment period. When considering annual assessments with hourly resolution and multi-order failure combinations, the state space becomes extremely large, and the method of calling the solver one by one is computationally inefficient.

[0079] This invention observes that, under the same network topology, different power generation and load scenarios only change the right-hand vector in the standard linear programming problem. The constraint coefficient matrix and objective function coefficient vector It remains unchanged. According to the optimality condition of the simplex method for linear programming, if the basis matrix corresponding to the set of basic variables remains unchanged... To be optimal, the feasibility condition must be met simultaneously. and optimality conditions ,in and They are respectively The column matrices corresponding to the basic and non-basic variables. and These are the coefficients of the corresponding objective function. When both conditions are met, the optimal solution and the objective function value can be obtained directly through matrix operations:

[0080]

[0081] vector on the right end When changes occur, due to and Unchanged, in the optimality condition Unaffected, therefore only feasibility conditions need to be verified. Does this property hold true? If it does, then the original optimal basis remains optimal under the new state, and there is no need to resolve the linear programming problem. This property forms the theoretical basis of state similarity: for different power generation and load scenarios, if their corresponding linear programming problems share the same optimal basis, then these scenarios are said to have state similarity.

[0082] Based on the above analysis, such as Figure 3 As shown, the frequency-constrained reliability assessment process based on state similarity proposed in this invention is as follows.

[0083] Construct a complete set of system states, including the network topology state set. Power generation and load scenario set For each topological state Perform the following process: when the power generation and load scenarios are combined When not empty, from Select a scenario, call the solver to solve the corresponding standard linear programming problem and obtain its optimal basis matrix. ;Will The right-hand vectors of all scenes are assembled into a matrix column-wise. ,calculate Check whether each column in the calculation result satisfies the condition that all components are non-negative, and form a set of the scenario indices that meet the condition. ; For sets All scenarios directly utilize and Calculate its optimal load shedding amount; then from Remove from For the corresponding scenario, repeat the above process for the remaining scenarios until... Empty. After traversing all topology states, calculate the expected power shortage based on the load shedding amount and probability of occurrence for each system state:

[0084]

[0085] in For system status index, The set of all enumerated states. For state The total sheared load obtained from solving the optimal power flow model under frequency constraints. Let be the probability of this state occurring. To assess the time span of the period.

[0086] V. Specific Application Examples

[0087] To verify the effectiveness of the method of this invention, a frequency-constrained reliability assessment was performed on an improved standard testing system. For example... Figure 4As shown, the test system comprises 39 busbars, 46 transmission lines, and 10 conventional generator sets, with a total installed capacity of 7367 MW and a peak load of 6254 MW. To simulate renewable energy grid connection scenarios, 5% of the total capacity of the conventional generator sets is replaced with renewable energy, corresponding to a renewable energy installed capacity of 368.35 MW. The evaluation period is set to 8760 hours, and a set of generation and load scenarios is constructed using standardized annual renewable energy generation and load data. Network topology state set By considering to The fault combination is constructed, where faults of order three and above are only considered for generator faults. It contains a total of 2179 topological states. The complete state space. Include The system state is defined. The potential active power imbalance is set at 300 MW, and the system inertia is... Megawatt-seconds, maximum permissible frequency deviation Hertz, response parameter set to Second, Second, Second, The convergence tolerance of the asymptotic vertex search method is seconds. .

[0088] The calculations were performed using methods based on the minimum frequency point constraint of the original mixed-integer second-order cone, the convex hull approximation method, the convex hull approximation method accelerated by state similarity, and the state similarity method without considering frequency constraints. The results show that the expected power shortage considering the frequency constraint is 273.47 MWh, significantly higher than the 128.24 MWh without frequency constraints. This is because the frequency constraint requires conventional generators and renewable energy units to reserve primary frequency regulation capacity, reducing available generation capacity and thus increasing load shedding. The expected power shortage obtained using the original mixed-integer second-order cone constraint and the convex hull approximation constraint are completely consistent, verifying the approximate accuracy of the asymptotic vertex search method. The results obtained by the accelerated method based on state similarity are also consistent with the previous two, indicating the accuracy of this method based on the optimality conditions of linear programming. In terms of computational efficiency, the state similarity method achieves an acceleration of approximately 30 times, with the solver called only 10624 times, averaging about 4.87 calls per topology state. The remaining states obtain their optimal solutions precisely through matrix operations.

