Active power distribution network security domain description method considering inertia and voltage support

Abstract

The invention discloses an active power distribution network security domain description method considering inertia and voltage support, which comprises the following steps: firstly, establishing a branch load flow model of an active power distribution network, then establishing an energy storage system operation model considering virtual inertia support capability, secondly, establishing an operation model considering voltage-reactive V-Q droop control of the photovoltaic inverter, wherein the model comprises droop control constraint and photovoltaic capacity constraint; and finally, proposing an adaptive piecewise linear reconstruction algorithm, and efficiently and accurately describing a P-Q security domain of interaction between the active power distribution network and the main network, which meets the inertia requirement and the voltage reactive power control, by adaptively adjusting the sampling step length, and further constructing a P-Q-inertia three-dimensional security domain which meets the system inertia requirement and the voltage reactive power control constraint.

Description

A method for characterizing the security domain of an active distribution network considering inertia and voltage support Technical Field

[0001] This invention belongs to the technical field of active distribution network operation capability assessment and safety boundary analysis, specifically relating to a method for characterizing the safety domain of an active distribution network that considers inertia and voltage support. Background Technology

[0002] As the penetration rate of distributed photovoltaic and energy storage systems in distribution networks continues to increase, traditional distribution networks primarily relying on unidirectional power supply are gradually evolving into active distribution networks with source-load-storage coordinated control capabilities. Simultaneously, the replacement of synchronous rotating motors with a large number of power electronic interface devices has led to a decrease in the system's equivalent inertia level and a weakening of its frequency response capability. During power disturbances or power deficits, the system's frequency change rate may increase, potentially causing malfunctions or actuations of protection devices, thus threatening operational safety. It should be noted that in the context of power electronic distribution networks, the role provided by energy storage devices through virtual inertia control primarily manifests as the availability of inertia support capabilities. Its purpose is to meet the operational requirements and constraints for inertia support, rather than equating it with complete suppression or significant improvement of the frequency change rate.

[0003] The Proportional Qualifying (PQ) safety domain is used to characterize the feasible boundary for the exchange of active / reactive power between the root node of a distribution network and the upstream grid. It is an important tool for measuring the regulation capability and flexibility of a distribution network and can provide a basis for operation verification, boundary assessment, and control decisions. Existing PQ safety domain construction methods are mostly based on steady-state optimal power flow, mainly considering static safety constraints such as node voltage exceeding limits and line capacity exceeding limits. However, in actively managed distribution networks with a high proportion of power electronics, operational feasibility is not only affected by steady-state power flow constraints but also by frequency-related operational constraints such as the capacity to provide inertia support, as well as control characteristic constraints such as inverter voltage-reactive power droop control. If these constraints are ignored during the construction process, the resulting PQ safety domain may be difficult to achieve in actual operation due to insufficient inertia support configuration or limited control characteristics, thereby reducing the engineering applicability and reliability of the safety domain results.

[0004] Therefore, it is necessary to propose a PQ security domain construction method that explicitly incorporates inertia support to provide capacity constraints and inverter droop control constraints on the basis of steady-state security constraints, so as to achieve a more accurate characterization of the interaction capability boundary between the active distribution network and the main grid, and to provide support for the evaluation of the operating boundary under different inertia support requirement levels. Summary of the Invention

[0005] Objective: The technical problem to be solved by this invention is to provide a method for characterizing the safety domain of an active distribution network that considers inertia and voltage support, addressing the shortcomings of existing technologies. This invention introduces virtual inertia demand constraints for energy storage and minimum system inertia demand constraints into the distribution network branch power flow model. Combined with photovoltaic inverter droop control constraints and photovoltaic capacity constraints, an adaptive piecewise linear reconfiguration algorithm is used to efficiently and accurately characterize the PQ feasible domain of the interaction between the root node and the main grid in the active distribution network. Furthermore, a PQ-inertia three-dimensional safety domain can be constructed.

