A multi-constraint coupling evaluation method for load capacity of a receiving power grid with multiple direct current feeders

Abstract

The present application relates to the technical field of power system operation control, and particularly relates to a multi-constraint coupling evaluation method for load-carrying capacity of a receiving-end power grid with multiple DC feed-in, comprising the following steps: S1, obtaining a receiving-end power grid topology, real-time environmental temperature and initial load parameters, calculating temperature-sensitive load amounts of each node in the receiving-end power grid topology and dynamic thermal stability limits of each AC line according to the real-time environmental temperature, and constructing an equivalent model of the receiving-end power grid; S2, calculating commutation voltage interaction factors between drop points of each feed-in DC based on the equivalent model of the receiving-end power grid. In the present application, by extracting real-time environmental temperature and initial load parameters, dynamically calculating temperature-sensitive load amounts of each node in the receiving-end power grid and thermal stability limits of AC lines, and directly introducing meteorological environmental factors into the modeling process of bottom-layer physical parameters, the equivalent model constructed can objectively reflect real system operation boundaries under actual meteorological working conditions.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, and in particular to a multi-constraint coupling evaluation method for the carrying capacity of multiple DC feeders in a receiving-end power grid. Background Technology

[0002] With the development of DC transmission technology, receiving-end power grids generally exhibit a multi-DC centralized feed-in operation mode. Accurately assessing the carrying capacity of multiple DC feed-ins is crucial for ensuring the safe operation of the system. In actual power grid operation, the node load level and the current-carrying capacity of AC transmission lines are the fundamental physical boundaries that determine the system's power acceptance limit, and these underlying network parameters have a close physical coupling relationship with the external meteorological environment.

[0003] Existing methods for assessing load capacity typically use fixed static load values ​​and constant line rated thermal stability limits for calculation, failing to effectively consider the impact of real-time ambient temperature on system load fluctuations and line dynamic current-carrying capacity. This fixed-parameter modeling approach is detached from actual meteorological conditions and struggles to reflect the dynamic evolution of the power grid's physical boundaries under varying ambient temperatures, easily leading to the final calculated multi-DC feed-in load capacity assessment results deviating from the system's actual operating level. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides a multi-constraint coupled evaluation method for the carrying capacity of multiple DC feeders in the receiving-end power grid, aiming to improve the problem that existing carrying capacity evaluation methods usually use fixed static load values ​​and constant line rated thermal stability limits for calculation.

[0005] This invention provides the following technical solution: a multi-constraint coupled evaluation method for the carrying capacity of multiple DC feeders in a receiving-end power grid, comprising the following steps: S1. Obtain the receiving-end power grid topology, real-time ambient temperature and initial load parameters. Calculate the temperature-sensitive load of each node in the receiving-end power grid topology and the dynamic thermal stability limit of each AC line based on the real-time ambient temperature, and construct an equivalent model of the receiving-end power grid. S2. Based on the equivalent model of the receiving-end power grid, calculate the commutation voltage interaction factor between the landing points of each DC feed, and generate a multi-feed coupling matrix. S3. Combining the multi-infeed coupling matrix, generate analytical expressions for line thermal stability, multi-infeed short-circuit ratio, frequency drop deviation, and commutation failure risk of the receiving-end power grid, and construct a multi-constraint feasible domain space by combining the analytical expressions. S4. Within the multi-constraint feasible domain space, with the goal of solving the upper limit value of the total power of each input DC, the continuous boundary tracking algorithm is used to solve the constraint boundary in the critical state, and the upper limit value of the carrying power of each input DC and the dominant constraint margin are calculated. S5. Based on the upper limit of the carrying power of each feed DC and the dominant constraint margin, calculate the over-limit risk index of the receiving-end power grid and output the multi-constraint coupling evaluation result.

[0006] Preferably, in S1, the construction of the equivalent model of the receiving-end power grid specifically includes the following steps: Extract the basic load value and temperature elasticity coefficient from the initial load parameters, and calculate the temperature-sensitive load of each node in combination with the real-time ambient temperature. Extract the AC line parameters from the receiving-end power grid topology, and calculate the dynamic thermal stability limit of each AC line in combination with the real-time ambient temperature; The temperature-sensitive load of each node and the dynamic thermal stability limit of each AC line are updated to the corresponding nodes and AC lines in the receiving-end power grid topology to form an equivalent model of the receiving-end power grid.

[0007] Preferably, in S2, generating the multi-feed coupling matrix specifically includes the following steps: Generate the node impedance matrix based on the equivalent model of the receiving-end power grid; Extract the self-impedance and mutual impedance values ​​corresponding to each DC feed point in the node impedance matrix, substitute them into the preset commutation voltage interaction equation, and calculate the commutation voltage interaction factor between each DC feed point. The commutation voltage interaction factors between the landing points of each DC feed are matrix-combined to generate a multi-feed coupling matrix.

[0008] Preferably, in S3, the construction of the multi-constraint feasible domain space by simultaneously formulating the analytical expressions specifically includes the following steps: Substituting the multi-feed coupling matrix into the preset calculation formulas for various indicators, the analytical formulas for line thermal stability, multi-feed short-circuit ratio, frequency drop deviation, and commutation failure risk of the receiving-end power grid are generated respectively. Obtain the thermal stability threshold, short-circuit ratio threshold, frequency deviation threshold, and commutation failure threshold, and use the thermal stability threshold, short-circuit ratio threshold, frequency deviation threshold, and commutation failure threshold as boundary conditions for each analytical expression to generate multiple constraint inequalities; Using the power of each DC feed as the solution variable, the common solution set region is solved by simultaneously solving the multiple constraint inequalities, and the common solution set region is determined as the multi-constraint feasible region space.