[0089] Sensitivity analysis was conducted on reliability at different renewable energy penetration levels. The results show that as the renewable energy penetration rate increases from 5% to 25%, the expected power shortage first decreases and then increases. Moderately increasing the renewable energy penetration rate can enhance frequency support by leveraging its rapid frequency response capability, reducing the primary frequency regulation reserve requirement of conventional generator units, and lowering the load shedding; however, when the penetration rate is too high, the uncertainty of renewable energy output increases, which may lead to increased load shedding in extreme scenarios.

[0090] In practical applications, the parameter values ​​of the method described in this invention can be adjusted according to the characteristics of a specific power system. System inertia parameter The primary frequency regulation response parameters should be calculated based on the parameters of the actual grid-connected synchronous generator units. , , and The maximum permissible frequency deviation should be set according to the actual frequency regulation characteristics of various types of generating units. The convergence tolerance of the asymptotic vertex search method should be determined based on power system operation standards. The tolerance can be set according to the need for a balance between computational accuracy and efficiency. A smaller tolerance will yield a more accurate convex hull approximation but requires more iterations, while a larger tolerance can reduce iterations but may introduce some approximation error. The selection of the above parameters falls within the scope that can be directly determined by those skilled in the art based on actual engineering conditions, and does not affect the applicability and technical effect of the method of the present invention.

[0091] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A power system frequency-constrained reliability assessment method based on state similarity and convex hull approximation, characterized in that, Includes the following steps: Based on the swing equation, a dynamic model of the system frequency after disturbance is established. The primary frequency regulation response process of conventional generator sets and renewable energy is linearized. The analytical expression of frequency deviation is derived. Based on the condition that the derivative of frequency deviation with respect to time is zero, the time interval of the frequency minimum point is determined. A piecewise frequency minimum point constraint is established and the constraint is transformed into a mixed integer second-order cone form. The asymptotic vertex search method is used to approximate the feasible region of the frequency minimum point constraint in the form of a mixed integer second-order cone within the first frequency modulation spare space. The boundary vertices of the convex hull are obtained by iteratively solving the optimization problem with the search direction as the objective. The convex hull is gradually expanded until the convergence accuracy requirement is met, and the frequency minimum point constraint is transformed into a set of linear inequality constraints. The linearized minimum frequency constraint and quasi-steady-state frequency constraint are embedded into the DC optimal power flow model to construct a frequency-constrained optimal power flow model with the goal of minimizing load shedding. The frequency-constrained optimal power flow model is then transformed into a standard linear programming form. Based on the optimality conditions of linear programming, the state similarity of the optimal power flow problem corresponding to different power generation and load scenarios is determined. By reusing the obtained optimal basis and verifying the feasibility of the basic feasible solution under the new state, matrix operations are used to replace repeated calls to the solver, and the optimal load shedding amount of each state is obtained efficiently. Calculate the expected power shortage based on the load shedding amount and probability of occurrence for each system state.

2. The power system frequency-constrained reliability assessment method based on state similarity and convex hull approximation according to claim 1, characterized in that, The analytical expression for the frequency deviation is: ; in, For system inertia parameters, For the rated frequency, and These are the primary frequency regulation reserve capacities for conventional generating units and renewable energy units, respectively. and These are the corresponding first-order frequency modulation response times. and These are the corresponding response dead time, This refers to the imbalance of active power. This indicates a positive operation; the lowest frequency point occurs in one of the following three time intervals: the renewable energy response phase only, the phase where conventional generators and renewable energy respond simultaneously, and the phase where conventional generators respond only. The constraint on the lowest frequency point in each interval has a second-order cone structure.

3. The power system frequency-constrained reliability assessment method based on state similarity and convex hull approximation according to claim 1, characterized in that, The asymptotic vertex search method includes: In the initialization phase, the mixed integer second-order cone optimization problem is solved along the positive and negative coordinate axes of the first frequency modulation backup variable to obtain four initial vertices and construct the initial convex hull. In the iterative expansion phase, for each face of the current convex hull, the mixed integer second-order cone optimization problem is solved with the outward normal vector of that face as the search direction to obtain new boundary vertices and update the convex hull; During the convergence determination phase, the expansion degree of the convex hull is evaluated based on the normalized distance from the new vertex to the corresponding face. The iteration is terminated when the maximum expansion distance does not exceed the preset convergence threshold.