[0006] Technical Solution: To solve the above-mentioned technical problems, this invention provides a method for characterizing the safety domain of an active distribution network considering inertia and voltage support. The method includes the following steps:

[0007] Step 1: Obtain the network parameters and operating parameters of the active distribution network. The network parameters include line resistance, reactance, and topology. The operating parameters include the rated capacity of photovoltaic units and upper and lower limits of reactive power regulation, energy storage system capacity, virtual inertia time constant, and maximum allowable frequency change rate.

[0008] Step 2: Obtain the load demand and photovoltaic power output data of the distribution network, and establish a branch power flow model of the active distribution network. The model includes power balance constraints of the distribution network, node voltage and branch current constraints, voltage amplitude and line capacity constraints.

[0009] Step 3: Establish an energy storage system operation model that considers virtual inertia support capability. The model includes virtual inertia reserve constraints and system minimum inertia requirement constraints.

[0010] Step 4: Establish an operation model that considers the voltage-reactive power VQ droop control of the photovoltaic inverter. The model includes photovoltaic inverter droop control constraints and photovoltaic capacity constraints.

[0011] Step 5: Based on the mathematical model constructed in Steps 2 to 4, the active power P and reactive power Q exchanged between the substation root node of the distribution network and the main network are used as boundary variables. An adaptive piecewise linear reconstruction algorithm is used to solve for a series of (P,Q) boundary points. The boundary points are then enveloped using the convex hull algorithm to obtain the PQ security domain of the active distribution network. The above construction process is repeated for different minimum inertia requirements by hierarchical slicing to obtain the PQ security domain under different inertia support levels, and the PQ-inertia three-dimensional security domain is output.

[0012] Furthermore, in step 2, the branch power flow model is as follows:

[0013] (2.1) Power balance constraints of distribution network

[0014] (A-1)

[0015] (A-2)

[0016] (A-3)

[0017] (A-4)

[0018] In the formula, For node indexes in the distribution network, This represents the branch from node i to node j. Let j be the set of branches flowing into node j. Let J be the set of branches flowing out of node j; These are the active power and reactive power flowing through branch ij, respectively; These are the active power and reactive power flowing through branch jk, respectively; These represent the net injected active power and reactive power at node j, respectively. Let be the amplitude of the current in branch ij; and Let be the resistance and reactance of branch ij, respectively; These are the active and reactive power exchanged between the distribution network and the upstream main network through the root node, respectively. These are the active and reactive power of the load at node j, respectively. This refers to the maximum power point tracking power of photovoltaics. This represents the active power of energy stored at node j, where discharging is positive and charging is negative; The reactive power output of the photovoltaic inverter at node j;

[0019] (2.2) Node voltage and branch current constraints

[0020] (A-5)

[0021] (A-6)

[0022] In the formula, and These are the voltage magnitudes at nodes i and j, respectively.

[0023] (2.3) Voltage amplitude and line capacity constraints

[0024] (A-7)

[0025] (A-8)

[0026] In the formula, and These are the minimum and maximum allowable voltage amplitudes for the node, respectively; The maximum apparent power transmission capacity of branch ij.

[0027] Furthermore, in step 3, the energy storage system operation model considering virtual inertia support capability includes:

[0028] (3.1) Virtual inertia reserve constraint:

[0029] (A-9)

[0030] (A-10)

[0031] (A-11)

[0032] In the formula, This represents the amount of virtual inertial power reserved for energy storage at node j; This indicates the maximum allowable rate of frequency change of the system; Indicates the system's nominal frequency; This represents the virtual inertia provided by the energy storage at node j; This represents the maximum charging and discharging power of the energy stored at node j;

[0033] (3.2) Minimum inertia requirement constraint of the system:

[0034] (A-12)

[0035] (A-13)

[0036] In the formula, Represents an energy storage collection; This represents the minimum inertia required to maintain the system. This represents the virtual inertia time constant of the energy stored at node j.

