Method for evaluating power flow regulation capability of a flexible straight back-to-back system

Abstract

The present application relates to the technical field of power system operation analysis and regulation, and specifically discloses a kind of VSC-HVDC system power flow regulation capability evaluation method, comprising the following steps: S1, the power flow regulation range mathematical model of establishing containing back-to-back flexible HVDC transmission system BTB;S2, establish new energy output uncertainty model;S3, construct power flow over-limit risk and risk adaptive power regulation mechanism;S4, generalized polynomial chaos matrix method is used to evaluate the two-way power flow regulation range;S5, output power flow regulation range evaluation results and visual index.The present application uses the above-mentioned VSC-HVDC system power flow regulation capability evaluation method, realizes the collaborative quantification of new energy randomness, operation risk and BTB regulation capacity, improves the accuracy and engineering practicability of the evaluation results, and provides a decision basis for power system planning and design, operation control.

Description

Technical Field

[0001] This invention relates to the field of power system operation analysis and control technology, and in particular to a method for evaluating the power flow regulation capability of a flexible DC back-to-back system. Background Technology

[0002] With the continuous surge in installed capacity of new energy sources such as wind power and photovoltaics, the power system is gradually transforming towards a form with a high proportion of new energy penetration. Consequently, the power flow distribution of the power grid exhibits strong time-varying and random characteristics, posing a severe challenge to the safe and stable operation of the system. Back-to-back flexible DC transmission systems (BTB) have become key core devices for solving regional power grid interconnection, new energy consumption, and optimized power flow configuration due to their core advantages such as rapid bidirectional regulation, independent control of active and reactive power, and enhanced grid stability.

[0003] However, with the large-scale integration of wind and solar power, power flow in the grid exhibits strong time-varying and random characteristics. Traditional power flow regulation capacity assessment methods are mostly based on deterministic power flow or Jacobi sensitivity analysis, which can only characterize the system characteristics under static and deterministic operating conditions. They are difficult to accurately capture the dynamic changes in power flow caused by the fluctuation and randomness of new energy output, and cannot fully reflect the dynamic boundary of BTB bidirectional power regulation.

[0004] On the other hand, the reactive power support capability of new energy inverters is affected by control strategies and capacity constraints, and exhibits significant randomness and uncertainty. Furthermore, in the power grid, power flow constraints, bus voltage, line capacity, and equipment capacity constraints can all be affected by random disturbances.

[0005] Existing assessment systems often lack quantitative analysis of power flow over-limit risks in extreme scenarios and have not constructed risk-adaptive adjustment mechanisms. This makes it difficult to meet the engineering requirements of high-proportion renewable energy power grids for accurate assessment of BTB regulation capabilities, thus restricting the full application of BTB devices in power grid safe operation and optimized regulation. Summary of the Invention

[0006] The purpose of this invention is to provide a method for evaluating the power flow regulation capability of a flexible DC back-to-back system. This method can accurately calculate the power flow regulation range of the transmission network under the combined effects of stochastic renewable energy output, operational risk constraints, and the bidirectional regulation characteristics of the BTB (Browser-to-Built) system, thereby providing a quantifiable decision-making basis for operation control and planning design.

[0007] To achieve the above objectives, the present invention provides a method for evaluating the power flow regulation capability of a flexible back-to-back system, comprising the following steps: S1. Establish a mathematical model of the power flow regulation range including the back-to-back flexible DC transmission system (BTB). S2. Establish an uncertainty model for new energy output; S3. Construct a power regulation mechanism to address power flow over-limit risk and risk-adaptive power adjustment. S4. The generalized polynomial chaotic matrix method is used to evaluate the bidirectional power flow regulation range. S5 outputs power flow regulation range assessment results and visualization indicators.

[0008] Preferably, S1 specifically includes: S11. Construct bidirectional active power constraints for the BTB back-to-back flexible DC transmission system, equating the BTB back-to-back flexible DC transmission system to a system located at the bus. i With busbar j A controllable bidirectional power exchange device between them, its active power satisfy: ; in, This represents the active power transmission of the BTB under the current operating conditions. Rated active power transmission capacity for BTB; >0 indicates that power is transmitted from the sending end to the receiving end. <0 indicates that power is fed back from the receiving end to the sending end; S12. Construct reactive power and capacity curve constraints for the BTB back-to-back flexible DC transmission system, and the reactive power of the BTB converter station. Constrained by converter capacity and control strategy, the following conditions must be met: ; Using a circular capacity curve: ; in, Q BTB Reactive power injected into the BTB converter station; These are the upper and lower boundary functions of reactive power regulation related to active power, respectively. Rated apparent capacity for BTB; S13. Establish the power flow equations for the AC power grid including the BTB back-to-back flexible DC transmission system, that is, establish the active and reactive power balance equations for each bus of the AC power grid including the BTB back-to-back flexible DC transmission system: ; in, busbars i The active and reactive power injected; busbar i busbar j The voltage amplitude; busbar i With busbar j The voltage phase angle difference; These are the real and imaginary elements of the network admittance matrix, respectively. N This represents the total number of busbars. S14. Establish the AC power flow equation and the mathematical model of the power flow regulation range, and inject power into the BTB converter station. P BTB , Q BTB Superimposed on the power balance equations of the corresponding bus, a set of power flow equations including the busbar (BTB) is formed: ; in, x It is a set of state variables, including the magnitude and phase angle of all bus voltages; u The set of control variables includes BTB active / reactive power output and other adjustable resources; x It is a random perturbation vector; The power flow regulation range is defined as follows: ; in, It is a set of inequality constraints that includes upper and lower limits of bus voltage, upper limit of branch power flow, and equipment capacity constraints. This represents the feasible region of active / reactive power values ​​that BTB can take while satisfying the above constraints.