[0009] Preferably, the step of solving the common solution set region of the multiple constraint inequalities, and defining the common solution set region as the multi-constraint feasible region space, specifically includes: Extract the nonlinear and linear constraint terms from the aforementioned multi-constraint inequalities; Calculate the partial derivatives of the nonlinear constraint terms with respect to the power of each fed DC source, and generate the partial derivative sensitivity matrix; The partial derivative sensitivity matrix is ​​used to perform a Taylor expansion calculation on the nonlinear constraint term to generate a set of linearized constraint hyperplanes; Solve for the geometric intersection of the set of linearized constraint hyperplanes and the linear constraint terms, and determine the geometric intersection as the common solution set region of the multinomial constraint inequalities.

[0010] Preferably, in step S4, calculating the upper limit of the carrying power and the dominant constraint margin of each fed-in DC power source specifically includes the following steps: The initial power value and power step value of each DC feed are obtained. The initial power value is used as the starting point for calculation, and a tracking calculation trajectory is generated based on the power step value. The continuous boundary tracing algorithm is used to verify each analytical expression along the tracing calculation trajectory, extract the solution coordinate points that reach the critical state conditions of each analytical expression, determine the boundary where the solution coordinate points are located as the constraint boundary in the critical state, and determine the analytical expression that reaches the critical state conditions as the dominant constraint analytical expression. The power values ​​of each input DC corresponding to the solution coordinate point are extracted as the upper limit of the carrying power of each input DC. The difference between the index value corresponding to the dominant constraint analytical expression and the preset threshold is calculated, and the difference is determined as the dominant constraint margin.

[0011] Preferably, the step of using the continuous boundary tracing algorithm to verify each of the analytical expressions along the tracing calculation trajectory and extracting the solution coordinate points that reach the critical state conditions of each analytical expression specifically includes: Calculate the tangent direction vector of the calculation starting point, and perform mapping calculation along the tangent direction vector in combination with the power step size value to generate the estimated coordinate point; Substitute the estimated coordinate points into the preset power flow equation of the receiving-end power grid, calculate the power imbalance that deviates from the equilibrium state, and use the power imbalance to perform projection iteration correction on the estimated coordinate points in combination with the Jacobian matrix to generate corrected coordinate points. Based on the power imbalance, the power step value is scaled, the correction coordinate point is updated to the calculation starting point, and the step of generating the estimated coordinate point is executed repeatedly until the calculation result after substituting the correction coordinate point into the power flow equation of the receiving end grid and each of the analytical expressions satisfies the preset error convergence threshold. The correction coordinate point corresponding to the calculation result satisfying the error convergence threshold is extracted as the solution coordinate point.

[0012] Preferably, in step S5, the output of the multi-constraint coupling evaluation result specifically includes the following steps: Obtain the risk assessment weight matrix, and combine the upper limit of the carrying power of each DC feed into the dominant constraint margin with the risk assessment weight matrix to perform weighted calculation to generate the over-limit risk index of the receiving-end power grid; The risk level label is generated by comparing the over-limit risk index of the receiving power grid with a preset set of risk classification thresholds. By combining the risk level label, the over-limit risk index of the receiving-end power grid, the upper limit of the carrying capacity of each feeder DC, and the dominant constraint margin, a multi-constraint coupling evaluation result is output.

[0013] The present invention has the following beneficial effects: 1. In this invention, by extracting real-time ambient temperature and initial load parameters, the temperature-sensitive load of each node in the receiving-end power grid and the thermal stability limit of the AC line are dynamically calculated. Meteorological environmental factors are directly introduced into the modeling process of the underlying physical parameters, so that the constructed equivalent model can objectively reflect the real operating boundary of the system under actual meteorological conditions.

[0014] 2. In this invention, a continuous boundary tracking algorithm combined with Taylor dimensionality reduction is used to transform the electrical interaction between multiple DC lines and the power grid safety boundary into a unified mathematical constraint space. This avoids the calculation divergence of high-dimensional nonlinear equations near the limit point, thereby enabling efficient and accurate determination of the upper limit value of each feed-in DC power carrying capacity under multiple constraint conditions.

[0015] 3. In this invention, the upper limit of the carrying capacity and the dominant constraint margin obtained by solving are used to perform quantitative weighted calculation of the risk dimension in combination with the weight matrix. The generated over-limit risk index is compared with the preset threshold to output an intuitive risk level label, which provides a clear auxiliary decision-making basis for dispatching and operation personnel to formulate DC power transmission and reception plans. Attached Figure Description

[0016] Figure 1 This is a flowchart of a multi-constraint coupling evaluation method for the carrying capacity of multiple DC feeders in a receiving-end power grid, as proposed in this invention. Detailed Implementation

[0017] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] This invention provides a multi-constraint coupled evaluation method for the carrying capacity of multiple DC feeders in a receiving-end power grid, such as... Figure 1 As shown, it includes the following steps: S1. Obtain the receiving-end power grid topology, real-time ambient temperature and initial load parameters. Calculate the temperature-sensitive load of each node in the receiving-end power grid topology and the dynamic thermal stability limit of each AC line based on the real-time ambient temperature, and construct an equivalent model of the receiving-end power grid. Furthermore, in step S1, constructing the equivalent model of the receiving-end power grid specifically includes the following steps: Extract the basic load value and temperature elasticity coefficient from the initial load parameters, and calculate the temperature-sensitive load of each node in combination with the real-time ambient temperature. Extract the AC line parameters from the receiving-end power grid topology and calculate the dynamic thermal stability limit of each AC line in combination with the real-time ambient temperature. The temperature-sensitive load of each node and the dynamic thermal stability limit of each AC line are updated to the corresponding nodes and AC lines in the receiving-end power grid topology to form an equivalent model of the receiving-end power grid.

[0019] Specifically, the receiving-end power grid topology, real-time ambient temperature, and initial load parameters are obtained. The receiving-end power grid topology includes the connection relationships between nodes and the impedance parameters of each AC line. The real-time ambient temperature is collected in real time by meteorological sensors deployed in various areas of the receiving-end power grid. The initial load parameters include the base load values ​​of each node and the corresponding temperature elasticity coefficient. The temperature elasticity coefficient is obtained by performing linear regression analysis on the historical electricity consumption data and corresponding historical ambient temperature data of each node, reflecting the proportion of load change caused by a unit temperature change, with dimensions of _____. Reference ambient temperature The standard reference value of 20°C, as stipulated in the State Grid Operation Regulations, is taken as the corresponding temperature condition between the load baseline state and the line rated current carrying capacity.

