A back-to-back flexible direct current system site selection method considering stability and risk

Abstract

The application belongs to the technical field of flexible direct current power transmission, and particularly discloses a back-to-back flexible direct current system site selection method considering stability and risk, which comprises the following steps: first, a cross-voltage level power grid power flow and device model containing a back-to-back flexible direct current power transmission system BTB is established; then, a node frequency dynamic response model containing inertia characteristics is established; a risk modeling and adaptive control model considering new energy output uncertainty and power flow constraints is constructed; a multi-objective optimization model considering cost, loss, dynamic stability, minimum frequency value and risk level is established; finally, a Pareto optimal solution set is solved by a multi-objective evolutionary algorithm, and a site selection result is output. The back-to-back flexible direct current system site selection method considering stability and risk is adopted, intelligent site selection and capacity configuration of the cross-voltage level BTB flexible direct current device are realized, and the voltage stability, frequency stability and risk robustness of the power grid under the condition of high proportion of new energy are improved.

Description

Technical Field

[0001] This invention relates to the field of flexible DC transmission technology, and in particular to a back-to-back flexible DC system location method that takes into account stability and risk. Background Technology

[0002] With the high proportion of new energy sources such as wind power and photovoltaics being integrated into the power system, the following significant changes are occurring: (1) The system's equivalent inertia decreases, and its frequency stability deteriorates: Since renewable energy inverters do not provide rotational inertia, the overall grid inertia constant HeqH_{eq}Heq decreases significantly, leading to a sharp increase in RoCoF (Rate of Change of Frequency). Under large disturbance scenarios, the system frequency may drop rapidly within tens of milliseconds, triggering low-frequency load shedding or even unit tripping, creating a chain reaction of fault risks.

[0003] (2) Increased complexity of power flow interaction across voltage levels: The power flow of high voltage (such as 500 kV) and medium and low voltage (such as 220 kV) is coupled with each other. In some areas, there are problems such as power flow bottlenecks, reverse flow and circulation, which makes it difficult for power flow analysis of a single voltage level to reflect the actual operating status.

[0004] (3) The randomness of new energy sources renders traditional power flow location strategies ineffective: The output of new energy sources is highly time-varying and uncertain. Traditional optimization methods based on deterministic power flow, Jacobian matrix or sensitivity calculation cannot reflect the risk of exceeding limits under extreme scenarios (such as low wind and low light).

[0005] (4) Existing site selection methods lack dynamic response modeling: BTB converter stations can output a large amount of active power support within 20–50 ms, significantly suppressing RoCoF and improving the frequency nadir. However, existing methods are mostly based on static power flow models and do not incorporate the dynamic adjustment characteristics of BTB into the optimization framework.

[0006] (5) Lack of quantifiable risk description.

[0007] In high uncertainty scenarios, problems such as node voltage exceeding limits and line power flow exceeding limits have probabilistic and tail risk characteristics. Traditional optimization methods based on constraint "hard limits" cannot measure the losses in extreme scenarios.

[0008] Therefore, a location selection method that can simultaneously satisfy the following characteristics is needed: (1) Power flow modeling across voltage levels; (2) Includes dynamic response of inertia and nodal frequency; (3) Modeling the stochastic characteristics of new energy sources in multiple scenarios; (4) Quantitative Risk (CVaR); (5) Supports BTB rapid adjustment capability; (6) It possesses engineering feasibility and explainability; This invention is proposed to solve the above-mentioned problems. Summary of the Invention

[0009] The purpose of this invention is to provide a back-to-back flexible DC system (BTB) location method that considers stability and risk. This method is a smart BTB location method that comprehensively considers power flow safety, frequency stability, dynamic robustness, and risk control under complex operating conditions such as multi-voltage power grids, random power output from new energy sources, and decreased system inertia. This method can be used to determine the optimal location, rated transmission capacity, and dynamic adjustment strategy of the BTB, thereby improving the stability and operational reliability of the power grid under extreme conditions.

[0010] To achieve the above objectives, the present invention provides a back-to-back flexible direct current system location method that considers stability and risk, comprising the following steps: Step 1: Establish a cross-voltage level power flow and equipment model for a power grid including a back-to-back flexible DC transmission system (BTB). Step 2: Establish a node frequency dynamic response model that includes inertia characteristics; Step 3: Construct a risk modeling and adaptive control model that considers the uncertainty of new energy output and power flow constraints; Step 4: Establish a multi-objective optimization model that comprehensively considers cost, loss, dynamic stability, minimum frequency, and risk level; Step 5: Solve for the Pareto optimal solution set using a multi-objective evolutionary algorithm and output the location selection results.