[0009] Preferably, S2 specifically includes: S21, New Energy Power Station k Contributing to the cause P ren,k With no effort Q ren,k Treat as a vector of random perturbation x =( x 1, x 2,…, x m ) T A changing random function, expressed as: ; in, m P,k , m Q,k They are new energy power stations k Expected values ​​of active and reactive power output during the study period; s P,k , s Q,k These are the standard deviations of the corresponding outputs; x k To describe new energy power stations k The standardized random variable of output fluctuation follows a distribution with zero mean and unit variance; mThe dimension of the random variable is given, and the corresponding disturbance factors include wind speed, irradiance, temperature, and prediction error. S22. Using one or more methods, such as probability distribution models, Monte Carlo simulations, or interval analysis, generate a set of scenarios for renewable energy output: ; In each scene s The corresponding output set is obtained below: ; in, S Number of scenes; x (s) For the first s A random vector for each scene; For the scene s New energy power station k The active and passive output values; S23, in each scene s The corresponding output set is obtained and embedded as an external disturbance input into the power flow equations containing BTB, defining the following... x Changing power flow state quantity With control quantity : ; in, V ( x () is a vector of the magnitudes of all bus voltages under random disturbances; i ( x () is the vector of the bus voltage phase angle under random disturbance; P BTB ( x ) and Q BTB ( x ) for in scene x The active and inactive contributions of BTB.

[0010] Preferably, S3 specifically includes: S31. Set the power flow constraint over-limit loss function. L ( x Its expression is as follows: ; in, V i ( x (This refers to a random scene) x Lower busbar i voltage amplitude; Δ V lim The allowable voltage deviation threshold; S l ( x(This refers to a random scene) x Downline l The complex power or its amplitude; S l max For the line l Maximum permissible power transfer capacity; loss function L ( x ) is used for quantization in random scenarios x The extent to which voltage and power flow constraints are exceeded; S32. The Conditional Value at Risk (CVaR) is used to quantify the risk of extreme scenarios, and its indicator is expressed as follows: ; in, α Confidence level; or As an auxiliary variable, it is used to determine the approximate location of VaR; E[⋅] represents the relationship between the random variable and the target variable. x The mathematical expectation; CVaR α ( L Characterization loss function L In the worst case (1- α The average level in percentage scenarios; S33. Define the risk mitigation function. The BTB adjustment strategy is adaptively adjusted based on risk indicators. ; in, The BTB active power reference command is taken into account after risk mitigation. This is the BTB reference power setting value without considering risks; k r This is a risk adjustment coefficient, used to adjust the impact of risk on the correction magnitude of the reference power. For a monotonically non-decreasing function, when CVaR α ( L The output value increases as the number of digits increases. S34, Risk Mitigation Function The output is also used to adjust the reactive power support level: ; in, BTB reactive power reference output when considering risks; The reactive power reference output without considering risks; This is the reactive power regulation coefficient.

[0011] Preferably, S4 specifically includes: S41. Selection of Random Vectors x The corresponding family of orthogonal polynomials ,in, For the first The order generalized polynomial chaotic basis functions satisfy: ; in, [⋅] is for... x The expectation operator; K The highest polynomial order in the expansion; Depend on x The probability distribution determines; i and j The index subscripts of the basis functions in the orthogonal polynomial family represent the i-th, j ... i The and the first j A generalized polynomial chaotic basis function; S42. Perform gPC expansion on the power flow state variables and BTB control variables involving stochasticity, and on the bus voltage vector. V ( x )have: ; For BTB active power: ; in, In order to be with the first The bus voltage coefficient vector corresponding to the order generalized polynomial chaotic basis functions; In order to be with the first The BTB active power coefficient scalar or vector corresponding to the order generalized polynomial chaotic basis function. K The highest polynomial order in the expansion; S43, will x ( x )and u ( x Substituting the gPC expansion of ) into the power flow equations containing BTB: ; Obtain information about the basis functions Residual expansion: ; For each basis function Φ j ( x Apply the Galerkin orthogonality condition: ; A set of algebraic equations concerning the gPC coefficients is obtained, and solving them yields the coefficient matrix: ; in, c x,K State variables xThe K Expansion coefficients of a polynomial of order 1; C x It is a generalized polynomial chaotic coefficient matrix, reflecting the mapping relationship between random disturbances and system states; S44, will C x Treating it as a generalized polynomial chaotic matrix, a rapid assessment of the power flow over-limit probability and state response under various stochastic scenarios is performed within a given BTB bidirectional power regulation range, and this is achieved through scanning. The range of values ​​for is used to solve for the boundary of the feasible region that satisfies the safety probability constraint, thereby determining the power flow regulation range: ; in, {⋅} represents a probability operator; e The maximum acceptable probability of default; g (⋅) is a constraint function that includes bus voltage and line power.