4. The power system frequency-constrained reliability assessment method based on state similarity and convex hull approximation according to claim 3, characterized in that, In the convergence determination phase, the measure of the convex hull expansion degree is defined as: ; in, For the first The set of faces of the convex hull at the next iteration. For noodles The outer normal vector, The corresponding intercept, For the surface The new vertex is obtained by searching the direction of the outer normal vector; when The iteration terminates at time. The preset convergence tolerance; the minimum frequency constraint after convex hull approximation is expressed as: ,in The normal vector matrix, The intercept vector, This is the standby variable vector for primary frequency regulation.

5. The power system frequency-constrained reliability assessment method based on state similarity and convex hull approximation according to claim 1, characterized in that, The frequency-constrained optimal power flow model includes node power balance constraints, upper and lower bound constraints on load shedding, constraints on the output and reserve capacity of conventional generator sets, constraints on the output and reserve capacity of renewable energy sources, constraints on line transmission capacity, constraints on the lowest frequency point, and constraints on quasi-steady-state frequency. The quasi-steady-state frequency constraint requires that the sum of the primary frequency regulation reserve capacity of conventional generator sets and renewable energy sources is not less than the active power imbalance.

6. The power system frequency-constrained reliability assessment method based on state similarity and convex hull approximation according to claim 1, characterized in that, The steps of determining and reusing the optimal basis based on state similarity include: The frequency-constrained optimal power flow model is transformed into a standard linear programming form. , ; For a given set of power generation and load scenarios with a specific topological state, select one scenario and solve a linear programming problem to obtain the optimal basis matrix. ; Assemble the right-hand vectors of all scenes in the scene set into a matrix, and calculate... The product with this matrix is ​​used to filter out scenarios where all components of the product result are non-negative, and these scenarios are identified as having state similarity to the current scenario. For scenarios with similar states, the optimal solution can be directly calculated using the optimal basis. and objective function value No need to call the solver again; Remove the solved scenarios from the set, and repeat the above process for the remaining scenarios until all scenarios have been solved.

7. A power system frequency-constrained reliability assessment system based on state similarity and convex hull approximation, characterized in that, include: The frequency constraint modeling module is used to establish a dynamic frequency model of the system after disturbance based on the swing equation, derive the analytical expression of the minimum frequency constraint, and transform it into a mixed integer second-order cone form. The convex hull approximation module is used to perform convex hull approximation on the feasible region of the minimum frequency constraint in the primary frequency modulation spare space using the asymptotic vertex search method, transforming the minimum frequency constraint into a set of linear inequality constraints. The optimal power flow construction module is used to embed the linearized frequency constraints into the DC optimal power flow model, construct the frequency-constrained optimal power flow model, and transform it into a standard linear programming form. The state similarity solution module is used to efficiently obtain the optimal load shedding amount under each system state based on the optimality conditions of linear programming through optimal basis reuse and matrix operations. The reliability index calculation module is used to calculate the expected power shortage based on the load shedding amount and the probability of occurrence of each state.

8. The power system frequency-constrained reliability assessment system based on state similarity and convex hull approximation according to claim 7, characterized in that, In the convex hull approximation module, the convergence of the asymptotic vertex search method is guaranteed by the property that the projection of the minimum frequency constraint onto the primary frequency modulation reserve space is a convex set. This convexity is determined by the linear structure of the minimum frequency constraint with respect to the primary frequency modulation reserve variable.

9. The power system frequency-constrained reliability assessment system based on state similarity and convex hull approximation according to claim 7, characterized in that, In the state similarity solving module, the condition for determining state similarity is: the change in the right-hand vector corresponding to the new power generation and load scenario. ,verify Whether it is valid, among which Given the known optimal basis matrix, if this condition holds, the new scenario shares the same optimal basis as the known scenario.

10. The power system frequency-constrained reliability assessment system based on state similarity and convex hull approximation according to claim 7, characterized in that, In the reliability index calculation module, the formula for calculating the expected power shortage is as follows: ,in For system status index, The set of all enumerated states. For state The total load shedding amount obtained from the optimal power flow solution under lower frequency constraints. Let be the probability of this state occurring. To assess the duration of the evaluation period.

Images