[0011] Preferably, step one specifically involves: Let the set of power grid nodes be 𝒩 and the set of voltage levels be R, where R = {H, L}, and H and L represent high voltage level and low voltage level, respectively; The system node state vector is defined as follows: ; in, For nodes i The active power of power generation, For nodes i The active power of the load, For nodes i Voltage amplitude, For nodes i Voltage phase angle; Establish the AC power flow equilibrium equation: ; ; In the formula, P i , Q i They are nodes i The active and reactive power injected; G ij , B ij They are nodes i With nodes j The real and imaginary parts of the admittance; The BTB back-to-back flexible DC transmission system is considered as a connection to the high-voltage side node. i With low voltage side node j A bidirectional controllable active power exchange device whose active power satisfies: ; In the formula, For BTB at the high voltage side node i Injected active power, For BTB at the low voltage side node j Injected active power; Corresponding reactive power Constrained by converter capacity and control strategy, by The power balance equations at the corresponding nodes are superimposed to form a cross-voltage level AC power flow model that includes the power balancing model (BTB).

[0012] Preferably, step two specifically involves: The overall equivalent inertia constant of the power grid is defined as H eq The rated frequency is defined as f n The net loss of active power in a system caused by a fault or disturbance is defined as follows: Ignoring higher-order dynamics, the system frequency change rate RoCoF is expressed as: ; In the formula, f ( t (time) t The system frequency, Let RoCoF be the first derivative of frequency with respect to time; H eq The smaller the value, the better for the same Δ P imb The faster the frequency decreases; When considering BTB's participation in frequency support, BTB-supported active power is introduced. The effective power loss after the disturbance is defined as: ; The rate of change of frequency is now corrected to: .

[0013] Preferably, the node frequency dynamic response model in step two also includes calculating the lowest frequency after the disturbance, and the calculation method is as follows: Active power loss measurement corresponding to a given typical disturbance Given the combined response time Δt of primary frequency modulation and BTB fast support, the minimum system frequency value is determined. f min Represented as: ; In the formula, f min The lowest frequency value after the disturbance, Δ t This is a critical time window before the main supporting measures have been fully implemented.

[0014] Preferably, step three specifically involves: New energy power stations k Contributing to the cause With no effort Consider it as a random perturbation vector x =( x 1, x 2,…, x m ) T The random function is: ; ; In the formula, They are new energy power stations k Expected value of effort, whether it is productive or not. These are the standard deviations of the corresponding outputs. x k To describe new energy power stations k Standardized random variables of output fluctuations m The dimension of the random variable; a set of new energy power output scenarios is obtained through Monte Carlo simulation or scenario sampling, which is used to drive the power flow equations and frequency response models containing BTB; Define power flow and voltage over-limit loss functions L ( x ), used to measure random scenarios x Lower node voltage V i ( x Constraints, line power S l ( x The degree of breach of the constraint; Based on the loss function, a confidence level is introduced. α Conditional Value at Risk (CVaR) CVaR α (L), for the worst (1- α Quantify the average loss for percentage-based scenarios; Reconstruct the risk mitigation function F risk ( CVaR α ( L This is then superimposed onto the BTB active and reactive power reference commands to form a risk-adaptive BTB power regulation strategy.

[0015] Preferably, in step three, risk modeling and adaptive control also include a safety probability constraint in the form of an opportunity constraint, specifically: Apply chance constraints to node voltages and line power flows respectively: ; ; in, V i min and V i max They are nodes i Lower and upper limits of voltage amplitude , This represents the maximum probability of default allowed by voltage and power flow constraints. S l ( x ) for scene x Downline l Apparent power S l max For the line l The maximum allowed transmission capacity.

[0016] Preferably, in step three, the risk-adaptive BTB power regulation strategy includes the following forms: Define the risk mitigation function: ; in, (⋅) is a monotonically non-decreasing function, when CVaR α ( L When it increases F risk Consequently, the active power reference value of BTB is increased; the value is then corrected to: ; The reactive power reference value is corrected to: ; In the formula, These are the BTB active and reactive power reference values ​​when no risk is considered, and are the active and reactive power risk adjustment coefficients.