[0037] Furthermore, in step 4, the photovoltaic inverter voltage-reactive power VQ droop control operation model includes:

[0038] (4.1) Sag control constraint

[0039] (A-14)

[0040] (A-15)

[0041] (A-16)

[0042] (A-17)

[0043] In the formula, The reactive power command value is calculated for the j-th photovoltaic inverter according to V-Q droop control. Let s be the droop coefficient of the photovoltaic inverter at node j; Let be the amplitude of the voltage at node j. The droop control voltage intercept of the photovoltaic inverter at node j is the input. Number of busbars Inject the partial derivative of the bus voltage amplitude into the reactive power at node j; The maximum reactive power output of the photovoltaic inverter at node j is the maximum reactive power output. These are the minimum and maximum voltage intercepts for droop control of the photovoltaic inverter, respectively.

[0044] (4.2) Photovoltaic capacity constraints

[0045] (A-18)

[0046] (A-19)

[0047] In the formula, The total active power provided to the photovoltaic system; This represents the rated apparent power of the photovoltaic system.

[0048] Furthermore, in step 5, the adaptive piecewise linear reconstruction algorithm specifically includes the following sub-steps:

[0049] (5.1) Determine the range of boundary variables: while satisfying the power balance constraints of the distribution network Under the constraints of node voltage and branch current, voltage amplitude and line capacity, virtual inertia reserve, system minimum inertia requirement, droop control, and photovoltaic capacity, the optimization problem is solved using equations (A-20) and (A-21) as objective functions, respectively, to obtain the two boundary points of the PQ safety domain. , ;

[0050] (A-20)

[0051] (A-21)

[0052] In the formula, and These are the minimum and maximum objective function values, respectively. These are the minimum and maximum active power values ​​in the PQ safety domain, respectively. They are respectively The reactive power value at the corresponding boundary point;

[0053] (5.2) Initialize the upper boundary point set: set the points and The initial endpoints of the upper boundary are used to form the initial set of upper boundary points; and an error threshold is set. The maximum number of points is used to control the segmentation precision and computational scale;

[0054] (5.3) For any two adjacent points in the upper boundary point set and Calculate the x-coordinate of the midpoint of the line segment formed:

[0055] (A-22)

[0056] In the formula, and The root node corresponding to the k-th boundary point exchanges active and reactive power with the main network, respectively. and The root node corresponding to the (k+1)th boundary point exchanges active and reactive power with the main network, respectively. for and The x-coordinate of the midpoint between two points;

[0057] The reference reactive power value corresponding to this midpoint is obtained based on linear interpolation:

[0058] (A-23)

[0059] In the formula, for and The reference reactive power value obtained by linear interpolation on the connecting line segment;

[0060] (5.4) Find the active power at the fixed midpoint and the reactive power at the true boundary: Solve the equations (A-1)-(A-19) simultaneously, and add equality constraints. The optimization problem is solved using equation (A-21) as the objective function to obtain the feasible upper boundary true reactive power value under the fixed active power condition. This forms candidate new boundary points. ;

[0061] (5.5) Error Criterion and Adaptive Subdivision Update: Calculate the subdivision error of the line segment:

[0062] (A-24)

[0063] In the formula, This represents the error value of the line segment. The feasible upper boundary real reactive power value under fixed active power;

[0064] like Greater than the preset absolute error threshold Then the new point Add the upper boundary point set, split the original line segment into two segments, and continue to repeat sub-steps (5.3) to (5.5) on the updated upper boundary point set; if Or section length If the value is less than the preset value, the line segment is determined to meet the accuracy requirements and the splitting of the line segment is stopped. When all line segments meet the accuracy requirements, the upper boundary of the safety domain is obtained.

[0065] (5.6) Repeat sub-steps (5.2) to (5.5) for the lower boundary, wherein the objective function of sub-step (5.4) is changed to equation (A-20) to obtain the set of boundary points of the lower boundary. Merge the set of boundary points of the upper and lower boundaries and use the convex hull algorithm to perform envelope processing on the merged point set to form a closed PQ safe domain convex polygon.