[0020] Extract the base load value and temperature elasticity coefficient from the initial load parameters, and calculate the temperature-sensitive load at each node based on the real-time ambient temperature. The calculation formula is as follows: ; in For the first Temperature-sensitive load of each node, in MW; For the first Each node at the reference ambient temperature The base load value is in MW; For the first The temperature elastic coefficient of each node, in units of It is obtained by regression from historical data; This is the real-time ambient temperature, in °C. The ambient temperature is taken as 20°C. This formula is used to convert real-time meteorological data into actual electrical power load values ​​for each node.

[0021] The AC line parameters in the receiving-end power grid topology are extracted, and the dynamic thermal stability limits of each AC line are calculated in conjunction with the real-time ambient temperature. This step uses a simplified calculation model derived from the conductor heat balance equation. This model holds true under the condition of neglecting the effects of wind speed and solar radiation and considering only the single meteorological variable of ambient temperature. It is suitable for thermal stability boundary assessment under steady-state operating conditions of the receiving-end power grid. The AC line parameters include the basic thermal stability current carrying capacity and the maximum allowable operating temperature of each line at the reference ambient temperature. These parameters are determined by the conductor type and manufacturer's technical specifications. The calculation formula is as follows: ; in For the first AC lines under real-time ambient temperature The dynamic thermal stability limit under the given conditions, expressed in Å; For the first AC lines at reference ambient temperature The basic thermally stable current carrying capacity, in A; For the first The maximum allowable operating temperature of an AC line conductor, in °C, is determined by the conductor material properties and is typically between 70°C and 90°C. This is the real-time ambient temperature, in °C. For reference ambient temperature, 20°C is used. When the real-time ambient temperature... When it rises, The decrease reflects the reduced current-carrying capacity due to the decreased heat dissipation capacity of the circuit under high-temperature conditions.

[0022] The temperature-sensitive loads of each node and the dynamic thermal stability limits of each AC line are updated to the corresponding nodes and AC lines in the receiving-end power grid topology, respectively, to form an equivalent model of the receiving-end power grid. The specific execution process is as follows: The temperature-sensitive loads of each node are updated... Replacing the nodal load power term in the power balance equations of the receiving-end power grid, the nodal power balance equations become: ; in For nodes The power generation capacity, measured in MW; For nodes Temperature-sensitive load, in MW; This represents the system's baseline capacity; the unit is MVA. , They are nodes ,node The voltage amplitude is expressed in per-unit value, in pu. , The nodes in the node admittance matrix are respectively With nodes The per-unit values ​​of conductivity and susceptance, in pu, are consistent with the per-unit values ​​of voltage. For nodes With nodes The voltage phase angle difference between them, in rad; The set of all nodes in the receiving-end power grid. This represents a summation over all nodes in the receiving-end power grid. Simultaneously, it uses the dynamic thermal stability limit of each AC line. Update the maximum allowable current carrying capacity limit constraint for the corresponding line and complete the construction of the equivalent model of the receiving-end power grid.

[0023] By incorporating real-time meteorological environmental factors into the modeling process of the underlying physical parameters of the power grid, the nodal load boundaries and line current-carrying constraints of the equivalent model can be dynamically adjusted with the ambient temperature, providing a foundation for the accurate construction of subsequent multi-constraint feasible regions.

[0024] S2. Based on the equivalent model of the receiving-end power grid, calculate the commutation voltage interaction factor between the landing points of each DC feeder and generate a multi-feeder coupling matrix. Furthermore, in S2, generating the multi-feed coupling matrix specifically includes the following steps: Generate the node impedance matrix based on the equivalent model of the receiving-end power grid; Extract the self-impedance and mutual impedance values ​​corresponding to each DC input point in the node impedance matrix, substitute them into the preset commutation voltage interaction equation, and calculate the commutation voltage interaction factor between each DC input point. The commutation voltage interaction factors between the landing points of each DC feed are matrix-combined to generate a multi-feed coupling matrix.

[0025] Specifically, based on the receiving-end power grid equivalent model constructed in the aforementioned steps, the system baseline capacity is used. (Unit: MVA) serves as the per-unit reference. Under the condition that the operating voltage of each node is approximately equal to the reference voltage, the updated temperature-sensitive load values ​​of each node in the equivalent model are converted into constant parallel admittance per-unit values. The conversion formula is: ; in For the first The constant parallel admittance per unit value of each node, in pu; The first step calculated by the aforementioned steps Temperature-sensitive load of each node, in MW; The system baseline capacity, in MVA, is taken from the baseline value uniformly specified by the receiving-end power grid. The rated voltage of each voltage level in the receiving-end power grid is extracted as the baseline voltage for each node. (Unit: kV), using the system's reference capacity Reference voltages at each node The impedance parameters of each AC line are normalized to per-unit values. Combining the normalized per-unit impedance parameters of each AC line with the previously calculated constant parallel admittance per-unit values ​​of each node, a node admittance matrix for the receiving-end power grid is constructed. The node admittance matrix is ​​then inverted to generate a node impedance matrix. This node impedance matrix contains the self-impedance and mutual impedance information of all nodes within the receiving-end power grid, reflecting the overall network structure and electrical connectivity after considering real-time weather conditions.

[0026] Extract the self-impedance and mutual impedance values ​​corresponding to each DC feed point in the node impedance matrix, substitute them into the preset commutation voltage interaction equation, and calculate the commutation voltage interaction factor between each DC feed point. This step uses a linearized approximation calculation method based on the node impedance matrix. This method holds true under the condition of neglecting the influence of the system's operating state before the fault on voltage changes, and is suitable for assessing the voltage interaction impact between multiple DC feed points under steady-state operation of the receiving-end power grid. The calculation formula is: ; in DC landing point When a three-phase short-circuit fault occurs on the AC side, the DC landing point The resulting commutation voltage interaction factor is dimensionless. and , This represents the total number of DC feed-in points in the receiving-end power grid. DC landing point extracted from the nodal impedance matrix With DC landing point The per-unit value of the mutual impedance between them, in pu; DC landing point extracted from the nodal impedance matrix The per-unit value of the self-impedance, in units of pu; and These represent the magnitudes of the corresponding complex impedances. This formula transforms the nodal impedance parameters into quantitative indicators characterizing the degree of voltage perturbation between different DC landing points.