[0017] Preferably, step four specifically involves: Let the BTB site selection and capacity configuration scheme be the set of decision variables. u The steady-state and dynamic states of the power grid are x Under the premise of satisfying the power flow balance equation, equipment operation constraints, dynamic stability constraints, and risk constraints, a set of multi-objective functions is constructed: ; in, To take into account both investment and operating costs, For system active power loss, As a dynamic stability index, As a risk indicator, It is the negative value of the minimum frequency of the critical node after the perturbation, used to achieve the goal of maximizing the minimum frequency of the node; The above multi-objective problem can be transformed into a multi-objective minimization form: ; Apply constraints on node voltage upper and lower limits, line power upper limit, BTB active / reactive capacity, and RoCoF and minimum frequency.

[0018] Preferably, in step four, the constraints of the multi-objective optimization model include: Current balance constraints: ; in, h For the AC power flow equations that include BTB; Running constraint set: ; in, g Including node voltage constraints Line power constraints BTB active power constraint BTB reactive power constraint And inertia and RoCoF safety constraints; RoCoF and Frequency Security Constraints: ; in, RoCoF max The maximum allowable rate of change threshold for the system.f safe This is the minimum safe frequency threshold.

[0019] Preferably, step five specifically includes: An improved multi-objective particle swarm optimization algorithm is used to solve the multi-objective model, and the Pareto optimal solution set is obtained by balancing cost, loss, dynamic stability, frequency safety margin and risk level. Then, the solution with the best comprehensive index is selected from the Pareto set by fuzzy comprehensive evaluation or weighted aggregation method, and the candidate node combination, rated capacity, frequency support strategy and risk control parameters of BTB are output. The improvement process of the multi-objective particle swarm optimization algorithm is as follows: A linearly decreasing inertia weight strategy is adopted: ; In the formula, The inertia weight is the number of iterations when iter is given. These are the initial and final inertia weights, respectively, iter max This represents the maximum number of iterations. An adaptive target weight adjustment mechanism is introduced to dynamically update the target weights based on the current distribution of the group across targets; An external elite library is set up to store non-dominated solutions, and the elite library is updated using the crowding distance metric; The penalty function method is used to penalize particles that violate power flow constraints, dynamic stability constraints, and risk constraints, thereby guiding particles to converge toward the feasible region.

[0020] Therefore, the present invention employs the aforementioned back-to-back flexible vertical system location method that considers stability and risk, and the beneficial effects are as follows: (1) By coupling system inertia, RoCoF dynamic and BTB rapid adjustment, the present invention can provide active power support within tens of milliseconds, suppress frequency drop under high proportion of new energy, avoid low frequency load reduction and unit tripping, and improve frequency safety margin in the scenario of inertia decline.

[0021] (2) This invention breaks through the limitations of single voltage level analysis and solves the high-low voltage power flow coupling problem by cross-voltage power flow modeling; combined with new energy stochastic model and CVaR, it accurately assesses the risk of exceeding limits in extreme scenarios and improves the operational robustness of the power grid under high uncertainty.

[0022] (3) This invention uses risk adaptive adjustment to match the risk intensity of the system on demand, combined with multi-objective optimization and Pareto optimal solution, to output the optimal location and capacity scheme of BTB, taking into account both grid stability and investment economy, and has engineering feasibility.

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 This is an overall flowchart of an embodiment of the back-to-back flexible direct current system location method considering stability and risk according to the present invention; Figure 2 This is a schematic diagram of a cross-voltage level transmission network structure including BTB, according to an embodiment of the back-to-back flexible DC system location method considering stability and risk of the present invention. Figure 3 This is a flowchart illustrating the quantification of new energy randomness and CVaR risk in an embodiment of the back-to-back flexible DC system location method considering stability and risk according to the present invention. Figure 4 This is a schematic diagram of the BTB risk adaptive adjustment strategy in Embodiment 1 of the back-to-back flexible direct current system location method that considers stability and risk according to the present invention. Detailed Implementation

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects.

[0027] like Figure 1 As shown, a back-to-back flexible CRT system location method considering stability and risk includes the following steps: Step 1: Establish a cross-voltage level power flow and equipment model for the BTB (Back-to-Back Flexible DC Transmission System), specifically as follows: like Figure 2 As shown, under the given conditions of multi-voltage level AC power grid topology and parameters, let the set of power grid nodes be 𝒩 and the set of voltage levels be R, where R={H,L}, H and L represent high voltage level and low voltage level, respectively.