[0012] Preferably, in S5, a unified model integrating power flow constraints, new energy uncertainty constraints, and risk index constraints is constructed during the evaluation. The maximum feasible boundary of power transmission from the sending end to the receiving end and from the receiving end to the sending end of the BTB is solved respectively. The boundary volume, coverage, and risk robustness engineering evaluation index are calculated to quantitatively evaluate and visualize the power flow regulation capability of the BTB flexible DC system. The evaluation results and visualization indexes are presented.

[0013] Preferably, S5 specifically includes: S51. Establish power flow and equipment operation constraints, including bus voltage constraints: ; Branch power constraints: ; Operational constraints include the transformer tap position and the switching status of reactive power compensation equipment; in, V i min , V i max busbar i Voltage amplitude upper and lower limits; S l For the line l The complex power or its amplitude; S l max This represents the maximum permissible transmission power of line l; S52. Establish uncertainty constraints for new energy sources; the power output scenario for new energy sources is determined by random variables. xThe drive, whose boundaries are given by historical data, prediction intervals, or probability distributions, corresponds to the following output range: ; in, , They are new energy power stations k The contribution of effort and the contribution without effort, They are new energy power stations k The lower and upper levels that have contributed merit and effort; These are the lower and upper boundaries of no productive output, respectively. S53. Establish risk indicator constraints, through... CVaR Or, opportunity constraints set an upper limit on the risk of exceeding the trend limit: ; in, This represents the upper limit allowed for the loss function; e The maximum acceptable probability of default; For probability operators; S54. Incorporate power flow constraints, new energy uncertainty constraints, and risk indicator constraints into the power flow regulation range assessment model to form a model that includes decision variables ( P BTB ,Q BTB ), state variables x and random variables x Multi-constraint coordination optimization problem: ; Wherein, Φ( x , u This is a comprehensive objective function that reflects the extent of the expansion of the power flow regulation range boundary, the risk of loss, or the operating cost. h For the power flow equilibrium equation; g For the set of constraints to run; x , u The decision variable should include at least the active / reactive output of BTB.

[0014] Therefore, the present invention employs the above-mentioned method for evaluating the power flow regulation capability of a flexible back-to-back system, and the beneficial effects are as follows: (1) Compared with existing systems, the present invention can systematically characterize the bidirectional active and reactive power regulation capabilities of BTB.

[0015] (2) This invention can directly integrate the randomness of new energy into the power flow model, thereby improving the realism of the adjustment range.

[0016] (3) The risk assessment mechanism of this invention makes the results more practical for engineering applications; the gPC method is used to reduce the amount of power flow calculation in multiple scenarios and improve the calculation efficiency.

[0017] (4) The present invention can output adjustment range graphs and indicators, which are convenient for engineering applications.

[0018] 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

[0019] Figure 1 This is an overall method flowchart of an embodiment of the method for evaluating the power flow regulation capability of a flexible straight back-to-back system according to the present invention; Figure 2 This is a schematic diagram of an AC power grid structure containing a BTB, according to an embodiment of the present invention, which provides a method for evaluating the power flow regulation capability of a flexible back-to-back system. Figure 3 This is a schematic diagram of the risk adaptive adjustment mechanism of an embodiment of the power flow regulation capability assessment method for a flexible straight back-to-back system according to the present invention; Figure 4 This is a flowchart illustrating the construction of a generalized polynomial chaotic matrix in an embodiment of the present invention, which describes a method for evaluating the power flow regulation capability of a flexible back-to-back system. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] 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.

[0022] The generalized polynomial chaotic gPC method can approximate the influence of random variables on the system state through polynomial basis functions, thus efficiently solving stochastic power flows without performing extensive Monte Carlo power flow calculations. This invention combines the BTB regulation model, new energy uncertainty, risk assessment, and gPC to construct a power flow regulation range assessment method suitable for engineering applications.

[0023] like Figure 1 As shown, a method for evaluating the power flow regulation capability of a flexible back-to-back system includes the following steps: S1. Establish a mathematical model of the power flow regulation range including the back-to-back flexible DC transmission system (BTB).

[0024] like Figure 2As shown, under given AC grid topology and parameters, a cross-voltage level BTB back-to-back flexible DC transmission system is introduced between the 500kV and 1000kV AC grids. The BTB converter station is considered as a controllable power source or controllable bus with bidirectional active / reactive power regulation capability. A set of power flow equations and constraints for the AC grid including the BTB are established, resulting in a mathematical model describing the adjustable power range under BTB bidirectional power regulation. Specifically, this includes: S11. Construct bidirectional active power constraints for the BTB back-to-back flexible DC transmission system, equating the BTB back-to-back flexible DC transmission system to a system located at the bus. i With busbar j A controllable bidirectional power exchange device between them, its active power satisfy: ; in, This represents the active power transmission of the BTB under the current operating conditions. Rated active power transmission capacity for BTB; >0 indicates that power is transmitted from the sending end to the receiving end. <0 indicates that power is fed back from the receiving end to the sending end.

[0025] S12. Construct reactive power and capacity curve constraints for the BTB back-to-back flexible DC transmission system, and the reactive power of the BTB converter station. Constrained by converter capacity and control strategy, the following conditions must be met: ; A circular capacity curve can be used: ; in, Q BTB Reactive power injected into the BTB converter station; These are the upper and lower boundary functions of reactive power regulation related to active power, respectively. The nominal apparent capacity of BTB.