[0027] The commutation voltage interaction factors between the various DC feed points are matrix-combined to generate a multi-feed coupling matrix. Assume the receiving-end power grid contains... One DC feed point, constructing a A real square matrix of order 1. The calculated commutation voltage interaction factor is then used. Fill the first square in this matrix Line 1 The array. For the elements on the main diagonal of the matrix, representing the voltage interaction of each DC landing point, their values ​​are uniformly set to... Finally, the complete multi-feed coupling matrix is ​​output.

[0028] By transforming the underlying grid impedance parameters into intuitive voltage interaction factors, the electrical coupling strength between multiple DC feed-in systems is quantified, providing a data foundation for the subsequent construction of constraint analytical expressions such as multi-feed-in short-circuit ratio and commutation failure.

[0029] S3. Combining the multi-infeed coupling matrix, generate analytical expressions for line thermal stability, multi-infeed short-circuit ratio, frequency drop deviation, and commutation failure risk of the receiving-end power grid, respectively, and construct a multi-constraint feasible domain space by combining the analytical expressions. Furthermore, in S3, constructing the multi-constraint feasible domain space by simultaneously solving the analytical expressions specifically includes the following steps: Substituting the multi-infeed coupling matrix into the preset calculation formulas for various indicators, analytical expressions for line thermal stability, multi-infeed short-circuit ratio, frequency drop deviation, and commutation failure risk of the receiving-end power grid are generated respectively. Obtain the thermal stability threshold, short-circuit ratio threshold, frequency deviation threshold, and commutation failure threshold. Use the thermal stability threshold, short-circuit ratio threshold, frequency deviation threshold, and commutation failure threshold as boundary conditions for each analytical expression to generate multiple constraint inequalities. Using the power of each DC feed as the solution variable, a common solution set region is solved by simultaneously solving multiple constraint inequalities, and the common solution set region is determined as the multi-constraint feasible region space.

[0030] Furthermore, finding the common solution set region for solving multiple constraint inequalities, and defining the common solution set region as the multi-constraint feasible region space specifically includes: Extract the nonlinear and linear constraint terms from the multinomial constraint inequalities; Calculate the partial derivatives of the nonlinear constraint terms with respect to the power of each DC feed, and generate the partial derivative sensitivity matrix; The nonlinear constraint terms are calculated by Taylor expansion using the partial derivative sensitivity matrix to generate a set of linearized constraint hyperplanes; Solve for the geometric intersection of the set of linearized constrained hyperplanes and the linear constraint terms, and define the geometric intersection as the common solution set region of the multinomial constraint inequalities.

[0031] Specifically, combining the multi-infeed coupling matrix generated in the aforementioned steps, which includes the interaction factors of each commutation voltage, and substituting this multi-infeed coupling matrix into the preset calculation formulas for various indicators, analytical expressions for line thermal stability, multi-infeed short-circuit ratio, frequency sag deviation, and commutation failure risk of the receiving-end power grid are generated respectively. The power vector is formed by the power of each DC feeder in the receiving-end power grid. As the solution variables, construct the analytical expression, where The total amount of DC feed in. For the first The power of the DC feed, measured in MW. .

[0032] The analytical expression for the multi-infeed short-circuit ratio is constructed as follows: ; in DC landing point Multi-infeed short-circuit ratio, dimensionless ; DC landing point The AC-side short-circuit capacity, in MVA, is determined by the DC landing point in the node impedance matrix generated in the preceding steps. The self-impedance per-unit value is derived, and the calculation formula is as follows: ,in This is the system baseline capacity, in MVA. DC landing point The magnitude of the self-impedance, in units of pu; The first of the aforementioned multi-feed coupling matrices Line 1 The commutation voltage interaction factor of the column is dimensionless.

[0033] The analytical formula for commutation failure risk is constructed as follows: ; in DC landing point The commutation failure risk index is dimensionless. ; This represents the system's baseline capacity, measured in MVA.

[0034] The analytical equation for line thermal stability is constructed using a sensitivity analysis method based on AC power flow equations. The measured power values ​​of each DC feeder under the current actual operating conditions of the receiving-end grid are taken as the initial operating power point. The unit is MW, which serves as the linearization reference point for sensitivity calculation. At the initial operating power point... At point 1, the Jacobian matrix of the AC power flow equation is used to calculate the first... AC line current amplitude For each input DC power Sensitivity coefficient The unit is A / MW. The sensitivity coefficients are combined to form the line current sensitivity row vector. The analytical expression for the thermal stability of the circuit is constructed as follows: ; in For the first AC lines in power vector The current amplitude, in amperes (A). , This represents the total number of AC lines in the receiving-end power grid. Initial operating power point Next The initial current amplitude of the AC line, in amperes (A).

[0035] The analytical expression for frequency sag deviation is constructed based on the frequency response of the receiving-end power grid under a single-circuit DC blocking fault. When the... When the DC feed is blocked, the resulting frequency drop is: ; in For the first The frequency drop caused by DC feedout blocking, in Hz; The frequency regulation effect coefficient of the receiving-end power grid, in MW / Hz, comprehensively reflects the system's inertial response and the governor's regulation capability. The calculation formula is as follows: ; in The system inertia constant is expressed in seconds (s). The rated capacity of the receiving-end power grid is expressed in MW. The system's rated frequency is set to 50Hz. The speed controller response time is expressed in seconds (s). The governor droop coefficient is a per-unit value and dimensionless. The first term in the above formula... The unit is MW / Hz, the second item The unit is MW / Hz, and both quantities have the same dimension. To cover all single-circuit DC blocking scenarios, each component in the power vector... Apply frequency constraints to all, that is, for all satisfy The equivalent constraint form is .

