Novel power system constant volume site selection method considering photovoltaic power generation bearing limit

Abstract

The invention discloses a novel electric power system constant-volume site selection method considering photovoltaic power generation bearing limit, and the method comprises the steps: firstly building a critical inertia and critical photovoltaic permeability model under the constraints of RoCoF and SSFD, taking the equivalent inertia of a power grid as the core, taking the maximum frequency change rate and steady-state frequency deviation as the constraints, and carrying out the constant-volume site selection of the power grid; and solving the critical inertia and the critical photovoltaic permeability of the novel power system. Secondly, taking active loss, a voltage deviation index and a voltage stability index as optimization targets, taking critical inertia and critical photovoltaic permeability as constraints, and establishing a multi-target photovoltaic power station constant-volume site selection model; and finally, solving the multi-target photovoltaic power station constant-volume site selection model by adopting a genetic algorithm to obtain an optimal constant-volume site selection plan. The critical inertia and the critical photovoltaic permeability of the power system are considered, the active loss of the power distribution network can be remarkably reduced, the voltage distribution is improved, and the voltage stability of the power grid is improved.

Description

Technical Field

[0001] The present invention belongs to the field of power system operation, and in particular relates to a novel power system capacity determination and site selection method taking into account the load limit of photovoltaic power generation. Background Art

[0002] With the proposal of the "dual carbon" goal, my country's new energy industry has ushered in a leapfrog development, and the proportion of clean energy installed capacity has increased significantly. Against this background, the proportion of photovoltaic power stations in the power grid has continued to increase. By the end of 2022, my country's cumulative photovoltaic installed capacity will reach 415 million kilowatts, and the annual photovoltaic power generation will be 435 billion kilowatt-hours. However, the increase in the penetration rate of renewable energy will affect the safe and stable operation of the power system. After large-scale photovoltaics are connected to the power grid, the power system will show low inertia characteristics, which will seriously weaken the inertia support and frequency regulation capabilities of the power system under active disturbances, posing a threat to the safe and stable operation of the power system that cannot be underestimated. On the one hand, if the inertia of the power system is maintained at a level far higher than the safety critical value, it may aggravate the phenomenon of abandoned light; on the other hand, insufficient inertia of the power system will bring the risk of frequency instability.

[0003] In the power system dispatch, the frequency stability problem caused by the low inertia of the power system with a high proportion of renewable energy connected to the grid can be fully considered to improve the level of new energy power consumption and reduce the phenomenon of abandoned light. In addition, the improper location and capacity of photovoltaic access to the grid may have adverse effects. After the photovoltaic power station is connected to the grid, the voltage at each load node along the feeder is raised due to the reduction of transmission power on the feeder, which may cause the voltage deviation of some load nodes to exceed the standard. The excess amount is closely related to the location and total capacity of the photovoltaic power source connected. Since the access of large-scale photovoltaic power stations to the grid is an important way to solve the problem of new energy consumption and build a green and low-carbon power system, the frequency stability problem caused by the low inertia of the power system with a high proportion of renewable energy connected to the grid in the power system, and the photovoltaic access location and capacity are optimized, which can improve the level of new energy power consumption and reduce the phenomenon of abandoned light.

[0004] In this context, when solving the problem of sizing and site selection for new power systems, introducing the equivalent inertia of photovoltaic power stations and the load limit of photovoltaic power generation is an effective measure to ensure the long-term stable operation of the power system. Therefore, while ensuring the maximum access capacity of photovoltaic power stations, the present invention also takes into account the stable operation of the power system. Based on the critical inertia of the power system, the load limit of photovoltaic power stations is introduced to improve energy utilization. With the goal of minimizing the combined active power loss, voltage stability index and voltage deviation index of the new power system after connecting to the photovoltaic power station, the modeling of sizing and site selection for the new power system is completed. Summary of the invention

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

[0006] Aiming at the new power system, a modeling method for the photovoltaic power generation load limit of the new power system considering the rate of change of frequency (RoCoF) and steady state frequency deviation (SSFD) constraints is proposed.

[0007] A new method for determining the capacity and site selection of a power system considering the load limit of photovoltaic power generation is proposed, which includes the following steps:

[0008] Step 1: Establish the critical inertia and critical PV penetration model under RoCoF and SSFD constraints, take the equivalent inertia of the power grid as the core, and take the maximum frequency change rate and steady-state frequency deviation as constraints to solve the critical inertia and critical PV penetration of the new power system.

