A power system location method considering the photovoltaic power generation carrying capacity limit

Abstract

This invention discloses a power system capacity selection and location method considering the photovoltaic (PV) power generation carrying capacity limit. The method first establishes critical inertia and critical PV penetration rate models under RoCoF and SSFD constraints, using the grid's equivalent inertia as the core and the maximum rate of frequency change and steady-state frequency deviation as constraints to solve for the power system's critical inertia and critical PV penetration rate. Secondly, using active power loss, voltage deviation index, and voltage stability index as optimization objectives, and with critical inertia and critical PV penetration rate as constraints, a multi-objective PV power plant capacity selection and location model is established. Finally, a genetic algorithm is used to solve the multi-objective PV power plant capacity selection and location model to obtain the optimal capacity selection and location plan. This invention takes into account both the power system's critical inertia and critical PV penetration rate, significantly reducing active power loss in the distribution network, improving voltage distribution, and enhancing grid voltage stability.

Description

Technical Field

[0001] This invention belongs to the field of power system operation, and specifically relates to a power system capacity selection and site selection method that takes into account the photovoltaic power generation carrying capacity limit. Background Technology

[0002] With the introduction of the "dual carbon" target, my country's new energy industry has ushered in a leapfrog development, with a significant increase in the proportion of clean energy installed capacity. Against this backdrop, the proportion of photovoltaic power plants in the power grid has continued to increase. By the end of 2022, my country's cumulative installed photovoltaic capacity reached 415 million kilowatts, and the annual photovoltaic power generation was 435 billion kilowatt-hours. However, the increased penetration rate of renewable energy will affect the safe and stable operation of the power system. After large-scale photovoltaic grid connection, the power system will exhibit low inertia characteristics, severely weakening the power system's inertia support and frequency regulation capabilities under active power disturbances, posing a considerable threat to the safe and stable operation of the power system. On the one hand, if the power system inertia remains at a level far above the safety threshold, it may exacerbate the curtailment of solar power; on the other hand, insufficient power system inertia will bring the risk of frequency instability.

[0003] In power system dispatching, fully considering the frequency stability issues caused by the low inertia of a power system with a high proportion of renewable energy grid connection can improve the absorption of new energy power and reduce curtailment. Furthermore, improper location and capacity of photovoltaic (PV) grid connection can have adverse effects. After a PV power plant is connected to the grid, the reduced transmission power on the feeder causes a rise in voltage at each load node along the feeder, potentially leading to excessive voltage deviations at some load nodes. The extent of this deviation is closely related to the location and total capacity of the connected PV power source. Since large-scale PV grid connection is a crucial way to address renewable energy absorption and build a green, low-carbon power system, fully considering the frequency stability issues caused by the low inertia of a power system with a high proportion of renewable energy grid connection, and optimizing the location and capacity of PV grid connection, can improve the absorption of new energy power and reduce curtailment.

[0004] Against this backdrop, introducing the equivalent inertia of photovoltaic (PV) power plants and the PV power generation capacity limit is an effective measure to ensure the long-term stable operation of the power system when solving the power system capacity and location problem. Therefore, this invention, while ensuring the maximum grid connection capacity of PV power plants, also takes into account the stable operation of the power system. Based on the critical inertia of the power system, it introduces the PV power plant capacity limit to improve energy utilization. The modeling of power system capacity and location is completed with the goal of minimizing the combined active power loss, voltage stability index, and voltage deviation index of the power system after the PV power plant is connected. Summary of the Invention

[0005] The problem to be solved by the present invention

[0006] Based on the power system, a modeling method for the photovoltaic power generation carrying capacity limit of the power system is proposed, which considers the constraints of the rate of change of frequency (RoCoF) and the steady state frequency feviation (SSFD).

[0007] A power system capacity selection method considering the photovoltaic power generation carrying capacity limit is proposed, including the following steps:

[0008] Step 1: Establish critical inertia and critical photovoltaic penetration rate models under RoCoF and SSFD constraints. With the equivalent inertia of the power grid as the core and the maximum rate of frequency change and steady-state frequency deviation as constraints, solve for the critical inertia and critical photovoltaic penetration rate of the power system.

[0009] Step 2: Using active power loss, voltage deviation index, and voltage stability index as optimization objectives, and the critical inertia and critical photovoltaic penetration rate obtained in Step 1 as constraints, establish a multi-objective photovoltaic power plant capacity selection and site selection model.