[0026] S13. Establish the power flow equations for the AC power grid including the BTB back-to-back flexible DC transmission system, that is, establish the active and reactive power balance equations for each bus of the AC power grid including the BTB back-to-back flexible DC transmission system: ; in, busbars i Active and reactive power injection (positive values ​​indicate injection, negative values ​​indicate absorption); busbar i busbar j The voltage amplitude; busbari With busbar j The voltage phase angle difference; These are the real and imaginary elements of the network admittance matrix, respectively. N This represents the total number of busbars.

[0027] S14. Establish the AC power flow equation and the mathematical model of the power flow regulation range, and inject power into the BTB converter station. P BTB , Q BTB Superimposed on the power balance equations of the corresponding bus, a set of power flow equations including the busbar (BTB) is formed: ; in, x It is a set of state variables, including the magnitude and phase angle of all bus voltages; u The set of control variables includes BTB active / reactive power output and other adjustable resources; x It is a random disturbance vector (such as new energy output, load deviation, etc.).

[0028] Based on this, the power flow regulation range is defined as follows: ; in, It is a set of inequality constraints that includes upper and lower limits of bus voltage, upper limits of branch power flow, and equipment capacity constraints. This represents the feasible region of active / reactive power values ​​that BTB can take while satisfying the above constraints.

[0029] S2. Establish an uncertainty model for new energy output.

[0030] The active and reactive power injected by wind power, photovoltaic and other new energy power plants are treated as stochastic processes. A stochastic vector representing disturbance factors such as weather and load is introduced to construct a probabilistic or interval model of new energy output, forming a set of new energy output for multiple scenarios. This set is then embedded into the power flow regulation range model in step one, specifically including: S21. Expression of random function for new energy output: Wind power, photovoltaic and other new energy power stations k Contributing to the cause P ren,k With no effort Q ren,k Treat as a vector of random perturbation x =( x 1, x 2,…, x m ) T A changing random function, expressed as: ; in, m P,k , m Q,k They are new energy power stations k Expected values ​​of active and reactive power output during the study period; s P,k , s Q,k These are the standard deviations of the corresponding outputs; x k To describe new energy power stations k The standardized random variable of output fluctuation can follow a distribution with zero mean and unit variance; m The dimension of the random variable can correspond to disturbance factors such as wind speed, irradiance, temperature, and prediction error.

[0031] S22, Probability Distribution and Scene Generation: Using one or more methods among probability distribution models (such as Beta distribution, Weibull distribution, normal distribution, or empirical distribution based on wind speed / irradiance), Monte Carlo simulation, or interval analysis, generate a set of scenarios for renewable energy output: ; In each scene s The corresponding output set is obtained below: ; in, S Number of scenes; x (s) For the first s A random vector for each scene; For the scene s New energy power station k The effective and ineffective output values.

[0032] S23. Embedding new energy scenarios into the power flow equation containing BTB: In each of the above scenarios s The corresponding output set is obtained and embedded as an external disturbance input into the power flow equations containing BTB, defining the following... x Changing power flow state quantity With control quantity : ; in, V ( x () is a vector of the magnitudes of all bus voltages under random disturbances; i ( x () is the vector of the bus voltage phase angle under random disturbance; P BTB( x )and Q BTB ( x ) for in scene x The active and inactive contributions of BTB. x ( x ),u( x It is used for subsequent generalized polynomial chaos expansion and risk assessment.

[0033] S3. Construct a power flow over-limit risk and risk-adaptive power regulation mechanism.

[0034] like Figure 3 As shown, a risk assessment index and risk mitigation function reflecting the risk of power flow exceeding limits are established. Based on the risk assessment results, the power control parameters and active / reactive power output commands of the BTB flexible DC system are dynamically adjusted to achieve adaptive correction of the risk within the bidirectional power flow regulation range. Specifically, this includes: S31. Construction of the power flow over-limit loss function: Set the power flow constraint over-limit loss function L ( x Its expression is as follows: ; in, V i ( x (This refers to a random scene) x Lower busbar i voltage amplitude; Δ V lim The allowable voltage deviation threshold; S l ( x (This refers to a random scene) x Downline l The complex power or its amplitude; S l max For the line l Maximum permissible power transfer capacity; loss function L ( x ) is used for quantization in random scenarios x The extent to which voltage and power flow constraints are exceeded.

[0035] S32. Conditional Value at Risk (CVaR) indicator: Conditional Value at Risk (CVaR) is used to quantify the risk of extreme scenarios, and its metric can be expressed as: ; in, α The confidence level is 0.95 or 0.99. orAs an auxiliary variable, it is used to determine the approximate location of VaR (Value-at-Risk); [⋅] indicates that the random variable x The mathematical expectation; CVaR α ( L Characterization loss function L In the worst case (1- α The average level in percentage scenarios.

[0036] S33. Risk-based BTB active power adaptive adjustment strategy: Define risk mitigation function The BTB adjustment strategy is adaptively adjusted based on risk indicators. ; in, The BTB active power reference command is taken into account after risk mitigation. This is the BTB reference power setting value without considering risks; k r This is a risk adjustment coefficient, used to adjust the impact of risk on the correction magnitude of the reference power. For a monotonically non-decreasing function, when CVaR α ( L When the output value increases, the output value increases, thereby prompting the BTB output to adjust in a direction with lower risk.