[0009] Step 2: Taking active power loss, voltage deviation index and voltage stability index as optimization targets, and the critical inertia and critical photovoltaic penetration rate solved in step 1 as constraints, a multi-objective photovoltaic power station capacity selection model is established.

[0010] Multi-objective photovoltaic power station capacity selection model F:

[0011]

[0012] Where: i is the weight factor describing the importance of the i-th objective function and satisfies f i * Represents the function value of the i-th objective function after numerical normalization. Each objective function in formula (1) needs to be numerically normalized so that each objective function is dimensionless to prevent the objective function fitness scaling problem 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 main goal of connecting a photovoltaic power station 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 by formula (3).

[0018]

[0019] Where: P j and Q j denote the injected active power and reactive power of node j respectively; r ij represents the real part of the i-th row and j-th column in the node impedance matrix; U i represents the voltage amplitude of node i; δ i represents the voltage phase angle of node i; is the number of all nodes in the power system.

[0020] (2) Improve grid voltage

[0021] The reactive power injected by the photovoltaic power station is conducive to reducing the reactive power flow of the power grid and reducing the voltage loss of the branch. Therefore, the voltage deviation index (VDI) is used as the second objective function:

[0022]

[0023] Where: U i It is represented as the voltage of node i; U norm It is represented by the voltage at the substation node in the power grid and can usually be set to 1.

[0024] (3) Improve voltage stability

[0025] Although minimizing the voltage deviation can improve the node voltage curve, in order to ensure the stable operation of the new power system, a third objective function is constructed based on the voltage stability index (VSI), as shown in formula (5). VSI represents the static voltage stability of the branch. The larger the VSI, the more sensitive it is to voltage collapse and the worse the stability. Therefore, it is necessary to maximize the minimum value in the node VSI to improve the voltage stability level of the new power system, as shown in formula (6).

[0026]

[0027]

[0028] Where: R ij , X ij Respectively represent the resistance and reactance of the line between node i and node j; It is the collection of substation access nodes in the network.

[0029] Step 3: Use genetic algorithm to solve the multi-objective photovoltaic power station capacity and site selection model to obtain the optimal capacity and site selection plan.

[0030] Regarding the solution of the multi-objective optimization model for the site selection and capacity determination of photovoltaic power stations, the genetic algorithm is mainly used to simulate and solve the IEEE30-node system. First, the objective function values ​​of adding 1-11 photovoltaic power stations (PV) are solved and compared to find the minimum value of the objective function. The number and capacity of the added photovoltaic power stations corresponding to the objective function value are the optimal solution.

[0031] The present invention is different from the existing research work and has the following beneficial effects.

[0032] (1) Different from the traditional power system capacity selection, the present invention takes into account both the critical inertia and critical photovoltaic penetration of the power system.

[0033] (2) Solve the specific value of the equivalent inertia of the photovoltaic power station, and then calculate the overall inertia of the power system. Apply it to the power system site selection and sizing model, which can significantly reduce the active power loss of the distribution network, improve the voltage distribution, and enhance the voltage stability of the power grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the topological diagram of IEEE 30-node power system structure;

[0035] Figure 2 A specific implementation flow chart for site selection and capacity determination of IEEE 30-node power system;

[0036] Figure 3 This is a schematic diagram for comparing the configuration results of connecting different numbers of photovoltaic power stations;

[0037] Figure 4 This is a schematic diagram comparing the voltage deviation results of each node after connecting to different numbers of photovoltaic power stations;

[0038] Figure 5 This is the topological diagram of the power system structure after the capacity and site selection are completed. DETAILED DESCRIPTION

[0039] The method of the present invention is described in detail below with reference to the accompanying drawings:

[0040] A novel power system capacity determination and site selection method considering the photovoltaic power generation load limit includes the following steps:

[0041] Step 1: Solve the critical inertia and critical PV penetration under RoCoF and SSFD constraints.

[0042] ROCOF constraint: The frequency constraint is usually based on the system maximum bus frequency or a specific bus frequency, which is usually located near the disturbance point. To prevent PV disconnection after a disturbance, RoCoF must not exceed its protection setting value.