[0036] Obtain the thermal stability threshold, short-circuit ratio threshold, frequency deviation threshold, and commutation failure threshold. Set the thermal stability threshold to the dynamic thermal stability limit of each AC line calculated in the preceding steps. The unit is ampere-ampere (A); the short-circuit ratio threshold is set to a preset safe operating lower limit constant. Dimensionless; the frequency deviation threshold is set as the allowable drop constant specified in the power grid guidelines. The unit is Hz; the commutation failure threshold is set to a preset risk upper limit constant. Dimensionless. Using the aforementioned threshold values ​​as boundary conditions for each analytical expression, multiple constraint inequalities are generated, specifically line current constraints. Multi-infeed short-circuit ratio constraint Frequency drop constraint and commutation failure risk constraints .

[0037] Extract the nonlinear and linear constraint terms from the above multiple constraint inequalities. Since the power variable in the multi-infeed short-circuit ratio analytical expression is in the denominator, the short-circuit ratio constraint is classified as a nonlinear constraint term. The short-circuit ratio constraint is then uniformly rewritten in the form of less than or equal to, i.e. With line thermal stability constraints Together they form a set of nonlinear constraint terms, denoted as The nonlinear constraint vector The former Each component represents the current amplitude of each line. ,back Each component is ; the corresponding nonlinear boundary threshold vector The former Each component represents the dynamic thermal stability limit of each line. ,back Each component is The frequency drop constraint and the commutation failure risk constraint are categorized into a set of linear constraint terms, denoted as . The linear coefficient matrix The upper part is identity matrix of order Corresponding to the frequency drop constraint, the lower half is 1-th order matrix Corresponding to the commutation failure risk constraint, For all The constructed multi-feed coupling matrix; linear boundary threshold vector The former Each component is ,back Each component is .

[0038] Calculate the partial derivatives of the nonlinear constraint terms with respect to the power of each DC input, and generate the partial derivative sensitivity matrix. This is done for the set of nonlinear constraint terms. At the initial operating power point At each location, the power variable of each DC feed is... Calculate the first-order partial derivatives to generate the partial derivative sensitivity matrix. Its dimensions are .matrix The former The partial derivatives of the line corresponding to the thermal stability constraints are given by the element. The unit is A / MW, calculated from the Jacobian matrix of the aforementioned AC power flow equations; later The partial derivatives of the row corresponding to the short-circuit ratio constraint have the following elements: ; in Initial operating power point The Middle The initial power value of the DC feed, in MW; .

[0039] Taylor expansion of the nonlinear constraint terms is performed using the partial derivative sensitivity matrix to generate a set of linearized constraint hyperplanes. This is based on the partial derivative sensitivity matrix. Retaining the first-order terms of the Taylor series expansion, the calculation formula is: ; By combining and rearranging the constant terms in the above equation, we obtain the linearized expression: ; This dimensionality reduction process transforms the high-order nonlinear boundary into a power vector. Let be the set of linearized constraint hyperplanes for the independent variables.

[0040] Solve for the geometric intersection of the set of linearized constraint hyperplanes and the linear constraint terms, defining this geometric intersection as the common solution set region for the multinomial constraint inequalities. Simultaneously solve the system of linearized nonlinear constraint inequalities. With linear constraint inequalities In a coordinate system with each input DC power as the axis In the Euclidean space, find the set of polyhedra that satisfy all the above half-space constraints for the power vector, and output the closed geometric intersection polyhedra as the multi-constraint feasible domain space.

[0041] This step transforms the electrical interaction between multiple DC lines and the physical security boundary of the power grid into a unified set of mathematical constraint inequalities. It also eliminates the computational obstacles of high-dimensional nonlinearity through Taylor first-order expansion, thus constructing a solution space with clear boundaries for evaluating the maximum power carrying capacity of multiple DC feeds into the receiving-end power grid.

[0042] S4. Within the multi-constraint feasible domain space, with the goal of solving the upper limit of the total power of each feed DC, the continuous boundary tracking algorithm is used to solve the constraint boundary in the critical state, and the upper limit of the carrying power of each feed DC and the dominant constraint margin are calculated. Furthermore, in S4, calculating the upper limit of the carrying capacity and the dominant constraint margin of each fed-in DC power source specifically includes the following steps: The initial power value and power step value of each DC feed are obtained. The initial power value is used as the starting point for calculation, and the tracking calculation trajectory is generated based on the power step value. The continuous boundary tracing algorithm is used to verify each analytical expression along the tracing calculation trajectory, extract the solution coordinate points that reach the critical state conditions of each analytical expression, determine the boundary where the solution coordinate points are located as the constraint boundary in the critical state, and determine the analytical expression that reaches the critical state conditions as the dominant constraint analytical expression. The power values ​​of each input DC corresponding to the solution coordinate point are extracted as the upper limit of the carrying power of each input DC. The difference between the index value corresponding to the dominant constraint analytical expression and the preset threshold is calculated, and the difference is determined as the dominant constraint margin.

[0043] Furthermore, a continuous boundary tracing algorithm is used to verify each analytical expression along the tracing calculation trajectory, and the solution coordinate points that reach the critical state conditions of each analytical expression are extracted, specifically including: Calculate the tangent direction vector at the starting point of the calculation, and perform mapping calculations along the tangent direction vector in combination with the power step size value to generate the estimated coordinate point; Substitute the estimated coordinate points into the preset power flow equation of the receiving-end power grid, calculate the power imbalance that deviates from the equilibrium state, and use the power imbalance to perform projection iteration correction on the estimated coordinate points in combination with the Jacobian matrix to generate corrected coordinate points. Based on the power imbalance, the power step size is scaled, the correction coordinate point is updated as the calculation starting point, and the step of generating the estimated coordinate point is executed repeatedly until the calculation result after substituting the correction coordinate point into the power flow equation of the receiving end grid and each analytical expression meets the preset error convergence threshold. The correction coordinate point corresponding to the calculation result meeting the error convergence threshold is extracted as the solution coordinate point.