[0066] (5.7) For different minimum inertia requirements, perform hierarchical slicing and repeat sub-steps (5.1)-(5.6) to obtain a set of PQ safety domains under different inertia support levels. Then, superimpose the PQ safety domains corresponding to each slice according to the inertia dimension to output the PQ-inertia three-dimensional safety domain.

[0067] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0068] This invention introduces virtual inertia reserve constraints and system minimum inertia requirement constraints during the construction of the PQ safety domain, combined with photovoltaic droop control constraints and photovoltaic capacity constraints. This ensures that the obtained PQ safety domain satisfies steady-state safety constraints such as node voltage and line capacity while also considering inertia support capability configuration requirements and inverter control characteristics, thereby improving the engineering feasibility and operational reliability of the safety domain results. Simultaneously, this invention employs an adaptive piecewise linear reconstruction algorithm for iterative boundary approximation. Compared to the fixed-step scanning method, this significantly reduces the number of optimization solutions and improves computational efficiency while maintaining boundary fitting accuracy, making it suitable for active distribution network power interaction boundary assessment and online analysis applications. Based on consideration of distribution network inertia support and voltage-reactive power control constraints, this invention achieves rapid construction of the PQ safety domain and its three-dimensional safety domain, providing a basis for active distribution network operation scheduling and safety verification. Attached Figure Description

[0069] Figure 1 is a flowchart of the method of the present invention;

[0070] Figure 2 is a system diagram of the improved IEEE 33-node computational example;

[0071] Figure 3 shows the three-dimensional security domain of P–Q–inertia for an active distribution network considering virtual inertia and voltage reactive power control constraints. Detailed Implementation

[0072] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0073] As shown in Figure 1, this invention provides a method for characterizing the safety domain of an active distribution network considering inertia and voltage support. The method includes the following steps:

[0074] Step 1: Obtain the network parameters and operating parameters of the active distribution network. The network parameters include line resistance, reactance, and topology. The operating parameters include the rated capacity of photovoltaic units and upper and lower limits of reactive power regulation, energy storage system capacity, virtual inertia time constant, and maximum allowable frequency change rate.

[0075] Step 2: Obtain the load demand and photovoltaic power output data of the distribution network, and establish a branch power flow model of the active distribution network. The model includes power balance constraints of the distribution network, node voltage and branch current constraints, voltage amplitude and line capacity constraints.

[0076] Step 3: Establish an energy storage system operation model that considers virtual inertia support capability. The model includes virtual inertia reserve constraints and system minimum inertia requirement constraints.

[0077] Step 4: Establish an operation model that considers the voltage-reactive power VQ droop control of the photovoltaic inverter. The model includes photovoltaic inverter droop control constraints and photovoltaic capacity constraints.

[0078] Step 5: Based on the mathematical model constructed in Steps 2 to 4, the active power P and reactive power Q exchanged between the substation root node of the distribution network and the main network are used as boundary variables. An adaptive piecewise linear reconstruction algorithm is used to solve for a series of (P,Q) boundary points. The boundary points are then enveloped using the convex hull algorithm to obtain the PQ security domain of the active distribution network. The above construction process is repeated for different minimum inertia requirements by hierarchical slicing to obtain the PQ security domain under different inertia support levels, and the PQ-inertia three-dimensional security domain is output.

[0079] Furthermore, in step 2, the branch power flow model is as follows:

[0080] (2.1) Power balance constraints of distribution network

[0081] (A-1)

[0082] (A-2)

[0083] (A-3)

[0084] (A-4)

[0085] In the formula, For node indexes in the distribution network, This represents the branch from node i to node j. Let j be the set of branches flowing into node j. Let J be the set of branches flowing out of node j; These are the active power and reactive power flowing through branch ij, respectively; These are the active power and reactive power flowing through branch jk, respectively; These represent the net injected active power and reactive power at node j, respectively. Let be the amplitude of the current in branch ij; and Let be the resistance and reactance of branch ij, respectively; These are the active and reactive power exchanged between the distribution network and the upstream main network through the root node, respectively. These are the active and reactive power of the load at node j, respectively. This refers to the maximum power point tracking power of photovoltaics. This represents the active power of energy stored at node j, where discharging is positive and charging is negative; The reactive power output of the photovoltaic inverter at node j;

[0086] (2.2) Node voltage and branch current constraints

[0087] (A-5)

[0088] (A-6)

[0089] In the formula, and These are the voltage magnitudes at nodes i and j, respectively.