[0043] SSFD constraint: The system steady-state frequency difference is mainly determined by the unit regulation power of the synchronous machine and the frequency regulation effect of the load. The grid operation criteria stipulate that the system must meet the maximum frequency drop value of no more than 1.0Hz and the steady-state frequency deviation of no more than 0.2Hz, that is, Δf(t∞)≤0.2Hz.

[0044] (1) Calculation of equivalent inertia of power grid:

[0045] IEEE 30-bus power system Figure 1 As shown. The IEEE 30-node power system has a total of 41 transmission lines and 30 nodes, with node numbers 1 to 30, and each node is connected by a transmission line. There are 6 generators, namely G1 to G6, located at nodes 1, 2, 5, 8, 11 and 13 respectively; 4 intermediate nodes without load or power generation, which are mainly used as transmission nodes for connecting lines or transformers in the power network, are located at nodes 7, 12, 15 and 18 respectively; the remaining 20 nodes are all load nodes; in addition, there are 4 adjustable transformers connected to nodes 6 and 9, nodes 6 and 10, nodes 4 and 12, nodes 28 and 27.

[0046] After the new energy is connected, for the new power system consisting of n synchronous machine units and m photovoltaic motor units, the equivalent inertia of the power system H sys for:

[0047]

[0048] Where: m is the number of photovoltaic generators; S PV,j is the capacity of the jth photovoltaic generator; n is the number of synchronous machines; S G,j is the capacity of the i-th synchronous machine; H G,i The equivalent inertia of the i-th synchronous machine; H PV,j The equivalent inertia of the jth photovoltaic motor; S PV is the total installed capacity of photovoltaic units; S G is the total capacity of synchronous units; S sys is the total installed capacity of the new power system.

[0049] The equivalent inertia H obtained by replacing the synchronous generator set with photovoltaic power generation is PV The expression is shown in formula (2):

[0050]

[0051] Where: 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.

[0052] The equivalent inertia H PVSubstitute into the power system equivalent inertia H sys When the power increment ΔP is generated by the difference between the load increment and the power output increment in the power system sys When the regulation effect of photovoltaic units and loads is ignored, ΔP sys , H sys And the relationship of the initial RoCoF is:

[0053]

[0054] Where: f0 is the initial frequency, P e and P t are the electromagnetic power and mechanical power of the equivalent synchronous machine respectively; f is the frequency, and df / dt is the initial RoCoF.

[0055] The unit regulation power of a single synchronous machine is represented by K, which refers to the change in frequency when the power changes by a unit amount. If the power system contains n synchronous machine units, the equivalent unit regulation power K sys for:

[0056]

[0057] Where: i is the adjustment coefficient of the ith synchronous machine unit, S i is the capacity of the i-th synchronous machine unit.

[0058] The power increment ΔP generated by the difference between the load increment and the power output increment in the power system sys , Equivalent unit adjustment power K sys And the relationship between the steady-state frequency deviation Δf is:

[0059]

[0060] By combining the right sides of equations (4) and (5) to form a new equation, we can obtain:

[0061]

[0062] In this context, exploring the intrinsic relationship between the inertia of the power system and the frequency response index of the new energy power system has become a key link in quantifying the minimum inertia limit and the maximum photovoltaic access ratio. By controlling the start and stop of the relevant units in the photovoltaic power station and the traditional power plant to change the photovoltaic penetration rate, the safe operation premise of the power system under the inertia-frequency constraint can be met, and the maximum safe access amount of photovoltaic can be determined.

[0063] The ratio of the installed capacity of photovoltaic generators to the total capacity of the power system is defined as the photovoltaic penetration rate ξ, that is:

[0064]

[0065] Where: m is the number of photovoltaic generators; S PV,j is the capacity of the jth photovoltaic generator; n is the number of synchronous machines; S G,j is the capacity of the i-th synchronous machine; S PV is the total installed capacity of photovoltaic units; S G is the total capacity of synchronous units.

[0066] (2) Critical inertia of maximum frequency change rate constraint

[0067] If the difference in equivalent inertia of each synchronous unit is ignored and the maximum total load power increment of the power system is known Then formula (8) can be transformed into:

[0068]

[0069] Therefore, when the RoCoF limit value is known, the critical inertia H under the maximum frequency change rate constraint can be obtained: RoCoF .