[0044] Specifically, the initial power values ​​of each fed DC source are obtained to form an initial power vector. The unit is MW, and the power growth direction vector for tracking and searching is set. The unit is MW, reflecting the weighting of each feed-in DC power increase. Obtain the initial power step size value. , dimensionless, is the initial scaling factor for the tracking step size in the continuous boundary tracking algorithm. It controls the advance magnitude along the tangential direction in each step and is independent of the physical dimensions of power. Construct the system synthesis state vector for the continuous boundary tracking algorithm. ,in This is the voltage phase angle vector of the receiving-end power grid node, in rad; This is a per-unit vector of node voltage magnitudes, in units of pu; The scaling parameter for continuous load is dimensionless. At any tracking step size, the power vector of each input DC is given by the formula... Dynamically generated, with units unified to MW. The initial steady-state solution of the system corresponding to that time is set as the starting point for calculation. The tracking trajectory is generated based on the power step size value.

[0045] Calculate the tangent direction vector at the starting point, and combine it with the power step size value to perform mapping calculations along the tangent direction vector, generating the estimated coordinate point. In the... The starting point for step tracking calculation At this point, construct the power flow equations of the receiving-end power grid that include continuous load scaling parameters. By taking the partial derivative of the power flow equation and combining it with the locally parameterized equation, the tangent direction vector is calculated. ,in , and These represent the tangential increments of the node voltage phase angle, voltage magnitude, and load scaling parameter, respectively. The tangential direction vector satisfies the equation... ,in It is the augmented Jacobian matrix that includes the regular power flow Jacobian matrix and the continuous parameter partial derivatives; This is the unit column vector corresponding to the current local parameterized variable. Using the first... Power step size value for step tracking Explicit Euler mapping is performed along the tangent direction vector to generate the estimated coordinate points. .

[0046] Substitute the estimated coordinate points into the preset power flow equations of the receiving-end power grid to calculate the power imbalance that deviates from the equilibrium state. Substituting into the nonlinear power flow equation The active and reactive power deviations of each node under the current state are calculated and denoted as the power imbalance. The unit is MVA. Combined with the augmented Jacobian matrix... The estimated coordinate points are projected and iteratively corrected using the power imbalance to generate corrected coordinate points. The state correction is then calculated using the Newton-Raphson method. , where the scalar at the end of the matrix This indicates that the residual of the corresponding locally parameterized equation is zero. The state correction is then superimposed onto the estimated coordinate points to complete a single correction iteration and update the state value.

[0047] Based on the power imbalance, the power step size is scaled, the correction coordinate point is updated as the calculation starting point, and the step of generating the estimated coordinate point is executed iteratively. This projection iterative correction process is repeated until the power imbalance is reached. The norm is less than the preset power flow error convergence threshold. At this point, the fully converged correction coordinate point is obtained. The DC power vector contained in the calibration coordinate points. Substitute the analytical expressions established in the preceding steps into the equations to determine whether they exceed the preset boundary thresholds. To correct the coordinate point The continuous load scaling parameters extracted are dimensionless. If all analytical expressions are within the safe region, the power step size is scaled based on the iterative convergence rate of the current step, using the following scaling formula: ,in This is the preset optimal number of iterations; This represents the actual number of iterations consumed. Update the correction coordinates to the new calculation starting point. And continue moving forward to generate the next estimated coordinate point.

[0048] The calculation results, after substituting the corrected coordinate points into the power flow equations and analytical expressions of the receiving-end power grid, reach the critical state conditions of each analytical expression, and the calculation results satisfy the preset boundary critical error convergence threshold. The corresponding correction coordinate points are extracted as solution coordinate points. The boundary where the solution coordinate point is located is defined as the constraint boundary in a critical state, and the analytical expression that reaches the condition of this critical state is defined as the dominant constraint analytical expression. For example, if a certain correction coordinate point first satisfies... If the short-circuit ratio reaches the critical boundary, then the multi-feed short-circuit ratio analytical expression is the dominant constraint analytical expression.

[0049] The power values ​​of each input DC power source corresponding to the solution coordinate points are extracted as the upper limit of the carrying capacity of each input DC power source. Using the solution coordinate points... Critical load scaling parameters in Calculate the vector of upper limit values ​​of the carrying capacity of each DC feeder. The unit is MW. Calculate the absolute value of the difference between the index value corresponding to the dominant constraint analytical expression and the preset threshold, and determine this difference as the dominant constraint margin. Through the formula Perform calculations, where The index calculation function is the dominant constraint analytical expression; This corresponds to a preset threshold. Because the tracking process accurately stops at the critical boundary, this dominant constraint margin... It approaches 0 numerically.

[0050] This step solves for the critical boundary of the multi-constraint feasible region and outputs the upper limit of the carrying power of each feed DC and the corresponding margin index.

[0051] S5. Based on the upper limit of the carrying capacity of each DC feed and the dominant constraint margin, calculate the over-limit risk index of the receiving-end power grid and output the multi-constraint coupling evaluation results.

[0052] Furthermore, in S5, the output of the multi-constraint coupling evaluation results specifically includes the following steps: Obtain the risk assessment weight matrix, combine the upper limit of the carrying capacity of each DC feeder with the dominant constraint margin and perform weighted calculation based on the risk assessment weight matrix to generate the over-limit risk index of the receiving-end power grid; The risk level label is generated by comparing the over-limit risk index of the receiving power grid with the preset risk classification threshold set. The combined risk level label, the over-limit risk index of the receiving-end grid, the upper limit of the carrying capacity of each feeder DC and the dominant constraint margin are used to output the multi-constraint coupled evaluation results.