[0010] Multi-objective photovoltaic power plant gradation and site selection model F:

[0011]

[0012] In the formula: ω i Let be a weighting factor describing the importance of the i-th objective function, and satisfy . f i * Let represent the value of the i-th objective function after numerical normalization. Equation (1) requires that each objective function be numerically normalized to make it dimensionless, in order to prevent the fitness scaling problem of the objective function from occurring during the optimization process, thereby ensuring the objective accuracy of the optimization model.

[0013] The objective function F includes the following three sub-objective functions.

[0014] (1) Reduce power loss

[0015] The primary objective of connecting photovoltaic power plants to the power system is to minimize network power loss. Therefore, taking power loss as the first objective function f1, it can be expressed as:

[0016]

[0017] In the above formula, α ij With β ij It can be obtained from equation (3).

[0018]

[0019] In the formula: P j and Q j These represent the injected active power and reactive power at node j, respectively; r ij U represents the real part of the i-th row and j-th column of the nodal impedance matrix; i δ represents the voltage magnitude at node i; i This represents the voltage phase angle at node i; This represents the total number of nodes in the power system.

[0020] (2) Improve grid voltage

[0021] The reactive power injected by photovoltaic power plants helps reduce reactive power flow in the power grid and decreases branch voltage losses. Therefore, the voltage deviation index (VDI) is used as the second objective function.

[0022]

[0023] In the formula: U i Represented as the voltage at node i; U norm This represents the voltage at a substation node in the power grid, and can usually be set to 1.

[0024] (3) Improve voltage stability

[0025] While minimizing voltage deviation can improve node voltage curves, a third objective function is constructed based on the Voltage Stability Index (VSI) to ensure the stable operation of the power system, as shown in Equation (5). VSI represents the static voltage stability of a branch; the larger the VSI, the more sensitive it is to voltage collapse and the worse its stability. Therefore, it is necessary to maximize the minimum value of the node VSI to improve the voltage stability level of the power system, as shown in Equation (6).

[0026]

[0027] In the formula: R ij X ij These represent the resistance and reactance of the line between node i and node j, respectively. This refers to the set of substation access nodes in the network.

[0028] Step 3: Use a genetic algorithm to solve the multi-objective photovoltaic power plant capacity and location model to obtain the optimal capacity and location plan.

[0029] The solution to the multi-objective optimization model for photovoltaic power plant site selection and capacity determination mainly employs a genetic algorithm to simulate and solve the IEEE 30-node system. First, the objective function values ​​for adding 1-11 photovoltaic (PV) power plants are calculated and compared. The minimum objective function value is then identified, and the corresponding number and capacity of added PV power plants is the optimal solution.

[0030] This invention patent differs from existing research in the following ways and has the following beneficial effects.

[0031] (1) Unlike the traditional power system fixed capacity and location selection, the present invention takes into account both the critical inertia and critical photovoltaic penetration rate of the power system.

[0032] (2) Solve for the specific value of the equivalent inertia of the photovoltaic power station, and then calculate the overall inertia of the power system. Apply this to the power system location and capacity model to significantly reduce the active power loss of the distribution network, improve voltage distribution, and enhance the voltage stability of the power grid. Attached Figure Description

[0033] Figure 1 This is a topology diagram of the IEEE 30-node power system.

[0034] Figure 2 Flowchart for the specific implementation of site selection and capacity determination for the IEEE 30-bus power system;

[0035] Figure 3 A diagram comparing configuration results for different numbers of connected photovoltaic power plants;

[0036] Figure 4 This is a schematic diagram comparing the voltage deviation results of each node after connecting different numbers of photovoltaic power plants;

[0037] Figure 5 This is a diagram of the power system topology after the power system has been determined and its location selected. Detailed Implementation

[0038] The method of the present invention will be described in detail below with reference to the accompanying drawings:

[0039] A power system capacity selection and location method considering the photovoltaic power generation carrying capacity limit includes the following steps:

[0040] Step 1: Solve for the critical inertia and critical photovoltaic penetration rate under RoCoF and SSFD constraints.

[0041] ROCOF constraint: Frequency constraints are usually based on the system's maximum bus frequency or a specific bus frequency, and are generally located near the disturbance point. To prevent photovoltaic grid disconnection after a disturbance, RoCoF must not exceed its protection setting value.