[0037] S34. Risk-based adaptive adjustment of reactive power support: Risk mitigation function The output can also be used to adjust the reactive power support level: ; in, BTB reactive power reference output when considering risks; The reactive power reference output without considering risks; This is the reactive power regulation coefficient.

[0038] Through the above adjustments, when an increased risk of power flow exceeding limits is predicted, the voltage support capability is automatically increased or the power flow regulation range is narrowed, thereby achieving robust protection against extreme operating conditions.

[0039] S4. The generalized polynomial chaotic matrix method is used to evaluate the bidirectional power flow regulation range.

[0040] like Figure 4As shown, considering the uncertainty of new energy output and the risk adaptive mechanism, a generalized polynomial chaos (gPC) expansion is introduced to perform a polynomial expansion on the power flow state variables involving random variables, constructing a generalized polynomial chaos matrix describing the mapping relationship between BTB power regulation, bus power distribution, and voltage level. Based on this matrix, the adjustable boundary of the power flow is calculated under bidirectional power regulation conditions, specifically including: S41. Selection of Random Vectors x The corresponding family of orthogonal polynomials ,in, For the first The order generalized polynomial chaotic basis functions satisfy: ; in, [⋅] is for... x The expectation operator; K The highest polynomial order in the expansion; Depend on x The probability distribution determines; i and j The index subscripts of the basis functions in the orthogonal polynomial family represent the i-th, j ... i The and the first j A generalized polynomial chaotic basis function. This formula describes the orthogonality property of the basis functions, that is, for any two distinct basis functions, their product is orthogonal with respect to the random variable. x The expected value is 0.

[0041] For example, the Gaussian distribution corresponds to the Hermite multinomial, and the Beta distribution corresponds to the Jacobi multinomial.

[0042] S42. Perform gPC expansion on the power flow state variables and BTB control variables involving stochasticity, and on the bus voltage vector. V ( x )have: ; For BTB active power: ; in, In order to be with the first The bus voltage coefficient vector corresponding to the order generalized polynomial chaotic basis functions; In order to be with the first The BTB active power coefficient scalar or vector corresponding to the order generalized polynomial chaotic basis function. K Let be the order of the highest polynomial in the expansion.

[0043] The above expansion can be generalized to all state variables. x and control quantityu .

[0044] S43. Substitute the gPC expansion into the power flow equations containing BTB, and solve for the coefficient matrix using Galerkin projection. Specifically: Will x ( x )and u ( x Substituting the gPC expansion form of the equation into the power flow equation containing BTB: .

[0045] Obtain information about the basis functions Residual expansion: .

[0046] For each basis function Φ j ( x Apply the Galerkin orthogonality condition: .

[0047] A set of algebraic equations about the gPC coefficients can be obtained, and solving them yields the coefficient matrix: ; in, c x,K State variables x The K Expansion coefficients of a polynomial of order 1; C x It is a generalized polynomial chaotic coefficient matrix, which reflects the mapping relationship between random disturbances and system states.

[0048] S44. Evaluating the power flow regulation range based on the generalized polynomial chaotic matrix: Will C x Treated as a "generalized polynomial chaotic matrix," the power flow exceedance probability and state response under various stochastic scenarios are rapidly evaluated within a given BTB bidirectional power regulation range, and this is achieved through scanning. The range of values ​​for is used to solve for the boundary of the feasible region that satisfies the safety probability constraint, thereby determining the power flow regulation range: ; in, {⋅} represents a probability operator; e The maximum acceptable probability of default; g (⋅) is a constraint function that includes bus voltage and line power.

[0049] S5 outputs power flow regulation range assessment results and visualization indicators.

[0050] During the evaluation, under the constraints of bidirectional power regulation capability, AC grid security, and risk indicators, a unified model integrating grid power flow constraints, new energy uncertainty constraints, and risk indicator constraints is constructed. The maximum feasible boundary of power transmission from the (forward) sender to the receiver and from the (reverse) receiver to the sender in the BTB system is solved separately to obtain a multidimensional boundary set of power flow regulation range. The boundary volume, coverage, and risk robustness engineering evaluation indicators are calculated to quantitatively evaluate and visualize the power flow regulation capability of the BTB flexible DC system. The evaluation results and visualization indicators are presented.

[0051] Specifically, it includes: S51. Establish power flow and equipment operation constraints, including bus voltage constraints: ; Branch power constraints: ; And operational constraints, including transformer tap positions and the switching status of reactive power compensation equipment.

[0052] in, V i min , V i max busbar i Voltage amplitude upper and lower limits; S l For the line l The complex power or its amplitude; S l max This represents the maximum permissible transmission power of line l.

[0053] S52. Establishing Uncertainty Constraints for New Energy Sources: New energy power output scenarios are composed of random variables x The drive, whose boundaries are given by historical data, prediction intervals, or probability distributions, corresponds to the following output range: ; in, , They are new energy power stations k The contribution of effort and the contribution without effort, They are new energy power stations k The lower and upper levels that have contributed merit and effort; These are the lower and upper boundaries for no effort exertion, respectively.

[0054] The aforementioned intervals can be determined by historical statistics, forecasting models, or operational strategies.

[0055] S53. Establish risk indicator constraints: pass CVaR Or, opportunity constraints set an upper limit on the risk of exceeding the trend limit: ; in, This represents the upper limit allowed for the loss function; e The maximum acceptable probability of default; It is a probability operator.