[0053] Specifically, obtain the vector of upper limit values ​​of the carrying power of each DC feeder calculated in the aforementioned steps. With dominant constraint margin Obtain the rated operating power of each DC feeder. The unit is MW. A comprehensive risk feature vector is constructed to characterize the degree to which the system approaches the limit. Among them, the former Each component represents the power limitation risk level of each input DC, calculated using the following formula: , dimensionless, of which For the first The maximum carrying capacity of the DC feed is expressed in MW. ;No. Each component represents the boundary approximation risk level, calculated using the following formula: , dimensionless, of which This is the preset threshold corresponding to the dominant constraint expression in the preceding steps. The dimension to be obtained is... Risk assessment weight matrix This matrix is ​​pre-calibrated based on scheduling and operational experience, and its elements represent the severity weights of various risk indicators and satisfy the following conditions: Dimensionless. The comprehensive risk feature vector and the risk assessment weight matrix are weighted together to generate the over-limit risk index of the receiving-end power grid. The calculation formula is: This index is a dimensionless scalar; the larger the value, the higher the risk of multiple DC coupling exceeding the limit in the receiving-end power grid.

[0054] Obtain the preset set of risk classification thresholds ,in The low-risk threshold The threshold for moderate risk is [missing information]. The above thresholds are all dimensionless constants and represent high-risk thresholds. The over-limit risk index of the receiving-end power grid is... Perform an interval comparison with the risk classification threshold set. The specific comparison logic is as follows: when... When the risk level label is generated, it is considered a safe state; when... When the risk level label is low, it is generated; when When the risk level label is generated, it is classified as medium risk; when At that time, a risk level label of "high risk" is generated. Through this interval division calculation, the continuous risk index is discretized into a qualitative assessment conclusion.

[0055] The generated risk level labels and the over-limit risk index of the receiving-end power grid will be used to... The vector of upper limit values ​​of the carrying capacity of each DC feed obtained in the aforementioned steps. and dominant constraint margin The data is combined and packaged into a structured comprehensive evaluation result file. This multi-constraint coupled evaluation result is then output to the receiving-end power grid dispatching terminal system as auxiliary decision-making data for formulating DC power transmission and reception plans and for preventing extreme weather disasters.

[0056] This enables a quantitative mapping from underlying physical limit data to system risk indicators, providing power grid operators with intuitive assessment conclusions on multi-DC carrying capacity.