[0028] The system node state vector is defined as follows: ; in, For nodes i The active power of power generation, For nodes iThe active power of the load, For nodes i Voltage amplitude, For nodes i Voltage phase angle.

[0029] Based on this, the AC power flow equilibrium equation is established: ; ; In the formula, P i , Q i They are nodes i The active and reactive power injected are positive values, indicating that they are injected into the grid and negative values ​​indicate that they are absorbed from the grid. G ij , B ij They are nodes i With nodes j The real and imaginary parts of the admittance.

[0030] The BTB back-to-back flexible DC transmission system is considered as a connection to the high-voltage side node. i With low voltage side node j A bidirectional controllable active power exchange device whose active power satisfies: ; In the formula, For BTB at the high voltage side node i Injected active power, For BTB at the low voltage side node j The injected active power is the opposite when commutation losses are ignored.

[0031] Corresponding reactive power Constrained by converter capacity and control strategy. By... The power balance equations at the corresponding nodes are superimposed to form a cross-voltage level AC power flow model that includes the power balancing model (BTB).

[0032] Step 2: Establish a node frequency dynamic response model that includes inertia characteristics, specifically as follows: To address the issue of reduced system equivalent inertia due to high-proportion renewable energy integration, the overall equivalent inertia constant of the power grid is defined as follows: H eq The rated frequency is defined as f n The net loss of active power in a system caused by a fault or disturbance is defined as follows: Ignoring higher-order dynamics, the system's rate of change of frequency (RoCoF) is approximately expressed as: ; In the formula, f ( t (time) t The system frequency, Let RoCoF be the first derivative of frequency with respect to time; H eq The smaller the value, the better for the same Δ P imb The lower the frequency, the faster it decreases.

[0033] When considering BTB's participation in frequency support, BTB-supported active power is introduced. The effective power loss after the disturbance is defined as: .

[0034] The rate of change of frequency is now corrected to: .

[0035] Through the above relationships, BTB quickly adjusts the active power to reduce RoCoF, thereby supporting the system frequency; at the same time, at the node level, the speed deviation of each generator and the corresponding node frequency offset are incorporated into the state vector to form a node dynamic response model with frequency state.

[0036] The node frequency dynamic response model of this invention also includes an approximate calculation of the lowest frequency after perturbation, used to construct an optimization objective of "maximum lowest node frequency after perturbation". The calculation method is as follows: Given a typical disturbance such as the disconnection of active power corresponding to the shutdown of a single large generating unit, the loss of power is measured. Given the combined response time Δt of primary frequency modulation and BTB rapid support, the approximate relationship of linear frequency decline in the initial stage of disturbance is obtained using the approximate formula of system frequency change rate, thus determining the minimum system frequency. f min Approximately expressed as: ; In the formula, f min The lowest frequency value after the disturbance, Δ t This is a critical time window before the main support measures have been fully implemented, through... f min As the objective function f 5 ( u The basic quantity, combined with the BTB support power Δ PHVD ( t The correction of effective loss measurement enables quantitative evaluation of frequency security margin for different site selection schemes.

[0037] Step 3: Construct a risk modeling and adaptive control model that considers the uncertainty of new energy output and power flow constraints, specifically as follows: Wind power, photovoltaic and other new energy power stations k Contributing to the cause With no effort Consider it as a random perturbation vector x =( x 1, x 2,…, x m ) T The random function can be: ; ; In the formula, They are new energy power stations k Expected value of effort, whether it is productive or not. These are the standard deviations of the corresponding outputs. x k To describe new energy power stations k Standardized random variables of output fluctuations m The dimension of the random variable is used to obtain a set of new energy power output scenarios through Monte Carlo simulation or scenario sampling, which are used to drive the power flow equations and frequency response models containing BTB.

[0038] like Figure 3 As shown, the power flow and voltage over-limit loss functions are defined. L ( x ), used to measure random scenarios x Lower node voltage V i ( x Constraints, line power S l ( x The degree of breach of constraints, etc.

[0039] Based on the loss function, a confidence level is introduced. α Conditional Value at Risk (CVaR) CVaR α (L), for the worst (1- α The average loss in percentage scenarios is quantified.

[0040] Reconstruct the risk mitigation function F risk ( CVaR α (L This is then superimposed onto the BTB active and reactive power reference commands to form a risk-adaptive BTB power regulation strategy.