[0056] S54, Unified Power Flow Regulation Range Assessment Model: The aforementioned power flow constraints, renewable energy uncertainty constraints, and risk indicator constraints are uniformly incorporated into the power flow regulation range assessment model, forming a model that includes decision variables ( P BTB ,Q BTB ), state variables x and random variables x Multi-constraint coordination optimization problem: ; Wherein, Φ( x , u It can be a comprehensive objective function that reflects the extent of the expansion of the power flow regulation range boundary, loss risk, or operating cost; h For the power flow equilibrium equation; g For the set of constraints to run; x , u The decision variable should include at least the active / reactive output of BTB.

[0057] Example 1: (i) Establishing a mathematical model for the power flow regulation range of a back-to-back flexible DC transmission system (BTB): The power flow of a transmission network containing busbars (BTB) can be represented by an improved busbar power balance equation. At the busbar... i In the steady-state power flow equation, considering the power injection from traditional power sources, loads, renewable energy sources, and BTB (Build-Transfer-Based Power), the active and reactive power balance can be written as: ; ; in, V i and V j busbar i , j voltage amplitude, i ij This is the phase angle difference; G ij and B ij These are the real and imaginary parts of the admittance matrix, respectively.P BTB and Q BTB Indicates BTB on the busbar i Active and reactive power injection. As a bidirectional controllable power source, the BTB can achieve forward (sender end → receiver end) or reverse (receiver end → sender end) energy control by adjusting the converter controller.

[0058] The regulation capability of a BTB is limited by its converter capacity, and there is a coupling relationship between active and reactive power, which is usually expressed by a capacity circle: ; in, S max The rated apparent capacity of the converter reflects the engineering reality that reactive power regulation space is limited when active power output is high.

[0059] Based on this, the active power regulation range of BTB can be represented by a two-way limit: ; in, P max For the rated active power transmission capacity, the adjustment limit of BTB in different directions is defined.

[0060] The power flow regulation range is defined as: all conditions that meet the constraints of power flow balance, bus voltage, line power, and BTB capacity. P BTB , Q BTB The feasible region formed by the combination of )

[0061] (II) Establishing an uncertainty model for new energy output: Renewable energy power plants are significantly affected by weather changes, and their power output typically exhibits a stochastic process. In short-term regulation range assessments, this stochastic variation can be represented using a mean-perturbation form: ; ; in, m P,k and m Q,k They are new energy power stations k The average active and reactive power output; s P,k and s Q,k Indicates the amplitude of output fluctuation; x kThis is a zero-mean random variable used to characterize the volatility of wind speed, irradiance, or prediction errors. The model reflects the linear stochastic characteristics of new energy sources over a short period, and its mean and variance can be estimated using historical data.

[0062] The reactive power response of new energy sources is also affected by the inverter control strategy, and its dynamic characteristics can be represented by control functions, such as: ; in, V k Bus voltage, control parameters x This can include droop coefficients, virtual inertia coefficients, etc. This function describes the adaptive adjustment mechanism of reactive power as voltage changes.

[0063] After generating a batch of random samples, a set of power outputs for multiple scenarios of new energy can be formed, which can be used to represent the power flow changes of the system under different disturbance scenarios.

[0064] (III) Risk Adaptive Adjustment Mechanism: Power grid operation requires consideration of safety constraints such as bus voltage limits and line power flow limits, which may be exceeded under random disturbances. To quantify this risk, a power flow limit exceedance loss function is defined: ; in, V i ( x ) is the busbar i voltage, Δ V Indicates the allowable voltage deviation range; S l ( x ( ) is the line l The trend S l max This is its thermal stability limit. This loss function comprehensively describes the degree of voltage and line over-limit violations.

[0065] To further describe the impact of extreme scenarios, we introduce Conditional Value at Risk (CVaR): ; in, α The confidence level can take values ​​such as 0.95 or 0.99. or It is an auxiliary variable. CVaR reflects the average degree of exceeding the limit under the worst case and is a robust indicator commonly used in power grid risk assessment.

[0066] Based on the risk assessment results, a risk-adaptive adjustment strategy for BTB can be constructed. For example, the adjustment range can be narrowed when the risk is high. ; in,P BTB This is the original reference value. k r For adjustment coefficients, This is the risk mitigation function. This strategy can achieve a dynamic balance between regulatory capacity and safety risk.

[0067] (iv) Power flow regulation assessment method based on generalized polynomial chaotic matrix: To avoid performing power flow calculations for every random scenario, a generalized multinomial chaotic expansion (gPC) is introduced to approximate the power flow state as it changes with random variables. Let... x To influence the random vectors of the system, one can choose a family of orthogonal polynomials that correspond to their distribution: ; This makes polynomials of different orders orthogonal in the probability space.

[0068] System state variables (such as voltage) can be expressed as: ; The active power output of BTB is: ; in, The coefficient to be determined represents the weight of the influence of random disturbances on the power flow state.

[0069] By using the Galerkin projection method, the residuals of the power flow equations can be made orthogonal to each basis function, thereby establishing an algebraic equation about the coefficients and solving for the coefficient matrix. ; After obtaining the gPC coefficients, it is possible to quickly calculate whether the constraints are satisfied in any scenario. Based on this, the adjustment range boundary satisfying the specified probability requirement can be further obtained, i.e., all conditions that satisfy: ; of( P BTB , Q BTB )combination.