[0042] SSFD constraint: The steady-state frequency deviation of the system is mainly determined by the unit regulating power of the synchronous machine and the frequency regulation effect of the load. The power grid operation guidelines stipulate that the system must meet the requirement that the maximum frequency drop does not exceed 1.0 Hz and the steady-state frequency deviation does not exceed 0.2 Hz, i.e., Δf(t∞) ≤ 0.2 Hz.

[0043] (1) Calculation of the equivalent inertia of the power grid:

[0044] IEEE 30-bus power system, such as Figure 1 As shown, this IEEE 30-node power system has 41 transmission lines and 30 nodes, numbered 1 to 30, connected by these transmission lines. There are 6 generators, G1 to G6, located at nodes 1, 2, 5, 8, 11, and 13 respectively; 4 intermediate nodes without loads or generators, primarily serving as transmission nodes for connecting lines or transformers in the power network, located at nodes 7, 12, 15, and 18 respectively; the remaining 20 nodes are load nodes; additionally, 4 adjustable transformers are connected to nodes 6 and 9, 6 and 10, 4 and 12, and nodes 28 and 27.

[0045] After the integration of new energy sources, for a power system containing n synchronous machine units and m photovoltaic motor units, the equivalent inertia H of the power system is... sys for:

[0046]

[0047] Where: m is the number of photovoltaic generators; S PV,j S represents the capacity of the j-th photovoltaic generator; n represents the number of synchronous generators; S G,j H represents the capacity of the i-th synchronous machine; G,i The equivalent inertia of the i-th synchronous machine; H PV,j The equivalent inertia of the j-th photovoltaic motor; S PV S represents the total installed capacity of the photovoltaic units. G S represents the total capacity of the synchronous generator units. sys This refers to the total installed capacity of the power system.

[0048] The equivalent inertia H obtained by replacing synchronous generator sets with photovoltaic power in the power system PV The expression is shown in equation (2):

[0049]

[0050] In the formula: C is the capacitance value; U dc is the steady-state value of DC voltage; k is the control parameter of the virtual inertia control branch; s is time.

[0051] The obtained equivalent inertia H PVSubstituting into the equivalent inertia H of the power system sys In a power system, the power increment ΔP is generated by the difference between the load increment and the power output increment. sys At that time, neglecting the regulating effect of photovoltaic units and load, ΔP sys H sys The relationship between the initial RoCoF and the following is:

[0052]

[0053] In the formula: f0 is the initial frequency, P e and P t df and dt are the electromagnetic power and mechanical power of the equivalent synchronous machine, respectively; f is the frequency, and df / dt is the initial RoCoF.

[0054] The unit regulating power of a single synchronous machine is denoted by K, which refers to the change in frequency when the power changes by a unit amount. If a power system contains n synchronous machine units, their equivalent unit regulating power K is... sys for:

[0055]

[0056] In the formula: σ i S is the droop coefficient of the i-th synchronous machine unit. i Let be the capacity of the i-th synchronous machine unit.

[0057] In a power system, the power increment ΔP is generated by the difference between the load increment and the power output increment. sys Equivalent unit of regulating power K sys The relationship between the steady-state frequency deviation Δf and the following formula is:

[0058]

[0059] By constructing a new equation from the right sides of equations (4) and (5), we obtain:

[0060]

[0061] Against this backdrop, exploring the intrinsic relationship between power system inertia and the frequency response index of new energy power systems becomes a crucial step in quantifying the minimum inertia limit and the maximum photovoltaic (PV) integration ratio. By controlling the start-up and shutdown of relevant units in PV power plants and traditional power plants to alter the PV penetration rate, the safe operation prerequisite of the power system under inertia-frequency constraints can be met, thus determining the maximum safe PV integration ratio.

[0062] The ratio of installed photovoltaic (PV) capacity to the total power system capacity is defined as PV penetration rate ξ, i.e.:

[0063]

[0064] Where: m is the number of photovoltaic generators; S PV,j S represents the capacity of the j-th photovoltaic generator; n represents the number of synchronous generators; S G,j S represents the capacity of the i-th synchronizer; PV S represents the total installed capacity of the photovoltaic units. G This represents the total capacity of the synchronous generator units.

[0065] (2) Critical inertia constrained by maximum rate of change of frequency

[0066] If the difference in equivalent inertia of each synchronous generator unit is neglected, and the maximum total load power increment of the power system is known... but:

[0067]

[0068] Therefore, when the RoCoF limit is known, the critical inertia H under the maximum rate of change constraint can be obtained. RoCoF .