[0041] In this invention, risk modeling and adaptive control also include safety probability constraints in the form of opportunity constraints, specifically: Apply chance constraints to node voltages and line power flows respectively: ; ; in, V i min and V i max They are nodes i Lower and upper limits of voltage amplitude , This represents the maximum probability of default allowed by voltage and power flow constraints. S l ( x ) for scene x Downline l Apparent power S l max For the line l The maximum allowable transmission capacity is determined by combining the above opportunity constraints with the CVaRα(L) risk index to achieve unified risk control for typical operating conditions and extreme scenarios.

[0042] The risk-adaptive BTB power regulation strategy in this invention includes the following forms: Define the risk mitigation function: ; in, (⋅) is a monotonically non-decreasing function, when CVaR α ( L When it increases F risk Consequently, the active power reference value of BTB is increased; the value is then corrected to: .

[0043] The reactive power reference value is corrected to: .

[0044] In the formula, These are the active and reactive power reference values ​​of BTB when no risk is considered, and are the active and reactive power risk adjustment coefficients. Through the above relationship, BTB can automatically increase its support capacity or shrink its boundary when the risk level increases, thereby realizing the risk adaptive correction of the power flow adjustment range.

[0045] Step 4: Establish a multi-objective optimization model that comprehensively considers cost, loss, dynamic stability, minimum frequency, and risk level, specifically as follows: Let the BTB site selection and capacity configuration scheme be the set of decision variables. u The steady-state and dynamic states of the power grid are x Under the premise of satisfying the power flow balance equation, equipment operation constraints, dynamic stability constraints, and risk constraints, a set of multi-objective functions is constructed: ; in, To take into account both investment and operating costs, For system active power loss, It is a function of dynamic stability indices (such as indices related to the real part of eigenvalues). For risk indicators (such as) CVaR α ( L ), It is the negative value of the minimum frequency of the critical node after the perturbation, used to achieve the goal of maximizing the minimum frequency of the node.

[0046] The above multi-objective problem can be transformed into a multi-objective minimization form: .

[0047] It also applies node voltage upper and lower limit constraints, line power upper limit constraints, BTB active / reactive capacity constraints, and RoCoF and minimum frequency constraints.

[0048] The constraints of the multi-objective optimization model of this invention specifically include: Current balance constraints: ; in, h This is a set of AC power flow equations that include BTB.

[0049] Running constraint set: ; in, g Including node voltage constraints Line power constraints BTB active power constraint BTB reactive power constraint And inertia and RoCoF safety constraints.

[0050] RoCoF and Frequency Security Constraints: ; in, RoCoF max The maximum allowable rate of change threshold for the system. f safe The minimum safe frequency threshold is used to ensure that the flexible DC addressing scheme meets the frequency safety operation requirements after disturbances through the above constraints.

[0051] Step 5: Solve for the Pareto optimal solution set using a multi-objective evolutionary algorithm and output the location selection results, specifically as follows: An improved multi-objective particle swarm optimization algorithm is used to solve the multi-objective model, and the Pareto optimal solution set is obtained by balancing cost, loss, dynamic stability, frequency safety margin and risk level.

[0052] Then, by using fuzzy comprehensive evaluation or weighted aggregation method, the solution with the best comprehensive index is selected from the Pareto set, and the results such as candidate node combination, rated capacity, frequency support strategy and risk control parameters of BTB are output to guide the site selection and control strategy design of flexible DC system engineering across voltage levels.

[0053] The improvement process of the multi-objective particle swarm optimization algorithm of this invention is as follows: (1) Adopting a linearly decreasing inertia weight strategy: ; In the formula, The inertia weight is the number of iterations when iter is given. These are the initial and final inertia weights, respectively, iter max This represents the maximum number of iterations.

[0054] (2) An adaptive target weight adjustment mechanism is introduced to dynamically update the target weights based on the current distribution of the group on each target, so as to enhance the algorithm’s attention to weak targets (such as targets with the lowest frequency).

[0055] (3) Set up an external elite library to store non-dominated solutions and use the crowding distance index to update the elite library in order to maintain the uniformity of the Pareto front distribution.

[0056] (4) By using the penalty function method, particles that violate the power flow constraint, dynamic stability constraint and risk constraint are penalized, and the particles are guided to converge toward the feasible region, thereby improving the convergence quality of the algorithm and the engineering feasibility of the solution.