[0070] (v) Output and visualization of power flow regulation range: The final evaluation results can be projected onto P BTB - Q BTB The plane provides an adjustable area in both forward and reverse directions, and can further calculate indicators such as coverage and boundary volume to compare the adjustment capabilities of BTB under different operating conditions.

[0071] Therefore, the present invention adopts the above-mentioned method for evaluating the power flow regulation capability of a flexible DC back-to-back system, which is applicable to power flow analysis, regulation strategy formulation, and operation safety assessment of power transmission networks with a high proportion of new energy penetration.

[0072] 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 method for evaluating the power flow regulation capability of a flexible back-to-back system, characterized by, Includes the following steps: S1. Establish a mathematical model of the power flow regulation range including the back-to-back flexible DC transmission system (BTB). S2. Establish an uncertainty model for new energy output; S3. Construct a power regulation mechanism to address power flow over-limit risk and risk-adaptive power adjustment. S4. The generalized polynomial chaotic matrix method is used to evaluate the bidirectional power flow regulation range. S5 outputs power flow regulation range assessment results and visualization indicators.

2. The method for evaluating the power flow regulation capability of a flexible straight back-to-back system according to claim 1, characterized in that, S1 specifically includes: S11. Construct bidirectional active power constraints for the BTB back-to-back flexible DC transmission system, equating the BTB back-to-back flexible DC transmission system to a system located at the bus. i With busbar j A controllable bidirectional power exchange device between them, its active power satisfy: ； in, This represents the active power transmission of the BTB under the current operating conditions. Rated active power transmission capacity for BTB; >0 indicates that power is transmitted from the sending end to the receiving end. <0 indicates that power is fed back from the receiving end to the sending end; S12. Construct reactive power and capacity curve constraints for the BTB back-to-back flexible DC transmission system, and the reactive power of the BTB converter station. Constrained by converter capacity and control strategy, the following conditions must be met: ； Using a circular capacity curve: ； in, Q BTB Reactive power injected into the BTB converter station; These are the upper and lower boundary functions of reactive power regulation related to active power, respectively. Rated apparent capacity for BTB; S13. Establish the power flow equations for the AC power grid including the BTB back-to-back flexible DC transmission system, that is, establish the active and reactive power balance equations for each bus of the AC power grid including the BTB back-to-back flexible DC transmission system: ； in, busbars i The active and reactive power injected; busbar i busbar j The voltage amplitude; busbar i With busbar j The voltage phase angle difference; These are the real and imaginary elements of the network admittance matrix, respectively. N This represents the total number of busbars. S14. Establish the AC power flow equation and the mathematical model of the power flow regulation range, and inject power into the BTB converter station. P BTB , Q BTB Superimposed on the power balance equations of the corresponding bus, a set of power flow equations including the busbar (BTB) is formed: ； in, x It is a set of state variables, including the magnitude and phase angle of all bus voltages; u The set of control variables includes BTB active / reactive power output and other adjustable resources; ξ It is a random perturbation vector; The power flow regulation range is defined as follows: ； in, It is a set of inequality constraints that includes upper and lower limits of bus voltage, upper limit of branch power flow, and equipment capacity constraints. This represents the feasible region of active / reactive power values ​​that BTB can take while satisfying the above constraints.

3. The method for evaluating the power flow regulation capability of a flexible straight back-to-back system according to claim 2, characterized in that, S2 specifically includes: S21, New Energy Power Station k Contributing to the cause P ren,k With no effort Q ren,k Treat as a vector of random perturbation ξ =( ξ 1, ξ 2,…, ξ m ) T A changing random function, expressed as: ； in, μ P,k , μ Q,k They are new energy power stations k Expected values ​​of active and reactive power output during the study period; σ P,k , σ Q,k These are the standard deviations of the corresponding outputs; ξ k To describe new energy power stations k The standardized random variable of output fluctuation follows a distribution with zero mean and unit variance; m The dimension of the random variable is given, and the corresponding disturbance factors include wind speed, irradiance, temperature, and prediction error. S22. Using one or more methods, such as probability distribution models, Monte Carlo simulations, or interval analysis, generate a set of scenarios for renewable energy output: ； In each scene s The corresponding output set is obtained below: ； in, S Number of scenes; ξ (s) For the first s A random vector for each scene; For the scene s New energy power station k The active and passive output values; S23, in each scene s The corresponding output set is obtained and embedded as an external disturbance input into the power flow equations containing BTB, defining the following... ξ Changing power flow state quantity With control quantity : ； in, V ( ξ () is a vector of the magnitudes of all bus voltages under random disturbances; θ ( ξ () is the vector of the bus voltage phase angle under random disturbance; P BTB ( ξ )and Q BTB ( ξ ) for in scene ξ The active and inactive contributions of BTB.