[0069] (3) Critical photovoltaic penetration rate

[0070] If the power increment ΔP in the power system is caused by the difference between the load increment and the power output increment of synchronous generators and photovoltaic generators... sys Given that the critical photovoltaic penetration rate under RoCoF and SSFD constraints can be calculated, the answer can be determined.

[0071] Power increment in the power system Critical photovoltaic penetration rate ξ under RoCoF constraints lim，1 As shown in the following formula:

[0072]

[0073] If the maximum total load power increment of the power system is known Furthermore, disregarding the differences in droop coefficients among the synchronous generator units, the critical photovoltaic penetration rate ξ under SSFD constraints is... lim,2 As shown in the following formula:

[0074]

[0075] In summary, the maximum photovoltaic penetration rate that a power system can withstand while satisfying both RoCoF and SSFD safety constraints is:

[0076] ξ lim =min(ξ) lim,1 ,ξ lim,2 (11)

[0077] Step 2: Establish a photovoltaic power plant site selection and capacity determination model

[0078] After completing the modeling in step one and obtaining the critical inertia and critical photovoltaic penetration rate under RoCoF and SSFD constraints, the objective function of the power system is established. This invention takes the stable operation of the power system as its principle and aims to minimize the combined power system losses, voltage deviation index, and voltage stability index.

[0079] The objective function for establishing a photovoltaic power plant site selection and capacity determination model is:

[0080]

[0081] In the formula: ω i Let be a weighting factor describing the importance of the i-th objective function, and satisfy . Based on the author's multiple simulations, the values ​​can be set to 1 / 3, 1 / 3, and 1 / 3 respectively to obtain the most balanced result for the objective function; f i * This represents the value of the i-th objective function after numerical normalization.

[0082] Each objective function in the formula needs to be numerically normalized to make each objective function dimensionless in order to prevent the objective function fitness scaling problem from occurring during the optimization process, thereby ensuring the objective accuracy of the optimization model, as shown in Equation (13).

[0083]

[0084] In the formula: f i Aft and f i Bef Let i represent the i-th objective function before and after photovoltaic power is connected to the power system, respectively.

[0085] The power plant site selection and gradation model F includes the following three sub-objective functions.

[0086] (1) Reduce power loss

[0087] The primary objective of connecting photovoltaic power plants to the power system is to minimize network power loss. Therefore, power loss as the first objective function f1 can be expressed as:

[0088]

[0089] In the above formula, α ij With β ij It can be obtained from equation (15).

[0090]

[0091] In the formula: P j and Q jThese represent the injected active power and reactive power at node j, respectively; r ij U represents the real part of the i-th row and j-th column of the nodal impedance matrix; i δ represents the voltage magnitude at node i; i This represents the voltage phase angle at node i.

[0092] (2) Improve grid voltage

[0093] The reactive power injected by photovoltaic power plants helps reduce reactive power flow in the power grid and decrease branch voltage losses. Therefore, the Voltage Deviation Index (VDI) is used as the second objective function f2.

[0094]

[0095] In the formula: U i Represented as the voltage at node i; U norm This represents the voltage at a substation node in the power grid, and can usually be set to 1.

[0096] (3) Improve voltage stability

[0097] Although minimizing voltage deviation can improve node voltage curves, to ensure stable operation of the power system, the Voltage Stability Index (VSI) should be used as the third objective function f3, as shown in Equation (17). VSI represents the static voltage stability of a branch. The larger the VSI, the more sensitive it is to voltage collapse and the worse its stability. Therefore, it is necessary to maximize the minimum value of the node VSI to improve the voltage stability level of the power system, as shown in Equation (18).

[0098]

[0099] In the formula: R ij X ij These represent the resistance and reactance of the line between node i and node j, respectively. It is the set of all nodes in the power system; This refers to the set of substation access nodes in the network.

[0100] Step 3: Solve based on the objective function to obtain the optimal plan.

[0101] The solution to the multi-objective optimization model for photovoltaic power plant site selection and capacity determination mainly employs a genetic algorithm. This algorithm records the optimal total capacity of the photovoltaic power plant configuration corresponding to the best individual during the iteration process, along with the network topology and corresponding total photovoltaic power configuration for each time period during which the photovoltaic system participates in scheduling. Constraints are added as penalty terms to the objective function, and the optimal solution is found through iteration and nonlinear optimization. The flowchart of the genetic algorithm solution is shown below. Figure 2 .