[0057] Example 1: (1) Construct a cross-voltage level power flow model including a back-to-back flexible DC transmission system (BTB): ① Construct the node power balance equations: node i Active power balance: ; node i Reactive power balance: ; in, They are nodes i ,node j Voltage amplitude (per unit value pu). Represents a node i With nodes j The voltage phase angle difference between them These are the real and imaginary parts of the nodal admittance matrix, respectively. Is BTB at the node i Injected active and reactive power, N This represents the total number of nodes in the power grid.

[0058] ② Construct a BTB bidirectional active power transmission model: ; in, i For high-voltage side nodes, such as 500 kV; j For low-voltage side nodes, such as 220 kV.

[0059] ③ Construct a capability constraint model (capability circle): ; in, It is the active power output of the BTB converter. It is the reactive power output of the BTB converter. It is the rated apparent capacity of the converter.

[0060] ④ Bidirectional adjustment range: ; (2) Establish a model that includes inertia characteristics and dynamic response of node frequencies: ① Constructing a system inertia model: The equivalent inertia of the system is expressed as follows: ; in, For the first g The inertia constant of the synchronous machine, Indicates the first g Rated capacity of the unit For the number of synchronizers, This represents the system's baseline capacity.

[0061] ②RoCoF dynamic equations: ; in, It is the rate of change of frequency (Hz / s). It is a measure of active power loss after a fault. It is the system's equivalent inertia. It is the rated frequency, such as 50 Hz.

[0062] ③BTB fast support corrected frequency response: ; The corrected RoCoF is: ; ④ The approximate formula for the lowest frequency point (Nadir) is: .

[0063] (3) Constructing a model for uncertainty in new energy output and risk of tidal current exceeding limits: The output of new energy sources (wind power and photovoltaic) is characterized by abrupt changes, time correlation, and cumulative prediction errors. This randomness directly leads to fluctuations in node voltage, power flow, and converter station load. This invention uses a random variable model and risk indicators to characterize these fluctuations.

[0064] ① Construct a stochastic model for active power output from new energy sources: Wind power or solar power plants k The active power output can be modeled as follows: ; in, For new energy power stations k Power contribution (MW). This represents the average active power output within the operating range. This represents the standard deviation of active power output fluctuation. It is a standardized random variable with a mean of 0 and a variance of 1.

[0065] ② Construct a reactive power stochastic model for new energy sources: ; in, This indicates the reactive power output (MVar) of the power station. To average reactive power output, This represents the standard deviation of reactive power fluctuation.

[0066] ③ Nodal voltage over-limit loss function: Node voltage in random scenarios x The loss function is as follows: ; in, For the scene x Next node i Voltage (per unit value pu) These are the upper and lower limits of the voltage.

[0067] ④ Line power flow over-limit loss function: ; in, For the line l Flow dynamics (MVA) in random scenarios For the line l The thermal stability limit.

[0068] ⑤ Comprehensive over-limit loss function: ; in, These represent the voltage and power flow loss weighting coefficients, respectively.

[0069] ⑥ Introduce Conditional Value at Risk (CVaR): CVaR (confidence level) of the loss function α ) is defined as: ; in, or These are auxiliary variables (i.e., points corresponding to VaR). Represents the mathematical expectation. α The confidence level is set to, for example, 0.95 or 0.99.

[0070] (4) such as Figure 4 As shown, a risk-adaptive BTB active / reactive power regulation strategy is designed: BTB converter stations have the capability to output supporting power within tens of milliseconds, but the regulation intensity should be increased when system risks intensify and reduced when the system is in a safe state. Therefore, a risk-adaptive regulation mechanism should be constructed.

[0071] ① Risk mitigation function design: Define the risk mitigation function: ; in, (⋅) is a monotonically non-decreasing function, and can be chosen as a linear, logarithmic, or piecewise function; F risk A scalar measure (dimensionless) that represents the level of risk.

[0072] Commonly used linear form: ; in, This is a risk amplification factor. As a risk threshold, This is the step activation function.

[0073] ② Adaptive active power regulation strategy: ; When the system is at high risk, BTB will proactively enhance support by either reducing the power sent out or increasing the power injected into the system.

[0074] ③ Adaptive reactive power regulation strategy: ; This strategy can enhance the node's voltage support capability.

[0075] (5) Construct a multi-objective optimization model and solve for BTB location and capacity configuration: The optimization model uses the node location, rated capacity, and adjustment strategy parameters of the BTB as decision variables.

[0076] ① Decision variables: ; in, Install node combinations for BTB. Indicates the rated capacity. This is the risk adjustment coefficient.