[0070] (3) Critical photovoltaic penetration

[0071] If the power increment ΔP generated by the difference between the load increment and the output increment of the synchronous unit and the photovoltaic unit in the power system sys It is known that the critical photovoltaic penetration under the RoCoF constraint and SSFD constraint can be obtained at this time.

[0072] Power increase in the power system The critical photovoltaic penetration ξ under RoCoF constraint is lim，1 , as follows:

[0073]

[0074] If the maximum total load power increment in the power system is known Ignoring the differences in the regulation coefficients of the synchronous units, the critical PV penetration rate ξ under the SSFD constraint is lim,2 As follows:

[0075]

[0076] In summary, the maximum PV penetration rate that the power system can withstand while satisfying both the RoCoF and SSFD security constraints is:

[0077] ξ lim =min(ξ lim,1 ,ξ lim,2 ) (11)

[0078] Step 2: Establish a photovoltaic power station site selection and capacity determination model

[0079] After completing the modeling in step 1 and obtaining the critical inertia and critical photovoltaic penetration under RoCoF and SSFD constraints, the objective function of the new power system is established. The present invention takes the stable operation of the power system as the principle and the comprehensive minimization of the power system loss, voltage offset index and voltage stability index as the goal:

[0080] The objective function of establishing the photovoltaic power station site selection and capacity determination model is as follows:

[0081]

[0082] Where: i is the weight factor describing the importance of the i-th objective function and satisfies According to the author's multiple simulations, the values ​​can be set to 1 / 3, 1 / 3, and 1 / 3 respectively to obtain the most compromised result of the objective function; f i * Represents the function value of the i-th objective function after numerical normalization.

[0083] In the formula, each objective function needs to be normalized numerically so that each objective function is dimensionless to prevent the fitness scaling problem of the objective function during the optimization process, thereby ensuring the objective accuracy of the optimization model, as shown in formula (13).

[0084]

[0085] Where: f i Aft and f i Bef They represent the i-th objective function after and before photovoltaics are connected to the new power system.

[0086] The power station site selection and sizing model F includes the following three sub-objective functions.

[0087] (1) Reduce power loss

[0088] The main goal of connecting a photovoltaic power station 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:

[0089]

[0090] In the above formula, α ij With β ij It can be obtained by formula (15).

[0091]

[0092] Where: P j and Q jdenote the injected active power and reactive power of node j respectively; r ij represents the real part of the i-th row and j-th column in the node impedance matrix; U i represents the voltage amplitude of node i; δ i represents the voltage phase angle of node i.

[0093] (2) Improve grid voltage

[0094] The reactive power injected by the photovoltaic power station is conducive to reducing the reactive power flow of the power grid and reducing the voltage loss of the branch. Therefore, the voltage deviation index (VDI) is used as the second objective function f2:

[0095]

[0096] Where: U i It is represented as the voltage of node i; U norm It is represented by the voltage at the substation node in the power grid and can usually be set to 1.

[0097] (3) Improve voltage stability

[0098] Although minimizing the voltage deviation can improve the node voltage curve, in order to ensure the stable operation of the new power system, the voltage stability index (VSI) should be used as the third objective function f3, as shown in formula (17). VSI represents the static voltage stability of the branch. The larger the VSI, the more sensitive it is to voltage collapse and the worse the stability. Therefore, it is necessary to maximize the minimum value in the node VSI to improve the voltage stability level of the power system, as shown in formula (18).

[0099]

[0100]

[0101] Where: R ij , X ij Respectively represent the resistance and reactance of the line between node i and node j; is the set of all nodes in the power system; It is the collection of substation access nodes in the network.

[0102] Step 3: Solve based on the objective function to obtain the optimal plan.

[0103] The genetic algorithm is mainly used to solve the multi-objective optimization model for photovoltaic power station site selection and capacity determination. The optimal photovoltaic power station configuration total capacity corresponding to the optimal individual in the iteration process and the network topology and corresponding photovoltaic configuration total power of each period of photovoltaic scheduling are recorded, and each constraint condition is added as a penalty term to the objective function. The optimal solution is found through iteration and nonlinear optimization. The genetic algorithm solution flow chart is shown in Figure 2 .