4. The method for evaluating the power flow regulation capability of a flexible straight back-to-back system according to claim 3, characterized in that, S3 specifically includes: S31. Set the power flow constraint over-limit loss function. L ( ξ Its expression is as follows: ； in, V i ( ξ (This refers to a random scene) ξ Lower busbar i voltage amplitude; Δ V lim The allowable voltage deviation threshold; S l ( ξ (This refers to a random scene) ξ Downline l The complex power or its amplitude; S l max For the line l Maximum permissible power transfer capacity; loss function L ( ξ ) is used for quantization in random scenarios ξ The extent to which voltage and power flow constraints are exceeded; S32. The Conditional Value at Risk (CVaR) is used to quantify the risk of extreme scenarios, and its indicator is expressed as follows: ； in, α Confidence level; η As an auxiliary variable, it is used to determine the approximate location of VaR; E[⋅] represents the relationship between the random variable and the target variable. ξ The mathematical expectation; CVaR α ( L Characterization loss function L In the worst case (1- α The average level in percentage scenarios; S33. Define the risk mitigation function. The BTB adjustment strategy is adaptively adjusted based on risk indicators. ； in, The BTB active power reference command is taken into account after risk mitigation. This is the BTB reference power setting value without considering risks; k r This is a risk adjustment coefficient, used to adjust the impact of risk on the correction magnitude of the reference power. For a monotonically non-decreasing function, when CVaR α ( L The output value increases as the number of digits increases. S34, Risk Mitigation Function The output is also used to adjust the reactive power support level: ； in, BTB reactive power reference output when considering risks; The reactive power reference output without considering risks; This is the reactive power regulation coefficient.

5. The method for evaluating the power flow regulation capability of a flexible straight back-to-back system according to claim 4, characterized in that, S4 specifically includes: S41. Selection of Random Vectors ξ The corresponding family of orthogonal polynomials ,in, For the first The order generalized polynomial chaotic basis functions satisfy: ； in, [⋅] is for... ξ The expectation operator; K The highest polynomial order in the expansion; Depend on ξ The probability distribution determines; i and j The index subscripts of the basis functions in the orthogonal polynomial family represent the i-th, j ... i The and the first j A generalized polynomial chaotic basis function; S42. Perform gPC expansion on the power flow state variables and BTB control variables involving stochasticity, and on the bus voltage vector. V ( ξ )have: ； For BTB active power: ； in, In order to be with the first The bus voltage coefficient vector corresponding to the order generalized polynomial chaotic basis functions; In order to be with the first The BTB active power coefficient scalar or vector corresponding to the order generalized polynomial chaotic basis function. K The highest polynomial order in the expansion; S43, will x ( ξ )and u ( ξ Substituting the gPC expansion of ) into the power flow equations containing BTB: ； Obtain information about the basis functions Residual expansion: ； For each basis function Φ j ( ξ Apply the Galerkin orthogonality condition: ； A set of algebraic equations concerning the gPC coefficients is obtained, and solving them yields the coefficient matrix: ； in, c x,K State variables x The K Expansion coefficients of a polynomial of order 1; C x It is a generalized polynomial chaotic coefficient matrix, reflecting the mapping relationship between random disturbances and system states; S44, will C x Treating it as a generalized polynomial chaotic matrix, a rapid assessment of the power flow over-limit probability and state response under various stochastic scenarios is performed within a given BTB bidirectional power regulation range, and this is achieved through scanning. The range of values ​​for is used to solve for the boundary of the feasible region that satisfies the safety probability constraint, thereby determining the power flow regulation range: ； in, {⋅} represents a probability operator; ε The maximum acceptable probability of default; g (⋅) is a constraint function that includes bus voltage and line power.

6. The method for evaluating the power flow regulation capability of a flexible straight back-to-back system according to claim 5, characterized in that, In S5, a unified model is constructed to integrate power flow constraints, new energy uncertainty constraints, and risk index constraints during the evaluation. The maximum feasible boundary of power transmission from the sending end to the receiving end and from the receiving end to the sending end of the BTB is solved separately. The boundary volume, coverage, and risk robustness engineering evaluation index are calculated to quantitatively evaluate and visualize the power flow regulation capability of the BTB flexible DC system. The evaluation results and visualization indexes are presented.

7. The method for evaluating the power flow regulation capability of a flexible straight back-to-back system according to claim 6, characterized in that, S5 specifically includes: S51. Establish power flow and equipment operation constraints, including bus voltage constraints: ； Branch power constraints: ； Operational constraints include the transformer tap position and the switching status of reactive power compensation equipment; in, V i min , V i max busbar i Voltage amplitude upper and lower limits; S l For the line l The complex power or its amplitude; S l max This represents the maximum permissible transmission power of line l; S52. Establish uncertainty constraints for new energy sources; the power output scenario for new energy sources is determined by random variables. ξ The drive, whose boundaries are given by historical data, prediction intervals, or probability distributions, corresponds to the following output range: ； in, , They are new energy power stations k The contribution of effort and the contribution without effort, They are new energy power stations k The lower and upper levels that have contributed merit and effort; These are the lower and upper boundaries of no productive output, respectively. S53. Establish risk indicator constraints, through... CVaR Or, opportunity constraints set an upper limit on the risk of exceeding the trend limit: ； in, This represents the upper limit allowed for the loss function; ε The maximum acceptable probability of default; For probability operators; S54. Incorporate power flow constraints, new energy uncertainty constraints, and risk indicator constraints into the power flow regulation range assessment model to form a model that includes decision variables ( P BTB ,Q BTB ), state variables x and random variables ξ Multi-constraint coordination optimization problem: ； Wherein, Φ( x , u This is a comprehensive objective function that reflects the extent of the expansion of the power flow regulation range boundary, the risk of loss, or the operating cost. h For the power flow equilibrium equation; g For the set of constraints to run; x , u The decision variable should include at least the active / reactive output of BTB.

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