[0090] (2.3) Voltage amplitude and line capacity constraints

[0091] (A-7)

[0092] (A-8)

[0093] In the formula, and These are the minimum and maximum allowable voltage amplitudes for the node, respectively; The maximum apparent power transmission capacity of branch ij.

[0094] Furthermore, in step 3, the energy storage system operation model considering virtual inertia support capability includes:

[0095] (3.1) Virtual inertia reserve constraint:

[0096] (A-9)

[0097] (A-10)

[0098] (A-11)

[0099] In the formula, This represents the amount of virtual inertial power reserved for energy storage at node j; This indicates the maximum allowable rate of frequency change of the system; Indicates the system's nominal frequency; This represents the virtual inertia provided by the energy storage at node j; This represents the maximum charging and discharging power of the energy stored at node j;

[0100] (3.2) Minimum inertia requirement constraint of the system:

[0101] (A-12)

[0102] (A-13)

[0103] In the formula, Represents an energy storage collection; This represents the minimum inertia required to maintain the system. This represents the virtual inertia time constant of the energy stored at node j.

[0104] Furthermore, in step 4, the photovoltaic inverter voltage-reactive power VQ droop control operation model includes:

[0105] (4.1) Sag control constraint

[0106] (A-14)

[0107] (A-15)

[0108] (A-16)

[0109] (A-17)

[0110] In the formula, The reactive power command value is calculated for the j-th photovoltaic inverter according to V-Q droop control. Let s be the droop coefficient of the photovoltaic inverter at node j; Let be the amplitude of the voltage at node j. The droop control voltage intercept of the photovoltaic inverter at node j is the input. Number of busbars Inject the partial derivative of the bus voltage amplitude into the reactive power at node j; The maximum reactive power output of the photovoltaic inverter at node j is the maximum reactive power output. These are the minimum and maximum voltage intercepts for droop control of the photovoltaic inverter, respectively.

[0111] (4.2) Photovoltaic capacity constraints

[0112] (A-18)

[0113] (A-19)

[0114] In the formula, The total active power provided to the photovoltaic system; This represents the rated apparent power of the photovoltaic system.

[0115] Furthermore, in step 5, the adaptive piecewise linear reconstruction algorithm specifically includes the following sub-steps:

[0116] (5.1) Determine the range of boundary variables: while satisfying the power balance constraints of the distribution network Under the constraints of node voltage and branch current, voltage amplitude and line capacity, virtual inertia reserve, system minimum inertia requirement, droop control, and photovoltaic capacity, the optimization problem is solved using equations (A-20) and (A-21) as objective functions, respectively, to obtain the two boundary points of the PQ safety domain. , ;

[0117] (A-20)

[0118] (A-21)

[0119] In the formula, and These are the minimum and maximum objective function values, respectively. These are the minimum and maximum active power values ​​in the PQ safety domain, respectively. They are respectively The reactive power value at the corresponding boundary point;

[0120] (5.2) Initialize the upper boundary point set: set the points and The initial endpoints of the upper boundary are used to form the initial set of upper boundary points; and an error threshold is set. The maximum number of points is used to control the segmentation precision and computational scale;

[0121] (5.3) For any two adjacent points in the upper boundary point set and Calculate the x-coordinate of the midpoint of the line segment formed:

[0122] (A-22)