[0104] (1) Encoding method for PV location capacity optimization

[0105] The optimization of photovoltaic power stations includes both the position optimization of discrete variables and the capacity optimization of continuous variables. Real number coding is used. The specific coding method is shown in formula (19):

[0106] g=[P PV1 ,P PV2 ,…,P PVi …,P PVN ] (19)

[0107] Where N is the number of nodes; P PV1 ,P PV2 ,…,P PVi …,P PVN is a real number, indicating the installed photovoltaic capacity. If P PVi If it is 0, it means that the node has no photovoltaic installed.

[0108] (2) Fitness function

[0109] Select F as the fitness function. In the genetic algorithm, we hope that F will achieve the minimum value.

[0110] (3) Select operation

[0111] 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 of pi is shown in formula (20):

[0112]

[0113] In the formula, f(x i ) represents the fitness of the ith individual.

[0114] (4) Crossover operation

[0115] The multi-point crossover method is adopted. The selected individuals generate new offspring through crossover operation. If the crossover point is k, and two x are considered i and x j , descendants x new It can be expressed as:

[0116] x new =(xi1 ,x i2 ,...,x ik ,x j(k+1) ,...,x jn ) (twenty one)

[0117] (5) Mutation Operation

[0118] Modify some genes of newborn individuals with a small probability μ to introduce mutations and increase the diversity of the population. nk , which can be expressed as:

[0119] x' nk =x nk +δ+μ (22)

[0120] Where δ represents a small random change and μ represents the mutation rate.

[0121] (6) Nonlinear Optimization

[0122] After the genetic algorithm evolves for a certain number of generations, the obtained results are used as the initial value, and the linear programming function fmincon in the MATLAB optimization toolbox is used to perform local optimization, and the local optimal value found is used as the new individual chromosome to continue evolving.

[0123] The specific implementation process is as follows Figure 2 shown.

[0124] The critical inertia H of the new power system is obtained RoCoF is 6.672, and the critical photovoltaic penetration rate is 44.45%. Under the constraints of critical inertia and critical photovoltaic penetration rate, the number and capacity of photovoltaic power stations added are analyzed. As the number of photovoltaic power stations added increases, the photovoltaic penetration rate increases and the comprehensive objective function decreases, indicating that the power system operation is more stable and the network loss is reduced.

[0125] Figure 3 The configuration results of the model with 1 to 11 photovoltaic power stations connected to the IEEE 30-node power system are given. It can be seen that as the number of photovoltaic power stations connected increases, the objective function F value decreases significantly. Figure 4 The voltage deviation of each node after connecting different numbers of photovoltaic power stations to the IEEE 30-node power system. It can be seen that as the number of photovoltaic power stations connected increases, the voltage deviation of each node decreases significantly. Compared with the cases of no photovoltaic connection, three photovoltaic connection, and six photovoltaic connection, the voltage deviation is the smallest and the energy utilization rate is the highest when nine photovoltaic power stations are connected.

[0126] The following conclusions can be drawn: When 8 photovoltaic power stations are connected, the objective function F is the smallest, with a value of 0.2962. At this time, the photovoltaic penetration rate is 42.76%. The network topology at this time is as follows: Figure 5 The photovoltaic location and capacity connected to each node are shown in Table 1.

[0127] Table 1 Capacity of each photovoltaic power station connected

[0128]

[0129] The results show that after configuring the appropriate capacity at the optimal location, the operating loss of the IEEE30-node power system is reduced, the voltage distribution is improved, and the voltage stability is enhanced.

Claims

1. A new method for determining the capacity and site selection of a power system considering the load limit of photovoltaic power generation, characterized in that: The steps include: Step 1: Establish the critical inertia and critical PV penetration model under RoCoF and SSFD constraints, take the equivalent inertia of the power grid as the core, and take the maximum frequency change rate and steady-state frequency deviation as constraints to solve the critical inertia and critical PV penetration of the new power system; Step 2: Taking active power loss, voltage deviation index and voltage stability index as optimization targets, and critical inertia and critical photovoltaic penetration rate as constraints, a multi-objective photovoltaic power station capacity selection model is established; Step 3: Use genetic algorithm to solve the multi-objective photovoltaic power station capacity and site selection model to obtain the optimal capacity and site selection plan.