[0102] (1) Encoding method for PV location capacity optimization

[0103] The optimization of photovoltaic power plants includes both discrete variable location optimization and continuous variable capacity optimization. Real number encoding is adopted, and the specific encoding method is shown in equation (19):

[0104] g = [P] PV1 ,P PV2 ,…,P PVi …,P PVN (19)

[0105] In the formula, N is the number of nodes; P PV1 ,P PV2 ,…,P PVi …,P PVN Let P be a real number, representing the installed photovoltaic capacity. PVi A value of 0 indicates that no photovoltaic system is installed on this node.

[0106] (2) Fitness function

[0107] We choose F as the fitness function, and in the genetic algorithm, we hope that F will reach its minimum value.

[0108] (3) Select operation

[0109] The probability of an individual being selected for reproduction is proportional to its fitness. The probability of the i-th individual being selected is pi, and the expression for pi is shown in equation (20):

[0110]

[0111] In the formula, f(x) i ) represents the fitness of the i-th individual.

[0112] (4) Cross operation

[0113] A multi-point crossover method is adopted. Selected individuals generate new offspring through crossover operations. If the crossover point is k, and two individuals x are considered... i and x j , descendants x new It can be represented as:

[0114] x new =(x i1 ,x i2 ,...,x ik ,x j(k+1) ,...,x jn ) (twenty one)

[0115] (5) Mutation operation

[0116] With a small probability μ, certain genes of newborn individuals are modified to introduce variation and increase population diversity. For gene x... nk , can be represented as:

[0117] x' nk =x nk +δ+μ (22)

[0118] In the formula, δ represents a small, random change; μ represents the mutation rate.

[0119] (6) Nonlinear optimization

[0120] After a certain number of generations, the genetic algorithm uses the obtained result as the initial value, employs the linear programming function fmincon in the MATLAB optimization toolbox to perform local optimization, and uses the found local optimum as the new individual chromosome to continue the evolution.

[0121] The specific implementation process is as follows: Figure 2 As shown.

[0122] The critical inertia H of the power system is obtained by solving. RoCoF The critical photovoltaic penetration rate is 44.45%, which is 6.672. Under the constraints of critical inertia and critical photovoltaic penetration rate, the analysis considers different numbers and capacities of photovoltaic power plants. As the number of photovoltaic power plants increases, the photovoltaic penetration rate increases, the overall objective function decreases, indicating that the power system operates more stably and network losses decrease.

[0123] Figure 3 The model is presented with configuration results for connecting 1 to 11 photovoltaic power plants in the IEEE 30-node power system. It can be seen that the objective function F-value decreases significantly as the number of connected photovoltaic power plants increases. Figure 4 The voltage deviation of each node in the IEEE 30-node power system after connecting different numbers of photovoltaic (PV) power plants is shown. It can be seen that as the number of PV power plants connected increases, the voltage deviation of each node decreases significantly. Compared to the cases of no PV connection, 3 PV connections, and 6 PV connections, the voltage deviation is smallest and the energy utilization rate is highest when 9 PV power plants are connected.

[0124] The following conclusions can be drawn: When eight photovoltaic power stations are connected, the objective function F is minimized to a value of 0.2962, and the photovoltaic penetration rate is 42.76%. The network topology at this point is as follows: Figure 5 As shown in Table 1, the location and capacity of the photovoltaic system connected to each node are as follows.

[0125] Table 1. Capacity of photovoltaic power plants connected to the grid

[0126]

[0127] The results show that configuring appropriate capacity at the optimal location reduces operating losses, improves voltage distribution, and enhances voltage stability in the IEEE 30-bus power system.