[0123] In the formula, and The root node corresponding to the k-th boundary point exchanges active and reactive power with the main network, respectively. and The root node corresponding to the (k+1)th boundary point exchanges active and reactive power with the main network, respectively. for and The x-coordinate of the midpoint between two points;

[0124] The reference reactive power value corresponding to this midpoint is obtained based on linear interpolation:

[0125] (A-23)

[0126] In the formula, for and The reference reactive power value obtained by linear interpolation on the connecting line segment;

[0127] (5.4) Find the active power at the fixed midpoint and the reactive power at the true boundary: Solve the equations (A-1)-(A-19) simultaneously, and add equality constraints. The optimization problem is solved using equation (A-21) as the objective function to obtain the feasible upper boundary true reactive power value under the fixed active power condition. This forms candidate new boundary points. ;

[0128] (5.5) Error Criterion and Adaptive Subdivision Update: Calculate the subdivision error of the line segment:

[0129] (A-24)

[0130] In the formula, This represents the error value of the line segment. The feasible upper boundary real reactive power value under fixed active power;

[0131] like Greater than the preset absolute error threshold Then the new point Add the upper boundary point set, split the original line segment into two segments, and continue to repeat sub-steps (5.3) to (5.5) on the updated upper boundary point set; if Or section length If the value is less than the preset value, the line segment is determined to meet the accuracy requirements and the splitting of the line segment is stopped. When all line segments meet the accuracy requirements, the upper boundary of the safety domain is obtained.

[0132] (5.6) Repeat sub-steps (5.2) to (5.5) for the lower boundary, wherein the objective function of sub-step (5.4) is changed to equation (A-20) to obtain the set of boundary points of the lower boundary. Merge the set of boundary points of the upper and lower boundaries and use the convex hull algorithm to perform envelope processing on the merged point set to form a closed PQ safe domain convex polygon.

[0133] (5.7) For different minimum inertia requirements, perform hierarchical slicing and repeat sub-steps (5.1)-(5.6) to obtain a set of PQ safety domains under different inertia support levels. Then, superimpose the PQ safety domains corresponding to each slice according to the inertia dimension to output the PQ-inertia three-dimensional safety domain.

[0134] Case Analysis

[0135] The following example illustrates the superiority of the active distribution network security domain characterization method considering inertia and voltage support described in this invention. This invention uses an improved IEEE 33-node distribution system as the test object, as shown in Figure 2. Five photovoltaic and energy storage devices are configured in the system. The photovoltaic system employs a voltage-reactive power (VQ) droop control strategy, while the energy storage provides virtual inertia support capabilities. In this example, this invention constructs the security domain through the GAMS optimization platform.

[0136] To demonstrate the impact of virtual inertia constraints on the power interaction boundary of the distribution network, this invention sets different minimum inertia demand levels and constructs the root node PQ safety domain boundary under each inertia slice using a hierarchical slicing method. Then, the slice results are superimposed along the inertia dimension to obtain the PQ-inertia three-dimensional safety domain surface, as shown in Figure 3. As can be seen from Figure 3, as the minimum inertia demand level gradually increases, the safety domain boundary of the exchangeable active and reactive power between the distribution network root node and the main grid generally shows a shrinking trend, and the P-Q safety domain area decreases. This is because when the inertia demand increases, it occupies the available power margin of the energy storage device, thus reducing the range of active power adjustment that can be exchanged between the distribution network root node and the main grid, hence the decrease in the P-Q safety domain area.

[0137] Furthermore, this invention employs an adaptive piecewise linear reconstruction method to construct the P–Q–inertia three-dimensional safety domain boundary. Compared with the traditional fixed-step radial point-by-point scanning method, this invention can significantly reduce the number of optimal power flow solutions and shorten the overall computation time while maintaining accuracy requirements. At the same time, a comparison of domain volume indices shows that the safety domain volume obtained by this invention is on the same order of magnitude as that of the fixed-step method with a small deviation, indicating that this method still has good three-dimensional safety domain approximation capability while improving efficiency, and is more suitable for rapid reconstruction and online evaluation applications under multi-inertia slice conditions.