2. The new power system capacity determination and site selection method considering the photovoltaic power generation load limit according to claim 1 is characterized in that: The calculation process of the equivalent inertia is as follows: After the new energy is connected, for the new power system consisting of n synchronous machine units and m photovoltaic motor units, the equivalent inertia of the power system H sys for: Where: m is the number of photovoltaic generators; S PV,j is the capacity of the jth photovoltaic generator; n is the number of synchronous machines; S G,j is the capacity of the i-th synchronous machine; H G,i The equivalent inertia of the i-th synchronous machine; H PV,j The equivalent inertia of the jth photovoltaic motor; S PV is the total installed capacity of photovoltaic units; S G is the total capacity of synchronous units; S sys is the total installed capacity of the new power system; The equivalent inertia H obtained by replacing the synchronous generator set with photovoltaic power generation PV The expression is: Where: 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 equivalent inertia H PV Substitute into the power system equivalent inertia H sys When the power increment ΔP is generated by the difference between the load increment and the power output increment in the power system sys When the regulation effect of photovoltaic units and loads is ignored, ΔP sys , H sys And the relationship of the initial RoCoF is: Where: f0 is the initial frequency, P e and P t are the electromagnetic power and mechanical power of the equivalent synchronous machine, respectively; f is the frequency, df / dt is the initial RoCoF; If the power system contains n synchronous machine units, the equivalent unit regulation power K sys for: Where: i is the adjustment coefficient of the ith synchronous machine unit, S i is the capacity of the i-th synchronous machine unit; The power increment ΔP generated by the difference between the load increment and the power output increment in the power system sys , Equivalent unit adjustment power K sys And the relationship between the steady-state frequency deviation Δf is: The right sides of equations (4) and (5) are combined to form a new equation, and we get:

3. The new power system capacity determination and site selection method considering the photovoltaic power generation load limit according to claim 2 is characterized in that: The specific process of solving the critical inertia of the new power system is as follows: If the difference in equivalent inertia of each synchronous unit is ignored and the maximum total load power increment of the power system is known Then formula (7) becomes: Where ξ is the photovoltaic penetration rate; when the RoCoF limit value is known, the critical inertia H under the maximum frequency change rate constraint is obtained RoCoF .

4. The new power system capacity determination and site selection method considering the photovoltaic power generation load limit according to claim 3 is characterized in that: The specific process of solving the critical photovoltaic permeability is as follows: If the power increment ΔP generated by the difference between the load increment and the output increment of the synchronous unit and the photovoltaic unit in the power system sys It is known that at this time, the critical photovoltaic penetration under the RoCoF constraint and SSFD constraint is obtained; Power increase in the power system The critical photovoltaic penetration ξ under RoCoF constraint is lim,1 : If the maximum total load power increment in the power system is known Ignoring the differences in the regulation coefficients of the synchronous units, the critical PV penetration rate ξ under the SSFD constraint is lim,2 As follows: In summary, the maximum PV penetration rate that the power system can withstand while satisfying both the RoCoF and SSFD security constraints is: x lim =min(ξ lim,1 ,x lim,2 ) (10).

5. The new power system capacity determination and site selection method considering the photovoltaic power generation load limit according to claim 4 is characterized in that: The multi-objective photovoltaic power station capacity determination and site selection model is established as follows: Multi-objective photovoltaic power station capacity selection model F: Where: i is the weight factor describing the importance of the i-th objective function and satisfies f i * Represents the function value of the i-th objective function after numerical normalization; F includes the following three sub-objective functions, each of which is subjected to numerical normalization operation; The power loss is expressed as the first objective function f1 as: Where: P j and Q j denote the injected active power and reactive power of node j respectively; r ij represents the real part of the i-th row and j-th column in the node impedance matrix; U i represents the voltage amplitude of node i; δ i represents the voltage phase angle of node i; is the number of all nodes in the power system; The voltage deviation index VDI is used as the second objective function: Where: U i It is represented as the voltage of node i; U norm It is expressed as the voltage at the substation node in the power grid; The third objective function is constructed based on the voltage stability index VSI, which is specifically shown in formula (15): Where: R ij , X ij Respectively represent the resistance and reactance of the line between node i and node j; It is the collection of substation access nodes in the network.

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