[0077] ② Set of multi-objective functions: ; in, This indicates that the risk indicator minimizes investment or operating costs. This indicates the system's active power loss. To maximize the minimum frequency value (taking the negative sign as the objective). This indicates that the risk indicator has been minimized.

[0078] ③The main constraints are as follows: (a) Power flow balance constraint: .

[0079] (b) Operational safety constraints: ; This includes node voltage range, line power flow limits, and BTB capacity limits.

[0080] (c) RoCoF safety constraints: ; (d) Minimum frequency constraint: .

[0081] ④ Solution method: A multi-objective evolutionary algorithm (such as the improved particle swarm optimization algorithm or NSGA-II) is adopted to successively perform elite library maintenance, crowding distance sorting, dynamic inertia weighting, and penalty function feasibility correction; finally, the Pareto optimal set is obtained, and the final location scheme is output through fuzzy weighting method.

[0082] Therefore, the above-mentioned back-to-back flexible DC system location method that considers stability and risk can be applied to scenarios such as power grid planning and design, operation optimization, new energy base transmission projects, and stability improvement of multi-voltage level hub power grids.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A back-to-back flexible DC system location method considering stability and risk, characterized in that, Includes the following steps: Step 1: Establish a cross-voltage level power flow and equipment model for a power grid including a back-to-back flexible DC transmission system (BTB). Step 2: Establish a node frequency dynamic response model that includes inertia characteristics; Step 3: Construct a risk modeling and adaptive control model that considers the uncertainty of new energy output and power flow constraints; Step 4: Establish a multi-objective optimization model that comprehensively considers cost, loss, dynamic stability, minimum frequency, and risk level; Step 5: Solve for the Pareto optimal solution set using a multi-objective evolutionary algorithm and output the location selection results.

2. The back-to-back flexible vertical transmission system location method considering stability and risk according to claim 1, characterized in that, Step one is as follows: Let the set of power grid nodes be 𝒩 and the set of voltage levels be R, where R = {H, L}, and H and L represent high voltage level and low voltage level, respectively; The system node state vector is defined as follows: ； in, For nodes i The active power of power generation, For nodes i The active power of the load, For nodes i Voltage amplitude, For nodes i Voltage phase angle; Establish the AC power flow equilibrium equation: ； ； In the formula, P i , Q i They are nodes i The active and reactive power injected; G ij , B ij They are nodes i With nodes j The real and imaginary parts of the admittance; The BTB back-to-back flexible DC transmission system is considered as a connection to the high-voltage side node. i With low voltage side node j A bidirectional controllable active power exchange device whose active power satisfies: ； In the formula, For BTB at the high voltage side node i Injected active power, For BTB at the low voltage side node j Injected active power; Corresponding reactive power Constrained by converter capacity and control strategy, by The power balance equations at the corresponding nodes are superimposed to form a cross-voltage level AC power flow model that includes the power balancing model (BTB).

3. The back-to-back flexible vertical transmission system location method considering stability and risk according to claim 2, characterized in that, Step two is as follows: The overall equivalent inertia constant of the power grid is defined as H eq The rated frequency is defined as f n The net loss of active power in a system caused by a fault or disturbance is defined as follows: Ignoring higher-order dynamics, the system frequency change rate RoCoF is expressed as: ； In the formula, f ( t (time) t The system frequency, Let RoCoF be the first derivative of frequency with respect to time; H eq The smaller the value, the better for the same Δ P imb The faster the frequency decreases; When considering BTB's participation in frequency support, BTB-supported active power is introduced. The effective power loss after the disturbance is defined as: ； The rate of change of frequency is now corrected to: 。 4. The back-to-back flexible vertical transmission system location method considering stability and risk according to claim 3, characterized in that, The node frequency dynamic response model in step two also includes calculating the lowest frequency after the disturbance, and the calculation method is as follows: Active power loss measurement corresponding to a given typical disturbance Given the combined response time Δt of primary frequency modulation and BTB fast support, the minimum system frequency value is determined. f min Represented as: ； In the formula, f min The lowest frequency value after the disturbance, Δ t This is a critical time window before the main supporting measures have been fully implemented.