[0138] Table 1 Comparison of time consumption of different methods

[0139] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for characterizing the safety domain of an active distribution network considering inertia and voltage support, characterized in that, The method includes the following steps: Step 1, obtaining network parameters and operating parameters of the active distribution network. The network parameters include line resistance, reactance, and topology. The operating parameters include the rated capacity and reactive power regulation limits of photovoltaic units, the capacity of the energy storage system, the virtual inertia time constant, and the maximum allowable frequency change rate. Step 2, obtaining distribution network load demand and photovoltaic predicted output data, and establishing a branch power flow model of the active distribution network. The model includes distribution network power balance constraints, node voltage and branch current constraints, voltage amplitude and line capacity constraints. Step 3, establishing an energy storage system operating model considering virtual inertia support capability. The model includes virtual inertia reserve constraints and the minimum system inertia requirement. Step 4: Establish an operation model considering the voltage-reactive power (VQ) droop control of the photovoltaic inverter. The model includes photovoltaic inverter droop control constraints and photovoltaic capacity constraints. Step 5: Based on the mathematical model constructed in steps 2 to 4, using the active power P and reactive power Q exchanged between the substation root node of the distribution network and the main network as boundary variables, an adaptive piecewise linear reconstruction algorithm is used to solve for a series of (P,Q) boundary points. The boundary points are then enveloped using the convex hull algorithm to obtain the PQ security domain of the active distribution network. The above construction process is repeated for different minimum inertia requirements by hierarchical slicing to obtain the PQ security domain under different inertia support levels, and the PQ-inertia three-dimensional security domain is output.

2. The method for characterizing the safety domain of an active distribution network considering inertia and voltage support according to claim 1, characterized in that, In step 2, the branch power flow model is as follows: (2.1) Distribution network power balance constraints: （A-1） （A-2） （A-3） In formula (A-4), For node indexes in the distribution network, This represents the branch from node i to node j. Let j be the set of branches flowing into node j. Let J be the set of branches flowing out of node j; These are the active power and reactive power flowing through branch ij, respectively; These are the active power and reactive power flowing through branch jk, respectively; These represent the net injected active power and reactive power at node j, respectively. Let be the amplitude of the current in branch ij; and Let be the resistance and reactance of branch ij, respectively; These are the active and reactive power exchanged between the distribution network and the upstream main network through the root node, respectively. These are the active and reactive power of the load at node j, respectively. This refers to the maximum power point tracking power of photovoltaics. This represents the active power of energy stored at node j, where discharging is positive and charging is negative; (2.2) Reactive power output of the photovoltaic inverter at node j; (3) Node voltage and branch current constraints （A-5） In formula (A-6), and The voltage amplitudes at nodes i and j are respectively; (2.3) Voltage amplitude and line capacity constraints （A-7） In formula (A-8), and These are the minimum and maximum allowable voltage amplitudes for the node, respectively; The maximum apparent power transmission capacity of branch ij.

3. The method for characterizing the safety domain of an active distribution network considering inertia and voltage support according to claim 2, characterized in that, In step 3, the energy storage system operation model considering virtual inertia support capability includes: (3.1) Virtual inertia reserve constraint: （A-9） （A-10） In formula (A-11), This represents the amount of virtual inertial power reserved for energy storage at node j; This indicates the maximum allowable rate of frequency change of the system; Indicates the system's nominal frequency; This represents the virtual inertia provided by the energy storage at node j; Represents the maximum charging and discharging power of the energy stored at node j; (3.2) Minimum inertia requirement constraint of the system: （A-12） In formula (A-13), Represents an energy storage collection; This represents the minimum inertia required to maintain the system. This represents the virtual inertia time constant of the energy stored at node j.