Claims

1. A power system capacity selection and site selection method considering the photovoltaic power generation carrying capacity limit, characterized in that, Includes the following steps: Step 1: Establish critical inertia and critical photovoltaic penetration rate models under the constraints of frequency change rate RoCoF and steady-state frequency deviation SSFD. Taking the equivalent inertia of the power grid as the core and the maximum frequency change rate and steady-state frequency deviation as constraints, solve for the critical inertia and critical photovoltaic penetration rate of the power system. The specific process for solving the critical inertia of the power system is as follows: If the difference in equivalent inertia of each synchronous generator unit is neglected, and the maximum total load power increment of the power system is known... but: Where ξ is the photovoltaic penetration rate; when the RoCoF limit is known, the critical inertia H under the maximum rate of change constraint is obtained. RoCoF ; The specific process for calculating the critical photovoltaic penetration rate is as follows: If the power increment ΔP in the power system is caused by the difference between the load increment and the power output increment of synchronous generators and photovoltaic generators... sys Given this, the critical photovoltaic penetration rate under RoCoF and SSFD constraints can be calculated. Power increment in the power system Critical photovoltaic penetration rate ξ under RoCoF constraints lim,1 : If the maximum total load power increment of the power system is known Furthermore, disregarding the differences in droop coefficients among the synchronous generator units, the critical photovoltaic penetration rate ξ under SSFD constraints is... lim,2 As shown in the following formula: In summary, the maximum photovoltaic penetration rate that a power system can withstand while satisfying both RoCoF and SSFD safety constraints is: x lim =min(ξ lim,1 ,x lim,2 ) (4); Step 2: Using active power loss, voltage deviation index, and voltage stability index as optimization objectives, and critical inertia and critical photovoltaic penetration rate as constraints, establish a multi-objective photovoltaic power plant capacity selection and site selection model; Step 3: Use a genetic algorithm to solve the multi-objective photovoltaic power plant capacity and location model to obtain the optimal capacity and location plan.

2. The power system capacity selection and site selection method considering the photovoltaic power generation carrying capacity limit according to claim 1, characterized in that, The calculation process for the equivalent inertia is as follows: After the integration of new energy sources, for a power system containing n synchronous machine units and m photovoltaic motor units, the equivalent inertia H of the power system is... sys for: In the formula: m is the number of photovoltaic generators; S PV,j S represents the capacity of the j-th photovoltaic generator; n represents the number of synchronous generators; S G,j H represents the capacity of the i-th synchronous machine; G,i The equivalent inertia of the i-th synchronous machine; H PV,j The equivalent inertia of the j-th photovoltaic motor; S PV S represents the total installed capacity of the photovoltaic units. G S represents the total capacity of the synchronous generator units. sys This refers to the total installed capacity of the power system. The equivalent inertia H obtained by replacing synchronous generator sets with photovoltaic power in the power system PV The expression is: In the formula: C is the capacitance value; U dc is the steady-state value of DC voltage; k is the control parameter of the virtual inertia control branch; s is time; The obtained equivalent inertia H PV Substituting into the equivalent inertia H of the power system sys In a power system, the power increment ΔP is generated by the difference between the load increment and the power output increment. sys At that time, neglecting the regulating effect of photovoltaic units and load, ΔP sys H sys The relationship between the initial RoCoF and the following is: In the formula: f0 is the initial frequency, P e and P t These represent the electromagnetic power and mechanical power of the equivalent synchronous machine, respectively; f is the frequency, and df / dt is the initial RoCoF; If a power system contains n synchronous machine units, its equivalent regulating power K sys for: In the formula: σ i S is the droop coefficient of the i-th synchronous machine unit. i Let be the capacity of the i-th synchronous machine unit; In a power system, the power increment ΔP is generated by the difference between the load increment and the power output increment. sys Equivalent unit of regulating power K sys The relationship between the steady-state frequency deviation Δf and the following formula is: By constructing a new equation from the right sides of equations (8) and (9), we obtain:

3. The power system capacity selection and site selection method considering the photovoltaic power generation carrying capacity limit according to claim 2, characterized in that, The multi-objective photovoltaic power plant capacity and site selection model is established as follows: Multi-objective photovoltaic power plant gradation and site selection model F: In the formula: ω i Let be a weighting factor describing the importance of the i-th objective function, and satisfy . f i * This represents the numerically normalized value of the i-th objective function. F includes the following three sub-objective functions, each of which has been numerically normalized. The power loss is expressed as the first objective function f1: In the formula: P j and Q j These represent the injected active power and reactive power at node j, respectively; r ij U represents the real part of the i-th row and j-th column of the nodal impedance matrix; i δ represents the voltage magnitude at node i; i This represents the voltage phase angle at node i; This represents the total number of nodes in the power system. The voltage offset index VDI is used as the second objective function: In the formula: U i Represented as the voltage at node i; U norm Represented as the voltage at a substation node in the power grid; A third objective function is constructed based on the voltage stability index VSI, as shown in equation (15): In the formula: R ij X ij These represent the resistance and reactance of the line between node i and node j, respectively. This refers to the set of substation access nodes in the network.

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