5. The back-to-back flexible direct current system location method considering stability and risk according to claim 4, characterized in that, Step three specifically involves: New energy power stations k Contributing to the cause With no effort Consider it as a random perturbation vector ξ =( ξ 1, ξ 2,…, ξ m ) T The random function is: ； ； In the formula, They are new energy power stations k Expected value of effort, whether it is productive or not. These are the standard deviations of the corresponding outputs. ξ k To describe new energy power stations k Standardized random variables of output fluctuations m The dimension of the random variable; a set of new energy power output scenarios is obtained through Monte Carlo simulation or scenario sampling, which is used to drive the power flow equations and frequency response models containing BTB; Define power flow and voltage limit loss functions L ( ξ ), used to measure random scenarios ξ Lower node voltage V i ( ξ Constraints, line power S l ( ξ The degree of breach of the constraint; Based on the loss function, a confidence level is introduced. α Conditional Value at Risk (CVaR) CVaR α (L), for the worst (1- α Quantify the average loss for percentage-based scenarios; Reconstruct the risk mitigation function F risk ( CVaR α ( L This is then superimposed onto the BTB active and reactive power reference commands to form a risk-adaptive BTB power regulation strategy.

6. The back-to-back flexible direct current system location method considering stability and risk according to claim 5, characterized in that, In step three, risk modeling and adaptive control also include safety probability constraints in the form of opportunity constraints, specifically: Apply chance constraints to node voltages and line power flows respectively: ； ； in, V i min and V i max They are nodes i Lower and upper limits of voltage amplitude , This represents the maximum probability of failure allowed by voltage and power flow constraints. S l ( ξ ) for scene ξ Downline l Apparent power S l max For the line l The maximum allowed transmission capacity.

7. The back-to-back flexible direct current system location method considering stability and risk according to claim 6, characterized in that, In step three, the risk-adaptive BTB power regulation strategy includes the following forms: Define the risk mitigation function: ； in, (⋅) is a monotonically non-decreasing function, when CVaR α ( L When it increases F risk Consequently, the active power reference value of BTB is increased; the value is then corrected to: ； The reactive power reference value is corrected to: ； In the formula, These are the BTB active and reactive power reference values ​​when no risk is considered, and are the active and reactive power risk adjustment coefficients.

8. The back-to-back flexible direct current system location method considering stability and risk according to claim 7, characterized in that, Step four is as follows: Let the BTB site selection and capacity configuration scheme be the set of decision variables. u The steady-state and dynamic states of the power grid are x Under the premise of satisfying the power flow balance equation, equipment operation constraints, dynamic stability constraints, and risk constraints, a set of multi-objective functions is constructed: ； in, To take into account both investment and operating costs, For system active power loss, As a dynamic stability index, As a risk indicator, It is the negative value of the minimum frequency of the critical node after the perturbation, used to achieve the goal of maximizing the minimum frequency of the node; The above multi-objective problem can be transformed into a multi-objective minimization form: ； Apply constraints on node voltage upper and lower limits, line power upper limit, BTB active / reactive capacity, and RoCoF and minimum frequency.

9. The back-to-back flexible vertical transmission system location method considering stability and risk according to claim 1, characterized in that, In step four, the constraints of the multi-objective optimization model include: Current balance constraints: ； in, h For the AC power flow equations that include BTB; Running constraint set: ； in, g Including node voltage constraints Line power constraints BTB active power constraint BTB reactive power constraint And inertia and RoCoF safety constraints; RoCoF and Frequency Security Constraints: ； in, RoCoF max The maximum allowable rate of change threshold for the system. f safe This is the minimum safe frequency threshold.

10. The back-to-back flexible direct current system location method considering stability and risk according to claim 1, characterized in that, Step five is as follows: An improved multi-objective particle swarm optimization algorithm is used to solve the multi-objective model, and the Pareto optimal solution set is obtained by balancing cost, loss, dynamic stability, frequency safety margin and risk level. Then, the solution with the best comprehensive index is selected from the Pareto set by fuzzy comprehensive evaluation or weighted aggregation method, and the candidate node combination, rated capacity, frequency support strategy and risk control parameters of BTB are output. The improvement process of the multi-objective particle swarm optimization algorithm is as follows: A linearly decreasing inertia weight strategy is adopted: ； In the formula, The inertia weight is the number of iterations when iter is given. These are the initial and final inertia weights, respectively, iter max This represents the maximum number of iterations. An adaptive target weight adjustment mechanism is introduced to dynamically update the target weights based on the current distribution of the group across targets; An external elite library is set up to store non-dominated solutions, and the elite library is updated using the crowding distance metric; The penalty function method is used to penalize particles that violate power flow constraints, dynamic stability constraints, and risk constraints, thereby guiding particles to converge toward the feasible region.

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