4. The method for characterizing the safety domain of an active distribution network considering inertia and voltage support according to claim 3, characterized in that, In step 4, the photovoltaic inverter voltage-reactive power VQ droop control operation model includes: (4.1) droop control constraints （A-14） （A-15） （A-16） In formula (A-17), The reactive power command value is calculated for the j-th photovoltaic inverter according to V-Q droop control. Let s be the droop coefficient of the photovoltaic inverter at node j; Let be the amplitude of the voltage at node j. The droop control voltage intercept of the photovoltaic inverter at node j is the input. Number of busbars Inject the partial derivative of the bus voltage amplitude into the reactive power at node j; The maximum reactive power output of the photovoltaic inverter at node j is the maximum reactive power output. These are the minimum and maximum voltage intercepts for droop control of the photovoltaic inverter, respectively; (4.2) Photovoltaic capacity constraints （A-18） In formula (A-19), The total active power provided to the photovoltaic system; This represents the rated apparent power of the photovoltaic system.

5. The method for characterizing the safety domain of an active distribution network considering inertia and voltage support according to claim 4, characterized in that, In step 5, the adaptive piecewise linear reconstruction algorithm specifically includes the following sub-steps: (5.1) Determine the range of boundary variables: while satisfying the power balance constraints of the distribution network. Under the constraints of node voltage and branch current, voltage amplitude and line capacity, virtual inertia reserve, system minimum inertia requirement, droop control, and photovoltaic capacity, the optimization problem is solved using equations (A-20) and (A-21) as objective functions, respectively, to obtain the two boundary points of the PQ safety domain. ， ； （A-20） In formula (A-21), and These are the minimum and maximum objective function values, respectively. These are the minimum and maximum active power values ​​in the PQ safety domain, respectively. They are respectively The reactive power value of the corresponding boundary point; (5.2) Initialize the upper boundary point set: set the points and As the initial endpoints of the upper boundary, they form the initial set of upper boundary points; And set the error threshold The maximum number of points is used to control the segmentation accuracy and computational scale; (5.3) For any two adjacent points in the upper boundary point set and Calculate the x-coordinate of the midpoint of the line segment formed: In formula (A-22), and The root node corresponding to the k-th boundary point exchanges active and reactive power with the main network, respectively. and The root node corresponding to the (k+1)th boundary point exchanges active and reactive power with the main network, respectively. for and The x-coordinate of the midpoint between the two points; the reference reactive power value corresponding to this midpoint is obtained based on linear interpolation: In formula (A-23), for and Reference reactive power obtained by linear interpolation on the connecting line segment; (5.4) Fix the midpoint active power and find the true boundary reactive power: solve equations (A-1)-(A-19) simultaneously, and add equality constraints. The optimization problem is solved using equation (A-21) as the objective function to obtain the feasible upper boundary true reactive power value under the fixed active power condition. This forms candidate new boundary points. (5.5) Error criterion and adaptive subdivision update: Calculate the subdivision error of the line segment. In formula (A-24), This represents the error value of the line segment. The feasible upper boundary real reactive power value under fixed active power; like Greater than the preset absolute error threshold Then the new point Add the upper boundary point set, split the original line segment into two segments, and continue to repeat sub-steps (5.3) to (5.5) on the updated upper boundary point set; if Or section length If the value is less than the preset value, the line segment is determined to meet the accuracy requirements and the splitting of the line segment is stopped. When all line segments meet the accuracy requirements, the upper boundary of the safety domain is obtained; (5.6) Repeat sub-steps (5.2) to (5.5) for the lower boundary, where the objective function of sub-step (5.4) is changed to equation (A-20) to obtain the set of boundary points of the lower boundary. The set of boundary points of the upper and lower boundaries are merged, and the convex hull algorithm is used to envelop the merged point set to form a closed PQ safety domain convex polygon; (5.7) For different minimum inertia requirements, the slices are graded and the sub-steps (5.1)-(5.6) are repeated to obtain the set of PQ safety domains under different inertia support levels. The PQ safety domains corresponding to each slice are superimposed according to the inertia dimension to output the PQ-inertia three-dimensional safety domain.

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