[0057] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-constraint coupled evaluation method for the carrying capacity of multiple DC feeders in a receiving-end power grid, characterized in that, Includes the following steps: S1. Obtain the receiving-end power grid topology, real-time ambient temperature and initial load parameters. Calculate the temperature-sensitive load of each node in the receiving-end power grid topology and the dynamic thermal stability limit of each AC line based on the real-time ambient temperature, and construct an equivalent model of the receiving-end power grid. In S1, the construction of the equivalent model of the receiving-end power grid specifically includes the following steps: Extract the basic load value and temperature elasticity coefficient from the initial load parameters, and calculate the temperature-sensitive load of each node in combination with the real-time ambient temperature. The formula for calculating the temperature-sensitive load is: ； in For the first Temperature-sensitive load of each node, in MW; For the first Each node is at the reference ambient temperature. The base load value is in MW; For the first The temperature elastic coefficient of each node, in units of It is obtained by regression from historical data; This is the real-time ambient temperature, in °C. For reference ambient temperature; Extract the AC line parameters from the receiving-end power grid topology, and calculate the dynamic thermal stability limit of each AC line in combination with the real-time ambient temperature; The formula for calculating the dynamic thermal stability limit is: ； in For the first AC lines under real-time ambient temperature The dynamic thermal stability limit under the given conditions, expressed in amperes (A); For the first AC lines at reference ambient temperature The basic thermally stable current carrying capacity, in A; For the first The maximum allowable operating temperature of an AC line conductor, in °C, is determined by the conductor material properties and is typically between 70°C and 90°C. This is the real-time ambient temperature, in °C. For reference ambient temperature; S2. Based on the equivalent model of the receiving-end power grid, calculate the commutation voltage interaction factor between the landing points of each DC feed, and generate a multi-feed coupling matrix. In S2, the generation of the multi-feed coupling matrix specifically includes the following steps: Generate the node impedance matrix based on the equivalent model of the receiving-end power grid; Extract the self-impedance and mutual impedance values ​​corresponding to each DC feed point in the node impedance matrix, substitute them into the preset commutation voltage interaction equation, and calculate the commutation voltage interaction factor between each DC feed point. The calculation formula is: ； in DC landing point When a three-phase short-circuit fault occurs on the AC side, the DC landing point The resulting commutation voltage interaction factor is dimensionless. and , This represents the total number of DC feed-in points in the receiving-end power grid. DC landing point extracted from the nodal impedance matrix With DC landing point The per-unit value of the mutual impedance between them, in pu; DC landing point extracted from the nodal impedance matrix The per-unit value of the self-impedance, in units of pu; and These represent the magnitudes of the corresponding complex impedances; S3. Combining the multi-infeed coupling matrix, generate analytical expressions for line thermal stability, multi-infeed short-circuit ratio, frequency drop deviation, and commutation failure risk of the receiving-end power grid, and construct a multi-constraint feasible domain space by combining the analytical expressions. In S3, the construction of the multi-constraint feasible domain space by simultaneously combining the analytical expressions specifically includes the following steps: Substituting the multi-feed coupling matrix into the preset calculation formulas for various indicators, the analytical formulas for line thermal stability, multi-feed short-circuit ratio, frequency drop deviation, and commutation failure risk of the receiving-end power grid are generated respectively. Obtain the thermal stability threshold, short-circuit ratio threshold, frequency deviation threshold, and commutation failure threshold, and use the thermal stability threshold, short-circuit ratio threshold, frequency deviation threshold, and commutation failure threshold as boundary conditions for each analytical expression to generate multiple constraint inequalities; Using the power of each DC feed as the solution variable, the common solution set region is solved by simultaneously solving the multiple constraint inequalities, and the common solution set region is determined as the multi-constraint feasible domain space. The step of finding the common solution set region of the multiple constraint inequalities, and defining the common solution set region as the multi-constraint feasible region space, specifically includes: Extract the nonlinear and linear constraint terms from the aforementioned multi-constraint inequalities; Calculate the partial derivatives of the nonlinear constraint terms with respect to the power of each fed DC source, and generate the partial derivative sensitivity matrix; The partial derivative sensitivity matrix is ​​used to perform a Taylor expansion calculation on the nonlinear constraint term to generate a set of linearized constraint hyperplanes; Solve for the geometric intersection of the set of linearized constraint hyperplanes and the linear constraint terms, and determine the geometric intersection as the common solution set region of the multinomial constraint inequalities; The analytical expression for the multi-infeed short-circuit ratio is constructed as follows: ； in DC landing point The multi-feed short-circuit ratio is dimensionless. ; DC landing point The AC-side short-circuit capacity, in MVA, is determined by the DC landing point in the node impedance matrix generated in the preceding steps. The self-impedance per-unit value is derived, and the calculation formula is as follows: ,in This is the system baseline capacity, in MVA. DC landing point The magnitude of the self-impedance, in units of pu; The first of the aforementioned multi-feed coupling matrices Line 1 The commutation voltage interaction factor of the column is dimensionless. The analytical formula for commutation failure risk is constructed as follows: ； in DC landing point The commutation failure risk index, dimensionless. ; This is the system baseline capacity, in MVA. S4. Within the multi-constraint feasible domain space, with the goal of solving the upper limit value of the total power of each input DC, the continuous boundary tracking algorithm is used to solve the constraint boundary in the critical state, and the upper limit value of the carrying power of each input DC and the dominant constraint margin are calculated. In S4, calculating the upper limit of the carrying power and the dominant constraint margin of each fed-in DC power source specifically includes the following steps: The initial power value and power step value of each DC feed are obtained. The initial power value is used as the starting point for calculation, and a tracking calculation trajectory is generated based on the power step value. The continuous boundary tracing algorithm is used to verify each analytical expression along the tracing calculation trajectory, extract the solution coordinate points that reach the critical state conditions of each analytical expression, determine the boundary where the solution coordinate points are located as the constraint boundary in the critical state, and determine the analytical expression that reaches the critical state conditions as the dominant constraint analytical expression. The power values ​​of each input DC corresponding to the solution coordinate point are extracted as the upper limit of the carrying power of each input DC. The difference between the index value corresponding to the dominant constraint analytical expression and the preset threshold is calculated, and the difference is determined as the dominant constraint margin. The step of using the continuous boundary tracing algorithm to verify each analytical expression along the tracing calculation trajectory and extracting the solution coordinate points that reach the critical state conditions of each analytical expression specifically includes: Calculate the tangent direction vector of the calculation starting point, and perform mapping calculation along the tangent direction vector in combination with the power step size value to generate the estimated coordinate point; Substitute the estimated coordinate points into the preset power flow equation of the receiving-end power grid, calculate the power imbalance that deviates from the equilibrium state, and use the power imbalance to perform projection iteration correction on the estimated coordinate points in combination with the Jacobian matrix to generate corrected coordinate points. Based on the power imbalance, the power step value is scaled, the correction coordinate point is updated to the calculation starting point, and the step of generating the estimated coordinate point is executed repeatedly until the calculation result after substituting the correction coordinate point into the power flow equation of the receiving end power grid and each of the analytical expressions satisfies the preset error convergence threshold. The correction coordinate point corresponding to the calculation result satisfying the error convergence threshold is extracted as the solution coordinate point. S5. Based on the upper limit of the carrying power of each feed-in DC and the dominant constraint margin, calculate the over-limit risk index of the receiving-end power grid and output the multi-constraint coupling evaluation result. In S5, the output of the multi-constraint coupling evaluation result specifically includes the following steps: Obtain the risk assessment weight matrix, and combine the upper limit of the carrying power of each DC feed into the dominant constraint margin with the risk assessment weight matrix to perform weighted calculation to generate the over-limit risk index of the receiving-end power grid; Specifically, this includes: obtaining the vector of upper limit values ​​of the carrying power of each feed-in DC obtained from the aforementioned steps. With dominant constraint margin Obtain the rated operating power of each DC feeder. The unit is MW. Construct a comprehensive risk feature vector to characterize the degree to which the system approaches the limit. , among which the former Each component represents the power limitation risk level of each input DC, calculated using the following formula: , dimensionless, of which For the first The maximum carrying capacity of the DC feed is expressed in MW. ;No. Each component represents the boundary approximation risk level, calculated using the following formula: , dimensionless, of which The preset threshold corresponding to the dominant constraint expression in the aforementioned steps is used to obtain the dimension. Risk assessment weight matrix This matrix is ​​pre-calibrated based on scheduling and operational experience, and its elements represent the severity weights of various risk indicators and satisfy the following conditions: The dimensionless method generates the over-limit risk index of the receiving-end power grid by weighting the comprehensive risk feature vector with the risk assessment weight matrix. The calculation formula is: .

2. The multi-constraint coupled evaluation method for the carrying capacity of multiple DC feeders in a receiving-end power grid according to claim 1, characterized in that, In S1, the construction of the equivalent model of the receiving-end power grid further includes the following steps: The temperature-sensitive load of each node and the dynamic thermal stability limit of each AC line are updated to the corresponding nodes and AC lines in the receiving-end power grid topology to form an equivalent model of the receiving-end power grid.

3. The multi-constraint coupled evaluation method for the carrying capacity of multiple DC feeders in a receiving-end power grid according to claim 1, characterized in that, In S2, the generation of the multi-feed coupling matrix further includes the following steps: The commutation voltage interaction factors between the landing points of each DC feed are matrix-combined to generate a multi-feed coupling matrix.

4. The multi-constraint coupled evaluation method for the carrying capacity of multiple DC feeders in a receiving-end power grid according to claim 1, characterized in that, In S5, the output of the multi-constraint coupling evaluation result further includes the following steps: The risk level label is generated by comparing the over-limit risk index of the receiving power grid with a preset set of risk classification thresholds. By combining the risk level label, the over-limit risk index of the receiving-end power grid, the upper limit of the carrying capacity of each feeder DC, and the dominant constraint margin, a multi-constraint coupling evaluation result is output.

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